prompt,prompt_tokens,compression_time,compressed_tokens,compression_ratio,compressed_text,gpt_o1_saving,compression_ratio_normalized
"Incremental class learning involves sequentially learning classes in bursts of examples from the same class. This violates the assumptions that underlie  methods for training standard deep neural networks, and will cause them to suffer from catastrophic forgetting. Arguably, the best method for incremental class learning is iCaRL, but it requires storing  training examples for each class, making it challenging to scale. Here, we propose FearNet for incremental class learning. FearNet is a generative model that does not store previous examples, making it memory efficient. FearNet uses a brain-inspired dual-memory system in which new memories are consolidated from a network for recent memories inspired by the mammalian hippocampal complex to a network for long-term storage inspired by medial prefrontal cortex. Memory consolidation is inspired by mechanisms that occur during sleep. FearNet also uses a module inspired by the basolateral amygdala for determining which memory system to use for recall.   FearNet achieves state-of-the-art performance at incremental class learning on image (CIFAR-100, CUB-200) and audio classification (AudioSet) benchmarks.
 In incremental classification, an agent must sequentially learn to classify training examples, without necessarily having the ability to re-study previously seen examples. While deep neural networks (DNNs) have revolutionized machine perception BID26 , off-the-shelf DNNs cannot incrementally learn classes due to catastrophic forgetting. Catastrophic forgetting is a phenomenon in which a DNN completely fails to learn new data without forgetting much of its previously learned knowledge BID29 . While methods have been developed to try and mitigate catastrophic forgetting, as shown in BID23 , these methods are not sufficient and perform poorly on larger datasets. In this paper, we propose FearNet, a brain-inspired system for incrementally learning categories that significantly outperforms previous methods.The standard way for dealing with catastrophic forgetting in DNNs is to avoid it altogether by mixing new training examples with old ones and completely re-training the model offline. For large datasets, this may require weeks of time, and it is not a scalable solution. An ideal incremental learning system would be able to assimilate new information without the need to store the entire training dataset. A major application for incremental learning includes real-time operation on-board embedded platforms that have limited computing power, storage, and memory, e.g., smart toys, smartphone applications, and robots. For example, a toy robot may need to learn to recognize objects within its local environment and of interest to its owner. Using cloud computing to overcome these resource limitations may pose privacy risks and may not be scalable to a large number of embedded devices. A better solution is on-device incremental learning, which requires the model to use less storage and computational power.In this paper, we propose an incremental learning framework called FearNet (see Fig. 1 ). FearNet has three brain-inspired sub-systems: 1) a recent memory system for quick recall, 2) a memory system for long-term storage, and 3) a sub-system that determines which memory system to use for a particular example. FearNet mitigates catastrophic forgetting by consolidating recent memories into long-term storage using pseudorehearsal BID34 . Pseudorehearsal allows the network to revisit previous memories during incremental training without the need to store previous training examples, which is more memory efficient.Figure 1: FearNet consists of three braininspired modules based on 1) mPFC (longterm storage), 2) HC (recent storage), and 3) BLA for determining whether to use mPFC or HC for recall.Problem Formulation: Here, incremental class learning consists of T study-sessions. At time t, the learner receives a batch of data B t , which contains N t labeled training samples, i.e., B t = {(x j , y j )} Nt j=1 , where x j ∈ R d is the input feature vector to be classified and y j is its corresponding label. The number of training samples N t may vary between sessions, and the data inside a study-session is not assumed to be independent and identically distributed (iid). During a study session, the learner only has access to its current batch, but it may use its own memory to store information from prior study sessions. We refer to the first session as the model's ""base-knowledge,"" which contains exemplars from M ≥ 1 classes. The batches learned in all subsequent sessions contain only one class, i.e., all y j will be identical within those sessions.Novel Contributions: Our contributions include:1. FearNet's architecture includes three neural networks: one inspired by the hippocampal complex (HC) for recent memories, one inspired by the medial prefrontal cortex (mPFC) for long-term storage, and one inspired by the basolateral amygdala (BLA) that determines whether to use HC or mPFC for recall.2. Motivated by memory replay during sleep, FearNet employs a generative autoencoder for pseudorehearsal, which mitigates catastrophic forgetting by generating previously learned examples that are replayed alongside novel information during consolidation. This process does not involve storing previous training data.3. FearNet achieves state-of-the-art results on large image and audio datasets with a relatively small memory footprint, demonstrating how dual-memory models can be scaled. FearNet's mPFC is trained to both discriminate examples and also generate new examples. While the main use of mPFC's generative abilities is to enable psuedorehearsal, this ability may also help make the model more robust to catastrophic forgetting. BID18 observed that unsupervised networks are more robust (but not immune) to catastrophic forgetting because there are no target outputs to be forgotten. Since the pseudoexample generator is learned as a unsupervised reconstruction task, this could explain why FearNet is slow to forget old information. Table 5 : Memory requirements to train CIFAR-100 and the amount of memory that would be required if these models were trained up to 1,000 classes. Table 5 shows the memory requirements for each model in Sec. 6.1 for learning CIFAR-100 and a hypothetical extrapolation for learning 1,000 classes. This chart accounts for a fixed model capacity and storage of any data or class statistics. FearNet's memory footprint is comparatively small because it only stores class statistics rather than some or all of the raw training data, which makes it better suited for deployment.An open question is how to deal with storage and updating of class statistics if classes are seen in more than one study sessions. One possibility is to use a running update for the class means and covariances, but it may be better to favor the data from the most recent study session due to learning in the autoencoder.FearNet assumed that the output of the mPFC encoder was normally distributed for each class, which may not be the case. It would be interesting to consider modeling the classes with a more complex model, e.g., a Gaussian Mixture Model. BID34 showed that pseudorehearsal worked reasonably well with randomly generated vectors because they were associated with the weights of a given class. Replaying these vectors strengthened their corresponding weights, which could be what is happening with the pseudo-examples generated by FearNet's decoder. The largest impact on model size is the stored covariance matrix Σ c for each class. We tested a variant of FearNet that used a diagonal Σ c instead of a full covariance matrix. TAB5 shows that performance degrades, but FearNet still works.FearNet can be adapted to other paradigms, such as unsupervised learning and regression. For unsupervised learning, FearNet's mPFC already does a form of it implicitly. For regression, this would require changing mPFC's loss function and may require grouping input feature vectors into similar collections. FearNet could also be adapted to perform the supervised data permutation experiment performed by BID20 and BID24 . This would likely require storing statistics from previous permutations and classes. FearNet would sleep between learning different permutations; however, if the number of classes was high, recent recall may suffer. In this paper, we proposed a brain-inspired framework capable of incrementally learning data with different modalities and object classes. FearNet outperforms existing methods for incremental class learning on large image and audio classification benchmarks, demonstrating that FearNet is capable of recalling and consolidating recently learned information while also retaining old information. In addition, we showed that FearNet is more memory efficient, making it ideal for platforms where size, weight, and power requirements are limited. Future work will include 1) integrating BLA directly into the model (versus training it independently); 2) replacing HC with a semi-parametric model; 3) learning the feature embedding from raw inputs; and 4) replacing the pseduorehearsal mechanism with a generative model that does not require the storage of class statistics, which would be more memory efficient.A SUPPLEMENTAL MATERIAL A.1 MODEL HYPERPARAMETERS TAB1 shows the training parameters for the FearNet model for each dataset. We also experimented with various dropout rates, weight decay, and various activation functions; however, weight decay did not work well with FearNet's mPFC. TAB1 : FearNet Training Parameters TAB2 shows the training parameters for the iCaRL framework used in this paper. We adapted the code from the author's GitHub page for our own experiments. The ResNet-18 convolutional neural network was replaced with a fully-connected neural network. We experimented with various regularization strategies to increase the initial base-knowledge accuracy with weight decay working the best. The values that are given as a range of values are the hyperparameter search spaces. TAB9 shows the training parameters for GeppNet and GeppNet+STM. Parameters not listed here are the default parameters defined by BID17 . The values that are given as a range of values are the hyperparameter search spaces. A.3 BLA VARIANTS Our BLA model is a classifier that determines whether a prediction should be made using HC (recent memory) or mPFC (remote memory). An alternative approach would be to use an outlier detection algorithm that determines whether the data being processed by a sub-network is an outlier for that sub-network and should therefore be processed by the other sub-network. To explore this alternative BLA formulation, we experimented with three outlier detection algorithms: 1) one-class support vector machine (SVM) BID36 , 2) determining if the data fits into a Gaussian distribution using a minimum covariance determinant estimation (i.e., elliptical envelope) (Rousseeuw BID35 , and 3) the isolation forest BID27 . All three of these methods set a rejection criterion for if the test sample exists in HC; whereas the binary MLP reports a probability on how likely the test sample resides in HC. TAB5 : Performance of different BLA variants.",2233,1.973,1345,1.6602230483271376,"Incremental class learning involves sequentially classes bursts examples This violates the assumptions underlie methods training standard deep neural networks will cause suffer catastrophic forgetting incremental class learning iCaRL storing training examples making challenging scale Here, propose FearNet for incremental class learning FearNet a generative model does store previous examples making memory FearNet uses a brain-inspired dual-memory system in new memories consolidated from a network for recent memories inspired the mammalian hippocampal complex to a network inspired Memory consolidation inspired mechanisms sleep FearNet also uses a module inspired the basolateral amygdala for determining which memory system recall FearNet achieves state performance at incremental class learning on image (CIFAR-100 CUB-200 audio classificationAudioSet benchmarks In incremental classification an agent sequentially learn training examples without necessarily restudy previously seen While deep neural networks machine perception BID26 , off incrementally classes due catastrophic forgetting Catastrophic forgetting a DNN completely new data without forgetting much BID29 . While methods try mitigate catastrophic forgetting as shown BID23 , sufficient and perform larger datasets In this paper FearNet a brain-inspired system incrementally learning categories significantlyThe standard way dealing catastrophic forgetting DNNs avoid it mixing new training examples completely re offline For large datasets weeks time a scalable solution An ideal incremental learning system would assimilate store A major application incremental learning includes real operation on-board embedded platforms have limited storage smart toys smartphone applications robots For example a toy robot need learn recognize within of interest Using cloud computing overcome these resource limitations pose privacy risks scalable embedded devices A better solution on-device incremental learning requires the model use less storageIn called FearNet Fig 1 ). FearNet three brain-inspired sub 1) a recent memory system for quick recall determines a particular example FearNet mitigates catastrophic forgetting consolidating recent memories using pseudorehearsal BID34 . Pseudorehearsal allows the network revisit previous memories during incremental training without store previous training examples more memoryFigure FearNet consists three braininspired modules based 1) mPFClongterm storage HC (recent storage for determining recallProblem Formulation Here incremental class learning consists T study-sessions At time t, the learner receives a batch data B t N t labeled training samples {(x j Nt j=1 is the input feature vector to classified its corresponding label The number training samples N t may vary sessions the data inside a study-session assumed independent and identically (iid During a study session the learner only has access its current batch, use We refer the first session the model's ""base-knowledge contains exemplars M ≥ 1 classes The batches learned in all subsequent sessions contain only one class all y j will identical within those sessionsNovel Contributions Our contributions FearNet's architecture includes three neural networks inspired the hippocampal complex (HC for recent memories that determines whether to use HC recall.2. Motivated memory replay during employs pseudorehearsal, catastrophic forgetting previously learned examples alongside novel information during consolidation This process does storing previous training data.3. FearNet achieves state results large image and demonstrating dual-memory models scaled FearNet's mPFC trained both discriminate examples also generate new examples While the main use mPFC's generative abilities enable psuedorehearsal, this ability help make the model robust catastrophic forgetting BID18 observed unsupervised networks robust (but immune catastrophic forgetting because there no target outputs forgotten Since the pseudoexample generator learned as a unsupervised reconstruction task this could explain FearNet slow forget old information Table 5 : Memory requirements to train CIFAR-100 the amount would if these models trained up to 1,000 classes Table 5 shows the memory requirements each model Sec 6.1 for learning CIFAR-100 a hypothetical extrapolation 1,000 classes This chart accounts a fixed model capacity storage any data or class statistics FearNet's memory footprint comparatively because class statistics rather some or the raw training data better deploymentAn open question deal storage updating if classes seen more than one study sessions One possibility a running update the class means and covariances favor the data the most recent study session due learning inFearNet assumed the output the mPFC encoder normally for It would interesting consider modeling the classes with BID34 showed pseudorehearsal worked reasonably randomly generated vectors because associated the weights a given class Replaying these vectors strengthened their corresponding weights could what the pseudoexamples generated FearNet's decoder The largest impact model size the stored covariance matrix �� c for each class We tested a variant FearNet used a diagonal �� c instead TAB5 shows performance degrades, FearNet still worksFearNet can adapted regression For unsupervised learning FearNet's mPFC already does a form it implicitly For regression this would changing mPFC's loss function may grouping input feature vectors similar collections FearNet could also adapted perform the supervised data permutation experiment performed BID20 . This would likely require storing statistics previous permutations classes FearNet would sleep between learning different permutations; however the number classes high recent recall may suffer In this paper proposed a brain-inspired framework capable incrementally learning data with different modalities object classes FearNet outperforms existing methods incremental class learning on large image and audio classification benchmarks demonstrating FearNet recalling recently learned information while old information In addition showed FearNet more memory making ideal platforms size, weight limited Future work 1 integrating BLA directly the modelversus training independently replacing HC learning the feature embedding from raw inputs replacing the pseduorehearsal mechanism does the storage class statistics memoryA SUPPLEMENTAL MATERIAL A.1 MODEL HYPERPARAMETERS TAB1 shows the FearNet model for each dataset We also experimented various dropout rates weight decay various activation functions; weight decay did FearNet's mPFC TAB1 : FearNet Training Parameters TAB2 shows the iCaRL framework used We adapted our own experiments The ResNet-18 convolutional neural network replaced We experimented various regularization strategies increase the initial base-knowledge accuracy with weight decay working the best The values given a range the hyperparameter search spaces TAB9 shows the training parameters GeppNet GeppNet+STM Parameters not listed defined BID17 . The values given a range the hyperparameter search spaces A.3 BLA VARIANTS Our BLA model a classifier determines a prediction should HC (recent memory mPFCremote memory An alternative approach an outlier detection determines being processed a subnetwork for should processed To explore this alternative BLA formulation experimented three outlier detection 1) one-class support vector machineSVM) BID36 , determining if fits a minimum covariance determinant estimationRousseeuw BID35 and 3 the isolation forest BID27 All three these methods set a rejection criterion if the test sample exists HC; whereas the binary MLP reports on how resides TAB5 : Performance different BLA variants",0.01,0.3862694902585724
"Multi-view learning can provide self-supervision when different views are available of the same data. Distributional hypothesis provides another form of useful self-supervision from adjacent sentences which are plentiful in large unlabelled corpora. Motivated by the asymmetry in the two hemispheres of the human brain as well as the observation that different learning architectures tend to emphasise different aspects of sentence meaning, we present two multi-view frameworks for learning sentence representations in an unsupervised fashion. One framework uses a generative objective and the other a discriminative one. In both frameworks, the final representation is an ensemble of two views, in which, one view encodes the input sentence with a Recurrent Neural Network (RNN), and the other view encodes it with a simple linear model. We show that, after learning, the vectors produced by our multi-view frameworks provide improved representations over their single-view learnt counterparts, and the combination of different views gives representational improvement over each view and demonstrates solid transferability on standard downstream tasks. Multi-view learning methods provide the ability to extract information from different views of the data and enable self-supervised learning of useful features for future prediction when annotated data is not available BID16 . Minimising the disagreement among multiple views helps the model to learn rich feature representations of the data and, also after learning, the ensemble of the feature vectors from multiple views can provide an even stronger generalisation ability.Distributional hypothesis BID22 noted that words that occur in similar contexts tend to have similar meaning BID51 , and distributional similarity BID19 consolidated this idea by stating that the meaning of a word can be determined by the company it has. The hypothesis has been widely used in machine learning community to learn vector representations of human languages. Models built upon distributional similarity don't explicitly require humanannotated training data; the supervision comes from the semantic continuity of the language data.Large quantities of annotated data are usually hard and costly to obtain, thus it is important to study unsupervised and self-supervised learning. Our goal is to propose learning algorithms built upon the ideas of multi-view learning and distributional hypothesis to learn from unlabelled data. We draw inspiration from the lateralisation and asymmetry in information processing of the two hemispheres of the human brain where, for most adults, sequential processing dominates the left hemisphere, and the right hemisphere has a focus on parallel processing BID9 , but both hemispheres have been shown to have roles in literal and non-literal language comprehension BID15 BID14 .Our proposed multi-view frameworks aim to leverage the functionality of both RNN-based models, which have been widely applied in sentiment analysis tasks BID57 , and the linear/loglinear models, which have excelled at capturing attributional similarities of words and sentences BID5 BID24 BID51 for learning sentence representations. Previous work on unsupervised sentence representation learning based on distributional hypothesis can be roughly categorised into two types:Generative objective: These models generally follow the encoder-decoder structure. The encoder learns to produce a vector representation for the current input, and the decoder learns to generate sentences in the adjacent context given the produced vector BID24 BID20 BID50 . The idea is straightforward, yet its scalability for very large corpora is hindered by the slow decoding process that dominates training time, and also the decoder in each model is discarded after learning as the quality of generated sequences is not the main concern, which is a waste of parameters and learning effort.Our first multi-view framework has a generative objective and uses an RNN as the encoder and an invertible linear projection as the decoder. The training time is drastically reduced as the decoder is simple, and the decoder is also utilised after learning. A regularisation is applied on the linear decoder to enforce invertibility, so that after learning, the inverse of the decoder can be applied as a linear encoder in addition to the RNN encoder.Discriminative Objective: In these models, a classifier is learnt on top of the encoders to distinguish adjacent sentences from those that are not BID31 BID26 BID40 BID33 ; these models make a prediction using a predefined differentiable similarity function on the representations of the input sentence pairs or triplets.Our second multi-view framework has a discriminative objective and uses an RNN encoder and a linear encoder; it learns to maximise agreement among adjacent sentences. Compared to earlier work on multi-view learning BID16 BID17 BID52 that takes data from various sources or splits data into disjoint populations, our framework processes the exact same data in two distinctive ways. The two distinctive information processing views tend to encode different aspects of an input sentence; forcing agreement/alignment between these views encourages each view to be a better representation, and is beneficial to the future use of the learnt representations.Our contribution is threefold:• Two multi-view frameworks for learning sentence representations are proposed, in which one framework uses a generative objective and the other one adopts a discriminative objective. Two encoding functions , an RNN and a linear model, are learnt in both frameworks.• The results show that in both frameworks, aligning representations from two views gives improved performance of each individual view on all evaluation tasks compared to their single-view trained counterparts, and furthermore ensures that the ensemble of two views provides even better results than each improved view alone.• Models trained under our proposed frameworks achieve good performance on the unsupervised tasks, and overall outperform existing unsupervised learning models, and armed with various pooling functions, they also show solid results on supervised tasks, which are either comparable to or better than those of the best unsupervised transfer model. It is shown BID24 that the consistency between supervised and unsupervised evaluation tasks is much lower than that within either supervised or unsupervised evaluation tasks alone and that a model that performs well on supervised evaluation tasks may fail on unsupervised tasks. It is subsequently showed BID13 BID48 ) that, with large-scale labelled training corpora, the resulting representations of the sentences from the trained model excel in both supervised and unsupervised tasks, while the labelling process is costly. Our model is able to achieve good results on both groups of tasks without labelled information. In both frameworks, RNN encoder and linear encoder perform well on all tasks, and generative objective and discriminative objective give similar performance. We proposed multi-view sentence representation learning frameworks with generative and discriminative objectives; each framework combines an RNN-based encoder and an average-on-wordvectors linear encoder and can be efficiently trained within a few hours on a large unlabelled corpus. The experiments were conducted on three large unlabelled corpora, and meaningful comparisons were made to demonstrate the generalisation ability and transferability of our learning frameworks and consolidate our claim. The produced sentence representations outperform existing unsupervised transfer methods on unsupervised evaluation tasks, and match the performance of the best unsupervised model on supervised evaluation tasks.Our experimental results support the finding BID24 ) that linear/log-linear models (g in our frameworks) tend to work better on the unsupervised tasks, while RNN-based models (f in our frameworks) generally perform better on the supervised tasks. As presented in our experiments, multi-view learning helps align f and g to produce better individual representations than when they are learned separately. In addition, the ensemble of both views leveraged the advantages of both, and provides rich semantic information of the input sentence. Future work should explore the impact of having various encoding architectures and learning under the multi-view framework.Our multi-view learning frameworks were inspired by the asymmetric information processing in the two hemispheres of the human brain, in which the left hemisphere is thought to emphasise sequential processing and the right one more parallel processing BID9 . Our experimental results raise an intriguing hypothesis about how these two types of information processing may complementarily help learning.",1560,0.693,879,1.7747440273037542,"Multi-view learning can provide self-supervision when different views of Distributional hypothesis provides another form useful self-supervision from adjacent sentences which plentiful large unlabelled corpora Motivated the asymmetry as the observation different learning architectures tend emphasise sentence meaning present two multi-view frameworks sentence representations One framework uses a generative objective and In both frameworks the final representation an ensemble two views in, encodes the input sentence with We show, learning, the vectors produced our multi-view frameworks provide improved representations over their single-view learnt counterparts the combination different views gives representational improvement and demonstrates solid transferability on standard downstream tasks Multi-view learning methods provide extract different views enable useful features for future prediction when annotated data available BID16 . Minimising the disagreement multiple views helps the model learn rich feature representations, also after the ensemble the feature vectors from provide an even stronger generalisation abilityDistributional hypothesis BID22 noted words that occur similar similar meaning BID51 distributional similarity consolidated stating the company it has. The hypothesis has widely used machine learning community learn vector representations human languages Models built upon distributional similarity do explicitly require humanannotated training data; the supervision comes the semantic continuity the language dataLarge quantities usually hard and costly thus study Our goal propose learning algorithms built multi-view learning distributional hypothesis to learn unlabelled data We draw the lateralisation information processing of where, most adults sequential processing dominates has a focus parallel processing BID9 , but roles .Our proposed multi-view frameworks aim leverage the functionality sentiment analysis tasks BID57 the linear/loglinear models excelled capturing attributional similarities words for learning sentence representations Previous work unsupervised sentence representation learning based distributional hypothesis can roughlyGenerative objective: These models generally follow The encoder learns produce a vector representation sentences the adjacent context given the produced vector BID24 BID20 BID50 The idea straightforward yet its scalability for very large corpora hindered the slow decoding process dominates training time also in each model discarded learning as the quality generated sequences the main concern a waste parameters learning effortOur first multi-view framework a generative objective uses an RNN an invertible linear projection The training time drastically the decoder simple also utilised after learning A regularisation applied on the linear decoder enforce invertibility after learning in additionDiscriminative Objective In these models learnt on top distinguish adjacent sentences BID31 BID26 BID40 BID33 ; these models make a prediction using a predefined differentiable similarity function on the representations or tripletsOur second multi-view framework uses; learns maximise agreement Compared earlier work multi learning BID16 BID17 BID52 that takes data various sources or splits data disjoint populations our framework processes two distinctive ways The two distinctive information processing views tend encode an input sentence; forcing agreement/alignment encourages, is beneficial the future use the learnt representationsOur contribution threefold:• Two multi-view frameworks sentence representations in uses a generative objective Two encoding functions , an RNN learnt both frameworks.• The results in aligning representations from two views gives of each individual view on all evaluation tasks compared their single-view trained counterparts furthermore ensures the ensemble provides each improved view Models trained under our proposed frameworks achieve overall armed various pooling functions solid results either comparable It shown BID24 that the consistency supervised and unsupervised evaluation tasks much within alone and a model performs fail It subsequently showed BID13 BID48 ), large-scale labelled training corpora the resulting representations the sentences from the trained model excel the labelling process costly Our model able achieve good results both groups tasks labelled information In both frameworks RNN encoder linear encoder perform well all tasks generative objective and give We proposed multi-view sentence representation learning frameworks with generative and discriminative objectives; each framework combines averageonwordvectors linear can efficiently within a large unlabelled corpus The experiments three large unlabelled corpora and meaningful comparisons demonstrate the generalisation ability and transferability our learning frameworks consolidate our claim. The produced sentence representations outperform existing unsupervised transfer methods on matchOur experimental results BID24 ) that linear/log-linear models (g in our frameworks tend work generally As presented our experiments multi-view learning helps align f and produce better individual representations than when they learned In addition the ensemble both views leveraged the advantages both, provides rich semantic information of the input sentence Future work explore having various encoding architectures learning under the multi-view frameworkOur multi learning frameworks were inspired the asymmetric information processing in thought emphasise sequential processing one more parallel BID9 . Our experimental results raise an intriguing hypothesis these two types information processing complementarily help learning",0.01,0.678058882987794
"We show how discrete objects can be learnt in an unsupervised fashion from pixels, and how to perform reinforcement learning using this object representation.

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

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

 This gives the first reinforcement learning agent for Atari with an interpretable object representation, and opens the avenue for agents that can conduct object-based exploration and generalization. Humans are able to parse the world as a collection of objects, that are discrete, persistent, and can be interacted with. Humans can use this representation for planning, reasoning, and exploration. When playing a game such as Montezuma's Revenge in Atari, a human can identify the different objects, such as an avatar that moves in a 2-D plane, a rolling skull, and a key. Even if they do not know initially what to do, they can explore the state space using the prior knowledge that objects persist, move around contiguously, and can interact with other objects in local proximity.This explicit representation of objects and prior knowledge is missing from artificial reinforcement learning agents, such as DQN BID11 ). Although architectures such as DQN attain superhuman performance on many games, in particular those whose reward signal is dense (see e.g., BID1 ), its performance on games with sparse rewards, or greater planning complexity, is often below that of humans. Perhaps explicit object knowledge is one missing ingredient, which would allow for more powerful exploration than existing epsilon-greedy methods (that simply execute a random walk in action space).In this paper we set forth a method to learn objects from pixels in an unsupervised manner. By an object representation, we mean a ""tabular"" representation, where there is a list of objects, and each object has a position and a set of features (represented by a vector).Learning such a representation from input pixels is a non-trivial challenge. The space of possible inputs is a connected manifold, but the space of object representations is disconnected; for example, there is no continuous transformation from 4 objects to 5. We address this challenge by introducing an object presence value between 0 and 1, which is a continuous relaxation of whether an object is present or not.We give a method of tracking the same object across multiple frames (object persistence), and give an architecture that can perform calculations using the object representation. We test this model in the Atari domain, and show that it is possible to do reinforcement learning on a learnt object representation. Objects such as the ball and paddles in Pong, and the submarine and fish in Seaquest, emerge naturally without supervision. We give results and insights into how best to calculate global values from a collection of objects using an ""interaction net"" style architecture, where calculations are invariant to object order.",654,0.332,381,1.7165354330708662,"We show discrete objects learnt from pixels perform this object representation More precisely construct a differentiable mapping an image a discrete tabular list consists a differentiable position feature vector scalar presence value that allows the representation learnt using an attention mechanism Applying this mapping Atari games together an interaction net-style architecture calculating quantities from objects construct agents play objects learnt During training many natural objects emerge the ball paddles in Pong the submarine and fish Seaquest This gives the first reinforcement learning agent Atari with an interpretable object representation opens the avenue agents conduct object-based exploration generalization Humans able parse as objects that discrete persistent can interacted Humans can use this representation planning reasoning exploration When playing such Montezuma's Revenge in Atari a human identify the different objects such an avatar that moves a rolling skull a key Even do know initially explore the state space using the prior knowledge objects persist move contiguously can interact local proximityThis explicit representation prior knowledge missing artificial reinforcement learning agents DQN BID11 ). Although architectures DQN attain superhuman performance on many games in particular those whose reward signal densesee BID1 its performance games sparse rewards, or greater planning complexity below humans Perhaps explicit object knowledge one missing ingredient, which would more powerful exploration than existing epsilon-greedy methods (that simply execute a random walk action space).In set forth learn objects pixels By an object representation a ""tabular"" representation there featuresrepresented a vector).Learning from input pixels The space of possible inputs a connected manifold but object representations disconnected; no continuous transformation 4 objects We address this challenge introducing an object presence value between a continuous relaxation whetherWe give a method tracking across multiple framesobject persistence give an architecture perform calculations We test this model the Atari domain show do reinforcement learning a learnt object representation Objects such the ball paddles in Pong the submarine and fish Seaquest emerge naturally without supervision We give results best calculate global values from a collection objects using an ""interaction net"" style architecture calculations invariant object order",0.0,0.5297484990335661
"Most recent gains in visual recognition have originated from the inclusion of attention mechanisms in deep convolutional networks (DCNs). Because these networks are optimized for object recognition, they learn where to attend using only a weak form of supervision derived from image class labels. Here, we demonstrate the benefit of using stronger supervisory signals by teaching DCNs to attend to image regions that humans deem important for object recognition. We first describe a large-scale online experiment (ClickMe) used to supplement ImageNet with nearly half a million human-derived ""top-down"" attention maps. Using human psychophysics, we confirm that the identified top-down features from ClickMe are more diagnostic than ""bottom-up"" saliency features for rapid image categorization. As a proof of concept, we extend a state-of-the-art attention network and demonstrate that adding ClickMe supervision significantly improves its accuracy and yields visual features that are more interpretable and more similar to those used by human observers. Attention has become the subject of intensive research within the deep learning community. While biology is sometimes mentioned as a source of inspiration BID34 BID23 BID2 You et al., 2016; BID3 BID41 BID1 , the attentional mechanisms that have been considered remain limited in comparison to the rich and diverse array of processes used by the human visual system (see BID15 , for a review). In addition, whereas human attention is controlled by varying task demands, attention networks used in computer vision are solely optimized for object recognition. This means that, unlike infants who can rely on a myriad of visual cues and supervision to learn to focus their attention BID15 , DCNs must solve this challenging problem with weak supervisory signals derived from statistical associations between image pixels and class labels. Here, we investigate how explicit human supervision -teaching DCNs what and where to attend -affects their performance and interpretability. We have described the ClickMe dataset, which is aimed at supplementing ImageNet with nearly a half-million human-derived attention maps. The approach was validated with human psychophysics, which indicated the sufficiency of ClickMe features for rapid visual categorization. When participants viewed images that were masked to reveal commonly selected ClickMe map locations, they reached ceiling recognition accuracy when only 6% of image pixels were visible. By comparison, participants viewing images masked according to bottom-up saliency map locations did not reach ceiling performance until the full image was visible. These results indicate that ClickMe.ai may also provide novel insights into human vision with a measure of feature diagnosticity that goes beyond classic bottom-up saliency measures. While a detailed analysis of the ClickMe features falls outside the scope of the present study, we expect a more systematic analysis of this data, including the timecourse of feature selection BID4 BID11 , will aid our understanding of the different attention mechanisms responsible for the selection of diagnostic image features.We also extended the squeeze-and-excitation (SE) module which constituted the building block of the winning architecture in the ILSVRC17 challenge. We trained an SE-ResNet-50 on a reduced amount of data (∼ 300K samples) and found that the architecture overfits compared to a standard ResNet-50. We described a novel global-and-local attention (GALA) module and found that the proposed GALA-ResNet-50, however, significantly increases accuracy in this regime and cuts down top-5 error by ∼ 25% over both . In addition, we described an approach to co-train GALA using ClickMe supervision and cue the network to attend to image regions that are diagnostic to humans for object recognition. The routine casts ClickMe map prediction as an auxiliary task that can be combined with a primary visual categorization task. We found a trade-off between learning visual representations that are more similar to those used by human observers vs. learning visual representations that are more optimal for ILSVRC. The proper trade-off resulted in a model with better classification accuracy and more interpretable visual representations (both qualitatively and according to quantitative experiments on the ClickMe dataset and Microsoft COCO images).While recent advancements in DCNs have led to models that perform on par with human observers in basic visual recognition tasks, there is also growing evidence of qualitative differences in the visual strategies that they employ BID30 BID38 BID8 BID22 . It is not known whether these discrepancies arise because of differences in mechanisms for visual inference or fundamentally different training routines. However , our success in encouraging DCNs to learn more human-like representations with ClickMe map supervision suggests that improved training regimens can help close this gap. In particular , DCNs lack explicit mechanisms for perceptual grouping and figure-ground segmentation which are known to play a key role in the development of our visual system BID18 BID27 ) by simplifying the process of discarding background clutter. In the absence of figure-ground mechanisms, DCNs are compelled to associate foreground objects and their context as single perceptual units. This leads to DCN representations that are significantly more distributed compared to those used by humans BID22 . We hope that this work will help catalyze interest in the development of novel training paradigms that leverage combinations of visual cues (depth, motion, etc) for figure-ground segregation in order to substitute for the human supervision used here for co-training GALA.",1060,0.582,633,1.6745655608214849,"Most recent gains visual recognition originated attention mechanisms Because these networks optimized object recognition learn where attend using only a weak form supervision derived image class labels Here demonstrate stronger supervisory signals by teaching DCNs attend image regions humans deem object recognition We first describeClickMe used supplement ImageNet Using human psychophysics confirm the identified top-down features from ClickMe more diagnostic for rapid image categorization As a proof extend state attention network demonstrate adding ClickMe supervision significantly its accuracy yields visual features interpretable similar Attention has become intensive research within While biology sometimes mentioned BID34 BID23 You et; , the attentional mechanisms have considered remain limited comparison the rich and diverse array processes used , In addition whereas human attention controlled varying task demands attention networks used solely optimized This means unlike infants rely a myriad supervision focus BID15 , DCNs must solve this challenging problem weak supervisory signals derived statistical associations image pixels class labels Here investigate how explicit human supervision -teaching DCNs what and attend interpretability We described the ClickMe dataset aimed ImageNet nearly a half-million human-derived attention maps The approach validated human psychophysics indicated the sufficiency ClickMe features rapid visual categorization When participants viewed masked commonly selected ClickMe map locations reached ceiling recognition accuracy when only 6% image pixels By comparison participants viewing images masked according bottom-up saliency map locations did reach ceiling performance until visible These results ClickMe.ai may also novel insights human vision with a measure feature diagnosticity goes classic bottom-up saliency measures While a detailed analysis the ClickMe features falls outside expect the timecourse feature selection BID4 BID11 , aid the different attention mechanisms responsible diagnostic image featuresWe extended the squeeze-and-excitation (SE) module which constituted the winning architecture the ILSVRC17 challenge We trained an SEResNet-50 on a reduced amount� 300K samples found the architecture overfits compared We described a novel global-and-local attention (GALA) module and found-ResNet-50, however significantly accuracy this regime cuts top-5 error ∼ 25 both . In addition described co-train GALA using ClickMe supervision cue the network attend image regions diagnostic to humans for object recognition The routine casts ClickMe map prediction an auxiliary task combined a primary visual categorization task We found learning visual representations that similar human observers learning visual representations that optimal ILSVRC The proper trade-off resulted a model better classification accuracy more interpretable visual representationsboth qualitatively according quantitative experiments on the ClickMe dataset and Microsoft COCO images).While recent advancements DCNs models perform on par human observers qualitative differences the visual strategies they BID30 BID38 BID8 BID22 . It these discrepancies arise mechanisms visual inference fundamentally different training routines However , our success encouraging DCNs learn more human-like representations with ClickMe map supervision suggests improved training regimens close In particular , DCNs lack explicit mechanisms perceptual grouping and figure-ground segmentation which known BID18 BID27 ) by discarding background clutter In figure-ground mechanisms DCNs compelled associate foreground objects their context as single perceptual units This leads DCN representations significantly distributed compared those used humans BID22 . We hope this work interest leverage combinations visual cuesdepth motion figure-ground segregation substitute the human supervision used here co-training GALA",0.01,0.42281295197479973
"In recent years, deep neural networks have demonstrated outstanding performancein many machine learning tasks. However, researchers have discovered that thesestate-of-the-art models are vulnerable to adversarial examples:  legitimate examples added by small perturbations which are unnoticeable to human eyes. Adversarial training, which augments the training data with adversarial examples duringthe training process,  is a well known defense to improve the robustness of themodel against adversarial attacks.   However, this robustness is only effective tothe same attack method used for adversarial training.   Madry et al. (2017) suggest that effectiveness of iterative multi-step adversarial attacks and particularlythat projected gradient descent (PGD) may be considered the universal first order adversary and applying the adversarial training with PGD implies resistanceagainst many other first order attacks.    However,  the computational cost of theadversarial training with PGD and other multi-step adversarial examples is muchhigher than that of the adversarial training with other simpler attack techniques. In this paper, we show how strong adversarial examples can be generated only ata cost similar to that of two runs of the fast gradient sign method (FGSM), allowing defense against adversarial attacks with a robustness level comparable to thatof the adversarial training with multi-step adversarial examples.   We empiricallydemonstrate the effectiveness of the proposed two-step defense approach againstdifferent attack methods and its improvements over existing defense strategies. Despite the fact that deep neural networks demonstrate outstanding performance for many machine learning tasks, researchers have found that they are susceptible to attacks by adversarial examples BID18 ; BID2 ). Adversarial examples which are generated by adding crafted perturbations to legitimate input samples are indistinguishable to human eyes. For classification tasks, these perturbations may cause the legitimate samples to be misclassified by the model at the inference time. While there exists no widely agreed conclusion, several studies attempted to explain the underlying causes of the susceptibility of deep neural networks toward adversarial examples. The vulnerability is ascribed to the linearity of the model BID2 ), low flexibility BID1 ), or the flatness/curvedness of the decision boundaries BID10 ), but a more general cause is still under research. The recent literature considered two types of threat models: black-box and white-box attacks. In black-box attacks, the attacker is assumed to have no access to the architecture and parameters of the model, whereas in white-box attacks, the attacker has complete access to such information. Several white-box attack methods were proposed BID2 , BID12 , BID17 , BID0 , BID9 ). In response, several defenses have been proposed to mitigate the effect of adversarial attacks. These defenses were developed along three main directions: (1) expanding the training data to make the classifier more robustly learn the underlying function, e.g., by adversarial training which augments the training data set with adversarial examples generated by certain attack methods BID18 , BID2 , BID5 ); (2) modifying the training procedure to reduce the gradients of the model w.r.t. the input such that the classifier becomes more robust to input perturbations, e.g., via input gradient regularization BID15 , or defensive distillation BID14 ; and (3) using external models as network add-ons when classifying unseen examples (feature squeezing BID19 , MagNet BID8 , and Defense-GAN) BID16 ).Adversarial training, a simple but effective method to improve the robustness of a deep neural network against white-box adversarial attacks, uses the same white-box attack mechanism to generate adversarial examples for augmenting the training data set. However, if the attacker applies a different attack strategy, adversarial training does not work well due to gradient masking BID13 . BID7 have suggested the effectiveness of iterative multi-step adversarial attacks. In particular, it was suggested that projected gradient descent (PGD) PGD may be considered the strongest first-order attack so that the adversarial training with PGD can boost the resistance against many other first-order attacks. However, in the literature a large number (e.g. 40) of steps of back propagation are typically used in the iterative attack method of PGD or its closely related variant iterative fast gradient (IFGSM) BID5 to find strong adversarial examples to be used in each adversarial training step, incurring a prohibitively high computational complexity particularly for large DNNs or training datasets.In this paper, we propose an efficient two-step adversarial defense technique, called e2SAD, to facilitate defense against multiple types of whitebox and blackbox attacks with a quality on a par with the expensive adversarial training using the well-known multi-step attack the iterative fast gradient method (IFGSM) BID5 . The first step of e2SAD is similar to the basic adversarial training, where an adversarial example is generated by applying a simple one-step attack method such as the fast gradient sign method (FGSM). Then in the second step, e2SAD attemps to generate a second adversarial example at which the vulnerability of the current model is maximally revealed such that the resulting defense is at the same quality level of the much more expensive IFGSMbased adversarial training. Finally, the two adversarial examples are taken into consideration in the proposed loss function according to which a more robust model is trained, resulting strong defense to both one-step and multi-step iterative attacks with a training time much less less than that of the adversarial training using IFGSM. The main contributions of this paper are as follows:• We propose a computationally efficient method to generate two adversarial examples per input example while effectively revealing the vulnerability of the learned classifier in the neighborhood of each clean data point;• We show that by considering the generated adversarial examples as part of a well-designed final loss function, the resulting model is robust to both one-step and iterative white box attacks;• We further demonstrate that by adopting other techniques in our two-step approach like the use of soft labels and hyper parameter tuning, robust defense against black box attacks can be achieved. We have aimed to improve the robustness of deep neural networks by presenting an efficient twostep adversarial defense technique e2SAD, particularly w.r.t to strong iterative multi-step attacks. This objective is achieved by finding a combination of two adversarial points to best reveal the vulnerability of the model around each clean input. In particular, we have demonstrated that using a dissimilarity measure between the first and second adversarial examples we are able to appropriately locate the second adversary in a way such that including both types of adversaries in the final training loss function leads to improved robustness against multi-step adversarial attacks. We have demonstrated the effectiveness of e2SAD in terms of defense against while-box one-step FGSM and multi-step IFGSM attacks and black-box IFGSM attacks under various settings.e2SAD provides a general mechanism for defending both one-step and multiple attacks and for balancing between these two defense needs, the latter of which can be achieved by properly tuning the corresponding weight hyperparameters in the training loss function. In the future work, we will explore hyperparameter tuning and other new techniques to provide a more balanced or further improved defense quality for a wider range of white and black box attacks.",1474,0.657,865,1.7040462427745664,"In deep neural networks demonstrated outstanding performancein However researchers thesestate-of models vulnerable adversarial examples: legitimate examples added small perturbations which Adversarial training augments the training data with adversarial examples duringthe training process a well known defense to improve themodel against However this robustness only effective tothe same attack method adversarial training Madry et al (2017 suggest effectiveness iterative multi-step adversarial attacks and particularlythat projected gradient descentPGD considered the universal first order adversary and applying with PGD implies resistanceagainst many other first order attacks However the computational cost theadversarial training with PGD and other multi-step adversarial examples muchhigher other simpler attack techniques In this paper how strong adversarial examples only ata cost similar two runs the fast gradient sign methodFGSM allowing defense a robustness level thatof with We empiricallydemonstrate the proposed two-step defense approach againstdifferent attack methods its improvements Despite deep neural networks demonstrate outstanding performance for researchers susceptible attacks adversarial examples BID18 ; BID2 Adversarial examples which generated adding crafted perturbations legitimate input samples indistinguishable to human eyes For classification tasks these perturbations cause the legitimate samples the model at the inference time While exists no widely agreed conclusion several studies attempted explain the susceptibility deep neural networks toward adversarial examples The vulnerability ascribed the linearity the model BID2 ), low flexibility or flatness/ the decision boundaries a more general cause still under research The recent literature considered two types threat models In black-box attacks assumed no access the architecture parameters the model whereas such information Several white-box attack methods proposed BID2 , ). In response several defenses mitigate adversarial attacks These defenses along three main directions expanding the training data make the classifier robustly learn the underlying function adversarial training which augments set generated certain attack methods BID18 , ); modifying reduce the input such becomes input via input gradient regularization BID15 or defensive distillation BID14 external models network add-ons when unseen examplesfeature squeezing MagNet BID8 Defense-GAN ).Adversarial training against uses to augmenting However if the attacker applies adversarial training does due gradient masking BID13 . BID7 have suggested the effectiveness iterative multi-step adversarial attacks In particular suggested projected gradient descent (PGD) PGD considered the strongest first-order attack so the adversarial training with boost the resistance against However the literature ( 40 steps of back propagation typically the iterative attack method PGD or its closely related variant iterative fast gradient (IFGSM) BID5 to find strong adversarial examples to be each adversarial training step incurring particularly large DNNs or training datasetsIn called e2SAD facilitate defense multiple types whitebox and with a quality on a par the expensive adversarial training using . The first step e2SAD similar the basic adversarial training generated applying such the fast gradient sign methodFGSM Then in the second step e2SAD attemps generate a second adversarial example at which the vulnerability the current model maximally revealed such the resulting defense at the same quality level the much more expensive IFGSMbased adversarial training Finally the two adversarial examples taken into the proposed loss function according a more robust model trained resulting strong defense to both one-step and multi-step iterative attacks with a training time much less using IFGSM The main contributions as We propose two adversarial examples per input example while effectively revealing the vulnerability the learned classifier the neighborhood each clean data by considering part a well-designed final loss function both one-step and iterative white box further adopting other techniques like the use soft labels hyper parameter tuning robust defense We aimed improve deep neural networks presenting an efficient twostep adversarial defense technique e2SAD particularly w.r.t to strong iterative multi-step attacks This objective achieved finding a combination two adversarial points to best reveal the vulnerability the model around each clean input In particular demonstrated using a dissimilarity measure between the first and second adversarial examples we are appropriately locate the second adversary a way such including both types adversaries the final training loss function leads improved robustness against We demonstrated e2SAD terms defense while-box one-step FGSM multi-step IFGSM attacks and under a general mechanism defending for balancing these two defense needs the properly tuning the corresponding weight hyperparameters the training loss function In the future work, explore hyperparameter tuning provide a more balanced or further improved defense quality white and black box attacks",0.01,0.49792713944685585
"Recently several different deep learning architectures have been proposed that take a string of characters as the raw input signal and automatically derive features for text classification. Little studies are available that compare the effectiveness of these approaches for character based text classification with each other. In this paper we perform such an empirical comparison for the important cybersecurity problem of DGA detection: classifying domain names as either benign vs. produced by malware (i.e., by a Domain Generation Algorithm). Training and evaluating on a dataset with 2M domain names shows that there is surprisingly little difference between various convolutional neural network (CNN) and recurrent neural network (RNN) based architectures in terms of accuracy, prompting a preference for the simpler architectures, since they are faster to train and less prone to overfitting. Malware is software that infects computers in order to perform unauthorized malicious activities. In order to successfully achieve its goals, the malware needs to be able to connect to a command and control (C&C) center. To this end, both the controller behind the C&C center (hereafter called botmaster) and the malware on the infected machines can run a Domain Generation Algorithm (DGA) that generates hundreds or even thousands of domains automatically. The malware then attempts at resolving each one of these domains with its local DNS server. The botmaster will have registered one or a few of these automatically generated domains. For these domains that have been actually registered, the malware will obtain a valid IP address and will be able to communicate with the C&C center.The binary text classification task that we address in this paper is: given a domain name string as input, classify it as either malicious, i.e. generated by a DGA, or as benign. Deep neural networks have recently appeared in the literature on DGA detection ; BID8 ; BID15 . They significantly outperform traditional machine learning methods in accuracy, at the price of increasing the complexity of training the model and requiring larger datasets. Independent of the work on deep networks for DGA detection, other deep learning approaches for character based text classification have recently been proposed, including deep neural network architectures designed for processing and classification of tweets BID2 ; BID11 ) as well as general natural language text BID16 ). No systematic study is available that compares the predictive accuracy of all these different character based deep learning architectures, leaving one to wonder which one works best for DGA detection.To answer this open question, in this paper we compare the performance of five different deep learning architectures for character based text classification (see TAB0 ) for the problem of detecting DGAs. They all rely on character-level embeddings, and they all use a deep learning architecture based on convolutional neural network (CNN) layers, recurrent neural network (RNN) layers, or a combination of both. Our most important finding is that for DGA detection, which can be thought of as classification of short character strings, despite of vast differences in the deep network architectures, there is remarkably little difference among the methods in terms of accuracy and false positive rates, while they all comfortably outperform a random forest trained on human engineered features. This finding is of practical value for the design of deep neural network based classifiers for short text classification in industry and academia: it provides evidence that one can select an architecture that BID16 is faster to train, without loss of accuracy. In the context of DGA detection, optimizing the training time is of particular importance, as the models need to be retrained on a regular basis to stay current with respect to new, emerging malware. DGA detection, i.e. the classification task of distinguishing between benign domain names and those generated by malware (Domain Generation Algorithms), has become a central topic in information security. In this paper we have compared five different deep neural network architectures that perform this classification task based purely on the domain name string, given as a raw input signal at character level. All five models, i.e. two RNN based architectures, two CNN based architectures, and one hybrid RNN/CNN architecture perform equally well, catching around 97-98% of malicious domain names against a false positive rate of 0.001. This roughly means that for every 970 malicious domain names that the deep networks catch, they flag only one benign domain name erroneously as malicious. A Random Forest based on human defined linguistic features achieves a recall of only 83% against the same 0.001 false positive rate when trained and tested on the same data that was used for the deep networks. The use of a deep neural network that automatically learns features is attractive in a cybersecurity setting because it is a lot harder to craft malware to avoid detection by a system that relies on automatically learned features instead of on human engineered features. An interesting direction for future work is to test the trained deep networks more extensively on domain names generated by new and previously unseen malware families.A KERAS CODE FOR DEEP NETWORKS main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) lstm = LSTM(128, return sequences=False)(embedding) drop = Dropout(0.5) (lstm) output = Dense(1, activation ='sigmoid') (drop) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam')Listing 1: Endgame model with single LSTM layer, adapted from main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) bi lstm = Bidirectional ( layer =LSTM(64, return sequences=False), merge mode='concat')(embedding) output = Dense(1, activation ='sigmoid') ( bi lstm ) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 2: CMU model with bidirectional LSTM, adapted from BID2 main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) conv1 = Conv1D( filters =128, kernel size =3, padding='same', strides =1)(embedding) thresh1 = ThresholdedReLU(1e−6)(conv1) max pool1 = MaxPooling1D(pool size=2, padding='same')(thresh1 ) conv2 = Conv1D( filters =128, kernel size =2, padding='same', strides =1)(max pool1) thresh2 = ThresholdedReLU(1e−6)(conv2) max pool2 = MaxPooling1D(pool size=2, padding='same')(thresh2 ) flatten = Flatten () (max pool2) fc = Dense(64)( flatten ) thresh fc = ThresholdedReLU(1e−6)(fc) drop = Dropout(0.5) ( thresh fc ) output = Dense(1, activation ='sigmoid') (drop) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 3: NYU model with stacked CNN layers, adapted from BID16 def getconvmodel( self , kernel size , filters ) : model = Sequential () model.add( Conv1D( filters = filters , input shape =(128, 128), kernel size = kernel size , padding='same', activation =' relu ', strides =1)) model.add(Lambda(lambda x: K.sum(x, axis=1), output shape =( filters , ) ) ) model.add(Dropout(0.5) ) return model main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) conv1 = getconvmodel(2, 256)(embedding) conv2 = getconvmodel(3, 256)(embedding) conv3 = getconvmodel(4, 256)(embedding) conv4 = getconvmodel(5, 256)(embedding) merged = Concatenate () ([ conv1, conv2, conv3, conv4] ) middle = Dense(1024, activation =' relu ') (merged) middle = Dropout(0.5) (middle) middle = Dense(1024, activation =' relu ') (middle) middle = Dropout(0.5) (middle) output = Dense(1, activation ='sigmoid') (middle) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 4: Invincea CNN model with parallel CNN layers, adapted from BID8 main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) conv = Conv1D( filters =128, kernel size =3, padding='same', activation =' relu ', strides =1)(embedding) max pool = MaxPooling1D(pool size=2, padding='same')(conv) encode = LSTM(64, return sequences=False) (max pool) output = Dense(1, activation ='sigmoid') (encode) model = Model(inputs=main input, outputs =output) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 5: MIT model with a stacked CNN and LSTM layer, adapted from BID11 main input = Input (shape=(75, ) , dtype='int32 ', name='main input') embedding = Embedding(input dim=128, output dim=128, input length =75)(main input ) flatten = Flatten () (embedding) output = Dense(1, activation ='sigmoid') ( flatten ) model = Model(inputs=main input, outputs =output) print (model.summary()) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 6: Baseline Model with only Embedding Layer main input = Input (shape=(11, ) , name='main input') dense = Dense(128, activation =' relu ') ( main input ) output = Dense(1, activation ='sigmoid') (dense) model = Model(inputs=main input, outputs =output) print (model.summary()) model.compile( loss =' binary crossentropy ', optimizer ='adam') Listing 7: MLP Model with 128 Nodes Dense Layer",2178,0.736,1258,1.7313195548489666,"Recently several different deep learning architectures proposed that take a string characters as the raw input signal automatically derive features for text classification Little studies are available that compare the effectiveness these approaches for character based text classification with each In this paper perform such an empirical comparison for the important cybersecurity problem DGA detection: classifying domain names either benign vs. produced malware ( by a Domain Generation Algorithm Training and evaluating on a dataset with 2M domain names shows there surprisingly little difference various convolutional neural network ( based architectures in accuracy, prompting a preference the simpler architectures, since faster to less Malware is software in order perform unauthorized malicious activities In order successfully achieve its goals the malware needs connect To this end both the controller behind the C&C center (hereafter called botmaster the malware on the infected machines can run a Domain Generation Algorithm that generates hundreds or domains automatically The malware then attempts at resolving each one these domains with its local DNS server The botmaster will have registered one or a of these automatically generated domains For these domains that have actually registered the malware will obtain a valid IP address and will be communicate the C&C centerThe binary text classification task that we address this paper: given a domain name string as input classify either malicious, i.e. generated a DGA as benign Deep neural networks have recently appeared the literature on DGA detection ; BID8 ; BID15 . They significantly outperform traditional machine learning methods accuracy at the price increasing the complexity training the model and requiring larger datasets Independent of the work on deep networks for DGA detection other deep learning approaches for character based text classification recently proposed, including deep neural network architectures designed processing and classification tweets BID2 ; BID11 ) as general natural language text BID16 ). No systematic study is that the predictive accuracy all these different character based deep learning architectures, leaving one which one works DGA detectionTo answer this open question in compare five different deep learning for character based text classification (see TAB0 ) for the problem detecting DGAs They all rely character-level embeddings, and they use a deep learning architecture based convolutional neural network layers, recurrent neural network or a combination both Our most important finding for DGA detection which can thought classification short character strings despite of vast differences the deep network architectures there remarkably little difference among the methods in terms accuracy and false positive rates, while they all comfortably a random forest trained human engineered features This finding is of practical value for the design deep neural network based classifiers for short text classification in industry and: it provides evidence one can select an architecture BID16 is faster to train, without loss accuracy In the context DGA detection optimizing the training time is of, the models need retrained on stay current respect new, emerging malware DGA detection, i.e. the classification task of distinguishing benign domain names those generated malware (Domain Generation Algorithms has become a central topic information security. In this paper have compared five different deep neural network architectures that perform this classification task based purely the domain name string, given as a raw input signal at character level All five models, i.e. two RNN based architectures two CNN based architectures one hybrid RNN/CNN architecture perform equally, catching around 97-98% malicious domain names against a false positive rate of 0.001. This roughly means for every 970 malicious domain names that the deep networks catch they flag only one benign domain name erroneously as A Random Forest based human defined linguistic features achieves a recall of only 83% against the same 0.001 false positive rate when trained and tested on the same data that was the deep networks The use a deep neural network that automatically features is attractive in cybersecurity setting is a lot harder craft malware to avoid by a system relies automatically learned features instead on human engineered features An interesting direction future work is test the trained deep networks more extensively on domain names generated new and previously unseen malware familiesA KERAS CODE FOR DEEP NETWORKS main input = Input (shape=(75 ) , dtype='int32 ', name='main input embedding = Embedding(input dim=128 output input length =75)(main input ) lstm = LSTM(128 return sequencesFalse)(embedding) drop Dropout(0.5 (lstm) output = Dense(1 activation ='sigmoid (drop) model Model(inputsmain input outputs =output) model.compile loss' binary crossentropy optimizer =adam')Listing 1: Endgame model with single LSTM layer, adapted main input = Input bi lstm = Bidirectional ( layerLSTM(64 merge mode='concat')(embedding) output = Dense(1 bi lstm ) model CMU model, BID2 main input conv1 = Conv1D( filters128 kernel size =3 padding='same strides1)(embedding thresh1 ThresholdedReLU(1e−6)(conv1 max pool1 MaxPooling1D(pool size=2 ) conv2 Conv1D21)(max flatten Flatten () (max fc Dense(64)( flatten ) thresh fc drop NYU model stacked CNN layers BID16 def getconvmodel( self , kernel size , filters ) model = Sequential () model.add Conv1D filters input shape =(128 128 kernel kernel size , activation relu ', model.add(Lambda(lambda x: K.sum(x axis=1 output shape filters , ) ) ) return main input getconvmodel(2 256)(embedding merged = Concatenate () ([ conv1] middle = Dense(1024 activation)mergedmiddle middlesigmoid Listing 4: Invincea CNN model parallel CNN layers ', optimizeradam Listing 4: Invincea CNN model with parallel CNN layers, adapted BID8 main input = Input (shape=(75 ) , dtype='int32 ', name='main input embedding = Embedding(input dim=128 output input length =75)(main ) conv Conv1D filters128 kernel size =3 padding='same activation relu ', strides1)(embedding) max pool MaxPooling1D(pool size=2 padding='same')(conv) encode = LSTM(64 return sequencesFalse (max output (encode) model Listing 5: MIT model a stacked CNN and LSTM layer flatten Flatten ()embedding flatten model Baseline Model only Embedding Layer main input (shape=(11 name='main dense = Dense(128 ') print MLP Model 128 Nodes Dense Layer",0.01,0.567417142405429
"Recognizing the relationship between two texts is an important aspect of natural language understanding (NLU), and a variety of neural network models have been proposed for solving NLU tasks. Unfortunately, recent work showed that the datasets these models are trained on often contain biases that allow models to achieve non-trivial performance without possibly learning the relationship between the two texts. We propose a framework for building robust models by using adversarial learning to encourage models to learn latent, bias-free representations. We test our approach in a Natural Language Inference (NLI) scenario, and show that our adversarially-trained models learn robust representations that ignore known dataset-specific biases. Our experiments demonstrate that our models are more robust to new NLI datasets. Recognizing the relationship between two texts is a significant aspect of general natural language understanding (NLU) BID2 . Natural Language Inference (NLI) is often used to gauge a model's ability to understand such a relationship between two texts BID11 BID12 . In NLI, a model is tasked with determining whether a hypothesis (the animal moved) would likely be inferred from a premise (a black cat ran). The development of new large-scale datasets has led to a flurry of various neural network architectures for solving NLI. However, recent work has found that many NLI datasets contain biases that enable hypothesis-only models -models that are given access to the hypothesis alone -to perform surprisingly well without possibly learning the relationship between two texts. For instance, annotation artifacts and statistical irregularities in the popular Stanford Natural Language Inference dataset (SNLI) BID5 allowed hypothesis-only models to perform at double the majority class baseline, and at least 5 other recent NLI datasets contain similar biases BID21 BID43 BID54 . We will use the terms ""artifacts"" and ""biases"" interchangeably.The existence of annotation artifacts in large-scale NLI datasets is detrimental for making progress in deep learning research for NLU. How can we trust the performance of top models if it is possible to infer the relationship without even looking at the premise? Solutions to this concern are so far unsatisfactory: constructing new datasets BID50 ) is costly and may still result in other artifacts; filtering ""easy"" examples and defining a harder subset is useful for evaluation purposes BID21 , but difficult to do on a large scale that will enable training; and compiling adversarial examples BID18 ) is informative but again limited by scale or diversity. Furthermore, these solutions do not address a lingering question: can we develop models that will generalize well despite many NLI datasets containing specific hypothesis-only biases?Inspired by domain-adversarial training of neural networks BID16 BID17 , we propose two architectures (Figure 1 ) that enable a model to perform well on other NLI datasets regardless of what annotation artifacts exist in the training corpus's hypotheses. While learning to classify the relationship between two texts, we simultaneously use adversarial learning to discourage our model from using dataset-specific biases.In this way, the resulting representations contain fewer biases, and the model is encouraged to learn the relationship between the two texts. Our experiments demonstrate that our architectures generate sentence representations that are more robust to annotation artifacts, and also transfer better: when trained on one dataset and evaluated on another, they perform better than a non-adversarial model in 9 out of 12 target datasets. The methodology can also be extended to other NLU tasks, and we outline the necessary changes to our architectures in the conclusion. To our knowledge , this is the first study that explores methods to ignore hypothesis-only biases when training NLI models. Biases in annotations are a major source of concern for the quality of NLI datasets and systems. In this paper, we presented a solution for combating annotation biases based on adversarial learning. We designed two architectures that discourage the hypothesis encoder from learning the biases, and instead obtain a more unbiased representation. We empirically evaluated our approach in a transfer learning scenario, where we found our models to perform better than a non-adversarial baseline on a range of datasets. We also investigated what biases remain in the latent representations.The methodology developed in this work can be extended to deal with biases in other NLU tasks, where one is concerned with finding the relationship between two objects. For example, in Reading Comprehension, a question is being asked about a passage; in story cloze completion, an ending is judged with respect to a context; and in Visual Question Answering, a question is asked about an image. In all these cases, the second element (question, ending, and question, respectively) may contain biases. Our adversarial architectures naturally apply to any model that relies on encoding this biased element, and may help remove such biases from the latent representation. We hope to encourage such investigation in the broader research community. TAB1 we consider the range {1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0}. In each dataset, we choose the best-performing model on the development set and report its quality on the test set.We follow the InferSent training regime, using SGD with an initial learning rate of 0.1. See BID9 for details.",1059,0.56,626,1.6916932907348243,"Recognizing the relationship two texts natural language understanding (NLU a variety neural network models solving Unfortunately recent work showed the datasets these models trained often biases allow models achieve without possibly learning the relationship the two texts We propose building robust models by adversarial learning encourage models latent, bias-free representations We test our approach Natural Inference scenario show our adversarially-trained models learn robust representations ignore known dataset-specific biases Our experiments demonstrate our models new NLI datasets Recognizing the relationship two texts general natural language understandingNLU BID2 . Natural Language Inference often gauge such a relationship two texts BID11 BID12 . In NLI a model tasked a hypothesisthe animal moved would likely inferred a premisea black cat ran The development new large-scale datasets various neural network solving NLI However recent work many NLI datasets biases enable hypothesis-only models -models given access the hypothesis alone surprisingly without possibly learning the relationship two texts For instance annotation artifacts statistical irregularities the popular Stanford Natural Language Inference dataset (SNLI) BID5 allowed hypothesis-only models perform at double the majority class baseline at least 5 other recent NLI datasets contain BID21 BID43 BID54 We will use ""artifacts ""biasesThe existence annotation artifacts large-scale NLI datasets detrimental making progress deep learning research for NLU How trust the performance top models if possible infer the relationship without even the premise Solutions this concern so unsatisfactory constructing new datasets BID50 ) costly may still other artifacts; filtering ""easy"" examples defining a harder subset useful evaluation purposes BID21 difficult on that enable training; compiling adversarial examples informative again limited scale or diversity Furthermore these solutions a lingering question can develop models generalize well despite many NLI datasets containing specific hypothesisonly biases?Inspired domain-adversarial training BID16 BID17 two architectures (Figure enable regardless what annotation artifacts the training corpus's hypotheses While learning classify the relationship two texts simultaneously use adversarial learning discourage our model dataset-specific biasesIn the resulting representations contain encouraged Our experiments demonstrate our architectures generate sentence representations annotation artifacts also transfer better: trained one dataset evaluated 9 12 target datasets The methodology can extended other NLU tasks and we outline the necessary changes our architectures the conclusion To our knowledge , explores methods ignore hypothesis-only biases training NLI models Biases in annotations concern the quality NLI datasets systems In presented a solution combating annotation biases based adversarial learning We designed two architectures discourage the hypothesis encoder learning the biases instead obtain We empirically evaluated our approach a transfer learning scenario found our models a non-adversarial baseline a range datasets We also investigated what biases remain the latent representations.The methodology developed can extended deal biases other NLU tasks where one is concerned finding the relationship two objects For example Reading Comprehension a question being; story cloze completion an ending judged with a context Visual Question Answering In the second element (question, ending may contain biases Our adversarial architectures naturally apply any model relies encoding this biased element may help remove the latent representation We hope encourage such investigation the broader research community TAB1 we consider the range { In each dataset choose on the development set report its qualityWe follow the InferSent training regime SGD with See BID9",0.01,0.46645290296809233
"We study the problem of learning representations of entities and relations in knowledge graphs for predicting missing links. The success of such a task heavily relies on the ability of modeling and inferring the patterns of (or between) the relations. In this paper, we present a new approach for knowledge graph embedding called RotatE, which is able to model and infer various relation patterns including: symmetry/antisymmetry, inversion, and composition. Specifically, the RotatE model defines each relation as a rotation from the source entity to the target entity in the complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Experimental results on multiple benchmark knowledge graphs show that the proposed RotatE model is not only scalable, but also able to infer and model various relation patterns and significantly outperform existing state-of-the-art models for link prediction. Knowledge graphs are collections of factual triplets, where each triplet (h, r, t) represents a relation r between a head entity h and a tail entity t. Examples of real-world knowledge graphs include Freebase BID0 , Yago (Suchanek et al., 2007) , and WordNet (Miller, 1995) . Knowledge graphs are potentially useful to a variety of applications such as question-answering BID10 , information retrieval BID30 , recommender systems BID34 , and natural language processing BID31 . Research on knowledge graphs is attracting growing interests in both academia and industry communities.Since knowledge graphs are usually incomplete, a fundamental problem for knowledge graph is predicting the missing links. Recently, extensive studies have been done on learning low-dimensional representations of entities and relations for missing link prediction (a.k.a., knowledge graph embedding) BID3 BID28 BID7 . These methods have been shown to be scalable and effective. The general intuition of these methods is to model and infer the connectivity patterns in knowledge graphs according to the observed knowledge facts. For example, some relations are symmetric (e.g., marriage) while others are antisymmetric (e.g., filiation); some relations are the inverse of other relations (e.g., hypernym and hyponym); and some relations may be composed by others (e.g., my mother's husband is my father). It is critical to find ways to model and infer these patterns, i.e., symmetry/antisymmetry, inversion, and composition, from the observed facts in order to predict missing links.Indeed, many existing approaches have been trying to either implicitly or explicitly model one or a few of the above relation patterns BID3 BID29 BID17 Table 1: The score functions f r (h, t) of several knowledge graph embedding models, where · denotes the generalized dot product, • denotes the Hadamard product, ⊗ denotes circular correlation, σ denotes activation function and * denotes 2D convolution. · denotes conjugate for complex vectors, and 2D reshaping for real vectors in ConvE model. TransX represents a wide range of TransE's variants, such as TransH BID29 , TransR BID17 , and STransE BID23 , where g r,i (·) denotes a matrix multiplication with respect to relation r. BID32 BID28 . For example, the TransE model BID2 , which represents relations as translations, aims to model the inversion and composition patterns; the DisMult model BID32 , which models the three-way interactions between head entities, relations, and tail entities, aims to model the symmetry pattern. However, none of existing models is capable of modeling and inferring all the above patterns. Therefore, we are looking for an approach that is able to model and infer all the three types of relation patterns.In this paper, we propose such an approach called RotatE for knowledge graph embedding. Our motivation is from Euler's identity e iθ = cos θ + i sin θ, which indicates that a unitary complex number can be regarded as a rotation in the complex plane. Specifically, the RotatE model maps the entities and relations to the complex vector space and defines each relation as a rotation from the source entity to the target entity. Given a triplet (h, r, t), we expect that t = h • r, where h, r, t ∈ C k are the embeddings, the modulus |r i | = 1 and • denotes the Hadamard (element-wise) product. Specifically, for each dimension in the complex space, we expect that:t i = h i r i , where h i , r i , t i ∈ C and |r i | = 1.It turns out that such a simple operation can effectively model all the three relation patterns: symmetric/antisymmetric, inversion, and composition. For example, a relation r is symmetric if and only if each element of its embedding r, i.e. r i , satisfies r i = e 0/iπ = ±1; two relations r 1 and r 2 are inverse if and only if their embeddings are conjugates: r 2 =r 1 ; a relation r 3 = e iθ3 is a combination of other two relations r 1 = e iθ1 and r 2 = e iθ2 if and only if r 3 = r 1 • r 2 (i.e. θ 3 = θ 1 + θ 2 ). Moreover, the RotatE model is scalable to large knowledge graphs as it remains linear in both time and memory.To effectively optimizing the RotatE, we further propose a novel self-adversarial negative sampling technique, which generates negative samples according to the current entity and relation embeddings. The proposed technique is very general and can be applied to many existing knowledge graph embedding models. We evaluate the RotatE on four large knowledge graph benchmark datasets including FB15k BID3 , WN18 BID3 ), FB15k-237 (Toutanova & Chen, 2015 and WN18RR BID7 . Experimental results show that the RotatE model significantly outperforms existing state-of-the-art approaches. In addition, RotatE also outperforms state-of-the-art models on Countries BID4 , a benchmark explicitly designed for composition pattern inference and modeling. To the best of our knowledge, RotatE is the first model that achieves state-of-the-art performance on all the benchmarks. 2 The p-norm of a complex vector v is defined as v p = p |vi| p . We use L1-norm for all distancebased models in this paper and drop the subscript of · 1 for brevity. We have proposed a new knowledge graph embedding method called RotatE, which represents entities as complex vectors and relations as rotations in complex vector space. In addition, we propose a novel self-adversarial negative sampling technique for efficiently and effectively training the RotatE model. Our experimental results show that the RotatE model outperforms all existing state-of-theart models on four large-scale benchmarks. Moreover, RotatE also achieves state-of-the-art results on a benchmark that is explicitly designed for composition pattern inference and modeling. A deep investigation into RotatE relation embeddings shows that the three relation patterns are implicitly represented in the relation embeddings. In the future, we plan to evaluate the RotatE model on more datasets and leverage a probabilistic framework to model the uncertainties of entities and relations. No existing models are capable of modeling all the three relation patterns. For example, TransE cannot model the symmetry pattern because it would yield r = 0 for symmetric relations; TransX can infer and model the symmetry/antisymmetry pattern when g r,1 = g r,2 , e.g. in TransH BID29 , but cannot infer inversion and composition as g r,1 and g r,2 are invertible matrix multiplications; due to its symmetric nature, DistMult is difficult to model the asymmetric and inversion pattern; ComplEx addresses the problem of DisMult and is able to infer both the symmetry and asymmetric patterns with complex embeddings. Moreover, it can infer inversion rules because the complex conjugate of the solution to arg max r Re( x, r, y ) is exactly the solution to arg max r Re( y, r, x ). However, ComplEx cannot infer composition rules, since it does not model a bijection mapping from h to t via relation r. These concerns are summarized in TAB0 .B PROOF OF LEMMA 1Proof. if r(x, y) and r(y, x) hold, we have y = r • x ∧ x = r • y ⇒ r • r = 1 Otherwise, if r(x, y) and ¬r(y, x) hold, we have DISPLAYFORM0 Proof. if r 1 (x, y) and r 2 (y, x) hold, we have DISPLAYFORM1 Proof. if r 1 (x, z) , r 2 (x, y ) and r 3 (y, z) hold, we have DISPLAYFORM2",1844,0.932,1109,1.6627592425608657,"We study the problem learning representations entities relations knowledge graphs for predicting missing links The success such a task heavily modeling inferring the patterns ( between the relations In this paper knowledge graph embedding called RotatE, able model and infer various relation patterns including symmetry/antisymmetry inversion composition Specifically the RotatE model defines each relation a rotation from the source entity the complex vector space In addition propose a novel self-adversarial negative sampling technique efficiently and training the RotatE model Experimental results on multiple benchmark knowledge graphs the proposed RotatE model scalable able infer and model various relation patterns significantly existing state for link prediction Knowledge graphs collections factual triplets where (h, r a relation r between a head entity h Examples real-world knowledge graphs include Freebase BID0 , Yago (Suchanek et WordNetMiller 1995 Knowledge graphs potentially a variety such question-answering BID10 , information BID30 recommender systems BID34 natural Research knowledge graphs attracting growing interests both academia industry communitiesSince knowledge graphs usually incomplete a fundamental problem knowledge graph is predicting the missing links Recently extensive studies learning low-dimensional representations entities relations for missing link prediction knowledge graph embedding BID3 BID28 BID7 . These methods scalable The general intuition these methods model and infer the connectivity patterns knowledge graphs according the observed knowledge facts For example some relations the inverse and hyponym may composed by others my mother's husband It critical find model infer these patterns symmetry/ inversion composition from the observed facts in predict missing linksIndeed many existing approaches trying either implicitly one a the above relation patterns BID3 BID29 BID17 Table score functions f rh t of several knowledge graph embedding models where · denotes the generalized dot product • the Hadamard product circular correlation, �� denotes activation function and * denotes 2D convolution · denotes conjugate for complex vectors 2D reshaping real vectors in ConvE model TransX represents TransE's variants such TransH BID29 , STransE where g r,i (· denotes a matrix multiplication with respect relation r. BID32 BID28 . For example the TransE model BID2 , represents relations as translations aims model the inversion and composition patterns; the DisMult model BID32 models head entities relations tail entities the symmetry pattern However none existing models is capable modeling and inferring all the above patterns Therefore looking an approach able model infer all the three types relation patternsIn called RotatE for knowledge graph embedding Our motivation from Euler's identity e i� = cos + indicates a unitary complex number regarded a rotation the complex plane Specifically the RotatE model maps the entities and relations the complex vector space defines each relation a rotation from the source entity Given a triplet (h r expect that t = h • r, t � C k are, the modulus |r i • denotes the Hadamard (element-wise) product Specifically for each dimension the complex space expect:t i h r , , t i � and |r 1.It turns such a simple operation effectively model all the three relation patterns inversion composition For example a relation r symmetric each element its embedding r, satisfies = e 0/iπ = ±1; two relations 1 inverse conjugates: 2r ; = e i�3 is a combination if • ( � � Moreover the RotatE model scalable large knowledge graphs as remains linear both time memoryTo effectively optimizing, further propose a novel self-adversarial negative sampling technique generates negative samples according the current entity and relation embeddings The proposed technique very general many existing knowledge graph embedding models We evaluate the RotatE on four large knowledge graph benchmark datasets including FB15k BID3 , WN18 BID3 ), FB15k-237 (Toutanova & Chen and WN18RR BID7 . Experimental results the RotatE model significantly existing state approaches In addition RotatE also outperforms state models on Countries BID4 , a benchmark explicitly composition pattern inference modeling To RotatE the first model achieves state all the benchmarks 2 The p-norm of a complex vector v defined v p = p |vi| p We use L1-norm for all distancebased models in drop the subscript of · 1 brevity We proposed a new knowledge graph embedding method RotatE, represents entities complex vectors and relations as rotations In addition propose a novel self-adversarial negative sampling technique efficiently and training the RotatE model Our experimental results the RotatE model all existing statetheart on four large-scale benchmarks Moreover RotatE also achieves state results a benchmark that explicitly composition pattern inference modeling A deep investigation RotatE relation embeddings shows the three relation patterns implicitly represented In the future plan evaluate the RotatE model on more datasets leverage model the uncertainties entities relations No existing models capable modeling all the three relation patterns For example TransE cannot model the symmetry pattern because would yield r symmetric relations; TransX infer and when g r,1 , TransH BID29 , inversion composition as and invertible matrix multiplications; due DistMult difficult; ComplEx addresses DisMult is infer with complex embeddings Moreover can infer inversion rules because the complex conjugate the solution arg max r Re x, r, y exactly the solution y However ComplEx infer composition rules since model a bijection mapping from h via relation r. These concerns summarized TAB0 .B PROOF LEMMA 1Proof. if r(x and hold we y = r • x �� � Otherwise � DISPLAYFORM0 Proof if r 1 (x and hold we DISPLAYFORM1 Proof. if r 1 (x z , ) and hold we DISPLAYFORM2",0.01,0.3927314903385226
"Deep learning algorithms have been known to be vulnerable to adversarial perturbations in various tasks such as image classification. This problem was addressed by employing several defense methods for detection and rejection of particular types of attacks. However, training and manipulating networks according to particular defense schemes increases computational complexity of the learning algorithms. In this work, we propose a simple yet effective method to improve robustness of convolutional neural networks (CNNs) to adversarial attacks by using data dependent adaptive convolution kernels. To this end, we propose a new type of HyperNetwork in order to employ statistical properties of input data and features for computation of statistical adaptive maps. Then, we filter convolution weights of CNNs with the learned statistical maps to compute dynamic kernels. Thereby, weights and kernels are collectively optimized for learning of image classification models robust to
 adversarial attacks without employment of additional target detection and rejection algorithms.
 We empirically demonstrate that the proposed method enables CNNs to spontaneously defend against different types of attacks, e.g. attacks generated by Gaussian noise, fast gradient sign methods (Goodfellow et al., 2014) and a black-box attack (Narodytska & Kasiviswanathan, 2016). Deep convolutional neural networks are powerful and popular algorithms that achieve state-of-the-art performance in various computer vision tasks, such as object recognition. Despite the advances made by the recent architectures BID7 BID16 BID18 BID5 , they are discovered to be fragile to small but carefully directed perturbations of images BID17 , such that the targeted images can be classified to incorrect categories with high confidence, while humans are still able to correctly classify the attacked images, being undisturbed or even unaware of the perturbations. The vulnerability of these networks to these, so called adversarial examples, may lead to undesirable consequences in safety-and security-critical applications. provide an example of misclassification of traffic signs which could be a significant threat for autonomous driving systems that employ deep learning algorithms. Various adversarial attack methods for neural networks have been studied in numerous works. The majority of attack methods can be catalogued in three groups.1. Methods which use unspecific statistical noise: In this group, input images are perturbed using unspecific statistical noise, e.g. Gaussian noise, salt and pepper noise and blurring. Since shape and parameters of distribution functions that are used to generate noise are not determined, it is usually not easy to obtain a highly confident misclassification results with imperceptible perturbations BID17 . 2. Gradient based attack methods: They are used to generate high confidence imperceptible adversarial examples within few steps or one-shot gradient based noise. Some examples of the methods considered in this group are (Iterative) Fast Gradient Sign Method BID3 BID8 , L-BFGS BID19 , Jacobian-based Saliency Map BID12 and DeepFool . These methods require a white-box environment in order to make attacks. In other words, the full network architecture and weights are required to be accessible in order to obtain gradients towards input images.3. Black-box attack methods. These methods assume that only the output of the networks can be accessed. Substitute networks and greedy search of noisy pixels BID11 are considered in this group. It is worth mentioning that, methods such as transferring adversarial examples from another network, which is optimized with a sufficient part or the whole training datasets, are not considered as a genuine black-box method.In this work, inspired by the recent works BID0 BID4 that construct neural networks with data dependent weights, we propose a simple yet effective method to train CNNs by improving their robustness to adversarial perturbations. Our main idea is to adaptively filter convolution weights of CNNs by using statistical properties of input data and features. Concretely, we propose a HyperNetwork to compute statistical adaptive maps using these statistical properties (mean and variance) of input data and features for each input channel. Then, we obtain data dependent kernels for convolution operations by computing Hadamard (element-wise) product of computed maps and convolution weights. Our main contributions can be summarized as follows:1. We propose a new type of CNN architecture that employ HyperNetworks to dynamically generate data dependent convolution kernels with statistical properties of input data and features. 2. We empirically verify the robustness of our proposed models using large scale vision dataset, and demonstrate that their robustness is improved without using additional aforementioned computationally complex defense methods or spending effort to generate adversarial examples for training. In this work, we propose a simple yet effective method to improve robustness of convolutional neural networks (CNNs) to adversarial attacks by training CNNs using data dependent adaptive convolution kernels. To this end, we employ HyperNetworks to dynamically generate data dependent convolution kernels with statistical properties of input data and features. The robustness of our proposed method is verified using 3 different types of attack with state-of-the-art CNN models trained on the ILSVRC-2012 dataset. Moreover, the robustness is obtained spontaneously during a normal training progress without losing any performance in the original tasks. This shed light on building practical deep learning systems that focus on the target without a concern of attacker. On the other hand, there still exists uncertainty on the mechanism of the robustness remains to be solved in the future works. Furthermore, designing of network architectures that employ more powerful HyperNetworks with better adversarial robustness is still an open problem.",1081,0.637,652,1.6579754601226995,"Deep learning algorithms known vulnerable various tasks This problem addressed employing several defense methods detection rejection particular types attacks However training and manipulating networks according particular defense schemes increases computational complexity the learning In this work propose robustness adversarial attacks data dependent adaptive convolution kernels To this end propose HyperNetwork in employ statistical properties input data features for computation statistical adaptive maps Then we filter convolution weights of CNNs the learned statistical maps compute dynamic kernels Thereby weights kernels collectively optimized learning of image classification models robust adversarial attacks without employment additional target detection rejection algorithms We empirically demonstrate the proposed method enables CNNs spontaneously defend different types generated Gaussian noise fast gradient sign methodsGoodfellow a blackNarodytska Kasiviswanathan powerful and popular algorithms achieve state Despite the advances the recent architectures BID7 BID16 BID18 BID5 , they discovered fragile to small but carefully directed perturbations images BID17 such the targeted images classified to incorrect categories with while humans correctly the attacked images being or unaware The vulnerability these networks these, so adversarial examples lead undesirable consequences safety-and security-critical applications provide misclassification traffic signs which a significant threat for autonomous driving systems that employ Various adversarial attack methods for neural networks studied numerous works The majority attack methods can catalogued three groups.1 Methods unspecific statistical noise: In input images perturbed salt pepper Since shape parameters distribution functions that noise determined usually easy obtain a highly confident misclassification results BID17 . 2 Gradient based attack methods They high confidence imperceptible adversarial examples within few steps or one-shot gradient based noise Some examples the methods considered this group (Iterative) Fast Gradient Sign Method BID3 BID8 , L-BFGS BID19 Jacobian-based Saliency Map BID12 and DeepFool . These methods require a white-box environment make attacks In the full network architecture weights required accessible obtain gradients towards input images.3. Black-box attack methods These methods assume only the output the networks Substitute networks greedy search of noisy pixels BID11 are considered in It worth methods transferring adversarial examples another network optimized with a sufficient part or the whole training datasets considered a genuine black-box methodIn inspired BID0 BID4 that construct data dependent weights CNNs by improving Our main idea adaptively filter convolution weights of CNNs statistical properties input data features Concretely propose a HyperNetwork to compute statistical adaptive maps these statistical propertiesmean input data features for each input channel Then we obtain data dependent kernels convolution operations by computing Hadamard (element-wise) product computed maps Our main contributions can We propose CNN architecture employ HyperNetworks dynamically data dependent convolution kernels with statistical properties input data features 2 We empirically verify large scale vision dataset demonstrate improved without additional aforementioned computationally complex defense methods or spending effort generate adversarial examples for training In this work propose robustness adversarial attacks data dependent adaptive convolution kernels To this end employ HyperNetworks dynamically data dependent convolution kernels with statistical properties input data features The robustness our proposed method verified 3 different types attack with state CNN models trained the ILSVRC-2012 dataset Moreover the robustness is obtained spontaneously during a normal training progress without losing the original tasks This shed light building practical deep learning systems focus the target without a concern attacker On still uncertainty the mechanism the robustness remains solved the future works Furthermore designing of network architectures employ more powerful HyperNetworks with better adversarial robustness still",0.01,0.38054283298460445
"Adapting deep networks to new concepts from a few examples is challenging, due to the high computational requirements of standard fine-tuning procedures.
 Most work on few-shot learning has thus focused on simple learning techniques for adaptation, such as nearest neighbours or gradient descent.
 Nonetheless, the machine learning literature contains a wealth of methods that learn non-deep models very efficiently.
 In this paper, we propose to use these fast convergent methods as the main adaptation mechanism for few-shot learning.
 The main idea is to teach a deep network to use standard machine learning tools, such as ridge regression, as part of its own internal model, enabling it to quickly adapt to novel data.
 This requires back-propagating errors through the solver steps.
 While normally the cost of the matrix operations involved in such a process would be significant, by using the Woodbury identity we can make the small number of examples work to our advantage.
 We propose both closed-form and iterative solvers, based on ridge regression and logistic regression components.
 Our methods constitute a simple and novel approach to the problem of few-shot learning and achieve performance competitive with or superior to the state of the art on three benchmarks. Humans can efficiently perform fast mapping BID7 BID8 , i.e. learning a new concept after a single exposure. By contrast, supervised learning algorithms -and neural networks in particular -typically need to be trained using a vast amount of data in order to generalize well. This requirement is problematic, as the availability of large labelled datasets cannot always be taken for granted. Labels can be costly to acquire: in drug discovery, for instance, campaign budgets often limits researchers to only operate with a small amount of biological data that can be used to form predictions about properties and activities of compounds BID0 . In other circumstances, data itself can be scarce, as it can happen for example with the problem of classifying rare animal species, whose exemplars are not easy to observe. Such a scenario, in which just one or a handful of training examples is provided, is referred to as one-shot or few-shot learning BID28 BID12 BID25 BID18 and has recently seen a tremendous surge in interest within the machine learning community (e.g. ; BID4 ; BID39 ; BID14 ).Currently , most methods tackling few-shot learning operate within the general paradigm of metalearning, which allows one to develop algorithms in which the process of learning can improve with the number of training episodes BID53 BID57 . This can be achieved by distilling and transferring knowledge across episodes. In practice , for the problem of few-shot classification, meta-learning is often implemented using two ""nested training loops"". The base learner works at the level of individual episodes, which correspond to learning problems characterised by having only a small set of labelled training images available. The meta learner , by contrast, learns from a collection of such episodes, with the goal of improving the performance of the base learner across episodes. Episode N Figure 1 : Diagram of the proposed method for one episode, of which several are seen during meta-training. The task is to learn new classes given just a few sample images per class. In this illustrative example, there are 3 classes and 2 samples per class, making each episode a 3-way, 2-shot classification problem. At the base learning level, learning is accomplished by a differentiable ridge regression layer (R.R.), which computes episode-specific weights (referred to as w E in Section 3.1 and as W in Section 3.2). At the meta-training level, by back-propagating errors through many of these small learning problems, we train a network whose weights are shared across episodes, together with the hyper-parameters of the R.R. layer. In this way, the R.R. base learner can improve its learning capabilities as the number of experienced episodes increases.Clearly, in any meta-learning algorithm, it is of paramount importance to choose the base learner carefully. On one side of the spectrum , methods related to nearest-neighbours, such as learning similarity functions BID23 BID48 , are fast but rely solely on the quality of the similarity metric, with no additional data-dependent adaptation at test-time. On the other side of the spectrum , methods that optimize standard iterative learning algorithms, such as backpropagating through gradient descent BID14 BID35 or explicitly learning the learner's update rule BID1 BID39 , are slower but allow more adaptability to different problems/datasets.In this paper, we take a different perspective. As base learners, we propose to adopt simple learning algorithms that admit a closed-form solution such as ridge regression. Crucially, the simplicity and differentiability of these solutions allow us to backpropagate through learning problems. Moreover, these algorithms are particularly suitable for use within a meta-learning framework for few-shot classification for two main reasons. First, their closed-form solution allows learning problems to be solved efficiently. Second, in a data regime characterized by few examples of high dimensionality, the Woodbury's identity (Petersen et al., 2008, Chapter 3.2) can be used to obtain a very significant gain in terms of computational speed.We demonstrate the strength of our approach by performing extensive experiments on Omniglot (Lake et al., 2015), CIFAR-100 BID24 ) (adapted to the few-shot problem) and miniImageNet . Our base learners are fast, simple to implement, and can achieve performance that is competitive with or superior to the state of the art in terms of accuracy. With the aim of allowing efficient adaptation to unseen learning problems, in this paper we explored the feasibility of incorporating fast solvers with closed-form solutions as the base learning component of a meta-learning system. Importantly, the use of the Woodbury identity allows significant computational gains in a scenario presenting only a few samples with high dimensionality, like one-shot of few-shot learning. R2-D2, the differentiable ridge regression base learner we introduce, is almost as fast as prototypical networks and strikes a useful compromise between not performing adaptation for new episodes (like metric-learning-based approaches) and conducting a costly iterative approach (like MAML or LSTM-based meta-learners). In general, we showed that our base learners work remarkably well, with excellent results on few-shot learning benchmarks, generalizing to episodes with new classes that were not seen during training. We believe that our findings point in an exciting direction of more sophisticated yet efficient online adaptation methods, able to leverage the potential of prior knowledge distilled in an offline training phase. In future work, we would like to explore Newton's methods with more complicated second-order structure than ridge regression. Contributions within the few-shot learning paradigm. In this work, we evaluated our proposed methods R2-D2 and LR-D2 in the few-shot learning scenario BID12 BID25 BID39 BID18 , which consists in learning how to discriminate between images given one or very few examples. For methods tackling this problem, it is common practice to organise the training procedure in two nested loops. The inner loop is used to solve the actual few-shot classification problem, while the outer loop serves as a guidance for the former by gradually modifying the inductive bias of the base learner BID57 . Differently from standard classification benchmarks, the few-shot ones enforce that classes are disjoint between dataset splits.In the literature (e.g. ), the very small classification problems with unseen classes solved within the inner loop have often been referred to as episodes or tasks. Considering the general few-shot learning paradigm just described, methods in the recent literature mostly differ for the type of learner they use in the inner loop and the amount of per-episode adaptability they allow. For example, at the one end of the spectrum in terms of ""amount of adaptability"", we can find methods such as MAML Finn et al. (2017) , which learns how to efficiently fine-tune the parameters of a neural-network with few iterations of SGD. On the other end, we have methods based on metric learning such as prototypical networks BID48 and relation network BID50 , which are fast but do not perform adaptation. Note that the amount of adaptation to a new episode (i.e.a new classification problem with unseen classes) is not at all indicative of the performance in few-shot learning benchmarks. As a matter of fact, both BID48 and BID50 achieve higher accuracy than MAML. Nonetheless, adaptability is a desirable property, as it allows more design flexibility.Within this landscape, our work proposes a novel technique (R2-D2) that does allow per-episode adaptation while at the same time being fast TAB6 ) and achieving strong performance TAB0 . The key innovation is to use a simple (and differentiable) solver such as ridge regression within the inner loop, which requires back-propagating through the solution of a learning problem. Crucially, its closed-form solution and the use of the Woodbury identity (particularly advantageous in the low data regime) allow this non-trivial endeavour to be efficient. We further demonstrate that this strategy is not limited to the ridge regression case, but it can also be extended to other solvers (LR-D2) by dividing the problem into a short series of weighted least squares problems ( (Murphy, 2012, Chapter 8.3.4",1871,0.992,1092,1.7133699633699633,"Adapting deep networks new concepts from a few examples challenging due standard fine-tuning procedures Most work few-shot learning has thus focused simple learning techniques adaptation nearest neighbours gradient descent Nonetheless the machine learning literature contains methods learn non-deep models very In these fast convergent methods as the main adaptation mechanism few-shot learning The main idea teach a deep network use standard machine learning tools ridge regression as part its own internal model enabling quickly adapt novel data This requires back-propagating errors through the solver steps While normally the cost the matrix operations involved significant by the Woodbury identity we the small number examples work to We propose both closed-form and iterative solvers ridge regression logistic regression components Our methods constitute few-shot learning achieve performance competitive or superior the state on three benchmarks Humans efficiently perform fast mapping BID7 BID8 , learning after By contrast supervised learning algorithms -and in need well This requirement problematic the availability large labelled datasets taken Labels can costly acquire: in drug discovery campaign budgets limits researchers operate biological data that form predictions properties activities compounds BID0 . In other circumstances data itself scarce happen for the problem classifying rare animal species whose exemplars easy observe Such a scenario just training examples provided referred oneshot or few learning BID28 BID12 BID25 BID18 and recently seen within ( ; BID4 ;.Currently , most methods tackling operate within metalearning allows develop algorithms which improve episodes BID53 This can achieved distilling transferring knowledge across episodes In practice , for the problem few-shot classification meta-learning implemented two ""nested training loops The base learner works the level individual episodes correspond learning problems characterised having labelled training images available The meta learner , by contrast learns a collection such episodes across Episode N Figure : Diagram the proposed method one episode of several seen during meta-training The task learn new classes given just a few sample images per In there 3 classes and 2 samples per making each episode 3,shot classification problem At the base learning level learning accomplished a differentiable ridge regression layer episode-specific weightsreferred w E in Section and At the meta-training level by back-propagating errors through many of these small learning problems train a network whose weights shared episodes together the hyper the R.R. layer In this way the R.R. base learner improve its learning capabilities experienced episodes increasesClearly in any meta-learning algorithm of choose carefully On , methods related learning similarity functions BID23 BID48 fast but rely solely the quality the similarity metric with no additional data-dependent adaptation at test-time On , methods optimize standard iterative learning through BID14 BID35 explicitly the learner's update rule slower allow different problems/In take As base learners propose adopt simple learning algorithms admit a closed-form solution such ridge regression Crucially the simplicity differentiability these solutions allow backpropagate through learning problems Moreover these algorithms particularly suitable use within few-shot classification for two main reasons First their closed-form solution allows learning problems efficiently Second a data regime characterized few examples high dimensionality the Woodbury's identity ( Chapter obtain a very significant gain terms computational speedWe demonstrate the strength performing extensive experiments Omniglot 2015 CIFAR-100 BID24 )adapted to the few-shot problem miniImageNet . Our base learners fast, simple implement achieve performance competitive or superior the state terms accuracy With the aim allowing efficient adaptation unseen learning problems in explored incorporating fast solvers closed-form solutions as the base learning component Importantly the Woodbury identity allows significant computational gains a scenario presenting with high dimensionality like one-shot of few-shot learning the differentiable ridge regression base learner we introduce almost fast prototypical networks strikes a useful compromise not performing adaptation for new episodes metric-learning-based approaches conducting MAML In general showed our base learners work remarkably excellent results few-shot learning benchmarks generalizing episodes new classes seen training We believe our findings point of more sophisticated yet efficient online adaptation methods able leverage prior knowledge distilled an offline training phase In future work explore Newton's methods with more complicated second-order structure than ridge regression Contributions within the few-shot learning paradigm. In this work evaluated our proposed methods R2-D2 the few-shot learning scenario BID12 BID25 BID39 BID18 , consists in how discriminate images given one or very few examples For methods tackling organise the training procedure two nested loops The inner loop used solve the actual few-shot classification problem while serves a guidance former by gradually modifying the inductive bias the base learner BID57 . Differently standard classification benchmarks the few-shot ones enforce classes between dataset splitsIn the literature ( the very small classification problems unseen classes solved within the inner loop often referred episodes tasks Considering the general few-shot learning paradigm just methods in mostly differ for they in the inner loop perepisode adaptability allow For example at the one end in ""amount adaptability methods MAML Finn et al (2017 , which learns the parameters with few iterations SGD On methods based metric learning such prototypical networks BID48 and relation network BID50 , fast adaptation Note the amount adaptation (i.e.a new classification problem with unseen classes at indicative in few-shot learning benchmarks As both BID48 achieve higher accuracy MAML Nonetheless adaptability a desirable property more design flexibilityWithin this landscape our work proposes ( does allow perepisode while being fast TAB6 ) achieving strong performance TAB0 The key innovation simple ( differentiable solver such ridge regression within the inner loop requires back through the solution Crucially its closed-form solution and the use the Woodbury identity (particularly advantageous the low data regime efficient We further demonstrate this strategy the ridge regression case it other solvers (LR-D2 by dividing weighted least squares problems ( (Murphy 2012, Chapter",0.01,0.5216831603507924
"While many active learning papers assume that the learner can simply ask for a label and receive it, real annotation often presents a mismatch between the form of a label (say, one among many classes), and the form of an annotation (typically yes/no binary feedback). To annotate examples corpora for multiclass classification, we might need to ask multiple yes/no questions, exploiting a label hierarchy if one is available. To address this more realistic setting, we propose active learning with partial feedback (ALPF), where the learner must actively choose both which example to label and which binary question to ask. At each step, the learner selects an example, asking if it belongs to a chosen (possibly composite) class. Each answer eliminates some classes, leaving the learner with a partial label. The learner may then either ask more questions about the same example (until an exact label is uncovered) or move on immediately, leaving the first example partially labeled. Active learning with partial labels requires (i) a sampling strategy to choose (example, class) pairs, and (ii) learning from partial labels between rounds. Experiments on Tiny ImageNet demonstrate that our most effective method improves 26% (relative) in top-1 classification accuracy compared to i.i.d. baselines and standard active learners given 30% of the annotation budget that would be required (naively) to annotate the dataset. Moreover, ALPF-learners fully annotate TinyImageNet at 42% lower cost. Surprisingly, we observe that accounting for per-example annotation costs can alter the conventional wisdom that active learners should solicit labels for hard examples. Given a large set of unlabeled images, and a budget to collect annotations, how can we learn an accurate image classifier most economically? Active Learning (AL) seeks to increase data efficiency by strategically choosing which examples to annotate. Typically, AL treats the labeling process as atomic: every annotation costs the same and produces a correct label. However, large-scale multi-class annotation is seldom atomic; we can't simply ask a crowd-worker to select one among 1000 classes if they aren't familiar with our ontology. Instead, annotation pipelines typically solicit feedback through simpler mechanisms such as yes/no questions. For example, to construct the 1000-class ImageNet dataset, researchers first filtered candidates for each class via Google Image Search, then asking crowd-workers questions like ""Is there a Burmese cat in this image?"" BID5 . For tasks where the Google trick won't work, we might exploit class hierarchies to drill down to the exact label. Costs scale with the number of questions asked. Thus, real-world annotation costs can vary per example BID24 .We propose Active Learning with Partial Feedback (ALPF), asking, can we cut costs by actively choosing both which examples to annotate, and which questions to ask? Say that for a new image, our current classifier places 99% of the predicted probability mass on various dog breeds. Why start at the top of the tree -""is this an artificial object?"" -when we can cut costs by jumping straight to dog breeds ( FIG0 )? ALPF proceeds as follows: In addition to the class labels, the learner possesses a pre-defined collection of composite classes, e.g. dog ⊃ bulldog, mastiff, .... At each round, the learner selects an (example, class) pair. The annotator responds with binary feedback, leaving the learner with a partial label. If only the atomic class label remains, the learner has obtained an exact label. For simplicity, we focus on hierarchically-organized collections-trees with atomic classes as leaves and composite classes as internal nodes. For this to work, we need a hierarchy of concepts familiar to the annotator. Imagine asking an annotator ""is this a foo?"" where foo represents a category comprised of 500 random ImageNet classes. Determining class membership would be onerous for the same reason that providing an exact label is: It requires the annotator be familiar with an enormous list of seemingly-unrelated options before answering. On the other hand , answering ""is this an animal?"" is easy despite animal being an extremely coarse-grained category -because most people already know what an animal is.We use active questions in a few ways. To start, in the simplest setup, we can select samples at random but then once each sample is selected, choose questions actively until finding the label:ML: ""Is it a dog?"" Human: Yes! ML: ""Is it a poodle ?"" Human: No! ML: ""Is it a hound ?"" Human: Yes! ML: "" Is it a Rhodesian ?"" Human: No! ML: ""Is it a Dachsund ?"" Human: Yes!In ALPF, we go one step further. Since our goal is to produce accurate classifiers on tight budget, should we necessarily label each example to completion? After each question, ALPF learners have the option of choosing a different example for the next binary query. Efficient learning under ALPF requires (i) good strategies for choosing (example , class) pairs, and (ii) techniques for learning from the partially-labeled data that results when labeling examples to completion isn't required.We first demonstrate an effective scheme for learning from partial labels. The predictive distribution is parameterized by a softmax over all classes. On a per-example basis, we convert the multiclass problem to a binary classification problem, where the two classes correspond to the subsets of potential and eliminated classes. We determine the total probability assigned to potential classes by summing over their softmax probabilities. For active learning with partial feedback, we introduce several acquisition functions for soliciting partial labels, selecting questions among all (example, class) pairs. One natural method, expected information gain (EIG) generalizes the classic maximum entropy heuristic to the ALPF setting. Our two other heuristics, EDC and ERC, select based on the number of labels that we expect to see eliminated from and remaining in a given partial label, respectively.We evaluate ALPF learners on CIFAR10, CIFAR100, and Tiny ImageNet datasets. In all cases, we use WordNet to impose a hierarchy on our labels. Each of our experiments simulates rounds of active learning, starting with a small amount of i. 2 ACTIVE LEARNING WITH PARTIAL FEEDBACK By x ∈ R d and y ∈ Y for Y = {{1}, ..., {k}}, we denote feature vectors and labels. Here d is the feature dimension and k is the number of atomic classes . By atomic class, we mean that they are indivisible. As in conventional AL, the agent starts off with an unlabeled training set D = {x 1 , ..., x n }.Composite classes We also consider a pre-specified collection of composite classes C = {c 1 , ..., c m }, where each composite class c i ⊂ {1, ..., k} is a subset of labels such that |c i | ≥ 1. Note that C includes both the atomic and composite classes. In this paper's empirical section, we generate composite classes by imposing an existing lexical hierarchy on the class labels BID19 . Our experiments validate the active learning with partial feedback framework on large-scale classification benchmarks. The best among our proposed ALPF learners fully labels the data with 42% fewer binary questions as compared to traditional active learners. Our diagnostic analysis suggests that in ALPF, it's sometimes more efficient to start with ""easier"" examples that can be cheaply annotated rather than with ""harder"" data as often suggested by traditional active learning.A WARM-STARTING PLOT ALPF -ERC -0% ALPF -ERC -5% ALPF -ERC -10% FIG4 : This plot compares our models under various amounts of warm-starting with pre-labeled i.i.d. data. We find that on the investigated datasets, ERC does benefit from warm-starting. However, absent warm-starting, EIG performs significantly worse and EDC suffers even more. We find that 5% warmstarting helps these two models and that for both, increasing warm-starting from 5% up to 10% does not lead to further improvements.",1645,0.957,971,1.694129763130793,"While many active learning papers assume ask a label receive real annotation often presents (say one among many classestypically yes/no binary feedback To annotate examples corpora for multiclass classification might ask multiple yes exploiting a label hierarchy if one To address this more realistic setting propose active learning partial feedbackALPF must actively both which example label binary question At each step selects asking belongs a chosen (possibly composite) class Each answer eliminates some classes leaving a partial label The learner then either ask the same exampleuntil an exact label uncovered move immediately leaving partially labeled Active learning with partial labels requires ( a sampling strategy choose (example, class) pairs learning between rounds Experiments Tiny ImageNet demonstrate our most effective method improves 26% (relative in top-1 classification accuracy standard active learners given 30% the annotation budget that (naively Moreover ALPF-learners fully annotate TinyImageNet at 42% lower cost Surprisingly observe accounting perexample annotation costs alter active learners solicit labels hard examples Given a large set a budget to collect annotations how learn an accurate image classifier most economically Active Learning seeks data efficiency strategically choosing which examples Typically AL treats the labeling process atomic: every annotation costs and produces However large-scale multi-class annotation seldom atomic; ask a crowd-worker select among 1000 classes if are familiar our ontology Instead annotation pipelines typically solicit feedback simpler mechanisms yes For example to construct the 1000-class ImageNet dataset researchers filtered candidates via asking crowd-workers questions BID5 . For tasks where the Google trick wo might exploit class hierarchies drill the exact label Costs scale questions Thus real-world annotation costs per example BID24 .We propose Active Learning Partial FeedbackALPF asking, can cut costs actively choosing both which examples questions Say that for a new image our current classifier places 99% the predicted probability mass various dog breeds Why start at -""is an artificial object -when cut costs jumping dog breeds FIG0 ALPF proceeds as follows In the class labels possesses composite classes dog � bulldog .... At each round the learner selects an (example, class) pair The annotator responds binary feedback leaving a partial label If only the atomic class label remains the learner obtained an exact label For simplicity focus hierarchically-organized collections-trees atomic classes as leaves composite classes internal nodes For this to a hierarchy concepts familiar the annotator Imagine asking an annotator ""is a foo where foo represents comprised 500 random ImageNet classes Determining class membership would providing an exact label: the annotator be an enormous list seemingly-unrelated options before answering On , answeringis an animal easy despite animal being coarse- category -because alreadyWe use active questions To start in the simplest setup select samples at but once choose questions actively until finding the label:ML ""Is Human! ML Is a Rhodesian a Dachsund Yes!In ALPF go one Since our goal produce accurate classifiers on tight budget should necessarily label each example to completion After each question ALPF learners a different example the next binary query Efficient learning under ALPF requires ( good strategies choosing (example , class) pairs techniques that results when labeling examples completion isWe first demonstrate an effective scheme The predictive distribution parameterized a softmax over all classes On perexample convert the multiclass problem correspond potential and eliminated classes We determine assigned potential classes over their softmax probabilities For active learning with partial feedback introduce several acquisition functions soliciting partial labels selecting questions among all (example, class) pairs One natural method, expected information gain generalizes classic maximum heuristic the ALPF setting Our two other heuristics EDC select based labels expect eliminated and remaining a given partial labelWe evaluate ALPF learners CIFAR10 Tiny ImageNet datasets In all cases use WordNet impose a hierarchy our labels Each our experiments rounds active learning starting i. 2 ACTIVE WITH PARTIAL FEEDBACK By x �� R d and y �� Y for Y = {{ ...k we denote feature vectors labels Here d is the feature dimension k atomic classes . By atomic class they As in conventional AL, the agent starts D = { 1 ....Composite classes We consider c i ��� {1 k labels such |c ≥ Note C includes both the atomic and composite classes In this paper's empirical section generate composite classes by imposing an existing lexical hierarchy labels BID19 . Our experiments validate the active learning with partial feedback framework on large classification benchmarks best among our proposed ALPF learners fully labels with 42% fewer binary questions as traditional active learners Our diagnostic analysis suggests in ALPF it's sometimes start ""easier"" examples cheaply rather with as often suggested traditional active learningA WARM-STARTING PLOT ALPF -ERC -0% FIG4 : This plot our models under various amounts warm-starting with pre We find on the investigated datasets ERC does benefit warm-starting However absent warmstarting EIG performs significantly and EDC We find 5% warmstarting helps these two models and for increasing- up further improvements",0.01,0.47266082056689634
"Despite their prevalence, Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete probability distributions in a Wasserstein space, endowed with an optimal transport metric. Wasserstein spaces are much larger and more flexible than Euclidean spaces, in that they can successfully embed a wider variety of metric structures. We propose to exploit this flexibility by learning an embedding that captures the semantic information in the Wasserstein distance between embedded distributions. We examine empirically the representational capacity of such learned Wasserstein embeddings, showing that they can embed a wide variety of complex metric structures with smaller distortion than an equivalent Euclidean embedding. We also investigate an application to word embedding, demonstrating a unique advantage of Wasserstein embeddings: we can directly visualize the high-dimensional embedding, as it is a probability distribution on a low-dimensional space. This obviates the need for dimensionality reduction techniques such as t-SNE for visualization. Learned embeddings form the basis for many state-of-the-art learning systems. Word embeddings like word2vec BID34 , GloVe BID42 , fastText BID5 , and ELMo BID43 are ubiquitous in natural language processing, where they are used for tasks like machine translation BID38 , while graph embeddings BID41 like node2vec BID21 are used to represent knowledge graphs and pre-trained image models BID47 appear in many computer vision pipelines.An effective embedding should capture the semantic structure of the data with high fidelity, in a way that is amenable to downstream tasks. This makes the choice of a target space for the embedding important, since different spaces can represent different types of semantic structure. The most common choice is to embed data into Euclidean space, where distances and angles between vectors encode their levels of association BID34 BID56 BID27 BID36 . Euclidean spaces, however, are limited in their ability to represent complex relationships between inputs, since they make restrictive assumptions about neighborhood sizes and connectivity. This drawback has been documented recently for tree-structured data, for example, where spaces of negative curvature are required due to exponential scaling of neighborhood sizes BID39 BID49 .In this paper, we embed input data as probability distributions in a Wasserstein space. Wasserstein spaces endow probability distributions with an optimal transport metric, which measures the distance traveled in transporting the mass in one distribution to match another. Recent theory has shown that Wasserstein spaces are quite flexible-more so than Euclidean spaces-allowing a variety of other metric spaces to be embedded within them while preserving their original distance metrics. As such, they make attractive targets for embeddings in machine learning, where this flexibility might capture complex relationships between objects when other embeddings fail to do so.Unlike prior work on Wasserstein embeddings, which has focused on embedding into Gaussian distributions BID37 BID58 , we embed input data as discrete distributions supported at a fixed number of points. In doing so, we attempt to access the full flexibility of Wasserstein spaces to represent a wide variety of structures.Optimal transport metrics and their gradients are costly to compute, requiring the solution of a linear program. For efficiency , we use an approximation to the Wasserstein distance called the Sinkhorn divergence BID15 , in which the underlying transport problem is regularized to make it more tractable. While less well-characterized theoretically with respect to embedding capacity, the Sinkhorn divergence is computed efficiently by a fixed-point iteration. Moreover, recent work has shown that it is suitable for gradient-based optimization via automatic differentiation BID20 . To our knowledge, our work is the first to explore embedding properties of the Sinkhorn divergence.We empirically investigate two settings for Wasserstein embeddings. First, we demonstrate their representational capacity by embedding a variety of complex networks, for which Wasserstein embeddings achieve higher fidelity than both Euclidean and hyperbolic embeddings. Second, we compute Wasserstein word embeddings , which show retrieval performance comparable to existing methods. One major benefit of our embedding is that the distributions can be visualized directly, unlike most embeddings, which require a dimensionality reduction step such as t-SNE before visualization. We demonstrate the power of this approach by visualizing the learned word embeddings. Several characteristics determine the value and effectiveness of an embedding space for representation learning. The space must be large enough to embed a variety of metrics, while admitting a mathematical description compatible with learning algorithms; additional features, including direct interpretability, make it easier to understand, analyze, and potentially debug the output of a representation learning procedure. Based on their theoretical properties, Wasserstein spaces are strong candidates for representing complex semantic structures, when the capacity of Euclidean space does not suffice. Empirically, entropy-regularized Wasserstein distances are effective for embedding a wide variety of semantic structures, while enabling direct visualization of the embedding.Our work suggests several directions for additional research. Beyond simple extensions like weighting points in the point cloud, one observation is that we can lift nearly any representation space X to distributions over that space W(X ) represented as point clouds; in this paper we focused on the case X = R n . Since X embeds within W(X ) using δ-functions, this might be viewed as a general ""lifting"" procedure increasing the capacity of a representation. We can also consider other tasks, such as co-embedding of different modalities into the same transport space. Additionally, our empirical results suggest that theoretical study of the embedding capacity of Sinkhorn divergences may be profitable. Finally, following recent work on computing geodesics in Wasserstein space BID45 , it may be interesting to invert the learned mappings and use them for interpolation.",1127,0.619,666,1.6921921921921923,"Despite their prevalence Euclidean embeddings data fundamentally limited latent semantic structures need conform Here consider embeds data as discrete probability distributions a Wasserstein space endowed an optimal transport metric Wasserstein spaces much flexible in successfully embed metric structures We propose exploit this flexibility learning an that captures the Wasserstein distance embedded distributions We examine empirically the representational capacity such learned Wasserstein embeddings showing embed complex metric structures with smaller distortion We also investigate an application word demonstrating a unique advantage we directly visualize, a probability distribution on This obviates dimensionality reduction techniques t-SNE visualization Learned embeddings form state learning Word embeddings like word2vec BID34 , GloVe BID42 fastText ELMo BID43 ubiquitous where tasks BID38 while like knowledge graphs pre-trained image models appear many computer vision pipelinesAn effective should capture with in amenable downstream tasks This makes the choice a target space embedding important since different spaces represent semantic structure The most common choice embed data distances between vectors encode their levels association BID34 BID56 BID27 BID36 Euclidean spaces however limited represent complex relationships inputs since make restrictive assumptions neighborhood sizes connectivity This drawback documented recently for tree-structured data for where spaces of negative curvature required due exponential scaling neighborhood sizes BID39 BID49 .In embed input data probability distributions a Wasserstein space Wasserstein spaces endow probability distributions an optimal transport metric measures traveled transporting in one distribution match Recent theory shown Wasserstein spaces quite flexible-moreallowing other metric spaces embedded while their original distance metrics As such they make attractive targets embeddings machine learning where this flexibility might capture complex relationships objects when failUnlike prior work has into Gaussian distributions BID37 BID58 embed input data discrete distributions supported at In doing attempt access the full flexibility Wasserstein spaces to represent structuresOptimal transport metrics their gradients costly requiring the solution a linear program For efficiency , an approximation the Wasserstein distance called the Sinkhorn divergence BID15 the underlying transport problem regularized make While lesscharacterized theoretically with embedding capacity the Sinkhorn divergence computed efficiently a fixed-point iteration Moreover recent work it suitable gradient-based optimization via automatic differentiation BID20 . To our knowledge our work explore embedding properties the Sinkhorn divergenceWe empirically investigate two settings Wasserstein embeddings First demonstrate their representational capacity a variety complex networks for Wasserstein embeddings achieve higher fidelity both Second compute Wasserstein word embeddings , show retrieval performance comparable existing methods One major benefit our embedding the distributions directly unlike a dimensionality reduction step such t-SNE before visualization We demonstrate this approach the learned word embeddings Several characteristics determine effectiveness an embedding space representation learning The space must large embed a variety metrics while admitting a mathematical description compatible learning algorithms; additional features direct interpretability make analyze potentially debug the output a representation learning procedure Based their theoretical properties Wasserstein spaces strong candidates representing complex semantic structures when the capacity does suffice entropy-regularized Wasserstein distances effective embedding semantic structures while enabling direct visualization.Our work several directions additional research Beyond simple extensions weighting points the point cloud one observation we lift nearly any representation space X distributions over W(X ) represented as point clouds; focused X = R n Since X embeds within W(X ) using ��-functions might viewed a general ""lifting"" procedure increasing a representation We consider other tasks coembedding of different modalities the same transport space Additionally our empirical results theoretical study the embedding capacity Sinkhorn divergences profitable Finally following recent work computing geodesics Wasserstein space BID45 , may interesting invert the learned mappings interpolation",0.01,0.4677240600484631
"Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The data is embedded into a lower-dimensional space by a deep autoencoder. The autoencoder is optimized as part of the clustering process. The resulting network produces clustered data. The presented approach does not rely on prior knowledge of the number of ground-truth clusters. Joint nonlinear dimensionality reduction and clustering are formulated as optimization of a global continuous objective. We thus avoid discrete reconfigurations of the objective that characterize prior clustering algorithms. Experiments on datasets from multiple domains demonstrate that the presented algorithm outperforms state-of-the-art clustering schemes, including recent methods that use deep networks. Clustering is a fundamental procedure in machine learning and data analysis. Well-known approaches include center-based methods and their generalizations BID2 BID26 , and spectral methods BID20 BID34 . Despite decades of progress, reliable clustering of noisy high-dimensional datasets remains an open problem. High dimensionality poses a particular challenge because assumptions made by many algorithms break down in high-dimensional spaces BID1 BID3 BID24 .There are techniques that reduce the dimensionality of data by embedding it in a lower-dimensional space . Such general techniques, based on preserving variance or dissimilarity, may not be optimal when the goal is to discover cluster structure. Dedicated algorithms have been developed that combine dimensionality reduction and clustering by fitting low-dimensional subspaces BID14 BID31 . Such algorithms can achieve better results than pipelines that first apply generic dimensionality reduction and then cluster in the reduced space. However, frameworks such as subspace clustering and projected clustering operate on linear subspaces and are therefore limited in their ability to handle datasets that lie on nonlinear manifolds.Recent approaches have sought to overcome this limitation by constructing a nonlinear embedding of the data into a low-dimensional space in which it is clustered BID7 BID36 BID38 . Ultimately, the goal is to perform nonlinear embedding and clustering jointly, such that the embedding is optimized to bring out the latent cluster structure. These works have achieved impressive results. Nevertheless, they are based on classic center-based, divergencebased, or hierarchical clustering formulations and thus inherit some limitations from these classic methods. In particular, these algorithms require setting the number of clusters a priori. And the optimization procedures they employ involve discrete reconfigurations of the objective, such as discrete reassignments of datapoints to centroids or merging of putative clusters in an agglomerative procedure. Thus it is challenging to integrate them with an optimization procedure that modifies the embedding of the data itself.We seek a procedure for joint nonlinear embedding and clustering that overcomes some of the limitations of prior formulations. There are a number of characteristics we consider desirable. First, we wish to express the joint problem as optimization of a single continuous objective. Second, this optimization should be amenable to scalable gradient-based solvers such as modern variants of SGD. Third, the formulation should not require setting the number of clusters a priori, since this number is often not known in advance.While any one of these desiderata can be fulfilled by some existing approaches, the combination is challenging. For example, it has long been known that the k-means objective can be optimized by SGD BID5 . But this family of formulations requires positing the number of clusters k in advance. Furthermore, the optimization is punctuated by discrete reassignments of datapoints to centroids, and is thus hard to integrate with continuous embedding of the data.In this paper, we present a formulation for joint nonlinear embedding and clustering that possesses all of the aforementioned desirable characteristics. Our approach is rooted in Robust Continuous Clustering (RCC), a recent formulation of clustering as continuous optimization of a robust objective BID22 . The basic RCC formulation has the characteristics we seek , such as a clear continuous objective and no prior knowledge of the number of clusters. However, integrating it with deep nonlinear embedding is still a challenge. For example, Shah & Koltun (2017) presented a formulation for joint linear embedding and clustering (RCC-DR), but this formulation relies on a complex alternating optimization scheme with linear least-squares subproblems, and does not apply to nonlinear embeddings.We present an integration of the RCC objective with dimensionality reduction that is simpler and more direct than RCC-DR, while naturally handling deep nonlinear embeddings. Our formulation avoids alternating optimization and the introduction of auxiliary dual variables. A deep nonlinear embedding of the data into a low-dimensional space is optimized while the data is clustered in the reduced space. The optimization is expressed by a global continuous objective and conducted by standard gradient-based solvers.The presented algorithm is evaluated on high-dimensional datasets of images and documents. Experiments demonstrate that our formulation performs on par or better than state-of-the-art clustering algorithms across all datasets. This includes recent approaches that utilize deep networks and rely on prior knowledge of the number of ground-truth clusters. Controlled experiments confirm that joint dimensionality reduction and clustering is more effective than a stagewise approach, and that the high accuracy achieved by the presented algorithm is stable across different dimensionalities of the latent space. We have presented a clustering algorithm that combines nonlinear dimensionality reduction and clustering. Dimensionality reduction is performed by a deep network that embeds the data into a lower-dimensional space. The embedding is optimized as part of the clustering process and the resulting network produces clustered data. The presented algorithm does not rely on a priori knowledge of the number of ground-truth clusters. Nonlinear dimensionality reduction and clustering are performed by optimizing a global continuous objective using scalable gradient-based solvers.B CONVOLUTIONAL NETWORK ARCHITECTURE TAB4 summarizes the architecture of the convolutional encoder used for the convolutional configuration of DCC. Convolutional kernels are applied with a stride of two. The encoder is followed by a fully-connected layer with output dimension d and a convolutional decoder with kernel size that matches the output dimension of conv5. The decoder architecture mirrors the encoder and the output from each layer is appropriately zero-padded to match the input size of the corresponding encoding layer. All convolutional and transposed convolutional layers are followed by batch normalization and rectified linear units BID12 BID18 . C HYPERPARAMETERS DCC uses three hyperparameters: the nearest neighbor graph (mkNN) parameter k, the embedding dimensionality d, and the update period M for graduated nonconvexity. For fair comparison to RCC and RCC-DR, we fix k = 10 (the setting used in BID22 ). The other two hyperparameters were set to d = 10 and M = 20 based on grid search on MNIST. The hyperparameters are fixed at these values across all datasets. No dataset-specific tuning is done. However, note that the hyperparameter M is architecture-specific. We set M = 10 for convolutional autoencoders and it is varied for varying dimensionality d during the controlled experiment reported in FIG1 . The other hyperparameters such as λ, δ i , µ i are set automatically as described in Sections 3.2 and 3.3 and in BID22 . DISPLAYFORM0",1433,0.958,848,1.6898584905660377,"Clustering high-dimensional datasets hard interpoint distances become less informative We present performs nonlinear dimensionality reduction jointly The data embedded a lower-dimensional space The autoencoder optimized as part The resulting network produces clustered data The presented approach does prior knowledge the number ground-truth clusters Joint nonlinear dimensionality reduction are formulated optimization a global continuous objective We thus avoid discrete reconfigurations the objective that characterize prior clustering algorithms Experiments datasets multiple domains demonstrate the presented algorithm state schemes recent methods deep networks Clustering a fundamental procedure Well-known approaches include center-based methods their generalizations BID2 BID26 , spectral methods Despite decades progress reliable clustering noisy high-dimensional datasets High dimensionality poses because assumptions made many algorithms break BID1 .There techniques reduce . Such general techniques based preserving variance or optimal the goal discover cluster structure Dedicated algorithms combine dimensionality reduction by fitting low-dimensional subspaces BID14 BID31 . Such algorithms achieve pipelines first apply generic dimensionality reduction cluster the reduced space However frameworks subspace clustering projected linear subspaces limited handle datasets lieRecent approaches sought constructing embedding of in it clustered BID7 BID36 BID38 Ultimately perform nonlinear embedding jointly such optimized bring the latent cluster structure These works achieved Nevertheless they based classic centerbased, divergencebased or hierarchical clustering formulations and thus inherit some limitations these classic methods In particular these algorithms require setting clusters a priori And the optimization procedures they involve discrete reconfigurations the objective discrete reassignments centroids merging putative clusters in Thus challenging integrate them an optimization procedure modifies itselfWe seek joint nonlinear clustering overcomes some prior formulations There characteristics we consider desirable First wish the joint problem as optimization a single continuous objective Second this optimization should amenable scalable gradient-based solvers such modern variants SGD Third the formulation should require setting clusters a this numberWhile any one fulfilled some existing approaches the combination is challenging For example it has long the k-means objective can optimized SGD BID5 . But this family formulations requires positing the number clusters k advance Furthermore the optimization punctuated discrete reassignments centroids is hard integrate continuous embeddingIn a formulation joint nonlinear and possesses all the aforementioned desirable characteristics Our approach rooted Robust Continuous ClusteringRCC a recent formulation as continuous optimization a robust objective BID22 The basic RCC formulation has the characteristics we seek , a clear continuous objective no prior knowledge the number clusters However integrating it deep nonlinear embedding For example Shah & Koltun (2017 presented a formulation joint linear embeddingRCC-DR but relies a complex alternating optimization scheme applyWe an integration the RCC objective dimensionality reduction that simpler direct while naturally handling Our formulation avoids alternating optimization the introduction auxiliary dual variables A deep nonlinear embedding optimized while clustered the reduced space The optimization expressed a global continuous objective and conducted standard gradient-based solversThe presented algorithm evaluated images documents Experiments demonstrate our formulation performs on par or state clustering across all datasets This includes recent approaches utilize deep networks rely prior knowledge the number ground-truth clusters Controlled experiments confirm that joint dimensionality reduction and clustering more a stagewise approach the high accuracy achieved the presented algorithm stable different dimensionalities the latent space We presented combines nonlinear dimensionality reduction Dimensionality reduction performed a deep network that embedding is optimized as the resulting network produces clustered data The presented algorithm does rely ground-truth clusters Nonlinear dimensionality reduction are performed optimizing a global continuous objective using scalable gradient-based solversB CONVOLUTIONAL NETWORK ARCHITECTURE TAB4 summarizes the convolutional encoder used DCC Convolutional kernels applied with a stride two The encoder followed a fully-connected layer output dimension d kernel size that matches conv5 The decoder architecture mirrors from each layer appropriately zeropadded match All convolutional and transposed convolutional layers followed batch normalization rectified linear units BID12 BID18 C HYPERPARAMETERS DCC uses the nearest neighbor graph (mkNN) parameter k the embedding dimensionality d the update period M for graduated nonconvexity For fair comparison RCC and fix k = 10the setting BID22 The other two hyperparameters set d 10 M based grid search on MNIST The hyperparameters fixed these values across all datasets No dataset-specific tuning done However note hyperparameter M architecture We set M = 10 it varied varying dimensionality d during the controlled experiment reported FIG1 The other hyperparameters such ��� i µ set automatically as described Sections in BID22 . DISPLAYFORM0",0.01,0.4617779933418041
"Deep convolutional neural networks (CNNs) are deployed in various applications but demand immense computational requirements. Pruning techniques and Winograd convolution are two typical methods to reduce the CNN computation. However, they cannot be directly combined because Winograd transformation fills in the sparsity resulting from pruning. Li et al. (2017) propose sparse Winograd convolution in which weights are directly pruned in the Winograd domain, but this technique is not very practical because Winograd-domain retraining requires low learning rates and hence significantly longer training time. Besides, Liu et al. (2018) move the ReLU function into the Winograd domain, which can help increase the weight sparsity but requires changes in the network structure. To achieve a high Winograd-domain weight sparsity without changing network structures, we propose a new pruning method, spatial-Winograd pruning. As the first step, spatial-domain weights are pruned in a structured way, which efficiently transfers the spatial-domain sparsity into the Winograd domain and avoids Winograd-domain retraining. For the next step, we also perform pruning and retraining directly in the Winograd domain but propose to use an importance factor matrix to adjust weight importance and weight gradients. This adjustment makes it possible to effectively retrain the pruned Winograd-domain network without changing the network structure. For the three models on the datasets of CIFAR-10, CIFAR-100, and ImageNet, our proposed method can achieve the Winograd-domain sparsities of 63%, 50%, and 74%, respectively. Deep convolutional neural networks (CNNs) have been ubiquitously utilized in various application domains. However, their performance comes at the cost of a significant amount of computation which keeps growing over time. As an example, for the ImageNet challenge BID12 , BID5 proposed AlexNet which requires more than 1.1 × 10 9 multiplications. Later, in 2016, the ResNet-152 model BID3 increased the computation cost to 11.3 × 10 9 multiplications. This high computation cost limits the deployment of larger and deeper CNN models.There are two primary methods to reduce the required computation of CNN models: pruning techniques and Winograd/FFT convolution. Pruning removes redundant weight parameters, inducing sparsity into the network. On the other hand, Winograd convolution BID6 and FFT convolution BID10 transform the computation into different domains. The convolution operations can then be replaced by element-wise multiplications. For the typical convolution kernel size of 3 × 3, Winograd convolution can achieve more than twofold speedup over highly optimized spatial convolution algorithms, and typically requires fewer flops than FFT-based approaches BID7 . Therefore, in this paper, we focus on the Winograd convolution.The pruning techniques and Winograd convolution are not directly compatible with each other. Sparse weight matrices, which are generated by pruning, lose most of the sparsity after the Winograd transformation from the spatial (original) domain to the Winograd domain. The remaining sparsity is much lower than what we need for improving computation performance.To increase the Winograd-domain sparsity, BID7 propose to perform pruning and retraining directly on Winograd-domain weights. However, it requires using an extremely small learning rate, e.g., 200x smaller for AlexNet, in retraining and is difficult to be applied to deep networks. Besides, Winograd-ReLU pruning BID9 moves ReLU function into the Winograd domain, which helps increase Winograd-domain sparsity but requires changes in the network structure.In this paper, to further improve the sparsity of Winograd-domain weights without changing the network structure, we propose a new pruning method, spatial-Winograd pruning. It includes two parts: spatial structured pruning and Winograd direct pruning. In spatial structured pruning, we prune the spatial-domain weights in a structured way, in which the structures are designed to transfer the spatial-domain sparsity into the Winograd domain efficiently. After spatial structured pruning, weights of the pruned layers will be converted to and kept in the Winograd domain. Then, for Winograd direct pruning, we perform pruning and retraining entirely in the Winograd domain to improve the sparsity further. This paper makes the following contributions:• We propose a new pruning method, spatial-Winograd pruning. Without changing the network structure, it can achieve higher sparsity in Winograd-domain weights compared with previous methods.• As the first part of spatial-Winograd pruning, we provide a structured pruning method to transfer the spatial-domain sparsity into the Winograd domain efficiently. It can help avoid Winograd-domain retraining in this part and accelerate the pruning process.• In the second part, to perform pruning directly in the Winograd domain, we present a new approach to measuring the importance of each Winograd-domain weight based on its impact on output activations. Also , we propose to use an importance factor matrix to adjust the gradients of Winograd-domain weights, which makes it much faster to retrain deep networks directly in the Winograd domain without changing the network structure. In this paper, we present a new pruning method, spatial-Winograd pruning, to improve the Winograd-domain weight sparsity without changing network structures. It includes two steps: spatial structured pruning and Winograd direct pruning. In spatial structured pruning, we prune the spatial-domain weights based on the internal structure in the Winograd transformation. It can help efficiently transfer the spatial-domain sparsity into the Winograd domain. For Winograd direct pruning, we perform both pruning and retraining in the Winograd domain. An importance factor matrix is proposed to adjust the weight gradients in Winograd retraining, which makes it possible to effectively retrain the Winograd-domain network to regain the original accuracy without changing the network structure. We evaluate spatial-Winograd pruning on three datasets, CIFAR-10, CIFAR-100, ImageNet, and it can achieve the Winograd-domain sparsities of 63%, 50%, and 74%, respectively.",1212,0.691,702,1.7264957264957266," deployed but demand immense computational requirements Pruning techniques Winograd convolution two typical methods reduce the CNN computation However they directly combined because Winograd transformation fills the sparsity resulting pruning Li et al (2017 propose sparse Winograd convolution in weights directly pruned this technique very low learning rates Besides Liu et (2018 move the ReLU function the Winograd domain help increase the weight sparsity but requires changes To achieve a high Winograd-domain weight sparsity without changing network structures propose spatial-Winograd pruning As spatial-domain weights pruned efficiently transfers the Winograd domain avoids Winograd-domain retraining For the next step also perform pruning retraining directly the Winograd domain but propose an importance factor matrix adjust weight importance This adjustment makes effectively retrain the pruned Winograd-domain network without For the three models on the datasets of ImageNet our proposed method can achieve the Winograd-domain sparsities 63% ubiquitously utilized various application domains However their performance comes computation which keeps growing As for the ImageNet challenge BID12 , proposed AlexNet which requires more than 1.1 × 10 9 multiplications Later 2016 the ResNet-152 model BID3 increased the computation cost 11.3 × 10 9 multiplications This high computation cost limits the deployment larger and deeper CNN modelsThere of pruning techniques Winograd/FFT convolution Pruning removes redundant weight parameters inducing sparsity into On Winograd convolution BID6 and transform the computation different domains The convolution operations can then replaced element-wise multiplications For the typical convolution kernel size 3 ×, Winograd convolution can achieve more highly optimized spatial convolution algorithms typically fewer flops BID7 . Therefore focus the Winograd convolution.The pruning techniques and not compatible Sparse weight matrices generated pruning lose most after the Winograd transformation from the spatial (original) domain The remaining sparsity much need improving computation performanceTo increase the Winograd-domain sparsity BID7 propose perform pruning retraining directly However requires using an extremely small learning rate 200x smaller AlexNet in retraining and is difficult be applied deep networks Besides Winograd-ReLU pruning BID9 moves ReLU function helps increase Winograd-domain sparsity but requires changesIn to further without spatial-Winograd pruning It includes two parts spatial structured pruning Winograd direct pruning In spatial structured pruning prune the spatial-domain weights a structured way the structures designed transfer the Winograd domain efficiently After spatial structured pruning weights will converted and kept the Winograd domain Then for Winograd direct pruning perform retraining entirely to the sparsity further This paper makes the following contributions:• spatial-Winograd pruning Without changing the network structure achieve higher sparsity Winograd-domain weights compared previous methods.• As the first part spatial-Winograd pruning provide transfer efficiently It can help avoid Winograd-domain retraining this part and accelerate process.• In to perform directly present measuring the importance based its impact output activations Also , we propose an importance factor matrix adjust Winograd-domain weights makes faster retrain deep networks directly without changing In spatialWinograd pruning the Winograd-domain weight sparsity without network structures It includes two steps spatial structured pruning Winograd direct pruning In spatial structured pruning prune the spatial-domain weights based in the Winograd transformation It can help efficiently transfer the spatial-domain sparsity the Winograd domain For Winograd direct pruning perform both retraining the Winograd domain An importance factor matrix proposed adjust Winograd retraining makes effectively the Winograd-domain network regain the original accuracy without We evaluate spatial-Winograd pruning ImageNet it can achieve the Winograd-domain sparsities 63%",0.01,0.5551264515782985
"In federated learning problems, data is scattered across different servers and exchanging or pooling it is often impractical or prohibited. We develop a Bayesian nonparametric framework for federated learning with neural networks. Each data server is assumed to train local neural network weights, which are modeled through our framework. We then develop an inference approach that allows us to synthesize a more expressive global network without additional supervision or data pooling. We then demonstrate the efficacy of our approach on federated learning problems simulated from two popular image classification datasets. The standard machine learning paradigm involves algorithms that learn from centralized data, possibly pooled together from multiple data sources. The computations involved may be done on a single machine or farmed out to a cluster of machines. However, in the real world, data often lives in silos and amalgamating them may be rendered prohibitively expensive by communication costs, time sensitivity, or privacy concerns. Consider, for instance, data recorded from sensors embedded in wearable devices. Such data is inherently private, can be voluminous depending on the sampling rate of the sensing modality, and may be time sensitive depending on the analysis of interest. Pooling data from many users is technically challenging owing to the severe computational burden of moving large amounts of data, and fraught with privacy concerns stemming from potential data breaches that may expose the user's protected health information (PHI).Federated learning avoids these pitfalls by obviating the need for centralized data and instead designs algorithms that learn from sequestered data sources with different data distributions. To be effective , such algorithms must be able to extract and distill important statistical patterns from various independent local learners coherently into an effective global model without centralizing data. This will allow us to avoid the prohibitively expensive cost of data communication. To achieve this , we develop and investigate a probabilistic federated learning framework with a particular emphasis on training and aggregating neural network models on siloed data.We proceed by training local models for each data source, in parallel. We then match the estimated local model parameters (groups of weight vectors in the case of neural networks) across data sources to construct a global network. The matching, to be formally defined later, is governed by the posterior of a Beta-Bernoulli process (BBP) (Thibaux & Jordan, 2007; Yurochkin et al., 2018) , a Bayesian nonparametric model that allows the local parameters to either match existing global ones or create a new global parameter if existing ones are poor matches. Our construction allows the size of the global network to flexibly grow or shrink as needed to best explain the observed data. Crucially, we make no assumptions about how the data is distributed between the different sources or even about the local learning algorithms. These may be adapted as necessary, for instance to account for non-identically distributed data. Further, we only require communication after the local algorithms have converged. This is in contrast with popular distributed training algorithms that rely on frequent communication between the local machines. Our construction also leads to compressed global models with fewer parameters than the set of all local parameters. Unlike naive ensembles of local models, this allows us to store fewer parameters and leads to more efficient inference at test time, requiring only a single forward pass through the compressed model as opposed to J forward passes, once for each local model. While techniques such as distillation allow for the cost of multiple forward passes to be amortized, training the distilled model itself requires access to data pooled across all sources, a luxury unavailable in our federated learning scenario. In summary, the key question we seek to answer in this paper is the following: given pre-trained neural networks trained locally on non-centralized data, can we learn a compressed federated model without accessing the original data, while improving on the performance of the local networks?The remainder of the paper is organized as follows. We briefly introduce the Beta-Bernoulli process in Section 2 before describing our model for federated learning in Section 3. We thoroughly vet the proposed models and demonstrate the utility of the proposed approach in Section 4. Finally, Section 5 discusses limitations and open questions. In this work we have developed models for matching fully connected networks, and experimentally demonstrated the capabilities of our methodology, particularly when prediction time is limited and communication is expensive. We also observed the importance of convergent local neural networks that serve as inputs to our matching algorithms. Poor quality local neural network weights will affect the quality of the master network. In future work we plan to explore more sophisticated ways to account for uncertainty in the weights of small batches. Additionally, our matching approach is completely unsupervised -incorporating some form of supervised signal may help to improve the performance of the global network when local networks are low quality. Finally, it is of interest to extend our modeling framework to other architectures such as Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). The permutation invariance necessitating matching inference arises in CNNs too -any permutation of the filters results in same output, however additional bookkeeping is needed due to pooling operations.Ohad Shamir, Nati Srebro, and Tong Zhang. Communication-efficient distributed optimization using an approximate newton-type method. In International conference on machine learning, pp. The goal of maximum a posteriori (MAP) estimation is to maximize posterior probability of the latent variables: global atoms DISPLAYFORM0 and assignments of observed neural network weight estimates to global atoms {B j } J j=1 , given estimates of the batch weights DISPLAYFORM1 arg max DISPLAYFORM2 MAP estimates given matching (Proposition 1 in the main text) First we note that given {B j } it is straightforward to find MAP estimates of {✓ i } based on Gaussian-Gaussian conjugacy: DISPLAYFORM3 where L = max{i : DISPLAYFORM4 . . , J} is the number of active global atoms, which is an (unknown) latent random variable identified by {B j }. For simplicity we assume ⌃ 0 = I 2 0 , ⌃ j = I 2 j and µ 0 = 0.Inference of atom assignment. We can now cast optimization corresponding to (1) with respect to only {B j } J j=1 . Taking natural logarithm we obtain: DISPLAYFORM5 Let us first simplify the first term of (3):1 2 DISPLAYFORM6 We consider an iterative optimization approach: fixing all but one B j we find corresponding optimal assignment, then pick a new j at random and proceed until convergence. In the following we will use notation j to say ""all but j"". Let L j = max{i : B j i,l = 1} denote number of active global weights outside of group j. We now rearrange (4) by partitioning it into i = 1, . . . , L j and i = L j + 1, . . . , L j + L j . We are interested in solving for B j , hence we can modify objective function by subtracting terms independent of B j : DISPLAYFORM7 Now observe that P l B j i,l 2 {0, 1}, i.e. it is 1 if some neuron from batch j is matched to global neuron i and 0 otherwise. Due to this we can rewrite (5) as a linear sum assignment problem: DISPLAYFORM8 Now we consider second term of FORMULA12 : DISPLAYFORM9 First, because we are optimizing for B j , we can ignore log P (B j ). Second, due to exchangeability of batches (i.e. customers of the IBP), we can always consider B j to be the last batch (i.e. last customer of the IBP). Let m j i = P j,l B j i,l denote number of times batch weights were assigned to global atom i outside of group j. We now obtain the following: DISPLAYFORM10 We now rearrange (7) as linear sum assignment problem: DISPLAYFORM11 Combining FORMULA20 and FORMULA25 we arrive at the cost specification for finding B j as minimizer of DISPLAYFORM12 , where: DISPLAYFORM13 This completes the proof of Proposition 2 in the main text. FIG3 illustrates the overall multilayer inference procedure visually, and Algorithm 1 provides the details. Nodes in the graphs indicate neurons, neurons of the same color have been matched. On the left, the individual layer matching approach is shown, consisting of using the matching assignments of the next highest layer to convert the neurons in each of the J servers to weight vectors referencing the global previous layer. These weight vectors are then used to form a cost matrix, which the Hungarian algorithm then uses to do the matching. Finally, the matched neurons are then aggregated and averaged to form the new layer of the global model. As shown on the right, in the multilayer setting the resulting global layer is then used to match the next lower layer, etc. until the bottom hidden layer is reached FIG3 ,... in order).",1827,1.101,1048,1.743320610687023,"In federated learning problems data scattered exchanging or pooling impractical prohibited We develop federated learning Each data server assumed train local neural network weights modeled through our framework We then develop an inference approach a more expressive global network without additional supervision data pooling We then demonstrate our approach federated learning problems simulated two popular image classification datasets The standard machine learning paradigm involves algorithms centralized data possibly pooled The computations involved may done farmed However data often lives amalgamating may rendered communication costs time sensitivity Consider, data recorded sensors embedded Such data inherently private can depending the sampling rate the sensing modality time depending interest Pooling data many users technically challenging owing the severe computational burden moving fraught stemming that expose (PHI).Federated learning avoids obviating and designs learn sequestered data sources with different data distributions To effective , such algorithms extract distill important statistical patterns various independent local learners coherently into an effective global model without centralizing This will avoid data communication To achieve , develop investigate a probabilistic federated learning framework training aggregating on siloed dataWe proceed training local models in parallel We then match the estimated local model parametersgroups weight vectors neural networks across data sources construct The matching, to formally defined later governed the posterior a Beta-Bernoulli processBBPThibaux Jordan Yurochkin 2018 , the local parameters either match existing global ones create if poor matches Our construction allows the size the global network flexibly or best explain the observed data Crucially make distributed even the local learning algorithms These may adapted as necessary account non-identically distributed data Further only require communication after the local algorithms converged This in contrast popular distributed training algorithms frequent communication the local machines Our construction also leads compressed global models fewer parameters the set all local parameters Unlike naive ensembles local models allows store fewer parameters leads at test time requiring through the compressed model as J forward passes once for While techniques distillation allow the cost multiple forward passes training the distilled model itself access data pooled all sources a luxury unavailable our federated learning scenario In summary seek given pre-trained neural networks trained locally a compressed federated model without accessing improving the local networks?The remainder organized We briefly introduce the Beta-Bernoulli process Section before describing our model federated learning Section We thoroughly vet the proposed models demonstrate Section Finally Section discusses limitations open questions In this work models matching fully connected networks experimentally demonstrated our methodology prediction time communication expensive We also observed the importance convergent local neural networks that serve inputs our matching algorithms Poor quality local neural network weights will affect the master network In future work explore more sophisticated ways account uncertainty the weights small batches Additionally our matching approach completely -incorporating some form supervised signal may the global network when local networks low quality Finally of extend our modeling framework other architectures The permutation invariance necessitating matching inference arises CNNs too -any permutation the filters results same output however additional bookkeeping due pooling operationsOhad Shamir Nati Srebro Tong Zhang. Communication-efficient distributed optimization an approximate newton-type method In International conference machine learning pp The goal maximum a posteriori (MAP) estimation maximize the latent variables: global atoms DISPLAYFORM0 assignments observed neural network weight estimates {B j } J j=1 , given estimates the batch DISPLAYFORM1 arg max DISPLAYFORM2 MAP estimates given matching (Proposition in First note given { it straightforward find MAP estimates {�� i based Gaussian-Gaussian conjugacy where L max{i : . . , J} active global atoms an (unknown) latent random variable identified {B j. For simplicity ��� 0 I 0 j µ 0.Inference atom assignment We cast optimization corresponding ( with respect only {B j } J j=1 Taking natural logarithm we obtain DISPLAYFORM5 Let simplify ( consider an iterative optimization approach fixing all but one B j we corresponding optimal assignment pick at proceed until convergence In we use notation j sayall but j Let L j = max{i : B j il = 1} denote number active global weights outside group j. We now rearrange (4 by partitioning i = . . . , L j and i . . . , L j + L j . We interested solving for B j hence modify objective function by terms independent : DISPLAYFORM7 Now observe P l B i,l 2 {0 it 1 some neuron from batch j matched global neuron Due this we rewrite (5 as a linear sum assignment problem DISPLAYFORM8 Now consider second term FORMULA12 : First because optimizing B j ignore log P Second due exchangeability batches of the IBP always consider B j to Let m j i = P j,l B j il denote number batch weights assigned global atom i outside We now obtain DISPLAYFORM10 We rearrange (7 as linear sum assignment problem Combining FORMULA20 arrive the cost specification finding B j as minimizer , This completes Proposition FIG3 illustrates the overall multilayer inference procedure visually Algorithm Nodes the graphs indicate neurons have matched On the individual layer matching approach consisting using the matching assignments convert the neurons the J servers weight vectors referencing the global previous layer These weight vectors then form a cost matrix the Hungarian algorithm then do the matching Finally the matched neurons then averaged the global model As shown in setting the resulting global layer then match the next lower layer etc until the bottom hidden layer FIG3 ,... in order).",0.01,0.5979947782795595
"We present a general-purpose method to train Markov chain Monte Carlo kernels, parameterized by deep neural networks, that converge and mix quickly to their target distribution. Our method generalizes Hamiltonian Monte Carlo and is trained to maximize expected squared jumped distance, a proxy for mixing speed. We demonstrate large empirical gains on a collection of simple but challenging distributions, for instance achieving a 106x improvement in effective sample size in one case, and mixing when standard HMC makes no measurable progress in a second. Finally, we show quantitative and qualitative gains on a real-world task: latent-variable generative modeling. Python source code will be open-sourced with the camera-ready paper. High-dimensional distributions that are only analytically tractable up to a normalizing constant are ubiquitous in many fields. For instance, they arise in protein folding BID41 , physics simulations BID37 , and machine learning BID1 . Sampling from such distributions is a critical task for learning and inference BID31 , however it is an extremely hard problem in general.Markov Chain Monte Carlo (MCMC) methods promise a solution to this problem. They operate by generating a sequence of correlated samples that converge in distribution to the target. This convergence is most often guaranteed through detailed balance, a sufficient condition for the chain to have the target equilibrium distribution. In practice, for any proposal distribution, one can ensure detailed balance through a Metropolis-Hastings BID20 accept/reject step.Despite theoretical guarantees of eventual convergence, in practice convergence and mixing speed depend strongly on choosing a proposal that works well for the task at hand. What's more, it is often more art than science to know when an MCMC chain has converged (""burned-in""), and when the chain has produced a new uncorrelated sample (""mixed""). Additionally, the reliance on detailed balance, which assigns equal probability to the forward and reverse transitions, often encourages random-walk behavior and thus slows exploration of the space BID24 .For densities over continuous spaces, Hamiltonian Monte Carlo (HMC; BID12 BID36 introduces independent, auxiliary momentum variables, and computes a new state by integrating Hamiltonian dynamics. This method can traverse long distances in state space with a single Metropolis-Hastings test. This is the state-of-the-art method for sampling in many domains. However , HMC can perform poorly in a number of settings. While HMC mixes quickly spatially, it struggles at mixing across energy levels due to its volume-preserving dynamics. HMC also does not work well with multi-modal distributions, as the probability of sampling a large enough momentum to traverse a very low-density region is negligibly small. Furthermore , HMC struggles with ill-conditioned energy landscapes BID14 and deals poorly with rapidly changing gradients BID44 .Recently, probabilistic models parameterized by deep neural networks have achieved great success at approximately sampling from highly complex, multi-modal empirical distributions BID27 BID39 BID16 . Building on these successes , we present a method that, given an analytically described distribution, automatically returns an exact sampler with good convergence and mixing properties, from a class of highly expressive parametric models. The proposed family of samplers is a generalization of HMC; it transforms the HMC trajectory using parametric functions (deep networks in our experiments), while retaining theoretical guarantees with a tractable Metropolis-Hastings accept/reject step. The sampler is trained to minimize a variation on expected squared jumped distance (similar in spirit to BID38 ). Our parameterization reduces easily to standard HMC. It is further capable of emulating several common extensions of HMC such as withintrajectory tempering BID34 and diagonal mass matrices BID4 .We evaluate our method on distributions where HMC usually struggles, as well as on a the real-world task of training latent-variable generative models.Our contributions are as follows:• We introduce a generic training procedure which takes as input a distribution defined by an energy function, and returns a fast-mixing MCMC kernel.• We show significant empirical gains on various distributions where HMC performs poorly.• We finally evaluate our method on the real-world task of training and sampling from a latent variable generative model, where we show improvement in the model's log-likelihood, and greater complexity in the distribution of posterior samples. In this work, we presented a general method to train expressive MCMC kernels parameterized with deep neural networks. Given a target distribution p, analytically known up to a constant, our method provides a fast-mixing sampler, able to efficiently explore the state space. Our hope is that our method can be utilized in a ""black-box"" manner, in domains where sampling constitutes a huge bottleneck such as protein foldings BID41 or physics simulations BID37 .... DISPLAYFORM0 Figure 4: Diagram of our L2HMC-DGLM model. Nodes are functions of their parents. Round nodes are deterministic , diamond nodes are stochastic and the doubly-circled node is observed.",989,0.537,581,1.70223752151463,"We present train parameterized deep neural networks converge and mix quickly their target distribution Our method generalizes Hamiltonian Monte Carlo trained maximize expected squared jumped distance a proxy mixing speed We demonstrate large empirical gains on a collection simple but challenging distributions for achieving a 106x improvement effective sample size mixing when standard HMC makes no measurable progress Finally show quantitative gains latent-variable generative modeling Python source code will open with the camera-ready paper High-dimensional distributions that only analytically up a normalizing constant ubiquitous For instance they arise protein folding BID41 , physics simulations BID37 machine Sampling from such distributions learning inference BID31 howeverMarkov methods promise They operate generating a sequence correlated samples converge distribution This convergence most guaranteed detailed balance a sufficient condition the chain have the target equilibrium distribution In practice for any proposal distribution one ensure detailed balance through a Metropolis-Hastings BID20 accept/reject stepDespite theoretical guarantees eventual convergence and mixing speed depend strongly choosing works What often more art know an MCMC chain converged (""burned- produced a new uncorrelated sample Additionally the reliance detailed balance, assigns equal probability the forward and reverse transitions often encourages random-walk behavior thus slows exploration BID24 .For densities over continuous spaces Hamiltonian Monte Carlo; BID12 BID36 introduces independent, auxiliary momentum variables a new state integrating This method traverse state space a single Metropolis-Hastings test This state method sampling in many domains However , HMC can perform poorly settings While HMC mixes quickly spatially struggles at mixing across energy levels due its volume-preserving dynamics HMC also does work well the probability sampling a large enough momentum traverse negligibly Furthermore , HMC struggles ill-conditioned energy landscapes BID14 deals poorly rapidly changing gradients .Recently parameterized achieved approximately sampling from highly complex, multi-modal empirical distributions Building these successes , present, given an analytically described distribution automatically returns an exact sampler good convergence mixing from a class highly expressive parametric models The proposed family samplers a generalization HMC; transforms the HMC trajectory usingdeep networks in our experiments while theoretical guarantees with a tractable Metropolis-Hastings accept/reject step The sampler trained minimize a variation on expected squared jumped distancesimilar spirit BID38 Our parameterization reduces easily standard HMC It further capable emulating several common extensions HMC such withintrajectory tempering BID34 diagonal mass matrices .We evaluate our method distributions where usually struggles a the real-world task trainingOur contributions as defined an energy function a fast-mixing MCMC significant empirical gains various distributions performs finally evaluate and sampling from improvement greater complexity posterior samples In this work presented train expressive MCMC kernels parameterized Given a target distribution p analytically known up a constant our method provides a fast-mixing sampler able efficiently explore the state space Our hope our method utilized domains sampling constitutes such protein foldings BID41 or physics simulations .... DISPLAYFORM0 Figure our L2HMC-DGLM model Nodes functions their parents Round nodes deterministic , diamond nodes observed",0.01,0.49331867658905004
"This paper addresses the problem of evaluating learning systems in safety critical domains such as autonomous driving, where failures can have catastrophic consequences. We focus on two problems: searching for scenarios when learned agents fail and assessing their probability of failure. The standard method for agent evaluation in reinforcement learning, Vanilla Monte Carlo, can miss failures entirely, leading to the deployment of unsafe agents. We demonstrate this is an issue for current agents, where even matching the compute used for training is sometimes insufficient for evaluation. To address this shortcoming, we draw upon the rare event probability estimation literature and propose an adversarial evaluation approach. Our approach focuses evaluation on adversarially chosen situations, while still providing unbiased estimates of failure probabilities. The key difficulty is in identifying these adversarial situations -- since failures are rare there is little signal to drive optimization. To solve this we propose a continuation approach that learns failure modes in related but less robust agents. Our approach also allows reuse of data already collected for training the agent. We demonstrate the efficacy of adversarial evaluation on two standard domains: humanoid control and simulated driving. Experimental results show that our methods can find catastrophic failures and estimate failures rates of agents multiple orders of magnitude faster than standard evaluation schemes, in minutes to hours rather than days. How can we ensure machine learning systems do not make catastrophic mistakes? While machine learning systems have shown impressive results across a variety of domains BID6 BID11 BID26 , they may also fail badly on particular inputs, often in unexpected ways BID28 . As we start deploying these systems, it is important that we can reliably evaluate the risk of failure. This is particularly important for safety critical domains like autonomous driving where the negative consequences of a single mistake can overwhelm the positive benefits accrued during typical operation of the system.Limitations of random testing. The key problem we highlight is that for standard statistical evaluation, attaining confidence that the failure rate of a policy is below requires at least 1/ episodes. We now informally summarize this point, which we discuss further in Appendix A. For concreteness, consider a self-driving car company that decides that the cost of a single accident where the car is at fault outweighs the benefits of 100 million miles of faultless operation. The standard approach in machine learning is to estimate the expected return via i.i.d. samples from the data distribution (frequently a test set). For tightly bounded returns, the sample estimate is guaranteed to quickly converge to the true expectation. However, with catastrophic failures, this may be prohibitively inefficient. In our current example, any policy with a failure probability greater than = 10 −8 per mile has negative expected return. In other words, it would be better to not deploy the car. However, to achieve reasonable confidence that the car crashes with probability below 1e-8, the manufacturer would need to test-drive the car for at least 1e8 miles, which may be prohibitively expensive.Our Contributions. To overcome the above-mentioned problems, we develop a novel adversarial evaluation approach. The central motivation behind our algorithmic choices is the fact that realworld evaluation is typically dominated by the cost of running the agent in the real-world and/or human supervision. In the self-driving car example, both issues are present: testing requires both operating a physical car, and a human test driver behind the wheel. The overarching idea is thus to screen out situations that are unlikely to be problematic, and focus evaluation on the most difficult situations. The difficulty arises in identifying these situations -since failures are rare, there is little signal to drive optimization. To address this problem, we introduce a continuation approach to learning a failure probability predictor (AVF), which estimates the probability the agent fails given some initial conditions. The idea is to leverage data from less robust agents, which fail more frequently, to provide a stronger learning signal. In our implementation, this also allows the algorithm to reuse data gathered for training the agent, saving time and resources during evaluation. We note that adversarial testing is a well-established idea (see Section 5), but typically requires either a dense optimization signal or expert domain knowledge. We avoid these stumbling blocks by relying on the learned AVF, which guides the adversarially acting evaluator.We look at two settings where the AVF can be used. In the simplest setting, failure search, the problem is to efficiently find inputs (initial conditions) that cause failures (Section 2.1). This task has several uses. First, an adversary that solves this task efficiently allows one to identify and debug potentially unsafe policies. Second, as has been done previously in the supervised learning literature, efficient adversaries can be used for adversarial training, by folding the states causing failures back into the training algorithm BID9 . The second setting, risk estimation, is the problem of efficiently estimating the failure probability of an agent (Section 2.2), which also has a simple application to efficiently selecting the most reliable agent from a finite set (Section 4.3).Empirically , we demonstrate dramatic improvements in efficiency through adversarial testing on two domains (simulated driving and humanoid locomotion). In summary , we present 3 key contributions:1. We empirically demonstrate the limitations of random testing. We observe that with random testing, the cost of reliably obtaining even a single adversarial input can exceed the entire cost of training. Further, reliably estimating risk can exceed training costs.2. We describe a continuation approach for learning failure probability predictors even when failures are rare. We develop algorithms applying failure probability predictors to failure search, risk estimation, and model selection.3. We extensively evaluate our method on simulated driving and humanoid locomotion domains. Using adversarial evaluation, we find failures with 198 and 3100 times fewer samples respectively. On Humanoid, we bring the cost of reliable risk estimation down from greater than the cost of training to a practical budget. In this work, we argued that standard approaches to evaluating RL agents are highly inefficient in detecting rare, catastrophic failures, which can create a false sense of safety. We believe the approach and results here strongly demonstrate that adversarial testing can play an important role in assessing and improving agents, but are only scratching the surface. We hope this work lays the groundwork for future research into evaluating and developing robust, deployable agents.",1265,0.822,724,1.7472375690607735,"This paper addresses evaluating learning systems safety critical domains where failures We focus two problems searching scenarios when learned agents assessing The standard method agent evaluation reinforcement learning Vanilla Monte Carlo can miss failures entirely leading the deployment unsafe agents We demonstrate this is current agents even matching the compute used training sometimes evaluation To address draw the rare event probability estimation literature propose Our approach focuses evaluation adversarially chosen situations while still unbiased estimates failure probabilities The key difficulty these adversarial situations -- since failures there little signal drive optimization To solve we propose a continuation approach learns failure modes related but less robust agents Our approach also reuse already training the agent We demonstrate adversarial evaluation two standard domains humanoid control simulated driving Experimental results our methods find catastrophic failures estimate failures rates agents multiple orders standard evaluation schemes minutes to How ensure machine learning systems do make While machine learning systems shown across BID6 , they fail badly particular inputs often BID28 As start deploying these systems can reliably evaluate This particularly safety critical domains autonomous driving where the negative consequences a single mistake overwhelm accrued during typical operationLimitations random testing. The key problem we highlight for standard statistical evaluation attaining confidence that a policy below requires at least 1/ episodes We now informally summarize this point discuss further For concreteness consider decides a single accident where at faultless operation The standard approach machine learning estimate via i.i.d samples the data distributionfrequently a test set For tightly bounded returns the sample estimate guaranteed quickly the true expectation However with catastrophic failures this inefficient In our current example any policy with a failure probability = 10 −8 per mile has negative expected return In deploy the car However to achieve reasonable confidence the car crashes with probability below 1e-8 test- mayOur Contributions. To overcome develop a novel adversarial evaluation approach The central motivation our algorithmic choices realworld evaluation typically dominated the cost running the agent In the self-driving car example both issues present testing requires both operating a physical car test behind The overarching idea thus screen situations unlikely problematic focus evaluation The difficulty arises identifying these situations -since failures little signal drive optimization To address introduce a continuation approach learning a failure probability predictorAVF estimates the agent fails given The idea leverage data less robust agents fail a stronger learning signal In our implementation this also the algorithm reuse gathered training the agent saving during evaluation We note adversarial testing ( typically requires either a dense optimization signal expert domain knowledge We avoid these stumbling blocks relying the learned AVF, guides the adversarially acting evaluatorWe look two settings where In the simplest setting failure search, efficiently inputs (initial conditions cause failuresSection This task several uses First an adversary solves efficiently allows identify debug potentially unsafe policies Second as has done the supervised learning literature efficient adversaries by folding the states causing failures back the training algorithm BID9 . The second setting risk estimation efficientlySection also a simple application efficiently selecting from , demonstrate dramatic improvements efficiency through adversarial testing on two domainssimulated driving humanoid locomotion In summary , 3 key contributions:1 We empirically demonstrate the limitations random testing We observe with random testing the cost reliably obtaining even a single adversarial input training Further reliably estimating risk can exceed training costs.2. We describe a continuation approach learning failure probability predictors even failures rare We develop algorithms applying failure probability predictors failure search risk estimation model. extensively on simulated driving humanoid locomotion domains Using adversarial evaluation find failures 198 and 3100 times fewer samples respectively On Humanoid bring the cost reliable risk estimation down greater training a practical budget In this work argued standard approaches evaluating RL agents highly rare, catastrophic failures create We believe the approach and results here strongly adversarial testing play assessing agents, are scratching We hope this work lays evaluating robust, deployable agents",0.01,0.6079748440756761
"The variational autoencoder (VAE) is a popular combination of deep latent variable model and accompanying variational learning technique. By using a neural inference network to approximate the model's posterior on latent variables, VAEs efficiently parameterize a lower bound on marginal data likelihood that can be optimized directly via gradient methods. In practice, however, VAE training often results in a degenerate local optimum known as ""posterior collapse"" where the model learns to ignore the latent variable and the approximate posterior mimics the prior. In this paper, we investigate posterior collapse from the perspective of training dynamics. We find that during the initial stages of training the inference network fails to approximate the model's true posterior, which is a moving target. As a result, the model is encouraged to ignore the latent encoding and posterior collapse occurs. Based on this observation, we propose an extremely simple modification to VAE training to reduce inference lag: depending on the model's current mutual information between latent variable and observation, we aggressively optimize the inference network before performing each model update. Despite introducing neither new model components nor significant complexity over basic VAE, our approach is able to avoid the problem of collapse that has plagued a large amount of previous work. Empirically, our approach outperforms strong autoregressive baselines on text and image benchmarks in terms of held-out likelihood, and is competitive with more complex techniques for avoiding collapse while being substantially faster.",284,0.158,169,1.680473372781065,"The variational autoencoder deep latent variable model accompanying By using a neural inference network approximate on latent variables VAEs efficiently parameterize lower marginal data likelihood that optimized directly via gradient methods In practice VAE training often results a degenerate local optimum known the model learns the latent variable the approximate posterior mimics prior In posterior collapse from the perspective training dynamics We find during training the inference network fails approximate, a moving target As the model encouraged ignore the latent encoding posterior collapse occurs Based this observation an extremely simple modification VAE training inference lag depending the model's current mutual information between latent variable observation aggressively before each model update Despite introducing neither new model components significant complexity over basic VAE our approach able avoid collapse that a large amount previous work our approach outperforms strong autoregressive baselines text and image benchmarks held-out likelihood competitive more complex techniques avoiding collapse while being substantially",0.0,0.4378655377931265
"Online healthcare services can provide the general public with ubiquitous access to medical knowledge and reduce the information access cost for both individuals and societies. To promote these benefits, it is desired to effectively expand the scale of high-quality yet novel relational medical entity pairs that embody rich medical knowledge in a structured form. To fulfill this goal, we introduce a generative model called Conditional Relationship Variational Autoencoder (CRVAE), which can discover meaningful and novel relational medical entity pairs without the requirement of additional external knowledge. Rather than discriminatively identifying the relationship between two given medical entities in a free-text corpus, we directly model and understand medical relationships from diversely expressed medical entity pairs. The proposed model introduces the generative modeling capacity of variational autoencoder to entity pairs, and has the ability to discover new relational medical entity pairs solely based on the existing entity pairs. Beside entity pairs, relationship-enhanced entity representations are obtained as another appealing benefit of the proposed method. Both quantitative and qualitative evaluations on real-world medical datasets demonstrate the effectiveness of the proposed method in generating relational medical entity pairs that are meaningful and novel. Increasingly, people engage in health services on the Internet BID11 . The healthcare services can provide the general public with ubiquitous access to medical knowledge and reduce the information access cost significantly. The relational medical entity pair, which consists of two medical entities with a semantic connection between them, is an intuitive representation that distills human medical reasoning processes in a structured form. The medical relationships discussed in this paper are binary ones. For example, the Disease Cause − −−− →Symptom relationship indicates a ""Cause"" relationship from a disease entity to a symptom entity that is caused by this disease, such as the medical entity pairs <Synovitis, Joint Pain>. For the relationship Symptom Belongto − −−−−− →Department, we may have a relational medical entity pair such as <Stiffness of a Joint, Orthopedics>.The ability to understand, reason and generalize is central to human intelligence BID27 . However , it possesses significant challenges for machines to understand and reason about the relationships between two entities BID31 . Real-world relational medical entity pairs possess certain challenging properties to deal with: First, as the medical research develops, many medical relationships among medical entities that were once neglected due to the underdeveloped medical knowledge now need to be discovered. An increasing number of relationships will be formed among a large number of medical entities. Also, various linguistic expressions can be used for the same medical entity. For example, Nose Plugged, Blocked Nose and Sinus Congestion are symptom entities that share the same meaning but expressed very differently. Moreover, one medical relationship may instantiate entity pairs with varying granularities or relationship strength. For instance, Disease Cause − −−− →Symptom may include entity pairs like <Rhinitis, Nose Plugged> as a coarse-grained entity pair, while < Acute Rhinitis, Nose Plugged>, <Chronic Rhinitis, Nose Plugged> are considered fine-grained entity pairs. As for the relationship strength, <Cold, Fatigue> has greater relationship strength than <Cold, Ear Infections> as cold rarely cause serious complications such as ear infections.To effectively expand the scale of high-quality yet novel relational medical entity pairs, relation extraction methods BID8 BID2 are proposed to examine whether or not a semantic relationship exists between two given entities given a context. Although the existing relation extraction methods BID1 BID3 BID30 BID39 BID6 BID37 achieve decent performance in identifying the relationship for given entity pairs, those methods require contexts such as sentences retrieved from a large free-text corpus, from existing domain-specific knowledge graphs BID0 , or from web tables and links BID21 . As medical relationships in the real-world are becoming more and more complex and diversely expressed, existing relation extraction methods suffer from the data sparsity problem where it is hard to obtain additional external knowledge that covers all possible entity pairs, e.g. free-text corpus where two entities co-occur in the same sentence with a relationship between them. Therefore, it is crucial and appealing for us to discover meaningful relational medical entity pairs solely based on existing medical entity pairs, without the requirement of a well-maintained context as an additional external knowledge.Furthermore, most relation extraction methods adopt a discriminative approach that learns to distinguish entity pairs of one relationship from the other BID41 BID22 , or to identify meaningful entity pairs from randomly sampled negative entity pairs with no relationships BID4 BID32 . Those methods need to iterate over the combination of all possible entity pairs and check each of them to discover new entity pairs. Such discriminative approach is tedious and labor-intensive. It is challenging yet rewarding for us to understand medical relationships intrinsically from the existing entity pairs. Specifically, in the medical domain, the diversely expressed medical entity pairs offer great advantages for us to ultimately understand medical relationships and discover high-quality relational medical entity pairs solely from existing meaningful medical entity pairs.Problem Studied: We propose a novel research problem called RElational Medical Entity-pair DiscoverY (REMEDY), which aims at modeling relational medical entity pairs solely from the existing entity pairs. Also, it aims to discover meaningful and novel entity pairs pertaining to a certain medical relationship in a generative fashion, without sophisticated feature engineering and the requirement of external knowledge such as free-text corpora.Proposed Model: A generative model named Conditional Relationship Variational Autoencoder (CRVAE) is introduced for relational medical entity pair discovery. It is unlikely to create meaningful, novel relational medical entity pairs without intrinsically understanding each medical relationship, more specifically, understanding the relationships between every two medical entities that instantiate a particular relationship. CRVAE fully explores the generative modeling capacity which roots in Bayesian inference while incorporating deep learning for powerful hands-free feature engineering. CRVAE is trained to encode each relational medical entity pair into a latent space conditioned on the relationship type. The encoding process addresses relationship-enhanced entity representations, interactions between entities as well as expressive latent variables. The latent variables are decoded to reconstruct entity pairs. Once the model is trained, we can sample directly from the distribution of latent variables and decode them into high-quality and novel relational medical entity pairs.Overall, CRVAE has three notable strengths:CRVAE models the intrinsic relations between medical entity pairs directly based on the existing meaningful relational medical entity pairs, without the requirement of additional external contexts for entity pair extraction. Existing relation extraction methods usually rely on the free-text corpus to decide whether a candidate entity pair it mentions is meaningful or not. The CRVAE only utilizes the existing entity pairs and pre-trained word vector as initial entity representations which are trained separately.CRVAE is able to generate entity pairs for a particular relationship, even if it observes existing entity pairs only for that particular relationship. Unlike most discriminative methods which harness discrepancies among different relationships to distinguish the relationship of an entity pair from the other, or from randomly constructed negative entity pairs with no relations. The CRVAE understands the intrinsic medical relation from diversely expressed medical entity pairs and discovers meaningful, novel entity pairs of a particular relationship that we specified.CRVAE generates novel entity pairs by a density-based sampling strategy in the generator. The generator samples directly from the latent space based on the density of hidden parameters. With the hands-free feature engineering by deep neural networks, the model is able to discover meaningful and novel entity pairs which does not exist in the training data.The contributions of this paper can be summarized as follows:• We study the Relational Medical Entity-pair Discovery (REMEDY) problem, which aims to expand the scale of high-quality yet novel relational medical entity pairs without maintaining large-scale context information such as the free-text corpus.• We propose a generative model named Conditional Relationship Variational Autoencoder (CRVAE) that discovers relational medical entity pairs for a given relationship, solely from the diversely expressed entity pairs without sophisticated feature engineering.• We obtain relationship-enhanced entity representations as an appealing benefit of the proposed model. To effectively expand the scale of high-quality relational medical entity pairs which store the medical knowledge, a novel generative model named Conditional Relationship Variational Autoencoder (CRVAE) is introduced for Relational Medical Entity-pair Discovery (REMEDY). The proposed model fully explores the generative modeling ability while incorporates deep learning for powerful hands-free feature engineering. Unlike traditional relation extraction tasks which require additional contexts for extraction and need negative samples for discriminative training, the proposed method learns to intrinsically understand the medical relations from diversely expressed medical entity pairs, without the requirement of external context information. Moreover, it is able to generate meaningful, novel entity pairs for a given type of medical relationship. The relationshipenhanced entity representations have the potential to improve other NLP tasks. The performance of the proposed method is evaluated on real-world medical data both quantitatively and qualitatively.",1781,0.878,1065,1.6723004694835681,"Online healthcare services ubiquitous access reduce the information access cost societies To promote these benefits it desired effectively expand high-quality yet novel relational medical entity pairs embody rich medical knowledge To fulfill introduce called Conditional Relationship Variational AutoencoderCRVAE discover meaningful and novel relational medical entity pairs without additional external knowledge Rather discriminatively identifying the relationship two given medical entities a free-text corpus directly model understand medical relationships from diversely expressed medical entity pairs The proposed model introduces the generative modeling capacity to entity pairs has discover new relational medical entity solely entity pairs relationship-enhanced entity representations obtained another appealing benefit the proposed method Both quantitative and qualitative evaluations on real-world medical datasets demonstrate generating relational medical entity pairs meaningful novel engage health services on the Internet BID11 . The healthcare services can provide ubiquitous access reduce the information access cost significantly The relational medical entity pair a semantic connection that distills human medical reasoning processes The medical relationships discussed binary ones For example the Disease Cause − −−− →Symptom relationship indicates a ""Cause"" relationship from the medical entity pairs <Synovitis Joint Pain For the relationship Symptom Belongto − −−−−− →Department, we may a relational medical entity pair such <Stiffness a Joint, Orthopedics>.The ability understand reason central human intelligence BID27 . However , possesses significant challenges machines reason the relationships two entities BID31 Real-world relational medical entity pairs possess certain challenging properties to deal First as the medical research develops many medical relationships among that were neglected due now discovered An increasing number relationships will medical entities Also various linguistic expressions the same medical entity For example Nose Plugged Blocked Nose and Sinus Congestion symptom entities share expressed very Moreover one medical relationship instantiate entity pairs varying granularities or relationship strength For instance Disease Cause − −−− →Symptom may entity pairs like <Rhinitis Nose Plugged as while considered As for the relationship strength <Cold, Fatigue greater relationship strength cold rarely serious complications suchTo effectively expand the scale high-quality yet novel relational medical entity pairs relation extraction methods BID8 BID2 are examine or two given entities given Although the existing relation extraction methods achieve decent performance identifying the relationship for given entity pairs contexts such sentences retrieved from existing domain knowledge graphs BID0 , web tables links As medical relationships in diversely expressed existing relation extraction methods suffer the data sparsity problem where obtain additional external knowledge covers all possible entity pairs where co with a relationship Therefore crucial and appealing discover meaningful relational medical entity pairs solely as an additional external knowledgeFurthermore most relation extraction methods adopt learns one relationship the other BID41 BID22 , or to randomly sampled negative entity with no relationships Those methods need iterate the combination all possible entity pairs check discover Such discriminative approach tedious labor It challenging yet rewarding understand medical relationships intrinsically from the existing entity pairs Specifically the medical domain the diversely expressed medical entity pairs offer great advantages us ultimately medical relationships discover high-quality relational medical entity solely existing meaningful medical entity pairsProblem Studied We called RElational Medical Entity-pair DiscoverY solely Also aims discover meaningful and novel entity pairs pertaining a certain medical relationship without sophisticated feature engineering the requirement external knowledge such free-text corporaProposed Model named Conditional Relationship Variational AutoencoderCRVAE introduced relational medical entity pair discovery It unlikely create meaningful novel relational medical entity pairs without intrinsically understanding each medical relationship more understanding instantiate CRVAE fully explores the generative modeling capacity which roots while incorporating for powerful hands-free feature engineering CRVAE trained encode each relational medical entity pair a latent space conditioned The encoding process addresses relationship-enhanced entity representations interactions as expressive latent variables The latent variables decoded reconstruct entity pairs Once the model trained sample directly latent variables decode high-quality and novel relational medical entity pairsOverall CRVAE three notable strengthsCRVAE models the intrinsic relations directly based existing meaningful relational medical without additional external contexts entity pair extraction Existing relation extraction methods usually rely the free-text corpus decide a candidate entity pair it mentions meaningful The CRVAE only utilizes the existing entity pairs pre-trained word vector as initial entity representations which trained separately a particular relationship even observes only Unlike most discriminative methods which harness discrepancies among different relationships distinguish an entity pair or randomly constructed negative entity with. The CRVAE understands the intrinsic medical relation from diversely expressed medical entity pairs discovers meaningful, novel entity pairs a particular relationship we specified generates a density-based sampling strategy the generator The generator samples directly the latent space based hidden parameters With the hands-free feature engineering by deep neural networks the model discover meaningful and novel entity pairs which doesThe contributions study the Relational Medical Entity-pair Discovery (REMEDY) problem aims expand the scale high yet novel relational without maintaining large-scale context information such freetext named Conditional Relationship Variational AutoencoderCRVAE discovers solely the diversely expressed entity pairs without sophisticated feature obtain relationship-enhanced entity representations as an appealing benefit To effectively expand the scale high-quality relational medical entity pairs which store a novel generative model named Conditional Relationship Variational AutoencoderCRVAE introduced for Relational Medical Entity-pair DiscoveryREMEDY The proposed model fully explores the generative modeling ability while incorporates powerful hands-free feature engineering Unlike traditional relation extraction tasks which additional contexts extraction need negative samples the proposed method learns intrinsically understand the medical relations from diversely expressed medical entity pairs without external context information Moreover able generate meaningful novel entity pairs medical relationship The relationshipenhanced entity representations other NLP tasks The performance the proposed method evaluated both",0.01,0.4170416982545368
"Although variational autoencoders (VAEs) represent a widely influential deep generative model, many aspects of the underlying energy function remain poorly understood.  In particular, it is commonly believed that Gaussian encoder/decoder assumptions reduce the effectiveness of VAEs in generating realistic samples .  In this regard, we rigorously analyze the VAE objective, differentiating situations where this belief is and is not actually true .  We then leverage the corresponding insights to develop a simple VAE enhancement that requires no additional hyperparameters or sensitive tuning .  Quantitatively, this proposal produces crisp samples and stable FID scores that are actually competitive with a variety of GAN models, all while retaining desirable attributes of the original VAE architecture . The code for our model is available at \url{https://github.com/daib13/TwoStageVAE}. Our starting point is the desire to learn a probabilistic generative model of observable variables x ∈ χ, where χ is a r-dimensional manifold embedded in R d . Note that if r = d, then this assumption places no restriction on the distribution of x ∈ R d whatsoever; however, the added formalism is introduced to handle the frequently encountered case where x possesses low-dimensional structure relative to a high-dimensional ambient space, i.e., r d. In fact, the very utility of generative models of continuous data, and their attendant low-dimensional representations, often hinges on this assumption BID1 . It therefore behooves us to explicitly account for this situation.Beyond this, we assume that χ is a simple Riemannian manifold, which means there exists a diffeomorphism ϕ between χ and R r , or more explicitly, the mapping ϕ : χ → R r is invertible and differentiable. Denote a ground-truth probability measure on χ as µ gt such that the probability mass of an infinitesimal dx on the manifold is µ gt (dx) and χ µ gt (dx) = 1.The variational autoencoder (VAE) BID17 BID28 attempts to approximate this ground-truth measure using a parameterized density p θ (x) defined across all of R d since any underlying generative manifold is unknown in advance. This density is further assumed to admit the latent decomposition p θ (x) = p θ (x|z)p(z)dz, where z ∈ R κ serves as a lowdimensional representation, with κ ≈ r and prior p(z) = N (z|0, I).Ideally we might like to minimize the negative log-likelihood − log p θ (x) averaged across the ground-truth measure µ gt , i.e., solve min θ χ − log p θ (x)µ gt (dx). Unfortunately though, the required marginalization over z is generally infeasible. Instead the VAE model relies on tractable encoder q φ (z|x) and decoder p θ (x|z) distributions, where φ represents additional trainable parameters. The canonical VAE cost is a bound on the average negative log-likelihood given by L(θ, φ) χ {− log p θ (x) + KL [q φ (z|x)||p θ (z|x)]} µ gt (dx) ≥ χ − log p θ (x)µ gt (dx),where the inequality follows directly from the non-negativity of the KL-divergence. Here φ can be viewed as tuning the tightness of bound, while θ dictates the actual estimation of µ gt . Using a few standard manipulations, this bound can also be expressed as DISPLAYFORM0 which explicitly involves the encoder/decoder distributions and is conveniently amenable to SGD optimization of {θ, φ} via a reparameterization trick BID17 BID28 . The first term in (2 ) can be viewed as a reconstruction cost (or a stochastic analog of a traditional autoencoder), while the second penalizes posterior deviations from the prior p(z). Additionally, for any realizable implementation via SGD, the integration over χ must be approximated via a finite sum across training samples {x (i) } n i=1 drawn from µ gt . Nonetheless, examining the true objective L(θ, φ) can lead to important, practically-relevant insights.At least in principle, q φ (z|x) and p θ (x|z) can be arbitrary distributions, in which case we could simply enforce q φ (z|x) = p θ (z|x) ∝ p θ (x|z)p(z) such that the bound from (1) is tight. Unfortunately though, this is essentially always an intractable undertaking. Consequently, largely to facilitate practical implementation, a commonly adopted distributional assumption for continuous data is that both q φ (z|x) and p θ (x|z) are Gaussian. This design choice has previously been cited as a key limitation of VAEs BID5 BID18 , and existing quantitative tests of generative modeling quality thus far dramatically favor contemporary alternatives such as generative adversarial networks (GAN) BID13 . Regardless, because the VAE possesses certain desirable properties relative to GAN models (e.g., stable training BID29 , interpretable encoder/inference network BID4 , outlier-robustness BID9 , etc.), it remains a highly influential paradigm worthy of examination and enhancement.In Section 2 we closely investigate the implications of VAE Gaussian assumptions leading to a number of interesting diagnostic conclusions. In particular, we differentiate the situation where r = d, in which case we prove that recovering the ground-truth distribution is actually possible iff the VAE global optimum is reached, and r < d, in which case the VAE global optimum can be reached by solutions that reflect the ground-truth distribution almost everywhere, but not necessarily uniquely so. In other words, there could exist alternative solutions that both reach the global optimum and yet do not assign the same probability measure as µ gt .Section 3 then further probes this non-uniqueness issue by inspecting necessary conditions of global optima when r < d. This analysis reveals that an optimal VAE parameterization will provide an encoder/decoder pair capable of perfectly reconstructing all x ∈ χ using any z drawn from q φ (z|x). Moreover, we demonstrate that the VAE accomplishes this using a degenerate latent code whereby only r dimensions are effectively active. Collectively, these results indicate that the VAE global optimum can in fact uniquely learn a mapping to the correct ground-truth manifold when r < d, but not necessarily the correct probability measure within this manifold, a critical distinction.Next we leverage these analytical results in Section 4 to motivate an almost trivially-simple, twostage VAE enhancement for addressing typical regimes when r < d. In brief, the first stage just learns the manifold per the allowances from Section 3, and in doing so, provides a mapping to a lower dimensional intermediate representation with no degenerate dimensions that mirrors the r = d regime. The second (much smaller) stage then only needs to learn the correct probability measure on this intermediate representation, which is possible per the analysis from Section 2. Experiments from Sections 5 and 6 empirically corroborate motivational theory and reveal that the proposed two-stage procedure can generate high-quality samples, reducing the blurriness often attributed to VAE models in the past BID11 BID21 . And to the best of our knowledge, this is the first demonstration of a VAE pipeline that can produce stable FID scores, an influential recent metric for evaluating generated sample quality BID16 , that are comparable to GAN models under neutral testing conditions. Moreover, this is accomplished without additional penalties, cost function modifications, or sensitive tuning parameters. Finally, an extended version of this work can be found in BID8 ). There we include additional results, consideration of disentangled representations, as well as a comparative discussion of broader VAE modeling paradigms such as those involving normalizing flows or parameterized families for p(z). It is often assumed that there exists an unavoidable trade-off between the stable training, valuable attendant encoder network, and resistance to mode collapse of VAEs, versus the impressive visual quality of images produced by GANs. While we certainly are not claiming that our two-stage VAE model is superior to the latest and greatest GAN-based architecture in terms of the realism of generated samples, we do strongly believe that this work at least narrows that gap substantially such that VAEs are worth considering in a broader range of applications. For further results and discussion, including consideration of broader VAE modeling paradigms and the identifiability of disentangled representations, please see BID8 .",1753,0.763,1054,1.6631878557874762,"Although variational autoencodersVAEs represent a widely influential deep generative model many aspects the underlying energy function In particular commonly Gaussian encoder/decoder assumptions reduce VAEs generating realistic samples . In this regard rigorously analyze the VAE objective differentiating situations this belief and actually . We then leverage the corresponding insights a simple VAE enhancement requires sensitive tuning . Quantitatively this proposal produces crisp samples stable FID scores actually competitive a variety GAN models all while desirable attributes the original VAE architecture . The code our model \url{https://github.com/daib13/TwoStageVAE Our starting point the desire learn a probabilistic generative model observable variables x �� ��, a r-dimensional manifold embedded R d Note r = d this assumption places no restriction x �� R d whatsoever; the added formalism introduced handle the frequently encountered case possesses low-dimensional structure relative r d. In fact very utility generative models continuous data their attendant low-dimensional representations often hinges this assumption BID1 . It therefore explicitly account this situationBeyond assume �� there a diffeomorphism �� R r or more explicitly is differentiable Denote a ground-truth probability measure on �� as µ gt such the probability mass on the manifolddxVAE BID17 BID28 attempts a parameterized density p ��x defined across of R d since any underlying generative manifold unknown advance This density further assumed admit the latent decomposition p ��x z �� R �� serves a lowdimensional representation, prior p(z N I).Ideally like minimize averaged the ground-truth measure µ gt solve min �� �� − log)�dx Unfortunately though the required marginalization over z is generally Instead the VAE model relies tractable encoder q �z|x p � distributions additional trainable parameters The canonical VAE cost a bound on the average negative log-likelihood given by L� � {− log (x KL [q �z|x)||p µ gt (dx) ≥ �� −� the inequality follows directly non Here �� can viewed tuning the tightness bound, while dictates the actual estimation µ gt Using a few standard manipulations bound can also expressed DISPLAYFORM0 which explicitly involves conveniently amenable SGD optimization of {�� � via a reparameterization trick BID17 BID28 The first term (2 ) can viewed a reconstruction cost a stochastic analog penalizes posterior deviations the prior p(z Additionally for any realizable implementation via SGD the integration over �� must approximated via a finite sum across training samples {x (i n i=1 drawn µ gt Nonetheless examining the true objective L(�� can important, practically-relevant insightsAt q �z|x arbitrary distributions in simply enforce = such bound from tight Unfortunately though essentially always an intractable undertaking largely to facilitate practical implementation a commonly adopted distributional assumption continuous data both q ��z|x Gaussian This design choice previously cited VAEs BID5 BID18 , existing quantitative tests generative modeling quality thus dramatically favor contemporary alternativesGAN) BID13 Regardless because the VAE possesses certain desirable properties relative GAN modelse.g., stable training BID29 , interpretable encoder/inference network BID4 remains a highly influential paradigm worthy examination enhancementIn Section closely investigate VAE Gaussian assumptions leading a number interesting diagnostic conclusions In particular differentiate the situation r = d in prove recovering the ground-truth distribution actually iff the VAE global optimum reached r < can solutions reflect almost everywhere uniquely so In could exist alternative solutions both reach the global optimum yet assign the same probability measure µ gt .Section then further probes inspecting necessary conditions global optima when r < d. This analysis reveals an optimal VAE parameterization will provide capable perfectly all x �� �� using any z drawn q ��z|x Moreover demonstrate the VAE accomplishes using a degenerate latent code whereby only r dimensions effectively active Collectively the VAE global optimum can in uniquely learn a mapping to the correct ground-truth manifold when r < d, but not necessarily the correct probability measure within a critical distinctionNext leverage these analytical results Section motivate an almost trivially-simple, twostage VAE enhancement addressing typical regimes when In brief the first stage just learns the manifold per the allowances from Section in provides a mapping a lower dimensional intermediate representation with no degenerate dimensions that mirrors the r = d regime The second (much smaller) stage then only needs learn the correct probability measure on this intermediate representation possible per the analysis from Section Experiments from Sections 5 empirically motivational theory reveal the proposed two-stage procedure generate reducing often attributed VAE models BID11 BID21 . And to a VAE pipeline produce stable FID scores an influential recent metric generated sample quality BID16 , that are comparable GAN models under neutral testing conditions Moreover this accomplished without additional penalties cost function modifications sensitive tuning parameters Finally an extended version BID8 ). There we include additional results consideration disentangled representations as a comparative discussion broader VAE modeling paradigms such those involving normalizing flows or parameterized families for p(z It often there exists the stable training, valuable attendant encoder network resistance mode collapse of VAEs versus the impressive visual quality images GANs certainly are claiming our two-stage VAE model latest the realism generated samples strongly this work at narrows substantially such worth For further results discussion including consideration broader VAE modeling paradigms the identifiability disentangled representations BID8 .",0.01,0.39382355918237977
"We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions.   We focus on the high-dimensional regime where the canonical example is training a neural network with a large number of hyperparameters. The algorithm --- an iterative application of compressed sensing techniques for orthogonal polynomials --- requires only uniform sampling of the hyperparameters and is thus easily parallelizable.
 
 Experiments for training deep neural networks on Cifar-10 show that compared to state-of-the-art tools (e.g., Hyperband and Spearmint), our algorithm finds significantly improved solutions, in some cases better than what is attainable by hand-tuning.   In terms of overall running time (i.e., time required to sample various settings of hyperparameters plus additional computation time), we are at least an order of magnitude faster than Hyperband and Bayesian Optimization.   We also outperform Random Search $8\times$.
   
Our method is inspired by provably-efficient algorithms for learning decision trees using the discrete Fourier transform.   We obtain improved sample-complexty bounds for learning decision trees while matching state-of-the-art bounds on running time (polynomial and quasipolynomial, respectively). Large scale machine learning and optimization systems usually involve a large number of free parameters for the user to fix according to their application. A timely example is the training of deep neural networks for a signal processing application: the ML specialist needs to decide on an architecture, depth of the network, choice of connectivity per layer (convolutional, fully-connected, etc.), choice of optimization algorithm and recursively choice of parameters inside the optimization library itself (learning rate, momentum, etc.).Given a set of hyperparameters and their potential assignments, the naive practice is to search through the entire grid of parameter assignments and pick the one that performed the best, a.k.a. ""grid search"". As the number of hyperparameters increases, the number of possible assignments increases exponentially and a grid search becomes quickly infeasible. It is thus crucial to find a method for automatic tuning of these parameters.This auto-tuning, or finding a good setting of these parameters, is now referred to as hyperparameter optimization (HPO), or simply automatic machine learning (auto-ML). For continuous hyperparameters, gradient descent is usually the method of choice BID25 BID24 BID9 . Discrete parameters , however, such as choice of architecture, number of layers, connectivity and so forth are significantly more challenging. More formally, let DISPLAYFORM0 be a function mapping hyperparameter choices to test error of our model. That is, each dimension corresponds to a certain hyperparameter (number of layers, connectivity, etc.), and for simplicity of illustration we encode the choices for each parameter as binary numbers {−1, 1}. The goal of HPO is to approximate the minimizer x * = arg min x∈{0,1} n f (x) in the following setting:1. Oracle model: evaluation of f for a given choice of hyperparameters is assumed to be very expensive. Such is the case of training a given architecture of a huge dataset.2. Parallelism is crucial: testing several model hyperparameters in parallel is entirely possible in cloud architecture, and dramatically reduces overall optimization time.3. f is structured.The third point is very important since clearly HPO is information-theoretically hard and 2 n evaluations of the function are necessary in the worst case. Different works have considered exploiting one or more of the properties above. The approach of Bayesian optimization BID32 addresses the structure of f , and assumes that a useful prior distribution over the structure of f is known in advance. Multi-armed bandit algorithms BID22 , and Random Search BID2 , exploit computational parallelism very well, but do not exploit any particular structure of f 1 . These approaches are surveyed in more detail later .",773,0.415,455,1.6989010989010989,"We give a simple, fast algorithm hyperparameter optimization inspired techniques the analysis Boolean functions We focus the high-dimensional regime where the canonical example training The algorithm --- an iterative application compressed sensing techniques for requires only uniform sampling thus easily Experiments for training Cifar-10 show compared state tools ( Hyperband and Spearmint our algorithm finds significantly improved solutions in better what attainable In terms overall running time required sample various settings of hyperparameters plus additional computation Hyperband and Bayesian Optimization We also outperform Random Search $8\times$. Our method inspired provably-efficient algorithms for learning decision trees We obtain improved sample-complexty bounds learning decision trees while matching state bounds running time and quasipolynomial, Large scale machine learning and optimization systems usually free parameters for the user fix according their application A timely example the training deep neural networks a signal processing application: the ML specialist needs decide an architecture depth choice connectivity per, fully choice optimization algorithm recursively choice parameters inside the optimization library itselflearning rate momentum etc.).Given their potential assignments the naive practice search the entire grid parameter assignments pick performed ""grid search As the number hyperparameters increases possible assignments increases a grid search quickly It thus crucial find automatic tuning these parametersThis auto-tuning, finding a good setting now referred simply automatic machine learningauto-ML For continuous hyperparameters gradient descent usually BID25 BID24 BID9 . Discrete parameters , however such choice architecture number layers connectivity so significantly challenging More formally let DISPLAYFORM0 a function mapping hyperparameter choices test error of our model That each dimension correspondsnumber layers connectivity for simplicity encode the choices binary numbers {−1 The goal HPO approximate the minimizer x * = arg min x�� n f (x the following setting:1 Oracle model evaluation f for a given choice hyperparameters is assumed very expensive Such training a given architecture of a huge dataset.2. Parallelism crucial: testing several model hyperparameters entirely cloud architecture dramatically f is structured.The third point very since clearly HPO information-theoretically hard and 2 n evaluations the function necessary Different works have considered exploiting one above The approach Bayesian optimization BID32 addresses the structure f , assumes a useful prior distribution over the structure Multiarmed bandit algorithms BID22 , Random Search exploit computational parallelism very do exploit any particular structure f 1 These approaches surveyed later .",0.0,0.48481776490465855
"Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator.   Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms. In principle, deep networks can learn arbitrarily sophisticated mappings from inputs to outputs. However, in practice we must encode specific inductive biases in order to learn accurate models from limit data. In a variety of recent research efforts, practitioners have provided models with the ability to explicitly manipulate latent combinatorial objects such as stacks BID12 BID23 , memory slots BID16 BID45 , mathematical expressions BID33 , program traces BID13 BID6 , and first order logic . Operations on these discrete objects can be approximated using differentiable operations on continuous relaxations of the objects. As such, these operations can be included as modules in neural network models that can be trained end-toend by gradient descent.Matchings and permutations are a fundamental building block in a variety of applications, as they can be used to align, canonicalize, and sort data. Prior work has developed learning algorithms for supervised learning where the training data includes annotated matchings BID36 BID46 . However, we would like to learn models with latent matchings, where the matching is not provided to us as supervision. This is a common and relevant setting. For example, BID30 showed a problem from neuroscience involving the identification of neurons from the worm C. elegans can be cast as the inference of latent permutation on a larger hierarchical structure.Unfortunately, maximizing the marginal likelihood for problems with latent matchings is very challenging. Unlike for problems with categorical latent variables, we cannot obtain unbiased stochastic gradients of the marginal likelihood using the score function estimator BID54 , as computing the probability of a given matching requires computing an intractable partition function for a structured distribution. Instead, we draw on recent work that obtains biased stochastic gradients by relaxing the discrete latent variables into continuous random variables that support the reparametrization trick BID22 BID31 .Our contributions are the following: first, in Section 2 we present a theoretical result showing that the non-differentiable parameterization of a permutation can be approximated in terms of a differentiable relaxation, the so-called Sinkhorn operator. Based on this result, in Section 3 we introduce Sinkhorn networks, which generalize the work of method of BID1 for predicting rankings, and complements the concurrent work by BID9 , by focusing on more fundamental aspects. Further , in Section 4 we introduce the Gumbel-Sinkhorn, an analog of the Gumbel Softmax distribution BID22 BID31 for permutations. This enables optimization of the marginal likelihood by the reparametrization trick. Finally, in Section 5 we demonstrate that our methods outperform strong neural network baselines on the tasks of sorting numbers, solving jigsaw puzzles, and identifying neural signals from C. elegans worms. We have demonstrated Sinkhorn networks are able to learn to find the right permutation in the most elementary cases; where all training samples obey the same sequential structure; e.g., in sorted number and in pieces of faces, as we expect parts of faces occupy similar positions from sample to sample. This is already non-trivial, as indicates one can train a neural network to solve the linear assignment problem.However, the fact that Imagenet represented a much more challenging scenario indicates there are clear limits to our formulation. As the most obvious extension we propose to introduce a sequential stage, in which current solutions are kept on a memory buffer, and improved. One way to achieve this would be by exploring more complex parameterizations for permutations; i.e. replacing M (X) by a quadratic operator that may parameterize a notion of local distance between pieces. Alternatively, one may resort to reinforcement learning techniques, as suggested in BID3 . Either sequential improvement would help solve the ""Order Matters"" problem BID52 , and we deem our elementary work as a significant step in that direction.We have made available Tensorflow code for Gumbel-Sinkhorn networks featuring an implementation of the number sorting experiment at http://github.com/google/gumbel sinkhorn .",985,0.546,556,1.7715827338129497,"Permutations matchings core building blocks a variety latent variable models as align, canonicalize sort Learning in such models exact marginalization over these combinatorial objects In response this paper introduces new methods end learning such models approximate discrete maximum-weight matching the continuous Sinkhorn operator Sinkhorn iteration attractive functions the softmax operator With this define the Gumbel-Sinkhorn method an extension 2016, Maddison2016 et al 2016) to distributions over latent matchings We demonstrate our method outperforming competitive baselines sorting numbers solving identifying neural signals worms In principle deep networks learn arbitrarily sophisticated mappings inputs However practice we must encode specific inductive biases learn accurate models from limit data In a variety recent research efforts practitioners provided models with explicitly manipulate latent combinatorial objects stacks BID12 BID23 memory slots mathematical expressions program traces first order logic . Operations these discrete objects differentiable operations continuous relaxations As such these operations included modules neural network models end-toendMatchings a variety as align canonicalize sort Prior work developed learning algorithms supervised learning where includes annotated matchings BID36 BID46 . However we would learn models with latent matchings provided supervision This a common and relevant setting For example BID30 showed a problem from neuroscience involving from the worm elegans can cast the inference latent permutation on a larger hierarchical structureUnfortunately maximizing problems latent matchings Unlike for problems categorical latent variables obtain the marginal likelihood using the score function estimator BID54 , computing a given matching requires computing a structured distribution Instead draw recent work obtains biased stochastic gradients relaxing the discrete latent variables into support BID22 BID31 .Our contributions first in Section a theoretical result showing a differentiable relaxation, the so-called Sinkhorn operator Based this result in Section we introduce Sinkhorn networks generalize method of BID1 for predicting rankings complements the concurrent work , focusing more fundamental aspects Further , in Section we introduce the Gumbel-Sinkhorn, an analog BID22 BID31 for permutations This enables optimization the marginal likelihood by the reparametrization trick Finally in Section we demonstrate our methods strong neural network baselines the tasks sorting numbers solving identifying neural signals C. elegans worms We demonstrated Sinkhorn networks learn find the most elementary cases; where all training samples obey sorted number and in pieces faces as expect parts occupy from sample This already non indicates one train solve the linear assignment problemHowever Imagenet represented indicates clear limits our formulation As the most obvious extension we propose introduce a sequential stage current solutions kept a memory buffer improved. One way achieve exploring more complex parameterizations permutations; replacing M (X may parameterize a notion local distance pieces Alternatively one resort reinforcement learning techniques BID3 . Either sequential improvement would solve the ""Order Matters"" problem BID52 , deem our elementary workWe made available Tensorflow code Gumbel-Sinkhorn networks featuring an implementation the number sorting experiment at .",0.01,0.6700041849214333
"Recent work in network quantization has substantially reduced the time and space complexity of neural network inference, enabling their deployment on embedded and mobile devices with limited computational and memory resources. However, existing quantization methods often represent all weights and activations with the same precision (bit-width). In this paper, we explore a new dimension of the design space: quantizing different layers with different bit-widths. We formulate this problem as a neural architecture search problem and propose a novel differentiable neural architecture search (DNAS) framework to efficiently explore its exponential search space with gradient-based optimization. Experiments show we surpass the state-of-the-art compression of ResNet on CIFAR-10 and ImageNet. Our quantized models with 21.1x smaller model size or 103.9x lower computational cost can still outperform baseline quantized or even full precision models. Recently, ConvNets have become the de-facto method in a wide range of computer vision tasks, achieving state-of-the-art performance. However, due to high computation complexity, it is nontrivial to deploy ConvNets to embedded and mobile devices with limited computational and storage budgets. In recent years, research efforts in both software and hardware have focused on lowprecision inference of ConvNets. Most of the existing quantization methods use the same precision for all (or most of) the layers of a ConvNet. However, such uniform bit-width assignment can be suboptimal since quantizing different layers can have different impact on the accuracy and efficiency of the overall network. Although mixed precision computation is widely supported in a wide range of hardware platforms such as CPUs, FPGAs, and dedicated accelerators, prior efforts have not thoroughly explored the mixed precision quantization of ConvNets.For a ConvNet with N layers and M candidate precisions in each layer, we want to find an optimal assignment of precisions to minimize the cost in terms of model size, memory footprint or computation, while keeping the accuracy. An exhaustive combinatorial search has exponential time complexity (O(M N )). Therefore, we need a more efficient approach to explore the design space.In this work, we propose a novel, effective, and efficient differentiable neural architecture search (DNAS) framework to solve this problem. The idea is illustrated in FIG0 . The problem of neural architecture search (NAS) aims to find the optimal neural net architecture in a given search space.In the DNAS framework, we represent the architecture search space with a stochastic super net where nodes represent intermediate data tensors of the super net (e.g., feature maps of a ConvNet) and edges represent operators (e.g., convolution layers in a ConvNet). Any candidate architecture can be seen as a child network (sub-graph) of the super net. When executing the super net, edges are executed stochastically and the probability of execution is parameterized by some architecture parameters θ. Under this formulation, we can relax the NAS problem and focus on finding the optimal θ that gives the optimal expected performance of the stochastic super net. The child network can then be sampled from the optimal architecture distribution.We solve for the optimal architecture parameter θ by training the stochastic super net with SGD with respect to both the network's weights and the architecture parameter θ. To compute the gradient of θ, we need to back propagate gradients through discrete random variables that control the stochastic edge execution. To address this, we use the Gumbel SoftMax function BID9 ) to ""soft-control"" the edges. This allows us to directly compute the gradient estimation of θ with a controllable trade-off between bias and variance. Using this technique, the stochastic super net becomes fully differentiable and can be effectively and efficiently solved by SGD. We apply the DNAS framework to solve the mixed precision quantization problem, by constructing a super net whose macro architecture (number of layers, filter size of each layer, etc.) is the same as the target network. Each layer of the super net contains several parallel edges representing convolution operators with quantized weights and activations with different precisions. We show that using DNAS to search for layer-wise precision assignments for ResNet models on CIFAR10 and ImageNet, we surpass the state-of-the-art compression. Our quantized models with 21.1x smaller model size or 103.9x smaller computational cost can still outperform baseline quantized or even full precision models. The DNAS pipeline is very fast, taking less than 5 hours on 8 V100 GPUs to complete a search on ResNet18 for ImageNet, while previous NAS algorithms (such as Zoph & Le (2016)) typically take a few hundred GPUs for several days. Last, but not least, DNAS is a general architecture search framework that can be applied to other problems such as efficient ConvNet-structure discovery. Due to the page limit, we will leave the discussion to future publications. In this work we focus on the problem of mixed precision quantization of a ConvNet to determine its layer-wise bit-widths. We formulate this problem as a neural architecture search (NAS) problem and propose a novel, efficient, and effective differentiable neural architecture search (DNAS) framework to solve it. Under the DNAS framework, we efficiently explore the exponential search space of the NAS problem through gradient based optimization (SGD). We use DNAS to search for layer-wise precision assignment for ResNet on CIFAR10 and ImageNet. Our quantized models with 21.1x smaller model size or 103.9x smaller computational cost can still outperform baseline quantized or even full precision models. DNAS is very efficient, taking less than 5 hours to finish a search on ResNet18 for ImageNet. It is also a general architecture search framework that is not limited to the mixed precision quantization problem. Its other applications will be discussed in future publications. DISPLAYFORM0 w denotes the latent full-precision weight of a network. Q k (·) denotes a k-bit quantization function that quantizes a continuous value w ∈ [0, 1] to its nearest neighbor in { DISPLAYFORM1 To quantize activations, we follow to use a bounded activation function followed by a quantization function as DISPLAYFORM2 Here, x is the full precision activation, y k is the quantized activation. P ACT (·) is a function that bounds the output between [0, α]. α is a learnable upper bound of the activation function.",1302,0.726,770,1.690909090909091,"Recent work network quantization substantially neural network inference enabling their deployment However existing quantization methods often represent all weights activations withbit-width In explore a new dimension the design space quantizing different layers with We formulate this problem a neural architecture search problem propose efficiently explore its exponential search space with gradient-based optimization Experiments show we surpass state compression ResNet on ImageNet Our quantized models with 21.1x smaller model size or 103.9x lower computational cost can still baseline quantized or even full precision models Recently ConvNets have become in computer vision tasks achieving state However due high computation complexity deploy ConvNets limited computational and storage budgets In research efforts both software lowprecision inference ConvNets Most the existing quantization methods the same precision ( the layers a ConvNet However such uniform bit-width assignment since quantizing different layers have the overall network Although mixed precision computation widely supported such dedicated accelerators prior efforts thoroughly the mixed precision quantization ConvNetsFor a ConvNet with N layers M candidate precisions in want find an optimal assignment minimize in terms model size or, keeping. An exhaustive combinatorial search exponential time complexityO(M N Therefore explore the design spaceIn a novel, effective, and efficient differentiable neural architecture search (DNAS) framework solve The idea illustrated FIG0 . The problem neural architecture search (NAS aims findIn the DNAS framework represent a stochastic super net where nodes represent intermediate data tensors of a ConvNet edges operators in Any candidate architecture seen a child network (subgraph the super net When executing the super net edges executed stochastically execution parameterized some architecture parameters � Under this formulation relax the NAS problem finding the optimal �� that gives the optimal expected performance the stochastic super net The child network can then sampled the optimal architecture distributionWe solve training the stochastic super net SGD with respect both the network's weights To compute the gradient �� back propagate gradients through discrete random variables that control the stochastic edge execution To address use the Gumbel SoftMax function BID9 ) ""soft-control the edges This allows directly compute the gradient estimation �� bias variance Using the stochastic super net becomes fully differentiable effectively and solved SGD We apply the DNAS framework solve the mixed precision quantization problem constructing a super net whose macro architecture (number layers filter size of Each layer the super net contains several parallel edges representing convolution operators with quantized weights activations with different precisions We show using DNAS search layer-wise precision assignments ResNet models on CIFAR10 surpass state compression. Our quantized models with 21.1x smaller model size or can still baseline quantized or even full precision models The DNAS pipeline very fast taking on 8 V100 GPUs a search ResNet18 ImageNet while previous NAS algorithms ( Zoph & Le ( typically several days Last, DNAS a general architecture search framework other problems efficient ConvNet-structure discovery Due the page limit leave the discussion future publications In this work mixed precision quantization a ConvNet to determine its layer-wise bit-widths We formulate this problem a neural architecture search ( propose Under the DNAS framework we efficiently explore the exponential search space the NAS problem through gradient based optimizationSGD We use DNAS search layer-wise precision assignment ResNet on CIFAR10 ImageNet Our quantized models with 21.1x smaller model size or can still baseline quantized or even full precision models DNAS very efficient taking finish ResNet18 ImageNet It a general architecture search framework not the mixed precision quantization problem Its other applications will discussed future publications DISPLAYFORM0 w denotes the latent full-precision weight a network Q k (· denotes a k-bit quantization function continuous w � [ to in { DISPLAYFORM1 To activations follow to use a bounded activation function followed as Here x the full precision activation P ACT (· is a function bounds between [ α α is learnable upper the activation function",0.01,0.46445483071116694
"The top-$k$ error is a common measure of performance in machine learning and computer vision. In practice, top-$k$ classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed suggest that cross-entropy is an optimal learning objective for such a task in the limit of infinite data. In the context of limited and noisy data however, the use of a loss function that is specifically designed for top-$k$ classification can bring significant improvements.
 Our empirical evidence suggests that the loss function must be smooth and have non-sparse gradients in order to work well with deep neural networks. Consequently, we introduce a family of smoothed loss functions that are suited to top-$k$ optimization via deep learning. The widely used cross-entropy is a special case of our family. Evaluating our smooth loss functions is computationally challenging: a na{\""i}ve algorithm would require $\mathcal{O}(\binom{n}{k})$ operations, where $n$ is the number of classes. Thanks to a connection to polynomial algebra and a divide-and-conquer approach, we provide an algorithm with a time complexity of $\mathcal{O}(k n)$. Furthermore, we present a novel approximation to obtain fast and stable algorithms on GPUs with single floating point precision. We compare the performance of the cross-entropy loss and our margin-based losses in various regimes of noise and data size, for the predominant use case of $k=5$. Our investigation reveals that our loss is more robust to noise and overfitting than cross-entropy. In machine learning many classification tasks present inherent label confusion. The confusion can originate from a variety of factors, such as incorrect labeling, incomplete annotation, or some fundamental ambiguities that obfuscate the ground truth label even to a human expert. For example, consider the images from the ImageNet data set (Russakovsky et al., 2015) in Figure 1 , which illustrate the aforementioned factors. To mitigate these issues, one may require the model to predict the k most likely labels, where k is typically very small compared to the total number of labels. Then the prediction is considered incorrect if all of its k labels differ from the ground truth, and correct otherwise. This is commonly referred to as the top-k error. Learning such models is a longstanding task in machine learning, and many loss functions for top-k error have been suggested in the literature.In the context of correctly labeled large data, deep neural networks trained with cross-entropy have shown exemplary capacity to accurately approximate the data distribution. An illustration of this phenomenon is the performance attained by deep convolutional neural networks on the ImageNet challenge. Specifically, state-of-the-art models trained with cross-entropy yield remarkable success on the top-5 error, although cross-entropy is not tailored for top-5 error minimization. This phenomenon can be explained by the fact that cross-entropy is top-k calibrated for any k (Lapin et al., 2016) , an asymptotic property which is verified in practice in the large data setting. However, in cases where only a limited amount of data is available, learning large models with cross-entropy can be prone to over-fitting on incomplete or noisy labels.To alleviate the deficiency of cross-entropy, we present a new family of top-k classification loss functions for deep neural networks. Taking inspiration from multi-class SVMs, our loss creates a Figure 1 : Examples of images with label confusion, from the validation set of ImageNet. The top-left image is incorrectly labeled as ""red panda"", instead of ""giant panda"". The bottom-left image is labeled as ""strawberry"", although the categories ""apple"", ""banana"" and ""pineapple"" would be other valid labels. The center image is labeled as ""indigo bunting"", which is only valid for the lower bird of the image. The right-most image is labeled as a cocktail shaker, yet could arguably be a part of a music instrument (for example with label ""cornet, horn, trumpet, trump""). Such examples motivate the need to predict more than a single label per image.margin between the correct top-k predictions and the incorrect ones. Our empirical results show that traditional top-k loss functions do not perform well in combination with deep neural networks. We believe that the reason for this is the lack of smoothness and the sparsity of the derivatives that are used in backpropagation. In order to overcome this difficulty, we smooth the loss with a temperature parameter. The evaluation of the smooth function and its gradient is challenging, as smoothing increases the naïve time complexity from O(n) to O( n k ). With a connection to polynomial algebra and a divide-and-conquer method, we present an algorithm with O(kn) time complexity and training time comparable to cross-entropy in practice. We provide insights for numerical stability of the forward pass. To deal with instabilities of the backward pass, we derive a novel approximation. Our investigation reveals that our top-k loss outperforms cross-entropy in the presence of noisy labels or in the absence of large amounts of data. We further confirm that the difference of performance reduces with large correctly labeled data, which is consistent with known theoretical results. This work has introduced a new family of loss functions for the direct minimization of the top-k error (that is, without the need for fine-tuning). We have empirically shown that non-sparsity is essential for loss functions to work well with deep neural networks. Thanks to a connection to polynomial algebra and a novel approximation, we have presented efficient algorithms to compute the smooth loss and its gradient. The experimental results have demonstrated that our smooth top-5 loss function is more robust to noise and overfitting than cross-entropy when the amount of training data is limited.We have argued that smoothing the surrogate loss function helps the training of deep neural networks. This insight is not specific to top-k classification, and we hope that it will help the design of other surrogate loss functions. In particular, structured prediction problems could benefit from smoothed SVM losses.",1232,0.754,772,1.5958549222797926,"The top-$k$ error a common measure machine learning In practice top-$k$ classification typically performed deep neural networks trained the cross-entropy loss. Theoretical results indeed cross an optimal learning objective such a task in the limit infinite data In the context limited and noisy data however a loss function that specifically top-$k$ classification bring Our empirical evidence the loss function must smooth have non-sparse gradients work Consequently introduce a family smoothed loss functions suited top-$k$ optimization via deep learning The widely used crossentropy is our family. Evaluating our smooth loss functions computationally: a na{\""i}ve algorithm would $\mathcal{O}(\binom{n}{k})$ operations where classes. Thanks a connection polynomial algebra provide with a time complexity n)$. Furthermore we present a novel approximation obtain fast and stable algorithms on GPUs single floating point precision We compare the cross-entropy loss and our margin-based losses various regimes noise and data size for the predominant use case $k=5$. Our investigation our loss more robust to noise overfitting cross In machine many classification tasks present inherent label confusion The confusion can originate incorrect labeling incomplete annotation some fundamental ambiguities obfuscate the ground truth label even to a human expert For example consider the images from the ImageNet dataRussakovsky in , illustrate the aforementioned factors To mitigate one may require the model predict the k most likely labels where typically very compared Then the prediction considered incorrect if all its k labels differ the ground truth correct otherwise This commonly the top-k error Learning such models a longstanding task many loss functions for top-k error have suggestedIn correctly labeled large data deep neural networks trained cross have exemplary capacity accurately approximate the data distribution An illustration this phenomenon the performance attained on the ImageNet challenge Specifically state models trained with cross-entropy yield remarkable success on the top-5 error, although cross tailored error minimization This phenomenon cross top-k calibrated any k (Lapin 2016 , verified practice the large data setting However in cases learning large models with cross prone on incomplete or noisy labelsTo alleviate the deficiency present a new family top-k classification loss functions Taking inspiration multi-class SVMs our loss creates a Figure : Examples images label confusion from the validation set ImageNet The top-left image incorrectly ""red panda instead The bottom-left image labeledstrawberry although the categories ""apple would other valid labels The center image labeledindigo bunting only valid the lower bird the image The right-most image labeled a cocktail shaker yet could arguably a part a music instrument (for with label ""cornet, horn, trumpet, trump Such examples motivate the need predict more a single label per image.margin between the correct top-k predictions Our empirical results traditional top-k loss functions perform combination deep neural networks We believe the reason smoothness the sparsity the derivatives backpropagation In order overcome smooth the loss with a temperature parameter The evaluation the smooth function and its gradient is challenging smoothing increases the naïve time complexity from O(n n k With a connection polynomial algebra present with O(kn time complexity training time comparable cross in practice We provide insights for numerical stability the forward pass To deal instabilities the backward pass derive a novel approximation. Our investigation our top-k loss outperforms crossentropy the presence noisy labels or in large amounts data We further confirm the difference of performance reduces large correctly labeled data, known theoretical results This work introduced loss functions the direct minimization the top-k error (that without We empirically nonsparsity is essential loss functions work deep neural networks Thanks a connection polynomial algebra a novel approximation presented efficient algorithms compute the smooth loss and its gradient The experimental results have demonstrated our smooth top-5 loss function more to noise overfitting cross when the amount training dataWe argued the surrogate loss function helps the training This insight specific top-k classification and hope the design other surrogate loss functions In particular structured prediction problems could benefit smoothed SVM losses",0.01,0.22226516041165623
"Designing a molecule with desired properties is one of the biggest challenges in drug development, as it requires optimization of chemical compound structures with respect to many complex properties. To augment the compound design process we introduce Mol-CycleGAN -- a CycleGAN-based model that generates optimized compounds with a chemical scaffold of interest. Namely, given a molecule our model generates a structurally similar one with an optimized value of the considered property. We evaluate the performance of the model on selected optimization objectives related to structural properties (presence of halogen groups, number of aromatic rings) and to a physicochemical property (penalized logP). In the task of optimization of penalized logP of drug-like molecules our model significantly outperforms previous results. The principal goal of the drug design process is to find new chemical compounds that are able to modulate the activity of a given target (typically a protein) in a desired way BID27 ). However, finding such molecules in high-dimensional chemical space of all molecules without any prior knowledge is nearly impossible. In silico methods have been introduced to leverage the existing chemical, pharmacological and biological knowledge, thus forming a new branch of science -computer-aided drug design (CADD) BID26 BID0 . In particular, the recent advancements in deep learning encouraged its application to CADD BID4 . Computer methods are nowadays applied at every stage of drug design pipelines BID26 from the search of new, potentially active compounds BID22 , through optimization of their activity and physicochemical profile BID15 and simulating their scheme of interaction with the target protein BID9 , to assisting in planning the synthesis and evaluation of its difficulty BID30 .In the center of our interest are the hit-to-lead and lead optimization phases of the compound design process. Their goals are to optimize drug-like molecules identified in previous steps in terms of, respectively, the desired activity profile (increased potency towards given target protein and provision of inactivity towards undesired proteins) and the physicochemical and pharmacokinetic properties. The challenge here is to optimize a molecule with respect to multiple properties simultaneously BID15 .Our principal contribution is the introduction of Mol-CycleGAN, a generative model based on CycleGAN BID36 with the goal to augment the compound design process. We show that our model can generate molecules that possess desired properties 1 while retaining their chemical scaffolds. Given a starting molecule, the model generates a similar one but with a desired characteristics. The similarity between the two molecules is important in the context of multiparameter optimization, as it makes it easier to optimize the selected property without spoiling the previously optimized ones. To the best of our knowledge , this is the first approach to molecule generation that uses the CycleGAN architecture. We evaluate our model on its ability to perform structural transformations and molecular optimization. The former indicates that the model is able to do simple structural modifications such as a change in the presence of halogen groups or number of aromatic rings. In the latter, we aim to maximize penalized logP to assess the model's utility for compound design. Penalized logP is a physicochemical property often selected as a testing ground for molecule optimization models BID18 BID35 , as it is relevant in the drug design process. In the optimization of penalized logP for drug-like molecules our model significantly outperforms previous results. In this work, we introduced Mol-CycleGAN -a new model based on CycleGAN that can be used for the de novo generation of molecules. The advantage of the proposed model is the ability to learn transformation rules from the sets of compounds with desired and undesired values of the considered property. The model operates in the latent space trained by another model -in our work we use the latent space of JT-VAE. The model can generate molecules with desired properties -both structural and physicochemical. The generated molecules are close to the starting ones and the degree of similarity can be controlled via a hyperparameter. In the task of constrained optimization of druglike molecules our model significantly outperforms previous results. In future work we will extend the approach to multi-parameter optimization of molecules using StarGAN BID5 . It would also be interesting to test the model on cases where a small structural change leads to a drastic change in the property (e.g. on the so-called activity cliffs), which are hard for other approaches. Another interesting direction is the application of the model to working on text embeddings, where the X and Y sets could be characterized, e.g., by different sentiment.",902,0.528,524,1.7213740458015268,"Designing a molecule desired properties optimization chemical compound structures with respect many complex properties To augment the compound design process we introduce Mol-CycleGAN -- generates optimized compounds interest Namely given a molecule our model generates structurally one an optimized value the considered property We evaluate the model selected optimization objectives related structural propertiespresence halogen groups number aromatic rings to a physicochemical propertypenalized logP In the task optimization penalized logP of drug-like molecules our model significantly The principal goal the drug design process a given target ( BID27 However finding such molecules high-dimensional chemical space of all molecules without nearly In silico methods have leverage thus forming branch science -computer drug BID26 BID0 . In particular the recent advancements encouraged its application CADD BID4 . Computer methods nowadays applied at drug design pipelines BID26 from the search new, potentially active compounds BID22 , through optimization their activity simulating their scheme interaction to assisting planning evaluation its difficulty .In the center our interest hittolead optimization phases Their goals optimize drug-like molecules identified previous steps terms, respectively the desired activity profile towards given target protein provision inactivity towards undesired proteins The challenge here optimize a molecule respect multiple properties simultaneously BID15 .Our principal contribution Mol-CycleGAN CycleGAN BID36 with augment the compound design process We show our model generate molecules possess desired 1 while their chemical scaffolds Given a starting molecule the model generates a similar one but a desired characteristics The similarity important multiparameter optimization makes the selected property without the previously optimized ones To , molecule generation the CycleGAN architecture We evaluate our model its ability perform structural transformations molecular optimization former indicates the model able do simple structural modifications a change the presence halogen groups number aromatic rings In latter aim maximize penalized logP to assess compound design Penalized logP a physicochemical property often selected a testing ground molecule optimization models BID18 BID35 as relevant In the optimization penalized logP for drug-like molecules our model significantly In this work introduced Mol-CycleGAN -a new model based CycleGAN molecules The advantage the proposed model learn transformation rules the sets compounds desired and undesired values of the considered property The model operates the latent space trained another model -in our work JT-VAE The model can generate molecules desired properties -both structural The generated molecules close the starting ones the degree similarity can controlled via In the task constrained optimization druglike molecules our model significantly In future work extend the approach molecules StarGAN BID5 . It would also test the model cases a small structural change leads ( on the so-called activity cliffs hard other approaches Another interesting direction the application the model working on text embeddings the X and Y sets could characterized, different sentiment.",0.01,0.5420768591554229
"Knowledge distillation is a potential solution for model compression. The idea is to make a small student network imitate the target of a large teacher network, then the student network can be competitive to the teacher one. Most previous studies focus on model distillation in the classification task, where they propose different architectures and initializations for the student network. However, only the classification task is not enough, and other related tasks such as regression and retrieval are barely considered. To solve the problem, in this paper, we take face recognition as a breaking point and propose model distillation with knowledge transfer from face classification to alignment and verification. By selecting appropriate initializations and targets in the knowledge transfer, the distillation can be easier in non-classification tasks. Experiments on the CelebA and CASIA-WebFace datasets demonstrate that the student network can be competitive to the teacher one in alignment and verification, and even surpasses the teacher network under specific compression rates. In addition, to achieve stronger knowledge transfer, we also use a common initialization trick to improve the distillation performance of classification. Evaluations on the CASIA-Webface and large-scale MS-Celeb-1M datasets show the effectiveness of this simple trick. Since the emergence of Alexnet BID12 , larger and deeper networks have shown to be more powerful BID22 . However, as the network going larger and deeper, it becomes difficult to use it in mobile devices. Therefore, model compression has become necessary in compressing the large network into a small one. In recent years, many compression methods have been proposed, including knowledge distillation BID0 BID8 BID19 , weight quantization BID4 BID17 , weight pruning BID6 BID24 and weight decomposition BID2 BID16 . In this paper, we focus on the knowledge distillation, which is a potential approach for model compression.In knowledge distillation, there is usually a large teacher network and a small student one, and the objective is to make the student network competitive to the teacher one by learning specific targets of the teacher network. Previous studies mainly consider the selection of targets in the classification task, e.g., hidden layers BID15 , logits BID0 BID25 BID20 or soft predictions BID8 BID19 . However, only the distillation of the classification task is not enough, and some common tasks such as regression and retrieval should also be considered. In this paper, we take face recognition as a breaking point that we start with the knowledge distillation in face classification, and consider the distillation on two domain-similar tasks, including face alignment and verification. The objective of face alignment is to locate the key-point locations in each image; while in face verification, we have to determine if two images belong to the same identity.For distillation on non-classification tasks, one intuitive idea is to adopt a similar method as in face classification that trains teacher and student networks from scratch. In this way, the distillation on all tasks will be independent, and this is a possible solution. However, this independence cannot give the best distillation performance. There has been strong evidence that in object detection BID18 , object segmentation BID3 and image retrieval BID30 , they all used the pretrained classification model(on ImageNet) as initialization to boost performance. This success comes from the fact that their domains are similar, which makes them transfer a lot from low-level to high-level representation BID29 . Similarly, face classification, alignment and verification also share the similar domain, thus we propose to transfer the distilled knowledge of classification by taking its teacher and student networks to initialize corresponding networks in alignment and verification.Another problem in knowledge transfer is what targets should be used for distillation? In face classification, the knowledge is distilled from the teacher network by learning its soft-prediction, which has been proved to work well BID8 BID19 . However, in face alignment BID27 and verification BID27 , they have additional task-specific targets. As a result, selecting the classification or task-specific target for distillation remains a problem. One intuitive idea is to measure the relevance of objectives between non-classification and classification tasks. For example, it is not obvious to see the relation between face classification and alignment, but the classification can help a lot in verification. Therefore, it seems reasonable that if the tasks are highly related, the classification target is preferred, or the task-specific target is better.Inspired by the above thoughts, in this paper, we propose the model distillation in face alignment and verification by transferring the distilled knowledge from face classification. With appropriate selection of initializations and targets, we show that the distillation performance of alignment and verification on the CelebA and CASIA-WebFace BID28 datasets can be largely improved, and the student network can even exceed the teacher network under specific compression rates. This knowledge transfer is our main contribution. In addition, we realize that in the proposed method, the knowledge transfer depends on the distillation of classification, thus we use a common initialization trick to further boost the distillation performance of classification. Evaluations on the CASIA-WebFace and large-scale MS-Celeb-1M BID5 datasets show that this simple trick can give the best distillation results in the classification task. In this paper, we take face recognition as a breaking point, and propose the knowledge distillation on two non-classification tasks, including face alignment and verification. We extend the previous distillation framework by transferring the distilled knowledge from face classification to face alignment and verification. By selecting appropriate initializations and targets, the distillation on non-classification tasks can be easier. Besides, we also give some guidelines for target selection on non-classification tasks, and we hope these guidelines can be helpful for more tasks. Experiments on the datasets of CASIA-WebFace, CelebA and large-scale MS-Celeb-1M have demonstrated the effectiveness of the proposed method, which gives the student networks that can be competitive or exceed the teacher network under appropriate compression rates. In addition, we use a common initialization trick to further improve the distillation performance of classification, and this can boost the distillation on non-classification tasks. Experiments on CASIA-WebFace have demonstrated the effectiveness of this simple trick.",1242,0.685,745,1.6671140939597315,"Knowledge distillation a potential solution model compression The idea a small student network imitate the target then competitive one Most previous studies focus model distillation the classification task they propose different architectures initializations the student network However only the classification task not enough other related tasks regression retrieval barely To solve in take face recognition propose model distillation with knowledge transfer classification alignment verification By selecting appropriate initializations targets the knowledge transfer the distillation can easier in non-classification tasks Experiments the CelebA and CASIA-WebFace datasets demonstrate the student network competitive one in alignment verification even under specific compression rates In addition to achieve stronger knowledge transfer a common initialization trick improve the distillation performance classification Evaluations on the CASIA-Webface large-scale MS-Celeb-1M datasets the effectiveness this simple trick Since Alexnet BID12 , larger and deeper networks shown more powerful BID22 However the network going larger deeper difficult use mobile devices Therefore model compression necessary compressing the large network into In many compression methods proposed knowledge distillation BID0 BID8 BID19 pruning In focus the knowledge distillation which a potential approach model compressionIn a large teacher network one the objective competitive one learning specific targets Previous studies mainly consider the selection targets the classification task hidden layers BID15 logits soft predictions However only the distillation the classification task not some common tasks regression retrieval should In take face recognition that start with the knowledge distillation in face classification consider on two domain-similar tasks including face alignment verification The objective face alignment locate the key-point locations; while face verification have belongFor distillation on non-classification tasks one intuitive idea adopt classification that trains teacher and student networks from scratch In this way the distillation on all tasks independent this a possible solution However this independence give the best distillation performance There strong evidence in object detection BID18 , object segmentation image retrieval they all used the pretrained classification model(on ImageNet initialization to boost This success comes their domains similar transfer a from high-level representation BID29 . Similarly face classification alignment verification also share the similar domain thus we propose transfer the distilled knowledge classification by taking its teacher and student networks initialize corresponding networks alignmentAnother problem what targets distillation? In face classification the knowledge distilled the teacher network by learning its soft-prediction proved well BID8 BID19 . However face alignment BID27 and verification , they additional task-specific targets As selecting the classification or task-specific target distillation remains One intuitive idea measure the relevance objectives between For example obvious see the relation face classification alignment can help verification Therefore the tasks highly related the classification target preferred betterInspired the above thoughts in the model distillation in face alignment verification transferring the distilled knowledge face classification. With appropriate selection initializations targets show the distillation performance alignment verification on the CelebA and CASIA-WebFace BID28 datasets largely the student network even exceed under specific compression rates This knowledge transfer our main contribution In addition realize in the proposed method the knowledge transfer depends the distillation classification, thus use a common initialization trick further boost classification Evaluations on the CASIA-WebFace and large-scale MS-Celeb-1M BID5 datasets this simple trick give the best distillation results the classification task In take face recognition the knowledge distillation on two non-classification tasks including face alignment verification We extend the previous distillation framework transferring the distilled knowledge face classification face alignment verification By selecting appropriate initializations targets the distillation on non-classification tasks easier Besides also give some guidelines target selection on non-classification tasks hope more tasks Experiments the datasets CASIA-WebFace CelebA large-scale MS-Celeb-1M have the proposed method gives the student networks that competitive or exceed under appropriate compression rates In addition use a common initialization trick further the distillation performance classification this boost on Experiments CASIA-WebFace have this simple trick",0.01,0.40382726908977234
"RNNs have been shown to be excellent models for sequential data and in particular for session-based user behavior. The use of RNNs provides impressive performance benefits over classical methods in session-based recommendations. In this work we introduce a novel ranking loss function tailored for RNNs in recommendation settings. The better performance of such loss over alternatives, along with further tricks and improvements described in this work, allow to achieve an overall improvement of up to 35% in terms of MRR and Recall@20 over previous session-based RNN solutions and up to 51% over classical collaborative filtering approaches. Unlike data augmentation-based improvements, our method does not increase training times significantly. Session-based recommendation is a very common recommendation problem that is encountered in many domains such as e-commerce, classified sites, music and video recommendation. In the session-based setting, past user history logs are typically not available (either because the user is new or not logged-in or not tracked) and recommender systems have to rely only on the actions of the user in the current sessions to provide accurate recommendations. Until recently many of these recommendations tasks were tackled mainly using relatively simple methods such as item-based collaborative filtering BID16 or content-based methods. Recurrent Neural Networks (RNNs) have emerged from the deep learning literature as powerful methods for modeling sequential data. These models have been successfully applied in speech recognition, translation, time series forecasting and signal processing. In recommender systems RNNs have been recently applied to the session-based recommendation setting with impressive results BID7 .The advantage of RNNs over traditional similarity-based methods for recommendation is that they can effectively model the whole session of user interactions (clicks, views, etc.) . By modeling the whole session RNNs can in effect learn the 'theme' of the session and thus provide recommendations with increased accuracy (between 20%-30%) over traditional methods.RNNs in session-based recommendation have been adapted to the task of recommendation. One of the main objectives in recommendation is to rank items by user preference; i.e. the exact ranking or scoring of items in the tail of the item list (items that the user will not like) is not that important, but it is very important to rank correctly the items that the user will like at the top of the list (first 5, 10 or 20 positions). To achieve this with machine learning one has to typically utilize learning to rank techniques(see e.g. BID2 ) and in particular ranking objectives and loss functions. The current session-based RNN approaches use ranking loss functions and, in particular, pairwise ranking loss functions. As in most deep learning approaches the choice of a good ranking loss can have a very significant influence on performance. Since deep learning methods need to propagate gradients over several layers and in the case of RNNs 'back in time' over previous steps, to optimize the model parameters, the quality of these gradients originating from the loss function influences the quality of the optimization and the model parameters. Moreover the nature of the recommendation task, which typically entails large output spaces (due to large number of items), poses unique challenges that have to be taken into account as well when designing a proper ranking loss function. We will see that the way this large output space issue is tackled is very crucial in achieving good performance.In this work we analyze ranking loss functions used in RNNs for session-based recommendations, this analysis leads to a new set of ranking loss functions that increase the performance of the RNN up to 30% over previous commonly used losses without incurring in significant computational overheads. We essentially devise a new class of loss functions that combines learnings from the deep learning and the learning to rank literature. Experimental results on several datasets coming from industry validate these impressive improvements, in terms of Mean Reciprocal Rank (MRR) and Recall@20. With these improvements the difference between RNNs and conventional memory-based collaborative filtering jumps to 51% in terms of MRR and Recall@20 demonstrating the potential that deep learning methods bring to the area of Recommender Systems. We introduced a new class of loss function that together with an improved sampling strategy have provided impressive top-k gains for RNNs for session-based recommendations. We believe that these new losses could be more generally applicable and along with the corresponding sampling strategies also provide top-k gains for different recommendations settings and algorithms such as e.g. matrix factorization or autoencoders. It is also conceivable that these techniques could also provide similar benefits in the area of Natural Language Processing a domain that shares significant similarities to the recommendation domain in terms of machine learning (e.g. ranking, retrieval) and data structure (e.g. sparse large input and output space).",948,0.458,540,1.7555555555555555,"RNNs shown excellent models sequential data and in session-based user behavior The use RNNs provides impressive performance benefits classical methods session-based recommendations In this work introduce a novel ranking loss function tailored in recommendation settings The better performance such loss over alternatives along further tricks described this work allow achieve terms MRR Recall@20 over previous session-based RNN solutions and classical collaborative filtering approaches Unlike data augmentation-based improvements our method increase training times significantly Session-based recommendation is a very common recommendation problem encountered many domains e music video recommendation In the session-based setting past user history logs typically not (either new not- or tracked recommender systems rely only the actions accurate recommendations Until many these recommendations tasks tackled mainly using relatively simple methods item-based collaborative filtering BID16 Recurrent Neural Networks emerged powerful methods modeling sequential data These models successfully applied speech recognition translation time series forecasting signal processing In recommender systems RNNs recently applied session recommendation setting with impressive results BID7 .The advantage traditional similarity-based methods effectively model of user interactionsclicks views . By modeling the whole session RNNs in effect learn the 'theme thus provide recommendations with increased accuracy (between over traditional methods in session-based recommendation have adapted recommendation One recommendation rank items user preference; or scoring the tailitems that correctly atfirst 5, 10 or 20 positions To achieve with machine one typically utilize learning rank techniques(see BID2 ) in particular ranking objectives loss functions current session- RNN approaches use ranking loss functions, As in most deep learning approaches the choice a good ranking loss can Since deep learning methods need propagate gradients and in 'back in time over previous steps to optimize the model parameters the quality originating the loss function influences the optimization and Moreover the nature the recommendation task typically entails large output spacesdue items poses that as when a proper ranking loss function We will see the way this large output space issue tackled very crucial achieving good performanceIn this work analyze ranking loss functions used session-based recommendations this analysis leads increase up 30 previous commonly used losses without in significant computational overheads We essentially devise loss functions combines learnings the learning to rank literature Experimental results on several datasets coming industry validate these impressive improvements in Mean Reciprocal Rank Recall@20 With these improvements the difference RNNs conventional memory-based collaborative filtering jumps terms MRR Recall@20 demonstrating that deep learning methods bring the area Recommender Systems We introduced loss function together an improved sampling strategy have provided impressive top-k gains RNNs for session-based recommendations We believe these new losses could more generally applicable along the corresponding sampling strategies also top-k gains different recommendations settings algorithms such It conceivable these techniques provide similar benefits the area Natural Language Processing a domain shares the recommendation domain terms ( ranking retrieval) data structure sparse large input and output space",0.01,0.629168342854078
"In representational lifelong learning an agent aims to continually learn to solve novel tasks while updating its representation in light of previous tasks. Under the assumption that future tasks are related to previous tasks, representations should be learned in such a way that they capture the common structure across learned tasks, while allowing the learner sufficient flexibility to adapt to novel aspects of a new task. We develop a framework for lifelong learning in deep neural networks that is based on generalization bounds, developed within the PAC-Bayes framework. Learning takes place through the construction of a distribution over networks based on the tasks seen so far, and its utilization for learning a new task. Thus, prior knowledge is incorporated through setting a history-dependent prior for novel tasks. We develop a gradient-based algorithm implementing these ideas, based on minimizing an objective function motivated by generalization bounds, and demonstrate its effectiveness through numerical examples. Learning from examples is the process of inferring a general rule from a finite set of examples. It is well known in statistics (e.g., BID7 ) that learning cannot take place without prior assumptions. This idea has led in Machine Learning to the notion of inductive bias BID23 . Recent work in deep neural networks has achieved significant success in using prior knowledge in the implementation of structural constraints, e.g. the use of convolutions and weight sharing as building blocks, capturing the translational invariance of image classification. However, in general the relevant prior information for a given task is not always clear, and there is a need for building prior knowledge through learning from previous interactions with the world.Learning from previous experience can take several forms: Continual learning -a single model is trained to solve a task which changes over time (and hopefully not 'forget' the knowledge from previous times, (e.g., ). Multi-task learning -the goal is to learn how to solve several observed tasks, while exploiting their shared structure. Domain adaptation -the goal is to solve a 'target' learning task using a single 'source' learning task (both are observed, but usually the target has mainly unlabeled data). Lifelong Learning / Meta-Learning / Learning-to-Learnthe goal is to extract knowledge from several observed tasks to be used for future learning on new (not yet observed) learning tasks. In contrast to multi-task learning, the performance is evaluated on the new tasks.We work within the framework of lifelong learning, where an agent learns through interacting with the world, transferring the knowledge acquired along its path to any new task it encounters. This notion has been formulated by BID3 in a clear and simple context of 'task-environment'. In analogy to the standard single-task learning in which data is sampled from an unknown distribution, Baxter suggested to model a lifelong learning setting as if tasks are sampled from an unknown task distribution (environment), so that knowledge acquired from previous tasks can be used in order to improve performance on a novel task. Baxter's work not only provided an interesting and mathematically precise perspective for lifelong learning, but also provided generalization bounds demonstrating the potential improvement in performance due to prior knowledge. Baxter's seminal work, has led to a large number of extensions and developments.In this contribution we work within the framework formulated by BID3 , and, following the setup in BID25 , provide generalization error bounds within the PAC-Bayes framework. These bounds are then used to develop a practical learning algorithm that is applied to neural networks, demonstrating the utility of the approach. The main contributions of this work are the following. (i) An improved and tighter bound in the theoretical framework of BID25 which can utilize different single-task PAC-Bayesian bounds.(ii ) Developing a learning algorithm within this general framework and its implementation using probabilistic feedforward neural networks. This yields transfer of knowledge between tasks through constraining the prior distribution on a learning network. (iii ) Empirical demonstration of the performance enhancement compared to naive approaches and recent methods in this field.As noted above, BID3 provided a basic mathematical formulation and initial results for lifelong learning. While there have been many developments in this field since then (e.g., BID1 ; BID9 BID10 ; BID27 ), most of them were not based on generalization error bounds which is the focus of the present work. An elegant extension of generalization error bounds to lifelong learning was provided by BID25 , mentioned above (more recently extended in BID26 ). Their work , however, did not provide a practical algorithm applicable to deep neural networks. More recently , Dziugaite & Roy (2017) developed a single-task algorithm based on PAC-Bayes bounds that was demonstrated to yield good performance in simple classification tasks. Other recent theoretical approaches to lifelong or multitask learning (e.g. BID0 ; BID20 ) provide increasingly general bounds but have not led directly to practical learning algorithms. We have presented a framework for representational lifelong learning, motivated by PAC-Bayes generalization bounds, and implemented through the adjustment of a learned prior, based on tasks encountered so far. The framework bears conceptual similarity to the empirical Bayes method while not being Bayesian, and is implemented at the level of tasks rather than samples. Combining the general approach with the rich representational structure of deep neural networks, and learning through gradient based methods leads to an efficient procedure for lifelong learning, as motivated theoretically and demonstrated empirically. While our experimental results are preliminary, we believe that our work attests to the utility of using rigorous performance bounds to derive learning algorithms, and demonstrates that tighter bounds indeed lead to improved performance.There are several open issues to consider. First, the current version learns to solve all available tasks in parallel, while a more useful procedure should be sequential in nature. This can be easily incorporated into our framework by updating the prior following each novel task. Second, our method requires training stochastic models which is challenging due to the the high-variance gradients. We we would like to develop new methods within our framework which have more stable convergence and are easier to apply in larger scale problems. Third, there is much current effort in reinforcement learning to augment model free learning with model based components, where some aspects of the latter are often formulated as supervised learning tasks. Incorporating our approach in such a context would be a worthwhile challenge. In fact, a similar framework to ours was recently proposed within an RL setting BID33 , although it was not motivated from performance guarantees as was our approach, but rather from intuitive heuristic arguments.",1284,0.694,740,1.7351351351351352,"In representational lifelong an agent aims continually solve novel tasks while updating its representation light previous tasks Under future tasks related representations should learned capture the common structure across learned tasks while allowing novel aspects We develop lifelong learning deep neural networks generalization bounds developed within the PAC-Bayes framework Learning takes the construction a distribution over networks based the tasks seen so its utilization Thus prior knowledge incorporated through setting historydependent prior novel tasks We develop a gradient-based algorithm implementing these ideas minimizing an objective function motivated generalization bounds demonstrate through numerical examples Learning examples inferring It well statistics ( BID7 ) learning take prior assumptions This idea led in Machine Learning inductive bias BID23 . Recent work achieved using prior knowledge the implementation structural constraints convolutions weight sharing building, capturing the translational invariance image classification However general the relevant prior information building through learning previous interactions the worldLearning take Continual learning -a single model is trained solve which changesand hopefully ' the knowledge ( ). Multitask learning -the goal solve several observed tasks exploiting their shared structure Domain adaptation -the goal solve a 'target' learning taskboth are observed usually has mainly unlabeled data Lifelong Learning / Meta-toLearnthe goal extract several observed tasks be on new (not In contrast multi-task learning the performance is evaluated the new tasksWe work within lifelong learning an agent through interacting transferring acquired along any new task it This notion formulated BID3 in a clear and simple context 'task-environment In analogy the standard single-task learning in data sampled an unknown distribution Baxter suggested to model lifelong setting if tasks sampledenvironment so acquired order Baxter's work not provided an interesting and mathematically precise perspective for lifelong learning generalization bounds demonstrating the potential improvement due prior knowledge Baxter's seminal work has led extensions developmentsIn this contribution work within formulated BID3 ,, following the setup in BID25 generalization error bounds within the PAC-Bayes framework These bounds then develop a practical learning algorithm applied demonstrating The main contributions (i An improved and tighter bound in the theoretical framework BID25 which utilize different single-task PAC-Bayesian bounds.(ii ) Developing a learning algorithm within this general framework and its implementation This yields transfer knowledge tasks through constraining the prior distribution on a learning network (iii ) Empirical demonstration the performance enhancement compared naive approaches and recent methodsAs BID3 provided a basic mathematical formulation initial results lifelong learning While many developments ( BID1 ; most based generalization error bounds which the focus An elegant extension generalization error bounds to lifelong learning was provided BID25 , mentionedmore recently extended Their work , however did provide practical algorithm applicable More recently , Dziugaite & Roy2017 developed a single-task algorithm PAC-Bayes bounds demonstrated yield simple classification tasks Other recent theoretical approaches lifelong or multitask learning BID0 ; provide increasingly general bounds but led directly learning algorithms We presented representational lifelong learning motivated PAC-Bayes generalization bounds implemented through the adjustment learned prior, tasks encountered so The framework bears conceptual similarity the empirical Bayes method while not Bayesian implemented at tasks rather samples Combining the general approach the rich representational structure deep neural networks and learning through gradient based methods leads an efficient procedure lifelong learning motivated theoretically demonstrated While our experimental results attests using rigorous performance bounds derive learning algorithms demonstrates tighter bounds indeedThere First the current version learns solve all available tasks parallel while a more useful procedure should sequential in This can easily incorporated our framework updating prior following each novel task Second our method requires training which challenging We we would develop new methods within have more stable convergence apply larger scale problems Third much current effort reinforcement augment model free learning model based components where some aspects latter often formulated supervised learning tasks our approach a worthwhile challenge In fact a similar framework to ours recently within an RL setting BID33 , although motivated from performance guarantees was our approach intuitive heuristic arguments",0.01,0.5771389057413681
"Optimization algorithms for training deep models not only affects the convergence rate and stability of the training process, but are also highly related to the generalization performance of trained models. While adaptive algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in many scenarios, they often lead to worse generalization performance than SGD, when used for training deep neural networks (DNNs). In this work, we identify two problems regarding the direction and step size for updating the weight vectors of hidden units, which may degrade the generalization performance of Adam. As a solution, we propose the normalized direction-preserving Adam (ND-Adam) algorithm, which controls the update direction and step size more precisely, and thus bridges the generalization gap between Adam and SGD. Following a similar rationale, we further improve the generalization performance in classification tasks by regularizing the softmax logits. By bridging the gap between SGD and Adam, we also shed some light on why certain optimization algorithms generalize better than others. In contrast with the growing complexity of neural network architectures BID10 BID12 , the training methods remain relatively simple. Most practical optimization methods for deep neural networks (DNNs) are based on the stochastic gradient descent (SGD) algorithm. However, the learning rate of SGD, as a hyperparameter, is often difficult to tune, since the magnitudes of different parameters can vary widely, and adjustment is required throughout the training process.To tackle this problem, several adaptive variants of SGD have been developed, including Adagrad BID6 ), Adadelta (Zeiler, 2012 , RMSprop BID24 , Adam BID15 , etc. These algorithms aim to adapt the learning rate to different parameters automatically, based on the statistics of gradient. Although they usually simplify learning rate settings, and lead to faster convergence, it is observed that their generalization performance tend to be significantly worse than that of SGD in some scenarios BID25 . This intriguing phenomenon may explain why SGD (possibly with momentum) is still prevalent in training state-of-the-art deep models, especially feedforward DNNs BID10 BID12 . Furthermore, recent work has shown that DNNs are capable of fitting noise data BID31 , suggesting that their generalization capabilities are not the mere result of DNNs themselves, but are entwined with optimization BID2 .This work aims to bridge the gap between SGD and Adam in terms of the generalization performance. To this end, we identify two problems that may degrade the generalization performance of Adam, and show how these problems are (partially) avoided by using SGD with L2 weight decay. First, the updates of SGD lie in the span of historical gradients, whereas it is not the case for Adam. This difference has been discussed in rather recent literature BID25 , where the authors show that adaptive methods can find drastically different but worse solutions than SGD. Second, while the magnitudes of Adam parameter updates are invariant to rescaling of the gradient, the effect of the updates on the same overall network function still varies with the magnitudes of parameters. As a result, the effective learning rates of weight vectors tend to decrease during training, which leads to sharp local minima that do not generalize well BID11 .To fix the two problems for Adam, we propose the normalized direction-preserving Adam (NDAdam) algorithm, which controls the update direction and step size more precisely. We show that ND-Adam is able to achieve significantly better generalization performance than vanilla Adam, and matches that of SGD in image classification tasks.We summarize our contributions as follows:• We observe that the directions of Adam parameter updates are different from that of SGD, i.e., Adam does not preserve the directions of gradients as SGD does. We fix the problem by adapting the learning rate to each weight vector, instead of each individual weight, such that the direction of the gradient is preserved.• For both Adam and SGD without L2 weight decay, we observe that the magnitude of each vector's direction change depends on its L2-norm. We show that, using SGD with L2 weight decay implicitly normalizes the weight vectors, and thus remove the dependence in an approximate manner. We fix the problem for Adam by explicitly normalizing each weight vector, and by optimizing only its direction, such that the effective learning rate can be precisely controlled.• We further show that, without proper regularization, the learning signal backpropagated from the softmax layer may vary with the overall magnitude of the logits in an undesirable way. Based on the observation, we apply batch normalization or L2-regularization to the logits, which further improves the generalization performance in classification tasks.In essence, our proposed methods, ND-Adam and regularized softmax, improve the generalization performance of Adam by enabling more precise control over the directions of parameter updates, the learning rates, and the learning signals.",981,0.44,576,1.703125,"Optimization algorithms training deep models not affects the convergence rate stability are related While adaptive algorithms, Adam and RMSprop shown better optimization performance many scenarios often lead worse generalization performance when training In this work identify two problems regarding the direction and step size for updating the weight vectors hidden units degrade Adam. As a solution propose the normalized direction-preserving Adam (ND-Adam) algorithm controls the update direction step size more thus bridges Adam SGD Following a similar rationale further improve the generalization performance in classification tasks regularizing the softmax logits By bridging SGD Adam also shed why certain optimization algorithms generalize In contrast the growing complexity neural network BID10 BID12 , the training methods remain Most practical optimization methods However the learning rate SGD, a hyperparameter often difficult tune adjustment throughoutTo tackle several adaptive variants Adagrad BID6 ), Adadelta (Zeiler 2012 , RMSprop BID24 Adam BID15 etc These algorithms aim adapt the learning rate different parameters automatically based the statistics gradient. Although they usually simplify learning rate settings and lead faster convergence observed their generalization performance tend SGD in some scenarios BID25 . This intriguing phenomenon may SGD (possibly with momentum still prevalent training state- deep models feedforward BID10 BID12 . Furthermore recent work DNNs fitting noise data BID31 , suggesting their generalization capabilities the mere result themselves entwined optimization BID2 .This work aims bridge SGD Adam in. To this end identify two problems degrade the generalization performance Adam, show ( avoided SGD with L2 weight decay First the updates of SGD lie the span historical gradients whereas it Adam This difference has discussed rather recent literature BID25 , where show adaptive methods find drastically different but worse solutions SGD Second while the magnitudes Adam parameter updates invariant rescaling of the gradient the updates the same overall network function still parameters As the effective learning rates weight vectors tend during sharp local minima do generalize BID11 .To fix the two problems for Adam propose the normalized direction-preserving Adam (NDAdam) algorithm controls the update direction step size more We show ND-Adam achieve significantly better generalization performance vanilla Adam matches SGD in image classification tasksWe summarize our contributions as observe the directions Adam parameter updates different Adam does preserve gradients We fix adapting the learning rate each weight vector instead, such the direction preserved.• For both Adam SGD without L2 weight decay observe We show, using SGD with L2 weight decay implicitly normalizes the weight vectors remove in an approximate manner We fix for Adam by explicitly normalizing each weight vector optimizing only its direction such the effective learning rate can precisely controlled.• further show without proper regularization the learning signal backpropagated the softmax layer may vary the overall magnitude the logits an undesirable way Based the observation apply batch normalization or L2-regularization the logits further improves in classification tasksIn essence our proposed methods, ND-Adam regularized softmax improve Adam by enabling the directions parameter updates the learning rates the learning signals",0.01,0.4955798937967658
"Options in reinforcement learning allow agents to hierarchically decompose a task into subtasks, having the potential to speed up learning and planning. However, autonomously learning effective sets of options is still a major challenge in the field. In this paper we focus on the recently introduced idea of using representation learning methods to guide the option discovery process. Specifically, we look at eigenoptions, options obtained from representations that encode diffusive information flow in the environment. We extend the existing algorithms for eigenoption discovery to settings with stochastic transitions and in which handcrafted features are not available.   We propose an algorithm that discovers eigenoptions while learning non-linear state representations from raw pixels. It exploits recent successes in the deep reinforcement learning literature and the equivalence between proto-value functions and the successor representation. We use traditional tabular domains to provide intuition about our approach and Atari 2600 games to demonstrate its potential. Sequential decision making usually involves planning, acting, and learning about temporally extended courses of actions over different time scales. In the reinforcement learning framework, options are a well-known formalization of the notion of actions extended in time; and they have been shown to speed up learning and planning when appropriately defined (e.g., BID4 BID9 BID24 . In spite of that, autonomously identifying good options is still an open problem. This problem is known as the problem of option discovery.Option discovery has received ample attention over many years, with varied solutions being proposed (e.g., BID0 BID5 BID20 BID8 BID13 BID20 BID21 . Recently, Machado et al. (2017) and BID31 proposed the idea of learning options that traverse directions of a latent representation of the environment. In this paper we further explore this idea.More specifically, we focus on the concept of eigenoptions BID16 , options learned using a model of diffusive information flow in the environment. They have been shown to improve agents' performance by reducing the expected number of time steps a uniform random policy needs in order to traverse the state space. Eigenoptions are defined in terms of proto-value functions (PVFs; BID18 , basis functions learned from the environment's underlying state-transition graph. PVFs and eigenoptions have been defined and thoroughly evaluated in the tabular case. Currently, eigenoptions can be used in environments where it is infeasible to enumerate states only when a linear representation of these states is known beforehand.In this paper we extend the notion of eigenoptions to stochastic environments with non-enumerated states, which are commonly approximated by feature representations. Despite methods that learn representations generally being more flexible, more scalable, and often leading to better performance, current algorithms for eigenoption discovery cannot be combined with representation learn-ing. We introduce an algorithm that is capable of discovering eigenoptions while learning representations. The learned representations implicitly approximate the model of diffusive information flow (hereafter abbreviated as the DIF model) in the environment. We do so by exploiting the equivalence between PVFs and the successor representation (SR; BID7 . Notably, by using the SR we also start to be able to deal with stochastic transitions naturally, a limitation of previous algorithms.We evaluate our algorithm in a tabular domain as well as on Atari 2600 games. We use the tabular domain to provide intuition about our algorithm and to compare it to the algorithms in the literature. Our evaluation in Atari 2600 games provides promising evidence of the applicability of our algorithm in a setting in which a representation of the agent's observation is learned from raw pixels. In this paper we introduced a new algorithm for eigenoption discovery in RL. Our algorithm uses the successor representation (SR) to estimate the model of diffusive information flow in the environment, leveraging the equivalence between proto-value functions (PVFs) and the SR. This approach circumvents several limitations from previous work: (i) it builds increasingly accurate estimates using a constant-cost update-rule; (ii) it naturally deals with stochastic MDPs; (iii) it does not depend on the assumption that the transition matrix is symmetric; and (iv) it does not depend on handcrafted feature representations. The first three items were achieved by simply using the SR instead of the PVFs, while the latter was achieved by using a neural network to estimate the SR.The proposed framework opens up multiple possibilities for investigation in the future. It would be interesting to evaluate the compositionality of eigenoptions, or how transferable they are between similar environments, such as the different modes of Atari 2600 games BID17 . Finally, now that the fundamental algorithms have been introduced, it would be interesting to investigate whether one can use eigenoptions to accumulate rewards instead of using them for exploration.",938,0.544,568,1.6514084507042253,"Options in reinforcement learning allow agents hierarchically decompose a task subtasks having the potential speed planning However autonomously learning effective sets options In this paper focus the recently introduced idea using representation learning methods guide the option discovery process Specifically look eigenoptions options obtained representations that encode diffusive flow We extend the existing algorithms eigenoption discovery settings with stochastic transitions in handcrafted features We propose discovers eigenoptions while learning non-linear state representations from raw pixels It exploits recent successes the deep reinforcement learning literature the equivalence proto-value functions the successor representation We use traditional tabular domains intuition our approach and Atari 2600 games demonstrate its potential Sequential decision making usually planning acting learning temporally extended courses over In the reinforcement learning framework options a well-known formalization actions extended time; and speed planning when appropriately defined BID4 BID9 BID24 . In spite that autonomously identifying good options an open problem This problem known the problem option discoveryOption discovery has received ample attention many years varied solutions ( BID0 BID5 . Recently, Machado et al (2017 and BID31 proposed learning options traverse directions a latent representation In this paper further this ideaMore focus eigenoptions BID16 options learned using diffusive information flow They shown improve agents' performance the expected number time steps a uniform random policy needs in traverse the state space Eigenoptions are defined proto-value functionsPVFs; BID18 , basis functions learned the environment's underlying state-transition graph. PVFs eigenoptions defined thoroughly the tabular case Currently eigenoptions can environments states only when a linear representation known beforehandIn extend commonly approximated feature representations Despite methods learn representations generally being flexible more scalable often leading current algorithms eigenoption discovery combined representation learning We introduce an algorithm capable discovering eigenoptions while learning representations The learned representations implicitly approximate diffusive information flowhereafter the DIF model the environment We do so by exploiting the equivalence PVFs the successor representation (SR; BID7 . Notably by the SR we also start be deal stochastic transitions naturally a limitation previous algorithmsWe evaluate a tabular domain as on Atari 2600 games We use the tabular domain intuition our algorithm compare the algorithms Our evaluation in Atari 2600 games provides promising evidence our algorithm a setting in a representation the agent's observation learned raw pixels In this paper introduced eigenoption discovery RL Our algorithm the successor representation (SR estimate the model of diffusive information flow leveraging proto-value functions the SR This approach several limitations from: builds increasingly accurate estimates using a constant-cost update-rule naturally deals stochastic MDPs depend the assumption the transition matrix handcrafted feature representations The first three items achieved simply the SR instead the PVFs while latter a neural network estimate the SR.The proposed framework opens multiple possibilities investigation It would evaluate the compositionality eigenoptions how transferable between similar environments such the different modes Atari 2600 games BID17 . Finally now the fundamental algorithms introduced would investigate one eigenoptions accumulate rewards instead exploration",0.01,0.363810669957471
"One form of characterizing the expressiveness of a piecewise linear neural network is by the number of linear regions, or pieces, of the function modeled. We have observed substantial progress in this topic through lower and upper bounds on the maximum number of linear regions and a counting procedure. However, these bounds only account for the dimensions of the network and the exact counting may take a prohibitive amount of time, therefore making it infeasible to benchmark the expressiveness of networks. In this work, we approximate the number of linear regions of specific rectifier networks with an algorithm for probabilistic lower bounds of mixed-integer linear sets. In addition, we present a tighter upper bound that leverages network coefficients. We test both on trained networks. The algorithm for probabilistic lower bounds is several orders of magnitude faster than exact counting and the values reach similar orders of magnitude, hence making our approach a viable method to compare the expressiveness of such networks. The refined upper bound is particularly stronger on networks with narrow layers.   Neural networks with piecewise linear activations have become increasingly more common along the past decade, in particular since BID40 and BID25 . The simplest and most commonly used among such forms of activation is the Rectifier Linear Unit (ReLU), which outputs the maximum between 0 and its input argument BID30 BID35 . In the functions modeled by these networks, we can associate each part of the domain in which the network corresponds to an affine function with a particular set of units having positive outputs. We say that those are the active units for that part of the domain. Counting these ""pieces"" into which the domain is split, which are often denoted as linear regions or decision regions, is one way to compare the expressiveness of models defined by networks with different configurations or coefficients. The theoretical analysis of the number of input regions in deep learning dates back to at least BID8 , and more recently BID45 have shown empirical evidence that the accuracy of similar rectifier networks can be associated with the number of such regions.From the study of how many linear regions can be defined on such a rectifier network with n ReLUs, we already know that not all configurations -and in some cases none -can reach the ceiling of 2 n regions. We have learned that the number of regions may depend on the dimension of the input as well as on the number of layers and how the units are distributed among these layers. On the one hand, it is possible to obtain neural networks where the number of regions is exponential on network depth . On the other hand, there is a bottleneck effect by which the width of each layer affects how the regions are partitioned by subsequent layers due to the dimension of the space containing the image of the function, up to the point that shallow networks define the largest number of linear regions if the input dimension exceeds n BID45 .The literature on this topic has mainly focused on bounding the maximum number of linear regions. Lower bounds are obtained by constructing networks defining increasingly larger number of linear regions BID2 BID45 . Upper bounds are proven using the theory of hyperplane arrangements by BID54 along with other analytical insights BID44 BID38 BID45 . These bounds are only identical -and thus tight -in the case of one-dimensional inputs BID45 . Both of these lines have explored deepening connections with polyhedral theory, but some of these results have also been recently revisited using tropical algebra BID55 BID13 . In addition , BID45 have shown that the linear regions of a trained network correspond to a set of projected solutions of a Mixed-Integer Linear Program (MILP).Other methods to study neural network expressiveness include universal approximation theory BID16 , VC dimension BID5 , and trajectory length BID44 . Different networks can be compared by transforming one network to another with different number of layers or activation functions. For example, it has been shown that any continuous function can be modeled using a single hidden layer of sigmoid activation functions BID16 . In the context of ReLUs , BID36 have shown that the popular ResNet architecture BID31 with a single ReLU neuron in every hidden layer can be a universal approximator. Furthermore, BID2 have shown that a network with single hidden layer of ReLUs can be trained for global optimality with a runtime polynomial in the data size, but exponential in the input dimension. The use of trajectory length for expressiveness is related to linear regions, i.e., by changing the input along a one dimensional path we study the transition in the linear regions.Certain critical network architectures using leaky ReLUs (f (x) = max(x, αx), α ∈ (0, 1)) are identified to produce connected decision regions BID42 . In order to avoid such degenerate cases, we need to use sufficiently wide hidden layers. However, this result is mainly applicable for leaky ReLUs and not for the standard ReLUs BID7 .Although the number of linear regions has been long conjectured and recently shown to work for comparing similar networks, this metric would only be used in practice if we come up with faster methods to count or reasonably approximate such number. Our approach in this paper consists of introducing empirical upper and lower bounds, both of which based on the weight and bias coefficients of the networks, and thus able to compare networks having the same configuration of layers.In particular, we reframe the problem of determining the potential number of linear regions N of an architecture with that of estimating the representation efficiency η = log 2 N of a network, which can be interpreted as the minimum number of units to define as many linear regions, thereby providing a more practical and interpretable metric for expressiveness. We present the following contributions:(i ) We adapt approximate model counting methods for propositional satisfiability (SAT) to obtain probabilistic bounds on the number of solutions of MILP formulations, which we use to count regions. Interestingly, these methods are particularly simpler and faster when restricted to lower bounds on the order of magnitude. See results in FIG2 and algorithm in Section 5. (ii) We refine the best known upper bound by considering the coefficients of the trained network.With such information, we identify that unit activity further contributes to the bottleneck effect caused by narrow layers BID45 . Furthermore, we are able to compare networks with the same configuration of layers. See results in Table 1 and theory in Section 4. (iii) We also survey and contribute to the literature on MILP formulations of rectifier networks due to the impact of the formulation on obtaining better empirical bounds. See Section 3. This paper introduced methods to obtain upper and lower bounds on a rectifier network. The upper bound refines the best known result for the network configuration by taking into account the coefficients of the network. By analyzing how the network coefficients affect when each unit can be active, we break the commonly used theoretical assumption that the activation hyperplane of each unit intersects every linear region defined by the previous layers. The resulting bound is particularly stronger when the network has a narrow layer, hence evidencing that the bottleneck effected identified by BID45 can be even stronger in those cases. The lower bound is based on extending an approximate model counting algorithm of SAT formulas to MILP formulations, which can then be used on MILP formulations of rectifier networks. The resulting algorithm is orders of magnitude faster than exact counting on networks with a large number of linear regions. The probabilistic bounds obtained can be parameterized for a balance between precision and speed, but it is interesting to observe that the the bounds obtained for different networks preserve a certain ordering in their sizes as we make the estimate more precise. Hence, we have some indication that faster approximations could suffice if we just want to compare networks for their relative expressiveness.Algorithm 1 Computes probabilistic lower bounds on the number of distinct solutions on n binary variables of a formulation F using parity constraints of size k DISPLAYFORM0 end for 6:while Termination criterion not satisfied do 7:F ← F Start over with F as formulation F 8: DISPLAYFORM1 Number of times that we have made F infeasible 9:r ← 0 Number of parity constraints added this time 10:while F has some solution s do 11:repeat 12:Generate parity constraint C of size k among n variables 13: DISPLAYFORM2 r ← r + 1 15: until C removes s This loop is implemented as a lazy cut callback 16: end while 17: DISPLAYFORM3 Number of times that F is feasible after adding j constraints 19:end for 20:end while 21:for j ← 0 → n − 1 do Computes probabilities after last call to the solver 22: BID46 and BID47 used these functions to show that approximate counting can be done in polynomial time with an NP-oracle, whereas BID50 have shown that SAT formulas with unique solution are as hard as those with multiple solutions. Hence, from a theoretical standpoint, such approximations are not much harder than solving for a single solution. DISPLAYFORM4 The seminal work by BID26 introduced the MBound algorithm, where XOR constraints on sets of variables with a fixed size k are used to compute the probability that 2 r is either a lower or an upper bound. These probabilistic lower bounds are always valid but get better as k increases, whereas the probabilistic upper bound is only valid if k = |V |/2. However, BID29 have shown that these lower bounds can be very good in practice for small values of k. The same principles have also been applied to constraint satisfaction problems BID28 .With time, this topic has gradually shifted to more precise estimates and to reducing the value of k needed to obtain valid upper bounds. Some of the subsequent work has been influenced by uniform sampling results from BID27 , where the fixed size k is replaced with an independent probability p of including each variable in each XOR constraint. That work includes the ApproxMC and the WISH algorithms BID10 BID21 , which rely on finding more solutions of the restricted formulas but generate (σ, ) certificates by which, with probability 1 − σ, the result is within (1 ± )|S|. The following work by BID22 and BID56 aimed at providing upper bound guarantees when p < 1/2, showing that the size of those sets can be Θ log(|V |) . Other groups tackled this issue differently. BID11 and BID33 have limited the counting to any set of variables I for which any assignment leads to at most one solution in V , denoting those as minimal independent supports. BID0 and BID1 have broken with the independent probability p by using each variable the same number of times across the r XOR constraints.",2164,1.023,1231,1.7579203899268887,"One form characterizing the expressiveness a piecewise linear neural network linear regions pieces modeled We observed substantial progress this topic lower and upper bounds linear regions a counting procedure However these bounds only account the dimensions the exact counting may take therefore making benchmark the expressiveness networks In this work approximate linear regions specific rectifier networks an algorithm probabilistic lower bounds of mixed-integer linear sets In present tighter upper that leverages network coefficients We test both on trained networks The algorithm probabilistic lower bounds several orders exact counting the values reach similar orders hence making our approach compare the expressiveness such networks The refined upper bound particularly stronger networks narrow layers Neural networks with piecewise linear activations become more along in since BID40 . simplest commonly among such forms activation Rectifier Linear Unit outputs between its input argument BID30 BID35 In the functions modeled these networks associate each part corresponds units having positive outputs We say those are the active units that part Counting these ""pieces into which the domain split which often linear regions decision regions compare models defined networks different configurations or coefficients The theoretical analysis the number input regions deep learning dates at least BID8 , more have empirical evidence the accuracy similar rectifier networks associatedFrom how many linear regions defined with n ReLUs already not configurations -and none reach the ceiling 2 n regions We learned regions may depend the dimension as layers how the units On possible obtain neural networks where regions exponential on network depth . On a bottleneck effect by the width each layer affects the regions subsequent layers due the dimension containing of up shallow networks define linear regions if n BID45 .The literature mainly bounding the maximum number. Lower bounds obtained constructing networks defining increasingly larger number linear regions BID2 BID45 . Upper bounds proven using the theory hyperplane arrangements by BID54 along other analytical insights . These bounds only identical -and tight one-dimensional inputs BID45 . Both explored deepening connections polyhedral theory some recently using tropical algebra BID55 BID13 . In , BID45 have shown the linear regions a trained network correspond projected solutions a Mixed-Integer Linear Program study neural network expressiveness universal approximation theory BID16 VC dimension BID5 trajectory length BID44 Different networks compared transforming with different number layers activation functions For example any continuous function modeled a single hidden layer sigmoid activation functions BID16 . In ReLUs , BID36 have the popular ResNet architecture BID31 with a single ReLU neuron in every hidden layer a universal approximator Furthermore BID2 have shown a network single hidden layer ReLUs trained global optimality a runtime polynomial the data size exponential in The use trajectory length expressiveness related linear regions by changing along we studyCertain critical network using leaky ReLUsf ( αx α �� identified produce connected decision regions BID42 . In such degenerate cases use sufficiently wide hidden layers However this result mainly applicable leaky ReLUs not the standard ReLUs BID7 .Although linear regions long conjectured recently shown work comparing similar networks this metric would come faster methods count or reasonably approximate such number Our approach in consists introducing both based the weight and bias coefficients the networks thus able compare networks having layersIn reframe determining the potential number linear regions N an architecture that estimating the representation efficiency �� = log interpreted units define thereby expressiveness We present the following contributions:(i ) We adapt approximate model counting methods propositional satisfiabilitySAT obtain solutions MILP formulations count regions Interestingly these methods particularly simpler restricted lower bounds magnitude See results FIG2 algorithm Section (ii We refine best known upper the trained networkWith such information identify that unit activity further contributes the bottleneck effect caused narrow layers BID45 . Furthermore compare networks layers See results Table theory (iii We also survey contribute MILP formulations rectifier networks due obtaining better empirical bounds See Section This paper introduced methods obtain a rectifier network The upper bound refines the best known result the network configuration by taking the coefficients By analyzing the network coefficients when each unit can active break the commonly used theoretical assumption the activation hyperplane intersects every linear region defined the previous layers resulting bound particularly stronger the network a narrow layer hence evidencing effected identified BID45 can even lower bound based extending an approximate model counting algorithm of SAT formulas MILP formulations on rectifier networks The resulting algorithm orders exact counting networks linear regions The probabilistic bounds obtained can parameterized a balance precision speed interesting the the bounds different networks preserve a certain ordering their sizes as we make the estimate more Hence some indication faster approximations could suffice if just networks for their relative expressivenessAlgorithm 1 Computes lower bounds distinct solutions on n binary variables of a formulation F using parity constraints size k DISPLAYFORM0 end for 6:while Termination criterion not do 7:F �� F Start over as formulation F 8 times we made 9r 0 Number parity constraints added thiswhile has some solution s dorepeatGenerate parity constraint C of size among + 15 until removes s This loop implemented a lazy cut callback end while 17 feasible after adding j constraintsendend → − do Computes probabilities after last call BID46 and used these functions show approximate counting an NPoracle whereas have shown SAT formulas unique solution as Hence from such approximations much harder solving DISPLAYFORM4 The seminal work BID26 introduced the MBound algorithm where XOR constraints sets variables with k 2 r either lower These probabilistic lower bounds always valid but get better k increases whereas = |V |/2 However BID29 have shown these lower bounds very good practice small values The same principles constraint satisfaction problems BID28 .With time this topic gradually shifted more precise estimates reducing the value k needed valid upper bounds Some the subsequent work influenced uniform sampling results BID27 , where the fixed size k replaced p including each XOR constraint That work includes the ApproxMC and the WISH algorithms BID10 BID21 , rely finding more solutions of the restricted formulas but generate (σ ) certificates by which, with within (1 ± )|S| The following work by BID22 aimed upper bound guarantees when p < showing those sets �� log(|V | Other groups tackled differently BID11 and limited the counting any set variables I for which any assignment leads at most one solution in V , denoting those as minimal independent supports BID0 and broken with the independent probability p by each variable across the r XOR constraints",0.01,0.6351937330601588
"The ability to look multiple times through a series of pose-adjusted glimpses is fundamental to human vision. This critical faculty allows us to understand highly complex visual scenes. Short term memory plays an integral role in aggregating the information obtained from these glimpses and informing our interpretation of the scene. Computational models have attempted to address glimpsing and visual attention but have failed to incorporate the notion of memory. We introduce a novel, biologically inspired visual working memory architecture that we term the Hebb-Rosenblatt memory. We subsequently introduce a fully differentiable Short Term Attentive Working Memory model (STAWM) which uses transformational attention to learn a memory over each image it sees. The state of our Hebb-Rosenblatt memory is embedded in STAWM as the weights space of a layer. By projecting different queries through this layer we can obtain goal-oriented latent representations for tasks including classification and visual reconstruction. Our model obtains highly competitive classification performance on MNIST and CIFAR-10. As demonstrated through the CelebA dataset, to perform reconstruction the model learns to make a sequence of updates to a canvas which constitute a parts-based representation. Classification with the self supervised representation obtained from MNIST is shown to be in line with the state of the art models (none of which use a visual attention mechanism). Finally, we show that STAWM can be trained under the dual constraints of classification and reconstruction to provide an interpretable visual sketchpad which helps open the `black-box' of deep learning. Much of the current effort and literature in deep learning focuses on performance from a statistical pattern recognition perspective. In contrast, we go back to a biological motivation and look to build a model that includes aspects of the human visual system. The eminent computational neuroscientist David Marr posited that vision is composed of stages which lead from a two dimensional input to a three dimensional contextual model with an established notion of object BID27 . This higher order model is built up in the visual working memory as a visual sketchpad which integrates notions of pattern and texture with a notion of pose BID3 . Visual attention models often draw inspiration from some of these concepts and perform well at various tasks BID0 BID1 BID12 BID18 BID38 . Inspired by vision in nature, visual attention corresponds to adaptive filtering of the model input, typically, through the use of a glimpsing mechanism which allows the model to select a portion of the image to be processed at each step. Broadly speaking, visual attention models exist at the crux of two key challenges. The first is to separate notions of pose and object from visual features. The second is to effectively model long range dependencies over a sequence of observations.Various models have been proposed and studied which hope to enable deep networks to construct a notion of pose. For example, transformational attention models learn an implicit representation of object pose by applying a series of transforms to an image BID18 BID0 . Other models such as Transformational Autoencoders and Capsule Networks harness an explicit understanding of positional relationships between objects BID16 BID36 . Short term memories have previously been studied as a way of improving the ability of Recurrent Neural Networks (RNNs) to learn long range dependencies. The ubiquitous Long Short-Term Memory (LSTM) network is perhaps the most commonly used example of such a model BID17 . More recently, the fast weights model, proposed by BID2 provides a way of imbuing recurrent networks with an ability to attend to the recent past.From these approaches, it is evident that memory is a central requirement for any method which attempts to augment deep networks with the ability to attend to visual scenes. The core concept which underpins memory in neuroscience is synaptic plasticity, the notion that synaptic efficacy, the strength of a connection, changes as a result of experience BID33 . These changes occur at multiple time scales and, consequently, much of high level cognition can be explained in terms of the interplay between immediate, short and long term memories. An example of this can be found in vision, where each movement of our eyes requires an immediate contextual awareness and triggers a short term change. We then aggregate these changes to make meaningful observations over a long series of glimpses. Fast weights BID2 draw inspiration from the Hebbian theory of learning BID14 which gives a framework for how this plasticity may occur. Furthermore, differentiable plasticity BID28 combines neural network weights with weights updated by a Hebbian rule to demonstrate that backpropagation can be used to learn a substrate over which the plastic network acts as a content-addressable memory.In this paper, we propose augmenting transformational attention models with a visual working memory in order to move towards two key goals. Firstly, we wish to understand if visual attention and working memory provide more than just increased efficiency and enable functions that cannot otherwise be achieved. Secondly, we wish to understand and seek answers to some of the challenges faced when attempting to model such psychophysical concepts in deep networks. We demonstrate classification performance on MNIST (LeCun, 1998) and CIFAR-10 ( BID21 ) that is competitive with the state of the art and vastly superior to previous models of attention, demonstrating the value of a working memory. We then demonstrate that it is possible to learn this memory representation in an unsupervised manner by painting images, similar to the Deep Recurrent Attentive Writer (DRAW) network BID12 . Using this representation, we demonstrate competitive classification performance on MNIST with self supervised features. Furthermore, we demonstrate that the model can learn a disentangled space over the images in CelebA BID25 , shedding light on some of the higher order functions that are enabled by visual attention. Finally, we show that the model can perform multiple tasks in parallel and how a visual sketchpad can be used to produce interpretable classifiers. In this paper we have described a novel, biologically motivated short term attentive working memory model (STAWM) which demonstrates impressive results on a series of tasks and makes a strong case for further study of short term memories in deep networks. As well as demonstrating competitive classification results on MNIST and CIFAR-10, we have shown that the core model can be used for image reconstruction and for disentangling foreground from background in an unsupervised setting with CelebA. Finally, we have given a concrete example of how a model augmented with a visual sketchpad can 'describe what it sees' in a way that is naturally interpretable for humans. It is easy to see how similar systems could be used in future technologies to help open the 'black-box' and understand why a decision was made, through the eyes of the model that made it. Furthermore, we have explored the notion that building up a memory representation over an attention policy, coupled with a smooth changing latent space can result in a movement from simple to complex regions of a scene. This perhaps gives us some insight into how humans learn to attend to their environment when endowed with a highly capable visual memory. Future work will look to see if variants of this model can be used to good effect on higher resolution images. Experimentation and analysis should also be done to further understand the dynamics of the Hebb-Rosenblatt memory and the representation it learns. We further intend to investigate if the memory model can be used for other applications such as fusion of features from multi-modal inputs. Finally, we will look further into the relationship between visual memories and saliency.A STABILISING THE MEMORY The working memory model described in the paper exhibits a potential issue with stability. It is possible for the gradient to explode, causing damaging updates which halt learning and from which the model cannot recover. In this section we will briefly demonstrate some properties of the learning rule in Equation 2 and derive some conditions under which the dynamics are stable. We will broadly follow the method of with minor alterations for our approach. We use the terms stimuli and response to represent input to and output from a neuron respectively. We will consider a sequence of DISPLAYFORM0 Hg×Wg , presented to L I when attending to a single image. ν as the identity input to some ν ∈ L II . We then define γ DISPLAYFORM1 ν , the projection of e (i) through the weights matrix W ∈ R M ×M . The total input to ν if stimulus i is presented to L I at time t is the sum of these two terms given in Equation 9. DISPLAYFORM2 Suppose that a stimulus i is presented at time t 0 for some period ∆t. The subsequent change in the weight, w µν , of some connection is defined in Equation 10, where φ II is a nonlinear activation function of neurons in L II . Note that the change in the matrix W for this step is the learning rule in Equation 2. DISPLAYFORM3 From FORMULA1 and (8) we derive Equation 11 which gives the change in the weighted component γ (q) ν for some query stimulus q over a single time step. We omit the subscript ν for brevity. The response of L II to q is the latent representation derived from the memory during the glimpse sequence. DISPLAYFORM4 The next step in is to define some sequence over the set of possible stimuli to be presented in order. We deviate slightly here as our sequence is not drawn from a bounded set. Instead, as we have seen, each glimpse is a sample from the manifold space of affine transforms over the image. As such, in Equation 12 we generalise Equation 11 to represent the change in the query response for some arbitrary point, n, in the sequence, with stimulus g n at time t + n∆t. Summing over the whole sequence we obtain Equation 13. We can now obtain an expression for the gradient of Equation 13 by dividing by N ∆t in the limit of ∆t → 0 (Equation 14). DISPLAYFORM5 DISPLAYFORM6 Although Equation 14 is only an approximation of the dynamics of the system, we have demonstrated stability under certain conditions: firstly, the input to the memory network must not vary with time. This is satisfied in the case where the feature vector is not dependent on the output of a recurrent network. It is possible to extend this proof to incorporate such networks BID35 , however, that is outside the scope of this paper. Secondly, the activation functions must be nonnegative and have an upper bound (as with ReLU6 or Sigmoid). This introduces an interesting similarity as there is an upper bound to the number of times a real neuron can fire in a given window, governed by its refractory period. Finally, we can observe that Equation 15 is nondecreasing iff η is greater than δ, δ is positive and η and θ are nonnegative.",2164,1.25,1243,1.7409493161705552,"The ability look multiple through pose-adjusted glimpses fundamental This critical faculty allows understand highly complex visual scenes Short term memory plays aggregating obtained these glimpses informing the scene Computational models attempted glimpsing visual attention but incorporate memory We introduce biologically inspired visual working memory architecture we term We subsequently introduce a fully differentiable Short Term Attentive Working Memory model transformational attention learn a memory over each image it sees The state our Hebb-Rosenblatt memory embedded STAWM as the weights space a layer By projecting different queries through this layer obtain goal-oriented latent representations tasks including classification visual reconstruction Our model obtains highly competitive classification performance MNIST As demonstrated through the CelebA dataset to perform reconstruction the model learns make a sequence updates a canvas which constitute a parts-based representation Classification with the self supervised representation obtained MNIST to innone a visual attention mechanism Finally show STAWM can trained under the dual constraints classification reconstruction to an interpretable visual sketchpad which helps open the `black-box deep learning Much and literature deep learning performance from a statistical pattern recognition perspective In contrast we go a biological motivation look build includes aspects The eminent computational neuroscientist vision composed stages which lead a two dimensional input a three dimensional contextual model with an established notion object BID27 . This higher order model built up the visual working memory as a visual sketchpad which integrates notions pattern texture with a notion pose BID3 . Visual attention models often draw inspiration some these concepts perform well BID0 . Inspired vision in nature visual attention corresponds adaptive filtering the model input typically, a glimpsing mechanism which select at each step Broadly visual attention models exist at two key challenges first is separate notions pose object visual features second is to effectively model long range dependencies over a sequence observationsVarious models studied which hope enable deep networks construct a notion pose For example transformational attention models learn an implicit representation object pose transforms BID18 BID0 Other models such Transformational Autoencoders Capsule Networks harness an explicit understanding positional relationships objects BID16 BID36 . Short term memories have previously studied Recurrent Neural Networks long range dependencies perhaps BID17 . More recently the fast weights model proposed BID2 provides imbuing recurrent networks an ability attend the recent pastFrom these approaches evident any method which augment deep networks visual scenes The core concept which memory in neuroscience the notion synaptic efficacy the strength changes experience BID33 . These changes occur multiple time scales, consequently much high level cognition explained An example vision each movement requires an immediate contextual awareness triggers We then aggregate these changes meaningful observations over glimpses Fast weights BID2 draw inspiration the Hebbian theory learning BID14 which gives how this plasticity Furthermore differentiable plasticity BID28 combines neural network weights weights updated a Hebbian rule demonstrate learn a substrate over which the plastic network acts a content-addressable memoryIn augmenting transformational attention models a visual working memory in move towards two key goals Firstly wish understand if visual attention provide more just increased efficiency enable functions otherwise Secondly wish understand seek when attempting model such psychophysical concepts deep networks We demonstrate classification performance MNIST (LeCun 1998 ( BID21 that competitive vastly attention, demonstrating a working memory We then demonstrate it learn this memory representation painting images, similar the Deep Recurrent Attentive Writer network BID12 . Using this representation demonstrate competitive classification performance MNIST with self supervised features Furthermore demonstrate the model learn a disentangled space over the images CelebA BID25 , shedding some enabled visual attention Finally show the model perform multiple tasks how a visual sketchpad produce interpretable classifiers In a novel, biologically motivated short term attentive working memory modelSTAWM impressive results makes further study deep networks As well demonstrating competitive classification results MNIST the core model image reconstruction foreground from CelebA. Finally given a model augmented a visual sketchpad 'describe what naturally for humans It easy how similar systems future technologies open the 'black-box and understand why a decision through the model that made Furthermore explored building up a memory representation over an attention policy, coupled a smooth changing latent space can result a movement simple This perhaps gives humans learn attend when endowed a highly capable visual memory Future work see variants good effect higher resolution images Experimentation analysis should also further the Hebb-Rosenblatt memory the representation it learns We further intend investigate the memory model other applications fusion features Finally look further visual memories saliencyA STABILISING The working memory model described exhibits a potential issue stability It the gradient explode damaging updates which halt learning from the model In briefly demonstrate some properties the learning rule Equation derive some conditions under the dynamics stable We will broadly follow with minor alterations for our approach We use the terms stimuli response represent input and a neuron respectively We will consider a sequence DISPLAYFORM0 Hg×Wg , presented to L I when attending ν as the identity input some �� �� L II We then define �� DISPLAYFORM1 �� the projection ei the weights matrix W �� R M ×M The total input �� if stimulus i presented L I at these two terms given 9 DISPLAYFORM2 Suppose stimulus i 0 for some period �� The subsequent change the weight, w µν some connection defined 10 �� II a nonlinear activation function neurons L II Note the change the matrix W for this step the learning rule DISPLAYFORM3 From FORMULA1 ( we derive Equation 11 the change weighted component �q �� some query stimulus q over We omit the subscript �� The response L II q is the latent representation derived the memory during the glimpse sequence DISPLAYFORM4 The next step is define some sequence over possible stimuli We deviate here as our sequence drawn a bounded set Instead as each glimpse a sample the manifold space affine transforms over the image As such in Equation 12 generalise represent the query response for some arbitrary point n stimulus g n at +�� Summing over the whole sequence we obtain Equation 13 We obtain an expression the gradient Equation 13 by dividing N ��t in the limit → DISPLAYFORM5 Although Equation 14 the dynamics demonstrated stability under: firstly to the memory network vary This satisfied in the feature vector dependent a recurrent network It extend this proof incorporate such networks BID35 , however that outside Secondly the activation functions must nonnegativeas with ReLU6 or This introduces an interesting similarity as there upper a real neuron fire governed its refractory period Finally observe Equation 15 nondecreasing iff �� greater",0.01,0.5919529281912578
"Generative models have been successfully applied to image style transfer and domain translation. However, there is still a wide gap in the quality of results when learning such tasks on musical audio. Furthermore, most translation models only enable one-to-one or one-to-many transfer by relying on separate encoders or decoders and complex, computationally-heavy models. In this paper, we introduce the Modulated Variational auto-Encoders (MoVE) to perform musical timbre transfer. First, we define timbre transfer as applying parts of the auditory properties of a musical instrument onto another. We show that we can achieve and improve this task by conditioning existing domain translation techniques with Feature-wise Linear Modulation (FiLM). Then, by replacing the usual adversarial translation criterion by a Maximum Mean Discrepancy (MMD) objective, we alleviate the need for an auxiliary pair of discriminative networks. This allows a faster and more stable training, along with a controllable latent space encoder. By further conditioning our system on several different instruments, we can generalize to many-to-many transfer within a single variational architecture able to perform multi-domain transfers. Our models map inputs to 3-dimensional representations, successfully translating timbre from one instrument to another and supporting sound synthesis on a reduced set of control parameters. We evaluate our method in reconstruction and generation tasks while analyzing the auditory descriptor distributions across transferred domains. We show that this architecture incorporates generative controls in multi-domain transfer, yet remaining rather light, fast to train and effective on small datasets.",306,0.201,176,1.7386363636363635,"Generative models successfully image style transfer and domain translation However results learning such tasks on musical audio Furthermore most translation models only enable by relying complex, computationally-heavy models In the Modulated Variational auto-Encoders (MoVE to perform musical timbre transfer First define timbre transfer applying parts the auditory properties onto We show we achieve and this task conditioning existing domain translation techniques Feature-wise Linear ModulationFiLM Then by replacing the usual adversarial translation criterion by a Maximum Mean Discrepancy (MMD) objective alleviate an auxiliary pair This allows along a controllable latent space encoder By further conditioning on several different instruments within able Our models map inputs successfully timbre one instrument supporting sound synthesis on a reduced set We evaluate our method reconstruction generation tasks while analyzing the auditory descriptor distributions transferred domains We show this architecture incorporates generative controls multi-domain transfer yet remaining rather light, fast to train effective",0.0,0.5860597283479253
"We study the behavior of weight-tied multilayer vanilla autoencoders under the assumption of random weights. Via an exact characterization in the limit of large dimensions, our analysis reveals interesting phase transition phenomena when the depth becomes large. This, in particular, provides quantitative answers and insights to three questions that were yet fully understood in the literature. Firstly, we provide a precise answer on how the random deep weight-tied autoencoder model performs “approximate inference” as posed by Scellier et al. (2018), and its connection to reversibility considered by several theoretical studies. Secondly, we show that deep autoencoders display a higher degree of sensitivity to perturbations in the parameters, distinct from the shallow counterparts. Thirdly, we obtain insights on pitfalls in training initialization practice, and demonstrate experimentally that it is possible to train a deep autoencoder, even with the tanh activation and a depth as large as 200 layers, without resorting to techniques such as layer-wise pre-training or batch normalization. Our analysis is not specific to any depths or any Lipschitz activations, and our analytical techniques may have broader applicability. The autoencoder is a cornerstone in machine learning, first as a response to the unsupervised learning problem (Rumelhart & Zipser (1985) ), then with applications to dimensionality reduction (Hinton & Salakhutdinov (2006) ), unsupervised pre-training (Erhan et al. (2010) ), and also as a precursor to many modern generative models (Goodfellow et al. (2016) ). Its reconstruction power is well utilized in applications such as anomaly detection (Chandola et al. (2009) ) and image recovery (Mousavi et al. (2015) ). With the surge of deep learning, thousands of papers have studied multilayer variants of this architecture, but theoretical understanding has been limited, since analyzing the learning dynamics of a highly nonlinear structure is typically a difficult problem even for the shallow autoencoder. To get around this, we tackle the task with a critical assumption: the weights are random and the autoencoder is weight-tied. One enjoys much analytical tractability from the randomness assumption, whereas weight tying enforces the random autoencoder to perform ""autoencoding"". We also study this in the high-dimensional setting, where all dimensions are comparably large and ideally jointly approaching infinity. We consider the simplest setting: vanilla autoencoders (i.e., ones with fully connected layers only) and their reconstruction capability. This is done for the sake of understanding the effect of depth, while we note our techniques may have broader applicability.The aforementioned assumptions are not without justifications. There is a growing literature on deep neural networks with random weights, (Li & Saad (2018) ; Giryes et al. (2016) ; Poole et al. (2016) ; Schoenholz et al. (2016) ; Gabrié et al. (2018) ; Amari et al. (2018) ) to name a few, revealing certain properties of deep feedforward networks 1 . Several recent works have also studied random multilayer feedforward networks through the lens of statistical inference (Manoel et al. (2017) ; Reeves (2017); Fletcher et al. (2018) ). The idea of weight tying is considered in the important paper Vincent et al. (2010) with an empirical finding that autoencoders with and without weight tying perform comparably, and has become standard in autoencoders. Similar features of random connection and symmetry also appear in other neural models (Lillicrap et al. (2016) ; Scellier et al. (2018) ). Finally the high-dimensional setting is common in recent statistical learning advances (Bühlmann & Van De Geer (2011) ), and not too far from the actual practice where many large datasets have dimensions of at least a few hundreds and are harnessed by large-scaled models.We seek quantitative answers to three specific questions that are motivated by previous works:• In exactly what way does the (vanilla) random weight-tied autoencoder perform ""approximate inference""? This term is coined in Scellier et al. (2018) in connection with the theoretical results in Arora et al. (2015) , which implicitly studies the said model. In particular, Arora et al. (2015) proves an upper bound on x − x 2 , where x andx are the input and the output of the network, but is limited in the number of layers and specific to the ReLU activation. This direction has been recently extended by Gilbert et al. (2017) . In our work, we establish precisely what this approximate inference is by obtaining a general and asymptotically exact characterization 2 ofx, for any number of layers and any Lipschitz continuous activations (Theorem 1 and Section 3.3). Theorem 1 is the key theoretical result of our work and lays the foundation for all analyses that follow.• In what way is the deep autoencoder different from the shallow counterpart? Li & Saad (2018) ; Poole et al. (2016) reveal this in terms of the candidate function space and expressivity for feedforward networks. It is unclear how these notions are applicable to weighttied autoencoders, which seek replication of the input rather than a generic mapping. In this work, we show that the deep autoencoder exhibits a higher order of sensitivity to perturbations of the parameters (Section 3.4). Burkholz & Dubatovka (2018) demonstrate a connection between the study of random networks, or ones at initialization, and their trainability. Note that these works either do not study weight-tied structures, or assume the analysis of the untying case for weight-tied structures. In our work , we derive and experimentally verify insights on how (not) to initialize deep weight-tied autoencoders, demonstrating that it is possible to train them without resorting to techniques such as greedy layer-wise pretraining, drop-out and batch normalization (Section 3.5). Specifically we experiment with 200-layer autoencoders.No prior works have attempted all three tasks. The quantitative difference between weight-tied and weight-untied networks is in fact not negligible, yet the analysis is non-trivial due to the weight tying constraint (Arora et al. (2015) ; Chen et al. (2018) ). To address this issue and obtain Theorem 1, we apply the Gaussian conditioning technique, which first appears in the studies of TAP equations in spin glass theory (Bolthausen (2014) ) and is extensively used in the approximate message passing algorithm literature (Bayati & Montanari (2011); Javanmard & Montanari (2013) ; Berthier et al. (2017) ). This should be contrasted with untied random networks, whose analysis is typically more straightforward. More importantly , the difference is not only analytical: the overall picture of deep random weight-tied autoencoders is rich and drastically different from that of feedforward networks. An analysis in the limit of infinite depth reveals three fundamental equations governing the picture (Section 3.1), which displays multiple phase transition phenomena (Section 3.2) . Consider the following 2L-layers autoencoder with weight tying: DISPLAYFORM0 Here x ∈ R n0 is the input, W ∈ R n ×n −1 is the weight, b ∈ R n is the encoder bias, and v ∈ R n −1 is the decoder bias, for = 1, ..., L. Also ϕ : R → R and σ : R → R are the activations (where for a vector u ∈ R n and a function ϕ : R → R, we write ϕ (u) to denote the vector (ϕ (u 1 ) , ..., ϕ (u n )) ). It is usually the case in practice that σ 0 (u) = u the identity function. We introduce some convenient quantities inductively: FIG6 of Appendix A.1 for a schematic diagram. We assume weights are random . Specifically we generate the weights and biases according to DISPLAYFORM1 DISPLAYFORM2 independently of each other. The scaling of the variances accords with the literature and actual practice (Glorot & Bengio (2010); Vincent et al. (2010) ). We also consider the asymptotic highdimensional regime, indexed by n: DISPLAYFORM3 Here σ W, , σ b, , σ v, and α are finite constants independent of n. We enforce σ W, > 0, but allow σ b, and σ v, to be zero. We assume that all activations are Lipschitz continuous, and the encoder activations σ 's are non-trivial in the sense that for any τ > 0, E z σ (τ z) This paper has shown quantitative answers to the three questions posed in Section 1. This feat is enabled by an exact analysis via Theorem 1. The theorem is stated in a general setting, allowing varying activations, weight variances, etc, but our analyses in Section 3 have made several simplifications. This leaves a question of whether these simplifications can be relaxed, and how the picture changes accordingly, for instance, when the parameters vary across layers, similar to Yang & Schoenholz (2018) . Many other questions also remain. For example, what would be the covariance structure between the outputs of two distinct inputs? How does the network's Jacobian matrix look like? These questions have been answered in the feedforward case (Poole et al. (2016) ; Pennington et al. FORMULA12 ), but we believe answering them is more technically involved in our case. We have also seen that an autoencoder that shows initial progress may not necessarily produce meaningful reconstruction eventually after training, and hence much more work is needed to understand the training dynamics far beyond initialization. Recent works Mei et al. FORMULA12 In the following, we give an outline of the proof of Theorem 1, and the complete proof. First, we start with a few notations and definitions. DISPLAYFORM0",2112,1.362,1219,1.7325676784249384,"We study weight-tied multilayer vanilla autoencoders under random weights Via an exact characterization in the limit large dimensions our analysis interesting phase transition phenomena when the depth becomes This, particular provides quantitative answers and insights three questions yet fully Firstly provide a precise answer the random deep weight-tied autoencoder model performs �� inference�� posed Scellier et al (2018 and its connection reversibility considered several theoretical studies Secondly show deep autoencoders display sensitivity the parameters distinct the shallow counterparts Thirdly obtain insights pitfalls training initialization practice demonstrate experimentally even the tanh activation a depth as large as 200 layers techniques Our analysis not specific any depths any Lipschitz activations our analytical techniques The autoencoder a cornerstone first as a responseRumelhart Zipser (1985 with applications dimensionality reductionHinton Salakhutdinov preErhan (2010 ), also as many modern generative models (2016 ). Its reconstruction power well utilized applications anomaly detection (Chandola (2009 ) and image recoveryMousavi (2015 ). With the surge deep learning thousands papers studied multilayer variants this architecture theoretical understanding since analyzing the learning dynamics typically even the shallow autoencoder To tackle the task with a critical assumption the weights random weighttied One enjoys much analytical tractability from the randomness assumption whereas weight tying enforces to perform We also study this the high-dimensional setting all dimensions comparably ideally jointly approaching We consider the simplest setting vanilla autoencoders fully connected layers only their reconstruction capability This done understanding depth while we note our techniques mayThe aforementioned assumptions without justifications There deep neural networks with random weights (Li Saad (2018 ; Giryes (2016 ; Poole et (2016 ; Schoenholz (2016 ; Gabrié et (2018 ; Amari (2018 ) to name revealing certain properties deep feedforward networks 1 . Several recent works also studied random multilayer feedforward networks through (2017 ; Reeves Fletcher et (2018 ). The idea weight tying considered in the important paper Vincent et (2010 with an empirical finding with and weight tying perform, has become standard Similar features random connection symmetry also other neural modelsLillicrap (2016 ; Scellier (2018 ). Finally the high-dimensional setting common recent statistical learning advancesBühlmann Van De Geer ( not too where dimensions and harnessedWe seek quantitative answers motivated previous works:• In exactly what way the (vanilla) random weight-tied autoencoder ""approximate inference This term coined Scellier et (2018 in connection the theoretical results in Arora et (2015 , which implicitly studies the said model In particular, Arora et al (2015 proves an upper x − x 2 andx the input the network but is limited layers specific to the ReLU activation This direction recently extended Gilbert et (2017 . In our work establish precisely what this approximate inference by obtaining 2 ofx for any number layers any Lipschitz continuous activationsTheorem Section Theorem is the key theoretical result our work lays all analyses follow.• what way different the shallow counterpart Li & Saad2018 ; Poole et (2016 reveal this in terms the candidate function space expressivity for feedforward networks It unclear these notions applicable weighttied autoencoders seek replication the input rather a generic mapping In this work exhibits sensitivity the parametersSection Burkholz & Dubatovka2018 demonstrate a connection the study random networks or ones at initialization their trainability Note these works either study weight-tied structures assume the analysis the untying case In our work , derive and experimentally verify insights on (not initialize deep weight-tied autoencoders demonstrating train techniques greedy layer-wise pretraining, drop-out and batch normalizationSection Specifically we experiment 200-layer autoencodersNo prior works attempted all three tasks The quantitative difference weight-tied and weight-untied networks in negligible yet the analysis non due the weight tying constraintArora (2015 ; Chen (2018 ). To address obtain Theorem apply the Gaussian conditioning technique first appears the studies TAP equations spin glass theoryBolthausen (2014 ) extensively the approximate message passing algorithm literatureBayati Montanari Javanmard (2017 ). This should contrasted untied random networks whose analysis typically more straightforward More importantly , the difference analytical: the overall picture deep random weight-tied autoencoders rich drastically feedforward networks An analysis in the limit infinite depth three fundamental equations governing the picture (Section displays multiple phase transition phenomena . Consider the following 2L-layers autoencoder weight tying DISPLAYFORM0 Here x �� R n0 is is the encoder bias v for = ... L. Also � : the activationswhere for vector u n function :, write to ( 1 , ... It usually in practice � 0u the identity function We introduce some convenient quantities inductively: FIG6 of for We assume weights random . Specifically we generate the weights biases according DISPLAYFORM1 DISPLAYFORM2 independently The scaling the variances accords actual practice (Glorot Bengio ( Vincent (2010 ). We also consider the asymptotic highdimensional regime indexed n: DISPLAYFORM3 Here �� W, , α finite constants independent We enforce �� W > 0 but allow zero We assume all activations Lipschitz continuous encoder activations �� 's non for τ > E z � z This paper quantitative answers Section This feat enabled an exact analysis via Theorem The theorem stated a general setting allowing varying activations weight variances our analyses in Section have made This leaves these simplifications relaxed the picture changes accordingly the parameters vary layers similar Yang &2018 . Many other questions also For example what the covariance structure the outputs two distinct inputs How the network's Jacobian matrix These questions the feedforward casePoole (2016 ; Pennington FORMULA12 ), but we believe answering them technically involved in We also an autoencoder that shows initial progress may necessarily produce meaningful reconstruction eventually after training the training dynamics far initialization Recent works Mei et al FORMULA12 In, give the proof Theorem First start definitions DISPLAYFORM0",0.01,0.5705972516180668
"Assessing distance betweeen the true and the sample distribution is a key component of many state of the art generative models, such as Wasserstein Autoencoder (WAE). Inspired by prior work on Sliced-Wasserstein Autoencoders (SWAE) and
 kernel smoothing we construct a new generative model – Cramer-Wold AutoEncoder (CWAE). CWAE cost function, based on introduced Cramer-Wold distance between samples, has a simple closed-form in the case of normal prior. As a consequence, while simplifying the optimization procedure (no need of sampling necessary to evaluate the distance function in the training loop), CWAE performance matches quantitatively and qualitatively that of WAE-MMD (WAE using maximum mean discrepancy based distance function) and often improves upon SWAE. One of the crucial aspects in construction of generative models is devising effective method for computing and minimizing distance between the true and the model distribution. Originally in Variational Autencoder (VAE) BID10 this computation was carried out using variational methods. An important improvement was brought by the introduction of Wasserstein metric BID14 and the construction of WAE-GAN and WAE-MMD models, which relax the need for variational methods. WAE-GAN requires a separate optimization problem to be solved to approximate the used divergence measure, while in WAE-MMD the discriminator has the closed-form obtained from a characteristic kernel, i.e. one that is injective on distributions BID12 . A recent contribution to this trend of simplifying the construction of generative models is Sliced-Wasserstein Autoencoder (SWAE, BID11 ), where a significantly simpler AutoEncoder based model based on Wasserstein distance is proposed. The main innovation of SWAE was the introduction of the sliced-Wasserstein distance -a fast to estimate metric for comparing two distributions, based on the mean Wasserstein distance of one-dimensional projections. However, even in SWAE there is no close analytic formula that would enable computing the distance of the sample from the standard normal distribution. Consequently in SWAE two types of sampling are needed: (i) sampling from the prior distribution and (ii) sampling over one-dimensional projections.Our main contribution is introduction of the CramerWold distance between distributions, which has a closed-form for the distance of a sample from standard multivariate normal distribution. Its important feature is that it is given by a characteristic kernel which has a closed-form given by equation 7 for the product of radial Gaussians 1 . We use it to construct an AutoEncoder based generative model, called Cramer-Wold AutoEncoder (CWAE), in which the cost function, for a normal prior distribution, has a closed analytic formula. Thus In the paper we have presented a new autoencoder based generative model CWAE, which matches results of WAE-MMD, while using a cost function given by a simple closed analytic formula. We hope this result will encourage future work in developing simpler to optimize analogs of strong neural models.Crucial in the construction of CWAE is the use of the developed Cramer-Wold metric between samples and distributions, which can be effectively computed for Gaussian mixtures. As a consequence we obtain a reliable measure of the divergence from normality. Future work could explore use of the Cramer-Wold distance in other settings, in particular in adversarial models.",679,0.327,425,1.5976470588235294,"Assessing distance betweeen true the sample distribution many state of Wasserstein Autoencoder Inspired prior work Sliced-Wasserstein AutoencodersSWAE kernel smoothing we construct – Cramer-Wold AutoEncoder CWAE cost function based introduced Cramer-Wold distance samples a simple closed-form in normal prior As while simplifying the optimization procedureno of sampling necessary evaluate the training loop CWAE performance matches quantitatively and WAE-MMD using maximum mean discrepancy based distance function often improves SWAE One in construction generative models devising effective method for computing minimizing distance true the model distribution Originally in Variational AutencoderVAE BID10 this computation carried variational methods An important improvement brought Wasserstein metric BID14 WAE-GAN and WAE-MMD models relax variational methods WAE-GAN requires a separate optimization problem approximate the used divergence measure while in the closed-form obtained a characteristic kernel injective on distributions BID12 . A recent contribution this trend simplifying Sliced-Wasserstein Autoencoder (SWAE, BID11 ), where a significantly simpler AutoEncoder based model based The main innovation SWAE the sliced-Wasserstein distance -a fast to estimate metric comparing two distributions one-dimensional projections However even SWAE there no close analytic formula enable computing the sample in SWAE two types sampling sampling the prior distribution over one-dimensional projectionsOur main contribution introduction the CramerWold distance distributions a closed-form for standard multivariate normal distribution Its important feature given by a characteristic kernel a closed-form given equation 7 for radial Gaussians 1 . We use it construct an AutoEncoder based generative model called Cramer-Wold AutoEncoderCWAE cost function for a normal prior distribution has a closed analytic formula Thus In the paper based generative model CWAE matches results WAE-MMD while a cost function given a simple closed analytic formula We hope this result future work developing simpler to optimize analogs strong neural modelsCrucial in the construction CWAE the developed Cramer-Wold metric between samples distributions effectively computed Gaussian mixtures As we obtain a reliable measure the divergence Future work explore use the Cramer-Wold distance other settings in adversarial models",0.0,0.22683136686970243
"We propose a rejection sampling scheme using the discriminator of a GAN to
 approximately correct errors in the GAN generator distribution. We show that
 under quite strict assumptions, this will allow us to recover the data distribution
 exactly. We then examine where those strict assumptions break down and design a
 practical algorithm—called Discriminator Rejection Sampling (DRS)—that can be
 used on real data-sets. Finally, we demonstrate the efficacy of DRS on a mixture of
 Gaussians and on the state of the art SAGAN model. On ImageNet, we train an
 improved baseline that increases the best published Inception Score from 52.52 to
 62.36 and reduces the Frechet Inception Distance from 18.65 to 14.79. We then use
 DRS to further improve on this baseline, improving the Inception Score to 76.08
 and the FID to 13.75. Generative Adversarial Networks (GANs) BID5 are a powerful tool for image synthesis. They have also been applied successfully to semi-supervised and unsupervised learning BID25 BID20 BID11 , image editing BID31 BID12 , and image style transfer BID2 . Informally, the GAN training procedure pits two neural networks against each other, a generator and a discriminator. The discriminator is trained to distinguish between samples from the target distribution and samples from the generator. The generator is trained to fool the discriminator into thinking its outputs are real. The GAN training procedure is thus a two-player differentiable game, and the game dynamics are largely what distinguishes the study of GANs from the study of other generative models. These game dynamics have well-known and heavily studied stability issues. Addressing these issues is an active area of research BID17 BID7 .However , we are interested in studying something different: Instead of trying to improve the training procedure, we (temporarily) accept its flaws and attempt to improve the quality of trained generators by post-processing their samples using information from the trained discriminator. It's well known that (under certain very strict assumptions) the equilibrium of this training procedure is reached when sampling from the generator is identical to sampling from the target distribution and the discriminator always outputs 1/2. However, these assumptions don't hold in practice. In particular , GANs as presently trained don't learn to reproduce the target distribution BID1 . Moreover, trained GAN discriminators aren't just identically 1/2 -they can even be used to perform chess-type skill ratings of other trained generators .We ask if the information retained in the weights of the discriminator at the end of the training procedure can be used to ""improve"" the generator. At face value, this might seem unlikely. After all, if there is useful information left in the discriminator, why doesn't it find its way into the generator via the training procedure? Further reflection reveals that there are many possible reasons. First, the assumptions made in various analyses of the training procedure surely don't hold in practice (e.g. the discriminator and generator have finite capacity and are optimized in parameter space rather than density-space). Second, due to the concrete realization of the discriminator and the generator as neural networks, it may be that it is harder for the generator to model a given distribution than it is for the discriminator to tell that this distribution is not being modeled precisely. Finally, we may simply not train GANs long enough in practice for computational reasons.In this paper, we focus on using the discriminator as part of a probabilistic rejection sampling scheme. In particular, this paper makes the following contributions:• We propose a rejection sampling scheme using the GAN discriminator to approximately correct errors in the GAN generator distribution.• We show that under quite strict assumptions, this scheme allows us to recover the data distribution exactly.• We then examine where those strict assumptions break down and design a practical algorithm -called DRS -that takes this into account.• We conduct experiments demonstrating the effectiveness of DRS. First, as a baseline, we train an improved version of the Self-Attention GAN, improving its performance from the best published Inception Score of 52.52 up to 62.36, and from a Fréchet Inception Distance of 18.65 down to 14.79. We then show that DRS yields further improvement over this baseline, increasing the Inception Score to 76.08 and decreasing the Fréchet Inception Distance to 13.75. We have proposed a rejection sampling scheme using the GAN discriminator to approximately correct errors in the GAN generator distribution. We've shown that under strict assumptions, we can recover the data distribution exactly. We've also examined where those assumptions break down and Each row shows images synthesized by interpolating in latent space. The color bar above each row represents the acceptance probabilities for each sample: red for high and white for low. Subjective visual quality of samples with high acceptance probability is considerably better: objects are more coherent and more recognizable as belonging to a specific class. There are fewer indistinct textures, and fewer scenes without recognizable objects. • There's no reason that our scheme can only be applied to GAN generators. It seems worth investigating whether rejection sampling can improve e.g. VAE decoders. This seems like it might help, because VAEs may have trouble with ""spreading mass around"" too much.• In one ideal case, the critic used for rejection sampling would be a human. Can we use better proxies for the human visual system to improve rejection sampling's effect on image synthesis models?• It would be interesting to theoretically characterize the efficacy of rejection sampling under the breakdown-of-assumptions that we have described earlier. In addition , we represent Inception score as a function of acceptance rate in FIG5 -left. Different acceptance rates are achieved by changing γ from the 0 th percentile of F (x) (acceptance rate = 100%) to its 90 th percentile (acceptance rate = 14%). Decreasing the acceptance rate filters more non-realistic samples and increases the final Inception score. After an specific rate, rejecting more samples does not gain any benefit in collecting a better pool of samples.Moreover, FIG5 -right shows the correlation between the acceptance probabilities that DRS assigns to the synthesized samples and the recognizability of those samples from the view-point of a pre-trained Inception network. The latter is measured by computing max j p(y j |x i ) which is the probability of sample x i belonging to the category y j from the 1,000 ImageNet classes. As expected, there is a large mass of the recognizable images accepted with high acceptance probabilities on the top right corner. The small mass of images which cannot be easily classified into one of the 1,000 categories while having high acceptance probability scores (the top left corner of the graph) can be due to the non-optimal GAN discriminator in practice. Therefore, we expect that improving the discriminator performance boosts the final inception score even more substantially. , and the acceptance probability assigned to each sample x i by DRS versus the maximum probability of belonging to one of the 1K categories based on a pre-trained Inception network, max j p(y j |x i ) (right).",1453,0.781,861,1.6875725900116143,"We propose a rejection sampling scheme of a GAN approximately correct errors We show under quite strict assumptions this will allow recover the data distribution exactly We then examine where those strict assumptions break design a practical algorithm—called Discriminator Rejection Sampling on Finally demonstrate DRS on a mixture Gaussians on the state the art SAGAN model On ImageNet train an improved baseline that increases the best published Inception Score 52.52 reduces the Frechet Inception Distance We then use DRS further improve on this baseline improving the Inception Score 76.08 the FID to Generative Adversarial Networks (GANs) BID5 are image synthesis They also applied successfully semisupervised and BID25 BID20 BID11 , image editing image style transfer Informally the GAN training procedure pits a generator The discriminator trained samples the target distribution the generator The generator trained fool its outputs real The GAN training procedure thus a two-player differentiable game the game dynamics largely what distinguishes the study These game dynamics well-known and heavily studied stability issues Addressing an active area BID17 BID7 .However , interested studying something Instead trying improve the training procedure ( accept its flaws attempt trained generators post their samples information the trained discriminator It well (under certain very strict assumptions the equilibrium this training procedure reached sampling from the generator identical and always outputs However these assumptions do In particular , GANs as presently trained do learn reproduce the target distribution BID1 Moreover trained GAN discriminators are identically 1/2 -they perform chess-type skill ratings of other trained generators .We ask the information retained the weights at ""improve At face value unlikely After all useful information left the discriminator does find via the training procedure Further reflection. First the assumptions various analyses the training procedure surely do ( the discriminator and generator have finite capacity optimized parameter space rather density-space Second due the concrete realization the discriminator the generator as neural networks it harder model a given distribution tell that being precisely Finally may simply not train GANs long in practice computational reasonsIn focus using the discriminator part a probabilistic rejection sampling scheme In particular this paper makes the following contributions:• a rejection sampling scheme the GAN discriminator approximately correct errors under quite strict assumptions allows recover the data distribution then examine where those strict assumptions break design practical -called DRS takes this conduct demonstrating First as a baseline train an improved version the Self-Attention GAN improving from the best published Inception Score 52.52 up a Fréchet Inception Distance down We then show DRS yields further improvement this baseline increasing the Inception Score 76.08 decreasing the Fréchet Inception Distance We proposed a rejection sampling scheme using the GAN discriminator approximately correct errors the GAN generator distribution We shown under strict assumptions recover the data distribution exactly We also examined where those assumptions break Each row images synthesized interpolating in latent space The color bar above each row the acceptance probabilities: red for high Subjective visual quality samples with high acceptance probability considerably: objects coherent recognizable belonging There fewer indistinct textures fewer scenes without recognizable objects • There our scheme only GAN generators It worth investigating rejection sampling VAE decoders This seems help VAEs may trouble ""spreading mass around too much.• In one ideal case the critic used for rejection sampling a human. Can use better proxies the human visual system rejection sampling's effect image synthesis models?• It theoretically characterize rejection sampling under the breakdown that In addition , represent Inception score acceptance rate FIG5 -left Different acceptance rates achieved changing �� from 0 th Fx (acceptance 14 Decreasing the acceptance rate filters more non-realistic samples increases the final Inception score After an specific rate rejecting more samples does gain collecting a better poolMoreover FIG5 -right shows the correlation the acceptance probabilities that DRS assigns from the view-point a pre-trained Inception network latter measured computing max j p(y j |x i which sample belonging the category from the 1,000 ImageNet classes As expected a large mass the recognizable images accepted with high acceptance probabilities on The small mass images which easily classified one while having high acceptance probability scoresthe top left corner due the non-optimal GAN discriminator in practice Therefore expect improving the discriminator performance boosts the final inception score even substantially , the acceptance probability assigned x i by DRS versus belonging the 1K categories based a pre-trained Inception network max j p(y j |x (right",0.01,0.45595371956616015
"The quality of the features used in visual recognition is of fundamental importance for the overall system. For a long time, low-level hand-designed feature algorithms as SIFT and HOG have obtained the best results on image recognition. Visual features have recently been extracted from trained convolutional neural networks. Despite the high-quality results, one of the main drawbacks of this approach, when compared with hand-designed features, is the training time required during the learning process. In this paper, we propose a simple and fast way to train supervised convolutional models to feature extraction while still maintaining its high-quality. This methodology is evaluated on different datasets and compared with state-of-the-art approaches. The design of high-quality image features is essential to vision recognition related tasks. They are needed to provide high accuracy and scalability on processing large image data. Many approaches to building visual features have been proposed such as dictionary learning that aims to find a sparse representation of the data in the form of a linear combination of fundamental elements called atoms BID5 . Scattering approaches provide mathematical frameworks to build geometric image priors BID11 . Unsupervised bag of words methods identifies object categories using a corpus of unlabeled images BID15 . Unsupervised deep learning techniques are also used to extract features by using neural networks based models with many layers and frequently trained using contrastive divergence algorithms BID6 . All of them have been shown to improve the results of hand-crafted designed feature vectors such as SIFT BID10 or HOG BID1 with promising results BID0 BID11 .Another recent but very successful alternative is to use supervised Convolutional Neural Networks (CNN) to extract high-quality image features BID12 . These models take into consideration that images are symmetrical by a shift in position and therefore weight sharing and selective fields techniques are used to create filter banks that extract geometrically related features from the image dataset. The process is composed hierarchically over many layers to obtain higher level features after each layer. The network is typically trained using gradient backpropagation techniques. After the CNN training, the last layer (usually a fully connected layer) is removed to provide the learned features.A drawback of this approach is the time needed to thoroughly train a CNN to obtain high accuracy results. In this paper , we propose the Simple Fast Convolutional (SFC) feature learning technique to significantly reduce the time required to learning supervised convolutional features without losing much of the representation performance presented by such solutions. To accelerate the training time, we consider few training epochs combined with fast learning decay rate.To evaluate the proposed approach we combined SFC and alternative features methods with classical classifiers such as Support Vector Machines (SVM) BID18 and Extreme Learning Machines (ELM) . The results show that SFC provides better performance than alternative approaches while significantly reduces the training time. We evaluated the alternative feature methods over the MNIST (Lecun & Cortes) , CIFAR-10 and CIFAR-100 BID4 ). In this paper, we showed that convolutional feature learning can be performed in a fast way. Moreover, despite being very fast, it is still capable of generating representations that present better performance than other approaches. The proposed method is also flexible enough since a compromise can be obtained between the speed of the training and the final solution test accuracy. Naturally, the difference in test accuracy presented in this paper could be even greater if more training time is allowed to be used.We emphasize that transfer learning techniques can be used to extend the application of the proposed method. Finally, we show that despite efforts to the contrary, supervised convolutional method still provides state-of-the-art results for image feature generation. Moreover, the experiments showed that a quick change in the learning rate decay is a valid method to speed up the training of deep neural networks significantly.",752,0.451,435,1.728735632183908,"The quality the features used visual recognition of the overall system For low handdesigned feature algorithms as SIFT HOG obtained image recognition Visual features have recently extracted Despite one, when hand-designed features the training time during In train feature extraction while This methodology evaluated different datasets compared state approaches The design high-quality image features essential vision recognition related tasks They needed provide high accuracy on processing large image data Many approaches building visual features such dictionary learning that aims find a sparse representation a linear combination fundamental elements called atoms BID5 . Scattering approaches provide mathematical frameworks geometric image priors BID11 . Unsupervised bag of words methods identifies object categories a corpus unlabeled images BID15 . Unsupervised deep learning techniques also extract features by neural networks based models with many layers frequently trained using contrastive divergence BID6 . All shown improve the results hand-crafted designed feature vectors such SIFT BID10 HOG with promising results BID0 .Another recent but very successful alternative extract These models take into images symmetrical by a shift position therefore weight sharing selective fields techniques filter banks extract The process composed hierarchically over to obtain higher level features after The network typically trained using gradient backpropagation techniques After the CNN training the last layer (usually a fully connected layer provide the learned featuresA drawback thoroughly a CNN to obtain high accuracy results In , the Simple Fast Convolutional ( feature learning technique significantly learning without losing much the representation performance presented such solutions To accelerate the training time consider few training epochs combined fast learning decay rateTo evaluate the proposed approach combined SFC alternative features methods classical classifiers Support BID18 Extreme Learning Machines . The results show SFC provides alternative approaches while significantly reduces We evaluated the alternative feature methods over the MNIST (Lecun & Cortes , BID4 ). In showed convolutional feature learning Moreover despite very fast capable generating representations present better performance other approaches The proposed method also flexible since a compromise obtained the speed the training the final solution test accuracy Naturally the difference test accuracy presented could even more training time allowedWe emphasize transfer learning techniques extend the proposed method Finally show despite efforts the contrary supervised convolutional method still provides state results image feature generation Moreover the experiments a quick change the learning rate decay is a valid method speed significantly",0.0,0.5608335344758228
"We develop a framework for understanding and improving recurrent neural networks (RNNs) using max-affine spline operators (MASOs). We prove that RNNs using piecewise affine and convex nonlinearities can be written as a simple piecewise affine spline operator. The resulting representation provides several new perspectives for analyzing RNNs, three of which we study in this paper. First, we show that an RNN internally partitions the input space during training and that it builds up the partition through time. Second, we show that the affine slope parameter of an RNN corresponds to an input-specific template, from which we can interpret an RNN as performing a simple template matching (matched filtering) given the input. Third, by carefully examining the MASO RNN affine mapping, we prove that using a random initial hidden state corresponds to an explicit L2 regularization of the affine parameters, which can mollify exploding gradients and improve generalization. Extensive experiments on several datasets of various modalities demonstrate and validate each of the above conclusions. In particular, using a random initial hidden states elevates simple RNNs to near state-of-the-art performers on these datasets. Recurrent neural networks (RNNs) are a powerful class of models for processing sequential inputs and a basic building block for more advanced models that have found success in challenging problems involving sequential data, including sequence classification (e.g., sentiment analysis BID30 , sequence generation (e.g., machine translation BID1 ), speech recognition BID10 , and image captioning BID22 . Despite their success, however, our understanding of how RNNs work remains limited. For instance, an attractive theoretical result is the universal approximation property that states that an RNN can approximate an arbitrary function BID28 BID29 BID11 . These classical theoretical results have been obtained primarily from the dynamical system BID29 BID28 and measure theory BID11 perspectives. These theories provide approximation error bounds but unfortunately limited guidance on applying RNNs and understanding their performance and behavior in practice.In this paper, we provide a new angle for understanding RNNs using max-affine spline operators (MASOs) BID21 BID12 ) from approximation theory. The piecewise affine approximations made by compositions of MASOs provide a new and useful framework to study neural networks. For example, BID4 ; BID2 have provided a detailed analysis in the context of feedforward networks. Here, we go one step further and find new insights and interpretations from the MASO perspective for RNNs. We will see that the input space partitioning and matched filtering links developed in BID4 ; BID2 extend to RNNs and yield interesting insights into their inner workings. Moreover, the MASO formulation of RNNs enables us to theoretically justify the use of a random initial hidden state to improve RNN performance.For concreteness, we focus our analysis on a specific class of simple RNNs BID8 with piecewise affine and convex nonlinearities such as the ReLU BID9 . RNNs with such nonlinearities have recently gained considerable attention due to their ability to combat the exploding gradient problem; with proper initialization BID19 BID33 and clever parametrization of the recurrent weight BID0 BID39 BID16 BID15 BID24 BID13 , these RNNs achieve performance on par with more complex ones such as LSTMs. Below is a summary of our key contributions. Contribution 1. We prove that an RNN with piecewise affine and convex nonlinearities can be rewritten as a composition of MASOs, making it a piecewise affine spline operator with an elegant analytical form (Section 3).Contribution 2. We leverage the partitioning of piecewise affine spline operators to analyze the input space partitioning that an RNN implicitly performs. We show that an RNN calculates a new, high-dimensional representation (the partition code) of the input sequence that captures informative underlying characteristics of the input. We also provide a new perspective on RNN dynamics by visualizing the evolution of the RNN input space partitioning through time (Section 4).Contribution 3. We show the piecewise affine mapping in an RNN associated with a given input sequence corresponds to an input-dependent template, from which we can interpret the RNN as performing greedy template matching (matched filtering) at every RNN cell (Section 5).Contribution 4. We rigorously prove that using a random (rather than zero) initial hidden state in an RNN corresponds to an explicit regularizer that can mollify exploding gradients. We show empirically that such a regularization improves RNN performance (to state-of-the-art) on four datasets of different modalities (Section 6). We have developed and explored a novel perspective of RNNs in terms of max-affine spline operators (MASOs). RNNs with piecewise affine and convex nonlinearities are piecewise affine spline operators with a simple, elegant analytical form. The connections to input space partitioning (vector quantization) and matched filtering followed immediately. The spline viewpoint also suggested that the typical zero initial hidden state be replaced with a random one that mollifies the exploding gradient problem and improves generalization performance.There remain abundant promising research directions. First, we can extend the MASO RNN framework following BID3 to cover more general networks like gated RNNs (e.g, GRUs, LSTMs) that employ the sigmoid nonlinearity, which is neither piecewise affine nor convex. Second, we can apply recent random matrix theory results BID23 to the affine parameter A RNN (e.g., the change of the distribution of its singular values during training) to understand RNN training dynamics. t th time step of a discrete time-serie, DISPLAYFORM0 x Concatenation of the whole length T time-serie: DISPLAYFORM1 Output/prediction associated with input x y n True label (target variable) associated with the nth time-serie example x n . For classification y n ∈ {1, . . . , C}, C > 1; For regression y n ∈ R C , C ≥ 1 DISPLAYFORM2 Output of an RNN cell at layer and time step t; Alternatively, input to an RNN cell at layer + 1 and time step t − 1 DISPLAYFORM3 Concatenation of hidden state h ( ,t) of all time steps at layer : DISPLAYFORM4 Concatenated input to an RNN cell at layer and time step t: DISPLAYFORM5 th layer RNN weight associated with the input h ( ,t−1) from the previous time step: DISPLAYFORM6 th layer RNN weight associated with the input h ( −1,t) from the previous layer: DISPLAYFORM7 Bias of the last fully connected layer: DISPLAYFORM8 Pointwise nonlinearity in an RNN (assumed to be piecewise affine and convex in this paper) σ Standard deviation of noise injected into the initial hidden state h DISPLAYFORM9 MASO formula of the RNN activation σ(·) at layer and time step t: DISPLAYFORM10 MASO parameters of an RNN at layer and time step t: DISPLAYFORM11",1435,0.668,812,1.7672413793103448,"We develop understanding improving max-affine spline operatorsMASOs We prove RNNs using piecewise affine and convex nonlinearities written The resulting representation provides several new perspectives analyzing RNNs three we study First show an RNN internally partitions during training builds through time Second show that the affine slope parameter an RNN corresponds an input-specific template from interpret performing a simple template matchingmatched filtering given Third by carefully the MASO RNN affine mapping prove using a random initial hidden state corresponds an explicit L2 regularization mollify exploding gradients improve Extensive experiments several datasets various modalities demonstrate and each In particular using a random initial hidden states elevates simple RNNs near state performers on these datasets Recurrent neural networks a powerful class models processing sequential inputs a basic building block more advanced models have found success challenging problems involving sequential data, sequence classification sentiment BID30 , sequence generation ( image . Despite however our understanding RNNs work For instance an attractive theoretical result the universal approximation property states an RNN approximate BID28 BID29 BID11 These classical theoretical results obtained primarily BID29 BID28 measure theory BID11 perspectives These theories provide approximation error bounds but unfortunately limited guidance applying understanding behaviorIn a new angle max-affine spline operatorsMASOs BID21 BID12 ) from approximation theory The piecewise affine approximations made compositions MASOs provide For example BID4 ; have provided a detailed analysis in feedforward networks Here go one find new insights interpretations the MASO perspective for RNNs see the input space partitioning matched filtering links developed BID4 ; extend yield Moreover the MASO formulation RNNs enables theoretically justify a random initial hidden state improveFor concreteness focus a specific class simple RNNs BID8 with piecewise affine and such . RNNs with such nonlinearities recently gained combat the exploding gradient problem; with proper initialization BID19 BID33 clever parametrization , achieve performance on par more complex ones Below our key contributions Contribution 1 We prove an RNN with piecewise affine and rewritten a composition MASOs making spline operator an elegant analytical formSection 3).Contribution 2 We leverage the partitioning piecewise affine spline operators analyze the input space that an RNN implicitly We show an RNN calculates (the partition code captures informative underlying characteristics We also provide a new perspective RNN dynamics partitioning throughSection 4).Contribution 3 We show the piecewise affine mapping an RNN associated given input sequence corresponds an input-dependent template from interpret performing greedy template matchingmatched filtering at every RNN cellSection 5).Contribution 4 We rigorously prove using a random (rather than zero) initial hidden state an RNN corresponds an explicit regularizer mollify exploding gradients We show empirically such a regularization improves RNN performanceto state- four datasets different modalitiesSection We developed explored a novel perspective RNNs terms max-affine spline operatorsMASOs RNNs with piecewise affine and piecewise affine spline operators a simple, elegant analytical form The connections input space partitioningvector quantization matched filtering followed immediately The spline viewpoint also suggested the typical zero initial hidden state be replaced mollifies the exploding gradient problem improves generalization performanceThere remain abundant promising research directions First can extend the MASO RNN framework following BID3 to cover more general networks like gated RNNs, GRUs employ, neither piecewise affine Second apply recent random matrix theory results BID23 the affine parameter A RNN its singular values during training understand RNN training dynamics t th time step of a discrete time-serie DISPLAYFORM0 x Concatenation: DISPLAYFORM1 Output/prediction associated input x y n True labeltarget variable associated . For classification y n � { . . . , C}, > For regression y n � R C ≥ 1 DISPLAYFORM2 Output an RNN cell at layer and time step t; Alternatively input + − hidden state h ( ,t : input th layer RNN weight associated h from the last fully connected layer (assumed piecewise affine and this paper �� Standard deviation noise injected the initial hidden state h DISPLAYFORM9 MASO formula(· at MASO parameters",0.01,0.6589427950760319
"Reasoning over text and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering.  Transducing text to logical forms which can be operated on is a brittle and error-prone process . Operating directly on text by jointly learning representations and transformations thereof by means of neural architectures that lack the ability to learn and exploit general rules can be very data-inefficient and not generalise correctly . These issues are addressed by Neural Theorem Provers (NTPs) (Rocktäschel & Riedel, 2017), neuro-symbolic systems based on a continuous relaxation of Prolog’s backward chaining algorithm, where symbolic unification between atoms is replaced by a differentiable operator computing the similarity between their embedding representations . In this paper, we first propose Neighbourhood-approximated Neural Theorem Provers (NaNTPs) consisting of two extensions toNTPs, namely a) a method for drastically reducing the previously prohibitive time and space complexity during inference and learning, and b) an attention mechanism for improving the rule learning process, deeming them usable on real-world datasets. Then, we propose a novel approach for jointly reasoning over KB facts and textual mentions, by jointly embedding them in a shared embedding space. The proposed method is able to extract rules and provide explanations—involving both textual patterns and KB relations—from large KBs and text corpora. We show that NaNTPs perform on par with NTPs at a fraction of a cost, and can achieve competitive link prediction results on challenging large-scale datasets, including WN18, WN18RR, and FB15k-237 (with and without textual mentions) while being able to provide explanations for each prediction and extract interpretable rules. The main focus in Artificial Intelligence is building systems that exhibit intelligent behaviour BID38 . In particular, Natural Language Understanding (NLU) and Machine Reading (MR) aim at building models and systems with the ability to read text, extract meaningful knowledge, and actively reason with it BID18 BID45 . This ability enables both the synthesis of new knowledge and the possibility to verify and update a given assertion. For example, given the following statement:The River Thames is in the United Kingdom. NTPs combine the strengths of rule-based and neural models but, so far, they were unable to reason over large KBs, and therefore over natural language.In this paper, we proposed NaNTPs that utilise ANNS and attention as a solution to scaling issues of NTP. By efficiently considering only the subset of proof paths associated with the highest proof scores during the construction of a dynamic computation graph, NaNTPs yield drastic speedups and memory efficiency, while yielding the same or a better predictive accuracy than NTPs. This enables application of NaNTPs to mixed KB and natural language data by embedding logic atoms and textual mentions in a joint embedding space.Albeit results are still slightly lower than those yielded by state-of-the-art Neural Link Predictors on large datasets, NaNTPs is interpretable and is able to provide explanations of its reasoning at scale.",635,0.277,374,1.6978609625668448,"Reasoning over text Knowledge BasesKBs Artificial Intelligence applications machine reading dialogue question Transducing text logical forms which operated is . Operating directly text by jointly learning representations transformations thereof neural architectures lack learn exploit general rules can datainefficient not generalise correctly . These issues Neural Theorem ProversRocktäschel 2017 neuro-symbolic systems based a continuous relaxation Prolog��s backward chaining algorithm where symbolic unification between atoms replaced a differentiable operator computing the similarity their embedding representations . In first propose Neighbourhood-approximated Neural Theorem ProversNaNTPs consisting two extensions toNTPs) a method drastically the previously prohibitive time and space complexity during inference learning improving the rule learning process deeming usable on Then propose jointly reasoning over KB facts textual mentions jointly The proposed method able extract rules provide explanations— both textual patterns KB relations large KBs text corpora We show NaNTPs perform on par at a cost can competitive link prediction results challenging WN18 FB15k-237 (with and textual mentions while being provide explanations each prediction extract interpretable rules The main focus Artificial Intelligence building exhibit BID38 . In particular Natural Language Understanding Machine Reading aim building models systems with extract meaningful knowledge actively reason with BID18 BID45 . This ability enables both the synthesis new knowledge the possibility verify update a given assertion For example givenThe River Thames in NTPs combine rule-based and neural models but, so were reason over large KBs over natural languageIn proposed that ANNS attention as scaling By efficiently considering only the subset proof paths associated the highest proof scores during a dynamic computation graph NaNTPs yield drastic speedups memory efficiency, yielding or a better predictive accuracy enables application mixed KB natural language data by logic atoms textual mentions a joint embedding spaceAlbeit results slightly lower yielded state Neural Link Predictors on large datasets is interpretable explanations its reasoning at",0.0,0.4821675889103584
"We investigate the methods by which a Reservoir Computing Network (RCN) learns concepts such as 'similar' and 'different' between pairs of images using a small training dataset and generalizes these concepts to previously unseen types of data. Specifically, we show that an RCN trained to identify relationships between image-pairs drawn from a subset of digits from the MNIST database or the depth maps of subset of visual scenes from a moving camera generalizes the learned transformations to images of digits unseen during training or depth maps of different visual scenes. We infer, using Principal Component Analysis, that the high dimensional reservoir states generated from an input image pair with a specific transformation converge over time to a unique relationship. Thus, as opposed to training the entire high dimensional reservoir state, the reservoir only needs to train on these unique relationships, allowing the reservoir to perform well with very few training examples. Thus, generalization of learning to unseen images is interpretable in terms of clustering of the reservoir state onto the attractor corresponding to the transformation in reservoir space. We find that RCNs can identify and generalize linear and non-linear transformations, and combinations of transformations, naturally and be a robust and effective image classifier. Additionally, RCNs perform significantly better than state of the art neural network classification techniques such as deep Siamese Neural Networks (SNNs) in generalization tasks both on the MNIST dataset and more complex depth maps of visual scenes from a moving camera. This work helps bridge the gap between explainable machine learning and biological learning through analogies using small datasets, and points to new directions in the investigation of learning processes. Different types of Artificial Neural Networks (ANNs) have been used through time for the task of object recognition and classification. Feed-forward structures, such as convolutional neural networks, deep learning BID17 , stacked auto encoders etc. have been extensively studied and are the state of the art for classification. These architectures are well understood due to their feed-forward and non-dynamic nature.However, biological systems such as the visual cortex are known to have primarily ( 70 %) recurrent connections BID2 with less than 1 % of the connections being feedforward Da Costa and Martin (2009). RCN's (or closely related models) provides explanations of why biological brains can carry out accurate computations with an 'inaccurate' and noisy physical substrate BID11 , especially accurate timing BID16 , of the way in which visual spatio-temporal information is super-imposed and processed in primary visual cortex Danko Nikoli c and Maas (2006); BID1 . In addition, biological systems learn visual concepts through analogies, using only a handful of examples BID20 . In particular, in BID9 , bees were trained to fly towards the image from a pair of images that looked very similar to a previously displayed base image. On training bees to fly towards the visually similar image, the bees were presented with two scents, one very similar and one different from a base scent. As a consequence of the visual training that induced preference to the very similar category, the bees flew towards the very similar scent. Thus, biological systems have been found to translate learning of concepts of similarity across sensory inputs, leading us to believe that the brain has a common and fundamental mechanism that comprehends through analogies or through concepts of 'similarity'.Deriving inspiration from nature, we hope to develop a biologically plausible learning technique that learns through analogies.In our framework, we refer to generalization as the ability of a system to learn the relationships or transformations, both linear and non-linear, between a pair of images and be able to recognize the same transformation in unseen image-pairs. Feed-forward networks have, to the best of our knowledge, not been successful in developing an explainable model for this type of generalization of learning. In addition, learning of stand-alone images without drawing comparisons isn't biologically plausible. Networks that require large datasets and hence increasingly powerful GPUs do not scale well. It seems reasonable to say that humans learn through comparitively few training examples BID8 . For instance, a child would learn the features of a horse and the difference between a horse and a donkey, simply by observing at a handful of examples, contrary to deep learning. While research in learning from very few images, one shot learning BID23 etc. has gained momentum recently, integrating it with generalization of learning is a relatively unexplored area.In the ground-breaking work of BID12 , the success of Recurrent Neural Networks (RNNs) depend on the existence of attractors. In training, the dynamical system of the RNN is left running until it ends up in one of its several attractors. Similarly, in BID14 , a unique conceptor is found for each input pattern in a driven RNN. However, training of RNNs is difficult due to problems like the vanishing gradient. BID3 showed that much slower dynamics can be introduced in the RNN by using a random network of neurons with short term plasticity, thus allowing the system to work with training of only the output weights. Exploiting this property, Echo State Networks (ESN) BID13 and Liquid State Machine (LSM) BID18 , commonly falling under Reservoir Computing (RC) were introduced. RC is appealing because of its dynamical property and easy scalability since the recurrent connections in the network aren't trained. Applications of RC include many real world phenomena such as weather or stock market prediction, self driven cars, speech processing and language interpretation, gait generation and motion control in robots etc. RCNs and RNNs perform very well for generating chaotic dynamics BID15 . Models of spontaneously active neural circuits typically exhibit chaotic dynamics, as in RCNs BID19 . Such chaotic dynamics is found in spiking models of spontaneous activity in cortical circuits BID21 .In this work, we train RCNs on both the MNIST handwritten digit database as proof of concept as well as depth maps of visual scenes from a moving camera, to study generalization of the learned transformations between pairs of images. We classify pairs of images into very similar, rotated, zoomed , blurred or different. The reservoir activity is then studied to reveal the underlying features of the activity that are responsible for classification. We find that the relationships between reservoirstate pairs corresponding to input image pairs converge for image pairs with a common relationship between them. In other words, the reservoir only learns relationships between the images , not features of the individual images themselves. This allows for generalization of the learned relationships to all image pairs, seen and unseen by the reservoir. Additionally we compare its performance for a generalization task to a pair-based deep siamese neural network (SNN) built on the keras implementation and show that the reservoir performs significantly better, both for simpler MNIST images as well as for depth maps . We also show that the reservoir is able to recognize linear combinations of the individuals transformations it has learned. This work can useful in the field of computer vision to identify similar transformations between images, even if they are non-linear as in a moving camera, in a biological plausible and computationally efficient way. In this paper we have used RCNs to solve a class of image classification problems that generalize learning of relationships between images using a rather small training data. While image classification has been studied extensively before, here we present a biologically plausible method that not only generalizes learning, but also allows us to interpret the results analytically through a dynamical systems lens. We see that the differential reservoir states obtained from input image-pairs with a common transformation have principal components that are aligned closer together. From a dynamical systems perspective, this can be interpreted as the existence of attractors in reservoir space, each corresponding to a given image transformation. Thus, by reducing the dimensionality of the reservoir space, the reservoir as a dynamical system allows us to train on a much smaller training dataset, whereas contemporary methods such as deep learning require much larger datasets due partly to the lack of dynamics. This same property also allows the reservoir to generalizes the relationships learned to images it hasn't seen during training.In a reservoir, the image space is mapped onto the reservoir space in a way as to preserve the locality of common transformations in reservoir space. In addition, the reservoir performs significantly better than a deep SNN for the task of generalization. From a computation perspective, the reservoir is fast since only the output weights are being trained and the reservoir is sparsely connected. Further, we argue that our method is biologically plausible primarily due to the learning technique based on learning using concepts of similarity from a small training, and secondly due to the dynamics of the reservoir that have been shown to resemble neural cortex activity. We conclude that although state of the art machine learning techniques such as SNNs work exceedingly well for image classification, they do not work as well for generalization of learning, for whch RCNs outperform them, due to their ability to function as a dynamical system with 'memory'. Thus, we see the strength of our work as lying in not only its ability to generalize to untrained images, but also our ability to explain this in terms of the reservoir dynamics and PCA. This relates to new ideas in explainable Artificial Intelligence, a topic that continues to receive traction. An interesting direction would be to explore different reservoir architectures that model the human brain better. Another interesting direction would be to use RCNs to study videos which are naturally temporal, and and investigate how the reservoir generalizes in the action domain. Finally, although we get a fairly good performance with a sparse reservoir and few training images, we predict that as the image complexity increases, a more sophisticated reservoir would be required to match performance.",1954,1.017,1143,1.709536307961505,"We investigate the methods a Reservoir Computing Network learns concepts 'similar between pairs images using a small training dataset generalizes previously unseen types Specifically show an RCN trained identify relationships image-pairs drawn digits from or the depth maps subset visual scenes a moving camera generalizes the learned transformations digits unseen during training or depth maps We infer, using the high dimensional reservoir states generated an input image pair with a specific transformation converge over a unique relationship Thus as opposed training the entire high dimensional reservoir state only train on these unique relationships allowing perform very few training examples Thus generalization learning unseen images interpretable clustering the reservoir state onto the attractor corresponding the transformation reservoir space We find RCNs identify generalize combinations naturally be a robust and effective image classifier Additionally RCNs perform significantly state of deep Siamese Neural Networks generalization tasks both visual scenes from a moving camera This work helps bridge explainable machine learning biological learning through analogies using small datasets points the investigation learning processes Different types Artificial Neural Networks through time Feed-forward structures deep BID17 , stacked auto encoders etc have extensively are the state classification These architectures well understood dueHowever biological systems known primarily ( 70 % recurrent connections BID2 with being feedforward Da Costa Martin2009 RCN (or closely related models provides explanations biological brains carry accurate computations with an ' and noisy physical substrate BID11 , especially accurate timing BID16 of visual spatio super-imposed and primary visual cortex Danko Nikoli c and Maas2006 . In addition biological systems learn visual concepts analogies using only a handful examples BID20 . In particular in BID9 , bees trained fly towards the image from a pair images looked a previously displayed base image On training bees towards the visually similar image presented two scents very different a base scent As the visual training induced preference the very similar category the bees flew towards the very similar scent Thus biological systems found translate learning of concepts of similarity across sensory inputs leading us comprehends through or through concepts 'Deriving inspiration nature hope a biologically plausible learning technique learnsIn our framework refer generalization the relationships or transformations, both linear images be recognize the same transformation unseen image-pairs Feed-forward networks, to successful developing an explainable model this type generalization learning In addition learning stand-alone images without drawing comparisons is biologically Networks require large datasets hence increasingly powerful GPUs do scale It reasonable humans learn through comparitively few training examples BID8 . For instance a child would learn the features a horse the difference simply at a handful examples contrary deep learning While research learning from very few images one shot learning BID23 etc has gained momentum recently integrating it generalization learning isIn BID12 , the success depend attractors In training the dynamical system left running until ends one its several attractors Similarly BID14 , a unique conceptor found each input pattern a driven RNN However training RNNs difficult problems like the vanishing gradient BID3 showed much slower dynamics introduced the RNN a random network short term plasticity thus work training only the output weights Exploiting this property Echo State Networks BID13 and Liquid State Machine (LSM) BID18 , commonly falling Reservoir Computing were introduced RC is appealing because its dynamical property easy scalability since the recurrent connections are trained Applications RC include many real world phenomena weather or stock market prediction self driven cars speech processing language interpretation gait generation in robots etc RCNs perform very generating chaotic dynamics BID15 . Models spontaneously active neural circuits typically chaotic dynamics RCNs BID19 . Such chaotic dynamics is found spiking models spontaneous activity cortical circuits BID21 .In train RCNs both the MNIST handwritten digit database proof depth maps visual scenes a moving camera study generalization the learned transformations pairs We classify pairs images very, rotated , blurred different. The reservoir activity then studied reveal the underlying features classification We find the relationships reservoirstate pairs corresponding input image pairs converge a common relationship In the reservoir only learns relationships the images , features individual themselves This allows generalization the learned relationships all image pairs seen and the reservoir Additionally we compare its performance for a generalization task a pair-based deep siamese neural network built the keras implementation show the reservoir performs, both simpler MNIST images depth maps . We also show the reservoir able recognize linear combinations the individuals transformations it learned This work can useful to similar transformations even non as a moving camera a biological plausible and computationally efficient way In RCNs solve generalize learning relationships a rather small training data. While image classification studied before here not generalizes learning interpret through a dynamical systems lens We see the differential reservoir states obtained input image-pairs a common transformation have principal components aligned closer From a dynamical systems perspective can interpreted the existence attractors reservoir space each corresponding a given image transformation Thus by reducing the reservoir space as allows train on a much smaller training dataset whereas contemporary methods due partly dynamics This same property allows the reservoir generalizes the relationships learned to images it has during trainingIn a reservoir mapped as preserve common transformations reservoir space In addition the reservoir performs significantly a deep SNN for the task generalization From a computation perspective the reservoir fast since only the output weights being trained sparsely connected Further argue our method biologically primarily the learning technique based learning using concepts similarity from a small training, secondly the dynamics the reservoir have resemble neural cortex activity We conclude although state of such SNNs work exceedingly learning whch RCNs them due function 'memory Thus the strength our work lying generalize untrained images explain this the reservoir dynamics PCA This relates new ideas explainable Artificial Intelligence continues receive traction An interesting direction would explore different reservoir architectures model better Another interesting direction would RCNs study videos which naturally temporal and investigate reservoir generalizes the action domain Finally although get a fairly good performance a sparse reservoir few training images predict as image complexity a more sophisticated reservoir match performance",0.01,0.5119153431913219
"We present Generative Adversarial Privacy and Fairness (GAPF), a data-driven framework for learning private and fair representations of the data. GAPF leverages recent advances in adversarial learning to allow a data holder to learn ""universal"" representations that decouple a set of sensitive attributes from the rest of the dataset. Under GAPF, finding the optimal decorrelation scheme is formulated as a constrained minimax game between a generative decorrelator and an adversary. We show that for appropriately chosen adversarial loss functions, GAPF provides privacy guarantees against strong information-theoretic adversaries and enforces demographic parity. We also evaluate the performance of GAPF on multi-dimensional Gaussian mixture models and real datasets, and show how a designer can certify that representations learned under an adversary with a fixed architecture perform well against more complex adversaries. The use of deep learning algorithms for data analytics has recently seen unprecedented success for a variety of problems such as image classification, natural language processing, and prediction of consumer behavior, electricity use, political preferences, to name a few. The success of these algorithms hinges on the availability of large datasets, that often contain sensitive information, and thus, may facilitate learning models that inherit societal biases leading to unintended algorithmic discrimination on legally protected groups such as race or gender. This, in turn, has led to privacy and fairness concerns and a growing body of research focused on developing representations of the dataset with fairness and/or privacy guarantees. These techniques predominantly involve designing randomizing schemes, and in recent years, distinct approaches with provable statistical privacy or fairness guarantees have emerged.In the context of privacy, preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. While context-free privacy solutions, such as differential privacy BID10 a; BID7 BID8 , provide strong worst-case privacy guarantees, they often lead to a significant reduction in utility. In contrast, context-aware privacy solutions, e.g., mutual information privacy BID31 BID5 BID33 BID32 BID3 ), achieve improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics.In the context of fairness, machine learning models seek to maximize predictive accuracy. Fairness concerns arise when models learned from datasets that include patterns of societal bias and discrimination inherit such biases. Thus, there is a need for actively decorrelating sensitive and non-sensitive data. In the context of publishing datasets or meaningful representations that can be ""universally"" used for a variety of learning tasks, modifying the training data is the most appropriate and is the focus of this work. Fairness can then be achieved by carefully designing objective functions which approximate a specific fairness definition while simultaneously ensuring maximal utility (Zemel et al., 2013; BID6 BID16 . This, in turn, requires dataset statistics.Adversarial learning approaches for context-aware privacy and fairness have been studied extensively BID13 BID0 BID30 BID20 BID36 BID4 BID27 Zhang et al., 2018) . They allow the data curator to cleverly decorrelate the sensitive attributes from the rest of the dataset. These approaches overcome the lack of statistical knowledge by taking a data-driven approach that leverages recent advancements in generative adversarial networks (GANs) BID17 BID28 . However, most existing efforts focus on extensive empirical studies without theoretical verification and focus predominantly on providing guarantees for a specific classification task. This work introduces a general framework for context-aware privacy and fairness that we call generative adversarial privacy and fairness (GAPF) (see FIG0 . We provide precise connections to information-theoretic privacy and fairness formulations and derive game-theoretically optimal decorrelation schemes to compare against those learned directly from the data. While our framework can be generalized to learn an arbitrary representation using an encoder-decoder structure, this paper primarily focuses on learning private/fair representations of the data (of the same dimension).Our Contributions. We list our main contributions below.1. We introduce GAPF, a framework for creating private/fair representations of data using an adversarially trained conditional generative model. Unlike existing works, GAPF can create representations that are useful for a variety of classification tasks, without requiring the designer to model these tasks at training time. We validate this observation via experiments on the GENKI (Whitehill & Movellan, 2012) and HAR BID2 datasets.2. We show that via the choice of the adversarial loss function, our framework can capture a rich class of statistical and information-theoretic adversaries. This allows us to compare data-driven approaches directly against strong inferential adversaries (e.g., a maximum a posteriori probability (MAP) adversary with access to dataset statistics). We also show that by carefully designing the loss functions in the GAPF framework, we can enforce demographic parity.3. We make precise comparison between data-driven privacy/fairness methods and the minimax game-theoretic GAPF formulation. For Gaussian mixture data, we derive game-theoretically optimal decorrelation schemes and compare them with those that are directly learned in a datadriven fashion to show that the gap between theory and practice is negligible. Furthermore, we propose using mutual information estimators to verify that no adversary (regardless of their computational power) can reliably infer the sensitive attribute from the learned representation.Related work. In the context of publishing datasets with privacy and utility guarantees, a number of similar approaches have been recently considered. We briefly review them here. A detailed literature review is included in Appendix A. DP-based obfuscators for data publishing have been considered in BID18 BID26 . These novel approaches leverage non-generative minimax filters and deep auto-encoders to allow non-malicious entities to learn some public features from the filtered data, while preventing malicious entities from learning other sensitive features. However, DP can still incur a significant utility loss since it assumes worst-case dataset statistics. Our approach models a rich class of randomization-based schemes via a generative model that allows the generative decorrelator to tailor the noise to the dataset.Our work is closely related to adversarial neural cryptography BID0 , learning censored representations BID13 , privacy preserving image sharing BID30 , privacy-preserving adversarial networks BID36 , and adversarially learning fair representation BID27 in which adversarial learning is used to learn how to protect communications by encryption or hide/remove sensitive information or generate fair representation of the data. Similar to these problems, our model includes a minimax formulation and uses adversarial neural networks to learn decorrelation schemes that prevent an adversary from inferring the sensitive variable. However, most of these papers use non-generative auto-encoders to remove sensitive information. Instead, we use a GANs-like approach to learn decorrelation schemes . We also go beyond in formulating a game-theoretic setting subject to a distortion constraint which allows us to learn private/fair representation for a variety of learning tasks. Enforcing the distortion constraint calls for a new training process that relies on the Penalty method or Augmented Lagrangian method presented in Appendix C. We show that our framework captures a rich class of statistical and information-theoretic adversaries by changing the loss function. We also compare the performance of data-driven privacy/fairness methods and the minimax game-theoretic GAPF.Fair representations using information-theoretic objective functions and constrained optimization have been proposed in BID6 BID16 . However, both approaches require the knowledge of dataset statistics, which is very difficult to obtain for real datasets. We overcome the issue of statistical knowledge by taking a data-driven approach , i.e., learning the representation from the data directly via adversarial models. In contrast to in-processing approaches that modify learning algorithms to ensure fair predictions (e..g, using linear programs in BID11 BID14 or via adversarial learning approach in ( Zhang et al., 2018) ), we focus on a pre-processing approach to ensure fairness for a variety of learning tasks. Using GANs to generate synthetic non-sensitive attributes and labels which ensure fairness while preserving the utility of the data (predicting the label) has been studied in (Xu et al., 2018; BID34 . Rather than using a conditional-generative model to generate synthetic data, we focus on creating fair/private representations of the original data while preserving the utility of the representations for a variety of learning tasks by learning nonlinear compression and noise adding schemes via a generative adversarial model. We have introduced a novel adversarial learning framework for creating private/fair representations of the data with verifiable guarantees. GAPF allows the data holder to learn the decorrelation scheme directly from the dataset (to be published) without requiring access to dataset statistics. Under GAPF, finding the optimal decorrelation scheme is formulated as a game between two players: a generative decorrelator and an adversary. We have shown that for appropriately chosen loss functions, GAPF can provide guarantees against strong information-theoretic adversaries, such as MAP and MI adversaries. It can also enforce fairness, quantified via demographic parity by using the log-loss function. We have also validated the performance of GAPF on Gaussian mixture models and real datasets. There are several fundamental questions that we seek to address. An immediate one is to develop techniques to rigorously benchmark data-driven results for large datasets against computable theoretical guarantees. More broadly, it will be interesting to investigate the robustness and convergence speed of the decorrelation schemes learned in a data-driven fashion. In this paper, we connect our objective function in GAPF with demographic parity. Since there is no single metric for fairness, this leaves room for designing objective functions that link to other fairness metrics such as equalized odds and equal opportunity.",1957,1.02,1181,1.6570702794242167,"We present Generative Adversarial Privacy Fairness learning private and fair representations GAPF leverages recent advances adversarial learning allow a data holder ""universal"" representations decouple sensitive attributes Under GAPF finding the optimal decorrelation scheme formulated a constrained minimax game between a generative decorrelator an adversary We show for appropriately chosen adversarial loss functions GAPF provides privacy guarantees strong information-theoretic adversaries and enforces demographic parity We also evaluate GAPF real datasets a designer certify representations learned under an adversary with perform against more complex adversaries The use recently unprecedented success problems prediction electricity use political preferences to The success these algorithms hinges that often thus may facilitate learning models inherit societal biases leading unintended algorithmic discrimination on legally protected groups such race This, privacy and fairness concerns focused developing representations the dataset with fairness and/or privacy guarantees These techniques predominantly designing randomizing schemes distinct approaches with provable statistical privacy or fairness guaranteesIn preserving the utility published datasets while While context-free privacy solutions, differential privacy BID10 a; provide strong worst-case privacy guarantees lead utility In contrast, context-aware privacy solutions BID31 BID5 BID33 ), achieve improved privacy-utility tradeoff assume the data holder dataset statisticsIn fairness machine learning models seek Fairness concerns arise when models learned datasets include patterns societal bias discrimination inherit Thus actively decorrelating sensitive and non-sensitive data In publishing datasets or meaningful representations that "" learning tasks modifying is the focus Fairness can then carefully designing objective functions approximate a specific fairness definition while maximal utility (Zemel BID6 BID16 . This, requires dataset statisticsAdversarial learning approaches for context-aware privacy fairness studied BID13 BID0 Zhang 2018) . They allow the data curator cleverly decorrelate the sensitive attributes from the rest These approaches overcome statistical knowledge by taking recent advancements BID17 BID28 . However most existing efforts focus extensive empirical studies without theoretical verification focus predominantly providing guarantees a specific classification task This work introduces context-aware privacy fairness we FIG0 . We provide precise connections information-theoretic privacy fairness formulations derive game-theoretically optimal decorrelation schemes compare against those learned directly While our framework can generalized learn an arbitrary representation using this paper primarily private/fair representationsof the same dimension).Our Contributions. We list our main contributions below.1 We introduce GAPF private/fair representations using an adversarially trained conditional generative model Unlike existing works GAPF can create representations useful classification tasks without the designer model these tasks training time We validate this observation via experiments the GENKI (Whitehill & Movellan 2012 HAR BID2 datasets.2. via the choice the adversarial loss function our framework capture a rich class statistical and information-theoretic adversaries This allows compare directly strong inferential adversaries a maximum a probability ( access dataset statistics We also show by carefully designing the loss functions the GAPF framework enforce demographic parity.3. make precise comparison data-driven privacy/fairness methods For Gaussian mixture data derive game-theoretically optimal decorrelation schemes compare that directly learned a datadriven fashion show the gap theory Furthermore propose using mutual information estimators verify no adversary ( their computational power reliably the sensitive attribute the learned representationRelated work. In publishing datasets privacy and utility guarantees similar approaches recently We briefly review them A detailed literature review included DP-based obfuscators data publishing have considered BID18 BID26 . These novel approaches leverage non-generative minimax filters deep auto-encoders allow non-malicious entities learn some public features preventing other sensitive features However DP can incur a significant utility loss since assumes worst-case dataset statistics Our approach models a rich class randomization-based schemes via the generative decorrelator tailor the noiseOur work closely adversarial neural cryptography BID0 , learning censored representations BID13 privacy preserving image sharing learning fair representation BID27 in how protect communications by encryption hide/remove or generate Similar these problems our model includes a minimax formulation uses adversarial neural networks decorrelation schemes prevent the sensitive variable However most these papers use non-generative auto-encoders remove sensitive information Instead use a GANs-like approach learn decorrelation schemes . We also go beyond in formulating a game-theoretic setting subject a distortion constraint which learn private/fair representation learning tasks Enforcing the distortion constraint calls a new training process relies the Penalty method or Augmented Lagrangian method presented We show our framework captures a rich class statistical and information-theoretic adversaries by changing We also compare data-driven privacy/fairness methods the minimax game-theoretic GAPF.Fair representations using information-theoretic objective functions constrained optimization have BID6 BID16 . However both approaches require the knowledge dataset statistics very We overcome statistical knowledge taking , learning the representation from directly via In contrast inprocessing approaches modify learning ensure fair predictions.., using linear programs BID11 BID14 via adversarial learning approach ( Zhang et al 2018) focus ensure fairness Using GANs synthetic non-sensitive attributes labels which ensure fairness while the utility ( the label has studied ( 2018 BID34 . Rather using a conditional-generative model synthetic data focus creating fair/private representations while learning by learning nonlinear compression noise adding schemes via We introduced a novel adversarial learning framework creating private/fair representations with verifiable guarantees GAPF allows the data holder learn the decorrelation scheme directlyto published access dataset statistics Under GAPF finding the optimal decorrelation scheme formulated a game between a generative decorrelator an adversary We shown for appropriately chosen loss functions GAPF provide guarantees strong information-theoretic adversaries MAP and MI adversaries It can enforce fairness quantified via demographic parity by the log-loss function We also validated GAPF Gaussian mixture models real datasets There several fundamental questions seek An immediate one develop techniques rigorously benchmark against computable theoretical guarantees More broadly will investigate the robustness and convergence speed the decorrelation schemes learned In connect our objective function GAPF demographic parity Since there single metric fairness leaves room designing objective functions link other fairness metrics equalized odds equal opportunity",0.01,0.37823651209317694
"Current machine learning algorithms can be easily fooled by adversarial examples. One possible solution path is to make models that use confidence thresholding to avoid making mistakes. Such models refuse to make a prediction when they are not confident of their answer. We propose to evaluate such models in terms of tradeoff curves with the goal of high success rate on clean examples and low failure rate on adversarial examples. Existing untargeted attacks developed for models that do not use confidence thresholding tend to underestimate such models' vulnerability. We propose the MaxConfidence family of attacks, which are optimal in a variety of theoretical settings, including one realistic setting: attacks against linear models. Experiments show the attack attains good results in practice. We show that simple defenses are able to perform well on MNIST but not on CIFAR, contributing further to previous calls that MNIST should be retired as a benchmarking dataset for adversarial robustness research.   We release code for these evaluations as part of the cleverhans (Papernot et al 2018) library  (ICLR reviewers should be careful not to look at who contributed these features to cleverhans to avoid de-anonymizing this submission). We have made the following contributions:• We have shown that adversarial training on one kind of out-of-distribution data can actually worsen performance on other kinds of out-of-distribution data, relative to a baseline that uses confidence thresholding as the only defense.• We have introduced the evaluation methodology of success-fail curves, showing which success rates on clean data and failure rates on adversarial data are feasible for different confidence thresholds.• We have presented an attack that is optimal against a variety of confidence thresholding models. Specifically , it is optimal against linear classifiers and optimal against general models whenever the underlying optimization approximately succeeds.• We have shown an evaluation methodology that maps out an entire success-failure tradeoff curve without needing to re-train the model or re-run the evaluation for different thresholds.• We have shown that confidence thresholding with simple regularization is sufficient to achieve reasonable robustness to L ∞ attacks on MNIST, despite being roughly 40X cheaper to train than adversarial training.• We have shown that confidence thresholding can lead to robustness to a variety of attacks, without needing to anticipate and formally specify each attack type.Overall, we hope that our evaluation methodology will help to design and rigorously test low-cost, versatile defenses against a wide variety of adversarial examples. A set of points that should be equivalent to x. An adversarial example corresponding to x must be drawn from this set. x An adversarial example corresponding to x p model (y | x) The conditional distribution over the classes represented by the model c(x)arg max y p model (y | x), the confidence of the model for input x kThe number of classes tThe confidence threshold used by the model. An input x is covered only if c(x) > t. wThe weight vector for a logistic regression model η A perturbation applied to a clean input x B MODEL A Our ""Model A"" is a simple model that we tuned by trial and error to yield better success-fail curves than the baseline. We do not advocate ""Model A"" as the latest and greatest model that everyone should switch to. It is only included as a test point to show that our evaluation methodology can find interesting differences between models that have similar accuracy at 100% coverage on clean and adversarial data.Our trial-and-error design process was based on performance on clean data and on L ∞ adversarial examples. We did not use information about performance on semantic adversarial examples during the design process, so the defense was not designed in any specific way to handle these examples.The model architecture is straightforward to describe in cleverhans format: Conv2D(nb_filters, (3, 3) , (2, 2), ""SAME""), ReLU(), Add ([Conv2D(nb_filters, (3, 3) , (1, 1), ""SAME""), ReLU(), Conv2D(nb_filters, (3, 3) , (1, 1), ""SAME"")]), Conv2D(nb_filters * 2, (3, 3), (2, 2), ""SAME""), ReLU(), Conv2D(nb_filters * 2, (3, 3), (1, 1), ""VALID""), ReLU(), Flatten(), Linear(nb_classes), Softmax()] DISPLAYFORM0 In other words, it is a simple convolutional network, containing a convolution and 2X downsampling layer, a residual layer, two convolutional layers, and a fully connected layer to output the logits. There are no normalization layers, etc., and all of the hidden units are ReLUs BID9 BID14 BID3 .",969,0.402,589,1.6451612903225807,"Current machine learning algorithms easily fooled adversarial examples One possible solution path make models use confidence thresholding avoid making mistakes Such models refuse make a prediction when confident their answer We propose evaluate such models terms tradeoff curves with the goal high success rate on clean examples adversarial examples Existing untargeted attacks developed for models do use confidence thresholding tend underestimate such models' vulnerability We propose the MaxConfidence family attacks optimal a variety theoretical settings one realistic setting: attacks linear models Experiments show the attack attains good results practice We show simple defenses able perform on MNIST but CIFAR contributing further previous calls that retired as a benchmarking dataset adversarial robustness research We release code these evaluations as the cleverhans (Papernot et al 2018) library (ICLR reviewers should careful look who contributed these features cleverhans to avoid de this submission We made the following contributions:• We shown that adversarial training on one kind outdistribution data actually worsen relative a baseline that uses confidence thresholding as the only defense.• introduced the evaluation methodology success-fail curves showing which success rates on clean data and failure rates feasible confidence presented an attack that optimal against a variety confidence thresholding models Specifically , it optimal against linear classifiers optimal general models whenever underlying optimization approximately succeeds.• We an evaluation methodology maps out an entire success-failure tradeoff curve without needing retrain or rerun the evaluation for different thresholds.• confidence thresholding with simple regularization sufficient achieve reasonable robustness to L �� attacks on MNIST, despite being roughly 40X cheaper can lead a variety attacks without anticipate and formally specify each attack typeOverall hope design rigorously low-cost, versatile defenses adversarial examples A set points that should equivalent x. An adversarial example corresponding x must drawn this set x An adversarial example corresponding x p model (y |) The conditional distribution over the classes represented c(x)arg max y p model the confidence of for input kThe number classes tThe confidence threshold used. An input x is covered only c(x t. wThe weight vector a logistic regression model �� A perturbation applied a clean input x B MODEL A Our ""Model A we tuned by trial yield better success-fail curves the baseline We do advocate ""Model A as the latest and greatest model that everyone switch It only included as a test point to show our evaluation methodology can find interesting differences models similar accuracy at 100% coverage on clean and adversarial dataOur trial-and-error design process was performance on clean data L �� adversarial examples We did use information about performance on semantic adversarial examples during the defense was designed in handleThe model architecture straightforward describe cleverhans format Conv2D(nb_filters (3 , ""SAME, ReLU Add ([1 *VALID Flatten Linear(nb_classes Softmax] DISPLAYFORM0 In it containing and 2X downsampling layer a residual layer fully connected to output the logits There no normalization layers etc all the hidden units ReLUs BID9 BID14 BID3 .",0.01,0.3478934541745506
"Deep learning has achieved remarkable successes in solving challenging reinforcement learning (RL) problems when dense reward function is provided. However, in sparse reward environment it still often suffers from the need to carefully shape reward function to guide policy optimization. This limits the applicability of RL in the real world since both reinforcement learning and domain-specific knowledge are required. It is therefore of great practical importance to develop algorithms which can learn from a binary signal indicating successful task completion or other unshaped, sparse reward signals. We propose a novel method called competitive experience replay, which efficiently supplements a sparse reward by placing learning in the context of an exploration competition between a pair of agents. Our method complements the recently proposed hindsight experience replay (HER) by inducing an automatic exploratory curriculum. We evaluate our approach on the tasks of reaching various goal locations in an ant maze and manipulating objects with a robotic arm. Each task provides only binary rewards indicating whether or not the goal is achieved. Our method asymmetrically augments these sparse rewards for a pair of agents each learning the same task, creating a competitive game designed to drive exploration. Extensive experiments demonstrate that this method leads to faster converge and improved task performance. Recent progress in deep reinforcement learning has achieved very impressive results in domains ranging from playing games BID28 BID39 BID31 , to high dimensional continuous control , and robotics BID21 BID2 .Despite these successes, in robotics control and many other areas, deep reinforcement learning still suffers from the need to engineer a proper reward function to guide policy optimization (see e.g. BID36 BID29 . In robotic control as stacking bricks, reward function need to be sharped to very complex which consists of multiple terms BID36 . It is extremely hard and not applicable to engineer such reward function for each task in real world since both reinforcement learning expertise and domain-specific knowledge are required. Learning to perform well in environments with sparse rewards remains a major challenge. Therefore, it is of great practical importance to develop algorithms which can learn from binary signal indicating successful task completion or other unshaped reward signal.In environments where dense reward function is not available, only a small fraction of the agents' experiences will be useful to compute gradient to optimize policy, leading to substantial high sample complexity. Providing agents with useful signals to pursue in sparse reward environments becomes crucial in these scenarios.In the domain of goal-directed RL, the recently proposed hindsight experience replay (HER) BID0 addresses the challenge of learning from sparse rewards by re-labelling visited states as goal states during training. However, this technique continues to suffer from sample inefficiency, ostensibly due to difficulties related to exploration. In this work, we address these limitations by introducing a method called Competitive Experience Replay (CER). This technique attempts to emphasize exploration by introducing a competition between two agents attempting to learn the same task. Intuitively, agent A (the agent ultimately used for evaluation) receives a penalty for visiting states that the competitor agent (B) also visits; and B is rewarded for visiting states found by A. Our approach maintains the reward from the original task such that exploration is biased towards the behaviors best suited to accomplishing the task goals. We show that this competition between agents can automatically generate a curriculum of exploration and shape otherwise sparse reward. We jointly train both agents' policies by adopting methods from multi-agent RL. In addition, we propose two versions of CER, independent CER, and interact CER, which differ in the state initialization of agent B: whether it is sampled from the initial state distribution or sampled from off-policy samples of agent A, respectively.Whereas HER re-labels samples based on an agent's individual rollout, our method re-labels samples based on intra-agent behavior; as such, the two methods do not interfere with each other algorithmically and are easily combined during training. We evaluate our method both with and without HER on a variety of reinforcement learning tasks, including navigating an ant agent to reach a goal position and manipulating objects with a robotic arm. For each such task the default reward is sparse, corresponding to a binary indicator of goal completion. Ablation studies show that our method is important for achieving a high success rate and often demonstrates faster convergence. Interestingly, we find that CER and HER are complementary methods and employ both to reach peak efficiency and performance. Furthermore, we observe that, when combined with HER, CER outperforms curiosity-driven exploration. We introduce Competitive Experience Replay, a new and general method for encouraging exploration through implicit curriculum learning in sparse reward settings. We demonstrate an empirical advantage of our technique when combined with existing methods in several challenging RL tasks. In future work, we aim to investigate richer ways to re-label rewards based on intra-agent samples to further harness multi-agent competition, it's interesting to investigate counterfactual inference to promote efficient re-label off-policy samples. We hope that this will facilitate the application of our method to more open-end environments with even more challenging task structures. In addition, future work will explore integrating our method into approaches more closely related to model-based learning, where adequate exposure to the dynamics of the environment is often crucial. As BID0 and BID1 observe (and we also observe), performance depends on the batch size. We leverage this observation to tune the relative strengths of Agents A and B by separately manipulating the batch sizes used for updating each.For simplicity, we control the batch size by changing the number of MPI workers devoted to a particular update. Each MPI worker computes the gradients for a batch size of 256; averaging the gradients from each worker results in an effective batch size of N * 256. For our single-agent baselines, we choose N = 30 workers, and, when using CER, a default of N = 15 for each A and B In the following, AxBy denotes, for agent A, N = x and, for agent B, N = y. These results suggest that, while a sufficiently large batch size is important for achieving the best performance, the optimal configuration occurs when the batch sizes used for the two agents are balanced. Interestingly, we observe that batch size imbalance adversely effects both agents trained during CER.",1216,0.689,694,1.7521613832853027,"Deep learning achieved solving challenging reinforcement learning when dense reward function provided However sparse reward environment still often suffers carefully shape reward function guide policy optimization This limits RL in since both reinforcement learning It therefore develop algorithms learn a binary signal indicating successful task completion other unshaped, sparse reward We propose called competitive experience replay efficiently supplements a sparse reward by placing learning an exploration competition agents Our method complements the recently proposed hindsight experience replayHER inducing an automatic exploratory curriculum We evaluate our approach on the tasks reaching various goal locations an ant maze manipulating objects Each task provides only binary rewards indicating Our method asymmetrically augments these sparse rewards a pair agents each learning creating designed drive exploration Extensive experiments demonstrate this method leads faster converge improved Recent progress deep reinforcement learning achieved domains playing games BID28 BID39 BID31 high dimensional continuous control , robotics .Despite in robotics control engineer a proper reward function guide policy optimization In robotic control as stacking bricks reward function need sharped very complex which consists multiple terms BID36 . It extremely and not applicable engineer such reward function each task since both reinforcement learning expertise Learning perform well environments sparse rewards remains Therefore of develop algorithms learn binary signal indicating successful task completion other unshaped reward signalIn environments dense reward function the agents' experiences compute gradient to optimize policy leading substantial high sample complexity Providing agents useful signals pursue in sparse reward environments becomes crucial these scenariosIn the domain goal-directed RL the recently proposed hindsight experience replay (HER) BID0 addresses learning sparse rewards by relabelling visited states goal states during training However this technique continues suffer sample inefficiency ostensibly difficulties related exploration In address these limitations Competitive Experience Replay This technique attempts emphasize exploration introducing a competition attempting Intuitively agent A ultimately used evaluation receives a penalty visiting states the competitor agentB also; rewarded found Our approach maintains the reward from the original task such that exploration biased the behaviors best We show this competition agents automatically a curriculum exploration and shape otherwise sparse reward. We jointly train both agents' policies by adopting methods from multi-agent RL In propose two versions CER independent CER interact differ the state initialization agent B whether sampled off-policy samples respectivelyWhereas HER relabels samples based an agent's individual rollout our method re intra-agent behavior; as interfere algorithmically easily during training We evaluate our method both HER on reinforcement learning tasks navigating an ant agent to reach manipulating objects For each such task the default reward sparse corresponding a binary indicator goal completion Ablation studies our method important achieving often demonstrates faster convergence Interestingly CER and HER complementary methods and employ to reach peak efficiency performance Furthermore observe combined HER, CER outperforms curiosity-driven exploration We introduce Competitive Experience Replay a new and general method encouraging exploration implicit curriculum sparse reward settings We demonstrate an empirical advantage our technique combined several challenging RL tasks In future work aim investigate richer ways relabel rewards intra-agent samples further harness multi-agent competition it interesting investigate counterfactual inference promote efficient relabel off-policy samples We hope facilitate the application more open-end environments even more challenging task structures In future work explore integrating our method approaches more where adequate exposure often crucial As BID0 and observe ( also performance depends We leverage this observation tune Agents A separately manipulating used updating each.For simplicity control changing MPI workers devoted Each MPI worker computes the gradients a batch size 256; averaging results N * For our single-agent baselines choose N = 30 workers, CER a default each A In, AxBy denotes, agent A x, These results, a sufficiently large batch size achieving occurs used the two agents balanced Interestingly observe that batch size imbalance adversely effects both agents trained during CER.",0.01,0.6205202901181888
"This paper proposes a neural end-to-end text-to-speech (TTS) model which can control latent attributes in the generated speech that are rarely annotated in the training data, such as speaking style, accent, background noise, and recording conditions. The model is formulated as a conditional generative model with two levels of hierarchical latent variables. The first level is a categorical variable, which represents attribute groups (e.g. clean/noisy) and provides interpretability. The second level, conditioned on the first, is a multivariate Gaussian variable, which characterizes specific attribute configurations (e.g. noise level, speaking rate) and enables disentangled fine-grained control over these attributes. This amounts to using a Gaussian mixture model (GMM) for the latent distribution. Extensive evaluation demonstrates its ability to control the aforementioned attributes. In particular, it is capable of consistently synthesizing high-quality clean speech regardless of the quality of the training data for the target speaker. Recent development of neural sequence-to-sequence TTS models has shown promising results in generating high fidelity speech without the need of handcrafted linguistic features BID30 BID37 BID2 . These models rely heavily on a encoderdecoder neural network structure BID31 BID5 that maps a text sequence to a sequence of speech frames. Extensions to these models have shown that attributes such as speaker identity can be controlled by conditioning the decoder on additional attribute labels BID3 .There are many speech attributes aside from speaker identity that are difficult to annotate, such as speaking style, prosody, recording channel, and noise levels. ; model such latent attributes through conditional auto-encoding, by extending the decoder inputs to include a vector inferred from the target speech which aims to capture the residual attributes that are not specified by other input streams, in addition to text and a speaker label. These models have shown convincing results in synthesizing speech that resembles the prosody or the noise conditions of the reference speech, which may not have the same text or speaker identity as the target speech.Nevertheless, the presence of multiple latent attributes is common in crowdsourced data such as BID26 , in which prosody, speaker, and noise conditions all vary simultaneously. Using such data , simply copying the latent attributes from a reference is insufficient if one desires to synthesize speech that mimics the prosody of the reference, but is in the same noise condition as another. If the latent representation were disentangled, these generating factors could be controlled independently. Furthermore, it is can useful to construct a systematic method for synthesizing speech with random latent attributes, which would facilitate data augmentation BID33 BID12 BID8 by generating diverse examples. These properties were not explicitly addressed in the previous studies, which model variation of a single latent attribute.Motivated by the applications of sampling, inferring, and independently controlling individual attributes, we build off of and extend Tacotron 2 to model two separate latent spaces: one for labeled (i.e. related to speaker identity) and another for unlabeled attributes. Each latent variable is modeled in a variational autoencoding BID22 ) framework using Gaussian mixture priors. The resulting latent spaces (1) learn disentangled attribute representations, where each dimension controls a different generating factor; (2) discover a set of interpretable clusters, each of which corresponds to a representative mode in the training data (e.g., one cluster for clean speech and another for noisy speech); and (3) provide a systematic sampling mechanism from the learned prior. The proposed model is extensively evaluated on four datasets with subjective and objective quantitative metrics, as well as comprehensive qualitative studies. Experiments confirm that the proposed model is capable of controlling speaker, noise, and style independently, even when variation of all attributes is present but unannotated in the train set.Our main contributions are as follows:• We propose a principled probabilistic hierarchical generative model, which improves (1) sampling stability and disentangled attribute control compared to e.g. the GST model of , and (2) interpretability and quality compared to e.g. BID0 .• The model formulation explicitly factors the latent encoding by using two mixture distributions to separately model supervised speaker attributes and latent attributes in a disentangled fashion. This makes it straightforward to condition the model output on speaker and latent encodings inferred from different reference utterances.• To the best of our knowledge, this work is the first to train a high-quality controllable textto-speech system on real found data containing significant variation in recording condition, speaker identity, as well as prosody and style. Previous results on similar data focused on speaker modeling , and did not explicitly address modeling of prosody and background noise. Leveraging disentangled speaker and latent attribute encodings, the proposed model is capable of inferring the speaker attribute representation from a noisy utterance spoken by a previously unseen speaker, and using it to synthesize high-quality clean speech that approximates the voice of that speaker. We describe GMVAE-Tacotron, a TTS model which learns an interpretable and disentangled latent representation to enable fine-grained control of latent attributes and provides a systematic sampling scheme for them. If speaker labels are available, we demonstrate an extension of the model that learns a continuous space that captures speaker attributes, along with an inference model which enables one-shot learning of speaker attributes from unseen reference utterances.The proposed model was extensively evaluated on tasks spanning a wide range of signal variation. We demonstrated that it can independently control many latent attributes, and is able to cluster them without supervision. In particular, we verified using both subjective and objective tests that the model could synthesize high-quality clean speech for a target speaker even if the quality of data for that speaker does not meet high standard. These experimental results demonstrated the effectiveness of the model for training high-quality controllable TTS systems on large scale training data with rich styles by learning to factorize and independently control latent attributes underlying the speech signal.",1180,0.532,701,1.6833095577746078,"This paper neural end text which control latent attributes the generated speech that rarely speaking style accent background noise recording conditions The model formulated a conditional generative model two levels hierarchical latent variables The first level a categorical variable represents attribute groups clean/noisy provides interpretability The second level conditioned a multivariate Gaussian variable characterizes specific attribute configurations speaking rate enables This amounts using a Gaussian mixture model the latent distribution Extensive evaluation demonstrates its ability control the aforementioned attributes In particular capable consistently high-quality clean speech regardless the training data for Recent development neural sequenceto TTS models generating high fidelity speech without handcrafted linguistic features BID30 BID37 BID2 . These models rely a encoderdecoder neural network structure BID31 BID5 that maps a text sequence speech frames Extensions these models shown attributes speaker identity controlled conditioning additional attribute labels BID3 .There speech aside difficult annotate speaking style prosody recording channel noise levels ; model such latent attributes through conditional auto-encoding by extending the decoder inputs include inferred the target speech which aims capture the residual attributes that specified other input streams text a speaker label These models shown convincing results synthesizing speech that resembles or the noise conditions the reference speech not the same text speaker identityNevertheless multiple latent attributes common crowdsourced data such BID26 , in prosody speaker all vary simultaneously Using such data , simply copying the latent attributes a reference insufficient if one desires speech that the reference in the same noise condition another If the latent representation were these generating factors controlled independently Furthermore can useful construct a systematic method speech with random latent attributes facilitate data augmentation BID33 BID12 BID8 by diverse examples These properties explicitly addressed the previous studies model variation of a single latent attributeMotivated the applications sampling inferring independently controlling individual attributes build off and Tacotron 2 two separate latent spaces labeled ( related speaker identity Each latent variable modeled BID22 ) framework Gaussian mixture priors The resulting latent spaces1 learn disentangled attribute representations where each dimension controls a different generating factor; discover interpretable clusters corresponds a representative mode one cluster clean speech provide a systematic sampling mechanism from learned prior The proposed model extensively evaluated four datasets with subjective and objective quantitative metrics comprehensive qualitative studies Experiments confirm the proposed model capable controlling speaker, noise style independently variation all attributes but unannotated the train setOur main contributions as improves (1) sampling stability attribute control compared , quality compared The model formulation explicitly factors the latent encoding by two mixture distributions separately model supervised speaker attributes latent attributes This makes straightforward condition the model output speaker latent encodings inferred different reference utterances.• To the train a high-quality controllable textto-speech system real found data containing significant variation recording condition speaker identity as prosody style Previous results on similar data focused speaker modeling , did explicitly modeling prosody background noise Leveraging disentangled speaker latent attribute encodings the proposed model capable inferring attribute representation a noisy utterance spoken high-quality clean speech We describe GMVAE-Tacotron a TTS model learns an interpretable and disentangled latent representation to enable latent attributes provides a systematic sampling scheme them If speaker labels available demonstrate an extension learns a continuous space that captures speaker attributes along an inference model which enables one-shot learning unseen reference utterancesThe proposed model was extensively evaluated tasks spanning signal variation We demonstrated it independently control many latent attributes is cluster without supervision In particular verified using both subjective and objective tests the model could synthesize high-quality clean speech for a target speaker even data for does meet high standard These experimental results demonstrated the model training high-quality controllable TTS systems large scale training data with rich styles by learning factorize independently latent attributes underlying the speech signal",0.01,0.4450918879721845
"Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%. Consider the problem of counting how many cats there are in Figure 1 . Solving this involves several rough steps: understanding what instances of that type can look like, finding them in the image, and adding them up. This is a common task in Visual Question Answering (VQA) -answering questions about images -and is rated as among the tasks requiring the lowest human age to be able to answer (Antol et al., 2015) . However, current models for VQA on natural images struggle to answer any counting questions successfully outside of dataset biases (Jabri et al., 2016) .One reason for this is the presence of a fundamental problem with counting in the widely-used soft attention mechanisms (section 3). Another reason is that unlike standard counting tasks, there is no ground truth labeling of where the objects to count are. Coupled with the fact that models need to be able to count a large variety of objects and that, ideally, performance on non-counting questions should not be compromised, the task of counting in VQA seems very challenging.To make this task easier, we can use object proposals -pairs of a bounding box and object featuresfrom object detection networks as input instead of learning from pixels directly. In any moderately complex scene, this runs into the issue of double-counting overlapping object proposals. This is a problem present in many natural images, which leads to inaccurate counting in real-world scenarios.Our main contribution is a differentiable neural network component that tackles this problem and consequently can learn to count (section 4). Used alongside an attention mechanism, this component avoids a fundamental limitation of soft attention while producing strong counting features. We provide experimental evidence of the effectiveness of this component (section 5). On a toy dataset, we demonstrate that this component enables robust counting in a variety of scenarios. On the number category of the VQA v2 Open-Ended dataset (Goyal et al., 2017) , a relatively simple baseline model using the counting component outperforms all previous models -including large ensembles of state-of-the-art methods -without degrading performance on other categories. 1 2 RELATED WORK Usually, greedy non-maximum suppression (NMS) is used to eliminate duplicate bounding boxes. The main problem with using it as part of a model is that its gradient is piecewise constant. Various differentiable variants such as by Azadi et al. (2017) , Hosang et al. (2017) , and Henderson & Ferrari (2017) exist. The main difference is that, since we are interested in counting, our component does not need to make discrete decisions about which bounding boxes to keep; it outputs counting features, not a smaller set of bounding boxes. Our component is also easily integrated into standard VQA models that utilize soft attention without any need for other network architecture changes and can be used without using true bounding boxes for supervision.On the VQA v2 dataset (Goyal et al., 2017 ) that we apply our method on, only few advances on counting questions have been made. The main improvement in accuracy is due to the use of object proposals in the visual processing pipeline, proposed by BID0 . Their object proposal network is trained with classes in singular and plural forms, for example ""tree"" versus ""trees"", which only allows primitive counting information to be present in the object features after region-of-interest pooling. Our approach differs in the way that instead of relying on counting features being present in the input, we create counting features using information present in the attention map over object proposals. This has the benefit of being able to count anything that the attention mechanism can discriminate instead of only objects that belong to the predetermined set of classes that had plural forms.Using these object proposals, Trott et al. (2018) train a sequential counting mechanism with a reinforcement learning loss on the counting question subsets of VQA v2 and Visual Genome. They achieve a small increase in accuracy and can obtain an interpretable set of objects that their model counted, but it is unclear whether their method can be integrated into traditional VQA models due to their loss not applying to non-counting questions. Since they evaluate on their own dataset, their results can not be easily compared to existing results in VQA.Methods such as by Santoro et al. (2017) and Perez et al. (2017) can count on the synthetic CLEVR VQA dataset BID0 successfully without bounding boxes and supervision of where the objects to count are. They also use more training data (∼250,000 counting questions in the CLEVR training set versus ∼50,000 counting questions in the VQA v2 training set), much simpler objects, and synthetic question structures.More traditional approaches based on Lempitsky & Zisserman (2010) learn to produce a target density map, from which a count is computed by integrating over it. In this setting, Cohen et al. (2017) make use of overlaps of convolutional receptive fields to improve counting performance. Chattopadhyay et al. (2017) use an approach that divides the image into smaller non-overlapping chunks, each of which is counted individually and combined together at the end. In both of these contexts, the convolutional receptive fields or chunks can be seen as sets of bounding boxes with a fixed structure in their positioning. Note that while Chattopadhyay et al. (2017) evaluate their models on a small subset of counting questions in VQA, major differences in training setup make their results not comparable to our work. After understanding why VQA models struggle to count, we designed a counting component that alleviates this problem through differentiable bounding box deduplication. The component can readily be used alongside any future improvements in VQA models, as long as they still use soft attention as all current top models on VQA v2 do. It has uses outside of VQA as well: for many counting tasks, it can allow an object-proposal-based approach to work without ground-truth objects available as long as there is a -possibly learned -per-proposal scoring (for example using a classification score) and a notion of how dissimilar a pair of proposals are. Since each step in the component has a clear purpose and interpretation, the learned weights of the activation functions are also interpretable. The design of the counting component is an example showing how by encoding inductive biases into a deep learning model, challenging problems such as counting of arbitrary objects can be approached when only relatively little supervisory information is available.For future research, it should be kept in mind that VQA v2 requires a versatile skill set that current models do not have. To make progress on this dataset, we advocate focusing on understanding of what the current shortcomings of models are and finding ways to mitigate them.",1505,0.816,899,1.6740823136818688,"Visual Question Answering (VQA) models struggled counting objects natural images so We identify due soft attention these models as. To circumvent propose a neural network component robust counting from object proposals Experiments a toy task show the effectiveness this component and we obtain state accuracy the number category the VQA v2 dataset without negatively other categories outperforming ensemble models our single model On difficult balanced pair metric the component gives a substantial improvement counting over a strong baseline by Consider counting Figure . Solving involves several rough steps understanding what instances that type can look finding them the image adding up This a common task Visual Question Answering -answering questions images -and is rated among the tasks requiring the lowest human age ableAntol et However current models VQA on natural images struggle answer any counting questions successfully outside dataset biases .One reason counting the widely-used soft attention mechanismssection Another reason unlike standard counting tasks no ground truth labeling where to models need count a large variety that, ideally performance on non-counting questions counting in VQA seems veryTo can object proposals -pairs object featuresfrom object detection networks as input instead learning pixels directly In any moderately complex scene this runs double-counting overlapping object proposals This present many natural images leads inaccurate counting inOur main contribution a differentiable neural network component tackles consequently can learn (section Used alongside an attention mechanism this component avoids a fundamental limitation soft attention while producing strong counting features We provide experimental evidence this component (section On a toy dataset demonstrate this component enables robust counting On the number category the VQA v2 Open-Ended datasetGoyal et al , a relatively simple baseline model using the counting component outperforms -including state methods degrading performance other categories 1 2 RELATED WORK Usually greedy non-maximum suppression eliminate duplicate bounding boxes The main problem it part a model its gradient piecewise constant Various differentiable variants such by Azadi et al (2017 , Hosang et al (2017 , and Henderson Ferrari exist The main difference, since interested counting our component does make discrete decisions bounding; outputs counting features a smaller set Our component also easily standard VQA models utilize soft attention without other network architecture changes and using true bounding boxes supervisionOnGoyal et al ) that apply our method on only few advances on counting questions The main improvement accuracy due object proposals proposed BID0 . Their object proposal network trained classes singular and plural forms fortree versus only allows primitive counting information present features after regionof pooling Our approach differs instead relying counting features being create counting features information present the attention map over object proposals This has the benefit count anything the attention mechanism discriminate instead only objects belong the predetermined set classes had plural formsUsing these object proposals Trott et (2018 train a sequential counting mechanism a reinforcement learning loss on the counting question subsets VQA v2 Visual Genome They achieve a small increase accuracy can obtain an interpretable set objects their model counted integrated traditional VQA models due their loss not applying non-counting questions Since they evaluate on their own dataset not easily existing results VQA.Methods such by Santoro (2017 and Perez (2017 can count the synthetic CLEVR VQA dataset BID0 successfully without bounding supervision where to count They also use more training data (��250,000 counting questions in CLEVR training versus much simpler objects synthetic question structuresMore traditional approaches based Lempitsky & Zisserman learn produce a target density map from a count integrating over it In this setting Cohen et (2017 make use overlaps convolutional receptive fields counting performance Chattopadhyay et (2017 use an approach divides the image counted individually combined at In both contexts the convolutional receptive fields or chunks seen sets their positioning Note while et (2017 evaluate their models counting questions VQA major differences training setup make not comparable our work After understanding VQA models struggle count designed a counting component alleviates through differentiable bounding box deduplication The component can readily alongside any future improvements VQA models still soft attention as all current top models on It uses outside VQA: many counting tasks allow an object-proposal-based approach ground-truth objects available as long a -possibly learned -per-proposal scoring ( using a classification score) a notion how dissimilar a pair proposals Since each step the component has interpretation the learned weights the activation functions also The design the counting component showing by encoding inductive biases challenging problems counting of arbitrary objects approached when only relatively little supervisory informationFor future research kept VQA v2 requires a versatile skill current models To progress this dataset advocate focusing understanding of what the current shortcomings models finding mitigate",0.01,0.4215816807206873
"We propose a simple and robust training-free approach for building sentence representations. Inspired by the Gram-Schmidt Process in geometric theory, we build an orthogonal basis of the subspace spanned by a word and its surrounding context in a sentence. We model the semantic meaning of a word in a sentence based on two aspects. One is its relatedness to the word vector subspace already spanned by its contextual words. The other is its novel semantic meaning which shall be introduced as a new basis vector perpendicular to this existing subspace.   Following this motivation, we develop an innovative method based on orthogonal basis to combine pre-trained word embeddings into sentence representation. This approach requires zero training and zero parameters, along with efficient inference performance. We evaluate our approach on 11 downstream NLP tasks. Experimental results show that our model outperforms all existing zero-training alternatives in all the tasks and it is competitive to other approaches relying on either large amounts of labelled data or prolonged training time. The concept of word embeddings has been prevalent in NLP community in recent years, as they can characterize semantic similarity between any pair of words, achieving promising results in a large number of NLP tasks BID14 BID18 BID20 . However, due to the hierarchical nature of human language, it is not sufficient to comprehend text solely based on isolated understanding of each word. This has prompted a recent rise in search for semantically robust embeddings for longer pieces of text, such as sentences and paragraphs.Based on learning paradigms, the existing approaches to sentence embeddings can be categorized into two categories: i) parameterized methods and ii) non-parameterized methods.Parameterized sentence embeddings. These models are parameterized and require training to optimize their parameters. SkipThought BID11 is an encoder-decoder model that predicts adjacent sentences. BID15 proposes an unsupervised model, Sent2Vec, to learn an n-gram feature in a sentence to predict the center word from the surrounding context. Quick thoughts (QT) BID12 replaces the encoder with a classifier to predict context sentences from candidate sequences. BID10 proposesà la carte to learn a linear mapping to reconstruct the center word from its context. BID5 generates the sentence encoder InferSent using Natural Language Inference (NLI) dataset. Universal Sentence Encoder utilizes the transformer BID24 for sentence embeddings. The model is first trained on large scale of unsupervised data from Wikipedia and forums, and then trained on the Stanford Natural Language Inference (SNLI) dataset. BID27 propose the gated recurrent averaging network (GRAN), which is trained on Paraphrase Database (PPDB) and English Wikipedia. BID23 leverages a multi-task learning framework to generate sentence embeddings. BID28 learns the paraphrastic sentence representations as the simple average of updated word embeddings.Non-parameterized sentence embedding. Recent work BID0 shows that, surprisingly, a weighted sum or transformation of word representations can outperform many sophisticated neural network structures in sentence embedding tasks. These methods are parameter-free and require no further training upon pre-trained word vectors. BID0 constructs a sentence embedding called SIF as a sum of pre-trained word embeddings, weighted by reverse document frequency. BID19 concatenates different power mean word embeddings as a sentence vector in p-mean. As these methods do not have a parameterized model, they can be easily adapted to novel text domains with both fast inference speed and high-quality sentence embeddings. In view of this trend, our work aims to further advance the frontier of this group and make its new state-of-the-art.In this paper, we propose a novel sentence embedding algorithm, Geometric Embedding (GEM), based entirely on the geometric structure of word embedding space. Given a d-dim word embedding matrix A ∈ R d×n for a sentence with n words, any linear combination of the sentence's word embeddings lies in the subspace spanned by the n word vectors. We analyze the geometric structure of this subspace in R d . When we consider the words in a sentence one-by-one in order, each word may bring in a novel orthogonal basis to the existing subspace. This new basis can be considered as the new semantic meaning brought in by this word, while the length of projection in this direction can indicate the intensity of this new meaning. It follows that a word with a strong intensity should have a larger influence in the sentence's meaning. Thus, these intensities can be converted into weights to linearly combine all word embeddings to obtain the sentence embedding. In this paper, we theoretically frame the above approach in a QR factorization of the word embedding matrix A. Furthermore, since the meaning and importance of a word largely depends on its close neighborhood, we propose the sliding-window QR factorization method to capture the context of a word and characterize its significance within the context.In the last step, we adapt a similar approach as BID0 to remove top principal vectors before generating the final sentence embedding. This step is to ensure commonly shared background components, e.g. stop words, do not bias sentence similarity comparison. As we build a new orthogonal basis for each sentence, we propose to have disparate background components for each sentence. This motivates us to put forward a sentence-specific principal vector removal method, leading to better empirical results.We evaluate our algorithm on 11 NLP tasks. In all of these tasks, our algorithm outperforms all non-parameterized methods and many parameterized approaches. For example, compared to SIF BID0 , the performance is boosted by 5.5% on STS benchmark dataset, and by 2.5% on SST dataset. Plus, the running time of our model compares favorably with existing models.The rest of this paper is organized as following. In Section 2, we describe our sentence embedding algorithm GEM. We evaluate our model on various tasks in Section 3 and Section 4. Finally, we summarize our work in Section 5. Ablation Study. As shown in in Table 4 , every GEM weight (α n , α s , α u ) and proposed principal components removal methods contribute to the performance. As listed on the left, adding GEM weights improves the score by 8.6% on STS dataset compared with averaging three concatenated word vectors. The sentence-dependent principal component removal (SDR) proposed in GEM improves 0.3% compared to directly removing the top h corpus principal components (SIR). Using GEM weights and SDR together yields an overall improvement of 19.7%. As shown on the right in Table 4 , every weight contributes to the performance of our model. For example, three weights altogether improve the score in SUBJ task by 0.38% compared with only using α n . Sensitivity Study. We evaluate the effect of all four hyper-parameters in our model: the window size m in the contextual window matrix, the number of candidate principal components K, the number of principal components to remove h, and the power of the singular value in coarse sentence embedding, i.e. the power t in f (σ j ) = σ t j in Equation FORMULA9 . We sweep the hyper-parameters and test on STSB dev set, SUBJ, and MPQA. Unspecified parameters are fixed at m = 7, K = 45, h = 17 and t = 3. As shown in Figure 2 , our model is quite robust with respect to hyper-parameters. We proposed a simple non-parameterized method 1 to generate sentence embeddings, based entirely on the geometric structure of the subspace spanned by word embeddings. Our sentence embedding evolves from the new orthogonal basis vector brought in by each word, which represents novel semantic meaning. The evaluation shows that our method not only sets up the new state-of-the-art of non-parameterized models but also performs competitively when compared with models requiring either large amount of training data or prolonged training time. In future work, we plan to consider multi-characters, i.e. subwords, into the model and explore other geometric structures in sentences.",1619,1.002,958,1.6899791231732777,"We propose a simple and robust training-free approach building sentence representations Inspired the Gram-Schmidt Process in geometric theory build the subspace spanned a word its surrounding context a sentence We model the semantic meaning two aspects One is its relatedness the word vector subspace already spanned its contextual words other is its novel semantic meaning which shall introduced a new basis vector perpendicular this existing subspace Following this motivation develop based orthogonal basis combine sentence representation This approach requires zero training zero parameters along efficient inference performance We evaluate our approach on 11 downstream NLP tasks Experimental results our model all existing zero-training alternatives all the tasks and it competitive to other approaches relying either large amounts labelled data prolonged training time The concept word embeddings prevalent NLP community in they characterize semantic similarity any pair achieving promising results BID14 BID18 BID20 However due the hierarchical nature human language sufficient comprehend text solely based isolated understanding This has prompted a recent rise search for semantically robust embeddings longer pieces sentencesBased learning the existing approaches categorized i) parameterized methods. These models parameterized require training optimize SkipThought BID11 is an encoder-decoder model predicts adjacent sentences BID15 proposes an unsupervised model Sent2Vec learn an n-gram feature to the center word Quick thoughts (QT BID12 replaces the encoder predict context sentences candidate sequences BID10 proposesà la carte learn a linear mapping to reconstruct the center word its context BID5 generates the sentence encoder InferSent using Natural Inference dataset Universal Sentence Encoder utilizes the transformer BID24 The model first trained large scale of unsupervised data from Wikipedia forums Stanford Natural InferenceSNLI BID27 propose the gated recurrent averaging network trained Paraphrase DatabasePPDB English Wikipedia BID23 leverages generate BID28 learns the paraphrastic sentence representations as the simple average updated word embeddingsNon-parameterized sentence Recent work BID0 shows, surprisingly a weighted sum or transformation word representations many sophisticated neural network structures sentence These methods parameter- upon pre-trained word vectors BID0 constructs a sentence embedding called SIF as a sum weighted reverse document frequency BID19 concatenates different power mean word embeddings as a sentence vector p-mean As these methods do a parameterized model adapted novel text domains both fast inference speed In view this trend our work aims further advance the frontier this group make its new state-In a novel sentence algorithm entirely word space Given a d-dim word matrix A �� R d×n for a sentence any linear combination lies spanned We analyze the geometric structure this subspace R d When consider the words in one- in order, may bring in a novel orthogonal basis the existing subspace This new basis can considered the new semantic meaning brought in this word while the length projection this direction indicate the intensity It follows a word with a strong intensity should a larger influence Thus these intensities can converted weights linearly combine all word embeddings the sentence In theoretically frame the above approach a QR factorization of the word matrix A. Furthermore since the meaning and importance largely its close neighborhood propose the sliding-window QR factorization method capture characterizeIn adapt as BID0 remove top principal vectors before generating the final sentence This step commonly shared background components stop words bias sentence similarity comparison As build a new orthogonal basis each sentence propose have disparate background components This motivates put forward a sentence-specific principal vector removal method leading better empirical resultsWe evaluate our algorithm 11 NLP tasks In all these tasks our algorithm many parameterized approaches For example compared SIF BID0 , the performance is boosted STS benchmark dataset SST dataset Plus the running time our model compares existing modelsThe rest organized following In Section our sentence embedding algorithm GEM We evaluate our model various tasks Section Section Finally summarize Section Ablation Study. As shown in Table every GEM weightα n α proposed principal components removal methods contribute. As listed adding GEM weights improves the score STS dataset compared averaging three concatenated word vectors The sentence-dependent principal component removal proposed GEM improves compared directly the top h corpus principal componentsSIR Using GEM weights SDR together yields an overall improvement As shown Table every weight contributes our model For example three weights altogether improve the score SUBJ task using α n . Sensitivity Study. We evaluate all four hyper the window size m in the contextual window matrix candidate principal components K to remove h the singular value coarse sentence, fσ j in Equation FORMULA9 We sweep the hyper test on STSB dev set SUBJ MPQA Unspecified parameters fixed m = 7 K 45 h 17 t As shown our model quite hyper We proposed 1 generate entirely the geometric structure the subspace spanned Our sentence embedding evolves the new orthogonal basis vector brought each word represents novel semantic meaning The evaluation shows our method not sets the new state of non-parameterized models performs competitively when models requiring either large amount prolonged training time In future work consider multicharacters subwords into the model explore other geometric structures sentences",0.01,0.46208535462638667
"In few-shot classification, we are interested in learning algorithms that train a classifier from only a handful of labeled examples. Recent progress in few-shot classification has featured meta-learning, in which a parameterized model for a learning algorithm is defined and trained on episodes representing different classification problems, each with a small labeled training set and its corresponding test set. In this work, we advance this few-shot classification paradigm towards a scenario where unlabeled examples are also available within each episode. We consider two situations: one where all unlabeled examples are assumed to belong to the same set of classes as the labeled examples of the episode, as well as the more challenging situation where examples from other distractor classes are also provided. To address this paradigm, we propose novel extensions of Prototypical Networks (Snell et al., 2017) that are augmented with the ability to use unlabeled examples when producing prototypes. These models are trained in an end-to-end way on episodes, to learn to leverage the unlabeled examples successfully. We evaluate these methods on versions of the Omniglot and miniImageNet benchmarks, adapted to this new framework augmented with unlabeled examples. We also propose a new split of ImageNet, consisting of a large set of classes, with a hierarchical structure. Our experiments confirm that our Prototypical Networks can learn to improve their predictions due to unlabeled examples, much like a semi-supervised algorithm would. The availability of large quantities of labeled data has enabled deep learning methods to achieve impressive breakthroughs in several tasks related to artificial intelligence, such as speech recognition, object recognition and machine translation. However, current deep learning approaches struggle in tackling problems for which labeled data are scarce. Specifically, while current methods excel at tackling a single problem with lots of labeled data, methods that can simultaneously solve a large variety of problems that each have only a few labels are lacking. Humans on the other hand are readily able to rapidly learn new classes, such as new types of fruit when we visit a tropical country. This significant gap between human and machine learning provides fertile ground for deep learning developments.For this reason, recently there has been an increasing body of work on few-shot learning, which considers the design of learning algorithms that specifically allow for better generalization on problems with small labeled training sets. Here we focus on the case of few-shot classification, where the given classification problem is assumed to contain only a handful of labeled examples per class. One approach to few-shot learning follows a form of meta-learning 1 BID21 BID9 , which performs transfer learning from a pool of various classification problems generated from large quantities of available labeled data, to new classification problems from classes unseen at training time. Meta-learning may take the form of learning a shared metric BID23 BID20 , a common initialization for few-shot classifiers BID16 BID5 or a generic inference network BID19 BID15 . DISPLAYFORM0 Unlabeled Set Support Set Figure 1 : Consider a setup where the aim is to learn a classifier to distinguish between two previously unseen classes, goldfish and shark, given not only labeled examples of these two classes, but also a larger pool of unlabeled examples, some of which may belong to one of these two classes of interest. In this work we aim to move a step closer to this more natural learning framework by incorporating in our learning episodes unlabeled data from the classes we aim to learn representations for (shown with dashed red borders) as well as from distractor classes .These various meta-learning formulations have led to significant progress recently in few-shot classification. However , this progress has been limited in the setup of each few-shot learning episode, which differs from how humans learn new concepts in many dimensions. In this paper we aim to generalize the setup in two ways. First, we consider a scenario where the new classes are learned in the presence of additional unlabeled data. While there have been many successful applications of semisupervised learning to the regular setting of a single classification task BID2 where classes at training and test time are the same, such work has not addressed the challenge of performing transfer to new classes never seen at training time, which we consider here. Second , we consider the situation where the new classes to be learned are not viewed in isolation. Instead , many of the unlabeled examples are from different classes; the presence of such distractor classes introduces an additional and more realistic level of difficulty to the fewshot problem.This work is a first study of this challenging semi-supervised form of few-shot learning. First, we define the problem and propose benchmarks for evaluation that are adapted from the Omniglot and miniImageNet benchmarks used in ordinary few-shot learning. We perform an extensive empirical investigation of the two settings mentioned above, with and without distractor classes. Second, we propose and study three novel extensions of Prototypical Networks BID20 , a state-ofthe-art approach to few-shot learning, to the semi-supervised setting. Finally, we demonstrate in our experiments that our semi-supervised variants successfully learn to leverage unlabeled examples and outperform purely supervised Prototypical Networks. In this work, we propose a novel semi-supervised few-shot learning paradigm, where an unlabeled set is added to each episode. We also extend the setup to more realistic situations where the unlabeled set has novel classes distinct from the labeled classes. To address the problem that current fewshot classification datasets are too small for a labeled vs. unlabeled split and also lack hierarchical levels of labels, we introduce a new dataset, tieredImageNet. We propose several novel extensions of Prototypical Networks, and they show consistent improvements under semi-supervised settings compared to our baselines. As future work, we are working on incorporating fast weights BID0 BID5 into our framework so that examples can have different embedding representations given the contents in the episode.",1174,0.612,708,1.6581920903954803,"In few-shot classification interested learning algorithms train from labeled examples Recent progress few-shot classification featured meta-learning for defined episodes representing different classification problems each a small labeled training set In this work advance this few-shot classification paradigm towards a scenario unlabeled examples also available within each episode We consider two situations all unlabeled examples assumed belong classes as of the episode as examples other distractor classes provided To address this paradigm novel extensions Prototypical NetworksSnell 2017 augmented use unlabeled examples when producing prototypes These models trained an end way on episodes to learn leverage the unlabeled examples successfully We evaluate these methods versions the Omniglot and miniImageNet benchmarks adapted this new framework augmented unlabeled examples We also propose a new split ImageNet consisting classes Our experiments confirm our Prototypical Networks learn improve due unlabeled examples much semi would The availability large quantities labeled data enabled deep learning methods achieve several tasks related However current deep learning approaches struggle in tackling for labeled scarce Specifically while current methods excel tackling lots labeled data methods simultaneously that each lacking Humans on readily rapidly new classes new types fruit when we visit This significant gap providesFor recently there few-shot learning considers the design specifically allow on problems small labeled training sets Here focus few-shot classification the given classification problem assumed contain labeled examples per One approach few-shot learning follows a form meta-learning 1 BID21 BID9 , performs transfer a pool various classification problems generated large quantities available labeled data from classes unseen training time Meta-learning may take a shared metric BID23 BID20 , a common initialization few-shot classifiers BID16 BID5 or a generic inference network DISPLAYFORM0 Unlabeled Set Support Set Figure : Consider a setup the aim learn a classifier to two previously unseen classes goldfish shark given not only labeled examples a larger pool some belong of interest In this work aim move a step this more natural learning framework incorporating in episodes unlabeled data the classes aim representations (shown with dashed red borders distractor classes .These various meta-learning formulations led recently few-shot classification However , this progress limited the setup each few-shot learning episode differs how humans many dimensions In aim generalize the setup in First consider a scenario the new classes learned the presence additional unlabeled data While many successful applications semisupervised learning the regular setting a single classification task BID2 where classes at training the such work addressed performing transfer to never at we consider here. Second , consider the new classes to learned viewed Instead , many the unlabeled examples from different classes; the presence such distractor classes introduces an additional and more realistic level the fewshot problemThis work a first study this challenging semi-supervised form few-shot learning First define propose benchmarks evaluation that adapted the Omniglot and miniImageNet benchmarks used ordinary few-shot learning We perform an extensive empirical investigation the two settings mentioned and distractor classes Second propose and study three novel extensions Prototypical Networks BID20 , a state-ofthe-art approach few-shot learning the semi-supervised setting Finally demonstrate in our experiments our semi-supervised variants successfully learn leverage unlabeled examples outperform purely Prototypical Networks In this work propose a novel semi-supervised few-shot learning paradigm added each episode We also extend the setup more realistic situations the unlabeled set has novel classes distinct To address current fewshot classification datasets a labeled vs. unlabeled split and also lack hierarchical levels labels we introduce tieredImageNet We propose several novel extensions Prototypical Networks they show consistent improvements under compared our baselines As future work, we incorporating fast weights BID0 BID5 into examples have different embedding representations given the contents in the episode",0.01,0.3810947878867224
"We investigate the properties of multidimensional probability distributions in the context of latent space prior distributions of implicit generative models. Our work revolves around the phenomena arising while decoding linear interpolations between two random latent vectors -- regions of latent space in close proximity to the origin of the space are oversampled, which restricts the usability of linear interpolations as a tool to analyse the latent space. We show that the distribution mismatch can be eliminated completely by a proper choice of the latent probability distribution or using non-linear interpolations. We prove that there is a trade off between the interpolation being linear, and the latent distribution having even the most basic properties required for stable training, such as finite mean. We use the multidimensional Cauchy distribution as an example of the prior distribution, and also provide a general method of creating non-linear interpolations, that is easily applicable to a large family of commonly used latent distributions. Generative latent variable models have grown to be a very popular research topic, with Variational Auto-Encoders (VAEs) BID8 and Generative Adversarial Networks (GANs) BID4 gaining a lot of interest in the last few years. VAEs use a stochastic encoder network to embed input data in a typically lower dimensional space, using a conditional probability distribution p(z|x) over possible latent space codes z ∈ R D . A stochastic decoder network is then used to reconstruct the original sample. GANs, on the other hand, use a generator network that creates data samples from noise z ∼ p(z), where p(z) is a fixed prior distribution, and train a discriminator network jointly to distinguish between real and generated data. Both of these model families require a probability distribution to be defined on the latent space. The most popular variants are the multidimensional normal distribution and the uniform distribution on the zero-centred hypercube. Given a trained model, studying the structure of the latent space is a common way to measure generator capabilities.",392,0.207,241,1.6265560165975104,We investigate the properties multidimensional probability distributions latent space prior distributions implicit generative models Our work revolves the phenomena arising while decoding linear interpolations two random latent vectors -- regions latent space close proximity are which restricts the usability as analyse We show the distribution mismatch can eliminated completely a proper choice the latent probability distribution or using We prove there a trade the interpolation being linear the latent distribution having even the most basic properties required stable training such finite mean. We use the multidimensional Cauchy distribution the prior distribution also provide a general method creating that easily applicable a large family commonly used latent distributions Generative latent variable models grown Variational Auto-Encoders (VAEs) BID8 Generative gaining VAEs use a stochastic encoder network embed input data a typically lower dimensional space using a conditional probability distribution p(z|x over possible latent space codes z �� R D A stochastic decoder network then reconstruct the original sample GANs on use a generator network creates data samples noise z ∼ p(z a fixed prior distribution train jointly distinguish Both these model families require a probability distribution defined on the latent space The most popular variants the multidimensional normal distribution on the zero-centred hypercube Given a trained model studying the latent space measure generator capabilities,0.0,0.30048885136454745
"Deep neural networks (DNN) have shown promising performance in computer vision. In medical imaging, encouraging results have been achieved with deep learning for applications such as segmentation, lesion detection and classification. Nearly all of the deep learning based image analysis methods work on reconstructed images, which are obtained from original acquisitions via solving inverse problems (reconstruction). The reconstruction algorithms are designed for human observers, but not necessarily optimized for DNNs which can often observe features that are incomprehensible for human eyes. Hence, it is desirable to train the DNNs directly from the original data which lie in a different domain with the images. In this paper, we proposed an end-to-end DNN for abnormality detection in medical imaging. To align the acquisition with the annotations made by radiologists in the image domain, a DNN was built as the unrolled version of iterative reconstruction algorithms to map the acquisitions to images, and followed by a 3D convolutional neural network (CNN) to detect the abnormality in the reconstructed images. The two networks were trained jointly in order to optimize the entire DNN for the detection task from the original acquisitions. The DNN was implemented for lung nodule detection in low-dose chest computed tomography (CT), where a numerical simulation was done to generate acquisitions from 1,018 chest CT images with radiologists' annotations. The proposed end-to-end DNN demonstrated better sensitivity and accuracy for the task compared to a two-step approach, in which the reconstruction and detection DNNs were trained separately. A significant reduction of false positive rate on suspicious lesions were observed, which is crucial for the known over-diagnosis in low-dose lung CT imaging. The images reconstructed by the proposed end-to-end network also presented enhanced details in the region of interest. Deep neural networks (DNN) have shown promising performance in computer vision for various applications such as segmentation, detection and recognition. In medical imaging, DNNbased computer vision is also desirable because that radiologists' routine work requires handling of large amount of data, and the possibility exists that the intensive labor may lead to misdiagnosis BID14 BID38 . Furthermore, in some radiation related applications such as computed tomography (CT), low-dose scans are always preferred to decrease the potential harm that ionized radiation may do to human body. The increased noise level in lowdose data made it even more challenging for the radiologists to make correct decisions BID19 .Almost all the DNNs in medical image analysis are constructed in the image domain, which is the same domain where radiologists do the observations. However , in most medical imaging modalities, the acquired data are in a different domain from the images, and inverse problems have to be solved to reconstruct the images. For example , magnetic resonance imaging (MRI) acquires data in the Fourier domain, and CT acquires data in the Radon transform domain BID10 . During the reconstruction, there is great possibility of information lost due to the presence of noise in the measurements, especially for low-dose scans BID27 . To compensate for the noise, iterative methods that exploit prior knowledge about human body have been proposed BID11 BID30 . To achieve better representation of the med-ical images, DNN based reconstruction methods were also proposed recently BID36 b; BID12 . However, there is still gap between the objective image quality improvement and its utility in diagnosis, which means that both radiologists and computer aided diagnosis (CAD) systems are working with sub-optimal images.There is an emerging trend on task-based (end-to-end) signal processing with DNNs in recent years, where the decisions were directly made by the DNNs without explicit intermediate representations. BID13 used DNN for speech recognition directly from audio data without and intermediate phonetic representations. BID4 trained a DNN for self-driving cars which learned commands directly from images without recognition of land markers. BID18 used a classification criteria for the colorization of grey-scale images. BID35 detected words directly from scenes without doing a two-step text detection and optical character recognition (OCR). It was demonstrated that end-to-end DNNs had improved performance compared to multiple-step learning in these applications.In this paper, we proposed an end-to-end DNN which predicts the location of abnormalities in the images from the acquisitions. A reconstruction DNN was built first to map the acquired data to the images in order to align the data with annotations made by the radiologists. The DNN approximated a 10-iteration unrolled sequential quadratic surrogates (SQS) algorithm BID11 . A 3D convolutional neural network ( CNN) was used to detect abnormalities from the reconstructed images. The entire DNN was optimized jointly with regard to the total detection cross entropy loss. The method was implemented on The Lung Image Database Consortium image collection (LIDC-IDRI) from The Cancer Image Archive (TCIA), where we simulated ultra low-dose CT scans from the original patients' data BID2 BID8 BID3 . The task of the DNN was lung nodule detection , which is essential for early stage cancer screening (Team et al., 2011) . The performance of the end-to-end method was evaluated with entropy loss and receiver operating characteristic (ROC), and compared to a two-step approach, where the reconstruction DNN was trained first and the detection DNN was trained on the reconstructed images. Furthermore, the intermediate reconstructed images and features from the end-to-end network were studied for more comprehensive understanding of the DNN. In this paper a novel end-to-end DNN was proposed for abnormality detection in medical imaging. A reconstruction network and detection network were trained jointly to maximize the abnormality detection accuracy. We implemented the method on simulated chest CT data and achieved higher non-small lung nodule detection accuracy compared to two-step training scheme. There was significant false positive rate reduction on suspicious lesions (annotated non-nodules), and fair improvement on the overall detection sensitivity and accuracy. The images reconstructed by the end-to-end method resembled ordinary CT images, with more details and increased noise level compared to that from a two-step approach.Among the 102 validation cases, the mean entropy loss of nodule detection of the end-to-end method was smaller or similar than the two-step method for most of the cases, which indicated a statistical improvement on nodule detection from the proposed method. However, there was one case where the end-to-end entropy loss was significantly higher than the two-step loss. We studied the case further and confirmed that it was due to a strong misclassification of the positive samples, which was shown in figure 9(d).Although there was no significant improvement on the total AUC as shown in table 2, the ROC study in FIG4 indicated a significantly improved true positive rate at small false positive rate. The U.S. carried a national lung cancer screening with low-dose CT, which was considered to cause overdiagnosis due to the high false positive rate (Team et al., 2011; BID26 . The sensitivity improvement on the low false positive rate end indicated that the end-to-end DNN had great potential value to cancer screening tasks.There was great difference in the appearance of the reconstructed images from the two methods. The two-step training gave images with smaller overall noise level, but some of the details in lung were smoothed out, which caused misclassification for the detection network, as shown in FIG5 (a) and (b). The end-to-end training revealed more details in lung with higher spatial resolution, and the images were more suitable for the automatic nodule detection task. Though there were some misclassification due to the increased noise level, the overall performance of the nodule detection was improved with the end-to-end training scheme.The analysis on the intermediate results from the reconstruction network further revealed the difference between the two approaches. Whereas both methods kept similar structural component, the end-to-end method had more focus on the edges and tissues inside lung compared to the two-step method. As observed in FIG0 , the structures of the lung tissue were much more clearer in the end-to-end networks. This observation indicated that sharper edge and structures were of more importance for the detection network than the noise level in the reconstructed images, which is in accordance with human perceptions when radiologists perform the same task.Selecting appropriate representations of the data for further tasks such as detection is crucial, and the philosophy in end-to-end training is to leave the representation selection problem to machine rather than hand-crafting it. In this work, we demonstrated the feasibility of the end-to-end DNN for abnormality detection in medical imaging for a specific lung nodule detection problem in chest CT, and concluded that better results can be achieved for CAD systems by doing so. Nowadays most CAD systems are trained on reconstructed images, which are designed and tuned for radiologists rather than machines. By integrating the reconstruction process into the detection pipeline, better detection accuracy could be achieved for the CAD systems, and will increase its value to radiologists.",1802,0.945,1119,1.610366398570152,"Deep neural networks promising performance In medical imaging encouraging results deep learning for applications segmentation lesion detection classification Nearly all the deep learning based image analysis methods work reconstructed images obtained original acquisitions via solving inverse problemsreconstruction The reconstruction algorithms human observers not necessarily optimized DNNs which often observe features incomprehensible Hence desirable train the DNNs directly which lie a different domain with the images In this paper proposed end DNN abnormality detection medical imaging To align the acquisition the annotations made radiologists the image domain a DNN built as the unrolled version iterative reconstruction algorithms to map the acquisitions images followed detect the abnormality The two networks trained jointly order optimize the entire DNN for the detection task from the original acquisitions The DNN was implemented for lung nodule detection low-dose chest computed tomography where a numerical simulation done acquisitions 1,018 chest CT images radiologists' annotations proposed end DNN demonstrated better sensitivity the task compared the reconstruction and detection DNNs trained A significant reduction false positive rate on suspicious lesions were crucial the known over-diagnosis in low-dose lung CT imaging The images reconstructed proposed end network also presented enhanced details in interest Deep neural networks promising performance for various applications segmentation detection recognition In medical imaging DNNbased computer vision also desirable that radiologists' routine work requires handling large amount the possibility exists the intensive labor BID14 BID38 . Furthermore some radiation related applications low-dose scans always preferred decrease the potential harm that do The increased noise level lowdose data made even make correct decisions BID19 .Almost all the DNNs medical image analysis constructed do the observations However , in most medical imaging modalities the acquired data in a different domain inverse problems have reconstruct For example , magnetic resonance imaging acquires data the Fourier domain CT acquires the Radon transform domain BID10 During the reconstruction there great possibility information lost the presence noise the measurements low-dose scans BID27 . To compensate the noise iterative methods that exploit prior knowledge human body have BID11 BID30 . To achieve better representation the med-ical images DNN based reconstruction methods also proposed recently BID36 b; . However gap the objective image quality improvement its utility diagnosis which both radiologists computer aided diagnosis workingThere on task (end signal with DNNs the decisions were directly without explicit intermediate representations BID13 used DNN speech recognition directly audio data without and intermediate phonetic representations BID4 trained a DNN which learned commands directly images without recognition land markers BID18 used a classification criteria the colorization grey-scale images BID35 detected words directly scenes without doing a two-step text detection and optical character recognition It demonstrated end DNNs had improved multiple-step learning these applicationsIn proposed end which predicts abnormalities the images from the acquisitions A reconstruction DNN was first map the acquired data to the images align annotations made The DNN approximated a 10-iteration unrolled sequential quadratic surrogates BID11 . CNN) detect abnormalities from the reconstructed images The entire DNN was optimized jointly regard the total detection cross entropy loss The method was implemented The Lung Image Database Consortium image collectionLIDC-IDRI The Cancer Image ArchiveTCIA where we simulated ultra low-dose CT scans the original patients' data BID2 BID8 BID3 . The task the DNN was lung nodule detection , essential early stage cancer screening (Team et) The performance end method evaluated entropy loss receiver operating characteristic compared the reconstruction DNN trained first on the reconstructed images Furthermore the intermediate reconstructed images and features from end network studied more comprehensive understanding the DNN In this paper a novel end DNN was abnormality detection medical imaging A reconstruction network and detection network were trained jointly maximize the abnormality detection accuracy We implemented the method simulated chest CT data achieved higher non-small lung nodule detection accuracy two-step training scheme There significant false positive rate reduction on suspicious lesionsannotated nonnodules fair improvement the overall detection sensitivity accuracy The images reconstructed end method resembled ordinary CT images more details increased noise level compared that fromAmong the 102 validation cases mean entropy loss nodule detection of end smaller or similar most indicated a statistical improvement on from However one case end- entropy loss significantly We studied the case further confirmed it due a strong misclassification the positive samples shown figure 9(d).Although on the total AUC as shown table the ROC study in FIG4 indicated a significantly improved true positive rate small false positive rate carried a national lung cancer screening with, considered cause dueTeam et BID26 . The sensitivity improvement on the low false positive rate end indicated end DNN had great potential value cancer screening tasksThere great difference the appearance the reconstructed images The two-step training gave images with smaller overall noise level some in lung were smoothed caused misclassification for the detection network as shown FIG5 ( end- training revealed more details in lung with higher spatial resolution the images suitable the automatic nodule detection task Though some misclassification due the increased noise level the nodule detection improved end training schemeThe analysis on the intermediate results from the reconstruction network further the difference Whereas both methods kept similar structural component, end method had more focus the edges tissues inside lung compared As observed FIG0 the structures the lung tissue much clearer endto networks This observation indicated sharper edge and structures of the detection network the noise level the reconstructed images in human perceptions when radiologists performSelecting appropriate representations further tasks such detection is crucial the philosophy in end training leave the representation selection problem machine rather In this work demonstrated end DNN for abnormality detection medical imaging for a specific lung nodule detection problem chest CT concluded better results CAD systems doing Nowadays most CAD systems trained reconstructed images designed and tuned radiologists rather machines By integrating the reconstruction process the detection pipeline better detection accuracy the CAD systems will increase its value radiologists",0.01,0.2592391270351254
"Deep reinforcement learning (DRL) algorithms have demonstrated progress in learning to find a goal in challenging environments. As the title of the paper by Mirowski et al. (2016) suggests, one might assume that DRL-based algorithms are able to “learn to navigate” and are thus ready to replace classical mapping and path-planning algorithms, at least in simulated environments. Yet, from experiments and analysis in this earlier work, it is not clear what strategies are used by these algorithms in navigating the mazes and finding the goal. In this paper, we pose and study this underlying question: are DRL algorithms doing some form of mapping and/or path-planning? Our experiments show that the algorithms are not memorizing the maps of mazes at the testing stage but, rather, at the training stage. Hence, the DRL algorithms fall short of qualifying as mapping or path-planning algorithms with any reasonable definition of mapping. We extend the experiments in Mirowski et al. (2016) by separating the set of training and testing maps and by a more ablative coverage of the space of experiments. Our systematic experiments show that the NavA3C-D1-D2-L algorithm, when trained and tested on the same maps, is able to choose the shorter paths to the goal. However, when tested on unseen maps the algorithm utilizes a wall-following strategy to find the goal without doing any mapping or path planning. Navigation remains a fundamental problem in mobile robotics and artificial intelligence BID14 ; BID2 ). The problem is classically addressed by separating the task of navigation into two steps, exploration and exploitation. In the exploration stage, the environment is represented as some kind of map. In the exploitation stage, the map is used to plan a path to a given destination based on some optimality criterion. This classical approach has been quite successful in navigation using a variety of sensors. However, navigation in general unstructured environments, especially with texture-less BID17 , transparent and reflective surfaces BID5 , remains a challenge.Recently, end-to-end navigation methods-which attempt to solve the navigation problem without breaking it down into separate parts of mapping and path-planning-have gained traction. With the recent advances in Deep Reinforcement Learning (DRL), these end-to-end navigation methods, such as BID10 ; ; BID6 ; BID7 ; BID12 , forego decisions about the details that are required in the intermediate step of mapping. The potential for simpler yet more capable methods is rich; for example, the resulting trained agents can potentially optimize the amount of map information required for navigation tasks. One such algorithm by BID7 has shown promise in exploring and finding the goal efficiently within complex environments. Notably, this is done using only monocular first-person views.Despite such potential advances, DRL-based navigation remains a relatively unexplored field with its own limitations. The black-box nature of these methods make them difficult to study, and the patterns captured by the methods are not well understood. Recent work analyzing neural networks has shown that deep learning-based object detection methods can be easily fooled by introducing noise that is imperceptible to humans BID11 ); this level of sensitivity motivates why it is particularly important to analyze DRL methods across a wide variety of experiments: we need to understand their strengths and limitations. Figure 1 : Snapshots of the path taken by the agent while evaluating the model trained on the same random map with random goal and random spawn. The first row shows the top view of the robot moving through the maze with the goal location marked orange, the agent marked black and the agent's orientation marked red. The second row shows the first person view, which, besides reward, is the only input available to the agent and the top view is available only for human analysis.In this work, we develop a better understanding of recent DRL-based methods. In particular, we thoroughly explore and analyze the state-of-the-art BID7 methods across hundreds of maps with increasing difficulty levels. We set up the environment as a randomly generated map, as shown in Fig 1, with an agent and a goal. The agent is provided only with the first-person view and is tasked to find the goal as many times as possible within a fixed amount of time, re-spawning its location each time it reaches the goal. We train and evaluate the algorithms with increasing difficulty. In the easiest stage, we keep the goal location, spawn location and map constant over the training and testing. We call this set up static goal, static spawn, and static map. To increase the difficulty, we incrementally randomize the spawn locations, goal locations and map structures until all three are random. We discuss the design of experiments in Section 4.1 in more detail. BID7 do train and test their algorithms with randomized goals and spawns and show that their algorithm is able to exploit the knowledge of the goal location at evaluation time to maximize reward. However, following training and testing on constant map structures, this state-ofthe-art result is shown to be successful on only one map, which brings into question the repeatability of the results. It is also unclear whether these results generalize to unseen maps.Although disjoint training and testing sets are standard practice in machine learning, to the best of our knowledge, we are the first to evaluate any DRL-based navigation method on maps with unseen structures. We expand on the analysis in BID7 to address its limitations and ask whether DRL-based algorithms such as NavA3C+D 1 D 2 L perform any mapping followed by shortest path planning. Our experiments show no evidence of mapping in cases where algorithms are evaluated on unseen maps and no evidence of optimal path planning, even when the map is constant and only the goal is randomized.To better understand navigation, we compute attention-maps for models to show which portions of the input image are being used. We find that the models discard most of the image information, focusing attention on a small band in the middle of the image except around junctions, in which case the attention is distributed evenly throughout the image.These findings result from training and testing on multiple maps that were randomly selected from a set of 1100 randomly generated maps. We provide experimental results on ten randomly selected maps and a testing set of 100 unseen maps to ensure results are independent of map choice. We will make our code and data available following the blind review process. In this work, we comprehensively evaluate NavA3C+D 1 D 2 L BID7 ), a DRL-based navigation algorithms, through systematic set of experiments that are repeated over multiple randomly chosen maps. Our experiments show that DRL-based navigation models are able to perform some degree of path-planning and mapping when trained and tested on the same map even when spawn locations and goal locations are randomized. However the large variation in the evaluation metrics show that how such behaviour is not consistent across episodes. We also train and test these methods on disjoint set of maps and show that such trained models fail to perform any form of path-planning or mapping in unseen environments.In this work, we begin by asking: do DRL-based navigation algorithms really ""learn to navigate""? Our results answer this question negatively. At best, we can say that DRL-based algorithms learn to navigate in the exact same environment, rather than general technique of navigation which is what classical mapping and path planning provide. We hope that the systematic approach to the experiments in this work serve as a benchmark for future DRL-based navigation methods.",1508,0.84,902,1.671840354767184,"Deep reinforcement learning (DRL) algorithms demonstrated progress learning find a goal challenging environments As the title by (2016 suggests, one DRL-based algorithms able ��learn navigate�� ready replace classical mapping and path-planning algorithms at simulated environments Yet from experiments analysis this earlier work strategies these algorithms navigating finding the goal In pose and study this underlying question are DRL algorithms doing some form mapping and/or path-planning Our experiments the algorithms memorizing the maps mazes at the testing stage, at Hence the DRL algorithms fall qualifying mapping or with any reasonable definition We extend the experiments Mirowski et al (2016 by separating the set training and testing maps by a more ablative coverage experiments Our systematic experiments the NavA3C-D1-D2-L algorithm when trained and the same maps choose the shorter paths the goal However when tested unseen maps the algorithm utilizes a wall-following strategy the goal without doing any mapping or path planning Navigation remains a fundamental problem mobile robotics artificial intelligence BID14 ; BID2 The problem classically addressed separating the task navigation exploration exploitation In the exploration stage the environment represented map In the exploitation stage the map used plan a path based some optimality criterion This classical approach quite navigation using sensors However navigation general unstructured environments with textureless BID17 , transparent and reflective surfaces BID5 remainsRecently end navigation methods-which attempt solve without breaking it mapping path-planning With the recent advances these end navigation BID10 ; ; forego decisions the details that the intermediate step mapping. The potential simpler yet more capable methods rich; the resulting trained agents potentially optimize map information navigation tasks One such algorithm by BID7 shown exploring and finding the goal efficiently within complex environments Notably done only monocular first-person viewsDespite such potential advances DRL-based navigation The black-box nature these methods make study the patterns captured Recent work analyzing deep learning-based object detection methods easily fooled introducing noise that BID11 ); this level sensitivity motivates why particularly analyze DRL methods across experiments: we their strengths Figure : Snapshots the path taken the agent while evaluating trained the same random map random goal and random spawn The first row shows moving with the goal location marked orange the agent marked the agent's orientation The second row shows the first person view, besides reward the only input and available human analysisIn this work develop recent DRL-based methods In particular thoroughly explore and state BID7 methods across hundreds maps with increasing difficulty levels We set the environment as a randomly generated map as Fig an agent The agent provided only tasked find the goal as many within re its location each reaches We train evaluate the algorithms with increasing difficulty In the easiest stage keep the goal location spawn location map constant over the training We call set static goal static spawn To increase the difficulty incrementally randomize goal locations map structures until three random We discuss experiments Section in BID7 do train test their algorithms randomized goals spawns and show exploit the knowledge the goal location at evaluation time reward However following training testing constant map structures this state-ofthe-art result shown successful brings into It unclear these results generalize unseen mapsAlthough disjoint training testing sets standard practice to evaluate any DRL-based navigation method maps unseen structures We expand BID7 to its limitations ask DRL-based algorithms such NavA3C+D 1 D 2 L perform any mapping followed shortest path planning Our experiments mapping in cases algorithms evaluated unseen maps optimal path planning constant only the goal randomizedTo better navigation compute attention-maps models to show which portions the input image being We find the models discard most the image information focusing attention a small band in except around junctions the attention distributedThese findings result training multiple maps randomly 1100 randomly generated maps We provide experimental results ten randomly selected maps a testing 100 unseen maps ensure results independent map choice We will make our code data following the blind review process In this work comprehensively evaluate NavA3C+D 1 D 2 L BID7 ), a DRL-based navigation algorithms through systematic set experiments repeated multiple randomly chosen maps Our experiments DRL-based navigation models some degree path-planning mapping when trained and the same map even spawn locations goal locations randomized However the large variation the evaluation metrics show how such behaviour not consistent episodes. We also train test these methods disjoint set maps show such trained models fail any form path-planning mapping unseen environmentsIn begin asking do DRL-based navigation algorithms really ""learn Our results answer negatively At best DRL-based algorithms learn navigate in the exact same environment rather general technique navigation which what classical mapping path planning provide We hope the systematic approach the experiments serve future DRL-based navigation methods",0.01,0.41586936638242716
"In many robotic applications, it is crucial to maintain a belief about the state of 
 a system, like the location of a robot or the pose of an object.
 These state estimates serve as input for planning and decision making and 
 provide feedback during task execution. 
 Recursive Bayesian Filtering algorithms address the state estimation problem,
 but they require a model of the process dynamics and the sensory observations as well as 
 noise estimates that quantify the accuracy of these models. 
 Recently, multiple works have demonstrated that the process and sensor models can be 
 learned by end-to-end training through differentiable versions of Recursive Filtering methods.
 However, even if the predictive models are known, finding suitable noise models 
 remains challenging. Therefore, many practical applications rely on very simplistic noise 
 models. 
 Our hypothesis is that end-to-end training through differentiable Bayesian 
 Filters enables us to learn more complex heteroscedastic noise models for
 the system dynamics. We evaluate learning such models with different types of 
 filtering algorithms and on two different robotic tasks. Our experiments show that especially 
 for sampling-based filters like the Particle Filter, learning heteroscedastic noise 
 models can drastically improve the tracking performance in comparison to using 
 constant noise models. For many real-world systems that we would like to control, we cannot directly observe the current state directly. However, in order to stabilize a system at a goal state or make it track a trajectory, we need to have access to state feedback. An observer provides an estimate of the current system state from sensor measurements. Recursive Bayesian Filtering is a probabilistic approach towards estimating a belief about the current state. The method relies on a process model that predicts how the system behaves over time and an observation model that generates the expected observations given the predicted state. While the approach itself is general and makes few assumptions, the challenge is to formulate the process and observation models and to estimate the noise in these models. Process and observation noise quantify how certain the filter is about either the prediction or the observations. This information is used to determine how much the predicted state is updated based on the observation.Deep neural networks are well suited for tasks that require finding patterns or extracting information from raw, high-dimensional input signals and compressing them into a more compact representation. They have therefore become the method of choice especially in perception problems. For many robotics tasks like modeling dynamics, planning or tracking however, it has been shown that combining prior knowledge in the form of analytical models and/or algorithmic structure with trainable network components leads to better performance and generalizability than trying to learn the complete tasks from scratch BID17 BID11 BID9 BID23 BID19 BID8 BID6 BID12 .Specifically , BID8 BID6 BID9 BID12 have presented differentiable Bayesian Filtering algorithms. The authors focus on learning the observation and dynamics models end-to-end through the filters and demonstrate that the recursive filtering structure improves prediction results over using recurrent neural networks that were trained for the same task.In many robotic applications, it is possible to formulate the process and observation model based on first-order principles. However, finding appropriate values for the process and observation noise is often difficult and despite of much research on identification methods (e.g. BID2 BID25 ) they are often tuned manually. To reduce the tedious tuning effort, the noise models are typically assumed to be a Gaussian with zero mean and constant covariance. Many real systems can however be better modeled with heteroscedastic noise models, where the level of uncertainty depends on the state of the system and/or possible control inputs. Taking heterostochasticity into account has been demonstrated to improve filtering performance in many robotic tasks BID1 BID14 .In this work, we propose a method to learn heteroscedastic noise models from data by optimizing the prediction likelihood end-to-end through differentiable Bayesian Filters. In addition to differentiable Extended Kalman Filters and Particle Filters, which have been proposed in related work, we also propose two different versions of the Unscented Kalman Filter.In our experiments we focus on learning the noise models and therefore assume that observation and process models are known or at least pretrained. We evaluate the performance of the different filters and noise models on two different real-world robotic problems: (i) Visual Odometry for an driving car BID6 BID9 BID4 which has simple smooth dynamics and a low-dimensional state, and (ii) Visual tracking of an object that is pushed by a robot (Yu et al., 2016; BID17 . Planar pushing has challenging, discontinuous dynamics and was shown to have a heteroscedastic noise distribution BID1 . Furthermore, the dimensionality of the state is double of the Visual Odometry task.Our experiments show that using heteroscedastic process noise models drastically improves the tracking performance of the Particle Filter and Unscented Filter variants and facilitated learning as compared to learning a constant process noise model. While learning the noise models can be beneficial for all filters, the tracking performance of the EKF turned out to be least sensitive to the noise models. In comparison to the process noise, learning the observation noise did not improve the results much for the two tasks we evaluated. We proposed to optimize the process and observation noise for Bayesian Filters through end-to-end training and evaluated the method with different filtering algorithms and on two robotic applications. Our experiments showed that learning the process noise is especially important for filters that sample around the mean estimate of the state, like the Particle Filter but also the Unscented Kalman Filters. The Extended Kalman Filter in contrast proved to be most robust to suboptimal choices of the noise models. While this makes it a good choice for problems with simple and smooth dynamics, our experiments on the pushing task demonstrated that the (optimized) Unscented Filters can perform better on problems with more complex and even discontinuous dynamics.Training a state-dependent process noise model instead of a constant one improves the prediction accuracy for dynamic systems that are expected to have heteroscedastic noise. In our experiments, it also facilitated learning in general and lead to faster convergence of the models.We also used a heteroscedastic observation noise model in all our experiments. But different from the results in BID6 , we could not see a large benefit from it: Inspection on the pushing task showed that larger errors in the prediction of the preprocessing networks were not associated with higher observation noise. Identifying inputs that will lead to bad predictions is a difficult task if no obvious problems like occlusions are present to explain such outliers. Developing better methods for communicating uncertainty about the predictions of a neural network would thus be an impotent next step to further improve the performance of differentiable Bayesian Filters. The basic steps of the Extended Kalman Filter can be directly implemented in Tensorflow without any modifications. The only aspect of interest is how to compute the Jacobians of the process and observation model. Tensorflow implements auto differentiation, but has (as of now) no native support for computing Jacobians. While it can be done, it requires looping over the dimensions of the differentiated variable one by one, which we found to be relatively slow, especially during graph-construction. We therefore recommend to manually derive the Jacobians where applicable.",1434,0.739,857,1.6732788798133023,"In many robotic applications crucial a belief like the location the pose These state estimates serve input planning decision feedback during task execution Recursive Bayesian Filtering algorithms address the state estimation problem require the process dynamics the sensory observations as noise estimates that quantify Recently multiple works demonstrated the process and sensor models learned end through differentiable versions Recursive Filtering methods However even the predictive models known finding suitable noise models remains Therefore many practical applications rely very simplistic noise models Our hypothesis end training through differentiable Bayesian Filters enables learn more complex heteroscedastic noise models for the system dynamics We evaluate learning such models different types filtering algorithms on two different robotic tasks Our experiments especially sampling-based filters like the Particle Filter learning heteroscedastic noise models drastically in comparison using constant noise models For many real-world systems that we would control directly observe directly However stabilize a system at a goal state or make track a trajectory access state feedback An observer provides the current system state from sensor measurements Recursive Bayesian Filtering towards estimating a belief. The method relies a process model predicts behaves an observation model generates the expected observations given While the approach itself general makes few assumptions the challenge formulate the process and observation models estimate the noise Process and observation noise quantify how certain the filter about either the prediction This information used the predicted state updated the observationDeep neural networks well tasks finding extracting raw, high-dimensional input signals and compressing They therefore become the method especially perception problems For many robotics tasks like modeling dynamics planning or tracking however has shown combining prior knowledge the form analytical models algorithmic structure with trainable network components leads trying the complete tasks .Specifically , have presented differentiable Bayesian Filtering The authors focus learning the observation and dynamics models end the filters demonstrate the recursive filtering structure improves prediction results over using that wereIn many robotic applications formulate the process and observation model based However finding appropriate values the process and observation noise despite of much research identification methods (e.g. BID2 BID25 ) they tuned manually To reduce the tedious tuning effort the noise models typically assumed a Gaussian zero mean and constant covariance Many real systems however better modeled heteroscedastic noise models the level uncertainty depends possible control inputs Taking heterostochasticity has demonstrated filtering performance many robotic tasks BID1 BID14 .In propose learn heteroscedastic noise models data by optimizing the prediction likelihood end through differentiable Bayesian Filters In addition differentiable Extended Kalman Filters which proposed related workIn our experiments focus learning the noise models therefore assume observation and process models known or pretrained We evaluate the different filters noise models two different real-world robotic problems (i) Visual Odometry an driving car BID6 which simple smooth dynamics a low-dimensional state Visual tracking that pushedYu BID17 . Planar pushing has challenging, discontinuous dynamics was shown a heteroscedastic noise distribution BID1 . Furthermore the dimensionality the state double of the Visual Odometry taskOur experiments using heteroscedastic process noise models drastically the Particle Filter Unscented Filter variants and facilitated learning as learning While learning the noise models can beneficial all filters the tracking performance the EKF turned least sensitive In comparison the process noise learning the observation noise did much for we evaluated We proposed optimize the process and observation noise Bayesian Filters through end training evaluated different filtering algorithms on two robotic applications Our experiments learning the process noise especially filters sample around the mean estimate the state like the Particle Filter but Unscented Kalman The Extended Kalman Filter in contrast proved most robust suboptimal choices the noise models While this makes problems simple and smooth dynamics our experiments on the pushing task demonstrated the (optimized) Unscented Filters perform problemsTraining a state-dependent process noise model instead improves dynamic systems expected heteroscedastic noise In our experiments it also facilitated learning general lead faster convergenceWe a heteroscedastic observation noise model But different the results BID6 , could a large benefit it: Inspection on the pushing task showed larger errors the prediction the preprocessing networks higher observation noise Identifying inputs will bad predictions if no obvious problems like occlusions to such outliers Developing better methods communicating uncertainty the predictions would thus an impotent next further improve differentiable Bayesian Filters The basic steps the Extended Kalman Filter directly without The only aspect interest compute the Jacobians the process and observation model Tensorflow implements auto differentiation has (as computing Jacobians While can done looping the dimensions differentiated variable one we found relatively slow during graph-construction We therefore manually derive the Jacobians where",0.01,0.4195346018125077
"Graph convolutional neural networks have recently shown great potential for the task of zero-shot learning. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, we find that the extensive use of Laplacian smoothing at each layer in current approaches can easily dilute the knowledge from distant nodes and consequently decrease the performance in zero-shot learning. In order to still enjoy the benefit brought by the graph structure while preventing the dilution of knowledge from distant nodes, we propose a Dense Graph Propagation (DGP) module with carefully designed direct links among distant nodes. DGP allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants. A weighting scheme is further used to weigh their contribution depending on the distance to the node. Combined with finetuning of the representations in a two-stage training approach our method outperforms state-of-the-art zero-shot learning approaches. With the ever-growing supply of image data, from an ever-expanding number of classes, there is an increasing need to use prior knowledge to classify images from unseen classes into correct categories based on semantic relationships between seen and unseen classes. This task is called zero-shot image classification. To obtain satisfactory performance on this task, it is crucial to model precise class relationships based on prior class knowledge. Previously prior knowledge has been incorporated in form of semantic descriptions of classes, such as attributes BID0 BID27 BID18 or word embeddings BID29 BID10 , or by using semantic relations such as knowledge graphs BID23 BID26 BID28 BID19 . Approaches that use knowledge graphs are less-explored and generally are based on the assumption that unknown classes can exploit similarity to known classes. Recently the benefit of hybrid approaches that combine knowledge graph and semantic class descriptions has been illustrated BID31 .The current state-of-the-art approach BID31 processes knowledge graphs by making use of recent developments in applying neural network techniques to non-euclidean spaces, such as graph and manifold spaces BID1 . A deep graph convolutional neural network (GCN) BID13 ) is used and the problem is phrased as weight regression, where the GCN is trained to regress classifier weights for each class. GCNs balance model complexity and expressiveness with a simple scalable model relying on the idea of message passing, i.e. nodes pass knowledge to their neighbors. However, these models were originally designed for classification tasks, albeit semi-supervised, an arguably simpler task than regression. In recent work , it has been shown that GCNs perform a form of Laplacian smoothing, where feature representations will become more similar as depth increases leading to easier classification BID16 . In the regression setting, instead, the aim is to exchange information between nodes in the graph and extensive smoothing is not desired as it dilutes information and does not allow for accurate regression. For instance, in a connected graph all features in a GCN with n layers will converge to the same representation as n → ∞ under some conditions, hence washing out all information BID16 . Here, graph propagation represents the knowledge that a node receives in a single layer for previous approaches. b) Proposed dense graph propagation for node 'Cat'. The node receives knowledge from all its descendants during the descendant phase (blue arrows) and its ancestors during the ancestor phase (red arrows). This leads to a densely connected graph where knowledge can directly propagate between related nodes. Weights α k are used to weigh nodes that are k-hops away from a given node.We, therefore, argue that this approach is not ideal for the task of zero-shot learning and that the number of layers in the graph should be small in order to avoid smoothing. We illustrate this phenomenon in practice , by showing that a shallow GCN consistently outperforms previously reported results. We employ a model-of-models framework by training the method to predict a set of logistic regression classifier for each class on top of a set of extracted features produced by a CNN. Choosing a small number of layers, however , has the effect that knowledge will not propagate well through the graph. A 1-layer GCN for instance only considers neighbors that are two hops away in the graph such that only immediate neighbors influence a given node. Thus, we propose a dense connectivity scheme , where nodes are connected directly to descendants/ancestors in order to include distant information. These connections allow us to propagate information without many smoothing operations but leads to the problem that all descendants/ancestors are weighed equally when computing the regression weight vector for a given class. However, intuitively, nodes closer to a given node should have higher importance. To remedy this, we extend this framework by adding a weighting scheme that considers the distance between nodes in order to weigh the contribution of different nodes. Making use of shared weights based on the distance also has the advantage that it only adds a minimal amount of additional parameters, is computationally efficient, and provides a balance between increasing flexibility of the model and keeping it restrictive enough to allow good predictions for the nodes of the unseen classes. FIG0 illustrates the difference in the way knowledge is propagated in this proposed Dense Graph Propagation (DGP) module compared to a GCN layer.To allow the feature extraction stage of the pre-trained CNN to adjust to the newly learned classifiers we propose a two-phase training scheme. In the first step, the DGP is trained to predict the last layer CNN weights. In the second phase, we replace the last layer weights of the CNN with the weights predicted by the DGP, freeze the weights and finetune the remaining weights of the CNN by optimizing the cross entropy classification loss on the seen classes.Our contributions can be summarized as follows. We present• an analysis of our intuitions for zero-shot learning and illustrate how these intuitions can be combined to design a DGP that outperforms previous zero-shot learning results. In contrast to previous approaches using graph convolutional neural networks for zero-shot learning, we illustrate that the task of zero-shot learning benefits from shallow networks. Further, to avoid the lack of information propagation between distant nodes in shallow models, we propose DGP, which exploits the hierarchical structure of the knowledge graph by adding a dense connection scheme. Experiments illustrate the ability of the proposed methods, outperforming previous state-of-the-art methods for zero-shot learning. In future work, we aim to investigate the potential of more advanced weighting mechanisms to further improve the performance of DGP compared to the SGCN. The inclusion of additional semantic information for settings where these are available for a subset of nodes is another future direction.A QUALITATIVE RESULTS Figure 4 and 5 provide further qualitative results of our finetuned Graph Propagation Module GPM and Dense Graph Propagation Module DGP compared to a standard ResNet and GCNZ, our reimplementation of BID31 .upright , grand piano, organ, accordion, barbershop piano, spinet, keyboard instrument, concert grand, baby grand piano, spinet, concert grand, baby grand, keyboard instrument piano, baby grand, concert grand, spinet, keyboard instrument B TWO-PHASE PROPAGATION TAB4 illustrates the benefit of a two-phase directed propagation rule where ancestors and descendants are considered individually compared to two consecutive updates using the full adjacency matrix in the dense method. C ANALYSIS OF NUMBER OF LAYERS TAB5 illustrates the drop in performance that is caused by using additional hidden layers in the GCN for the 2-hops experiment. All hidden layers have dimensionality of 2048 with 0.5 dropout. TAB6 explains the performance difference between our SGCN, our reimplementation of GCNZ and the reported results in BID31 . Note, unless otherwise stated training is performed for 3000 epochs. Non-symmetric normalization (D −1 A) is denoted as non-sym in the normalization column, while a symmetric normalization (D −1/2 AD −1/2 ) is denoted as sym. No finetuning has been performed for SGCN in these results. TAB7 shows the mean and std for 3 runs for the 2-hops and All dataset. It can clearly be observed that as the number of classes increases (2-hops to all), results become more stable.",1680,0.878,974,1.7248459958932238,"Graph convolutional neural networks the task zero-shot learning These models highly sample efficient as related concepts the graph structure share statistical strength allowing generalization new classes when faced a lack However we find the extensive use smoothing at each layer in current approaches easily the knowledge from distant nodes consequently decrease in zero-shot learning In order still enjoy brought the graph structure while preventing the dilution knowledge distant nodes propose Dense module carefully designed direct links among distant nodes DGP allows us exploit the hierarchical graph structure the knowledge graph through additional connections These connections added based a node's relationship its ancestors descendants A weighting scheme further used weigh their contribution depending Combined finetuning the representations a two-stage training approach our method state zeroshot learning With image data from classes use prior knowledge classify unseen classes into correct categories based semantic relationships This task called zero-shot image classification To obtain satisfactory performance crucial model precise class relationships based prior class knowledge Previously prior knowledge has incorporated form semantic descriptions classes attributes BID0 BID27 BID18 , semantic relations knowledge graphs Approaches use knowledge graphs less-explored generally based unknown classes exploit similarity Recently the benefit hybrid approaches that knowledge graph semantic class descriptions illustrated BID31 .The current state- processes knowledge graphs making recent developments applying graph and manifold spaces BID1 A deep graph convolutional neural networkGCN) BID13 ) and the problem phrased weight regression regress classifier weights GCNs balance model complexity expressiveness a simple scalable model relying the idea message passing pass knowledge However these models originally classification tasks albeit semi-supervised, an arguably simpler task regression In recent work , it GCNs perform a form feature representations will become similar depth increases leading easier classification BID16 In regression setting instead, the aim exchange nodes extensive smoothing not desired as information does accurate regression For instance a connected graph all features a GCN with n layers converge n → �� under hence washing all information BID16 . Here graph propagation represents the knowledge receives a single layer for previous approaches b) Proposed dense graph propagation node 'Cat The node receives knowledge all its descendants during the descendant phaseblue arrows This leads a densely connected graph knowledge can directly propagate related nodes Weights α k are used weigh nodes khops awayWe, argue ideal zero-shot learning layers in smoothing We illustrate practice , a shallow GCN consistently previously results We employ model-ofmodels framework by training the method for on top extracted features produced a CNN Choosing a small number layers however , has knowledge will propagate well the graph A 1-layer GCN for instance only considers neighbors two hops in the graph such only immediate neighbors influence Thus propose a dense connectivity scheme , nodes directly descendants/ancestors include distant information These connections allow propagate without many smoothing operations but leads the problem all descendants/ancestors weighed equally computing the regression weight vector However, intuitively, nodes closer higher importance To remedy extend this framework considers nodes order weigh Making use shared weights based also only adds additional parameters is computationally a balance increasing flexibility keeping restrictive enough good predictions the nodes the unseen classes FIG0 illustrates the difference knowledge this proposed Dense Graph Propagation (DGP) module compared a GCN layerTo allow the feature extraction stage the pre-trained CNN adjust the newly learned classifiers propose In the DGP trained predict the last layer CNN weights In replace the last layer weights the CNN with predicted the DGP freeze finetune of optimizing the cross entropy classification loss on the seen classesOur contributions can We present• an analysis our intuitions for zero-shot learning illustrate combined design a DGP In contrast previous approaches using zero-shot learning illustrate shallow networks Further to the lack information propagation between distant nodes shallow models propose DGP, exploits the knowledge graph adding a dense connection scheme Experiments illustrate the proposed methods, outperforming state zero-shot learning In future work aim investigate more advanced weighting mechanisms further DGP compared the SGCN The inclusion additional semantic information for settings where these for a subset nodes another future directionA QUALITATIVE RESULTS Figure and our finetuned Graph Propagation Module GPM compared a standard ResNet and GCNZ, our reimplementation BID31 .upright , grand piano organ barbershop piano spinet keyboard instrument concert grand baby grand piano spinet concert grand keyboard instrument piano TWO-PHASE PROPAGATION TAB4 illustrates a two-phase directed propagation rule where ancestors considered individually compared two consecutive updates using in the dense method C ANALYSIS LAYERS TAB5 illustrates the drop performance that using additional hidden layers for the 2-hops experiment All hidden layers have dimensionality 2048 with TAB6 explains the performance difference our SGCN, our reimplementation GCNZ the reported results BID31 . Note, unless otherwise stated training performed 3000 epochs Non-symmetric normalization (D −1 A nonsym in AD ) sym No finetuning SGCN these results TAB7 shows the mean std for 3 runs for the 2-hops All dataset It can clearly observed as classes increases (2hops to all results stable",0.01,0.5509230829468674
"In this paper, we propose a capsule-based neural network model to solve the semantic segmentation problem. By taking advantage of the extractable part-whole dependencies available in capsule layers, we derive the probabilities of the class labels for individual capsules through a recursive, layer-by-layer procedure. We model this procedure as a traceback pipeline and take it as a central piece to build an end-to-end segmentation network. Under the proposed framework, image-level class labels and object boundaries are jointly sought in an explicit manner, which poses a significant advantage over the state-of-the-art fully convolutional network (FCN) solutions. Experiments conducted on modified MNIST and neuroimages demonstrate that our model considerably enhance the segmentation performance compared to the leading FCN variant.
 An effective segmentation solution should have a well-equipped mechanism to capture both semantic (i.e., what) and location (i.e., where) information. The fully convolutional network (FCN) BID19 and its variants BID24 BID21 BID1 constitute a popular class of solutions for this task, producing state-of-the-art results in a variety of applications. FCN and its variants (FCNs) are commonly constructed with an encoder-decoder architecture. In the encoding path, input images are processed through a number of ""convolution + pooling"" layers to generate high-level latent features, which are then progressively upsampled in the decoder to reconstruct the target pixel labels. The feature maps produced in higher (coarser) layers and those in lower (finer) layers contain complementary information: the former is richer in semantics, while the latter carries more spatial details that define class boundaries.Originated from and constructed upon convolutional neural networks (CNNs) BID13 BID26 , FCNs' encoders inherit some common drawbacks of CNNs, one of which is the lack of an internal mechanism in achieving viewpoint-invariant recognition. Traditional CNNs, as well as FCNs, rely on convolution operations to capture various visual patterns, and utilize poolings to enable multi-scale processing of the input images. Rotation invariance, however, is not readily available in both models. As a result, more data samples or additional network setups BID6 BID7 would be required for objects from different viewpoints to be correctly recognized. The absence of explicit part-whole relationships among objects imposes another limitation for FCNs -without such a mechanism, the rich semantic information residing in the higher layers and the precise boundary information in the lower layers can only be integrated in an implicit manner .Capsule nets BID25 BID10 , operating on a different paradigm, can provide a remedy. Capsule nets are built on capsules, each of which is a group of neurons representing one instance of a visual entity, i.e., an object or one of its parts BID9 . Capsules output both activation probabilities of their presence and the instantiation parameters that describe their properties, such as pose, deformation and texture, relative to a viewer BID9 . During inference propagation, the principle of coincidence filtering is employed to activate higher-level capsules and set up part-whole relationships among capsule entities. Such part-whole hierarchy equips capsule nets with a solid foundation for viewpoint-invariant recognition, which can be implemented through dynamic routing BID25 or EM routing BID10 . The same hierarchy , if properly embedded into a segmentation network, would provide a well-grounded platform to specify contextual constraints and enforce label consistency.With this thought, we develop a capsule-based semantic segmentation solution in this paper. Our approach treats capsule nets as probabilistic graphical models capable of inferring probabilistic dependences among visual entities, through which part-whole relationships can be explicitly constructed. As a concrete implementation , we propose a new operation sequence, which we call traceback pipeline, to capture such part-whole information through a recursive procedure to derive the class memberships for individual pixels. We term our model Tr-CapsNet .The contributions of our Tr-CapsNet can be summarized as:1. In Tr-CapsNet, the class labels for individual spatial coordinates within each capsule layer are analytically derived. The traceback pipeline in our model , taking advantage of the graphical properties of capsule nets, is mathematically rigorous. To the best of our knowledge, this is the first work to explore a capsule traceback approach for image segmentation. In addition, probability maps at each capsule layer are readily available, which makes it convenient to conduct feature visualization and layer interpretation.2. In parallel with segmentation, Tr-CapsNet carries out explicit class recognition at the same time. Such explicitness poses a powerful practical advantage over FCNs.3. The traceback pipeline is designed under a general context, making it applicable to many other potential tasks, including object localization and detection, action localization and network interpretation.",944,0.492,555,1.7009009009009008,"In solve By taking the extractable part-whole dependencies available capsule layers derive the probabilities the class labels individual capsules through recursive, layer procedure We model this procedure a traceback pipeline take a central piece build end segmentation network Under the proposed framework image-level class labels object boundaries jointly sought poses state fully network solutions Experiments conducted modified MNIST and neuroimages demonstrate our model considerably enhance compared the leading FCN variant An effective segmentation solution should a well-equipped mechanism capture The fully convolutional networkFCN) BID19 and constitute a popular class solutions this task producing state results FCN and its variants ( commonly constructed In the encoding path input images through ""convolution + pooling"" layers high-level latent features progressively upsampled reconstruct the target pixel labels The feature maps produced higher (coarser) layers and those contain complementary information: former richer semantics carries more spatial details define class boundariesOriginated and constructed upon BID13 BID26 FCNs' encoders inherit some common drawbacks one an internal mechanism in achieving viewpoint-invariant recognition Traditional CNNs as FCNs rely convolution operations capture various visual patterns utilize poolings enable multi-scale processing Rotation invariance however readily both models As more data samples or additional network setups BID6 BID7 would objects from different viewpoints correctly recognized The absence explicit part-whole relationships objects imposes another limitation for FCNs -without such a mechanism the rich semantic information residing the higher layers and the precise boundary information integrated an implicit manner .Capsule nets BID25 BID10 , operating a remedy Capsule nets built on capsules each a group neurons representing one instance a visual entity one BID9 . Capsules output both activation probabilities their presence the instantiation parameters that describe pose texture relative a viewer BID9 . During inference propagation the principle coincidence filtering employed activate higher-level capsules set part-whole relationships capsule entities Such part-whole hierarchy equips capsule nets viewpoint-invariant recognition implemented dynamic routing BID25 or EM routing . The same hierarchy , if properly embedded a segmentation network specify contextual constraints enforce label consistencyWith this thought develop Our approach treats capsule nets probabilistic graphical models capable among visual entities through part-whole relationships explicitly As a concrete implementation , propose a new operation sequence traceback pipeline capture such part-whole information through to derive the class memberships individual pixels We term our model Tr-CapsNet .The contributions can In Tr-CapsNet the class labels individual spatial coordinates within each capsule layer analytically derived The traceback pipeline in our model , taking the graphical properties capsule nets rigorous To explore a capsule traceback approach image segmentation In addition probability maps at each capsule layer readily convenient conduct feature visualization layer interpretation.2. In parallel segmentation Tr-CapsNet carries explicit class recognition at Such explicitness poses a powerful practical advantage FCNs.3 The traceback pipeline designed under a general context making applicable many other potential tasks object localization detection action localization network interpretation",0.01,0.4899130846994714
"Studying the evolution of information theoretic quantities during Stochastic Gradient Descent (SGD) learning of Artificial Neural Networks (ANNs) has gained popularity in recent years. 
 Nevertheless, these type of experiments require estimating mutual information and entropy which becomes intractable for moderately large problems. In this work we propose a framework for understanding SGD learning in the information plane which consists of observing entropy and conditional entropy of the output labels of ANN. Through experimental results and theoretical justifications it is shown that, under some assumptions, the SGD learning trajectories appear to be similar for different ANN architectures. First, the SGD learning is modeled as a Hidden Markov Process (HMP) whose entropy tends to increase to the maximum. Then, it is shown that the SGD learning trajectory appears to move close to the shortest path between the initial and final joint distributions in the space of probability measures equipped with the total variation metric. Furthermore, it is shown that the trajectory of learning in the information plane can provide an alternative for observing the learning process, with potentially richer information about the learning than the trajectories in training and test error. How do information theoretic quantities behave during the training of ANNs? This question was addressed by Shwartz-Ziv & Tishby (2017) in an attempt to explain the learning through the lens of the information bottleneck method (Tishby et al., 1999) . In that work, the layers of an ANNs are considered random variables forming a Markov chain. The authors constructed a 2D information plane by estimating the mutual information values between hidden layers, inputs, and outputs of ANNs. Using this approach it was observed that the information bottleneck method provides an approximate explanation for SGD learning. In addition, their experiments showed the role of compression in learning. That initial paper motivated further work on this line of research BID17 BID9 . The main practical limitation of that type of experiments is that it requires estimating mutual information between high dimensional continuous random variables. This becomes prohibitive as soon we move to moderately large problems, such as the CIFAR-100 dataset, where the large ANNs are employed. Other works dealing with information theoretic quantities tend to have these experimental limitations. For instance, BID16 ; Xu & Raginsky (2017) ; BID3 used generic chaining techniques to show that generalization error can be upper bounded by the mutual information between the training dataset and output of the learning algorithm. Nevertheless, estimating that mutual information to verify those results experimentally becomes intractable. Furthermore, in our previous work BID1 we defined a novel 2D information plane that only requires to estimate information theoretic quantities between the correct and estimated labels. Since these random variables are discrete and one-dimensional, this framework can be used to study learning in large recognition problems as well. Moreover, that work provides a preliminary empirical study on the behavior of those information theoretic quantities during learning along with some connections between error and conditional entropy.In this work, we extend the experiments from BID1 to more general scenarios and aim to characterize the observed behavior of SGD. Our main contributions are as follows:• We define a 2D-information plane, inspired by the works of Shwartz-Ziv & Tishby (2017) , and use it to study the behavior of ANNs during SGD learning. The main quantities are entropy of the output labels and its conditional entropy given true labels.• It is shown that if the learning is done perfectly and under some other mild assumptions, the entropy tends to increase to its maximum.• It is additionally shown that SGD learning trajectory follows approximately the shortest path in the space of probability measures equipped with the total variation metric. The shortest path is characterized well by a Markov chain defined on probabilities of estimate labels conditioned on true labels. To that end we provide theoretical and experimental justifications for constructing a simple Markovian model for learning, and compare it with SGD through experiments. These experiments are conducted using various datasets such as MNIST BID13 , CIFAR-10/ CIFAR-100, spirals BID1 , as well as different ANN architectures like Fully Connected Neural Networks (FCNNs), LeNet-5 (LeCun et al., 1999) , and DenseNet BID11 .• The trajectory, however, is not universal. Through a set of experiments, it is shown that SGD learning trajectory differs significantly for different learning strategies, noisy labels, overfitting, and underfitting. We show examples where this type of trajectories provide a richer view of the learning process than conventional training and test error, which allows us to spot undesired effects such as overfitting and underfitting.The paper is organized as follows: Section 2 introduces the notation as well as elementary notions from information theory. Section 3 formulates learning as a trajectory on the space of probability measures, defines the notion of shortest learning path, and provides a connection to Markov chains. Section 4 constructs a simple Markov chain model for gradient based learning that moves along the shortest learning path. Finally , Section 5 performs an empirical evaluation of the proposed model.",1027,0.532,600,1.7116666666666667,"Studying information theoretic quantities during learning of Artificial Neural Networks gained popularity Nevertheless these type experiments require estimating mutual information entropy which becomes moderately large problems In this work propose understanding SGD learning the information plane which consists observing entropy conditional entropy the output labels ANN Through experimental results theoretical justifications it shown under some assumptions the SGD learning trajectories appear similar ANN First the SGD learning is modeled a Hidden Markov Process whose entropy tends to Then shown the SGD learning trajectory appears move close between the initial and final joint distributions probability measures equipped the total variation metric Furthermore shown the trajectory learning the information plane provide observing potentially richer information than training test error How information theoretic quantities behave during the training ANNs This question addressed Shwartz-Ziv & Tishby the learning through the information bottleneck method 1999 . In that work the layers an ANNs considered random variables forming The authors constructed a 2D information plane estimating the mutual information values hidden layers inputs ANNs it observed the information bottleneck method provides an approximate explanation SGD learning In addition their experiments the role compression learning That initial paper motivated further work this line research BID17 BID9 . The main practical limitation that type experiments estimating mutual information high dimensional continuous random variables This becomes prohibitive as we move moderately large problems the CIFAR-100 dataset the large ANNs employed Other works dealing information theoretic quantities tend these experimental limitations For instance BID16 ; Xu & Raginsky2017 ; used generic chaining techniques show generalization error upper bounded the mutual information the training dataset output Nevertheless estimating mutual information to verify those results experimentally becomes Furthermore BID1 we defined a novel 2D information plane only requires to estimate information theoretic quantities between the correct and estimated labels Since these random variables discrete one this framework study learning large recognition problems as Moreover that work provides a preliminary empirical study those information theoretic quantities during learning along some connections error conditional entropyIn extend the experiments from BID1 more general scenarios aim characterize SGD Our main contributions as define a 2D-information plane inspired Shwartz-Ziv & Tishby2017 , study ANNs during SGD learning The main quantities entropy the output labels its conditional entropy given true labels.• It shown the learning perfectly under some other mild assumptions tends additionally SGD learning trajectory follows approximately the shortest path probability measures equipped the total variation metric The shortest path characterized well defined on probabilities estimate labels conditioned true labels To we provide theoretical and experimental justifications constructing a simple Markovian model learning compare SGD through experiments These experiments conducted various datasets such MNIST BID13 , spirals BID1 as different ANN architectures like Fully Connected Neural Networks LeNet-5LeCun et 1999 DenseNet BID11 .• The trajectory, however universal Through a set experiments it SGD learning trajectory differs for noisy labels overfitting We show examples where trajectories provide conventional training test error spot undesired effects suchThe paper organized Section introduces the notation as elementary notions from Section formulates learning as a trajectory on the space probability measures defines shortest learning path a connection Section constructs gradient based learning that moves Finally , Section performs",0.01,0.5173433100008048
"Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic model, even a simple modification of the underlying dynamical system requires significant physical intuition. This paper presents the first meta-learning algorithm that allows automated design for the underlying continuous dynamics of an SG-MCMC sampler. The learned sampler generalizes Hamiltonian dynamics with state-dependent drift and diffusion, enabling fast traversal and efficient exploration of energy landscapes. Experiments validate the proposed approach on Bayesian fully connected neural network, Bayesian convolutional neural network and Bayesian recurrent neural network tasks, showing that the learned sampler outperforms generic, hand-designed SG-MCMC algorithms, and generalizes to different datasets and larger architectures. There is a resurgence of research interests in Bayesian deep learning BID8 Blundell et al., 2015; BID10 BID9 BID4 BID33 , which applies Bayesian inference to neural networks for better uncertainty estimation. It is crucial for e.g. better exploration in reinforcement learning (Deisenroth & Rasmussen, 2011; Depeweg et al., 2017) , resisting adversarial attacks BID2 BID19 BID24 and continual learning BID28 . A popular approach to performing Bayesian inference on neural networks is stochastic gradient Markov chain Monte Carlo (SG-MCMC), which adds properly scaled Gaussian noise to a stochastic gradient ascent procedure BID46 . Recent advances in this area further introduced optimization techniques such as pre-conditioning BID1 BID30 , annealing (Ding et al., 2014 ) and adaptive learning rates BID16 Chen et al., 2016) . All these efforts have made SG-MCMC highly scalable to many deep learning tasks, including shape and texture modeling in computer vision BID17 and language modeling with recurrent neural networks BID5 . However, inventing novel dynamics for SG-MCMC requires significant mathematical work to ensure the sampler's stationary distribution is the target distribution, which is less friendly to practitioners. Furthermore, many of these algorithms are designed as a generic sampling procedure, and the associated physical mechanism might not be best suited for sampling neural network weights. This paper aims to automate the SG-MCMC proposal design by introducing meta-learning techniques BID36 Bengio et al., 1992; BID26 BID43 . The general idea is to train a learner on one or multiple tasks in order to acquire common knowledge that generalizes to future tasks. Recent applications of meta-learning include learning to transfer knowledge to unseen few-shot learning tasks BID35 BID32 BID3 , and learning algorithms such as gradient descent (Andrychowicz et al., 2016; BID18 BID47 , Bayesian optimization BID5 and reinforcement learning (Duan et al., 2016; . Unfortunately, these advances cannot be directly transferred to the world of MCMC samplers, as a naive neural network parameterization of the transition kernel does not guarantee the posterior distribution to be the stationary distribution of the sampler.• An SG-MCMC sampler that extends Hamiltonian dynamics with learnable diffusion and curl matrices. Once trained, the sampler can generalize to different datasets and architectures.• Extensive evaluation of the proposed sampler on Bayesian fully connected neural networks, Bayesian convolutional neural networks and Bayesian recurrent neural networks, with comparisons to popular SG-MCMC schemes based on e.g. Hamiltonian Monte Carlo (Chen et al., 2014) and pre-conditioned Langevin dynamics BID16 . We have presented a meta-learning algorithm that can learn an SG-MCMC sampler on simpler tasks and generalizes to more complicated densities in high dimensions. Experiments on Bayesian MLPs, Bayesian CNNs and Bayesian RNNs confirmed the strong generalization of the trained sampler to the long-time horizon as well as across datasets and network architectures. Future work will focus on better designs for both the sampler and the meta-learning procedure. For the former, temperature variable augmentation as well as moving average estimation will be explored. For the latter, better loss functions will be proposed for faster training, e.g. by reducing the unrolling steps of the sampler during training. Finally, the automated design of generic MCMC algorithms that might not be derived from continuous Markov processes remains an open challenge.A COMPARING MOMENTUM SGD AND SGHMC Similar to the relationship between SGLD and SGD, SGHMC is closely related SGD with momentum (SGD-M). First in HMC, the state space is augmented with an additional momentum variable denoted as p p p ∈ R D . We assume an identity mass matrix associated with that momentum term. Then the corresponding drift f f f (θ θ θ, p p p) and diffusion matrix D D D are: DISPLAYFORM0 where C C C is a positive definite matrix called friction coefficient. Thus, HMC's continuous-time dynamics is governed by the following SDE: DISPLAYFORM1 The discretized update rule (with simple Euler discretization) of HMC with step-size η is DISPLAYFORM2 If stochastic gradient ∇Ũ (θ θ θ) is used, we need to replace the covariance matrix of with 2η(C C C −B B B) whereB B B is the variance estimation of the gradients.On the other hand, the update equations of SGD with momentum (SGD-M) are the following: DISPLAYFORM3 where k and l are called momentum discount factor and learning rate, respectively. Also we can rewrite the SGHMC update equations by setting ηp p DISPLAYFORM4 Thus, the discretized SGHMC updates can be viewed as the SGD-M update injected with carefully controlled Gaussian noise. Therefore, the hyperparameter of SGHMC can be heuristically chosen based on the experience of SGD-M and vice versa. BID27 showed that in practice, simple Euler discretization for HMC simulation might cause divergence, therefore advanced discretization schemes such as Leapfrog and modified Euler are recommended. We use modified Euler discretization in our implementation of SGHMC and the meta sampler, resulting in the following update: DISPLAYFORM5 DISPLAYFORM6 Due to the two-stage update of Euler integrator, at time t, we have f DISPLAYFORM7 ), which is not exactly the history from the previous time. Therefore we further approximate it using delayed estimate: DISPLAYFORM8 Similarly, the Γ Γ Γ p p p term expands as DISPLAYFORM9 We further approximate DISPLAYFORM10 ∂U (θ θ θ) by the following DISPLAYFORM11 This only requires the storage of previous Q Q Q matrix. However, DISPLAYFORM12 ∂pi requires one further forward pass to obtainf DISPLAYFORM13 Therefore the proposed finite difference method only requires one more forward passes to computê f f f t−1 φ D and instead, save 3 back-propagations. As back-propagation is typically more expensive than forward pass, our approach reduces running time drastically, especially when the sampler are applied to large neural network.Time complexity figures Every SG-MCMC method (including the meta sampler) requires ∇ θ θ θŨ (θ θ θ). The main burden is the forward pass and back-propagation through the D D D(z z z) and Q Q Q(z z z) matrices, where the latter one has been replaced by the proposed finite difference scheme. The time complexity is O(HD) for both forward pass and finite difference with H the number of hidden units in the neural network of the meta sampler. Parallel computation with GPUs improves real-time speed, indeed in our MNIST experiment the meta sampler spends roughly 1.5x time when compared with SGHMC.",1532,0.691,924,1.658008658008658,"SG-MCMC become increasingly posterior samples However existing SG-MCMC schemes tailored even a simple modification requires significant physical intuition This paper the first meta-learning algorithm automated design for the underlying continuous dynamics an SG-MCMC sampler The learned sampler generalizes Hamiltonian dynamics state-dependent drift diffusion enabling fast traversal efficient exploration energy landscapes Experiments validate the proposed approach on Bayesian fully connected neural network showing the learned sampler outperforms generic, hand-designed SG-MCMC algorithms generalizes different datasets larger architectures There a resurgence research interests Bayesian deep BID8 Blundell et , which applies better uncertainty estimation It crucial e.g. better exploration reinforcement learningDeisenroth Rasmussen Depeweg 2017 , resisting BID2 BID19 BID24 continual learning A popular approach performing Bayesian inference onSG-MCMC adds properly scaled Gaussian noise BID46 . Recent advances further introduced optimization techniques such pre BID1 BID30 , annealing (Ding et adaptive learning rates BID16 Chen) All these efforts made SG-MCMC highly scalable many deep learning tasks shape and texture modeling in BID17 language . However inventing novel dynamics SG-MCMC requires significant mathematical work ensure the sampler's stationary distribution the target distribution less friendly practitioners Furthermore many these algorithms as a generic sampling procedure the associated physical mechanism might best sampling neural network weights This paper aims automate the SG-MCMC proposal design introducing meta-learning techniques BID36 Bengio 1992 BID26 BID43 . The general idea train a learner one or multiple tasks acquire common knowledge that generalizes future tasks Recent applications meta-learning include learning transfer unseen few-shot learning tasks BID35 BID32 , algorithms (Andrychowicz Bayesian optimization BID5 reinforcement learning (Duan . Unfortunately these advances directly transferred MCMC samplers a naive neural network parameterization the transition kernel does guarantee the posterior distribution to the stationary distribution the sampler.• that extends Hamiltonian dynamics learnable diffusion and curl Once trained the sampler generalize different datasets architectures.• Extensive evaluation the proposed sampler on fully connected neural networks recurrent with comparisons popular SG-MCMC schemes basedChen et al pre-conditioned Langevin dynamics BID16 . We presented a meta-learning algorithm an SG-MCMC sampler on simpler tasks generalizes more complicated densities high dimensions Experiments Bayesian MLPs confirmed the trained sampler the long-time horizon as across datasets network architectures Future work better designs both the sampler the meta-learning procedure For the former, temperature variable augmentation as moving average estimation will explored For latter better loss functions will proposed faster training the unrolling steps the sampler during Finally the automated design generic MCMC algorithms might not derived continuous Markov processes remainsA COMPARING MOMENTUM SGD AND SGHMC Similar the relationship SGLD closely related SGD momentum First in HMC the state space is augmented an additional momentum variable denoted p p p �� R D We assume an identity mass matrix associated that momentum term Then the corresponding drift f f f (�� �� �� diffusion matrix D D D are: DISPLAYFORM0 where a positive definite matrix called friction coefficient Thus HMC's continuous-time dynamics is governed the following SDE DISPLAYFORM1 The discretized update rulewith of with step-size �� If stochastic gradient ���� used need replace with 2��(C C C −B B B the variance estimationOn the update equations SGD with momentum where k and called momentum discount factor learning rate Also we rewrite the SGHMC update equations by setting ��p p DISPLAYFORM4 Thus viewed the SGD-M update injected carefully controlled Gaussian noise Therefore SGHMC heuristically chosen based the experience SGD-M vice BID27 showed in practice simple Euler discretization for HMC simulation might cause divergence, therefore advanced discretization schemes Leapfrog modified Euler We use modified Euler discretization our implementation SGHMC the meta sampler resulting the following update DISPLAYFORM5 DISPLAYFORM6 Due at time t f DISPLAYFORM7 ), exactly the history from Therefore further approximate it using delayed estimate: DISPLAYFORM8 Similarly the �� �� �� p p p term expands We DISPLAYFORM10 ��U This only requires the storage previous Q Q Q matrix However DISPLAYFORM12 ��pi requires one further forward pass obtainf Therefore the proposed finite difference method only passes computê f f f t−1 �� D and instead, save As back-propagation typically more forward pass our approach reduces running time drastically the sampler are applied large neural networkTime complexity figures Every SG-MCMC method ( �� �� �� ���� The main burden the forward pass through the D D D(z z z the latter one replaced the proposed finite difference scheme The time complexity O(HD both forward pass finite difference with H the number hidden units of the meta sampler Parallel computation GPUs improves indeed in our MNIST experiment the meta sampler spends when SGHMC",0.01,0.38062741828129226
"We propose a new, multi-component energy function for energy-based Generative Adversarial Networks (GANs) based on methods from the image quality assessment literature. Our approach expands on the Boundary Equilibrium Generative Adversarial Network (BEGAN) by outlining some of the short-comings of the original energy and loss functions. We address these short-comings by incorporating an l1 score, the Gradient Magnitude Similarity score, and a chrominance score into the new energy function. We then provide a set of systematic experiments that explore its hyper-parameters. We show that each of the energy function's components is able to represent a slightly different set of features, which require their own evaluation criteria to assess whether they have been adequately learned. We show that models using the new energy function are able to produce better image representations than the BEGAN model in predicted ways.",175,0.101,116,1.5086206896551724,"We propose a new, multi-component energy function energy-based Generative Adversarial Networks methods the image quality assessment literature Our approach expands the Boundary Equilibrium Generative Adversarial Network by outlining some the original energy and loss functions We address these short-comings incorporating an l1 score Gradient Magnitude Similarity a chrominance score the new energy function We then provide systematic experiments its hyper We show each the energy function's components able represent features require their own evaluation criteria assess whether have adequately learned We show models using the new energy function better image representations the BEGAN model in predicted ways",0.0,0.0
"Momentum is a simple and widely used trick which allows gradient-based optimizers to pick up speed along low curvature directions. Its performance depends crucially on a damping coefficient. Largecamping  coefficients can potentially deliver much larger speedups, but are prone to oscillations and instability; hence one typically resorts to small values such as 0.5 or 0.9. We propose Aggregated Momentum (AggMo), a variant of momentum which combines multiple velocity vectors with different damping coefficients. AggMo is trivial to implement, but significantly dampens oscillations, enabling it to remain stable even for aggressive damping coefficients such as 0.999. We reinterpret Nesterov's accelerated gradient descent as a special case of AggMo and analyze rates of convergence for quadratic objectives. Empirically, we find that AggMo is a suitable drop-in replacement for other momentum methods, and frequently delivers faster convergence with little to no tuning. In spite of a wide range of modern optimization research, gradient descent with momentum and its variants remain the tool of choice in machine learning. Momentum methods can help the optimizer pick up speed along low curvature directions without becoming unstable in high-curvature directions. The simplest of these methods, classical momentum BID24 , has an associated damping coefficient, 0 ≤ β < 1, which controls how quickly the momentum vector decays. The choice of β imposes a tradoff between speed and stability: in directions where the gradient is small but consistent, the terminal velocity is proportional to 1/(1 − β), suggesting that β slightly less than 1 could deliver much improved optimization performance. However, large β values are prone to oscillations and instability BID22 BID3 , requiring a smaller learning rate and hence slower convergence.Finding a way to dampen the oscillations while preserving the high terminal velocity of large beta values could dramatically speed up optimization. BID29 found that Nesterov accelerated gradient descent BID20 , which they reinterpreted as a momentum method, was more stable than classical momentum for large β values and gave substantial speedups for training neural networks. However, the reasons for the improved performance remain somewhat mysterious. O' Donoghue & Candes (2015) proposed to detect oscillations and eliminate them by resetting the velocity vector to zero. But in practice it is difficult to determine an appropriate restart condition.In this work, we introduce Aggregated Momentum (AggMo), a variant of classical momentum which maintains several velocity vectors with different β parameters. AggMo averages the velocity vectors when updating the parameters. We find that this combines the advantages of both small and large β values: the large values allow significant buildup of velocity along low curvature directions, while the small values dampen the oscillations, hence stabilizing the algorithm. AggMo is trivial to implement and incurs almost no computational overhead.We draw inspiration from the physics literature when we refer to our method as a form of passive damping. Resonance occurs when a system is driven at specific frequencies but may be prevented through careful design BID4 . Passive damping can address this in structures by making use of different materials with unique resonant frequencies. This prevents any single frequency from producing catastrophic resonance. By combining several momentum velocities together we achieve a similar effect -no single frequency is driving the system and so oscillation is prevented.In this paper we analyze rates of convergence on quadratic functions. We also provide theoretical convergence analysis showing that AggMo achieves converging average regret in online convex programming BID37 . To evaluate AggMo empirically we compare against other commonly used optimizers on a range of deep learning architectures: deep autoencoders, convolutional networks, and long-term short-term memory (LSTM).In all of these cases, we find that AggMo works as a drop-in replacement for classical momentum, in the sense that it works at least as well for a given β parameter. But due to its stability at higher β values, it often delivers substantially faster convergence than both classical and Nesterov momentum when its maximum β value is tuned.2 Background : momentum-based optimization Classical momentum We consider a function f : R d → R to be minimized with respect to some variable θ. Classical momentum (CM) minimizes this function by taking some initial point θ 0 and running the following iterative scheme, v t = βv t−1 − ∇ θ f (θ t−1 ), DISPLAYFORM0 where γ t denotes a learning rate schedule, β is the damping coefficient and we set v 0 = 0. Momentum can speed up convergence but it is often difficult to choose the right damping coefficient, β. Even with momentum, progress in a low curvature direction may be very slow. If the damping coefficient is increased to overcome this then high curvature directions may cause instability and oscillations.Nesterov momentum Nesterov's Accelerated Gradient BID20 BID21 ) is a modified version of the gradient descent algorithm with improved convergence and stability. It can be written as a momentum-based method BID29 , DISPLAYFORM1 Nesterov momentum seeks to solve stability issues by correcting the error made after moving in the direction of the velocity, v. In fact, it can be shown that for a quadratic function Nesterov momentum adapts to the curvature by effectively rescaling the damping coefficients by the eigenvalues of the quadratic BID29 . Aggregated Momentum is a simple extension to classical momentum which is easy to implement and has negligible computational overhead on modern deep learning tasks. We showed empirically that AggMo is able to remain stable even with large damping coefficients and enjoys faster convergence rates as a consequence of this. Nesterov momentum can be viewed as a special case of AggMo.(Incidentally , we found that despite its lack of adoption by deep learning practitioners, Nesterov momentum also showed substantial advantages compared to classical momentum.) On the tasks we explored, AggMo could be used as a drop-in replacement for existing optimizers with little-to-no additional hyperparameter tuning. But due to its stability at higher β values, it often delivered substantially faster convergence than both classical and Nesterov momentum.",1213,0.626,689,1.760522496371553," a simple and widely used trick which gradient-based optimizers pick speed along low curvature directions Its performance depends a damping coefficient Largecamping coefficients potentially deliver much larger speedups prone oscillations instability; hence one typically resorts small values such We Aggregated Momentum (AggMo momentum which multiple velocity vectors AggMo trivial significantly dampens oscillations enabling remain aggressive damping coefficients such We reinterpret Nesterov's accelerated gradient descent AggMo analyze rates convergence quadratic objectives find AggMo other momentum methods frequently delivers faster convergence little In spite modern optimization research gradient descent with momentum its variants remain the tool Momentum methods the optimizer pick speed along low curvature directions without becoming unstable simplest classical momentum BID24 , 0 ≤ β controls The choice β imposes a tradoff between speed directions small but consistent the terminal velocity proportional 1/(1 − β suggesting slightly less could deliver much improved optimization performance However large β values prone instability BID22 BID3 , requiring a smaller learning rate hence slower convergenceFinding dampen while the high terminal velocity dramatically optimization BID29 found Nesterov accelerated gradient descent BID20 , they reinterpreted a momentum method classical momentum for large β values gave substantial speedups training neural networks However the reasons remain somewhat O' Donoghue & Candes (2015 proposed detect oscillations eliminate resetting But practice an appropriate restart conditionIn this work introduce Aggregated Momentum (AggMo classical momentum which maintains several velocity vectors different β parameters AggMo averages the velocity vectors when updating We find this combines both small and large β values significant buildup velocity along low curvature directions dampen hence the algorithm AggMo trivial incursWe draw inspiration the physics literature refer our method a form passive damping Resonance occurs driven at specific frequencies but may prevented careful design BID4 . Passive damping can address in structures making use with unique resonant frequencies This prevents any single frequency producing catastrophic resonance By combining several momentum velocities we achieve -no single frequency driving so oscillation preventedIn analyze rates convergence We also provide theoretical convergence analysis showing AggMo achieves converging average regret online convex programming BID37 . To evaluate AggMo empirically compare against on deep learning deep long short all works classical momentum, in a given β parameter But due its stability at higher β values often delivers substantially faster convergence both classical and Nesterov momentum when tuned.2 Background : momentum optimization Classical momentum We a function f : R d → to minimized some variable �� Classical momentum (CM minimizes this function taking some initial point � 0 running v DISPLAYFORM0 where denotes a learning rate schedule β we set v can speed convergence but choose the right damping coefficient β Even momentum progress a low curvature direction very If the damping coefficient increased overcome then high curvature directions instabilityNesterov momentum Nesterov's Accelerated Gradient BID20 BID21 ) the gradient descent algorithm with improved convergence stability It can written a momentum-based method BID29 , DISPLAYFORM1 Nesterov momentum seeks solve stability issues correcting made after moving in v. In fact can shown for Nesterov momentum adapts by effectively rescaling the quadratic BID29 Aggregated Momentum classical momentum which easy negligible computational overhead on modern deep learning tasks We showed empirically AggMo remain large damping coefficients enjoys faster convergence rates as Nesterov momentum can viewed AggMo.(Incidentally , found despite its lack adoption deep learning practitioners also showed substantial advantages compared classical momentum On the tasks explored could existing optimizers with little- additional hyperparameter But due its stability at higher β values often delivered substantially faster convergence both classical and Nesterov momentum",0.01,0.6418236716625907
"Recurrent Neural Networks architectures excel at processing sequences by
 modelling dependencies over different timescales. The recently introduced
 Recurrent Weighted Average (RWA) unit captures long term dependencies
 far better than an LSTM on several challenging tasks. The RWA achieves
 this by applying attention to each input and computing a weighted average
 over the full history of its computations. Unfortunately, the RWA cannot
 change the attention it has assigned to previous timesteps, and so struggles
 with carrying out consecutive tasks or tasks with changing requirements.
 We present the Recurrent Discounted Attention (RDA) unit that builds on
 the RWA by additionally allowing the discounting of the past.
 We empirically compare our model to RWA, LSTM and GRU units on
 several challenging tasks. On tasks with a single output the RWA, RDA and
 GRU units learn much quicker than the LSTM and with better performance.
 On the multiple sequence copy task our RDA unit learns the task three
 times as quickly as the LSTM or GRU units while the RWA fails to learn at
 all. On the Wikipedia character prediction task the LSTM performs best
 but it followed closely by our RDA unit. Overall our RDA unit performs
 well and is sample efficient on a large variety of sequence tasks. Many types of information such as language, music and video can be represented as sequential data. Sequential data often contains related information separated by many timesteps, for instance a poem may start and end with the same line, a scenario which we call long term dependencies. Long term dependencies are difficult to model as we must retain information from the whole sequence and this increases the complexity of the model. A class of model capable of capturing long term dependencies are Recurrent Neural Networks (RNNs). A specific RNN architecture, known as Long Short-Term Memory (LSTM) BID13 , is the benchmark against which other RNNs are compared. LSTMs have been shown to learn many difficult sequential tasks effectively. They store information from the past within a hidden state that is combined with the latest input at each timestep. This hidden state can carry information right from the beginning of the input sequence, which allows long term dependencies to be captured. However, the hidden state tends to focus on the more recent past and while this mostly works well, in tasks requiring equal weighting between old and new information LSTMs can fail to learn.A technique for accessing information from anywhere in the input sequence is known as attention. The attention mechanism was introduced to RNNs by BID2 for neural machine translation. The text to translate is first encoded by a bidirectional-RNN producing a new sequence of encoded state. Different locations within the encoded state are focused on by multiplying each of them by an attention matrix and calculating the weighted average. This attention is calculated for each translated word. Computing the attention matrix for each encoded state and translated word combination provides a great deal of flexibility in choosing where in the sequence to attend to, but the cost of computing these matrices grows as a square of the number of words to translate. This cost limits this method to short sequences, typically only single sentences are processed at a time.The Recurrent Weighted Average (RWA) unit, recently introduced by BID17 , can apply attention to sequences of any length. It does this by only computing the attention for each input once and computing the weighted average by maintaining a running average up to the current timestep. Their experiments show that the RWA performs very well on tasks where information is needed from any point in the input sequence. Unfortunately, as it cannot change the attention it assigns to previous timesteps, it performs poorly when asked to carry out multiple tasks within the same sequence, or when asked to predict the next character in a sample of text, a task in which new information is more important than old.We introduce the Recurrent Discounted Attention (RDA) unit, which extends the RWA by allowing it to discount the attention applied to previous timesteps. As this adjustment is applied to all previous timesteps at once, it continues to be efficient. It performs very well both at tasks requiring equal weighting over all information seen and at tasks in which new information is more important than old.The main contributions of this paper are as follows:1. We analyse the Recurrent Weighted Average unit and show that it cannot output certain simple sequences.2. We propose the Recurrent Discounted Attention unit that extends the Recurrent Weighted Average by allowing it to discount the past.3. We run extensive experiments on the RWA, RDA, LSTM and GRU units and show that the RWA, RDA and GRU units are well suited to tasks with a single output, the RDA performs best on the multiple sequence copy task while the LSTM unit performs better on the Hutter Prize Wikipedia dataset.Our paper is setout as follows: we present the analysis of the RWA (sections 3 and 4) and propose the RDA (section 5). The experimental results (section 6), discussion (section 7) and conclusion follow (section 8). We analysed the Recurrent Weighted Average (RWA) unit and identified its weakness as the inability to forget the past. By adding this ability to forget the past we arrived at the Recurrent Discounted Attention (RDA). We implemented several varieties of the RDA and compared them to the RWA, LSTM and GRU units on several different tasks. We showed that in almost all cases the RDA should be used in preference to the RWA and is a flexible RNN unit that can perform well on all types of tasks.We also determined which types of tasks were more suited to each different RNN unit. For tasks involving a single output the RWA, RDA and GRU units performed best, for the multiple sequence copy task the RDA performed best, while on the Wikipedia character prediction task the LSTM unit performed best. We recommend taking these results into account when choosing a unit for real world applications.",1218,0.648,699,1.742489270386266,"Recurrent Neural Networks architectures excel processing sequences by modelling dependencies over The recently introduced Recurrent Weighted Average (RWA) unit captures long dependencies far on several challenging tasks The RWA achieves applying attention each input computing the full history Unfortunately the RWA change the attention assigned previous timesteps struggles carrying consecutive tasks or tasks changing requirements We present the Recurrent Discounted Attention (RDA) unit builds the RWA by additionally allowing the past. We empirically compare our model RWA GRU units on several challenging tasks On tasks a single output the RWA, GRU units learn much quicker with better performance On the multiple sequence copy task our RDA unit learns the task three as or GRU units while the RWA fails at On the Wikipedia character prediction task the LSTM performs best but followed closely by our RDA unit Overall our RDA unit performs sample efficient on sequence tasks Many types information such language music represented sequential data Sequential data often related information separated many timesteps for a poem may start a scenario which we long term dependencies Long term dependencies difficult model as we must retain information the whole sequence this increases A class model capable capturing long term dependencies are Recurrent Neural Networks A specific RNN architecture known Long Short BID13 , the benchmark against LSTMs shown learn many difficult sequential tasks effectively They store information from within a hidden state combined the latest input at each timestep This hidden state can carry information right the input sequence long term dependencies captured However the hidden state tends focus the more recent past while mostly in tasks requiring equal weighting between fail learnA technique accessing anywhere the input sequence attention. The attention mechanism was introduced RNNs BID2 for neural machine translation The text to translate first encoded a bidirectional-RNN producing encoded state Different locations within the encoded state focused by multiplying an attention matrix calculating This attention calculated for each translated word Computing the attention matrix each encoded state and translated word combination provides choosing where in attend the cost computing grows a square translate This cost limits this method short sequences typically only single sentences are processedThe Recurrent Weighted Average (RWA) unit recently BID17 , can apply attention sequences It does this only computing the attention for each input once computing by maintaining up Their experiments the RWA performs very tasks information needed from any point the input sequence Unfortunately as it cannot change the attention assigns previous timesteps performs asked carry multiple tasks within predict a sample text in new information moreWe introduce the Recurrent Discounted Attention (RDA) unit extends the RWA discount applied As this adjustment all previous timesteps at once continues efficient It performs both tasks requiring equal weighting over all information seen in new information moreThe main contributions We analyse the Recurrent Weighted Average unit and show output certain simple sequences.2. propose the Recurrent Discounted Attention unit that extends allowing discount run extensive experiments the RWA GRU units well tasks a single output performs the multiple sequence copy task while the Hutter Prize Wikipedia datasetOur paper setout wesections propose The experimental results (section discussion conclusion follow We analysed the Recurrent Weighted Average (RWA) unit identified its weakness the inability forget By adding this ability forget we arrived the Recurrent Discounted Attention We implemented several varieties the RDA compared the RWA LSTM GRU units on several different tasks We showed in the RDA should preference is a flexible RNN unit perform well tasksWe determined types suited For tasks involving a single output the RWA, GRU units performed best for the multiple sequence copy task on the Wikipedia character prediction We recommend taking these results a unit real world applications",0.01,0.595876596233991
"Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different kind of stochastic layers. Each weight of a variance layer follows a zero-mean distribution and is only parameterized by its variance. It means that each object is represented by a zero-mean distribution in the space of the activations. We show that such layers can learn surprisingly well, can serve as an efficient exploration tool in reinforcement learning tasks and provide a decent defense against adversarial attacks. We also show that a number of conventional Bayesian neural networks naturally converge to such zero-mean posteriors. We observe that in these cases such zero-mean parameterization leads to a much better training objective than more flexible conventional parameterizations where the mean is being learned. Modern deep neural networks are usually trained in a stochastic setting. They use different stochastic layers BID8 ; BID12 ) and stochastic optimization techniques BID14 ; Kingma & Ba (2014) ). Stochastic methods are used to reduce overfitting BID8 ; BID13 ; BID12 ), estimate uncertainty BID5 ; Malinin & Gales (2018) ) and to obtain more efficient exploration for reinforcement learning BID4 ; Plappert et al. (2017) ) algorithms.Bayesian deep learning provides a principled approach to training stochastic models (Kingma & Welling (2013) ; Rezende et al. (2014) ). Several existing stochastic training procedures have been reinterpreted as special cases of particular Bayesian models, including, but not limited to different versions of dropout BID5 ), drop-connect (Kingma et al. (2015) ), and even the stochastic gradient descent itself BID7 ). One way to create a stochastic neural network from an existing deterministic architecture is to replace deterministic weights w ij with random weightsŵ ij ∼ q(ŵ ij | φ ij ) (Hinton & Van Camp (1993) ; BID1 ). During training, a distribution over the weights is learned instead of a single point estimate. Ideally one would want to average the predictions over different samples of such distribution, which is known as test-time averaging, model averaging or ensembling. However, test-time averaging is impractical, so during inference the learned distribution is often discarded, and only the expected values of the weights are used instead. This heuristic is known as mean propagation or the weight scaling rule BID8 ; Goodfellow et al. (2016) ), and is widely and successfully used in practice BID8 ; Kingma et al. (2015) ; Molchanov et al. (2017) ).In our work we study the an extreme case of stochastic neural network where all the weights in one or more layers have zero means and trainable variances, e.g. w ij ∼ N (0, σ 2 ij ). Although no information get stored in the expected values of the weights, these models can learn surprisingly well and achieve competitive performance. Our key results can be summarized as follows:1. We introduce variance layers, a new kind of stochastic layers that store information only in the variances of its weights, keeping the means fixed at zero, and mapping the objects into zero-mean distributions over activations. The variance layer is a simple example when the weight scaling rule BID8 ) fails.2. We draw the connection between neural networks with variance layers (variance networks) and conventional Bayesian deep learning models. We show that several popular Bayesian models (Kingma et al. (2015) ; Molchanov et al. (2017) ) converge to variance networks, and demonstrate a surprising effect -a less flexible posterior approximation may lead to much better values of the variational inference objective (ELBO).3. Finally, we demonstrate that variance networks perform surprisingly well on a number of deep learning problems. They achieve competitive classification accuracy, are more robust to adversarial attacks and provide good exploration in reinforcement learning problems. In this paper we introduce variance networks, surprisingly stable stochastic neural networks that learn only the variances of the weights, while keeping the means fixed at zero in one or several layers.We show that such networks can still be trained well and match the performance of conventional models. Variance networks are more stable against adversarial attacks than conventional ensembling techniques, and can lead to better exploration in reinforcement learning tasks.The success of variance networks raises several counter-intuitive implications about the training of deep neural networks:• DNNs not only can withstand an extreme amount of noise during training, but can actually store information using only the variances of this noise. The fact that all samples from such zero-centered posterior yield approximately the same accuracy also provides additional evidence that the landscape of the loss function is much more complicated than was considered earlier BID6 ).• A popular trick, replacing some random variables in the network with their expected values, can lead to an arbitrarily large degradation of accuracy -up to a random guess quality prediction.• Previous works used the signal-to-noise ratio of the weights or the layer output to prune excessive units BID1 ; Molchanov et al. (2017); Neklyudov et al. (2017) ). However , we show that in a similar model weights or even a whole layer with an exactly zero SNR (due to the zero mean output) can be crucial for prediction and can't be pruned by SNR only.• We show that a more flexible parameterization of the approximate posterior does not necessarily yield a better value of the variational lower bound, and consequently does not necessarily approximate the posterior distribution better.We believe that variance networks may provide new insights on how neural networks learn from data as well as give new tools for building better deep models.A PROOF OF THEOREM 1 DISPLAYFORM0 t,i ) in terms of Maximum Mean Discrepancy: DISPLAYFORM1 Proof. By the definition of the Maximum Mean Discrepancy, we have DISPLAYFORM2 where the supremum is taken over the set of continuous functions, bounded by 1. Let's reparameterize and join the expectations: DISPLAYFORM3 (18) Since linear transformations of the argument do not change neither the norm of the function, nor its continuity, we can hide the component-wise multiplication of ε by √ α t µ t inside the function f (ε).This would not change the supremum. DISPLAYFORM4 There exists a rotation matrix R such that R( DISPLAYFORM5 αt , 0, . . . , 0) . As ε comes from an isotropic Gaussian ε ∼ N (0, I D ), its rotation Rε would follow the same distribution Rε ∼ N (0, I D ). Once again, we can incorporate this rotation into the function f without affecting the supremum. DISPLAYFORM6 Let's consider the integration over ε 1 separately (φ(ε 1 ) denotes the density of the standard Gaussian distribution): DISPLAYFORM7 Next, we view f (ε 1 , . . . ) as a function of ε 1 and denote its antiderivative as F 1 (ε) = f (ε)dε 1 . Note that as f is bounded by 1, hence F 1 is Lipschitz in ε 1 with a Lipschitz constant L = 1. It would allow us to bound its deviation DISPLAYFORM8 Let's use integration by parts: DISPLAYFORM9 The first term is equal to zero, as DISPLAYFORM10 Finally, we can use the Lipschitz property of F 1 (ε) to bound this value: DISPLAYFORM11 Thus, we obtain the following bound on the MMD: DISPLAYFORM12 This bound goes to zero as α t goes to infinity.As the output of a softmax network lies in the interval [0, 1], we obtain the following bound on the deviation of the prediction of the ensemble after applying the zero-mean approximation: Figure 8 : These are the learning curves for VGG-like architectures, trained on CIFAR-10 with layerwise parameterization and with different prior distributions. These plots show that all three priors are equivalent in practice: all three models converge to variance networks. The convergence for the Student 's prior is slower, because in this case the KL-term is estimated using one-sample MC estimate. This makes the stochastic gradient w.r.t. log α very noisy when α is large. DISPLAYFORM13",1725,0.917,998,1.7284569138276553,"Ordinary stochastic neural networks mostly the expected values the induced noise mostly used capture, prevent overfitting slightly boost through test-time averaging In variance layers a different kind Each weight a variance layer follows only It means each object a zero-mean distribution the activations We show such layers learn surprisingly can serve an efficient exploration tool reinforcement learning tasks a decent defense We also show a number conventional Bayesian neural networks naturally converge such zero-mean posteriors We observe such zero-mean parameterization leads a much better training objective more flexible conventional parameterizations where being learned Modern deep neural networks usually trained They use different stochastic layers BID8 ; ) Kingma & Ba (2014 Stochastic methods reduce BID8 ; BID13 ; ), estimate uncertainty Malinin & Gales2018 ) obtain more efficient exploration reinforcement Plappert (2017 ) algorithmsBayesian deep learning provides trainingKingma & Welling ( Rezende (2014 ). Several existing stochastic training procedures special cases particular Bayesian models, different versions dropout BID5 ), drop-connect (Kingma (2015 ), itself BID7 One way create from replace w ij random weights�� (Hinton Van Camp ( BID1 During training a distribution over the weights learned instead a single point estimate Ideally one average the predictions different samples such distribution known test-time averaging model averaging However test-time averaging impractical during inference the learned distribution often discarded instead This heuristic known mean propagation the weight scaling rule BID8 ; Goodfellow (2016 ), is widely and successfully practice BID8 ; Kingma (2015 ; Molchanov (2017 ).In our work study the an extreme case where zero means trainable variances e.g. w ij ∼ N (0, �� 2 ij Although no information get stored the expected values the weights these models learn surprisingly and achieve competitive performance Our key results can We introduce variance layers store only its weights keeping the means fixed mapping zero-mean distributions over activations The variance layer when weight scaling rule BID8 ) fails.2 draw the connection neural networks variance layers We show that several popular Bayesian modelsKingma et al (2015 ; Molchanov (2017 ) converge variance networks demonstrate a surprising effect -a less flexible posterior approximation may much better values the variational inference objectiveELBO).3 Finally demonstrate variance networks perform surprisingly They achieve competitive classification accuracy are robust good exploration in reinforcement learning problems In variance networks learn only the variances while keeping fixed in one or several layersWe still well match conventional models Variance networks more stable against conventional ensembling techniques lead better exploration in reinforcement learning tasksThe success raises about not withstand an extreme amount noise during actually store using only the variances this noise The fact all samples such zero-centered posterior yield also provides the landscape the loss function much considered earlier BID6 ).• A popular trick, replacing some random variables an arbitrarily large degradation accuracy -up a random guess quality prediction.• Previous works used signal or the layer output prune excessive units BID1 ; Molchanov (2017 Neklyudov (2017 ). However , show a similar model weights or even a whole layer with an exactly zero SNRdue the zero mean output crucial prediction can't pruned SNR only.• the approximate posterior does lower consequently does approximateWe believe variance networks may learn data as give building better deep modelsA PROOF OF THEOREM 1 DISPLAYFORM0 t,i ) in terms Maximum Mean Discrepancy DISPLAYFORM1 Proof By the definition the Maximum Mean Discrepancy DISPLAYFORM2 where the supremum taken over the set continuous functions bounded 1 Let reparameterize join the expectations: DISPLAYFORM3 (18 Since linear transformations the argument do neither the norm its continuity hide the component-wise multiplication �� α t µ inside fε).This would. DISPLAYFORM4 There exists a rotation matrix R DISPLAYFORM5 αt 0 . . . , 0) . As �� comes an isotropic Gaussian �� ∼ N0 I D its rotation Rε would follow Once can incorporate this rotation the function f without the supremum DISPLAYFORM6 Let consider the integration over � 1 separately (��(ε denotes): Next view f . . . ) as a function �� 1 denote its antiderivative as Fε (ε)dε Note as f is bounded hence F 1 Lipschitz in � with It would allow us bound its deviation DISPLAYFORM8 Let integration by parts The first term equal zero as Finally the Lipschitz property F 1ε bound this value Thus obtain bound on the MMD goes α t goesAs a softmax network lies the interval [ obtain the deviation the prediction the ensemble after applying the zero-mean approximation Figure : These the learning curves VGG-like architectures trained CIFAR-10 with layerwise parameterization different prior distributions These plots all three priors equivalent practice all three models variance networks The convergence for Student 's prior is slower because in the KL-term estimated using one-sample MC estimate This makes log α very noisy when α DISPLAYFORM13",0.01,0.5601233845920179
"Graph Convolutional Networks (GCNs) are a recently proposed architecture which has had success in semi-supervised learning on graph-structured data. At the same time, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper we propose a model, Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model achieves state-of-the-art performance on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations. Semi-supervised learning on graphs is important in many real-world applications, where the goal is to recover labels for all nodes given only a fraction of labeled ones. Some applications include social networks, where one wishes to predict user interests, or in health care, where one wishes to predict whether a patient should be screened for cancer. In many such cases, collecting node labels can be prohibitive. However, edges between nodes can be easier to obtain, either using an explicit graph (e.g. social network) or implicitly by calculating pairwise similarities (e.g. using a patient-patient similarity kernel, BID19 .Convolutional Neural Networks BID16 learn location-invariant hierarchical filters, enabling significant improvements on Computer Vision tasks BID15 BID23 BID12 . This success has motivated researchers BID7 to extend convolutions from spatial (i.e. regular lattice) domains to graph-structured (i.e. irregular) domains, yielding a class of algorithms known as Graph Convolutional Networks (GCNs).Formally, we are interested in semi-supervised learning where we are given a graph G = (V, E) with N = |V| nodes; adjacency matrix A; and matrix X ∈ R N ×F of node features. Labels for only a subset of nodes V L ⊂ V observed. In general, |V L | |V|. Our goal is to recover labels for all unlabeled nodes V U = V − V L , using the feature matrix X, the known labels for nodes in V L , and the graph G. In this setting, one treats the graph as the ""unsupervised"" and labels of V L as the ""supervised"" portions of the data.Depicted in FIG2 , our model for semi-supervised node classification builds on the GCN module proposed by BID14 , which operates on the normalized adjacency matrixÂ, as in GCN(Â), where = D , and D is diagonal matrix of node degrees. Our proposed extension of GCNs is inspired by the recent advancements in random walk based graph embeddings (e.g. BID22 BID9 BID1 . We make a Network of GCN modules (N-GCN), feeding each module a different power ofÂ, as in {GCN( 0 ), GCN( 1 ), GCN( 2 ), . . . }. The k-th power contains statistics from the k-th step of a random walk on the graph. Therefore, our N-GCN model is able to combine information from various step-sizes. We then combine the output of all GCN modules into a classification sub-network, and we jointly train all GCN modules and the classification sub-network on the upstream objective, Model architecture, where is the normalized normalized adjacency matrix, I is the identity matrix, X is node features matrix, and × is matrix-matrix multiply operator. We calculate K powers of the , feeding each power into r GCNs, along with X. The output of all K × r GCNs can be concatenated along the column dimension, then fed into fully-connected layers, outputting C channels per node, where C is size of label space. We calculate cross entropy error , between rows prediction N × C with known labels, and use them to update parameters of classification subnetwork and all GCNs. Right: pre-relu activations after the first fully-connected layer of a 2-layer classification sub-network. Activations are PCA-ed to 50 dimensions then visualized using t-SNE.semi-supervised node classification. Weights of the classification sub-network give us insight on how the N-GCN model works. For instance, in the presence of input perturbations , we observe that the classification sub-network weights shift towards GCN modules utilizing higher powers of the adjacency matrix, effectively widening the ""receptive field"" of the (spectral) convolutional filters. We achieve state-of-the-art on several semi-supervised graph learning tasks, showing that explicit random walks enhance the representational power of vanilla GCN's.The rest of this paper is organized as follows. Section 2 reviews background work that provides the foundation for this paper. In Section 3, we describe our proposed method, followed by experimental evaluation in Section 4. We compare our work with recent closely-related methods in Section 5 . Finally, we conclude with our contributions and future work in Section 6. In this paper, we propose a meta-model that can run arbitrary Graph Convolution models, such as GCN BID14 and SAGE BID10 , on the output of random walks. Traditional Graph Convolution models operate on the normalized adjacency matrix. We make multiple instantiations of such models, feeding each instantiation a power of the adjacency matrix, and then concatenating the output of all instances into a classification sub-network. Our model, Network of GCNs (and similarly, Network of SAGE), is end-to-end trainable, and is able to directly learn information across near or distant neighbors. We inspect the distribution of parameter weights in our classification sub-network, which reveal to us that our model is effectively able to circumvent adversarial perturbations on the input by shifting weights towards model instances consuming higher powers of the adjacency matrix. For future work, we plan to extend our methods to a stochastic implementation and tackle other (larger) graph datasets.",1291,0.681,743,1.737550471063257,"Graph Convolutional Networks had success on At unsupervised learning graph embeddings benefited the information contained random walks In, Network GCNs marries these two lines At N-GCN trains multiple instances GCNs over node pairs discovered random walks learns a combination the instance outputs which the classification objective Our experiments our proposed N-GCN model achieves state all the challenging node classification tasks we consider Cora Citeseer Pubmed PPI In addition our proposed method has other desirable properties generalization recently proposed semi-supervised learning methods GraphSAGE allowing propose N-SAGE resilience on graphs important recover labels all nodes given only a fraction labeled ones Some applications include where one wishes predict user interests in health care should screened In many such cases collecting node labels However edges between nodes easier obtain either an explicit graph implicitly calculating pairwise similarities using a patient-patient similarity kernel BID19 .Convolutional learn location-invariant hierarchical filters enabling significant improvements on Computer tasks This success motivated researchers BID7 to extend convolutions from yielding a class algorithms knownGCNs).Formally we where given G =V E N = |V| nodes; adjacency matrix A; matrix X �� R N ×F of node features Labels only a subset nodes V L ��� V observed In general |V L | |V|. Our goal recover labels all unlabeled nodes V U = − V L using the feature matrix X, the known labels G. In this setting one treats the graph ""unsupervised and labels of V L asDepicted FIG2 our model for builds the GCN module proposed BID14 operates matrixÂ, in GCN( where = D , diagonal matrix node degrees Our proposed extension GCNs inspired random walk based graph embeddingse.g. BID22 BID9 . We make a Network GCN modules feeding a different power ofÂ, as {GCN( 0 . . . }. The k-th power contains statistics a random walk on Therefore our N-GCN model able combine information various step-sizes We then combine all GCN modules a classification subnetwork jointly train the upstream objective Model architecture where is I is X node features matrix × matrix-matrix multiply operator We calculate K powers the , feeding each power r GCNs along X. The output all K × r GCNs along the column dimension then fed fully-connected layers outputting C channels per node where size label space We calculate cross entropy error , between rows prediction N × C with known labels them update parameters classification subnetwork and all GCNs Right: prerelu activations after the first fully-connected layer- Activations PCA-ed 50 dimensions then visualized t-SNE.semi-supervised node classification Weights the classification subnetwork give insight the N-GCN model For instance the presence input perturbations , classification subnetwork weights shift GCN modules utilizing higher powers effectively widening the ""receptive field We achieve state on several semi-supervised graph learning tasks showing that explicit random walks enhance vanilla GCN'sThe rest organized Section reviews background work that provides In Section our proposed method followed experimental evaluation in We compare our work recent closely-related methods Section . Finally conclude our contributions and future work Section In run arbitrary Graph Convolution models such GCN BID14 , random walks Traditional Graph Convolution models operate the normalized adjacency matrix We make multiple instantiations such models feeding a power the adjacency matrix all instances a classification subnetwork Our model, Network of GCNsand similarly Network SAGE end trainable directly learn information across near or distant neighbors We inspect the distribution parameter weights our classification subnetwork reveal to effectively able circumvent on by shifting towards model instances consuming higher powers For future work plan extend our methods a stochastic implementation tackle other (larger) graph datasets",0.01,0.5832929694771282
"Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers often with little or no drop in classification accuracy. However most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. In this paper we propose a cheap pruning algorithm based on difference of convex (DC) optimisation. We also provide theoretical analysis for the growth in the Generalisation Error (GE) of the new pruned network. Our method can be used with any convex regulariser and allows for a controlled degradation in classification accuracy while being orders of magnitude faster than competing approaches. Experiments on common feedforward neural networks show that for sparsity levels above 90% our method achieves 10% higher classification accuracy compared to Hard Thresholding. Recently, deep neural networks have achieved state-of-the art results in a number of machine learning tasks BID12 . Training such networks is computationally intensive and often requires dedicated and expensive hardware. Furthermore, the resulting networks often require a considerable amount of memory to be stored. Using a Pascal Titan X GPU the popular AlexNet and VGG-16 models require 13 hours and 7 days, respectively, to train, while requiring 200MB and 600MB, respectively, to store. The large memory requirements limit the use of DNNs in embedded systems and portable devices such as smartphones, which are now ubiquitous.A number of approaches have been proposed to reduce the DNN size during training time, often with little or no degradation to classification performance. Approaches include introducing bayesian, sparsity-inducing priors BID13 BID2 BID14 and binarization BID10 BID5 .Other methods include the hashing trick used in BID4 , tensorisation BID17 and efficient matrix factorisations BID11 .However , trained DNN models are used by researchers and developers that do not have dedicated hardware to train them, often as general feature extractors for transfer learning. In such settings it is important to introduce a cheap compression method, i.e., one that can be implemented as a postprocessing step with little or no retraining. Some first work in this direction has been BID11 BID8 BID9 although these still require a lengthy retraining procedure. Closer to our approach recently in BID0 the authors propose a convexified layerwise pruning algorithm termed Net-Trim. Building upon Net-Trim, the authors in BID6 propose LOBS, an algorithm for layerwise pruning by loss function approximation.Pruning a neural network layer introduces a pertubation to the latent signal representations generated by that layer. As the pertubated signal passes through layers of non-linear projections, the pertubation could become arbitrary large. In BID0 and BID6 the authors conduct a theoretical analysis using the Lipschitz properties of DNNs showing the stability of the latent representations, over the training set, after pruning. The methods employed have connections to recent work BID19 BID1 BID15 In this paper we have presented an efficient pruning algorithm for fully connected layers of DNNs, based on difference of convex functions optimisation. Our algorithm is orders of magnitude faster than competing approaches while allowing for a controlled degradation in the Generalization Error.We provided a theoretical analysis of the degradation in GE resulting from our pruning algorithm. This analysis validates the previously observed phenomenon that network layers closer to the input are exponentially less robust to pruning compared to layers close to the output. Our theoretical analysis is of value by itself as it holds for any kind of bounded pertubation to one or multiple hidden DNN layers. Experiments on common feedforward architectures validate our results. Proof. See BID3 for details, the derivation is not entirely trivial due to the nonsmoothness of the rectifier non-linearity. Proof. We see that: DISPLAYFORM0 1+exp(βx) ≤ 1. Therefore the smooth approximation to the rectifier non-linarity is Lipschitz smooth with Lipschitz constant k = 1. Then DISPLAYFORM1 We drop the W i from the layer notation for clarity. Using the triangle inequality DISPLAYFORM2 where we used Lemma 6.1 and Lemma 6.2 in line 5.B. PROOF OF THEOREM 3.2. We will proceed as follows. We first introduce some prior results which hold for the general class of robust classifiers. We will then give specific prior generalization error results for the case of classifiers operating on datapoints from C m -regular manifolds. Afterwards we will provide prior results for the specific case of DNN clasifiers. Finally we will prove our novel generalization error bound and provide a link with prior bounds.We first formalize robustness for generic classifiers g(x ). In the following we assume a loss function l(g(x) , y) that is positive and bounded DISPLAYFORM3 , such that ∀s i ∈ S m , ∀s ∈ S, DISPLAYFORM4 Now letl(·) and l emp (·) denote the expected error and the training error, i.e, DISPLAYFORM5 we can then state the following theorem from Xu & Mannor (2012): Theorem 6.3. If S m consists of m i.i.d. samples, and g(x) is (K, (S m ))-robust, then for any δ > 0, with probability at least 1 − δ, DISPLAYFORM6 The above generic bound can be specified for the case of C m -regular manifolds as in BID19 . We recall the definition of the sample margin γ(s i ) as well as the following theorem:Theorem 6.4. If there exists γ such that DISPLAYFORM7 By direct substitution of the above result and the definiton of a C m -regular manifold into Theorem 6.3 we get: Corollary 6.4.1. Assume that X is a (subset of) C M regular k−dimensional manifold, where DISPLAYFORM8 k . Assume also that classifier g(x) achieves a classification margin γ and take l(g(x), y) to be the 0 − 1 loss. Then for any δ > 0, with probability at least 1 − δ, DISPLAYFORM9 Note that in the above we have used the fact that l(g(x), y) ≤ 1 and therefore M = 1. The above holds for a wide range of algorithms that includes as an example SVMs. We are now ready to specify the above bound for the case of DNNs, adapted from BID19 , Theorem 6.5. Assume that a DNN classifier g(x), as defined in equation 8 , and letx be the training sample with the smallest score o(s) > 0. Then the classification margin is bounded as DISPLAYFORM10 We now prove our main result. We will denote byx = arg min si∈Sm min j =g(xi) v T g(xi)j f (x i ) the training sample with the smallest score. For this training sample we will denote j = arg min j =g(x) v T g(x)j f (x) the second best guess of the classifier g(·). Throughout the proof, we will use the notation DISPLAYFORM11 First we assume the score o 1 (x, g 1 (x)) of the pointx for the original classifier g 1 (x). Then , for the second classifier g 2 (x), we take a point x that lies on the decision boundary between g 2 (x) and j such that o 2 (x , g 2 (x)) = 0. We assume for simplicity that, after pruning, the classification decisions do not change such that g 1 (x) = g 2 (x). We then make the following calculations DISPLAYFORM12 where we used Theorem 3.1 in line 5, since x is not a training sample. From the above we can therefore write o 1 (x, g 1 (x)) − √ C 2 i>i ||W i || 2 DISPLAYFORM13 By following the derivation of the margin from the original paper BID19 and taking into account the definition of the margin we know that DISPLAYFORM14 Therefore we can finally write DISPLAYFORM15 The theorem follows from direct application of Corollary 3.1.1. Note that if γ − √ C2 i>i ||W i||2 i ||W i||2 < 0 the derived bound becomes vacuous, as by definition 0 ≤ γ 2 (x).C. PROOF OF THEOREM 3.3. We start as in theorem 3.2 by assuming the score o 1 (x, g 1 (x)) of the pointx for the original classifier g 1 (x). Then, for the second classifier g 2 (x), we take a point x that lies on the decision boundary between g 2 (x) and j such that o 2 (x , g 2 (x )) = 0. We assume as before that the classification decisions do not change such that g 1 (x) = g 2 ( x). We write DISPLAYFORM16 We can then write DISPLAYFORM17 Then as before DISPLAYFORM18 The theorem follows from direct application of Corollary 3.1.1.",1914,0.891,1087,1.7608095676172952,"Recent DNN pruning algorithms succeeded parameters fully connected layers often with classification accuracy However most the existing pruning schemes either applied during training require a costly retraining procedure after regain classification accuracy In a cheap pruning algorithm difference convex (DC) optimisation We also provide theoretical analysis the growth the Generalisation Error the new pruned network Our method can any convex regulariser allows a controlled degradation classification accuracy while being orders competing approaches Experiments common feedforward neural networks for sparsity levels above our method achieves 10% higher classification accuracy compared Hard Thresholding Recently deep neural networks achieved machine BID12 . Training such networks computationally Furthermore the resulting networks often stored Using a Pascal Titan X GPU the popular AlexNet and VGG-16 models require 13 hours, train requiring 200MB, The large memory requirements limit DNNs portable devices which now ubiquitousA number approaches during training time often classification performance Approaches include introducing bayesian, sparsity-inducing priors BID13 BID2 BID14 .Other the hashing trick used tensorisation BID17 and efficient matrix factorisations BID11 .However , trained DNN models used researchers developers that dedicated often as general feature extractors transfer learning In such settings introduce a cheap compression method with Some first work this direction BID11 BID8 BID9 although these still a lengthy retraining procedure Closer our approach recently in BID0 the authors propose a convexified layerwise pruning termed Net-Trim Building upon Net-Trim the authors in BID6 propose LOBS layerwise by loss function approximationPruning introduces a pertubation to the latent signal representations generated As the pertubated signal passes layers non-linear projections could arbitrary large In BID0 and the authors conduct the Lipschitz properties DNNs showing the stability the latent representations over the training set after pruning The methods employed have connections recent work BID19 BID1 In fully connected layers difference convex functions optimisation Our algorithm orders competing approaches while allowing a controlled degradation the Generalization ErrorWe provided GE resulting This analysis validates the previously observed phenomenon network layers closer exponentially robust pruning compared close Our theoretical analysis of value by as holds bounded pertubation to one or multiple hidden DNN layers Experiments common feedforward architectures validate Proof. See BID3 for the derivation is entirely trivial due the nonsmoothness the rectifier non Proof. We see: DISPLAYFORM0 1+exp(βx ≤ Therefore the smooth approximation the rectifier nonlinarity Lipschitz smooth with constant k Then DISPLAYFORM1 We drop the W i from the layer notation clarity Using the triangle inequality DISPLAYFORM2 where used Lemma in line 5.B. PROOF OF We proceed We first introduce some prior results which hold the general class robust classifiers We will then give specific prior generalization error results classifiers operating from C m -regular manifolds Afterwards we provide prior results the specific case DNN clasifiers Finally will prove our novel generalization error bound and provide with prior boundsWe first formalize robustness generic classifiers g(x ). In we assume a loss function l(g(x that positive bounded DISPLAYFORM3 such, Now letl(· l emp ( the training error, we then state from Xu & Mannor ( Theorem If S consists m i.i.d samples (K ()-robust for > with at − The above generic bound can specified C m -regular manifolds in BID19 We recall the definition the sample margin ��(s i well the following theoremTheorem If such that DISPLAYFORM7 By direct substitution the above result the definiton C m -regular manifold into Theorem Corollary Assume X a (subset of) C M regular k−dimensional manifold k . Assume also classifier g(x achieves a classification margin �� take the 0 − 1 loss Then for any �� > with probability DISPLAYFORM9 Note we used l(g(x therefore M above holds for algorithms includes as an example SVMs now specify above bound adapted BID19 , Theorem Assume classifier g(x as equation 8 , letx the training sample the smallest score o(s > Then the classification margin bounded as DISPLAYFORM10 We now prove our main result We will denote byx = arg min si��Sm min j =g(xi v T f the training sample the smallest score For this training sample denote j = arg min j =g(x v T g(x)j the second best guess the classifier g· Throughout the proof DISPLAYFORM11 First we assume the score o 1x g ( of the pointx for the original classifier g Then , for the second classifier g 2 take a point that lies the decision boundary g j such o , We assume for, pruning the classification decisions do such g 1x We then make DISPLAYFORM12 where used Theorem in line since x a training sample From the above therefore write o 1x g 1 − �� C i>i ||W || 2 DISPLAYFORM13 By following the margin from the original paper BID19 taking know Therefore finally The theorem follows direct application Note � − i < derived bound becomes vacuous by definition 0 ≤ � 2x).C. THEOREM We start as in theorem by assuming the score o 1 g ( the pointx for the original classifier g Then for the second classifier g 2 take a point lies the decision boundary g j such o , We assume as before the classification decisions do such g 1x x We write DISPLAYFORM16 We can then Then as The theorem follows direct application",0.01,0.6425551039749383
"Action segmentation as a milestone towards building automatic systems to understand untrimmed videos has received considerable attention in the recent years. It is typically being modeled as a sequence labeling problem but contains intrinsic and sufficient differences than text parsing or speech processing. In this paper, we introduce a novel hybrid temporal convolutional and recurrent network (TricorNet), which has an encoder-decoder architecture: the encoder consists of a hierarchy of temporal convolutional kernels that capture the local motion changes of different actions; the decoder is a hierarchy of recurrent neural networks that are able to learn and memorize long-term action dependencies after the encoding stage. Our model is simple but extremely effective in terms of video sequence labeling. The experimental results on three public action segmentation datasets have shown that the proposed model achieves superior performance over the state of the art. Action segmentation is a challenging problem in high-level video understanding. In its simplest form, action segmentation aims to segment a temporally untrimmed video by time and label each segmented part with one of k pre-defined action labels. For example, given a video of Making Hotdog (see FIG0 ), we label the first 10 seconds as take bread, and the next 20 seconds as take sausage, and the remaining video as pour ketchup following the procedure dependencies of making a hotdog. The results of action segmentation can be further used as input to various applications, such as video-to-text BID2 and action localization BID14 .Most current approaches for action segmentation BID26 BID19 use features extracted by convolutional neural networks, e.g., two-stream CNNs BID18 or local 3D ConvNets BID23 , at every frame after a downsampling as the input, and apply a one-dimensional sequence prediction model, such as recurrent neural networks, to label actions on frames. Despite the simplicity in handling video data, action segmentation is treated similar to text parsing BID1 , which results the local motion changes in various actions being under-explored. For example , the action pour ketchup may consist of a series of sub-actions, e.g., pick up the ketchup, squeeze and pour, and put down the ketchup. Furthermore , the time duration of performing the same action pour ketchup may vary according to different people and contexts.Indeed, the recent work by BID12 starts to explore the local motion changes in action segmentation. They propose an encoder-decoder framework, similar to the deconvolution networks in image semantic segmentation BID15 , for video sequence labeling. By using a hierarchy of 1D temporal convolutional and deconvolutional kernels in the encoder and decoder networks, respectively, their model is effective in terms of capturing the local motions and achieves state-of-theart performance in various action segmentation datasets. However, one obvious drawback is that it fails to capture the long-term dependencies of different actions in a video due to its fixed-size, local receptive fields. For example, pour ketchup usually happens after both take bread and take sausage for a typically video of Making Hotdog. In addition, a dilated temporal convolutional network, similar to the WavNet for speech processing BID24 , is also tested in BID12 , but has worse performance, which further suggests the existence of differences between video and speech data, despite they are both being represented as sequential features. To overcome the above limitations , we propose a novel hybrid TempoRal COnvolutional and Recurrent Network (TricorNet), that attends to both local motion changes and long-term action dependencies for modeling video action segmentation. TricorNet uses frame-level features as the input to an encoder-decoder architecture. The encoder is a temporal convolutional network that consists of a hierarchy of one-dimensional convolutional kernels, observing that the convolutional kernels are good at encoding the local motion changes; the decoder is a hierarchy of recurrent neural networks, in our case Bi-directional Long Short-Term Memory networks (Bi-LSTMs) BID5 , that are able to learn and memorize long-term action dependencies after the encoding process. Our network is simple but extremely effective in terms of dealing with different time durations of actions and modeling the dependencies among different actions.We conduct extensive experiments on three public action segmentation datasets, where we compare our proposed models with a set of recent action segmentation networks using three different evaluation metrics. The quantitative experimental results show that our proposed TricorNet achieves superior or competitive performance to state of the art on all three datasets. A further qualitative exploration on action dependencies shows that our model is good at capturing long-term action dependencies and produce smoother labeling.For the rest of the paper, we first survey related work in the domain of action segmentation and action detection in Sec. 2. We introduce our hybrid temporal convolutional and recurrent network with some implementation variants in Sec. 3. We present both quantitative and qualitative experimental results in Sec. 4, and conclude the paper in Sec. 5. In this paper, we propose TricorNet, a novel hybrid temporal convolutional and recurrent network for video action segmentation problems. Taking frame-level features as the input to an encoder-decoder architecture, TricorNet uses temporal convolutional kernels to model local motion changes and uses bi-directional LSTM units to learn long-term action dependencies. We provide three model variants to comprehensively evaluate our model design. Despite the simplicity in methods, experimental results on three public action segmentation datasets with different metrics show that our proposed model achieves superior performance over the state of the art. A further qualitative exploration on action dependencies shows that our model is good at capturing long-term action dependencies, which help to produce segmentation in a smoother and preciser manner.Limitations. In experiments we find that all the best results of TricorNet are achieved with number of layers K = 2. It will either over-fit or stuck in local optimum when adding more layers. Considering all three datasets are relatively small with limited training data (despite they are standard in evaluating action segmentation), using more data is likely going to further improve the performance.Future Work. We consider two directions for the future work. Firstly, the proposed TricorNet is good to be evaluated on other action segmentation datasets to further explore its strengths and limitations. Secondly, TricorNet can be extended to solve other video understanding problems, taking advantage of its flexible structural design and superior capability of capturing video information.",1267,0.678,732,1.7308743169398908,"Action segmentation as a milestone towards building automatic systems understand untrimmed videos has received It typically being modeled a sequence labeling problem but contains intrinsic and sufficient differences than text parsing speech processing In a novel hybrid temporal convolutional and recurrent network: consists a hierarchy capture the local motion changes different actions; learn long action dependencies after the encoding stage Our model simple extremely terms video sequence labeling The experimental results on three public action segmentation datasets the proposed model achieves superior performance Action segmentation high-level video understanding In action segmentation aims segment a temporally untrimmed video time label one k pre-defined action labels For example given a video Making Hotdogsee FIG0 label take bread sausage the remaining video pour ketchup following the procedure dependencies making The results action segmentation can further used input various applications videotext BID2 action localization BID14 .Most current approaches use features extracted, two-stream CNNs BID18 at every frame after as apply label actions frames Despite the simplicity in handling video data action segmentation treated similar text parsing BID1 , results the local motion changes various actions being under For example , the action pour ketchup consist sub pick squeeze put down Furthermore , the time duration performing the same action pour ketchup may different people contextsIndeed the recent work BID12 starts the local motion changes action segmentation They propose an encoder-decoder framework similar image semantic segmentation BID15 , video sequence labeling By using a hierarchy 1D temporal convolutional and deconvolutional kernels respectively their model effective terms capturing the local motions achieves statetheart various action segmentation datasets However one obvious drawback fails different actions a video due local receptive fields For example pour ketchup usually happens both take bread take sausage for a typically video of Making Hotdog In a dilated temporal convolutional network similar the WavNet for speech BID24 tested worse performance further differences video and speech data despite they being represented sequential features To overcome the above limitations , hybrid TempoRal COnvolutional and Recurrent Network attends both local motion changes for modeling video action segmentation TricorNet uses frame-level features as the input The encoder consists a hierarchy observing good encoding the local motion changes; in our case Bi Long networks BID5 , that learn long action dependencies after Our network simple extremely terms dealing different time durations actions modeling the dependencies amongWe conduct extensive experiments three public action segmentation datasets where compare our proposed models recent action segmentation networks using three different evaluation metrics The quantitative experimental results our proposed TricorNet achieves superior or competitive performance to state on A further qualitative exploration on action dependencies shows our model good capturing produce smoother labelingFor first survey related work action segmentation action detection Sec. 2 We introduce our hybrid temporal convolutional and recurrent network some implementation variants Sec 3 We present both quantitative experimental results Sec. 4 and conclude the paper Sec 5 In TricorNet a novel hybrid temporal convolutional and recurrent network video action segmentation problems Taking frame-level features as the input TricorNet temporal convolutional kernels model local motion changes uses learn long-term action dependencies We provide three model variants comprehensively our model design Despite the simplicity in methods experimental results on three public action segmentation datasets with different metrics our proposed model achieves the state A further qualitative exploration on action dependencies shows our model good capturing help produce segmentation in a smoother and preciser mannerLimitations. In experiments we find all the best results of TricorNet number layers K It will either overfit stuck local optimum when adding more layers Considering all three datasets relatively withdespite they standard evaluating action segmentation using going furtherFuture Work. We consider two directions the future work Firstly the proposed TricorNet good be evaluated other action segmentation datasets to further Secondly TricorNet can extended solve other video understanding problems taking its flexible structural design superior capability capturing",0.01,0.5662827153312788
"Convolutional Neural Networks (CNNs) become deeper and deeper in recent years, making the study of model acceleration imperative. It is a common practice to employ a shallow network, called student, to learn from a deep one, which is termed as teacher. Prior work made many attempts to transfer different types of knowledge from teacher to student, however, there are two problems remaining unsolved. Firstly, the knowledge used by existing methods is highly dependent on task and dataset, limiting their applications. Secondly, there lacks an effective training scheme for the transfer process, leading to degradation of performance. In this work, we argue that feature is the most important knowledge from teacher. It is sufficient for student to just learn good features regardless of the target task. From this discovery, we further present an efficient learning strategy to mimic features stage by stage. Extensive experiments demonstrate the importance of features and show that the proposed approach significantly narrows down the gap between student and teacher, outperforming the state-of-the-art methods.
 Over the past few years, Convolutional Neural Networks (CNNs) have advanced various tasks in computer vision field, such as image classification BID8 , object detection BID17 , semantic segmentation BID3 , etc. However, along with the architecture growing deeper BID12 BID20 BID5 , the great success of CNN is at the cost of large computational power, which can not be afforded by most devices in practice. Some lightweight models are presented by recent work BID7 to reduce the computing cost especially for mobile devices, but the performance drops severely compared with the state-of-the-art methods. Accordingly, it is crucial to balance the trade-off between efficiency and capability of a CNN model.To tackle this problem, knowledge distillation is introduced in BID6 for model acceleration. The core idea is to train shallow networks (student) to mimic deep ones (teacher) following two folds. First, teacher employs a very deep model to achieve satisfying performance by excavating information (knowledge) from labeled data. Second, student learns the knowledge from teacher with a shallow model to speed up without losing much accuracy. Accordingly, the main challenges, corresponding to the above two steps respectively, lie in (1) what kind of knowledge should be transferred to student, and (2) how to transfer the knowledge from teacher to student as much as possible.For the first issue, previous work usually make student to learn from both teacher and original labeled data. There are mainly two problems in doing so. On one hand, it is very sensitive to tasks and datasets. The hyper-parameters, e.g. the loss weights to balance these two objective functions, require careful adjustment, or otherwise, it may cause severe performance degradation. On the other hand, the purposes to learn from teacher and to learn from ground-truth are not always consistent with each other. For example, teacher model may eliminate some label errors during the training process. In this case, trying to minimize the loss to mimic teacher as well as the loss from target task may cause confusions to student. Furthermore, prior work has also characterized various types of knowledge from teacher model for student to learn, such as attention map BID23 , information flow BID22 , etc. However, all types of knowledge are manually defined, which may not fully conform with the information contained in the teacher network. In other words, teacher is trained independently from these handcraft definitions, but is required to guide the student with such knowledge, which may cause some ambiguities. For the second issue, previous approaches do not solve the problem caused by the gaps between the learning abilities of student and teacher. Intuitively, student model has much less parameters compared to teacher, resulting in lower representation capability. Training it from scratch may always lead to poor performance.In this paper, we address these weaknesses by proposing a task independent knowledge transfer approach, where student is trained to mimic features from teacher stage by stage. Here, for simplicity, we do not distinguish between feature and feature map. It has two appealing properties.First, we isolate the knowledge contained in teacher model from the information provided by ground-truth. This goal is achieved with two phases. In the first phase, student learns knowledge by mimicking the output features of teacher, while in the second phase, student is trained with task dependent objection function based on the features from first phase. In this way, student can focus on acquiring information from only one source in each phase, making the transfer process more accurate. Separating these two phases apart also makes our method more generic to various tasks. Besides, we directly treat features as knowledge in this work. Since teacher model just uses features for inference in practice, they are expected to contain the compete information extracted by teacher from training data.Second, instead of training all parameters of student together, we divide the transfer process into different stages and only train a sub-network at one time. Student network has far more limited representation ability than teacher, resulting in the huge difficulty to mimic the final features directly. To alleviate such obstacle, we let the student to learn from teacher gradually. In other words, both teacher network and student network are separated into sequential parts. Then, in each stage, one part of student will be trained to mimic the output of the corresponding part of teacher with all previous parts fixed. In doing so, the gap between learning powers between student and teacher is narrowed down. As long as each stage is well trained, they will finally collaborate to achieve appealing results.To summarize, the contributions of this work are as follows:• We demonstrate the effectiveness of mimicking features directly in task independent knowledge transfer.• We present a stage-by-stage training strategy to learn features accurately and efficiently.• We show experimentally that our approach surpasses the state-of-the-art methods on various tasks with higher performance and stronger stability. This work presents a stage-by-stage knowledge transfer approach by training student to mimic the output features of teacher network gradually. Compared to prior work, our method pays more attention to the information contained in the model, regardless of what task the model is applied for, making it a generic solution for model acceleration. The progressive training strategy helps reduce the learning difficulties of student in each stage, and all stages cooperate together for a better result.Extensive experimental results suggest that our scheme can significantly improve the performance of student model on various tasks with strong stability.",1263,0.756,699,1.8068669527896997," become deeper making the study model acceleration imperative It employ a shallow network called student, learn a deep one termed as teacher Prior work made many attempts transfer different types knowledge teacher however remaining unsolved Firstly the knowledge used existing methods highly task dataset limiting their applications Secondly lacks an effective training scheme the transfer process leading degradation performance In this work argue feature is from teacher. It sufficient student just learn good features regardless the target task From this discovery further present an efficient learning strategy mimic features stage Extensive experiments demonstrate features show the proposed approach significantly narrows student, outperforming state Over advanced various tasks image classification BID8 , object semantic etc However along the architecture growing deeper BID12 BID20 BID5 , the great success CNN at large computational power not afforded most devices practice Some lightweight models presented recent work BID7 to reduce the computing cost especially drops severely compared state methods Accordingly crucial balance efficiency capability a CNN modelTo tackle knowledge distillation introduced BID6 for model acceleration The core idea train shallow networksstudent) mimic deep ones following two folds First teacher employs a very deep model achieve satisfying performance by excavating information (knowledge labeled data Second student learns the knowledge from teacher with a shallow model to speed without losing much accuracy Accordingly the main challenges, corresponding respectively lie ( what kind knowledge transferred student teacher as muchFor previous work usually make student to learn original labeled data There mainly doing On sensitive tasks datasets The hyper the loss weights to balance these two objective functions require careful adjustment or otherwise it On the purposes to learn teacher to ground-truth consistent For example teacher model may eliminate some label errors during In trying minimize mimic teacher as from target task cause confusions to student Furthermore prior work also characterized various types knowledge from teacher model for student to learn attention map BID23 , etc However all types knowledge manually defined fully conform the teacher network In teacher is trained independently these handcraft definitions required guide with such knowledge cause For the second issue previous approaches do solve caused the gaps the learning abilities student Intuitively student model has much less parameters compared teacher, resulting lower representation capability Training it from may always leadIn address these weaknesses proposing a task independent knowledge transfer approach student is mimic features teacher stage by stage Here for simplicity do distinguish feature and feature map It two appealing propertiesFirst we isolate the knowledge contained teacher model ground-truth This goal achieved two phases In student learns knowledge by mimicking the output features teacher task dependent objection function based the features from In student can focus acquiring information each phase making accurate Separating these two phases apart also our method generic to various tasks Besides directly treat features knowledge in this work Since teacher model just uses features inference in practice they expected contain the compete information extracted teacher fromSecond instead training all parameters student together divide the transfer process only a subnetwork at Student network has far more limited representation ability teacher resulting the huge difficulty mimic the final features directly To alleviate such obstacle let to learn teacher gradually In both teacher network separated sequential parts Then each stage one part student will trained mimic the output with all previous parts fixed In doing the gap learning powers student narrowed down As long each stage well trained finally collaborate appealing resultsTo summarize the contributions this work We demonstrate mimicking features directly task independent knowledge present stage training learn features accurately experimentally surpasses state on various tasks with stronger stability This work presents stage knowledge transfer by training student to mimic the output features teacher network gradually Compared prior work our method pays regardless what task applied for making generic solution model acceleration The progressive training strategy helps reduce the learning difficulties student in each stage all stages cooperateExtensive experimental results our scheme significantly student model on with strong stability",0.01,0.759905274836609
"We augment adversarial training (AT) with worst case adversarial training
 (WCAT) which improves adversarial robustness by 11% over the current state-
 of-the-art result in the `2-norm on CIFAR-10. We interpret adversarial training as
 Total Variation Regularization, which is a fundamental tool in mathematical im-
 age processing, and WCAT as Lipschitz regularization, which appears in Image
 Inpainting. We obtain verifiable worst and average case robustness guarantees,
 based on the expected and maximum values of the norm of the gradient of the
 loss. We augment adversarial training (AT) with worst case adversarial training (WCAT) which improves adversarial robustness by 11% over the current state-of-the-art result BID27 in the 2 norm. The method also achieves results comparable to the state-of-the-art results of BID22 in the ∞ norm. Moreover, our adversarial training step uses only one gradient evaluation compared to seven steps in the BID22 work. The worst case adversarial training method is described as follows. During adversarial training, the gradient of the loss is computed for each perturbed image. WCAT records the largest of the gradients norms, and adds a penalty to the loss proportional to this term. In many cases we observe that models trained with AT and WCAT have improved test/validation error over the unregularized model.In §2 we show that the norm of the gradient of the loss of the model is a measure of the robustness of a model to adversarial examples. We obtain verifiable worst and average case robustness guarantees, based on the expected and maximum values of the norm of the gradient of the loss. We then compute these quantities empirically on trained models, and demonstrate that improving these quantities leads to proportional improvements in adversarial robustness.In §3 we interpret adversarial training as Total Variation (TV) Regularization, which is a fundamental tool in mathematical image processing. TV regularization was introduced for image denoising BID29 . It is a measure of the variation of a function, allowing for discontinuities. We also show that WCAT corresponds to Lipschitz regularization, which appears in Image Inpainting BID2 and function approximation BID7 BID25 . Lipschitz regularization was used in a recent proof of generalization of deep neural networks BID26 . Write (x) = • f (x) for the loss of the model. We show that training with AT and WCAT is equivalent to minimizing DISPLAYFORM0 where is the size of the adversarial training perturbation, and λ is the WCAT multiplier. The dual norm · * corresponds to · 1 for attacks measured in ∞ and to · 2 for attacks measured in 2 , 1 see §3.1.",564,0.313,330,1.709090909090909,"We augment adversarial trainingWCAT improves 11% of the `2-norm on We interpret adversarial training Total Variation Regularization a fundamental tool mathematical im- age processing WCAT appears Image Inpainting We obtain verifiable worst and average case robustness guarantees the expected and maximum values the norm of the gradient the loss We augment adversarial trainingWCAT improves 11% state result BID27 in the 2 norm. The method also achieves results state results BID22 the �� norm Moreover our adversarial training step uses only one gradient evaluation compared seven steps the BID22 work The worst case adversarial training method described follows During adversarial training the gradient the loss computed each perturbed image WCAT records largest of the gradients norms adds a penalty proportional this term In we observe models trained AT and WCAT improved test/validation error over the unregularized modelIn § we the norm the gradient the loss adversarial examples We obtain verifiable worst and average case robustness guarantees the expected and maximum values the norm of the gradient the loss We then compute these quantities trained models demonstrate improving proportional improvements adversarial robustnessIn § interpret TotalTV Regularization a fundamental tool mathematical image processing TV regularization was image denoising BID29 . It a measure the variation a function allowing We also show WCAT corresponds Lipschitz regularization appears Image Inpainting BID2 function approximation BID7 BID25 Lipschitz regularization a recent proof generalization BID26 Write (x = • f for the loss the model We show training AT and WCAT equivalent minimizing DISPLAYFORM0 where is �� WCAT multiplier The dual norm · * corresponds · for attacks measured to 2 , see §",0.0,0.5107805060013604
"The task of Reading Comprehension with Multiple Choice Questions, requires a human (or machine) to read a given \{\textit{passage, question}\} pair and select one of the $n$ given options. The current state of the art model for this task first computes a query-aware representation for the passage and then \textit{selects} the option which has the maximum similarity with this representation. However, when humans perform this task they do not just focus on option selection but use a combination of \textit{elimination} and \textit{selection}. Specifically, a human would first try to eliminate the most irrelevant option and then read the document again in the light of this new information (and perhaps ignore portions corresponding to the eliminated option). This process could be repeated multiple times till the reader is finally ready to select the correct option. We propose \textit{ElimiNet}, a neural network based model which tries to mimic this process. Specifically, it has gates which decide whether an option can be eliminated given the \{\textit{document, question}\} pair and if so it tries to make the document representation orthogonal to this eliminatedd option (akin to ignoring portions of the document corresponding to the eliminated option). The model makes multiple rounds of partial elimination to refine the document representation and finally uses a selection module to pick the best option. We evaluate our model on the recently released large scale RACE dataset and show that it outperforms the current state of the art model on 7 out of the 13 question types in this dataset. Further we show that taking an ensemble of our \textit{elimination-selection} based method with a \textit{selection} based method gives us an improvement of 7\% (relative) over the best reported performance on this dataset.    
 Reading comprehension is the task of answering questions from a given passage. An AI agent which can display such capabilities would be useful in a wide variety of commercial applications such as answering questions from financial reports of a company, troubleshooting using product manuals, answering general knowledge questions from Wikipedia documents, etc. Given its widespread applicability, several variants of this task have been studied in the literature. For example, given a passage and a question, the answer could either (i) match some span in the passage or (ii) be synthesized from the passage or (iii) be one of the n given candidate answers. The last variant is typically used in various high school, middle school and competitive examinations. We refer to this as Reading Comprehension with Multiple Choice Questions (RC-MCQ). There is an increasing interest in building AI agents with deep language understanding capabilities which can perform at par with humans on such competitive tests. For example, recently BID10 have released a large scale dataset for RC-MCQ collected from Chinese high school and middle school English examinations comprising of 28000 passages and 100000 questions. The large size of this dataset makes it possible to train and evaluate complex neural network based models and measure the scientific progress on RC-MCQ.While answering such Multiple Choice Questions (MCQs), humans typically use a combination of option elimination and option selection. More specifically, it makes sense to first try to eliminate options which are completely irrelevant for the given question. While doing so, we may also be able to discard certain portions of the document which are not relevant to the question (because they revolve around the option which has been eliminated). This process can then be repeated multiple times, each time eliminating an option and refining the document (by discarding irrelevant portions). Finally, when it is no longer possible to eliminate any option, we can pick the best option from the remaining options. In contrast, current state of the art models for RC-MCQ focus explicitly on option selection. Specifically, given a question and a passage, they first compute a question aware representation of the passage (say d q ). They then compute a representation for each of the n options and select an option whose representation is closest to d q . There is no iterative process where options get eliminated and the representation of the document gets refined in the light of this elimination.We propose a model which tries to mimic the human process of answering MCQs. Similar to the existing state of the art method BID3 , we first compute a query-aware representation of the document (which essentially tries to retain only those portions of the document which are relevant to the question). We then use an elimination gate which takes a soft decision as to whether an option needs to be eliminated or not. This gate depends on the question, document and option. Next, akin to the human process described above, we would like to discard portions of the document representation which are aligned with this eliminated option. We do this by subtracting the component of the document representation along the option representation (same as Gram-Schmidt orthogonalization). The amount of orthogonalization depends on the soft decision given by the elimination gate. We repeat this process multiple times, during each pass doing a soft elimination of the options and refining the document representation. At the end of a few passes, we expect the document representation to be orthogonal (hence dissimilar) to the irrelevant options. Finally, we use a selection module to select the option which is most similar to the refined document representation. We refer to this model as ElimiNet.We evaluate ElimiNet on the RACE dataset and compare it with Gated Attention Reader (GAR) BID3 which is the current state of the art method on this dataset. We show that of the 13 question types in this dataset our model outperforms GAR on 7 question types. We also visualize the soft elimination probabilities learnt by ElimiNet and observe that it indeed learns to iteratively refine the document representation and push the probability mass towards the correct option. Finally, we show that an ensemble model combining ElimiNet with GAR gives an accuracy of 47.2% which is 7% (relative) better than the best reported performance on this dataset. In this section, we discuss the results of our experiments as described above. We focus on the task of Reading Comprehension with Multiple Choice Questions and propose a model which mimics how humans approach this task. Specifically, the model uses a combination of elimination and selection to arrive at the correct option. This is achieved by introducing an elimination module which takes a soft decision as to whether an option should be eliminated or not. It then modifies the document representation to either align it with uneliminated options or orthogonalize it to eliminated options. The amount of orthogonalization or alignment is determined by two gating functions. This process is repeated multiple times to iteratively refine the document representation. We evaluate our model on the recently released RACE dataset and show that it outperforms current state of the art models on 7 out of 13 question types. Finally, using an ensemble of our eliminationselection approach with a state of the art selection approach, we get an improvement of 7% over the best reported performance on RACE dataset. As future work, instead of soft elimination we would like to use reinforcement learning techniques to learn a policy for hard elimination.",1445,0.812,864,1.6724537037037037,"The task Reading Comprehension with Multiple Choice Questions requires human ( machine read a given \{\textit{passage, question}\} pair and select The current state the art model this task first computes a query-aware representation the passage and then \textit{selects the option which has the maximum similarity with this representation However when humans perform just focus option selection use \textit{elimination Specifically a human would first try eliminate the most irrelevant option read the document again in the light ( ignore portions corresponding This process could till the reader finally select We propose \textit{ElimiNet a neural network based model tries mimic this process Specifically gates which decide an option eliminated given the \{\textit{document, question}\} pair if tries make the document representation this eliminatedd optionakin ignoring portions corresponding The model makes multiple rounds partial elimination to refine the document representation finally uses a selection module pick We evaluate our model the recently released large scale RACE dataset show on 7 out the 13 question types Further we show taking an ensemble our \textit{elimination-selection} based method gives 7\% (relative the best reported performance this dataset Reading comprehension answering from a given passage An AI agent which display such capabilities would answering financial reports of using product manuals answering general knowledge questions Wikipedia documents Given its widespread applicability several variants this task studied For example given a passage and could either ( match some span synthesized one the n given candidate answers The last variant typically various high school, competitive examinations We refer Reading Comprehension with Multiple Choice QuestionsRC-MCQ There building AI agents deep language understanding capabilities which perform at par on such competitive tests For example recently BID10 have a large scale dataset RC-MCQ collected Chinese high school and middle school English examinations comprising of 28000 passages 100000 questions The large size this dataset train and evaluate complex neural network based models and measure the scientific progress on RC-MCQ.While answering such Multiple Choice Questions humans typically option elimination option selection More specifically makes first try eliminate options which completely the given question While doing may discard certain portions which (because revolve the option which eliminated This process then each eliminating an option and refining the document (by discarding irrelevant portions Finally when is no eliminate any option pick In contrast current state RCMCQ focus explicitly option selection Specifically given a question and a passage they first compute a question aware representationsay d q They then compute a representation for the n options select whose representation closest d q There no iterative process where options get eliminated the representation the document refined the light this eliminationWe propose tries mimic answering MCQs Similar the existing state BID3 first compute a query-aware representation essentially tries retain only those portions We then use an elimination gate which takes a soft decision an option needs This gate depends the question document option Next akin the human process described would discard portions the document representation aligned this eliminated option We do subtracting the component the document representation along the option representationsame Gram-Schmidt orthogonalization The amount orthogonalization depends the soft decision given the elimination gate We repeat this process multiple during each pass doing a soft elimination the options refining the document representation At a few passes expect the document representation dissimilar the irrelevant options Finally use a selection module select the option which similar the refined document representation We refer ElimiNetWe evaluate the RACE dataset Gated Attention Reader (GAR) BID3 which on We show of the 13 question types our model GAR on We also visualize the soft elimination probabilities learnt ElimiNet observe indeed learns iteratively refine the document representation push the probability mass towards the correct option Finally show an ensemble model combining ElimiNet GAR gives an accuracy which 7% (relative the best reported performance In the results as described We focus the task Reading Comprehension with Multiple Choice Questions propose how humans approach Specifically the model uses elimination selection arrive the correct option This achieved introducing an elimination module a soft decision an option eliminated It then modifies the document representation either align uneliminated options eliminated options The amount orthogonalization or alignment two gating functions This process repeated multiple iteratively refine the document representation We evaluate our model the recently released RACE dataset show current state 7 out 13 question types Finally using an ensemble our eliminationselection approach with a state get an improvement 7% the best reported performance RACE dataset As future work, instead soft elimination we a policy hard elimination",0.01,0.41743212558443094
"Humans are capable of attributing latent mental contents such as beliefs, or intentions to others. The social skill is critical in everyday life to reason about the potential consequences of their behaviors so as to plan ahead. It is known that humans use this reasoning ability recursively, i.e. considering what others believe about their own beliefs.   In this paper, we start  from level-$1$ recursion and introduce a probabilistic recursive reasoning (PR2) framework for multi-agent reinforcement learning. Our hypothesis is that it is beneficial for each agent to account for how the opponents would react to its future behaviors. Under the PR2 framework, we adopt variational Bayes methods to approximate the opponents' conditional policy, to which each agent finds the  best response and then improve their own policy. We develop  decentralized-training-decentralized-execution  algorithms, PR2-Q and PR2-Actor-Critic, that are proved to converge in the self-play scenario when there is one Nash equilibrium. Our methods are tested on both the matrix game and the differential game, which have a non-trivial equilibrium where common gradient-based methods fail to converge. Our experiments show that it is critical to reason about how the opponents believe about what the agent believes. We expect our work to contribute a new idea of modeling the opponents to the multi-agent reinforcement learning community.",269,0.17,164,1.6402439024390243,Humans capable attributing latent mental contents such beliefs or intentions The social skill critical to reason the potential consequences their behaviors so plan It known humans use this reasoning ability recursively considering others In start level-$1$ recursion introduce a probabilistic recursive reasoning (PR2) framework Our hypothesis it beneficial each agent account how the opponents would its future behaviors Under the PR2 framework we adopt variational Bayes methods approximate the opponents' conditional policy to which each agent finds improve We develop decentralized-training-decentralized-execution algorithms PR2-Q PR2-Actor-Critic proved converge the self-play scenario when there one Nash equilibrium Our methods tested both the matrix game the differential game where common gradient-based methods fail Our experiments it critical reason the opponents believe the agent We expect our work contribute a new idea modeling the opponents the multi-agent reinforcement learning community,0.0,0.3353643818842243
"Due to the substantial computational cost, training state-of-the-art deep neural networks for large-scale datasets often requires distributed training using multiple computation workers. However, by nature, workers need to frequently communicate gradients, causing severe bottlenecks, especially on lower bandwidth connections. A few methods have been proposed to compress gradient for efficient communication, but they either suffer a low compression ratio or significantly harm the resulting model accuracy, particularly when applied to convolutional neural networks. To address these issues, we propose a method to reduce the communication overhead of distributed deep learning. Our key observation is that gradient updates can be delayed until an unambiguous (high amplitude, low variance) gradient has been calculated. We also present an efficient algorithm to compute the variance and prove that it can be obtained with negligible additional cost. We experimentally show that our method can achieve very high compression ratio while maintaining the result model accuracy. We also analyze the efficiency using computation and communication cost models and provide the evidence that this method enables distributed deep learning for many scenarios with commodity environments. Deep neural networks are attracting attention because of their outstanding prediction power in many application fields such as image recognition, natural language processing, and speech recognition. In addition, software frameworks are publicly available, making it easier to apply deep learning. However, their crucial drawback is the substantial computational cost on training. For example, it takes over a week to train ResNet-50 on the ImageNet dataset if using a single GPU. Such long training time limits the number of trials possible when creating models. Therefore, we must conduct distributed training using multiple computation workers (e.g., multiple GPUs in different nodes). However, by nature, workers need to frequently communicate gradients, which yields a severe bottleneck for scalability, especially when using lower bandwidth connections. For example, when using 1000BASE-T Ethernet, communication takes at least ten times longer than forward and backward computation for ResNet-50, making multiple nodes impractical. High performance interconnections such as InfiniBand and Omni-Path are an order of magnitude more expensive than commodity interconnections, which limits research and development of deep learning using large-scale datasets to a small number of researchers.Although several methods have been proposed to compress gradient for efficient communication, they either suffer a low compression ratio or significantly harm the resulting model accuracy, particularly when applied to convolutional neural networks. There are mainly two lines of research: quantization and sparsification. Quantization-based methods include 1-bit SGD BID9 and TernGrad (Wen et al., 2017) . Though they achieve small loss of accuracy by using at least one bit for each parameter, the compression ratio is limited. Sparsification-based methods include BID11 and QSGD (Alistarh et al., 2017) . While they can achieve high compression ratio, as we will see in our experiments, they harm the resulting model accuracy or suffer a low compression ratio, particularly when applied to convolutional neural networks.To address these issues, we propose a new gradient compression algorithm to reduce the communication overhead of distributed deep learning. The proposed method belongs to the sparsification approaches. Our key observation is that the variance of the gradient for each parameter point over iterations is a useful signal for compression. As almost all previous approaches of both sparsification and quantization only look at the magnitude of gradient, we believe that we are opening a new door for this field. In addition, we also show that our method can be combined with previous compression methods to further boost performance. We also present an efficient algorithm to compute the variance and prove that it can be obtained with negligible additional cost.We experimentally demonstrate that our method can achieve a high compression ratio while maintaining result model accuracy. We also analyze the efficiency using computation and communication cost models and provide evidence that our method enables distributed deep learning for many scenarios with commodity environments.Organization. The remainder of this paper is organized as follows: Section 2 provides the definitions and notations used in this paper. Section 3 reviews related work in this field. Section 4 presents the proposed method. Section 5 analyzes performance. Section 6 shows our experimental results, and we conclude in Section 7. We proposed a novel method for gradient compression. Our method can reduce communication cost significantly with no or only slight accuracy degradation. Contributions of our work can be summarized in the following three points. First, we proposed a novel measurement of ambiguity (high variance, low amplitude) to determine when a gradient update is required. Second, we showed the application of this measurement as a threshold for updates significantly reduces update requirements, while providing comparable accuracy. Third, we demonstrated this method can be combined with other efficient gradient compression approaches to further reduce communication cost.",942,0.613,549,1.715846994535519,"Due the substantial computational cost training state deep often distributed using multiple computation workers However by nature workers need frequently communicate gradients causing lower bandwidth connections A few methods compress gradient for efficient communication either suffer a low compression ratio significantly harm the resulting model accuracy particularly To address propose reduce the communication distributed deep learning Our key observation that gradient updates delayed until an unambiguous (high amplitude, low variance) gradient We also present an efficient algorithm prove obtained negligible additional cost We experimentally show our method achieve very high compression ratio while the result model accuracy We also analyze the efficiency using computation and communication cost models provide the evidence enables distributed deep learning many scenarios with commodity environments Deep neural networks attracting their outstanding prediction power many application fields In addition software frameworks publicly making apply deep learning However their crucial drawback the substantial computational cost on training For example it takes over train ResNet-50 the ImageNet dataset if using Such long training time limits the number trials possible when creating models Therefore conduct distributed training using multiple computation workers in different nodes However by nature workers need frequently communicate gradients yields a severe bottleneck scalability lower bandwidth connections For example using 1000BASE-T Ethernet communication takes at ten forward and backward computation ResNet-50 making multiple nodes impractical High performance interconnections such Omni-Path an order limits research deep learning using toAlthough several methods compress gradient for efficient communication they either suffer a low compression ratio significantly harm the resulting model accuracy particularly There mainly two lines research quantization sparsification Quantization-based methods include 1-bit SGD BID9 TernGrad (Wen 2017 . Though achieve small loss accuracy for the compression ratio limited Sparsification-based methods include BID11 QSGDAlistarh et 2017 . While they can achieve high compression ratio as our experiments harm the resulting model accuracy or suffer particularlyTo propose the communication distributed deep learning The proposed method belongs the sparsification approaches Our key observation the variance the gradient for each parameter point over iterations a useful signal compression As almost all previous approaches of both sparsification quantization only look the magnitude gradient believe opening this field In addition show our method combined previous compression methods further boost We also present an efficient algorithm prove obtained negligible additional costWe experimentally achieve while result model accuracy We also analyze the efficiency using computation and communication cost models provide evidence our method enables distributed deep learning many scenarios with commodity environmentsOrganization. The remainder organized Section provides notations Section reviews related work Section presents. Section analyzes performance. Section shows our experimental results conclude in We proposed gradient compression Our method can reduce communication cost significantly no or only slight accuracy degradation Contributions of our work summarized First proposed a novel measurement ambiguityhigh variance low amplitude when a gradient update Second showed the application this measurement as updates significantly reduces update requirements providing comparable accuracy Third demonstrated this method can combined other efficient gradient compression approaches further communication cost",0.01,0.5279944181310499
"In this work, we face the problem of unsupervised domain adaptation with a novel deep learning approach which leverages our finding that entropy minimization is induced by the optimal alignment of second order statistics between source and target domains. We formally demonstrate this hypothesis and, aiming at achieving an optimal alignment in practical cases, we adopt a more principled strategy which, differently from the current Euclidean approaches, deploys alignment along geodesics. Our pipeline can be implemented by adding to the standard classification loss (on the labeled source domain), a source-to-target regularizer that is weighted in an unsupervised and data-driven fashion. We provide extensive experiments to assess the superiority of our framework on standard domain and modality adaptation benchmarks. Learning visual representations that are invariant across different domains is an important task in computer vision. Actually, data labeling is onerous and even impossible in some cases. It is thus desirable to train a model with full supervision on a source, labeled domain and then learn how to transfer it on a target domain, as opposed to retrain it completely from scratch. Moreover, the latter stage is actually not possible if the target domain is totally unlabelled: this is the setting we consider in our work. In the literature, this problem is known as unsupervised domain adaptation which can be regarded as a special semi-supervised learning problem, where labeled and unlabeled data come from different domains. Since no labels are available in the target domain, source-to-target adaptation must be carried out in a fully unsupervised manner. Clearly, this is an arguably difficult task since transferring a model across domains is complicated by the so-called domain shift [Torralba & Efros (2011) ]. In fact, while switching from the source to the target, even if dealing with the same K visual categories in both domains, different biases may arise related to several factors. For instance, dissimilar points of view, illumination changes, background clutter, etc.In the previous years, a broad class of approaches has leveraged on entropy optimization as a proxy for (unsupervised) domain adaptation, borrowing this idea from semi-supervised learning [Grandvalet & Bengio (2004) ]. By either performing entropy regularization [Tzeng et al. (2015) ; Carlucci et al. (2017) ; Saito et al. (2017) ], explicit entropy minimization [Haeusser et al. (2017) ], or implicit entropy maximization through adversarial training [Ganin & Lempitsky (2015) ; Tzeng et al. (2017) ], this statistical tool has demonstrated to be powerful for adaptation purposes.Alternatively, there exist methods which try to align the source to the target domain by learning an explicit transformation between the two so that the target data distribution can be matched to the one of the source one [Glorot et al. (2011); Kan et al. (2015) ; Shekhar et al. (2013) ; Gopalan & Li (2011); Gong et al. (2012a) ]. Within this paradigm, correlation alignment minimizes the distance between second order statistics computed in the form of covariance representations between features from the source a [Fernando et al. (2013) ; Sun et al. (2016) ; Sun & Saenko (2016) ].Apparently , correlation alignment and entropy minimization may seem two unrelated and approaches in optimizing models for domain adaptation. However, in this paper, we will show that this is not the case and, indeed, we claim that the two classes of approaches are deeply intertwined. In addition to formally discuss the latter aspect, we also obtain a solution for the prickly problem of hyperparameter validation in unsupervised domain adaptation. Indeed, one can construct a validation set out of source data but the latter is not helpful since not representative of target data. At the same time, due to the lack of annotations on the target domain, usual (supervised) validation techniques can not be applied.In summary, this paper brings the following contributions.1. We explore the two paradigms of correlation alignment and entropy minimization, by formally demonstrating that, at its optimum, correlation alignment attains the minimum of the sum of cross-entropy on the source domain and of the entropy on the target.2. Motivated by the urgency of penalizing correlation misalignments in practical terms, we observe that an Euclidean penalty, as adopted in [Sun et al. (2016); Sun & Saenko (2016) ], is not taking into account the structure of the manifold where covariance matrices lie in. Hence, we propose a different loss function that is inspired by a geodesic distance that takes into account the manifold's curvature while computing distances.3. When aligning second order statistics, a hyper-parameter controls the balance between the reduction of the domain shift and the supervised classification on the source domain. In this respect , a manual cross-validation of the parameter is not straightforward: doing it on the source domain may not be representative, and it is not possible to do on the target due to the lack of annotations. Owing to our principled connection between correlation alignment and entropy regularization, we devise an entropy-based criterion to accomplish such validation in a data-driven fashion.4. We combine the geodesic correlation alignment with the entropy-based criterion in a unique pipeline that we call minimal-entropy correlation alignment. Through an extensive experimental analysis on publicly available benchmarks for transfer object categorization, we certify the effectiveness of the proposed approach in terms of systematic improvements over former alignment methods and state-of-the-art techniques for unsupervised domain adaptation in general.The rest of the paper is outlined as follows. In Section 2, we report the most relevant related work as background material. Section 3 presents our theoretical analysis which inspires our proposed method for domain adaptation (Section 4). We report a broad experimental validation in Section 5. Finally, Section 6 draws conclusions. In this paper we carried out a principled connection between correlation alignment and entropy minimization, formally demonstrating that the optimal solution to the former problem gives for free the optimal solution of the latter. This improved knowledge brought us to two algorithmic advances. First, we achieved a more effective alignment of covariance operators which guarantees a superior performance. Second, we derived a novel cross-validation approach for the hyper-parameter λ so that we can obtain the maximum performance on the target, even not having access to its labels. These two components, when combined in our proposed MECA pipeline, provide a solid performance against state-of-the-art methods for unsupervised domain adaptation.L.J.P van der Maaten and G.E. Hinton. Visualizing high-dimensional data using t-sne. For the problem of (unsupervised) domain adaptation, a first class of methods aims at learning transformations which align feature representations in the source and target sets. For instance, in [Glorot et al. (2011) ] auto-encoders are exploited to learn common features. In [Kan et al. (2015) ], a bi-shifting auto-encoder (BSA) is instead intended to shift source domain samples into target ones and, similarly, other methods approach the same problem by means of techniques based on dictionary learning (as in [Shekhar et al. (2013)] ). Geodesic methods (such as [Gopalan & Li (2011); Gong et al. (2012a) ] aim at projecting source and target datasets on a common manifold in such a way that the projection already solves the alignment problem. The approaches [Gong et al. (2012b) ; Gopalan et al. FORMULA0 ] learns a smooth transition between the source and data manifold by means of Principal Components Analysis and Partial Least Squares, respectively. Inspired by the idea of adapting second order statistics between the two domains, [Sun et al. (2016); Fernando et al. (2013) ] propose a transformation to minimize the distance between the covariances of source and target datasets in order to, ultimately, achieve correlation alignment. Due to the well known properties of covariance operators, in some cases [Sun et al. (2016) ], the alignment can be written down in closed-form. But, since the latter operation can be prohibitively expensive in terms of computational cost, Sun & Saenko (2016) implements correlation alignment in an end-to-end fashion by means of backpropagation.A complementary family of approaches exploit the powerful statistical tool of entropy optimization in order to carry out adaptation. Indeed, the notion of association [Haeusser et al. (2017) ] is actually implementing explicit entropy minimization [Grandvalet & Bengio (2004) ] to align the target to the source embedding by navigating the data manifold by means of closed cyclic paths that interconnect instances belonging to the same objects' classes. In parallel, there are cases [Ganin & Lempitsky (2015) ; Tzeng et al. (2017) ] where minimax optimization is responsible for doing the following adversarial training. One seeks for feature representations that are effective for the primary visual recognition task being at the same time invariant while changing from source to target. The latter stage is implemented as the attempt of devising a random chance classifier which is asked to detect whether a given feature vector has been computed from a source or target data instance. Therefore, those approaches are implicitly promoting entropy maximization 3 at the classifier level. Finally, entropy regularization is accomplished in [Tzeng et al. (2015); Carlucci et al. (2017); Saito et al. (2017) ] as a complementary step to boost adaptation. Indeed, already established techniques for adaptation such as Batch Normalization [Ioffe & Szegedy (2015) ; Li et al. (2016) ] are applied in low-level layers to align the representations. On top of that, adaptation is refined at the end of the feature hierarchy by introducing a entropy-based regularizer on the target domain based. Practically, the latter exploits network's prediction to generate pseudo-labels [Lee FORMULA0",2078,1.239,1196,1.7374581939799332,"In this work face unsupervised domain adaptation with which our finding entropy minimization induced the optimal alignment second order statistics We formally demonstrate, aiming achieving an optimal alignment practical cases adopt a more principled strategy which, differently alignment along geodesics Our pipeline can implemented to the standard classification losson the labeled source domain source regularizer weighted We provide extensive experiments the superiority our framework standard domain and modality adaptation benchmarks Learning visual representations that Actually data labeling onerous even It thus desirable train a model full supervision a source, labeled domain then learn transfer on retrain completely Moreover the latter stage actually possible the target domain totally this the setting we consider our work In the literature this problem unsupervised domain adaptation which regarded come Since no labels the target domain source adaptation Clearly an arguably difficult task since transferring a model across domains complicated [Torralba Efros ( In fact while switching the source even dealing the same K visual categories both domains different biases related several factors For instance dissimilar points illumination changes background clutterIn the previous years a broad class approaches leveraged on entropy optimization (unsupervised) domain adaptation borrowing this idea [Grandvalet Bengio By either performing entropy regularization [Tzeng (2015 ; Carlucci (2017 ; Saito (2017 ], explicit entropy minimizationHaeusser (2017 ], or implicit entropy maximization through adversarial trainingGanin Lempitsky Tzeng (2017 ], this statistical tool demonstrated to powerful adaptation purposesAlternatively there exist try align learning an explicit transformation so the target data distribution matched one one [Glorot et al (2011 Kan et (2015 ; Shekhar (2013 ; Gopalan & Li Gong (2012a ]. Within this paradigm correlation alignment minimizes second order statistics computed covariance representations between features from a [Fernando (2013 ; Sun (2016 ; Sun & Saenko ].Apparently , correlation alignment entropy minimization may seem two unrelated and approaches in optimizing models domain adaptation However this paper, claim approaches deeply In formally discuss the latter aspect obtain a solution the prickly problem hyperparameter validation unsupervised domain adaptation Indeed one construct a validation set out source data but latter helpful not representative target data At due annotations the target domain usual (supervised) validation techniquesIn summary brings following contributions.1 explore correlation alignment entropy by formally its optimum attains the sum cross on of Motivated the urgency practical terms observe an Euclidean penalty adopted [Sun (2016 Sun & Saenko ], is not taking the structure the manifold where lie. Hence propose a different loss function inspired a geodesic distance that takes while computing distances.3. When aligning second order statistics controls the balance the reduction the domain shift the supervised classification on the source domain In this respect , a manual cross the parameter straightforward doing the source domain may representative on due annotations Owing our principled connection between correlation alignment entropy regularization devise accomplish such validation. combine a unique pipeline minimal-entropy correlation alignment Through an extensive experimental analysis on publicly available benchmarks transfer object categorization certify the effectiveness systematic improvements former alignment methods state unsupervised domain adaptation generalThe rest outlined In Section report the most relevant related work as background material Section presents our theoretical analysis which inspires domain adaptation We report a broad experimental validation in Section Finally Section draws conclusions In carried a principled connection correlation alignment entropy minimization formally demonstrating gives for This improved knowledge brought two algorithmic advances First achieved a more effective alignment covariance operators which guarantees Second derived so obtain the maximum performance even not having access its labels These two components when our proposed MECA pipeline a solid performance against state methods unsupervised domain adaptationL.J.P van der Maaten. Visualizing high-dimensional data t-sne. For the problem (unsupervised) domain adaptation a first class of methods aims learning transformations which align feature representations For instance [Glorot (2011 ] auto-encoders are exploited learn common features In [Kan et al (2015 ], a bi-shifting auto-encoder (BSA instead intended shift source domain samples target ones, similarly other methods approach means techniques based dictionary learningas [Shekhar (2013)] ). Geodesic methods ( [Gopalan & Li ( Gong (2012a ] aim at projecting source and target datasets a common manifold the projection already solves The approaches [Gong (2012b ; Gopalan FORMULA0 ] learns a smooth transition the source data manifold by Principal Components Analysis respectively Inspired adapting second order statistics between [Sun et (2016 Fernando et al (2013 ] propose a transformation minimize source and target datasets, ultimately achieve correlation alignment Due the well known properties covariance operators in [Sun et al (2016 ], the alignment can written down closed-form But since the latter operation can computational cost Sun & Saenko implements correlation alignment end meansA complementary family approaches exploit the powerful statistical tool entropy optimization carry adaptation Indeed, the notion association [Haeusser (2017 ] is actually implementing explicit entropy minimization [Grandvalet Bengio2004 align embedding by navigating manifold means closed cyclic paths interconnect instances belonging the same objects' classes In parallel cases [Ganin Lempitsky ; Tzeng (2017 ] where minimax optimization responsible doing the following adversarial training One seeks for feature representations effective the primary visual recognition task being at invariant while changing from source The latter stage implemented the attempt devising a random chance classifier asked detect computed target data instance Therefore those approaches implicitly promoting entropy maximization 3 at the classifier level Finally entropy regularization accomplished [Tzeng (2015); Carlucci (2017 Saito (2017 ] as a complementary step boost adaptation Indeed already established techniques adaptation such Batch Normalization [Ioffe Szegedy ; (2016 ] are applied low-level layers align the representations On top adaptation refined at the feature hierarchy introducing a entropy-based regularizer on based. Practically, the latter exploits network's prediction to pseudolabels [Lee FORMULA0",0.01,0.5830578555761948
"Catastrophic interference has been a major roadblock in the research of continual learning. Here we propose a variant of the back-propagation algorithm, ""Conceptor-Aided Backprop"" (CAB), in which gradients are shielded by conceptors against degradation of previously learned tasks. Conceptors have their origin in reservoir computing, where they have been previously shown to overcome catastrophic forgetting. CAB extends these results to deep feedforward networks. On the disjoint and permuted MNIST tasks, CAB outperforms two other methods for coping with catastrophic interference that have recently been proposed. Agents with general artificial intelligence are supposed to learn and perform well on multiple tasks. Continual learning refers to the scenarios where a machine learning system can retain previously acquired skills while learning new ones. However, when trained on a sequence of tasks, neural networks usually forget about previous tasks after their weights are adjusted for a new task. This notorious problem known as catastrophic interference (CI) BID15 BID16 BID3 BID11 ) poses a serious challenge towards continual learning.Many approaches have been proposed to overcome or mitigate the problem of CI in the last three decades BID5 BID1 BID0 BID2 BID20 . Especially recently, an avalanche of new methods in the deep learning field has brought about dramatic improvements in continual learning in neural networks. BID10 introduced a regularization-based method called elastic weight consolidation (EWC), which uses the posterior distribution of parameters for the old tasks as a prior for the new task. They approximated the posterior by a Gaussian distribution with the parameters for old tasks as the mean and the inverse diagonal of the Fisher information matrix as the variance. BID13 introduced two incremental moment matching (IMM) methods called mean-IMM and mode-IMM. Mean-IMM approximates the distribution of parameters for both old and new tasks by a Gaussian distribution, which is estimated by minimizing its KL-divergence from the mixture of two Gaussian posteriors, one for the old task and the other one for the new task. Mode-IMM estimates the mode of this mixture of two Gaussians and uses it as the optimal parameters for both tasks.In the field of Reservoir Computing BID6 BID14 , an effective solution to CI using conceptors was proposed by BID7 to incrementally train a recurrent neural network to generate spatial-temporal signals. Conceptors are a general-purpose neuro-computational mechanism that can be used in a diversity of neural information processing tasks including temporal pattern classification, one-shot learning, human motion pattern generation, de-noising and signal separation BID8 . In this paper, we adopt and extend the method introduced in BID7 and propose a conceptor-aided backpropagation (CAB) algorithm to train feed-forward networks. For each layer of a network, CAB computes a conceptor to characterize the linear subspace spanned by the neural activations in that layer that have appeared in already learned tasks. When the network is trained on a new task, CAB uses the conceptor to adjust the gradients given by backpropagation so that the linear transformation restricted to the characterized subspace will be preserved after the gradient descent procedure. Experiment results of two benchmark tests showed highly competitive performance of CAB.The rest of this paper is structured as follows. Section 2 introduces conceptors and their application to incremental learning by ridge regression. Section 3 extends the method to stochastic gradient descent and describes the CAB algorithm. Section 4 compares its performance on the permuted and disjoint MNIST tasks to recent methods that address the same problem. Finally we conclude our paper in Section 5. In this work, we first reviewed the conceptor-based incremental ridge regression algorithm, introduced in section 3.11 of Jaeger (2014) for memory management in recurrent neural networks. Then we derived its stochastic gradient descent version for optimizing the same objective. Finally we designed a conceptor-aided backprop algorithm by applying a conceptor to every linear layer of a feed-forward network. This method uses conceptors to guide gradients of parameters during the backpropagation procedure. As a result, learning a new task interferes only minimally with previously learned tasks, and the amount of already used network capacity can be monitored via the singular value spectra and quota of conceptors.In Jaeger (2014), different scenarios for continual learning are investigated in a reservoir computing setting. Two extreme cases are obtained when (i) the involved learning tasks are entirely unrelated to each other, versus (ii) all tasks come from the same parametric family of learning tasks. The two cases differ conspicuously with regards to the geometry of involved conceptors, and with regards to opportunities to re-use previously acquired functionality in subsequent learning episodes. The permuted MNIST task is an example of (i) while the disjoint MNIST task rather is of type (ii).Conceptors provide an analytical tool to discuss the ""family relatedness"" and enabling/disabling conditions for continual learning in geometrical terms. Ongoing and future research is devoted to a comprehensive mathematical analysis of these phenomena which in our view lie at the heart of understanding continual learning.",1018,0.565,610,1.6688524590163933,"Catastrophic interference has the research continual learning Here propose a variant ""Conceptor-Aided Backprop"" gradients shielded conceptors against degradation previously learned tasks Conceptors their origin reservoir computing they have previously shown overcome catastrophic forgetting CAB extends these results deep feedforward networks On the disjoint and permuted MNIST tasks CAB outperforms two other methods coping catastrophic interference that recently Agents with general artificial intelligence supposed learn perform well Continual learning refers the scenarios retain previously acquired skills However when trained a sequence tasks neural networks usually forget after their weights adjusted This notorious problem known catastrophic interference (CI) BID15 BID16 BID3 BID11 ) poses towards continual learningMany approaches or in Especially recently an avalanche new methods in brought continual learning BID10 introduced a regularization-based method called elastic weight consolidation the posterior distribution parameters the old tasks prior for They approximated the posterior by the parameters old tasks the inverse diagonal the Fisher information matrix BID13 introduced two incremental moment matching called mean-IMM Mean-IMM approximates the distribution parameters both old and new tasks by estimated minimizing its KL-divergence from the mixture two Gaussian posteriors one Mode-IMM estimates the mode this mixture two Gaussians uses the optimal parameters both tasksIn the field Reservoir Computing BID6 BID14 , an effective solution CI using conceptors to incrementally train Conceptors a general-purpose neuro-computational mechanism a diversity including temporal pattern classification one-shot learning human motion pattern generation de-noising and signal separation BID8 . In adopt and introduced BID7 propose a conceptor-aided backpropagation train feed-forward networks For each layer a network CAB computes a conceptor to characterize the linear subspace spanned the neural activations that have appeared already learned tasks When the network trained CAB uses the conceptor adjust given so the linear transformation restricted the characterized subspace preserved after the gradient descent procedure Experiment results two benchmark tests highly competitive performance CAB.The rest structured Section introduces conceptors their application incremental learning by ridge regression Section extends describes the CAB algorithm Section compares its performance the permuted and disjoint MNIST tasks recent methods address Finally conclude our paper in Section In this work first reviewed the conceptor-based incremental ridge regression algorithm introduced section Jaeger (2014 memory management Then derived its stochastic gradient descent version for optimizing the same objective Finally designed a conceptor-aided backprop algorithm by applying every linear layer This method conceptors guide gradients parameters during As learning a new task interferes only previously learned tasks the amount already used network capacity monitored via the singular value spectra and quota of conceptorsIn Jaeger ( different scenarios continual learning a reservoir computing setting Two extreme cases obtained when ( the involved learning tasks entirely versus all tasks come the same parametric family The two cases differ conspicuously with the geometry involved conceptors opportunities re previously acquired functionality subsequent learning episodes The permuted MNIST task is (i while rather is of typeii).Conceptors provide an analytical tool discuss the ""family relatedness enabling/disabling conditions continual learning geometrical terms Ongoing and future research devoted a comprehensive mathematical analysis these phenomena which in lie understanding continual learning",0.01,0.40825647052306274
"Recent advances in neural Sequence-to-Sequence (Seq2Seq) models reveal a purely data-driven approach to the response generation task. Despite its diverse variants and applications, the existing Seq2Seq models are prone to producing short and generic replies, which blocks such neural network architectures from being utilized in practical open-domain response generation tasks. In this research, we analyze this critical issue from the perspective of the optimization goal of models and the specific characteristics of human-to-human conversational corpora. Our analysis is conducted by decomposing the goal of Neural Response Generation (NRG) into the optimizations of word selection and ordering. It can be derived from the decomposing that Seq2Seq based NRG models naturally tend to select common words to compose responses, and ignore the semantic of queries in word ordering. On the basis of the analysis, we propose a max-marginal ranking regularization term to avoid Seq2Seq models from producing the generic and uninformative responses. The empirical experiments on benchmarks with several metrics have validated our analysis and proposed methodology. Past years have witnessed the dramatic progress on the application of generative sequential models (also noted as seq2seq learning (Sutskever et Despite these promising results, current Sequence-to-Sequence (Seq2Seq) architectures for response generation are still far from steadily generating relevant and coherent replies. The essential issue identified by many studies is the Universal Replies: the model tends to generate short and general replies which contain limited information, such as ""That's great!"", ""I don't know"", etc. Nevertheless, most previous analysis over the issue are empirical and lack of statistical evidence. Therefore, in this paper, we conduct an in-depth investigation on the performance of seq2seq models on the NRG task. In our inspections on the existing dialog corpora, it is shown that those repeatedly appeared replies have two essential traits: 1) Most of them are composed of highly frequent words; 2) They cover a large portion of the dialog corpora that each universal reply stands for the response of various queries. Above characteristics of universal replies deviate the NRG from other successful applications of sea2seq model such as translation, and lead current generative NRG models to prefer common replies. To discuss the influences from the specific distributed corpus, we decompose the target sequence's probability into two parts and analyze the probability respectively. To break down the mentioned characteristics of dialog corpora in the model training step, we propose a ranking-oriented regularization term to prune the scores of those irrelevant replies. Experimental results reveal that the model with such regularization can produce better results and avoid generating ambiguous responses. Also, case studies show that the issue of generic response is alleviated that these common responses are ranked relatively lower than more appropriate answers.The main contributions of this paper are concluded as follows: 1) We analyze the loss function of Seq2seq models on NRG task and conclude several critical reasons that the NRG models prefer universal replies; 2) Based on the analysis, a max-marginal ranking regularization is presented to help the model converge to informative responses. On the basis of Lemma 1, the word ordering probability could be deducted as: DISPLAYFORM0 All the possible y i satisfying S(y i ) ⊆ S(y) can be divided into three categories: ground-truth reply y, universal replies y ur and other replies y o . From above, we can get the following direct proportion according to the Lemma 2 and Lemma 3, On the basis of Eq. 7 and Lemma 4, for any reply y not belonging to universal replies, the Eq. 6 can be further deducted as: DISPLAYFORM1 where = 1 + 2 > 0, which is also a sufficiently small positive value. Thus, optimizing the word ordering probability for the non-universal replies is partially equivalent to maximizing p(y|S(y)).In fact the term p(y|S(y)) is the language model probability and it is irrelevant with the query x FIG6 ). In the sequential models, it is performed as t p(y t |y 1:t−1 , S(y)), in other words the sequences are generated based only on previously outputted words. This equation indicates that optimizing the mainly seeks the grammatical competence based on the selected words. Eliminating generic responses is the essence for the widely practical utilization of the Seq2Seq based neural response generation architectures, and thus, this paper has conducted a thorough investigation on the cause of such uninformative responses and proposed the solution from the statistical perspective. The main contributions of this work can be summarized as follows: a) The theoretical analysis is performed to capture the root reason of NRG models producing generic responses through the optimization goal of models and the statistical characteristics of human-to-human conversational corpora, which has been little studied currently. In detail, we have decomposed the goal of NRG into the optimizations of word selection and word ordering, and finally derived that NRG models tend to select common words as responses and order words from the language model perspective which ignores queries. b) According to the analysis, a max-marginal ranking regularization term is proposed to cooperate with the learning target of Seq2Seq, so as to help NRG models converge to the status of producing informative responses, rather than merely manipulating the decoding procedure to constrain the generation of universal replies. Furthermore, the empirical experiments on the conversation dataset indicate that the models utilizing this strategy notably outperform the current baseline models.",1107,0.503,668,1.657185628742515,"Recent advances neural Sequenceto models reveal the response generation task Despite its diverse variants applications the existing Seq2Seq models prone producing short and generic replies blocks such neural network utilized practical open-domain response generation tasks In this research analyze this critical issue the optimization goal models the specific characteristics Our analysis conducted decomposing the goal Neural Response Generation the optimizations word selection ordering It can derived the decomposing that Seq2Seq based NRG models naturally tend select common words compose responses ignore semantic of queries word ordering On a max-marginal ranking regularization term avoid Seq2Seq models from producing the generic and uninformative responses The empirical experiments benchmarks with several metrics validated our analysis proposed methodology Past years the dramatic progress on the application generative sequential modelsalso noted seq2seq learning (Sutskever Despite these promising results current Sequenceto architectures for response generation steadily generating relevant and coherent replies The essential issue identified many studies the Universal Replies: the model tends generate short and general replies containThat great Nevertheless most previous analysis over the issue are empirical lack of Therefore conduct on seq2seq models the NRG task In our inspections on the existing dialog corpora shown those repeatedly appeared replies have two essential traits Most composed highly frequent words cover each universal reply stands the response various queries Above characteristics universal replies deviate the NRG other successful applications sea2seq model such translation and lead current generative NRG models prefer common replies To discuss the influences from the specific distributed corpus decompose the target sequence's probability into and respectively To break the mentioned characteristics dialog corpora the model training step propose a ranking-oriented regularization term prune the scores those irrelevant replies Experimental results reveal the model with such regularization and avoid generating ambiguous responses Also case studies the issue generic response alleviated that these common responses ranked relatively more appropriate answersThe main contributions concluded We analyze the loss function Seq2seq models NRG task conclude several critical reasons prefer universal replies; Based a max-marginal ranking regularization presented help converge informative On Lemma the word ordering probability could deducted: DISPLAYFORM0 All y i satisfying can divided ground-truth reply y, universal replies y ur o From above get the following direct proportion according the Lemma 2 and, On Eq for any reply y not belonging universal replies can further deducted: DISPLAYFORM1 where = + > a sufficiently small positive value Thus optimizing the word ordering probability the non-universal replies partially equivalent p(y|S(y)).In fact the the language model probability and irrelevant with the query x FIG6 In the sequential models it performed t p(y t |y: , S(y in the sequences generated based only previously outputted words This equation indicates optimizing mainly seeks the grammatical competence based generic responses the essence for the widely practical utilization the Seq2Seq based neural response generation architectures thus conducted the cause proposed from The main contributions can a performed capture the root reason NRG models producing generic responses through the optimization goal models the statistical characteristics has little currently In detail decomposed the goal NRG into the optimizations word selection word ordering finally derived that NRG models tend select responses and the language model perspective which ignores queries b According a max-marginal ranking regularization term proposed cooperate the learning target Seq2Seq so help NRG models converge the status producing informative responses manipulating the decoding procedure the generation universal replies Furthermore the empirical experiments the conversation dataset the models utilizing this strategy notably",0.01,0.37853041202172094
"The ability to generate natural language sequences from source code snippets has a variety of applications such as code summarization, documentation, and retrieval. Sequence-to-sequence (seq2seq) models, adopted from neural machine translation (NMT), have achieved state-of-the-art performance on these tasks by treating source code as a sequence of tokens. We present code2seq: an alternative approach that leverages the syntactic structure of programming languages to better encode source code. Our model represents a code snippet as the set of compositional paths in its abstract syntax tree (AST) and uses attention to select the relevant paths while decoding.
 We demonstrate the effectiveness of our approach for two tasks, two programming languages, and four datasets of up to 16M examples. Our model significantly outperforms previous models that were specifically designed for programming languages, as well as general state-of-the-art NMT models. An interactive online demo of our model is available at http://code2seq.org. Our code, data and trained models are available at http://github.com/tech-srl/code2seq. Modeling the relation between source code and natural language can be used for automatic code summarization BID2 , documentation BID19 , retrieval BID1 , and even generation BID7 BID28 BID40 BID14 BID24 . In this work, we consider the general problem of generating a natural language sequence from a given snippet of source code.A direct approach is to frame the problem as a machine translation problem, where the source sentence is the sequence of tokens in the code and the target sentence is a corresponding natural language sequence. This approach allows one to apply state-of-the-art neural machine translation (NMT) models from the sequence-to-sequence (seq2seq) paradigm BID23 BID39 , yielding state-ofthe-art performance on various code captioning and documentation benchmarks BID19 BID2 BID22 ) despite having extremely long source sequences.We present an alternative approach for encoding source code that leverages the syntactic structure of programming languages: CODE2SEQ. We represent a given code snippet as a set of compositional paths over its abstract syntax tree (AST), where each path is compressed to a fixed-length vector using LSTMs BID17 . During decoding, CODE2SEQ attends over a different weighted average of the path-vectors to produce each output token, much like NMT models attend over token representations in the source sentence.We show the effectiveness of our code2seq model on two tasks: (1) code summarization (Figure 1a) , where we predict a Java method's name given its body, and (2) code captioning (Figure 1b) , where we predict a natural language sentence that describes a given C# snippet. We presented a novel code-to-sequence model which considers the unique syntactic structure of source code with a sequential modeling of natural language. The core idea is to sample paths in the Abstract Syntax Tree of a code snippet, encode these paths with an LSTM, and attend to them while generating the target sequence.We demonstrate our approach by using it to predict method names across three datasets of varying sizes, predict natural language captions given partial and short code snippets, and to generate method documentation, in two programming languages. Our model performs significantly better than previous programming-language-oriented works and state-of-the-art NMT models applied in our settings.We believe that the principles presented in this paper can serve as a basis for a wide range of tasks which involve source code and natural language, and can be extended to other kinds of generated outputs. To this end, we make all our code, datasets, and trained models publicly available.",728,0.317,432,1.6851851851851851,"The ability generate natural language sequences source code snippets a variety such code summarization documentation retrieval Sequence-toseq2seq models, adopted neural machine translation achieved state these tasks treating source code tokens We present code2seq: an programming languages better encode source code Our model represents a code snippet as the set compositional paths its abstract syntax treeAST uses attention select while decoding We demonstrate our approach two tasks two programming languages four datasets up to 16M examples Our model significantly were specifically programming languages as general state NMT An interactive online demo our model is http://code2seq.org Our code, data trained models http://github.com/tech-srl/code2seq Modeling the relation source code natural language can used automatic code summarization BID2 , documentation BID19 retrieval BID1 even generation In this work consider the general problem generating a natural language sequence a given snippetA direct approach frame the source sentence tokens This approach allows one apply state neural machine translationNMT models from sequencetoseq2seq paradigm BID23 BID39 , yielding state-ofthe-art performance on various code captioning documentation benchmarks ) despite extremely long source sequencesWe encoding source code programming languages: CODE2SEQ We represent a given code snippet as compositional paths over its abstract syntax treeAST compressed using LSTMs BID17 . During decoding CODE2SEQ attends over a different weighted average the path-vectors produce each output token much NMT models attend token representations the source sentenceWe show the effectiveness our code2seq model two tasks , predict a Java method's name given its body captioning describes a given C# snippet We presented novel codetosequence model which considers the unique syntactic structure source code with a sequential modeling natural language. The core idea sample paths of a code snippet encode with attend while generating the target sequenceWe demonstrate it predict method names across three datasets varying sizes predict natural language captions given partial and short code snippets to method documentation, in two programming languages Our model performs significantly previous programming-language-oriented works and state NMT applied our settingsWe believe the principles presented serve tasks which involve source code natural language, can extended generated outputs To this end make all our code, datasets trained models publicly",0.0,0.4498708218235131
"We propose a novel attention mechanism to enhance Convolutional Neural Networks for fine-grained recognition. The proposed mechanism reuses CNN feature activations to find the most informative parts of the image at different depths with the help of gating mechanisms and without part annotations. Thus, it can be used to augment any layer of a CNN to extract low- and high-level local information to be more discriminative. 

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

 Experiments show that, when augmented with our approach, Wide Residual Networks systematically achieve superior performance on each of five different fine-grained recognition datasets: the Adience age and gender recognition benchmark, Caltech-UCSD Birds-200-2011, Stanford Dogs, Stanford Cars, and UEC Food-100, obtaining competitive and state-of-the-art scores. Humans and animals process vasts amounts of information with limited computational resources thanks to attention mechanisms which allow them to focus resources on the most informative chunks of information. These biological mechanisms have been extensively studied (see BID0 ; BID2 ), concretely those mechanisms concerning visual attention, e.g. the work done by BID25 .In this work, we inspire on the advantages of visual and biological attention mechanisms for finegrained visual recognition with Convolutional Neural Networks (CNN) (see BID11 ). This is a particularly difficult task since it involves looking for details in large amounts of data (images) while remaining robust to deformation and clutter. In this sense, different attention mechanisms for fine-grained recognition exist in the literature: (i) iterative methods that process images using ""glimpses"" with recurrent neural networks (RNN) or long short-term memory (LSTM) (e.g. the work done by BID22 ; BID35 ), (ii) feed-forward attention mechanisms that augment vanilla CNNs, such as the Spatial Transformer Networks (STN) by BID8 , or a top-down feed-forward attention mechanism (FAM) BID19 ). Although it is not applied to fine-grained recognition, the Residual Attention introduced by BID28 is another example of feed-forward attention mechanism that takes advantage of residual connections BID6 ) to enhance or dampen certain regions of the feature maps in an incremental manner.Inspired by all the previous research about attention mechanisms in computer vision, we propose a novel feed-forward attention architecture (see FIG0 ) that accumulates and enhances most of the desirable properties from previous approaches:1. Detect and process in detail the most informative parts of an image: more robust to deformation and clutter. 2. Feed-forward trainable with SGD: faster inference than iterative models, faster convergence rate than Reinforcement Learning-based (RL) methods like the ones presented by BID22 ; BID15 . The proposed mechanism. Feature maps at different levels are processed to generate spatial attention masks and use them to output a class hypothesis based on local information and a confidence score (C). The final prediction consists of the average of all the hypotheses weighted by the normalized confidence scores. We have presented a novel attention mechanism to improve CNNs for fine-grained recognition. The proposed mechanism finds the most informative parts of the CNN feature maps at different depth levels and combines them with a gating mechanism to update the output distribution.Moreover, we thoroughly tested all the components of the proposed mechanism on Cluttered Translated MNIST, and demonstrate that the augmented models generalize better on the test set than their plain counterparts. We hypothesize that attention helps to discard noisy uninformative regions, avoiding the network to memorize them.Unlike previous work, the proposed mechanism is modular, architecture independent, fast, and simple and yet WRN augmented with it show higher accuracy in each of the following tasks: Age and Gender Recognition (Adience dataset), CUB200-2011 birds, Stanford Dogs, Stanford Cars, and UEC Food-100. Moreover, state of the art performance is obtained on gender, dogs, and cars. Figure 6: Test accuracy logs for the five fine-grained datasets. As it can be seen, the augmented models (WRNA) achieve higher accuracy at similar convergence rates. For the sake of space we only show one of the five folds of the Adience dataset.",887,0.422,517,1.7156673114119922,"We propose a novel attention mechanism enhance for The proposed mechanism reuses CNN feature activations find the most informative parts at with gating mechanisms without part annotations Thus can used augment any layer a CNN to extract to Differently from other approaches the mechanism we just needs a single pass it trained end through SGD As a consequence the proposed mechanism modular architecture easy faster iterative approaches Experiments show, augmented our approach Wide Residual Networks systematically achieve each five different fine-grained recognition datasets the Adience age gender recognition benchmark Caltech-UCSD Birds-2002011 Stanford Dogs, Stanford Cars UEC Food-100 obtaining competitive state scores Humans process vasts with limited computational resources thanks attention mechanisms which focus resources the most informative chunks These biological mechanisms extensively ( BID0 ; concretely those mechanisms concerning visual attention work done BID25 .In inspire on the advantages visual and biological attention mechanisms finegrained visual recognition with This a particularly difficult task since looking details large amountsimages while remaining robust deformation clutter In this sense different attention mechanisms for exist the literature process images using with recurrent neural networks the work done BID22 ; feed-forward attention mechanisms augment vanilla CNNs the Spatial Transformer Networks by BID8FAM BID19 Although applied fine-grained recognition the Residual Attention introduced BID28 another example feed-forward attention mechanism takes residual connections BID6 ) enhance or certain regions the feature maps an incremental mannerInspired about attention mechanismssee FIG0 accumulates enhances most the desirable properties from previous approaches:1 Detect and process in detail the most informative parts an image: more robust to clutter 2 Feed- trainable with SGD: faster inference iterative models faster convergence rate like the ones presented BID22 ; BID15 . The proposed mechanism. Feature maps at different levels processed spatial attention masks use output a class hypothesis local information a confidence score The final prediction consists weighted the normalized confidence scores We presented a novel attention mechanism improve CNNs for The proposed mechanism finds the most informative parts the CNN feature maps at different depth levels combines a gating mechanism update the output distributionMoreover thoroughly Cluttered Translated MNIST demonstrate the augmented models generalize We hypothesize attention helps discard noisy uninformative regions avoiding the network to memorizeUnlike the proposed mechanism modular, architecture independent, fast, and simple and yet WRN augmented it show higher accuracy each Age GenderAdience dataset CUB2002011 birds Stanford Dogs Stanford Cars UEC Food-100 Moreover state of is obtained on gender dogs cars Figure Test accuracy logs the five fine-grained datasets As it can the augmented models (WRNA achieve higher accuracy similar convergence rates For space we only show one the five folds the Adience dataset",0.01,0.5275366013190903
"Most existing GANs architectures that generate images use transposed convolution or resize-convolution as their upsampling algorithm from lower to higher resolution feature maps in the generator. We argue that this kind of fixed operation is problematic for GANs to model objects that have very different visual appearances. We propose a novel adaptive convolution method that learns the upsampling algorithm based on the local context at each location to address this problem. We modify a baseline GANs architecture by replacing normal convolutions with adaptive convolutions in the generator. Experiments on CIFAR-10 dataset show that our modified models improve the baseline model by a large margin. Furthermore, our models achieve state-of-the-art performance on CIFAR-10 and STL-10 datasets in the unsupervised setting. Generative Adversarial Networks BID6 (GANs) are an unsupervised learning method that is able to generate realistic looking images from noise. GANs employs a minimax game where a generator network learns to generate synthesized data from random noise and in conjunction, a discriminator network learns to distinguish between real and generated data. Theoretically, the training processes of the two networks intertwine and iterate until both networks reach a Nash equilibrium where real and synthesized data are indistinguishable.However, in practice, GANs are notoriously hard to train. For the learning of the generator to happen effectively, hyper-parameters, as well as the architectures of the generator and discriminator, must be chosen carefully. Nevertheless, on datasets with visually similar images, such as bedroom scenes and faces , GANs have produced good results BID15 . This success, however, does not translate to datasets that have diverse visual categories. GANs models trained on ImageNet BID16 were only able to learn basic image statistics and some shapes, but they did not learn any object BID17 . Recent works address this problem by incorporating additional high-level information to guide the generator, such as training the discriminator in a semi-supervised manner BID17 , adding a second training objective to direct the generator toward similar samples from the training set BID19 or using artificial class labels by clustering in the representation space BID7 .We take a different approach to tackle this problem. We hypothesize that the rigidity of the normal convolution operator is partially responsible for the difficulty of GANs to learn on diverse visual datasets. Most GANs generators upsample low resolution feature maps toward higher resolution using fixed convolutions (note that a transposed convolution is equivalent to a convolution) or resize-convolution BID13 . Such operations are unintuitive, because, pixel locations have different local contexts and belong to diverse object categories. Consequently , different pixel locations should have different upsampling schemes. This shortcoming of normal convolution is especially problematic in the early upsampling layers where higher level information usually associates with the object shapes and the context of images.We propose the use of a novel adaptive convolution BID12 architecture, called Adaptive Convolution Block, that replaces normal convolutions to address the aforementioned shortcoming of GANs generators. Instead of learning a fixed convolution for the upsampling of all pixels from the lower to the higher resolution feature map, an AdaConvBlock learns to generate the convolution weights and biases of the upsampling operation adaptively based on the local feature map at each pixel location. AdaConvBlock helps the generator to learn to generate upsampling algorithms that take into account the local context. We believe that this kind of adaptive convolution is more intuitive and more akin to the process when a human draws something: the same thought process is used in the whole drawing but the style of each stroke should vary and depend on the local context around each pixel position.We conduct experiments to compare our adaptive convolution method to normal convolution in the unsupervised setting. We progressively replace all convolutions of a GANs generator with AdaConvBlocks from the lowest resolution to the highest resolution. Experiments on CIFAR-10 dataset show that the modified adaptive convolution models have superior qualitative and quantitative performance over the baseline architecture and just replacing convolution of the upsampling from the lowest resolution feature map with adaptive convolution can have significant impacts on the baseline model. Furthermore, our best models achieve state-of-the-art unsupervised performance on both CIFAR-10 and STL-10 datasets. Our code and models will be released. We have demonstrated that using adaptive convolutions to replace normal convolutions in a GANs generator can improve the performance of a weak baseline model significantly on visually diverse datasets. Our AdaGAN models were able to beat other state-of-the-art methods without using any augmented training objectives. The samples generated by our models show that they seem to be able to learn the global context pretty well and be able to learn the rough shapes of the objects in most cases and the sample quality is quite reasonable on CIFAR-10 dataset. Furthermore, there are not much visible convolution artifacts in the generated images. The success of our models suggests that non-trivial performance improvement can be gained from modifying architectures for GANs.The approach we take is different from other methods that try to inject high level information into the discriminator. These existing methods and AdaGAN can complement each other. More experiments need to be done, but we believe that our architectures can benefit from the augmented training objectives from existing methods.Our method is not without a downside. Even though we used depthwise separable convolution to reduce the cost, the amount of memory and computation is still extremely high. More tricks could be applied to alleviate this issue. For example, in a similar manner to BID12 work, both the local convolutions and the convolution to regress the adaptive weights for the local convolutions in our AdaConvBlock can be approximated by separate 1-D convolutions. This can reduce the cost by more than 50%. Another idea is to exploit locality. We expect the adaptive convolution weights and biases of a pixel location to be quite similar to its neighbors and can be interpolated in a certain way. We will address this issue in our future work.A SAMPLES GENERATED BY OUR MODELS ON CIFAR-10 AND STL-10",1203,0.653,703,1.7112375533428166,"Most existing GANs architectures that generate images use transposed convolution or resize-convolution as from lower higher resolution feature maps in the generator We argue this kind fixed operation problematic GANs to model objects very different visual appearances We propose a novel adaptive convolution method learns the upsampling algorithm at to address We modify a baseline GANs architecture replacing normal convolutions in the generator Experiments CIFAR-10 dataset show our modified models improve the baseline model Furthermore our models achieve state CIFAR-10 STL-10 datasets Generative Adversarial Networks BID6GANs realistic looking images noise GANs employs a minimax game where a generator network learns synthesized data random noise in conjunction distinguish Theoretically the training processes the two networks intertwine iterate until both networks a Nash equilibrium where real and synthesized dataHowever GANs notoriously For the learning the generator to happen effectively hyper, as the architectures discriminator chosen Nevertheless on datasets visually similar images bedroom scenes faces , GANs produced BID15 . This success, translate datasets diverse visual categories GANs models trained ImageNet BID16 were only learn basic image statistics some shapes any object BID17 . Recent works address incorporating guide the generator training in BID17 , adding a second training objective direct toward similar samples from or artificial class labels by in the representation space .We take tackle We hypothesize the rigidity the normal convolution operator partially GANs to learn on diverse visual datasets Most GANs generators upsample low resolution feature maps toward using fixed convolutionsnote equivalent) or resize-convolution BID13 . Such operations unintuitive, pixel locations have different local contexts belong diverse object categories , different pixel locations should This shortcoming normal convolution especially the early upsampling layers higher level information usually associates the object shapes the context imagesWe a novel adaptive convolution BID12 architecture called replaces to address GANs generators Instead learning a fixed convolution for the upsampling all pixels from lower the higher resolution feature map an AdaConvBlock learns generate biases adaptively based at AdaConvBlock helps the generator learn to upsampling algorithms take We believe this kind adaptive convolution more intuitive akin when draws something: the same thought process the whole drawing but the style each stroke should depend around each pixel positionWe conduct compare We progressively replace all convolutions a GANs generator AdaConvBlocks from the lowest resolution Experiments CIFAR-10 dataset show the modified adaptive convolution models superior qualitative and quantitative performance the baseline architecture just replacing of the upsampling from the lowest resolution feature map can Furthermore our best models achieve state unsupervised performance both CIFAR-10 STL-10 datasets Our code and models will. We demonstrated using adaptive convolutions replace a GANs generator a weak baseline model significantly on visually diverse datasets Our AdaGAN models able beat other state methods without any augmented training objectives The samples generated our models they seem learn the global context pretty be the rough shapes most cases and the sample quality reasonable on CIFAR-10 dataset Furthermore not much visible convolution artifacts The success our models suggests gained modifying architectures GANsThe approach take different try inject the discriminator These existing methods and AdaGAN can complement More experiments need our architectures benefit the augmented training objectives from existing methodsOur method not without a downside Even used depthwise separable convolution memory and computation extremely More tricks could applied alleviate For example BID12 work both the local convolutions to regress the adaptive weights in our AdaConvBlock can separate 1-D convolutions This can reduce by Another idea exploit locality We expect the adaptive convolution weights biases a pixel location quite its neighbors interpolated We will address our future workA SAMPLES OUR ON CIFAR-10 STL-10",0.01,0.5162499669531191
"Techniques such as ensembling and distillation promise model quality improvements when paired with almost any base model. However, due to increased test-time cost (for ensembles) and increased complexity of the training pipeline (for distillation), these techniques are challenging to use in industrial settings. In this paper we explore a variant of distillation which is relatively straightforward to use as it does not require a complicated multi-stage setup or many new hyperparameters. Our first claim is that online distillation enables us to use extra parallelism to fit very large datasets about twice as fast. Crucially, we can still speed up training even after we have already reached the point at which additional parallelism provides no benefit for synchronous or asynchronous stochastic gradient descent. Two neural networks trained on disjoint subsets of the data can share knowledge by encouraging each model to agree with the predictions the other model would have made. These predictions can come from a stale version of the other model so they can be safely computed using weights that only rarely get transmitted. Our second claim is that online distillation is a cost-effective way to make the exact predictions of a model dramatically more reproducible. We support our claims using experiments on the Criteo Display Ad Challenge dataset, ImageNet, and the largest to-date dataset used for neural language modeling, containing $6\times 10^{11}$ tokens and based on the Common Crawl repository of web data. For large-scale, commercially valuable neural net training problems, practitioners would be willing to devote many more machines to training if it sped up training time dramatically or improved the quality of the final model. Currently, distributed stochastic gradient descent (SGD), in both its synchronous and asynchronous forms , is the dominant algorithm for large-scale neural network training across multiple interconnected machines. Unfortunately, as the number of machines increases, there are diminishing improvements to the time needed to train a high quality model, to a point where adding workers does not further improve training time. A combination of infrastructure limitations and optimization barriers constrain the scalability of distributed minibatch SGD. The overhead of communicating weight updates and the long tail of the machine and network latency distributions slow down execution and produce thorny engineering challenges. For the synchronous algorithm, there are rapidly diminishing returns from increasing the effective batch size BID11 BID9 . For the asynchronous algorithm, gradient interference from inconsistent weights can cause updates to thrash and even, in some cases, result in worse final accuracy or completely stall learning progress. The precise scalability limit for distributed SGD will depend on implementation details of the algorithm, specifics of the infrastructure, and the capabilities of the hardware, but in our experience it can be very difficult to scale effectively much beyond a hundred GPU workers in realistic setups. No algorithm for training neural nets will be infinitely scalable, but even scaling a bit beyond the limits of distributed SGD would be extremely valuable.Once we have reached the limits of adding workers to distributed SGD, we could instead use extra machines to train another copy of the model and create an ensemble to improve accuracy (or trade this accuracy for training time by training the members of the ensemble for fewer steps). As an added benefit, the ensemble will make more stable and reproducible predictions, which can be useful in practical applications. However, ensembling increases the cost at test time, potentially violating latency or other cost constraints. Alternatively, to get nearly the same benefits of the ensemble without increasing test time costs, we can distill BID8 BID2 an n-way ensemble of models into a single still-servable model using a two-phase process: first we use nM machines to train an n-way ensemble with distributed SGD and then use M machines to train the servable student network to mimic the n-way ensemble. By adding another phase to the training process and using more machines, distillation in general increases training time and complexity in return for a quality improvement close to the larger teacher ensemble model.We believe that the additional training costs, in terms of both time and pipeline complexity, discourage practitioners from using ensemble distillation, even though it almost always would improve results. In this work, we describe a simpler online variant of distillation we call codistillation. Codistillation trains n copies of a model in parallel by adding a term to the loss function of the ith model to match the average prediction of the other models.Through large-scale experiments we show that, compared to distributed SGD, codistillation improves accuracy and speeds up training by allowing the productive use of more computational resources even beyond the point where adding more workers provides no additional speedup for SGD. Specifically, codistillation provides the benefits of distilling an ensemble of models without increasing training time. Codistillation is also quite simple to use in practice compared to a multi-phase distillation training procedure. Multi-phase distillation tends to encourage human intervention between the training phases to decide when to stop training the ensemble and start distilling it into a single model. We also show that codistillation does not lose the reproducibility benefits of ensembles of neural networks, reducing churn in the predictions of different retrains of the same model. Reducing prediction churn can be essential when testing and launching new versions of a model in a non-disruptive way in an existing service, although it is not as well-studied in the academic machine learning community.Given the obvious relationship to distillation, very similar algorithms to codistillation have been independently described by multiple researchers. For example, BID21 describes another simultaneous distillation algorithm but does not investigate the benefits in the distributed training case and only presents it as a potential quality improvement over regular distillation. We view the experimental validation of codistillation at scale as the primary contribution of our work. Another contribution of this work is our exploration of different design choices and implementation considerations for codistillation which we believe has produced recommendations of substantial practical utility.In general, we believe the quality gains of codistillation over well-tuned offline distillation will be minor in practice and the more interesting research direction is exploring codistillation as a distributed training algorithm that uses an additional form of communication that is far more delay tolerant. Distillation is a surprisingly flexible tool, especially when performed during model training instead of after. It can be used to accelerate training, improve quality, distribute training in new, more communication efficient ways, and reduce prediction churn. However, there are still many questions we would like to explore. For example, we mostly focused on pairs of models codistilling from each other. It stands to reason that if pairs are useful then so are other topologies. Fully connected graphs might make the models too similar, too quickly so ring structures might also be interesting. We also did not explore the limits of how accurate the predictions from the teacher models have to be. It might be possible to aggressively quantize the teacher model to make codistillation almost as cheap as normal training even for very large models.It is somewhat paradoxical that bad models codistilling from each other can learn faster than models training independently. Somehow the mistakes made by the teacher model carry enough information to help the student model do better than the teacher, and better than just seeing the actual label in the data. Characterizing the ideal properties of a teacher model is an exciting avenue for future work.In this work we only extract predictions from the checkpoints, as predictions are identifiable and, unlike the internal structure of the networks, have no spurious symmetries. That said, it might be possible to extract more information from a checkpoint than just predictions without hitting the same issues faced by workers communicating gradients, allowing the use of the teacher models as a stronger regularizer. Perhaps distillation-based methods could be used to augment federated learning BID12 in particularly bandwidth-constrained settings.",1540,0.786,900,1.711111111111111,"Techniques such ensembling and distillation promise model quality improvements when paired almost any base model However due increased test-time costfor ensembles the training pipeline distillation these techniques challenging industrial settings In explore a variant distillation which relatively straightforward it or many new hyperparameters Our first claim online distillation enables use extra parallelism fit very large datasets about twice Crucially still speed training even additional parallelism provides Two neural networks trained disjoint subsets the data can share knowledge by encouraging agree would These predictions can come a stale version the other model so safely computed weights only rarely get transmitted Our second claim online distillation the exact predictions a model dramatically We support our claims using experiments the Criteo Display Ad Challenge dataset ImageNet largest to- used neural language modeling containing $6\times 10^{11}$ tokens based the Common Crawl repository web data For large-scale, commercially valuable neural net training problems practitioners would willing devote many more machines if sped dramatically or Currently distributedSGD , across multiple interconnected machines Unfortunately as machines increases diminishing improvements train a high quality model to adding workers does further A combination infrastructure limitations optimization barriers constrain distributed minibatch SGD The overhead communicating weight updates the long tail the machine and network latency distributions slow execution produce thorny engineering challenges For the synchronous algorithm there rapidly from increasing the effective batch size BID11 BID9 . For the asynchronous algorithm gradient interference from inconsistent weights updates thrash even, result worse final accuracy or completely stall learning progress The precise scalability limit distributed SGD will specifics the infrastructure capabilities scale effectively much a hundred GPU workers realistic setups No algorithm for training will infinitely even scaling bit beyond distributed SGDOnce reached adding workers distributed instead extra machines another copy create an ensemble improve accuracy ( trade this accuracy training time by the members fewer steps As the ensemble make more stable and reproducible predictions practical applications However ensembling increases at test time potentially violating latency or other cost constraints Alternatively to nearly the same benefits the ensemble without increasing test time costs distill BID8 BID2 an n-way ensemble models into a single still-servable model using we nM machines train distributed SGD M machines the servable student network to mimic By adding another phase and using more machines distillation in general increases training time complexity return a quality improvement close the larger teacher ensemble modelWe additional costs pipeline complexity discourage practitioners ensemble distillation almost would results In this work a simpler online variant distillation we codistillation Codistillation trains n copies a model parallel by adding a term the loss function match the average predictionThrough compared distributed SGD improves speeds training allowing the productive use even beyond adding more workers provides Specifically codistillation provides the benefits distilling an ensemble models without increasing training time Codistillation also quite simple compared a multi-phase distillation training procedure Multiphase distillation tends encourage human intervention between the training phases decide training the ensemble start into We also show codistillation does lose reducing churn the predictions different retrains Reducing prediction churn can essential testing launching a model in in an existing service although wellGiven the obvious relationship to distillation very similar algorithms to codistillation independently multiple researchers For example BID21 describes another simultaneous distillation algorithm but investigate in the distributed training case and presents it We view the experimental validation codistillation at scale the primary contribution Another contribution this work our exploration different design choices implementation considerations codistillation which produced recommendations substantial practical utilityIn general the quality gains over well-tuned offline distillation will minor practice the more interesting research direction exploring a distributed training algorithm uses an additional form communication far delay Distillation is a surprisingly flexible tool performed during model training instead. It can used accelerate training quality distribute in new, more communication efficient ways prediction churn However we would explore For example we mostly focused pairs models codistilling from It stands pairs useful then other topologies Fully connected graphs might make the models too similar too quickly so ring structures also interesting We also did explore the limits how accurate from the teacher models have It might possible aggressively quantize the teacher model codistillation almost cheap normal training even very large modelsIt somewhat bad models codistilling from each learn faster models training independently Somehow the mistakes the teacher model carry enough information help the student model do better just seeing the actual label in Characterizing the ideal properties a teacher model an exciting avenue future workIn only extract predictions the checkpoints as predictions identifiable, unlike the internal structure the networks have no spurious symmetries That might extract a checkpoint just predictions without hitting faced workers communicating gradients allowing the use the teacher models a stronger regularizer Perhaps distillation-based methods could augment federated learning BID12 in particularly bandwidth-constrained settings",0.01,0.5159278032558264
"Support Vector Machines (SVMs) are one of the most popular algorithms for classification and regression analysis. Despite their popularity, even efficient implementations have proven to be computationally expensive to train at a large-scale, especially in streaming settings. In this paper, we propose a novel coreset construction algorithm for efficiently generating compact representations of massive data sets to speed up SVM training. A coreset is a weighted subset of the original data points such that SVMs trained on the coreset are provably competitive with those trained on the original (massive) data set. We provide both lower and upper bounds on the number of samples required to obtain accurate approximations to the SVM problem as a function of the complexity of the input data. Our analysis also establishes sufficient conditions on the existence of sufficiently compact and representative coresets for the SVM problem. We empirically evaluate the practical effectiveness of our algorithm against synthetic and real-world data sets. Popular machine learning algorithms are computationally expensive, or worse yet, intractable to train on Big Data. The notion of using coresets BID6 BID3 BID2 , small weighted subsets of the input points that provably approximate the original data set, has shown promise in accelerating machine learning algorithms such as kmeans clustering BID6 , mixture model training , and logistic regression BID12 .Coreset constructions were originally introduced in the context of computational geometry BID1 and subsequently generalized for applications to other problems BID14 BID6 . Coresets provide a compact representation of the structure of static and streaming data, with provable approximation guarantees with respect to specific algorithms. For instance , a data set consisting of K clusters would yield a coreset of size K, with each cluster represented by one coreset point. Even if the data has no structure (e.g., uniformly distributed), coresets will correctly down sample the data to within prescribed error bounds. For domains where the data has structure, the coreset representation has the potential to greatly and effectively reduce the time required to manually label data for training and the computation time for training, while at the same time providing a mechanism of supporting machine learning systems for applications with streaming data.Coresets are constructed by approximating the relative importance of each data point in the original data set to define a sampling distribution and sampling sufficiently many points in accordance with this distribution. This construction scheme suggests that beyond providing a means of conducting provably fast and accurate inference, coresets also serve as efficient representations of the full data set and may be used to automate laborious representation tasks, such as automatically generating semantic video representations or detecting outliers in data BID17 .The representative power and provable guarantees provided by coresets also motivate their use in training of one of the most popular algorithms for classification and regression analysis: Support Vector Machines (SVMs). Despite their popularity , SVMs are computationally expensive to train on massive data sets, which has proven to be computationally problematic with the rising availability of Big Data. In this paper, we present a novel coreset construction algorithm for efficient, large-scale Support Vector Machine training.1. A practical coreset construction algorithm for accelerating SVM training based on an efficient importance evaluation scheme for approximating the importance of each point.2. An analysis proving lower bounds on the number of samples required by any coreset construction algorithm to approximately represent the data.3. An analysis proving the efficiency and theoretical guarantees of our algorithm and characterizing the family of data sets for which applications of coresets are most suited.4. Evaluations against synthetic and real-world data sets that demonstrate the practical effectiveness of our algorithm for large-scale SVM training. We presented an efficient coreset construction algorithm for generating compact representations of the input data points that provide provably accurate inference. We presented both lower and upper bounds on the number of samples required to obtain accurate approximations to the SVM problem as a function of input data complexity and established sufficient conditions for the existence of compact representations. Our experimental results demonstrate the effectiveness of our approach in speeding up SVM training when compared to uniform sub-samplingThe method presented in this paper is also applicable to streaming settings, using the merge-andreduce technique from coresets literature BID3 .We conjecture that our coreset construction method can be extended to significantly speed up SVM training for nonlinear kernels as well as other popular machine learning algorithms, such as deep learning. 8 APPENDIX Figure 3 : The estimator variance of query evaluations. We note that due to the use of a judicious sampling distribution based on the points' sensitivities, the variance of our coreset estimator is lower than that of uniform sampling for all data sets.",934,0.398,555,1.6828828828828828,"Support Vector Machines ( are one classification regression Despite their popularity even efficient implementations proven computationally train at streaming settings In this paper a novel coreset construction algorithm efficiently compact representations massive data sets to speed SVM training A coreset is a weighted subset the original data points such that SVMs trained provably competitive We provide both lower and upper bounds samples obtain to the SVM problem as Our analysis also establishes sufficient conditions on the existence sufficiently compact and representative coresets the SVM problem We empirically evaluate the practical effectiveness our algorithm against Popular machine learning algorithms computationally or worse intractable train Big Data The notion using coresets BID6 BID3 BID2 , small weighted subsets the input points that provably approximate shown accelerating such kmeans mixture model training , BID12 .Coreset constructions were originally introduced computational geometry subsequently generalized applications to other problems BID14 BID6 Coresets provide a compact representation static and streaming data provable approximation guarantees with specific algorithms For instance , data consisting K clusters would yield a coreset size K represented one coreset point Even the data has no structure ( uniformly coresets will correctly down sample the within prescribed error bounds For domains where the data structure the coreset representation has the potential greatly and effectively reduce manually label data for training the computation time training a mechanism of supporting machine learning systems applications streaming dataCoresets constructed approximating the relative importance define a sampling distribution sampling sufficiently many points accordance This construction scheme suggests beyond providing conducting provably fast and accurate inference coresets also efficient representations the full data automate laborious representation tasks automatically semantic video representations detecting outliers data BID17 .The representative power and provable guarantees also motivate training of one of classification regression Support Vector Machines Despite their popularity , SVMs computationally train on massive data sets has proven computationally problematic with the rising availability In this paper a novel coreset construction algorithm efficient, large-scale Support Vector Machine training.1. accelerating based an efficient importance evaluation scheme approximating the importance each point.2 An analysis proving lower bounds samples by approximately represent theoretical guarantees and characterizing the family data sets applications of coresets most Evaluations against demonstrate the practical effectiveness We presented an efficient coreset construction algorithm generating compact representations the input data points that provide provably accurate inference We presented both lower and upper bounds samples to the SVM problem as input data complexity established sufficient conditions the existence compact representations Our experimental results our approach speeding SVM training when uniform sub-samplingThe method presented also streaming settings using the merge-andreduce technique from coresets literature BID3 .We conjecture our coreset construction method significantly for nonlinear kernels as other popular machine 8 APPENDIX Figure : The estimator variance query evaluations We note due a judicious sampling distribution based the points' sensitivities the variance our coreset estimator lower uniform sampling for",0.01,0.44400475783531534
"The sign stochastic gradient descent method (signSGD) utilizes only the sign of the stochastic gradient in its updates. Since signSGD carries out one-bit quantization of the gradients, it is extremely practical for distributed optimization where gradients need to be aggregated from different processors. For the first time, we establish convergence rates for signSGD on general non-convex functions under transparent conditions. We show that the rate of signSGD to reach first-order critical points matches that of SGD in terms of number of stochastic gradient calls, up to roughly a linear factor in the dimension. We carry out simple experiments to explore the behaviour of sign gradient descent (without the stochasticity) close to saddle points and show that it often helps completely avoid them without using either stochasticity or curvature information. Deep neural network training takes place in an error landscape that is high-dimensional, non-convex and stochastic. In practice, simple optimization techniques perform surprisingly well but have very limited theoretical understanding. While stochastic gradient descent (SGD) is widely used, algorithms like Adam (Kingma & Ba, 2015) , RMSprop BID19 and Rprop (Riedmiller & Braun, 1993) are also popular. These latter algorithms involve component-wise rescaling of gradients, and so bear closer relation to signSGD than SGD. Currently, convergence rates have only been derived for close variants of SGD for general non-convex functions, and indeed the Adam paper gives convex theory.Recently, another class of optimization algorithms has emerged which also pays attention to the resource requirements for training, in addition to obtaining good performance. Primarily, they focus on reducing costs for communicating gradients across different machines in a distributed training environment BID17 BID18 BID14 BID0 BID21 . Often, the techniques involve quantizing the stochastic gradients at radically low numerical precision. Empirically, it was demonstrated that one can get away with using only one-bit per dimension without losing much accuracy BID17 BID18 . The theoretical properties of these approaches are however not well-understood. In particular, it was not known until now how quickly signSGD (the simplest incarnation of one-bit SGD) converges or even whether it converges at all to the neighborhood of a meaningful solution. Our contribution: we supply the non-convex rate of convergence to first order critical points for signSGD. The algorithm updates parameter vector x k according to DISPLAYFORM0 whereḡ k is the mini-batch stochastic gradient and k is the learning rate. We show that for nonconvex problems, signSGD entertains convergence rates as good as SGD, up to a linear factor in the dimension. Our statements impose a particular learning rate and mini-batch schedule.Ours is the first work to provide non-convex convergence rates for a biased quantisation procedure as far as we know, and therefore does not require the randomisation that other gradient quantisation algorithms need to ensure unbiasedness. The technical challenge we overcome is in showing how to carry the stochasticity in the gradient through the sign non-linearity of the algorithm in a controlledfashion.Whilst our analysis is for first order critical points, we experimentally test the performance of sign gradient descent without stochasticity (signGD) around saddle points. We removed stochasticity in order to investigate whether signGD has an inherent ability to escape saddle points, which would suggest superiority over gradient descent (GD) which can take exponential time to escape saddle points if it gets too close to them BID5 .In our work we make three assumptions. Informally , we assume that the objective function is lowerbounded, smooth, and that each component of the stochastic gradient has bounded variance. These assumptions are very general and hold for a much wider class of functions than just the ones encountered in deep learning. Outline of paper: in Sections 3, 4 and 5 we give non-convex theory of signSGD. In Section 6 we experimentally test the ability of the signGD (without the S) to escape saddle points. And in Section 7 we pit signSGD against SGD and Adam on CIFAR-10. First we wish to discuss the connections between signSGD and Adam BID10 . Note that setting the Adam hyperparameters 1 = 2 = ✏ = 0, Adam and signSGD are equivalent. Indeed the authors of the Adam paper suggest that during optimisation the Adam step will commonly look like a binary vector of ±1 (multiplied by the learning rate) and thus resemble the sign gradient step. If this algorithmic correspondence is valid, then there seems to be a discrepancy between our theoretical results and the empirical good performance of Adam. Our convergence rates suggest that signSGD should be worse than SGD by roughly a factor of dimension d. In deep neural network applications d can easily be larger than 10 6 . We suggest a resolution to this proposed discrepancy-there is structure present in deep neural network error surfaces that is not captured by our simplistic theoretical assumptions. We have already discussed in Section 5 how the signSGD bound is improved by a factor d in the case of gradients distributed uniformly across dimensions. It is also reasonable to expect that neural network error surfaces might exhibit only weak coupling across dimensions. To provide intuition for how such an assumption can help improve the dimension scaling of signSGD, note that in the idealised case of total decoupling (the Hessian is everywhere diagonal) then the problem separates into d independent one dimensional problems, so the dimension dependence is lost.Next, let's talk about saddle points. Though general non-convex functions are littered with local minima, recent work rather characterises successful optimisation as the evasion of a web of saddle points BID4 . Current theoretical work focuses either on using noise Levy (2016); BID5 or curvature information (Allen-Zhu, 2017b) to establish bounds on the amount of time needed to escape saddle points. We noted that merely passing the gradient through the sign operation introduces an algorithmic instability close to saddle points, and we wanted to empirically investigate whether this could be enough to escape them. We removed stochasticity from the algorithm to focus purely on the effect of the sign function.We found that when the objective function was axis aligned, then sign gradient descent without stochasticity (signGD) made progress unhindered by the saddles. We suggest that this is because signGD has a greater ability to 'explore', meaning it typically takes larger steps in regions of small gradient than SGD, and it can take steps almost orthogonal to the true gradient direction. This exploration ability could potentially allow it to break out of subspaces convergent on saddle points without sacrificing its convergence rate-we hypothesise that this may contribute to the often more robust practical performance of algorithms like Rprop and Adam, which bear closer relation to signSGD than SGD. For non axis-aligned objectives, signGD could sometimes get stuck in perfect periodic orbits around saddle points, though we hypothesise that this behaviour may be much less likely for higher dimensional objectives (the testbed function had dimension 10) with non-constant learning rate.Finally we want to discuss the implications of our results for gradient quantisation schemes. Whilst we do not analyse the multi-machine case of distributed optimisation, we imagine that our results will extend naturally to that setting. In particular our results stand as a proof of concept that we can provide guarantees for biased gradient quantisation schemes. Existing quantisation schemes with guarantees require delicate randomisation to ensure unbiasedness. If a scheme as simple as ours can yield provable guarantees on convergence, then there is a hope that exploring further down this avenue can yield new and useful practical quantisation algorithms. BID8 of 91.25%. Note the broad similarity in general shape of the heatmap between Adam and signSGD, supporting a notion of algorithmic similarity. Also note that whilst SGD has a larger region of very high-scoring hyperparameter configurations, signSGD and Adam appear more stable for large learning rates. We have investigated the theoretical properties of the sign stochastic gradient method (signSGD) as an algorithm for non-convex optimisation. The study was motivated by links that the method has both to deep learning stalwarts like Adam and Rprop, as well as to newer quantisation algorithms that intend to cheapen the cost of gradient communication in distributed machine learning. We have proved non-convex convergence rates for signSGD to first order critical points. Insofar as the rates can directly be compared, they are of the same order as SGD in terms of number of gradient evaluations, but worse by a linear factor in dimension. SignSGD has the advantage over existing gradient quantisation schemes with provable guarantees, in that it doesn't need to employ randomisation tricks to remove bias from the quantised gradient.We wish to propose some interesting directions for future work. First our analysis only looks at convergence to first order critical points. Whilst we present preliminary experiments exhibiting success and failure modes of the algorithm around saddle points, a more detailed study attempting to pin down exactly when we can expect signSGD to escape saddle points efficiently would be welcome. This is an interesting direction seeing as existing work always relies on either stochasticity or second order curvature information to avoid saddles. Second the link that signSGD has to both Adam-like algorithms and gradient quantisation schemes is enticing. In future work we intend to investigate whether this connection can be exploited to develop large scale machine learning algorithms that get the best of both worlds in terms of optimisation speed and communication efficiency.",1929,1.014,1137,1.6965699208443272,"The sign stochastic gradient descent methodsignSGD utilizes only the sign its updates Since signSGD carries one-bit quantization extremely practical distributed optimization where need different processors For establish convergence rates signSGD on under transparent conditions We show signSGD to reach first critical points matches number stochastic gradient calls up roughly a linear factor in the dimension We carry simple experiments sign gradient descentwithout close saddle show often helps completely them without using Deep neural network training takes an error landscape high non In practice simple optimization techniques perform surprisingly but very limited theoretical understanding While stochastic gradient descent algorithms Adam (Kingma & Ba, , RMSprop BID19 RpropRiedmiller Braun 1993 These latter algorithms involve component-wise rescaling bear closer relation signSGD Currently convergence rates only derived close variants SGD for indeed the Adam paper gives convex theoryRecently another class optimization algorithms also pays the resource requirements training obtaining Primarily focus reducing costs communicating gradients different machines BID17 BID18 BID14 BID0 BID21 . Often the techniques involve quantizing at radically low numerical precision demonstrated one get per dimension without BID17 . The theoretical properties these approaches however In particular known until quickly signSGD (the simplest incarnation or the neighborhood a meaningful solution Our contribution: we supply the non-convex rate convergence first order critical points signSGD The algorithm updates parameter vector x k according DISPLAYFORM0 where�� k We show for nonconvex problems signSGD entertains convergence rates good, up a linear factor in the dimension Our statements impose a particular learning rate mini-batch scheduleOurs provide non-convex convergence rates a biased quantisation procedure as far therefore that other gradient quantisation algorithms need ensure unbiasedness The technical challenge we overcome showing carry through the sign non a controlledfashionWhilst our analysis for first order critical points experimentally sign gradient descent withoutsignGD around saddle points We removed stochasticity order investigate signGD has an inherent ability escape saddle points superiorityGD which take exponential time escape if gets BID5 .In make Informally , assume lowerbounded smooth that each component bounded variance These assumptions very general hold a much wider class functions encountered deep learning Outline paper in Sections give non-convex theory signSGD In Section we experimentally the signGDwithout the S) escape saddle points And Section we pit signSGD Adam on CIFAR-10 First we wish discuss the connections signSGD Adam BID10 . Note setting the Adam hyperparameters 1 = = �� = Adam and signSGD equivalent Indeed the authors the Adam paper suggest during optimisation the Adam step commonly look a binary vector ±1multiplied thus resemble the sign gradient step If this algorithmic correspondence valid seems our theoretical results the empirical good performance Adam. Our convergence rates suggest signSGD should worse by dimension d. In deep neural network applications d can easily larger 10 6 . We suggest a resolution this proposed discrepancy-there structure present deep neural network error surfaces captured our simplistic theoretical assumptions We already Section how signSGD bound improved a factor d in gradients distributed dimensions It reasonable neural network error surfaces might exhibit only weak coupling across dimensions To provide intuition such an assumption help improve the dimension scaling signSGD note the idealised case total decouplingthe Hessian is everywhere diagonal then separates d independent one dimensional problems so the dimension dependence lostNext talk saddle points Though general non-convex functions littered local minima recent work rather characterises successful optimisation the evasion a web saddle points BID4 . Current theoretical work focuses either using noise Levy2016 BID5 or curvature informationAllen-Zhu establish bounds escape saddle points We noted merely passing the gradient through the sign operation introduces close saddle points wanted empirically enough escape them We removed stochasticity focus purely the sign functionWe axis aligned sign gradient descent withoutsignGD made progress the saddles We suggest this signGD ' meaning typically larger steps regions small gradient than SGD steps almost the true gradient direction This exploration ability could it break subspaces convergent saddle points without sacrificing its convergence rate-we hypothesise contribute the often more robust practical performance algorithms Rprop Adam, bear closer relation signSGD For non axis-aligned objectives signGD could sometimes get perfect periodic orbits saddle points though hypothesise much higher dimensional objectivesthe testbed function had dimension 10 non-constant learning rateFinally want discuss gradient quantisation schemes Whilst analyse the multi-machine case distributed optimisation imagine our results extend naturally that setting In particular our results stand as provide guarantees biased gradient quantisation schemes Existing quantisation schemes with guarantees require delicate randomisation unbiasedness If a scheme as ours yield provable guarantees convergence a hope exploring further down practical quantisation algorithms BID8 of 91.25% Note the broad similarity general shape the heatmap between Adam signSGD supporting algorithmic similarity Also note whilst SGD a larger region very high-scoring hyperparameter configurations signSGD and Adam appear more large learning rates We investigated the sign stochastic gradient methodsignSGD The study motivated links that the method both to deep learning stalwarts Adam and Rprop newer quantisation algorithms intend cheapen gradient communication We proved non-convex convergence rates signSGD to first order critical points Insofar the rates can directly of SGD number gradient evaluations worse by a linear factor in dimension SignSGD the advantage existing gradient quantisation schemes provable guarantees in does employ randomisation tricks remove biasWe wish propose some interesting directions First our analysis only convergence to first order critical points Whilst present preliminary experiments exhibiting success and failure modes the algorithm around saddle points attempting pin exactly we signSGD escape efficiently This an interesting direction seeing existing work always relies second order curvature information avoid saddles Second the link that signSGD both Adam-like algorithms gradient quantisation schemes enticing In future work intend investigate this connection develop get",0.01,0.47887812803106905
"Deep learning has found numerous applications thanks to its versatility and accuracy on pattern recognition problems such as visual object detection. Learning and inference in deep neural networks, however, are memory and compute intensive and so improving efficiency is one of the major challenges for frameworks such as PyTorch, Tensorflow, and Caffe. While the efficiency problem can be partially addressed with specialized hardware and its corresponding proprietary libraries, we believe that neural network acceleration should be transparent to the user and should support all hardware platforms and deep learning libraries. 

 To this end, we introduce a transparent middleware layer for neural network acceleration. The system is built around a compiler for deep learning, allowing one to combine device-specific libraries and custom optimizations while supporting numerous hardware devices. In contrast to other projects, we explicitly target the optimization of both prediction and training of neural networks. We present the current development status and some preliminary but encouraging results: on a standard x86 server, using CPUs our system achieves a 11.8x speed-up for inference and a 8.0x for batched-prediction (128); on GPUs we achieve a 1.7x and 2.3x speed-up respectively.",236,0.122,126,1.873015873015873,Deep learning found numerous applications thanks accuracy on pattern recognition problems such visual object detection Learning and inference however memory compute intensive and so improving efficiency one frameworks While the efficiency problem can partially specialized hardware its corresponding proprietary libraries we neural network acceleration transparent support deep learning libraries To this end introduce a transparent middleware layer neural network acceleration The system built a compiler deep learning allowing one combine device-specific libraries custom optimizations while supporting numerous hardware devices In contrast other projects explicitly target the optimization both prediction training We present the current development status some preliminary but encouraging results: on a standard x86 server using CPUs our system achieves for inference for batched-prediction128); GPUs,0.0,0.928446911792314
"Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. In particular, to aid convolutional neural networks in learning rotation invariance, we consider a simple, efficient conic convolutional scheme that encodes rotational equivariance, along with a method for integrating the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) to encode global rotational invariance. We call our new method the Conic Convolution and DFT Network (CFNet). We evaluated the efficacy of CFNet as compared to a standard CNN and group-equivariant CNN (G-CNN) for several different image classification tasks and demonstrated improved performance, including classification accuracy, computational efficiency, and its robustness to hyperparameter selection. Taken together, we believe CFNet represents a new scheme that has the potential to improve many imaging analysis applications. Though the appeal of neural networks is their versatility for arbitrary classification tasks, there is still much benefit in designing them for particular problem settings. In particular, their effectiveness can be greatly increased by encoding invariance to uniformative augmentations of the data BID17 . If such invariance is not explicitly encoded, the network must learn it from the data, perhaps with the help of data augmentation, requiring more parameters and thereby increasing its susceptibility to overfitting.A key invariance inherent to several computer vision settings, including satellite imagery and all forms of microscopy imagery, is rotation BID3 BID1 . Recently, there have been a variety of proposed approaches for encoding rotation equivariance and invariance, the most promising of which have formulated convolution over groups BID6 BID24 . Notably, G-CNNs have been applied to several biological imaging tasks, producing state-of-the-art results BID24 BID0 BID18 .Here we propose a new rotation-equivariant convolutional scheme, called conic convolution, which, in contrast to group convolution, encodes equivariance while still operating over only the spatial domain. Rather than convolving each filter across the entire image, as in standard convolution, rotated filters are convolved over corresponding conic regions of the input feature map that emanate from the origin, thereby transforming rotations in the input directly to rotations in the output. This scheme is intuitive, simple to implement, and computationally efficient. We also show that the method yields improved performance over group convolution on several relevant applications.Additionally, we propose the integration of the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) into a transition layer between convolutional and fully-connected layers to encode rotational invariance. Though the insight of using the DFT to encode rotational invariance has been employed for texture classification using wavelets BID9 BID13 BID21 BID2 and for general image classification BID23 , as of yet, its application to CNNs has been overlooked. As in these prior works, rotations of the input are transformed to circular shifts, to which the magnitude response of the 2D-DFT is invariant, in the transformed space. Most other recently proposed rotationinvariance CNNs impose this invariance by applying a permutation-invariant operation, such as the average or maximum, over the rotation group, but since this operation is applied for each filter individually, possibly valuable pose information between filters is lost. In contrast, the 2D-DFT is able to integrate mutual pose information between different filter responses, yielding richer features for subsequent layers.We demonstrate the effectiveness of these two novel contributions for various applications: classifying rotated MNIST images, classifying synthetic images that model biomarker expression in microscopy images of cells, and localizing proteins in budding yeast cells BID15 . We show that CFNet improves classification accuracy generally over the standard raster convolution formulation and over the equivariant method of G-CNN across these settings. We also show that the 2D-DFT clearly improves performance across these diverse data sets, and that not only for conic convolution, but also for group convolution. Source code for the implementation of CFNet will be made available on GitHub.2 RELATED WORK BID6 introduced G-CNNs by formulating convolution over groups, including rotation, translation, and flips, for neural networks, which has inspired many subsequent improvements. By convolving over groups, equivariance to these groups is maintained throughout the convolutional layers, and invariance is enforced at the end of the network by pooling over groups. This work was improved upon by the design of steerable filters BID24 for convolution, similar to those proposed by BID25 , which allow for finer sampling of rotations of filters without inducing artifacts. Steerable filters were first proposed by BID10 and had been explored previously for image classification BID19 , but as shallow features in the context of HOG descriptors.An alternative means of encoding rotational equivariance is to transform the domain of the image to an alternative domain, such as the log-polar domain BID23 BID11 in which rotation becomes some other transformation that is easier to manage, in this case, translations. The suitability of this transformation depends upon the signal of interest, since this warping will introduce distortion, as pixels near the center of the image are sampled more densely than pixels near the perimeter. In addition, its stability to translations in the original domain is of concern. Our proposed CFNet, by convolving over conic regions, also encodes global rotation equivariance about the origin, but without introducing such distortion, which greatly helps mitigate its susceptibility to translation. The recently developed spatial transform layer BID12 and deformable convolutional layer BID7 allow the network to learn non-regular sampling patterns and can potentially help learning rotation invariance, though invariance is not explicitly enforced, which would most likely be a challenge for tasks with small training data.A simple means for achieving rotation equivariance and invariance was proposed by BID8 , in which feature maps of standard CNNs are made equivariant or invariant to rotation by combinations of cyclic slicing, stacking, rolling, and pooling. RotEqNet BID20 improved upon this idea by storing , for each feature map for a corresponding filter, only the maximal response across rotations and the value of the corresponding rotation, to preserve pose information. This approach yielded improved results and considerable storage savings over BID8 and G-CNN. These methods are most similar to our proposed conic convolution . However, in contrast, our method applies each filter only at the appropriate rotation within each conic region, which further saves on storage.To enforce rotation invariance, as noted, most of the previous methods apply some permutationinvariant, or pooling, operation over rotations. BID3 recently proposed a strategy of encouraging a network to learn a rotation invariant transform, and follow-up work improved this learning process by incorporating a Fisher discriminant penalty BID4 . However, the convolutional layers of the network do not maintain the property of rotation equivariance with the input image, which requires that the network learn this equivariance and could therefore hinder performance. Also, learning such a transform that generalizes to unseen data could prove difficult for settings with limited training data. BID23 previously proposed the 2D-DFT for rotational invariance. However , no method has yet been proposed to integrate the 2D-DFT into a rotation-equivariant CNN.",1475,0.674,881,1.674233825198638,"Performance can significantly encoding known invariance for particular tasks Many image classification tasks those related cellular imaging exhibit invariance rotation In particular to aid rotation invariance consider a simple, efficient conic convolutional scheme rotational equivariance along integrating the magnitude response the 2D-discrete-Fourier transform encode We call our new method the Conic Convolution and DFT NetworkCFNet We evaluated CFNet compared a standard CNN and group-equivariant CNN several different image classification tasks demonstrated, computational efficiency its robustness Taken we believe CFNet represents a new scheme many imaging analysis applications Though the appeal neural networks their versatility for arbitrary classification tasks much benefit designing particular problem settings In particular their effectiveness greatly encoding invariance to uniformative augmentations BID17 If such invariance explicitly encoded the network learn it perhaps data augmentation requiring more parameters thereby its susceptibilityA key invariance inherent several computer vision settings satellite imagery all forms microscopy imagery rotation BID3 BID1 Recently there proposed approaches encoding rotation equivariance the promising have formulated convolution over groups BID6 BID24 . Notably G-CNNs applied several biological imaging tasks producing state BID24 BID0 .Here propose a new rotation-equivariant convolutional scheme called conic convolution, equivariance while still operating over Rather convolving each filter across as rotated corresponding conic regions the input feature map that emanate thereby transforming rotations directly This scheme intuitive computationally We also show the method yields improved group convolution on several relevant applicationsAdditionally propose the integration the magnitude response a transition layer encode Though the insight using the DFT encode rotational invariance employed texture classification using wavelets BID9 BID13 BID21 BID2 for as of CNNs overlooked As in these prior works rotations the input are transformed circular shifts to which magnitude response the 2D-DFT the transformed space Most other recently proposed rotationinvariance CNNs impose this invariance by applying average maximum over the rotation group since for each filter individually, possibly valuable pose information between In contrast the 2D-DFT able integrate mutual pose information different filter responses yielding richer features subsequent layersWe demonstrate these two novel contributions various applications rotated synthetic images that model biomarker microscopy images cells localizing proteins budding yeast cells BID15 . We show CFNet improves classification accuracy generally over the standard raster convolution formulation the equivariant method G-CNN across these settings We also show the 2D-DFT clearly improves across these diverse data sets not for conic convolution Source code the implementation CFNet will made GitHub.2 RELATED WORK BID6 introduced G-CNNs by formulating convolution over groups including rotation translation flips has inspired many subsequent improvements By convolving over groups equivariance to these groups maintained throughout enforced pooling This work improved the design steerable filters BID24 for convolution similar proposed , allow finer sampling rotations filters without inducing Steerable filters were BID10 had explored previously image classification BID19 , as shallow features the context HOG descriptors.An alternative means encoding rotational equivariance transform the domain BID23 BID11 in rotation becomes some other transformation that easier manage in translations The suitability this transformation depends the signal interest since this warping will introduce distortion pixels near sampled In its stability to translations in the original domain Our proposed CFNet, by convolving over conic regions also encodes global rotation equivariance about introducing such distortion greatly helps mitigate its susceptibility translation The recently developed spatial transform layer BID12 and allow the network learn non-regular sampling patterns can potentially help learning rotation invariance though invariance explicitly enforced most tasks small training dataA simple means achieving rotation equivariance was , feature maps standard CNNs made equivariant or rotation by combinations cyclic slicing stacking rolling RotEqNet BID20 improved upon this idea storing , for each feature map for a corresponding filter only the maximal response across rotations to preserve pose This approach yielded improved results considerable storage savings BID8 G-CNN These methods most similar our proposed conic convolution . However contrast our method applies each filter at the appropriate rotation within each conic region further saves storageTo enforce as noted most some permutationinvariant pooling over rotations BID3 recently proposed encouraging a network learn a rotation invariant transform follow-up work improved incorporating a Fisher discriminant penalty BID4 However the convolutional layers maintain the property rotation equivariance with the input image requires learn could hinder Also learning such a transform that generalizes unseen data could settings BID23 previously proposed the 2D-DFT rotational invariance However , no method integrate the 2D-DFT a rotation-equivariant CNN",0.01,0.4219677187537588
"The problem of visual metamerism is defined as finding a family of perceptually
 indistinguishable, yet physically different images. In this paper, we propose our
 NeuroFovea metamer model, a foveated generative model that is based on a mixture
 of peripheral representations and style transfer forward-pass algorithms. Our
 gradient-descent free model is parametrized by a foveated VGG19 encoder-decoder
 which allows us to encode images in high dimensional space and interpolate
 between the content and texture information with adaptive instance normalization
 anywhere in the visual field. Our contributions include: 1) A framework for
computing metamers that resembles a noisy communication system via a foveated
feed-forward encoder-decoder network – We observe that metamerism arises as a
byproduct of noisy perturbations that partially lie in the perceptual null space; 2)
A perceptual optimization scheme as a solution to the hyperparametric nature of
our metamer model that requires tuning of the image-texture tradeoff coefficients
everywhere in the visual field which are a consequence of internal noise; 3) An
 ABX psychophysical evaluation of our metamers where we also find that the rate
 of growth of the receptive fields in our model match V1 for reference metamers
 and V2 between synthesized samples. Our model also renders metamers at roughly
 a second, presenting a ×1000 speed-up compared to the previous work, which now
 allows for tractable data-driven metamer experiments. The history of metamers originally started through color matching theory, where two light sources were used to match a test light's wavelength, until both light sources are indistinguishable from each other producing what is called a color metamer. This leads to the definition of visual metamerism: when two physically different stimuli produce the same perceptual response (See Figure 1 for an example). Motivated by BID1 's work of local texture matching in the periphery as a mechanism that explains visual crowding, BID7 were the first to create such point-of-fixation driven metamers through such local texture matching models that tile the entire visual field given log-polar pooling regions that simulate the V1 and V2 receptive field sizes, as well as having global image statistics that match the metamer with the original image. The essence of their algorithm is to use gradient descent to match the local texture BID22 ) and image statistics of the original image throughout the visual field given a point of fixation until convergence thus producing two images that are perceptually indistinguishable to each other.However, metamerism research currently faces 2 main limitations: The first is that metamer rendering faces no unique solution. Consider the potentially trivial examples of having an image I and its metamer M where all pixel values are identical except for one which is set to zero (making this difference unnoticeable), or the case where the metameric response arises from an imperceptible equal perturbation across all pixels as suggested in BID16 ; BID7 . This is a concept similar to Just Noticeable Differences BID21 BID5 ). However, like the work of BID7 ; BID17 ; BID23 ; BID1 , we are interested in creating point-of-fixation driven metamers, which create images that preserve information in the fovea, yet lose spatial information in the periphery such that this loss is unnoticeable contingent of a point of fixation (Figure 1 ). The second issue is that the current state of the art for a full field of view rendering of a 512px × 512px metamer takes 6 hours for a grayscale image and roughly a day for a color image. This computational constraint makes data- There has been a recent surge in interest with regards to developing and testing new metamer models: The SideEye model developed by BID8 , uses a fully convolutional network (FCN) as in BID20 and learns to map an input image into a Texture Tiling Model (TTM) mongrel BID23 ). Their end-to-end model is also feedforward like ours, but no use of noise is incorporated in the generation pipeline making their model fully deterministic. At first glance this seems to be an advantage rather a limitation, however it limits the biological plausilibility of metameric response as the same input image should be able to create more than one metamer. Another model which has recently been proposed is the CNN synthesis model developed by BID29 . The CNN synthesis model is gradient-descent based and is closest in flavor to the FS model, with the difference that their texture statistics are provided by a gramian matrix of filter activations of multiple layers of a VGGNet, rather than those used in BID22 .The question of whether the scaling parameter is the only parameter to be optimized for metamerism still seems to be open. This has been questioned early in BID23 , and recently proposed and studied by BID29 , who suggest that metamers are driven by image content, rather than bouma's law (scaling factor). FIG3 suggests that on average, it does seem that α must increase in proportion to retinal eccentricity, but this is conditioned by the image content of each receptive field. We believe that the hyperparametric nature of our model sheds some light into reconciling these two theories. Recall that in FIG0 , we found that certain images can be pushed stronger in the direction of it's texturized version versus others given their location in the encoded space, the local geometry of the surface, and their projection in the perceptual space. This suggests that the average maximal distortion one can do is fixed contingent on the size of the receptive field, but we are allowed to push further (increase α) for some images more than others, because the direction of the distortion lies closer to the perceptual null space (making this difference perceptually un-noticeable to the human observer). This is usually the case for regions of images that are periodic like skies, or grass. Along the same lines, we elaborate in the Supplementary Material on how our model may potentially explain why creating synthesized samples are metameric to each other at the scales of (V1;V2), but only generated samples at the scale of V1 (s = 0.25) are metameric to the reference image.Our model is also different to others (FS and recently Wallis et al. FORMULA0 ) given the role of noise in the computational pipeline. The previously mentioned models used noise as an initial seed for the texture matching pipeline via gradient-descent, while we use noise as a proxy for texture distortion that is directly associated with crowding in the visual field. One could argue that the same response is achieved via both approaches, but our approach seems to be more biologically plausible at the algorithmic level. In our model an image is fed through a non-linear hierarchical system (simulated through a deep-net), and is corrupted by noise that matches the texture properties of the input image (via AdaIN). This perceptual representation is perturbed along the direction of the texture-matched patch for each receptive field, and inverting such perturbed representation results in a metamer. FIG7 illustrates such perturbations which produce metamers when projected to a 2D subspace via the locally linear embedding (LLE) algorithm (Roweis & Saul FORMULA1 ). Indeed, the 10 encoded images do not fully overlap to each other and they are quite distant as seen in the 2D projection. However, foveated representations when perturbed with texture-like noise seem to finely tile the perceptual space, and might act as a type of biological regularizer for human observers who are consistently making eye-movements when processing visual information. This suggests that robust representations might be achieved in the human visual system given its foveated nature as non-uniform high-resolution imagery does not map to the same point in perceptual space. If this holds, perceptually invariant data-augmentation schemes driven by metamerism may be a useful enhancement for artificial systems that react oddly to adversarial perturbations that exploit coarse perceptual mappings (Goodfellow et al. FORMULA0 ; BID26 ; Berardino et al. FORMULA0 ).Understanding the underlying representations of metamerism in the human visual system still remains a challenge. In this paper we propose a model that emulates metameric responses via a foveated feed-forward style transfer network. We find that correctly calibrating such perturbations (a consequence of internal noise that match texture representation) in the perceptual space and inverting such encoded representation results in a metamer. Though our model is hyper-parametric in nature we propose a way to reduce the parametrization via a perceptual optimization scheme. Via a psychophysical experiment we empirically find that the critical scaling factor also matches the rate of growth of the receptive fields in V2 (s = 0.5) as in BID7 when performing visual discrimination between synthesized metamers, and match V1 (0.25) for reference metamers similar to BID29 . Finally, while our choice of texture statistics and transfer is relu4_1 of a VGG19 and AdaIN respectively, our ×1000-fold accelerated feed-forward metamer generation pipeline should be extendible to other models that correctly compute texture/style statistics and transfer. This opens the door to rapidly generating multiple flavors of visual metamers with applications in neuroscience and computer vision.6 Supplementary Material FIG0 : Reference Metamers at the scale of s = 0.25, at which they are indiscriminable to the human observer. The color coding scheme matches the data points of the optimization in Experiment 1 and the psychophysics of Experiment 2. All images used in the experiments were generated originally at 512 × 512 px subtending 26 × 26 d.v.a (degrees of visual angle). for each α ∈ [0 : DISPLAYFORM0 Compute metamer M NF (I) 9:end for 10:Find the α for each receptive field that minimizes: E(∆-SSIM) 2 . 11:Fit the γ s (•) function to collection of α values. 12:endfor 13: end for 14: Perform Permutation test on γ s for all s. 15: if γ s is independent of s then 16: γ s = γ 17: else 18:Perform regression of parameters of γ s as a function f of s. 19: DISPLAYFORM1 end if 21: end procedure",2149,0.923,1225,1.7542857142857142,"The problem visual metamerism defined finding a family perceptually yet In our NeuroFovea metamer model a mixture peripheral representations style transfer forward-pass algorithms Our gradient-descent free model a foveated VGG19 encoder-decoder which encode images the content texture information with adaptive instance normalization anywhere Our contributions include 1 A framework computing metamers resembles a noisy communication system via – We observe metamerism arises partially lie the perceptual null space; as requires tuning the image-texture tradeoff coefficients everywhere which internal noise 3) An ABX psychophysical evaluation where also rate growth our model match V1 for reference metamers between synthesized samples Our model also renders metamers roughly a second, presenting a ×1000 speed-up now allows tractable data-driven metamer experiments The history metamers originally through color matching theory a test light's wavelength until indistinguishable producing what This leads the definition visual metamerism when two physically different stimuli produceSee Motivated BID1 's work local texture matching the periphery as that explains visual crowding were the create such pointfixation driven metamers through such local texture matching models tile given log-polar pooling regions that simulate the V1 having global image statistics match the metamer with The essence their algorithm match the local texture BID22 ) image statistics throughout given fixation until thus producing toHowever metamerism research currently faces 2 main limitations that metamer rendering faces no unique solution Consider the potentially trivial examples having an image I and its metamer M where all pixel values identical which setmaking this difference the metameric response arises an imperceptible equal perturbation across as suggested BID16 ; BID7 This a concept similar Just Noticeable Differences BID21 BID5 ). However like the work BID7 ; creating pointfixation driven metamers create images preserve information yet lose spatial information such this loss unnoticeable contingent of The second issue that a full field view rendering a 512px × 512px metamer takes 6 hours roughly a This computational constraint makes data- There has with developing new metamer models: The SideEye model developed BID8 , uses in learns a Texture Tiling Model BID23 Their end model also feedforward like ours no use noise is incorporated the generation pipeline making their model fully At an advantage rather a limitation limits the biological plausilibility metameric response as the same input image should create. Another model which recently proposed the CNN synthesis model developed BID29 . The CNN synthesis model gradient-descent based closest in flavor their texture statistics provided a gramian matrix filter activations of multiple layers a VGGNet those used BID22 .The question the scaling parameter optimized metamerism still seems open This has questioned early BID23 , recently proposed and studied who suggest metamers driven image content bouma's lawscaling factor FIG3 suggests on it does seem α must increase proportion retinal eccentricity conditioned the image content each receptive field We believe the hyperparametric nature sheds reconciling Recall FIG0 , found certain images pushed stronger it texturized version versus others given their location the encoded space the local geometry projection This suggests the average maximal distortion one do fixed contingent allowed push further ( α some images more the direction lies closer the perceptual null spacemaking this difference un- This usually regions images periodic like skies grass Along elaborate in the Supplementary Material may potentially creating synthesized samples are metameric to each at the scales (V1;V2 but only generateds = are the reference imageOur model different othersFS and recently Wallis FORMULA0 ) given noise the computational pipeline The previously mentioned models used noise an initial seed the texture matching pipeline via gradient-descent while we texture distortion that directly crowding One could the same response achieved via both approaches our approach biologically at In our model an image fedsimulated through a deep-net corrupted noise that matches the texture propertiesvia AdaIN This perceptual representation perturbed along the texture-matched patch for each receptive field inverting such perturbed representation results a metamer. FIG7 illustrates such perturbations which produce metamers when projected via the locally linear embedding (LLE) algorithmRoweis Saul FORMULA1 Indeed the 10 encoded images do fully overlap to each quite distant as seen However foveated representations when perturbed texture-like noise seem finely tile might act biological regularizer human observers consistently making processing This suggests robust representations might achieved given its foveated nature does map perceptual space If this holds perceptually invariant data-augmentation schemes driven metamerism a useful enhancement artificial systems react oddly that exploit coarse perceptual mappingsGoodfellow FORMULA0 ; BID26 Berardino et FORMULA0 ).Understanding the underlying representations metamerism still In metameric responses via a foveated feed-forward style transfer network We find correctly such perturbationsa consequence internal noise that match texture representation in and inverting such encoded representation results a metamer. Though our model hyper we propose reduce via a perceptual optimization scheme Via a psychophysical we empirically find the critical scaling factor also matches the receptive fields V2s in BID7 when performing visual discrimination between synthesized metamers match similar . Finally while our choice texture statistics transfer is relu4_1 of a VGG19 and AdaIN respectively our ×1000-fold accelerated feed-forward metamer generation pipeline should extendible other models correctly texture/style This opens rapidly generating multiple flavors visual metamers applications neuroscience computer vision.6 Supplementary Material FIG0 : Reference Metamers at the scale s at they indiscriminable The color coding scheme matches the optimization Experiment the psychophysics All images used the experiments generated originally subtending 26 26 d.v.a (degrees visual angle for each α �� [ : DISPLAYFORM0 Compute metamer M NF (I 9end for 10Find each receptive field that: E(��-SSIM 2 . 11Fit the �� s (•) function collection α values 12endfor 13 end for Perform Permutation test �� s for 15 if � s independent 16 17 elsePerform regression of parameters f 19: DISPLAYFORM1 end if 21: end procedure",0.01,0.6259328988655564
"Past works have shown that, somewhat surprisingly, over-parametrization can help generalization in neural networks. Towards explaining this phenomenon, we adopt a margin-based perspective. We establish: 1) for multi-layer feedforward relu networks, the global minimizer of a weakly-regularized cross-entropy loss has the maximum normalized margin among all networks, 2) as a result, increasing the over-parametrization improves the normalized margin and generalization error bounds for deep networks. In the case of two-layer networks, an infinite-width neural network enjoys the best generalization guarantees. The typical infinite feature methods are kernel methods; we compare the neural net margin with that of kernel methods and construct natural instances where kernel methods have much weaker generalization guarantees. We validate this gap between the two approaches empirically. Finally, this infinite-neuron viewpoint is also fruitful for analyzing optimization. We show that a perturbed gradient flow on infinite-size networks finds a global optimizer in polynomial time. In deep learning, over-parametrization refers to the widely-adopted technique of using more parameters than necessary (Krizhevsky et al., 2012; Livni et al., 2014) . Both computationally and statistically, over-parametrization is crucial for learning neural nets. Controlled experiments demonstrate that over-parametrization eases optimization by smoothing the non-convex loss surface (Livni et al., 2014; Sagun et al., 2017) . Statistically, increasing model size without any regularization still improves generalization even after the model interpolates the data perfectly (Neyshabur et al., 2017b) . This is surprising given the conventional wisdom on the trade-off between model capacity and generalization.In the absence of an explicit regularizer, algorithmic regularization is likely the key contributor to good generalization. Recent works have shown that gradient descent finds the minimum norm solution fitting the data for problems including logistic regression, linearized neural networks, and matrix factorization (Soudry et al., 2018; BID17 Li et al., 2018; BID16 Ji & Telgarsky, 2018) . Many of these proofs require a delicate analysis of the algorithm's dynamics, and some are not fully rigorous due to assumptions on the iterates. To the best of our knowledge, it is an open question to prove analogous results for even two-layer relu networks. (For example, the technique of Li et al. (2018) on two-layer neural nets with quadratic activations still falls within the realm of linear algebraic tools, which apparently do not suffice for other activations.)We propose a different route towards understanding generalization: making the regularization explicit. The motivations are: 1) with an explicit regularizer, we can analyze generalization without fully understanding optimization; 2) it is unknown whether gradient descent provides additional implicit regularization beyond what 2 regularization already offers; 3) on the other hand, with a sufficiently weak 2 regularizer, we can prove stronger results that apply to multi-layer relu networks. Additionally , explicit regularization is perhaps more relevant because 2 regularization is typically used in practice.Concretely, we add a norm-based regularizer to the cross entropy loss of a multi-layer feedforward neural network with relu activations. We show that the global minimizer of the regularized objective achieves the maximum normalized margin among all the models with the same architecture, if the regularizer is sufficiently weak (Theorem 2.1). Informally, for models with norm 1 that perfectly classify the data, the margin is the smallest difference across all datapoints between the classifier score for the true label and the next best score. We are interested in normalized margin because its inverse bounds the generalization error (see recent work BID5 Neyshabur et al., 2017a; BID14 or Proposition 3.1). Our work explains why optimizing the training loss can lead to parameters with a large margin and thus, better generalization error (see Corollary 3.2). We further note that the maximum possible margin is non-decreasing in the width of the architecture, and therefore the generalization bound of Corollary 3.2 can only improve as the size of the network grows (see Theorem 3.3). Thus, even if the dataset is already separable, it could still be useful to increase the width to achieve larger margin and better generalization.At a first glance, it might seem counterintuitive that decreasing the regularizer is the right approach. At a high level, we show that the regularizer only serves as a tiebreaker to steer the model towards choosing the largest normalized margin. Our proofs are simple, oblivious to the optimization procedure, and apply to any norm-based regularizer. We also show that an exact global minimum is unnecessary: if we approximate the minimum loss within a constant factor, we obtain the max-margin within a constant factor (Theorem 2.2).To better understand the neural network max-margin, in Section 4 we compare the max-margin two-layer network obtained by optimizing both layers jointly to kernel methods corresponding to fixing random weights for the hidden layer and solving a 2-norm max-margin on the top layer. We design a simple data distribution ( FIG3 ) where neural net margin is large but the kernel margin is small. This translates to an Ω( √ d) factor gap between the generalization error bounds for the two approaches and demonstrates the power of neural nets compared to kernel methods. We experimentally confirm that a gap does indeed exist.In the setting of two-layer networks, we also study how over-parametrization helps optimization. Prior works (Mei et al., 2018; BID10 Sirignano & Spiliopoulos, 2018; Rotskoff & Vanden-Eijnden, 2018) show that gradient descent on two-layer networks becomes Wasserstein gradient flow over parameter distributions in the limit of infinite neurons. For this setting, we prove that perturbed Wasserstein gradient flow finds a global optimizer in polynomial time.Finally, we empirically validate several claims made in this paper. First, we confirm that neural networks do generalize better than kernel methods. Second, we show that for two-layer networks, the test error decreases and margin increases as the hidden layer grows, as predicted by our theory. Zhang et al. (2016) and Neyshabur et al. (2017b) show that neural network generalization defies conventional explanations and requires new ones. Neyshabur et al. (2014) initiate the search for the "" inductive bias"" of neural networks towards solutions with good generalization. Recent papers (Hardt et al., 2015; BID8 BID9 ) study inductive bias through training time and sharpness of local minima. Neyshabur et al. (2015a) propose a new steepest descent algorithm in a geometry invariant to weight rescaling and show that this improves generalization. Morcos et al. (2018) relate generalization in deep nets to the number of ""directions"" in the neurons. Other papers BID15 Soudry et al., 2018; Nacson et al., 2018; BID17 Li et al., 2018; BID16 ) study implicit regularization towards a specific solution. Ma et al. (2017) show that implicit regularization can help gradient descent avoid overshooting optima. Rosset et al. (2004a; b) study logistic regression with a weak regularization and show convergence to the max margin solution. We adopt their techniques and extend their results. We have made the case that maximizing margin is one of the inductive biases of relu networks obtained from optimizing weakly-regularized cross-entropy loss. Our framework allows us to directly analyze generalization properties of the network without considering the optimization algorithm used to obtain it. Using this perspective, we provide a simple explanation for why over-parametrization can improve generalization. It is a fascinating question for future work to characterize other generalization properties of the max-margin solution. On the optimization side, we make progress towards understanding over-parametrized gradient descent by analyzing infinite-size neural networks. A natural direction for future work is to apply our theory to optimize the margin of finite-sized neural networks. Proof. We will argue in the setting of Theorem 2.1 where L λ is the multi-class cross entropy loss, because the logistic loss case is analogous. We first note that L λ is continuous in Θ because f is continuous in Θ and the term inside the logarithm is always positive. DISPLAYFORM0 However, there must be a value Θ λ which attains inf Θ ≤M L λ (Θ), because {Θ : Θ ≤ M } is a compact set and L λ is continuous. Thus, inf Θ L λ (Θ) is attained by some Θ λ .",1830,1.175,1088,1.681985294117647,"Past works have, somewhat over-parametrization help generalization explaining this phenomenon adopt a margin-based perspective We establish: for multi-layer feedforward relu networks the global minimizer a weakly-regularized cross-entropy loss has the maximum normalized margin among as increasing improves the normalized margin and generalization error bounds deep networks. In two-layer networks an infinite-width neural network enjoys the best generalization guarantees The typical infinite feature methods kernel methods; we compare the neural net margin construct natural instances where have much weaker generalization guarantees We validate this gap empirically Finally this infinite-neuron viewpoint also fruitful analyzing optimization We show a perturbed gradient flow on infinite-size networks finds In deep learning refers more parameters necessary Livni . Both computationally and statistically, over-parametrization crucial learning neural nets Controlled experiments demonstrate over-parametrization eases optimization the non-convex loss surfaceLivni Sagun 2017 . Statistically increasing model size without any regularization still improves even interpolates perfectlyNeyshabur et al 2017b) . This surprising model capacity generalizationIn an explicit regularizer algorithmic regularization the key contributor Recent works that gradient descent finds the minimum norm solution fitting problems including linearized neural networks matrix factorizationSoudry 2018 BID17 Li Ji & Telgarsky . Many these proofs require a delicate analysis the algorithm's dynamics fully rigorous due assumptions on the iterates To prove analogous results even two-layer relu networks (For example technique Li (2018 on two-layer neural nets still falls linear algebraic tools apparently do suffice other activations.)We a different route towards generalization making regularization explicit The motivations: with an explicit regularizer analyze generalization without fully optimization unknown provides additional implicit regularization beyond 2 regularization already on with a sufficiently weak 2 regularizer prove stronger results apply multi-layer relu networks Additionally , explicit regularization perhaps relevant because 2 regularization typically practiceConcretely add the cross entropy loss of relu activations We show the global minimizer the regularized objective achieves the maximum normalized margin among if sufficiently weak (Theorem Informally for models norm 1 that perfectly classify the margin the smallest difference across between the classifier score for the true label the next best score We interested normalized margin because its inverse bounds the generalization errorsee recent work BID5 Neyshabur 2017a or Proposition Our work explains optimizing the training loss parameters with a large margin and thus errorsee Corollary We further the maximum possible margin non the width the architecture the generalization bound Corollary can improve as Theorem Thus even the dataset already separable could increase achieve larger margin and better generalizationAt decreasing the regularizer At show the regularizer only serves steer the model choosing the largest normalized margin Our proofs oblivious the optimization procedure apply any norm-based regularizer We also show an exact global minimum unnecessary: if approximate the minimum loss within a constant factor obtain the max-margin within better in Section compare obtained optimizing both layers jointly kernel methods corresponding fixing random weights solving on We design a simple data distribution ( FIG3 neural net margin large but the kernel margin This translates an ��( � d) factor gap the generalization error bounds demonstrates neural nets compared kernel methods We experimentally confirm a gap does indeedIn the setting two-layer networks also study helps optimization Prior works (Mei et 2018 BID10 Sirignano & Spiliopoulos Rotskoff Vanden-Eijnden show on two-layer networks becomes Wasserstein gradient flow over parameter distributions the limit infinite neurons For this setting prove perturbed Wasserstein gradient flow finds a global optimizerFinally validate several claims First confirm neural networks do generalize better kernel methods Second show for two-layer networks test error decreases and margin increases the hidden layer predicted our theory Zhang et al (2016 and Neyshabur et al (2017b show neural network generalization defies conventional explanations requires new ones Neyshabur et al (2014 initiate the search the "" inductive bias towards solutions Recent papers (Hardt BID8 BID9 ) study inductive bias through training time sharpness local minima Neyshabur et al (2015a propose a new steepest descent algorithm a geometry invariant to weight rescaling show improves Morcos (2018 relate generalization deep nets the number ""directions the neurons Other papers BID15 Soudry 2018 Nacson Li ) study implicit regularization towards a specific solution Ma et al (2017 show implicit regularization gradient descent avoid overshooting optima Rosset et (2004a; b) study logistic regression a weak regularization show convergence the max margin solution We adopt their techniques extend We made maximizing margin the inductive biases relu networks obtained optimizing weakly-regularized cross-entropy loss Our framework directly analyze generalization properties the network without considering algorithm obtain Using this perspective provide over-parametrization improve It future work characterize other generalization properties the max-margin solution On the optimization side make progress understanding by analyzing infinite-size neural networks A natural direction future work apply our theory optimize the margin finite-sized neural networks Proof. We will argue the setting Theorem where L �� the multi-class cross entropy loss because the logistic loss case analogous. We first note L �� continuous �� because f the term inside DISPLAYFORM0 However must a value �� �� attains inf �� ≤M L ��� because { : a compact set and continuous Thus inf �� L ��) attained .",0.01,0.4417177805227811
"We propose a distributed architecture for deep reinforcement learning at scale, that enables agents to learn effectively from orders of magnitude more data than previously possible. The algorithm decouples acting from learning: the actors interact with their own instances of the environment by selecting actions according to a shared neural network, and accumulate the resulting experience in a shared experience replay memory; the learner replays samples of experience and updates the neural network. The architecture relies on prioritized experience replay to focus only on the most significant data generated by the actors. Our architecture substantially improves the state of the art on the Arcade Learning Environment, achieving better final performance in a fraction of the wall-clock training time. A broad trend in deep learning is that combining more computation BID7 with more powerful models (Kaiser et al., 2017) and larger datasets BID8 ) yields more impressive results. It is reasonable to hope that a similar principle holds for deep reinforcement learning. There are a growing number of examples to justify this optimism: effective use of greater computational resources has been a critical factor in the success of such algorithms as Gorila (Nair et al., 2015) , A3C (Mnih et al., 2016) , GPU Advantage Actor Critic BID2 , Distributed PPO BID10 and AlphaGo (Silver et al., 2016) .Deep learning frameworks such as TensorFlow BID0 support distributed training, making large scale machine learning systems easier to implement and deploy. Despite this, much current research in deep reinforcement learning concerns itself with improving performance within the computational budget of a single machine, and the question of how to best harness more resources is comparatively underexplored.In this paper we describe an approach to scaling up deep reinforcement learning by generating more data and selecting from it in a prioritized fashion (Schaul et al., 2016) . Standard approaches to distributed training of neural networks focus on parallelizing the computation of gradients, to more rapidly optimize the parameters BID7 . In contrast , we distribute the generation and selection of experience data, and find that this alone suffices to improve results. This is complementary to distributing gradient computation, and the two approaches can be combined, but in this work we focus purely on data-generation.We use this distributed architecture to scale up variants of Deep Q-Networks (DQN) and Deep Deterministic Policy Gradient (DDPG), and we evaluate these on the Arcade Learning Environment benchmark BID4 , and on a range of continuous control tasks. Our architecture achieves a new state of the art performance on Atari games, using a fraction of the wall-clock time compared to the previous state of the art, and without per-game hyperparameter tuning.We empirically investigate the scalability of our framework, analysing how prioritization affects performance as we increase the number of data-generating workers. Our experiments include an analysis of factors such as the replay capacity, the recency of the experience, and the use of different data-generating policies for different workers. Finally, we discuss implications for deep reinforcement learning agents that may apply beyond our distributed framework. We have designed, implemented, and analyzed a distributed framework for prioritized replay in deep reinforcement learning. This architecture achieved state of the art results in a wide range of discrete and continuous tasks, both in terms of wall-clock learning speed and final performance.In this paper we focused on applying the Ape-X framework to DQN and DPG, but it could also be combined with any other off-policy reinforcement learning update. For methods that use temporally extended sequences (e.g., Mnih et al., 2016; BID10 , the Ape-X framework may be adapted to prioritize sequences of past experiences instead of individual transitions.Ape-X is designed for regimes in which it is possible to generate large quantities of data in parallel. This includes simulated environments but also a variety of real-world applications, such as robotic arm farms, self-driving cars, online recommender systems, or other multi-user systems in which data is generated by many instances of the same environment (c.f. Silver et al., 2013) . In applications where data is costly to obtain, our approach will not be directly applicable. With powerful function approximators, overfitting is an issue: generating more training data is the simplest way of addressing it, but may also provide guidance towards data-efficient solutions.Many deep reinforcement learning algorithms are fundamentally limited by their ability to explore effectively in large domains. Ape-X uses a naive yet effective mechanism to address this issue: generating a diverse set of experiences and then identifying and learning from the most useful events. The success of this approach suggests that simple and direct approaches to exploration may be feasible, even for synchronous agents.Our architecture illustrates that distributed systems are now practical both for research and, potentially, large-scale applications of deep reinforcement learning. We hope that the algorithms, architecture, and analysis we have presented will help to accelerate future efforts in this direction.Richard S Sutton and Andrew G Barto. fixed set of 6 values for . Blue: full range of values for . In both cases, the curve plotted is from a separate actor that does not add data to the replay memory, and which follows an -greedy policy with = 0.00164.",1042,0.481,613,1.699836867862969,"We propose a distributed architecture deep reinforcement learning at that enables agents effectively orders algorithm decouples acting learning: the actors interact their own instances the environment selecting actions according a shared neural network accumulate the resulting experience a shared experience replay memory; replays samples experience updates The architecture relies prioritized experience replay focus only generated the actors Our architecture substantially the state on the Arcade Learning Environment achieving better final performance the wall-clock training time A broad trend deep learning combining more computation BID7 more powerful modelsKaiser et al 2017 larger datasets ) yields It reasonable hope a similar principle holds deep reinforcement learning There examples to justify this optimism effective use greater computational resources has such algorithms GorilaNair , A3CMnih et GPU Advantage Actor Critic BID2 , Distributed PPO BID10 AlphaGoSilver .Deep frameworks TensorFlow BID0 support distributed training making easier deploy Despite this much current research in deep reinforcement learning concerns itself improving within the computational budget the question how to best harness more resources comparativelyIn scaling generating selecting from inSchaul . Standard approaches distributed training focus parallelizing gradients to more rapidly optimize the parameters BID7 . In contrast , distribute the generation and selection experience data find this alone suffices improve results This complementary distributing gradient computation, this work purely data-generationWe this distributed architecture scale variants Deep Q-Networks Deep Deterministic Policy Gradient evaluate on the Arcade Learning Environment benchmark BID4 , a range continuous control tasks Our architecture achieves a new state on Atari games using a fraction the wall-clock time compared the previous state without per hyperparameterWe empirically investigate our framework analysing prioritization as increase data-generating workers Our experiments include an analysis factors the replay capacity the experience different data-generating policies different workers Finally discuss implications deep reinforcement learning agents may apply beyond our distributed framework We designed, implemented analyzed a distributed framework prioritized replay in deep reinforcement learning This architecture achieved state discrete and continuous tasks both wall-clock learning speed final performanceIn focused applying the Ape-X framework DQN DPG, but it combined any other off-policy reinforcement learning update For methods temporally extended sequences Mnih et al 2016 BID10 , the Ape-X framework may adapted prioritize past experiences instead individual transitions. designed regimes it generate large quantities data This includes simulated environments but robotic arm farms online recommender systems or in data generated many instancesc.f Silver) . In applications data costly obtain our approach will not directly With powerful function approximators overfitting: generating more training data addressing may provide guidance towards data-efficient solutionsMany deep reinforcement learning algorithms fundamentally limited explore effectively in large domains Ape-X uses a naive yet effective mechanism address generating a diverse set experiences then identifying learning the most useful events The success this approach suggests simple and direct approaches exploration feasible synchronous agentsOur architecture illustrates distributed systems now practical both research, of We hope the algorithms, architecture analysis we presented accelerate future efforts this directionRichard S Sutton and Andrew G Barto. fixed set 6 values . Blue: full range values . In both cases the curve plotted from a separate actor that does add data the replay memory which follows an -greedy policy with = 0.00164",0.01,0.4872020220037415
"Designing neural networks for continuous-time stochastic processes is challenging, especially when observations are made irregularly. In this article, we analyze neural networks from a frame theoretic perspective to identify the sufficient conditions that enable smoothly recoverable representations of signals in L^2(R). Moreover, we show that, under certain assumptions, these properties hold even when signals are irregularly observed. As we converge to the family of (convolutional) neural networks that satisfy these conditions, we show that we can optimize our convolution filters while constraining them so that they effectively compute a Discrete Wavelet Transform. Such a neural network can efficiently divide the time-axis of a signal into orthogonal sub-spaces of different temporal scale and localization. We evaluate the resulting neural network on an assortment of synthetic and real-world tasks: parsimonious auto-encoding, video classification, and financial forecasting. The predominant assumption made in deep learning for time series analysis is that observations are made regularly, with the same duration of time separating each successive timestamps BID10 BID14 BID27 BID20 BID29 BID3 . However, this assumption is often inappropriate, as many real-world time series are observed irregularly and are, occasionally, event-driven (e.g., financial data, social networks, internet-of-things).One common approach in working with irregularly observed time series is to interpolate the observations to realign them to a regular time-grid. However , interpolation schemes may result in spurious statistical artifacts, as shown in BID17 BID4 . Fortunately , procedures for working with irregularly observed time series in their unaltered form have been devised, notably in the field of Gaussian-processes and kernel-learning BID17 BID4 and more recently in deep learning BID24 .In this article , we investigate the underlying representation of time series data as it is processed by a neural network. Our objective is to identify a class of neural networks that provably guarantee information preservation for certain irregularly observed signals. In doing so, we must analyze neural networks from a frame theoretic perspective, which has enabled a clear understanding of the impact discrete sampling has on representations of continuous-time signals BID7 BID5 BID6 BID13 BID15 BID22 .Although frame theory has historically been studied in the linear setting, recent work by BID26 has related frames with non-linear operators in Banach space, to what can be interpreted as non-linear frames. Here, we extend this generalization of frames to characterize entire families of neural networks. In doing so, we can show that the composition of certain non-linear neural layers (i.e., convolutions and fully-connected layers) form non-linear frames in L 2 (R), while others do not (i.e., recurrent layers).Moreover, frame theory can be used to analyze randomly-observed time series. In particular, when observations are made according to a family of self-exciting point processes known as Hawkes processes BID12 . We prove that such processes, under certain assumptions of stability, almost surely yield non-linear frames on a class of band-limited functions. That is to say , that despite having discrete and irregular observations, the signal of interest can still be smoothly recovered.As we obtain a family of convolutional neural networks that constitute non-linear frames, we show that under certain conditions, such networks can efficiently divide the time-axis of a time series into orthogonal sub-spaces of different temporal scale and localization. Namely, we optimize the weights of our convolution filters while constraining them so that they effectively compute a Discrete Wavelet Transform BID23 . Our numerical experiments on synthetic data highlight this unique capacity that allows neural networks to learn sparse representations of signals in L 2 (R), and how such a property is particularly powerful when training parsimoniously parameterized auto-encoders. Such auto-encoders learn optimal ways of compressing certain classes of input signals.Finally, we show that the ability of these networks to divide time series into a set sub-spaces, corresponding to different temporal scales and localization, can be composed with existing predictive frameworks to improve both accuracy and efficiency. This is demonstrated on real-world video classification and financial forecasting tasks. DISPLAYFORM0 We introduce the article with a theoretical analysis of the sufficient conditions on neural networks that enable smoothly recoverable representations of signals in L 2 (R) and prove that, under certain assumptions, this property holds true in the irregularly observed setting. In this article, we analyze neural networks from a frame theoretic perspective. In doing so, we come to the conclusion that by considering time series as an irregularly observed continuous-time stochastic processes, we are better able to devise robust and efficient convolutional neural networks. By leveraging recent contributions to frame theory, we prove properties about non-linear frames that allow us to make guarantees over an entire class of convolutional neural networks. Particularly regarding their capacity to produce discrete representations of continuous time signals that are both injective and bi-Lipschitz. Moreover, we show that, under certain conditions, these properties almost certainly hold, even when the signal is irregularly observed in an event-driven manner. Finally, we show that bounded-output recurrent neural networks do not satisfy the sufficient conditions to yield non-linear frames.This article is not limited to the theoretical statements it makes. In particular, we show that we can build a convolutional neural network that effectively computes a Discrete Wavelet Transform. The network's filters are dynamically learned while being constrained to produce outputs that preserve both orthogonality and the properties associated with non-linear frames. Our numerical experiments on real-world prediction tasks further demonstrate the benefits of such neural networks. Notably, their ability to produce compact representations that allow for efficient learning on latent continuous-time stochastic processes.",1143,0.563,695,1.6446043165467625,"Designing neural networks observations irregularly In analyze neural networks a frame theoretic perspective identify the sufficient conditions smoothly recoverable representations signals L^2(R Moreover we show under these properties hold signals irregularly observed As converge the family (convolutional) neural networks satisfy show optimize our convolution filters while constraining so effectively compute a Discrete Wavelet Transform Such a neural network efficiently divide the time-axis of different temporal scale localization We evaluate the resulting neural network on an assortment: auto video classification financial forecasting The predominant assumption made deep learning for observations made regularly the same duration separating each successive timestamps BID10 BID14 BID27 BID20 BID29 BID3 . However this assumption inappropriate many real-world time series observed irregularly, occasionally internet-of-things).One common approach in working realign a regular time-grid However , interpolation schemes result spurious statistical artifacts BID17 BID4 Fortunately , procedures working irregularly observed time series their unaltered form devised notably Gaussian-processes kernel-learning BID17 BID4 more deep learning BID24 .In investigate the underlying representation as it processed Our objective identify a class provably guarantee information preservation certain irregularly observed signals In doing analyze neural networks from a frame theoretic perspective enabled a clear understanding the impact discrete sampling representations continuous-time signals BID7 BID5 BID6 .Although frame theory historically studied the linear setting BID26 related frames non-linear operators Banach space to what can interpreted Here extend this generalization frames characterize entire families In doing show the composition certain non-linear neural layers fully-connected layers form L 2R others recurrent layers).Moreover frame theory analyze randomly-observed time series In particular when observations according a family self-exciting point processes known Hawkes processes BID12 . We prove such processes, under stability almost surely yield non-linear frames on a class band-limited functions That to , despite discrete and irregular observations the signal interest still smoothly recoveredAs obtain a family constitute non-linear frames show under such networks efficiently divide the time-axis of different temporal scale localization Namely we optimize the weights our convolution filters while constraining effectively compute a Discrete Wavelet Transform BID23 . Our numerical experiments synthetic data highlight this unique capacity that sparse representations signals L 2R how such a property particularly powerful training parsimoniously parameterized auto-encoders Such auto-encoders learn optimal ways compressing certain classes input signalsFinally these networks divide time series a set sub corresponding localization composed with existing predictive frameworks to both accuracy This demonstrated on real-world video classification and financial forecasting tasks DISPLAYFORM0 We introduce the article with a theoretical analysis the sufficient conditions on neural networks smoothly recoverable representations signals L 2R prove, under certain assumptions this property holds the irregularly observed setting In analyze neural networks a frame theoretic perspective In doing come by considering time series an irregularly observed continuous-time stochastic processes better devise By leveraging recent contributions frame theory prove properties about non-linear frames allow make guarantees over an entire class Particularly regarding their capacity produce discrete representations continuous time signals that both injective and bi-Lipschitz. Moreover we show under these properties almost hold, the signal irregularly observed Finally show bounded-output recurrent neural networks do satisfy the sufficient conditions yield non-linear framesThis article limited the theoretical statements it In particular show we build effectively a Discrete Wavelet Transform The network's filters dynamically learned while being constrained produce outputs preserve both orthogonality the properties associated non-linear frames Our numerical experiments real-world prediction tasks further Notably, their ability produce compact representations that efficient learning on latent continuous-time stochastic processes.",0.01,0.34647433392894667
"Most state-of-the-art neural machine translation systems, despite being different
 in architectural skeletons (e.g., recurrence, convolutional), share an indispensable
 feature: the Attention. However, most existing attention methods are token-based
 and ignore the importance of phrasal alignments, the key ingredient for the success
 of phrase-based statistical machine translation. In this paper, we propose
 novel phrase-based attention methods to model n-grams of tokens as attention
 entities. We incorporate our phrase-based attentions into the recently proposed
 Transformer network, and demonstrate that our approach yields improvements of
 1.3 BLEU for English-to-German and 0.5 BLEU for German-to-English translation
 tasks, and 1.75 and 1.35 BLEU points in English-to-Russian and Russian-to-English translation tasks 
 on WMT newstest2014 using WMT’16 training data.
 Neural Machine Translation (NMT) has established breakthroughs in many different translation tasks, and has quickly become the standard approach to machine translation. NMT offers a simple encoder-decoder architecture that is trained end-to-end. Most NMT models (except a few like BID5 and BID4 ) possess attention mechanisms to perform alignments of the target tokens to the source tokens. The attention module plays a role analogous to the word alignment model in Statistical Machine Translation or SMT BID9 . In fact, the Transformer network introduced recently by BID19 achieves state-of-the-art performance in both speed and BLEU scores BID12 by using only attention modules.On the other hand, phrasal interpretation is an important aspect for many language processing tasks, and forms the basis of Phrase-Based Machine Translation BID9 . Phrasal alignments BID10 can model one-to-one, one-to-many, many-to-one, and many-to-many relations between source and target tokens, and use local context for translation. They are also robust to non-compositional phrases. Despite the advantages, the concept of phrasal attentions has largely been neglected in NMT, as most NMT models generate translations token-by-token autoregressively, and use the token-based attention method which is order invariant. Therefore, the intuition of phrase-based translation is vague in existing NMT systems that solely depend on the underlying neural architectures (recurrent, convolutional, or self-attention) to incorporate contextual information. However, the information aggregation strategies employed by the underlying neural architectures provide context-relevant clues only to represent the current token, and do not explicitly model phrasal alignments. We argue that having an explicit inductive bias for phrases and phrasal alignments is necessary for NMT to exploit the strong correlation between source and target phrases.In this paper, we propose phrase-based attention methods for phrase-level alignments in NMT. Specifically, we propose two novel phrase-based attentions, namely CONVKV and QUERYK, designed to assign attention scores directly to phrases in the source and compute phrase-level attention vector for the target. We also introduce three new attention structures, which apply these methods to conduct phrasal alignments. Our homogeneous and heterogeneous attention structures perform token-to-token and token-to-phrase mappings, while the interleaved heterogeneous attention structure models all token-to-token, token-to-phrase, phrase-to-token, and phrase-to-phrase alignments.To show the effectiveness of our approach, we apply our phrase-based attention methods to all multi-head attention layers of the Transformer. Our experiments on WMT'14 translation tasks show improvements of up to 1.3 and 0.5 BLEU points for English-to-German and German-to-English respectively, and up to 1.75 and 1.35 BLEU points for English-to-Russian and Russian-to-English respectively, compared to the baseline Transformer network trained in identical settings.",770,0.351,475,1.6210526315789473,"Most stateof neural machine translation despite different architectural skeletons ( recurrence share an indispensable feature the Attention. However most existing attention methods token ignore the importance phrasal alignments, the key ingredient the success phrase-based statistical machine translation In this paper novel phrase-based attention methods model n tokens as attention entities We incorporate our phrase-based attentions the recently proposed Transformer network demonstrate yields improvements of 1.3 BLEU for EnglishtoGerman and points in on WMT newstest2014 using WMT��16 training data Neural Machine Translation has established breakthroughs many different translation tasks quickly NMT offers a simple encoder-decoder architecture trained end Most NMT models (except a like BID5 ) possess attention mechanisms to perform alignments the target tokens the source tokens The attention module plays analogous the word alignment model Statistical Machine Translation or SMT BID9 . In fact the Transformer network introduced recently BID19 achieves state both speed BLEU scores BID12 by only attention modulesOn phrasal interpretation many language processing tasks forms Phrase-Based Machine Translation BID9 . Phrasal alignments BID10 can model source target tokens use local context for translation They also robust to non-compositional phrases Despite the advantages the concept phrasal attentions largely NMT most NMT models generate translations token-by autoregressively use the token-based attention method which order Therefore the intuition phrase-based translation vague in existing NMT systems that solely depend the underlying neural architectures (recurrent, selfattention incorporate However the information aggregation strategies employed the underlying neural architectures provide context-relevant clues only represent current token, do explicitly model phrasal alignments We argue having an explicit inductive bias for phrases phrasal alignments necessary NMT exploit the strong correlation source and target phrasesIn phrase-based attention methods phrase-level alignments Specifically propose two novel phrase-based attentions namely CONVKV QUERYK designed assign attention scores directly phrases the source and compute phrase-level attention vector for We also introduce three new attention structures apply these methods conduct phrasal alignments Our homogeneous and heterogeneous attention structures perform tokento and tokenphrase mappings while heterogeneous models all, phrasetoken alignmentsTo show the effectiveness apply our phrase-based attention methods all multi-head attention layers the Transformer Our experiments on WMT'14 translation tasks improvements up to 1.3 and 0.5 BLEU points Englishto respectively up compared the baseline Transformer network trained identical settings",0.0,0.2864667098593696
"Intuitively, unfamiliarity should lead to lack of confidence. In reality, current algorithms often make highly confident yet wrong predictions when faced with unexpected test samples from an unknown distribution different from training. Unlike domain adaptation methods, we cannot gather an ""unexpected dataset"" prior to test, and unlike novelty detection methods, a best-effort original task prediction is still expected. We compare a number of methods from related fields such as calibration and epistemic uncertainty modeling, as well as two proposed methods that reduce overconfident errors of samples from an unknown novel distribution without drastically increasing evaluation time: (1) G-distillation, training an ensemble of classifiers and then distill into a single model using both labeled and unlabeled examples, or (2) NCR, reducing prediction confidence based on its novelty detection score. Experimentally, we investigate the overconfidence problem and evaluate our solution by creating ""familiar"" and ""novel"" test splits, where ""familiar"" are identically distributed with training and ""novel"" are not. We discover that calibrating using temperature scaling on familiar data is the best single-model method for improving novel confidence, followed by our proposed methods. In addition, some methods' NLL performance are roughly equivalent to a regularly trained model with certain degree of smoothing. Calibrating can also reduce confident errors, for example, in gender recognition by 95% on demographic groups different from the training data. In machine learning and computer vision, the i.i.d. assumption, that training and test sets are sampled from the same distribution (henceforth ""familiar"" distribution), is so prevalent as to be left unwritten. In experiments, it is easy to satisfy the i.i.d. condition by randomly sampling training and test data from a single pool, such as photos of employees' faces. But in real-life applications, test samples are often sampled differently (e.g., faces of internet users) and may not be well-represented, if at all, by the training samples.Prior work BID24 has shown networks to be unreliable when tested on semantically unrelated input (e.g. feeding CIFAR into MNIST-trained networks), but users would not expect useful predictions on these data. However, we find this issue extends to semantically related input as well, such as gender classifiers applied to faces of older or younger people than those seen during training, which is a more common occurrence in practice and more problematic from a user's perspective. We demonstrate that, counter to the intuition that unfamiliarity should lead to lack of confidence, current algorithms (deep networks) are more likely to make highly confident wrong predictions when faced with such ""novel"" samples, both for real-world image datasets (Figure 1 ; see caption) and for toy datasets FIG1 ; see subcaption 2(a) and Appendix A). The reason is simple: the classification function, such as a deep network, is undefined or loosely regulated for areas of the feature space that are unobserved in training, so the learner may extrapolate wildly without penalty.Confident errors on novel samples can be catastrophic. Whether one would ride in a self-driving car with a 99.9% accurate vision system, probably depends on how well-behaved the car is on the 0.1% mistakes. When a trained model labeled a person as a gorilla BID52 , the public trust in that system was reduced. When a driving vision system confidently mistook a tractor trailer BID50 , a person died. Scholars that study the impact of AI on society consider differently distributed samples to be a major risk BID47 : ""This is one form of epistemic Novel herptile, model: 99.4% bird (ours: 76.5%) Novel fish, model: 99.0% bird (ours: 92.0%)Figure 1: Deep networks can often make highly confident mistakes when samples are drawn from outside the distribution observed during training. Shown are example images that have ages, breeds, or species that are not observed during training and are misclassified by a deep network model with high confidence. Using our methods (shown here is G-distillation, to distill an ensemble of networks on both training and unsupervised examples) makes fewer confident errors for novel examples, increasing the reliability of prediction confidence overall.uncertainty that is quite relevant to safety because training on a dataset from a different distribution can cause much harm."" Our trust in a system requires its ability to avoid confident errors.Unfortunately, these novel samples may differ from training in both expected and unexpected ways. This means gathering a set of ""unexpected"" training samples, though required by covariate shift and domain adaptation methods, becomes unviable BID47 . One may use novelty detection methods to identify novel samples at test time (to report an error or seek human guidance), but this may be insufficient. These ""outliers"" (e.g. underrepresented faces that users upload) are perfectly normal samples in the eyes of a user and they would reasonably expect a prediction. Also, human guidance may not be fast enough or affordable.In this paper, our aim is to reduce confident errors for predictions on samples from a different (often non-overlapping) but unknown distribution (henceforth ""novel"" distribution). In contrast with most recent work, we focus on the confidence of the prediction rather than only the most likely prediction (accuracy) or the confidence ordering (average precision or ROC). In addition to reviewing the effectiveness of established methods, we propose and evaluate two ideas that are straightforward extensions to ensemble and rejection methods. One is that multiple learners, with different initializations or subsamples of training data, may make different predictions on novel data (see BID24 ). Hence, ensembles of classifiers tend to be better behaved. But ensembles are slow to evaluate. If we distill BID18 an ensemble into a single model using the training data, the distilled classifier will have the original problem of being undefined for novel areas of the feature space. Fortunately, it is often possible to acquire many unlabeled examples, such as faces from a celebrity dataset. By distilling the ensemble on both the training set and on unsupervised examples, we can produce a single model that outperforms, in terms of prediction confidence, single and standard distilled models on both identically and differently distributed samples.Another idea is that if the training set does not provide enough information for the unseen data, therefore it may be desired to simply avoid confident predictions. We can lower their confidence according to the output of an off-the-shelf novelty detector. This means reducing confident errors by reducing confidence, regardless of correctness. It may improve novel sample prediction quality, but in turn degrade performance on familiar samples. Although this idea sounds like a natural extension to novelty detection, we are unaware of any implementation or analysis in the literature.Experimentally, we investigate the confidence problem and perform an extensive study by creating ""familiar"" and ""novel"" test splits, where ""familiar"" are identically distributed with training and (a) Demonstration of deep networks' generalization behavior with a 2-dimensional toy dataset ""square"". Column 1: we design a binary ground truth for classification on a 2-dimensional feature space. Column 2: for training, we only provide samples on the left and lower portions (the ""familiar"" distribution), and reserve the upper-right only for testing (the ""novel"" distribution). Column 3-7: we show negative log likelihood (NLL) predicted for each point in the feature space. A small NLL indicates correct prediction, while a very large NLL indicates a confident error. Column 3, 4: multiple runs of the network have similar performances on familiar regions but vary substantially in novel regions where the training data imposes little or no regulation, due to optimization randomness. Column 5: an ensemble of 10 such networks can smooth the predictions and reduce confident errors at the sacrifice of test efficiency. Column 6: distilling the ensemble using the training samples results in the same irregularities as single models. Column 7: one of our proposals is to distill the ensemble into a single model using both the labeled training data and unsupervised data from a ""general"" distribution. ""novel"" are not. For example, in cat vs. dog classification, the novel examples are from breeds not seen during training, or in gender classification, the novel examples are people that are older or younger than those seen during training. Our evaluation focuses on negative log likelihood (NLL) and the fraction of highly confident predictions that are misclassified (""E99""). They measure both prediction accuracy and how often confident errors occur. To summarize, our contributions are:• Draw attention to a counter-intuitive yet important problem of highly confident wrong predictions when samples are drawn from a unknown distribution that is different than training.• Evaluate and compare the effectiveness of methods in related fields, including two proposed methods to reduce such overconfident errors.• Propose an experimental methodology to study the problem by explicitly creating familiar and novel test splits and measuring performance with NLL and E99. In this paper, we draw attention to the importance of minimizing harm from confident errors in unexpected novel samples different from training. We propose an experiment methodology to explicitly study generalization issues with unseen novel data, and compare methods from several related fields. We propose two simple methods that use an ensemble and distillation to better regularize network behavior outside the training distribution, or reduce confidence on detected novel samples, and consequently reduce confident errors. For future work, it can be beneficial to investigate the ability to handle adversarial examples using this framework, and improve calibration with unexpected novel samples taken into account.",1959,0.947,1115,1.75695067264574,"Intuitively unfamiliarity should lack In reality current algorithms often highly confident yet wrong predictions faced unexpected test samples different training Unlike domain adaptation methods gather an ""unexpected dataset prior test unlike novelty detection methods a best-effort original task prediction still expected We compare methods from related fields calibration epistemic uncertainty modeling two proposed methods reduce overconfident errors of samples an unknown novel distribution without drastically increasing evaluation time training an ensemble classifiers then distill into reducing prediction confidence based its novelty detection score Experimentally investigate the overconfidence problem evaluate our solution creating "" are identically with training We discover calibrating using temperature scaling on familiar data the best single-model method improving novel confidence, followed our proposed methods In some methods' NLL performance roughly a regularly trained model certain degree Calibrating can reduce confident errors for gender recognition 95% on demographic groups different the training data In machine learning the i.i.d. assumption, training and test sets sampledhenceforth ""familiar"" distribution so prevalent left In experiments it easy satisfy randomly sampling training such photos employees' faces But real-life applications test samples sampled differently (, faces internet users well, if by the training samplesPrior work BID24 networks unreliable semantically unrelated input feeding CIFAR into users would expect useful predictions However we find this issue extends semantically related input as gender classifiers applied faces than seen training practice more problematic from We demonstrate counter unfamiliarity should lack confidence current algorithms (deep networks make highly confident wrong predictions faced such ""novel"" samples bothFigure ; caption toy datasets FIG1 ; subcaption The reason the classification function such a deep network undefined or loosely regulated for areas the feature space unobserved training extrapolate wildly penaltyConfident errors on novel samples catastrophic Whether one would ride with probably depends- on the 0.1% mistakes When a trained model labeled a gorilla BID52 , the public trust that system When a driving vision system confidently mistook BID50 , a person died Scholars that AI consider differently distributed samples to BID47 : "" one form epistemic Novel herptile, model: 99.4% bird (ours: Novel fish model 92.0%)Figure Deep networks can often make highly confident mistakes when samples drawn outside observed during training Shown example images ages breeds observed during training misclassified a deep network model with Using our methods (shown is G-distillation to an ensemble networks on both training unsupervised examples makes fewer confident errors for novel examples increasing prediction confidence overall.uncertainty that quite relevant safety because training on from much harm Our trust a system requires its ability avoid confident errorsUnfortunately these novel samples differ training This means gathering ""unexpected"" training samples though required covariate shift and domain adaptation methods becomes BID47 . One may use novelty detection methods novel samples at test timeto report seek human guidance insufficient These ""outliers (e.g. underrepresented faces that users upload perfectly normal samples in would reasonably a prediction Also human guidance may fast affordableIn our aim reduce confident errors for predictions on samples different (often but unknown distribution In contrast most recent work the confidence rather only the most likely predictionaccuracy orderingaverage precision ROC In reviewing established methods propose and two ideas straightforward extensions ensemble rejection One is multiple learners different initializations or subsamples make novel data BID24 Hence ensembles classifiers tend better behaved But ensembles slow evaluate If distill BID18 an ensemble into using the distilled classifier the original problem being undefined novel areas Fortunately often acquire many unlabeled examples faces a celebrity dataset By distilling the ensemble on both the training set unsupervised examples produce, prediction confidence single and standard distilled models identically and differently distributedAnother idea does the unseen data therefore desired simply avoid confident predictions We lower their confidence according the output an off novelty detector This means reducing confident errors confidence, regardless correctness It may improve novel sample prediction quality turn degrade familiar samples Although this idea sounds novelty detection unaware analysisExperimentally investigate the confidence problem perform by creating "" are identically with training (a) Demonstration deep networks' generalization behavior a 2-dimensional toy dataset ""square Column 1 we design a binary ground truth classification on Column 2 for training only provide samples on the left and lower portions (the ""familiar"" distribution reserve only testing Column 3- we show negative log likelihood (NLL predicted each point the feature space A small NLL indicates correct prediction a confident error Column 3 4 multiple runs the network have similar performances familiar regions vary novel regions where imposes due optimization randomness Column 5 an ensemble 10 such networks can smooth the predictions reduce confident errors at the sacrifice test efficiency Column 6 distilling the ensemble using the training samples results the same irregularities single models Column 7 one our proposals distill the ensemble using both the labeled training data a ""general"" distribution ""novel are. For example cat dog classification the novel examples from breeds not seen during training gender classification people older Our evaluation focuses negative log likelihood the fraction highly confident predictions misclassifiedE99 They measure both prediction accuracy how often confident errors To summarize our contributions are:• Draw attention a counter highly confident wrong predictions when samples a unknown distribution different compare methods related fields two proposed methods reduce such overconfident by explicitly creating familiar and novel test splits measuring performance NLL E99 In draw minimizing harm confident errors unexpected novel samples different training We propose an experiment methodology explicitly study generalization issues unseen novel data compare methods from several related fields We propose two simple methods use an ensemble and distillation better regularize network behavior outside the training distribution or reduce confidence on detected novel samples consequently confident errors For future work it beneficial investigate handle adversarial examples this framework improve calibration with unexpected novel samples taken into",0.01,0.6327229786262207
"Progress in deep learning is slowed by the days or weeks it takes to train large models. The natural solution of using more hardware is limited by diminishing returns, and leads to inefficient use of additional resources. In this paper, we present a large batch, stochastic optimization algorithm that is both faster than widely used algorithms for fixed amounts of computation, and also scales up substantially better as more computational resources become available. Our algorithm implicitly computes the inverse Hessian of each mini-batch to produce descent directions; we do so without either an explicit approximation to the Hessian or Hessian-vector products. We demonstrate the effectiveness of our algorithm by successfully training large ImageNet models (InceptionV3, ResnetV1-50, ResnetV1-101 and InceptionResnetV2) with mini-batch sizes of up to 32000 with no loss in validation error relative to current baselines, and no increase in the total number of steps. At smaller mini-batch sizes, our optimizer improves the validation error in these models by 0.8-0.9\%. Alternatively, we can trade off this accuracy to reduce the number of training steps needed by roughly 10-30\%. Our work is practical and easily usable by others -- only one hyperparameter (learning rate) needs tuning, and furthermore, the algorithm is as computationally cheap as the commonly used Adam optimizer. Large deep neural networks trained on massive data sets have led to major advances in machine learning performance BID21 ). Current practice is to train networks using gradient descent (SGD) and momentum optimizers, along with natural-gradient-like methods BID16 ; Zeiler (2012); BID10 ; BID20 ). As distributed computation availability increases, total wall-time to train large models has become a substantial bottleneck, and approaches that decrease total wall-time without sacrificing model generalization are very valuable.In the simplest version of mini-batch SGD, one computes the average gradient of the loss over a small set of examples, and takes a step in the direction of the negative gradient. It is well known that the convergence of the original SGD algorithm BID28 ) has two terms, one of which depends on the variance of the gradient estimate. In practice, decreasing the variance by increasing the batch size suffers from diminishing returns, often resulting in speedups that are sublinear in batch size, and even worse, in degraded generalization performance BID19 ). Some recent work BID12 ; BID40 b) ) suggests that by carefully tuning learning rates and other hyperparameter schedules, it is possible to train architectures like ResNets and AlexNet on Imagenet with large mini-batches of up to 8192 with no loss of accuracy, shortening training time to hours instead of days or weeks.There have been many attempts to incorporate second-order Hessian information into stochastic optimizers (see related work below). Such algorithms either explicitly approximate the Hessian (or its inverse), or exploit the use of Hessian-vector products. Unfortunately, the additional computational cost and implementation complexity often outweigh the benefit of improved descent directions. Con-sequently, their adoption has been limited, and it has largely been unclear whether such algorithms would be successful on large modern machine learning tasks.In this work, we attack the problem of training with reduced wall-time via a novel stochastic optimization algorithm that uses (limited) second order information without explicit approximations of Hessian matrices or even Hessian-vector products. On each mini-batch, our algorithm computes a descent direction by solving an intermediate optimization problem, and inverting the Hessian of the mini-batch. Explicit computations with Hessian matrices are extremely expensive, so we develop an inner loop iteration that applies the Hessian inverse without explicitly representing the Hessian, or computing a Hessian vector product. The key ingredients in this iteration are the Neumann series expansion for the matrix inverse, and an observation that allows us to replace each occurrence of the Hessian with a single gradient evaluation.We conduct large-scale experiments using real models (Inception-V3, Resnet-50, Resnet-101, Inception-Resnet-V2) on the ImageNet dataset. Compared to recent work, our algorithm has favourable scaling properties; we are able to obtain linear speedup up to a batch size of 32000, while maintaining or even improving model quality compared to the baseline. Additionally, our algorithm when run using smaller mini-batches is able to improve the validation error by 0.8-0.9% across all the models we try; alternatively, we can maintain baseline model quality and obtain a 10-30% decrease in the number of steps. Our algorithm is easy to use in practice, with the learning rate as the sole hyperparameter. In this paper, we have presented a large batch optimization algorithm for training deep neural nets; roughly speaking, our algorithm implicitly inverts the Hessian of individual mini-batches. Our algorithm is practical, and the only hyperparameter that needs tuning is the learning rate. Experimentally, we have shown the optimizer is able to handle very large mini-batch sizes up to 32000 without any degradation in quality relative to current baseline models. Intriguingly, at smaller mini-batch sizes, the optimizer is able to produce models that generalize better, and improve top-1 validation error by 0.8-0.9% across a variety of architectures with no attendant drop in the classification loss.We believe the latter phenomenon is worth further investigation, especially since the Neumann optimizer does not improve the training loss. This indicates that, somehow, the optimizer has found a different local optimum. We think that this confirms the general idea that optimization and generalization can not be decoupled in deep neural nets.Matthew D Zeiler. Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701, 2012.",1183,0.548,683,1.7320644216691068,"Progress deep learning slowed the days or large models The natural solution of using more hardware limited diminishing leads In this paper a large batch, both faster widely algorithms fixed amounts computation scales substantially better as Our algorithm implicitly the inverse Hessian each minibatch to descent directions; without either an explicit approximation Hessian-vector products We demonstrate our algorithm successfully training large ImageNet modelsInceptionV3 ResnetV1-50101 mini-batch sizes 32000 with no loss validation error relative current baselines no increase steps At smaller mini-batch sizes our optimizer improves the validation error these models Alternatively we trade off this accuracy reduce training steps by roughly 10-30\% Our work practical easily usable by others -- only one hyperparameter (learning rate needs tuning furthermore as computationally cheap the commonly used Adam optimizer Large deep neural networks trained led machine learning performance BID21 ). Current practice train networks gradient descentSGD momentum optimizers along natural-gradient-like methods BID16 ; Zeiler BID10 As distributed computation availability increases total wall-time to train large models approaches decrease without sacrificing model generalization very valuableIn the simplest version mini-batch SGD one computes the average gradient the loss over examples takes the negative gradient It well the convergence the original SGD algorithm BID28 ) two terms one depends the variance the gradient estimate In practice decreasing the variance by increasing suffers diminishing often speedups sublinear batch size even in degraded generalization performance BID19 ). Some recent work BID12 ; b) ) suggests by carefully tuning learning rates other hyperparameter schedules train architectures like ResNets AlexNet on Imagenet with large minibatches up 8192 with shortening hours insteadThere incorporate second-order Hessian information stochastic optimizers related work below Such algorithms either explicitly approximate the Hessian ( its inverse exploit the use Hessian-vector products Unfortunately the additional computational cost and implementation complexity often improved descent directions Con-sequently their adoption limited largely unclear such algorithms successful on large modern machine learning tasksIn attack training with reduced wall-time via (limited second information without Hessian matrices even Hessian-vector products On each minibatch our algorithm a descent direction solving an intermediate optimization problem inverting the Hessian the mini Explicit computations with Hessian matrices extremely expensive develop an inner loop iteration applies inverse without explicitly representing, computing The key ingredients this iteration the Neumann series expansion for the matrix inverse an observation allows replace each occurrence the Hessian a single gradient evaluationWe conduct real models (Inception-V3 Resnet-50 the ImageNet dataset Compared recent work our algorithm favourable scaling properties; obtain linear speedup up a batch size 32000 or model quality compared the baseline Additionally our algorithm when run using smaller minibatches improve the validation error by across try; alternatively maintain baseline model quality obtain steps Our algorithm easy in practice the learning rate as the sole hyperparameter In this paper have presented a large batch optimization training deep neural nets; roughly speaking implicitly inverts individual minibatches Our algorithm practical the only hyperparameter tuning Experimentally the optimizer handle very large mini-batch sizes up 32000 without quality relative current baseline models at smaller mini-batch sizes the optimizer produce models generalize improve top-1 validation error by across architectures with no attendant drop the classification lossWe believe the latter phenomenon worth further the Neumann optimizer does improve the training loss This indicates, somehow the optimizer found a different local optimum We think confirms optimization not deep neural netsMatthew D Zeiler. Adadelta: an adaptive learning rate method, 2012",0.01,0.5693149976198629
"Recent work has shown that performing inference with fast, very-low-bitwidth
 (e.g., 1 to 2 bits) representations of values in models can yield surprisingly accurate
 results. However, although 2-bit approximated networks have been shown to
 be quite accurate, 1 bit approximations, which are twice as fast, have restrictively
 low accuracy. We propose a method to train models whose weights are a mixture
 of bitwidths, that allows us to more finely tune the accuracy/speed trade-off. We
 present the “middle-out” criterion for determining the bitwidth for each value, and
 show how to integrate it into training models with a desired mixture of bitwidths.
 We evaluate several architectures and binarization techniques on the ImageNet
 dataset. We show that our heterogeneous bitwidth approximation achieves superlinear
 scaling of accuracy with bitwidth. Using an average of only 1.4 bits, we are
 able to outperform state-of-the-art 2-bit architectures. With Convolutional Neural Nets (CNNs) now outperforming humans in vision classification tasks BID11 , it is clear that CNNs will be a mainstay of AI applications. However, CNNs are known to be computationally demanding, and are most comfortably run on GPUs. For execution in mobile and embedded settings, or when a given CNN is evaluated many times, using a GPU may be too costly. The search for inexpensive variants of CNNs has yielded techniques such as hashing BID0 , vector quantization BID4 , and pruning BID5 . One particularly promising track is binarization BID1 , which replaces 32-bit floating point values with single bits, either +1 or -1, and (optionally) replaces floating point multiplies with packed bitwise popcount-xnors . Binarization can reduce the size of models by up to 32×, and reduce the number of operations executed by up to 64×.Binarized CNNs are faster and smaller, but also less accurate. Much research has therefore focused on reducing the accuracy gap between binary models and their floating point counterparts. The typical approach is to add bits to the activations and weights of a network, giving a better approximation of the true values. However, the cost of extra bits is quite high. Using n bits to approximate just the weights increases the computation and memory required by a factor of n compared to 1-bit binarization. Further using n bits to approximate activations as well requires n 2 times the resources as one bit. There is thus a strong motivation to use as few bits as possible while still achieving acceptable accuracy. However, today's binary approximations are locked to use the same number of bits for all approximated values, and the gap in accuracy between bits can be substantial. For example, recent work concludes 1-bit accuracy is unsatisfactory while 2-bit accuracy is quite high BID12 (also see TAB0 ).In order to bridge the gap between integer bits, we introduce Heterogeneous Bitwidth Neural Networks (HBNNs), which use a mix of integer bitwidths to allow values to have effectively (i.e., on average) fractional bitwidths. The freedom to select from multiple bitwidths allows HBNNs to approximate each value better than fixed-bitwidth schemes, giving them disproportionate accuracy gains for the number of effective bits used. For instance, Alexnet trained with an average of 1.4 bits has comparable (actually, slightly higher) accuracy to training with a fixed two bits TAB0 .Our main contributions are:(1) We propose HBNNs as a way to break the integer-bitwidth barrier in binarized networks.(2) We study several techniques for distributing the bitwidths in a HBNN, and introduce the middle-out bitwidth selection algorithm, which uses the full representational power of heterogeneous bitwidths to learn good bitwidth distributions. (3) We perform a comprehensive study of heterogeneous binarization on the ImageNet dataset using an AlexNet architecture. We evaluate many fractional bitwidths and compare to state of the art results. HBNNs typically yield the smallest and fastest networks at each accuracy. Further, we show that it is usually possible to equal, or improve upon, 2-bitbinarized networks with an average of 1.4 bits. (4) We show that heterogeneous binarization is applicable to MobileNet BID6 , demonstrating that its benefits apply even to modern, optimized architectures. In this paper, we present Heterogeneous Bitwidth Neural Networks (HBNNs), a new type of binary network that is not restricted to integer bitwidths. Allowing effectively fractional bitwidths in networks gives a vastly improved ability to tune the trade-offs between accuracy, compression, and speed that come with binarization. We show a simple method of distributing bits across a tensor lead to a linear relationship between accuracy and number of bits, but using a more informed method allows higher accuracy with fewer bits. We introduce middle-out bit selection as the top performing technique for determining where to place bits in a heterogeneous bitwidth tensor and find that Middle-Out enables a heterogeneous representation to be more powerful than a homogeneous one. On the ImageNet dataset with AlexNet and MobileNet models, we perform extensive experiments to validate the effectiveness of HBNNs compared to the state of the art and full precision accuracy. The results of these experiments are highly compelling, with HBNNs matching or outperforming competing binarization techniques while using fewer average bits. The use of HBNNs enables applications which require higher compression and speeds offered by a low bitwidth but also need the accuracy of a high bitwidth. As future work, we will investigate modifying the bit selection method to make heterogeneous bit tensors more amenable for CPU computation as well as develop a HBNN FPGA implementation which can showcase both the speed and accuracy benefits of heterogeneous binarization.",1198,0.604,700,1.7114285714285715,"Recent work performing inference fast, very-low-bitwidth values models However although 2-bit approximated networks, twice restrictively low accuracy We propose train models whose weights a mixture bitwidths that allows more finely the accuracy/speed trade-off We present the ��middle-out�� criterion the bitwidth each value integrate training models a desired mixture We evaluate several architectures binarization techniques on We show our heterogeneous bitwidth approximation achieves superlinear scaling accuracy Using an average only 1.4 bits outperform state 2 architectures With Convolutional Neural Nets now outperforming humans vision classification tasks BID11 , However CNNs are known computationally demanding are most comfortably run For execution mobile and embedded settings or a given CNN evaluated many using too The search inexpensive variants CNNs yielded techniques such hashing BID0 , vector quantization BID4 pruning One particularly promising track binarization BID1 , replaces single bits either +1 ( replaces packed bitwise popcount-xnors Binarization can reduce models 32× operations executed up faster smaller also Much research therefore reducing the accuracy gap binary models their floating point counterparts The typical approach add bits the activations weights a network giving However the cost extra bits quite Using n bits approximate just the weights increases and memory required a factor n compared 1-bit binarization Further using n bits approximate activations as requires n 2 times the resources as one bit There thus use as few bits while achieving acceptable accuracy However today's binary approximations locked use all approximated values the gap accuracy bits can substantial For example recent work concludes 1-bit accuracy unsatisfactory while quite high BID12 (also TAB0 ).In bridge integer bits introduce Heterogeneous Bitwidth Neural Networks a mix integer bitwidths allow values have effectively ( on The freedom select multiple bitwidths HBNNs approximate each value better giving disproportionate accuracy gains effective bits For instance Alexnet trained an average 1.4 bits has comparable (actually, slightly higher) accuracy training a fixed two bits TAB0 .Our main contributions are:(1 We propose HBNNs break the integer-bitwidth barrier binarized networks.(2 study several techniques distributing a HBNN introduce the middle-out bitwidth selection algorithm the full representational power learn good bitwidth distributions (3 We perform heterogeneous binarization on the ImageNet dataset an AlexNet architecture We evaluate many fractional bitwidths compare to state HBNNs typically yield the smallest and fastest networks at each accuracy Further show it usually possible equal, improve 2-bitbinarized networks an average (4 We show heterogeneous binarization applicable MobileNet BID6 , demonstrating its benefits apply modern, optimized architectures In Heterogeneous Bitwidth Neural Networks binary network not restricted Allowing effectively fractional bitwidths networks gives a vastly improved ability tune accuracy compression that come binarization We show distributing bits across a tensor lead a linear relationship accuracy number but using a more informed method allows higher accuracy with We introduce middle-out bit selection as the top performing technique determining where bits a heterogeneous bitwidth tensor and find enables to more powerful On the ImageNet dataset with AlexNet and MobileNet models perform extensive experiments validate HBNNs compared the state and full precision accuracy The results these experiments highly compelling HBNNs matching or competing binarization techniques while fewer average bits The use HBNNs enables applications which higher compression speeds offered a low bitwidth but need the accuracy As future work, we investigate modifying the bit selection method heterogeneous bit tensors amenable CPU computation as develop a HBNN FPGA implementation which showcase accuracy benefits",0.01,0.5167366642529573
"Pruning units in a deep network can help speed up inference and training as well as reduce the size of the model. We show that bias propagation is a pruning technique which consistently outperforms the common approach of merely removing units,  regardless of the architecture and the dataset.   We also show how a simple adaptation to an existing scoring function allows us to select the best units to prune.   Finally,  we show that the units selected by the best performing scoring functions are somewhat consistent over the course of training, implying the dead parts of the network appear during the stages of training. Pruning is a successful method for reducing the size of a trained neural network and accelerating inference. Pruning consists of deleting the parts of the network whose removal least affects the network performance. Many pruning methods proposed in the literature differ in computational cost and in effectiveness in ways that are hard to assess.In an interesting recent work, BID3 argue for the so called ""winning ticket"" hypothesis. More precisely, they train a large network after saving the random initial value of each parameter. After training, they prune the large network to produce a smaller network with one fifth of the weights. Setting its weights to their saved initial values and retraining achieves a performance close to that of the large trained network with a much reduced computational cost. This result opens up a new frontier for pruning methods, where they are used to detect useless units early in the training and therefore accelerating the inference.This contribution studies the effect of pruning methods throughout the training process. We also present mean replacement, a unit pruning method that extends the idea of bias propagation introduced in (Ye et al., 2018) to the non-constrained training setting. The main observations of our work can then be summarized as follows:• Regardless of the scoring function used, bias propagation reduces the pruning penalty for networks without batch normalization.• Fine-tuning the pruned network with additional training iterations reduces the bias propagation advantage but not very quickly.• Absolute valued approximation of the pruning penalty provides superior performance over the normal first order approximation. This finding confirms the observations made by BID11 .• Units that are selected by the best performing scoring function seem to come from a small subset of units. This finding confirms BID3 's comments on the lottery ticket and BID2 's claims about dead units.The rest of the paper is organized as follows. After reviewing the related work in Section 2. we define our pruning methods and scoring functions in Section 3. Section 4 provides an empirical evaluation comparing various combinations of scoring functions and methods under varying pruning fractions, datasets, and models. We briefly provide some concluding remarks and discuss future work in Section 5. This work presents an experimental comparison of unit pruning strategies throughout the training process. We introduce the mean replacement approach and show that it substantially reduces the impact of the unit removal on the loss function. We also show that fine-tuning the pruned networks does not reduce the mean replacement advantage very quickly. We argue that direct first order approximation of the pruning penalty are poor predictors of the pruning penalty incurred by the simultaneous removal of multiple units because the neglected high order terms can become significant. In contrast the absolute value versions of these approximations achieve the best performance. Finally we provide some evidence showing that our best pruning methods identify a stable set of prunable units relatively early in the training process.This last observation begs for future work. Can we combine pruning and training in a manner that reduces the computational training cost to a quantity comparable to training the ""winning ticket"" network? If we decided that we will be using Mean Replacement as our pruning method, we can define a new scoring function, i.e. the first order Taylor approximation of the pruning penalty after mean replacement. We name this new saliency function as Mean Replacement Saliency (MRS) Let us parameterize the loss as a function with activations and write down the first order approximation of the absolute change in the loss. DISPLAYFORM0 where DISPLAYFORM1 If we were interested in the average change in the loss we can write down the Equation 5 without the absolute values. In other words approximations on absolute change penalizes both directions, emphasizing the change in the neural network itself rather then the loss function.",845,0.494,471,1.7940552016985138,"Pruning units a deep network speed inference training as We show bias propagation consistently merely removing units, regardless the architecture the dataset We also show a simple adaptation an existing scoring function allows select prune Finally show the units selected the best performing scoring functions somewhat consistent training implying the dead parts appear during the stages Pruning reducing accelerating inference Pruning consists deleting the parts whose removal least Many pruning methods proposed differ computational cost in effectiveness ways hardIn an interesting recent work BID3 argue the so called ""winning ticket"" hypothesis More precisely train a large network after saving the random initial value After training prune the large network to produce one fifth Setting its weights their saved initial values retraining achieves close the large trained network This result opens pruning methods where they detect useless units early therefore accelerating the inferenceThis contribution studies throughout We also present mean replacement, a unit pruning method extends bias propagation introduced (Ye 2018 The main observations can then Regardless the scoring function bias propagation reduces the pruning penalty networks without batch Fine additional training iterations but very quickly.• Absolute valued approximation provides the normal first order approximation This finding the observations BID11 .• Units that selected the best performing scoring function seem come units This finding BID3 's comments the lottery ticket and dead unitsThe rest organized After reviewing the related work Section we define our pruning methods scoring functions Section Section provides an empirical evaluation comparing various combinations scoring functions methods under varying pruning fractions datasets models We briefly provide some concluding remarks discuss future work Section This work presents unit pruning strategies throughout We introduce the mean replacement approach show substantially the unit removal the loss function We also show fine the pruned networks does reduce the mean replacement advantage very quickly We argue direct first order approximation the pruning penalty are incurred the simultaneous removal multiple units because the neglected high order terms become significant In contrast the absolute value versions achieve Finally provide some evidence showing our best pruning methods identify a stable set prunable units relativelyThis last observation begs for future work Can combine pruning training reduces the computational training cost a quantity comparable training the ""winning ticket"" network If decided will Mean Replacement as our pruning method define after We name this new saliency function Mean Replacement Saliency Let parameterize the loss as with activations write the first order approximation DISPLAYFORM0 where If we interested the average change the loss we write the Equation 5 without In other words approximations on absolute change penalizes both directions emphasizing the neural network itself then loss function",0.01,0.7272620586844106
"Due to the phenomenon of “posterior collapse,” current latent variable generative models pose a challenging design choice that either weakens the capacity of the decoder or requires altering the training objective. We develop an alternative that utilizes the most powerful generative models as decoders, optimize the variational lower bound, and ensures that the latent variables preserve and encode useful information. Our proposed δ-VAEs achieve this by constraining the variational family for the posterior to have a minimum distance to the prior. For sequential latent variable models, our approach resembles the classic representation learning approach of slow feature analysis. We demonstrate our method’s efficacy at modeling text on LM1B and modeling images: learning representations, improving sample quality, and achieving state of the art log-likelihood on CIFAR-10 and ImageNet 32 × 32. Deep latent variable models trained with amortized variational inference have led to advances in representation learning on high-dimensional datasets BID25 BID33 . These latent variable models typically have simple decoders, where the mapping from the latent variable to the input space is unimodal, for example using a conditional Gaussian decoder. This typically results in representations that are good at capturing the global structure in the input, but fail at capturing more complex local structure (e.g. texture BID28 ). In parallel, advances in autoregressive models have led to drastic improvements in density modeling and sample quality without explicit latent variables BID39 . While these models are good at capturing local statistics, they often fail to produce globally coherent structures BID30 .Combining the power of tractable densities from autoregressive models with the representation learning capabilities of latent variable models could result in higher-quality generative models with useful latent representations. While much prior work has attempted to join these two models, a common problem remains. If the autoregressive decoder is expressive enough to model the data density, then the model can learn to ignore the latent variables, resulting in a trivial posterior that collapses to the prior. This phenomenon has been frequently observed in prior work and has been referred to as optimization challenges of VAEs by BID5 , the information preference property by , and the posterior collapse problems by several others (e.g. van den BID40 BID14 . Ideally, an approach that mitigates posterior collapse would not alter the evidence lower bound (ELBO) training objective, and would allow the practitioner to leverage the most recent advances in powerful autoregressive decoders to improve performance. To the best of our knowledge , no prior work has succeeded at this goal. Most common approaches either change the objective BID20 BID1 Zhao et al., 2017; BID29 Goyal et al., 2017) , or weaken the decoder BID5 BID18 . Additionally, these approaches are often challenging to tune and highly sensitive to hyperparameters BID1 .In this paper, we propose δ-VAEs , a simple framework for selecting variational families that prevent posterior collapse without altering the ELBO training objective or weakening the decoder. By restricting the parameters or family of the posterior, we ensure that there is a minimum KL divergence, δ, between the posterior and the prior.We demonstrate the effectiveness of this approach at learning latent-variable models with powerful decoders on images (CIFAR-10, and ImageNet 32 × 32), and text (LM1B). We achieve state of the art log-likelihood results with image models by additionally introducing a sequential latent-variable model with an anti-causal encoder structure. Our experiments demonstrate the utility of δ-VAEs at learning useful representations for downstream tasks without sacrificing performance on density modeling. In this work, we have demonstrated that δ-VAEs provide a simple, intuitive, and effective solution to posterior collapse in latent variable models, enabling them to be paired with powerful decoders. Unlike prior work, we do not require changes to the objective or weakening of the decoder, and we can learn useful representations as well as achieving state-of-the-art likelihoods. While our work presents two simple posterior-prior pairs, there are a number of other possibilities that could be explored in future work. Our work also points to at least two interesting challenges for latentvariable models: (1) can they exceed the performance of a strong autoregressive baseline, and (2) can they learn representations that improve downstream applications such as classification? DISPLAYFORM0 B DERIVATION OF THE KL-DIVERGENCE BETWEEN AR(1) AND DIAGONAL GAUSSIAN, AND ITS LOWER-BOUND DISPLAYFORM1 Noting the analytic form for the KL-divergence for two uni-variate Gaussian distributions: DISPLAYFORM2 we now derive the lower-bound for KL-divergence. To avoid clutter we assume a single dimension per timestep but extend the results to the general multivariate case at the end of this section. DISPLAYFORM3 C DERIVATION OF THE LOWER-BOUND Removing non-negative quadratic terms involving µ i in equation 3 and expanding back f inside the summation yields DISPLAYFORM4 Consider f a (x) = ax − ln(x) − 1 and its first and second order derivatives, f a (x) = a − 1 x and f a (x) ≥ 0. Thus, f a is convex and obtains its minimum value of ln(a) at x = a −1 . Substituting σ DISPLAYFORM5 When using multi-dimensional z i at each timestep, the committed rate is the sum of the KL for each individual dimension: DISPLAYFORM6 The most common choice for variational families is to assume that the components of the posterior are independent, for example using a multivariate Gaussian with a diagonal covariance: q φ (z|x) = N (z; µ q (x), σ q (x)). When paired with a standard Gaussian prior, p(z) = N (z; 0, 1), we can guarantee a committed information rate δ by constraining the mean and variance of the variational family (see Appendix C) DISPLAYFORM7 We can, thus, numerically solve DISPLAYFORM8 where the above equation has a solution for µ q , and the committed rate δ. Posterior parameters can thus be parameterised as: DISPLAYFORM9 Where φ parameterises the data-dependent part of µ q ad σ q , which allow the rate to go above the designated lower-bound δ.We compare this model with the temporal version of δ-VAE discussed in the paper and report the results in Table 3 . While independent δ-VAE also prevents the posterior from collapsing to prior, its performance in density modeling lags behind temporal δ-VAE.",1320,0.592,777,1.6988416988416988,"Due the phenomenon ��posterior collapse�� current latent variable generative models pose a challenging design choice either the decoder requires altering the training objective We develop an alternative that utilizes as optimize variational lower ensures preserve and encode useful Our proposed ��-VAEs achieve this constraining the variational family for the posterior to have prior For sequential latent variable models our approach resembles the classic representation learning approach slow feature analysis We demonstrate our method��s efficacy modeling text on LM1B and modeling images: learning representations improving sample quality achieving state on ImageNet 32 × Deep latent variable models trained led advances representation learning on BID25 BID33 . These latent variable models typically simple decoders the mapping from the input space unimodal for using This typically representations good capturing the global structure in fail more complex local structure BID28 In parallel advances autoregressive models drastic improvements density modeling sample quality without explicit latent variables BID39 . While these models good capturing local statistics produce globally coherent structures BID30 .Combining the power tractable densities from autoregressive models the representation learning capabilities latent variable models could result useful latent representations While much prior work attempted join these two models a common problem If the autoregressive decoder expressive model the data density learn ignore resulting a trivial posterior that collapses prior This phenomenon frequently prior work referred optimization challenges of VAEs BID5 , the information preference property by , the posterior collapse problems several others van BID40 BID14 . Ideally an approach mitigates posterior collapse alter lower bound (ELBO) training objective allow the practitioner leverage the most recent advances powerful autoregressive decoders To , no prior work succeeded Most common approaches either change the objective BID20 BID1 Zhao , weaken the decoder . Additionally these approaches challenging tune highly sensitive BID1 .In ��-VAEs , selecting variational families prevent posterior collapse without altering the ELBO training objective or weakening the decoder By restricting the parameters or family posterior ensure a minimum KL divergence �� priorWe demonstrate the effectiveness at learning powerful decoders on imagesCIFAR-10 and 32 × textLM1B We achieve state the art log-likelihood results image models by additionally introducing a sequential latent-variable model an anti-causal encoder structure Our experiments demonstrate ��-VAEs at learning useful representations downstream tasks without sacrificing density modeling In this work demonstrated �-VAEs provide posterior collapse latent variable models enabling paired powerful decoders Unlike prior work require changes the objective weakening the decoder learn useful representations as achieving state likelihoods While our work presents two simple posterior-prior pairs Our work also points at least two interesting challenges latentvariable models can exceed a strong autoregressive baseline learn representations improve downstream applications such classification DISPLAYFORM0 B DERIVATION THE KL-DIVERGENCE AR(1 GAUSSIAN ITS LOWER Noting the analytic form for for two uni-variate Gaussian distributions: we derive lower To avoid clutter we assume a single dimension per timestep but extend the results the general multivariate case at DISPLAYFORM3 C DERIVATION THE LOWER-BOUND Removing non-negative quadratic terms involving µ i equation expanding back f inside yields Consider f ax − its first and second order derivatives ≥ Thus f a convex obtains its minimum value a −1 �� DISPLAYFORM5 When multi-dimensional z i at each timestep the committed rate the KL for each individual dimension: The most common choice variational families assume the components the posterior independent for using q ��z|x N; µ q ( When paired standard Gaussian prior p(z N (z; guarantee committed information rate � by constraining the variational family Appendix C DISPLAYFORM7 We, thus numerically solve where the above equation has a solution for µ q. Posterior parameters can thus parameterised DISPLAYFORM9 Where �� parameterises the data-dependent part µ q ad �� q allow the rate go above designated lower �.We compare the temporal version-VAE discussed and report While independent ��-VAE also prevents posterior from collapsing prior its performance density modeling lags temporal ��",0.01,0.4846664187721393
"Mini-batch gradient descent and its variants are commonly used in deep learning. The principle of mini-batch gradient descent is to use noisy gradient calculated on a batch to estimate the real gradient, thus balancing the computation cost per iteration and the uncertainty of noisy gradient. However, its batch size is a fixed hyper-parameter requiring manual setting before training the neural network. Yin et al. (2017) proposed a batch adaptive stochastic gradient descent (BA-SGD) that can dynamically choose a proper batch size as learning proceeds. We extend the BA-SGD to momentum algorithm and evaluate both the BA-SGD and the batch adaptive momentum (BA-Momentum) on two deep learning tasks from natural language processing to image classification. Experiments confirm that batch adaptive methods can achieve a lower loss compared with mini-batch methods after scanning the same epochs of data. Furthermore, our BA-Momentum is more robust against larger step sizes, in that it can dynamically enlarge the batch size to reduce the larger uncertainty brought by larger step sizes. We also identified an interesting phenomenon, batch size boom. The code implementing batch adaptive framework is now open source, applicable to any gradient-based optimization problems. Efficiency of training large neural networks becomes increasingly important as deep neural networks tend to have more parameters and require more training data to achieve the state-of-the-art performance on a wide variety of tasks BID4 . For training deep neural networks, stochastic gradient descent (SGD) (Robbins & Monro, 1951) and its variants, including momentum, which utilizes past updates with an exponential decay BID11 , and other methods that can adapt different learning rates for each dimension, such as ADAGRAD BID1 , ADADELTA BID19 and ADAM BID6 , are commonly used. SGD approximates the gradient by only using a single data instance in each iteration, which may lead to uncertainty of approximation. This uncertainty can be reduced by adopting a batch of instances to do the approximation. In mini-batch SGD, the batch size is a fixed hyper parameter requiring manual setting before training the neural network. Setting the batch size typically involves a tuning procedure in which the best batch size is chosen by a series of attempts. BID18 has developed a batch adaptive stochastic gradient descent (BA-SGD) that can dynamically choose a proper batch size as learning proceeds. BA-SGD models the decrease of objective value as a Gaussian random walk game with rebound on the basis of Taylor extension and central limit theorem. Its core idea is to only update the parameters when the ratio between the expected decrease of objective value and the current batch size is large enough, otherwise enlarge the batch size to better approximate the gradient. It claimed that by smartly choosing the batch size, the BA-SGD not only conserves the fast convergence of SGD algorithm but also avoids too frequent model updates, and compared with mini-batch SGD, its objective value decreases more, after scanning the same amount of data.However, the experiment in BID18 was only conducted on some simple classification tasks using fully connected neural network with one input layer, one output layer and two hidden layers. What about the evaluation on some complex neural networks, such as convolutional neural network (CNN) and recurrent neural network (RNN)? How well would the batch adaptive algorithm perform on other complicated tasks related to natural language processing and computer vision? Furthermore, empirical studies reveal that SGD usually performs not so well in some deep and complex neural networks BID15 . Can this batch adaptive framework be extended to other gradient based optimization algorithms except SGD? Therefore, in this paper we extend the batch adaptive framework to momentum algorithm, and evaluate both the batch adaptive SGD (BA-SGD) and the batch adaptive momentum (BA-Momentum) on two deep learning tasks from natural language processing to image classification. These two tasks use RNN and CNN respectively, which cover most of the deep learning models.In our experiments, we have the following observations. First, for batch adaptive methods, their loss functions converge to lower values after scanning same epoches of data, compared with fixedbatch-size methods. Second, BA-Momentum is more robust against large step sizes by dynamically enlarging the batch size to counteract with the larger noise brought by larger step sizes. Third, we observed a batch size boom, a concentrated period where the batch size frequently increases to larger values, in the training of BA-Momentum. The batch size boom is of significance in that it always appears at the point where mini-batch method starts to reach its lowest possible loss and it helps BA-Momentum keep dropping to even lower loss. More details on these observations and their analysis can be found in Section 4. The code implementing the batch adaptive framework using Theano (AlR) is now open source 1 , which is applicable to any gradient-based optimization problems.This paper is organized as follows. In Section 2, we briefly introduce the batch adaptive framework proposed by BID18 . In Section 3, we extend the batch adaptive framework to momentum algorithm. In Section 4, we demonstrate the performance of BA-M and BA-SGD on Fashion-MNIST BID17 and relation extraction task, and then reveal the robustness of BA-Momentum against large step sizes. In Section 5, we discuss some efficiency issue concerned with implementing this batch adaptive framework, and also propose several promising applications based on this framework. In this work we developed BA-Momentum algorithm, an extension of the BA-SGD proposed by BID18 . We also evaluate the two algorithms on natural language processing and image classification tasks using RNN and CNN respectively. The experiments show that in most cases both batch adaptive methods can achieve lower loss than mini-batch methods after scanning same epochs of data. Furthermore, we also confirm that within a certain range of step sizes, BA-Momentum is more robust against large step size compared with mini-batch methods.In the experiments, we did not evaluate the decrease of training loss with respect to training time. This is because, in the BA-SGD and BA-Momentum algorithm, we have to calculate the derivatives of the loss of each instance from a batch with respect to parameters, and then derive a covariance matrix through Equation 4 from the derivatives. Computing derivatives by backpropagation is time consuming, and now we have to compute all the derivatives of every instance in a batch. However, in mini-batch gradient descent, it is a common practice to calculate an average loss from a batch and then the derivative of this average loss, which requires less time. A feasible approach to reduce the computation cost might be to modify the way Theano do the derivation for a batch of instances and return the square sum of the derivatives, which we plan to study in future work.The batch adaptive framework can have many important applications. It can be adapted to accelerate distributed deep learning. For distributed deep learning, communication cost for synchronizing gradients and parameters among workers and parameter server is its well-known bottleneck BID7 b; BID16 . A larger batch may help make more accurate updates, thus reducing the total number of iterations needed to converge, lowering the communication cost. However, a larger batch also causes a higher computation cost per iteration. In this update-costly environment, the batch adaptive framework may be modified to take both the computation and communication cost into consideration when deciding a proper batch size, which is worth further exploring.Another application is that the batch adaptive framework may help remedy the generalization degradation of using large batch studied by BID5 . They provided solid numeric evidence suggesting that using a larger batch will degrade the quality of the model, as measured by its ability to generalize. They also studied the cause for this generalization drop and presented evidence supporting the view that large-batch methods tend to converge to sharp minimizers of the training and testing functions, which causes this generalization drop. Several strategies to help large-batch methods eliminate this generalization drop was proposed in their work. The most promising one is to warm-start with certain epochs of small-batch regime, and then use large batch for the rest of the training. However, the number of epochs needed to warm start with small batch varies for different data sets, thus a batch adaptive method that can dynamically change the batch size against the characteristics of data is the key to solving this problem. The batch adaptive framework sheds light on this issue. Difficulty lies in how to identify a sharp minima accurately and efficiently in the process of learning and limit the batch size when encountering a sharp minima, which we plan to study in future work.",1703,0.938,982,1.734215885947047,"Mini-batch gradient descent its variants commonly The principle mini-batch gradient descent noisy gradient calculated to thus balancing per uncertainty noisy gradient However its batch size a fixed hyper requiring manual setting before training Yin et (2017 proposed a batch adaptive stochastic gradient descentBA-SGD dynamically choose a proper batch size as learning We extend the BA-SGD momentum algorithm evaluate the batch adaptive momentum on two deep learning tasks from Experiments confirm batch adaptive methods achieve a lower loss compared after scanning the same epochs Furthermore our BA-Momentum is more robust against larger step sizes in dynamically enlarge reduce the larger uncertainty brought We also identified an interesting phenomenon, batch size boom The code implementing batch adaptive framework applicable any gradient-based optimization problems Efficiency training large neural networks becomes tend more parameters require state on BID4 . For training deep neural networks ( Monro 1951 its variants including momentum which utilizes past updates with BID11 , adapt different learning rates each dimension ADAGRAD BID1 ADADELTA BID19 commonly SGD approximates the gradient by only a single data instance uncertainty approximation This uncertainty reduced adopting a batch instances do the approximation In mini-batch SGD the batch size a fixed hyper parameter requiring manual setting before training Setting the batch size typically a tuning procedure attempts BID18 has developed a batch adaptive stochastic gradient descentBA-SGD dynamically choose a proper batch size as learning BA-SGD models the decrease objective value a Gaussian random walk game rebound on Taylor extension central limit theorem Its core idea only update the parameters the ratio between the expected decrease objective value the current batch size large otherwise enlarge better approximate the gradient It claimed by smartly the batch size the BA-SGD not the fast convergence SGD algorithm avoids too frequent model updates compared its objective value decreases more, after scanningHowever in BID18 only some simple classification tasks using fully connected neural network one input layer What about the evaluation on some complex neural networks How well would the batch adaptive algorithm other complicated tasks related Furthermore empirical studies reveal SGD usually performs not so some deep and complex neural networks BID15 . Can this batch adaptive framework extended other gradient based optimization algorithms except SGD Therefore extend the batch adaptive framework momentum algorithm evaluate both the batch adaptive SGD on two deep learning tasks from These two tasks use RNN CNN respectively cover mostIn First for batch adaptive methods their loss functions converge lower after scanning same epoches compared fixedbatch-size methods Second BA-Momentum more robust against large step sizes by dynamically enlarging counteract with the larger noise brought Third observed a batch size boom a concentrated period where frequently increases larger values the training BA-Momentum The batch size boom of significance always appears mini-batch method starts reach its lowest possible loss helps BA-Momentum keep dropping even lower loss More details these observations their analysis Section The code implementing the batch adaptive framework using Theano (AlR 1 , applicable any gradient-based optimization problemsThis paper organized In Section briefly introduce the batch adaptive framework proposed BID18 . In Section extend the batch adaptive framework momentum algorithm In Section demonstrate BA-M and BA-SGD Fashion-MNIST BID17 and relation extraction task then reveal against large step sizes In Section some efficiency issue concerned implementing this batch adaptive framework propose several promising applications based In this work developed BA-Momentum algorithm the BA-SGD proposed BID18 . We also evaluate the two algorithms on RNN CNN respectively The experiments in both batch adaptive methods can achieve lower loss after scanning same epochs Furthermore confirm within step sizes BA-Momentum robust against large step size compared mini-batch methodsIn did evaluate the decrease training loss respect This because the BA-SGD and BA-Momentum algorithm calculate the derivatives the loss each instance from a batch with respect parameters derive through Equation from Computing derivatives by time now compute every instance However mini-batch gradient descent calculate an average loss and then the derivative requires A feasible approach reduce the computation cost might modify Theano do a batch instances return the square sum plan studyThe batch adaptive framework have It can adapted accelerate distributed deep learning For distributed deep learning communication cost for synchronizing gradients parameters among workers parameter server its well-known bottleneck BID7 b; . A larger batch may help make more accurate updates thus iterations converge lowering the communication cost However a larger batch also causes a higher computation cost per iteration In this update-costly environment the batch adaptive framework may modified take both the computation and communication cost a proper batch size worth further exploringAnother application help remedy the generalization degradation using studied BID5 . They provided solid numeric evidence suggesting using a larger batch will degrade measured its ability generalize They also studied the cause for this generalization drop presented large-batch methods tend converge sharp minimizers the training and testing functions causes Several strategies large-batch methods eliminate this generalization drop was their work most promising one to warm-start with certain epochs small-batch regime, use large batch However epochs needed warm start small batch varies for thus a batch adaptive method that dynamically against the characteristics data the key solving The batch adaptive framework sheds Difficulty lies identify a sharp minima accurately limit the batch size when encountering we plan study",0.01,0.5747967395744698
"Deep learning models for graphs have advanced the state of the art on many tasks. Despite their recent success, little is known about their robustness. We investigate training time attacks on graph neural networks for node classification that perturb the discrete graph structure.   Our core principle is to use meta-gradients to solve the bilevel problem underlying training-time attacks, essentially treating the graph as a hyperparameter to optimize. Our experiments show that small graph perturbations consistently lead to a strong decrease in performance for graph convolutional networks, and even transfer to unsupervised embeddings. Remarkably, the perturbations created by our algorithm can misguide the graph neural networks such that they perform worse than a simple baseline that ignores all relational information. Our attacks do not assume any knowledge about or access to the target classifiers. Graphs are a powerful representation that can model diverse data from virtually any domain, such as biology (protein interaction networks), chemistry (molecules), or social networks (Facebook). Not surprisingly, machine learning on graph data has a longstanding history, with tasks ranging from node classification, over community detection, to generative modeling.In this paper, we study node classification, which is an instance of semi-supervised classification: given a single (attributed) network and a subset of nodes whose class labels are known (e.g., the topic of a paper in a citation graph), the goal is to infer the classes of the unlabeled nodes. While there exist many classical approaches to node classification (London & Getoor, 2014; Chapelle et al., 2006) , recently deep learning on graphs has gained much attention BID7 Bojchevski & Günnemann, 2018a; BID2 BID11 Bojchevski et al., 2018; Klicpera et al., 2019) . Specifically, graph convolutional approaches (Kipf & Welling, 2017; BID12 have improved the state of the art in node classification.However, recent works have also shown that such approaches are vulnerable to adversarial attacks both at test time (evasion) as well as training time (poisoning attacks) BID18 Dai et al., 2018) . A core strength of models using graph convolution -exploiting the information in a node's neighborhood to improve classification -is also a major vulnerability: because of these propagation effects, an attacker can change a single node's prediction without even changing any of its attributes or edges. This is because the foundational assumption that all samples are independent of each other does not hold for node classification. Network effects such as homophily (London & Getoor, 2014) support the classification, while on the other hand they enable indirect adversarial attacks.So far, all existing attacks on node classification models are targeted, that is, aim to provoke misclassification of a specific single node, e.g. a person in a social network. In this work, we propose the first algorithm for poisoning attacks that is able to compromise the global node classification performance of a model. We show that even under restrictive attack settings and without access to the target classifier, our attacks can render it near-useless for use in production (i.e., on test data).Our approach is based on the principle of meta learning, which has traditionally been used for hyperparameter optimization BID4 , or, more recently, few-shot learning (Finn et al., 2017) . In essence, we turn the gradient-based optimization procedure of deep learning models upside down and treat the input data -the graph at hand -as a hyperparameter to learn. We propose an algorithm for training-time adversarial attacks on (attributed) graphs, focusing on the task of node classification. We use meta-gradients to solve the bilevel optimization problem underlying the challenging class of poisoning adversarial attacks. Our experiments show that attacks created using our meta-gradient approach consistently lead to a strong decrease in classification performance of graph convolutional models and even transfer to unsupervised models. Remarkably, even small perturbations to a graph based on our approach can lead to graph neural networks performing worse than a baseline ignoring all relational information. We further propose approximations of the metagradients that are less expensive to compute and, in many cases, have a similarly destructive impact on the training of node classification models. While we are able to show small statistical differences of adversarial and 'normal' edges, it is still an open question what makes the edges inserted/removed by our algorithm so destructive, which could then be used to detect or defend against attacks.",919,0.423,542,1.6955719557195572,"Deep learning models graphs advanced the state on many tasks Despite little their robustness We investigate training time attacks graph neural networks for node classification that perturb the discrete graph structure Our core principle use meta-gradients solve the bilevel problem underlying training-time attacks essentially treating the graph to optimize. Our experiments small graph perturbations consistently performance even transfer created our algorithm misguide the graph neural networks such perform a simple baseline that ignores all relational information Our attacks do assume or access the target classifiers Graphs a powerful representation that model diverse data from virtually any domain such biology (protein interaction networks social networksFacebook Not surprisingly machine learning on graph data a longstanding history tasks node classification over community detection generative modelingIn study node classification an instance: given whose class labels known the topic a citation graph infer While exist many classical approaches node classificationLondon & Getoor 2014 Chapelle 2006 , recently deep learning on graphs BID7 Bojchevski 2018a; Klicpera 2019 Specifically graph convolutional approaches (Kipf & Welling 2017 BID12 have improved the state node classification.However recent works also vulnerable both at test time (evasion as training time (poisoning attacks BID18 Dai et al . A core strength models using graph convolution -exploiting the information a node's neighborhood improve classification also a major vulnerability: because these propagation effects change changing edges This because the foundational assumption all samples independent does node classification Network effects such homophilyLondon & Getoor 2014 support the classification, while on they enable indirect adversarial attacksSo all existing attacks node classification models targeted, that aim provoke a specific single node in In this work propose the first algorithm poisoning attacks compromise the global node classification performance a model We show even under restrictive attack settings and without access the target classifier our attacks render it nearuseless use production ( on test data).Our approach meta learning has traditionally BID4 , or, more recently, few-shot learningFinn 2017) In essence we turn the gradient-based optimization procedure deep learning models upside treat the input data -the graph at to learn We propose training-time adversarial attacks (attributed) graphs focusing the task node classification We use meta-gradients solve the bilevel optimization problem underlying the challenging class poisoning adversarial attacks Our experiments attacks created using our meta-gradient approach consistently a strong decrease classification performance graph convolutional models even transfer to even small perturbations a graph based our approach graph neural networks performing worse a baseline ignoring all relational information We further propose approximations the metagradients less expensive compute, have a similarly destructive impact the training node classification models While able show small statistical differences of adversarial and 'normal' edges makes inserted/ destructive which could then detect or defend",0.01,0.4763354005734122
"Numerous models for grounded language understanding have been recently proposed, including (i) generic models that can be easily adapted to any given task and (ii) intuitively appealing modular models that require background knowledge to be instantiated. We compare both types of models in how much they lend themselves to a particular form of systematic generalization. Using a synthetic VQA test, we evaluate which models are capable of reasoning about all possible object pairs after training on only a small subset of them. Our findings show that the generalization of modular models is much more systematic and that it is highly sensitive to the module layout, i.e. to how exactly the modules are connected. We furthermore investigate if modular models that generalize well could be made more end-to-end by learning their layout and parametrization. We find that end-to-end methods from prior work often learn inappropriate layouts or parametrizations that do not facilitate systematic generalization. Our results suggest that, in addition to modularity, systematic generalization in language understanding may require explicit regularizers or priors.
 In recent years, neural network based models have become the workhorse of natural language understanding and generation. They empower industrial machine translation BID34 ) and text generation BID20 systems and show state-of-the-art performance on numerous benchmarks including Recognizing Textual Entailment BID8 , Visual Question Answering BID17 , and Reading Comprehension BID33 . Despite these successes, a growing body of literature suggests that these approaches do not generalize outside of the specific distributions on which they are trained, something that is necessary for a language understanding system to be widely deployed in the real world. Investigations on the three aforementioned tasks have shown that neural models easily latch onto statistical regularities which are omnipresent in existing datasets BID0 BID10 BID16 and extremely hard to avoid in large scale data collection. Having learned such dataset-specific solutions, neural networks fail to make correct predictions for examples that are even slightly out of domain, yet are trivial for humans. These findings have been corroborated by a recent investigation on a synthetic instruction-following task , in which seq2seq models BID32 BID2 have shown little systematicity BID6 in how they generalize, that is they do not learn general rules on how to compose words and fail spectacularly when for example asked to interpret ""jump twice"" after training on ""jump"", ""run twice"" and ""walk twice"".An appealing direction to improve the generalization capabilities of neural models is to add modularity and structure to their design to make them structurally resemble the kind of rules they are supposed to learn BID1 BID7 . For example, in the Neural Module Network paradigm (NMN, BID1 ), a neural network is assembled from several neural modules, where each module is meant to perform a particular subtask of the input processing, much like a computer program composed of functions. The NMN approach is intuitively appealing but its widespread adoption has been hindered by the large amount of domain knowledge that is required to decide BID1 or predict BID19 BID12 how the modules should be created (parametrization) and how they should be connected (layout) based on a natural language utterance. Besides , their performance has often been matched by more traditional neural models, such as FiLM BID28 , Relations Networks BID29 , and MAC networks BID14 . Lastly , generalization properties of NMNs, to the best of our knowledge, have not been rigorously studied prior to this work.Here, we investigate the impact of explicit modularity and structure on systematic generalization of NMNs and contrast their generalization abilities to those of generic models. For this case study, we focus on the task of visual question answering (VQA), in particular its simplest binary form, when the answer is either ""yes"" or ""no"". Such a binary VQA task can be seen as a fundamental task of language understanding, as it requires one to evaluate the truth value of the utterance with respect to the state of the world. Among many systematic generalization requirements that are desirable for a VQA model, we choose the following basic one: a good model should be able to reason about all possible object combinations despite being trained on a very small subset of them. We believe that this is a key prerequisite to using VQA models in the real world, because they should be robust at handling unlikely combinations of objects. We implement our generalization demands in the form of a new synthetic dataset, called Spatial Queries On Object Pairs (SQOOP), in which a model has to perform spatial relational reasoning about pairs of randomly scattered letters and digits in the image (e.g. answering the question ""Is there a letter A left of a letter B?""). The main challenge in SQOOP is that models are evaluated on all possible object pairs, but trained on only a subset of them.Our first finding is that NMNs do generalize better than other neural models when layout and parametrization are chosen appropriately. We then investigate which factors contribute to improved generalization performance and find that using a layout that matches the task (i.e. a tree layout, as opposed to a chain layout), is crucial for solving the hardest version of our dataset. Lastly, and perhaps most importantly , we experiment with existing methods for making NMNs more end-to-end by inducing the module layout BID19 or learning module parametrization through soft-attention over the question BID12 . Our experiments show that such end-to-end approaches often fail by not converging to tree layouts or by learning a blurred parameterization for modules, which results in poor generalization on the hardest version of our dataset. We believe that our findings challenge the intuition of researchers in the field and provide a foundation for improving systematic generalization of neural approaches to language understanding. We have conducted a rigorous investigation of an important form of systematic generalization required for grounded language understanding: the ability to reason about all possible pairs of objects despite being trained on a small subset of such pairs. Our results allow one to draw two important conclusions. For one, the intuitive appeal of modularity and structure in designing neural architectures for language understanding is now supported by our results, which show how a modular model consisting of general purpose residual blocks generalizes much better than a number of baselines, including architectures such as MAC, FiLM and RelNet that were designed specifically for visual reasoning. While this may seem unsurprising, to the best of our knowledge, the literature has lacked such a clear empirical evidence in favor of modular and structured networks before this work. Importantly, we have also shown how sensitive the high performance of the modular models is to the layout of modules, and how a tree-like structure generalizes much stronger than a typical chain of layers.Our second key conclusion is that coming up with an end-to-end and/or soft version of modular models may be not sufficient for strong generalization. In the very setting where strong generalization is required, end-to-end methods often converge to a different, less compositional solution (e.g. a chain layout or blurred attention). This can be observed especially clearly in our NMN layout and parametrization induction experiments on the #rhs/lhs=1 version of SQOOP, but notably, strong initialization sensitivity of layout induction remains an issue even on the #rhs/lhs=18 split. This conclusion is relevant in the view of recent work in the direction of making NMNs more end-toend BID31 BID13 BID14 BID9 . Our findings suggest that merely replacing hard-coded components with learnable counterparts can be insufficient, and that research on regularizers or priors that steer the learning towards more systematic solutions can be required. That said, our parametrization induction results on the #rhs/lhs=2 split are encouraging, as they show that compared to generic models, a weaker nudge (in the form of a richer training signal or a prior) towards systematicity may suffice for end-to-end NMNs.While our investigation has been performed on a synthetic dataset, we believe that it is the realworld language understanding where our findings may be most relevant. It is possible to construct a synthetic dataset that is bias-free and that can only be solved if the model has understood the entirety of the dataset's language. It is, on the contrary, much harder to collect real-world datasets that do not permit highly dataset-specific solutions, as numerous dataset analysis papers of recent years have shown (see Section 5 for a review). We believe that approaches that can generalize strongly from imperfect and biased data will likely be required, and our experiments can be seen as a simulation of such a scenario. We hope, therefore, that our findings will inform researchers working on language understanding and provide them with a useful intuition about what facilitates strong generalization and what is likely to inhibit it. We can observe a clear correlation between κ and error rate for 1, 2 and 4 rhs/lhs. Also note that perfect generalization is always associated with κ close to 1.Next, we experiment with a hard-coded variation of MAC. In this model, we use hard-coded control scores such that given a SQOOP question X R Y, the first half of all modules focuses on X while the second half focuses on Y. The relationship between MAC and hardcoded MAC is similar to that between NMN-Tree and end-to-end NMN with parameterization induction. However, this model has not performed as well as the successful runs of MAC. We hypothesize that this could be due to the interactions between the control scores and the visual attention part of the model.",1920,0.871,1168,1.643835616438356,"Numerous models for grounded language understanding recently (i) generic models easily any given task intuitively appealing modular models require background knowledge instantiated We compare both types models how they lend a particular form systematic generalization Using a synthetic VQA test evaluate which models capable reasoning all possible object pairs after training them Our findings the generalization modular models much systematic highly sensitive the module layout how exactly We furthermore investigate if modular models that generalize well could made more end by learning their layout We find end methods from prior work often learn inappropriate layouts or parametrizations facilitate systematic generalization Our results, modularity systematic generalization in language understanding require explicit regularizers or priors In neural network based models natural language understanding generation They empower industrial machine translation BID34 ) text generation BID20 systems and show state performance on numerous benchmarks Recognizing Textual Entailment BID8 Visual Question Answering BID17 Despite these successes these approaches generalize outside the specific distributions on trained something necessary a language understanding system widely deployed Investigations on the three aforementioned tasks neural models easily latch statistical regularities which omnipresent existing datasets BID0 BID10 BID16 and extremely hard avoid large scale data collection Having learned such dataset-specific solutions neural networks fail make correct predictions examples even slightly out domain yet trivial humans These findings on a synthetic instruction-following task , seq2seq models BID32 BID2 have shown little systematicity BID6 in how generalize, that they learn general rules on compose words fail spectacularly for asked interpret ""jump twice after training onrunwalkAn appealing direction improve the generalization capabilities neural models add modularity structure their design structurally resemble the kind rules For example the Neural Module Network paradigmNMN, BID1 ), assembled several neural modules where meant perform a particular subtask the input processing much composed functions The NMN approach intuitively appealing but its widespread adoption domain knowledge decide BID1 or predict BID19 BID12 how the modules created (parametrization connected (layout based a natural language utterance Besides , their performance often matched more traditional neural models FiLM BID28 Relations Networks BID29 MAC networks BID14 Lastly , generalization properties NMNs to priorHere investigate explicit modularity structure systematic generalization contrast those generic models For this case study focus the task visual question answering particular its simplest binary when either Such a binary VQA task seen a fundamental task language understanding requires one evaluate the truth value the utterance with the state Among many systematic generalization requirements that desirable a VQA model choose basic one a good model reason all possible object combinations despite being trained We believe this a key prerequisite using VQA models because should robust at handling unlikely combinations objects We implement our generalization demands a new synthetic dataset called Spatial Queries On Object Pairs a model has perform spatial relational reasoning about pairs randomly scattered letters digits the image answering A left of The main challenge SQOOP models evaluated all possible object pairs trainedOur first finding NMNs generalize other neural models layout chosen appropriately We then investigate which factors improved generalization performance find using a layout matches the task as crucial solving the hardest version our dataset Lastly and , experiment existing methods making NMNs more end by inducing the module layout BID19 or learning module parametrization through soft-attention over the question BID12 Our experiments such end approaches often by not converging tree layouts learning a blurred parameterization for modules results poor generalization on the hardest version our dataset We believe our findings challenge the intuition researchers improving systematic generalization neural approaches language understanding We conducted an important form systematic generalization required grounded language understanding the ability reason all possible pairs objects despite being trained Our results allow one draw two important conclusions For one the intuitive appeal modularity structure in designing neural architectures for language understanding now supported our results how a modular model consisting general purpose residual blocks generalizes much a number baselines architectures MAC FiLM RelNet that were specifically visual reasoning While this unsurprising to best the literature lacked such a clear empirical evidence in modular and structured networks before this work Importantly also shown how sensitive the high performance the modular models the layout modules a tree-like structure generalizes much stronger a typical chain layersOur second key conclusion coming end and/or soft version modular models may not sufficient strong generalization In the very setting strong generalization required end methods often converge a different, less compositional solution (e.g. a chain layout blurred attention This can observed especially clearly our NMN layout and parametrization induction experiments on the #rhs/lhs=1 version SQOOP but notably strong initialization sensitivity layout induction remains even This conclusion relevant the view recent work the direction making NMNs more end-toend BID31 BID13 BID14 BID9 . Our findings merely replacing hard-coded components learnable counterparts insufficient, that research regularizers or priors that steer towards more systematic solutions required That said our parametrization induction results on the #rhs/lhs=2 split encouraging compared generic models a weaker nudge (in a richer training signal or prior) towards systematicity may suffice end NMNsWhile our investigation performed a synthetic dataset believe the realworld language understanding where may It possible construct a synthetic dataset bias that only solved understood the entirety It, on much harder collect real-world datasets do permit highly dataset-specific solutions numerous dataset analysis papers of ( Section for We believe approaches can generalize strongly imperfect and biased data likely required our experiments can seen a simulation We hope, therefore our findings inform researchers working language understanding provide a useful intuition facilitates strong generalization what likely inhibit We can observe a clear correlation �� error rate for 1 rhs/lhs Also note perfect generalization always associated �� close 1.Next experiment a hard-coded variation MAC. In this model hard-coded control scores such given a SQOOP question X R Y all modules focuses X while The relationship MAC hardcoded MAC similar NMN-Tree end NMN with parameterization induction However this model performed the successful runs MAC. We hypothesize this could the interactions the control scores the visual attention part",0.01,0.34451575358998004
"The behavioral dynamics of multi-agent systems have a rich and orderly structure, which can be leveraged to understand these systems, and to improve how artificial agents learn to operate in them. Here we introduce Relational Forward Models (RFM) for multi-agent learning, networks that can learn to make accurate predictions of agents' future behavior in multi-agent environments. Because these models operate on the discrete entities and relations present in the environment, they produce interpretable intermediate representations which offer insights into what drives agents' behavior, and what events mediate the intensity and valence of social interactions. Furthermore, we show that embedding RFM modules inside agents results in faster learning systems compared to non-augmented baselines. 
 As more and more of the autonomous systems we develop and interact with become multi-agent in nature, developing richer analysis tools for characterizing how and why agents make decisions is increasingly necessary. Moreover, developing artificial agents that quickly and safely learn to coordinate with one another, and with humans in shared environments, is crucial. The study of multi-agent systems has received considerable attention in recent years and some of the most advanced autonomous systems in the world today are multi-agent in nature (e.g. assembly lines and warehouse management systems). In particular, research in multi-agent reinforcement learning (MARL), where multiple learning agents perceive and act in a shared environment, has produced impressive results BID15 BID23 BID14 BID26 BID19 BID0 .One of the outstanding challenges in this domain is how to foster coordinated behavior among learning agents. In hand-engineered multi-agent systems (e.g. assembly lines), it is possible to obtain coordination by design, where expert engineers carefully orchestrate each agent's behavior and role in the system. This , however, rules out situations where either humans or artificial learning agents are present in the environment. In learning-based systems, there have been some successes by introducing a centralized controller BID4 BID6 BID12 BID20 . However , these cannot scale to large number of agents or to mixed human-robot ensembles. There is thus an increasing focus on multi-agent systems that learn how to coordinate on their own BID15 BID23 .Alongside the challenges of learning coordinated behaviors, there are also the challenges of measuring them. In learning-based systems, the analysis tools currently available to researchers focus on the functioning of each single agent, and are ill-equipped to characterize systems of diverse agents as a whole. Moreover, there has been little development of tools for measuring the contextual interdependence of agents' behaviors in complex environment, which will be valuable for identifying the conditions under which agents are successfully coordinating.Here we address these two challenges by developing Relational Forward Models (RFM) for multiagent systems. We build on recent advances in neural networks that effectively perform relational reasoning with graph networks (GN) BID2 to construct models that learn to predict the forward dynamics of multi-agent systems. First, we show that our models can surpass previous top methods on this task BID16 Hoshen, 2017) . Perhaps more importantly , they produce intermediate representations that support the social analysis of multi-agent systems: we use our models to propose a new way to characterize what drives each agent's behavior, track when agents influence each other, and identify which factors in the environment mediate the presence and valence of social interactions. Finally, we embed our models inside agents and use them to augment the host agent's observations with predictions of others' behavior. Our results show that this leads to agents that learn to coordinate with one another faster than non-augmented baselines. Here we showed that our Relational Forward Model can capture the rich social dynamics of multiagent environments, that its intermediate representations contained valuable interpretable information, and that providing this information to learning agents results in faster learning system. The analysis tools we introduced allow researchers to answer new questions, which are specifically tailored to multi-agent systems, such as what entities, relations and social interactions drive agents' behaviors, and what environment events or behavior patterns mediate these social and non-social influence signals. Importantly our methods require no access to agents internals, only to behavioral trajectories, making them amenable to analyzing human behavior, sports and ecological systems.Providing agents with access the output of RFM modules results in agents that learn to coordinate with one another faster than non-augmented baselines. We posit that explicit modeling of teammates and opponents is an important research direction in multi-agent RL, and one that might alleviate the need for communication, parameter sharing or centralized controllers to achieve coordination. Future work will see our methods applied to more complex and varied domains where artificial and non-artificial agents interact and learn in shared environments. We will focus on identifying entire patterns of behavior for in-agent modeling, so as to adapt the host agent policy more efficiently.",957,0.469,553,1.7305605786618445,"The behavioral dynamics multi-agent systems a rich and orderly structure leveraged understand these systems improve how artificial agents learn Here introduce Relational Forward Models multi-agent learning networks that learn make Because these models operate the discrete entities relations present produce interpretable intermediate representations which offer insights what drives what events mediate the intensity valence social interactions Furthermore show embedding RFM modules inside agents results faster learning systems compared non-augmented baselines As more the autonomous systems develop and interact multiagent in developing richer analysis tools characterizing how agents make Moreover developing artificial agents quickly safely learn coordinate with humans shared environments crucial The study multi-agent systems received some the most advanced autonomous systems today multi in warehouse In particular research multi-agent reinforcement learningMARL where multiple learning agents perceive act produced BID15 BID23 .One foster coordinated behavior learning In hand-engineered multi-agent systems obtain coordination by design where expert engineers carefully role This , however rules situations either humans artificial learning agents In learning-based systems have by introducing a centralized controller BID4 BID6 BID12 BID20 . However , these cannot scale large number agents mixed human-robot ensembles There thus an increasing focus multi-agent systems learn coordinate on their own BID15 BID23 .Alongside the challenges learning coordinated behaviors measuring them In learning-based systems the analysis tools currently focus the functioning each single agent ill characterize systems diverse agents as Moreover little development tools measuring the contextual interdependence agents' behaviors complex environment, will valuable identifying the conditions successfully coordinatingHere address Relational Forward Models multiagent systems We build recent advances effectively perform relational reasoning with graph networksGN) BID2 to construct models learn the forward dynamics multi-agent systems First show our models surpass previous top methods on this task BID16 Hoshen 2017) . Perhaps more , they produce intermediate representations support the social analysis multi-agent systems: we use our models propose characterize what drives track when influence identify which factors in mediate the presence valence Finally embed our models inside agents use augment the host agent's observations predictions Our results this leads agents learn coordinate faster Here showed our Relational Forward Model capture the rich social dynamics multiagent environments that its intermediate representations contained valuable interpretable information providing learning faster learning system The analysis tools introduced allow researchers answer, which specifically multi-agent systems what entities relations social interactions drive agents' behaviors what environment events or mediate Importantly our methods require no access agents internals only behavioral trajectories making amenable analyzing sports ecologicalProviding agents the output RFM modules results agents learn coordinate one faster non-augmented baselines We posit that explicit modeling teammates multi-agent RL one might alleviate communication, parameter sharing or centralized controllers achieve coordination Future work see our methods applied more complex and varied domains where artificial and non-artificial agents interact learn in shared environments We will focus identifying entire patterns for inagent modeling so as adapt the host agent policy more",0.01,0.5654833377635606
"We show that gradient descent on an unregularized logistic regression
 problem, for almost all separable datasets, converges to the same direction as the max-margin solution. The result generalizes also to other monotone decreasing loss functions with an infimum at infinity, and we also discuss a multi-class generalizations to the cross entropy loss. Furthermore,
 we show this convergence is very slow, and only logarithmic in the
 convergence of the loss itself. This can help explain the benefit
 of continuing to optimize the logistic or cross-entropy loss even
 after the training error is zero and the training loss is extremely
 small, and, as we show, even if the validation loss increases. Our
 methodology can also aid in understanding implicit regularization
 in more complex models and with other optimization methods. It is becoming increasingly clear that implicit biases introduced by the optimization algorithm play a crucial role in deep learning and in the generalization ability of the learned models BID7 BID1 BID15 BID5 Wilson et al., 2017) . In particular, minimizing the training error, without any explicit regularization, over models with more parameters and more capacity then the number of training examples, often yields good generalization, despite the empirical optimization problem being highly underdetermined. That is, there are many global minima of the training objective, most of which will not generalize well, but the optimization algorithm (e.g. gradient descent) biases us toward a particular minimum that does generalize well. Unfortunately, we still do not have a good understanding of the biases introduced by different optimization algorithms in different situations.We do have a decent understanding of the implicit regularization introduced by early stopping of stochastic methods or, at an extreme, of one-pass (no repetition) stochastic optimization. However, as discussed above, in deep learning we often benefit from implicit bias even when optimizing the (unregularized) training error to convergence, using stochastic or batch methods. For loss functions with attainable, finite, minimizers, such as the squared loss, we have some understanding of this: In particular, when minimizing an underdetermined least squares problem using gradient descent starting from the origin, we know we will converge to the minimum Euclidean norm solution. But the logistic loss, and its generalization the cross-entropy loss which is often used in deep learning, do not admit a finite minimizer on separable problems. Instead, to drive the loss toward zero and thus minimize it, the predictor must diverge toward infinity. Do we still benefit from implicit regularization when minimizing the logistic loss on separable data? Clearly the norm of the predictor itself is not minimized, since it grows to infinity. However, for prediction, only the direction of the predictor, i.e. the normalized w(t)/ w(t) , is important. How does w(t)/ w(t) behave as t → ∞ when we minimize the logistic (or similar) loss using gradient descent on separable data, i.e., when it is possible to get zero misclassification error and thus drive the loss to zero?In this paper, we show that even without any explicit regularization, for all most all datasets (except a zero measure set), when minimizing linearly separable logistic regression problems using gradient descent, we have that w(t)/ w(t) converges to the L 2 maximum margin separator, i.e. to the solution of the hard margin SVM. This happens even though the norm w , nor the margin constraint, are in no way part of the objective nor explicitly introduced into optimization. More generally, we show the same behavior for generalized linear problems with any smooth, monotone strictly decreasing, lower bounded loss with an exponential tail. Furthermore , we characterize the rate of this convergence, and show that it is rather slow, with the distance to the max-margin predictor decreasing only as O(1/ log(t)). This explains why the predictor continues to improve even when the training loss is already extremely small. We emphasize and demonstrate that this bias is specific to gradient descent, and changing the optimization algorithm, e.g. using adaptive learning rate methods such as ADAM BID6 , changes this implicit bias.",837,0.39,468,1.7884615384615385,"We show that gradient descent on an unregularized logistic regression problem for almost all separable datasets the max-margin solution The result generalizes also other monotone decreasing loss functions with an infimum at infinity we discuss a multi-class generalizations the cross entropy loss Furthermore show this convergence very slow only the convergence the loss itself This can explain the benefit continuing optimize the logistic or cross-entropy loss even the training error zero extremely, show validation loss increases. Our methodology can aid implicit regularization with other optimization methods It becoming implicit biases introduced the optimization algorithm play deep learning the generalization ability the learned models BID7 BID1 Wilson) . In particular minimizing the training error, without any explicit regularization over models more parameters more capacity then the number often yields despite the empirical optimization problem being highly underdetermined That there many global minima the training objective most generalize well, the optimization algorithm biases us a particular minimum that does Unfortunately the biases introduced different optimization algorithmsWe the implicit regularization introduced early stopping of or, an extreme one-pass However discussed in deep learning benefit implicit bias even optimizing convergence using For loss functions with attainable, finite minimizers such the squared loss some understanding this In particular minimizing an underdetermined least squares problem using starting we converge But the logistic loss, its generalization the cross-entropy loss which deep learning do admit a finite minimizer on separable problems Instead to drive the loss toward zero thus minimize the predictor diverge toward infinity Do still benefit implicit regularization minimizing the logistic loss on separable data Clearly the norm the predictor itself minimized grows infinity However for prediction only the direction the predictor important How w(t)/ behave t → � when minimize using on separable data it get zero misclassification error thus drive even without any explicit regularization for all most all datasets a zero measure set when minimizing that the L 2 maximum margin separator the solution the hard margin SVM This happens even norm w , nor the margin constraint in part the objective nor explicitly introduced optimization More generally show the same behavior generalized linear problems any smooth, monotone strictly decreasing, lower bounded loss with an exponential tail Furthermore , characterize this convergence rather slow the distance the max-margin predictor only O(1/ log(t This explains the predictor continues improve the training loss already extremely We emphasize and demonstrate this bias specific gradient descent changing the optimization, adaptive learning rate methods ADAM BID6 changes",0.01,0.713009896210476
"Despite impressive performance as evaluated on i.i.d. holdout data, deep neural networks depend heavily on superficial statistics of the training data and are liable to break under distribution shift. For example, subtle changes to the background or texture of an image can break a seemingly powerful classifier. Building on previous work on domain generalization, we hope to produce a classifier that will generalize to previously unseen domains, even when domain identifiers are not available during training. This setting is challenging because the model may extract many distribution-specific (superficial) signals together with distribution-agnostic (semantic) signals. To overcome this challenge, we incorporate the gray-level co-occurrence matrix (GLCM) to extract patterns that our prior knowledge suggests are superficial: they are sensitive to the texture but unable to capture the gestalt of an image. Then we introduce two techniques for improving our networks' out-of-sample performance. The first method is built on the reverse gradient method that pushes our model to learn representations from which the GLCM representation is not predictable. The second method is built on the independence introduced by projecting the model's representation onto the subspace orthogonal to GLCM representation's.
 We test our method on the battery of standard domain generalization data sets and, interestingly, achieve comparable or better performance as compared to other domain generalization methods that explicitly require samples from the target distribution for training. Imagine training an image classifier to recognize facial expressions. In the training data, while all images labeled ""smile"" may actually depict smiling people, the ""smile"" label might also be correlated with other aspects of the image. For example, people might tend to smile more often while outdoors, and to frown more in airports. In the future, we might encounter photographs with previously unseen backgrounds, and thus we prefer models that rely as little as possible on the superficial signal.The problem of learning classifiers robust to distribution shift, commonly called Domain Adaptation (DA), has a rich history. Under restrictive assumptions, such as covariate shift BID43 BID16 , and label shift (also known as target shift or prior probability shift) BID44 BID41 BID48 BID30 , principled methods exist for estimating the shifts and retraining under the importance-weighted ERM framework. Other papers bound worst-case performance under bounded shifts as measured by divergence measures on the train v.s. test distributions BID3 BID33 BID20 .While many impossibility results for DA have been proven BID4 , humans nevertheless exhibit a remarkable ability to function out-of-sample, even when confronting dramatic Example illustration of train/validation/test data. The first row is ""happiness"" sentiment and the second row is ""sadness"" sentiment. The background and sentiment labels are correlated in training and validation set, but independent in testing set.distribution shift. Few would doubt that given photographs of smiling and frowning astronauts on the Martian plains, we could (mostly) agree upon the correct labels.While we lack a mathematical description of how precisely humans are able to generalize so easily out-of-sample, we can often point to certain classes of perturbations that should not effect the semantics of an image. For example for many tasks, we know that the background should not influence the predictions made about an image. Similarly, other superficial statistics of the data, such as textures or subtle coloring changes should not matter. The essential assumption of this paper is that by making our model depend less on known superficial aspects, we can push the model to rely more on the difference that makes a difference. This paper focuses on visual applications, and we focus on high-frequency textural information as the relevant notion of superficial statistics that we do not want our model to depend upon.The contribution of this paper can be summarized as follows.• We propose a new differentiable neural network building block (neural gray-level cooccurrence matrix) that captures textural information only from images without modeling the lower-frequency semantic information that we care about (Section 3.1).• We propose an architecture-agnostic , parameter-free method that is designed to discard this superficial information, (Section 3.2).• We introduce two synthetic datasets for DA/DG studies that are more challenging than regular DA/DG scenario in the sense that the domain-specific information is correlated with semantic information. FIG0 is a toy example (Section 4). We introduced two novel components: NGLCM that only extracts textural information from an image, and HEX that projects the textural information out and forces the model to focus on semantic information. Limitations still exist. For example, NGLCM cannot be completely free of semantic information of an image. As a result, if we apply our method on standard MNIST data set, we will 3 ) learns garbage information and HEX degenerates to the baseline model. To overcome these limitations, we invented several training heuristics, such as optimizing F P and F G sequentially and then fix some weights. However, we did not report results with training heuristics (expect for PACS experiment) because we hope to simplify the methods. Another limitation we observe is that sometimes the training performance of HEX fluctuates dramatically during training, but fortunately, the model picked up by highest validation accuracy generally performs better than competing methods. Despite these limitations, we still achieved impressive performance on both synthetic and popular DG data sets.",1076,0.545,623,1.7271268057784912,"Despite impressive performance as evaluated i.i.d. holdout data deep neural networks depend superficial statistics liable break under distribution shift For example subtle changes texture break a seemingly powerful classifier Building domain generalization hope produce previously unseen domains even domain identifiers during training This setting challenging the model may extract many distribution-specific (superficial) signals together To overcome incorporate the gray-level co-occurrence matrix extract patterns our prior knowledge superficial: they sensitive the texture but unable capture the gestalt Then introduce two techniques networks' outsample The first method built the reverse gradient method pushes our model learn representations which the GLCM representation not predictable The second method built the independence introduced projecting the model's representation GLCM representation's We test our method the battery standard domain generalization data sets, interestingly achieve as compared that explicitly require samples the target distribution for training Imagine training an image classifier In the training data while all images labeled ""smile may actually depict might correlated other aspects For example people might tend smile while outdoors to frown in airports In encounter photographs with previously unseen backgrounds thus prefer models rely as little the superficial signalThe problem learning classifiers robust distribution shift commonly Domain AdaptationDA Under restrictive assumptions such covariate shift BID43 BID16 label shift (also target shift prior probability shift principled methods exist the shifts retraining under the importance-weighted ERM framework Other papers bound worst-case performance under bounded shifts as measured divergence measures on the train v.s. test distributions BID3 BID33 .While many impossibility results DA have proven BID4 humans nevertheless function out confronting dramatic Example illustration train/validation/test data The first row ""happiness"" sentiment The background and sentiment labels correlated training validation set independent in testing set.distribution shift Few would doubt given photographs smiling astronauts the Martian plains (mostly upon the correct labelsWhile lack a mathematical description precisely generalize so out-sample often point certain classes should effect the semantics For example for many tasks know the background should influence the predictions an image Similarly other superficial statistics textures subtle coloring changes should matter The essential assumption by making our model depend less known superficial aspects push rely the difference that makes This paper focuses visual applications we high-frequency textural information as the relevant notion superficial statistics that do our model dependThe contribution can a new differentiable neural network building blockneural gray-level cooccurrence matrix captures only images without modeling careSection an architecture-agnostic , parameter-free method designed discard this superficial information ( introduce two synthetic datasets DA/DG studies more challenging in correlated FIG0 is a toy example (Section We introduced two novel components NGLCM that only extracts textural information HEX that projects out and forces the model focus Limitations still For example NGLCM completely free semantic information of an image As if apply standard MNIST data set 3 ) learns garbage information HEX degenerates the baseline model To overcome invented several training heuristics optimizing F P sequentially fix some weights However we report results with training heuristicsexpect for PACS experiment hope simplify Another limitation we observe sometimes the training performance HEX fluctuates dramatically fortunately picked by highest validation accuracy generally performs competing methods Despite these limitations still achieved impressive performance both synthetic and popular DG data sets",0.01,0.5567343861447632
"In this paper, we conduct an intriguing experimental study about the physical adversarial attack on object detectors in the wild. In particular, we learn a camouflage pattern to hide vehicles from being detected by state-of-the-art convolutional neural network based detectors. Our approach alternates between two threads. In the first, we train a neural approximation function to imitate how a simulator applies a camouflage to vehicles and how a vehicle detector performs given images of the camouflaged vehicles. In the second, we minimize the approximated detection score by searching for the optimal camouflage. Experiments show that the learned camouflage can not only hide a vehicle from the image-based detectors under many test cases but also generalizes to different environments, vehicles, and object detectors. Is it possible to paint a unique pattern on a vehicle's body and hence hide it from being detected by surveillance cameras? We conjecture the answer is affirmative mainly for two reasons. First, deep neural networks will be widely used in modern surveillance and autonomous driving systems for automatic vehicle detection. Second, unfortunately, these neural networks are intriguingly vulnerable to adversarial examples BID1 . BID39 found that adding imperceptible perturbations to clean images can result in the failure of neural networks trained for image classification. This motivates a rich line of work on developing defense techniques for the neural networks BID1 and powerful attack methods to defeat those defenses BID3 . Moreover, the adversarial attack has been extended to other tasks, such as semantic segmentation BID2 , object detection BID44 , image captioning BID9 , etc.Figure 1: A Toyota Camry XLE in the center of the image fools the Mask R-CNN object detector after we apply the learned camouflage to it (on the right), whereas neither plain colors (on the left) nor a random camouflage (in the middle) is able to escape the Camry from being detected.It is worth noting that the adversarial examples in the works mentioned above are not physical, i.e., the adversary directly manipulates image pixels. Although it is arguably more challenging to create physical adversarial objects than to produce adversarial images, some existing works have shown promising results with adversarial patches BID7 , stop signs BID14 BID11 , and small objects like baseballs and 3D turtle models BID4 .To this end, we are reasonably optimistic about designing a special pattern to camouflage a 3D car, in order to make it difficult to detect by the deep learning based vehicle detectors.It is undoubtedly challenging to run experiments in the real world considering financial and time constraints. In this paper, we instead demonstrate results using a simulation engine (Unreal) with a high-fidelity 3D sedan model and a 3D SUV. Fig. 1 shows that the vehicle in the simulation is photo-realistic such that, even covered with random camouflage, it can still be detected by the Mask R-CNN detector BID18 ) trained on COCO BID21 .The simulation engine enables us to test the physically adversarial cars under a considerable spectrum of environmental conditions: lighting, backgrounds, camera-to-object distances, viewing angles, occlusions, etc. In contrast, existing experiments on physical adversarial attacks are all executed in simplified scenarios. BID14 , BID13 , and BID11 attack neural classifiers and detectors of stop signs. While projective transformations could be used to render the planar stop signs to various images, it is more involved to image the nonplanar 3D vehicles considered in this paper; we learn a neural approximation function instead. BID4 synthesize objects (e.g., baseball , turtle, etc.) which are adversarial within a small range of camera-to-object distances and viewing angles.Given a 3D vehicle model in the simulation engine, we learn a camouflage for it by following the expectation over transformation (EoT) principle first formalized by BID4 . The main idea is to consider a variety of transformations under which the camouflage can consistently hide the vehicle from a neural detector. A transformation imitates the imaging procedure and produces an image of the 3D vehicle model in the simulated environment. If a camouflage works under many transformations seen in the training phase, it is expected to also generalize to unseen transformations in the test phase.One of the major challenges is that the simulator's image generation procedure is non-differentiable. A seemingly plausible solution is to train a neural network to approximate this procedure. The network takes as input the environment, a camouflage pattern, and the 3D vehicle model and outputs an image as close as possible to the one rendered by the simulator. Although this approach is viable, it is extremely difficult to generate high-resolution images. State-of-the-art methods (e.g., RenderNet (Nguyen-Phuoc et al., 2018) ) can only generate simple 3D objects without any backgrounds.We tackle the above challenge by drawing the following observation. In EoT BID4 BID11 , the gradients propagate back to the physical object from the detector/classifier's decision values. If we jointly consider the object detector and the imaging procedure of the simulator as a whole black box, it is easier to learn a function to approximate this black box's behavior than to train the image generation neural network. Hence, we learn a substitute neural network which takes as input a camouflage , the vehicle model, and the environment and outputs the vehicle detector's decision value. Equipped with this substitute network, we can readily run the EoT algorithm BID4 over our simulator in order to infer an adversarial camouflage for the vehicles.Finally, we make some remarks about the significance and potential impact of this work. In the real world, multiclass visual object detection neural networks BID18 BID32 have become the cornerstone of multiple industrial applications, such as surveillance systems BID27 , autonomous driving BID19 , and military systems BID30 . Among these applications, cars are one of the most crucial objects. Attacking vehicle detectors in the physical world will be enormously valuable and impactful from the perspective of the malicious adversaries. Compared with the stop sign, it is legal in the United States to paint a car while defacing a stop sign is criminal. This poses a more significant threat to autonomous driving systems since anyone has access to perturb public machine learning based systems legally. This observation motivates us to focus our approach on cars. We limit our camouflage within the legally paintable car body parts, which means that we will leave discriminative visual cues, such as the tires, windows, grille, lights, etc. unaltered for the detectors. In this paper, we investigate whether it is possible to physically camouflage 3D objects of complex shapes, i.e., vehicles, in order to hide them from state-of-the-art object detectors. We conduct extensive experimental studies with a photo-realistic simulation engine. We propose to use a clone network to mimic the simulator and the detector's joint response to the 3D vehicles. Then, we infer a camouflage for a 3D vehicle by minimizing the output of the clone network. Our learned camouflage significantly reduces the detectability of a Toyota Camry and a SUV. Moreover, we find that the camouflage is transferable across different environments. For future work, We plan to look into possible ways to white-box the entire process so as to propose a more effective camouflage.",1467,0.798,876,1.6746575342465753,"In conduct an intriguing experimental study about the physical adversarial attack object detectors the wild In particular learn a camouflage pattern hide vehicles being state convolutional based detectors Our approach alternates two threads In, train a neural approximation function imitate how a simulator applies a camouflage vehicles a vehicle detector given images In second, minimize the approximated detection score searching the optimal camouflage Experiments the learned camouflage not hide a vehicle the image-based detectors under many test cases generalizes vehicles object detectors Is paint a unique pattern hence hide being We conjecture the answer affirmative mainly for First deep neural networks will widely modern surveillance autonomous driving systems for automatic vehicle detection Second unfortunately these neural networks intriguingly vulnerable adversarial examples BID1 . BID39 found adding imperceptible perturbations clean images the failure trained This motivates a rich line work developing defense techniques the neural networks BID1 powerful attack methods those defenses BID3 . Moreover the adversarial attack extended other tasks semantic segmentation BID2 , object detection BID44 imageFigure A Toyota Camry XLE in fools the Mask R-CNN object detector after we apply the learned camouflageon whereas neither plain colorson a random camouflagein able escape from beingIt the adversarial examples the works mentioned physical directly image pixels Although arguably challenging physical adversarial objects produce some existing works adversarial patches BID7 , stop signs small objects like baseballs 3D turtle models .To this are reasonably designing a special pattern camouflage by the deep learning based vehicle detectorsIt undoubtedly challenging run experiments considering financial and time constraints In instead demonstrate results using a simulation engineUnreal) Fig 1 shows that the vehicle in the simulation photo such, covered random camouflage detected the Mask R-CNN detector BID18 ) trained COCO BID21 .The simulation engine enables test the physically adversarial cars under a considerable spectrum: lighting backgrounds camera-toobject distances viewing angles In contrast existing experiments physical adversarial attacks all executed simplified scenarios BID14 , BID11 attack neural classifiers detectors of stop signs While projective transformations could render the planar stop signs to various images involved image the nonplanar 3D vehicles considered; we learn a neural approximation function instead BID4 synthesize objects ( baseball , turtle which adversarial within camerato viewing anglesGiven a 3D vehicle model in the simulation engine learn a camouflage for it following the expectation over transformationEoT principle first formalized The main idea consider transformations under the camouflage can consistently hide a neural detector A transformation imitates the imaging procedure and produces the 3D vehicle model If a camouflage works under many transformations seen the training phase expected also generalize unseen transformationsOne the simulator's image generation procedure nondifferentiable A seemingly plausible solution train approximate this procedure The network takes as input the environment a camouflage pattern the 3D vehicle model outputs as close rendered Although this approach viable extremely generate State methods ( RenderNet (Nguyen-Phuoc et 2018 ) only generate without any backgroundsWe tackle the above challenge drawing the following observation In EoT BID4 BID11 , the gradients propagate back the physical object from the detector/classifier's decision values If jointly consider the object detector the imaging procedure the simulator as a whole black box easier learn a function approximate train the image generation neural network Hence learn a substitute neural network which takes as a camouflage , the vehicle model the environment the vehicle detector's decision value Equipped this substitute network readily run the EoT algorithm BID4 over our simulator in infer an adversarial camouflage the vehiclesFinally make some remarks the significance and In multiclass visual object detection neural networks BID18 BID32 have become multiple industrial applications surveillance systems BID27 , military systems Among these applications cars Attacking vehicle detectors the physical world will enormously valuable impactful from the malicious adversaries Compared the stop sign legal paint while defacing is criminal This poses autonomous driving systems since anyone has perturb public machine based systems legally This observation motivates focus our approach cars We limit our camouflage within the legally paintable car body parts leave discriminative visual cues the tires windows lights unaltered for the detectors In it physically camouflage of complex shapes hide state object We conduct extensive experimental studies a photo-realistic simulation engine We propose a clone network mimic the simulator the detector's joint response the 3D vehicles Then infer a camouflage for a 3D vehicle minimizing the output the clone network Our learned camouflage significantly a Toyota Camry a SUV Moreover the camouflage transferable different environments For future work We plan look white-box as propose a more effective camouflage",0.01,0.4230472921812332
"As deep learning-based classifiers are increasingly adopted in real-world applications, the importance of understanding how a particular label is chosen grows. Single decision trees are an example of a simple, interpretable classifier, but are unsuitable for use with complex, high-dimensional data. On the other hand, the variational autoencoder (VAE) is designed to learn a factored, low-dimensional representation of data, but typically encodes high-likelihood data in an intrinsically non-separable way.   We introduce the differentiable decision tree (DDT) as a modular component of deep networks and a simple, differentiable loss function that allows for end-to-end optimization of a deep network to compress high-dimensional data for classification by a single decision tree.   We also explore the power of labeled data in a  supervised VAE (SVAE) with a Gaussian mixture prior, which leverages label information to produce a high-quality generative model with improved bounds on log-likelihood.   We combine the SVAE with the DDT to get our classifier+VAE (C+VAE), which is competitive in both classification error and log-likelihood, despite optimizing both simultaneously and using a very simple encoder/decoder architecture. While deep learning approaches are very effective in many classification problems, interpretability of the classifier (why a particular classification was made) can be very difficult, yet critical for many applications. Decision trees are highly interpretable classifiers, so long as the data is encoded such that the classes can be easily separated. We present a differentiable decision tree (DDT) that we connect to a variational autoencoder (VAE) to learn an embedding of the data that the tree can classify with low expected loss. The expected loss of the DDT is differentiable, so standard gradient-based methods may be applied in training.Since we work in a supervised learning setting, it is natural to exploit the label information when training the VAE. Thus, we employ a supervised VAE (SVAE) that uses a class-specific Gaussian mixture distribution as its prior distribution. We found that the SVAE was very effective in exploiting label information, resulting in improved log-likelihood due to separation of classes in latent space. Further, when we combined SVAE with DDT (yielding our Classifier+VAE, or C+VAE), we got a model that is competitive in both classification error and log-likelihood, despite optimizing both simultaneously and using a very simple encoder/decoder architecture. Further, the resultant decision tree revealed clear semantic meanings in its internal nodes.",513,0.249,300,1.71,"As deep learning-based classifiers adopted understanding a particular label chosen grows Single decision trees an example a simple, interpretable classifier are unsuitable use On the variational autoencoderVAE designed learn a factored, low-dimensional representation data typically encodes high-likelihood data an intrinsically non-separable way We introduce the differentiable decision tree a modular component deep networks a simple, differentiable loss function end optimization to compress for classification by We also explore the power labeled data a supervised VAESVAE with a Gaussian mixture prior, which leverages label information produce improved bounds We combine the SVAE with the DDT get our classifier+VAE (C+VAE competitive both classification error despite optimizing both simultaneously and While deep learning approaches very effective many classification problems interpretability (why was made yet critical Decision trees highly interpretable classifiers so long encoded such the classes separated We present a differentiable decision tree (DDT we connectVAE learn of that the tree classify with low expected loss The expected loss the DDT is differentiable so standard gradient-based methods trainingSince work a supervised learning setting natural exploit the label information when the VAE Thus employ a supervised VAE that a class-specific Gaussian mixture distribution its prior distribution We found the SVAE very exploiting label information resulting improved log-likelihood due separation classes latent space Further when combined SVAE DDTyielding our Classifier+VAE, or got a model competitive both classification error despite optimizing both simultaneously and Further the resultant decision tree revealed clear semantic meanings its internal nodes",0.0,0.5130967897658703
"We propose Regularized Learning under Label shifts (RLLS), a principled and a practical domain-adaptation algorithm to correct for shifts in the label distribution between a source and a target domain. We first estimate importance weights using labeled source data and unlabeled target data, and then train a classifier on the weighted source samples. We derive a generalization bound for the classifier on the target domain which is independent of the (ambient) data dimensions, and instead only depends on the complexity of the function class. To the best of our knowledge, this is the first generalization bound for the label-shift problem where the labels in the target domain are not available. Based on this bound, we propose a regularized estimator for the small-sample regime which accounts for the uncertainty in the estimated weights. Experiments on the CIFAR-10 and MNIST datasets show that RLLS improves classification accuracy, especially in the low sample and large-shift regimes, compared to previous methods. When machine learning models are employed ""in the wild"", the distribution of the data of interest(target distribution) can be significantly shifted compared to the distribution of the data on which the model was trained (source distribution). In many cases, the publicly available large-scale datasets with which the models are trained do not represent and reflect the statistics of a particular dataset of interest. This is for example relevant in managed services on cloud providers used by clients in different domains and regions, or medical diagnostic tools trained on data collected in a small number of hospitals and deployed on previously unobserved populations and time frames. In this work, we establish the first generalization guarantee for the label shift setting and propose an importance weighting procedure for which no prior knowledge of q(y)/p(y ) is required. Although RLLS is inspired by BBSL, it leads to a more robust importance weight estimator as well as generalization guarantees in particular for the small sample regime, which BBSL does not allow for. RLLS is also equipped with a sample-size-dependent regularization technique and further improves the classifier in both regimes.We consider this work a necessary step in the direction of solving shifts of this type, although the label shift assumption itself might be too simplified in the real world. In future work, we plan to also study the setting when it is slightly violated. For instance , x in practice cannot be solely explained by the wanted label y, but may also depend on attributes z which might not be observable. In the disease prediction task for example, the symptoms might not only depend on the disease but also on the city and living conditions of its population. In such a case , the label shift assumption only holds in a slightly modified sense, i.e. P(X|Y = y, Z = z) = Q(X|Y = y, Z = z). If the attributes Z are observed, then our framework can readily be used to perform importance weighting.Furthermore, it is not clear whether the final predictor is in fact ""better"" or more robust to shifts just because it achieves a better target accuracy than a vanilla unweighted estimator. In fact, there is a reason to believe that under certain shift scenarios, the predictor might learn to use spurious correlations to boost accuracy. Finding a procedure which can both learn a robust model and achieve high accuracies on new target sets remains to be an ongoing challenge. Moreover, the current choice of regularization depends on the number of samples rather than data-driven regularization which is more desirable.An important direction towards active learning for the same disease-symptoms scenario is when we also have an expert for diagnosing a limited number of patients in the target location. Now the question is which patients would be most ""useful"" to diagnose to obtain a high accuracy on the entire target set? Furthermore, in the case of high risk , we might be able to choose some of the patients for further medical diagnosis or treatment, up to some varying cost. We plan to extend the current framework to the active learning setting where we actively query the label of certain x's BID5 as well as the cost-sensitive setting where we also consider the cost of querying labels (Krishnamurthy et al., 2017) .Consider a realizable and over-parameterized setting, where there exists a deterministic mapping from x to y, and also suppose a perfect interpolation of the source data with a minimum proper norm is desired. In this case, weighting the samples in the empirical loss might not alter the trained classifier BID3 . Therefore, our results might not directly help the design of better classifiers in this particular regime. However, for the general overparameterized settings, it remains an open problem of how the importance weighting can improve the generalization. We leave this study for future work.",957,0.477,560,1.7089285714285714,"We propose Regularized Learning under Label shifts a principled and a practical domain-adaptation algorithm correct shifts the label distribution a source We first estimate importance weights labeled source data train the weighted source samples We derive bound on the target domain which independent the (ambient) data dimensions instead only depends the complexity the function class. To bound the label-shift problem where in the target domain available Based this bound propose a regularized estimator the small-sample regime which accounts Experiments MNIST datasets RLLS improves especially the low sample and large-shift regimes previous methods When machine learning models employed "" wild the distribution of interest(target distribution significantly shifted compared onsource distribution In publicly large datasets with the models trained do represent and reflect the statistics of This for example relevant managed services on cloud providers used clients different domains regions medical diagnostic tools trained data deployed previously unobserved populations and time frames In this work establish the first generalization guarantee the label shift setting propose an importance weighting procedure which q(y)/p(y ) Although RLLS inspired BBSL leads a more robust importance weight estimator as generalization guarantees particular the small sample regime RLLS is also equipped a sample-size-dependent regularization technique and further improves in both regimesWe consider work a necessary solving shifts this type although the label shift assumption itself might too simplified In future work also study the setting when slightly violated For instance , x in practice solely explained the wanted label y may depend attributes z which might observable In the disease prediction task for example the symptoms might only depend the city and living conditions its population In , the label shift assumption only a slightly modified sense P(X|Y = y If the attributes Z are observed our framework readily perform importance weightingFurthermore the final predictor in ""better more robust to shifts just achieves a better target accuracy In fact to under certain shift scenarios the predictor might learn use spurious correlations boost accuracy Finding a procedure which both learn a robust model achieve new target sets remains Moreover the current choice regularization depends samples rather data-driven regularization which desirableAn important direction towards active learning for the same disease-symptoms scenario when also an expert for a limited number the target location Now the question which patients "" diagnose to obtain a high accuracy on entire target set Furthermore high risk , might choose some further medical diagnosis up some varying cost We plan extend the current framework the active learning setting where actively query the label certain x's BID5 as the cost-sensitive setting also consider ( 2017 .Consider a realizable and over-parameterized setting there exists from also suppose a perfect interpolation a minimum proper norm is desired In weighting the samples the empirical loss might alter the trained classifier BID3 . Therefore our results might directly help the design better classifiers this particular regime However for the general overparameterized settings remains an open problem of the importance weighting improve We leave this study future work",0.01,0.5103668839005552
"The statistics of the real visual world presents a long-tailed distribution: a few classes have significantly more training instances than the remaining classes in a dataset. This is because the real visual world has a few classes that are common while others are rare. Unfortunately, the performance of a convolutional neural network is typically unsatisfactory when trained using a long-tailed dataset. To alleviate this issue, we propose a method that discriminatively learns an embedding in which a simple Bayesian classifier can balance the class-priors to generalize well for rare classes. To this end, the proposed approach uses a Gaussian mixture model to factor out class-likelihoods and class-priors in a long-tailed dataset. The proposed method is simple and easy-to-implement in existing deep learning frameworks. Experiments on publicly available datasets show that the proposed approach improves the performance on classes with few training instances, while maintaining a comparable performance to the state-of-the-art on classes with abundant training examples. Deep convolutional neural networks (CNN) have achieved impressive results in large-scale visual recognition tasks BID13 BID25 BID29 BID18 BID8 BID10 . However, despite the significant impact in visual perception, the vast majority of these advancements learn from artificially balanced largescale datasets that are not representative of the real visual world BID19 BID5 BID3 BID21 BID15 BID23 . The statistics of the real visual world follow a long-tailed distribution BID36 BID32 BID24 BID33 BID34 . This means that a few classes are predominant in the world while others are rare. Consequently, representative real-world datasets have a few classes with significantly more training instances than the remaining classes in the set; see Fig. 1 (a) for an illustration of a long-tailed dataset. We refer to classes with abundant training instances as classes in the head, and unrepresented classes as classes in the tail.As BID32 note, the main motivation for visual recognition is to understand and learn from the real visual world. Thus, while the state-of-the-art can challenge humans in visual recognition tasks, it misses a mechanism that effectively learns from long-tailed datasets. As BID32 found, training models using long-tailed datasets often leads to unsatisfying performance. This is because classifiers tend to generalize well for classes in the head, but lack generalization for classes in the tail.To alleviate this issue, learned classifiers need to generalize for classes in the tail while maintaining a good performance for all the classes. Recent efforts that aim to learn from long-tailed datasets consider penalities in the optimization-learning problem BID9 , sampling-based methods BID7 , and transfer-learning algorithms BID33 BID34 . In contrast with these solutions, the proposed method aims to learn an embedding in which the distribution of the real visual world allows a simple Bayesian classifier to predict robustly given a long-tailed dataset.Long-tailed datasets have class-prior statistics that heavily skew towards classes in the head. This skew can bias classifiers towards classes in the head, and consequently can reduce generalization for classes in the tail. To remove this skew, we appeal to Bayesian classifiers that can explicitly Figure 1: (a) The real visual world yields long-tailed datasets. Classes in the head are common (e.g., cats) while classes in the tail are rare (e.g., white reindeers). (b) The proposed approach builds a generative (Bayesian) classifier over a learned embedding to compute class-posterior probabilities. In an empirical Bayesian framework, posteriors are computed through class likelihoods and priors fit to the data (e.g., sample means, variances, and counts assuming Gaussian Mixture Models). We introduce an end-to-end pipeline for jointly learning embeddings and Bayesian models built upon them. (c) Bayesian models are particularly well-suited for long-tailed datasets because class priors and likelihoods can be fixed to be uniform and isotropic, ensuring that the learned representation is balanced across the head and tail.factor out the likelihood and prior when computing posteriors over class labels. Thus, the main goal of this work is to learn a feature embedding in which class prior statistics do not affect/skew class likelihoods. The proposed approach uses a simple Gaussian mixture model (GMM) to describe the statistics of a long-tailed dataset. This is because it enables a clean factorization of the class-likelihoods and class-priors. Moreover, it easily fits within an empirical Bayesian classification framework, because a GMM enables the computation of closed-form maximum likelihood estimation (MLE) of class-specific means, covariance matrices, and priors. We show that such closed-form estimates can be integrated into existing deep learning optimizers without much effort. By fixing the covariance matrices of all the classes to be the identity and the priors over each class to be uniform, we can explicitly enforce that both rare classes in the tail and dominant classes in the head have equal weight for Bayesian classification. In simple terms: we learn a discriminative embedding of training data such that Bayesian classifiers with balanced priors produce accurate class posteriors. As a point of clarity, the proposed approach does not learn an embedding in the traditional Bayesian sense, which might define a prior distribution over embeddings that is then combined with training data to produce a posterior embedding. Rather, it learns a single embedding that is discriminatively trained to produce accurate features for Bayesian classifiers. See Fig. 1 for an illustration about the proposed approach.A GMM not only is useful for learning an embedding using a long-tailed dataset, but also provides flexibility at the evaluation stage. This is because it enables the measurement of generalization for classes in the tail by simply setting equal class-prior probabilities. In addition, it enables the possibility of giving more importance to the most frequent classes by adjusting their respective class-prior probabilities.In sum, the proposed approach aims to learn an embedding in which a GMM enables a Bayesian classifier to generalize well for classes in the tail by balancing out class-priors. The proposed method is simple, easy-to-train using deep learning frameworks, and increases classification performance for classes in the tail. The experiments on publicly available datasets show that this approach tends to perform better on classes in the tail than the competing methods, while performing comparable to the state-of-the-art on classes with abundant training instances. Other probabilistic models: Our analysis and experiments focus on Gaussian Mixture Models, but the general learning problem from Eq. (4) holds for other probabilistic models. For example, deep embeddings can be learned for rectified (nonnegative) or binary features BID0 BID4 . For such embeddings, likelihood models based on rectified Gaussians or multivariate Bernoulli distributions may be more appropriate BID27 BID30 . Such models do not appear to have closed form maximum likelihood estimates, and so may be challenging to formulate precisely as a constrained optimization problem.Relationship to softmax: The GMM-based formulation has a direct relationship with softmax classifiers. This relationship can be obtained by expanding the squared distance terms in the classposterior probability, yielding the following: DISPLAYFORM0 where v j = µ j and DISPLAYFORM1 2 is a common term between the numerator and denominator. This relationship thus indicates that the proposed approach fits linear classifiers with restricted biases. This relationship is useful for an easy implementation in many deep learning frameworks. This is because this approach can be implemented using a dense layer without the bias terms. In addition, this relationship shows that the proposed approach requires fewer parametersto-learn in comparison with classical CNN-softmax models. An more intuitive comparison between GMMs and softmax classifiers can be made with respect to to their parameter updates. Intuitively, during softmax training, an ""easy"" example of a class will not generate a model update. In some sense, this might be considered paradoxical. When children learn a new concept (for say, a neverbefore-seen animal), they tend to be presented with an easy or ""protypical"" example. On the other hand, an easy example of a class will change its centroid, generating a signal for learning -see FIG1 . This work introduced a method that improves the classification performance for classes in the tail. The proposed approach is based on a Gaussian mixture model that allows a Bayesian classifier to represent the distribution of a long-tailed dataset and to compute the class-prediction probabilities. The experiments on publicly available dataset show that the proposed approach tends to increase the classification accuracy for classes in the tail while maintaining a comparable accuracy to that of a softmax classifier for classes in the head. In addition, this work introduced an evaluation method for methods that tackle the learning of concepts from a long-tailed dataset. Finally, this work demon-strated that class-centroid approaches overall tend to generalize well for classes in the tail while maintaining a comparable performance to that of a softmax classifiers for classes in the head.",1792,0.993,1041,1.7214217098943323,"The statistics the real visual world presents a few classes significantly more training instances This because the real visual world a few classes common while Unfortunately the performance typically trained a long-tailed dataset To alleviate propose discriminatively learns an embedding in which balance the class-priors generalize well for rare classes To this end the proposed approach uses factor class-likelihoods class-priors a long-tailed dataset The proposed method simple- in existing deep Experiments publicly available datasets the proposed approach improves on classes few training instances maintaining on abundant training examples achieved . However despite in visual perception these advancements learn artificially balanced largescale datasets . The statistics the real visual world follow BID36 BID32 . This means a few classes predominant while rare representative real-world datasets a few classes with significantly more training instances the remaining classes; Fig 1 (a for an illustration a long-tailed dataset We refer classes with abundant training instances the head unrepresented classesAs BID32 note the main motivation visual recognition the real visual world Thus while can challenge humans visual recognition tasks misses a mechanism effectively learns long-tailed datasets As BID32 found training models using long-tailed datasets often leads unsatisfying performance This because classifiers tend well for the head lack generalizationTo alleviate learned classifiers need while Recent efforts that aim learn long-tailed datasets consider penalities the optimization-learning problem BID9 , sampling-based methods BID7 transfer In contrast these solutions the proposed method aims learn an embedding in which the distribution the real visual world allows robustly given a long-tailed datasetLong-tailed datasets class-prior statistics heavily skew towards classes the head This skew can bias classifiers towards classes in the head consequently reduce for classes To remove this skew appeal Bayesian classifiers explicitly Figure: The real visual world yields long-tailed datasets Classes the head are while (b The proposed approach builds over learned embedding to compute class-posterior probabilities In an empirical Bayesian framework posteriors computed through class likelihoods fit sample means counts assuming Gaussian Mixture Models We introduce end pipeline jointly learning embeddings Bayesian models built them (c) Bayesian models particularly long-tailed datasets class priors fixed uniform ensuring the learned representation balanced the head tail.factor out the likelihood prior when computing posteriors over class labels Thus learn a feature embedding which class prior statistics do/skew class likelihoods The proposed approach uses the statistics a long-tailed dataset This because enables a clean factorization the class-likelihoods class-priors Moreover easily fits an empirical Bayesian classification framework a GMM enables the computation closed-form maximum likelihood estimation class-specific means We show such closed-form estimates integrated existing deep learning optimizers without By fixing to the identity over uniform explicitly enforce both rare classes in the tail and dominant classes Bayesian classification In simple terms learn a discriminative embedding of training data such Bayesian classifiers balanced priors produce accurate class posteriors As a point clarity the proposed approach learn an embedding in the traditional Bayesian sense might define a prior distribution that then combined training data embedding Rather learns a single embedding that discriminatively trained accurate features Bayesian classifiers See Fig 1 for an illustration about the proposed approachA GMM not useful learning an embedding using a long-tailed dataset flexibility at This because enables the measurement generalization for classes the tail by simply setting equal class-prior probabilities In addition enables the possibility giving more importance the most frequent classes by adjusting their respective class-prior probabilitiesIn sum aims learn an embedding in which a GMM enables well for the tail by balancing The proposed method simple easytrain using deep learning frameworks increases classification performance classes the tail The experiments publicly available datasets this approach tends perform classes in the tail the competing methods while performing comparable on abundant training instances Other probabilistic models: Our analysis and experiments focus Gaussian Mixture Models the general learning problem from Eq holds For example deep embeddings learned rectified (nonnegative or binary features BID0 BID4 For such embeddings likelihood models based rectified Gaussians more appropriate BID27 BID30 . Such models do closed form maximum likelihood estimates may challenging formulate precisely as a constrained optimization problemRelationship softmax: The GMM-based formulation This relationship obtained expanding the squared distance terms the classposterior probability, yielding DISPLAYFORM0 where v j µ 2 a common term between This relationship thus indicates the proposed approach fits linear classifiers restricted biases This relationship useful an easy implementation many deep learning frameworks This because this approach implemented a dense layer without the bias terms In addition this relationship shows the proposed approach requires fewer parametersto-learn in comparison classical CNN-softmax models An more intuitive comparison GMMs softmax classifiers respect to their parameter updates Intuitively during softmax training an ""easy"" example a class will not generate a model update In some sense might considered When children learn (for say presented an easy or ""protypical"" example On an easy example a class will change its centroid generating a signal learning -see FIG1 This work introduced improves the classification performance classes the tail The proposed approach a Gaussian mixture model allows represent a long-tailed dataset The experiments publicly available dataset show the proposed approach tends for classes the tail while maintaining for In addition this work introduced an evaluation method methods tackle the learning concepts a long-tailed dataset Finally this work demon- class-centroid approaches overall tend generalize well for classes the tail while maintaining a comparable performance a softmax classifiers",0.01,0.5421983030761701
"As deep reinforcement learning is being applied to more and more tasks, there is a growing need to better understand and probe the learned agents. Visualizing and understanding the decision making process can be very valuable to comprehend and identify problems in the learned behavior. However, this topic has been relatively under-explored in the reinforcement learning community. In this work we present a method for synthesizing states of interest for a trained agent. Such states could be situations (e.g. crashing or damaging a car) in which specific actions are necessary. Further, critical states in which a very high or a very low reward can be achieved (e.g. risky states) are often interesting to understand the situational awareness of the system. To this end, we learn a generative model over the state space of the environment and use its latent space to optimize a target function for the state of interest. In our experiments we show that this method can generate insightful visualizations for a variety of environments and reinforcement learning methods. We explore these issues in the standard Atari benchmark games as well as in an autonomous driving simulator. Based on the efficiency with which we have been able to identify significant decision scenarios with this technique, we believe this general approach could serve as an important tool for AI safety applications. Humans can naturally learn and perform well at a wide variety of tasks, driven by instinct and practice; more importantly, they are able to justify why they would take a certain action. Artificial agents should be equipped with the same capability, so that their decision making process is interpretable by researchers. Following the enormous success of deep learning in various domains, such as the application of convolutional neural networks (CNNs) to computer vision BID19 BID18 BID20 BID33 , a need for understanding and analyzing the trained models has arisen. Several such methods have been proposed and work well in this domain, for example for image classification BID35 BID44 BID8 , sequential models BID12 or through attention BID41 .Deep reinforcement learning (RL) agents also use CNNs to gain perception and learn policies directly from image sequences. However , little work has been so far done in analyzing RL networks. We found that directly applying common visualization techniques to RL agents often leads to poor results. In this paper, we present a novel technique to generate insightful visualizations for pre-trained agents.Currently, the generalization capability of an agent is-in the best case-evaluated on a validation set of scenarios. However , this means that this validation set has to be carefully crafted to encompass as many potential failure cases as possible. As an example, consider the case of a self-driving agent, where it is near impossible to exhaustively model all interactions of the agent with other drivers, pedestrians, cyclists, weather conditions, even in simulation. Our goal is to extrapolate from the training scenes to novel states that induce a specified behavior in the agent.In our work, we learn a generative model of the environment as an input to the agent. This allows us to probe the agent's behavior in novel states created by an optimization scheme to induce specific actions in the agent. For example we could optimize for states in which the agent sees the only option as being to slam on the brakes; or states in which the agent expects to score exceptionally low. Visualizing such states allows to observe the agent's interaction with the environment in critical scenarios to understand its shortcomings. Furthermore , it is possible to generate states based on an objective function specified by the user. Lastly, our method does not affect and does not depend on the training of the agent and thus is applicable to a wide variety of reinforcement learning algorithms. We have presented a method to synthesize inputs to deep reinforcement learning agents based on generative modeling of the environment and user-defined objective functions. Training the generator to produce states that the agent perceives as those from the real environment enables optimizing its latent space to sample states of interest. We believe that understanding and visualizing agent behavior in safety critical situations is a crucial step towards creating safer and more robust agents using reinforcement learning. We have found that the methods explored here can indeed help accelerate the detection of problematic situations for a given learned agent. As such we intend to build upon this work.",843,0.493,480,1.75625,"As deep reinforcement learning better probe the learned agents Visualizing and understanding valuable comprehend identify problems the learned behavior However this topic relatively under the reinforcement learning community In this work present states interest a trained agent Such states could situations ( crashing damaging specific actions Further critical states in a very or a reward interesting understand the situational awareness To this end learn a generative model over the state space the environment use its latent space optimize a target function interest In our experiments show this method generate insightful visualizations for environments reinforcement learning methods We explore these issues the standard Atari benchmark games as an autonomous driving simulator Based the efficiency with we have identify significant decision scenarios with this technique this general approach could serve AI safety applications Humans can naturally learn perform well driven instinct practice; more justify why would take Artificial agents should equipped the same capability so their decision making process interpretable researchers Following the enormous success deep learning various domains such the application BID19 BID18 BID20 BID33 , a need understanding analyzing the trained models Several such methods work for for image classification BID35 BID44 , sequential models or through attention BID41 .Deep reinforcement learning (RL) agents also CNNs gain perception learn policies directly image sequences However , little work so analyzing RL networks We found directly applying common visualization techniques RL agents often poor results In this paper generate insightful visualizations for pre-trained agentsCurrently the generalization capability-in bestevaluated on a validation set scenarios However , means this validation set carefully crafted encompass as many potential failure cases As an example a self-driving agent where near exhaustively model all interactions pedestrians weather conditions even in simulation Our goal extrapolate the training scenes novel states that induce a specified behavior the agentIn our work learn a generative model the environment as This allows probe the agent's behavior novel states created an optimization scheme to induce specific actions For example we could optimize for states the agent sees the only option as slam on; states expects score exceptionally Visualizing such states allows to observe the agent's interaction critical scenarios to its shortcomings Furthermore , generate states an objective function specified Lastly our method does affect and depend the training the agent and thus applicable reinforcement learning We presented inputs deep reinforcement learning agents based generative modeling the environment user-defined objective functions Training the generator states the agent those from the real environment enables optimizing its latent space sample We believe understanding visualizing agent behavior safety critical situations creating using We found the methods explored indeed accelerate problematic situations for a given learned agent As such we intend build upon",0.01,0.630937726285301
"We introduce the deep abstaining classifier -- a deep neural network trained with a novel loss function that provides an abstention option during training. This allows the  DNN to abstain on confusing or difficult-to-learn examples while improving performance on the non-abstained samples. We show that such deep abstaining classifiers can: (i) learn representations for structured noise -- where noisy training labels or confusing examples are correlated with underlying features -- and then learn to abstain based on such features; (ii) enable robust learning in the presence of arbitrary or unstructured noise by identifying noisy samples; and (iii) be used as an effective out-of-category detector that learns to reliably abstain when presented with samples from  unknown classes. We provide analytical results on loss function behavior that enable automatic tuning of accuracy and coverage, and demonstrate the utility of the deep abstaining classifier using multiple image benchmarks, Results indicate significant improvement in learning in the presence of label noise. Machine learning algorithms are expected to increasingly replace humans in decision-making pipelines. With the deployment of AI-based systems in high risk fields such as medical diagnosis BID23 , autonomous vehicle control BID19 and the legal sector BID3 , an erroneous prediction that should have otherwise been flagged for human interventionbecause the system has not robustly learned when it is likely to get the wrong answer -can have severe consequences.In these situations, the quality of ""knowing when it doesn't know"" and abstaining from predicting is an essential trait for a classifier to possess. This allows the decision-making to be routed to a human or another more accurate, but possibly more expensive, classifier, with the assumption being that the additional cost incurred is greatly surpassed by the consequences of a wrong prediction.Since learning systems have been around for multiple decades, there has been extensive theoretical and empirical investigation into rejection (or abstention) classification with the bulk of this being in the area of shallow learners BID5 BID7 BID10 and multilayer perceptrons BID8 . A framework for ""self-aware learning"" was analyzed in the context of Markov decision processes in BID20 . In the context of deep networks, this has been an under-explored area with BID11 recently proposing an effective technique of selective classification for optimizing risk-vs-coverage profiles based on the output of a trained model.The abstention formulations in all the previous works have been in a post-processing setting i.e., a classifier is first trained as usual, and an abstention threshold is determined based on post-training performance on a calibration set. In this paper, we introduce a method to train DNNs that utilizes an abstention option while training. Using a novel loss function -a modified version of the multi-class categorical cross-entropy loss that includes an abstention output -the representational capacity of a DNN is exploited for learning when abstention is a better option, while at the same improving performance on the non-abstained samples. We illustrate the utility of a DNN trained in this way in multiple situations: first, when labeling errors are correlated with some underlying feature of the data (systematic or structured label noise), abstention training allows the DNN to learn features that are indicative of unreliable training signals and which are thus likely to lead to uncertain predictions. This kind of representation learning for abstention is useful both for effectively eliminating structured noise and also for interpreting the reasons for abstention. Second, we show how an abstention-based approach can be used as a very effective data cleaner when training data contains arbitrary (or unstructured) label noise: a DNN trained with an abstention option can be used to identify and filter out noisy training data leading to significant performance benefits for downstream training using a cleaner set. Finally, we also consider the problem of open-set detection since real-world systems are often deployed in open-domain situations; when presented with samples from unknown classes, abstention is often the safest choice. We describe a method for utilizing abstention training for effective open-set detection by training the DNN to pickup only features associated with known classes, and abstain when such features are absent. To summarize, the contributions of this paper are:• The introduction of the deep abstaining classifier (DAC) -a DNN trained with a novel loss function that uses an abstention class while training -enabling robust learning in the presence of label noise.• The demonstration of the ability of the DAC to learn features associated with systematic label noise. Through numerous experiments, we show how the DAC is able to pick up (and then abstain on) such features with remarkable precision.• Demonstration of the utility of the DAC as a highly effective data cleaner in the presence of arbitrary label noise. We provide results on learning with noisy labels on multiple image benchmarks (CIFAR-10, CIFAR-100 and Fashion-MNIST) that are competitive and in many cases, significantly improve performance compared to existing methods.• Illustration of the DAC as an effective open-set detector that learns to reliably abstain when presented with samples from unknown classes.We note that, while ideally such an abstaining classifier should also learn to reliably abstain when presented with adversarially perturbed samples BID26 BID35 MoosaviDezfooli et al., 2017) , in this work we do not consider adversarial settings and leave that for future exploration. The rest of the paper is organized as follows: Section 2 describes the loss function formulation and an algorithm for automatically tuning abstention behavior. Section 3 discusses learning in the presence of structured noise, including experimental results and visual interpretations of abstention. Section 4 presents the utility of the DAC for data cleaning in the presence of unstructured (arbitrary) noise. Section 5 has further discussions on abstention behavior in the context of memorization. Section 6 discusses open set detection with the DAC. We conclude in Section 7. We introduced and the illustrated the utility of a deep abstaining classifier -a DNN trained on a novel loss function that learns to abstain as opposed to abstention calibration after training. We illustrated the utility of the DAC in multiple situations: as a representation learner in the presence of structured noise, as an effective data cleaner in the presence of arbitrary noise, and as an effective out-of-category detector. While adversarial settings were not considered in this work, the DAC, and abstention in general, might be considered as part of the defense arsenal against adversarial attacks; we leave this for future work. In summary, our results here indicate that the representational power of DNNs can be used very effectively as a means of self-calibration -""knowing when it doesn't know"". Figure 6 : Results on blurred-image experiment with noisy labels (a)20% of the images are blurred in the train set, and their labels randomized (b) Validation accuracy for baseline vs DAC (non-abstained) (c)Abstention behavior for the DAC during training (d) Distribution of predictions on the blurred validation images for the DAC. We also observed (not shown) that for the baseline DNN, the accuracy on the blurred images in the validation set is no better than random.Results The DAC abstains remarkably well on the blurred images in the test set (Figure 6d ), while maintaining classification accuracy over the remaining samples in the validation set (≈ 79%). The baseline DNN accuracy drops to 63% (Figure 6b ), while the basline accuracy over the smudged images alone is no better than random (≈ 9.8%) . The abstention behavior of the DAC on the blurred images in the test set can be explained by how abstention evolves during training (Figure 6c ). Once abstention is introduced at epoch 20, the DAC initially opts to abstain on a high percentage of the traning data, while continuing to learn (since the gradients w.r.t the true-class pre-activations are always negative.). In the later epochs, sufficient learning has taken place on the non-randomized samples but the DAC continues to abstain on about 20% of the training data, which corresponds to the blurred images indicating that a strong association has been made between blurring and abstention.",1648,0.677,981,1.6799184505606524,"We introduce the deep abstaining classifier -- a novel loss function provides an abstention option during This allows the DNN abstain on confusing or difficult-to-learn examples while improving the non-abstained samples We show such deep abstaining classifiers: learn representations for structured noise -- where noisy training labels or confusing examples correlated underlying features then abstain based enable robust learning by identifying noisy samples be used outcategory detector that learns reliably presented samples unknown classes We provide analytical results loss function behavior that enable automatic tuning accuracy coverage demonstrate the deep abstaining classifier using multiple image benchmarks Results indicate learning in label noise Machine learning algorithms expected increasingly replace decision-making pipelines With the deployment high risk fields medical diagnosis BID23 , autonomous vehicle control BID19 the legal sector an erroneous prediction that should otherwise flagged human interventionbecause robustly learned when likely get -canIn the quality ""knowing when does abstaining predicting an essential trait a classifier possess This allows routed a human or another more accurate but possibly expensive classifier with the assumption being the additional cost incurred greatly surpassed the consequences a wrong predictionSince learning systems multiple decades extensive theoretical and empirical investigation rejection (or abstention) classification with the bulk being shallow learners BID5 BID7 BID10 multilayer perceptrons . A framework ""self-aware learning was analyzed Markov decision processes BID20 . In the context deep networks has with BID11 recently proposing an effective technique selective classification optimizing riskvscoverage profiles the output a trained modelThe abstention formulations all the previous works in first as usual an abstention threshold determined post-training performance a calibration set In train utilizes an abstention option while training Using a novel loss function -a modified version that includes an abstention output -the representational capacity a DNN exploited learning when abstention a better option while at the same improving performance the non-abstained samples We illustrate a DNN trained multiple situations first labeling errors are correlated some underlying featuresystematic or structured label noise abstention training allows features indicative unreliable training signals which thus uncertain predictions This kind representation learning for abstention useful both effectively eliminating structured noise also interpreting the reasons Second show as very data cleaner when training data contains arbitrary (or unstructured) label noise: a DNN trained identify filter leading significant performance benefits downstream training using a cleaner set. Finally also consider open-set detection since deployed open-domain situations; when presented samples unknown classes abstention We describe utilizing abstention training effective open-set detection by training the DNN pickup only features associated known classes, abstain when To summarize, the contributions are:• The introduction the deep abstaining classifierDAC) -a DNN trained with a novel loss function while training -enabling robust learning label the DAC features associated systematic label noise Through numerous experiments show the DAC pick ( then abstain on such features with remarkable precision.• Demonstration the utility highly data cleaner arbitrary label noise We provide results learning with noisy labels on multiple image benchmarks Fashion-MNIST competitive in significantly improve compared existing methods.• Illustration the DAC as an effective open-set detector that learns reliably abstain when presented samples unknown classesWe note, ideally such an abstaining classifier also learn adversarially perturbed samples BID26 BID35 MoosaviDezfooli) , in adversarial settings leave that The rest organized Section describes the loss function formulation an algorithm automatically tuning abstention behavior Section discusses learning in the presence structured noise experimental results visual interpretations abstention Section presents the utility the DAC data cleaning Section has further discussions abstention behavior memorization Section discusses open set detection the DAC We conclude in Section 7 We introduced and the illustrated the utility a deep abstaining classifier -a DNN trained a novel loss function learns as opposed abstention calibration after We illustrated the utility the DAC multiple situations as a representation learner structured noise effective data cleaner outcategory detector While adversarial settings were this work the DAC, abstention general might part the defense arsenal; we leave In summary our results here the representational power DNNs very self-calibration -""knowing it does know Figure : Results on blurred-image experiment noisy labelsa)20 the train set their labels randomized (b) Validation accuracy baseline vs DACnonabstainedc)Abstention behavior the DAC during predictions the blurred validation images We also observed (not for the baseline DNN the accuracy on the blurred images in the validation set no randomResults The DAC abstains remarkably testFigure 6d maintaining classification accuracy over� 79% The baseline DNN accuracy dropsFigure 6b the basline accuracy over the smudged images alone no random (�� . The abstention behavior the DAC on the blurred images can how abstention evolves trainingFigure 6c Once abstention introduced at epoch 20 the DAC initially opts on a high percentage the traning data while continuing learn (since the true-class preactivations negative In the later epochs sufficient learning but the DAC continues abstain on about 20% corresponds the blurred images indicating a strong association blurring abstention",0.01,0.4364516447304483
"Temporal Difference learning with function approximation has been widely used recently and has led to several successful results.   However, compared with the original tabular-based methods, one major drawback of temporal difference learning with neural networks and other function approximators is that they tend to over-generalize across temporally successive states, resulting in slow convergence and even instability. In this work, we propose a novel TD learning method, Hadamard product Regularized TD (HR-TD), that reduces over-generalization and thus leads to faster convergence. This approach can be easily applied to both linear and nonlinear function approximators. 
 HR-TD is evaluated on several linear and nonlinear benchmark domains, where we show improvement in learning behavior and performance. Temporal Difference (TD) learning is one of the most important paradigms in Reinforcement Learning BID15 . Techniques based on combining TD learning with nonlinear function approximators and stochastic gradient descent, such as deep networks, have led to significant breakthroughs in large-scale problems to which these methods can be applied BID8 BID12 .At its heart, the TD learning update is straightforward. v(s ) estimates the value of being in a state s. After an action a that transitions the agent from s to next state s , v(s) is altered to be closer to the (discounted) estimated value of s , v(s ) (plus any received reward, r). The difference between these estimated values is called the temporal difference error (TD error) and is typically denoted as δ. Formally, δ = r + γv(s ) − v(s), where γ is the discount factor, and r + γv(s ) is known as the TD target.When states are represented individually (the tabular case), v(s) can be altered independently from v(s ) using the update rule v(s) ← v(s) + αδ, where α is the learning rate. In fully deterministic environments , α can be set to 1, thus causing v(s) to change all the way to the TD target. Otherwise, in a stochastic environment , α is set less than 1 so that v(s) only moves part of the way towards the TD target, thus avoiding over-generalization from a single example. When, on the other hand, states are represented with a function approximator, as is necessary in large or continuous environments, v(s) can no longer be updated independently from v(s ). That is because s and s are likely to be similar (assuming actions have local effects), any change to v(s) is likely to also alter v(s ). While such generalization is desirable in principle, it also has the unintended consequence of changing the TD target, which in turn can cause the TD update to lead to an increase in the TD error between s and s . This unintended consequence can be seen as a second form of over-generalization: one that can be much more difficult to avoid.Past work has identified this form of over-generalization in RL, has observed that it is particularly relevant in methods that use neural network function approximators such as DQN BID8 , and has proposed initial solutions BID4 BID10 . In this paper, we present a deeper analysis of the reasons for this form of over-generalization and introduce a novel learning algorithm termed HR-TD, based on the recursive proximal mapping formulation of TD learning BID1 , which offers a mathematical framework for parameter regularization that allows one to control for this form of over-generalization. Empirical results across multiple domains demonstrate that our novel algorithm learns more efficiently (from fewer samples) than prior approaches.The rest of the paper is organized as follows. Section 2 offers a brief background on TD learning, the over-generalization problem, and optimization techniques used in the derivation of our algorithm. In Section 3, we discuss the state-of-the-art research in this direction. The motivation and the design of our algorithm are presented in Section 4. Finally , the experimental results of Section 5 validate the effectiveness of the proposed algorithm. In this paper, we analyze the problem of over-generalization in TD learning with function approximation. This analysis points to the potential pitfalls of over-generalization in TD-learning. Based on the analysis, we propose a novel regularization scheme based on the Hadamard product. We also show that with the right weight on the regularization, the solution of this method is the same as that of TD. Finally, we experimentally validate the effectiveness of our algorithm on benchmarks of varying complexity.",901,0.469,534,1.6872659176029963,"Temporal Difference learning with function approximation has widely recently led several successful results However compared the original tabular-based methods one major drawback temporal difference learning with and other function approximators over across temporally successive states slow convergence even instability In this work propose a novel TD learning method Hadamard product Regularized TDHR-TD reduces over thus leads faster convergence This approach can easily both linear and nonlinear function approximators HR-TD is evaluated several linear and nonlinear benchmark domains where we show improvement learning behavior Temporal Difference (TD) learning one Reinforcement Learning BID15 . Techniques based combining TD learning nonlinear function approximators deep networks led to which these methods BID8 BID12 .At its heart the TD learning update straightforward v(s ) estimates being a state s. After an action a that transitions the agent s next state s , v(s altered be closer the (discounted) estimated value ) (plus any received reward, r The difference these estimated values called the temporal difference errorTD error typically denoted �� Formally, �� = r + ��v(s ) the discount factor known the TD targetWhen states represented individuallythe tabular case can altered independently ) α�, the learning rate In fully deterministic environments , α can set thus causing v(s change the TD target Otherwise in a stochastic environment , α set less so v(s only moves part the TD target thus avoiding over-generalization from a single example When, states represented with a function approximator as necessary large or continuous environments v(s no updated independently That because s and likely similar (assuming actions have local effects any change v(s also alter ). While such generalization desirable principle also changing the TD target in the TD update lead the TD error between s . This unintended consequence as a second form one can muchPast work identified this form RL has observed particularly relevant methods neural network function approximators DQN BID8 , initial solutions BID4 BID10 In this paper a deeper analysis the reasons this form introduce novel learning termed HR-TD the recursive proximal mapping formulation TD learning BID1 , offers parameter regularization that one control this form Empirical results across multiple domains demonstrate our novel algorithm learns more (from fewer samples prior approachesThe rest organized Section offers a brief background TD learning over problem optimization techniques the derivation our algorithm In Section state- research this direction The motivation and the design our algorithm presented Section Finally , the experimental results Section validate the proposed algorithm In this paper analyze the problem over-generalization TD learning with function approximation This analysis points the potential pitfalls TD-learning Based the analysis propose a novel regularization scheme the Hadamard product We also show with the right weight on the regularization the solution this method the TD. Finally experimentally validate our algorithm benchmarks varying complexity",0.01,0.4551723452129446
"We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. 
 To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficient neural networks that match or outperform state-of-the-art network architectures in terms of performance but with a significantly lower number of network parameters. We evaluate our algorithm in an extensive series of experiments on a variety of computer vision and climate science tasks, including shape classification, climate pattern segmentation, and omnidirectional image semantic segmentation. Overall, we present (1) a novel CNN approach on unstructured grids using parameterized differential operators for spherical signals, and (2) we show that our unique kernel parameterization allows our model to achieve the same or higher accuracy with significantly fewer network parameters. A wide range of machine learning problems in computer vision and related areas require processing signals in the spherical domain; for instance, omnidirectional RGBD images from commercially available panorama cameras, such as Matterport , panaramic videos coupled with LIDAR scans from self-driving cars BID17 , or planetary signals in scientific domains such as climate science BID31 . Unfortunately, naively mapping spherical signals to planar domains results in undesirable distortions. Specifically, projection artifacts near polar regions and handling of boundaries makes learning with 2D convolutional neural networks (CNNs) particularly challenging and inefficient. Very recent work, such as BID10 and BID16 , propose network architectures that operate natively in the spherical domain, and are invariant to rotations in the SO(3) group. Such invariances are desirable in a set of problems -e.g., machine learning problems of molecules -where gravitational effects are negligible and orientation is arbitrary. However, for other different classes of problems at large, assumed orientation information is crucial to the predictive capability of the network. A good example of such problems is the MNIST digit recognition problem, where orientation plays an important role in distinguishing digits ""6"" and ""9"". Other examples include omnidirectional images, where images are naturally oriented by gravity; and planetary signals, where planets are naturally oriented by their axis of rotation.In this work, we present a new convolution kernel for CNNs on arbitrary manifolds and topologies, discretized by an unstructured grid (i.e., mesh), and focus on its applications in the spherical domain approximated by an icosahedral spherical mesh. We propose and evaluate the use of a new parameterization scheme for CNN convolution kernels, which we call Parameterized Differential Operators (PDOs), which is easy to implement on unstructured grids. We call the resulting convolution operator that operates on the mesh using such kernels the MeshConv operator. This parameterization scheme utilizes only 4 parameters for each kernel, and achieves significantly better performance Illustration for the MeshConv operator using parameterized differential operators to replace conventional learnable convolutional kernels. Similar to classic convolution kernels that establish patterns between neighboring values, differential operators computes ""differences"", and a linear combination of differential operators establishes similar patterns.than competing methods, with much fewer parameters. In particular, we illustrate its use in various machine learning problems in computer vision and climate science.In summary, our contributions are as follows:• We present a general approach for orientable CNNs on unstructured grids using parameterized differential operators.• We show that our spherical model achieves significantly higher parameter efficiency compared to state-of-the-art network architectures for 3D classification tasks and spherical image semantic segmentation.• We release and open-source the codes developed and used in this study for other potential extended applications 1 .We organize the structure of the paper as follows. We first provide an overview of related studies in the literature in Sec. 2; we then introduce details of our methodology in Sec. 3, followed by an empirical assessment of the effectiveness of our model in Sec. 4. Finally , we evaluate the design choices of our kernel parameterization scheme in Sec. 5. We have presented a novel method for performing convolution on unstructured grids using parameterized differential operators as convolution kernels. Our results demonstrate its applicability to machine learning problems with spherical signals and show significant improvements in terms of overall performance and parameter efficiency. We believe that these advances are particularly valuable with the increasing relevance of omnidirectional signals, for instance, as captured by real-world 3D or LIDAR panorama sensors.",929,0.477,559,1.661896243291592,"We present an efficient convolution kernel on unstructured grids parameterized differential operators while focusing spherical signals such panorama images planetary signals To this end replace conventional convolution kernels linear combinations differential operators weighted learnable parameters Differential operators efficiently estimated on unstructured grids one-ring neighbors learnable parameters optimized through As obtain extremely efficient neural networks match or state network but network parameters We evaluate our algorithm an extensive series computer vision climate science tasks shape classification climate pattern segmentation Overall present (1) a novel CNN approach on unstructured grids parameterized differential operators spherical signals we our unique kernel parameterization our model achieve significantly fewer network parameters A wide range machine problems in require processing signals the spherical domain; RGBD from commercially available panorama cameras Matterport , panaramic videos coupled LIDAR scans from BID17 planetary signals scientific domains climate science Unfortunately naively mapping spherical signals planar domains results undesirable distortions Specifically projection artifacts near polar regions and handling boundaries makes learning with particularly inefficient Very recent work, such BID10 , propose network architectures operate natively the spherical domain rotations the SO(3) group Such invariances desirable a set problems -e.g machine learning problems of molecules -where gravitational effects negligible orientation arbitrary However for other different classes problems at large, assumed orientation information crucial the predictive capability the network A good example such problems the MNIST digit recognition problem orientation plays distinguishing digits ""6 Other examples include omnidirectional images where naturally oriented gravity; planetary signals planets naturally their axisIn a new convolution kernel CNNs on arbitrary manifolds topologies discretized focus its applications the spherical domain approximated an icosahedral spherical mesh We propose and evaluate CNN convolution kernels easy unstructured grids We call the resulting convolution operator that operates the mesh using such kernels the MeshConv operator This parameterization scheme utilizes only 4 parameters each kernel achieves significantly better performance Illustration for the MeshConv operator using parameterized differential operators to replace conventional learnable convolutional kernels Similar classic convolution kernels that establish patterns between neighboring values differential operators computes ""differences a linear combination establishes similar patterns.than competing methods with much fewer parameters In particular illustrate its use various machine learning problems climate scienceIn summary our contributions as orientable CNNs on parameterized differential operators.• our spherical model achieves significantly higher parameter efficiency compared state network 3D classification tasks spherical image semantic release and the codes developed and other potential extended applications 1 .We organize the structure the paper We first provide related studies in Sec 2; we then introduce details our methodology Sec 3, followed an empirical assessment our model Sec 4 Finally , evaluate the design choices our kernel parameterization scheme Sec 5 We presented performing convolution parameterized differential operators as Our results demonstrate its applicability machine learning problems spherical signals show significant improvements terms parameter efficiency We believe these advances particularly valuable with the increasing relevance omnidirectional signals for as captured or LIDAR panorama sensors",0.01,0.3905326440227
"Prediction is arguably one of the most basic functions of an intelligent system. In general, the problem of predicting events in the future or between two waypoints is exceedingly difficult. However, most phenomena naturally pass through relatively predictable bottlenecks---while we cannot predict the precise trajectory of a robot arm between being at rest and holding an object up, we can be certain that it must have picked the object up. To exploit this, we decouple visual prediction from a rigid notion of time. While conventional approaches predict frames at regularly spaced temporal intervals, our time-agnostic predictors (TAP) are not tied to specific times so that they may instead discover predictable ""bottleneck"" frames no matter when they occur. We evaluate our approach for future and intermediate frame prediction across three robotic manipulation tasks. Our predictions are not only of higher visual quality, but also correspond to coherent semantic subgoals in temporally extended tasks. Imagine taking a bottle of water and laying it on its side. Consider what happens to the surface of the water as you do this: which times can you confidently make predictions about? The surface is initially flat, then becomes turbulent, until it is flat again, as shown in Fig 1. Predicting the exact shape of the turbulent liquid is extremely hard, but its easy to say that it will eventually settle down.Prediction is thought to be fundamental to intelligence BID2 BID3 BID10 . If an agent can learn to predict the future, it can take anticipatory actions, plan through its predictions, and use prediction as a proxy for representation learning. The key difficulty in prediction is uncertainty. Visual prediction approaches attempt to mitigate uncertainty by predicting iteratively in heuristically chosen small timesteps, such as, say, 0.1s. In the bottle-tilting case, such approaches generate blurry images of the chaotic states at t = 0.1s, 0.2s, . . ., and this blurriness compounds to make predictions unusable within a few steps. Sophisticated probabilistic approaches have been proposed to better handle this uncertainty BID0 BID19 BID4 BID39 .What if we instead change the goal of our prediction models? Fixed time intervals in prediction are in many ways an artifact of the fact that cameras and monitors record and display video at fixed frequencies. Rather than requiring predictions at regularly spaced future frames, we ask: if a frame prediction is treated as a bet on that frame occurring at some future point, what should we predict? Such time-agnostic prediction (TAP) has two immediate effects: (i) the predictor may skip more uncertain states in favor of less uncertain ones, and (ii) while in the standard approach, a prediction is wrong if it occurs at t ± rather than at t, our formulation considers such predictions equally correct.Recall the bottle-tilting uncertainty profile. Fig 1 depicts uncertainty profiles for several other prediction settings, including both forward/future prediction (given a start frame) and intermediate prediction (given start and end frames). Our time-agnostic reframing of the prediction problem targets the minima of these profiles, where prediction is intuitively easiest. We refer to these minima states as ""bottlenecks.""At this point, one might ask: are these ""easy"" bottlenecks actually useful to predict? Intuitively, bottlenecks naturally correspond to reliable subgoals-an agent hoping to solve the maze in Fig 1 (e) would do well to target its bottlenecks as subgoals. In our experiments, we evaluate the usefulness of our predictions as subgoals in simulated robotic manipulation tasks.Figure 1: (a) Over time as the bottle is tilted, the uncertainty first rises and then falls as the bottle is held steady after tilting. (b)-(e) Similar uncertainty profiles corresponding to various scenarios-a ball rolling down the side of a bowl, a car driving on a highway with an exit 100m away, an iron pellet tossed in the direction of a magnet, and intermediate frame prediction in a maze traversal given start and end states. The red asterisks along the x-axis correspond to the asterisks in the maze-these ""bottleneck"" states must occur in any successful traversal.Our main contributions are: (i) we reframe the video prediction problem to be time-agnostic, (ii) we propose a novel technical approach to solve this problem, (iii) we show that our approach effectively identifies ""bottleneck states"" across several tasks, and (iv) we show that these bottlenecks correspond to subgoals that aid in planning towards complex end goals. The standard paradigm for prediction tasks demands that a predictor not only make good predictions, but that it make them on a set schedule. We have argued for redefining the prediction task so that the predictor need only care that its prediction occur at some time, rather than that it occur at a specific scheduled time. We define this time-agnostic prediction task and propose novel technical approaches to solve it, that require relatively small changes to standard prediction methods. Our results show that reframing prediction objectives in this way yields higher quality predictions that are also semantically coherent-unattached to a rigid schedule of regularly specified timestamps, model predictions instead naturally attach to specific semantic ""bottleneck"" events, like a grasp. In our preliminary experiments with a hierarchical visual planner, our results suggest that such predictions could serve as useful subgoals for complex tasks.In future work, we would like to address some limitations of our TAP formulation, of which we will mention two here. First, TAP currently benefits not only from selecting which times to predict, but also from not having to provide timestamps attached to its predictions. We would like to study: could we retain the benefits of time-agnostic prediction while also providing timestamps for when each predicted state will occur? Second, our current TAP formulation may not generalize to prediction problems in all settings of interest. As an example, for videos of juggling or waving, which involve repeated frames, TAP might collapse to predicting the input state repeatedly. We would like to investigate more general TAP formulations: for example, rather than choosing E t in Eq 5 to encourage predicting farther away times, we could conceivably penalize predictions that look too similar to the input context frames. More broadly, we believe that our results thus far hold great promise for many applications of prediction including hierarchical planning and model-based reinforcement learning, and we hope to build further on these results. In these appendices, we provide details omitted in the main text for space. Note that more supplementary material, such as video examples, is hosted at: https://sites.google.com/view/ ta-pred",1355,0.711,789,1.717363751584284,"Prediction is arguably an intelligent system In general the problem predicting events or between two waypoints exceedingly However most phenomena naturally pass relatively predictable bottlenecks---while we a robot arm between being at holding up be must picked the object To exploit decouple visual prediction a rigid notion While conventional approaches predict frames at regularly spaced temporal intervals our time-agnostic predictorsTAP tied specific times so instead discover predictable ""bottleneck no matter We evaluate our approach future and intermediate frame prediction across three robotic manipulation tasks Our predictions not only of higher visual quality correspond coherent semantic subgoals temporally extended tasks Imagine taking a bottle laying Consider what the surface as do which times can confidently make predictions? The surface initially flat turbulent until flat as Predicting the exact shape the turbulent liquid extremely its easy say eventuallyPrediction thought fundamental intelligence BID2 BID3 BID10 . If an agent learn predict take anticipatory actions plan through its predictions prediction representation learning The key difficulty prediction uncertainty Visual prediction approaches attempt mitigate uncertainty predicting iteratively in heuristically chosen small timesteps, In the bottle-tilting case such approaches generate blurry images the chaotic states at t = . . ., and this blurriness compounds make predictions unusable within Sophisticated probabilistic approaches better handle this uncertainty BID0 BID19 BID4 BID39 .What if instead change the goal our prediction models Fixed time intervals prediction are in many ways an artifact cameras monitors record and video fixed frequencies Rather requiring predictions at regularly spaced future frames ask if a frame prediction treated that frame occurring predict Such time-agnostic prediction (TAP two immediate effects the predictor may skip more uncertain states favor while in the standard approach wrong occurs t ± rather, our formulation considers such predictions equally correctRecall the bottle-tilting uncertainty profile Fig depicts uncertainty profiles several other prediction settings both forward/future predictiongiven a start frame intermediate prediction Our time-agnostic reframing the prediction problem targets the minima these profiles prediction intuitively easiest We refer these minima states""At one are actually useful predict Intuitively naturally correspond reliable subgoals-an agent hoping solve the maze in Fige) would do target In our experiments evaluate our predictions subgoals simulated robotic manipulation tasksFigure as the bottle tilted the uncertainty first rises held steady after (b)-(e) Similar uncertainty profiles corresponding various scenarios-a ball rolling down a bowl with an exit 100m iron pellet tossed a magnet intermediate frame prediction in a maze traversal given start states The red asterisks along the maze-these ""bottleneck"" states must occur any successful traversalOur main contributions we reframe the video prediction problem timeagnostic propose a novel technical approach show effectively identifies across several tasks correspond subgoals aid planning towards complex end goals The standard paradigm prediction tasks demands a predictor not make that on a set schedule We argued redefining the prediction task so the predictor need care that occur a specific scheduled time We define this time-agnostic prediction task and propose novel technical approaches solve that require relatively small changes standard prediction methods Our results reframing prediction objectives this way yields higher quality predictions also semantically coherent-unattached a rigid schedule regularly specified timestamps model predictions instead naturally attach specific semantic ""bottleneck"" events like a grasp. In our preliminary experiments a hierarchical visual planner such predictions could serve useful subgoals complex tasksIn future work address some limitations our TAP formulation of mention two First TAP currently benefits not selecting which times predict not provide attached its predictions We would study: could retain time-agnostic prediction while timestamps when each predicted state Second our current TAP formulation may generalize prediction problems all settings interest As for videos juggling or waving which involve repeated frames TAP might collapse predicting the input state repeatedly We would investigate more general TAP formulations: for rather choosing E t in Eq 5 to encourage predicting farther times conceivably penalize predictions look similar the input context frames More broadly our results thus hold many applications prediction including hierarchical planning build on In these appendices details omitted for space Note more supplementary material video examples hosted tapred",0.01,0.5318589818304855
"In cities with tall buildings, emergency responders need an accurate floor level location to find 911 callers quickly. We introduce a system to estimate a victim's floor level via their mobile device's sensor data in a two-step process. First, we train a neural network to determine when a smartphone enters or exits a building via GPS signal changes. Second, we use a barometer equipped smartphone to measure the change in barometric pressure from the entrance of the building to the victim's indoor location. Unlike impractical previous approaches, our system is the first that does not require the use of beacons, prior knowledge of the building infrastructure, or knowledge of user behavior. We demonstrate real-world feasibility through 63 experiments across five different tall buildings throughout New York City where our system predicted the correct floor level with 100% accuracy.
 Indoor caller floor level location plays a critical role during 911 emergency calls. In one use case, it can help pinpoint heart attack victims or a child calling on behalf of an incapacitated adult. In another use case, it can help locate firefighters and other emergency personnel within a tall or burning building. In cities with tall buildings, traditional methods that rely on GPS or Wi-Fi fail to provide reliable accuracy for these situations. In these emergency situations knowing the floor level of a victim can speed up the victim search by a factor proportional to the number of floors in that building. In recent years methods that rely on smartphone sensors and Wi-Fi positioning BID28 have been used to formulate solutions to this problem.In this paper we introduce a system that delivers an estimated floor level by combining deep learning with barometric pressure data obtained from a Bosch bmp280 sensor designed for ""floor level accuracy"" BID3 and available in most smartphones today 1 . We make two contributions: the first is an LSTM BID13 trained to classify a smartphone as either indoors or outdoors (IO) using GPS, RSSI, and magnetometer sensor readings. Our model improves on a previous classifier developed by BID1 . We compare the LSTM against feedforward neural networks, logistic regression, SVM, HMM and Random Forests as baselines. The second is an algorithm that uses the classifier output to measure the change in barometric pressure of the smartphone from the building entrance to the smartphone's current location within the building. The algorithm estimates the floor level by clustering height measurements through repeated building visits or a heuristic value detailed in section 4.5.We designed our method to provide the most accurate floor level estimate without relying on external sensors placed inside the building, prior knowledge of the building, or user movement behavior. It merely relies on a smartphone equipped with GPS and barometer sensors and assumes an arbitrary user could use our system at a random time and place. We offer an extensive discussion of potential real-world problems and provide solutions in (appendix B).We conducted 63 test experiments across six different buildings in New York City to show that the system can estimate the floor level inside a building with 65.0% accuracy when the floor-ceiling distance in the building is unknown. However , when repeated visit data can be collected, our simple clustering method can learn the floor-ceiling distances and improve the accuracy to 100%. All code , data and data collection app are available open-source on github.2 . In this paper we presented a system that predicted a device's floor level with 100% accuracy in 63 trials across New York City. Unlike previous systems explored by BID1 , BID26 , BID20 , BID17 BID27 , our system is completely selfcontained and can generalize to various types of tall buildings which can exceed 19 or more stories. This makes our system realistic for real-world deployment with no infrastructure support required.We also introduced an LSTM, that solves the indoor-outdoor classification problem with 90.3% accuracy. The LSTM matched our baseline feedforward network, and outperformed SVMs, random forests, logistic regression and previous systems designed by BID22 and BID30 . The LSTM model also serves as a first step for future work modeling the overall system end-to-end within the LSTM.Finally, we showed that we could learn the distribution of floor heights within a building by aggregating m ∆ measurements across different visits to the building. This method allows us to generate precise floor level estimates via unsupervised methods. Our overall system marries these various elements to make it a feasible approach to speed up real-world emergency rescues in cities with tall buildings.",899,0.492,500,1.798,"In cities tall buildings emergency responders an accurate floor level location quickly We introduce estimate a victim's floor level via their mobile device's sensor data in First train determine a smartphone enters via signal changes Second use a barometer equipped smartphone the entrance the victim's indoor location Unlike impractical previous approaches our system the beacons prior knowledge the building infrastructure knowledge We demonstrate real-world feasibility through 63 experiments across five different tall buildings throughout where our system predicted the correct floor level with Indoor caller floor level location plays during In one use case pinpoint heart attack victims or a child calling on behalf In another use case locate firefighters within a tall or burning building In cities tall buildings traditional methods that GPS fail reliable accuracy these situations In these emergency situations knowing the floor level a victim speed the victim search proportional floors In recent years methods rely smartphone sensors BID28 have formulate solutionsIn delivers an estimated floor level by combining deep learning obtained a Bosch bmp280 sensor designed ""floor level accuracy"" BID3 available most smartphones 1 We make two contributions an LSTM BID13 trained to classify a smartphone either indoorsIO GPS RSSI magnetometer sensor readings Our model improves a previous classifier developed BID1 . We compare against feedforward neural networks HMM Random Forests as baselines second is an algorithm the classifier output measure the smartphone from the building entrance within The algorithm estimates the floor level by clustering height measurements through repeated building visits or a heuristic value detailed section designed provide without external sensors placed prior user movement behavior It merely relies a smartphone equipped barometer sensors assumes an arbitrary user could our system at We offer an extensive discussion potential real-world problems provide (appendix conducted 63 test experiments across six different buildings show estimate the floor level inside when in unknown However , when repeated visit data can our simple clustering method learn the floor-ceiling distances improve to All code , data collection app are open github.2 . In presented predicted a device's floor level with 63 trials across Unlike previous systems explored BID1 , BID26 our system completely selfcontained generalize various types tall buildings which exceed 19 or more stories This makes our system realistic with no infrastructure supportWe introduced, that solves the indoor-outdoor classification problem The LSTM matched our baseline feedforward network outperformed SVMs random forests previous systems designed BID22 . The LSTM model also serves future work modeling the overall system end within showed we learn the distribution floor heights aggregating m �� measurements across different visits This method generate precise floor level estimates via Our overall system marries these various elements feasible approach speed cities tall buildings",0.01,0.7373130581704083
"Sparse reward is one of the most challenging problems in reinforcement learning (RL). Hindsight Experience Replay (HER) attempts to address this issue by converting a failure experience to a successful one by relabeling the goals. Despite its effectiveness, HER has limited applicability because it lacks a compact and universal goal representation. We present Augmenting experienCe via TeacheR's adviCE (ACTRCE), an efficient reinforcement learning technique that extends the HER framework using natural language as the goal representation. We first analyze the differences among goal representation, and show that ACTRCE can efficiently solve difficult reinforcement learning problems in challenging 3D navigation tasks, whereas HER with non-language goal representation failed to learn. We also show that with language goal representations, the agent can generalize to unseen instructions, and even generalize to instructions with unseen lexicons. We further demonstrate it is crucial to use hindsight advice to solve challenging tasks, but we also found that little amount of hindsight advice is sufficient for the learning to take off, showing the practical aspect of the method. Many impressive deep reinforcement learning (deep RL) applications rely on carefully-crafted reward functions to encourage the desired behavior. However, designing a good reward function is nontrivial (Ng et al., 1999) , and requires a significant engineering effort. For example, even for the seemingly simple task of stacking Lego blocks, Popov et al. (2017) needed 5 complicated reward terms with different importance weights. Moreover, handcrafted reward shaping BID9 can lead to biased learning, which may cause the agent to learn unexpected and undesired behaviors BID6 .One approach to avoid defining a complicated reward function is to use a sparse and binary reward function, i.e., give only a positive or negative reward at the terminal state, depending on the success of the task. However , the sparse reward makes learning difficult.Hindsight Experience Replay (HER) BID1 attempts to address this issue. The main idea of HER is to utilize failed experiences by substituting with a fake goal in order to convert them to successful experiences. For their algorithm to work, Andrychowicz et al. made the non-trivial assumption that for every state in the environment, there exists a goal which is achieved in that state. As the authors pointed out, this assumption can be trivially satisfied by choosing the goal space to be the state space. However, representing the goal using the enormous state space is very inefficient and contains much redundant information. For example, if we want to ask an agent to avoid collisions while driving where the state is the raw pixel value from the camera, then there can be many states (i.e. frames) that achieve this goal. It is redundant to represent the goal using each state.Therefore, we need a goal representation that is (1) expressive and flexible enough to satisfy the assumption in HER, while also being (2) compact and informative where similar goals are represented using similar features. Natural language representation of goals satisfies both requirements. First, language can flexibly describe goals across tasks and environments. Second, language representation is abstract , hence able to compress any redundant information in the states. Recall the previous driving example, for which we can simply describe ""avoid collisions"" to represent all states that satisfy this goal. Moreover, the compositional nature of language provides transferable features for generalizing across goals.In this paper, we combine the HER framework with natural language goal representation, and propose an efficient technique called Augmenting experienCe via TeacheR's adviCE (ACTRCE; pronounced ""actress"") to a broad range of reinforcement learning problems. Our method works as follows. Whenever an agent finishes an episode, a teacher gives advice in natural language to the agent based on the episode. The agent takes the advice to form a new experience with a corresponding reward, alleviating the sparse reward problem. For example, a teacher can describe what the agent has achieved in the episode, and the agent can replace the original goal with the advice and a reward of 1. We show many benefits brought by language goal representation when combining with hindsight advice. The agent can efficiently solve reinforcement learning problems in challenging 2D and 3D environments; it can generalize to unseen instructions, and even generalize to instruction with unseen lexicons. We further demonstrate it is crucial to use hindsight advice to solve challenging tasks, but we also found that little amount of hindsight advice is sufficient for the learning to take off, showing the practical aspect of the method.We note that our work is also interesting from a language learning perspective. Learning to achieve goals described in natural language is part of a class of problem called language grounding BID10 , which has recently received increasing interest, as grounding is believed to be necessary for more general understanding of natural language. Early attempts to ground language in a simulated physical world (Winograd, 1972; Siskind, 1994) consisted of hard coded rules which could not scale beyond their original domain. Recent work has been using reinforcement learning techniques to address this problem BID12 BID4 . Our work combines reinforcement learning and rich language advice , providing an efficient technique for language grounding. In this work, we propose the ACTRCE method that uses natural language as a goal representation for hindsight advice. The main point of the paper is to show that using language as goal representations can bring many benefits, when combined with hindsight advice. We analyzed the differences among goal representation, and show that ACTRCE can efficiently solve difficult reinforcement learning problems in challenging 3D navigation tasks, whereas HER with non-language goal representation failed to learn. We also show that with language goal representations, the agent can generalize to unseen instructions. With pre-trained language component, the agent can even generalize to instructions with unseen lexicons, demonstrating its potential to deal with noisy natural language advice from humans. Although ACTRCE algorithm crucially relies on hindsight advice, we showed that little amount of advice is sufficient for the learning to take off, showing its great practicality.",1207,0.694,687,1.7569141193595341,"Sparse reward (RL Hindsight Experience Replay (HER attempts address converting a failure experience the goals Despite its effectiveness HER has limited a compact and universal goal representation We present Augmenting experienCe via TeacheR's adviCE (ACTRCE extends the HER framework using as the goal representation We first analyze goal representation show ACTRCE efficiently solve difficult reinforcement learning problems challenging 3D navigation tasks whereas HER with non-language goal representation failed learn We also show with language goal representations the agent unseen instructions even instructions unseen lexicons We further demonstrate it crucial hindsight advice solve challenging tasks found little amount off showing the practical aspect Many impressive deep reinforcement learningdeep RL rely carefully-crafted reward functions encourage However designing a good reward function (Ng , requires For example even for stacking Popov et al (2017 needed 5 complicated reward terms with different importance weights Moreover handcrafted reward shaping BID9 can lead biased learning the agent learn BID6 .One approach avoid defining a complicated reward function a sparse and give at the terminal state depending However , the sparse reward makes learningHindsight Experience ReplayHER BID1 attempts address The main idea HER is utilize failed experiences by with a fake goal convert successful experiences For their algorithm Andrychowicz made for the environment a goal achieved As the authors pointed this assumption satisfied choosing the goal space However representing the goal using the enormous state space inefficient contains For example ask an agent avoid collisions while where the state the raw pixel value from there can many states achieve It redundant represent using each stateTherefore a goal representation ( expressive flexible in HER while ( compact informative where similar goals similar features Natural language representation goals satisfies both requirements First language can flexibly describe goals across tasks Second language representation abstract , hence able compress any redundant information the states Recall the previous driving example for simply describe ""avoid collisions to represent all states satisfy Moreover the compositional nature language provides transferable features generalizing across goalsIn combine the HER framework natural language goal representation called experienCe via TeacheR's adviCE (ACTRCE; pronounced ""actress a broad range reinforcement learning problems Our method works Whenever an agent finishes an episode a teacher gives advice in natural language based The agent takes to form a corresponding reward alleviating the sparse reward problem For example a teacher describe the agent achieved the episode replace the advice a reward We show many benefits brought language goal representation when combining with hindsight advice The agent can efficiently solve reinforcement learning problems; unseen instructions even instruction with unseen lexicons We further demonstrate it crucial hindsight advice solve challenging tasks found little amount off showing the practical aspectWe note also interesting from Learning achieve goals described natural language part a class problem called language grounding BID10 , grounding believed necessary more general understanding Early attempts ground language a simulated physical world (Winograd 1972 Siskind consisted hard coded rules scale beyond their original domain Recent work using address BID12 BID4 . Our work combines reinforcement learning rich language advice , providing an efficient technique language grounding In propose the ACTRCE method natural language as a goal representation hindsight advice The main point using language goal representations bring when hindsight advice We analyzed goal representation show ACTRCE can efficiently solve difficult reinforcement learning problems challenging 3D navigation tasks whereas HER with non-language goal representation failed learn We also show with language goal representations the agent unseen instructions With pre-trained language component the agent even generalize instructions unseen lexicons demonstrating deal noisy natural language advice from humans Although ACTRCE algorithm crucially relies hindsight advice showed little amount advice the learning off showing its great practicality",0.01,0.6326298440645047
"Learning rich and compact representations is an open topic in many fields such as word embedding, visual question-answering, object recognition or image retrieval. Although deep neural networks (convolutional or not) have made a major breakthrough during the last few years by providing hierarchical, semantic and abstract representations for all of these tasks, these representations are not necessary as rich as needed nor as compact as expected. Models using higher order statistics, such as bilinear pooling, provide richer representations at the cost of higher dimensional features. Factorization schemes have been proposed but without being able to reach the original compactness of first order models, or at a heavy loss in performances. This paper addresses these two points by extending factorization schemes to codebook strategies, allowing compact representations with the same dimensionality as first order representations, but with second order performances. Moreover, we extend this framework with a joint codebook and factorization scheme, granting a reduction both in terms of parameters and computation cost. This formulation leads to state-of-the-art results and compact second-order models with few additional parameters and intermediate representations with a dimension similar to that of first-order statistics. Learning rich and compact representations is an open topic in many fields such as word embedding BID16 ), visual question-answering ), object recognition BID23 ) or image retrieval BID19 ). The standard approach extracts features from the input data (text, image, etc.) and builds a representation that will be next processed for a given task (classification, retrieval, etc.) . These features are usually extracted with deep neural networks and the representation is trained in an end-to-end manner. Recently, representations that compute first order statistics over input data have been outperformed by improved models that compute higher order statistics such as bilinear models. This embedding strategy generates richer representations and has been applied in a wide range of tasks : word embedding BID2 ), VQA BID9 ), fine grained classification BID28 ), etc. and gets state-of-the-art results. For instance, Bilinear models perform the best for fine grained visual classification tasks by producing efficient representations that model more details within an image than classical first order statistics BID14 ).However , even if the increase in performances is unquestionable, second order models suffer from a collection of drawbacks: Their intermediate dimension increases quadratically with respect to input features dimension, they require a projection to lower dimension that is costly both in number of parameters and in computation, they are harder to train than first order models due to the increased dimension, they lack a proper adapted pooling scheme which leads to sub-optimal representations.The two main downsides, namely the high dimensional output representations and the sub-efficient pooling scheme, have been widely studied over the last decade. On one hand, the dimensionality issue has been studied through factorization scheme, either representation oriented such as Compact Bilinear Pooling ) and Hadamard Product for Low Rank Bilinear Pooling BID9 ), or task oriented as Low-rank Bilinear Pooling BID10 ). While these factorization schemes are efficient in term of computation cost and number of parameters, the intermediate representation is still too large (typically 10k dimension) to ease the training process and using lower dimension greatly deteriorate performances.On the other hand, it is well-known that global average pooling schemes aggregate unrelated features. This problem has been tackled by the use of codebooks such as VLAD BID0 ) or, in the case of second-order information, Fisher Vectors BID20 ). These strategies have been enhanced to be trainable in an end-to-end manner BID1 ; BID24 ). However , using a codebook on end-to-end trainable second order features leads to an unreasonably large model, since the already large second order model has to be duplicated for each entry of the codebook. This is for example the case in MFAFVNet BID13 ) for which the second order layer alone (i.e., without the CNN part) already costs over 25M parameters and 40 GFLOP, or about as much as an entire ResNet50.In this paper, we tackle both of these shortcomings (intermediate representation cost and lack of proper pooling) by exploring joint factorization and codebook strategies. Our main results are the following:-We first show that state-of-the-art factorization schemes can already be improved by the use of a codebook pooling, albeit at a prohibitive cost. -We then propose our main contribution, a joint codebook and factorization scheme that achieves similar results at a much reduced cost.Since our approach focuses on representation learning and is task agnostic, we validate it in a retrieval context on several image datasets to show the relevance of the learned representations. We show our model achieves competitive results on these datasets at a very reasonable cost.The remaining of this paper is organized as follows: in the next section, we present the related work on second order pooling, factorization schemes and codebook strategies. In section 3, we present our factorization with the codebook strategy and how we improve its integration. In section 4, we show an ablation study on the Stanford Online Products dataset BID18 ). Finally, we compare our approach to the state-of-the-art methods on three image retrieval datasets (Stanford Online Products, CUB-200-2001, Cars-196) . In this paper, we propose a new pooling scheme based which is both efficient in performances (rich representation) and in representation dimension (compact representation). This is thanks to the second-order information that allows richer representation than first-order statistics and thanks to a codebook strategy which pools only related features. To control the computational cost, we extend this pooling scheme with a factorization that shares sets of projections between each entry of the codebook, trading fewer parameters and fewer computation for a small loss in performance. We achieve state-of-the-art results on Stanford Online Products and Cars-196, two image retrieval datasets. Even if our tests are performed on image retrieval datasets, we believe our method can readily be used in place of global average pooling for any task.",1210,0.568,709,1.7066290550070522,"Learning rich and compact representations an open topic such word visual question object or image retrieval Although deep neural networks or not made during by providing hierarchical, semantic and abstract representations all these representations necessary as rich needed nor compact expected Models using higher order statistics pooling provide richer representations at Factorization schemes but without being reach the original compactness first order models or a heavy loss performances This paper addresses these two points extending factorization schemes codebook strategies allowing compact representations with first order representations second order performances Moreover extend with a joint codebook and factorization scheme granting a reduction both terms parameters computation cost This formulation leads state results compact second-order models few additional parameters intermediate representations with a dimension similar Learning rich and compact representations an open topic such word BID16 ), visual question ), object or image retrieval The standard approach extracts featurestext builds will next processedclassification retrieval . These features usually extracted with deep neural networks the representation trained an end Recently representations that compute first order statistics over input data outperformed improved models compute such This embedding strategy generates richer representations has tasks : word BID2 ), VQA BID9 fine classification etc and gets state results For instance Bilinear models perform best fine grained visual classification tasks by producing efficient representations model more details within classical first order statistics BID14 ).However , even the increase performances unquestionable second order models suffer a collection drawbacks Their intermediate dimension increases respect input features dimension they a projection to lower dimension that costly both number parameters computation, harder train lack a proper adapted pooling scheme which leads, namely the high dimensional output representations widely over On the dimensionality issue studied through factorization scheme either representation oriented such Compact Bilinear Pooling ) and Hadamard Product for Low Rank Bilinear Pooling BID9 task as While these factorization schemes efficient term computation cost number parameters the intermediate representation too large (typically 10k dimension ease using lower dimension greatly deteriorate performancesOn well global average pooling schemes aggregate unrelated features This problem tackled the use codebooks such VLAD BID0 ), second-order information Fisher Vectors BID20 These strategies enhanced to be trainable an end BID1 ; BID24 However , using a codebook on end-to-end trainable second order features leads since duplicated each entry This for example MFAFVNet BID13 ) for the second order layer alone without the CNN part already costs over 25M parameters 40 GFLOP, as an entire ResNet50.In tackle both (intermediate representation cost lack proper pooling exploring joint factorization and codebook strategies Our main results the following:-We first show state factorization schemes already improved a codebook pooling, albeit -We then propose our main contribution a joint codebook and factorization scheme achieves atSince focuses representation learning task validate a retrieval context on several image datasets to the learned representations We show our model achieves competitive results these datasets atThe remaining of organized in the related work second pooling factorization schemes codebook strategies In section present our factorization with the codebook strategy improve its integration In section show an ablation study the Stanford Online Products dataset BID18 ). Finally compare our approach state methods on three image retrieval datasetsStanford Online Products CUB-2002001 Cars-196) . In which both performancesrich representation representation dimension This thanks the second-order information allows richer representation than thanks a codebook strategy pools only related features To control the computational cost extend this pooling scheme that shares sets projections between each entry the codebook trading fewer parameters fewer computation for a small loss performance We achieve state results Stanford Online Products Cars-196 two image retrieval datasets Even our tests performed image retrieval datasets believe readily place global average pooling any task",0.01,0.5045079180918282
"Natural language understanding research has recently shifted towards complex Machine Learning and Deep Learning algorithms. Such models often outperform their simpler counterparts significantly. However, their performance relies on the availability of large amounts of labeled data, which are rarely available. To tackle this problem, we propose a methodology for extending training datasets to arbitrarily big sizes and training complex, data-hungry models using weak supervision. We apply this methodology on biomedical relation extraction, a task where training datasets are excessively time-consuming and expensive to create, yet has a major impact on downstream applications such as drug discovery. We demonstrate in two small-scale controlled experiments that our method consistently enhances the performance of an LSTM network, with performance improvements comparable to hand-labeled training data. Finally, we discuss the optimal setting for applying weak supervision using this methodology. The amount of scientific papers in the biomedical field is ever increasing. Published papers contain important information, however, encoded in unstructured text, making it difficult for researchers to locate it. Extracting this information in a structured format and storing it within a knowledge base can have a remarkable impact on a variety of important tasks, ranging from drug design to detecting adverse drug effects. During the past decade, there have been efforts towards automation of Information Extraction BID15 , due to the fact that manual annotation of documents from domain experts is labor-intensive to perform on a large scale BID16 .The broader focus of this work is to help automation of semantic triple extraction from biomedical abstracts. We apply our methodology on two different relations: (a ) Regulations, indicating that a Chemical increases (up-regulates) or decreases (down-regulates) the production of a Protein (CPR) and ( b) Chemically Induced Diseases (CID). Both relations are particularly important for areas such as drug design, safety, and discovery, as it will enable researchers to filter out or select chemical substances with specific properties, faster BID16 . We have shown that weak supervision is a tool which can be used for enhancing the performance of complex models, such as deep neural networks, while utilizing both unlabeled data and multiple base learners. Additionally, we have shown that the proposed methodology is practically feasible for the task at hand, as we have succeeded on defining a combination of base learners, which model the problem space sufficiently and allow us to take advantage of additional, unlabeled data. This comes under the requirement that the unlabeled data are drawn from the same domain/distribution as our labeled data, so that our base learners can generalize and perform adequately on D U . In practice, our methodology shifts the human effort from hand-labeling examples to feature engineering and construction of diverse learners. More importantly, once a satisfactory set of diverse learners is available, we can use this method to scale the training datasets in arbitrarily high levels while consistently improving the performance over the supervised learning paradigm. Moreover, the same pipeline can be re-used on similar tasks with the only requirement of providing the appropriate datasets. On the contrary, in the typical supervised learning paradigm, we would have to repeatedly hand-label large datasets.Despite demonstrating the usability of our method using a controlled, small-scale dataset, it is crucial to further explore the requirements of constructing a large enough unlabelled dataset and perform the same experiments there. That would likely improve the metalearner performance further (which is currently upper-bounded by the small dataset size) and allow us to draw stronger conclusions on the research questions of Subsection 6.2. Additionally it would allow us to inspect how performance improves with the increase of D U in a different scale of magnitude and if there seems to be a certain performance threshold, which we cannot surpass using weak supervision. Our preliminary experiments demonstrate that collecting an appropriate unlabeled dataset given a labeled one is a challenging task itself, along with the definition of ""appropriate"", and semi-supervised algorithms should not take the existence of an appropriate unlabeled dataset for granted.Further, it would be very important to conclude on a more appropriate metric than the F1 score for the evaluation of marginal weak labels. Currently, the absence of an appropriate metric prevents us from drawing conclusions directly from the weak labels, without having to introduce an additional step (train the meta-learner). This would also allow us to select the optimal hyperparameters of the Generative Model and could have a significant impact upon the final performance.Other areas for further investigation include experimenting with the meta-learner (eg. using pre-trained word embeddings or other model architectures) and defining a more appropriate selection method for the Base Learners. Last, it would be interesting to examine how this system would behave if the Base Learners abstained from voting on the examples they are less certain about. One could simply delete a percentage of the votes which are closer to the classification boundary, or perform a probability calibration on the output of the Base Learners and set a minimum confidence threshold below which they would abstain voting. This could also provide the Generative Model with a modeling advantage, compared to unweighted methods (such as Majority Voting), as described in an analysis related to the trade-offs of weak supervision BID29 .",1021,0.503,603,1.693200663349917,"Natural language understanding research recently shifted complex Machine Learning Such models often significantly However their performance relies the availability labeled data rarely To tackle propose a methodology extending training datasets arbitrarily big sizes training complex weak supervision We apply this methodology on biomedical relation extraction a task training datasets excessively time expensive yet has downstream applications We demonstrate in two small-scale controlled experiments our method consistently enhances an LSTM network performance improvements hand-labeled training data Finally discuss the optimal setting applying weak supervision using this methodology The amount scientific papers ever Published papers contain however encoded making locate Extracting in and storing within a knowledge base have a variety important tasks ranging drug design detecting adverse drug effects During efforts towards automation Information Extraction BID15 , due manual annotation documents from domain experts labor to on BID16 .The broader focus help automation semantic triple extraction biomedical abstracts We apply our methodology on two different relations (a ) Regulations indicating Chemical increases ( a Protein (CPR ( b) Chemically Induced Diseases Both relations particularly areas drug design safety discovery it filter or select chemical substances specific properties faster BID16 . We shown weak supervision a tool which enhancing complex models while utilizing both unlabeled data multiple base learners Additionally shown the proposed methodology practically feasible the task succeeded on defining a combination base learners which model the problem space sufficiently and allow take additional, unlabeled data This comes under the requirement the unlabeled data are drawn the same domain/distribution our labeled data our base learners generalize perform adequately D U In practice our methodology shifts the human effort hand-labeling examples feature engineering construction diverse learners More importantly once a satisfactory set diverse learners scale the training datasets arbitrarily high levels while consistently over the supervised learning paradigm Moreover the same pipeline can re similar tasks the only requirement providing the appropriate datasets On in the typical supervised learning paradigm would to repeatedly hand-label large datasetsDespite demonstrating the usability our method using crucial further the requirements constructing a large enough unlabelled dataset perform there That would likely improve the metalearner performance further (which currently upperbounded the small dataset size draw the research questions of Subsection Additionally it inspect how performance improves the increase D U in a different scale magnitude if seems a certain performance threshold surpass using weak supervision Our preliminary experiments demonstrate collecting an appropriate unlabeled dataset given a labeled one itself along the definitionappropriate semi-supervised algorithms should take the existence for grantedFurther would very conclude on appropriate metric the F1 score the evaluation marginal weak labels Currently the absence appropriate metric prevents drawing directly the weak labels without introducetrain the meta-learner This would also allow select the optimal hyperparameters the Generative Model could have uponOther areas for experimenting the meta-learner (eg using or other model architectures) defining a more appropriate selection method the Base Learners Last, it would examine this system behave the Base Learners abstained voting the examples are less certain One could simply delete a percentage which closer the classification boundary perform a probability calibration the Base Learners and set below they abstain voting This could provide the Generative Model a modeling advantage compared unweighted methods ( Majority Voting described an analysis related weak supervision BID29 .",0.01,0.47029355595503863
"We introduce contextual explanation networks (CENs)---a class of models that learn to predict by generating and leveraging intermediate explanations. CENs are deep networks that generate parameters for context-specific probabilistic graphical models which are further used for prediction and play the role of explanations. Contrary to the existing post-hoc model-explanation tools, CENs learn to predict and to explain jointly. Our approach offers two major advantages: (i) for each prediction, valid instance-specific explanations are generated with no computational overhead and (ii) prediction via explanation acts as a regularization and boosts performance in low-resource settings. We prove that local approximations to the decision boundary of our networks are consistent with the generated explanations. Our results on image and text classification and survival analysis tasks demonstrate that CENs are competitive with the state-of-the-art while offering additional insights behind each prediction, valuable for decision support. Model interpretability is a long-standing problem in machine learning that has become quite acute with the accelerating pace of widespread adoption of complex predictive algorithms. While high performance often supports our belief in predictive capabilities of a system, perturbation analysis reveals that black-box models can be easily broken in an unintuitive and unexpected manner BID0 BID1 . Therefore, for a machine learning system to be used in a social context (e.g., in healthcare) it is imperative to provide a sound reasoning for each decision.Restricting the class of models to only human-intelligible BID2 ) is a potential remedy, but often is limiting in modern practical settings. Alternatively, we may fit a complex model and explain its predictions post-hoc, e.g., by searching for linear local approximations of the decision boundary BID22 . While such approaches achieve their goal, the explanations are generated a posteriori, require additional computation per data instance, and most importantly are never the basis for the predictions made in the first place which may lead to erroneous interpretations.Explanation is a fundamental part of the human learning and decision process (Lombrozo, 2006) . Inspired by this fact, we introduce contextual explanation networks (CENs)-a class of deep neural networks that generate parameters for probabilistic graphical models. The generated models not only play the role of explanations but are used for prediction and can encode arbitrary prior knowledge. The data often consists of two representations: (1) low-level or unstructured features (e.g., text, image pixels, sensory inputs), and (2) high-level or human-interpretable features (e.g., categorical variables). To ensure interpretability, CENs use deep networks to process the low-level representation (called the context) and construct explanations as context-specific probabilistic models on the high-level features (cf. Koller & Friedman, 2009, Ch. 5.3) . Importantly, the explanation mechanism is an integral part of CEN, and our models are trained to predict and to explain jointly.A motivating example. Consider a CEN for diagnosing the risk of developing heart arrhythmia ( FIG0 ). The causes of the condition are quite diverse, ranging from smoking and diabetes to an injury from previous heart attacks, and may carry different effects on the risk of arrhythmia in different contexts. Assume that the data for each patient consists of medical notes in the form of raw text (which is used as the context) and a number of specific attributes (such as high blood pressure, diabetes, smoking, etc.). Further, assume that we have access to a parametric class of expert-designed models that relate the attributes to the condition. The CEN maps the medical notes to the parameters of the model class to produce a context-specific hypothesis, which is further used to make a prediction. In the sequel, we formalize these intuitions and refer to this toy example in our discussion to illustrate different aspects of the framework. The main contributions of the paper are as follows:(i ) We formally define CENs as a class of probabilistic models, consider special cases (e.g., Jacobs et al., 1991) , and derive learning and inference algorithms for simple and structured outputs. ( ii) We prove that post-hoc approximations of CEN's decision boundary are consistent with the generated explanations and show that, in practice, while both methods tend to produce virtually identical explanations, CENs construct them orders of magnitude faster. (iii) It turns out that noisy features can render post-hoc methods inconsistent and misleading, and we show how CENs can help to detect and avoid such situations. (iv) We implement CENs by extending a number of established domain-specific deep architectures for image and text data and design new architectures for survival analysis. Experimentally, we demonstrate the value of learning with explanations for prediction and model diagnostics. Moreover, we find that explanations can act as a regularizer and improve sample efficiency. In this paper, we have introduced contextual explanation networks (CENs)-a class of models that learn to predict by generating and leveraging intermediate context-specific explanations. We have formally defined CENs as a class of probabilistic models, considered a number of special cases (e.g., the mixture of experts), and derived learning and inference procedures within the encoder-decoder framework for simple and sequentially-structured outputs. We have shown that, while explanations generated by CENs are provably equivalent to those generated post-hoc under certain conditions, there are cases when post-hoc explanations are misleading. Such cases are hard to detect unless explanation is a part of the prediction process itself. Besides, learning to predict and to explain jointly turned out to have a number of benefits, including strong regularization, consistency, and ability to generate explanations with no computational overhead.We would like to point out a few limitations of our approach and potential ways of addressing those in the future work. Firstly, while each prediction made by CEN comes with an explanation, the process of conditioning on the context is still uninterpretable. Ideas similar to context selection (Liu et al., 2017) or rationale generation (Lei et al., 2016) may help improve interpretability of the conditioning. Secondly, the space of explanations considered in this work assumes the same graphical structure and parameterization for all explanations and uses a simple sparse dictionary constraint. This might be limiting, and one could imagine using a more hierarchically structured space of explanations instead, bringing to bear amortized inference techniques (Rudolph et al., 2017) . Nonetheless, we believe that the proposed class of models is useful not only for improving prediction capabilities, but also for model diagnostics, pattern discovery, and general data analysis, especially when machine learning is used for decision support in high-stakes applications.",1351,0.684,776,1.740979381443299,"We introduce contextual explanation networksCENs)---a class models learn by generating leveraging intermediate explanations CENs deep networks generate parameters context-specific probabilistic graphical models which further used prediction play explanations Contrary the existing post-hoc model-explanation tools CENs learn predict to explain jointly Our approach offers for each prediction valid instance-specific explanations generated with no computational overhead via explanation acts boosts low-resource settings We prove local approximations to the decision boundary our networks consistent the generated explanations Our results on image and survival analysis tasks demonstrate CENs competitive the state while offering additional insights behind each prediction valuable decision support Model interpretability that become quite acute the accelerating pace widespread adoption complex predictive algorithms While high performance often supports our belief predictive capabilities perturbation analysis reveals black-box models easily broken in an unintuitive and unexpected manner BID0 BID1 . Therefore for a machine learning system used healthcare imperative a sound reasoning forRestricting the class models only human-intelligible BID2 ) a potential remedy often is limiting modern practical settings Alternatively we fit a complex model explain its predictions post searching linear local approximations the decision boundary BID22 . While such approaches achieve the explanations generated a posteriori require additional computation per data instance most never the basis the predictions which erroneous interpretationsExplanation is the human learning and decision process (Lombrozo . Inspired this fact introduce contextual explanation networksCENs)-a class generate parameters The generated models not play explanations prediction can encode arbitrary prior knowledge The data often consists two representations sensory inputs To ensure interpretability CENs use deep networks process the low-level representation (called the context construct explanations as oncf Koller & Friedman 2009 Ch) . Importantly the explanation mechanism CEN, our models trained and to explain jointlyA motivating example. Consider a CEN for diagnosing the risk developing FIG0 The causes the condition quite smoking diabetes an injury from previous heart attacks may carry different contexts Assume the data each patient consists medical notes in raw textwhich used the context number specific attributes high blood pressure smoking Further assume we access a parametric class expert-designed models relate the attributes the condition The CEN maps the medical notes to the parameters the model class to produce a context-specific hypothesis further used make In the sequel we formalize these intuitions refer this toy example to different aspects The main contributions follows:(i ) We formally CENs consider special cases Jacobs 1991 , derive learning simple and structured outputs ( ii We prove CEN's decision boundary the generated explanations show, while both methods tend virtually identical explanations CENs construct them orders faster (iii It turns noisy features render post-hoc methods inconsistent misleading we show CENs detect (iv We implement CENs by extending a number established domain-specific deep architectures image and and design survival analysis Experimentally demonstrate the value learning with explanations prediction and model diagnostics Moreover we find explanations can act a regularizer and improve sample efficiency In this paper have introduced contextual explanation networksCENs)-a class models learn by generating leveraging intermediate context-specific explanations We formally defined CENs considered a number experts derived learning and within for simple and sequentially-structured outputs We shown, explanations generated CENs provably equivalent those generated post under cases misleading Such cases hard detect unless explanation a part the prediction process itself Besides learning predict to explain jointly turned have strong regularization consistency ability generate explanations with no computational overheadWe would point potential ways addressing in the future work Firstly while each prediction made CEN comes conditioning on the context still uninterpretable Ideas similar context selectionLiu 2017 rationale generation improve interpretability the conditioning. Secondly the space explanations considered assumes the same graphical structure parameterization for all explanations uses a simple sparse dictionary constraint This might limiting and one imagine using a more hierarchically structured space explanations instead bringing to amortized inference techniquesRudolph 2017 . Nonetheless we the proposed class models useful not improving prediction capabilities model diagnostics pattern discovery machine learning decision support",0.01,0.5920295318647031
"The goal of imitation learning (IL) is to enable a learner to imitate an expert’s behavior given the expert’s demonstrations. Recently, generative adversarial imitation learning (GAIL) has successfully achieved it even on complex continuous control tasks. However, GAIL requires a huge number of interactions with environment during training. We believe that IL algorithm could be more applicable to the real-world environments if the number of interactions could be reduced. To this end, we propose a model free, off-policy IL algorithm for continuous control. The keys of our algorithm are two folds: 1) adopting deterministic policy that allows us to derive a novel type of policy gradient which we call deterministic policy imitation gradient (DPIG), 2) introducing a function which we call state screening function (SSF) to avoid noisy policy updates with states that are not typical of those appeared on the expert’s demonstrations. Experimental results show that our algorithm can achieve the goal of IL with at least tens of times less interactions than GAIL on a variety of continuous control tasks. Recent advances in reinforcement learning (RL) have achieved super-human performance on several domains BID16 BID17 BID13 . However, on most of domains with the success of RL, the design of reward, that explains what agent's behavior is favorable, is clear enough for humans. Conversely, on domains where it is unclear how to design the reward, agents trained by RL algorithms often obtain poor policies and their behavior is far from what we want them to do. Imitation learning (IL) comes in such cases. The goal of IL is to enable the learner to imitate the expert's behavior given the expert's demonstrations but the reward signals. We are interested in IL because we desire an algorithm that can be applied in real-world environments where it is often hard to design the reward. Besides, since it is generally hard to model a variety of the real-world environments with an algorithm, and the state-action pairs in a vast majority of the real-world applications such as robotics control can be naturally represented in continuous spaces, we focus on model free IL for continuous control.A widely used approach of existing model free IL methods is the combination of Inverse Reinforcement Learning (IRL) BID22 BID18 BID1 BID32 and RL. Recently, BID10 has proposed generative adversarial imitation learning (GAIL) on the line of those works. GAIL has achieved state-of-the art performance on a variety of continuous control tasks. However, as pointed out by BID10 , a crucial drawback of GAIL is requirement of a huge number of interactions between the learner and the environments during training 1 . Since the interactions with environment can be too much time-consuming especially in the real-world environments, we believe that model free IL could be more applicable to the real-world environments if the number could be reduced while keeping the imitation capability satisfied as well as GAIL.To reduce the number of interactions, we propose a model free, off-policy IL algorithm for continuous control. As opposed to GAIL and its variants BID2 BID30 BID8 BID12 those of which adopt a stochastic policy as the learner's policy, we adopt a deterministic policy while following adversarial training fashion as GAIL. We show that combining the deterministic policy into the adversarial off-policy IL objective derives a novel type of policy gradient which we call deterministic policy imitation gradient (DPIG). Because DPIG only integrates over the state space as deterministic policy gradient (DPG) algorithms BID25 , the number of the interactions is expected to be less than that for stochastic policy gradient (PG) which integrates over the state-action space. Besides, we introduce a function which we call state screening function (SSF) to avoid noisy policy update with states that are not typical of those appeared on the experts demonstrations.In order to evaluate our algorithm, we used 6 physics-based control tasks that were simulated with MuJoCo physics simulator BID29 . The experimental results show that our algorithm enables the learner to achieve the same performance as the expert does with at least tens of times less interactions than GAIL. It indicates that our algorithm is more applicable to the real-world environments than GAIL. A wide variety of IL methods have been proposed in these last few decades. The simplest IL method among those is BC (Pomerleau, 1991) which learns a mapping from states to actions in the expert's demonstrations using supervised learning. Since the learner with the mapping learned by BC does not interacts with the environments, inaccuracies of the mapping are never corrected once the training has done, whereas our algorithm corrects the learner's behavior through the interactions. A noticeable point in common between BC and our algorithm is that the both just consider the relationship between single time-step state-action pairs but information over entire trajectories of the behavior in the optimizations. In other words, the both assume that the reward structure is dense and the reasonable rewards for the states s ∈ S \ S E can not be defined. A drawback of BC due to ignorance of the information over the trajectories is referred to as the problem of compounding error BID21 ) -the inaccuracies compounds over time and can lead the learner to encounter unseen states in th expert's demonstrations. For the state s ∈ S β * E , it is assumed in our algorithm that the immediate reward is greater if the learner's behavior is more likely to the expert's behavior, and the expert's behavior yields the greatest cumulative reward. That is, maximizing the immediate reward for the state s ∈ S β * E ⊂ S E implies maximizing the cumulative reward for trajectories stating from the state in our algorithm, and thus the information over the trajectories is implicitly incorporated in log R ω of the objective (11). Therefore, our algorithm is less affected by the compounding error than BC.Another widely used approach for IL the combination of IRL and RL that we considered in this paper. The concept of IRL was originally proposed by BID22 , and a variety of IRL algorithms have been proposed so far. Early works on IRL BID18 BID1 BID32 represented the parameterized reward function as a linear combination of hand-designed features. Thus, its capabilities to represent the reward were limited in comparison with that of nonlinear functional representation. Indeed, applications of the early works were often limited in small discrete domains. The early works were extended to algorithms that enable to learn nonlinear functions for representing the reward BID11 BID6 . A variety of complex tasks including continuous control in the real-world environment have succeeded with the nonlinear functional representation BID6 . As well as those methods, our algorithm can utilize the nonlinear functions if it is differentiable with respect to the action.In recent years, the connection between GANs and the IL approach has been pointed out BID10 BID5 . BID10 showed that IRL is a dual problem of RL which can be deemed as a problem to match the learner's occupancy measure BID28 to that of the expert, and found a choice of regularizer for the cost function yields an objective which is analogous to that of GANs. After that, their algorithm, namely GAIL, has become a popular choice for IL and some extensions of GAIL have been proposed BID2 BID30 BID8 BID12 . However, those extensions have never addressed reducing the number of interactions during training whereas we address it, and our algorithm significantly reduce the number while keeping the imitation capability as well as GAIL.The way of deriving policy gradients using gradients of the parameterized reward function with respect to actions executed by the current learner's policy is similar to DPG BID25 and deep DPG BID13 . However, they require parameterized Q-function approximator with known reward function whereas our algorithm does not use Q-function besides the parameterized reward function learned by IRL. In IL literature, MGAIL BID2 uses the gradients derived from parameterized discriminator to update the learner's policy. However, MGAIL is modelbased method and requires to train parameterized forward-model to derive the gradients whereas our algorithm is model free. Although model based methods have been thought to need less environment interactions than model free methods in general, the experimental results showed that MGAIL needs more interactions than our model free algorithm. We think that the reasons are the need for training the forward model besides that for the policy, and lack of care for the noisy policy updates issue that MGAIL essentially has. In this paper, we proposed a model free, off-policy IL algorithm for continuous control. The experimental results showed that our algorithm enables the learner to achieve the same performance as the expert does with several tens of times less interactions than GAIL.Although we implemented shallow neural networks to represent the parameterized functions in the experiment, deep neural networks can also be applied to represent the functions in our algorithm. We expect that the that advanced techniques used in deep GANs enable us to apply our algorithm to more complex tasks.A DETAILED DESCRIPTION OF EXPERIMENT TAB2 summarizes the description of each task, an agents performance with random policy, and the performance of the experts.",1807,0.883,1060,1.7047169811320755,"The goal imitation learning (IL enable imitate an expert��s behavior given Recently generative adversarial imitation learning successfully achieved it even on complex continuous control tasks However GAIL requires a huge number interactions environment during training We believe IL algorithm could more applicable if the number interactions To this end propose a model free, off-policy IL algorithm continuous control The keys our algorithm two folds adopting deterministic policy derive a novel type policy gradient which deterministic policy imitation gradientDPIG introducing state screening function avoid noisy policy updates with states typical those appeared the expert��s demonstrations Experimental results our algorithm achieve IL with at least tens of times less interactions GAIL on continuous control tasks Recent advances reinforcement learningRL achieved BID16 BID17 BID13 . However on most domains the success RL design reward, that explains what agent's behavior favorable clear enough humans Conversely on domains unclear design the reward agents trained RL algorithms obtain poor policies their behavior far what Imitation learning (IL comes such cases The goal IL is enable imitate the expert's behavior given the expert's demonstrations but the reward signals. We interested IL because desire an algorithm often design the reward Besides since generally hard model a variety an algorithm the state-action pairs a vast majority such robotics control naturally represented continuous spaces focus model free IL for continuous controlA widely used approach of existing model free IL methods the combination BID22 BID18 RL. Recently BID10 proposed generative adversarial imitation learning on the line those works GAIL has achieved continuous control tasks However pointed BID10 , a crucial drawback GAIL requirement interactions the environments during 1 Since the interactions environment too time especially believe model free IL could more applicable if the number could while the imitation capability satisfied as GAIL.To reduce a model free, off-policy IL algorithm continuous control As opposed GAIL its variants BID2 those of which adopt as the learner's policy we adopt while following adversarial training fashion GAIL We show combining the deterministic policy into the adversarial off-policy IL objective derives a novel type policy gradient deterministic policy imitation gradientDPIG Because DPIG only integrates over the state space as deterministic policy gradient algorithms BID25 , the interactions expectedPG which integrates Besides introduce a function state screening function avoid noisy policy update with states typical those appeared the experts demonstrationsIn evaluate 6 physics-based control tasks simulated MuJoCo physics simulator BID29 . The experimental results our algorithm enables achieve does at least tens of times less interactions GAIL It indicates our algorithm more applicable GAIL A wide variety IL methods The simplest IL method among is BC (Pomerleau learns a mapping states actions the expert's demonstrations using supervised learning Since the learner with the mapping learned by BC does interacts the environments inaccuracies never once done whereas our algorithm through A noticeable point common BC our algorithm the both just consider the relationship single time-step state-action pairs but information over entire trajectories the optimizations In the both assume the reward structure dense the reasonable rewards the states s �� S \ S E can not defined A drawback BC due ignorance the information over the trajectories referred compounding error BID21 ) -the inaccuracies compounds encounter unseen states th expert's demonstrations For the state s �� S β * E assumed in our algorithm the immediate reward greater likely the expert's behavior yields That maximizing the immediate reward the state s �� S β * E ��� S E implies trajectories stating from in our algorithm the information over implicitly incorporated log R �� of the objective (11 Therefore our algorithm less affected the compounding error BC.Another widely IL the combination IRL RL that considered The concept IRL BID22 , a variety so Early works IRL BID18 BID1 represented the parameterized reward function hand-designed features Thus its capabilities represent the reward were nonlinear functional representation Indeed applications the early works were limited small discrete domains The early works extended algorithms enable to learn nonlinear functions for representing the reward BID11 BID6 A variety complex tasks including continuous control in succeeded the nonlinear functional representation BID6 . As well those methods our algorithm utilize if differentiable the actionIn the connection GANs the IL approach pointed BID10 BID5 . BID10 showed IRL a dual problem RL which deemed to match the learner's occupancy measure BID28 to the expert found a choice regularizer the cost function yields an objective which analogous GANs After that their algorithm, namely GAIL become IL some extensions BID2 . However those extensions addressed reducing interactions during training whereas we address, our algorithm significantly reduce while the imitation capability as GAIL.The way of deriving policy gradients using the parameterized reward function with actions executed the current learner's policy DPG BID25 . However they require parameterized Q-function approximator known reward function whereas our algorithm besides learned IRL In IL literature MGAIL BID2 uses the gradients derived parameterized discriminator to update the learner's policy However MGAIL modelbased method requires to train parameterized forward-model derive whereas our algorithm free Although model based methods thought need less environment interactions model free methods showed MGAIL needs our model free algorithm We think the reasons the need training the forward model besides for the policy lack care the noisy policy updates issue MGAIL essentially In proposed a model free, off-policy IL algorithm continuous control The experimental results our algorithm enables achieve does several tens times less interactions GAIL.Although implemented shallow neural networks represent the parameterized functions We expect the that advanced techniques deep GANs enable apply our algorithm TAB2 summarizes each task an agents performance with random policy the experts",0.01,0.4996361218513612
"Convolution acts as a local feature extractor in convolutional neural networks (CNNs). However, the convolution operation is not applicable when the input data is supported on an irregular graph such as with social networks, citation networks, or knowledge graphs. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network that generalizes CNN architectures to graph-structured data and provides a systematic way to design a set of fixed-size learnable filters to perform convolutions on graphs. The topologies of these filters are adaptive to the topology of the graph when they scan the graph to perform convolution, replacing the square filter for the grid-structured data in traditional CNNs. The outputs are the weighted sum of these filters’ outputs, extraction of both vertex features and strength of correlation between vertices. It
 can be used with both directed and undirected graphs. The proposed TAGCN not only inherits the properties of convolutions in CNN for grid-structured data, but it is also consistent with convolution as defined in graph signal processing. Further, as no approximation to the convolution is needed, TAGCN exhibits better performance than existing graph-convolution-approximation methods on a number
 of data sets. As only the polynomials of degree two of the adjacency matrix are used, TAGCN is also computationally simpler than other recent methods. Convolutional neural network (CNN) architectures exhibit state-of-the-art performance on a variety of learning tasks dealing with 1D, 2D, and 3D grid-structured data such as acoustic signals, images, and videos, in which convolution serves as a feature extractor BID12 . However, the (usual) convolution operation is not applicable when applying CNN to data that is supported on an arbitrary graph rather than on a regular grid structure, since the number of neighbors of each vertex on the graph varies, and it is difficult to design a fixed-size filter scanning over the graph-structured data for feature extraction.Recently, there has been an increasing interest in graph CNNs (Bruna et al., 2014; BID3 BID10 BID13 , attempting to generalize deep learning methods to graph-structured data, specifically focusing on the design of graph CNN . In this paper, we propose the topology adaptive graph convolutional network (TAGCN), a unified convolutional neural network to learn nonlinear representations for the graph-structured data. It slides a set of fixed-size learnable filters on the graph simultaneously, and the output is the weighted sum of these filters' outputs, which extract both vertex features and strength of correlation between vertices. Each filter is adaptive to the topology of the local region on the graph where it is applied. TAGCN unifies filtering in both the spectrum and vertex domains; and applies to both directed and undirected graphs.In general, the existing graph CNNs can be grouped into two types: spectral domain techniques and vertex domain techniques. In Bruna et al. (2014) , CNNs have been generalized to graph-structured data, where convolution is achieved by a pointwise product in the spectrum domain according to the convolution theorem. Later, BID3 and BID13 proposed spectrum filtering based methods that utilize Chebyshev polynomials and Cayley polynomials, respectively. The assumption of symmetric adjacency matrix in these spectrum based methods restrict the application to undirected graphs. BID10 simplified this spectrum method and obtained a filter in the vertex domain, which achieves state-of-the-art performance. Other researchers BID0 worked on designing feature propagation models in the vertex domain for graph CNNs. BID22 ; BID2 ; Grover & Leskovec (2016) ; BID5 study transforming graph-structured data to embedding vectors for learning problems. Nevertheless, it still remains open how to extend CNNs from grid-structured data to arbitrary graph-structured data with local feature extraction capability. This paper proposes a modification to the graph convolution step in CNNs that is particularly relevant for graph structured data. Our proposed TAGCN is graph-based convolution and draws on techniques from graph signal processing. We define rigorously the graph convolution operation on the vertex domain as multiplication by polynomials of the graph adjacency matrix, which is consistent with the notion of convolution in graph signal processing. In graph signal processing, polynomials of the adjacency matrix are graph filters, extending to graph based data from the usual concept of filters in traditional time or image based signal processing. Thus, comparing ours with existing work on graph CNNs, our paper provides a solid theoretical foundation for our proposed convolution step instead of an ad-hoc approach to convolution in CNNs for graph structured data.Further, our method avoids computing the spectrum of the graph Laplacian as in Bruna et al. (2014) , or approximating the spectrum using high degree Chebyshev polynomials of the graph Laplacian matrix (in BID3 , it is suggested that one needs a 25 th degree Chebyshev polynomial to provide a good approximation to the graph Laplacian spectrum) or using high degree Cayley polynomials of the graph Laplacian matrix (in BID13 , 12 th degree Cayley polynomials are needed). We also clarify that the GCN method in BID10 is a first order approximation of the Chebyshev polynomials approximation in BID3 , which is very different from our method. Our method has a much lower computational complexity than the complexity of the methods proposed in Bruna et al. (2014) ; BID3 ; BID13 , since our method only uses polynomials of the adjacency matrix with maximum degree 2 as shown in our experiments. Finally, the method that we propose exhibits better performance than existing methods. Our contributions are summarized follows:• We propose a general K-localized filter for graph convolution in the vertex domain to extract local features on a set of size-1 up to size-K receptive fields. The topologies of these filters are adaptive to the topology of the graph as they scan the graph to perform convolution. It replaces the fixed square filters in traditional CNNs for the input gridstructured data volumes in traditional CNNs. Thus, our convolution definition that we use in the convolution step for the vertex domain is consistent with convolution in traditional CNNs.• TAGCN is based on the graph signal processing and it is consistent with the convolution in graph signal processing. It applies to both directed and undirected graphs. Moreover , it has a much lower computational complexity compared with recent methods since it only needs polynomials of the adjacency matrix with maximum degree 2 compared with the 25 th and 12 th degree Laplacian matrix polynomials in BID3 and BID13 .• As no approximation to the convolution is needed in TAGCN, it achieves better performance compared with existing methods. We contrast TAGCN with recently proposed graph CNN including both spectrum filtering methods (Bruna et al., 2014; BID3 and vertex domain propagation methods BID10 BID0 , evaluating their performances on three commonly used data sets for graph vertices classification. Our experimental tests show that TAGCN outperforms consistently all other approaches for each of these data sets. We have defined a novel graph convolutional network that rearchitects the CNN architecture for graph-structured data. The proposed method, known as TAGCN, is adaptive to the graph topology as the filter scans the graph. Further, TAGCN inherits properties of the convolutional layer in classical CNN, i.e., local feature extraction and weight sharing. It can further extract the strength of correlation between vertices in the filtering region. On the other hand, by the convolution theorem, TAGCN that implements in the vertex domain offers implement in the spectrum domain unifying graph CNN in both the spectrum domain and the vertex domain. TAGCN is consistent with convolution in graph signal processing. These nice properties lead to a noticeable performance advantage in classification accuracy on different graph-structured datasets for semi-supervised graph vertex classification problems with low computational complexity.",1588,0.788,899,1.7664071190211346,"Convolution acts a local feature extractor However the convolution operation applicable supported on an irregular graph with social networks citation networks knowledge graphs This paper proposes the topology adaptive graph convolutional networkTAGCN generalizes CNN architectures a systematic way design fixed-size learnable filters perform convolutions graphs The topologies these filters adaptive the graph when scan to perform convolution replacing the square filter the grid-structured data traditional CNNs The outputs the weighted sum�� outputs extraction of both vertex features strength correlation It can used both directed and undirected graphs The proposed TAGCN not inherits the properties convolutions in CNN for grid-structured data consistent as graph signal processing Further as no approximation the convolution is needed TAGCN exhibits better existing graph-convolution-approximation methods on As only the polynomials degree two the adjacency matrix used TAGCN computationally simpler other recent methods architectures exhibit state learning dealing 1D such acoustic signals images videos in which serves a feature extractor BID12 . However the (usual) convolution operation applicable applying CNN data supported on an arbitrary graph rather a regular grid structure neighbors on varies, design a fixed-size filter scanning over for feature extractionRecently there graph CNNsBruna BID3 BID10 BID13 , attempting deep learning methods specifically focusing the design . In the topology adaptive graph convolutional networkTAGCN to learn nonlinear representations It slides a set fixed-size learnable filters the graph simultaneously the weighted sum extract both vertex features strength correlation Each filter adaptive the local region on where TAGCN unifies filtering in both the spectrum and vertex domains; and applies toIn general the existing graph CNNs spectral domain techniques In Bruna et al (2014 , CNNs have generalized graph-structured data convolution achieved a pointwise product in the spectrum domain according Later BID3 and proposed spectrum filtering based methods utilize The assumption symmetric adjacency matrix in these spectrum based methods restrict undirected graphs BID10 simplified this spectrum method obtained a filter in the vertex domain achieves state Other researchers BID0 worked designing feature propagation models the vertex domain graph CNNs BID22 ; BID2 ; Grover & Leskovec (2016) ; BID5 study transforming embedding vectors learning problems Nevertheless still open how extend CNNs from grid-structured data with local feature extraction capability This paper proposes a modification the graph convolution step CNNs particularly graph structured data Our proposed TAGCN is graph-based convolution and draws techniques graph signal processing We define rigorously the graph convolution operation on the vertex domain multiplication consistent graph signal processing In graph signal processing of graph filters extending to graph based data from the usual concept filters in traditional time or image based signal processing Thus comparing ours existing work graph CNNs our paper provides our proposed convolution step instead in for graph structured dataFurther avoids computing the spectrum as in Bruna (2014 , or approximating the spectrum usingin BID3 , it one needs provide or 12 needed We also clarify the GCN method in BID10 a first order approximation , very Our method has a much lower computational complexity the complexity proposed Bruna (2014 ; BID3 ; , since our method only of with maximum degree 2 as shown our experiments Finally the method propose exhibits better performance existing methods Our contributions summarized follows:• propose a general K-localized filter graph convolution the vertex domain to extract local features on size-1 up size-K receptive fields The topologies these filters adaptive the graph as scan perform convolution It replaces the fixed square filters traditional CNNs for the input gridstructured data volumes in Thus our convolution definition that the vertex domain consistent traditional CNNs.• TAGCN is based the graph signal processing it consistent It applies both directed and undirected graphs Moreover , a much lower computational complexity compared recent methods since only with maximum degree 2 compared in BID3 .• As no approximation is TAGCN achieves We contrast TAGCN recently proposed graph CNN including both spectrum filtering methodsBruna BID3 and vertex domain propagation methods BID10 BID0 , evaluating their performances three commonly used data sets for graph vertices classification Our experimental tests that TAGCN outperforms consistently all other approaches each We defined a novel graph convolutional network the CNN architecture The proposed method, TAGCN adaptive the graph topology as the filter scans Further, TAGCN inherits properties the convolutional layer classical CNN weight sharing It can further extract correlation vertices the filtering region On by the convolution theorem TAGCN that implements in the vertex domain offers implement in the spectrum domain unifying graph CNN in TAGCN is consistent convolution in graph signal processing These nice properties lead a noticeable performance advantage classification accuracy on different graph-structured datasets for semi-supervised graph vertex classification problems with",0.01,0.6568171731564318
"Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a ``forgetting event'' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance. Many machine learning models, in particular neural networks, cannot perform continual learning. They have a tendency to forget previously learnt information when trained on new tasks, a phenomenon usually called catastrophic forgetting BID17 BID29 . One of the hypothesized causes of catastrophic forgetting in neural networks is the shift in the input distribution across different tasks-e.g., a lack of common factors or structure in the inputs of different tasks might lead standard optimization techniques to converge to radically different solutions each time a new task is presented. In this paper, we draw inspiration from this phenomenon and investigate the extent to which a related forgetting process occurs as a model learns examples traditionally considered to belong to the same task.Similarly to the continual learning setting, in stochastic gradient descent (SGD) optimization, each mini-batch can be considered as a mini-""task"" presented to the network sequentially. In this context, we are interested in characterizing the learning dynamics of neural networks by analyzing (catastrophic) example forgetting events. These occur when examples that have been ""learnt"" (i.e., correctly classified) at some time t in the optimization process are subsequently misclassifiedor in other terms forgotten -at a time t > t. We thus switch the focus from studying interactions between sequentially presented tasks to studying interactions between sequentially presented dataset examples during SGD optimization. Our starting point is to understand whether there exist examples that are consistently forgotten across subsequent training presentations and, conversely, examples that are never forgotten. We will call the latter unforgettable examples. We hypothesize that specific examples consistently forgotten between subsequent presentations, if they exist, must not share commonalities with other examples from the same task. We therefore analyze the proportion of forgettable/unforgettable examples for a given task and what effects these examples have on a model's decision boundary and generalization error.The goal of our investigation is two-fold. First, we attempt to gain insight into the optimization process by analyzing interactions among examples during learning and their influence on the final decision boundary. We are particularly interested in whether we can glean insight on the compressibility of a dataset, and thereby increase data efficiency without compromising generalization accuracy. It is a timely problem that has been the recent focus of few-shot learning approaches via meta-learning BID8 BID28 . Second, we aim to characterize whether forgetting statistics can be used to identify ""important"" samples and detect outliers and examples with noisy labels BID12 BID3 BID32 BID11 .Identifying important, or most informative examples is an important line of work and was extensively studied in the literature. Techniques of note -among others -are predefined curricula of examples BID1 , self-paced learning BID21 , and more recently meta-learning BID7 . These research directions usually define ""hardness"" or ""commonality"" of an example as a function of the loss on that particular example at some point during training (or possibly at convergence). They do not consider whether some examples are consistently forgotten throughout learning. Very recently, BID4 consider re-weighting examples by accounting for the variance of their predictive distribution. This is related to our definition of forgetting events, but the authors provide little analysis of the extent to which the phenomenon occurs in their proposed tasks. Our purpose is to study this phenomenon from an empirical standpoint and characterize its prevalence in different datasets and across different model architectures.Our experimental findings suggest that: a) there exist a large number of unforgettable examples, i.e., examples that are never forgotten once learnt, those examples are stable across seeds and strongly correlated from one neural architecture to another; b) examples with noisy labels are among the most forgotten examples, along with images with ""uncommon"" features, visually complicated to classify; c) training a neural network on a dataset where a very large fraction of the least forgotten examples have been removed still results in extremely competitive performance on the test set. In this paper, inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks when training on single classification tasks. We show that catastrophic forgetting can occur in the context of what is usually considered to be a single task. Inspired by this result, we find that some examples within a task are more prone to being forgotten, while others are consistently unforgettable. We also find that forgetting statistics seem to be fairly stable with respect to the various characteristics of training, suggesting that they actually uncover intrinsic properties of the data rather than idiosyncrasies of the training schemes. Furthermore, the unforgettable examples seem to play little part in the final performance of the classifier as they can be removed from the training set without hurting generalization. This supports recent research interpreting deep neural networks as max margin classifiers in the linear case. Future work involves understanding forgetting events better from a theoretical perspective, exploring potential applications to other areas of supervised learning, such as speech or text and to reinforcement learning where forgetting is prevalent due to the continual shift of the underlying distribution. permutedMNIST The permutedMNIST data set is obtained by applying a fixed random permutation of the pixels to all the images of the standard MNIST data set. This typically makes the data set harder to learn for convolutional neural networks as local patterns, e.g. the horizontal bar of the 7, get shuffled. This statement is supported by the two following facts:",1207,0.608,686,1.7594752186588922,"Inspired the phenomenon catastrophic forgetting investigate the learning dynamics as train on single classification tasks Our goal understand whether a related phenomenon data does undergo a clear distributional shift We define a ``forgetting event have individual training example transitions being classified correctly incorrectly over learning Across several benchmark data sets: certain examples forgotten with high frequency some not a data set's (un)forgettable examples generalize neural architectures based forgetting dynamics can omitted while state performance Many machine learning models in perform continual learning They a tendency forget previously learnt information trained new tasks usually called catastrophic BID17 BID29 . One the hypothesized causes catastrophic forgetting neural networks the shift the input distribution across- a lack common factors structure might standard optimization techniques converge radically different solutions each In draw inspiration this phenomenon investigate a related forgetting process as a model learns examples traditionally considered belong the same taskSimilarly the continual learning setting in stochastic gradient descent each mini can considered a mini-""task presented sequentially In this context characterizing the learning dynamics by (catastrophic) example forgetting events These occur examples that ""learnt correctly classified at some time t in the optimization process subsequently misclassifiedor in other terms forgotten -at > We thus switch studying interactions sequentially presented tasks sequentially presented dataset examples during SGD optimization Our starting point understand whether exist examples consistently forgotten across subsequent training presentations,, examples never We will call the latter unforgettable examples We hypothesize specific examples consistently forgotten between subsequent presentations if must not share commonalities from We therefore analyze forgettable/unforgettable examples for what effects a model's decision boundary generalization errorThe goal two First attempt gain the optimization process interactions examples during learning their influence the final decision boundary We particularly whether we glean on the compressibility a dataset thereby increase data efficiency without generalization accuracy It a timely problem the recent focus few-shot learning approaches via meta-learning BID8 BID28 . Second aim characterize whether forgetting statistics ""important"" samples detect and examples with noisy labels BID12 BID3 BID32 BID11 .Identifying important, or most informative examples an important line and was extensively Techniques note -among predefined curricula of examples BID1 , self-paced learning BID21 These research directions usually define ""hardness an example as the loss on that particular example at training possibly convergence They do consider whether some examples consistently forgotten throughout learning Very recently BID4 consider reweighting examples by accounting the variance their predictive distribution This related our definition forgetting events the authors provide little analysis their proposed tasks Our purpose study this phenomenon from characterize different datasets modelOur experimental findings: a there exist unforgettable examples never forgotten once learnt those examples stable across seeds strongly from one neural architecture noisy labels among along images ""uncommon"" features visually complicated to classify training where the least forgotten examples removed still results extremely competitive performance In inspired the phenomenon catastrophic forgetting the learning dynamics when training on single classification tasks We show catastrophic forgetting what usually a single task Inspired this result find some examples within a task prone forgotten consistently unforgettable We also find forgetting statistics seem fairly stable the various characteristics training suggesting actually uncover intrinsic properties the training schemes Furthermore the unforgettable examples seem play little part the final performance the classifier as can removed hurting generalization This supports recent interpreting deep neural networks max margin classifiers the linear case Future work involves understanding forgetting events better from exploring potential applications to other areas supervised learning such speech or text and to where forgetting prevalent due the continual shift the underlying distribution permutedMNIST obtained the pixels This typically makes the data set harder learn for as local patterns, 7, get This statement supported the two following facts",0.01,0.6391553000635452
"Discovering objects and their attributes is of great importance for autonomous agents to effectively operate in human environments. This task is particularly challenging due to the ubiquitousness of objects and all their nuances in perceptual and semantic detail. In this paper we present an unsupervised approach for learning disentangled representations of objects entirely from unlabeled monocular videos. These continuous representations are not biased by or limited by a discrete set of labels determined by human labelers. The proposed representation is trained with a metric learning loss, where objects with homogeneous features are pushed together, while those with heterogeneous features are pulled apart. We show these unsupervised embeddings allow to discover object attributes and can enable robots to self-supervise in previously unseen environments. We quantitatively evaluate performance on a large-scale synthetic dataset with 12k object models, as well as on a real dataset collected by a robot and show that our unsupervised object understanding generalizes to previously unseen objects. Specifically, we demonstrate the effectiveness of our approach on robotic manipulation tasks, such as pointing at and grasping of objects. An interesting and perhaps surprising finding in this approach is that given a limited set of objects, object correspondences will naturally emerge when using metric learning without requiring explicit positive pairs. The ability to autonomously train to recognize and differentiate previously unseen objects as well as infer general properties and attributes is an important skill for robotic agents. Increased autonomy leads to robustness, one of the main challenges real-world robotics faces. It also renders scaling up data collection practical. Additionally, removing human supervision from the loop has the potential to enable learning richer and less biased continuous representations than ones supervised by a limited set of discrete labels. Unbiased representations can prove useful in unknown future environments different from the ones seen during supervision, a typical challenge for robotics.In this work we present an unsupervised method that learns representations that disentangle perceptual and semantic object attributes such as class, function, and color. We automatically acquire training data by capturing videos with a real robot; a robot base moves around a table to capture objects in various arrangements. Assuming a pre-existing objectness detector, we extract objects from random frames within a same scene containing the same objects, and let the metric learning system decide how to assign positive and negative pairs of embeddings. Representations that generalize across objects naturally emerge despite not being given groundtruth matches. Unlike previous methods, we abstain from employing additional self-supervisory training signals such as tracking or depth. The only inputs to the system are monocular videos. This simplifies data collection and allows our embedding to integrate into existing end-to-end learning pipelines. We demonstrate that a trained Object-Contrastive Network (OCN) embedding allows us to reliably identify object instances based on their visual features such as color and shape. Moreover, we show that objects are also organized along their semantic or functional properties. For example, a cup might not only be associated with other cups, but also with other containers like bowls or vases.The key contributions of this work are: (1) an unsupervised algorithm for learning representations of objects (naturally encoding attributes like class, color, texture and function) which generalize to previously unseen objects; (2) showing monocular videos are sufficient to contrast similar and dissimilar objects pairs naturally without requiring explicit correspondences; (3) demonstrating the autonomy of the system, using a robot from data collection to tasks such as pointing and grasping similar objects to ones presented to it. We introduced a novel unsupervised representation learning algorithm that allows us to differentiate object attributes, such as color, shape, and function. An OCN embedding is learned by contrasting the features of objects captured from two frames of single view camera trajectories of table-top indoor environments. We specifically attend to individual objects by detecting object bounding boxes and leverage a metric learning loss to disentangle subtle variations of object attributes. The resulting embedding space allows to organize objects along multiple dimensions and serves as representation for robotic learning. We show that an OCN embedding can be used on real robotic tasks such as Figure 7 : Robot experiment of grasping the object that is closest to the query object (held by hand). Images on the left are captured by the robot camera, and the images on the right are the video frames from a third person view camera. The leftmost object (black border) is the query object and its nearest neighbors are listed in descending order. The top row and the bottom row show the robot successfully identifies and grasps the object with similar color and shape attribute respectively.grasping and pointing, where it is important to differentiate visual and semantic attributes of individual object instances. Finally, we show that an OCN can be trained efficiently from RGB videos that are automatically obtained from a real robotic agent.",950,0.543,555,1.7117117117117118,Discovering objects their attributes of autonomous agents effectively operate This task particularly the ubiquitousness objects all their nuances perceptual and semantic detail In representations objects entirely unlabeled monocular videos These continuous representations biased or a discrete set labels determined human labelers The proposed representation trained with a metric learning loss objects homogeneous features pushed together pulled We show these unsupervised embeddings allow to discover object attributes can enable robots previously unseen environments We quantitatively performance 12k object models collected a robot show our unsupervised object understanding previously unseen objects Specifically demonstrate our approach robotic manipulation tasks pointing and of An interesting and perhaps surprising finding this approach given objects object correspondences will naturally emerge using metric learning without requiring explicit positive pairs The ability autonomously train to recognize differentiate previously unseen objects as infer general properties attributes robotic agents Increased autonomy leads robustness one real-world robotics It also renders scaling up data collection practical Additionally removing human supervision the loop enable learning richer and less biased continuous representations than ones supervised discrete labels Unbiased representations can prove unknown future environments different seen during supervision a typical challenge roboticsIn learns representations perceptual and semantic object attributes such class function color We automatically acquire training data capturing videos with a real robot; a robot base moves objects various arrangements Assuming a pre-existing objectness detector extract objects random frames within a same scene containing let the metric learning system assign Representations that generalize across objects naturally emerge despite not given groundtruth matches Unlike previous methods abstain employing additional self-supervisory training signals such tracking depth. The only inputs monocular videos This simplifies data collection allows our embedding to integrate end learning pipelines We demonstrate a trained Object-Contrastive Network embedding allows reliably object instances based such Moreover show objects also organized along their semantic or functional properties For example a cup might not only associated other cups other containers bowlsThe key contributions learning representations objectsnaturally encoding attributes class texture function generalize previously unseen objects showing monocular videos are sufficient contrast similar and pairs naturally without requiring explicit correspondences the autonomy a robot from data collection tasks pointing grasping similar objects ones presented We introduced a novel unsupervised representation learning differentiate object attributes function An OCN embedding is learned contrasting objects captured two frames single view camera trajectories of table-top indoor environments We specifically attend individual objects by detecting object bounding boxes leverage a metric learning loss subtle variations object attributes The resulting embedding space to organize objects along serves representation robotic learning We show an OCN embedding can on real robotic tasks Figure : Robot experiment of grasping that closest the query objectheld Images on captured the robot camera the video frames camera The leftmost object (black border the query object its nearest neighbors listed The top row and the robot successfully identifies similar color and shape attribute respectively.grasping pointing where important differentiate visual and semantic attributes individual object instances Finally show an OCN can trained efficiently RGB videos that automatically obtained a real robotic agent,0.01,0.5174580808179653
"Learning from a scalar reward in continuous action space environments is difficult and often requires millions if not billions of interactions.   We introduce state aligned vector rewards, which are easily defined in metric state spaces and allow our deep reinforcement learning agent to tackle the curse of dimensionality.   Our agent learns to map from action distributions to state change distributions implicitly defined in a quantile function neural network.    We further introduce a new reinforcement learning technique inspired by quantile regression which does not limit agents to explicitly parameterized action distributions.   Our results in high dimensional state spaces show that training with vector rewards allows our agent to learn multiple times faster than an agent training with scalar rewards. Reinforcement learning BID32 ) is a powerful paradigm in which an agent learns about an environment through interaction. The common formulation consists of a Markov Decision Process (MDP) modeled as a 5-tuple (S, A, P, r, γ) where S is the (possibly infinite) set of states, A is the (possibly infinite) set of actions available to the agent, P : (S × A × S) → [0, 1] : P (s |s, a) is the transition probability of reaching state s ∈ S given state s ∈ S and action a ∈ A, r : (S × A) → R : r(s, a) is the reward received for taking action a in state s and γ is the reward discount factor. The goal of the agent is to maximize the cumulative discounted reward R = ∞ t=0 γ t r(s t , a t ) by choosing actions a t according to some (possibly stochastic) policy π : (S × A) → [0, 1] : π(a t |s t ). Sometimes it is further useful to make a distinction between the actual state space S and the correlated observation space O of the agent. In this case π : (O × A) → [0, 1] : π(a t |o t ) with o t ∈ O. The use of deep neural networks allowed this formulation to scale to high dimensional visual inputs approaching continuity in state space BID20 while others extended deep reinforcement learning to continuous action spaces BID15 BID21 . While neural networks are powerful function approximators, they require large amounts of training data to converge. In the case of reinforcement learning this means interactions with the environment, a requirement easy to fulfill in simulation, yet impractical when the agent should interact with the real world. This problem is aggravated by the weak training signal of classical reinforcement learning -a simple scalar reward.While originally the dopamine activity in mammal brains was linked to general ""rewarding"" events, BID28 point out that the diversity of dopamine circuits in the mid brain is better modeled by viral vector strategies. BID8 also show that human reinforcement learning incorporates effector specific value estimations to cope with the high dimensional action space. Inspired by these biological insights, we improve the sample efficiency of a deep reinforcement learning algorithm in this work by modeling a d-dimensional vector reward. A vector reward can in some domains easily be defined in alignment with the state space. We say that two vector spaces are aligned if their dimensions correlate and show that if state and action space are not aligned, a mapping from action distribution to state change distribution can be learned.As a motivating example, consider the agent in Figure 1 (a) trying to reach the goal (marked by the blue dot). If we take p as the position vector of the agent relative to the goal, a sensible reward to guide the agent to the goal in this environment would be r = ||p|| − ||p + a|| where || · || can be any norm in the vector space of the environment. For illustration purposes we'll focus on the L 1 norm in this example and throughout this paper. During training the agent might try action a which moves Figure 1: (a) An agent freely moving in a 2D world might try to reach a goal at position (0, 0) by taking action a. A sensible reward in this environment is the change in absolute distance to the goal. With a scalar reward this would be summarized as r = r x − r y , whereas a vector reward would keep the two reward dimensions distinguishable. (b) In most cases action and state space are however not aligned, therefore a mapping from action to state change must be learned.it closer to the goal in x direction, but a bit further away from the goal in y direction. The scalar reward would then just convey the information, that the action was rather positive (since the agent got closer to the goal) but miss out on the distinction that the action was good in x-direction but bad in y-direction. To provide this distinction, a more informative reward would keep the dimensions separate and therefore be a vector itself: r = |p| − |p + a| where | · | denotes the element-wise absolute value here. Note that this reward is dimension wise aligned with the position p, the state, of the agent. Since we focus on reaching problems in this work, we'll use the terms ""position"" and ""state"" interchangeably.The problem with such a state aligned vector reward is however that the action space is in most cases not state aligned. To see this, consider the schematic robot arm in Figure 1 (b): The action dimensions a 1 and a 2 correspond to the torques of the robot arm and do not directly translate to a shift in x and y dimension, respectively. To address this issue we use the method proposed by BID5 a) to train a deep neural network to approximate the quantile function, in our case of the position change, given the current observation and quantile target. Additionally we give a parameterization of the action probability distribution as input to this position change prediction network (short PCPN). We then train the agent, parameterized by another neural network which maps from observations to action probability distributions, through a new reinforcement learning method we call quantile regression reinforcement learning (short QRRL). A schematic overview of our setup can be seen in FIG1 .To summarize, the contributions of this paper are the following:• We extend the reinforcement learning paradigm to allow for faster training based on more informative state aligned vector rewards.• We present an architecture that learns a probability distribution over possible state changes based on a probability distribution over possible actions.• We introduce a new reinforcement learning algorithm to train stochastic continuous action policies with arbitrary action probability distributions. In this work we present the idea of state aligned vector rewards for faster reinforcement learning. While the idea is straight forward and simple, we are unaware of any work that addresses it so far. Additionally, we also present a new reinforcement learning technique based on quantile regression in this work which we term QRRL. QRRL allows for complex stochastic policies in continuous action spaces, not limiting agents to Gaussian actions. Combining both, we show that the agent network in our SAVER agent can be trained through a quantile network pretrained in the environment. We show that SAVER is capable of training orders of magnitudes faster in high dimensional metric spaces. While d-dimensional metric spaces are mainly mathematical constructs for d > 3, we see a lot of potential in SAVER to be applied to problems in mathematics and related fields, including the field of deep (reinforcement) learning itself.",1490,0.713,843,1.767497034400949,"Learning a scalar reward in continuous action space environments difficult millions if interactions We introduce state aligned vector rewards easily defined metric state spaces allow our deep reinforcement agent tackle the curse dimensionality Our agent learns to map from action distributions state change distributions implicitly defined a quantile function neural network We further introduce a new reinforcement learning technique inspired quantile regression which does limit agents explicitly parameterized action distributions Our results in high dimensional state spaces training vector rewards allows our agent multiple times an agent training Reinforcement learning BID32 ) a powerful paradigm about interaction The common formulation consists a Markov Decision Process modeled (possibly set states actions available : S → [0 : P (s |s the transition probability reaching given action r received taking the reward discount factor The goal the agent maximize the cumulative discounted reward R = �� t=0 �� t r(s t by choosing actions a t according some :S × A → [0( Sometimes further useful make the actual state space S the correlated observation space O of the agent In � :O × A [0 :(a t |o t with The use allowed this formulation scale high dimensional visual inputs approaching continuity state space BID20 while others extended deep reinforcement learning continuous action spaces . While neural networks powerful function approximators require converge In reinforcement learning this interactions a requirement easy fulfill simulation yet impractical the agent should This problem aggravated the weak training signal classical reinforcement learning -a simple scalar rewardWhile originally the dopamine activity mammal brains linked BID28 point the diversity dopamine circuits the mid brain better modeled viral vector strategies BID8 also show human reinforcement learning incorporates effector specific value estimations cope the high dimensional action space Inspired these biological insights improve the sample efficiency a deep reinforcement in this work modeling a d-dimensional vector reward A vector reward can in some domains easily defined alignment the state space We say two vector spaces aligned if their dimensions correlate and show if state and action space a mapping from action distribution state change distribution learnedAs a motivating example the agent in Figure trying reachmarked If take p as the position vector the agent relative a sensible reward to guide in r ||p|| − + a|| where || · || can any norm in For illustration purposes we the L 1 norm in throughout During training the agent might action a which moves Figure: ( An agent freely moving might reach at position0 taking A sensible reward in this environment the change absolute distance With a scalar reward this would summarized whereas keep the two reward dimensions distinguishable (b In most cases action and state space however aligned therefore a mapping action state change learned.it closer in x direction bit The scalar reward would then just convey, that the action rather positive (since the agent got closer miss the distinction that good x but To provide this distinction a more informative reward keep the dimensions separate therefore a vector itself r |p| − a| · denotes here Note this reward dimension wise aligned the position p, the state, of the agent Since we focus reaching problems this work use ""positionstateThe problem such a state aligned vector reward however the action space in state To consider the schematic robot arm (b): The action dimensions a 1 do directly translate a shift x To address use the method proposed BID5 a) train approximate the quantile function in of the position change given the current observation quantile target Additionally we give a parameterization the action probability distribution input this position change prediction networkshort PCPN We then train the agent parameterized another neural network which maps from observations through we quantile regression reinforcement learningshort QRRL A schematic overview our setup can FIG1 .To summarize the contributions this paper extend the reinforcement learning paradigm allow faster training based more informative state aligned vector rewards.• present learns possible state changes reinforcement stochastic continuous action policies arbitrary action probability distributions In this work state aligned vector rewards faster reinforcement learning While the idea straight we unaware addresses so Additionally present a new reinforcement learning technique quantile regression this work which term QRRL QRRL allows complex stochastic policies continuous action spaces not limiting agents Gaussian actions Combining both, show the agent network our SAVER agent can trained through a quantile network pretrained the environment We show SAVER capable training orders magnitudes faster in high dimensional metric spaces While d-dimensional metric spaces mainly mathematical constructs for d > see potential SAVER to applied problems mathematics deep (reinforcement itself",0.01,0.6595941817852811
"We propose Episodic Backward Update - a new algorithm to boost the performance of a deep reinforcement learning agent by fast reward propagation. In contrast to the conventional use of the replay memory with uniform random sampling, our agent samples a whole episode and successively propagates the value of a state into its previous states. Our computationally efficient recursive algorithm allows sparse and delayed rewards to propagate effectively throughout the sampled episode. We evaluate our algorithm on 2D MNIST Maze Environment and 49 games of the Atari 2600 Environment and show that our agent improves sample efficiency with a competitive computational cost. Recently, deep reinforcement learning (RL) has been very successful in many complex environments such as the Arcade Learning Environment (Bellemare et al., 2013) and Go . Deep Q-Network (DQN) algorithm BID11 with the help of experience replay BID8 BID9 enjoys more stable and sample-efficient learning process, so is able to achieve super-human performance on many tasks. Unlike simple online reinforcement learning, the use of experience replay with random sampling breaks down the strong ties between correlated transitions and also allows the transitions to be reused multiple times throughout the training process.Although DQN has shown impressive performances, it is still impractical in terms of data efficiency. To achieve a human-level performance in the Arcade Learning Environment, DQN requires 200 million frames of experience for training, which is approximately 39 days of game play in real time. Remind that it usually takes no more than a couple of hours for a skilled human player to get used to such games. So we notice that there is still a tremendous amount of gap between the learning process of humans and that of a deep reinforcement learning agent. This problem is even more crucial in environments such as autonomous driving, where we cannot risk many trials and errors due to the high cost of samples.One of the reasons why the DQN agent suffers from such low sample efficiency could be the sampling method over the replay memory. In many practical problems, the agent observes sparse and delayed reward signals. There are two problems when we sample one-step transitions uniformly at random from the replay memory. First, we have a very low chance of sampling the transitions with rewards for its sparsity. The transitions with rewards should always be updated, otherwise the agent cannot figure out which action maximizes its expected return in such situations. Second, there is no point in updating a one-step transition if the future transitions have not been updated yet. Without the future reward signals propagated, the sampled transition will always be trained to return a zero value.In this work, we propose Episodic Backward Update (EBU) to come up with solutions for such problems. Our idea originates from a naive human strategy to solve such RL problems. When we observe an event, we scan through our memory and seek for another event that has led to the former one. Such episodic control method is how humans normally recognize the cause and effect relationship BID7 . We can take a similar approach to train an RL agent. We can solve the first problem above by sampling transitions in an episodic manner. Then, we can be assured that at least one transition with non-zero reward is being updated. We can solve the second problem by updating transitions in a backward way in which the transitions were made. By then, we can perform an efficient reward propagation without any meaningless updates. This method faithfully follows the principle of dynamic programing.We evaluate our update algorithm on 2D MNIST Maze Environment and the Arcade Learning Environment. We observe that our algorithm outperforms other baselines in many of the environments with a notable amount of performance boosts.",728,0.438,442,1.6470588235294117,We propose Episodic Backward Update - boost a deep reinforcement learning agent fast reward propagation In contrast the conventional use the replay memory with uniform random sampling our agent samples a whole episode successively the value a state its previous states Our computationally efficient recursive algorithm allows sparse delayed rewards propagate effectively throughout the sampled episode We evaluate our algorithm 2D MNIST Maze Environment 49 games the Atari 2600 Environment show our agent improves sample efficiency a competitive computational cost Recently deep reinforcement learningRL very many complex environments the Arcade Learning EnvironmentBellemare et Go . Deep QNetwork algorithm BID11 with the help experience replay BID8 BID9 enjoys more stable and sample-efficient learning process is achieve Unlike simple online reinforcement learning experience replay with random sampling breaks the strong ties correlated transitions also the transitions reused multiple throughoutAlthough DQN impressive performances impractical terms data efficiency To achieve the Arcade Learning Environment DQN 200 million frames experience training approximately 39 days in Remind that usually a skilled human player used such games So notice still gap the learning process humans a deep reinforcement learning agent This problem even crucial environments autonomous driving we risk many trials samplesOne the DQN agent suffers such low sample efficiency could the sampling method over the replay memory In many practical problems the agent observes sparse delayed reward signals There when we sample one-step transitions uniformly at the replay memory First sampling the transitions with rewards its sparsity The transitions with rewards should updated otherwise the agent figure maximizes its expected return such situations Second updating a one-step transition the future transitions updated Without the future reward signals propagated the sampled transition always trained returnIn this work propose Episodic Backward UpdateEBU come solutions Our idea originates a naive human strategy solve such RL problems When observe scan seek led former one Such episodic control method how humans normally recognize the cause relationship BID7 . We take train an RL agent We solve above sampling transitions Then be at least one transition with non-zero reward being updated We solve updating transitions a backward way in which were By then we can perform an efficient reward propagation without any meaningless updates This method faithfully follows dynamic programingWe evaluate our update algorithm 2D MNIST Maze Environment the Arcade Learning Environment We observe our algorithm other baselines many the environments with a notable amount performance boosts,0.0,0.35272820207011113
"Survival Analysis (time-to-event analysis) in the presence of multiple possible adverse events, i.e., competing risks, is a challenging, yet very important problem in medicine, finance, manufacturing, etc. Extending classical survival analysis to competing risks is not trivial since only one event (e.g. one cause of death) is observed and hence, the incidence of an event of interest is often obscured by other related competing events. This leads to the nonidentifiability of the event times’ distribution parameters, which makes the problem significantly more challenging. In this work we introduce Siamese Survival Prognosis Network, a novel Siamese Deep Neural Network architecture that is able to effectively learn from data in the presence of multiple adverse events. The Siamese Survival Network is especially crafted to issue pairwise concordant time-dependent risks, in which longer event times are assigned lower risks. Furthermore, our architecture is able to directly optimize an approximation to the C-discrimination index, rather than relying on well-known metrics of cross-entropy etc., and which are not able to capture the unique requirements of survival analysis with competing risks. Our results show consistent performance improvements on a number of publicly available medical datasets over both statistical and deep learning state-of-the-art methods. Competing risks settings are ubiquitous in medicine. They can be encountered in cardiovascular diseases, in cancer, and in the geriatric population suffering from multiple diseases. To solve the challenging problem of learning the model parameters from time-to-event data while handling right censoring, we have developed a novel deep learning architecture for estimating personalized risk scores in the presence of competing risks which is based on the well-known Siamese network architecture. Our method is able to capture complex non-linear representations missed out by classical machine learning and statistical models. Experimental results show that our method is able to outperform existing competing risk methods by successfully learning representations which can flexibly describe non-proportional hazard rates with complex interactions between covariates and survival times that are common in many diseases with heterogeneous phenotypes.",403,0.215,253,1.592885375494071,"Survival Analysis (timeevent in the presence multiple possible adverse events a challenging, yet very important problem medicine finance manufacturing etc Extending classical survival analysis competing risks trivial since only one event observed and hence the incidence of often obscured other related competing events This leads the nonidentifiability the event times�� distribution parameters makes the problem significantly challenging In this work introduce Siamese Survival Prognosis Network Siamese Deep Neural Network architecture effectively learn data multiple adverse events The Siamese Survival Network especially crafted issue pairwise concordant time-dependent risks in longer event assigned lower risks Furthermore our architecture able directly optimize an approximation the C-discrimination index rather well-known metrics of cross etc which able capture the unique requirements survival analysis with competing risks Our results consistent performance improvements publicly available medical datasets both statistical deep state Competing risks settings are ubiquitous medicine They can encountered cardiovascular diseases in suffering multiple diseases To solve the challenging problem learning the model parameters from time data while handling right censoring a novel deep learning architecture estimating personalized risk scores competing risks which the well-known Siamese network architecture Our method able capture complex non-linear representations missed out classical machine learning and statistical models Experimental results our method existing competing risk methods successfully learning representations which flexibly describe non-proportional hazard rates with complex interactions survival times that common many diseases with",0.0,0.2146990161031655
"The digitization of data has resulted in making datasets available to millions of users in the form of relational databases and spreadsheet tables. However, a majority of these users come from diverse backgrounds and lack the programming expertise to query and analyze such tables. We present a system that allows for querying data tables using natural language questions, where the system translates the question into an executable SQL query. We use a deep sequence to sequence model in wich the decoder uses a simple type system of SQL expressions to structure the output prediction. Based on the type, the decoder either copies an output token from the input question using an attention-based copying mechanism or generates it from a fixed vocabulary. We also introduce a value-based loss function that transforms a distribution over locations to copy from into a distribution over the set of input tokens to improve training of our model. We evaluate our model on the recently released WikiSQL dataset and show that our model trained using only supervised learning significantly outperforms the current state-of-the-art Seq2SQL model that uses reinforcement learning. The IT revolution of the past few decades has resulted in a large-scale digitization of data, making it accessible to millions of users in the form of databases and spreadsheet tables. Despite advances in designing new high-level programming languages and user interfaces, querying and analyzing such tables usually still requires users to write small programs in languages such as SQL or Excel, which is unfortunately beyond the programming expertise of a majority of end-users BID8 . Thus, building effective semantic parsers that can translate natural language questions into executable programs has been a long-standing goal to improve end-user data accessibility BID22 BID30 BID20 BID15 BID9 .Recent work has shown that recurrent neural networks with attention and copying mechanisms BID4 BID18 BID13 can be used effectively to build successful semantic parsers. Notably , BID32 recently introduced the state-ofthe-art Seq2SQL model for question to SQL translation in the supervised setting, where programs are explicitly provided with their corresponding questions. The Seq2SQL model shows that using separate decoders for different parts of a query (i.e., aggregation operation, target column, and where predicates) increases prediction accuracy, and reinforcement learning further improves the model by allowing it to learn semantically equivalent queries beyond supervision.In this paper, we present a new encoder-decoder model as an extension of the attentional seq2seq model for natural language to SQL program translation and a training approach that is capable of learning the model in an effective and stable manner. FIG0 shows an example table-question pair and how our system generates the answer by executing the synthesized SQL program.First, we present a simple type system to control the decoding mode at each decoding step (cf. Sect. 2). Based on the SQL grammar, a decoder cell is specialized to either select a token from the SQL built-in vocabulary, generate a pointer over the table header and the input question to copy a table column, or generate a pointer to copy a constant from the user's question. The type system allows us to have a fine-grain control over the decoding process while retaining the simplicity of the sequence structure, as opposed to designing multiple decoders for different language components or adding extra controllers for expansion of production rules . FIG0 . The model encodes table columns as well as the user question with a bidirectional LSTM and then decodes the hidden state with a typed LSTM, where the decoding action for each cell is statically determined.Second, we constructed an objective function that allows us to effectively train our model to copy correct values (cf. Sect. 3). Training copying decoders can be challenging when the value to be copied appears in multiple places in the input (i.e. both in the question and the table headers). Our solution to the problem is to use a new value-based loss function that transfers the distribution over the pointer locations in the input into a distribution over the set of tokens observed in the input, by summing up the probabilities of the same vocabulary value appearing at different input indices. Our results show that our training strategy performs better than alternatives (e.g., direct supervision on pointers). Our approach is very robust and consistently converges to high-accuracy models starting from random initializations.We have evaluated our approach on the recently released WikiSQL dataset BID32 , a corpus consisting of over 80,000 natural language question and pairs. Our results in Sect. 4 show that our model can significantly outperform the current state-of-the-art Seq2SQL model BID32 , without requiring a reinforcement learning refinement phase (59.5% vs 48.3% for exact syntactic match and 65.1% vs 59.4% for execution accuracy). Also, with a series of ablation experiments, we analyze the influence of different components of our model on the overall results. We presented a new sequence to sequence based neural architecture to translate natural language questions over tables into executable SQL queries. Our approach uses a simple type system to guide the decoder to either copy a token from the input using a pointer-based copying mechanism or generate a token from a finite vocabulary. We presented a sum-transfer value based loss function that transforms a distribution over pointer locations into a distribution over token values in the input to efficiently train the architecture. Our evaluation on the WikiSQL dataset showed that our model significantly outperforms the current state-of-the-art Seq2SQL model.",1074,0.562,605,1.7752066115702478,"The digitization resulted making datasets millions spreadsheet tables However a majority these users come lack the programming expertise query such tables We present querying data tables natural language questions where the system translates We use a deep sequence to sequence model in wich the decoder of SQL expressions structure the output prediction Based the type, the decoder either copies an output token the input question using an attention-based copying mechanism generates a fixed vocabulary We also introduce a value-based loss function transforms a distribution locations copy from into the set input tokens to improve training We evaluate our model the recently released WikiSQL dataset show trained using only supervised learning significantly current state Seq2SQL that The IT revolution of resulted making databases spreadsheet tables Despite advances designing querying such tables usually still users languages SQL Excel unfortunately beyond the programming expertise end-users BID8 . Thus building effective semantic parsers that translate natural language questions executable programs to end-user data accessibility BID22 BID30 BID20 BID15 BID9 .Recent work attention and copying mechanisms can effectively Notably , BID32 recently the state-ofthe-art Seq2SQL model question to SQL translation in the supervised setting programs explicitly provided their corresponding questions The Seq2SQL model shows using separate decoders target column where predicates) increases prediction accuracy reinforcement learning further semantically equivalent queries beyond supervisionIn as the attentional seq2seq model to SQL program translation a training approach capable FIG0 shows an example table-question pair how our system generates by executing the synthesized SQL programFirst present control the decoding mode at each decoding step (cf Sect. 2 Based the SQL grammar a decoder cell specialized either select a token built-in vocabulary generate over the table header the input question copy a table column copy a constant the user's question The type system allows have the decoding process while retaining the sequence structure designing different language components or adding extra controllers expansion production rules . FIG0 . The model encodes table columns the user question with then the hidden state with where the decoding action for staticallySecond constructed an objective function allows effectively train copy correct values (cf Sect. 3 Training copying decoders can challenging when the value to appears ( both in the question the table headers Our solution a new value-based loss function transfers the distribution over the pointer locations into a distribution tokens observed by the same vocabulary value appearing different input indices Our results our training strategy performs alternatives on pointers Our approach very robust and consistently converges high-accuracy models starting random initializationsWe evaluated the recently released WikiSQL dataset BID32 , a corpus consisting and pairs Our results in Sect. 4 show that our model significantly state- Seq2SQL BID32 , without requiring a reinforcement learning refinement phase59.5% exact syntactic match execution accuracy Also with a series ablation experiments analyze different components our model We presented a new sequence to sequence based neural architecture to translate natural language questions over tables executable SQL queries Our approach uses guide either copy a token using generate a finite vocabulary We presented a sum-transfer value based loss function transforms pointer locations token values in to efficiently train the architecture Our evaluation on the WikiSQL dataset showed our model significantly current state Seq2SQL",0.01,0.6792375070566105
"To backpropagate the gradients through stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator that is unbiased, exhibits low variance, and has low computational complexity. Exploiting variable augmentation, REINFORCE, and reparameterization, the ARM estimator achieves adaptive variance reduction for Monte Carlo integration by merging two expectations via common random numbers. The variance-reduction mechanism of the ARM estimator can also be attributed to either antithetic sampling in an augmented space, or the use of an optimal anti-symmetric ""self-control"" baseline function together with the REINFORCE estimator in that augmented space. Experimental results show the ARM estimator provides state-of-the-art performance in auto-encoding variational inference and maximum likelihood estimation, for discrete latent variable models with one or multiple stochastic binary layers. Python code for reproducible research is publicly available. Given a function f (z) of a random variable z = (z 1 , . . . , z V )T , which follows a distribution q φ (z) parameterized by φ, there has been significant recent interest in estimating φ to maximize (or minimize) the expectation of f (z) with respect to z ∼ q φ (z), expressed as DISPLAYFORM0 In particular, this expectation objective appears in both maximizing the evidence lower bound (ELBO) for variational inference BID12 and approximately maximizing the log marginal likelihood of a hierarchal Bayesian model BID1 , two fundamental problems in statistical inference. To maximize (1), if ∇ z f (z) is tractable to compute and z ∼ q φ (z) can be generated via reparameterization as z = T φ ( ), ∼ p( ), where are random noises and T φ (·) denotes a deterministic transform parameterized by φ, then one may apply the reparameterization trick BID14 BID27 to compute the gradient as DISPLAYFORM1 This trick, however, is often inapplicable to discrete random variables, as widely used to construct discrete latent variable models such as sigmoid belief networks BID22 BID31 .To maximize (1) for discrete z, using the score function ∇ φ log q φ (z) = ∇ φ q φ (z)/q φ (z), one may compute ∇ φ E(φ) via REINFORCE BID38 as its high Monte-Carlo-integration variance often limits its use in practice. Note that if f (z) depends on φ, then we assume it is true that E z∼q φ (z) [∇ φ f (z)] = 0. For example, in variational inference, we need to maximize the ELBO as E z∼q φ (z) [f (z)], where f (z) = log[p(x | z)p(z)/q φ (z)]. In this case, although f (z) depends on φ, as E z∼q φ (z) [∇ φ log q φ (z)] = ∇ φ q φ (z)dz = ∇ φ q φ (z)dz = 0, we have E z∼q φ (z) [∇ φ f (z)] = 0.To address the high-variance issue, one may introduce an appropriate baseline (a.k.a. control variate) to reduce the variance of REINFORCE BID24 BID26 BID19 BID9 BID20 BID29 BID21 . Alternatively , one may first relax the discrete random variables with continuous ones and then apply the reparameterization trick to estimate the gradients, which reduces the variance of Monte Carlo integration at the expense of introducing bias BID11 . Combining both REINFORCE and the continuous relaxation of discrete random variables, REBAR of BID35 and RELAX of BID7 both aim to produce a low-variance and unbiased gradient estimator by introducing a continuous relaxation based baseline function, whose parameters, however, need to be estimated at each mini-batch by minimizing the sample variance of the estimator with stochastic gradient descent (SGD). Estimating the baseline parameters often clearly increases the computation. Moreover, the potential conflict, between minimizing the sample variance of the gradient estimate and maximizing the expectation objective, could slow down or even prevent convergence and increase the risk of overfitting. Another interesting variance-control idea applicable to discrete latent variables is using local expectation gradients, which estimates the gradients based on REINFORCE, by performing Monte Carlo integration using a single global sample together with exact integration of the local variable for each latent dimension BID34 .Distinct from the usual idea of introducing baseline functions and optimizing their parameters to reduce the estimation variance of REINFORCE, we propose the augment-REINFORCE-merge (ARM) estimator, a novel unbiased and low-variance gradient estimator for binary latent variables that is also simple to implement and has low computational complexity. We show by rewriting the expectation with respect to Bernoulli random variables as one with respect to augmented exponential random variables, and then expressing the gradient as an expectation via REINFORCE, one can derive the ARM estimator in the augmented space with the assistance of appropriate reparameterization. In particular, in the augmented space, one can derive the ARM estimator by using either the strategy of sharing common random numbers between two expectations, or the strategy of applying antithetic sampling. Both strategies, as detailedly discussed in BID23 , can be used to explain why the ARM estimator is unbiased and could lead to significant variance reduction. Moreover, we show that the ARM estimator can be considered as improving the REINFORCE estimator in an augmented space by introducing an optimal baseline function subject to an anti-symmetric constraint; this baseline function can be considered as a ""self-control"" one, as it exploits the function f itself and correlated random noises for variance reduction, and adds no extra parameters to learn. This ""self-control"" feature makes the ARM estimator distinct from both REBAR and RELAX, which rely on minimizing the sample variance of the gradient estimate to optimize the baseline function.We perform experiments on a representative toy optimization problem and both auto-encoding variational inference and maximum likelihood estimation for discrete latent variable models, with one or multiple binary stochastic layers. Our extensive experiments show that the ARM estimator is unbiased, exhibits low variance, converges fast, has low computation, and provides state-of-the-art out-of-sample prediction performance for discrete latent variable models, suggesting the effectiveness of using the ARM estimator for gradient backpropagation through stochastic binary layers. Python code for reproducible research is available at https://github.com/mingzhang-yin/ARM-gradient. To train a discrete latent variable model with one or multiple stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator to provide unbiased and low-variance gradient estimates of the parameters of Bernoulli distributions. With a single Monte Carlo sample, the estimated gradient is the product of uniform random noises and the difference of a function of two vectors of correlated binary latent variables. Without relying on estimating a baseline function with extra learnable parameters for variance reduction, it maintains efficient computation and avoids increasing the risk of overfitting. Applying the ARM gradient leads to not only fast convergence, but also low test negative log-likelihoods (and low test negative evidence lower bounds for variational inference), on both auto-encoding variational inference and maximum likelihood estimation for stochastic binary feedforward neural networks. Some natural extensions of the proposed ARM estimator include generalizing it to multivariate categorical latent variables, combining it with a baseline or local-expectation based variance reduction method, and applying it to reinforcement learning whose action space is discrete.Initialize w1:T , ψ randomly; while not converged do Sample a mini-batch of x from data; DISPLAYFORM0 ) T ∇w t Tw t (bt−1) ; end wt = wt + ρtgw t with step-size ρt end ψ = ψ + ηt∇ ψ f (b1:T ; ψ) with step-size ηt end",1630,0.621,995,1.6381909547738693,"To backpropagate the gradients through stochastic binary layers propose the augment-REINFORCE-merge (ARM) estimator unbiased exhibits low variance Exploiting variable augmentation REINFORCE reparameterization the ARM estimator achieves adaptive variance reduction Monte Carlo integration merging two expectations via common random numbers The variance-reduction mechanism the ARM estimator also attributed either antithetic sampling in an augmented space an optimal anti-symmetric ""self-control baseline function together in that augmented space Experimental results the ARM estimator provides state auto-encoding variational inference for discrete latent variable models one or multiple stochastic binary layers Python code for reproducible research publicly Given a function f (z = 1 . . . , z V )T which follows distribution q �z parameterized, there has significant recent interest estimating to maximize ( the expectation f with z ∼ q �� expressed DISPLAYFORM0 In this expectation objective appears in both maximizing the evidence lowerELBO variational inference BID12 approximately the log marginal likelihood a hierarchal Bayesian model two fundamental problems To maximize (1 if � z f tractable to compute and z ∼ q � can generated via reparameterization as z = T �� ), ∼ p( ), are random noises· a deterministic transform parameterized, then one apply BID14 BID27 the gradient as DISPLAYFORM1 This trick often discrete random variables widely construct discrete latent variable models sigmoid belief networks BID22 .To discrete z using score � � log q via BID38 as its high Monte-Carlo-integration variance often limits practice Note f (z depends �� assume it true E z��q �� [�� � For example variational inference need maximize the ELBO as E z��q ��z [f (z log[p(x | � In although f (z depends �� as E z��q �� [�� � log q =, we 0.To address one introduce an appropriate baseline reduce REINFORCE . Alternatively , one first relax the discrete random variables with continuous ones the reparameterization trick estimate reduces Monte Carlo integration at introducing bias BID11 Combining both REINFORCE the continuous relaxation discrete random variables REBAR of BID35 and RELAX both aim produce and unbiased gradient estimator by introducing based baseline function whose parameters, however need estimated each mini by minimizing with Estimating the baseline parameters often clearly increases the computation. Moreover the potential conflict, between minimizing the sample variance the gradient estimate the expectation objective slow or convergence and increase Another interesting variance-control idea applicable discrete latent variables using local expectation gradients estimates based REINFORCE by performing Monte Carlo integration using a single global sample together exact integration for BID34 .Distinct from the usual idea introducing baseline functions optimizing their parameters reduce the estimation variance the augment-REINFORCE-merge (ARM) estimator simple We show by rewriting the expectation with Bernoulli random variables as one with augmented exponential random variables expressing the gradient an expectation via REINFORCE, one can the ARM estimator in the augmented space the assistance appropriate reparameterization In particular in the augmented space one derive the ARM estimator by either the strategy sharing common random numbers two expectations applying antithetic sampling Both strategies, detailedly BID23 , explain the ARM estimator unbiased could lead significant variance reduction Moreover we show the ARM estimator considered improving an augmented space introducing an optimal baseline function subject; ""selfcontrol one exploits the function f itself correlated random noises for variance reduction adds no extra parameters learn This ""self-control"" feature makes the ARM estimator distinct both REBAR RELAX rely minimizing the sample variance the gradient estimate optimize the baseline functionWe perform experiments a representative toy optimization problem both auto-encoding variational inference discrete latent variable models one or multiple binary stochastic layers Our extensive experiments the ARM estimator unbiased exhibits low variance converges fast has low computation, provides state outsample prediction performance discrete latent variable models suggesting the effectiveness using gradient backpropagation through stochastic binary layers Python code for reproducible research https://github.com/mingzhang-yin/ARM-gradient To train a discrete latent variable model one or multiple stochastic binary layers propose the augment-REINFORCE-merge (ARM) estimator provide unbiased and low-variance gradient estimates Bernoulli distributions With a single Monte Carlo sample the estimated gradient the product uniform random noises the difference a function two vectors correlated binary latent variables Without relying estimating a baseline function with extra learnable parameters for variance reduction maintains efficient computation avoids increasing Applying the ARM gradient leads not only fast convergence low test negative log-likelihoodsand low test negative evidence lower bounds variational inference on both auto-encoding variational inference for stochastic binary feedforward neural networks Some natural extensions the proposed ARM estimator include generalizing it multivariate categorical latent variables combining a baseline or local-expectation based variance reduction method reinforcement learning whose action space discreteInitialize w1:T , �� randomly; while not converged do Sample a mini x from data; DISPLAYFORM0 ) T ��w t Tw tbt−1 ; end wttgw with step-size ��t end �� � f: ; �) with",0.01,0.3301336516034191
"Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speed-up with respect to the number of workers, but this is rarely seen in practice as the scheme often suffers from large network delays and bandwidth limits. To overcome this communication bottleneck recent works propose to reduce the communication frequency. An algorithm of this type is local SGD that runs SGD independently in parallel on different workers and averages the sequences only once in a while. This scheme shows promising results in practice, but eluded thorough theoretical analysis.
    
 We prove concise convergence rates for local SGD on convex problems and show that it converges at the same rate as mini-batch SGD in terms of number of evaluated gradients, that is, the scheme achieves linear speed-up in the number of workers and mini-batch size. The number of  communication rounds can be reduced up to a factor of T^{1/2}---where T denotes the number of total steps---compared to mini-batch SGD. This also holds for asynchronous implementations.

 Local SGD can also be used for large scale training of deep learning models. The results shown here aim serving as a guideline to further explore the theoretical and practical aspects of local SGD in these applications. Stochastic Gradient Descent (SGD) BID29 consists of iterations of the form DISPLAYFORM0 for iterates (weights) x t , x t+1 ∈ R d , stepsize (learning rate) η t > 0, and stochastic gradient g t ∈ R d with the property E g t = ∇f (x t ), for a loss function f : R d → R. This scheme can easily be parallelized by replacing g t in (1) by an average of stochastic gradients that are independently computed in parallel on separate workers (parallel SGD). This simple scheme has a major drawback: in each iteration the results of the computations on the workers have to be shared with the other workers to compute the next iterate x t+1 . Communication has been reported to be a major bottleneck for many large scale deep learning applications, see e.g. BID32 BID17 . Mini-batch parallel SGD addresses this issue by increasing the compute to communication ratio. Each worker computes a mini-batch of size b ≥ 1 before communication. This scheme is implemented in state-of-the-art distributed deep learning frameworks BID0 BID26 BID31 . Recent work in BID43 BID10 explores various limitations of this approach, as in general it is reported that performance degrades for too large mini-batch sizes BID13 BID18 BID42 .In this work we follow an orthogonal approach, still with the goal to increase the compute to communication ratio: Instead of increasing the mini-batch size, we reduce the communication frequency. Rather than keeping the sequences on different machines in sync, we allow them to evolve locally on each machine, independent from each other, and only average the sequences once in a while (local SGD). Such strategies have been explored widely in the literature, under various names.An extreme instance of this concept is one-shot SGD (McDonald et al., 2009; BID53 where the local sequences are only exchanged once, after the local runs have converged. Zhang et al. (2013 ) show statistical convergence (see also BID33 BID9 BID12 ), but the analysis restricts the algorithm to at most one pass over the data, which is in general not enough for the training error to converge. More practical are schemes that perform more frequent averaging of the parallel sequences, as e.g. BID22 for perceptron training (iterative parameter mixing), see also BID6 , BID48 BID4 BID46 for the training of deep neural networks (model averaging) or in federated learning BID23 .The question of how often communication rounds need to be initiated has eluded a concise theoretical answer so far. Whilst there is practical evidence, the theory does not even resolve the question whether averaging helps when optimizing convex functions. Concretely, whether running local SGD on K workers is K times faster than running just a single instance of SGD on one worker. Theorem 2.2. Let f be L-smooth and µ-strongly convex, DISPLAYFORM0 are generated according to (4) with gap(I T ) ≤ H and for stepsizes η t = 4 µ(a+t) with shift parameter a > max{16κ, H}, for DISPLAYFORM1 DISPLAYFORM2 We were not especially careful to optimize the constants (and the lower order terms) in (5), so we now state the asymptotic result. Corollary 2.3. Letx T be as defined as in Theorem 2.2, for parameter a = max{16κ, H}. Then DISPLAYFORM3 For the last estimate we used E µ x 0 − x ≤ 2G for µ-strongly convex f , as derived in (Rakhlin et al., 2012, Lemma 2) . Remark 2.4 (Mini-batch local SGD). So far, we assumed that each worker only computes a single stochastic gradient. In mini-batch local SGD, each worker computes a mini-batch of size b in each iteration. This reduces the variance by a factor of b, and thus Theorem (2.2) gives the convergence rate of mini-batch local SGD when σ 2 is replaced by DISPLAYFORM4 We now state some consequences of equation FORMULA17 . For the ease of the exposition we omit the dependency on L, µ, σ 2 and G 2 below, but depict the dependency on the local mini-batch size b.Convergence rate. For T large enough and assuming σ > 0, the very first term is dominating in (6) and local SGD converges at rate O(1/(KT b)). That is, local SGD achieves a linear speedup in both, the number of workers K and the mini-batch size b. Global synchronization steps. It needs to hold H = O( T /(Kb)) to get the linear speedup. This yields a reduction of the number of communication rounds by a factor O( T /(Kb)) compared to parallel mini-batch SGD without hurting the convergence rate. Extreme Cases. We have not optimized the result for extreme settings of H, K, L or σ. For instance, we do not recover convergence for the one-shot averaging, i.e. the setting H = T (though convergence for H = o(T ), but at a lower rate). Unknown Time Horizon/Adaptive Communication Frequency BID46 empirically observe that more frequent communication at the beginning of the optimization can help to get faster time-to-accuracy (see also BID16 ). Indeed, when the number of total iterations T is not known beforehand (as it e.g. depends on the target accuracy, cf. (6) and also Section 4 below), then increasing the communication frequency seems to be a good strategy to keep the communication low, why still respecting the constraint H = O( T /(Kb)) for all T . DISPLAYFORM5 . It will be useful to define DISPLAYFORM6 Observex t+1 =x t − η t g t and E g t =ḡ t .Now the proof proceeds as follows: we show (i) that the virtual sequence {x t } t≥0 almost behaves like mini-batch SGD with batch size K (Lemma 3.1 and 3.2), and (ii ) the true iterates {x k t } t≥0,k∈[K] do not deviate much from the virtual sequence FIG6 . These are the main ingredients in the proof. To obtain the rate we exploit a technical lemma from BID35 . Lemma 3.1 . Let {x t } t≥0 and {x t } t≥0 for k ∈ [K] be defined as in (4) and (7) and let f be L-smooth and µ-strongly convex and η t ≤ 1 4L . Then DISPLAYFORM7 Bounding the variance. From equation FORMULA21 it becomes clear that we should derive an upper bound on E g t −ḡ t 2 . We will relate this to the variance σ 2 . DISPLAYFORM8 Bounding the deviation. Further, we need to bound DISPLAYFORM9 For this we impose a condition on I T and an additional condition on the stepsize η t . Lemma 3.3. If gap(I T ) ≤ H and sequence of decreasing positive stepsizes {η t } t≥0 satisfying η t ≤ 2η t+H for all t ≥ 0, then DISPLAYFORM10 where G 2 is a constant such that DISPLAYFORM11 Optimal Averaging. Similar as in BID14 BID34 BID28 we define a suitable averaging scheme for the iterates {x t } t≥0 to get the optimal convergence rate. In contrast to BID14 ) that use linearly increasing weights, we use quadratically increasing weights, as for instance BID34 BID35 . Lemma 3.4 ((Stich et al., 2018) ). Let {a t } t≥0 , a t ≥ 0, {e t } t≥0 , e t ≥ 0 be sequences satisfying DISPLAYFORM12 DISPLAYFORM13 for w t = (a + t) 2 and S T := T −1 DISPLAYFORM14 Proof. This is a reformulation of Lemma 3.3 in BID35 . We prove convergence of synchronous and asynchronous local SGD and are the first to show that local SGD (for nontrivial values of H) attains theoretically linear speedup on strongly convex functions when parallelized among K workers. We show that local SGD saves up to a factor of O(T 1/2 ) in global communication rounds compared to mini-batch SGD, while still converging at the same rate in terms of total stochastic gradient computations.Deriving more concise convergence rates for local SGD could be an interesting future direction that could deepen our understanding of the scheme. For instance one could aim for a more fine grained analysis in terms of bias and variance terms (similar as e.g. in BID7 BID12 ), relaxing the assumptions (here we relied on the bounded gradient assumption), or investigating the data dependence (e.g. by considering data-depentent measures like e.g. gradient diversity BID42 ). There are also no apparent reasons that would limit the extension of the theory to non-convex objective functions; Lemma 3.3 does neither use the smoothness nor the strong convexity assumption, so this can be applied in the non-convex setting as well. We feel that the positive results shown here can motivate and spark further research on non-convex problems. Indeed, very recent work (Zhou & Cong, 2018; BID44 analyzes local SGD for non-convex optimization problems and shows convergence of SGD to a stationary point, though the restrictions on H are stronger than here.",2243,1.145,1281,1.750975800156128,"Mini-batch stochastic gradient descent state large scale distributed training The scheme can reach a linear speed-up respect workers rarely often suffers large network delays bandwidth limits To overcome this communication bottleneck recent works propose reduce. An algorithm of local SGD that runs SGD independently in different workers averages the sequences only This scheme shows promising practice eluded thorough theoretical analysis We prove concise convergence rates local SGD on convex problems show mini terms number evaluated gradients that the scheme achieves linear speed-up workers The number communication rounds can up T^{1/2}---where T denotes total steps--- mini-batch SGD This also holds asynchronous implementations Local SGD can large scale training deep learning models The results shown aim serving further local SGD these applications Stochastic Gradient Descent BID29 consists iterations the form DISPLAYFORM0 iteratesweights x t x � R d stepsizelearning � > g t � with the property E gf for a loss function f : → R. This scheme can easily parallelized replacing g t ( an average that independently computed on separate workersparallel SGD This simple scheme in each iteration results on the workers shared to compute x t+1 Communication has reported many large scale deep learning applications see e.g. BID32 BID17 . Mini-batch parallel SGD addresses this issue increasing the compute to communication ratio Each worker computes a minibatch size b ≥ before communication This scheme implemented state distributed deep learning BID0 BID26 BID31 . Recent work BID43 BID10 explores various limitations in general reported performance for too large mini-batch sizes follow still with increase the compute to communication ratio: Instead Rather keeping the sequences on different machines sync allow evolve locally independent only average oncelocal SGD Such strategies explored widely underAn extreme instance one-shot SGDMcDonald BID53 where the local sequences only exchanged after the local runs Zhang et al (2013 ) show statistical convergence BID33 BID9 BID12 the analysis restricts the algorithm at most one pass over in general the training error converge More practical are schemes perform more frequent averaging the parallel sequences e.g. BID22 for perceptron trainingiterative parameter mixing see , the trainingmodel averaging in federated BID23 .The question how often communication rounds need initiated has eluded a concise theoretical answer so Whilst practical evidence, the theory even resolve averaging helps when optimizing convex functions Concretely whether running local SGD on K workers K times faster just a single instance Theorem Let f Lsmooth µ-strongly DISPLAYFORM0 are generated according ( gap(I T ≤ H and for stepsizes � 4 µ(a+t shift parameter a > max{16κ H We were especially optimize the constantsand lower terms now state Corollary Letx T be as Theorem for parameter a = max{16κ H Then DISPLAYFORM3 For the last estimate E µ x 0 − x ≤ 2G µ-strongly convex f , derived in (Rakhlin, Lemma Remark 2.4 (Minibatch local SGD So assumed each worker only computes In mini-batch local SGD each worker computes size b each iteration This reduces by b thus Theorem gives the convergence rate mini-batch local SGD when � 2 replaced DISPLAYFORM4 We now state some consequences equation FORMULA17 For the ease the exposition we omit the dependency L, µ � 2 G below depict the local mini-batch size b.Convergence rate For T large enough assuming �� > the very first term dominating (6 local SGD converges rate O(1/(KT b That local SGD achieves a linear speedup both, workers K and b. Global synchronization steps It needs hold H = O( T /(Kb the linear speedup This yields a reduction communication rounds O T /(Kb compared parallel mini-batch SGD without hurting Extreme Cases. We not optimized the result extreme settings of H, K �� For instance do recover convergence for the one-shot averaging (though convergence H o(T but at Unknown Time Horizon/Adaptive Communication Frequency BID46 empirically observe more frequent communication at the optimization can get faster timesee Indeed the number total iterations T beforehand depends the target accuracy cf (6 and also Section below then increasing the communication frequency seems low why still respecting the constraint H = O( T /(Kb all T . DISPLAYFORM5 . It will useful define DISPLAYFORM6 Observex t+1 =x t − �� t g t and E g t =�� t .Now the proof proceeds we show ( the virtual sequence {� almost behaves mini-batch SGD batch size KLemma and ) the true iterates {[K do FIG6 These the proof. To obtain the rate we exploit a technical lemma from BID35 . Lemma . Let { t t� for [K be defined in f L-smooth µ-strongly �� 1 4L Then DISPLAYFORM7 Bounding the variance. From equation FORMULA21 it becomes derive upper E g t −�� t 2 We relate the variance � 2 DISPLAYFORM8 Bounding the deviation. Further bound DISPLAYFORM9 For impose I T and the stepsize �� t Lemma If gap(I T ) ≤ H and sequence decreasing positive stepsizes {�� t } t��0 satisfying for DISPLAYFORM10 where G 2. Similar as BID14 BID34 BID28 we define a suitable averaging scheme the iterates {x t } t� to get In contrast BID14 ) that use linearly increasing weights for instance Lemma ((Stich et 2018 Let {a t } t�0 , ≥e be sequences satisfying DISPLAYFORM12 DISPLAYFORM13 for w t = ( 2 S T T −1. This a reformulation Lemma BID35 . We prove convergence synchronous and asynchronous local SGD are (for nontrivial values H) attains theoretically linear speedup strongly convex functions when among K workers We show local SGD saves up O(T global communication rounds compared mini convergingDeriving more concise convergence rates could that deepen the scheme For instance one aim more fine in bias variance termssimilar as BID7 BID12 relaxinghere relied the bounded gradient assumption investigating the data dependence considering data-depentent measures like gradient diversity BID42 There also no apparent reasons would limit the extension the theory non-convex objective functions; Lemma neither use smoothness nor can We feel the positive results shown motivate spark Indeed very recent work (Zhou & Cong 2018 BID44 analyzes local SGD for convergence a stationary point though the restrictions H are stronger here",0.01,0.6174995284692464
"Extracting relevant information, causally inferring and predicting the future states with high accuracy is a crucial task for modeling complex systems. The endeavor to address these tasks is made even more challenging when we have to deal with high-dimensional heterogeneous data streams. Such data streams often have higher-order inter-dependencies across spatial and temporal dimensions. We propose to perform a soft-clustering of the data and learn its dynamics to produce a compact dynamical model while still ensuring the original objectives of causal inference and accurate predictions. To efficiently and rigorously process the dynamics of soft-clustering, we advocate for an information theory inspired approach that incorporates stochastic calculus and seeks to determine a trade-off between the predictive accuracy and compactness of the mathematical representation. We cast the model construction as a maximization of the compression of the state variables such that the predictive ability and causal interdependence (relatedness) constraints between the original data streams and the compact model are closely bounded. We provide theoretical guarantees concerning the convergence of the proposed learning algorithm. To further test the proposed framework, we consider a high-dimensional Gaussian case study and describe an iterative scheme for updating the new model parameters. Using numerical experiments, we demonstrate the benefits on compression and prediction accuracy for a class of dynamical systems. Finally, we apply the proposed algorithm to the real-world dataset of multimodal sentiment intensity and show improvements in prediction with reduced dimensions. The use of machine learning for making inference and prediction from the real-world data has shown unprecedented growth. There exist a plethora of approaches for complex system (CS) modeling (e.g., multi-input multi-output state space identification (Stoica & Jansson, 2000) , expectation maximization (EM) BID17 , regularization BID6 , graphical models (Meinshausen & Buhlmann, 2006) , combined regularization and Bayesian learning BID11 BID10 BID3 , kernel-based regularization (Pillonetto & Chiuso, 2015) ). With the increase in the size of data, the complexity of the accurate models also increases, making inference and predictions slower. The major challenges of the upcoming era, hence, are likely to deal with the massive and diverse data sources, and still making quick decisions. Therefore, the compact modeling of time-varying complex systems 1 is a challenging task and appealing for more investigation. The real-world data has complex inter-dependencies across spatial and temporal dimensions. We aim to identify such dependencies and carefully construct a compact representation of the given CS model while still ensuring accurate predictions. We do so by performing a soft-clustering of such inter-dependencies to preserve only the relevant information. For the CS model in the form of a dynamical system, we additionally argue that similar to the data, the most relevant information also gets transformed at each hop in an alternate dynamical system. From a bird's-eye view, we track how the most relevant information propagates across the given dynamical system. We represent this propagation via an alternate dynamical system (compact model) and develop an unsupervised learning technique of such process.The most relevant work in this regard is information bottleneck (IB) principle (Tishby et al., 2000) . For fixed two random variables, it performs a soft-clustering to compress one variable while predicting another, given the joint probability distribution. The IB has been successfully applied to speech recognition (Hecht & Tishby, 2005) , document classification (Slonim & Tishby, 2000) , gene expression BID12 ) and deep learning (Tishby & Zaslavsky, 2015) , etc., and it has shown good performance. In contrast, we aim to learn a dynamics of the soft-clustering across the given dynamical system, and propose a general optimization framework to study the trade-offs between compactness and the resulting accuracies.The problem statement addressed in this work is: Given a dynamical system, we aim to develop a compact model by learning the dynamics of the soft-clustering in an unsupervised manner, or alternate dynamical process, through Information Bottleneck hierarchy (IBH). The main contributions of the present work are as follows: (i) By learning the dynamics of the soft-clustering, we propose an alternate compact dynamical system of the given process, with emphasis on the prediction accuracies. (ii) We formulate a novel optimization setup, compact perception problem, and characterize general solution to the information theoretic problem. (iii) We quantify how most relevant information about future gets transformed at each hop in the alternatively designed dynamical system.A brief mention of the mathematical notations is provided in the next part. In this paper, we have introduced a novel information-theoretic inspired approach to learn the compact dynamics of a time-varying complex system. The trade-off between the predictive accuracy and the compactness of the mathematical representation is formulated as a multi-hop compact perception optimization problem. A key ingredient to solve the aforementioned problem is to exploit variational calculus in order to derive the general solution expressions. Additionally, we have investigated the guaranteed convergence of the proposed iterative algorithm. Moreover, considering a specific class of distributions (Gaussian), we have provided closed-form expressions for the model parameters' update in our algorithm. Interestingly, the proposed compact perception shows improvements in prediction with reduced dimension on challenging real-world problems.The quantification of information flow across a dynamical system can have an enormous impact on understanding and improving the current state-of-the-art in neural networks as realized in (Tishby & Zaslavsky, 2015) . Moreover, modeling with dynamical systems is a standard approach, and by using the proposed framework, we can make a better compact representation of the system. The driving force of a dynamical system can enforce different behaviors of information flow, as realized in defining dynamical entropy by (Sinai, 1959) . Therefore, measuring the information flow can help in estimating/differentiating the actual driving component behind the observed activities. Such concepts are useful in predicting brain imagined tasks from observed electroencephalogram activities.The appendix is arranged as follows: In the Section A, we provide the proof of Theorem 1. In the Section B, we provide the iterative procedure (mentioned as Corollary 1) to minimize the functional in (4). Next, in Section C, we present the detailed proof of the Lemma 1, and finally, in Section D, a detailed proof of Theorem 2 is presented.A PROOF OF THEOREM 1Proof. For the sake of simplicity, a sketch of the proof is given for discrete variables. The Lagrangian associated with the minimization problem is the following DISPLAYFORM0 where α 1 (X k−1 ) and α 2 (B k ) are Lagrange multipliers for the normalization of the distributions p(B k |X k−1 ) and p(B k+1 |B k ), respectively. Taking the derivative of each term of the Lagrangian L with respect to p(B k |X k−1 ), we have DISPLAYFORM1 Setting the derivative of the Lagrangian equal to zero and arranging the terms we obtain the self consistent equation FORMULA7 . Note that all the constant terms in the derivative independent of B k will be captured by the Lagrange multiplier α 1 (X k−1 ). The derivative of the Lagrangian L with respect to p(B k+1 |B k ) involves only the two last terms from the functional F and the term that ensures the normalization condition. Then, we have DISPLAYFORM2 DISPLAYFORM3 Thus, the variational condition is written as follows DISPLAYFORM4 where α 2 (B k ) is the summation of the Lagrange multiplier α 2 (B k ) and the terms independent of B k+1 , and hence the equation FORMULA8 follows.",1594,0.784,936,1.702991452991453,"Extracting relevant information, causally inferring and predicting with high accuracy modeling complex systems The endeavor address these tasks made even high-dimensional heterogeneous data streams Such data streams often higher-order inter across We propose perform learn its dynamics produce while ensuring the original objectives causal inference accurate predictions To efficiently process the dynamics softclustering advocate an information theory inspired seeks determine the predictive accuracy the mathematical representation We cast the model construction as a maximization the compression the state variables such predictive ability and causal (relatedness constraints between the original data streams the compact model closely bounded We provide theoretical guarantees concerning the convergence the proposed learning algorithm To further test the proposed framework consider highdimensional case study and describe updating Using numerical experiments demonstrate the benefits on compression and prediction accuracy a class Finally apply the proposed algorithm multimodal sentiment intensity show improvements prediction with reduced dimensions The use machine making inference from shown unprecedented growth There exist approaches complex system (CSStoica & Jansson , expectation maximizationEM) BID17 regularization BID6 graphical modelsMeinshausen combined regularization learning BID10 kernelPillonetto Chiuso 2015 With the increase data the complexity the accurate models also inference predictions slower The major challenges the upcoming era, hence, likely deal the massive and diverse data sources still making quick decisions Therefore the compact modeling 1 appealing more investigation The real-world data has complex inter across We aim identify such dependencies carefully construct a compact representation the given CS model while accurate predictions We do so by performing a soft-clustering such inter preserve only the relevant information For the CS model in the form a dynamical system additionally argue similar the data the most relevant information also gets transformed at each hop From we track how the most relevant information propagates the given dynamical system We represent this propagation via an alternate dynamical systemcompact model develop of such processThe most relevant work information bottleneckIB) principle (Tishby . For fixed two random variables it performs soft to compress while predicting given the joint probability distribution The IB has successfully applied speech recognition (Hecht & Tishby , document classificationSlonim gene expression BID12 ) deep learning 2015 etc In contrast we aim learn a dynamics the soft-clustering across the given dynamical system propose a general optimization framework study compactness the resulting accuraciesThe problem statement addressed Given aim develop by learning or alternate through Information Bottleneck hierarchy The main contributions as By learning the dynamics the soft-clustering, propose an alternate compact dynamical system the given process emphasis the prediction accuracies (ii We formulate a novel optimization setup compact perception problem characterize general solution (iii We quantify how most relevant information future gets transformed at each hop the alternatively designed dynamical systemA brief mention the mathematical notations In have a novel information-theoretic inspired approach learn the compact dynamics The trade-off the predictive accuracy the compactness the mathematical representation formulated a multi-hop compact perception optimization problem A key ingredient solve exploit variational calculus derive the general solution expressions Additionally investigated the guaranteed convergence the proposed iterative algorithm. Moreover considering a specific class distributionsGaussian provided closed-form expressions the model parameters' update in our algorithm Interestingly the proposed compact perception shows improvements prediction with reduced dimension on challenging real-world problemsThe quantification information flow across have understanding improving- as realized (Tishby Moreover modeling with dynamical systems a standard approach by the proposed framework a better compact representation The driving force a dynamical system can enforce different behaviors of information flow realized defining dynamical entropy by (Sinai 1959 . Therefore measuring the information flow can in estimating/ the actual driving component behind the observed activities Such concepts useful predicting brain imagined tasks from observed electroencephalogram activitiesThe appendix arranged In the Section A the proof Theorem In the Section B provide the iterative procedure (mentioned as Corollary minimize functional in (4 Next in Section C present the detailed proof the Lemma 1 finally isA PROOF THEOREM 1Proof For a sketch the proof discrete variables The Lagrangian associated the minimization problem the following DISPLAYFORM0 where α 1 (X k−1 ) Lagrange multipliers the distributions p(B Taking the derivative each term the Lagrangian L with p(B k |X k−1 DISPLAYFORM1 Setting equal zero arranging we obtain the self consistent equation FORMULA7 Note all the constant terms the derivative independent B k will captured the Lagrange multiplier α 1 (X k−1 The derivative the Lagrangian L with p(B k+1 |B k involves only the two last terms from the functional F that ensures the normalization condition Then we DISPLAYFORM2 DISPLAYFORM3 Thus the variational condition written where α 2 (B k the Lagrange the terms independent hence the equation FORMULA8 follows",0.01,0.49523962775229974
"We propose the dense RNN, which has the fully connections from each hidden state to multiple preceding hidden states of all layers directly. As the density of the connection increases, the number of paths through which the gradient flows can be increased. It increases the magnitude of gradients, which help to prevent the vanishing gradient problem in time. Larger gradients, however, can also cause exploding gradient problem. To complement the trade-off between two problems, we propose an attention gate, which controls the amounts of gradient flows. We describe the relation between the attention gate and the gradient flows by approximation. The experiment on the language modeling using Penn Treebank corpus shows dense connections with the attention gate improve the model’s performance. In order to analyze sequential data, it is important to choose an appropriate model to represent the data. Recurrent neural network (RNN), as one of the model capturing sequential data, has been applied to many problems such as natural language , machine translation BID0 , speech recognition BID6 . There are two main research issues to improve the RNNs performance: 1) vanishing and exploding gradient problems and 2) regularization.The vanishing and exploding gradient problems occur as the sequential data has long-term dependency BID10 BID18 . One of the solutions is to add gate functions such as the long short-term memory (LSTM) and gated recurrent unit (GRU). The LSTM has additional gate functions and memory cells BID11 . The gate function can prevent the gradient from being vanished during back propagation through time. Gated recurrent unit (GRU) has similar performance with less gate functions BID1 .The part of sequential data whose boundary to distinguish the consecutive other parts, has the hierarchical structures. To handle the hierarchy, the model should capture the multiple timescales. In hierarchical multiple recurrent neural network (HM-RNN, Chung et al. (2016) ), the boundary information is also learned by implementing three operations such as update, copy and flush operator. In clockwork RNN BID14 , the hidden states are divided into multiple sub-modules, which act with different periods to capture multiple timescales. As all previous states within the recurrent depth do not always affect the next state, memory-augmented neural network (MANN, BID7 ) uses the memory to remember previous states and retrieve some of previous states if necessary.The basic way to handle multiple timescales along with preventing the vanishing gradient problem is to increases both of feedforward depth and recurrent depth to capture multiple timescales. Feedforward depth is the longest path from the input layer to the output layer. Recurrent depth is the longest path from arbitrary hidden state at time t to same hidden sate at time t + t . Increasing feedforward depth means stacking multiple recurrent layers deeply. It can capture fast and slow changing components in the sequential data BID19 BID3 BID9 . The low level layer in the stacked RNN captures short-term dependency. As the layer is higher , the aggregated information from lower layer is abstracted. Thus, as the layer is higher, the capacity to model long-term dependency increases. The number of nonlinearities in the stacked RNN, however, is proportional to the number of unfolded time steps regardless of the feedforward depth. Thus, the simple RNN and stacked RNN act identically in terms of long run.Increasing recurrent depth also increases the capability to capture long-term dependency in the data. The hidden state in vanilla RNN has only connection to previous time step's hidden state in the same layer. Adding the connections to multiple previous time steps hidden states can make the shortcut paths, which alleviates the vanishing problem. Nonlinear autoregressive exogenous model (NARX) handles the vanishing gradient problem by adding direct connections from the distant past in the same layer BID15 . Similarly, higher-order RNN (HO-RNN ) has the direct connections to multiple previous states with gating to each time step BID20 . Unlike other recurrent models that use one connection between two consecutive time steps, the recurrent highway network (RHN) adds multiple connections with sharing parameters between transitions in the same layer BID23 .The vanilla RNN has only one path connected with previous hidden states. Thus, it is hard to apply standard dropout technique for regularization as the information is being diluted during training of long-term sequences. By selecting the same dropout mask for feedforward , recurrent connections, respectively, the dropout can apply to the RNN, which is called a variational dropout BID4 . This paper proposes a dense RNN that has both of feedforward and recurrent depths. The stacked RNN increases the complexity by increasing feedforward depth. NARX-RNN and HO-RNN increase the complexity by increasing recurrent depth. The model with the feedforward depth can be combined with the model with the recurrent depth, as the feedforward depth and recurrent depth have an orthogonal relationship. Gated feedback RNN has the fully connection between two consecutive timesteps. As the connection of gated feedback is not overlapped with the model with orthogonal depths, all three features, adding feedforward depth, recurrent depth, and gated feedback, can be modeled jointly . With the three features, we propose the attention gate, which controls the flows from each state so that it enhances the overall performance.The contributions of this paper are summarized: 1) dense RNN that is aggregated model with feedforward depth, recurrent depth and gated feedback function, 2) extension of the variational dropout to the dense RNN. This paper proposed dense RNN, which has fully connections from each hidden state to multiple preceding hidden states of all layers directly. Each previous hidden state has its attention gate that controls the amount of information flows. To evaluate the effect of dense connections, we used Penn Treebank corpus (PTB). The result of dense connection was confirmed by varying the recurrent depth with the attention gate. The dense connections with the attention gate made the model's perplexity less than conventional RNN.",1204,0.758,717,1.6792189679218967,"We propose the dense RNN the fully connections each hidden state multiple preceding hidden states of all layers directly As the density the connection increases paths the gradient flows It increases gradients help prevent the vanishing gradient problem time Larger gradients however exploding gradient problem To complement two problems an attention gate controls gradient flows We describe the attention gate gradient flows by approximation The experiment on the language modeling using Penn Treebank corpus dense connections the attention gate improve the model��s performance analyze sequential data choose Recurrent neural network as one capturing sequential data applied , machine translation BID0 There two main research issues improve vanishing exploding gradient problemsThe the sequential data has long-term dependency BID10 BID18 One gate functions such gated recurrent unit The LSTM additional gate functions memory cells BID11 . The gate function prevent the gradient vanished during back propagation through time Gated recurrent unit similar performance less gate functions BID1 .The part sequential data whose boundary to distinguish the consecutive other parts, has the hierarchical structures To handle the hierarchy the model capture hierarchical multiple recurrent neural networkHM-RNN, Chung (2016 ), the boundary information also learned implementing three operations such update copy flush operator clockwork RNN BID14 , the hidden states dividedmodules act with different periods capture As all previous states within the recurrent depth do always affectMANN, BID7 ) uses remember retrieve some ifThe basic way handle along preventing the vanishing gradient problem increases both feedforward depth capture Feedforward depth the longest path Recurrent depth the longest path arbitrary hidden state at same hidden sate + Increasing feedforward depth means stacking multiple recurrent layers deeply It can capture fast slow changing components the sequential data BID19 BID3 BID9 . The low level layer the stacked RNN captures short-term dependency. As the layer higher , lower layer abstracted Thus the layer higher capacity model nonlinearities the stacked RNN however proportional unfolded time steps regardless the feedforward depth Thus, the simple RNN and stacked long run.Increasing recurrent depth also capture long-term dependency The hidden state vanilla RNN only connection previous time step's hidden state Adding the connections multiple previous time steps hidden states the shortcut paths, alleviates the vanishing problem Nonlinear autoregressive exogenous model handles the vanishing gradient problem adding direct connections the distant past in BID15 . Similarly higher-order RNN ( the direct connections multiple previous states gating to each time BID20 Unlike other recurrent models one connection the recurrent highway network adds sharing parameters between transitions BID23 .The vanilla RNN connected previous hidden states Thus hard apply standard dropout technique regularization as the information being diluted during of long-term sequences By selecting the same dropout mask feedforward , recurrent connections respectively can apply called BID4 This paper a dense RNN of feedforward and recurrent depths The stacked RNN increases by feedforward depth NARX-RNN and increase the complexity by recurrent depth The model with the feedforward depth can combined Gated feedback RNN has the fully connection two consecutive timesteps As the connection gated feedback not overlapped the model with orthogonal depths all three features adding feedforward depth recurrent depth modeled jointly . With the three features propose the attention gate controls the flows from each state so enhancesThe contributions this paper: 1) dense RNN that aggregated model feedforward depth, recurrent depth and gated feedback function, 2) extension This paper proposed dense RNN, fully connections from each hidden state multiple preceding hidden states all layers directly Each previous hidden state its attention gate flows To evaluate dense connections Penn Treebank corpus The result dense connection was confirmed varying the recurrent depth with the attention gate The dense connections with the attention gate made the model's perplexity conventional RNN",0.01,0.4346694244227716
"We propose a new algorithm for training generative adversarial networks to jointly learn latent codes for both identities (e.g. individual humans) and observations (e.g. specific photographs). In practice, this means that by fixing the identity portion of latent codes, we can generate diverse images of the same subject, and by fixing the observation portion we can traverse the manifold of subjects while maintaining contingent aspects such as lighting and pose. Our algorithm features a pairwise training scheme in which each sample from the generator consists of two images with a common identity code. Corresponding samples from the real dataset consist of two distinct photographs of the same subject. In order to fool the discriminator, the generator must produce images that are both photorealistic, distinct, and appear to depict the same person. We augment both the DCGAN and BEGAN approaches with Siamese discriminators to accommodate pairwise training. Experiments with human judges and an off-the-shelf face verification system demonstrate our algorithm’s ability to generate convincing, identity-matched photographs. In many domains, a suitable generative process might consist of several stages. To generate a photograph of a product, we might wish to first sample from the space of products, and then from the space of photographs of that product. Given such disentangled representations in a multistage generative process, an online retailer might diversify its catalog, depicting products in a wider variety of settings. A retailer could also flip the process, imagining new products in a fixed setting. Datasets for such domains often contain many labeled identities with fewer observations of each (e.g. a collection of face portraits with thousands of people and ten photos of each). While we may know the identity of the subject in each photograph, we may not know the contingent aspects of the observation (such as lighting, pose and background). This kind of data is ubiquitous; given a set of commonalities, we might want to incorporate this structure into our latent representations.Generative adversarial networks (GANs) learn mappings from latent codes z in some low-dimensional space Z to points in the space of natural data X BID9 . They achieve this power through an adversarial training scheme pitting a generative model G : Z → X against a discriminative model D : X → [0, 1] in a minimax game. While GANs are popular, owing to their ability to generate high-fidelity images, they do not, in their original form, explicitly disentangle the latent factors according to known commonalities.In this paper, we propose Semantically Decomposed GANs (SD-GANs), which encourage a specified portion of the latent space to correspond to a known source of variation.1,2 The technique Figure 1 : Generated samples from SD-BEGAN. Each of the four rows has the same identity code z I and each of the fourteen columns has the same observation code z O .decomposes the latent code Z into one portion Z I corresponding to identity, and the remaining portion Z O corresponding to the other contingent aspects of observations. SD-GANs learn through a pairwise training scheme in which each sample from the real dataset consists of two distinct images with a common identity. Each sample from the generator consists of a pair of images with common z I ∈ Z I but differing z O ∈ Z O . In order to fool the discriminator, the generator must not only produce diverse and photorealistic images, but also images that depict the same identity when z I is fixed. For SD-GANs, we modify the discriminator so that it can determine whether a pair of samples constitutes a match.As a case study, we experiment with a dataset of face photographs, demonstrating that SD-GANs can generate contrasting images of the same subject ( Figure 1 ; interactive web demo in footnote on previous page). The generator learns that certain properties are free to vary across observations but not identity. For example, SD-GANs learn that pose, facial expression, hirsuteness, grayscale vs. color, and lighting can all vary across different photographs of the same individual. On the other hand, the aspects that are more salient for facial verification remain consistent as we vary the observation code z O . We also train SD-GANs on a dataset of product images, containing multiple photographs of each product from various perspectives FIG2 ).We demonstrate that SD-GANs trained on faces generate stylistically-contrasting, identity-matched image pairs that human annotators and a state-of-the-art face verification algorithm recognize as depicting the same subject. On measures of identity coherence and image diversity, SD-GANs perform comparably to a recent conditional GAN method (Odena et al., 2017) ; SD-GANs can also imagine new identities, while conditional GANs are limited to generating existing identities from the training data. Our evaluation demonstrates that SD-GANs can disentangle those factors of variation corresponding to identity from the rest. Moreover, with SD-GANs we can sample never-before-seen identities, a benefit not shared by conditional GANs. In FIG1 , we demonstrate that by varying the observation vector z O , SD-GANs can change the color of clothing, add or remove sunnies, or change facial pose. They can also perturb the lighting, color saturation, and contrast of an image, all while keeping the apparent identity fixed. We note, subjectively, that samples from SD-DCGAN tend to appear less photorealistic than those from SD-BEGAN. Given a generator trained with SD-GAN, we can independently interpolate along the identity and observation manifolds ( FIG4 ).On the shoe dataset, we find that the SD-DCGAN model produces convincing results. As desired, manipulating z I while keeping z O fixed yields distinct shoes in consistent poses FIG2 . The identity code z I appears to capture the broad categories of shoes (sneakers, flip-flops, boots, etc.) . Surprisingly , neither original BEGAN nor SD-BEGAN can produce diverse shoe images (Appendix G).In this paper , we presented SD-GANs, a new algorithm capable of disentangling factors of variation according to known commonalities. We see several promising directions for future work. One logical extension is to disentangle latent factors corresponding to more than one known commonality. We also plan to apply our approach in other domains such as identity-conditioned speech synthesis. We estimate latent vectors for unseen images and demonstrate that the disentangled representations of SD-GANs can be used to depict the estimated identity with different contingent factors. In order to find a latent vectorẑ such that G(ẑ) (pretrained G) is similar to an unseen image x, we can minimize the distance between x and G(ẑ): minẑ ||G(ẑ) − x|| In FIG5 , we depict estimation and linear interpolation across both subspaces for two pairs of images using SD-BEGAN. We also display the corresponding source images being estimated. For both pairs,ẑ I (identity) is consistent in each row andẑ O (observation) is consistent in each column.",1447,0.748,803,1.8019925280199254,"We propose training jointly latent codes both identities observations In practice by fixing the identity portion latent codes generate diverse images by fixing traverse the manifold subjects while contingent aspects lighting pose Our algorithm features a pairwise training scheme from the generator consists two images a common identity code Corresponding samples the real dataset consist two distinct photographs In order fool the discriminator the generator produce images both, distinct appear depict We augment both the DCGAN BEGAN approaches Siamese discriminators accommodate pairwise training Experiments human judges an off face verification demonstrate our algorithm��s ability generate convincing identitymatched photographs In many domains a suitable generative process might consist several stages To generate a photograph a product might wish first sample from products from photographs Given such disentangled representations a multistage generative process an online retailer diversify depicting settings A retailer could also flip the process imagining new products a fixed setting Datasets such domains often many labeled identities with fewer observations face portraits thousands people ten photos While may know each photograph the contingent aspects the observation ( lighting pose This kind data ubiquitous; given commonalities incorporate this structure our latent representationsGenerative learn mappings latent codes z in some low-dimensional space Z to points natural data X BID9 They achieve this power an adversarial training scheme pitting a generative model G : Z → X D [0 a minimax game While GANs popular owing generate, explicitly the latent factors according known commonalitiesIn Semantically Decomposed GANsSD-GANs encourage a specified portion correspond variation.1,2 The technique Figure : Generated samples. Each the same identity code z I each O .decomposes the latent code Z into one portion Z corresponding identity, the other contingent aspects observations SD-GANs learn through a pairwise training scheme in each sample from the real dataset consists two distinct images Each sample from the generator consists images common z I �� Z I but In order fool the discriminator the generator not produce diverse and photorealistic images images depict when z I fixed For SD-GANs modify the discriminator so determine samples constitutesAs experiment face photographs demonstrating generate contrasting images Figure ; interactive web demo in footnote on The generator learns certain properties free vary across observations but not identity For example SD-GANs learn pose hirsuteness grayscale vs. color, and lighting can vary across different photographs On the aspects more salient facial verification remain consistent as we vary the observation code z O We also train SD-GANs a dataset product images containing multiple photographs from FIG2 ).We demonstrate trained faces generate stylistically identitymatched image human annotators a state face verification recognize depicting On measures identity coherence image diversity SD-GANs perform a recent conditional GAN methodOdena 2017 ; imagine new identities while limited generating from Our evaluation demonstrates SD-GANs those factors of variation corresponding identity Moreover with SD-GANs we sample a benefit shared conditional GANs FIG1 by varying the observation vector z O change clothing add sunnies facial pose They can perturb the lighting color saturation contrast all while the apparent identity fixed We note subjectively samples SD-DCGAN tend appear Given a generator trained with SD-GAN independently interpolate along the identity and observation manifolds FIG4.On the shoe dataset produces convincing results As desired manipulating z I while O fixed yields distinct shoes consistent poses FIG2 identity code z I appears capture the broad categories shoes ( boots . Surprisingly , neither original BEGAN can produce diverse shoe imagesAppendix G).In presented SD-GANs capable factors variation according known commonalities We see several promising directions future work One logical extension latent factors corresponding more than one known commonality We also plan apply our approach identity-conditioned speech synthesis We estimate latent vectors unseen images demonstrate the disentangled representations SD-GANs depict the estimated identity with different contingent factors In order find a latent vector��� such (pretrained G similar an unseen image x minimize): min��� ||G − x|| In FIG5 depict estimation across both subspaces for two pairs using SD-BEGAN We also display the corresponding source images being estimated For both pairs��� I (identity consistent",0.01,0.7474856687855017
"The goal of unpaired cross-domain translation is to learn useful mappings between two domains, given unpaired sets of datapoints from these domains. While this formulation is highly underconstrained, recent work has shown that it is possible to learn mappings useful for downstream tasks by encouraging approximate cycle consistency in the mappings between the two domains [Zhu et al., 2017]. In this work, we propose AlignFlow, a framework for unpaired cross-domain translation that ensures exact cycle consistency in the learned mappings. Our framework uses a normalizing flow model to specify a single invertible mapping between the two domains. In contrast to prior works in cycle-consistent translations, we can learn AlignFlow via adversarial training, maximum likelihood estimation, or a hybrid of the two methods. Theoretically, we derive consistency results for AlignFlow which guarantee recovery of desirable mappings under suitable assumptions. Empirically, AlignFlow demonstrates significant improvements over relevant baselines on image-to-image translation and unsupervised domain adaptation tasks on benchmark datasets. Given data from two domains, cross-domain translation refers to the task of learning a mapping from one domain to another, such as translating text across two languages or image colorization. This ability to learn a meaningful alignment between two domains has a broad range of applications across machine learning, including relational learning BID1 , domain adaptation BID2 BID4 , image and video translation for computer vision BID6 , and machine translation for natural language processing BID7 .Broadly , there are two learning paradigms for cross-domain translation: paired and unpaired. In paired cross-domain translation, we assume access to pairs of datapoints across the two domains, e.g., black and white images and their respective colorizations. However, paired data can be expensive to obtain or may not even exist, as in neural style transfer BID8 where the goal is to translate across the works of two artists that typically do not exhibit a direct correspondence.Unpaired cross-domain translation tackles this regime where paired data is not available and learns an alignment between two domains given only unpaired sets of datapoints from the domains. Formally , we seek to learn a joint distribution over two domains, say A and B, given samples only from the marginal distributions over A and B. CycleGAN BID0 , a highly successful approach to this problem, learns a pair of conditional generative models, say G A→B and G B→A , to match the marginal distributions over A and B via an adversarial objective BID9 . The marginal matching constraints alone are insufficient to learn the desired joint distribution, both in theory and practice. To further constrain the problem, an additional desideratum is imposed in the form of cycle-consistency. That is, given any datapoint A = a, the cycle-consistency term in the learning objective prefers mappings G A→B and G B→A such that G B→A (G A→B (a)) ≈ a. Symmetrically, cycle-consistency in the reverse direction implies G A→B (G B→A (b)) ≈ b for all datapoints B = b. Intuitively , this encourages the learning of approximately bijective mappings.While empirically effective, the CycleGAN objective only imposes a soft cycle-consistency penalty and provides no guarantee that G A→B and G B→A are true inverses of each other. A natural question, then, is whether the cycle-consistency objective can be replaced with a single, invertible model G A→B . Drawing inspiration from the literature on invertible generative models (Rezende and BID10 BID11 BID13 , we propose AlignFlow, a learning framework for cross-domain translations which uses normalizing flow models to represent the mappings. In AlignFlow, we compose a pair of invertible flow models G Z→A and G Z→B , to represent the mapping G A→B = G Z→B • G −1 Z→A . Here, Z is a shared latent space between the two domains. Since composition of invertible mappings preserves invertibility , the mapping G A→B is invertible and the reverse mapping from B → A is simply given as G B→A = G −1 A→B . Hence, AlignFlow guarantees exact cycle-consistency by design and simplifies the standard CycleGAN learning objective by learning a single, invertible mapping.Furthermore, AlignFlow provides flexibility in specifying the training objective. In addition to adversarial training, we can also specify a prior distribution over the latent variables Z and train the two component models G Z→B and G Z→A via maximum likelihood estimation (MLE). MLE is statistically efficient, exhibits stable training dynamics , and can have a regularizing effect when used in conjunction with adversarial training of invertible generative models BID14 . In this work, we presented AlignFlow, a learning framework for cross-domain translations based on normalizing flow models. The use of normalizing flow models is an attractive choice for several reasons we highlight: it guarantees exact cycle-consistency via a single cross-domain mapping, learns a shared latent space across two domains, and permits a flexible training objective which is a hybrid of terms corresponding to adversarial training and exact maximum likelihood estimation. Theoretically, we derived conditions under which the AlignFlow model learns marginals that are consistent with the underlying data distributions. Finally, our empirical evaluation demonstrated significant gains on the tasks of image-to-image translation and unsupervised domain adaptation, along with an increase in inference capabilities due to the use of invertible models, e.g., paired interpolations in the latent space for two domains.In the future, we would like to consider extensions of AlignFlow to learning stochastic, multimodal mappings BID37 and translations across more than two domains BID38 . In spite of strong empirical results in domain alignments in the last few years, a well-established theory explaining such results is lacking. With a handle on model likelihoods and exact invertibility for inference, we are optimistic that AlignFlow can potentially aid the development of such a theory and characterize structure that leads to provably identifiable recovery of cross-domain mappings. Exploring the latent space of AlignFlow from a manifold learning perspective to domain alignment BID44 is also an interesting direction for future research.",1257,0.592,746,1.6849865951742626,"The goal unpaired cross-domain translation learn useful mappings given unpaired sets from While this formulation highly underconstrained recent work learn mappings useful downstream tasks encouraging approximate cycle consistency between 2017 In this work propose AlignFlow unpaired cross-domain translation ensures exact cycle consistency the learned mappings Our framework uses a normalizing flow model specify a single invertible mapping In contrast prior works cycle-consistent translations can learn AlignFlow via adversarial training maximum likelihood estimation a hybrid Theoretically derive consistency results AlignFlow which guarantee recovery desirable mappings under suitable assumptions AlignFlow demonstrates significant improvements relevant baselines on image translation unsupervised domain adaptation tasks on benchmark datasets Given data two domains cross-domain translation refers the task learning a mapping across image colorization This ability learn a meaningful alignment two domains machine learning relational BID1 , image and video translation for .Broadly , there paired. In paired cross-domain translation assume access pairs across black and white images their respective colorizations However paired data can expensive or may in neural style transfer BID8 where the goal translate across the works that typically exhibit a direct correspondenceUnpaired cross-domain translation tackles this regime where learns an alignment two domains given only unpaired sets from the domains Formally , seek learn a joint distribution over two domains say A given samples only the marginal distributions over CycleGAN BID0 , a highly successful approach learns a pair conditional generative models say G A→B match the marginal distributions over A via an adversarial objective BID9 The marginal matching constraints alone learn the desired joint distribution both theory To further an additional desideratum imposed cycle-consistency That given any datapoint A = a, the cycle-consistency term the learning objective prefers mappings G A→B such ( (a � Symmetrically cycle-consistency implies G A→B (b � b for B = Intuitively , encourages the learning approximately bijective mappingsWhile empirically effective the CycleGAN objective only imposes a soft cycle-consistency penalty provides G A→B and true inverses A natural question the cycle-consistency objective replaced a single, invertible model G A→B Drawing the literature invertible generative modelsRezende BID10 BID11 BID13 , we AlignFlow cross-domain translations which normalizing flow models represent. In AlignFlow compose a pair invertible flow models G Z→A the mapping G = • −1 Here Z is a shared latent space between Since composition invertible mappings preserves , the mapping G A→B from simply given = −1 Hence AlignFlow guarantees exact cycle-consistency by design the standard CycleGAN learning objective learning a single, invertible mappingFurthermore flexibility specifying the training objective In addition adversarial training can specify a prior distribution the latent variables Z train the two component models G Z→B via maximum likelihood estimation MLE is statistically efficient exhibits stable training dynamics , have of invertible generative models BID14 In this work presented AlignFlow cross-domain translations based normalizing flow models The use normalizing flow models an attractive choice we highlight it guarantees exact cycle-consistency via learns a shared latent space across permits a flexible training objective which a hybrid terms corresponding adversarial training exact maximum likelihood estimation Theoretically derived conditions under the AlignFlow model learns marginals that consistent the underlying data distributions Finally our empirical evaluation demonstrated significant gains on the tasks imageto translation unsupervised domain adaptation along inference capabilities due invertible models paired interpolations for two domainsIn consider extensions AlignFlow learning, multimodal mappings BID37 translations across . In spite strong empirical results domain alignments explaining such results lacking With a handle model likelihoods exact invertibility for inference are optimistic AlignFlow potentially aid such a theory characterize structure that leads provably identifiable recovery cross-domain mappings Exploring the latent space AlignFlow from a manifold learning perspective to domain alignment BID44 is also",0.01,0.4493648319236102
"Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, that maps the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, it is commonly formulated as a constraint satisfaction problem, where input-output examples are expressed constraints, and solved with a constraint solver. A key challenge of this formulation is that of scalability: While constraint solvers work well with few well-chosen examples, constraining the entire set of example constitutes a significant overhead in both time and memory. In this paper we address this challenge by constructing a representative subset of examples that is both small and is able to constrain the solver sufficiently. We build the subset one example at a time, using a trained discriminator to predict the probability of unchosen input-output examples conditioned on the chosen input-output examples, adding the least probable example to the subset. Experiment on a diagram drawing domain shows our approach produces subset of examples that are small and representative for the constraint solver. Program synthesis (or synthesis for short) is a special class of regression problems where rather than minimizing the error on an example dataset, one seeks an exact fit of the examples in the form of a program. Applications include synthesizing database relations BID19 ), inferring excelformulas BID11 ), and compilation BID16 ). In these domains, the synthesizer was able to come up with complex programs consisting of branches, loops, and other programming constructs. Recent efforts BID5 ; BID19 ) show an interest in applying the synthesis technique to large sets of examples, but scalability remains an open problem. In this paper we present a technique to select from a large dataset of examples a representative subset that is sufficient to synthesize a correct program, yet small enough to solve efficiently.There are two key ingredients to a synthesis problem: a domain specific language (DSL for short) and a specification. The DSL defines a space of candidate programs which serve as the model class. The specification is commonly expressed as a set of example input-output pairs which the candidate program needs to fit exactly. The DSL restricts the structure of the programs in such a way that it is difficult to fit the input-output examples in an ad-hoc fashion: This structure aids generalization to an unseen input despite ""over"" fitting the input-output examples during training.Given the precise and combinatorial nature of a synthesis problem, gradient-descent based approaches perform poorly and an explicit search over the solution space is required ). For this reason, synthesis is commonly casted as a constraint satisfaction problem (CSP) (Solar-Lezama (2013) ; BID12 ). In such a setting, the DSL and its execution can be thought of as a parametrized function F , which is encoded as a logical formula. Its free variables s ∈ S correspond to different parametrization within the DSL, and the input-output examples D are expressed as constraints which the instantiated program needs to satisfy, namely, producing the correct output on a given input.",598,0.303,335,1.7850746268656716,"Program synthesis a class regression problems seeks, maps exactly Due its precise and combinatorial nature commonly formulated a constraint satisfaction problem input-output examples expressed constraints solved A key challenge this formulation of scalability While constraint solvers work few well-chosen examples constraining example constitutes both time In address this challenge constructing a representative subset examples is both small is able constrain sufficiently We build the subset one example a trained discriminator predict unchosen input-output examples conditioned adding the least probable example Experiment on a diagram drawing domain shows our approach produces subset examples small representative for the constraint Program synthesis (or for a special class regression problems rather minimizing on an example dataset seeks an exact fit the examples Applications include synthesizing database relations BID19 ), inferring excelformulas compilation BID16 In these domains the synthesizer was able come complex programs consisting branches programming Recent efforts BID5 ; ) show an interest applying the synthesis technique large sets examples scalability remains In select from examples a representative subset that sufficient a correct program yet small solve efficientlyThere two key ingredients a synthesis problem a domain specific language for The DSL defines a space candidate programs serve the model class The specification commonly expressed example which the candidate program needs fit exactly The DSL restricts the structure the programs fit the input-output examples: This structure aids generalization an unseen input despite ""over"" fitting during trainingGiven a synthesis problem gradient-descent based approaches perform an explicit search over the solution space ). For synthesis commonly casted a constraint satisfaction problemCSPSolar-Lezama ( BID12 In such a setting the DSL and its execution thought F encoded a logical formula Its free variables s �� S correspond within the DSL the input-output examples D are expressed constraints which the instantiated program needs namely producing on",0.0,0.7043803430350063
"Humans possess an ability to abstractly reason about objects and their interactions, an ability not shared with state-of-the-art deep learning models. Relational networks, introduced by Santoro et al. (2017), add the capacity for relational reasoning to deep neural networks, but are limited in the complexity of the reasoning tasks they can address. We introduce recurrent relational networks which increase the suite of solvable tasks to those that require an order of magnitude more steps of relational reasoning. We use recurrent relational networks to solve Sudoku puzzles and achieve state-of-the-art results by solving 96.6% of the hardest Sudoku puzzles, where relational networks fail to solve any. We also apply our model to the BaBi textual QA dataset solving 19/20 tasks which is competitive with state-of-the-art sparse differentiable neural computers. The recurrent relational network is a general purpose module that can augment any neural network model with the capacity to do many-step relational reasoning.",190,0.115,115,1.6521739130434783,Humans possess abstractly reason objects an not state deep Relational networks introduced Santoro et (2017 add the capacity relational reasoning deep neural networks but are limited the complexity address We introduce recurrent relational networks which increase the suite solvable tasks to those an order of relational reasoning We use recurrent relational networks Sudoku puzzles achieve state 96.6% where relational networks fail. We also apply our model the BaBi textual QA dataset solving 19/20 tasks which is competitive state sparse differentiable neural computers The recurrent relational network a general purpose module augment the capacity do many-step relational reasoning,0.0,0.3657610007451019
"Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrary binary classifier in an unbiased manner given a single set of U data, but it becomes possible given two sets of U data with different class priors. These two facts answer a fundamental question---what the minimal supervision is for training any binary classifier from only U data. Following these findings, we propose an ERM-based learning method from two sets of U data, and then prove it is consistent. Experiments demonstrate the proposed method could train deep models and outperform state-of-the-art methods for learning from two sets of U data. With some properly chosen loss function (e.g., BID2 BID50 BID39 and regularization (e.g., BID51 BID46 , empirical risk minimization (ERM) is the common practice of supervised classification BID54 . Actually, ERM is used in not only supervised learning but also weakly-supervised learning. For example, in semi-supervised learning (Chapelle et al., 2006) , we have very limited labeled (L) data and a lot of unlabeled (U) data, where L data share the same form with supervised learning. Thus, it is easy to estimate the risk from only L data in order to carry out ERM, and U data are needed exclusively in regularization (including but not limited to BID16 BID3 BID25 BID29 BID20 BID49 BID24 Kamnitsas et al., 2018) .Nevertheless , L data may differ from supervised learning in not only the amount but also the form. For instance , in positive-unlabeled learning BID12 BID55 ), all L data are from the positive class, and due to the lack of L data from the negative class it becomes impossible to estimate the risk from only L data. To this end , a two-step approach to ERM has been considered (du BID9 BID34 BID18 . Firstly, the risk is rewritten into an equivalent expression, such that it just involves the same distributions from which L and U data are sampled-this step leads to certain risk estimators. Secondly, the risk is estimated from both L and U data, and the resulted empirical training risk is minimized (e.g. by BID41 Kingma & Ba, 2015) . In this two-step approach, U data are needed absolutely in ERM itself. This indicates that risk rewrite (i.e., the technique of making the risk estimable from observable data via an equivalent expression) enables ERM in positive-unlabeled learning and is the key of success.One step further from positive-unlabeled learning is learning from only U data without any L data. This is significantly harder than previous learning problems (cf. FIG1 ). However, we would still like to train arbitrary binary classifier, in particular, deep networks BID15 . Note that for this purpose clustering is suboptimal for two major reasons. First, successful translation of clusters into meaningful classes completely relies on the critical assumption that one cluster exactly In the left panel, (a) and (b) show positive (P) and negative (N) components of the Gaussian mixture; (c) and (d) show two distributions (with class priors 0.9 and 0.4) where U training data are drawn (marked as black points). The right panel shows the test distribution (with class prior 0.3) and data (marked as blue for P and red for N), as well as four learned classifiers. In the legend, ""CCN"" refers to BID31 , ""UU-biased "" means supervised learning taking larger-/smaller-class-prior U data as P/N data, ""UU"" is the proposed method, and ""Oracle"" means supervised learning from the same amount of L data. See Appendix B for more information. We can see that UU is almost identical to Oracle and much better than the other two methods. corresponds to one class, and hence even perfect clustering might still result in poor classification. Second, clustering must introduce additional geometric or information-theoretic assumptions upon which the learning objectives of clustering are built (e.g., BID57 BID14 . As a consequence, we prefer ERM to clustering and then no more assumption is required.The difficulty is how to estimate the risk from only U data, and our solution is again ERM-enabling risk rewrite in the aforementioned two-step approach. The first step should lead to an unbiased risk estimator that will be used in the second step. Subsequently, we can evaluate the empirical training and/or validation risk by plugging only U training/validation data into the risk estimator. Thus, this two-step ERM needs no L validation data for hyperparameter tuning, which is a huge advantage in training deep models nowadays. Note that given only U data, by no means could we learn the class priors BID27 , so that we assume all necessary class priors are also given. This is the unique type of supervision we will leverage throughout this paper, and hence this learning problem still belongs to weakly-supervised learning rather than unsupervised learning.In this paper, we raise a fundamental question in weakly-supervised learning-how many sets of U data with different class priors are necessary for rewriting the risk? Our answer has two aspects:• Risk rewrite is impossible given a single set of U data (see Theorem 2 in Sec. 3);• Risk rewrite becomes possible given two sets of U data (see Theorem 4 in Sec. 4).This suggests that three class priors 1 are all you need to train deep models from only U data, while any two 2 should not be enough. The impossibility is a proof by contradiction, and the possibility is a proof by construction, following which we explicitly design an unbiased risk estimator. Therefore, with the help of this risk estimator, we propose an ERM-based learning method from two sets of U data. Thanks to the unbiasedness of our risk estimator, we derive an estimation error bound which certainly guarantees the consistency of learning BID30 BID44 .3 Experiments demonstrate that the proposed method could train multilayer perceptron, AllConvNet BID45 and ResNet (He et al., 2016) from two sets of U data; it could outperform state-of-the-art methods for learning from two sets of U data. See FIG1 for how the proposed method works on a Gaussian mixture of two components .As mentioned earlier, learning from two sets of U data is already studied in du BID8 and BID27 . Both of them adopt (4) as the performance measure. In the former paper, g is learned by estimating sign(p tr (x) − p tr (x)). In the latter paper, g is learned by taking noisy L data from p tr (x) and p tr (x) as clean L data from p p (x) and p n (x), and then its threshold is moved to the correct value by post-processing. In summary, instead of ERM, they evidence the possibility of empirical balanced risk minimization , and no impossibility is proven.Our findings are compatible with learning from label proportions BID36 BID58 . BID36 proves that the minimal number of U sets is equal to the number of classes. However, their finding only holds for the linear model, the logistic loss, and their proposed method based on mean operators. On the other hand, BID58 is not ERM-based; it is based on discriminative clustering together with expectation regularization BID25 .At first glance, our data generation process, using the names from BID27 , looks quite similar to class-conditional noise (CCN, BID0 in learning with noisy labels (cf. BID31 . 4 In fact, BID27 makes use of mutually contaminated distributions (MCD, BID43 that is more general than CCN . Denote byỹ andp(·) the corrupted label and distributions. Then, CCN and MCD are defined by DISPLAYFORM0 where both of T CCN and T MCD are 2-by-2 matrices but T CCN is column normalized and T MCD is row normalized. It has been proven in BID27 that CCN is a strict special case of MCD. To DISPLAYFORM1 Due to this covariate shift, CCN methods do not fit MCD problem setting, though MCD methods fit CCN problem setting. To the best of our knowledge, the proposed method is the first MCD method based on ERM.3 LEARNING FROM ONE SET OF U DATA From now on, we prove that knowing π p and θ is insufficient for rewriting R(g). We focused on training arbitrary binary classifier, ranging from linear to deep models, from only U data by ERM. We proved that risk rewrite as the core of ERM is impossible given a single set of U data, but it becomes possible given two sets of U data with different class priors, after we assumed that all necessary class priors are also given. This possibility led to an unbiased risk estimator, and with the help of this risk estimator we proposed UU learning, the first ERM-based learning method from two sets of U data. Experiments demonstrated that UU learning could successfully train fully connected, all convolutional and residual networks, and it compared favorably with state-of-the-art methods for learning from two sets of U data.",1942,0.989,1137,1.7080035180299034,"Empirical risk minimization with proper loss function regularization supervised classification In study training arbitrary (from linear deep) binary classifier from only unlabeled (U) data by ERM We prove estimate an arbitrary binary classifier given U data becomes given different class priors These two facts answer--- the minimal supervision training any binary classifier from only U data Following these findings an ERM-based learning method from two sets U data prove consistent Experiments demonstrate the proposed method could train deep models and outperform state learning two sets U data With some properly chosen loss function BID2 BID50 BID39 and regularization is the common practice supervised classification BID54 . Actually ERM used not only supervised learning For exampleChapelle , very limited labeled (L) data a lot where share supervised learning Thus easy estimate from only L data order carry ERM, U data are needed exclusively regularizationincluding but BID16 BID3 BID25 BID29 BID20 BID49 BID24 Kamnitsas et 2018 .Nevertheless , differ supervised learning but For instance , positiveunlabeled learning BID12 BID55 ), all L data from the positive class due it becomes estimate the risk from To this end , ERM considered (du BID9 BID34 BID18 . Firstly the risk rewritten into an equivalent expression such just involves the same distributions from L and U data sampled-this step leads certain risk estimators Secondly the risk estimated both L and U data the resulted empirical training risk minimized BID41 Kingma & Ba, 2015 In U data are needed absolutely ERM itself This indicates that risk rewrite making estimable observable data via an equivalent expression enables ERM positive-unlabeled learning of successOne step from learning only U data without any L data This significantly harder previous learning problemscf FIG1 ). However we would train arbitrary binary classifier in particular, deep networks BID15 . Note for clustering First, successful translation clusters meaningful classes completely relies the critical assumption one cluster exactly In the left panel ( and show positive (P components two distributionswith class priors U training data drawnmarked black points The right panel shows the test distributionwith class prior 0.3 datamarked blue for P and four learned classifiers In the legend ""CCN BID31 , ""UUbiased "" means supervised learning taking larger-/smaller-class-prior U data as P/N data the proposed methodOracle supervised from the same amount L data See Appendix B We that UU almost identical Oracle much corresponds one class hence even perfect clustering might still poor classification Second clustering must introduce additional geometric or information-theoretic assumptions upon the learning objectives built BID57 BID14 . As prefer ERM clustering then no more assumptionThe difficulty how estimate only U data our solution again ERM-enabling risk rewrite in the aforementioned two-step approach should lead an unbiased risk estimator Subsequently can evaluate the empirical training and/or validation risk by plugging only U training/validation data Thus this two-step ERM needs no L validation data hyperparameter tuning training deep models nowadays Note given only U data by could learn the class priors BID27 , so assume also This the unique type supervision will leverage throughout this paper hence this learning problem still belongs ratherIn raise U data with different class priors rewriting the risk? Our answer has two aspects:• Risk rewrite impossible given U datasee Theorem in Sec 3);• Risk rewrite becomes possible given two sets U datasee Theorem in Sec 4).This suggests three class priors 1 are all you train deep models from only U data any 2 should not The impossibility is a proof by contradiction construction following explicitly design an unbiased risk estimator Therefore with this risk estimator propose an ERM-based learning method from two sets U data Thanks the unbiasedness our risk estimator derive bound which certainly guarantees the consistency learning BID30 BID44 .3 Experiments demonstrate the proposed method could train multilayer perceptron, AllConvNet ResNet (He et from two sets U data; it state from See FIG1 for how the proposed method works on two components .As learning two sets U data already studied du BID8 Both adopt (4 as the performance measure In the former paper g is learned estimating sign(p tr ( In the latter paper g is learned taking noisy L data p trx clean L data n its threshold moved post In summary instead ERM they evidence empirical balanced risk minimization , no impossibility provenOur findings compatible learning label proportions BID36 BID58 BID36 proves the minimal number U sets equal classes However their finding only holds the linear model the logistic loss their proposed method based mean operators On BID58 ERM discriminative together expectation regularization BID25 .At our data generation process, using the names from looks class-conditional noise, in learning with noisy labels (cf BID31 . 4 In fact BID27 makes mutually contaminated distributionsMCD that more general CCN . Denote by��� andp(· the corrupted label distributions Then CCN and MCD defined DISPLAYFORM0 where both T CCN but column normalized It proven BID27 CCN a strict special case MCD To DISPLAYFORM1 Due this covariate shift CCN methods fit MCD problem setting though To the proposed method the first MCD method based ERM.3 LEARNING FROM ONE SET U DATA From now prove knowing �� p and �� insufficient rewriting R(g We focused training arbitrary binary classifier ranging linear deep models only U data by ERM We proved that risk rewrite as the core ERM impossible given U data becomes given different class priors after assumed also This possibility led an unbiased risk estimator with proposed UU learning, from two sets U data Experiments demonstrated UU learning successfully train fully connected, all convolutional and residual networks it compared favorably state two sets U data",0.01,0.508009929115052
"Deep Neural Networks (DNNs) excel on many complex perceptual tasks but it has proven notoriously difficult to understand how they reach their decisions. We here introduce a high-performance DNN architecture on ImageNet whose decisions are considerably easier to explain. Our model, a simple variant of the ResNet-50 architecture called BagNet, classifies an image based on the occurrences of small local image features without taking into account their spatial ordering. This strategy is closely related to the bag-of-feature (BoF) models popular before the onset of deep learning and reaches a surprisingly high accuracy on ImageNet (87.6% top-5 for 32 x 32 px features and Alexnet performance for 16 x16 px features). The constraint on local features makes it straight-forward to analyse how exactly each part of the image influences the classification. Furthermore, the BagNets behave similar to state-of-the art deep neural networks such as VGG-16, ResNet-152 or DenseNet-169 in terms of feature sensitivity, error distribution and interactions between image parts. This suggests that the improvements of DNNs over previous bag-of-feature classifiers in the last few years is mostly achieved by better fine-tuning rather than by qualitatively different decision strategies. A big obstacle in understanding the decision-making of DNNs is due to the complex dependencies between input and hidden activations: for one, the effect of any part of the input on a hidden activation depends on the state of many other parts of the input. Likewise, the role of a hidden unit on downstream representations depends on the activity of many other units. This dependency makes it extremely difficult to understand how DNNs reach their decisions.To circumvent this problem we here formulate a new DNN architecture that is easier to interpret by design. Our architecture is inspired by bag-of-feature (BoF) models which -alongside extensions such as VLAD encoding or Fisher Vectors -have been the most successful approaches to large-scale object recognition before the advent of deep learning (up to 75% top-5 on ImageNet) and classify images based on the counts, but not the spatial relationships, of a set of local image features. This structure makes the decisions of BoF models particularly easy to explain.To be concise, throughout this manuscript the concept of interpretability refers to the way in which evidence from small image patches is integrated to reach an image-level decision. While basic BoF models perform just a simple and transparent spatial aggregate of the patch-wise evidences, DNNs non-linearly integrate information across the whole image.In this paper we show that it is possible to combine the performance and flexibility of DNNs with the interpretability of BoF models, and that the resulting model family (called BagNets) is able to reach high accuracy on ImageNet even if limited to fairly small image patches. Given the simplicity of BoF models we imagine many use cases for which it can be desirable to trade a bit of accuracy for better interpretability, just as this is common e.g. for linear function approximation. This includes diagnosing failure cases (e.g. adversarial examples) or non-iid. settings (e.g. domain transfer), benchmarking diagnostic tools (e.g. attribution methods) or serving as interpretable parts of a computer vision pipeline (e.g. with a relational network on top of the local features).In addition, we demonstrate similarities between the decision-making behaviour of BagNets and popular DNNs in computer vision. These similarities suggest that current network architectures base their decisions on a large number of relatively weak and local statistical regularities and are not sufficiently encouraged -either through their architecture, training procedure or task specification -to learn more holistic features that can better appreciate causal relationships between different parts of the image. In this paper we introduced and analysed a novel interpretable DNN architecture -coined BagNets -that classifies images based on linear bag-of-local-features representations. The results demonstrate that even complex perceptual tasks like ImageNet can be solved just based on small image features and without any notion of spatial relationships. In addition we showed that the key properties of BagNets, in particlar invariance to spatial relationships as well as weak interactions between image features, are also present to varying degrees in many common computer vision models like ResNet-50 Table 1 : Average probability of leading class after masking the 100 patches (8 × 8 pixels) with the highest attribution according to different heatmaps (columns).or VGG-16, suggesting that the decision-making of many DNNs trained on ImageNet follows at least in part a similar bag-of-feature strategy. In contrast to the perceived ""leap"" in performance from bag-of-feature models to deep neural networks, the representations learnt by DNNs may in the end still be similar to the pre-deep learning era.VGG-16 is particularly close to bag-of-feature models, as demonstrated by the weak interactions (Figure 6 ) and the sensitivity to the same small image patches as BagNets (Figure 8 ). Deeper networks, on the other hand, exhibit stronger nonlinear interactions between image parts and are less sensitive to local maskings. This might explain why texturisation (Figure 5 ) works well in VGG-16 but fails for ResNet-and DenseNet-architectures.Clearly, ImageNet alone is not sufficient to force DNNs to learn more physical and causal representation of the world -simply because such a representation is not necessary to solve the task (local image features are enough). This might explain why DNNs generalise poorly to distribution shifts: a DNN trained on natural images has learnt to recognize the textures and local image features associated with different objects (like the fur and eyes of a cat or the keys of a typewriter) and will inevitably fail if presented with cartoon-like images as they lack the key local image features upon which it bases its decisions.One way forward is to define novel tasks that cannot be solved using local statistical regularities. Here the BagNets can serve as a way to evaluate a lower-bound on the task performance as a function of the observable length-scales. Furthermore, BagNets can be an interesting tool in any application in which it is desirable to trade some accuracy for better interpretability. For example, BagNets can make it much easier to spot the relevant spatial locations and image features that are predictive of certain diseases in medical imaging. Likewise, they can serve as diagnostic tools to benchmark feature attribution techniques since ground-truth attributions are directly available. BagNets can also serve as interpretable parts of a larger computer vision pipeline (e.g. in autonomous cars) as they make it easier to understand edge and failure cases. We released the pretrained BagNets (BagNet-9, BagNet-17 and BagNet-33) for PyTorch and Keras at https://github.com/wielandbrendel/ bag-of-local-features-models.Taken together, DNNs might be more powerful than previous hand-tuned bag-of-feature algorithms in discovering weak statistical regularities, but that does not necessarily mean that they learn substantially different representations. We hope that this work will encourage and inspire future work to adapt tasks, architectures and training algorithms to encourage models to learn more causal models of the world.A APPENDIXThe architecture of the BagNets is detailed in Figure A. 1. Training of the models was performed in PyTorch using the default ImageNet training script of Torchvision (https://github.com/ pytorch/vision, commit 8a4786a) with default parameters. In brief, we used SGD with momentum (0.9), a batchsize of 256 and an initial learning rate of 0.01 which we decreased by a factor of 10 every 30 epochs. Images were resized to 256 pixels (shortest side) after which we extracted a random crop of size 224 × 224 pixels.",1609,0.669,970,1.6587628865979382,"Deep Neural Networks excel on but it proven notoriously reach their decisions We here introduce a high-performance DNN architecture on ImageNet whose decisions considerably explain Our model, a simple variant the ResNet-50 architecture called BagNet classifies an image based the occurrences small local image features without taking their spatial ordering This strategy closely bagoffeature ( models popular before the onset deep learning reaches on ImageNet top-5 for 32 x 32 px features Alexnet performance The constraint local features makes straight analyse how exactly each part influences the classification Furthermore the BagNets behave similar such VGG-16 ResNet-152 DenseNet-169 in feature sensitivity error distribution interactions image parts This suggests the improvements of DNNs over bagfeature classifiers in is mostly achieved rather qualitatively different decision strategies A big obstacle understanding DNNs due the complex dependencies input hidden activations: for one the effect any part on Likewise the role a hidden unit on downstream representations depends the activity This dependency makes extremely understand DNNs reach their decisionsTo circumvent here formulate easier interpret by design Our architecture bagoffeature ( models which -alongside extensions VLAD encoding Fisher Vectors the most successful approaches beforeup to 75% top-5 on classify based the counts but a set local image features This structure makes the decisions BoF models particularly explainTo concise throughout this manuscript interpretability refers evidence from small image patches integrated to reach While basic BoF models perform just a simple and transparent spatial aggregate the patch-wise evidences DNNs non integrate information acrossIn it the performance flexibility the interpretability the resulting model family (called BagNets reach high accuracy ImageNet even limited fairly small image patches Given the simplicity BoF models we imagine many use cases desirable trade a bit accuracy better interpretability just this common linear function approximation This includes diagnosing failure cases (e.g. adversarial examples noniid. settings (e.g. domain transfer benchmarking diagnostic tools serving interpretable parts a computer vision pipeline with a relational network on the local features).In addition demonstrate similarities BagNets popular DNNs These similarities suggest current network architectures base relatively weak and local statistical regularities encouraged -either their architecture training procedure task specification learn more holistic features better appreciate causal relationships the image In introduced and analysed a novel interpretable DNN architecture -coined BagNets classifies images linear bagoflocal-features representations The results demonstrate even complex perceptual tasks ImageNet solved just based small image features without any notion spatial relationships In addition we showed the key properties BagNets in particlar invariance to spatial relationships as weak interactions image features present to many common computer vision models like ResNet-50 Table : Average probability leading class after the 100 patches8 × 8 pixels the highest attribution according different heatmapscolumns).or VGG-16 suggesting many DNNs trained follows at bagoffeature strategy In contrast the perceived ""leap performance bag-feature models deep neural networks the representations learnt may in still similar the pre-deep learning eraVGG-16 particularly close bag demonstrated the weak interactions (Figure ) the sensitivity the same small image patches BagNets Deeper networks on exhibit stronger nonlinear interactions image parts are local maskings This might explain texturisation (Figure ) works VGG-16 but fails ResNetand DenseNet-architecturesClearly ImageNet alone force learn more physical and causal representation -simply such a representation necessary solvelocal image features enough This might explain DNNs generalise poorly distribution shifts trained natural images learnt recognize the textures local image features associated different objectslike the fur eyes the keys will inevitably fail presented cartoon-like images as lack the key local image features upon basesOne forward define novel tasks local statistical regularities Here the BagNets can serve evaluate lowerbound the task performance as the observable length-scales Furthermore BagNets an interesting tool any application in desirable trade some accuracy better interpretability For example BagNets make much spot the relevant spatial locations image features predictive certain diseases medical imaging Likewise they can serve diagnostic tools benchmark feature attribution techniques since ground-truth attributions directly available BagNets can serve interpretable parts a larger computer vision pipeline ( in autonomous cars make edge and failure cases We released the pretrained BagNets (BagNet-9 PyTorch Keras atoflocal-features-modelsTaken DNNs might previous handfeature algorithms discovering weak statistical regularities does necessarily learn substantially different representations We hope this work and future work adapt tasks architectures training algorithms encourage models more causal modelsA APPENDIXThe architecture the BagNets detailed 1 Training of the models PyTorch the default ImageNet training script of Torchvision, commit 8a4786a) default parameters In brief used SGD with momentum a batchsize 256 and which decreased 10 every 30 epochs Images were resized 256 pixels (shortest side after which extracted a random crop size 224",0.01,0.38254912646097916
"Somatic cancer mutation detection at ultra-low variant allele frequencies (VAFs) is an unmet challenge that is intractable with current state-of-the-art mutation calling methods. Specifically, the limit of VAF detection is closely related to the depth of coverage, due to the requirement of multiple supporting reads in extant methods, precluding the detection of mutations at VAFs that are orders of magnitude lower than the depth of coverage. Nevertheless, the ability to detect cancer-associated mutations in ultra low VAFs is a fundamental requirement for low-tumor burden cancer diagnostics applications such as early detection, monitoring, and therapy nomination using liquid biopsy methods (cell-free DNA). Here we defined a spatial representation of sequencing information adapted for convolutional architecture that enables variant detection at VAFs, in a manner independent of the depth of sequencing. This method enables the detection of cancer mutations even in VAFs as low as 10x-4^, >2 orders of magnitude below the current state-of-the-art. We validated our method on both simulated plasma and on clinical cfDNA plasma samples from cancer patients and non-cancer controls. This method introduces a new domain within bioinformatics and personalized medicine – somatic whole genome mutation calling for liquid biopsy. The cancer genome acquires somatic mutations which drive its proliferative capacity BID8 . Mutations in the cancer genome also provide critical information regarding the evolutionary history and mutational processes active in each cancer (Martincorena et al., 2017; BID0 . Cancer mutation calling in patient tumor biopsies has become a pivotal step in determining patient outcomes and nomination of personalized therapeutics.Identifying cancer mutations in liquid biopsy techniques, such as cell-free circulating DNA (cfDNA), has been suggested as a transformative platform for early-stage cancer screening and residual disease monitoring. cfDNA released from dying tumor cells enables surveys the somatic genome dynamically over time for clinical purposes, empowered by the ability to obtain cancer-related genetic material non-invasively through a simple blood draw. Circulating tumor DNA (ctDNA) can be found and measured in the plasma cfDNA of cancer patients. ctDNA was shown to correlate with tumor burden and change in response to treatment or surgery BID4 . For example, ctDNA can be detected even in early stage non-small cell lung cancer (NSCLC) and therefore has the potential to transform NSCLC diagnosis and treatment BID15 BID17 BID1 BID20 . Nevertheless, the fraction of ctDNA of the total cfDNA is typically exceedingly low, especially in low disease-burden contexts such as early detection or detection of residual disease after therapeutic interventions. While detection of cancer through cfDNA in the low disease-burden setting may be of significant clinical benefit, it challenges our current methods for identifying somatic mutations due to the ultra-low VAFs compared with the available depth of sequencing.The most common type of somatic mutations is single-nucleotide variants (SNVs) , which occur at a frequency of 1-100 per million bases. These variants are typically identified in sequencing data through a careful comparison of the DNA sequencing reads which map to a particular genomic locus in both the cancer DNA and the matched germline DNA. This process has been enabled through tools of ever-increasing sophistication that refine the statistical comparison between the number of reads supporting a candidate mutated variant in the cancer vs. the germline sample BID39 BID42 .These statistical methods fundamentally require multiple independent observations (supporting reads) of the somatic variant at any given genomic location to distinguish true mutations from sequencing artifacts. Mutect , a state-of-the-art low-allele frequency somatic mutation caller, subjects each SNV to Bayesian classifiers that assume that the SNV either results from sequencing noise or that the site contains a true cancer variant. A true cancer-related SNV call is made when the log-likelihood ratio from the two models strongly favors the true cancer Bayesian classifier. This "" locus-centric"" type of cancer mutation detection can be readily achieved through increased depth of sequencing -so long as the tumor sample contains a high proportion of tumor DNA. However , these methods are significantly challenged in the ctDNA setting where the VAF is expected to be well below 1%. For example , a decrease of VAF to 5% and sequencing depth to 10X resulted in a decreased in the sensitivity of Mutect to below 0.1 BID39 BID42 . Thus, locus-centric mutation callers are unable to perform effective mutation calling in the ultra-low VAFs observed in low disease-burden cfDNA settings.We reasoned that to tackle this challenge, we would need a novel mutation detection framework. Specifically, we would need methodology to accurately distinguish true somatic cancer mutations from sequencing artifacts, even in ultra low tumor fractions that preclude the presence of multiple supporting independent observations (reads) in any given genomic location. We propose a ""readcentric "" alternative approach, and developed a convolutional neural network classifier -Kittyhawk -trained to discriminate between individual sequencing reads containing sequencing artifacts and sequencing reads harboring somatic cancer mutations. We take advantage of the fact that both cancer mutations and sequencing errors are systemic and governed by distinct signatures that can be learned and used for efficient signal to noise discrimination (e.g., mutagenesis processes such as exposure to tobacco or UV light are enriched in specific sequence contexts; BID0 ) 0.01%-1%, as well as with cfDNA samples from patients with early stage lung cancer and an individual with non-malignant lung nodules as controls. Ultra-low tumor fraction such as observed in cfDNA fundamentally challenge the prevailing mutation calling paradigm. State-of-the-art mutation callers share a common unifying principle: mutation calling at a particular genomic location based on the observation of the cancer variant in multiple FIG6 : PPV, enrichment, and sensitivity of CA0044 synthetic cfDNA.overlapping reads. However, in the ultra-low tumor fraction context, at best, only a single mutated read is observed, limiting the ability of traditional mutation calling.The need for extending the mutation-calling framework to ultra-low tumor fraction contexts motivated us to rethink the mutation calling process from a locus-centric approach to a read-centric approach. This approach uses every individual read as input for a classifier and lends itself to the application of convolutional neuronal network learning. To realize this novel methodology, we embodied the information captured in the sequencing read (nucleotide sequence, context, quality metrics) in a spatial representation typically applied for image analysis. While we anticipate that our ongoing efforts to include larger training datasets, will result in further performance improvement, even at this proof-of-principle stage the algorithm is providing a 30-fold enrichment in a manner that is completely independent from variant allele fraction or depth of coverage, a unique performance feature that addresses a major emerging unmet need. Indeed, stable enrichment performance extends to tumor fractions as low as 10 4 .While Kittyhawk captures position in the read by using a fully connected sigmoid layer, there are other architectures, which may be suited for capturing relative position on the read. Additionally , we have excluded an extra source of information contained in the read-pair that comes from the DNA fragment. The read pair can be used to determine both the strand of origin (Watson or Crick) and to estimate the DNA fragment size. It has been observed that ctDNA have a distinct fragment size distribution compared to other cfDNA from normal cells BID19 . It has been shown that recurrent neural networks (RNN) are a powerful tool for using length as a feature in bioinformatics at distances even up to 1kb, far beyond the size of a ctDNA fragment BID6 . These results suggest that integrating an RNN instead of a logistic regression layer could increase performance even further. In addition, while Kittyhawk was developed for the context of low tumor fraction mutation calling in cfDNA, we note that this framework can be adapted to other contexts. For example, it may be used in mutation (or germline SNP) detection in low pass genome sequencing (0.01-1X) across a wide range of applications. Furthermore, a read-centric approach may be also integrated with a more traditional locus-centric mutation calling approach, by adding Kittyhawk predictions as an additional input metric for extant statistical or machine learning mutation calling algorithms.In summary, Kittyhawk is the first somatic mutation caller designed specifically to function in the ultra-low allele frequency setting where at best a single supporting read is available for candidate mutation identification, such as liquid biopsy for early stage cancer detection. We apply a novel representation of a read together with a hand-engineered architecture to capture the entirety of informative features associated with a read and its alignment. This work sets the stage for a new family of somatic mutation callers to aid detection in liquid biopsy, paving the way for pivotal non-invasive screening and prognosis.",1778,0.839,1066,1.6679174484052532,"Somatic cancer mutation detection at ultra-low variant allele frequenciesVAFs an unmet challenge with state mutation calling Specifically the limit VAF detection closely coverage due multiple supporting reads extant methods precluding mutations orders lower Nevertheless the ability detect cancer-associated mutations ultra low VAFs low-tumor burden cancer diagnostics applications such monitoring therapy nomination using liquid biopsy methodscell-free DNA Here defined a spatial representation sequencing information adapted convolutional architecture that enables variant detection at VAFs independent the depth sequencing This method enables the detection cancer mutations even VAFs as 10x-4^, >2 orders- We validated both simulated plasma on clinical cfDNA plasma samples This method introduces within personalized medicine – somatic whole genome mutation calling liquid biopsy The cancer genome acquires somatic mutations drive BID8 . Mutations the cancer genome also provide mutational processes active (Martincorena 2017 BID0 . Cancer mutation calling in patient tumor biopsies has a pivotal step determining patient outcomes nomination personalized therapeuticsIdentifying liquid biopsy techniques cell-free circulating DNAcfDNA suggested a transformative platform residual disease monitoring cfDNA released from dying tumor cells enables surveys the somatic genome dynamically over for clinical purposes empowered obtain non a simple blood draw Circulating tumor DNActDNA and measured the plasma cfDNA ctDNA was shown correlate tumor burden change response or surgery BID4 . For example ctDNA even early stage therefore transform BID15 BID17 . Nevertheless the fraction ctDNA of the total cfDNA typically exceedingly especially low disease-burden contexts early detection detection residual disease after therapeutic interventions While detection cancer through cfDNA in the low disease-burden setting of challenges our current methods due the ultra-low VAFs compared the available depth sequencingThe most common type , These variants typically identified sequencing through a careful comparison the DNA sequencing reads which map both the cancer DNA This process enabled tools of refine the statistical comparison reads supporting a candidate mutated variant the cancer vs. the germline sample BID39 BID42 .These statistical methods fundamentally require multiple independent observations (supporting reads at distinguish true mutations sequencing artifacts Mutect , state lowallele frequency somatic mutation caller subjects each SNV Bayesian classifiers assume either results sequencing noise the site contains a true cancer variant A true cancer-related SNV call made the log-likelihood ratio from the two models strongly the true cancer Bayesian classifier This "" locus-centric"" type cancer mutation detection readily increased depth -so However , these methods significantly challenged ctDNA setting the VAF expected well below For example , decrease VAF to sequencing depth 10X resulted decreased in the sensitivity Mutect to below 0.1 BID39 BID42 Thus locus-centric mutation callers unable perform effective mutation calling the ultra-low VAFs observed low disease-burden cfDNA settingsWe reasoned to tackle a novel mutation detection framework Specifically would need methodology accurately distinguish true somatic cancer mutations sequencing artifacts even ultra low tumor fractions preclude multiple supporting independent observationsreads We propose a ""readcentric "" alternative approach and developed a convolutional neural network classifier -Kittyhawk -trained discriminate individual sequencing reads containing sequencing artifacts harboring somatic cancer mutations We take advantage both cancer mutations sequencing errors systemic governed distinct signatures learned used efficient signal to discrimination such exposure enriched specific sequence contexts BID0 ) 0.01%-1 with cfDNA samples an individual as controls Ultra-low tumor fraction such observed cfDNA fundamentally challenge the prevailing mutation calling paradigm State mutation callers share mutation calling at a particular genomic location based the observation the cancer variant multiple FIG6 : PPV, enrichment sensitivity CA0044 synthetic cfDNA.overlapping reads However the ultra-low tumor fraction context at best only a single mutated read observed limiting traditional mutation calling.The need extending motivated rethink from This approach uses every individual read as lends the application convolutional neuronal network learning To realize this novel methodology embodied the information captured the sequencing read ( context quality metrics a spatial representation typically applied image analysis While anticipate our ongoing efforts include larger training datasets will result further performance improvement even proof stage the algorithm providing a 30-fold enrichment a manner completely variant allele fraction or depth a unique performance addresses a major emerging unmet need Indeed stable enrichment performance extends tumor fractions low 4 .While Kittyhawk captures position the read by a fully connected sigmoid layer other architectures suited capturing relative position Additionally , excluded an extra source contained the read-pair that comes the DNA fragment The read pair can determine both the strand originWatson or Crick to estimate the DNA fragment size It observed ctDNA have a distinct fragment size distribution compared other cfDNA from normal cells BID19 . It shown recurrent neural networks using length at distances even up to 1kb far a ctDNA fragment BID6 . These results integrating an RNN instead increase even In addition while Kittyhawk developed the context low tumor fraction mutation calling cfDNA note this framework adapted For example it used mutation ( germline SNP) detection low pass genome across applications Furthermore a read-centric approach may also integrated a more traditional locus-centric mutation calling approach by adding Kittyhawk predictions as metric extant statistical or machine learning mutation callingIn the first somatic mutation caller designed function the ultra-low allele frequency setting where at best a single supporting read candidate mutation identification such liquid biopsy for early stage cancer detection We apply a novel representation a read together a hand-engineered architecture capture the entirety informative features associated its alignment This work sets a new family somatic mutation callers aid detection liquid biopsy paving",0.01,0.40587414563501184
"This paper presents the formal release of {\em MedMentions}, a new manually annotated resource for the recognition of biomedical concepts. What distinguishes MedMentions from other annotated biomedical corpora is its size (over 4,000 abstracts and over 350,000 linked mentions), as well as the size of the concept ontology (over 3 million concepts from UMLS 2017) and its broad coverage of biomedical disciplines. In addition to the full corpus, a sub-corpus of MedMentions is also presented, comprising annotations for a subset of UMLS 2017 targeted towards document retrieval. To encourage research in Biomedical Named Entity Recognition and Linking, data splits for training and testing are included in the release, and a baseline model and its metrics for entity linking are also described. One recognized challenge in developing automated biomedical entity extraction systems is the lack of richly annotated training datasets. While there are a few such datasets available, the annotated corpus often contains no more than a few thousand annotated entity mentions. Additionally, the annotated entities are limited to a few types of biomedical concepts such as diseases BID4 , gene ontology terms BID18 , or chemicals and diseases BID9 . Researchers targeting the recognition of multiple biomedical entity types have had to resort to specialized machine learning techniques for combining datasets labelled with subsets of the full target set, e.g. using multi-task learning BID3 , or a modified Conditional Random Field cost which allows un-labeled tokens to take any labels not in the current dataset's target set BID5 . To promote the development of state-of-the-art entity linkers targeting a more comprehensive coverage of biomedical concepts, we decided to create a large concept-mention annotated gold standard dataset named 'MedMentions' BID11 .With the release of MedMentions, we hope to address two key needs for developing better biomedical concept recognition systems: (i) a much broader coverage of the fields of biology and medicine through the use of the Unified Medical Language System (UMLS) as the target ontology, and (ii ) a significantly larger annotated corpus than available today, to meet the data demands of today's more complex machine learning models for concept recognition.The paper begins with an introduction to the MedMentions annotated corpus, including a subcorpus aimed at information retrieval systems. This is followed by a comparison with a few other large datasets annotated with biomedical entities. Finally , to promote further research on large ontology named entity recognition and linking, we present metrics for a baseline end-to-end concept recognition (entity type recognition and entity linking) model trained on the MedMentions corpus. We presented the formal release of a new resource, named MedMentions, for biomedical concept recognition, with a large manually annotated annotated corpus of over 4,000 abstracts targeting a very large fine-grained concept ontology consisting of over 3 million concepts. We also included in this release a targeted sub-corpus (MedMentions ST21pv), with standard training, development and test splits of the data, and the metrics of a baseline concept recognition model trained on this subset, to allow researchers to compare the metrics of their concept recognition models.",621,0.257,377,1.6472148541114058,"This paper the formal release {\em MedMentions a new manually annotated resource the recognition biomedical concepts What distinguishes MedMentions other annotated biomedical corpora its size over 350,000 linked mentions as the concept ontology (over 3 million concepts from UMLS 2017 its broad coverage In addition the full corpus a sub-corpus MedMentions presented comprising annotations UMLS 2017 targeted towards document retrieval To encourage research Biomedical Named Entity Recognition Linking data splits for training included, a baseline model and its metrics entity linking described One recognized challenge automated biomedical entity extraction systems richly annotated training datasets While there a few such datasets the annotated corpus often no more than a few thousand annotated entity mentions Additionally the annotated entities limited biomedical concepts diseases BID4 , gene terms Researchers targeting the recognition multiple biomedical entity types had resort combining datasets labelled subsets the full target set using multi-task learning BID3 , a modified Conditional Random Field cost which un-labeled tokens take any labels not BID5 To promote state entity linkers targeting a more comprehensive coverage biomedical concepts decided a large concept-mention annotated gold standard dataset named 'MedMentions' BID11 .With hope address two key needs developing better biomedical concept recognition systems a much broader coverage the fields biology through the Unified Medical Language System as the target ontology than available today meet forThe paper begins including a subcorpus aimed information retrieval systems This followed a few other large datasets annotated biomedical entities Finally , to promote further research large ontology named entity recognition linking present metrics a baseline end concept recognitionentity type recognition linking trained the MedMentions corpus We presented the formal release a new resource named MedMentions biomedical concept recognition with a large manually annotated annotated corpus targeting a very large fine-grained concept ontology consisting We also included in a targeted sub-corpus (MedMentions ST21pv with standard training, development test splits the data the metrics a baseline concept recognition model trained, allow researchers the metrics",0.0,0.35312575428433507
"In this paper we propose a Deep Autoencoder Mixture Clustering (DAMIC) algorithm. It is based on a mixture of deep autoencoders where each cluster is represented by an autoencoder. A clustering network transforms the data into another space and then selects one of the clusters. Next, the autoencoder associated with this cluster is used to reconstruct the data-point. The clustering algorithm jointly learns the nonlinear data representation and the set of autoencoders. The optimal clustering is found by minimizing the reconstruction loss of the mixture of autoencoder network. Unlike other deep clustering algorithms, no regularization term is needed to avoid data collapsing to a single point. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods. Effective automatic grouping of objects into clusters is one of the fundamental problems in machine learning and data analysis. In many approaches, the first step toward clustering a dataset is extracting a feature vector from each object. This reduces the problem to the aggregation of groups of vectors in a feature space. A commonly used clustering algorithm in this case is the k-means. Clustering high-dimensional datasets is, however, hard because inter-point distances become less informative in high-dimensional spaces. As a result, representation learning has been used to map the input data into a low-dimensional feature space. In recent years, motivated by the success of deep neural network in supervised learning, there are many attempts to apply unsupervised deep learning approaches for clustering. Most methods are focused on clustering over a low-dimensional feature space of an autoencoder or a variational autoencoder. Recent good overviews of deep clustering methods can be found in BID1 and BID14 .Using deep neural networks, it is possible to learn nonlinear mappings allowing to transform the data into more clustering-friendly representations. A deep version of k-means is based on learning a data representation and applying k-means in the embedded space. A straightforward implementation of the deep k-means algorithm would lead, however, to a trivial solution where the features are collapsed to a single point in the embedded space and the centroids are collapsed into a single entity. The objective function of most deep clustering algorithms is, therefore, composed of a clustering term computed in the embedded space and a regularization term in the form of reconstruction error to avoid data collapsing. Deep Embedded Clustering (DEC) BID16 ) is first pre-trained using an autoencoder reconstruction loss and then optimizes cluster centroids in the embedded space through a Kullback-Leibeler divergence loss. Deep Clustering network (DCN) BID17 ) is another autoencoder-based method that uses k-means for clustering. Similar to DEC, in the first phase, the network is pre-trained using the autoencoder reconstruction loss. In the second phase, in contrast to DEC, the network is jointly trained using a mathematical combination of the autoencoder reconstruction loss and the k-means clustering loss function. Thus, due to the fact that strict cluster assignments were used during the training (instead of probabilities such as in DEC) the method requires an alternation process between the network training and the cluster updates.In this paper we propose an algorithm to perform unsupervised clustering within the mixture-ofexperts framework BID8 ). Each cluster is represented by an autoencoder neuralnetwork and the clustering itself is performed in a low-dimensional embedded space by a softmax classification layer that directs the input data to the most suitable autoencoder. Unlike most deep clustering algorithms the proposed algorithm is deep in nature and not a deep variant of a classical clustering algorithm. The proposed algorithm does not suffer from the clustering collapsing problem and therefore there is no need for regularization terms that have to be tuned separately for each dataset. Note that parameter tuning in clustering is problematic since it is based, either explicitly or implicitly, on the data labels which are not supposed to be available in the clustering process. Another major difference of the proposed method from previous approaches is the learning method of the embedding latent space where the actual clustering operation is taking place. In most previous methods, the embedded space is controlled by an autoencoder. Thus, in order to gain a good reconstruction, it requires to encode into the embedded space information that can be entirely irrelevant to the clustering process. In contrast, in our algorithm no decoding is applied to the clustering embedded space and the only goal of the embedded space is to find a good organization of the data into separated clusters.We validate the method on standard real datasets including various document and image corpora. Evidently, visible improvement from the respective state-of-art is observed for all the tested datasets. The contribution of this paper is twofold: (i) a novel deep learning clustering method that unlike deep variants of k-means, does not require a tuned regularization term to avoid clustering collapsing to a single point; and (ii) state-of-the-art performance on standard datasets. In this study we presented a clustering technique which leverages the strength of deep neural network. Our technique has two major properties: first, unlike most previous methods, the clusters are represented by an autoencoder network instead of a single centroid vector in the embedded space. This enables a much richer representation of each cluster. Second, The algorithm does not cause a data collapsing problem. Hence, there is no need for regularization terms that have to be tuned for each dataset separately. Experiments on a variety of real datasets showed the improved performance of the proposed algorithm.",1084,0.653,637,1.7017268445839875,"In this paper a Deep Autoencoder Mixture Clustering It based a mixture deep autoencoders where each cluster represented A clustering network transforms another space selects Next the autoencoder associated this cluster reconstruct the data-point The clustering algorithm jointly learns the nonlinear data representation the set The optimal clustering is found minimizing the reconstruction loss the mixture autoencoder network. Unlike other deep clustering algorithms no regularization term avoid data collapsing to Our experimental evaluations on image and text corpora significant improvement state Effective automatic grouping objects clusters one In many approaches clustering extracting a feature vector each object This reduces the problem the aggregation groups vectors a feature space A commonly used clustering algorithm this case. Clustering high-dimensional datasets, hard because inter-point distances become less informative As representation learning used map the input data In motivated deep neural network in supervised learning there are apply for clustering Most methods focused clustering over of Recent good overviews deep clustering methods can BID1 .Using learn nonlinear mappings allowing transform more clustering-friendly representations A deep version k-means based learning a data representation applying the embedded space A straightforward implementation the deep k-means would lead, however a trivial solution where the features collapsed the embedded space the centroids collapsed The objective function most deep clustering algorithms, therefore composed a clustering term computed the embedded space reconstruction error to avoid data collapsing Deep Embedded Clustering (DEC) BID16 ) first pretrained an autoencoder reconstruction loss and optimizes cluster centroids the embedded space through a Kullback-Leibeler divergence loss Deep Clustering network (DCN) BID17 ) another autoencoder-based method k for Similar DEC in the network pretrained the autoencoder reconstruction loss. In in contrast DEC the network jointly trained using a mathematical combination the autoencoder reconstruction loss Thus due strict cluster assignments during (instead probabilities such DEC) the method requires an alternation process the network training the cluster updatesIn within the mixture-ofexperts framework BID8 ). Each cluster represented an autoencoder neuralnetwork itself performed a low-dimensional embedded space by a softmax classification layer that directs Unlike most deep clustering algorithms the proposed algorithm deep not a deep variant The proposed algorithm does suffer the clustering collapsing problem and therefore there regularization terms that tuned separately Note parameter tuning clustering problematic since based, either explicitly the data labels which supposed available Another major difference of the proposed method from previous approaches the learning method the embedding latent space where the actual clustering operation taking In most previous methods the embedded space controlled Thus gain a good reconstruction requires to encode into the embedded space information can entirely irrelevant In contrast our algorithm no decoding applied the clustering embedded space and the only goal a good organization into separated clustersWe validate the method on standard real datasets including various document and image corpora Evidently visible improvement from the respective state-of-art is observed for all the tested datasets The contribution this paper twofold a novel deep clustering method unlike deep variants a tuned regularization term avoid collapsing state performance standard datasets In presented which the strength deep neural network. Our technique two major properties unlike most previous methods the clusters represented instead a single centroid vector in the embedded space This enables a much richer representation each cluster Second The algorithm does cause a data collapsing problem Hence there regularization terms that tuned each dataset separately Experiments a variety real datasets showed the improved performance the proposed algorithm",0.01,0.49201751663735765
"We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure mu. We show that the Sobolev IPM compares two distributions in high dimensions based on weighted conditional Cumulative Distribution Functions (CDF) of each coordinate on a leave one out basis. The Dominant measure mu plays a crucial role as it defines the support on which conditional CDFs are compared. Sobolev IPM can be seen as an extension of the one dimensional Von-Mises Cramer statistics to high dimensional distributions. We show how Sobolev IPM can be used to train Generative Adversarial Networks (GANs). We then exploit the intrinsic conditioning implied by Sobolev IPM in text generation. Finally we show that a variant of Sobolev GAN achieves competitive results in semi-supervised learning on CIFAR-10, thanks to the smoothness enforced on the critic by Sobolev GAN which relates to Laplacian regularization. In order to learn Generative Adversarial Networks BID14 , it is now well established that the generator should mimic the distribution of real data, in the sense of a certain discrepancy measure. Discrepancies between distributions that measure the goodness of the fit of the neural generator to the real data distribution has been the subject of many recent studies BID1 BID36 BID20 BID30 BID17 , most of which focus on training stability.In terms of data modalities, most success was booked in plausible natural image generation after the introduction of Deep Convolutional Generative Adversarial Networks (DCGAN) BID39 . This success is not only due to advances in training generative adversarial networks in terms of loss functions and stable algorithms, but also to the representation power of convolutional neural networks in modeling images and in finding sufficient statistics that capture the continuous density function of natural images. When moving to neural generators of discrete sequences generative adversarial networks theory and practice are still not very well understood. Maximum likelihood pre-training or augmentation, in conjunction with the use of reinforcement learning techniques were proposed in many recent works for training GAN for discrete sequences generation BID50 BID40 . Other methods included using the Gumbel Softmax trick BID23 ) and the use of auto-encoders to generate adversarially discrete sequences from a continuous space BID51 . End to end training of GANs for discrete sequence generation is still an open problem BID38 . Empirical successes of end to end training have been reported within the framework of WGAN-GP BID17 , using a proxy for the Wasserstein distance via a pointwise gradient penalty on the critic. Inspired by this success, we propose in this paper a new Integral Probability Metric (IPM) between distributions that we coin Sobolev IPM. Intuitively an IPM BID35 between two probability distributions looks for a witness function f , called critic, that maximally discriminates between samples coming from the two distributions: DISPLAYFORM0 Traditionally, the function f is defined over a function class F that is independent to the distributions at hand BID48 . The Wasserstein-1 distance corresponds for instance to an IPM where the witness functions are defined over the space of Lipschitz functions; The MMD distance corresponds to witness functions defined over a ball in a Reproducing Kernel Hilbert Space (RKHS).We will revisit in this paper Fisher IPM defined in , which extends the IPM definition to function classes defined with norms that depend on the distributions. Fisher IPM can be seen as restricting the critic to a Lebsegue ball defined with respect to a dominant measure µ. The Lebsegue norm is defined as follows: DISPLAYFORM1 where µ is a dominant measure of P and Q.In this paper we extend the IPM framework to critics bounded in the Sobolev norm: DISPLAYFORM2 In contrast to Fisher IPM, which compares joint probability density functions of all coordinates between two distributions, we will show that Sobolev IPM compares weighted (coordinate-wise) conditional Cumulative Distribution Functions for all coordinates on a leave on out basis. Matching conditional dependencies between coordinates is crucial for sequence modeling.Our analysis and empirical verification show that the modeling of the conditional dependencies can be built in to the metric used to learn GANs as in Sobolev IPM. For instance, this gives an advantage to Sobolev IPM in comparing sequences over Fisher IPM. Nevertheless, in sequence modeling when we parametrize the critic and the generator with a neural network, we find an interesting tradeoff between the metric used and the architectures used to parametrize the critic and the generator as well as the conditioning used in the generator. The burden of modeling the conditional long term dependencies can be handled by the IPM loss function as in Sobolev IPM (more accurately the choice of the data dependent function class of the critic) or by a simpler metric such as Fisher IPM together with a powerful architecture for the critic that models conditional long term dependencies such as LSTM or GRUs in conjunction with a curriculum conditioning of the generator as done in BID38 . Highlighting those interesting tradeoffs between metrics, data dependent functions classes for the critic (Fisher or Sobolev) and architectures is crucial to advance sequence modeling and more broadly structured data generation using GANs.3. The intrinsic conditioning and the CDF matching make Sobolev IPM suitable for discrete sequence matching and explain the success of the gradient pernalty in WGAN-GP and Sobolev GAN in discrete sequence generation. 4. We give in Section 5 an ALM (Augmented Lagrangian Multiplier) algorithm for training Sobolev GAN. Similar to Fisher GAN, this algorithm is stable and does not compromise the capacity of the critic. 5. We show in Appendix A that the critic of Sobolev IPM satisfies an elliptic Partial Differential Equation (PDE). We relate this diffusion to the Fokker-Planck equation and show the behavior of the gradient of the optimal Sobolev critic as a transportation plan between distributions. 6. We empirically study Sobolev GAN in character level text generation (Section 6.1). We validate that the conditioning implied by Sobolev GAN is crucial for the success and stability of GAN in text generation. As a take home message from this study, we see that text generation succeeds either by implicit conditioning i.e using Sobolev GAN (or WGAN-GP) together with convolutional critics and generators, or by explicit conditioning i.e using Fisher IPM together with recurrent critic and generator and curriculum learning. 7. We finally show in Section 6.2 that a variant of Sobolev GAN achieves competitive semisupervised learning results on CIFAR-10, thanks to the smoothness implied by the Sobolev regularizer. We introduced the Sobolev IPM and showed that it amounts to a comparison between weighted (coordinate-wise) CDFs. We presented an ALM algorithm for training Sobolev GAN. The intrinsic conditioning implied by the Sobolev IPM explains the success of gradient regularization in Sobolev GAN and WGAN-GP on discrete sequence data, and particularly in text generation. We highlighted the important tradeoffs between the implicit conditioning introduced by the gradient regularizer in Sobolev IPM, and the explicit conditioning of Fisher IPM via recurrent critics and generators in conjunction with the curriculum conditioning. Both approaches succeed in text generation. We showed that Sobolev GAN achieves competitive semi-supervised learning results without the need of any normalization, thanks to the smoothness induced by the gradient regularizer. We think the Sobolev IPM point of view will open the door for designing new regularizers that induce different types of conditioning for general structured/discrete/graph data beyond sequences.",1600,0.765,930,1.7204301075268817,"We propose between distributions: IPM The Sobolev IPM compares the mean discrepancy functionscritic) restricted defined a dominant measure mu We show the Sobolev IPM compares two distributions high dimensions based weighted conditional Cumulative Distribution Functions each coordinate on leave one out The Dominant measure mu plays defines the support on conditional CDFs compared Sobolev IPM can seen the one dimensional Von-Mises Cramer statistics to high dimensional distributions We show Sobolev IPM train We then exploit the intrinsic conditioning implied Sobolev IPM text generation Finally show a variant Sobolev GAN achieves competitive results thanks smoothness enforced the critic by which relates learn Generative Adversarial Networks BID14 , now well the generator should mimic a certain discrepancy measure Discrepancies distributions that measure the goodness the neural generator has most training stabilityIn terms data modalities most success was booked plausible natural image generation after This success advances training generative adversarial networks terms loss functions stable algorithms the representation power modeling images finding sufficient statistics that capture the continuous density function When moving neural generators discrete sequences generative are still Maximum likelihood pre-training or were proposed many recent works for GAN for discrete sequences generation BID50 BID40 . Other methods included the Gumbel Softmax trick BID23 ) adversarially discrete sequences a continuous space BID51 End to training GANs discrete sequence generation is still BID38 . end to within WGAN-GP BID17 , a proxy the Wasserstein distance via a pointwise gradient penalty on the critic. Inspired this success propose in between distributions coin Sobolev IPM Intuitively an IPM BID35 between two probability distributions looks a witness function f called critic maximally samples coming DISPLAYFORM0 Traditionally over a function class F independent to at BID48 Wasserstein-1 distance corresponds for instance an IPM where the witness functions defined over Lipschitz functions; The MMD distance witness a ball in a Reproducing Kernel Hilbert Space revisit Fisher IPM defined , extends function classes with norms depend the distributions Fisher IPM can seen restricting the critic a Lebsegue ball defined with respect a dominant measure µ. The Lebsegue norm DISPLAYFORM1 where µ a dominant measure P Q.In paper extend the IPM framework critics bounded in In Fisher IPM compares joint probability density functions all coordinates show weighted ( conditional Cumulative Distribution Functions a leave on out basis Matching conditional dependencies coordinates crucial sequence modelingOur analysis and empirical verification the modeling built to the metric used learn GANs as in Sobolev IPM For instance this gives Sobolev IPM comparing sequences over Fisher IPM Nevertheless sequence modeling when the critic the generator metric used the architectures as the conditioning used The burden modeling the conditional long term dependencies can handled the IPM loss function in Sobolev IPMmore accurately choice the data dependent function class the critic a simpler metric Fisher IPM together a powerful architecture the critic models such GRUs conjunction a curriculum conditioning of the generator done BID38 Highlighting those interesting tradeoffs metrics data dependent functions classes for the criticFisher or architectures is crucial advance sequence modeling more broadly structured data generation using The intrinsic conditioning the CDF matching make Sobolev IPM suitable discrete sequence matching explain the gradient pernalty WGAN-GP in discrete sequence generation 4 We give in Section an ALM ( training Sobolev GAN Similar Fisher GAN this algorithm stable compromise the capacity the critic 5 We show the critic Sobolev IPM satisfies We relate this diffusion show the behavior the optimal Sobolev critic as a transportation plan between distributions 6 We empirically study Sobolev GAN character level text generationSection We validate the conditioning implied Sobolev GAN crucial and text generation As a take home message this study see that text generation succeeds either implicit conditioning using Sobolev GAN WGAN-GP together convolutional critics generators Fisher IPM together recurrent critic and curriculum learning 7 We finally show in Section a variant Sobolev GAN achieves competitive semisupervised learning results thanks smoothness implied We introduced the Sobolev IPM and showed amounts a comparison weighted (coordinate-wise) CDFs presented an ALM algorithm training The intrinsic conditioning implied the Sobolev IPM explains gradient regularization Sobolev GAN WGAN-GP on discrete sequence data particularly text generation We highlighted the implicit conditioning introduced the gradient regularizer Sobolev IPM Fisher IPM via recurrent critics generators conjunction the curriculum conditioning Both approaches succeed text generation We showed Sobolev GAN achieves competitive semi-supervised learning results thanks smoothness induced the gradient regularizer We think the Sobolev IPM point will open designing new regularizers induce different types conditioning general structured/discrete/graph data beyond sequences",0.01,0.5396717873651375
"We propose in this paper a new approach to train the Generative Adversarial Nets (GANs) with a mixture of generators to overcome the mode collapsing problem. The main intuition is to employ multiple generators, instead of using a single one as in the original GAN. The idea is simple, yet proven to be extremely effective at covering diverse data modes, easily overcoming the mode collapsing problem and delivering state-of-the-art results. A minimax formulation was able to establish among a classifier, a discriminator, and a set of generators in a similar spirit with GAN. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. The distinguishing feature is that internal samples are created from multiple generators, and then one of them will be randomly selected as final output similar to the mechanism of a probabilistic mixture model. We term our method Mixture Generative Adversarial Nets (MGAN). We develop theoretical analysis to prove that, at the equilibrium, the Jensen-Shannon divergence (JSD) between the mixture of generators’ distributions and the empirical data distribution is minimal, whilst the JSD among generators’ distributions is maximal, hence effectively avoiding the mode collapsing problem. By utilizing parameter sharing, our proposed model adds minimal computational cost to the standard GAN, and thus can also efficiently scale to large-scale datasets. We conduct extensive experiments on synthetic 2D data and natural image databases (CIFAR-10, STL-10 and ImageNet) to demonstrate the superior performance of our MGAN in achieving state-of-the-art Inception scores over latest baselines, generating diverse and appealing recognizable objects at different resolutions, and specializing in capturing different types of objects by the generators. Generative Adversarial Nets (GANs) BID10 are a recent novel class of deep generative models that are successfully applied to a large variety of applications such as image, video generation, image inpainting, semantic segmentation, image-to-image translation, and text-to-image synthesis, to name a few BID9 . From the game theory metaphor, the model consists of a discriminator and a generator playing a two-player minimax game, wherein the generator aims to generate samples that resemble those in the training data whilst the discriminator tries to distinguish between the two as narrated in BID10 . Training GAN, however, is challenging as it can be easily trapped into the mode collapsing problem where the generator only concentrates on producing samples lying on a few modes instead of the whole data space BID9 .Many GAN variants have been recently proposed to address this problem. They can be grouped into two main categories: training either a single generator or many generators. Methods in the former include modifying the discriminator's objective (Salimans et al., 2016; BID22 , modifying the generator's objective (Warde-Farley & Bengio, 2016) , or employing additional discriminators to yield more useful gradient signals for the generators (Nguyen et al., 2017; BID7 . The common theme in these variants is that generators are shown, at equilibrium, to be able to recover the data distribution, but convergence remains elusive in practice. Most experiments are conducted on toy datasets or on narrow-domain datasets such as LSUN (Yu et al., 2015) or CelebA BID20 . To our knowledge , only Warde-Farley & Bengio (2016) and Nguyen et al. (2017) perform quantitative evaluation of models trained on much more diverse datasets such as STL-10 (Coates et al., 2011) and ImageNet (Russakovsky et al., 2015) .Given current limitations in the training of single-generator GANs, some very recent attempts have been made following the multi-generator approach. Tolstikhin et al. (2017) apply boosting techniques to train a mixture of generators by sequentially training and adding new generators to the mixture. However, sequentially training many generators is computational expensive. Moreover, this approach is built on the implicit assumption that a single-generator GAN can generate very good images of some modes, so reweighing the training data and incrementally training new generators will result in a mixture that covers the whole data space. This assumption is not true in practice since current single-generator GANs trained on diverse datasets such as ImageNet tend to generate images of unrecognizable objects. BID2 train a mixture of generators and discriminators, and optimize the minimax game with the reward function being the weighted average reward function between any pair of generator and discriminator. This model is computationally expensive and lacks a mechanism to enforce the divergence among generators. BID8 train many generators by using a multi-class discriminator that, in addition to detecting whether a data sample is fake, predicts which generator produces the sample. The objective function in this model punishes generators for generating samples that are detected as fake but does not directly encourage generators to specialize in generating different types of data.We propose in this paper a novel approach to train a mixture of generators. Unlike aforementioned multi-generator GANs, our proposed model simultaneously trains a set of generators with the objective that the mixture of their induced distributions would approximate the data distribution, whilst encouraging them to specialize in different data modes. The result is a novel adversarial architecture formulated as a minimax game among three parties: a classifier, a discriminator, and a set of generators. Generators create samples that are intended to come from the same distribution as the training data, whilst the discriminator determines whether samples are true data or generated by generators, and the classifier specifies which generator a sample comes from. We term our proposed model as Mixture Generative Adversarial Nets (MGAN). We provide analysis that our model is optimized towards minimizing the Jensen-Shannon Divergence (JSD) between the mixture of distributions induced by the generators and the data distribution while maximizing the JSD among generators.Empirically, our proposed model can be trained efficiently by utilizing parameter sharing among generators, and between the classifier and the discriminator. In addition, simultaneously training many generators while enforcing JSD among generators helps each of them focus on some modes of the data space and learn better. Trained on CIFAR-10, each generator learned to specialize in generating samples from a different class such as horse, car, ship, dog, bird or airplane. Overall, the models trained on the CIFAR-10, STL-10 and ImageNet datasets successfully generated diverse, recognizable objects and achieved state-of-the-art Inception scores (Salimans et al., 2016) . The model trained on the CIFAR-10 even outperformed GANs trained in a semi-supervised fashion (Salimans et al., 2016; Odena et al., 2016) .In short, our main contributions are: (i) a novel adversarial model to efficiently train a mixture of generators while enforcing the JSD among the generators; (ii) a theoretical analysis that our objective function is optimized towards minimizing the JSD between the mixture of all generators' distributions and the real data distribution, while maximizing the JSD among generators; and (iii) a comprehensive evaluation on the performance of our method on both synthetic and real-world large-scale datasets of diverse natural scenes. We have presented a novel adversarial model to address the mode collapse in GANs. Our idea is to approximate data distribution using a mixture of multiple distributions wherein each distribution captures a subset of data modes separately from those of others. To achieve this goal, we propose a minimax game of one discriminator, one classifier and many generators to formulate an optimization problem that minimizes the JSD between P data and P model , i.e., a mixture of distributions induced by the generators, whilst maximizes JSD among such generator distributions. This helps our model generate diverse images to better cover data modes, thus effectively avoids mode collapse. We term our proposed model Mixture Generative Adversarial Network (MGAN).The MGAN can be efficiently trained by sharing parameters between its discriminator and classifier, and among its generators, thus our model is scalable to be evaluated on real-world largescale datasets. Comprehensive experiments on synthetic 2D data, CIFAR-10, STL-10 and ImageNet databases demonstrate the following capabilities of our model: (i) achieving state-of-the-art Inception scores; (ii) generating diverse and appealing recognizable objects at different resolutions; and (iv) specializing in capturing different types of objects by the generators. In our proposed method, generators G 1 , G 2 , ... G K are deep convolutional neural networks parameterized by θ G . These networks share parameters in all layers except for the input layers. The input layer for generator G k is parameterized by the mapping f θ G ,k (z) that maps the sampled noise z to the first hidden layer activation h. The shared layers are parameterized by the mapping g θ G (h) that maps the first hidden layer to the generated data. The pseudo-code of sampling from the mixture is described in Alg. 1. Classifier C and classifier D are also deep convolutional neural networks that are both parameterized by θ CD . They share parameters in all layers except for the last layer . The pseudo-code of alternatively learning θ G and θ CD using stochastic gradient descend is described in Alg. 2.Algorithm 1 Sampling from MGAN's mixture of generators. 1: Sample noise z from the prior P z . 2: Sample a generator index u from Mult (π 1 , π 2 , ..., π K ) with predefined mixing probability π = (π 1 , π 2 , ..., π K ). DISPLAYFORM0 Return generated data x and the index u.Algorithm 2 Alternative training of MGAN using stochastic gradient descent.1: for number of training iterations do 2:Sample a minibatch of M data points DISPLAYFORM1 Sample a minibatch of N generated data points ) and N indices (u 1 , u 2 , ..., u N ) from the current mixture. DISPLAYFORM2 4: DISPLAYFORM3 5: DISPLAYFORM4 Update classifier C and discriminator D by descending along their gradient: DISPLAYFORM5 Sample a minibatch of N generated data points ) and N indices (u 1 , u 2 , ..., u N ) from the current mixture. DISPLAYFORM6 8: DISPLAYFORM7 Update the mixture of generators G by ascending along its gradient: ∇ θ G L G . 10: end for B APPENDIX: PROOFS FOR SECTION 3.1 Proposition 1 FIG0 . For fixed generators G 1 , G 2 , ..., G K and mixture weights π 1 , π 2 , ..., π K , the optimal classifier C * = C * 1:K and discriminator D * for J (G, C, D) are: DISPLAYFORM8 Proof. The optimal D * was proved in Prop. 1 in BID9 . This section shows a similar proof for the optimal C * . Assuming that C * can be optimized in the functional space, we can calculate the functional derivatives of J (G, C, D)with respect to each C k (x) for k ∈ {2, ..., K} and set them equal to zero: DISPLAYFORM9 Setting DISPLAYFORM10 to 0 for k ∈ {2, ..., K}, we get: DISPLAYFORM11 DISPLAYFORM12 results from Eq. (6) due to the fact that DISPLAYFORM13 Reformulation of L (G 1:K ). Replacing the optimal C * and D * into Eq. (2), we can reformulate the objective function for the generator as follows: DISPLAYFORM14 The sum of the first two terms in Eq. FORMULA29 was shown in BID10 to be 2 · JSD (P data P model ) − log 4. The last term β{ * } of Eq. FORMULA29 is related to the JSD for the K distributions: DISPLAYFORM15 where H (P ) is the Shannon entropy for distribution P . Thus, L (G 1:K ) can be rewritten as: DISPLAYFORM16 Theorem 3 (Thm. 3 restated). If the data distribution has the form: DISPLAYFORM17 where the mixture components q k (x)(s) are well-separated, the minimax problem in Eq. (2) or the optimization problem in Eq. (3) has the following solution: DISPLAYFORM18 , and the corresponding objective value of the optimization problem in Eq. (3) DISPLAYFORM19 Proof. We first recap the optimization problem for finding the optimal G * : DISPLAYFORM20 The JSD in Eq. FORMULA30 is given by: DISPLAYFORM21 The i-th expectation in Eq. (9) can be derived as follows: DISPLAYFORM22 and the equality occurs if DISPLAYFORM23 = 1 almost everywhere or equivalently for almost every x except for those in a zero measure set, we have: DISPLAYFORM24 Therefore, we obtain the following inequality: DISPLAYFORM25 and the equality occurs if for almost every x except for those in a zero measure set, we have: DISPLAYFORM26 and we peak the minimum if p G k = q k , ∀k since this solution satisfies both DISPLAYFORM27 and the conditions depicted in Eq. (10). That concludes our proof.C APPENDIX: ADDITIONAL EXPERIMENTS DISPLAYFORM28 The true data is sampled from a 2D mixture of 8 Gaussian distributions with a covariance matrix 0.02I and means arranged in a circle of zero centroid and radius 2.0. We use a simple architecture of 8 generators with two fully connected hidden layers and a classifier and a discriminator with one shared hidden layer. All hidden layers contain the same number of 128 ReLU units. The input layer of generators contains 256 noise units sampled from isotropic multivariate Gaussian distribution N (0, I). We do not use batch normalization in any layer. We refer to Tab. 3 for more specifications of the network and hyperparameters. ""Shared"" is short for parameter sharing among generators or between the classifier and the discriminator . Feature maps of 8/1 in the last layer for C and D means that two separate fully connected layers are applied to the penultimate layer, one for C that outputs 8 logits and another for D that outputs 1 logit. Optimizer Adam(β 1 = 0.5, β 2 = 0.999) Weight, bias initialization N (µ = 0, σ = 0.02I), 0The effect of the number of generators on generated samples. Fig. 6 shows samples produced by MGANs with different numbers of generators trained on synthetic data for 25,000 epochs . The model with 1 generator behaves similarly to the standard GAN as expected. The models with 2, 3 and 4 generators all successfully cover 8 modes, but the ones with more generators draw fewer points scattered between adjacent modes. Finally, the model with 10 generators also covers 8 modes wherein 2 generators share one mode and one generator hovering around another mode. Figure 6: Samples generated by MGAN models trained on synthetic data with 2, 3, 4 and 10 generators. Data samples from the 8 Gaussians are in red, and generated data by each generator are in a different color.The effect of β on generated samples. To examine the behavior of the diversity coefficient β, Fig. 7 compares samples produced by our MGAN with 4 generators after 25,000 epochs of training with different values of β. Without the JSD force (β = 0), generated samples cluster around one mode. When β = 0.25, generated data clusters near 4 different modes. When β = 0.75 or 1.0, the JSD force is too strong and causes the generators to collapse, generating 4 increasingly tight clusters. When β = 0.5, generators successfully cover all of the 8 modes. DISPLAYFORM29 Figure 7: Samples generated by MGAN models trained on synthetic data with different values of diversity coefficient β. Generated data are in blue and data samples from the 8 Gaussians are in red.",3329,1.65,1894,1.7576557550158396,"We propose in train the Generative Adversarial Nets a mixture generators overcome the mode collapsing problem The main intuition employ multiple generators instead as in the original GAN The idea yet proven at covering diverse data modes easily overcoming the mode collapsing problem delivering state A minimax formulation was able establish among a classifier generators in a similar spirit with GAN Generators create samples intended come whilst determines true data generated generators specifies comes The distinguishing feature internal samples created multiple generators one randomly final output similar the mechanism We term our method Mixture Generative Adversarial Nets We develop theoretical analysis prove, the equilibrium the Jensen-Shannon divergence the mixture generators�� distributions the empirical data distribution minimal whilst among maximal hence effectively avoiding the mode collapsing problem By utilizing parameter sharing our proposed model adds minimal computational cost the standard GAN also efficiently We conduct extensive experiments synthetic 2D data natural image databases STL-10 demonstrate our MGAN in achieving state Inception scores over latest baselines generating diverse appealing recognizable objects at specializing capturing by the generators Generative Adversarial Nets BID10 are a recent novel class deep generative models successfully image, video generation image inpainting semantic segmentationimage synthesis . From the game theory metaphor the model consists a discriminator playing wherein aims samples resemble whilst distinguish as narrated BID10 . Training GAN, however challenging easily trapped the mode collapsing problem where the generator only concentrates producing samples lying a few modes instead BID9 .Many recently proposed They can grouped training either a single generator Methods in former include modifying the discriminator's objectiveSalimans 2016 BID22 , modifying (Warde-Farley & Bengio employing yield more useful gradient signals the generators . The common theme these variants generators shown, at equilibrium able recover the data distribution convergence remains practice Most experiments toy datasets narrow-domain datasets LSUNYu CelebA BID20 . To our knowledge , only Warde-Farley & Bengio2016 (2017 perform quantitative evaluation models trained much more diverse datasets such STL-10CoatesRussakovsky .Given current limitations single-generator GANs some very recent attempts following Tolstikhin et (2017 apply boosting techniques train a mixture generators by sequentially training and adding However sequentially training many generators computational expensive Moreover this approach built a single-generator GAN very good images some modes reweighing incrementally training new generators a mixture that covers This assumption since current single-generator GANs trained diverse datasets such ImageNet tend generate images unrecognizable objects BID2 train a mixture generators discriminators optimize the minimax game the reward function being the weighted average reward function between any pair This model computationally lacks a mechanism enforce the divergence among generators BID8 train many generators by a multi-class discriminator, detecting whether a data sample fake predicts produces The objective function in punishes generators samples detected fake but does directly encourage generators specializeWe in train a mixture Unlike aforementioned multi-generator GANs our proposed model simultaneously trains generators the objective that the mixture their induced distributions would approximate whilst encouraging them specialize different data modes The result a novel adversarial architecture formulated a minimax game among three parties a classifier generators Generators create samples intended come whilst determines true data generated generators specifies comes We term our proposed model Mixture Generative Adversarial Nets We provide analysis that our model optimized towards minimizing the Jensen-Shannon Divergence the mixture distributions induced the generators the data distribution while maximizing among generatorsEmpirically trained efficiently utilizing parameter sharing among between In addition simultaneously training many generators while enforcing JSD among generators helps each focus some modes the data space learn better Trained on CIFAR-10 each generator learned specialize generating samples a different class such horse car ship dog airplane Overall the models trained, STL-10 and ImageNet datasets successfully generated diverse, recognizable objects achieved state Inception scoresSalimans . The model trained even outperformed GANs trained inSalimans 2016 Odena .In short our main contributions efficiently a mixture generators while enforcing the JSD among theoretical analysis our objective function optimized towards between the mixture all generators' distributions generators comprehensive evaluation on of diverse natural scenes We presented a novel adversarial model address the mode collapse GANs Our idea approximate data distribution a mixture multiple distributions wherein captures modes separately To achieve propose a minimax game one discriminator many generators formulate the JSD between P data P model , distributions induced the generators whilst maximizes among such generator distributions This helps our model generate diverse images better cover data modes thus effectively avoids mode collapse We term our proposed model Mixture Generative Adversarial NetworkMGAN).The MGAN can efficiently trained sharing parameters its discriminator among thus scalable evaluated Comprehensive experiments synthetic 2D data CIFAR-10 STL-10 ImageNet databases demonstrate the following capabilities our model achieving state Inception scores generating diverse appealing recognizable objects ativ specializing capturing by the generators In our proposed method generators G 1 ... G K are parameterized �� G These networks share parameters in all layers except the input layers The input layer generator G k parameterized the mapping f �kz that the sampled noise z the first hidden layer activation h. The shared layers parameterized the mapping g �� G (h that the generated data The pseudocode sampling from the mixture described Alg. 1 Classifier C and also both parameterized �� CD They share parameters all layers except . The pseudocode alternatively learning �� G and �� CD using stochastic gradient descend is Alg. 2.Algorithm 1 Sampling from MGAN's mixture generators 1: Sample noise z from the prior P z 2: Sample a generator index u from Mult (π 1 ... predefined mixing probability �� = DISPLAYFORM0 Return generated data x and the index u.Algorithm 2 Alternative training MGAN using: for number do 2Sample a minibatch M data points generated ) and N indicesu 1 N from the current mixture DISPLAYFORM2 4 and discriminator D by descending along their gradient: a minibatch N generated data points ) N indicesu 1 ... N the current mixture DISPLAYFORM6 8: DISPLAYFORM7 Update the mixture generators G by ascending along its gradient: �� �� G L G . 10: end for B APPENDIX PROOFS SECTION Proposition FIG0 . For fixed generators G 1 ... K mixture weights � the optimal classifier C *:K and discriminator D for J (G DISPLAYFORM8 Proof. The optimal D * was proved Prop 1 in BID9 . This section shows a similar proof for the optimal C * . Assuming C * can optimized the functional space the functional derivatives JG D)with respect each C kx for { ... K set equal zero DISPLAYFORM9 Setting Eq due Reformulation L 1:K Replacing the optimal C * into Eq reformulate the objective function the generator DISPLAYFORM14 The sum FORMULA29 was shown BID10 2 · JSD (P data P model − log 4 The last term β{ * of FORMULA29 related the JSD for the K distributions: DISPLAYFORM15 where H (P ) distribution P Thus L (G 1:K can DISPLAYFORM16 Theorem 3Thm 3 restated). If the data distribution has the form DISPLAYFORM17 where the mixture components q k (x)(s well-separated, the minimax problem in Eq or optimization has the following solution , the corresponding objective value Proof We first recap the optimization problem finding * : DISPLAYFORM20 The JSD in Eq FORMULA30 given The i-th expectation (9 can derived and the equality occurs = almost everywhere or for almost x except those zero measure set we Therefore obtain for we peak the minimum if p G k = q k , ��k since this solution satisfies conditions depicted That concludes our proof.C APPENDIX DISPLAYFORM28 The true data sampled a 2D mixture 8 Gaussian distributions 0.02I and means arranged zero centroid radius a simple architecture 8 generators two fully connected hidden layers one shared hidden layer All hidden layers contain 128 ReLU units The input layer generators contains 256 noise units sampled isotropic multivariate N0 I We do use batch normalization any layer We refer Tab. 3 for more specifications of the network hyperparametersShared short parameter sharing among generators or between the classifier . Feature maps 8/1 in the last layer for C and means two separate fully connected layers applied one that outputs 8 logits Optimizer Adam(β 1 Weight, bias initialization N� = 0.02I 0The effect generators generated samples Fig 6 shows samples produced MGANs with different numbers generators trained synthetic data for . The model with 1 generator behaves the standard GAN as expected The models with 2, 3 and 4 generators all successfully cover 8 modes draw fewer points scattered between adjacent modes Finally the model with 10 generators also covers 8 modes wherein share one mode hovering Figure Samples generated MGAN models trained synthetic data with Data samples the 8 Gaussians in red generated data by each generatorThe effect β on generated samples. To examine the diversity coefficient β Fig 7 compares samples produced our MGAN with 4 generators after training different values β Without the JSD force (β generated samples cluster one mode When β = generated data clusters near 4 different modes. When β = or the JSD force too causes the generators collapse generating 4 increasingly tight clusters When β = generators successfully cover the 8 modes DISPLAYFORM29 Figure Samples generated MGAN models trained synthetic data with different values diversity coefficient β Generated data in blue and data samples from the 8 Gaussians",0.02,0.6345194665573748
"Allowing humans to interactively train artificial agents to understand language instructions is desirable for both practical and scientific reasons.   Though, given  the lack of sample efficiency in current learning methods, reaching this goal may require substantial research efforts. We introduce the BabyAI research platform, with the goal of supporting investigations towards including humans in the loop for grounded language learning. The BabyAI platform comprises an extensible suite of 19 levels of increasing difficulty. Each level gradually leads the agent towards acquiring a combinatorially rich synthetic language, which is a proper subset of English. The platform also provides a hand-crafted bot agent, which simulates a human teacher.   We report estimated amount of supervision required for training neural reinforcement and behavioral-cloning agents on some BabyAI levels. We put forward strong evidence that current deep learning methods are not yet sufficiently sample-efficient in the context of learning a language with compositional properties. How can a human train an intelligent agent to understand natural language instructions? We believe that this research question is important from both technological and scientific perspectives. No matter how advanced AI technology becomes, human users will likely want to customize their intelligent helpers to better understand their desires and needs. On the other hand, developmental psychology, cognitive science and linguistics study similar questions but applied to human children, and a synergy is possible between research in grounded language learning by computers and research in human language acquisition.In this work, we present the BabyAI research platform, whose purpose is to facilitate research on grounded language learning. In our platform we substitute a simulated human expert for a real human; yet our aspiration is that BabyAI-based studies enable substantial progress towards putting an actual human in the loop. The current domain of BabyAI is a 2D gridworld in which synthetic natural-looking instructions (e.g. ""put the red ball next to the box on your left"") require the agent to navigate the world (including unlocking doors) and move objects to specified locations. BabyAI improves upon similar prior setups BID16 BID7 BID41 by supporting simulation of certain essential aspects of the future human in the loop agent training: curriculum learning and interactive teaching. The usefulness of curriculum learning for training machine learning models has been demonstrated numerous times in the literature BID6 BID23 BID42 BID15 , and we believe that gradually increasing the difficulty of the task will likely be essential for achieving efficient humanmachine teaching, as in the case of human-human teaching. To facilitate curriculum learning studies, BabyAI currently features 19 levels in which the difficulty of the environment configuration and the complexity of the instruction language are gradually increased. Interactive teaching, i.e. teaching differently based on what the learner can currently achieve, is another key capability of human teachers. Many advanced agent training methods, including DAGGER BID28 , TAMER BID35 and learning from human preferences BID38 BID11 , assume that interaction between the learner and the teacher is possible. To support interactive experiments, BabyAI provides a bot agent that can be used to generate new demonstrations on the fly and advise the learner on how to continue acting.Arguably, the main obstacle to language learning with a human in the loop is the amount of data (and thus human-machine interactions) that would be required. Deep learning methods that are used in the context of imitation learning or reinforcement learning paradigms have been shown to be very effective in both simulated language learning settings BID25 BID16 and applications BID32 BID3 BID39 . These methods, however, require enormous amounts of data, either in terms of millions of reward function queries or hundreds of thousands of demonstrations. To show how our BabyAI platform can be used for sample efficiency research, we perform several case studies. In particular, we estimate the number of demonstrations/episodes required to solve several levels with imitation and reinforcement learning baselines. As a first step towards improving sample efficiency, we additionally investigate to which extent pretraining and interactive imitation learning can improve sample efficiency.The concrete contributions of this paper are two-fold. First, we contribute the BabyAI research platform for learning to perform language instructions with a simulated human in the loop. The platform already contains 19 levels and can easily be extended. Second, we establish baseline results for all levels and report sample efficiency results for a number of learning approaches. The platform and pretrained models are available online. We hope that BabyAI will spur further research towards improving sample efficiency of grounded language learning, ultimately allowing human-in-the-loop training. We present the BabyAI research platform to study language learning with a human in the loop. The platform includes 19 levels of increasing difficulty, based on a decomposition of tasks into a set of basic competencies. Solving the levels requires understanding the Baby Language, a subset of English with a formally defined grammar which exhibits compositional properties. The language is minimalistic and the levels seem simple, but empirically we have found them quite challenging to solve. The platform is open source and extensible, meaning new levels and language concepts can be integrated easily.The results in Section 4 suggest that current imitation learning and reinforcement learning methods scale and generalize poorly when it comes to learning tasks with a compositional structure. Hundreds of thousands of demonstrations are needed to learn tasks which seem trivial by human standards. Methods such as curriculum learning and interactive learning can provide measurable improvements in terms of sample efficiency, but, in order for learning with an actual human in the loop to become realistic, an improvement of at least three orders of magnitude is required.An obvious direction of future research to find strategies to improve sample efficiency of language learning. Tackling this challenge will likely require new models and new teaching methods. Approaches that involve an explicit notion of modularity and subroutines, such as Neural Module Networks BID1 or Neural Programmer-Interpreters BID27 , seem like a promising direction. It is our hope that the BabyAI platform can serve as a challenge and a benchmark for the sample efficiency of language learning for years to come.",1185,0.704,702,1.688034188034188,"Allowing humans interactively train artificial agents understand language instructions desirable Though, given sample efficiency current learning methods reaching substantial research efforts We introduce the BabyAI research platform with supporting investigations towards including humans the loop grounded language learning The BabyAI platform comprises an extensible suite 19 levels increasing difficulty Each level gradually leads the agent acquiring a combinatorially rich synthetic language a proper subset English The platform also a hand-crafted bot agent a human teacher We report estimated amount supervision training neural reinforcement and behavioral-cloning agents some BabyAI levels We put forward strong evidence current deep learning methods yet sampleefficient learning a language with compositional properties How a human train an intelligent agent understand natural language instructions We believe this research question from No advanced AI technology human users want customize their intelligent helpers better their desires On developmental psychology cognitive science and linguistics study similar questions but applied human children a synergy possible research grounded language by computersIn the BabyAI research platform whose purpose facilitate In our platform substitute a simulated human expert; yet our aspiration BabyAI-based studies enable substantial progress putting The current domain BabyAI a 2D gridworld in synthetic natural-looking instructions (put the red ball next require the agent navigate (including unlocking move specified BabyAI improves similar prior setups BID16 BID7 BID41 by supporting simulation certain essential aspects the future human in the loop agent training: curriculum learning interactive teaching The usefulness curriculum learning training machine learning models numerous BID6 BID23 BID42 BID15 , we gradually the task likely essential achieving efficient humanmachine teaching in human-human teaching To facilitate curriculum learning studies BabyAI currently features 19 levels in which the difficulty the environment configuration the instruction language gradually Interactive teaching, differently based can currently achieve another key capability human teachers Many advanced agent training methods DAGGER BID28 , TAMER BID35 learning from human preferences BID38 BID11 assume interaction possible To support interactive experiments BabyAI a bot agent new demonstrations on advise continue actingArguably language with a human in the loop ( would Deep learning methods the context imitation learning or both simulated language learning settings BID25 BID16 applications . These methods, enormous amounts either millions reward function queries demonstrations To show our BabyAI platform sample efficiency research perform several case studies In particular estimate demonstrations/episodes required solve several levels with imitation reinforcement baselines As improving sample efficiency additionally investigate to pretraining interactive imitationThe concrete contributions two First contribute the BabyAI research platform learning perform language instructions a simulated human in the loop The platform already contains 19 levels easily extended Second establish baseline results all levels and report sample efficiency results a number learning approaches The platform and pretrained models available online We hope BabyAI spur towards improving sample efficiency of grounded language learning ultimately humanin training We present the BabyAI research platform study language with a human in the loop The platform includes 19 levels increasing difficulty based a decomposition tasks into basic competencies Solving the levels requires understanding the Baby Language a subset English with a formally defined grammar which exhibits compositional properties The language minimalistic the levels seem empirically them quite solve The platform extensible new levels and language concepts integratedThe results in Section suggest current imitation learning and scale and generalize poorly tasks a compositional structure Hundreds of thousands demonstrations needed learn tasks which seem trivial by Methods such curriculum learning interactive learning measurable improvements terms sample efficiency, learning with an actual human in the loop realistic an improvement ofAn obvious direction to find strategies of. Tackling this challenge likely new models new teaching methods Approaches that involve an explicit notion modularity Neural Module Networks BID1 , seem like It the BabyAI platform serve a challenge the sample efficiency language for years",0.01,0.45712983077211916
"Recently, there has been growing interest in methods that perform neural network compression, namely techniques that attempt to substantially reduce the size of a neural network without significant reduction in performance. However, most existing methods are post-processing approaches in that they take a learned neural network as input and output a compressed network by either forcing several parameters to take the same value (parameter tying via quantization) or pruning irrelevant edges (pruning) or both. In this paper, we propose a novel algorithm that jointly learns and compresses a neural network. The key idea in our approach is to change the optimization criteria by adding $k$ independent Gaussian priors over the parameters and a sparsity penalty. We show that our approach is easy to implement using existing neural network libraries, generalizes L1 and L2 regularization and elegantly enforces parameter tying as well as pruning constraints. Experimentally, we demonstrate that our new algorithm yields state-of-the-art compression on several standard benchmarks with minimal loss in accuracy while requiring little to no hyperparameter tuning as compared with related, competing approaches. Neural networks represent a family of highly flexible and scalable models that have rapidly achieved state-of-the-art performance in diverse domains including computer vision BID18 BID8 BID14 , speech BID5 , and sentiment analysis BID10 . Despite their successes, the storage requirements of large, modern neural networks make them impractical for certain applications with storage limitations (e.g., mobile devices). Moreover, as they are often trained on small datasets compared to their number of parameters (typically in the millions for state-of-the-art models), they can potentially overfit. In recent work, BID6 showed that a large proportion of neural network parameters are in fact not required for their generalization performance, and interest in model compression has surged.A variety of methods have been proposed to perform compression including pruning BID20 BID12 , quantization BID13 , lowrank approximation BID6 BID7 BID16 , group lasso BID27 , variational dropout BID23 , teacher-student training BID25 , etc. Here, we focus on the quantization/parameter tying approach to compression combined with pruning. Parameter tying assumptions occur naturally in the construction of convolutional neural networks (CNNs), but in these applications, the parameters to be tied are usually selected in advance of training. Recent work has focused on automatic parameter tying, i.e., automatically discovering which parameters of the model should be tied together. BID24 proposed a soft parameter tying scheme based on a mixtures of Gaussians prior and suggested a gradient descent method to jointly optimize both the weights in the network and the parameters of the mixture model. proposed a random parameter tying scheme based on hashing functions. BID13 proposed a compression pipeline that involved thresholding to prune low-magnitude parameters, k-means clustering to tie parameters layer-wise, and a final retraining stage to fine-tune tied parameters. This work demonstrated that high compression rates are achievable without much loss in accuracy. Building on the work of BID24 , K. Ullrich (2017) imposed a Gaussian mixture prior on the parameters to encourage clustering. At convergence, they proposed clustering the weights by assigning them to the mixture component that generates each weight with highest probability. BID22 proposed a full Bayesian approach to compression using scale mixture priors. This approach has the advantage that posterior distributions can be used to estimate the significance of individual bits in the learned weights. BID22 demonstrated that this approach can yield state-of-the-art compression results for some problems. BID1 recently proposed a soft-to-hard quantization approach in which scalar quantization is gradually learned through annealing a softened version of quantization distortion; compression is achieved with low-entropy parameter distribution instead of pruning.While much of the previous work has demonstrated that significant compression can be achieved while preserving the accuracy of the final network (in many cases ≈ 1% loss in accuracy), many of these approaches have potential drawbacks that can limit their applications. The Gaussian mixture approach of BID24 and K. Ullrich (2017) can be computationally expensive, as the time and memory requirements for backpropagation is increased K-fold under a K-component GMM prior, in addition to its large number of sensitive hyperparameters that can require extensive tuning. Moreover, the GMM objective itself suffers from well known local (and often pathological) minima issues. These local minimas are in addition to the ones encountered while training a neural network which in turn incurs high computational cost. The approach of BID13 uses separate pruning and parameter tying stages, which potentially limits its compression efficiency; additionally, the required layer-wise codebook storage can become expensive especially for deep networks. The parameter tying approach of is also only applied layerwise, and it typically requires more clusters, i.e., larger K, before the random weight sharing is effective (our experiments confirm that random parameter tying yields poor results when the number of distinct parameters is too small). The soft-to-hard quantization approach of BID1 resembles our method, but is essentially probabilistic like the GMM prior as it uses soft assignment for quantization which can be expensive. Finally, the full Bayesian approach, similar to the GMM approach, has a number of additional parameters to tune (e.g., constraints on variances, careful initialization of each of the variational parameters, etc.). The Bayesian approach also requires sampling for prediction (which can be done deterministically but with some additional loss). We hope to argue that such sophisticated methods may not be necessary to achieve good compression in practice.The approach to compression in this work uses quantization and sparsity inducing priors. For quantization, we consider an independent Gaussian prior, that is, each parameter is non-probabilistically assigned to one of K independent Gaussian distributions, and the prior penalizes each weight by its 2 distance to the mean of its respective Gaussian. This prior places no restriction on which weights can be tied together (e.g., weights from the input could be tied to weights into the output), reduces the number of hyperparameters that need to be tuned compared to probabilistic methods like Gaussian mixtures, and requires only a small change to the typical gradient descent updates with only linear time and memory overhead. We observe that quantization alone is not enough to achieve the desired level of compression, and introduce pruning by adding a standard 1 penalty on top of the quantization prior; we demonstrate experimentally that the combined prior yields state-of-the-art compression results on standard benchmark data sets.",1290,0.857,764,1.6884816753926701,"Recently there growing methods perform neural network compression namely techniques attempt substantially without significant reduction However most existing methods post-processing approaches in a learned neural network output a compressed network by either forcing several parameters takeparameter tying via quantization pruning irrelevant edges) or both In jointly learns compresses The key idea our approach change the optimization criteria $k$ independent Gaussian priors over a sparsity penalty We show our approach easy existing neural network libraries generalizes L1 and L2 regularization elegantly enforces parameter tying as pruning constraints Experimentally demonstrate our new algorithm yields state compression on several standard benchmarks with minimal loss accuracy while requiring as related, competing approaches Neural networks represent a family highly flexible and scalable models have rapidly achieved state computer vision BID18 BID8 BID14 , sentiment Despite their successes the storage requirements large, modern neural networks make certain applications with storage limitations ( Moreover as they trained small datasets compared their number parameterstypically for state models potentially overfit. In recent work BID6 showed neural network parameters in not required their generalization performance interest model compression surgedA variety methods perform including pruning BID20 BID12 quantization lowrank approximation group lasso etc Here, focus the quantization/parameter tying approach compression combined pruning Parameter tying assumptions occur naturally the construction these applications to selected Recent work focused automatic parameter tying automatically discovering of together BID24 proposed a soft parameter tying scheme based a mixtures Gaussians prior suggested jointly optimize both the weights in the mixture model proposed a random parameter tying scheme based hashing functions BID13 proposed a compression pipeline involved thresholding to prune low-magnitude parameters tie parameters layer a final retraining stage This work demonstrated high compression rates achievable much loss accuracy Building BID24 , K. Ullrich (2017 imposed a Gaussian mixture prior on the parameters to encourage At convergence they proposed clustering the weights by assigning the mixture component that generates with highest probability BID22 proposed a full Bayesian approach compression scale mixture priors This approach posterior distributions individual bits the learned weights BID22 demonstrated this approach yield state compression results some problems BID1 recently proposed a soft-to-hard quantization approach gradually learned through annealing a softened version quantization distortion; compression achieved low-entropy parameter distribution instead pruningWhile much demonstrated significant compression while the accuracy the final networkin � 1 loss accuracy many potential drawbacks The Gaussian mixture approach of BID24 K. Ullrich (2017 can computationally the time and memory requirements is increased K under a K-component GMM prior, in its large number sensitive hyperparameters that require extensive tuning Moreover the GMM objective itself suffers well known local (and often pathological) minima issues These local minimas in addition encountered while training a neural network which in incurs high computational cost The approach BID13 uses separate pruning parameter tying stages potentially limits its compression efficiency; additionally the required layer-wise codebook storage can become expensive especially deep networks The parameter tying approach of is also only applied layerwise typically more clusters, before the random weight sharingour experiments confirm random parameter yields poor when distinct parameters The soft-to-hard quantization approach BID1 resembles our method essentially like the GMM prior as soft assignment for which expensive Finally the full Bayesian approach similar the GMM approach a number additional parameters tune variances careful initialization each of The Bayesian approach also requires sampling for prediction (which but with some additional loss We hope argue such sophisticated methods may good compression practiceThe approach this work uses quantization sparsity inducing priors For quantization consider independent Gaussian prior that each parameter non assigned K independent Gaussian distributions the prior penalizes each weight by its 2 distance to This prior places no restriction which weights tied ( weights the input could into reduces hyperparameters tuned compared probabilistic methods like Gaussian mixtures requires the typical gradient descent updates with only linear time memory overhead We observe quantization alone achieve compression introduce pruning by a standard 1 penalty top prior; demonstrate experimentally combined prior yields state results on standard benchmark data sets",0.01,0.4582699892457221
"The application of stochastic variance reduction to optimization has shown remarkable recent theoretical and practical success. The applicability of these techniques to the hard non-convex optimization problems encountered during training of modern deep neural networks is an open problem. We show that naive application of the SVRG technique and related approaches fail, and explore why. Stochastic variance reduction (SVR) consists of a collection of techniques for the minimization of finite-sum problems: DISPLAYFORM0 such as those encountered in empirical risk minimization, where each f i is the loss on a single training data point. Principle techniques include SVRG BID15 , SAGA BID7 , and their variants. SVR methods use control variates to reduce the variance of the traditional stochastic gradient descent (SGD) estimate f i (w) of the full gradient f (w). Control variates are a classical technique for reducing the variance of a stochastic quantity without introducing bias. Say we have some random variable X. Although we could use X as an estimate of E[X] =X, we can often do better through the use of a control variate Y . If Y is a random variable correlated with X (i.e. Cov[X, Y ] > 0), then we can estimateX with the quantity Remarkably, these methods are able to achieve linear convergence rates for smooth strongly-convex optimization problems, a significant improvement on the sub-linear rate of SGD. SVR methods are part of a larger class of methods that explicitly exploit finite-sum structures, either by dual (SDCA, BID25 MISO, Mairal, 2014; Finito, Defazio et al., 2014b) or primal (SAG, Schmidt et al., 2017) approaches. DISPLAYFORM1 Recent work has seen the fusion of acceleration with variance reduction BID26 ; BID21 ; BID6 ; BID1 ), and the extension of SVR approaches to general non-convex BID2 BID23 as well as saddle point problems BID3 .In this work we study the behavior of variance reduction methods on a prototypical non-convex problem in machine learning: A deep convolutional neural network designed for image classification. We discuss in Section 2 how standard training and modeling techniques significantly complicate the application of variance reduction methods in practice, and how to overcome some of these issues. In Sections 3 & 5 we study empirically the amount of variance reduction seen in practice on modern CNN architectures, and we quantify the properties of the network that affect the amount of variance reduction. In Sections 6 & 7 we show that streaming variants of SVRG do not improve over regular SVRG despite their theoretical ability to handle data augmentation. In Section 8 we study properties of DNN problems that actually give stochastic gradient descent an advantage over variance reduction techniques. The negative results presented here are disheartening, however we don't believe that they rule out the use of stochastic variance reduction on deep learning problems. Rather, they suggest avenues for further research. For instance, SVR can be applied adaptively; or on a meta level to learning rates; or scaling matrices; and can potentially be combined with methods like Adagrad BID9 and ADAM BID17 to yield hybrid methods.",653,0.359,363,1.7988980716253444,"The application stochastic variance reduction optimization has shown remarkable recent theoretical and practical success The applicability these techniques the hard non-convex optimization problems encountered during training an open problem We show naive application the SVRG technique and related approaches fail, explore Stochastic variance reduction consists a collection techniques the minimization finite-sum problems: DISPLAYFORM0 such those encountered empirical risk minimization where each f i the loss on a single training data point Principle techniques include SVRG BID15 , their variants SVR methods use control variates reduce estimate f iw f Control variates a classical technique reducing without bias Say we some random variable X. Although we could X as an estimate E[X =X often do through a control variate Y . If Y is correlated X ] > estimateX the quantity Remarkably these methods able achieve linear convergence rates smooth strongly-convex optimization problems a significant improvement the sub-linear rate SGD SVR methods part explicitly exploit finite-sum structures either dual (SDCA BID25 MISO Mairal 2014 Finito Defazio primalSAG 2017 DISPLAYFORM1 Recent work seen the fusion acceleration variance reduction BID26 ; ), the extension SVR approaches as saddle point problems BID3 .In study variance reduction methods machine learning: designed image classification We discuss in Section standard training modeling significantly complicate variance reduction methods practice overcome some In Sections study empirically the amount variance reduction seen practice on modern CNN architectures quantify the properties affect In Sections & streaming variants SVRG do improve over despite their theoretical ability handle data augmentation In Section we study properties DNN problems actually give variance reduction techniques The negative results presented however we do rule stochastic variance reduction on deep learning problems Rather suggest avenues For instance SVR can applied adaptively; or on a meta level to learning rates scaling matrices can potentially combined methods Adagrad BID9 yield hybrid methods",0.0,0.7396012657680755
"The ground-breaking performance obtained by deep convolutional neural networks (CNNs) for image processing tasks is inspiring research efforts attempting to extend it for 3D geometric tasks. One of the main challenge in applying CNNs to 3D shape analysis is how to define a natural convolution operator on non-euclidean surfaces. In this paper, we present a method for applying deep learning to 3D surfaces using their spherical descriptors and alt-az anisotropic convolution on 2-sphere. A cascade set of geodesic disk filters rotate on the 2-sphere and collect spherical patterns and so to extract geometric features for various 3D shape analysis tasks. We demonstrate theoretically and experimentally that our proposed method has the possibility to bridge the gap between 2D images and 3D shapes with the desired rotation equivariance/invariance, and its effectiveness is evaluated in applications of non-rigid/ rigid shape classification and shape retrieval. A recent research effort in computer vision and geometric processing communities is towards replicating the incredible success of deep convolutional neural networks (CNNs) from the image analysis to 3D shape analysis. A straightforward extension is to treat a 3D shape as a voxel grid BID38 ; BID16 ; BID30 ; BID36 ; BID22 . ) Alternative methods include encoding a 3D shape as a collection of 2D renderings from multiple cameras BID20 ; BID31 ; ,) or projecting a 3D object onto geometric entities which can be flattened as 2D images BID27 ; BID4 ; BID25 . ) All these methods convert a 3D shape into an Euclidean grid structure which supports shift (translational) equivariance/invariance, such that conventional CNNs can work out-of-the box.Although embedded in R 3 , 3D shapes are typically represented as manifold surfaces. Recent research has particularly focused on convolutional networks for non-Euclidean domains such as manifolds or graphs. One of the main difficulties of adopting CNNs and similar methods in these nonEuclidean domains is the lack of shift-invariance on surfaces or graphs BID15 . ) Our motivation comes from the representation of 3D shapes as functions on spheres. We transfer the problem of manifold surface convolution into spherical convolution with the primary benefit of rotation invariance. Although shift-invariance is hard to achieve on general surfaces, by replacing filter translations with filter rotations, rotation equivariance/invariance can be obtained on the 2-sphere. Furthermore, spherical descriptors of 3D shapes are compact and require a network of lower capacity, compared to voxel or multi-view representations. In this work, we are primarily interested in analyzing 3D geometric data using a specific type of spherical convolution either for classification or retrieval tasks. In this paper, we presented and analyzed a convolutional neural network based on alt-az anisotropic spherical convolution operator which is different from the existing types of networks. Numerically, we implemented an efficient algorithm for computing spherical convolution with locally-supported geodesic filters using icosahedron-sphere grid. We demonstrated the efficacy of our approach for non-rigid/ rigid shape classification and retrieval and showed that it compares favorably to competing methods. Furthermore, we have shown that the proposed method can effectively generalize across rotations, and achieve state-of-the-art results on competitive 3D shape recognition tasks, without excessive data augmentation, feature engineering and task-tuning.",688,0.38,394,1.7461928934010151,"The ground-breaking performance obtained for inspiring research efforts attempting extend for 3D geometric tasks One the main challenge applying CNNs 3D shape analysis define a natural convolution operator on In applying deep learning 3D surfaces their spherical descriptors alt-az anisotropic convolution on 2-sphere. A cascade set geodesic disk filters rotate and collect spherical patterns and so to extract geometric features for various 3D shape analysis tasks We demonstrate theoretically and our proposed method has bridge 2D images the desired rotation equivariance/invariance its effectiveness evaluated applications non-rigid/ rigid shape classification and shape retrieval A recent research effort computer vision geometric processing communities towards replicating the incredible success from the image analysis to A straightforward extension is treat BID38 ; BID16 ) Alternative methods include encoding from BID20 ; ,) or projecting geometric entities which flattened as . ) All these methods convert which supports shift (translational) equivariance/invariance such conventional CNNs work-Although embedded R 3 typically represented manifold surfaces Recent research particularly graphs One adopting CNNs similar methods these nonEuclidean domains shift-invariance on surfaces or graphs BID15 . ) Our motivation comes the representation 3D shapes functions on spheres We transfer the problem manifold surface convolution spherical convolution with the primary benefit rotation invariance Although shift-invariance hard achieve general surfaces by replacing filter translations filter rotations rotation equivariance/invariance obtained on the 2-sphere Furthermore spherical descriptors compact require a network lower capacity compared or In this work primarily analyzing 3D geometric data a specific type spherical convolution either classification or retrieval tasks In presented and alt-az anisotropic spherical convolution operator which different the existing types networks Numerically implemented computing spherical convolution with locally-supported geodesic filters icosahedron-sphere grid We demonstrated our approach non-rigid/ rigid shape classification retrieval and showed compares competing methods Furthermore shown the proposed method can effectively generalize across rotations achieve state competitive 3D shape recognition tasks without excessive data augmentation feature engineering task-tuning",0.0,0.6053131022788116
"Recent breakthroughs in computer vision make use of large deep neural networks, utilizing the substantial speedup offered by GPUs. For applications running on limited hardware, however, high precision real-time processing can still be a challenge.   One approach to solving this problem is training networks with binary or ternary weights, thus removing the need to calculate multiplications and significantly reducing memory size. In this work, we introduce LR-nets (Local reparameterization networks), a new method for training neural networks with discrete weights using stochastic parameters. We show how a simple modification to the local reparameterization trick, previously used to train Gaussian distributed weights, enables the training of discrete weights. Using the proposed training we test both binary and ternary models on MNIST, CIFAR-10 and ImageNet benchmarks and reach state-of-the-art results on most experiments. Deep Neural Networks have been the main driving force behind recent advancement in machine learning, notably in computer vision applications. While deep learning has become the standard approach for many tasks, performing inference on low power and constrained memory hardware is still challenging. This is especially challenging in autonomous driving in electric vehicles where high precision and high throughput constraints are added on top of the low power requirements.One approach for tackling this challenge is by training networks with binary {±1} or ternary {−1, 0, 1} weights BID0 BID15 that require an order of magnitude less memory and no multiplications, leading to significantly faster inference on dedicated hardware. The problem arises when trying to backpropagate errors as the weights are discrete. One heuristic suggested in BID0 is to use stochastic weights w, sample binary weights w b according to w for the forward pass and gradient computation and then update the stochastic weights w instead. Another idea, used by BID5 and BID15 , is to apply a ""straight-through"" estimator ∂sign ∂r = r1[|r| ≤ 1]. While these ideas were able to produce good results, even on reasonably large networks such as ResNet-18 BID4 , there is still a large gap in prediction accuracy between the full-precision network and the discrete networks.In this paper, we attempt to train neural networks with discrete weights using a more principled approach. Instead of trying to find a good ""derivative"" to a non-continuous function, we show how we can find a good smooth approximation and use its derivative to train the network. This is based on the simple observation that if at layer l we have stochastic (independent) weights w (CLT) . This allows us to model the pre-activation using a smooth distribution and use the reparameterization trick BID9 to compute derivatives. The idea of mod-eling the distribution of pre-activation, instead of the distribution of weights, was used in for Gaussian weight distributions where it was called the local reparameterization trick. We show here that with small modifications it can be used to train discrete weights and not just continuous Gaussian distributions. DISPLAYFORM0 Figure 1: The top histogram in each subfigure shows the pre-activation of a random neuron, z l i , which is calculated in a regular feed-forward setting when explicitly sampling the weights. The bottom shows samples from the approximated pre-activation using Lyapunov CLT. (a) refers to the first hidden layer whereas (b) refers to the last. We can see the approximation is very close to the actual pre-activation when sampling weights and performing standard feed-forward. In addition, we see it even holds for the first hidden layer, where the number of elements is not large (in this example, 27 elements for a 3 × 3 × 3 convolution).We experimented with both binary and ternary weights, and while the results on some datasets are quite similar, ternary weights were considerably easier to train. From a modeling perspective restricting weights to binary values {±1} forces each neuron to affect all neurons in the subsequent layer making it hard to learn representations that need to capture several independent features.In this work, we present a novel and simple method for training neural networks with discrete weights. We show experimentally that we can train binary and ternary networks to achieve stateof-the-art results on several datasets, including ResNet-18 on ImageNet, compared to previously proposed binary or ternary training algorithms. On MNIST and CIFAR-10 we can also almost match the performance of the original full-precision network using discrete weights. In this work we presented a simple, novel and effective algorithm to train neural networks with discrete weights. We showed results on various image classification datasets and reached state-ofthe-art results in both the binary and ternary settings on most datasets, paving the way for easier and more efficient training and inference of efficient low-power consuming neural networks.Moreover, comparing binary and ternary networks we advocate further research into ternary weights as a much more reasonable model than binary weights, with a modest computation and memory overhead. Further work into sparse ternary networks might help reduce, or even eliminate, this overhead compared to binary networks.",1021,0.574,576,1.7725694444444444,"Recent breakthroughs make use utilizing the substantial speedup offered For applications running limited hardware however still One approach solving training networks binary or ternary weights thus removing calculate multiplications significantly memory size In this work introduce LR-netsLocal reparameterization networks training discrete weights using We show a simple modification the local reparameterization trick, previously train Gaussian distributed weights enables discrete weights Using the proposed training we test both binary and ternary models MNIST ImageNet benchmarks reach state most experiments Deep Neural Networks have recent advancement notably While deep learning many tasks performing inference low power constrained memory hardware This especially challenging autonomous driving in electric vehicles where high precision high throughput constraints added onOne approach tackling training networks binary {±1, 0 weights BID0 BID15 that require an order no multiplications leading significantly faster inference on dedicated hardware The problem arises trying backpropagate errors as the weights discrete One heuristic suggested BID0 stochastic weights w sample binary weights according w for the forward pass and gradient computation update instead Another idea used BID5 , apply a ""straight-through"" estimator ��sign ��r = r1[|r| ≤ While these ideas able produce even on reasonably large networks ResNet-18 BID4 , prediction accuracyIn attempt train discrete weights a more principled approach Instead trying find show find a good smooth approximation and its derivative train the network This based the simple observation at layer l (independent) weights w (CLT . This allows model the pre-activation using a smooth distribution use the reparameterization trick BID9 compute derivatives The idea mod-eling the distribution preactivation, instead weights used for Gaussian weight distributions where called the local reparameterization trick We show here with small modifications train discrete weights not just continuous Gaussian distributions DISPLAYFORM0 Figure The top histogram in each subfigure the preactivation a random neuron z l i which calculated a regular feed-forward setting when explicitly sampling the weights The bottom shows samples the approximated pre-activation using Lyapunov CLT (a refers the first hidden layer whereas. We the approximation is the actual preactivation when sampling weights performing standard feed. In addition see it even holds for the first hidden layer largein 27 elements for 3 × × 3 convolution).We experimented while on some datasets considerably easier train From a modeling perspective restricting weights binary values {±1} forces each neuron affect all neurons the subsequent layer making learn representations need capture several independent featuresIn and We show experimentally we train binary and ternary networks achieve several datasets ResNet-18 on compared On MNIST and CIFAR-10 we can also almost match the original full-precision network using discrete weights In this work presented train discrete weights We showed results various image classification datasets reached state-ofthe-art results on most datasets paving efficient low-power consuming neural networksMoreover comparing advocate further research a much more reasonable model a modest computation memory Further work into sparse ternary networks might reduce, overhead compared binary networks",0.01,0.6725182369190337
"We present Optimal Completion Distillation (OCD), a training procedure for optimizing sequence to sequence models based on edit distance. OCD is efficient, has no hyper-parameters of its own, and does not require pre-training or joint optimization with conditional log-likelihood. Given a partial sequence generated by the model, we first identify the set of optimal suffixes that minimize the total edit distance, using an efficient dynamic programming algorithm.   Then, for each position of the generated sequence, we use a target distribution which puts equal probability on the first token of all the optimal suffixes. OCD achieves the state-of-the-art performance on end-to-end speech recognition, on both Wall Street Journal and Librispeech datasets, achieving $9.3\%$ WER and $4.5\%$ WER, respectively. Recent advances in natural language processing and speech recognition hinge on the development of expressive neural network architectures for sequence to sequence (seq2seq) learning BID54 BID1 . Such encoder-decoder architectures are adopted in both machine translation BID1 BID24 and speech recognition systems BID7 BID2 BID11 achieving impressive performance above traditional multi-stage pipelines BID29 BID41 . Improving the building blocks of seq2seq models can fundamentally advance machine translation and speech recognition, and positively impact other domains such as image captioning BID62 , parsing , summarization BID47 , and program synthesis BID65 .To improve the key components of seq2seq models, one can either design better architectures, or develop better learning algorithms. Recent architectures using convolution BID20 and self attention BID57 have proved to be useful, especially to facilitate efficient training. On the other hand, despite many attempts to mitigate the limitations of Maximum Likelihood Estimation (MLE) BID43 BID60 BID4 BID30 , MLE is still considered the dominant approach for training seq2seq models. Current alternative approaches require pre-training or joint optimization with conditional log-likelihood. They are difficult to implement and require careful tuning of new hyper-parameters (e.g. mixing ratios). In addition , alternative approaches typically do not offer a substantial performance improvement over a well tuned MLE baseline, especially when label smoothing BID40 BID18 and scheduled sampling are used.In this paper, we borrow ideas from search-based structured prediction BID15 BID46 and policy distillation BID48 and develop an efficient algorithm for optimizing seq2seq models based on edit distance 1 . Our key observation is that given an arbitrary prefix (e.g. a partial sequence generated by sampling from the model), we can exactly and efficiently identify all of the suffixes that result in a minimum total edit distance (v.s. the ground truth target). Our training procedure , called Optimal Completion Distillation (OCD), is summarized as follows:The proposed OCD algorithm is efficient, straightforward to implement, and has no tunable hyperparameters of its own. Our key contributions include:• We propose OCD, a stand-alone algorithm for optimizing seq2seq models based on edit distance. OCD is scalable to real-world datasets with long sequences and large vocabularies, and consistently outperforms Maximum Likelihood Estimation (MLE) by a large margin.• Given a target sequence of length m and a generated sequence of length n, we present an O(nm) algorithm that identifies all of the optimal extensions for each prefix of the generated sequence.• We demonstrate the effectiveness of OCD on end-to-end speech recognition using attentionbased seq2seq models. On the Wall Street Journal dataset, OCD achieves a Character Error Rate (CER) of 3.1% and a Word Error Rate (WER) of 9.3% without language model rescoring, outperforming all prior work TAB1 . On Librispeech, OCD achieves state-of-the-art WER of 4.5% on ""test-clean"" and 13.3% on ""test-other"" sets TAB2 ).",777,0.384,475,1.6357894736842105,"We present Optimal Completion Distillation a training procedure optimizing sequence to sequence models based edit distance OCD is efficient has no hyper of pre-training or joint optimization with conditional log-likelihood Given a partial sequence generated the model first identify the set optimal suffixes minimize the total edit distance using an efficient dynamic programming algorithm Then for each position the generated sequence a target distribution which puts equal probability the first token all the optimal suffixes OCD achieves state performance on end speech on both Wall Street Journal and Librispeech datasets achieving $9.3\%$ WER and Recent advances natural language processing and speech recognition hinge expressive neural network sequence to (seq2seq learning BID54 BID1 . Such encoder-decoder architectures adopted both machine translation BID1 achieving impressive performance above traditional multi-stage pipelines . Improving the building blocks seq2seq models fundamentally advance machine translation speech recognition positively other domains image captioning BID62 , parsing , summarization BID47 , and program synthesis BID65 .To the key components one either design better architectures Recent architectures using convolution BID20 self attention proved, to facilitate efficient training On despite many attempts mitigate the limitations Maximum Likelihood BID43 BID60 BID4 , considered training seq2seq models Current alternative approaches require pre-training or joint optimization with conditional log-likelihood They difficult implement require careful tuning new hyper ( mixing ratios In addition , alternative approaches typically do offer a well tuned MLE baseline label smoothing BID40 BID18 scheduled samplingIn borrow ideas search-based structured prediction BID15 BID46 policy distillation BID48 develop an efficient algorithm optimizing seq2seq models edit distance 1 Our key observation given an arbitrary prefix generated sampling the model exactly and identify all result a minimum total edit distancev.s. the ground truth target Our training procedure , called Optimal Completion Distillation summarized asThe proposed OCD algorithm efficient straightforward no tunable hyperparameters of Our key contributions include:• We propose OCD a stand-alone algorithm optimizing seq2seq models edit distance OCD is scalable real-world datasets long sequences consistently Maximum Likelihood Estimation a large margin.• Given a target sequence length m a generated sequence present an O(nm identifies all the optimal extensions each prefix OCD end speech attentionbased seq2seq models On the Wall Street Journal dataset OCD achieves a Character Error RateWER without language model rescoring outperforming all prior work TAB1 . On Librispeech OCD achieves state WER of on ""testcleanother sets TAB2 ).",0.0,0.32401488877878987
"As an emerging field, federated learning has recently attracted considerable attention.
 Compared to distributed learning in the datacenter setting, federated learning
 has more strict constraints on computate efficiency of the learned model and communication
 cost during the training process. In this work, we propose an efficient
 federated learning framework based on variational dropout. Our approach is able
 to jointly learn a sparse model while reducing the amount of gradients exchanged
 during the iterative training process. We demonstrate the superior performance
 of our approach on achieving significant model compression and communication
 reduction ratios with no accuracy loss. Federated Learning is an emerging machine learning approach that has recently attracted considerable attention due to its wide range of applications in mobile scenarios BID18 BID12 BID24 . It enables geographically distributed devices such as mobile phones to collaboratively learn a shared model while keeping the training data on each phone. This is different from standard machine learning approach which requires all the training data to be centralized in a server or in a datacenter. As such, federated learning enables distributing the knowledge across phones without sharing users' private data.Federated Learning uses some form of distributed stochastic gradient descent (SGD) and requires a parameter server to coordinate the training process. The server initializes the model and distributes it to all the participating devices. In each distributed SGD iteration, each device computes the gradients of the model parameters using its local data. The server aggregates the gradients from each device, averages them, and sends the averaged gradients back. Each device then updates the model parameters using the averaged gradients. In such manner, each device benefits from obtaining a better model than the one trained only on the locally stored private data.While federated learning shares some common features with distributed learning in the datacenter setting BID3 BID16 since they both use distributed SGD as the core training technique, federated learning has two more strict constraints which datacenter setting does not have:Model Constraint: Compared to datacenters, mobile devices have much less compute resources. This requires the final model learned in the federated learning setting to be computationally efficient so that it can efficiently run on mobile devices.Communication Constraint: In datacenters, communication between the server and working nodes during SGD is conducted via Gbps Ethernet or InfiniBand network with even higher bandwidth BID26 . In contrast, communication in the federated learning setting relies on wireless networks such as 4G and Wi-Fi. Both uplink and downlink bandwidths of those wireless networks are at Mbps scale, which is much lower than the Gbps scale in the datacenter setting. The limited bandwidth in the federated learning setting illustrates the necessity of reducing the communication cost to accelerate the training process.In this work, we propose an efficient federated learning framework that meets both model and communication constraints. Our approach is inspired by variational dropout BID10 . Our key idea is to jointly and iteratively sparsify the parameters of the shared model to be learned as well as the gradients exchanged between the server and the participating devices during the distributed SGD training process. By sparsifying parameters, only important parameters are kept, and the final model learned thus becomes computationally efficient run on mobile devices. By sparsifying gradients, only important gradients are transmitted, and the communication cost is thus significantly reduced. We examine the performance of our framework on three deep neural networks and five datasets that fit the federated learning setting and are appropriate to be deployed on resource-limited mobile devices. Our experiment results show that our framework is able to achieve significant model compression and communication reduction ratios with no accuracy loss.",713,0.428,410,1.7390243902439024,"As an emerging field federated learning recently attracted Compared distributed learning more strict constraints computate efficiency of the learned model and communication cost during In this work propose an efficient federated learning framework variational dropout Our approach able jointly learn a sparse model while reducing gradients exchanged during We demonstrate the superior performance our approach on achieving significant model compression and communication reduction ratios no accuracy loss Federated Learning is an emerging machine learning approach attracted mobile scenarios BID18 BID12 BID24 . It enables geographically distributed devices collaboratively learn a shared model while the training data each phone This different standard machine learning approach centralized As such, federated learning enables distributing phones without sharing uses some formSGD requires a parameter server coordinate The server initializes the model distributes all the participating devices In each distributed SGD iteration each device computes the gradients its local data The server aggregates the gradients each device averages sends Each device then updates the model parameters using the averaged gradients In such manner each device benefits obtaining a better model trained only the locally stored private dataWhile federated learning shares in setting BID3 BID16 since distributed SGD the core training technique two more strict constraints which datacenter setting doesModel Constraint Compared This requires the final model learned the federated learning setting computationally so efficiently runCommunication Constraint In datacenters communication during SGD conducted Gbps Ethernet InfiniBand network with even higher bandwidth BID26 . In contrast communication the federated learning setting relies wireless networks such 4 of at Mbps scale The limited bandwidth in the federated learning setting illustrates reducing accelerateIn propose meets both model and communication constraints Our approach inspired variational dropout BID10 . Our key idea jointly and sparsify the parameters the shared model learned as exchanged the server the participating devices during the distributed SGD training process By sparsifying parameters only important parameters kept the final model learned thus becomes computationally efficient run mobile devices By sparsifying gradients only important gradients transmitted the communication cost thus significantly We examine our framework three deep neural networks five datasets fit the federated learning setting appropriate be deployed resource-limited mobile devices Our experiment results our framework achieve significant model compression and communication reduction ratios no accuracy loss",0.0,0.5870483860522894
"We prove a multiclass boosting theory for the ResNet architectures which simultaneously creates a new technique for multiclass boosting and provides a new algorithm for ResNet-style architectures.   Our proposed training algorithm, BoostResNet, is particularly suitable in non-differentiable architectures.   Our method only requires the relatively inexpensive sequential training of T ""shallow ResNets"". We prove that the training error decays exponentially with the depth T if the weak module classifiers that we train perform slightly better than some weak baseline.   In other words, we propose a weak learning condition and prove a boosting theory for ResNet under the weak learning condition.   A generalization error bound based on margin theory is proved and suggests that ResNet could be resistant to overfitting using a network with l_1 norm bounded weights. Why do residual neural networks (ResNets) BID14 and the related highway networks BID35 work? And if we study closely why they work, can we come up with new understandings of how to train them and how to define working algorithms?Deep neural networks have elicited breakthrough successes in machine learning, especially in image classification and object recognition BID19 BID32 BID34 Zeiler & Fergus, 2014) in recent years. As the number of layers increases, the nonlinear network becomes more powerful, deriving richer features from input data. Empirical studies suggest that challenging tasks in image classification BID15 BID34 and object recognition BID7 BID8 BID12 BID23 often require ""deep"" networks, consisting of tens or hundreds of layers. Theoretical analyses have further justified the power of deep networks BID24 compared to shallow networks.However, deep neural networks are difficult to train despite their intrinsic representational power. Stochastic gradient descent with back-propagation (BP) BID20 and its variants are commonly used to solve the non-convex optimization problems. A major challenge that exists for training both shallow and deep networks is vanishing or exploding gradients BID1 BID9 . Recent works have proposed normalization techniques BID9 BID22 BID15 BID31 to effectively ease the problem and achieve convergence. In training deep networks, however, a surprising training performance degradation is observed BID35 BID14 : the training performance degrades rapidly with increased network depth after some saturation point. This training performance degradation is representationally surprising as one can easily construct a deep network identical to a shallow network by forcing any part of the deep network to be the same as the shallow network with the remaining layers functioning as identity maps. He et al. BID14 presented a residual network (ResNet) learning framework to ease the training of networks that are substantially deeper than those used previously. And they explicitly reformulate the layers as learning residual functions with reference to the layer inputs by adding identity loops to the layers. It is shown in BID10 that identity loops ease the problem of spurious local optima in shallow networks. BID35 introduce a novel architecture that enables the optimization of networks with virtually arbitrary depth through the use of a learned gating mechanism for regulating information flow.Empirical evidence overwhelmingly shows that these deep residual networks are easier to optimize than non-residual ones. Can we develop a theoretical justification for this observation? And does that justification point us towards new algorithms with better characteristics? Our proposed BoostResNet algorithm achieves exponentially decaying (with the depth T ) training error under the weak learning condition. BoostResNet is much more computationally efficient compared to end-to-end back-propagation in deep ResNet. More importantly, the memory required by BoostResNet is trivial compared to end-to-end back-propagation. It is particularly beneficial given the limited GPU memory and large network depth. Our learning framework is natural for nondifferentiable data. For instance, our learning framework is amenable to take weak learning oracles using tensor decomposition techniques. Tensor decomposition, a spectral learning framework with theoretical guarantees, is applied to learning one layer MLP in BID16 . We plan to extend our learning framework to non-differentiable data using general weak learning oracles. In neural network optimization, there are many commonly-used loss functions and criteria, e.g., mean squared error, negative log likelihood, margin criterion, etc. There are extensive works BID7 BID30 BID37 on selecting or modifying loss functions to prevent empirical difficulties such as exploding/vanishing gradients or slow learning BID0 . However, there are no rigorous principles for selecting a loss function in general. Other works consider variations of the multilayer perceptron (MLP) or convolutional neural network (CNN) by adding identity skip connections BID14 , allowing information to bypass particular layers. However, no theoretical guarantees on the training error are provided despite breakthrough empirical successes. Hardt et al. BID10 have shown the advantage of identity loops in linear neural networks with theoretical justifications; however the linear setting is unrealistic in practice.",975,0.795,563,1.7317939609236235,"We prove a multiclass boosting theory the ResNet architectures which simultaneously creates Our proposed training algorithm BoostResNet particularly non-differentiable architectures Our method only the relatively inexpensive sequential training T ""shallow ResNets We prove training error decays exponentially the depth T if the weak module classifiers that train perform slightly some weak baseline In propose a weak learning condition prove a boosting theory ResNet under A generalization error bound based margin theory proved and suggests ResNet resistant using l_1 norm bounded weights Why residual neural networksResNets) BID14 the related highway And study closely why work can come train define working algorithms?Deep elicited breakthrough successes especially BID19 BID32 BID34 Zeiler & Fergus) As layers increases the nonlinear network powerful deriving richer features input data challenging tasks image classification BID15 BID34 often ""deep"" networks consisting tens Theoretical analyses further justified the power deep networks BID24 comparedHowever train despite their intrinsic representational power backBP BID20 its variants commonly solve A major challenge exists training both shallow and deep networks vanishing or exploding gradients BID1 BID9 . Recent works proposed normalization techniques BID9 BID22 BID15 BID31 to effectively ease and achieve convergence In training deep networks however a surprising training performance degradation BID35 BID14 : increased network depth after some saturation point This training performance degradation representationally surprising one construct a deep network identical forcing any part with functioning identity maps He et BID14 presented a residual network ( learning ease networks substantially deeper previously And explicitly reformulate the layers as learning residual functions with reference layer inputs by identity loops It shown BID10 identity loops ease spurious local optima shallow networks BID35 introduce the optimization networks virtually arbitrary depth through a learned gating mechanism regulating overwhelmingly these deep residual networks easier Can develop a theoretical justification this observation And does that justification point new algorithms with better characteristics Our proposed BoostResNet algorithm achieves exponentially decayingwith the depth T training error under the weak learning condition BoostResNet much computationally compared deep ResNet More importantly the memory required BoostResNet trivial It particularly beneficial given the limited GPU memory large network depth Our learning framework natural nondifferentiable data For instance our learning framework amenable take weak learning oracles using Tensor decomposition a spectral learning framework theoretical guarantees applied learning one layer MLP BID16 . We plan extend our learning framework non-differentiable data using general weak learning oracles In neural network optimization criteria negative log likelihood margin criterion There extensive works BID7 BID30 BID37 on selecting or loss functions empirical difficulties such exploding/vanishing gradients slow learning BID0 . However no rigorous principles selecting a loss function general Other works consider variations by adding identity skip connections BID14 , allowing information bypass particular layers However no theoretical guarantees the training error despite breakthrough empirical successes Hardt et BID10 have shown the advantage identity loops theoretical justifications; the linear setting unrealistic",0.01,0.5686258874027927
"We consider the problem of learning a one-hidden-layer neural network: we assume the input x is from Gaussian distribution and the label $y = a \sigma(Bx) + \xi$, where a is a nonnegative vector and  $B$ is a full-rank weight matrix, and $\xi$ is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. 
	
 Inspired by the formula, we design a non-convex objective function $G$ whose landscape is guaranteed to have the following properties:	

1. All local minima of $G$ are also global minima.
 2. All global minima of $G$ correspond to the ground truth parameters.
 3. The value and gradient of $G$ can be estimated using samples.
	
 With these properties, stochastic gradient descent on $G$ provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity results and validate the results by simulations. Scalable optimization has played an important role in the success of deep learning, which has immense applications in artificial intelligence. Remarkably, optimization issues are often addressed through designing new models that make the resulting training objective functions easier to be optimized. For example, over-parameterization BID19 , batch-normalization BID14 , and residual networks BID12 b) are often considered as ways to improve the optimization landscape of the resulting objective functions.How do we design models and objective functions that allow efficient optimization with guarantees? Towards understanding this question in a principled way, this paper studies learning neural networks with one hidden layer. Roughly speaking, we will show that when the input is from Gaussian distribution and under certain simplifying assumptions on the weights, we can design an objective function G(·), such that[a] all local minima of G(·) are global minima [b] all the global minima are the desired solutions, namely, the ground-truth parameters (up to permutation and some fixed transformation).We note that designing such objective functions is challenging because 1) the natural 2 loss objective does have bad local minimum, and 2) due to the permutation invariance 1 , the objective function inherently has to contain an exponential number of isolated local minima. In this paper we first give an analytic formula for the population risk of the standard 2 loss, which empirically may converge to a spurious local minimum. We then design a novel population loss that is guaranteed to have no spurious local minimum.Designing objective functions with well-behaved landscape is an intriguing and potentially fruitful direction. We hope that our techniques can be useful for characterizing and designing the optimization landscape for other settings.We conjecture that the objective αf 2 + βf 4 12 has no spurious local minimum when α, β are reasonable constants and the ground-truth parameters are in general position. We provided empirical evidence to support the conjecture.Our results assume that the input distribution is Gaussian. Extending them to other input distributions is a very interesting open problem. 2 /2 ) in the following sense 13 . For two functions f, g that map R to R, define the inner product f, g with respect to the Gaussian measure as DISPLAYFORM0 The polynomials h 0 , . . . , h m , . . . are orthogonal to each other under this inner product: DISPLAYFORM1 2 /2 ) , let the k-th Hermite coefficient of σ be defined asσ DISPLAYFORM2 Since h 0 , . . . , h m , . . . , forms a complete orthonormal basis, we have the expansion that DISPLAYFORM3 We will leverage several other nice properties of the Hermite polynomials in our proofs. The following claim connects the Hermite polynomial to the coefficients of Taylor expansion of a certain exponential function. It can also serve as a definition of Hermite polynomials. 13 We denote by Donnell, 2014, Equation 11 .8)). We have that for t, z ∈ R, DISPLAYFORM4 DISPLAYFORM5 The following Claims shows that the expectation E [h n (x)h m (y)] can be computed easily when x, y are (correlated) Gaussian random variables. Claim A.2 ((O'Donnell, 2014, Section 11.2)). Let (x, y) be ρ-correlated standard normal variables (that is, both x,y have marginal distribution N (0, 1) and E[xy] = ρ). Then, DISPLAYFORM6 As a direct corollary, we can compute Ex∼N (0,Id d×d ) σ(u x)γ(v x) by expanding in the Hermite basis and applying the Claim above. Claim A.3. Let σ, γ be two functions from R to R such that DISPLAYFORM7 2 /2 ). Then, for any unit vectors u, v ∈ R d , we have that DISPLAYFORM8 Proof of Claim A.3. Let s = u x and t = v x. Then s, t are two spherical standard normal random variables that are u, v -correlated, and we have that DISPLAYFORM9 We expand σ(s ) and γ(t ) in the Fourier basis and obtain that DISPLAYFORM10 In this section we prove Theorem 2.1 and Theorem 2.2, which both follow from the following more general Theorem. DISPLAYFORM11 2 /2 ), andŷ = a γ(Bx) with parameter a ∈ R and B ∈ R ×d . Define the population risk f γ as DISPLAYFORM12 DISPLAYFORM13 whereσ k ,γ k are the k-th Hermite coefficients of the function σ and γ respectively.We can see that Theorem 2.1 follows from choosing γ = σ and Theorem 2.2 follows from choosing γ =σ 2 h 2 +σ 4 h 4 . The key intuition here is that we can decompose σ into a weighted combination of Hermite polynomials, and each Hermite polynomial influence the population risk more or less independently (because they are orthogonal polynomials with respect to the Gaussian measure).Proof of Theorem A.4. We have DISPLAYFORM14",1291,0.777,754,1.7122015915119364,"We consider learning a one-hidden-layer neural network: x from Gaussian distribution the label $y a \sigma(Bx + We first give an analytic formula the population risk the standard squared loss and demonstrate implicitly attempts a sequence low-rank tensors simultaneously Inspired the formula design a non-convex objective function $G$ whose landscape guaranteed 1 All local minima $G$ also 2 All global minima $G$ correspond the ground truth parameters 3 The value and gradient $G$ samples With these properties stochastic on $G$ provably converges the global minimum learn the ground-truth parameters We also prove finite sample complexity results validate simulations Scalable optimization has played immense applications optimization issues designing new models make the resulting training objective functions be optimized For example over- BID19 , batch residual networks b often considered ways the optimization landscape the resulting objective functionsHow design models objective functions with guarantees understanding in this studies learning neural networks one hidden layer speaking will show when the input from Gaussian distribution under on design an objective function G· such all local minima [ the desired solutions namely the ground-truth parametersup permutation some fixed transformation).We note designing challenging 1 the natural 2 loss objective does have bad local minimum due 1 , inherently contain an exponential number In first give an analytic formula the population risk the standard 2 loss, empirically may converge a spurious local minimum We then design a novel population loss that guaranteed no spurious local minimumDesigning objective functions well-behaved landscape We hope our techniques characterizing designing the optimization landscape other settingsWe conjecture αf 2 + 12 has no spurious local minimum when, are reasonable constants the ground-truth parameters in general position We provided empirical evidence the conjectureOur results assume the input distribution Extending them other input distributions 2 /2 ) in the following sense 13 . For two functions f, that map R define the inner product the Gaussian measure as DISPLAYFORM0 The polynomials h 0 . . . , h m . . . are orthogonal under this inner product: DISPLAYFORM1 2 /2 ) , let the k-th Hermite coefficient �� defined Since h 0 . . . , h m . . . , forms a complete orthonormal basis we the expansion that DISPLAYFORM3 We leverage several other nice properties our proofs The following claim connects the Hermite polynomial the coefficients Taylor expansion of It can serve a definition Hermite polynomials 13 We denote Donnell 2014 Equation 11 .8 We that for t, z �� R DISPLAYFORM4 The following Claims shows expectation E [h n ( m can easily when (correlated Gaussian random Claim A.2 ((O'Donnell 2014 Section Let (x �-correlated standard normal variablesthat, have marginal distribution N0 E[xy Then DISPLAYFORM6 As compute Ex��N (0,Id d×d ) ��u x)γ(v by expanding in the Hermite basis the Claim above Claim A.3 Let ��, two functions from R such DISPLAYFORM7 2 /2 ). Then for any unit vectors u that DISPLAYFORM8 Proof Claim A.3 Let x and Then s, t are two spherical standard normal random variables u -correlated we that DISPLAYFORM9 We expand �� ) the Fourier basis obtain In prove Theorem both DISPLAYFORM11 2 /2 ),�� = a ��Bx parameter a �� R and B �� R ×d Define the population risk f �� as DISPLAYFORM12 DISPLAYFORM13 whereσ k ,γ k the k-th Hermite coefficients respectivelyWe Theorem follows choosingσ 2 h + 4 The key intuition decompose �� a weighted combination each influence the population risk more independentlybecause the Gaussian measure).Proof We DISPLAYFORM14",0.01,0.5187062515085691
"Open information extraction (OIE) systems extract relations and their
  arguments from natural language text in an unsupervised manner. The resulting
  extractions are a valuable resource for downstream tasks such as knowledge
  base construction, open question answering, or event schema induction. In this
  paper, we release, describe, and analyze an OIE corpus called OPIEC, which was
  extracted from the text of English Wikipedia. OPIEC complements the available
  OIE resources: It is the largest OIE corpus publicly available to date (over
  340M triples) and contains valuable metadata such as provenance information,
  confidence scores, linguistic annotations, and semantic annotations including
  spatial and temporal information. We analyze the OPIEC corpus by comparing its
  content with knowledge bases such as DBpedia or YAGO, which are also based on
  Wikipedia. We found that most of the facts between entities present in OPIEC
  cannot be found in DBpedia and/or YAGO, that OIE facts 
  often differ in the level of specificity compared to knowledge base facts, and
  that OIE open relations are generally highly polysemous. We believe that the
  OPIEC corpus is a valuable resource for future research on automated knowledge
  base construction. Open information extraction (OIE) is the task of extracting relations and their arguments from natural language text in an unsupervised manner BID3 . The output of such systems is usually structured in the form of (subject, relation, object)-triples. For example, from the sentence ""Bell is a telecommunication company, which is based in L. A.,"" an OIE system may yield the extractions (""Bell""; ""is""; ""telecommunication company"") and (""Bell""; ""is based in""; ""L. A.""). The extractions of OIE systems from large corpora are a valuable resource for downstream tasks BID11 BID21 such as automated knowledge base construction BID28 BID34 BID33 BID30 , open question answering BID13 , event schema induction BID2 , generating inference rules BID18 , or for improving OIE systems themselves BID35 . A number of derived resources have been produced from OIE extractions, including as entailment rules BID18 , question paraphrases BID13 , Relgrams BID1 , and OIE-based embeddings BID32 .In this paper, we release a new OIE corpus called OPIEC. 1 The OPIEC corpus has been extracted from the full text of the English Wikipedia using the Stanford CoreNLP pipeline and the state-of-the-art OIE system MinIE BID15 . OPIEC complements available OIE resources BID12 BID19 BID26 BID24 BID9 : It is the largest OIE corpus publicly available to date (with over 340M triples) and contains valuable metadata information for each of its extractions not available in existing resources (see Tab. 1 for an overview). In particular , OPIEC provides for each triple detailed provenance information, syntactic annotations (such as POS tags, lemmas, dependency parses), semantic annotations (such as polarity, modality, attribution, space, time), entity annotations (NER types and, when available, Wikipedia links), as well as confidence scores.We performed a detailed data profiling study of the OPIEC corpus to analyze its contents and potential usefulness for downstream applications. We observed that a substantial fraction of the OIE extractions was not self-contained (e.g., because no anaphora resolution was performed) or overly specific (e.g., because arguments were complex phrases). Since these extractions are more difficult to work with, we created the OPIEC-Clean subcorpus (104M triples), in which we only retained triples that express relations between concepts. In particular , OPIEC-Clean contains triples in which arguments are either named entities (as recognized by an NER system), match a Wikipedia page title (e.g., concepts such as political party or movie), or link directly to a Wikipedia page. Although OPIEC-Clean is substantially smaller than the full OPIEC corpus, it is nevertheless four times larger than the largest prior OIE corpus.To gain insight into the information present in the OPIEC corpus, we compared its content with the DBpedia BID4 and YAGO BID17 knowledge bases, which are also constructed from Wikipedia (e.g., from infoboxes). Since such an analysis is difficult to perform due to the openness and ambiguity of OIE extractions, we followed standard practice and used a simple form of distant supervision. In particular, we analyze the OPIEC-Linked subcorpus (5.8M triples), which contains only those triples in which both arguments are linked to Wikipedia articles, i.e., where we have golden labels for disambiguation. We found that most of the facts between entities present in OPIECLinked cannot be found in DBpedia and/or YAGO, that OIE facts often differ in the level of specificity compared to knowledge base facts, and that frequent OIE open relations are generally highly polysemous.Along with the OPIEC corpus as well as the OPIEC-Clean and OPIEC-Linked subcorpora, we release the codebase used to construct the corpus as well as a number of derived resources, most notably a corpus of open relations between arguments of various entity types along with their frequencies. We believe that the OPIEC corpus is a valuable resource for future research on automated knowledge base construction. We created OPIEC, a large open information extraction corpus extracted from Wikipedia. OPIEC consists of hundreds of millions of triples, along with rich metadata such as provenance information, syntactic annotations, semantic annotations, and confidence scores. We reported on a data profiling study of the OPIEC corpus as well as subcorpora. In particular, we analyzed to what extent OPIEC overlaps with the DBpedia and YAGO knowledge bases. Our study indicates that most open facts do not have counterparts in the KB such that OIE corpora contain complementary information. For the information that overlaps, open relation are often more specific, more generic, or simply correlated to KB relations (instead of semantically equivalent). We hope that the OPIEC corpus, its subcorpora, derived statistics, as well as the codebase used to create the corpus are a valuable resource for automated KB construction and downstream applications (for example, an independent study showed the utility of OPIEC in entity-aspect linking BID27 ).",1323,0.594,794,1.6662468513853905,"Open information extraction (OIE) systems extract relations their arguments natural language text in The resulting extractions a valuable resource downstream tasks knowledge base construction open question answering event schema induction In release, describe an OIE corpus called OPIEC, extracted the text English Wikipedia OPIEC complements the available OIE resources: It corpus publicly to (over 340M triples valuable metadata provenance information confidence scores linguistic annotations semantic annotations including We analyze the OPIEC corpus by comparing knowledge bases such DBpedia YAGO also based We found most the facts between entities present OPIEC cannot DBpedia YAGO that OIE facts often the level specificity compared knowledge base facts OIE open relations highly polysemous We believe the OPIEC corpus automated knowledge base construction Open information extraction the task relations their arguments natural language text in BID3 . The output such systems structured (subject, relation, object)-triples For example from the sentenceBell a telecommunication company based A.,"" an OIE system may yield the extractions (""Bell"";is ""telecommunication company (""Bell basedL. A.""). The extractions OIE systems large corpora downstream tasks BID11 BID21 such , open question answering , event schema induction BID2 generating inference rules or for improving themselves A number derived resources produced OIE extractions as entailment rules BID18 , question paraphrases Relgrams BID1 .In release called OPIEC. 1 The OPIEC corpus has extracted using the Stanford CoreNLP pipeline state OIE system MinIE BID15 . OPIEC complements available OIE resources BID12 BID19 BID26 BID24 BID9 : It largest corpus publiclywith over 340M triples valuable metadata information each its extractions not existing resources Tab 1 for an overview). In particular , OPIEC provides for each triple detailed provenance information syntactic annotations ( POS tags lemmas dependency parses polarity modality attribution space time entity annotationsNER types, when available, Wikipedia links as confidence scoresWe performed a detailed data profiling study analyze its contents potential usefulness downstream applications We observed a substantial fraction the OIE extractions was self because no anaphora resolution overly specific arguments complex phrases Since these extractions more work created the OPIEC-Clean subcorpus104M triples in only retained triples express relations concepts In particular , OPIEC-Clean contains triples in which arguments either named entities recognized an NER system match a Wikipedia page title political party movie link Although OPIEC-Clean substantially the full OPIEC corpus nevertheless four the largest prior OIE corpusTo gain the information present compared its content the DBpedia BID4 and YAGO BID17 knowledge bases also constructed Wikipedia ( from Since such an analysis due the openness ambiguity OIE extractions followed standard practice a simple form distant supervision In particular analyze the OPIEC-Linked subcorpus5.8M triples only those triples both arguments linked Wikipedia articles where we golden labels We found most the facts between entities present OPIECLinked DBpedia YAGO that OIE facts often differ the level specificity compared knowledge base facts that frequent OIE open relations generally highly polysemousAlong the OPIEC corpus as release the codebase used construct derived resources open relations between arguments various entity types along their frequencies We believe the OPIEC corpus automated knowledge base construction We created OPIEC a large open information extraction corpus extracted OPIEC consists hundreds of millions triples along rich metadata such provenance information syntactic annotations confidence scores We reported a data profiling study the OPIEC corpus as subcorpora. In particular analyzed to OPIEC overlaps the DBpedia and YAGO knowledge bases Our study indicates most open facts do counterparts the KB such OIE corpora contain complementary information For the information that overlaps open relation are often more specific generic simply correlated KB relationsinstead semantically We hope the OPIEC corpus, its subcorpora derived statistics as the codebase used automated KB construction and downstream applications ( an independent study showed the utility entity-aspect linking BID27",0.01,0.4016176112054509
"The process of designing neural architectures requires expert knowledge and extensive trial and error.
 While automated architecture search may simplify these requirements, the recurrent neural network (RNN) architectures generated by existing methods are limited in both flexibility and components.
 We propose a domain-specific language (DSL) for use in automated architecture search which can produce novel RNNs of arbitrary depth and width.
 The DSL is flexible enough to define standard architectures such as the Gated Recurrent Unit and Long Short Term Memory and allows the introduction of non-standard RNN components such as trigonometric curves and layer normalization.   Using two different candidate generation techniques, random search with a ranking function and reinforcement learning, 
we explore the novel architectures produced by the RNN DSL for language modeling and machine translation domains.
 The resulting architectures do not follow human intuition yet perform well on their targeted tasks, suggesting the space of usable RNN architectures is far larger than previously assumed. Developing novel neural network architectures is at the core of many recent AI advances BID28 BID14 BID35 . The process of architecture search and engineering is slow, costly, and laborious. Human experts, guided by intuition, explore an extensive space of potential architectures where even minor modifications can produce unexpected results. Ideally, an automated architecture search algorithm would find the optimal model architecture for a given task.Many explorations into the automation of machine learning have been made, including the optimization of hyperparameters BID3 BID24 and various methods of producing novel model architectures BID27 BID1 Zoph and Le, 2017) . For architecture search, ensuring these automated methods are able to produce results similar to humans usually requires traversing an impractically large search space, assuming high quality architectures exist in the search space at all. The choice of underlying operators composing an architecture is further typically constrained to a standard set across architectures even though recent work has found promising results in the use of non-standard operators BID31 .We propose a meta-learning strategy for flexible automated architecture search of recurrent neural networks (RNNs) which explicitly includes novel operators in the search. It consists of three stages, outlined in Figure 1 , for which we instantiate two versions.1. A candidate architecture generation function produces potential RNN architectures using a highly flexible DSL. The DSL enforces no constraints on the size or complexity of the generated tree and can be incrementally constructed using either a random policy or with an RL agent. 2. A ranking function processes each candidate architecture's DSL via a recursive neural network, predicting the architecture's performance. By unrolling the RNN representation, the ranking function can also model the interactions of a candidate architecture's hidden state over time. Figure 1: A generator produces candidate architectures by iteratively sampling the next node (either randomly or using an RL agent trained with REINFORCE). Full architectures are processed by a ranking function and the most promising candidates are evaluated. The results from running the model against a baseline experiment are then used to improve the generator and the ranking function.3. An evaluator, which takes the most promising candidate architectures, compiles their DSLs to executable code and trains each model on a specified task. The results of these evaluations form architecture-performance pairs that are then used to train the ranking function and RL generator. We introduced a flexible domain specific language for defining recurrent neural network architectures that can represent most human designed architectures. It is this flexibility that allowed our generators to come up with novel combinations in two tasks. These architectures used both core operators that are already used in current architectures as well as operators that are largely unstudied such as division or sine curves. The resulting architectures do not follow human intuition yet perform well on their targeted tasks, suggesting the space of usable RNN architectures is far larger than previously assumed. We also introduce a component-based concept for architecture search from which we instantiated two approaches: a ranking function driven search which allows for richer representations of complex RNN architectures that involve long term memory (c t ) nodes, and a Reinforcement Learning agent that internalizes knowledge about the search space to propose increasingly better architectures. As computing resources continue to grow, we see automated architecture generation as a promising avenue for future research.APPENDIX A: DOMAIN SPECIFIC LANGUAGE DISPLAYFORM0",845,0.448,504,1.6765873015873016,"The process designing neural architectures requires expert knowledge extensive trial While automated architecture search may simplify these requirements architectures generated existing methods limited both flexibility components We propose use automated architecture search which produce of arbitrary depth width The DSL flexible define standard architectures such the Gated Recurrent Unit and allows the introduction non-standard RNN components layer normalization Using two different candidate generation techniques random search with a ranking function reinforcement learning explore the novel architectures produced the RNN DSL language modeling and machine translation domains The resulting architectures do follow human intuition yet perform their targeted tasks suggesting the space usable RNN architectures Developing novel neural network architectures at recent AI BID28 BID14 BID35 . The process architecture search engineering slow costly Human experts guided intuition explore an extensive space potential architectures where even minor modifications produce Ideally an automated architecture search algorithm find the optimal model architectureMany explorations the automation BID3 BID24 various methods producing novel model BID27 BID1 Zoph and Le, 2017) . For architecture search ensuring these automated methods able produce similar humans usually traversing assuming high quality architectures exist The choice underlying operators composing an architecture further typically constrained standard across even recent work promising results BID31 .We flexible automated architecture search of which explicitly novel operators It consists outlined , for instantiate two versions.1 A candidate architecture generation function produces potential RNN architectures a highly flexible DSL The DSL enforces no constraints complexity the generated tree incrementally constructed either a random policy with an RL agent 2 A ranking function processes each candidate architecture's DSL via predicting By unrolling the RNN representation the ranking function also model a candidate architecture's hidden state over Figure A generator produces candidate architectures by samplingeither randomly an RL agent trained REINFORCE Full architectures processed a ranking function the most promising candidates evaluated The results running against a baseline experiment then improve the generator the ranking function.3. takes the most promising candidate architectures their DSLs executable code trains each model a specified task The results these evaluations form architecture-performance pairs then train the ranking function RL generator We introduced a flexible domain specific language defining represent most human designed architectures It this flexibility allowed our generators come novel combinations in two tasks These architectures used both core operators that already current architectures largely such division sine curves The resulting architectures do follow human intuition yet perform their targeted tasks suggesting the space usable RNN architectures We also introduce a component-based concept architecture search from which instantiated two approaches a ranking function driven search which richer representations complex RNN architectures that involve (c t ) nodes internalizes knowledge propose increasingly better architectures As computing resources automated architecture generationAPPENDIX A DISPLAYFORM0",0.01,0.4279641698178993
"Researches on deep neural networks with discrete parameters and their deployment in embedded systems have been active and promising topics. Although previous works have successfully reduced precision in inference, transferring both training and inference processes to low-bitwidth integers has not been demonstrated simultaneously. In this work, we develop a new method termed as ``""WAGE"" to discretize both training and inference, where weights (W), activations (A), gradients (G) and errors (E) among layers are shifted and linearly constrained to low-bitwidth integers. To perform pure discrete dataflow for fixed-point devices, we further replace batch normalization by a constant scaling layer and simplify other components that are arduous for integer implementation. Improved accuracies can be obtained on multiple datasets, which indicates that WAGE somehow acts as a type of regularization. Empirically, we demonstrate the potential to deploy training in hardware systems such as integer-based deep learning accelerators and neuromorphic chips with comparable accuracy and higher energy efficiency, which is crucial to future AI applications in variable scenarios with transfer and continual learning demands. Recently deep neural networks (DNNs) are being widely used for numerous AI applications BID11 BID21 . Depending on the massive tunable parameters, DNNs are considered to have powerful multi-level feature extraction and representation abilities. However, training DNNs needs energy-intensive devices such as GPU and CPU with high precision (float32) processing units and abundant memory, which has greatly challenged their extensive applications for portable devices. In addition, a state-of-art network often has far more weights and effective capacity to shatter all training samples , leading to overfitting easily.As a result, there is much interest in reducing the size of network during inference BID8 BID17 BID14 , as well as dedicated hardware for commercial solutions BID10 BID20 . Due to the accumulation in stochastic gradient descent (SGD) optimization, the precision demand for training is usually higher than inference BID8 . Therefore, most of the existing techniques only focus on the deployment of a well-trained compressed network, while still keeping high precision and computational complexity during training. In this work, we address this problem as how to process both training and inference with low-bitwidth integers, which is essential for implementing DNNs in dedicated hardware. To this end, two fundamental issues are addressed for discretely training DNNs: i) how to quantize all the operands and operations, and ii) how many bits or states are needed for SGD computation and accumulation.With respect to the issues, we propose a framework termed as ""WAGE"" that constrains weights (W), activations (A), gradients (G) and errors (E) among all layers to low-bitwidth integers in both training and inference. Firstly, for operands, linear mapping and orientation-preserved shifting are applied to achieve ternary weights, 8-bit integers for activations and gradients accumulation. Secondly, for operations, batch normalization BID9 is replaced by a constant scaling factor. Other techniques for fine-tuning such as SGD optimizer with momentum and L2 regularization are simplified or abandoned with little performance degradation. Considering the overall bidirectional propagation, we completely streamline inference into accumulate-compare cycles and training into low-bitwidth multiply-accumulate (MAC) cycles with alignment operations, respectively.We heuristically explore the bitwidth requirements of integers for error computation and gradient accumulation, which have rarely been discussed in previous works. Experiments indicate that it is the relative values (orientations) rather than absolute values (orders of magnitude) in error that guides previous layers to converge. Moreover, small values have negligible effects on previous orientations though propagated layer by layer, which can be partially discarded in quantization. We leverage these phenomena and use an orientation-preserved shifting operation to constrain errors. As for the gradient accumulation, though weights are quantized to ternary values in inference, a relatively higher bitwidth is indispensable to store and accumulate gradient updates.The proposed framework is evaluated on MNIST, CIFAR10, SVHN, ImageNet datasets. Comparing to those who only discretize weights and activations at inference time, it has comparable accuracy and can further alleviate overfitting, indicating some type of regularization. WAGE produces pure bidirectional low-precision integer dataflow for DNNs, which can be applied for training and inference in dedicated hardware neatly. We publish the code on GitHub 1 .",882,0.44,539,1.6363636363636365,"Researches deep neural networks with discrete parameters their deployment active topics Although previous works successfully reduced precision inference transferring both training and inference processes low-bitwidth integers simultaneously In this work develop termed as""WAGE"" discretize both training inference where weights (W activations gradients errors among layers shifted linearly constrained low-bitwidth integers To perform pure discrete dataflow for fixed-point devices further replace batch normalization a constant scaling layer simplify other components arduous integer implementation Improved accuracies can on multiple datasets indicates WAGE somehow acts regularization demonstrate deploy training hardware systems integer-based deep learning accelerators comparable accuracy higher energy efficiency variable scenarios with transfer and continual learning demands Recently deep neural networks widely numerous AI applications BID11 BID21 . Depending the massive tunable parameters DNNs considered powerful multi-level feature extraction and representation abilities However training DNNs needs energy-intensive devices GPU with high precision (float32) processing units abundant memory has greatly challenged their extensive applications portable devices In addition stateart network often far more weights effective capacity shatter all training samples , leading overfitting easilyAs much interest reducing network during inference BID8 BID17 BID14 dedicated hardware commercial solutions Due the accumulation in the precision demand training usually inference BID8 . Therefore most the existing techniques only focus the deployment a well-trained compressed network still high precision computational complexity during training In this work address this problem as how process both training inference with low-bitwidth integers essential implementing dedicated hardware To this end two fundamental issues for discretely training DNNs i quantize operations or states SGD computation accumulationWith respect the issues, termed asWAGE weightsW activations errors among all layers low-bitwidth integers both training Firstly for operands linear mapping orientation-preserved shifting applied achieve ternary weights for activations gradients accumulation Secondly for operations batch normalization BID9 replaced a constant scaling factor Other techniques such SGD optimizer with momentum L2 regularization simplified or abandoned with little performance degradation Considering the overall bidirectional propagation completely streamline inference into accumulate-compare cycles training into lowbitwidth multiply (MAC cycles alignment operations respectivelyWe heuristically explore the bitwidth requirements integers error computation gradient accumulation have rarely previous works Experiments indicate it the relative values (orientations ratherorders error guides previous layers converge Moreover small values negligible effects previous orientations though propagated layer by partially discarded quantization We leverage these phenomena use an orientation-preserved shifting operation errors As for the gradient accumulation though weights quantized ternary inference a relatively higher bitwidth indispensable store accumulate gradient updatesThe proposed framework evaluated MNIST CIFAR10 SVHN ImageNet datasets Comparing to those only discretize weights activations at inference time has comparable accuracy can further alleviate indicating some type regularization WAGE produces pure bidirectional low-precision integer dataflow training dedicated hardware neatly We publish 1 .",0.01,0.32547780484058586
"Modern Convolutional Neural Networks (CNNs) are complex, encompassing millions of parameters. Their deployment exerts computational, storage and energy demands, particularly on embedded platforms. Existing approaches to prune or sparsify CNNs require retraining to maintain inference accuracy. Such retraining is not feasible in some contexts. In this paper, we explore the sparsification of CNNs by proposing three model-independent methods. Our methods are applied on-the-fly and require no retraining. We show that the state-of-the-art models' weights can be reduced by up to 73% (compression factor of 3.7x) without incurring more than 5% loss in Top-5 accuracy. Additional fine-tuning gains only 8% in sparsity, which indicates that our fast on-the-fly methods are effective. There has been a significant growth in the number of parameters (i.e., layer weights), and the corresponding number of multiply-accumulate operations (MACs), in state-of-the-art CNNs BID14 BID13 BID19 BID23 BID8 BID11 BID24 BID22 . Thus, it is to no surprise that several techniques exist for ""pruning"" or ""sparsifying"" CNNs (i.e., forcing some model weights to 0) to both compress the model and to save computations during inference. Examples of these techniques include: iterative pruning and retraining BID2 BID7 BID3 BID20 BID17 , Huffman coding BID5 , exploiting granularity BID15 BID4 , structural pruning of network connections BID25 BID16 BID0 BID18 , and Knowledge Distillation (KD) BID9 .A common theme to the aforementioned techniques is that they require a retraining of the model to fine-tune the remaining non-zero weights and maintain inference accuracy. Such retraining, while feasible in some contexts, is not feasible in others, particularly industrial ones. For example, for mobile platforms, a machine learning model is typically embedded within an app for the platform that the user directly downloads. The app utilizes the vendor's platform runtime support (often in the form of a library) to load and use the model. Thus , the platform vendor must sparsify the model at runtime, i.e., on-the-fly, within the library with no opportunity to retrain the model. Further , the vendor rarely has access to the labelled data used to train the model. While techniques such as Knowledge Distillation BID9 can address this lack of access, it is not possible to apply it on-the-fly.In this paper, we develop fast retraining-free sparsification methods that can be deployed for on-thefly sparsification of CNNs in the contexts described above. There is an inherent trade-off between sparsity and inference accuracy. Our goal is to develop model-independent methods that result in large sparsity with little loss to inference accuracy. We develop three model-independent sparsification methods: flat, triangular, and relative. We implement these methods in TensorFlow and use the framework to evaluate the sparsification of several pretrained models: Inception-v3, MobileNet-v1, ResNet, VGG, and AlexNet. Our evaluation shows that up to 81% of layer weights in some models may be forced to 0, incurring only a 5% loss in inference accuracy. While the relative method appears to be more effective for some models, the triangular method is more effective for others. Thus, a predictive modeling autotuning BID6 BID1 is needed to identify, at run-time, the optimal choice of method and it hyper-parameters.",718,0.393,415,1.730120481927711,"Modern Convolutional Neural Networks complex encompassing millions parameters Their deployment exerts computational, storage energy particularly embedded platforms Existing approaches prune or sparsify CNNs require retraining to maintain inference accuracy Such retraining feasible some contexts In this paper explore the sparsification CNNs proposing three model-independent methods Our methods applied on- require We show state models' weights reducedcompression factor without Top-5 accuracy Additional fine-tuning gains only 8% sparsity indicates our fast on methods effective There has a significant growth parameters ( layer weights the corresponding number multiply-accumulate operations state CNNs BID14 BID13 BID19 BID23 BID8 . Thus to no surprise several techniques exist ""pruning or ""sparsifying"" CNNs ( forcing some model weights 0 both compress save computations during inference Examples these techniques iterative pruning retraining BID2 BID7 BID3 BID20 BID17 , Huffman coding exploiting structural pruning of network connections Knowledge Distillation .A common theme to the model the remaining non-zero weights maintain inference accuracy Such retraining while feasible feasible particularly industrial ones For example for mobile platforms a machine learning model typically embedded for directly downloads The app utilizes the vendor's platform runtime supportoften in load use the model Thus , the platform vendor must sparsify the model at on- within with no opportunity retrain Further , the vendor rarely has access the labelled data used train While techniques Knowledge Distillation BID9 can address this lack access apply it on-In develop fast retraining-free sparsification methods deployed for onthefly CNNs the contexts described There sparsity inference accuracy Our goal develop model-independent methods result large sparsity with little loss inference accuracy We develop three model-independent sparsification methods flat triangular relative We implement these methods use the framework evaluate the sparsification several pretrained models Inception-v3 MobileNet-v1 ResNet, VGG AlexNet Our evaluation shows up to 81% layer weights some models may forced 0, incurring inference accuracy While the relative method appears some models the triangular method Thus a predictive modeling autotuning BID6 BID1 is needed identify, at the optimal choice method it hyper",0.0,0.5643620099514646
"Curriculum learning and Self paced learning are popular topics in the machine learning that suggest to put the training samples in order by considering their difficulty levels. Studies in these topics show that starting with a small training set and adding new samples according to difficulty levels improves the learning performance. In this paper we experimented that we can also obtain good results by adding the samples randomly without a meaningful order. We compared our method with classical training, Curriculum learning, Self paced learning and their reverse ordered versions. Results of the statistical tests show that the proposed method is better than classical method and similar with the others. These results point a new training regime that removes the process of difficulty level determination in Curriculum and Self paced learning and as successful as these methods.  BID1 named Curriculum learning the idea of following an order related with difficulty of the samples during training which provides an optimization for non convex objectives. After this many researchers tried to find the most efficient curriculum to get the best yield with this approach. In BID15 's study conventional curriculum learning did not work so well and they developed a new version. BID14 proposed three different curriculum strategies for language model adaptation of recurrent neural networks. In the field of computer vision BID13 looked for the best order of tasks to learn. Although these models have better generalization performance with the proposed curriculum methods it is not known whether the tried methods ensures the best curriculum.A curriculum is work-specific so could not be applicable for another work. In order to use the curriculum logic in different applications BID10 suggested a method that the learner decides itself which samples are easy or difficult at every stage. This method called Self paced learning was combined with Curriculum learning which provides prior information by BID9 . In another work BID7 introduced a method to automatically select the syllabus to follow for the neural networks. BID12 also proposed a way to learn simple subtasks before the complex tasks and achieved better results than using manually designed curriculum.In some cases higher learning performance could be obtainable by adding some noises to easy-tohard ordering of the samples. BID8 gave preference to both easy and diverse samples and outperform the conventional Self paced learning BID10 ) algorithm. Emphasizing the uncertain samples suggested by BID3 lead to more accurate and robust SGD training. BID0 explored the inversed versions of the Self paced learning and Self paced learning with diversity BID8 ) and demonstrated that these methods performed slightly better than their standard variants. Consistent with the literature we have showed in our previous work () that using both curriculum and anti-curriculum strategies improving generalization performance in a wide application area. These researches brings a question to minds: While it is natural and logical to obtain better results by sorting the samples from easy-to-hard why it is also better to sort the samples from hard-to-easy?In this study we point that to start with a small training set and add new samples in both curriculum and anti-curriculum learning makes these methods better. So we claim that it is possible to have better results only by adding new samples stage-by-stage without a meaningful order. We experimented two ordering types related with difficulty (easy-to-hard and hard-to-easy) and our method without a meaningful order. Training was carried out by adding a new group to the training set at every stage. We compared the proposed method with two strategies. First one is Curriculum learning which we give the difficulty levels of the samples as pre-information. Second one is Self paced learning which the trained network determines the difficulty levels of the samples at each stage. All methods including usual baseline training have been compared by using paired T-test and the results are examined. We drew our attention that both versions of training with easy-to-hard ordered and hard-to easy ordered samples have better performance. That led us to investigate what common issues they have. We considered that their common point is growing the training sets during training. Therefore, instead of ordering the samples according to difficulty we only added some samples randomly at each stage. In these experiments we obtained similar results with Curriculum, Anti-curriculum, Self Paced and Self Paced-Inversed methods which are related to difficulty levels. According to these results, we can claim that the success of Curriculum learning and Self paced learning approaches not comes from the fact that they follow a meaningful order but trained by growing training sets.In FIG0 we showed some examples for the individual instances. We started the optimization from θ A , instances under this point are considered as easy and above are difficult. If we take an easy instance it is possible or not to guide the optimization to a better minimum. It will be stop at the local minimum θ B in the worst case. Similarly if we take a difficult instance it is possible or not to obtain a better result. Implementation results also showed that both easy-to-hard and hard-to-easy ordered methods can be successful. Therefore ordering of the samples are not so important to guide the optimization.It is a better situation to shorten the distance between θ B and θ C in FIG2 to bypass the local minimum. When the points are same for a saddle point, training with growing sets will probably overcome this point and find a better minimum. This is a good condition when considering saddle points are so much than local minimums in high dimensional functions as mentioned in BID4 .On many data sets with different distributions we used ensemble method to automatically determine the difficulty of the samples for curriculum learning. Pre-processing for difficulty level determination can be thought to caused slowdown. However it has provided a faster neural network training than SPL. Also it could be said that ensemble method set a better ordering than SPL by considering their number of wins against Baseline.ACL and SPLI, which are the inverse versions of the CL and SPL methods, has performed poorly in some high error rated data sets. The effect of giving the samples at different points during the training has been studied in BID5 . In these methods , noisy examples may be effecting the output more because of giving at the beginning. Nevertheless, the inverse versions of the approaches have better performance than their standard versions. However, CL and SPL methods did not lose in any data set so this shows they have a robust aspect. It is thought that these methods must have a theoretical explanation about ensuring resistance to noises. BID6 studied on why these methods are effectiveness especially on big and noisy data.SPLI method has the most winning against Baseline. In this method strategy of selecting the samples to learn at each stage reminds pool-based active learning BID11 ) in which the learner wants to learn the uncertain samples of the unlabeled data pool. Also non-loss of CL and SPL, and more wins of ACL and SPLI shows the necessity of determining the valuable-example-based curriculum instead of easiness-based-curriculum for the future work.",1346,0.853,762,1.7664041994750657," learning Self paced that suggest put the training samples by considering Studies these topics starting new samples according difficulty levels improves experimented that also obtain adding the samples randomly without a meaningful order We compared our method classical training Curriculum learning Self paced their reverse ordered versions Results the proposed method classical method similar with These results point a new training regime removes the process difficulty level determination Curriculum Self paced as successful these methods BID1 named Curriculum learning the idea following an order related with difficulty the samples during training which provides an optimization non convex objectives After this many researchers tried the most efficient curriculum with BID15 's study conventional curriculum learning did work so they developed BID14 proposed three different curriculum strategies language model adaptation of BID13 looked the best order tasks learn Although these models better generalization performance the proposed curriculum methods the tried methods ensuresA curriculum work so could applicable another work the curriculum logic different applications BID10 suggested decides itself samples easy at This method called Self paced learning combined learning prior information by BID9 . another work BID7 introduced automatically select the syllabus follow the neural networks BID12 also proposed learn simple subtasks before achieved manually designed curriculumIn higher learning performance obtainable some noises easy-tohard ordering BID8 gave preference both easy and diverse samples outperform the conventional Self paced learning BID10 ) algorithm the uncertain samples suggested BID3 lead more accurate and robust SGD training BID0 explored the inversed versions the Self paced learning Self diversity BID8 ) demonstrated performed slightly their standard variants Consistent showed using both curriculum improving generalization performance a wide application area. These researches brings a question minds While natural obtain sorting easyhard why it also sorteasy?In point that to start add both curriculum makes these methods So claim better results only adding new samples stage without a meaningful order We experimented two ordering types related with difficultyeasyhard our method without a meaningful order Training was carried adding set every stage We compared the proposed method two strategies First one Curriculum learning give the difficulty levels the samples preinformation Second one Self paced learning the trained network determines the samples at All methods including usual baseline training the results examined We drew that both versions training with easy-to-hard ordered and hard-to easy ordered samples That led investigate what common issues they We considered their common point growing the training sets during Therefore instead ordering the samples according difficulty we added randomly at these experiments obtained Curriculum Anti Self Paced which related difficulty levels According these results claim Curriculum learning Self paced not comes follow a meaningful order trained growing training setsIn FIG0 for the individual instances We started the optimization from �� A instances under this point easy above difficult If an easy instance it or guide the optimization stop the local minimum �� B in Similarly if a difficult instance it or obtain Implementation results also successful Therefore ordering are so guideIt a better situation shorten �� B FIG2 bypass the local minimum When the points same a saddle point training growing sets probably overcome find a better minimum This a good condition when considering saddle points are so than local minimums high dimensional functions as mentioned BID4 .On many data sets different distributions used ensemble method automatically the difficulty the samples curriculum learning Preprocessing difficulty level determination can thought to caused slowdown However provided a faster neural network training SPL Also it could ensemble method set a better ordering SPL by their number wins against BaselineACL SPLI the inverse versions has performed poorly some high error rated The effect giving the samples has BID5 . these methods , noisy examples effecting more because giving at. Nevertheless the inverse versions the approaches better performance However CL and SPL methods lose in any data so shows a robust aspect thought these methods must a theoretical explanation about ensuring resistance noises BID6 studied on why these methods effectiveness especially big and noisy dataSPLI method winning against Baseline this method strategy selecting the samples learn at reminds pool-based active learning BID11 ) wants the uncertain samples Also nonloss CL and SPL more wins ACL SPLI shows the necessity determining the valuable-example-based curriculum instead",0.01,0.6568097344095569
"We study the problem of learning to map, in an unsupervised way, between domains $A$ and $B$, such that the samples $\vb \in B$ contain all the information that exists in samples $\va\in A$ and some additional information. For example, ignoring occlusions, $B$ can be people with glasses, $A$ people without, and the glasses, would be the added information. When mapping a sample $\va$ from the first domain to the other domain, the missing information is replicated from an independent reference sample $\vb\in B$. Thus, in the above example, we can create, for every person without glasses a version with the glasses observed in any face image. 

 Our solution employs a single two-pathway encoder and a single decoder for both domains. The common part of the two domains and the separate part are encoded as two vectors, and the separate part is fixed at zero for domain $A$. The loss terms are minimal and involve reconstruction losses for the two domains and a domain confusion term. Our analysis shows that under mild assumptions, this architecture, which is much simpler than the literature guided-translation methods, is enough to ensure disentanglement between the two domains. We present convincing results in a few visual domains, such as no-glasses to glasses, adding facial hair based on a reference image, etc. In the problem of unsupervised domain translation, the algorithm receives two sets of samples, one from each domain, and learns a function that maps between a sample in one domain to the analogous sample in the other domain BID37 BID5 BID28 BID29 BID10 BID11 BID38 b; BID26 . The term unsupervised means, in this context, that the two sets are unpaired.In this paper, we consider the problem of domain B, which contains a type of content that is not present at A. As a running example, we consider the problem of mapping between a face without eyewear (domain A) to a face with glasses (domain B). While most methods would map to a person with any glasses, our solution is guided and we attach to an image a ∈ A, the glasses that are present in a reference image b ∈ B.In comparison to other guided image to image translation methods, our method is considerably simpler. It relies on having a latent space with two parts: (i) a shared part that is common to both A and B, and (ii) a specific part that encodes the added content in B. By setting the second part to be the zero vector for all samples in A, a disentanglement emerges. Our analysis shows that this Table 1 : A comparison to other unsupervised guided image to image translation methods.† k = 5 is the number of pre-segmented face parts.‡ Used for domain confusion, not on the output.MUNIT EG-UNIT BID30 DRIT BID27 PairedCycleGAN (Chang' domains. The networks are of four types: encoders, which map images to a latent space, generators (also known as decoders), which generate images from a latent representation, discriminators that are used as part of an adversarial loss, and other, less-standard, networks.It is apparent that our method is considerably simpler than the literature methods. The main reason is that our method is based on the emergence of disentanglement, as detailed in Sec. 4. This allows us to to train with many less parameters and without the need to apply excessive tuning, in order to balance or calibrate the various components of the compound loss.The MUNIT architecture by , like our architecture, employs a shared latent space, in addition to a domain specific latent space. Their architecture is not limited to two domains 1 and unlike ours, employs separate encoders and decoders for the various domains. The type of guiding that is obtained from the target domain in MUNIT is referred to as style, while in our case, the guidance provides content. Therefore , MUNIT, as can be seen in our experiments, cannot add specific glasses, when shifting from the no-glasses domain to the faces with eyewear domain.The EG-UNIT architecture by BID30 presents a few novelties, including an adaptive method of masking-out a varying set of the features in the shared latent space. In our latent representation of domain A, some of the features are constantly zero, which is much simpler. This method also focuses on guiding for style and not for content, as is apparent form their experiments.The very recent DRIT work by BID27 learns to map between two domains using a disentangled representation. Unlike our work, this work seems to focus on style rather than content. The proposed solution differs from us in many ways: (1) it relies on two-way mapping, while we only map from A to B. (2) it relies on shared weights in order to ensure that the common representation is shared. (3) it adds a VAE-like BID24 statistical characterization of the latent space, which results in the ability to sample random attributes. As can be seen in Tab. 1, the solution of BID27 is considerably more involved than our solution.DRIT (and also MUNIT) employ two different types of encoders that enforce a separation of the latent space representations to either style or content vectors. For example, the style encoder , unlike the content encoder, employs spatial pooling and it also results in a smaller representation than the content one. This is important, in the context of these methods, in order to ensure that the two representations encode different aspects of the image. If DRIT or MUNIT were to use the same type of encoder twice, then one encoder could capture all the information, and the image-based guiding (mixing representations from two images) would become mute. In contrast, our method (i) does not separate style and content, and (ii) has a representation that is geared toward capturing the additional content.The work most similar to us in its goal, but not in method, is the PairedCycleGAN work by BID7 . This work explores the single application of applying the makeup of a reference face to a source face image. Unfortunately, the method was only demonstrated on a proprietary unshared dataset and the code is also not publicly available, making a direct comparison impossible at this time. The method itself is completely different from ours and does not employ disentanglement. Instead, a generator with two image inputs is used to produce an output image, where the makeup is transfered between the input images, and a second generator is trained to remove makeup. The generation is done separately to k = 5 pre-segmented facial regions, and the generators do not employ an encoder-decoder architecture.Lastly, there are guided methods, which are trained in the supervised domain, i.e., when there are matches between domain A and B. Unlike the earlier one-to-one work, such as pix2pix BID22 , these methods produce multiple outputs based on a reference image in the target domain. Examples include the Bicycle GAN by , who also applied, as baseline in their experiments, the methods of BID2 BID15 .Other Disentanglement Work InfoGAN BID9 learns a representation in which, due to the statistical properties of the representations, specific classes are encoded as a one-hot encoding of part of the latent vector. In the work of ; BID16 , the representation is disentangled by reducing the class based information within it. The separate class based information is different in nature from our multi-dimensional added content. BID6 , which builds upon BID16 , performs guided image to image translation, but assumes the availability of class based information, which we do not. When converting between two domains, there is an inherent ambiguity that arises from the domainspecific information in the target domain. In guided translation, the reference image in the target domain provides the missing information. Previous work has focused on the missing information that is highly tied to the texture of the image. For example, when translating between paintings and photos, DRIT adds considerable content from the reference photo. However, this is unstructured content, which is not well localized and is highly related to subsets of the image patches that exist in the target domain. In addition, the content from the reference photo that is out of the domain of paintings is not guaranteed to be fully present in the output.Our work focuses on transformations in which the domain specific content is well structured, and guarantees to replicate all of the domain specific information from the reference image. This is done using a small number of networks and a surprisingly simple set of loss terms, which, due to the emergence of a disentangled representation, solves the problem convincingly. In this section we provide notations and terminology that are were not introduced in Sec. 4 but are necessary for the proofs of the claims in this section.We say that three random variables (discrete or continuous) X 1 , X 2 , X 3 form a Markov chain, indicated with DISPLAYFORM0 The Data Processing Inequality (DPI) for a Markov chain X 1 → X 2 → X 3 ensures that I(X 1 ; X 3 ) ≤ min (I(X 1 ; X 2 ), I(X 2 ; X 3 )). In particular, it holds for X 2 = f (X 1 ) and X 3 = g(X 2 ), where f, g are deterministic processes.We denote by x ∼ log N (µ, σ 2 ) a random variable that is distributed by a log-normal distribution, i.e., log x ∼ N (µ, σ 2 ). We consider that the mean and variance of a log-normal distribution log N (µ, σ 2 ) are exp(µ + σ 2 /2) and (exp(σ 2 ) − 1) exp(2µ + σ 2 ) respectively. We denote by W U := (W k,j · U k,j ) k≤m,j≤m the Hadamard product of two matrices W , U ∈ R m×n . For a given vector x ∈ R m , we denote dim(x) := m and for a matrix W ∈ R m×n , we denote dim(W ) := mn. In addition, we denote x 2 = x x = (x 2 1 , . . . , x 2 m ) and DISPLAYFORM1",2121,1.066,1236,1.7160194174757282,"We study the problem learning map in between domains $ such the samples $\vb \in contain exists samples\va\in. For example ignoring occlusions $B$ people glasses the glasses, would the added information When mapping a sample $\va$ the first domain the missing information replicated from an independent reference sample Thus create, every person without glasses a version with the glasses observed any face image Our solution employs a single two-pathway encoder both domains The common part the two domains and the separate part encoded two vectors fixed zero for domain $ The loss terms minimal involve reconstruction losses the two domains a domain confusion term Our analysis under mild assumptions this architecture, much the literature guided-translation methods enough ensure We present convincing results a few visual domains no-glasses to glasses adding facial hair based a reference image etc In the problem unsupervised domain translation the algorithm receives two sets samples learns between a sample the analogous sample BID37 BID5 b; . The term unsupervised means, the two sets are unpairedIn consider domain B contains a type content present at A. As a running example consider mapping between a face without eyeweardomain A While most methods would map a person with any glasses our solution guided and we attach to an image a �� A, the glasses present a reference image b �� B.In comparison other guided image to considerably It relies having a latent space two parts a shared part common both A encodes the added content By setting the second part to the zero vector for all samples A a disentanglement emerges Our analysis this Table : A comparison to other unsupervised guided image to image translation methods.† k 5 is pre-segmented face parts Used domain confusion not on the outputMUNIT EGUNIT BID30 DRIT BID27 PairedCycleGAN (Chang' domains. The networks of four types encoders which map images a latent space generators (also discriminators that are as part an adversarial loss other, less-standard, networksIt apparent our method considerably the literature methods The main reason our method the emergence as detailed Sec 4 This allows to train with many less parameters without apply excessive tuning in balance or the compound lossThe MUNIT architecture by , like our architecture employs a shared latent space addition Their architecture not limited two domains 1 unlike ours employs separate encoders The type guiding that obtained the target domain MUNIT referred style while in provides content. Therefore , MUNIT as can our experiments add specific glasses when shifting the no-glasses domain the faces withThe EG-UNIT architecture by BID30 presents a few novelties an adaptive method masking-out a varying set the features the shared latent space In our latent representation domain A some constantly zero much simpler This method also focuses guiding for style not for content is apparent form their experimentsThe very recent DRIT work BID27 learns map between two domains using a disentangled representation Unlike our work seems focus style The proposed solution differs us ( relies two-way mapping while we only map from A (2 it relies shared weights the common representation shared (3 it adds a VAE-like BID24 statistical characterization the latent space results sample random attributes As can Tab. 1, the solution BID27 considerably involved our solutionDRIT (and also MUNIT employ enforce a separation the latent space representations to either style content vectors For example the style encoder , unlike employs spatial pooling it also results a smaller representation one This important in these methods in the two representations encode different aspects If DRIT or MUNIT use encoder twice capture the image-based guiding (mixing representations from become mute In contrast our method (i separate style a representation geared capturing the additional contentThe work most similar us its goal method the PairedCycleGAN work BID7 . This work explores the single application applying the makeup a reference face a source face image Unfortunately the method was only demonstrated a proprietary unshared dataset the code also making a direct comparison at The method itself completely ours does employ disentanglement Instead a generator with two image inputs where the makeup transfered between trained remove makeup The generation is done separately to k = 5 pre-segmented facial regions the generators do employLastly guided methods trained the supervised domain when matches domain A Unlike the earlier one-to-one work such pix2pix BID22 , these methods produce multiple outputs based a reference image in the target domain Examples include the Bicycle GAN by , who also applied, baseline in methods BID2 BID15 .Other Disentanglement Work InfoGAN BID9 learns a representation in, due the statistical properties specific classes encoded a one-hot encoding part the latent vector In the work ; BID16 , the representation disentangled reducing the class based information within The separate class based information different nature our multi-dimensional added content BID6 , which builds performs guided image to but assumes the availability class based information we When converting between two domains the domainspecific information In guided translation the reference image the target domain provides the missing information Previous work the missing information highly tied the texture For example translating between paintings photos DRIT adds considerable content from the reference photo However unstructured content well localized highly related subsets the image patches exist the target domain In addition the content from the reference photo that out the domain paintings guaranteed fully present the outputOur work focuses transformations which the domain specific content well structured guarantees replicate This done a small number networks a surprisingly simple set loss terms, due the emergence a disentangled representation solves convincingly In provide notations terminology were introduced Sec 4 but are necessary the proofs the claimsWe say three random variablesdiscrete or continuous) X 1 form indicated DISPLAYFORM0 The Data Processing Inequality for ensures ; 3 ≤ min In particular holds for X 2 = fX, are deterministic processesWe denote ∼ log N (��, 2 a random variable distributed We consider the mean variance log log N� 2 are exp /2 (exp(σ� respectively We denote W U := (W k,j · U k k�m the Hadamard product two matrices W , U �� R m×n For a given vector x �� R m denote dim(x and for a matrix W �� R m×n ) mn In addition denote x 2 x 1 . . . , x 2 m ) and DISPLAYFORM1",0.01,0.5284337366337889
"Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test spits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.
 Deep learning, powered by convolutional and recurrent networks, has had remarkable success in areas involving pattern matching (such as in images BID12 , machine translation BID2 BID25 , and reinforcement learning BID17 BID22 ). However, deep models are far from achieving the robustness and flexibility exhibited by humans. They are limited in their ability to generalize beyond the environments they have experienced and are extremely brittle in the presence of adversarially constructed inputs BID23 .One area where human intelligence still differs and excels compared to neural models is discrete compositional reasoning about objects and entities, that ""algebraically generalize"" BID15 . Our ability to generalise within this domain is complex, multi-faceted, and patently different from the sorts of generalisations that permit us to, for example, translate new sentence of French into English. For example, consider the following question from mathematics, with answer ""−70x − 165"".What is g(h(f (x))), where f (x) = 2x + 3, g(x) = 7x − 4, and h(x) = −5x − 8?To solve this problem, humans use a variety of cognitive skills:• Parsing the characters into entities such as numbers, arithmetic operators, variables (which together form functions) and words (determining the question).• Planning (for example, identifying the functions in the correct order to compose).• Using sub-algorithms for function composition (addition, multiplication).• Exploiting working memory to store intermediate values (such as the composition h(f (x))).• Generally applying acquired knowledge of rules, transformations, processes, and axioms.In this paper, we introduce a dataset consisting of many different types of mathematics problems, with the motivation that it should be harder for a model to do well across a range of problem types (including generalization, which we detail below) without possessing at least some part of these abilities that allow for algebraic generalization.This domain is an important one for the analysis of neural architectures in general. In addition to providing a wide range of questions, there are several other advantages: Mathematics offers a self-consistent universe; notation is the same across different problem types, which allows for an easily extendable dataset; and rules and methods learnt on one problem type often apply elsewhere. Addition of numbers (for example ) obeys the same rules everywhere, and occurs as a ""subroutine"" in other problems (such as concretely in multiplication, and both concretely and more abstractly in addition of polynomials); models that possess the ability to transfer knowledge will do well on the dataset (and knowledge transfer may be a necessity for solving harder problems).Mathematics is also an interesting domain in its own right; although models solving the mostly school-level problems in this dataset would not themselves have applications, they may lead on to more powerful models that can solve interesting and substantial new mathematical problems. But more generally, it is no coincidence that experiments seeking to validate new architectures which aim capture algorithmic/systematic reasoning have often been drawn from this domain BID10 , and thus in providing a large scale training and evaluation framework for such models, we hope to provide a solid foundation upon which to continue such research into machine reasoning beyond mathematics.Question: Solve -42 * r + 27 * c = -1167 and 130 * r + 4 * c = 372 for r. Answer: 4 Question: Calculate -841880142.544 + 411127. Answer: -841469015.544 Question: Let x(g) = 9 * g + 1. Let q(c) = 2 * c + 1. Let f(i) = 3 * i -39. Let w(j) = q(x(j)). Calculate f(w(a )). Answer: 54 * a -30 Question: Let e(l ) = l -6. Is 2 a factor of both e(9) and 2? Answer: False Question: Let u(n) = -n ** 3 -n ** 2. Let e(c) = -2 * c ** 3 + c. Let l(j) = -118 * e(j) + 54 * u(j ). What is the derivative of l(a)? Answer: 546 * a ** 2 -108 * a -118 Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql. Answer: 1/110Figure 1: Examples from the dataset. We have created a dataset on which current state-of-the-art neural models obtain moderate performance. Some modules are largely unsolved (for example those requiring several intermediate calculations), for which a human would find easy, and extrapolation performance is low. We hope this dataset will become a robust analyzable benchmark for developing models with more algebraic/symbolic reasoning abilities.The dataset is easily extendable, since it is modular, with all modules using a common input/output format and the common language of mathematics. The main restriction is that the answers must be well-determined (i.e. unique), but this still allows for covering a lot of mathematics up to university level. At some point it becomes harder to cover more of mathematics (for example, proofs) while maintaining the sequence-to-sequence format, but hopefully by this point the dataset in its current format will have served its purpose in developing models that can reason mathematically. Alternatively, we could consider methods for assessing answers where there is not a single unique answer; for now the full scope of possibilities is too large to include in this paper, but a few possibilities include metrics such as BLEU BID18 , by extending the data generation process to provide several reference answers, or by obtaining human paraphrases following the data augmentation process proposed by BID27 .We have not addressed linguistic variation or complexity in this dataset. Although to some extent linguistic complexity is orthogonal to the difficulty of the maths problems involved, the two cannot be entirely separated. The most obvious example of this for school-level mathematics is in algebraic word problems, where much of the difficulty lies in translating the description of the problem into an algebraic problem. Thus it would be useful to extend the dataset with ""linguistic complexity"", where the same underlying mathematical problem is phrased in quite distinct, and not-at-first-obvious, translations. One option may be to do joint training on this dataset, and that of BID14 another would be to obtain more question templates via mechanical turking, as proposed by BID27 .Finally one completely distinct direction the dataset could be extended is to include visual (e.g. geometry) problems as well. For humans, visual reasoning is an important part of mathematical reasoning, even concerning problems that are not specified in a visual format. Therefore we want to develop questions along these lines, including those that require ""intermediate visual representations"" (in a similar way to how the textual module composition requires intermediate digital representations) and visual working memory. Note that reasoning with intermediate visual representations or ideas is richer than simply analyzing a visual domain (such as is typical in visual question-answering datasets).",1655,0.745,946,1.7494714587737843,"Mathematical reasoning---a core ability within human intelligencepresents as a domain: we do come primarily on the back experience evidence inferring learning exploiting laws symbol manipulation rules In this paper a new challenge the evaluation ( eventually the design neural architectures similar system, developing a task suite mathematics problems involving sequential questions answers The structured nature the mathematics domain covering calculus enables training test spits designed clearly illuminate failure-modes different architectures evaluate their ability compose relate knowledge learned processes Having described the data generation process its potential future expansions conduct models from two broad classes the most powerful sequenceto architectures find notable differences resolve mathematical problems generalize their knowledge Deep learning powered had areas involving pattern matching ( in images BID12 , machine translation BID2 BID25 reinforcement However deep models far achieving flexibility exhibited humans They limited generalize beyond the environments extremely brittle adversarially constructed inputs BID23 .One area human intelligence still differs and excels compared neural models discrete compositional reasoning about objects entities that ""algebraically generalize BID15 Our ability generalise within this domain complex multi patently different the sorts permit, translate new sentence of French For example consider from mathematics, with answer ""−70x − 165""What g(h(f (, solve humans cognitive skills:• Parsing the characters into entities such arithmetic operators variables (which together form functions words (for identifying the functions to Using sub function compositionaddition working memory store intermediate values the composition h(f Generally applying acquired knowledge rules transformations processesIn introduce a dataset consisting mathematics problems the motivation that harder a model do acrossincluding which detail possessing at least some part these abilities that allowThis domain neural architectures In addition providing questions there several other advantages: Mathematics offers a self-consistent universe; notation the across different problem types which an easily extendable dataset rules methods learnt on often apply elsewhere Addition numbers (for ) obeys everywhere occurs other problems concretely in multiplication both more addition of models possess transfer knowledge will do on the dataset knowledge transfer may a necessity solving harder problems).Mathematics although models solving the mostly school-level problems this dataset would not themselves applications lead on interesting and substantial new mathematical problems But more generally no coincidence experiments seeking validate new architectures which aim capture algorithmic/systematic reasoning drawn this domain BID10 , in providing a large scale training and evaluation framework such models we hope upon continue into machine reasoning beyond mathematicsQuestion Solve -42 * r + 27 -1167 and 130 * r 4 372 for r. Answer 4 Question Calculate -841880142.544 + 411127. Answer -841469015.544 Question Let x(g 9 * Let q(c 2 Let f(i 3 -39 Let w(j Calculate f(w(a ) Answer 54 * a -30 Question Let e(l ) l -6 Is 2 a factor both e(9 2 Answer: False Question Let u(n = -n ** Let e(c -2 Let l(j -118 * 54 ). What the derivative l(a Answer 546 * a 2 -108 a -118 Question Three letters picked without replacement from qqqkkklkqkkk Give prob of sequence qql Answer 1/110Figure Examples from the dataset We created a dataset on which current state- neural models obtain moderate performance Some modules largely unsolved (for those requiring several intermediate calculations for a human find easy, extrapolation performance low We hope this dataset become a robust analyzable benchmark developing models more algebraic/symbolic reasoning abilitiesThe dataset easily since modular all modules using the common language mathematics The main restriction the answers welldetermined ( unique still allows covering mathematics up university level At it harder cover more mathematics (for proofs while sequence-to format hopefully by the dataset in served in developing models reason mathematically Alternatively we methods assessing answers where not; now the full scope possibilities too large include metrics BLEU BID18 , by extending the data generation process provide several reference answers obtaining human paraphrases following proposed BID27 .We not addressed linguistic variation complexity this dataset Although to some extent linguistic complexity the difficulty the maths problems two entirely The most obvious example for school-level mathematics algebraic word problems much translating the description Thus would useful extend the dataset with ""linguistic complexity the same underlying mathematical problem phrased quite distinct, notatfirstobvious translations One option may do joint training this dataset that of BID14 another would obtain more question templates via mechanical turking proposed BID27 .Finally one completely distinct direction the dataset extended visual (e.g. geometry) problems For humans visual reasoning mathematical reasoning even concerning problems specified a visual format Therefore want develop questions along including require ""intermediate visual representationsin the textual module composition requires intermediate digital representations visual working memory Note reasoning intermediate visual representations or ideas richer simply analyzing a visual domain is typical visual question-answering datasets",0.01,0.6136665987970235
"Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported stencils and point-wise nonlinearities.
 Commonly, the convolution operators couple features from all channels.
 For wide networks, this leads to immense computational cost in the training of and prediction with CNNs.
 In this paper, we present novel ways to parameterize the convolution more efficiently, aiming to decrease the number of parameters in CNNs and their computational complexity.
 We propose new architectures that use a sparser coupling between the channels and thereby reduce both the number of trainable weights and the computational cost of the CNN.
 Our architectures arise as new types of residual neural network (ResNet) that can be seen as discretizations of a Partial Differential Equations (PDEs) and thus have predictable theoretical properties. Our first architecture involves a convolution operator with a special sparsity structure, and is applicable to a large class of CNNs. Next, we present an architecture that can be seen as a discretization of a diffusion reaction PDE, and use it with three different convolution operators. We outline in our experiments that the proposed architectures,  although considerably reducing the number of trainable weights, yield comparable accuracy to existing CNNs that are fully coupled in the channel dimension.
 Convolutional Neural Networks (CNNs) BID18 are among the most effective machine learning approaches for processing structured high-dimensional input data and are indispensable in, e.g., in recognition tasks involving speech BID22 and image data BID16 . The essential idea behind CNNs is to replace some or all of the affine linear transformations in a neural network by convolution operators that are typically parameterized using small-dimensional stencils. This has a number of benefits including the increase of computational efficiency of the network due to the sparse connections between features, and a considerable reduction in the number of weights since stencils are shared across the whole feature map BID6 .In practical applications of CNNs, the features can be grouped into channels whose number is associated with the width of the network. This gives one several opportunities to define interactions between the different channels. Perhaps , the most common approach in CNNs is to fully couple features across channels BID7 BID6 BID16 . Following this approach, the number of convolution operators at a layer is proportional to the product of the number of input and output channels. Given that performing convolutions is often the computationally most expensive part in training of and prediction with CNNs and the number of channels is large in many applications, this scaling can be problematic for wide architectures or high-dimensional data. Another disadvantage of this type of architecture is the number of weights. Indeed, for deep neural networks, the number of weights that are associated with a wide network can easily reach millions and beyond. This makes the deployment of such networks challenging, especially on devices with limited memory.In this paper, we propose four novel ways to parameterize CNNs more efficiently, based on ideas from Partial Differential Equations (PDEs). Our goal is to dramatically reduce the number of weights in the networks and the computational costs of training and evaluating the CNNs. One ides, similar to BID13 , is to use spatial convolutions for each channel individually and add Table 1 : Cost comparison of different convolution layers for an image with n pixels, stencil of size m × m, and c input and output channels. RD denotes a reaction-diffusion architecture.no. of weights computational costs fully-coupled DISPLAYFORM0 1 × 1 convolutions to impose coupling between them. Our architectures are motivated by the interpretation of residual neural networks (ResNets) BID11 BID18 as time-dependent nonlinear PDEs BID24 . More specifically, we consider a simple Reaction-Diffusion (RD) model, that can model highly nonlinear processes. We derive new architectures by discretizing this continuous model, using 1×1 convolutions as a reaction term, together with cheap forms of a spatial convolution, that are similar to a depth-wise convolution in the number of parameters and cost. This spatial convolution acts similarly to a linear diffusion term that smooths the feature channels. Since the networks we propose originate in continuous models they have distinct theoretical properties that can be predicted using the standard theory of ODEs and PDEs BID0 .Our first approach is designed to be employed in any existing CNN layer with equal number of input and output channels. We simply replace the traditional fully coupled convolution with a linear sum of depth-wise and 1 × 1 convolution, like a mask that can be placed on a traditional convolution in any existing CNN. Our second ""explicit"" RD architecture applies the operators separately with a non-linear activation function operating only following the 1 × 1 convolution, as the non-linear reaction part of the diffusion reaction equation. The third architecture is more unique . To improve the stability of the forward propagation and increase the spatial coupling of the features, we propose a semi-implicit scheme for the forward propagation through the network. Unlike traditional CNN operators, the semi-implicit scheme applies an inverse of the depth-wise (block diagonal) convolution preceded by a non-linear step involving the 1 × 1 convolution. This way, the scheme couples all the pixels in the image in one layer, even though we are using a depth-wise 3 × 3 convolution. The inverse of the convolution operator can be efficiently computed using Fast Fourier Transforms (FFT) and over the channels and kernels.The last idea is to replace the depth-wise convolution structure with a circulant connectivity between the channels. This is motivated by the interpretation of the features as tensors and follows the definition of an efficient tensor product in BID14 whose associated tensor singular value decomposition has been successfully used for image classification in BID20 . The circulant structure renders the number of trainable convolution stencils proportional to the width of the layer. Using periodic boundary conditions in the other feature dimensions, this convolution can be computed efficiently by extending the FFT-based convolutions in BID19 BID26 along the channel dimension, which reduces the cost from O(c 2 ) to O(c log c) where c is the number of channels. Table 1 compares the number of weights and the computational complexity associated with the forward propagation through a layer for the standard and reduced architectures. In the table we assume that the explicit RD architecture is directly computed without using FFT, but the FFT-based implementation, which is necessary for the implicit scheme, can also be used for the explicit one.Our architectures pursue a similar goal than the recently proposed MobileNet architectures that are also based on a mix of 1 × 1 and ""depth-wise"" convolutions BID13 BID25 . The MobileNet architecture involves with significantly less parameters, and in particular avoids the fully coupled convolutions, except for 1 × 1 convolutions which are cheaper in both computational cost and number of parameters. What sets our work apart from these architectures is that our architectures can be seen as discretization of PDEs, which allows to control their stability and offers new ways for their analysis.The remainder of the paper is organized as follows. We first describe the mathematical formulation of the supervised classification problem with deep residual neural networks used in this paper. Subsequently, we propose the novel parameterizations of CNNs, describe their efficient implementation, and their computational costs. We perform experiments using the CIFAR10, CIFAR 100, and STL10 datasets and demonstrate that the performance of the new architectures, despite a considerable reduction in the number of trainable weights, is comparable to residual neural networks using fully-coupled convolutions. Finally, we summarize and conclude the paper. We present four new convolution models with the common goal of reducing the number of parameters and computational costs of CNNs. To this end, we propose alternative ways to the traditional full coupling of channels, and thereby obtain architectures that involve fewer expensive convolutions, avoid redundancies in the network parametrization, and thereby can be deployed more widely. Our work is similar to that of BID13 BID25 . However, our unique angle is the close relation of our architectures to continuous models given in terms of PDEs that are well understood. This highlights stability of our CNNs and paves the way toward more extensive theory.Our numerical experiments for image classification show that the new architectures can be almost as effective as more expensive fully coupled CNN architectures. We expect that our architectures will be able to replace the traditional convolutions in classification of audio and video, and also in other tasks that are treated with CNNs. It is important to realize that our new architectures become even more advantageous for 3D or 4D problems, e.g., when analyzing time series of medical or geophysical images. In these cases, the cost of each convolution is much more expensive and the computational complexity makes using 3D CNNs difficult. Here, also the number of weights imposes challenges when using computational hardware with moderate memory.",1783,0.889,1041,1.712776176753122," filter spatial convolution operators with compactly supported stencils Commonly the convolution operators couple features all channels For wide networks leads immense computational cost in the training and prediction with CNNs novel ways parameterize more aiming decrease parameters We propose new architectures a sparser coupling the channels thereby trainable weights the CNN Our architectures arise as new types residual neural networkResNet that seen discretizations a Partial Differential Equations thus have predictable theoretical properties Our first architecture involves a convolution operator a special sparsity structure is applicable a large class CNNs Next present seen a diffusion reaction PDE use with We outline in our experiments the proposed architectures although considerably reducing trainable weights yield comparable accuracy existing CNNs that fully coupled the channel dimension Convolutional BID18 are among processing indispensable, in recognition tasks involving speech BID22 The essential idea CNNs replace some the affine linear transformations convolution operators typically parameterized small-dimensional stencils This has a number including the increase computational efficiency due the sparse connections features a considerable reduction weights since stencils shared the whole feature map BID6 .In practical applications CNNs the features grouped channels whose number associated the width This gives one several opportunities define interactions the different channels Perhaps , CNNs fully couple features across channels BID7 BID6 BID16 . Following this approach convolution operators at a layer proportional the product Given performing convolutions often in training of and prediction with CNNs the number channels large this scaling can problematic wide architectures or Another disadvantage architecture weights Indeed for deep neural networks weights associated a wide network easily millions beyond This makes the deployment such networks challenging on devicesIn four novel ways parameterize CNNs more based ideas Partial Differential Equations Our goal dramatically weights the networks the computational costs evaluating the CNNs One ides, similar BID13 , spatial convolutions each channel individually add Table : Cost comparison an image n pixels stencil of size m c input and output channels RD denotes a reaction-diffusion architecture.no of weights computational costs fully- DISPLAYFORM0 1 × convolutions to impose coupling them Our architectures motivated the interpretation residual neural networksResNets BID11 BID18 as . More specifically consider a simple Reaction-Diffusion (RD) model that model highly nonlinear processes We derive new architectures by discretizing this continuous model 1×1 convolutions a reaction term together cheap forms a spatial convolution that similar the number parameters cost This spatial convolution acts similarly a linear diffusion term smooths the feature channels Since the networks we propose originate continuous models they distinct theoretical properties predicted the standard theory PDEs BID0 .Our designed employed any existing CNN layer equal number We simply replace the traditional fully coupled convolution with a linear sum depthwise like a mask that placed in any existing CNN Our second ""explicit"" RD architecture applies the operators separately with operating only following the 1 × 1 convolution, the non-linear reaction part the diffusion reaction equation The third architecture more unique . To improve the forward propagation increase the spatial coupling the features propose a semi-implicit scheme through Unlike traditional CNN operators the semi-implicit scheme applies an inverse the depth-wise (block diagonal) convolution preceded involving This way, the scheme couples all the pixels in even a depth-wise 3 × 3 convolution The inverse the convolution operator can efficiently over the channels kernelsThe last idea replace the depth-wise convolution structure a circulant connectivity between This motivated the interpretation the features as tensors follows an efficient tensor product BID14 whose associated tensor singular value decomposition has successfully image classification The circulant structure renders the number trainable convolution stencils proportional Using periodic boundary conditions the other feature dimensions this convolution can computed efficiently extending BID19 BID26 along the channel dimension reduces from O(c 2 Table 1 compares weights the computational complexity associated the forward propagation through a layer for the standard and reduced architectures In the table we assume the explicit RD architecture directly computed without FFT, necessary the implicit scheme oneOur architectures pursue than the recently proposed MobileNet architectures that also a mix 1 × 1 and ""depth-wise"" convolutions BID13 BID25 The MobileNet architecture involves with significantly less parameters in avoids the fully coupled convolutions except 1 × 1 convolutions cheaper both computational cost number What sets our work these architectures seen discretization PDEs allows to control their stability offers their analysisThe remainder organized We first describe the mathematical formulation the supervised classification problem deep residual neural networks used Subsequently propose the novel parameterizations CNNs describe their efficient implementation their computational costs We perform experiments the CIFAR10, 100 STL10 datasets demonstrate the new architectures, despite trainable weights residual neural networks using Finally summarize conclude We present four new convolution models the common goal reducing parameters computational costs CNNs To alternative ways the traditional full coupling channels thereby obtain architectures involve fewer expensive convolutions avoid thereby can deployed widely Our work similar BID13 BID25 . However our unique angle the close relation our architectures continuous models given in terms PDEs that well understood This highlights stability our CNNs paves toward more extensive theoryOur numerical experiments for image classification the new architectures almost more fully coupled CNN architectures We expect our architectures replace the traditional convolutions classification audio also in other tasks treated CNNs It become advantageous analyzing medical or geophysical images In these cases the cost each convolution much and makes using 3D CNNs Here also the number weights imposes challenges when using computational hardware with moderate memory",0.01,0.5201702442206027
"In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equivalently a lower bound on the negative log likelihood) that the model can assign to some data as one varies the prior and/or the likelihood function in a latent variable model. The core of our contribution is to formally show that the problem of optimizing priors in latent variable models is exactly an instance of the variational optimization problem that information theorists solve when computing rate-distortion functions, and then to use this to derive a lower bound on negative log likelihood. Moreover, we will show that if changing the prior can improve the log likelihood, then there is a way to change the likelihood function instead and attain the same log likelihood, and thus rate-distortion theory is of relevance to both optimizing priors as well as optimizing likelihood functions. We will experimentally argue for the usefulness of quantities derived from rate-distortion theory in latent variable modeling by applying them to a problem in image modeling. A statistician plans to use a latent variable model DISPLAYFORM0 where p(z) is known as the prior over the latent variables, and (x|z) is the likelihood of the data conditional on the latent variables; we will often use (p(z), (x|z)) as a shorthand for the model. Frequently, both the prior and the likelihood are parametrized and the statistician's job is to find reasonable parametric families for both -an optimization algorithm then chooses the parameter within those families. The task of designing these parametric families can sometimes be time consuming -this is one of the key modeling tasks when one adopts the representation learning viewpoint in machine learning.In this article we ask the question of how much p(z) can be improved if one fixes (x|z) and viceversa, with the goal of equipping the statistician with tools to make decisions on where to invest her time. One way to answer whether p(z) can be improved for fixed (x|z) is to drop the assumption that p(z) must belong to a particular family and ask how a model could improve in an unrestricted setting. Mathematically, given data {x 1 , · · · , x N } the first problem we study is the following optimization problem: for a fixed (x|z), DISPLAYFORM1 which as we will show, is also indirectly connected to the problem of determining if (x|z) can be improved for a given fixed p(z). The quantity being optimized in (2) is called the average negative log likelihood of the data, and is used whenever one assumes that the data {x 1 , · · · , x N } have been drawn statistically independently at random. Note that in this paper we are overloading the meaning of p(z): in (1) it refers to prior in the ""current"" latent variable model in the statistician's hands, and in (2) and other similar equations, it refers to a prior that can be optimized. We believe that the meaning will be clear depending on the context.Obviously, for any given (x|z), p(z), from the definition (1) we have the trivial upper bound DISPLAYFORM2 Can we give a good lower bound? A lower bound could tell us how far we can improve the model by changing the prior. The answer turns out to be in the affirmative. In an important paper, BID14 proved several facts about the problem of optimizing priors in latent variable models. In particular, he showed that DISPLAYFORM3 This result is very general -it holds for both discrete and continuous latent variable spaces, scalar or vector. It is also sharp -if you plug in the right prior, the upper and lower bounds match. It also has the advantage that the lower bound is written as a function of the trivial upper bound (3) -if someone proposes a latent variable model p(x) which uses a likelihood function (x|z), the optimal negative log likelihood value when we optimize the prior is thus known to be within a gap of DISPLAYFORM4 bits. The individual quantities under the sup c(z) DISPLAYFORM5 have a specific functional meaning: they can be regarded as multiplicative factors that tell you how to modify the prior to improve the log likelihood (see the Blahut-Arimoto algorithm BID3 ): DISPLAYFORM6 Lindsay (1983) derived his results with no apparent reference to earlier published work on ratedistortion theory, which is how information theorists study the problem of lossy compression BID19 . There is no reason for why this connection could be reasonably made, as it is not immediately obvious that the problems are connected; However, the quantity c(z) and the lower bound (4) in fact can be derived from ideas in Berger's book on rate-distortion theory BID2 ; in fact Lindsey's classical result that the optimal prior in a latent variable model has finite support with size equal to the size of the training data can be, drawing the appropriate connection, seen as a result of a similar result in rate-distortion theory also contained in BID2 .With time, the fundamental connection between the log likelihood optimization in latent variable modeling and the computation of rate-distortion functions became more clear. Although not explicitly mentioned in these terms, BID18 BID16 restate the optimal log likelihood as a problem of minimizing the variational free energy of a certain statistical system; this expression is identical to the one that is optimized in rate-distortion theory. The Information Bottleneck method of BID22 is a highly successful idea that exists in this boundary, having created a subfield of research that remains relevant nowadays BID23 ) BID20 . BID21 showed a fundamental connection between maximum likelihood and the information bottleneck method: ""every fixed point of the IB-functional defines a fixed point of the (log) likelihood and vice versa"". BID1 defined a rate-distortion problem where the output alphabet Z is finite and is jointly optimized with the test channel. By specializing to the case of where the distortion measure is a Bregman divergence, they showed the mathematical equivalence between this problem and that of maximum likelihood estimation where the likelihood function is an exponential family distribution derived from the Bregman divergence. BID27 study a variation of the maximum likelihood estimation for latent variable models where the maximum likelihood criterion is instead replaced with the entropic risk measure. The autoencoder concept extensively used in the neural network community is arguably directly motivated by the encoder/decoder concepts in lossy/lossless compression. BID7 proposed using a matrix based expression motivated by rate-distortion ideas in order to train autoencoders while avoiding estimating mutual information directly. Recently, BID0 exploited the β-VAE loss function of BID8 to explicitly introduce a trade-off between rate and distortion in the latent variable modeling problem, where the notions of rate and distortion have similarities to those used in our article.Latent Variable Modeling is undergoing an exciting moment as it is a form of representation learning, the latter having shown to be an important tool in reaching remarkable performance in difficult machine learning problems while simultaneously avoiding feature engineering. This prompted us to look deeper into rate-distortion theory as a tool for developing a theory of representation learning. What excites us is the possibility of using a large repertoire of tools, algorithms and theoretical results in lossy compression in meaningful ways in latent variable modeling; notably, we believe that beyond what we will state in this article, Shannon's famous lossy source coding theorem, the information theory of multiple senders and receivers, and the rich Shannon-style equalities and inequalities involving entropy and mutual information are all of fundamental relevance to the classical problem (1) and more complex variations of it.The goal of this article is laying down a firm foundation that we can use to build towards the program above. We start by proving the fundamental equivalence between these two fields by using simple convexity arguments, avoiding the variational calculus arguments that had been used before. We then take an alternate path to proving (2) also involving simple convexity arguments inspired by earlier results in rate-distortion theory.We then focus on what is a common problem -instead of improving a prior for a fixed likelihood function, improve the likelihood function for a fixed prior but for a fixed prior. Interestingly, ratedistortion theory still is relevant to this problem, although the question that we are able to answer with it is smaller in scope. Through a simple change of variable argument , we will argue that if the negative log likelihood can be improved by modifying the prior, exactly the same negative log likelihood can be attained by modifying the likelihood function instead. Thus if rate-distortion theory predicts that there is scope for improvement for a prior, the same holds for the likelihood function but conversely, while rate-distortion theory can precisely determine when it is that a prior can no longer be improved, the same cannot be said for the likelihood function.Finally, we test whether the lower bound derived and the corresponding fundamental quantity c(z) are useful in practice when making modeling decisions by applying these ideas to a problem in image modeling for which there have been several recent results involving Variational Autoencoders. The main goal for this article was to argue strongly for the inclusion of rate-distortion theory as key for developing a theory of representation learning. In the article we showed how some classical results in latent variable modeling can be seen as relatively simple consequences of results in ratedistortion function computation, and further argued that these results help in understanding whether prior or likelihood functions can be improved further (the latter with some limitations), demonstrating this with some experimental results in an image modeling problem. There is a large repertoire of tools, algorithms and theoretical results in lossy compression that we believe can be applied in meaningful ways to latent variable modeling. For example, while rate-distortion function computation is an important subject in information theory, the true crown jewel is Shannon's famous source coding theorem; to-date we are not aware of this important result being connected directly to the problem of latent variable modeling. Similarly, rate-distortion theory has evolved since Shannon's original publication to treat multiple sources and sinks; we believe that these are of relevance in more complex modeling tasks. This research will be the subject of future work.",2092,0.852,1253,1.6695929768555466,"In use rate-distortion theory a branch information theory devoted lossy compression shed latent variable modeling is room One way address find an upper bound (equivalently a lower the negative log likelihood can assign some data as one varies prior likelihood function The core our contribution formally show optimizing priors latent variable models exactly an instance information theorists solve computing rate-distortion functions then use derive lower negative log likelihood Moreover we will show if changing prior can improve the log likelihood there instead and attain rate-distortion theory of relevance both optimizing priors as optimizing We will experimentally argue the usefulness quantities derived rate-distortion theory latent variable modeling by applying a problem image modeling A statistician plans a latent variable model DISPLAYFORM0 where p(z known prior over ( conditional; we often ( Frequently, both prior the likelihood and the statistician's job reasonable parametric families both -an optimization algorithm then chooses within The task designing these parametric families can sometimes time -this the key modeling tasks when one the representation learning viewpointIn ask how much p(z improved if fixes ( viceversa with equipping the statistician tools decisions where invest her time One way answer whether p(z improved for fixed (x|z drop must belong a particular family ask a model improve in an unrestricted setting Mathematically given data { 1 · · N } the first problem we study the following optimization problem for a fixed (x|z DISPLAYFORM1 which as show also indirectly connected determining ( improved for a given fixed p(z The quantity being optimized (2 called the average negative log likelihood whenever one {x 1 · · , N have drawn statistically independently at Note overloading the meaning p(z): in ( prior in the ""current"" latent variable model in the statistician's hands and other similar equations optimized We believe the meaning will dependingObviously for any (x|z, p(z from ( we the trivial upper bound DISPLAYFORM2 Can give good lower A lower bound could tell improve the model changing prior. The answer turns in In an important paper BID14 proved several facts optimizing priors latent variable models In particular he showed DISPLAYFORM3 This result very general -it holds both discrete and continuous latent variable spaces scalar It sharp -if plug right prior the upper and lower bounds match It also lower bound written trivial upper3 -if someone proposes a latent variable model p(x uses a likelihood functionx|z the optimal negative log likelihood value when we optimize prior thus known within a gap DISPLAYFORM4 bits The individual quantities under the sup c(z DISPLAYFORM5 have a specific functional meaning: regarded multiplicative factors tell to modify prior to improve the log likelihood the Blahut-Arimoto algorithm BID3 ): DISPLAYFORM6 Lindsay1983 derived his results with no apparent reference earlier published work ratedistortion theory how information theorists study lossy compression BID19 There why this connection reasonably immediately the problems; However, the quantity c(z lower4 in fact can derived ideas Berger's book rate-distortion theory BID2 ; in Lindsey classical result that optimal prior in a latent variable model finite support with size equal, drawing the appropriate connection seen a similar result also contained the fundamental connection the log likelihood optimization in the computation became Although not explicitly these terms BID18 BID16 restate the optimal log likelihood as a problem minimizing the variational free energy a certain statistical system; this expression identical optimized rate-distortion theory The Information Bottleneck method BID22 a highly successful idea exists this boundary, having created a subfield research remains nowadays BID23 ) . BID21 showed a fundamental connection maximum likelihood the information bottleneck method: ""every fixed point the IB-functional defines the (log) likelihood and vice BID1 defined a rate-distortion problem the output alphabet Z finite is jointly optimized the test channel By specializing to the case where the distortion measure a Bregman divergence they showed the mathematical equivalence this problem maximum likelihood estimation where an exponential family distribution derived BID27 study a variation the maximum likelihood estimation for latent variable models where instead replaced the entropic risk measure The autoencoder concept extensively the neural network community arguably directly motivated lossy/lossless compression BID7 proposed using a matrix based expression motivated rate-distortion ideas train while estimating mutual information directly Recently BID0 exploited the β-VAE loss function BID8 explicitly introduce rate distortion the latent variable modeling problem the notions rate similarities our articleLatent Variable Modeling undergoing an exciting moment a form representation learning the latter having shown reaching remarkable performance difficult machine learning problems while avoiding feature engineering This prompted deeper rate-distortion theory as developing representation learning What excites using a large repertoire algorithms theoretical results lossy compression in meaningful ways in latent variable modeling; notably believe beyond what will state Shannon's famous lossy source coding theorem the information theory multiple senders the rich Shannon-style equalities and involving entropy mutual information of the classical problem ( more complex variationsThe goal laying towards the program above We start proving the fundamental equivalence these two fields simple convexity arguments avoiding the variational calculus arguments had We then take an alternate path proving (2 also involving simple convexity arguments inspired earlier results rate-distortion theoryWe focus what a common problem -instead improving a prior for a fixed likelihood function improve prior but for prior Interestingly ratedistortion theory still is relevant this problem that able smaller Through a simple change variable argument , will argue the negative log likelihood can improved modifying prior attained instead Thus if rate-distortion theory predicts there scope improvement for prior, same holds the likelihood function but conversely while can precisely determine when that noFinally test lower derived and corresponding fundamental quantity c(z useful practice when making modeling decisions by applying these ideas image modeling for have several recent results involving The main goal argue strongly rate-distortion theory key for developing representation learning In the article showed some classical results latent variable modeling seen relatively simple consequences results ratedistortion function computation further argued help whether prior or likelihood functions improved further (the with some limitations demonstrating this with an image modeling problem There a large repertoire tools algorithms theoretical results lossy compression believe meaningful ways latent variable modeling For example while rate-distortion function computation an important subject information theory the true crown jewel Shannon's famous source coding theorem; to- we this important result being connected latent variable modeling Similarly rate-distortion theory evolved Shannon's original publication to treat multiple sources and sinks; we believe of relevance more complex modeling tasks This research will the subject",0.01,0.4101432449160394
"Backprop is the primary learning algorithm used in many machine learning algorithms. In practice, however, Backprop in deep neural networks is a highly sensitive learning algorithm and successful learning depends on numerous conditions and constraints. One set of constraints is to avoid weights that lead to saturated units. The motivation for avoiding unit saturation is that gradients vanish and as a result learning comes to a halt. Careful weight initialization and re-scaling schemes such as batch normalization ensure that input activity to the neuron is within the linear regime where gradients are not vanished and can flow. Here we investigate backpropagating error terms only linearly. That is, we ignore the saturation that arise by ensuring gradients always flow. We refer to this learning rule as Linear Backprop since in the backward pass the network appears to be linear. In addition to ensuring persistent gradient flow, Linear Backprop is also favorable when computation is expensive since gradients are never computed. Our early results suggest that learning with Linear Backprop is competitive with Backprop and saves expensive gradient computations.",204,0.154,124,1.6451612903225807,Backprop is the primary learning algorithm practice Backprop in deep neural networks learning successful learning numerous conditions constraints One set constraints weights lead saturated units The motivation avoiding unit saturation gradients vanish as comes Careful weight initialization and re-scaling schemes such batch normalization ensure input activity to the neuron within the linear regime where gradients vanished flow Here investigate backpropagating error terms only linearly That ignore the saturation arise ensuring gradients always flow We refer this learning rule Linear Backprop since the backward pass the network appears ensuring persistent gradient flow Linear Backprop favorable computation expensive since never computed Our early results learning with Linear Backprop is competitive saves expensive gradient computations,0.0,0.3478934541745506
"Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning  abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models,  however, despite several recent improvements, the training of discrete latent variable models has remained  challenging and their performance has mostly failed to match their continuous counterparts. Recent work on vector quantized autoencoders (VQ-VAE) has made substantial progress in this direction, with its perplexity almost matching that of a VAE on datasets such as CIFAR-10. In this work, we investigate an alternate training technique for VQ-VAE, inspired by its connection to the Expectation Maximization (EM) algorithm. Training the discrete autoencoder with EM and combining it with sequence  level knowledge distillation alows us to develop a non-autoregressive machine translation model whose accuracy almost matches a strong greedy autoregressive baseline Transformer, while being 3.3 times faster at inference.
 Unsupervised learning of meaningful representations is a fundamental problem in machine learning since obtaining labeled data can often be very expensive. Continuous representations have largely been the workhorse of unsupervised deep learning models of images BID4 BID16 BID28 BID25 , audio BID27 , and video . However, it is often the case that datasets are more naturally modeled as a sequence of discrete symbols rather than continuous ones. For example, language and speech are inherently discrete in nature and images are often concisely described by language, see e.g., . Improved discrete latent variable models could also prove useful for learning novel data compression algorithms BID32 , while having far more interpretable representations of the data.We build on Vector Quantized Variational Autoencoder (VQ-VAE) , a recently proposed training technique for learning discrete latent variables. The method uses a learned code-book combined with nearest neighbor search to train the discrete latent variable model. The nearest neighbor search is performed between the encoder output and the embedding of the latent code using the 2 distance metric. VQ-VAE adopts the standard latent variable model generative process, first sampling latent codes from a prior, P (z), which are then consumed by the decoder to generate data from P (x | z). In van den , the authors use both uniform and autoregressive priors for P (z). The resulting discrete autoencoder obtains impressive results on unconditional image, speech, and video generation. In particular, on image generation, VQ-VAE was shown to perform almost on par with continuous VAEs on datasets such as CIFAR-10 (van den ). An extension of this method to conditional supervised generation, out-performs continuous autoencoders on WMT English-German translation task .The work of introduced the Latent Transformer, which set a new stateof-the-art in non-autoregressive Neural Machine Translation. However , additional training heuristics, namely, exponential moving averages (EMA) of cluster assignment counts, and product quantization BID24 were essential to achieve competitive results with VQ-VAE. In this work, we show that tuning for the code-book size can significantly outperform the results presented in . We also exploit VQ-VAE's connection with the expectation maximization (EM) algorithm BID3 , yielding additional improvements. With both improvements, we achieve a BLEU score of 22.4 on English to German translation, outperforming by 2.6 BLEU. Knowledge distillation BID7 BID12 ) provides significant gains with our best models and EM, achieving 26.7 BLEU, which almost matches the autoregressive transformer model with no beam search at 27.0 BLEU, while being 3.3× faster.Our contributions can be summarized as follows:1. We show that VQ-VAE from van den can outperform previous state-of-the-art without product quantization. 2. Inspired by the EM algorithm, we introduce a new training algorithm for training discrete variational autoencoders, that outperforms the previous best result with discrete latent autoencoders for neural machine translation. 3. Using EM training, and combining it sequence level knowledge distillation BID7 BID12 , allows us to develop a non-autoregressive machine translation model whose accuracy almost matches a strong greedy autoregressive baseline Transformer, while being 3.3 times faster at inference. 4. On the larger English-French dataset, we show that denoising discrete autoencoders gives us a significant improvement (1.0 BLEU) on top of our non-autoregressive baseline (see Section D). We investigate an alternate training technique for VQ-VAE inspired by its connection to the EM algorithm. Training the discrete autoencoder with EM and combining it with sequence level knowledge distillation, allows us to develop a non-autoregressive machine translation model whose accuracy almost matches a greedy autoregressive baseline, while being 3.3 times faster at inference. While sequence distillation is very important for training our best model, we find that the improvements from EM on harder tasks is quite significant. We hope that our results will inspire further research on using vector quantization for fast decoding of autoregressive sequence models.",1039,0.553,640,1.6234375,"Deep neural networks with discrete latent variables offer better symbolic reasoning learning abstractions useful new tasks There discrete latent variable models however despite several recent improvements the training challenging their performance mostly their continuous counterparts Recent work vector quantized autoencodersVQ-VAE made its perplexity almost matching a VAE on datasets In this work investigate an alternate training technique VQ-VAE inspired its connection the Expectation Maximization Training the discrete autoencoder EM and combining sequence level knowledge distillation alows whose accuracy almost a strong greedy autoregressive baseline Transformer, while being 3.3 inference Unsupervised learning meaningful representations since obtaining labeled data Continuous representations have largely images BID4 BID16 BID28 BID25 , audio BID27 . However often datasets naturally modeled as discrete symbols continuous ones For example language speech inherently discrete images concisely see . Improved discrete latent variable models could prove learning novel data compression algorithms BID32 , while having far more interpretable representationsWe build Vector Quantized Variational Autoencoder , The method uses a learned code-book combined nearest neighbor search train the discrete latent variable model The nearest neighbor search performed between the encoder output the latent code using 2 distance metric VQ-VAE adopts the standard latent variable model generative process first sampling latent codes a prior, P (z which are consumed data | In van den , use both uniform P (z The resulting discrete autoencoder obtains impressive results unconditional image, speech video generation In particular on image generation VQ-VAE shown perform almost on continuous VAEs datasets suchvan den ). An extension this method conditional supervised generation out-performs continuous autoencoders WMT English-German translation task .The work introduced the Latent Transformer set non-autoregressive Neural Machine Translation However , additional training heuristics namely, exponential moving averagesEMA cluster assignment counts product quantization BID24 essential achieve competitive results VQ-VAE In this work tuning the code-book size the results presented . We also exploit VQ-VAE's connection the expectation maximizationEM) algorithm BID3 , yielding additional improvements With both improvements achieve a BLEU score English to German translation outperforming by Knowledge distillation BID7 BID12 ) provides significant gains our best models EM, achieving 26.7 BLEU almost the autoregressive transformer model no beam search at being 3.3×Our contributions can We show VQ-VAE from van den can previous state without product quantization 2 Inspired the EM algorithm introduce the previous best result for neural machine translation 3 Using EM training and combining it sequence level knowledge distillation BID7 BID12 , allows a non-autoregressive machine translation model whose accuracy almost a strong greedy autoregressive baseline Transformer while being 3.3 inference 4 On the larger English-French dataset denoising discrete autoencoders gives (1.0 BLEU top our non-autoregressive baseline Section D We investigate an alternate training technique VQ-VAE inspired its connection the EM algorithm Training the discrete autoencoder EM and combining sequence level knowledge distillation allows whose accuracy almost a greedy autoregressive baseline being 3.3 inference While sequence distillation very training our best model find the improvements from EM on harder tasks is We hope our results using vector quantization fast decoding autoregressive sequence models",0.01,0.2925431450639637
"Recent research about margin theory has proved that maximizing the minimum margin like support vector machines does not necessarily lead to better performance, and instead, it is crucial to optimize the margin distribution. In the meantime, margin theory has been used to explain the empirical success of deep network in recent studies. In this paper, we present ODN (the Optimal margin Distribution Network), a network which embeds a loss function in regard to the optimal margin distribution. We give a theoretical analysis for our method using the PAC-Bayesian framework, which confirms the significance of the margin distribution for classification within the framework of deep networks. In addition, empirical results show that the ODN model always outperforms the baseline cross-entropy loss model consistently across different regularization situations. And our ODN
 model also outperforms the cross-entropy loss (Xent), hinge loss and soft hinge loss model in generalization task through limited training data. In the history of machine learning research, the large margin principle has played an important role in theoretical analysis of generalization ability, meanwhile, it also achieves remarkable practical results for classification BID3 and regression problems BID4 . More than that, this powerful principle has been used to explain the empirical success of deep neural network. BID1 and present a margin-based multi-class generalization bound for neural networks that scales with their margin-normalized spectral complexity using two different proving tools. Moreover, BID0 proposes a stronger generalization bounds for deep networks via a compression approach, which are orders of magnitude better in practice.As for margin theory, BID17 first introduces it to explain the phenomenon that AdaBoost seems resistant to overfitting problem. Two years later, BID2 indicates that the minimum margin is important to achieve a good performance. However, BID16 conjectures that the margin distribution, rather than the minimum margin, plays a key role in being empirically resistant to overfitting problem; this has been finally proved by BID6 . In order to restrict the complexity of hypothesis space suitably, a possible way is to design a classifier to obtain optimal margin distribution. BID6 proves that, to attain the optimal margin distribution, it is crucial to consider not only the margin mean but also the margin variance. Inspired by this idea, Zhang & Zhou (2016) proposes the optimal margin distribution machine (ODM) for binary classification, which optimizes the margin distribution through the first-and second-order statistics, i.e., maximizing the margin mean and minimizing the margin variance simultaneously. To expand this method to the multi-class classification problem, Zhang & Zhou (2017) presents a multi-class version of ODM.Based on these recent works, we consider the expansion of the optimal margin distribution principle on deep neural networks. In this paper, we propose an optimal margin distribution loss for convolution neural networks, which is not only maximizing the margin mean but also minimizing the margin variance as ODM does. Moreover, we use the PAC-Bayesian framework to derive a novel generalization bound based on margin distribution. Comparing to the spectrally-normalized margin bounds of BID1 and , our generalization bound shows that we can restrict the capacity of the model by setting an appropriate ratio between the first-order statistic and the second-order statistic rather than trying to control the whole product of the spectral norms of each layer. And we empirically evaluate our loss function on deep network across different datasets and model structures. Specifically, we consider the performance of these models in generalization task through limited training data.Recently, many researchers try to explain the experimental success of deep neural network. One of the research direction is to explain why the deep learning does not have serious overfitting problem. Although several common techniques, such as dropout (Srivastava et al., 2014) , batch normalization BID7 , and weight decay BID10 , do improve the generalization performance of the over-parameterized deep models, these techniques do not have a solid theoretical foundation to explain the corresponding effects. As for our optimal margin distribution loss, it has a generalization bound to prove that we can restrict the complexity of hypothesis space reasonably through searching appropriate statistics dependent on data distribution. In experimental section, we compare our optimal margin distribution loss with the baseline cross-entropy loss under different regularization methods. Recent studies disclose that maximizing the minimum margin for decision boundary does not necessarily lead to better generalization performance, and instead, it is crucial to optimize the margin distribution. However, the influence of margin distribution for deep networks still remains undiscussed. We propose ODN model trying to design a loss function which aims to control the ratio between the margin mean and the margin variance. Moreover, we present a theoretical analysis for our method, which confirms the significance of margin distribution in generalization performance. As for experiments, the results validate the superiority of our method in limited data problem. And our optimal margin distribution loss function can cooperate with batch normalization and dropout, achieving a better generalization performance.",988,0.529,580,1.703448275862069,"Recent research about margin theory proved maximizing like support vector machines instead crucial optimize In margin theory the empirical success deep network in recent studies In ODNthe Optimal margin Distribution Network which regard We give a theoretical analysis for our method using the PAC-Bayesian framework confirms the margin distribution classification within deep networks In addition empirical results the ODN model always the baseline cross-entropy loss model consistently different regularization situations And our ODN model also outperforms the cross-entropy lossXent hinge loss soft hinge loss model generalization task through limited training data In the history machine learning research the large margin principle played theoretical analysis generalization ability meanwhile also achieves remarkable practical results classification BID3 regression problems . More that this powerful principle explain the empirical success deep neural network. BID1 and present a margin-based multi-class generalization bound neural networks scales their margin-normalized spectral complexity using two different proving tools Moreover BID0 proposes a stronger generalization bounds deep networks via a compression approach are orders inAs margin theory BID17 first it explain AdaBoost seems resistant problem Two BID2 indicates the minimum margin important achieve However BID16 conjectures the margin distribution, rather plays being empirically resistant problem; has finally . In order restrict the complexity hypothesis space suitably a possible way design obtain optimal margin distribution BID6 proves, to attain the optimal margin distribution consider not margin mean Inspired this idea Zhang & Zhou2016 proposes the optimal margin distribution machineODM binary classification through maximizing mean simultaneously To expand this method the multi-class classification problem Zhang & Zhou presents ODM.Based these recent works consider the expansion the optimal margin distribution principle on In an optimal margin distribution loss convolution neural networks not maximizing the margin mean as ODM does Moreover use the PAC-Bayesian framework derive a novel generalization bound based margin distribution Comparing to the spectrally-normalized margin bounds BID1 , our generalization bound shows restrict the capacity setting an appropriate ratio the first-order statistic rather trying control the whole product the spectral norms each layer And we empirically evaluate our loss function deep network across different datasets model structures Specifically consider these models generalization task through limited training dataRecently try the experimental success. One the research direction is explain the deep learning does serious overfitting problem Although several common techniques dropout ( , batch normalization BID7 weight decay do improve the over-parameterized deep models the corresponding effects As for our optimal margin distribution loss has a generalization bound prove restrict the complexity hypothesis space reasonably through searching appropriate statistics dependent data distribution In experimental section compare our optimal margin distribution loss under different regularization methods Recent studies disclose maximizing the minimum margin decision boundary does better generalization performance instead crucial optimize the margin distribution However the influence margin distribution for deep networks still We propose ODN model trying design a loss function aims control the margin mean Moreover present for our method confirms margin distribution generalization performance As for experiments validate the superiority our method limited data problem And our optimal margin distribution loss function can cooperate batch normalization dropout, achieving",0.01,0.49640357229061105
"Deep network compression seeks to reduce the number of parameters in the network while maintaining a certain level of performance.   Deep network distillation seeks to train a smaller network that matches soft-max performance of a larger network.   While both regimes have led to impressive performance for their respective goals, neither provide insight into the importance of a given layer in the original model, which is useful if we are to improve our understanding of these highly parameterized models.   In this paper, we present the concept of deep net triage, which individually assesses small blocks of convolution layers to understand their collective contribution to the overall performance, which we call \emph{criticality}.  We call it triage because we assess this criticality by answering the question: what is the impact to the health of the overall network if we compress a block of layers into a single layer.
 We propose a suite of triage methods and compare them on problem spaces of varying complexity.   We ultimately show that, across these problem spaces, deep net triage is able to indicate the of relative importance of different layers.   Surprisingly, our local structural compression technique also leads to an improvement in overall accuracy when the final model is fine-tuned globally. As computational devices and methods become more powerful, deep learning models are able to grow ever deeper BID16 . To grow so deep, the most modern of networks have relied on clever intermediary layers-such as shortcut connection layers in BID5 -to overcome overfitting. While these methods allow for learning representations afforded only by very deep architectures, it is known that there are still more extraneous features and connections learned by these networks BID13 . The question of how to best remove these redundancies has been the focus of deep compression methods BID13 BID2 BID4 BID9 . Still others have investigated the ability of smaller-difficult to trainnetworks to learn from parent models via a method known as Knowledge Distillation BID6 BID14 .Both of these classes of approaches have demonstrated impressive performance for their respective goals; essentially, both lead to smaller networks that can match the performance of their larger, parent network. This performance is achieved in a variety of ways. For example, BID4 reduces the number of network parameters via low-threshold pruning, followed by retraining, weight quantization and sharing, in tandem with low-rank approximations to ensure removal of redundant and unimportant weights. These methods can be thought of as finding a sparser, compressed model which best approximates the original.Similarly, knowledge distillation methods leverage the soft-max outputs of previously trained ""teacher"" networks and network ensembles as guidance to train a smaller network, which would have otherwise been too difficult to train BID6 BID14 BID15 . These knowledge distillation networks globally train the smaller network to best approximate the soft-max output of the original network, sometimes with per-layer, intermediary targets incorporated BID0 BID11 BID17 .While impressive, these two methods do not shed any light on the criticality, or the relative importance of a given layer or block of layers to the overall output. Such layer-based analysis is important to understanding these increasingly deep networks, even if only in an empirical sense.To that end, we propose an idea called deep net triage that independently assesses small blocks of layers with respect to their importance to the overall network health. We drive the triage by using the initial parent network as an initialization, like BID1 , rather than as a means of globally retraining. Triage works by removing a connected block of network layers and replacing them with a single layer; we focus on convolution layers in this paper. We iterate over all connected blocks of layers separately thereby assessing the role each set plays in the original parent network.Our means for this triage is local structural compression, which approximates a section of a disassembled network and assesses the ability to approximate and relearn the original model. With structural compression we compress segments of a deep network-VGG16-and attempt to recover the compressed layer of the network via various initialization and training methodologies BID16 . We structure this as a compression problem as we are approximating multiple convolutional layers' representational abilities with a single, selectively initialized and trained layer. Distinctly, though , our primary goal is not to seek maximal compressive performance. Rather we seek to investigate the robustness of a network when faced with structural alterations, and how various learning techniques affect this behavior across data sets of assorted complexity. We seek overarching trends between these methods, layers, and data sets in hopes of developing a greater understanding for the representational ability, and robustness of neural networks.We perform our analysis using five approaches to structural compression for deep net triage, and four different data sets. We find that of the five approaches, methods which fine-tune over the entirety of the network achieve best performance across all data sets. Furthermore, these fine-tuned models are able to match or even exceed the performance of the baseline model. This suggests that for superior performance, a network cannot be altered without again retraining over the entire network. We additionally demonstrate that the criticality of any single layer in the network is not sufficient to inhibit relearning of the representations of the parent network. Finally, we show that knowledge distillation is an effective means of transferring the learned representations from a teacher to a student at any given intermediate point, even when the layer is altered or compressed, and improves a model's convergence. We present a novel method of analyzing deep learning methods which we refer to as deep net triage. By drawing from the field of deep network compression and knowledge distillation we design experiments which question the criticality of layers within a network structure, and assess the representations learned therein. We structurally compress a layer at a time, while conducting a series of experiments across these layers on various data sets to infer about the layer's ability to learn representations, recover from compression, and integrate itself into the global network.We show through experimentation that structurally compressed and fine-tuned models can perform equivalent to, or better than parent, uncompressed models in a layer invariant manner. Additionally, we show that parent-inspired initialization regimes applied only at the layer are unable to compete with fine-tuning over the entire global model. Lastly, we show that Student-Teacher models evaluated at intermediate layers in the form of hints from uncompressed parent models promote faster convergence to maximal accuracies, despite being unable to outperform full model training methods.Through this work, we hope to spur others to devise and rigorously test targeted assessments of deep networks, as we do in our deep net triage. While, as a community, we may continue to develop ever better performing methods for given problem spaces, we will never truly advance as a field until further intuition for and understanding of deep networks is developed. As optimization and statistical theory progresses on one side, so too must experimentalists approach from the other.",1377,0.693,779,1.7676508344030808,"Deep network compression seeks parameters while Deep network distillation seeks train a smaller network that matches soft-max performance While both regimes led impressive performance neither provide insight a given layer in the original model useful improve these highly parameterized models In deep net triage individually small blocks convolution layers understand their collective contribution, which \emph{criticality We call triage assess this criticality answering to the overall network if compress a block layers. We propose a suite triage methods compare on problem spaces We ultimately show, across these problem spaces deep net triage able indicate of relative importance different layers Surprisingly our local structural compression technique also leads overall accuracy the final model fine globally As computational devices methods deep learning models able grow ever deeper BID16 . To grow so deep most modern networks relied clever intermediary layers-such shortcut connection layers in BID5 -to overcome overfitting While these methods allow learning representations afforded only very deep architectures known more extraneous features connections learned these networks BID13 . The question best remove these redundancies deep compression methods BID13 BID2 . Still others investigated the ability smaller-difficult trainnetworks learn parent models via a method Knowledge Distillation BID6 BID14 .Both approaches demonstrated their respective goals; essentially both lead smaller networks match This performance achieved For example BID4 reduces network parameters via followed retraining weight quantization sharing tandem removal redundant and unimportant weights These methods thought finding a sparser compressed model which best originalSimilarly knowledge distillation methods leverage the soft-max outputs previously trained ""teacher"" networks network ensembles as guidance train a smaller network would otherwise BID6 BID14 BID15 These knowledge distillation networks globally train the smaller network best approximate the soft-max output sometimes perlayer, intermediary targets incorporated BID0 .While impressive these two methods shed the criticality, block layers Such layer-based analysis important these increasingly deep networks even onlyTo propose deep net triage independently small blocks layers with We drive the triage by the initial parent network an initialization, like BID1 rather globally retraining Triage works removing a connected block network layers replacing; we focus convolution layers We iterate all connected blocks layers separately thereby assessing each set the original parent networkOur means this triage local structural compression a section approximate and relearn With structural compression we compress segments a deep network-VGG16and attempt recover the compressed layer via various initialization and training methodologies BID16 . We structure as a compression problem as approximating multiple convolutional layers' representational abilities a single, selectively initialized and trained layer Distinctly though , our primary goal seek maximal compressive performance Rather we seek investigate a network when faced structural alterations how various learning techniques affect across of assorted complexity We seek overarching trends between these methods layers hopes for the representational ability, robustnessWe perform five approaches structural compression for deep net triage We find of the five approaches methods over the entirety achieve across Furthermore able match the baseline model This suggests for superior performance a network altered again retraining over We additionally demonstrate the criticality any single layer inhibit relearning the representations the parent network Finally show knowledge distillation transferring the learned representations a teacher at any given intermediate point the layer altered compressed improves a model's convergence We present analyzing deep learning methods which we refer deep net triage By drawing the field deep network compression knowledge distillation we design experiments question layers within assess the representations learned therein We structurally compress a layer at while conducting experiments across on infer about learn representations recover compression integrate itselfWe show through experimentation equivalent, parent, Additionally show parent-inspired initialization regimes applied only at the layer are unable compete fine over the entire global model Lastly show Student-Teacher models evaluated intermediate layers hints from uncompressed parent models promote faster convergence maximal accuracies despite unable full model training methodsThrough spur others devise rigorously targeted assessments deep networks our deep net triage While, a community may continue develop ever better performing methods given problem spaces truly advance further intuition for and deep networks As optimization statistical theory progresses on one side must experimentalists approach from",0.01,0.6599860506779922
"In this paper, we show a phenomenon, which we named ``super-convergence'', where residual networks can be trained using an order of magnitude fewer iterations than is used with standard training methods.    The existence of super-convergence is relevant to understanding why deep networks generalize well.   One of the key elements of super-convergence is training with cyclical learning rates and a large maximum learning rate.   Furthermore, we present evidence that training with large learning rates improves performance by regularizing the network. In addition, we show that super-convergence provides a  greater boost in performance relative to standard training when the amount of labeled training data is limited.   We also derive a simplification of the Hessian Free optimization method to compute an estimate of the optimal learning rate.   The architectures to replicate this work will be made available upon publication.
 While deep neural networks have achieved amazing successes in a range of applications, understanding why stochastic gradient descent (SGD) works so well remains an open and active area of research. This paper provides unique empirical evidence that supports the theories in some papers but not others. Specifically, we show that, for certain datasets, residual network architectures BID15 , and hyper-parameter values, using very large learning rates with the cyclical learning rate (CLR) method BID29 BID30 can speed up training by an order of magnitude. Analogous to the phenomenon of super-conductivity that only happens in limited circumstances and provides theoretical insights of materials, we named this phenomenon ""super-convergence."" While super-convergence might be of some practical value, the primary purpose of this paper is to provide empirical support and theoretical insights to the active discussions in the literature on SGD and understanding generalization. FIG0 provides a comparison of test accuracies from a super-convergence example and the result of a typical (piecewise constant) training regime for Cifar-10, both using a 56 layer residual network architecture. Piecewise constant training reaches a peak accuracy of 91.2% after approximately 80,000 iterations, while the super-convergence method reaches a higher accuracy (92.4%) after only 10,000 iterations. FIG1 shows the results for a range of CLR stepsize values, where training lasted only one cycle. This modified learning rate schedule achieves a higher final test accuracy (92.1%) than typical training (91.2%) after only 6,000 iterations. In addition, as the total number of iterations increases from 2,000 to 20,000, the final accuracy improves from 89.7% to 92.7%.The contributions of this paper are:1. We demonstrate a new training phenomenon and systematically investigate it. 2. We show evidence that large learning rates regularize the trained network and hypothesize that this allows SGD to find a flat local minima that generalizes well. 3. We derive a simplification of the second order, Hessian-free optimization method to estimate optimal learning rates which demonstrates that large learning rates find wide, flat minima. 4. We demonstrate that the effects of super-convergence are increasingly dramatic when less labeled training data is available. There is substantial discussion in the literature on stochastic gradient descent (SGD) and understanding why solutions generalize so well (i.e, Chaudhari et al. FORMULA1 BID20 ). Super-convergence provides empirical evidence that supports some theories, contradicts some others, and points to the need for further theoretical understanding. We hope the response to super-convergence is similar to the reaction to the initial report of network memorization , which sparked an active discussion within the deep learning research community on better understanding of the factors in SGD leading to solutions that generalize well (i.e., ).Our work impacts the line of research on SGD and the importance of noise for generalization. In this paper we focused on the use of CLR with very large learning rates, which adds noise in the middle part of training. Recently , stated that higher levels of noise lead SGD to solutions with better generalization. Specifically , they showed that the ratio of the learning rate to the batch size, along with the variance of the gradients, controlled the width of the local minima found by SGD. Independently , BID6 show that SGD performs regularization by causing SGD to be out of equilibrium, which is crucial to obtain good generalization performance, and derive that the ratio of the learning rate to batch size alone controls the entropic regularization term. They also state that data augmentation increases the diversity of SGD's gradients, leading to better generalization. These two papers provide theoretical support for the super-convergence phenomenon. In addition there are several other papers in the literature which state that wide, flat local minima produce solutions that generalize better than sharp minima BID16 BID21 BID36 . Our super-convergence results align with these results.In addition, there are several recent papers on the generalization gap between small and large minibatches and the relationship between gradient noise, learning rate, and batch size. Our results here supplements this other work by illustrating the possibility of time varying high noise levels during training. As mentioned above, showed that SGD noise is proportional to the learning rate, the variance of the loss gradients, divided by the batch size. Similarly Smith and Le derived the noise scale as g ≈ N/B(1 − m), where g is the gradient noise, the learning rate, N the number of training samples, and m is the momentum coefficient. Furthermore, showed an equivalence of increasing batch sizes instead of a decreasing learning rate schedule. Importantly, these authors demonstrated that the noise scale g is relevant to training and not the learning rate or batch size. BID21 study the generalization gap between small and large mini-batches, stating that small mini-batch sizes lead to wide, flat minima and large batch sizes lead to sharp minima. They also suggest a batch size warm start for the first few epochs, then using a large batch size, which amounts to training with large gradient noise for a few epochs and then removing it. Our results contradicts this suggestion as we found it preferable to start training with little or no noise and let it increase (i.e., curriculum training), reach a noise peak, and reduce the noise level in the last part of training (i.e., simulated annealing). BID12 use a very large mini-batch size of up to 8,192 and adjust the learning rate linearly with the batch size. They also suggest a gradual warmup of the learning rate, which is a discretized version of CLR and matches our experience with an increasing learning rate. They make a point relevant to adjusting the batch size; if the network uses batch normalization, different mini-batch sizes leads to different statistics, which must be handled. BID17 made a similar point about batch norm and suggested using ghost statistics. Also, BID17 show that longer training lengths is a form of regularization that improves generalization. On the other hand, our results show a different form of regularization that comes from training with very large learning rates, which permits much shorter training lengths.Furthermore, this paper points the way towards new research directions, such as the following three:1. Characterizing ""good noise"" that improves the trained network's ability to generalize versus ""bad noise"" that interferes with finding a good solution (i.e., ). We find that there is a lack of a unified framework for treating SGD noise/diversity, such as architectural noise (e.g., dropout BID33 , dropconnect BID35 ), noise from hyper-parameter settings (e.g., learning rate, mini-batch size), adding gradient noise, adding noise to weights BID9 , and input diversity (e.g., data augmentation, noise). Gradient diversity has been shown to lead to flatter local minimum and better generalization. A unified framework should resolve conflicting claims in the literature on the value of each of these, such as for architectural noise BID33 ) versus Hoffer et al. (2017 ). Furthermore, many papers study each of these factors independently and by focusing on the trees, one might miss the forest. 2. Time dependent application of good noise during training: As described above, combining curriculum learning with simulated annealing leads to cyclical application. To the best of our knowledge, this has only been applied sporadically in a few methods such as CLR BID30 or cyclical batch sizes but these all fall under a single umbrella of time dependent gradient diversity (i.e., noise). Also, one might learn an optimal noise level while training the network. 3. Discovering new ways to stabilize optimization (i.e., SGD) with large noise levels: Our evidence indicates that normalization (and batch normalization in particular) is the catalyst enabling super-convergence in the face of destabilizing noise from the large learning rates. Normalization methods (batch norm, layer normalization BID2 , streaming normalization BID23 ) and new techniques (i.e., cyclical gradient clipping) to stabilize training need further investigation to discover better ways to keep SGD stable in the presence of enormous good noise.Classical physics was insufficient for explaining super-conductivity when it was discovered and pointed to the need for new theories, such as quantum mechanics. Similarly, super-convergence indicates a need for new theories of SGD and generalization.The Resnet-56 architecture used consists of three stages. Within each stage, the same residual block structure is sequentially repeated . This structure is given in TAB1 . Between stages, a different residual block structure is used to reduce the spatial dimension of the channels. TAB2 shows this structure. The overall architecture is described in TAB3 . Following the Caffe convention, each Batch Norm layer was followed by a scaling layer to achieve true batch normalization behavior. This and the other architectures necessary to replicate this work will be made available upon publication. We ran a wide variety of experiments and due to space limitations in the main article, we report some of the more interesting results here that did not fit in the main article.In the main text we only showed the results of super-convergence for the Cifar-10 dataset. In fact, the super-convergence phenomenon also occurs with Cifar-100, which implies an independence of this phenomenon on the number of classes. FIG0 shows the results of the LR range test for Resnet-56 with the Cifar-100 training data. The curve is smooth and accuracy remains high over the entire range from 0 to 3 indicating a potential for super-convergence. An example of super-convergence with Cifar-100 with Resnet-56 is given in FIG16 , where there is also a comparison to the results from a piecewise constant training regime. Furthermore, the final accuracy for the super-convergence curve is 68.6%, while the accuracy for the piecewise constant method is 59.8%, which is an 8.8% improvement.As discussed in the main text, we tested various adaptive learning rate methods with Resnet-56 training on Cifar-10 to determine if they are capable of recognizing the need for using very large learning rates. FIG0 shows the results of this training for Nesterov momentum BID34 BID27 , AdaDelta BID8 ), AdaGrad (Zeiler, 2012 , and Adam (Kingma BID22 . We found no sign that any of these methods discovered the utility of large learning rates nor any indication of super-convergence-like behavior. We also ran CLR with these adaptive learning methods and found that Nesterov, AdaDelta, and AdaGrad allowed super-convergence to occur, but we were unable to create this phenomenon with Adam. For example, FIG18 shows a comparison of super-convergence to a piecewise constant training regime with the Nesterov momentum method. Here super-convergence yields a final test accuracy after 10,000 iterations of 92.1% while the piecewise constant training regime at iteration 80,000 has an accuracy of 90.9%. FIG1 shows a comparison of runs of the super-convergence phenomenon, both with and without dropout. The LR range test with and without dropout is shown in FIG0 . FIG1 shows the results of training for 10,000 iterations . In both cases, the dropout ratio was set to 0.2 and the Figure shows a small improvement with dropout. We also ran with other values for the dropout ratio and consistently saw similar improvements.The effect of mini-batch size is discussed in the main paper but here we present a table containing the final accuracies of super-convergence training with various mini-batch sizes. One can see in Table 5 the final test accuracy results and this table shows that the larger the mini-batch size, the better the final accuracy, which differs from the results shown in the literature 4 . Most of results reported in this paper are with a total mini-batch size of 1,000.In addition, we ran experiments on Resnet-56 on Cifar-10 with modified values for momentum and weight decay to determine if they might hinder the super-convergence phenomenon. FIG0 shows the results for momentum set to 0.8, 0.85, 0.9, and 0.95 and the final test accuracies are listed in TAB5 . These results indicate only a small change in the results, with a setting of 0.9 being a bit better than the other values. In FIG1 are the results for weight decay values of 10 −3 , 10 −4 , 10 −5 , and 10 −6 . In this case, a weight decay value of 10 −3 prevents super-convergence, while the smaller values do not. This FIG0 shows that a weight decay value of 10 −4 performs well. Table 5 : Comparison of accuracy results for various total training batch sizes with Resnet-56 on Cifar-10 using CLR=0.1-3 and stepsize=5,000.",2819,1.578,1611,1.7498448168839231,"In a phenomenon, named ``super residual networks trained using an order is with The existence super relevant deep networks generalize One super training with cyclical learning rates Furthermore present training large learning rates improves by regularizing the network In addition show super provides a greater boost relative standard training when labeled training data We also derive the Hessian Free optimization method an estimate The architectures to replicate made upon publication While deep neural networks achieved amazing successes a range applications understanding why This paper unique empirical evidence supports the theories in some papers but Specifically show certain datasets residual network architectures BID15 , hyper values using very large learning rates with the cyclical learning rate method BID29 BID30 speed training Analogous the phenomenon super that only limited circumstances provides theoretical insights of materials we named While might of the primary purpose and the active discussions SGD understanding generalization FIG0 provides test accuracies from a super-convergence example the result a typical (piecewise constant) training regime Cifar-10 both a 56 layer residual network architecture Piecewise constant training reaches a peak accuracy after approximately 80,000 iterations FIG1 shows for a range CLR stepsize values where training lasted This modified learning rate schedule achieves a higher final test accuracy typical training ( after only 6,000 iterations In addition as iterations from the final accuracy improves this paper We demonstrate a new training phenomenon and systematically 2 We show evidence large learning rates regularize the trained network hypothesize allows SGD find a flat local minima generalizes 3 We derive, Hessian-free optimization method to estimate optimal learning rates which demonstrates find wide, flat minima 4 We demonstrate super increasingly dramatic less labeled training data There substantial discussion understanding why solutions generalize so, Chaudhari FORMULA1 BID20 ). Superconvergence provides empirical evidence supports some theories contradicts points further theoretical understanding We hope the response super similar the initial report network memorization , sparked within better understanding the factors in SGD leading solutions generalize ( ).Our impacts the line the importance noise for In focused CLR with very large learning rates adds noise the middle part training Recently , stated higher levels noise lead SGD solutions Specifically , they showed the ratio the learning rate the batch size, along controlled the width the local minima found SGD Independently , BID6 show SGD performs regularization causing out equilibrium crucial obtain good generalization performance derive that the ratio the learning rate batch alone controls the entropic regularization term They also state data augmentation increases the diversity SGD's gradients leading These two papers theoretical support In addition there several other papers state that wide, flat local minima produce solutions generalize better sharp minima BID16 BID21 BID36 . Our super-convergence results alignIn there several recent papers the generalization gap gradient noise learning rate batch size Our results here supplements this other work illustrating time varying high noise levels training As mentioned showed SGD noise proportional the variance the loss gradients divided Similarly Smith Le derived the noise scale as g �� N/B(1 − m the learning N the training samples the momentum coefficient Furthermore showed an equivalence increasing batch sizes instead a decreasing learning rate schedule Importantly these authors demonstrated the noise scale g relevant training not learning or batch BID21 study the generalization gap small and large minibatches stating lead wide, flat minima They also suggest a batch size warm start then using amounts training with large gradient noise removing Our results contradicts this suggestion as it preferable start training let increase (i.e., curriculum training reach a noise peak reduce simulated BID12 use a very large mini-batch size up 8,192 and adjust the learning rate They also suggest a gradual warmup the learning rate a discretized version CLR and matches our experience They make relevant adjusting the batch size; the network uses batch normalization different mini-batch sizes leads different statistics must handled BID17 made batch norm and suggested ghost statistics Also BID17 show longer training lengths is a form regularization improves generalization On our results a different form regularization that comes training very large learning rates permits much shorter training lengthsFurthermore points new research directions the following three:1 Characterizing ""good noise that improves the trained network's ability generalize versus finding ). We find a unified framework treating SGD noise/diversity such architectural noise dropout BID33 , dropconnect noise hyper-parameter settings mini-batch size adding gradient noise adding weights BID9 input diversity Gradient diversity lead flatter local minimum and better generalization A unified framework should resolve conflicting claims the literature each, such for architectural noise BID33 ) versus Hoffer (2017 ). Furthermore many papers study each by focusing the trees one miss 2 Time dependent application good noise during training: As described combining curriculum learning simulated annealing leads cyclical application To only applied a few methods such CLR BID30 cyclical batch sizes but these all fall time dependent gradient diversity Also one might learn an optimal noise level while training the network 3 Discovering stabilize optimization ( with large noise levels: Our evidence normalizationand batch in the catalyst enabling super the face destabilizing noise from the large learning rates Normalization methodsbatch norm, layer normalization BID2 , and new techniques cyclical gradient clipping to stabilize training need further investigation discover keep SGD stable enormous good noiseClassical physics was insufficient explaining super when discovered and pointed Similarly super indicates a need new theories SGD generalizationThe Resnet-56 architecture used consists Within each stage the same residual block structure sequentially repeated . This structure given TAB1 . Between stages a different residual block structure used reduce the spatial dimension the channels TAB2 shows this structure The overall architecture described TAB3 . Following the Caffe convention each Batch Norm layer followed a scaling layer achieve true batch normalization behavior This and architectures necessary replicate made upon publication We ran experiments due space limitations in the main article report some here that didIn the main text only showed super for the Cifar-10 dataset In fact the super-convergence phenomenon also Cifar-100 implies an independence this phenomenon on the number classes FIG0 shows the LR range test Resnet-56 the Cifar-100 training data The curve smooth accuracy remains over from 3 indicating a potential super An example super with Cifar-100 with Resnet-56 given FIG16 there also a comparison to the results a piecewise constant training regime Furthermore the final accuracy for the super-convergence curve the piecewise constant methodAs discussed tested various adaptive learning rate methods Resnet-56 training on Cifar-10 to recognizing the need using FIG0 shows this training for Nesterov momentum BID34 BID27 , AdaDelta BID8 ), AdaGrad (Zeiler 2012 , and Adam (Kingma BID22 . We found no sign these methods discovered the utility large learning rates nor We also ran CLR with these adaptive learning methods Nesterov, AdaDelta AdaGrad allowed super create this phenomenon Adam For example FIG18 super to a piecewise constant training regime the Nesterov momentum method Here super-convergence yields a final test accuracy after 92.1% while the piecewise constant training regime at iteration 80,000 has FIG1 shows runs the super-convergence phenomenon both dropout The LR range test with and dropout shown FIG0 . FIG1 shows training 10,000 iterations . In both cases the dropout ratio set the Figure a small improvement dropout We also ran with other values the dropout ratio consistently similar improvementsThe effect mini-batch size discussed but present containing the final accuracies super-convergence training One can Table the final test accuracy results and this table that the larger the mini-batch size differs the literature 4 Most results reported with a total mini-batch size ran experiments Resnet-56 on Cifar-10 modified values momentum and weight decay to might hinder FIG0 shows momentum set and the final test accuracies listed TAB5 . These results only a small change, a setting being bit In FIG1 are the results for weight decay values 10 −3 In a weight decay value 10 −3 prevents super the smaller values do This FIG0 shows that weight decay value 10 −4 performs. Table 5 : Comparison accuracy results various total training batch sizes with Resnet-56 on Cifar-10 using CLR=0.1-3 stepsize=5,000",0.02,0.6146178824587722
"Infinite-width neural networks have been extensively used to study the theoretical properties underlying the extraordinary empirical success of standard, finite-width neural networks. Nevertheless, until now, infinite-width networks have been limited to at most two hidden layers. To address this shortcoming, we study the initialisation requirements of these networks and show that the main challenge for constructing them is defining the appropriate sampling distributions for the weights. Based on these observations, we propose a principled approach to weight initialisation that correctly accounts for the functional nature of the hidden layer activations and facilitates the construction of arbitrarily many infinite-width layers, thus enabling the construction of arbitrarily deep infinite-width networks. The main idea of our approach is to iteratively reparametrise the hidden-layer activations into appropriately defined reproducing kernel Hilbert spaces and use the canonical way of constructing probability distributions over these spaces for specifying the required weight distributions in a principled way. Furthermore, we examine the practical implications of this construction for standard, finite-width networks. In particular, we derive a novel weight initialisation scheme for standard, finite-width networks that takes into account the structure of the data and information about the task at hand. We demonstrate the effectiveness of this weight initialisation approach on the MNIST, CIFAR-10 and Year Prediction MSD datasets. While deep neural networks have achieved impressive empirical success on many tasks across a wide range of domains in recent years BID20 BID35 BID33 BID34 BID29 , they remain hard to interpret black boxes whose performance crucially depends on many heuristics. In an attempt to better understand them, significant research effort has been directed towards examining the theoretical properties of these models with one important line of research focusing on the profound connections between infinite-width networks and kernel methods. In particular, BID30 established a correspondence between single-layer infinite-width networks and Gaussian processes (GP) BID32 showing the equivalence of the prior over functions that is induced by the network and a GP with a particular covariance kernel. The appropriate covariance kernel has been analytically derived for a few particular activation functions and weight priors BID38 .Although there is a large body of research on infinite-width networks with surging recent interest in the topic BID13 BID24 BID27 , until now the construction of these networks has been limited to at most two hidden layers. In order to overcome this shortcoming and enable deep infinite-width networks, we propose a novel approach to the construction of networks with infinitely wide hidden layers. To the best of our knowledge, this is the first method that enables the construction of infinite-width networks with more than two hidden layers. The main challenge in constructing this type of networks lies in ensuring that the inner products between the hidden layer representations and the corresponding weights, which are both functions, are well-defined. In particular, this amounts to ensuring that the weights lie in the same function space as the hidden layer representations with which the inner product is taken. In other words, the weights connecting layers l and l + 1 need to be in the same function space as the activations of layer l. To construct the infinite-width layer l + 1, we need to construct infinitely many weights connecting layers l and l + 1 that fulfill this requirement, i.e. we need to define a probability distribution over the function space of activations of layer l. As the number of layers grows, the function spaces of activations grow increasingly more complex, thus making it increasingly more difficult to satisfy the requirements on the weights.In order to tackle this challenge, we propose a principled approach to weight initialisation that automatically ensures that the weights are in the appropriate function space. The main idea of our approach is to make use of the canonical way of defining probability distributions over reproducing kernel Hilbert spaces (RKHS) and iteratively define the appropriate weight distributions facilitating the composition of arbitrarily many layers of infinite width. To this end, we first construct a kernel corresponding to each hidden layer and examine the associated RKHS of functions that is induced by this kernel. Next, for every layer, we establish a correspondence between the space of activations at a layer and the corresponding RKHS by reparametrising the hidden layer activations of a datapoint with the RKHS function corresponding to that point. Establishing this correspondence allows us to use a principled approach to defining probability distributions over RKHSs for constructing the appropriate sampling distribution of the weights in the infinite-width network.We also examine some practical implications of this construction for the case of standard, finitewidth neural networks in terms of weight initialisation. Using Monte Carlo approximations, we derive a novel data-and task-dependent weight initialisation scheme for finite-width networks that incorporates the structure of the data and information about the task at hand into the network.The main contributions of this paper are• a novel approach to the construction of infinite-width networks that enables the construction of networks with arbitrarily many hidden layers of infinite-width,• a hierarchy of increasingly complex kernels that capture the geometry and inductive biases of individual layers in the network,• a novel weight initialisation scheme for deep neural networks with theoretical foundations established in the infinite-width case.The rest of the paper is organised as follows. Section 2 discusses related work and Section 3 introduces our proposed approach to the construction of deep infinite-width networks. In Section 4, we showcase the practical implications of our theoretical contribution for the case of standard, finite-width deep networks. Section 5 discusses the experimental results followed by a conclusion in Section 6. In this paper, we have studied the initialisation requirements of infinite-width networks and have shown that the main challenge in constructing these networks lies in defining the appropriate sampling distributions of the weights. To address this problem, we have presented a novel method for the construction of infinite-width networks that, unlike previous approaches, enables the construction of deep infinite-width networks with arbitrarily many hidden layers. In particular, we have proposed a principled approach to weight initialisation using the theory of reproducing kernel Hilbert spaces. In order to appropriately account for the functional form of the hidden layer activations and to facilitate the construction of arbitrarily many infinite-width layers, we proposed to construct the sampling distributions of the weights at every hidden layer as Gaussian processes with specific covariance kernels that take into account the geometry of the underlying space of activations. To achieve this, we have constructed a hierarchy of kernels that capture the geometry and inductive biases of individual layers in the neural network. Furthermore, using Monte Carlo approximations, we have examined the practical implications of this construction for standard, finite-width networks. In particular, we have derived a novel data-and task-dependent weight initialisation method for this type of network and showcased its competitive performance on three diverse datasets.7 SUPPLEMENTARY MATERIAL 7.1 PROOFS For completeness, we restate the proposition and lemma and provide the corresponding proofs.7.1.1 PROPOSITION 1 Proposition 1. Let x, x ∈ R d be inputs to an network with l infinite-width layers, k l be the kernel corresponding to the l-th layer with k l (·, x) the corresponding canonical feature maps and H k l the induced RKHS. We can extend the network with an (l + 1)-th layer of infinite width by sampling the weights w l connecting the l-th and (l + 1)-th layers from a Gaussian process with zero mean function and covariance function DISPLAYFORM0",1489,0.684,892,1.6692825112107623,"Infinite-width neural networks extensively the theoretical properties underlying the extraordinary empirical success Nevertheless until infinite-width networks limited at most two hidden layers To address study the initialisation requirements these networks show the main challenge constructing defining the appropriate sampling distributions the weights Based these observations a principled approach weight initialisation that correctly accounts the functional nature the hidden layer activations facilitates arbitrarily many infinite-width layers thus arbitrarily deep infinite-width networks The main idea our approach iteratively reparametrise the hidden-layer activations into appropriately defined reproducing kernel Hilbert spaces and use the canonical way constructing probability distributions over specifying the required weight distributions Furthermore examine this construction standard, finite-width networks In particular derive a novel weight initialisation scheme standard, finite-width networks takes information about the task We demonstrate this weight initialisation approach the MNIST, CIFAR-10 and Year Prediction MSD datasets While deep neural networks achieved impressive empirical success on across in BID20 BID35 , they remain hard interpret black boxes whose performance crucially many heuristics In better them significant research effort directed examining the theoretical properties these models with one important line focusing the profound connections infinite-width networks and kernel methods In particular BID30 established a correspondence single-layer infinite-width networks Gaussian processesGP) BID32 showing prior over functions that is induced a GP with a particular covariance kernel The appropriate covariance kernel analytically derived a few particular activation functions weight priors BID38 .Although infinite-width networks surging recent interest until the construction at most two hidden layers In order overcome and enable deep infinite-width networks propose the construction networks infinitely wide hidden layers To enables the construction infinite-width networks more than two hidden layers The main challenge constructing this type networks lies ensuring the inner products between the hidden layer representations the corresponding weights, both functions well In particular this amounts ensuring the weights lie the same function space the hidden layer representations with the inner product taken In the weights connecting layers l + need in the same function space the activations To construct the infinite-width layer l + 1 construct infinitely many weights connecting layers l that fulfill the function space activations As the number layers the function spaces activations grow increasingly thus more satisfy on the weightsIn tackle propose weight initialisation automatically ensures in The main idea our approach use the canonical way defining probability distributions over reproducing kernel Hilbert spacesRKHS iteratively define the appropriate weight distributions facilitating the composition arbitrarily many layers infinite width To this end first construct a kernel corresponding each hidden layer examine the associated RKHS functions is induced Next for every layer establish a correspondence the space activations at the corresponding RKHS by reparametrising with corresponding that point Establishing this correspondence allows use a principled approach defining probability distributions over RKHSs for constructing the appropriate sampling distribution the weights the infinite-width networkWe also examine some practical implications this construction the case standard, finitewidth neural networks terms weight initialisation Using derive a novel data-and task-dependent weight initialisation scheme finite-width networks incorporates the structure information at intoThe main contributions are• enables arbitrarily many hidden layers infinitewidth,• a hierarchy increasingly complex kernels capture the geometry inductive biases individual layers theoretical foundations established.The rest organised Section discusses related work Section introduces our proposed approach the construction deep infinite-width networks In Section showcase the practical implications our theoretical contribution for the case standard, finite-width deep networks Section discusses the experimental results followed a conclusion in In this paper have studied the initialisation requirements infinite-width networks have the main challenge lies defining the appropriate sampling distributions To address presented the construction infinite-width networks, unlike enables arbitrarily many hidden layers In particular proposed a principled approach weight initialisation using the theory reproducing kernel Hilbert spaces In order appropriately account the functional form the hidden layer activations facilitate the construction arbitrarily many infinite-width layers proposed the sampling distributions the weights at as processes specific covariance kernels that take of activations To achieve constructed a hierarchy kernels capture the geometry inductive biases individual layers Furthermore using examined the practical implications this construction standard, finite-width networks In particular derived a novel data-and task-dependent weight initialisation method this type network and showcased its competitive performance three diverse datasets.7 SUPPLEMENTARY MATERIAL 7.1 PROOFS For restate the proposition and lemma and Proposition Let x, x �� R d be inputs an network l infinite-width layers k l be the kernel corresponding with (· the corresponding canonical feature maps H l the induced RKHS We can extend the network an (l + 1)-th layer infinite width by sampling the weights w l connecting ( from zero mean function covariance function DISPLAYFORM0",0.01,0.4093522057303422
"Working memory requires information about external stimuli to be represented in the brain even after those stimuli go away. This information is encoded in the activities of neurons, and neural activities change over timescales of tens of milliseconds. Information in working memory, however, is retained for tens of seconds, suggesting the question of how time-varying neural activities maintain stable representations. Prior work shows that, if the neural dynamics are in the `  null space' of the representation - so that changes to neural activity do not affect the downstream read-out of stimulus information - then information can be retained for periods much longer than the time-scale of individual-neuronal activities. The prior work, however, requires precisely constructed synaptic connectivity matrices, without explaining how this would arise in a biological neural network. To identify mechanisms through which biological networks can self-organize to learn  memory function, we derived biologically plausible synaptic plasticity rules that dynamically modify the connectivity matrix to enable information storing. Networks implementing this plasticity rule can successfully learn to form memory representations even if only 10% of the synapses are plastic, they are robust to synaptic noise, and they can represent information about multiple stimuli. Working memory is a key cognitive function, and it relies on us retaining representations of external stimuli even after they go away. Stimulus-specific elevated firing rates have been observed in the prefrontal cortex during the delay period of working memory tasks, and are the main neural correlates of working memory BID6 BID7 . Perturbations to the delay period neural activities cause changes in the animal's subsequent report of the remembered stimulus representation BID12 BID19 . These elevated delay-period firing rates are not static but have time-varying dynamics with activities changing over timescales of tens of milliseconds BID0 BID18 ), yet information can be retained for tens of seconds FIG0 . This suggests the question of how time-varying neural activities keep representing the same information.Prior work from BID5 shows that, if the neural dynamics are in the ""null space"" of the representation -so that changes to neural activity do not affect the downstream read-out of stimulus information -then information can be retained for periods much longer than the timescale of individual neuronal activities (called the FEVER model; FIG0 . That model has a severe fine-tuning problem, discussed below. We identified a synaptic plasticity mechanism that overcomes this fine-tuning problem, enabling neural networks to learn to form stable representations.While the dynamics of neurons in the FEVER model match that which is observed in the monkey prefrontal cortex during a working memory task BID16 , the model itself requires that the network connectivity matrix have one or more eigenvalues very near to unity. According to the Gershgorin Circle Theorem, this will almost surely not happen in randomly-connected networks: fine-tuned connectivity is needed. BID5 suggest a mechanism of Hebbian learning by which this connectivity can be learned. That mechanism requires the read-out weights to form a 'tight frame' , which will not necessarily be true in biological circuits. Thus, the prior work leaves it unknown how synaptic plasticity can form and/or maintain functional working memory networks. Here, we identify biologically plausible synaptic plasticity rules that can solve this fine-tuning problem without making strong assumptions like 'tight frame' representations. Our plasticity rules dynamically re-tune the connectivity matrix to enable persistent representations of When presented with an external stimulus, s, neural activity patterns initially encode an internal representation of that stimulus,ŝ(t=0). These neural activity patterns change over time on timescales of tens of milliseconds, and yet somehow the same information is stored for up to tens of seconds. (B) While the firing rates, r i (t), change over time, information about stimulus,ŝ(t), can be remain unchanged as long as the projection of the firing rates onto the ""read-out"" vector d, remains constant BID5 .stimulus information. We specifically address parametric working memory, where the requirement is to remember continuous values describing several different variables or dimensions such as spatial locations or sound frequencies. For example, in the oculomotor delayed response task, subjects must remember the location of a target during a delay period BID6 . We perform experiments to demonstrate that networks using these plasticity rules are able to store information about multiple stimuli, work even if only a fraction of the synapses are tuned, and are robust to synaptic noise. We also show that these networks improve over time with multiple presented stimuli, and that the learning rules work within densely or sparsely connected networks. We derived biologically plausible synaptic plasticity rules through which networks self-organize to store information in working memory. Networks implementing these plasticity rules are robust to synaptic noise, to having only some of the synapses updated, and to partial connectivity. These networks can store multiple stimuli and have increased performance after previous training. We suggest two candidate sources for the global error signal necessary for the plasticity rule, and demonstrate that our networks can learn to store stimulus information while satisfying the added requirements imposed by these biological mechanisms. This flexibility suggests that other types of synaptic plasticity updates may also be able to organize working memory circuits.The results presented here were obtained for networks of 100 neurons -as opposed to larger networks -to speed up the simulations. Tests on networks with 10,000 neurons show that the update rule works in larger networks. The optimal learning rate, η, decreases as the network size increases. Aside from network size, a potential caveat in using a rate-based network model is losing information about spike-timing dependency. A future direction would be to create a spike-based model and determine what, if anything, must be adjusted to account for spike timing, and for the discretization that spiking neurons entail for the information shared between cells.Along with understanding how information is stored in working memory, this work may have implications in training recurrent neural networks (RNNs). Machine learning algorithms are generally unrealistic from a biological perspective: most rely on non-local synaptic updates or symmetric synapses. We show that recurrent networks can learn to store information using biologically plausible synaptic plasticity rules which require local information plus a global error signal (or signals), that can be calculated on the apical dendrite or via neuromodulators. This same setup could be utilized in RNNs to make them more biologically realistic. This would let us better understand how the brain learns, and could lead to novel biomimetic technologies: prior work on biologically realistic machine learning algorithms has led to hardware devices that use on-chip learning BID11 BID20 . Synaptically local updates do not have to be coordinated over all parts of the chip, enabling simpler and more efficient hardware implementations.",1367,0.714,780,1.7525641025641026,"Working memory requires information external stimuli represented even go This information encoded the activities neurons neural activities change Information in working memory however retained tens seconds suggesting the question maintain stable representations Prior work shows, the neural dynamics in the ` null space - so changes neural activity the downstream read-out stimulus information information retained periods much individual-neuronal activities The prior work however requires precisely constructed synaptic connectivity matrices without explaining would arise To identify mechanisms biological networks self to learn memory function derived biologically plausible synaptic plasticity rules dynamically the connectivity matrix to enable information storing Networks implementing this plasticity rule successfully learn form memory representations even plastic they robust synaptic noise represent multiple stimuli Working memory relies us retaining representations external stimuli even go Stimulus-specific elevated firing rates the delay period the main neural working memory BID6 BID7 the delay period neural activities cause the animal's subsequent report the remembered stimulus representation BID12 BID19 . These elevated delay-period firing rates static activities changing tens BID0 BID18 ), yet information can retained tens FIG0 This suggests the question keep representingPrior work from BID5 shows the neural dynamics in the ""null space the representation -so changes the downstream read-out retained periods much individual neuronal activitiescalled the FEVER model; FIG0 . That model discussed We identified a synaptic plasticity mechanism overcomes enabling neural networks form stable representationsWhile the dynamics neurons the FEVER model match which during a working memory task BID16 itself requires the network connectivity matrix have very near unity According the Gershgorin Circle Theorem this will almost surely randomly-connected networks: fine-tuned connectivity needed BID5 suggest a mechanism Hebbian learning this connectivity learned That mechanism requires the read-out weights form a 'tight frame , will necessarily true biological circuits Thus the prior work leaves it unknown synaptic plasticity form functional working memory networks Here identify biologically plausible synaptic plasticity rules solve without making strong assumptions like 'tight frame' representations Our plasticity rules dynamically re the connectivity matrix enable persistent representations When presented, s, neural activity patterns initially encode�� These neural activity patterns change on tens yet somehow seconds (B While the firing rates, r i (t change information stimulus,�� can remain as the projection onto the ""read-out"" vector d remains constant BID5 .stimulus information. We specifically address parametric working memory the requirement remember continuous values describing several different variables or dimensions such spatial locations sound frequencies For example delayed subjects must remember during BID6 . We perform experiments demonstrate networks using these plasticity rules store multiple stimuli work even tuned are robust synaptic noise We also show these networks improve over multiple presented stimuli learning rules work within densely or sparsely connected networks We derived biologically synaptic rules through which networks self store working memory Networks implementing these plasticity rules robust synaptic noise to having only some updated partial connectivity These networks store multiple stimuli increased after previous training We suggest two candidate sources the global error signal necessary the plasticity rule demonstrate our networks learn store stimulus information while satisfying the added requirements imposed these biological mechanisms This flexibility suggests other types updates able organize working memory circuitsThe results presented were for networks 100 neurons -as larger networks speed the simulations Tests networks the update rule larger networks The optimal learning rate, �� decreases Aside network size a potential caveat a rate-based network model losing information spike-timing dependency A future direction would a spike-based model and determine, must adjusted spike timing for the discretization that spiking neurons entail for the information shared cellsAlong understanding information working memory training Machine learning algorithms generally unrealistic from: most rely non-local synaptic updates We show recurrent networks learn store using biologically plausible synaptic plasticity rules which require local information plus a global error signalor signals that can calculated the apical dendrite via This same setup utilized RNNs make them biologically This would let better learns could: prior work biologically realistic machine learning algorithms led hardware devices use on BID11 BID20 . Synaptically local updates do coordinated over all parts enabling",0.01,0.6215463834580419
"Generative Adversarial Networks (GANs) have been proposed as an approach to learning generative models. While GANs have demonstrated promising performance on multiple vision tasks, their learning dynamics are not yet well understood, neither in theory nor in practice. In particular, the work in this domain has been focused so far only on understanding the properties of the stationary solutions that this dynamics might converge to, and of the behavior of that dynamics in this solutions’ immediate neighborhood.

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

 This methodology enables us to exhibit an interesting phenomena: a GAN with an optimal discriminator provably converges, while guiding the GAN training using only a first order approximation of the discriminator leads to unstable GAN dynamics and mode collapse. This suggests that such usage of the first order approximation of the discriminator, which is a de-facto standard in all the existing GAN dynamics, might be one of the factors that makes GAN training so challenging in practice. Additionally, our convergence result constitutes the first rigorous analysis of a dynamics of a concrete parametric GAN. Generative modeling is a fundamental learning task of growing importance. As we apply machine learning to increasingly sophisticated problems, we often aim to learn functions with an output domain that is significantly more complex than simple class labels. Common examples include image ""translation"" BID12 , speech synthesis BID16 , and robot trajectory prediction BID6 . Due to progress in deep learning, we now have access to powerful architectures that can represent generative models over such complex domains. However, training these generative models is a key challenge. Simpler learning problems such as classification have a clear notion of ""right"" and ""wrong,"" and the approaches based on minimizing the corresponding loss functions have been tremendously successful. In contrast, training a generative model is far more nuanced because it is often unclear how ""good"" a sample from the model is.Generative Adversarial Networks (GANs) have recently been proposed to address this issue BID8 . In a nutshell, the key idea of GANs is to learn both the generative model and the loss function at the same time. The resulting training dynamics are usually described as a game between a generator (the generative model) and a discriminator (the loss function). The goal of the generator is to produce realistic samples that fool the discriminator, while the discriminator is trained to distinguish between the true training data and samples from the generator. GANs have shown promising results on a variety of tasks, and there is now a large body of work that explores the power of this framework BID9 .Unfortunately , reliably training GANs is a challenging problem that often hinders further research in this area. Practitioners have encountered a variety of obstacles such as vanishing gradients, mode collapse, and diverging or oscillatory behavior BID9 . At the same time , the theoretical underpinnings of GAN dynamics are not yet well understood. To date, there were no convergence proofs for GAN models, even in very simple settings. As a result, the root cause of frequent failures of GAN dynamics in practice remains unclear.In this paper, we take a first step towards a principled understanding of GAN dynamics. Our general methodology is to propose and examine a problem setup that exhibits all common failure cases of GAN dynamics while remaining sufficiently simple to allow for a rigorous analysis. Concretely, we introduce and study the GMM-GAN: a variant of GAN dynamics that captures learning a mixture of two univariate Gaussians. We first show experimentally that standard gradient dynamics of the GMM-GAN often fail to converge due to mode collapse or oscillatory behavior. Interestingly, this also holds for techniques that were recently proposed to improve GAN training such as unrolled GANs (Metz et al., 2017 ). In contrast, we then show that GAN dynamics with an optimal discriminator do converge, both experimentally and provably. To the best of our knowledge, our theoretical analysis of the GMM-GAN is the first global convergence proof for parametric and non-trivial GAN dynamics.Our results show a clear dichotomy between the dynamics arising from applying simultaneous gradient descent and the one that is able to use an optimal discriminator. The GAN with optimal discriminator provably converges from (essentially) any starting point. On the other hand, the simultaneous gradient GAN empirically often fails to converge, even when the discriminator is allowed many more gradient steps than the generator. These findings go against the common wisdom that first order methods are sufficiently strong for all deep learning applications. By carefully inspecting our models, we are able to pinpoint some of the causes of this, and we highlight a phenomena we call discriminator collapse which often causes first order methods to fail in our setting. We haven taken a step towards a principled understanding of GAN dynamics. We define a simple yet rich model of GAN training and prove convergence of the corresponding dynamics. To the best of our knowledge, our work is the first to establish global convergence guarantees for a parametric GAN. We find an interesting dichotomy: If we take optimal discriminator steps, the training dynamics provably converge. In contrast, we show experimentally that the dynamics often fail if we take first order discriminator steps. We believe that our results provide new insights into GAN training and point towards a rich algorithmic landscape to be explored in order to further understand GAN dynamics.",1134,0.658,688,1.6482558139534884,"Generative Adversarial Networks learning While GANs demonstrated promising performance multiple vision tasks their learning dynamics neither theory In particular the work in this domain focused so only understanding the stationary solutions this dynamics might converge of that dynamics this solutions�� immediate neighborhood To address in this work take a principled study the GAN dynamics itself To this end propose, on exhibits several the common problematic convergence behaviorse.g., vanishing gradient, mode collapse diverging or oscillatory behavior sufficiently simple enable rigorous convergence analysis This methodology enables exhibit an interesting phenomena a GAN with an optimal discriminator provably converges, while guiding the GAN training using only a first order approximation leads unstable GAN dynamics and mode collapse This suggests such usage the first order approximation the discriminator, all the existing GAN dynamics one makes GAN training challenging in Additionally our convergence result constitutes a dynamics a concrete parametric GAN Generative modeling a fundamental learning task of growing importance As apply machine learning increasingly sophisticated problems often aim learn functions with an output domain significantly simple class labels Common examples image ""translation BID12 , speech synthesis robot trajectory prediction Due progress deep learning access powerful architectures represent generative models over such complex domains However training these generative models Simpler learning problems such classification have a clear notion ""right the approaches based minimizing the corresponding loss functions tremendously In contrast training a generative model far nuanced because often unclear ""good a sample fromGenerative Adversarial Networks recently BID8 . In a nutshell the key idea GANs learn both the generative model the loss function at The resulting training dynamics usually described a game a generatorthe generative model The goal the generator realistic samples fool while trained distinguish the true training data samples GANs have shown on tasks there explores the power this framework BID9 .Unfortunately , reliably training often hinders further research Practitioners have encountered obstacles such vanishing gradients mode collapse diverging or oscillatory behavior BID9 . At , GAN dynamics To date were no convergence proofs GAN models even in very simple settings As the root cause frequent failures GAN dynamics practice remainsIn take a principled understanding Our general methodology propose and examine a problem setup exhibits all common failure cases GAN dynamics while remaining sufficiently allow a rigorous analysis Concretely introduce and study the GMM-GAN: a variant GAN dynamics captures learning a mixture two univariate Gaussians We first show experimentally standard gradient dynamics the GMM-GAN often fail converge due mode collapse oscillatory behavior Interestingly also holds techniques were recently GAN training such unrolled GANsMetz et 2017 In contrast we then show GAN dynamics with an optimal discriminator do converge, both experimentally provably To our theoretical analysis the GMM-GAN the first global convergence proof parametric and non-trivial GAN dynamicsOur results a clear dichotomy arising applying simultaneous gradient descent able use an optimal discriminator The GAN with optimal discriminator provably from (essentially any starting point On the simultaneous gradient GAN empirically often converge allowed many more gradient steps the generator These findings go first order methods sufficiently strong all deep learning applications By carefully inspecting our models pinpoint some this, highlight a phenomena discriminator collapse which often first order methods our setting We haven taken a principled understanding GAN dynamics We define a simple yet rich model GAN training prove convergence the corresponding dynamics To our work establish global convergence guarantees a parametric GAN We find If take optimal discriminator steps the training dynamics provably converge In contrast we show experimentally the dynamics often fail if take first order discriminator steps We believe our results GAN training point towards a rich algorithmic landscape order further",0.01,0.3557780285042299
"The machine learning and computer vision community is witnessing an unprecedented rate of new tasks being proposed and addressed, thanks to the power of deep convolutional networks to find complex mappings from X to Y. The advent of each task often accompanies the release of a large-scale human-labeled dataset, for supervised training of the deep network. However, it is expensive and time-consuming to manually label sufficient amount of training data. Therefore, it is important to develop algorithms that can leverage off-the-shelf labeled dataset to learn useful knowledge for the target task. While previous works mostly focus on transfer learning from a single source, we study multi-source transfer across domains and tasks (MS-DTT), in a semi-supervised setting. We propose GradMix, a model-agnostic method applicable to any model trained with gradient-based learning rule. GradMix transfers knowledge via gradient descent, by weighting and mixing the gradients from all sources during training. Our method follows a meta-learning objective, by assigning layer-wise weights to the source gradients, such that the combined gradient follows the direction that can minimize the loss for a small set of samples from the target dataset. In addition, we propose to adaptively adjust the learning rate for each mini-batch based on its importance to the target task, and a pseudo-labeling method to leverage the unlabeled samples in the target domain. We perform experiments on two MS-DTT tasks: digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method against multiple baselines. Deep convolutional networks (ConvNets) have significantly improved the state-of-the-art for visual recognition, by finding complex mappings from X to Y. Unfortunately, these impressive gains in performance come only when massive amounts of paired labeled data (x, y) s.t. x ∈ X , y ∈ Y are available for supervised training. For many application domains, it is often prohibitive to manually label sufficient training data, due to the significant amount of human efforts involved. Hence, there is strong incentive to develop algorithms that can reduce the burden of manual labeling, typically by leveraging off-the-shelf labeled datasets from other related domains and tasks.There has been a large amount of efforts in the research community to address adapting deep models across domains BID5 BID16 BID31 , to transfer knowledge across tasks BID17 BID7 BID34 , and to learn efficiently in a few shot manner BID4 BID22 BID23 . However, most works focus on a single-source and single-target scenario. Recently, some works BID33 BID19 propose deep approaches for multi-source domain adaptation, but they assume that the source and target domains have shared label space (task).In many computer vision applications, there often exist multiple labeled datasets available from different domains and/or tasks related to the target application. Hence , it is important and practically valuable that we can transfer knowledge from as many source datasets as possible. In this work, we formalize this problem as multi-source domain and task transfer (MS-DTT). Given a set of labeled source dataset, S = {S 1 , S 2 , ..., S k }, we aim to transfer knowledge to a sparsely labeled target dataset T . Each source dataset S i could come from a different domain compared to T , or from a different task, or different in both domain and task. We focus on a semi-supervised setting, where only few samples in T have labels.Most works achieve domain transfer by aligning the feature distribution of source domain and target domain BID15 BID5 BID30 BID19 BID33 . However, this method could be suboptimal for MS-DTT. The reason is that in MS-DTT, the distribution of source data p(x Si , y Si ) and target data p(x T , y T ) could be significantly different in both input space and label space, thus simply aligning their input space may generate indiscriminative features for the target classes. In addition, feature alignment introduces additional layers and loss terms, which require careful design to perform well.In this work, we propose a generic and scalable method, namely GradMix, for semi-supervised MS-DTT. GradMix is a model-agnostic method, applicable to any model that uses gradient-based learning rule. Our method does not introduce extra layers or loss functions for feature alignment. Instead, we perform knowledge transfer via gradient descent, by weighting and mixing the gradients from all the source datasets during training. We follow a meta-learning paradigm and model the most basic assumption: the combined gradient should minimize the loss for a set of unbiased samples from the target dataset. We propose an online method to weight and mix the source gradients at each training iteration, such that the knowledge most useful for the target task is preserved through the gradient update. Our method can adaptively adjust the learning rate for each mini-batch based on its importance to the target task. In addition, we propose a pseudo-labeling method based on model ensemble to learn from the unlabeled data in target domain. We perform extensive experiments on two sets of MS-DTT task, including digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method compared to multiple baselines. Our code is available at https://www.url.com . In this work, we propose GradMix, a method for semi-supervised MS-DTT: multi-source domain and task transfer. GradMix assigns layer-wise weights to the gradients calculated from each source objective, in a way such that the combined gradient can optimize the target objective, measured by the loss on a small validation set. GradMix can adaptively adjust the learning rate for each mini-batch based on its importance to the target task. In addition, we assign pseudo-labels to the unlabeled samples using model ensembles, and consider the pseudo-labeled dataset as a source during training. We validate the effectiveness our method with extensive experiments on two MS-DTT settings, namely digit recognition and action recognition. GradMix is a generic framework applicable to any models trained with gradient descent. For future work, we intend to extend GradMix to other problems where labeled data for the target task is expensive to acquire, such as image captioning.",1227,0.737,687,1.7860262008733625,"The machine learning and computer vision community witnessing new tasks proposed addressed thanks to find complex mappings from X The advent each task often accompanies for supervised training the deep network However expensive manually label sufficient amount training data Therefore develop algorithms leverage off labeled dataset learn useful knowledge the target task While previous works mostly transfer learning from study across domains tasksMS-DTT We propose GradMix applicable any model trained gradient-based learning rule GradMix transfers knowledge via gradient descent by and mixing all sources during Our method follows a meta-learning objective by assigning layer-wise weights the source gradients such follows can minimize for samples from In addition propose adaptively adjust the learning rate each minibatch based its importance a pseudo-labeling method leverage We perform experiments two MS-DTT tasks digit recognition action recognition demonstrate the advantageous performance the proposed method against multiple baselines Deep convolutional networks significantly the state for visual recognition by finding complex mappings from X Unfortunately these impressive gains only massive amounts paired labeled datax s.t. x �� X , supervised training For many application domains manually label sufficient training data due human efforts Hence strong incentive develop algorithms reduce manual labeling typically leveraging off labeled datasets from other related domains tasksThere efforts adapting deep models across BID5 BID16 BID31 , to transfer tasks learn efficiently a few shot manner However most works focus Recently some works BID33 BID19 propose deep approaches multi-source domain adaptation assume shared label spacetask).In many computer vision applications often multiple labeled datasets available tasks related Hence , and practically valuable can transfer knowledge as many source datasets In this work formalize this problem as multi-source domain and task transferMS-DTT Given a set labeled source dataset S = {S 1 aim transfer knowledge a sparsely labeled target dataset T Each source dataset S i could come a different domain compared T , different in both domain We focus a semi-supervised setting only few samples in T have labelsMost works achieve domain transfer aligning the feature distribution source domain BID15 BID5 . However this method could MS-DTT The reason in MS-DTT the distribution source data p(x Si , target could significantly both input space label space simply their input space may generate indiscriminative features the target classes In addition feature alignment introduces additional layers loss terms require performIn propose, namely GradMix semi-supervised MS-DTT GradMix, applicable gradient-based learning rule Our method does introduce extra layers loss functions feature alignment Instead perform knowledge transfer by weighting and mixing from all the source datasets during We follow a meta-learning paradigm model the most basic assumption the combined gradient should minimize for unbiased samples We propose an online method weight mix the source gradients at each training iteration such the knowledge most useful preserved through the gradient update Our method can adaptively adjust each minibatch based its importance In addition propose a pseudo-labeling method model ensemble to learn target domain We perform extensive experiments two sets MS-DTT task including digit recognition action recognition demonstrate the advantageous performance the proposed method compared multiple baselines Our code . In this work propose GradMix semi-supervised MS-DTT: multi-source domain and task transfer GradMix assigns layer-wise weights calculated each source objective such can optimize the target objective measured the loss on a small validation set GradMix can adaptively adjust the learning rate each mini based its importance In addition assign pseudolabels model ensembles consider during training We validate our method with extensive experiments two MS-DTT settings digit recognition action recognition GradMix a generic framework applicable any models trained For future work intend extend GradMix other problems where labeled data for expensive acquire image captioning",0.01,0.7068048700022244
"Bayesian phylogenetic inference is currently done via Markov chain Monte Carlo with simple mechanisms for proposing new states, which hinders exploration efficiency and often requires long runs to deliver accurate posterior estimates. In this paper we present an alternative approach: a variational framework for Bayesian phylogenetic analysis. We approximate the true posterior using an expressive graphical model for tree distributions, called a subsplit Bayesian network, together with appropriate branch length distributions. We train the variational approximation via stochastic gradient ascent and adopt multi-sample based gradient estimators for different latent variables separately to handle the composite latent space of phylogenetic models. We show that our structured variational approximations are flexible enough to provide comparable posterior estimation to MCMC, while requiring less computation due to a more efficient tree exploration mechanism enabled by variational inference. Moreover, the variational approximations can be readily used for further statistical analysis such as marginal likelihood estimation for model comparison via importance sampling. Experiments on both synthetic data and real data Bayesian phylogenetic inference problems demonstrate the effectiveness and efficiency of our methods. Bayesian phylogenetic inference is an essential tool in modern evolutionary biology. Given an alignment of nucleotide or amino acid sequences and appropriate prior distributions, Bayesian methods provide principled ways to assess the phylogenetic uncertainty by positing and approximating a posterior distribution on phylogenetic trees . In addition to uncertainty quantification, Bayesian methods enable integrating out tree uncertainty in order to get more confident estimates of parameters of interest, such as factors in the transmission of Ebolavirus BID4 . Bayesian methods also allow complex substitution models BID24 , which are important in elucidating deep phylogenetic relationships (Feuda et al., 2017) .Ever since its introduction to the phylogenetic community in the 1990s, Bayesian phylogenetic inference has been dominated by random-walk Markov chain Monte Carlo (MCMC) approaches BID43 BID26 ). However , this approach is fundamentally limited by the complexities of tree space. A typical MCMC method for phylogenetic inference involves two steps in each iteration: first, a new tree is proposed by randomly perturbing the current tree, and second, the tree is accepted or rejected according to the Metropolis-Hastings acceptance probability. Any such random walk algorithm faces obstacles in the phylogenetic case, in which the high-posterior trees are a tiny fraction of the combinatorially exploding number of trees. Thus, major modifications of trees are likely to be rejected, restricting MCMC tree movement to local modifications that may have difficulty moving between multiple peaks in the posterior distribution BID41 . Although recent MCMC methods for distributions on Euclidean space use intelligent proposal mechanisms such as Hamiltonian Monte Carlo BID30 , it is not straightforward to extend such algorithms to the composite structure of tree space, which includes both tree topology (discrete object) and branch lengths (continuous positive vector) BID3 .Variational inference (VI) is an alternative approximate inference method for Bayesian analysis which is gaining in popularity BID17 BID40 BID0 . Unlike MCMC methods that sample from the posterior, VI selects the best candidate from a family of tractable distributions to minimize a statistical distance measure to the target posterior, usually the Kullback-Leibler (KL) divergence. By reformulating the inference problem into an optimization problem, VI tends to be faster and easier to scale to large data (via stochastic gradient descent) BID0 . However, VI can also introduce a large bias if the variational distribution is insufficiently flexible. The success of variational methods , therefore, relies on having appropriate tractable variational distributions and efficient training procedures.To our knowledge, there have been no previous variational formulations of Bayesian phylogenetic inference. This has been due to the lack of an appropriate family of approximating distributions on phylogenetic trees. However the prospects for variational inference have changed recently with the introduction of subsplit Bayesian networks (SBNs) BID46 , which provide a family of flexible distributions on tree topologies (i.e. trees without branch lengths). SBNs build on previous work BID13 BID23 , but in contrast to these previous efforts, SBNs are sufficiently flexible for real Bayesian phylogenetic posteriors BID46 .In this paper, we develop a general variational inference framework for Bayesian phylogenetics. We show that SBNs, when combined with appropriate approximations for the branch length distribution, can provide flexible variational approximations over the joint latent space of phylogenetic trees with branch lengths. We use recently-proposed unbiased gradient estimators for the discrete and continuous components separately to enable efficient stochastic gradient ascent. We also leverage the similarity of local structures among trees to reduce the complexity of the variational parameterization for the branch length distributions and provide an extension to better capture the between-tree variation. Finally, we demonstrate the effectiveness and efficiency of our methods on both synthetic data and a benchmark of challenging real data Bayesian phylogenetic inference problems. In this work we introduced VBPI, a general variational framework for Bayesian phylogenetic inference. By combining subsplit Bayesian networks, a recent framework that provides flexible distributions of trees, and efficient structured parameterizations for branch length distributions, VBPI exhibits guided exploration (enabled by SBNs) in tree space and provides competitive performance to MCMC methods with less computation. Moreover, variational approximations provided by VBPI can be readily used for further statistical analysis such as marginal likelihood estimation for model comparison via importance sampling, which, compared to MCMC based methods, dramatically reduces the cost at test time. We report promising numerical results demonstrating the effectiveness and efficiency of VBPI on a benchmark of real data Bayesian phylogenetic inference problems.When the data are weak and posteriors are diffuse, support estimation of CPTs becomes challenging. However, compared to classical MCMC approaches in phylogenetics that need to traverse the enormous support of posteriors on complete trees to accurately evaluate the posterior probabilities, the SBN parameterization in VBPI has a natural advantage in that it alleviates this issue by factorizing the uncertainty of complete tree topologies into local structures.Many topics remain for future work: constructing more flexible approximations for the branch length distributions (e.g., using normalizing flow BID33 for within-tree approximation and deep networks for the modeling of between-tree variation), deeper investigation of support estimation approaches in different data regimes, and efficient training algorithms for general variational inference on discrete / structured latent variables.",1300,0.627,771,1.6861219195849546,"Bayesian phylogenetic inference currently done via simple mechanisms proposing new states hinders exploration efficiency often long runs deliver In: We approximate the true posterior using an expressive graphical model tree distributions called a subsplit Bayesian network together appropriate branch length distributions We train the variational approximation via adopt multi-sample based gradient estimators different latent variables separately to handle the composite latent space phylogenetic models We show our structured variational approximations flexible provide comparable posterior estimation MCMC requiring due a more efficient tree exploration mechanism enabled Moreover the variational approximations can readily further statistical analysis such marginal likelihood estimation for model comparison via importance sampling Experiments both synthetic data Bayesian phylogenetic inference problems demonstrate our methods Bayesian phylogenetic inference Given an alignment appropriate prior distributions Bayesian methods provide principled ways by positing and on . In addition uncertainty quantification Bayesian methods enable integrating out tree uncertainty get more confident estimates parameters factors the transmission Ebolavirus BID4 . Bayesian methods also complex substitution models BID24 , importantFeuda 2017 .Ever its introduction to dominated BID43 BID26 However , this approach fundamentally limited tree space A typical MCMC method phylogenetic inference in each iteration proposed randomly accepted or according the Metropolis-Hastings acceptance probability Any such random walk algorithm faces obstacles the phylogenetic case in a tiny fraction the combinatorially exploding number Thus major modifications trees likely rejected restricting MCMC tree movement local modifications difficulty moving between multiple peaks BID41 . Although recent MCMC methods distributions on use intelligent proposal mechanisms Hamiltonian Monte Carlo BID30 , straightforward extend the composite structure tree space (discrete object branch lengthscontinuous positive vector BID3 .Variational inferenceVI an alternative approximate inference method Bayesian analysis which gaining BID17 BID40 BID0 Unlike MCMC methods sample the posterior, VI selects a family tractable distributions minimize a statistical distance measure posterior usually Kullback ( divergence By reformulating the inference problem into VI tends faster scale (via BID0 . However VI can introduce a large bias if the variational distribution insufficiently flexible The success variational methods , therefore relies having appropriate tractable variational distributions efficient training proceduresTo This has due an appropriate family of approximating distributions on However the prospects variational inference recently with subsplit Bayesian networks BID46 which a family flexible distributions on tree topologies without branch lengths SBNs build BID13 BID23 , in contrast these previous efforts sufficiently real Bayesian phylogenetic posteriors BID46 .In develop We show SBNs, when appropriate approximations the branch length distribution over the joint latent space branch lengths We use recently-proposed unbiased gradient estimators the discrete and continuous components separately to enable We also leverage the similarity local structures among trees reduce the variational parameterization for the branch length distributions provide an extension better capture between variation Finally demonstrate our methods both synthetic data a benchmark challenging real data Bayesian phylogenetic inference problems In this work introduced VBPI a general variational framework By combining subsplit Bayesian networks a recent framework flexible distributions trees efficient structured parameterizations branch length distributions VBPI exhibits guided exploration (enabled SBNs tree space provides competitive performance to MCMC methods less computation Moreover variational approximations provided VBPI readily further statistical analysis such marginal likelihood estimation for model comparison via importance sampling, compared MCMC based methods dramatically at test time We report promising numerical results demonstrating VBPI on a benchmark real data Bayesian phylogenetic inference problemsWhen weak posteriors diffuse support estimation CPTs becomes challenging However compared classical MCMC approaches phylogenetics that need traverse the enormous support posteriors on complete trees accurately evaluate the SBN parameterization VBPI a natural advantage alleviates this issue factorizing complete tree topologies local structuresMany topics remain for: constructing more flexible approximations the branch length distributions using normalizing flow BID33 within approximation deep networks the modeling between variation deeper investigation support estimation approaches different data regimes efficient training algorithms on discrete / structured latent variables",0.01,0.4522575387735413
"This paper introduces HybridNet, a hybrid neural network to speed-up autoregressive
 models for raw audio waveform generation. As an example, we propose
 a hybrid model that combines an autoregressive network named WaveNet and a
 conventional LSTM model to address speech synthesis. Instead of generating
 one sample per time-step, the proposed HybridNet generates multiple samples per
 time-step by exploiting the long-term memory utilization property of LSTMs. In
 the evaluation, when applied to text-to-speech, HybridNet yields state-of-art performance.
 HybridNet achieves a 3.83 subjective 5-scale mean opinion score on
 US English, largely outperforming the same size WaveNet in terms of naturalness
 and provide 2x speed up at inference. Speech synthesis, also known as text-to-speech (TTS) has variety of applications in human-computer interactions, assistive technology and entertainment productions. The traditional TTS system, which is done with complex hand-engineered pipelines, transforms textual features into high temporal resolution waveforms (e.g., 16KHz). Recent work on neural TTS has demonstrated state-of-the-art results BID0 b; BID14 . In particular, various neural network architectures (e.g., BID12 have been proposed as neural vocoders for waveform synthesis.Recurrent neural network (RNN), especially long short-term memory (LSTM) BID6 , is well-suited to address speech synthesis as it can model long-term dependencies in audio data (e.g., BID3 BID16 BID4 . RNNs have been successfully applied in many state-of-the-art neural TTS systems (e.g., BID14 BID1 , and were proven to be more effective than the conventional hidden Markov model (HMM)-based synthesizer. However, RNNs are unsuitable for raw waveform generation at high sampling rate (e.g. 16,000 samples per second), because RNNs process each state sequentially and the computation cannot be paralleled over elements of a sequence at training. In practice, RNNs are usually operated on spectral or hand-engineered features of audio (e.g., BID14 BID5 , which have much fewer time steps than the raw waveform. Most recently, SampleRNN was proposed to tackle this difficulty by combining autoregressive multilayer perceptrons and RNNs in a hierarchical architecture, where different RNN modules operate at different clock rates.Another line of research investigates the convolutional autoregressive model (e.g., WaveNet BID12 ) for waveform synthesis, where the computation over different time-step can be fully parallelized during training. WaveNet can be efficiently trained on audio data with tens of thousands of samples per second. In order to model the long-range dependencies in audio data, WaveNet uses dilated convolution BID15 to increase the receptive fields of output units, and demonstrates very good performance in speech synthesis. Several state-of-the-art neural TTS systems, such as Deep Voice 1 BID0 and Deep Voice 2 BID1 , use WaveNet to synthesize waveform conditioned on acoustic features (e.g., phoneme duration and fundamental frequency). Despite its full parallelism at training, WaveNet poses daunting computational problem at inference due to the autoregressive nature of the model (see FIG0 for an illustration).In addition, although the dilated convolution is very effective at increasing receptive fields, the very long-range connections in deep layer could potentially result in high variance in the output sampling distribution. In practice, some buzz noises are commonly observed in the audio samples generated by WaveNet. We present a hybrid neural architecture to speed up autoregressive models for audio synthesis. As a demonstration of effectiveness, we design and implement a hybrid model that consists of an autoregressive network named WaveNet and a LSTM model. The hybrid model exploits the long-term memory utilization property and short inference time of LSTMs. We evaluate HybridNet with both Mean Opinion Score (MOS) and validation error, and find that it outperforms WaveNet with the same layer in terms of naturalness and validation error. In addition, HybridNet provides 2x-4x speed-up at inference with comparable generation quality compared to WaveNet. The technique used in HybridNet can be easily applied to another autoregressive model and can be combined with existing inference time reduction techniques.",871,0.407,515,1.69126213592233,"This paper introduces HybridNet to speed-up autoregressive models raw audio waveform generation As propose a hybrid model an autoregressive network named WaveNet address speech synthesis Instead generating one sample time-step the proposed HybridNet generates by exploiting the evaluation when applied text yields stateart HybridNet achieves a 3.83 subjective 5-scale mean opinion score US English, largely outperforming the same size WaveNet naturalness provide 2x speed at inference Speech synthesis also text variety assistive technology entertainment productions The traditional TTS system done complex hand-engineered pipelines transforms textual features high temporal resolution waveforms ( 16KHz Recent work neural TTS state results BID0 b; BID14 . In particular, various neural network architectures BID12 have neural vocoders waveform synthesis.Recurrent neural network ( especially long short-term memory , well address speech synthesis model audio data . RNNs successfully applied state neural TTSe.g., BID14 BID1 , and were proven more the conventional hidden Markov modelHMM)-based synthesizer. However RNNs unsuitable raw waveform generation at high sampling rate process each state the computation paralleled over elements at training. In practice RNNs usually operated spectral or hand-engineered features audio ( BID14 BID5 , which have much fewer time steps. Most recently SampleRNN proposed tackle this difficulty combining autoregressive multilayer perceptrons a hierarchical architecture different RNN modules operate different clock ratesAnother line investigatese.g., WaveNet BID12 ) waveform synthesis the computation over different time-step can fully during training WaveNet can efficiently trained audio data In order model the long-range dependencies in audio data WaveNet dilated convolution BID15 increase the receptive fields output units demonstrates very good performance speech synthesis Several state- neural TTS Deep Voice 1 BID0 , use WaveNet waveform conditioned on acoustic features phoneme duration fundamental frequency Despite its full parallelism at training WaveNet poses daunting computational problem at inference due ( FIG0 for although the dilated convolution is very effective increasing receptive fields the very long-range connections deep layer could potentially result high variance the output sampling distribution In practice some buzz noises commonly observed the audio samples generated WaveNet We present a hybrid neural architecture speed autoregressive models audio synthesis As a demonstration effectiveness design a hybrid model consists an autoregressive network named WaveNet The hybrid model exploits the long-term memory utilization property short inference time We evaluate HybridNet both Mean Opinion Score validation error WaveNet the same layer in naturalness In addition HybridNet provides at inference with comparable generation quality compared WaveNet The technique HybridNet can easily another autoregressive model combined existing inference time reduction techniques",0.01,0.46535435838670464
"Visual Interpretation and explanation of deep models is critical towards wide adoption of systems that rely on them. In this paper, we propose a novel scheme for both interpretation as well as explanation in which, given a pretrained model, we automatically identify internal features relevant for the set of classes considered by the model, without relying on additional annotations. We interpret the model through average visualizations of this reduced set of features. Then, at test time, we explain the network prediction by accompanying the predicted class label with supporting visualizations derived from the identified features. In addition, we propose a method to address the artifacts introduced by strided operations in deconvNet-based visualizations. Moreover, we introduce an8Flower , a dataset specifically designed for objective quantitative evaluation of methods for visual explanation. Experiments on the MNIST , ILSVRC 12, Fashion 144k and an8Flower datasets show that our method produces detailed explanations with good coverage of relevant features of the classes of interest. Methods based on deep neural networks (DNNs) have achieved impressive results for several computer vision tasks, such as image classification, object detection and image generation. Combined with the general tendency in the Computer Vision community of developing methods with a focus on high quantitative performance, this has motivated the wide adoption of DNN-based methods, despite the initial skepticism due to their black-box characteristics. In this work, we aim for more visuallydescriptive predictions and propose means to improve the quality of the visual feedback capabilities of DNN-based methods. Our goal is to bridge the gap between methods aiming at model interpretation, i.e., understanding what a given trained model has actually learned, and methods aiming at model explanation, i.e., justifying the decisions made by a model.Model interpretation of DNNs is commonly achieved in two ways: either by a) manually inspecting visualizations of every single filter (or a random subset thereof) from every layer of the network BID28 ; BID29 ) or, more recently, by b) exhaustively comparing the internal activations produced by a given model w.r.t. a dataset with pixel-wise annotations of possibly relevant concepts BID1 ; BID7 ). These two paths have provided useful insights into the internal representations learned by DNNs. However, they both have their own weaknesses. For the first case, the manual inspection of filter responses introduces a subjective bias, as was evidenced by BID8 . In addition, the inspection of every filter from every layer becomes a cognitive-expensive practice for deeper models, which makes it a noisy process. For the second case, as stated by BID1 , the interpretation capabilities over the network are limited by the concepts for which annotation is available. Moreover, the cost of adding annotations for new concepts is quite high due to its pixel-wise nature. A third weakness, shared by both cases, is inherited by the way in which they generate spatial filter-wise responses, i.e., either through deconvolution-based heatmaps BID23 ; BID29 ) or by up-scaling the activation maps at a given layer/filter to the image space BID1 ; BID32 ). On the one hand, deconvolution methods are able to produce heatmaps with high level of detail from any filter in Figure 1 : Left: Proposed training/testing pipeline. Center: Visual explanations generated by our method.Predicted class labels are enriched with heatmaps indicating the pixel locations, associated to the features, that contributed to the prediction. Note these features may come from the object itself as well as from the context. On top of each heatmap we indicate the number of the layer where the features come from. The layer type is color-coded (green for convolutional and pink for fully connected). Right: Visualization comparison. Note how our heatmaps attenuate the grid-like artifacts introduced by deconvnet-based methods at lower layers. At the same time, our method is able to produce a more detailed visual feedback than up-scaled activation maps. the network. However, as can be seen in Fig. 1 (right), they suffer from artifacts introduced by strided operations in the back-propagation process. Up-scaled activation maps, on the other hand, can significantly lose details when displaying the response of filters with large receptive field from deeper layers. Moreover, they have the weakness of only being computable for convolutional layers.In order to alleviate these issues, we start from the hypothesis proven by BID1 ; BID28 , that only a small subset of the internal filters of a network encode features that are important for the task that the network addresses. Based on that assumption, we propose a method which, given a trained DNN model, automatically identifies a set of relevant internal filters whose encoded features serve as indicators for the class of interest to be predicted (Fig. 1 left) . These filters can originate from any type of internal layer of the network, i.e., convolutional, fully connected, etc. Selecting them is formulated as a µ-lasso optimization problem in which a sparse set of filter-wise responses are linearly combined in order to predict the class of interest. At test time, we move from interpretation to explanation. Given an image, a set of identified relevant filters, and a class prediction, we accompany the predicted class label with heatmap visualizations of the top-responding relevant filters for the predicted class, see Fig. 1 (center). In addition, by improving the resampling operations within deconvnet-based methods, we are able to address the artifacts introduced in the backpropagation process, see Fig. 1 (right) . The code and models used to generate our visual explanations can be found in the following link 1 . Overall, the proposed method removes the requirement of additional expensive pixel-wise annotation, by relying on the same annotations used to train the initial model. Moreover, by using our own variant of a deconvolution-based method, our method is able to consider the spatial response from any filter at any layer while still providing visually pleasant feedback. This allows our method to reach some level of explanation by interpretation.Finally, recent approaches to evaluate explanation methods measure the validity of an explanation either via user studies BID29 BID20 ) or by measuring its effect on a proxy task, e.g. object detection/segmentation BID33 ; BID30 ). While user studies inherently add subjectivity, benchmarking through a proxy task steers the optimization of the explanation method towards such task. Here we propose an objective evaluation via an8Flower, a synthetic dataset where the discriminative feature between the classes of interest is controlled. This allows us to produce ground-truth masks for the regions to be highlighted by the explanation. Furthermore, it allows us to quantitatively measure the performance of methods for model explanation.The main contributions of this work are four-fold. First, we propose an automatic method based on feature selection to identify the network-encoded features that are important for the prediction of a given class. This alleviates the requirement of exhaustive manual inspection or additional expensive pixel-wise annotations required by existing methods. Second, the proposed method is able to provide visual feedback with higher-level of detail over up-scaled raw activation maps and improved quality over recent deconvolution+guided back-propagation methods. Third, the proposed method is general enough to be applied to any type of network, independently of the type of layers that compose it. Fourth, we release a dataset and protocol specifically designed for the evaluation of methods for model explanation. To the best of our knowledge this is the first dataset aimed at such task. This paper is organized as follows: in Sec. 2 we position our work w.r.t. existing work. Sec. 3 presents the pipeline and inner-workings of the proposed method. In Sec. 4, we conduct a series of experiments evaluating different aspects of the proposed method. We draw conclusions in Sec. 5. We propose a method to enrich the prediction made by DNNs by indicating the visual features that contributed to such prediction. Our method identifies features encoded by the network that are relevant for the task addressed by the DNN. It allows interpretation of these features by the generation of average feature-wise visualizations. In addition, we proposed a method to attenuate the artifacts introduced by strided operations in visualizations made by Deconvnet-based methods. This empowers our method with richer visual feedback with pixel-level precision without requiring additional annotations for supervision. Finally, we have proposed a novel dataset designed for the objective evaluation of methods for explanation of DNNs.",1707,1.066,1013,1.6850937808489634,"Visual Interpretation explanation deep models is critical towards wide adoption systems rely them In both interpretation as explanation which, given a pretrained model automatically identify internal features relevant the set classes considered without relying additional annotations We interpret the model through average visualizations this reduced set features Then at test time explain the network prediction by accompanying the predicted class label supporting visualizations derived the identified features In addition propose address the artifacts introduced strided operations deconvNet-based visualizations Moreover introduce an8Flower , a dataset specifically objective quantitative evaluation methods visual explanation Experiments the MNIST , ILSVRC 12 Fashion 144k an8Flower datasets our method produces detailed explanations with good coverage relevant features the classes interest Methods based deep neural networks achieved Combined the general tendency the Computer Vision community of developing methods with high quantitative performance has motivated the wide adoption despite due their black-box characteristics In this work aim for more visuallydescriptive predictions propose means the visual feedback capabilities DNN-based methods Our goal bridge methods aiming model interpretation understanding a given trained model has actually model explanation justifyingModel interpretation of DNNs commonly achieved either a) manually inspecting visualizations every single filter a random subset from every layer BID28 ; ) b exhaustively the internal activations produced a dataset pixel-wise annotations possibly relevant concepts BID1 These two paths provided useful insights the internal representations learned DNNs both For the first case the manual inspection filter responses introduces a subjective bias was evidenced BID8 . In addition the inspection every filter from every layer becomes a cognitive-expensive practice deeper models noisy For the second case as stated BID1 , the interpretation capabilities over the concepts for annotation Moreover the cost adding annotations new concepts due its pixel-wise nature A third weakness, shared both cases inherited the way generate spatial filter-wise responses either through deconvolution-based heatmaps BID23 ; ) up the activation maps at a given layer/filter to the image space On deconvolution methods able heatmaps high level from any filter in Figure : Left Proposed training/testing pipeline Center Visual explanations generated our methodPredicted class labels enriched heatmaps indicating the pixel locations associated to the features that contributed Note these features come the object as On top each heatmap indicate the layer where the features come The layer type colorgreen pink fully connected Right: Visualization comparison Note how our heatmaps attenuate the grid-like artifacts introduced deconvnet-based methods at lower layers At our method able produce a more detailed visual feedback up-scaled activation maps the network However can Fig 1 (right they suffer artifacts introduced strided operations Up-scaled activation maps on significantly lose details displaying the response filters with large receptive field from deeper layers Moreover they the weakness only computableIn alleviate start the hypothesis proven BID1 ; BID28 the internal filters a network encode features important the task that addresses Based that assumption propose given a trained DNN model automatically identifies relevant internal filters whose encoded features serve indicators interest predictedFig 1 left) . These filters originate internal layer, fully Selecting them formulated a µ-lasso optimization problem a sparse filter-wise responses linearly combined predict the class interest At test time move interpretation explanation Given an image a set identified relevant filters a class prediction accompany the predicted class label heatmap visualizations the top-responding relevant filters see 1 (center In addition by improving the resampling operations within deconvnet-based methods address the artifacts see Fig 1 (right . The code and models our visual explanations 1 Overall the proposed method removes additional expensive pixel-wise annotation by relying the same annotations train Moreover by our own variant consider the spatial response from any filter at while visually pleasant feedback This allows our method reach some level explanation interpretationFinally recent approaches evaluate explanation methods measure either via user studies BID29 BID20 ) measuring a proxy task object ; While user studies inherently add subjectivity benchmarking through a proxy task steers the optimization the explanation method towards such task Here propose an objective evaluation via an8Flower a synthetic dataset where between the classes interest controlled This allows produce ground-truth masks the regions to highlighted the explanation Furthermore allows quantitatively methods model explanationThe main contributions four First propose an automatic method based feature selection identify the network-encoded features This alleviates the requirement exhaustive manual inspection or additional expensive pixel-wise annotations required existing methods Second the proposed method able visual feedback with of over up-scaled raw activation maps improved quality recent deconvolution+guided back-propagation methods Third the proposed method general network independently layers Fourth release a dataset and protocol specifically the evaluation methods model explanation To aimed such task This paper organized in Sec 2 we position our work w.r.t existing work Sec 3 presents the pipeline the proposed method In Sec 4, we conduct evaluating different aspects the proposed method We draw conclusions in Sec 5 We propose enrich the prediction made indicating the visual features contributed such prediction Our method identifies features encoded the network addressed It allows interpretation these features the generation average feature-wise visualizations In addition proposed attenuate the artifacts introduced strided operations visualizations made Deconvnet-based methods This empowers our method with richer visual feedback with pixel-level precision without additional annotations supervision Finally proposed a novel dataset designed the objective evaluation methods explanation DNNs",0.01,0.44963793160551746
"In this work we propose a simple and efficient framework for learning sentence representations from unlabelled data. Drawing inspiration from the distributional hypothesis and recent work on learning sentence representations, we reformulate the problem of predicting the context in which a sentence appears as a classification problem. Given a sentence and the context in which it appears, a classifier distinguishes context sentences from other contrastive sentences based on their vector representations. This allows us to efficiently learn different types of encoding functions, and we show that the model learns high-quality sentence representations. We demonstrate that our sentence representations outperform state-of-the-art unsupervised and supervised representation learning methods on several downstream NLP tasks that involve understanding sentence semantics while achieving an order of magnitude speedup in training time. Methods for learning meaningful representations of data have received widespread attention in recent years. It has become common practice to exploit these representations trained on large corpora for downstream tasks since they capture a lot of prior knowlege about the domain of interest and lead to improved performance. This is especially attractive in a transfer learning setting where only a small amount of labelled data is available for supervision.Unsupervised learning allows us to learn useful representations from large unlabelled corpora. The idea of self-supervision has recently become popular where representations are learned by designing learning objectives that exploit labels that are freely available with the data. Tasks such as predicting the relative spatial location of nearby image patches BID6 , inpainting BID30 and solving image jigsaw puzzles BID27 have been successfully used for learning visual feature representations. In the language domain, the distributional hypothesis has been integral in the development of learning methods for obtaining semantic vector representations of words BID24 . This is the assumption that the meaning of a word is characterized by the word-contexts in which it appears. Neural approaches based on this assumption have been successful at learning high quality representations from large text corpora.Recent methods have applied similar ideas for learning sentence representations Hill et al., 2016; BID8 . These are encoder-decoder models that learn to predict/reconstruct the context sentences of a given sentence. Despite their success, several modelling issues exist in these methods. There are numerous ways of expressing an idea in the form of a sentence. The ideal semantic representation is insensitive to the form in which meaning is expressed. Existing models are trained to reconstruct the surface form of a sentence, which forces the model to not only predict its semantics, but aspects that are irrelevant to the meaning of the sentence as well.The other problem associated with these models is computational cost. These methods have a word level reconstruction objective that involves sequentially decoding the words of target sentences. Training with an output softmax layer over the entire vocabulary is a significant source of slowdown in the training process. This further limits the size of the vocabulary and the model (Variations of the softmax layer such as hierarchical softmax BID26 , sampling based softmax BID9 and sub-word representations BID33 can help alleviate this issue).We circumvent these problems by proposing an objective that operates directly in the space of sentence embeddings. The generation objective is replaced by a discriminative approximation where the model attempts to identify the embedding of a correct target sentence given a set of sentence candidates. In this context, we interpret the 'meaning' of a sentence as the information in a sentence that allows it to predict and be predictable from the information in context sentences. We name our approach quick thoughts (QT), to mean efficient learning of thought vectors.Our key contributions in this work are the following:• We propose a simple and general framework for learning sentence representations efficiently. We train widely used encoder architectures an order of magnitude faster than previous methods, achieving better performance at the same time.• We establish a new state-of-the-art for unsupervised sentence representation learning methods across several downstream tasks that involve understanding sentence semantics.The pre-trained encoders will be made publicly available. We proposed a framework to learn generic sentence representations efficiently from large unlabelled text corpora. Our simple approach learns richer representations than prior unsupervised and supervised methods, consuming an order of magnitude less training time. We establish a new state-of-the-art for unsupervised sentence representation learning methods on several downstream tasks. We believe that exploring scalable approaches to learn data representations is key to exploit unlabelled data available in abundance.",857,0.49,490,1.7489795918367348,"In this work propose learning sentence representations Drawing inspiration the distributional hypothesis recent work learning sentence representations reformulate predicting the context appears as Given a sentence and appears a classifier distinguishes context sentences other contrastive sentences based their vector representations This allows efficiently learn different types encoding functions show the model learns high-quality sentence representations We demonstrate our sentence representations outperform state and representation learning methods on several downstream NLP tasks that understanding sentence semantics while achieving an order training time Methods learning meaningful representations have received It exploit these representations trained large corpora for downstream tasks since capture prior knowlege interest lead This especially attractive a transfer learning setting labelled data supervisionUnsupervised learning allows learn useful representations large unlabelled corpora The idea self-supervision recently where representations learned designing learning objectives exploit labels freely with Tasks such predicting the relative spatial location nearby image patches BID6 , inpainting BID30 solving have successfully learning visual feature representations In the language domain the distributional hypothesis integral learning methods obtaining semantic vector representations words BID24 . This the assumption the meaning characterized word-contexts Neural approaches based this assumption learning high quality representations large textRecent methods applied similar ideas for sentence representations Hill; BID8 . These encoder-decoder models learn predict/ the context sentences Despite several modelling issues exist these methods There expressing The ideal semantic representation insensitive in meaning Existing models trained reconstruct the surface form a sentence forces not predict its semantics aspects that irrelevant asThe other problem associated computational cost These methods a word level reconstruction objective involves sequentially decoding target sentences Training an output softmax layer over the entire vocabulary a significant source slowdown This further limits the vocabulary the model (Variations the softmax layer such hierarchical softmax BID26 , sampling sub-word representations can help alleviate issue).We circumvent proposing an objective that operates directly The generation objective replaced a discriminative approximation where attempts the embedding a correct target sentence given sentence candidates In this context interpret the 'meaning the information allows predict be predictable from context sentences We name our approach quick thoughts (QT to mean efficient learning thought vectorsOur key contributions propose sentence representations efficiently We train widely used encoder architectures an order previous methods achieving the same time.• establish unsupervised sentence representation learning methods across several downstream tasks understanding sentence semantics will made publicly We proposed learn generic sentence representations efficiently large unlabelled text corpora Our simple approach learns richer representations than prior unsupervised and supervised methods consuming an order We establish for unsupervised sentence representation learning methods on several downstream tasks We believe exploring scalable approaches learn data representations exploit unlabelled data available abundance",0.01,0.6124133650563779
"Many regularization methods have been proposed to prevent overfitting in neural networks. Recently, a regularization method has been proposed to optimize the variational lower bound of the Information Bottleneck Lagrangian. However, this method cannot be generalized to regular neural network architectures. We present the activation norm penalty that is derived from the information bottleneck principle and is theoretically grounded in a variation dropout framework. Unlike in previous literature, it can be applied to any general neural network. We demonstrate that this penalty can give consistent improvements to different state of the art architectures both in language modeling and image classification. We present analyses on the properties of this penalty and compare it to other methods that also reduce mutual information. Neural networks have been applied to many domains and are able to solve complex tasks such as image classification or machine translation, achieving higher performance than other families of learning algorithms. However, most neural networks used in these tasks are over-parameterized, and they are operating on inputs in high-dimensional space, thus prone to overfitting.For the task of supervised learning, the goal is to find a mapping from noisy input X to a set of corresponding labels Y . In the perspective of information theory, neural networks construct a mapping S and then decode from the resulting representation S(X) and obtain hypothesisŶ , forming the following Markov Chain: Y → X → S. By data processing inequality, I(Y ; X) ≥ I(Y ; S(X)). So if S captures the sufficient statistics of X, we have I(Y ; X) = I(Y ; S(X)) (Cover & BID2 . However, a trivial solution would satisfy this constraint: an identity mapping of X. To avoid this, we further require the minimum sufficient statistics of X to satisfy T * = arg min I(Y ;X)=I(Y ;S(X)) I(S(X); X). The minimum sufficient statistics should only capture the most relevant features in X. Intuitively, being able to compute T exactly would solve the overfitting problem.However, the minimum sufficient statistics does not exist for general distributions. BID16 relaxed the requirement and turn the problem into the Information Bottleneck Lagrangian: minimize βI(X; T ) − I(Y ; T ). We can work out a solution for P (T |X) if P (X, Y ) is known. We would also obtain a solution if we have deterministic mapping between T and X, namely for I(X; T ) = H(T ) − H(T |X), H(T |X) = 0, then minimizing the mutual information becomes minimizing the entropy of T . Since we don't know the distribution of T , we are not able to penalize towards this objective either.So we can only apply information bottleneck penalty in a principled way for probabilistic framework where T |X is a specified or known distribution. BID1 has proposed a variational lower bound of the information bottleneck objective when T |X ∼ N (µ(X), diag(σ 2 (X))) where both µ and σ are estimated by a neural network.We first extend BID1 's work naively to recurrent neural network. Then instead of relying on mean field approximation variational inference, which is not widely applicable to general neural network architecture, we extend the variational approximation of the information bottleneck objective to any neural network with dropout, which is shown to be mathematically equivalent to the lower bound of a Gaussian Process BID5 . We present an information bottleneck penalty that has a very simple equivalence in a neural network with dropout. From additional demonstration by BID6 , we can easily extend our case in recurrent neural networks as well.We validate this penalty on language modeling and image classification, we observe improvements over all near state of the art baselines. Finally, we show preliminary comparisons between this penalty and its variations. In this paper we present a simple way to extend information bottleneck principle to the training of recurrent neural network. We demonstrate how information bottleneck principle can be applied not only to Bayesian neural networks, but to general neural networks with dropout. We derived the activation norm penalty from the variational dropout framework, and observe consistent improvements to state of the art architectures when applied to language modeling and image classification.",851,0.468,485,1.754639175257732,"Many regularization methods prevent overfitting Recently a regularization method optimize variational lower the Information Bottleneck Lagrangian However this method generalized regular neural network architectures We present the activation norm penalty that derived the information bottleneck principle theoretically grounded a variation dropout framework Unlike in previous literature can applied any general neural network We demonstrate this penalty give consistent improvements different state of architectures both language modeling image We present analyses on the properties this penalty also reduce mutual information Neural networks applied able solve machine achieving other families learning However most neural networks used over operating inputs proneFor supervised learning a mapping from noisy input X a set corresponding labels Y In the perspective information theory neural networks construct a mapping S decode from obtain hypothesis�� , forming: By data processing inequality I(Y ; So if S captures the sufficient statistics X we I(Y ; (Cover & BID2 . However a trivial solution satisfy this constraint an identity mapping X. To avoid further require the minimum sufficient statistics X satisfy T * = arg min I(Y ;S(X X The minimum sufficient statistics should only capture X. Intuitively being compute T exactly would solveHowever the minimum sufficient statistics does general distributions BID16 relaxed and turn the problem the Information Bottleneck Lagrangian: minimize βI(X; T ) ; We work P (T |X if P, ) known We would obtain a solution have deterministic mapping T X namely for I(X; ) ) − |X minimizing the mutual information becomes minimizing . Since we do the distribution T , are penalize towards this objective eitherSo apply information bottleneck penalty for probabilistic framework where T |X is a specified or known distribution BID1 has proposed variational lower the information bottleneck objective when T |X ∼ N (��( diag(σ 2 (X where both µ estimatedWe extend naively recurrent. Then instead relying mean field approximation variational inference which widely general neural network architecture extend the information bottleneck objective dropout, shown a Gaussian Process BID5 . We present an information bottleneck penalty has a very simple equivalence a neural network dropout From additional demonstration by BID6 , easily extend our case in recurrent neural networks asWe validate this penalty language modeling and image classification we observe improvements over all near state of Finally show preliminary comparisons this penalty its variations In extend information bottleneck principle the training We demonstrate information bottleneck principle not dropout. We derived activation norm penalty the variational dropout framework observe consistent improvements to state of architectures applied language modeling image",0.01,0.6268334863675161
"Unsupervised learning of timeseries data is a challenging problem in machine learning. Here, 
we propose a novel algorithm, Deep Temporal Clustering (DTC), a fully unsupervised method, to naturally integrate dimensionality reduction and temporal clustering into a single end to end learning framework. The algorithm starts with an initial cluster estimates using an autoencoder for dimensionality reduction and a novel temporal clustering layer for cluster assignment. Then it jointly optimizes the clustering objective and the dimensionality reduction objective. Based on requirement and application, the temporal clustering layer can be customized with any temporal similarity metric. Several similarity metrics are considered and compared.   To gain insight into features that the network has learned for its clustering, we apply a visualization method that generates a heat map of regions of interest in the timeseries. The viability of the algorithm is demonstrated using timeseries data from diverse domains, ranging from earthquakes to sensor data from spacecraft. In each case, we show that our algorithm outperforms traditional methods. This performance is attributed to fully integrated temporal dimensionality reduction and clustering criterion. Deep learning has become the dominant approach to supervised learning of labeled data BID12 BID17 . However, in many applications the data labels may not be available or be reliable. A variety of techniques have been developed for unsupervised learning where the algorithms draw inferences from unlabeled data. However, the progress in learning of complex structure in the data has so far been largely restricted to labeled datasets, while relatively little attention was paid to learning of complex, high-level structure and features of unlabeled data. The standard unsupervised techniques include clustering approaches which organize similar objects into clusters. Such techniques differ in the method for organizing the data as well as the metrics to measure similarity. While clustering techniques have been successfully applied to static data, their extension to time series data remains an open problem. This has left a gap in technology for accurate unsupervised learning of time series data which encompass many areas of science and engineering such as financial trading, medical monitoring, and event detection BID0 .The problem of unsupervised time series clustering is particularly challenging. Time series data from different domains exhibit considerable variations in important properties and features, temporal scales, and dimensionality. Further , time series data from real world applications often have temporal gaps as well as high frequency noise due to the data acquisition method and/or the inherent nature of the data BID1 ).To address the issues and limitations of using standard clustering techniques on time series data, we present a novel algorithm called deep temporal clustering (DTC) . A key element of DTC is the transformation of the time series data into a low dimensional latent space using a trainable network, which here we choose to be a deep autoencoder network that is fully integrated with a novel temporal clustering layer. The overview of our method is illustrated in Figure 1 . The latent representation is compatible with any temporal similarity metric.The proposed DTC algorithm was designed based on the observation that time series data have informative features on all time scales. To disentangle the data manifolds , i.e., to uncover the latent dimension(s) along which the temporal or spatio-temporal unlabeled data split into two or more classes, we propose the following three-level approach. The first level, implemented as a CNN, reduces the data dimensionality and learns the dominant short-time-scale waveforms. The second level, implemented as a BI-LSTM, reduces the data dimensionality further and learns the temporal connections between waveforms across all time scales. The third level performs non-parametric clustering of BI-LSTM latent representations, finding one or more spatio-temporal dimensions along which the data split into two or more classes. The unique ability of this approach to untangle the data manifolds without discarding the information provided by the time course of the data (e.g., in contrast to PCA-based methods) allows our approach to achieve high performance on a variety of real-life and benchmark datasets without any parameter adjustment.DTC also includes an algorithm to visualize the cluster-assignment activations across time, a feature not available in traditional clustering algorithms. This allows the localization of events in unlabeled time series data, and provides explanation (as opposed to black-box approaches) regarding the most informative data features for class assignment.To the best of our knowledge, this is the first work on the application of deep learning in temporal clustering. The main contribution of our study is the formulation of an end-to-end deep learning algorithm that implements objective formulation to achieve meaningful temporal clustering. We carefully formulated the objective to encompass two crucial aspects essential for high clustering accuracy: an effective latent representation and a similarity metric which can be integrated into the learning structure. We demonstrate that the end-to-end optimization of our network for both reconstruction loss and clustering loss offers superior performance compared to cases where these two objectives are optimized separately. We also show that DTC outperforms current state-of-theart , k-Shape BID15 and hierarchical clustering with complete linkage, when evaluated on various real world time series datasets. In this work we addressed the question of unsupervised learning of patterns in temporal sequences, unsupervised event detection and clustering. Post-hoc labeling of the clusters, and comparison to ground-truth labels not used in training, reveals high degree of agreement between our unsupervised clustering results and human-labeled categories, on several types of datasets. This indicates graceful dimensionality reduction from inputs with extensive and complex temporal structure to one or fewdimensional space spanned by the cluster centroids. As most natural stimuli are time-continuous and unlabeled, the approach promises to be of great utility in real-world applications. Generalization to multichannel spatio-temporal input is straightforward and has been carried out as well; it will be described in more detail in a separate paper.",1162,0.645,681,1.7063142437591776,"Unsupervised learning of timeseries data Here, propose, Deep Temporal Clustering a fully unsupervised method, naturally integrate dimensionality reduction a single end to end learning framework The algorithm starts an initial cluster estimates using for dimensionality reduction a novel temporal clustering layer cluster assignment Then jointly optimizes the clustering objective Based requirement application the temporal clustering layer customized any temporal similarity metric Several similarity metrics considered and To gain insight features the network learned for its clustering apply a visualization method generates a heat map regions the timeseries The viability the algorithm demonstrated using timeseries data diverse domains earthquakes sensor spacecraft In each case we show our algorithm traditional methods This performance attributed fully integrated temporal dimensionality reduction clustering criterion Deep learning supervised learning of labeled data BID12 BID17 . However many applications the data labels available or be reliable A variety techniques where the algorithms draw However the progress learning of complex structure the data so restricted labeled datasets while relatively little attention learning and features The standard unsupervised techniques include clustering approaches which organize similar objects Such techniques differ the method for organizing as the metrics to measure similarity While clustering techniques successfully static data their extension time remains This has left technology accurate unsupervised learning which encompass many areas such financial trading medical monitoring event detection BID0 .The challenging Time series data different domains exhibit considerable variations important properties features temporal scales Further , time series data real world applications often temporal gaps as high frequency noise the data acquisition method the inherent nature BID1 ).To address and standard clustering techniques on called deep temporal clustering . A key element DTC the transformation a low dimensional latent space using a trainable network, here choose be that fully integrated a novel temporal clustering layer The overview our method illustrated The latent representation is compatible any temporal similarity metricThe proposed DTC algorithm was based time series data informative features on all time scales To the data manifolds , uncover along temporal or unlabeled split into propose The first level implemented a CNN, reduces the data dimensionality learns the dominant short-time-scale waveforms The second level implemented a BI-LSTM reduces the data dimensionality further learns the temporal connections waveforms across The third level performs BI-LSTM latent representations finding along which split The unique ability this approach untangle manifolds without discarding provided the time course ( contrast PCA-based methods our approach achieve real-life and benchmark datasets without any parameter adjustmentDTC also includes an algorithm visualize the cluster-assignment activations across a feature not This allows the localization events unlabeled time series data explanation ( black-box approaches regarding the most informative data features class assignmentTo the the application deep learning temporal clustering The main contribution the formulation end deep implements objective formulation to achieve meaningful temporal clustering We carefully formulated the objective encompass two crucial aspects essential high clustering accuracy an effective latent representation a similarity metric which integrated the learning structure We demonstrate end optimization our network for both reconstruction loss offers cases these two objectives optimized We also show DTC outperforms current statetheart , kShape BID15 hierarchical complete linkage when evaluated various real world time series datasets In this work addressed patterns temporal sequences unsupervised event detection Post-hoc labeling the clusters comparison ground-truth labels not training reveals high degree agreement our unsupervised clustering results human-labeled categories on several types datasets This indicates graceful dimensionality reduction from inputs with extensive and complex temporal structure one or fewdimensional space spanned the cluster centroids As most natural stimuli timecontinuous unlabeled the approach promises of Generalization to multichannel straightforward has carried as well; will described",0.01,0.5037058066912575
"We study many-class few-shot (MCFS) problem in both supervised learning and meta-learning scenarios. Compared to the well-studied many-class many-shot and few-class few-shot problems, MCFS problem commonly occurs in practical applications but is rarely studied. MCFS brings new challenges because it needs to distinguish between many classes, but only a few samples per class are available for training. In this paper, we propose ``memory-augmented hierarchical-classification network (MahiNet)'' for MCFS learning. It addresses the ``many-class'' problem by exploring the class hierarchy, e.g., the coarse-class label that covers a subset of fine classes, which helps to narrow down the candidates for the fine class and is cheaper to obtain. MahiNet uses a convolutional neural network (CNN) to extract features, and integrates a memory-augmented attention module with a multi-layer perceptron (MLP) to produce the probabilities over coarse and fine classes. While the MLP extends the linear classifier, the attention module extends a KNN classifier, both together targeting the ''`few-shot'' problem. We design different training strategies of MahiNet for supervised learning and meta-learning. Moreover, we propose two novel benchmark datasets ''mcfsImageNet'' (as a subset of ImageNet) and ''mcfsOmniglot'' (re-splitted Omniglot) specifically for MCFS problem. In experiments, we show that MahiNet outperforms several state-of-the-art models on MCFS classification tasks in both supervised learning and meta-learning scenarios. The representation power of deep neural networks (DNN) has dramatically improved in recent years, as deeper, wider and more complicated DNN architectures BID5 BID6 have emerged to match the increasing computation power of new hardwares. Although this brings hope for complex tasks that could be hardly solved by previous shallow models, more training data is usually required. Hence, the scarcity of annotated data has become a new bottleneck for training more powerful DNNs. For example, in image classification, the number of candidate classes can easily range from hundreds to tens of thousands (i.e., many-class), but the training samples available for each class can be less than 100 (i.e., few-shot). Additionally, in life-long learning, models are always updated once new training data becomes available, and those models are expected to quickly adapt to new classes with a few training samples. This ""many-class few-shot"" problem is very common in various applications, such as image search, robot navigation and video surveillance.Although enormous previous works have shown the remarkable power of DNN when ""many-class many-shot"" training data is available, their performance degrades dramatically when each class only has a few samples available for training. In practical applications, acquiring samples of rare species is usually difficult and often expensive. In these few-shot scenarios, the model's capacity cannot be fully utilized, and it becomes much harder to generalize the model to unseen data. Recently, several approaches have been proposed to address the few-shot learning problem. Most of them are based on the idea of ""meta-learning"", which trains a meta-learner that can generalize to different tasks. For classification, each task targets a different set of classes. Meta-learning can be categorized into two types: methods based on ""learning to optimize"", and methods based on metric learning. The former type adaptively modifies the optimizer (or some parts of it) applied to the training process. It includes methods that incorporate an RNN meta-learner BID0 BID13 BID16 , and model-agnostic meta-learning (MAML) methods aiming to learn a … Figure 1 : The MCFS problem with class hierarchy information. There are a few coarse classes (blue), but each coarse class contains a large number of fine classes (red), and the total number of fine classes is large. Only a few training samples are available for each fine class. The goal is to train a classifier to generate a prediction over all fine classes. In meta-learning, each task is an MCFS problem sampled from a certain distribution. The meta-learner's goal is to help train a classifier for any sampled task with better adaptation to few-shot data.generally compelling initialization BID4 . The latter type learns a similarity/distance metric BID22 or a support set of samples BID20 ) that can be generally used to build KNN classifiers for different tasks. Instead of using meta-learning, some other approaches, such as BID2 , address the few-shot learning problem through data augmentation by generating artificial samples for each class. However, most existing few-shot learning approaches only focus on ""few-class"" case (e.g., 5 or 10) per task, and performance usually collapses when the number of classes grows to hundreds or thousands. This is because the samples per class no longer provide enough information to distinguish them from other possible samples within a large number of other classes. And, in real-world problems, tasks are usually complicated involving many classes.Fortunately, in practice, class hierarchy is usually available or cheaper to obtain. As shown in Figure 1, coarse class labels might reveal the relationships among the targeted fine classes. Moreover, the samples per coarse class are sufficient to train a reliable coarse classifier, whose predictions are able to narrow down the candidates for fine classes. For example, a sheepdog with long hair could be easily mis-classified as mop when training samples of sheepdog are insufficient. However, if we could train a reliable dog classifier, it would be much simpler to predict an image as a sheepdog than a mop given a correct prediction of the coarse class as ""dog"". Hence, class hierarchy might provide weakly supervised information to help solve the ""many-class few-shot (MCFS)"" problem.",1171,0.644,710,1.6492957746478873,"We study many-class few-shot (MCFS) problem in both supervised learning and meta-learning scenarios Compared the well-studied many-class many-shot and few-class few-shot problems MCFS problem commonly practical applications but studied MCFS brings new challenges because needs distinguish many classes only a few samples per training In this paper ``memory-augmented hierarchical-classification networkMahiNet MCFS learning It addresses the ``many-class'' problem exploring the coarse-class label that covers fine classes helps narrow the candidates and is cheaper obtain MahiNet uses extract features, integrates a memory-augmented attention module the probabilities over coarse and fine classes While the MLP extends the linear classifier the attention module a KNN classifier both together targeting the ''`few-shot'' problem We design different training strategies of MahiNet supervised learning meta-learning Moreover we propose two novel benchmark datasets ''mcfsImageNetasre-splitted Omniglot specifically MCFS problem In experiments we show MahiNet outperforms several state models on MCFS classification tasks both supervised learning and meta-learning scenarios The representation power deep neural networks dramatically deeper, BID5 BID6 to match the increasing computation power new hardwares Although this brings hope complex tasks hardly previous shallow models more training data usually Hence the scarcity annotated data has become a new bottleneck training more powerful DNNs For image classification candidate classes can easily range the training samples available Additionally in life-long learning models always updated once new training data expected quickly new classes with a few training samples This ""many-class few-shot"" problem very various applications image search robot navigation video surveillanceAlthough enormous previous works the remarkable power DNN when "" their performance degrades each class only available In practical applications acquiring samples rare species usually often In these few-shot scenarios the model's capacity fully becomes much generalize unseen data Recently several approaches the few-shot learning problem Most them based ""meta-learning trains a meta-learner that can generalize For classification each task targets classes Meta-learning can categorized methods based ""learning to optimize metric learning The former type adaptively the optimizer some parts applied the training process It includes methods incorporate an RNN meta-learner BID0 BID13 BID16 , aiming learn a … Figure : The MCFS problem with class hierarchy information There a few coarse classes (blue each coarse class contains large Only a few training samples each fine class The goal train a classifier generate over all fine classes In meta-learning each task an MCFS problem sampled a certain distribution The meta-learner's goal train a classifier any sampled task with better adaptation few-shot data.generally compelling initialization BID4 . The latter type learns a similarity/distance metric BID22 or a support set samples ) generally build KNN classifiers different tasks Instead using meta-learning some other approaches BID2 , address the few-shot learning problem through data augmentation by generating artificial samples However most existing few-shot learning approaches only ""few-class"" case ( 5 or per task performance usually collapses hundreds This because the samples per class no provide distinguish within And real-world problems tasks usually complicated involving many classesFortunately in practice class hierarchy usually available or cheaper obtain As shown coarse class labels might reveal the relationships the targeted fine classes Moreover the samples per coarse class sufficient train a reliable coarse classifier whose predictions able narrow the candidates fine classes For example a sheepdog easily mis-classified mop when training samples are insufficient However if could train a reliable dog classifier predict an image as a sheepdog a mop given a correct prediction the coarse class as ""dog Hence class hierarchy might provide weakly supervised information help solve ""manyclass fewshot (MCFS",0.01,0.3584277569836108
"Learning a better representation with neural networks is a challenging problem, which has been tackled from different perspectives in the past few years. In this work, we focus on learning a representation that would be useful in a clustering task. We introduce two novel loss components that substantially improve the quality of produced clusters, are simple to apply to arbitrary models and cost functions, and do not require a complicated training procedure. We perform an extensive set of experiments, supervised and unsupervised, and evaluate the proposed loss components on two most common types of models, Recurrent Neural Networks and Convolutional Neural Networks, showing that the approach we propose consistently improves the quality of KMeans clustering in terms of mutual information scores and outperforms previously proposed methods. Representation learning is an important part of deep learning research, and the ability of deep neural networks to transform the input data into a space that is more suitable to the target task is one of the key reasons for their success. Consider the case of binary classification with a neural network with sigmoid activation function on the last layer, where a network transforms the input data x ∈ R n into a space R where two classes are linearly separable by applying a sequence of non-linear transformations f (x) : DISPLAYFORM0 Note that all representations, learned by the network in the sequence of transformations R i → R j , are devoted to one goal: binary classification. The learned intermediate representations can easily be used in tasks similar to the binary classification, but using them in a different task may be problematic.Consider the case of multivariate time series classification with an RNN model, depicted in Figure 1 with a sigmoid activation function in the last FC 2 layer and a ReLU activation function in the layer FC 1 . Note that ReLU activation produces non-negative vectors. During a regular training procedure with binary cross-entropy loss, the model will learn weights that produce two patterns of activation of the layer FC 1 : roughly orthogonal vectors for the samples that belong to different classes, and roughly parallel vectors for the samples that belong to the same class. Indeed, the value of the output scalar is the result of taking the dot product between the weights w of the final layer FC 2 (a single vector in this case) and the output h of the penultimate hidden layer FC 1 . Via the geometric interpretation of the dot product, this value is highest when the cosine between the vectors 1, and minimized when the cosine is −1. However, since the penultimate layer has the ReLU activation, the vectors cannot point in opposite directions, therefore, they must be orthogonal.",526,0.23,309,1.7022653721682848,"Learning a better representation with neural networks a challenging problem which tackled from In this work focus learning a representation that would a clustering task We introduce two novel loss components substantially produced clusters are simple apply arbitrary models cost functions do a complicated training procedure We perform an extensive set experiments, supervised and evaluate the proposed loss components on two most common types models showing the approach we consistently KMeans terms mutual information scores outperforms previously proposed methods Representation learning deep learning research the ability transform a space that the target task Consider binary classification with a neural network with sigmoid activation function on the last layer a network transforms the input data x �� R n a space R where two classes linearly applying a sequence f (x : DISPLAYFORM0 Note all representations, learned in the sequence R i → R j devoted one goal binary classification The learned intermediate representations can easily tasks similar the binary classification using problematicConsider multivariate time series classification with an RNN model depicted with in the last FC 2 layer the layer FC Note ReLU activation produces non-negative vectors During a regular training procedure with binary cross-entropy loss the model will learn weights produce two patterns activation the layer FC 1 : roughly orthogonal vectors for the samples that belong different classes roughly parallel vectors Indeed the value the output scalar the result taking the dot product between the weights w of the final layer FC 2 (a single vector in the output h the penultimate hidden layer Via the geometric interpretation the dot product this value highest between 1 and minimized −1 However since the penultimate layer the ReLU activation the vectors point therefore",0.0,0.49338963760763094
"In high dimensions, the performance of nearest neighbor algorithms depends crucially on structure in the data.
 While traditional nearest neighbor datasets consisted mostly of hand-crafted feature vectors, an increasing number of datasets comes from representations learned with neural networks.
 We study the interaction between nearest neighbor algorithms and neural networks in more detail.
 We find that the network architecture can significantly influence the efficacy of nearest neighbor algorithms even when the classification accuracy is unchanged.
 Based on our experiments, we propose a number of training modifications that lead to significantly better datasets for nearest neighbor algorithms.
 Our modifications lead to learned representations that can accelerate nearest neighbor queries by 5x. Learning representations has become a major field of study over the past decade, with many succesful applications in computer vision, speech recognition, and natural language processing. The primary focus in these directions has been accuracy, usually with a focus on classification tasks. Here, the main goal is to learn a representation that enables a standard classifier (e.g., a linear model such as softmax regression) to correctly label the transformed data. However, as learned representations have achieved high accuracy in a wide range of applications, additional goals are becoming increasingly important. One such desideratum is computational efficiency: how quickly can we process the learned representations? This is question is particularly relevant in the context of large databases, where the goal is to store many millions or even billions of images, texts, and videos. Common instantiations of such settings include web search, recommender systems, near-duplicate detection (e.g., for copyrighted content), and large-scale face recognition.In this paper, we study the problem of learning representations through the lenss of similarity search. Similarity search, also known as Nearest Neighbor Search (NNS), is a fundamental algorithmic problem with a wide range of applications in machine learning and broader data science . The most common example is similarity search in large corpora such as the aforementioned image databases, segments of speech, or document collections. More recently, NNS has also appeared as a sub-routine in other algorithms such as optimization methods BID4 , cryptography (Laarhoven, 2015) , and large-scale classification (Vijayanarasimhan et al., 2015) . A key challenge in the design of efficient NNS methods is the interaction between the data and the algorithms: How can we exploit structure in the data to enable fast and accurate search? Research on NNS has established a large set of techniques such as kd-trees, locality-sensitive hashing, and quantization methods that utilize various forms of structure in the data.Traditionally, NNS is used on hand-crafted feature vectors: image similarity search is often performed on SIFT vectors, speakers are identified via their i-vector, and document similarity is computed via tfidf representations. However, recent progress in deep learning is replacing many of these hand-crafted feature vectors with learned representations. There is often a clear reason: learned representations often lead to higher accuracy and semantically more meaningful NNS results. However, this raises an important question: Do existing NNS algorithms perform well on these new classes of feature vectors? Moreover, learning the representations in NNS also offers an interesting new design space: Instead of adapting the algorithm to the dataset, can we learn a representation that is particularly well suited for fast NNS? We have demonstrated how to learn representations specifically for faster similarity search in large datasets. To this end, we have studied multiple modifications to neural network training and architecture that lead to a smaller angle between the learned representation vectors produced by the network and the class vectors in the softmax layer. This angle is a crucial measure of performance for approximate nearest neighbor algorithms and enables a 5× speed-up in query times. An interesting direction for future research is whether these insights can also lead to faster training of large multiclass networks, which are common in language models or recommender systems. Figure 7 : Effect of our training modifications on the query times of nearest neighbor algorithms. We report the relative accuracies, i.e., the probability of finding the correct nearest neighbor conditioned on the model being correct. For LSH as implemented in the FALCONN library (left), our training yields a 5× speed-up in the relevant high accuracy regime. The variant of kd-trees implemented in the Annoy library (right) does not reach relative accuracy 1 when the softmax is trained using the standard approach. In contrast, the softmax resulting from our training techniques is more amenable to the kd-tree algorithm. Again, we obtain faster query times for fixed accuracy. A RELATED WORK The paper (Liu et al., 2016) also proposes a method for training with larger angular distance gaps. In contrast to our approach, the authors modify the loss function, not the training process or network architecture. The focus of their paper is also on classification accuracy and not fast similarity search. The authors do not quantify the improvements in angular distance and train on datasets with a relatively small number of classes (100 or less). ? also modifies the loss function for learning representations with angular distance gaps. Again, the focus of their paper is on accuracy and not fast similarity search. In particular, the authors do not investigate the effect of their changes on the angular gap on large datasets. The focus of our paper is on fast similarity search and we evaluate various network modifications with end-to-end experiments using state-of-the art NNS methods.",1088,0.685,669,1.6263079222720478,"In high dimensions the performance nearest neighbor algorithms depends structure in While traditional nearest neighbor datasets consisted hand-crafted feature vectors datasets comes representations learned with We study nearest neighbor algorithms We find the network architecture can significantly influence nearest algorithms even the classification accuracy unchanged Based our experiments propose a number training modifications lead significantly better datasets nearest neighbor algorithms Our modifications lead learned representations accelerate nearest neighbor queries 5x Learning representations has over The primary focus these directions accuracy usually classification tasks Here, the main goal learn a representation that enables a standard classifier ( linear such softmax regression correctly label the transformed data However as learned representations achieved high accuracy additional goals becoming One such desideratum computational efficiency process the learned representations This question is particularly large databases the goal store many millions images texts Common instantiations such settings web search recommender systems near-duplicate detection for copyrighted contentIn study the problem learning representations through the lenss similarity search Similarity search, also Nearest Neighbor Search a fundamental algorithmic problem with broader data science . The most common example similarity search large corpora such the aforementioned image databases segments speech document collections More recently NNS also appeared sub other algorithms optimization methods BID4 cryptography (LaarhovenVijayanarasimhan A key challenge efficient NNS methods: How exploit structure enable fast and accurate search Research NNS has established a large set techniques such kd-trees locality-sensitive hashing quantization methods utilize various forms structure inTraditionally on hand-crafted feature vectors: image similarity search is often SIFT vectors speakers identified via their i-vector document similarity via tfidf representations However recent progress deep learning replacing many these hand-crafted feature vectors learned representations There often a clear reason: learned representations often lead higher accuracy semantically more meaningful NNS results However this raises Do existing NNS algorithms perform these new classes feature vectors Moreover learning the representations NNS also offers an interesting new design space Instead adapting the algorithm the dataset can particularly fast NNS We demonstrated learn representations specifically faster similarity search large datasets To this end studied multiple modifications neural network training architecture lead a smaller angle between the learned representation vectors produced the class vectors in the softmax layer This angle a crucial measure performance approximate nearest neighbor algorithms and enables a 5× speed-up query times An interesting direction future research whether these insights also lead faster training large multiclass networks common language models or recommender systems Figure : Effect our training modifications the query times nearest neighbor algorithms We report the relative accuracies, the correct nearest neighbor conditioned the model being correct For LSH as implemented the FALCONN libraryleft our training yields a 5× speed-up the relevant high accuracy regime The variant kd-trees implemented the Annoy libraryright does reach relative accuracy 1 when the softmax trained using the standard approach In contrast the softmax resulting our training techniques more amenable the kd-tree algorithm Again obtain faster query times fixed accuracy A RELATED WORK The paper (Liu also proposes training with larger angular distance gaps In contrast our approach modify the loss function, not the training process or network architecture The focus their paper also classification accuracy not fast similarity search The authors do quantify the improvements angular distance train on datasets classes100 ? also modifies the loss function learning representations with angular distance gaps Again the focus their paper accuracy not fast similarity search In particular do investigate their changes the angular gap on large datasets The focus our paper fast similarity search we evaluate various network modifications with end experiments statethe art NNS methods",0.01,0.29985672882059794
"Neural network quantization has become an important research area due to its great impact on deployment of large models on resource constrained devices. In order to train networks that can be effectively discretized without loss of performance, we introduce a differentiable quantization procedure. Differentiability can be achieved by transforming continuous distributions over the weights and activations of the network to categorical distributions over the quantization grid. These are subsequently relaxed to continuous surrogates that can allow for efficient gradient-based optimization. We further show that stochastic rounding can be seen as a special case of the proposed approach and that under this formulation the quantization grid itself can also be optimized with gradient descent. We experimentally validate the performance of our method on MNIST, CIFAR 10 and Imagenet classification. Neural networks excel in a variety of large scale problems due to their highly flexible parametric nature. However, deploying big models on resource constrained devices, such as mobile phones, drones or IoT devices is still challenging because they require a large amount of power, memory and computation. Neural network compression is a means to tackle this issue and has therefore become an important research topic.Neural network compression can be, roughly, divided into two not mutually exclusive categories: pruning and quantization. While pruning BID18 BID10 aims to make the model ""smaller"" by altering the architecture, quantization aims to reduce the precision of the arithmetic operations in the network. In this paper we focus on the latter. Most network quantization methods either simulate or enforce discretization of the network during training, e.g. via rounding of the weights and activations. Although seemingly straighforward, the discontinuity of the discretization makes the gradient-based optimization infeasible. The reason is that there is no gradient of the loss with respect to the parameters. A workaround to the discontinuity are the ""pseudo-gradients"" according to the straight-through estimator BID3 , which have been successfully used for training low-bit width architectures at e.g. BID13 ; Zhu et al. (2016) .The purpose of this work is to introduce a novel quantization procedure, Relaxed Quantization (RQ). RQ can bypass the non-differentiability of the quantization operation during training by smoothing it appropriately. The contributions of this paper are four-fold: First, we show how to make the set of quantization targets part of the training process such that we can optimize them with gradient descent. Second , we introduce a way to discretize the network by converting distributions over the weights and activations to categorical distributions over the quantization grid. Third , we show that we can obtain a ""smooth"" quantization procedure by replacing the categorical distributions with (a) (b)Figure 1: The proposed discretization process. (a) Given a distribution p(x) over the real line we partition it into K intervals of width α where the center of each of the intervals is a grid point g i . The shaded area corresponds to the probability ofx falling inside the interval containing that specific g i .(b) Categorical distribution over the grid obtained after discretization. The probability of each of the grid points g i is equal to the probability ofx falling inside their respective intervals.concrete BID22 BID15 equivalents. Finally we show that stochastic rounding BID8 , one of the most popular quantization techniques, can be seen as a special case of the proposed framework. We present the details of our approach in Section 2, discuss related work in Section 3 and experimentally validate it in Section 4. Finally we conclude and provide fruitful directions for future research in Section 5. We have introduced Relaxed Quantization (RQ), a powerful and versatile algorithm for learning low-bit neural networks using a uniform quantization scheme. As such, the models trained by this method can be easily transferred and executed on low-bit fixed point chipsets. We have extensively evaluated RQ on various image classification benchmarks and have shown that it allows for the better trade-offs between accuracy and bit operations per second.Future hardware might enable us to cheaply do non-uniform quantization, for which this method can be easily extended. BID17 BID25 for example, show the benefits of low-bit floating point weights that can be efficiently implemented in hardware. The floating point quantization grid can be easily learned with RQ by redefiningĜ. General non-uniform quantization, as described TAB4 in the Appendix. We compare against multiple works that employ fixed-point quantization: SR+DR BID8 BID9 , LR Net BID29 , , TWN BID19 , INQ BID40 , BWN BID28 , XNORnet BID28 , DoReFa (Zhou et al., 2016) , HWGQ BID4 , ELQ Zhou et al. (2018) , SYQ BID7 , Apprentice , QSM BID30 and rounding.for example in BID2 , is a natural extension to RQ, whose exploration we leave to future work. For example, we could experiment with a base grid that is defined as in . Currently, the bit-width of every quantizer is determined beforehand, but in future work we will explore learning the required bit precision within this framework. In our experiments, batch normalization was implemented as a sequence of convolution, batch normalization and quantization. On a low-precision chip, however, batch normalization would be ""folded"" into the kernel and bias of the convolution, the result of which is then rounded to low precision. In order to accurately reflect this folding at test time, future work on the proposed algorithm will emulate folded batchnorm at training time and learn the corresponding quantization grid of the modified kernel and bias. For fast model evaluation on low-precision hardware, quantization goes hand-in-hand with network pruning. The proposed method is orthogonal to pruning methods such as, for example, L 0 regularization BID21 , which allows for group sparsity and pruning of hidden units.",1197,0.714,696,1.7198275862068966,"Neural network quantization due deployment large models resource constrained devices In order train networks effectively discretized without loss introduce a differentiable quantization procedure Differentiability can transforming continuous distributions the weights activations the network to the quantization grid These subsequently relaxed continuous surrogates that allow efficient gradient-based optimization We further show stochastic rounding seen the proposed approach and under the quantization grid itself also optimized gradient descent We experimentally validate our method MNIST 10 Imagenet classification Neural networks excel large scale problems due However deploying big models resource constrained devices drones challenging memory computation Neural network compression tackle has therefore can, roughly divided pruning quantization While pruning BID18 BID10 aims the model "" altering quantization aims the precision the network In focus latter Most network quantization methods either simulate enforce discretization during training via rounding activations Although seemingly straighforward the discontinuity the discretization makes the gradient-based optimization The reason no gradient the loss with the parameters A workaround the discontinuity are according the straight-through estimator BID3 , have successfully training lowbit width architectures at BID13 ; Zhu (2016 .The purpose introduce Relaxed Quantization RQ can bypass the nondifferentiability the quantization operation during training smoothing appropriately The contributions four the set quantization targets part such optimize gradient descent Second , introduce discretize the network by converting distributions the weights activations the quantization grid Third , show we obtain replacing the categorical distributions ( (b)Figure: (a Given a distribution p(x over the real line we partition K intervals width α where the center of a grid point g i The shaded area corresponds the probability ofx falling inside containing that specific g i .(b Categorical distribution over the grid obtained after The probability each the grid g i ofx falling inside their respective intervals.concrete BID22 BID15 equivalents Finally show stochastic rounding BID8 , one seen the proposed framework We present the details Section discuss related work experimentally validate Finally conclude and provide fruitful directions Section We introduced Relaxed Quantization learning low-bit neural networks a uniform quantization scheme As such the models trained this method transferred and executed low-bit fixed point chipsets We extensively evaluated RQ on various image classification benchmarks allows the better trade-offs bit operations perFuture hardware might enable cheaply do which this method BID17 BID25 for example show the benefits low-bit floating point weights that efficiently hardware The floating point quantization grid can learned RQ by redefining��. General non-uniform quantization TAB4 in We compare against multiple works employ fixed-point quantization: SR+DR BID8 BID9 , LR Net BID29 , TWN BID19 XNORnet BID28 , DoReFa (Zhou et al., 2016) , HWGQ BID4 ELQ Zhou (2018 , SYQ BID7 , Apprentice QSM BID30 and rounding.for example in BID2 is a natural extension RQ, whose exploration we leave future work For example experiment a base grid defined in . Currently the bit-width every quantizer beforehand future work explore learning the required bit precision within In our experiments batch normalization implemented, batch quantization On a low-precision chip however batch normalization would ""folded bias of, then rounded low precision In order accurately reflect this folding at test time future work the proposed algorithm emulate folded batchnorm at training time learn the corresponding quantization grid of the modified kernel and bias For fast model evaluation on quantization goes network pruning The proposed method orthogonal pruning methods, L 0 regularization BID21 allows group sparsity hidden units",0.01,0.5381366159787596
"In most current formulations of adversarial training, the discriminators can be expressed as single-input operators, that is, the mapping they define is separable over observations. In this work, we argue that this property might help explain the infamous mode collapse phenomenon in adversarially-trained generative models. Inspired by discrepancy measures and two-sample tests between probability distributions, we propose distributional adversaries that operate on samples, i.e., on sets of multiple points drawn from a distribution, rather than on single observations. We show how they can be easily implemented on top of existing models. Various experimental results show that generators trained in combination with our distributional adversaries are much more stable and are remarkably less prone to mode collapse than traditional models trained with observation-wise prediction discriminators. In addition, the application of our framework to domain adaptation results in strong improvement over recent state-of-the-art. Adversarial training of neural networks, especially Generative Adversarial Networks (GANs) BID10 , has proven to be a powerful tool for learning rich models, leading to outstanding results in various tasks such as realistic image generation, text to image synthesis, 3D object generation, and video prediction BID25 BID33 BID32 . Despite their success, GANs are known to be difficult to train. The generator and discriminator can oscillate significantly from iteration to iteration, and slight imbalances in their capacities frequently cause the training objective to diverge. Another common problem suffered by GANs is mode collapse, where the distribution learned by the generator concentrates on a few modes of the true data distribution, ignoring the rest of the space. In the case of images, this failure results in generated images that albeit realistic, lack diversity and reduce to a handful of prototypes.A flurry of recent research seeks to understand and address the causes of instability and mode collapse in adversarially-trained models. The first insights come from BID10 , who note that one of the main causes of training instability is saturation of the discriminator. BID1 formalize this idea by showing that if the two distributions have supports that are disjoint or concentrated on low-dimensional manifolds that do not perfectly align, then there exists an optimal discriminator with perfect classification accuracy almost everywhere and the usual divergences (Kullback-Leibler, Jensen-Shannon) max-out for this discriminator. In follow-up work, propose an alternative training scheme (WGAN) based on estimating the Wasserstein distance instead of the Jensen-Shannon divergence between real and generated distributions.In this work, we highlight a further view on mode collapse. The discriminator part of GANs and of variations like WGANs is separable over observations, which, as we will illustrate, can result in serious problems, even when minibatches are used. The underlying issue is that the stochastic gradients are essentially (sums of) functions of single observations (training points). Despite connections to two-sample tests based on Jensen-Shannon divergence, ultimately the updates based on gradients from different single observations are completely independent of each other. We show how this lack of sharing information between observations may explain mode collapses in GANs.Motivated by these insights, we take a different perspective on adversarial training and propose a framework that brings the discriminator closer to a truly distributional adversary, i.e., one that 1 (a set of observations) in its entirety, retaining and sharing global information between gradients. The key insight is that a carefully placed nonlinearity in the form of specific population comparisons can enable information-sharing and thereby stabilize training. We develop and test two such models, and also connect them to other popular ideas in deep learning and statistics.Contributions. The main contributions of this work are as follows:• We introduce a new distributional framework for adversarial training of neural networks that operates on a genuine sample, i.e., a collection of points, rather than an observation. This choice is orthogonal to modifications of the types of loss (e.g. logistic vs. Wasserstein) in the literature.• We show how off-the-shelf discriminator networks can be made distribution-aware via simple modifications to their architecture and how existing models can seamlessly fit into this framework.• Empirically, our distributional adversarial framework leads to more stable training and significantly better mode coverage than common single-observation methods. A direct application of our framework to domain adaptation results in strong improvements over state-of-the-art.",879,0.432,540,1.6277777777777778,"In most current formulations adversarial training the discriminators can expressed single-input operators that the mapping they define separable over observations In this work argue this property might help the infamous mode collapse phenomenon adversarially-trained generative models Inspired discrepancy measures two-sample tests between probability distributions propose distributional adversaries operate samples on sets multiple points drawn rather single observations We show they easily implemented existing models Various experimental results generators trained combination our distributional adversaries much stable are remarkably mode collapse traditional models trained observation-wise prediction discriminators In addition application our framework domain adaptation results strong improvement recent state. Adversarial training of neural networks especially Generative BID10 , has proven rich models leading outstanding results various tasks realistic image generation text to image synthesis 3D object generation video prediction BID25 BID33 BID32 Despite GANs known difficult train The generator and discriminator can oscillate significantly iteration slight imbalances their capacities frequently the training objective Another common problem suffered GANs mode collapse the distribution learned the generator concentrates a few modes the true data distribution ignoring the space In images failure results generated images albeit realistic, lack diversity reduce to prototypesA flurry recent research seeks and instability mode collapse adversarially-trained models The first insights come BID10 , note one training instability saturation the discriminator BID1 formalize this idea showing if the two distributions supports concentrated on perfectly exists perfect classification accuracy almost and usual (Kullback-Leibler Jensen-Shannon) max-out for In follow-up work propose an alternative training scheme (WGAN estimating the Wasserstein distance instead the Jensen-Shannon divergence between real and generated distributionsIn highlight a further view mode collapse The discriminator part GANs and of variations like WGANs separable over observations, illustrate result serious problems minibatches The underlying issue essentially (sums of) functions single observationstraining points Despite connections two-sample tests based Jensen-Shannon divergence ultimately the updates based gradients different single observations completely independent We show this lack sharing information between observations may explain mode collapses GANsMotivated these insights take adversarial training propose brings the discriminator closer a truly distributional adversary 1 (a set in retaining and global information between gradients The key insight a carefully placed nonlinearity specific population comparisons enable information-sharing thereby stabilize training We develop two such models also connect other popular ideas deep learning statisticsContributions. The main contributions We introduce adversarial training operates a genuine sample collection points rather observation This choice orthogonal modifications the types loss ( logistic vs. Wasserstein) in literature.• We show off discriminator networks made distributionaware via simple modifications their architecture existing models seamlessly fit our distributional adversarial framework leads more stable training significantly better mode coverage common single-observation methods A direct application our framework domain adaptation results strong improvements state.",0.01,0.3036017915091052
"Chemical information extraction is to convert chemical knowledge in text into true chemical database, which is a text processing task heavily relying on chemical compound name identification and standardization. Once a systematic name for a chemical compound is given, it will naturally and much simply convert the name into the eventually required molecular formula. However, for many chemical substances, they have been shown in many other names besides their systematic names which poses a great challenge for this task. In this paper, we propose a framework to do the auto standardization from the non-systematic names to the corresponding systematic names by using the spelling error correction, byte pair encoding tokenization and neural sequence to sequence model. Our framework is trained end to end and is fully data-driven. Our standardization accuracy on the test dataset achieves 54.04% which has a great improvement compared to previous state-of-the-art result. There are more than 100 million named chemical substances in the world. In order to uniquely identify every chemical substance, there are elaborate rules for assigning names to them on the basis of their structures. These names are called systematic names. The rules for these names are defined by International Union of Pure and Applied Chemistry (IUPAC) BID1 .However , besides the systematic name, there can be also many other names for a chemical substance due to many reasons. Firstly , many chemical are so much a part of our life that we know them by their familiar names which we call them common names or trivial names for the sake of simplicity. For example , sucrose is a kind of sugar which we are very familiar with. Its systematic name is much more complicated, which is (2R,3R,4S,5S,6R)-2-[(2S,3S,4S,5R)-3,4-dihydroxy-2,5-bis(hydroxymethyl)oxolan-2-yl]oxy-6-(hydroxymethyl)oxane-3,4,5-triol.Secondly, in chemistry industry, especially in pharmaceutical industry, many producers always generate new names to a chemical substance in order to distinguish their products from those of their competitors. We call these kind of names proprietary names. The most famous example is Aspirin. Its systematic name is 2-Acetoxybenzoic acid. So due to the history reasons and idiomatic usages, a chemical substance can have many other names.Chemical information extraction is a research that extracts useful chemical knowledge in text and converts it into a database, which strongly relies on the unique standard chemical names. Nowadays, there are many chemical databases such as PubChem and SciFinder, which are designed to store chemical information including chemical names, chemical structures, molecular formulas and other relevant information. For these databases , it is still an ongoing work to extract chemical information from chemical papers to update the databases. If all the chemical substances are expressed by the systematic names, it is easy to generate other information. For example, we can nearly perfectly convert the systematic name to other representations such as Simplified Molecular-Input Line-Entry System (SMILES) BID13 and International Chemical Identifier (InCHI) BID9 and then generate the structural formulas. Some online systems are already well developed for converting automatically systematic names to SMILES string with a very high precision such as Open Parser for Systematic IUPAC Nomenclature (OPSIN) BID7 developed by In the following passage, we consider the differences between non-systematic names and systematic names as ""error"" 2 . In view of natural language processing, the error types of non-systematic names can be summarized by four types: 1. Spelling error. It means that non-systematic names just have slightly differences from systematic names in spelling; 2. Ordering error. It means that the groups in a non-systematic name are in wrong order; 3. Common name error. As mentioned above, many chemical substances have common names or proprietary names which look totally different from their systematic names; 4. Synonym error. It means that the words in the nonsystematic names are different from those in the systematic names but they share the same root of word. In fact, it is the error type which happens most often. For example, 2-(Acetyloxy)benzoic Acid has synonyms Acetylsalicylic Acid and Acetysal and these three words share the same root of word ""Acety"". Some examples of different types of errors are shown in TAB0 . What is worth mentioning is that several types of error can appear at the same time in a single non-systematic name, especially for the ordering error and synonym error. The mixed types of error make this task very challenging .Based on these four error types, we propose a framework to convert automatically the non-systematic names to systematic names. Our framework is structured as followed: 1. Spelling error correction. It aims to correct the spelling errors; 2. Byte pair encoding (BPE) tokenization. It aims to split a name into small parts; 3. Sequence to sequence model. It aims to fix all the remaining ordering errors, common name errors and synonym errors.Actually, due to its great challenge, few work has been done on the chemical name standardization. To our best knowledge, BID2 is the only work deserving a citation which developed an online system ChemHits to do the standardization basing on several transformation rules and the queries to online chemical databases. The work of BID2 severely depends on chemical knowledge, limiting its application potential and effectiveness to some extent.Differently, we adopt sequence to sequence model that has been widely used on neural machine translation. The reason why we apply the sequence to sequence model is that our task has some similarities with the machine translation problem. In machine translation, there are source language and target language which correspond to the non-systematic names and the systematic names in our task. Two different languages can be different in: 1. Vocabularies, which corresponds to the common name error and synonym error; 2. Word order, which corresponds to the ordering error. Our framework is trained end-to-end , fully data-driven and without using external chemical knowledge.With this approach, we achieve an accuracy of 54.04% in our test data set.Our work will be done on a corpus containing chemical names extracted from report of Chemical Journals with High Impact factors (CJHIF) 3 . The corpus is collected and checked by paid manual work. It is a parallel corpus which includes non-systematic names and systematic names of chemical substances . In the following passage, we call a non-systematic name and the corresponding systematic name of a chemical substance data pair. In our corpus, there are 384816 data pairs. In FIG1 , we give an overview of the distribution of the Levenshtein distance between the non-systematic names and the systematic names to show how different the non-systematic names and the systematic names are. In the experiment, we use 80%, 19% and 1% data as training set, test set and development set respectively. In this work, we propose a framework to automatically convert non-systematic names to systematic names . Our framework consists of spelling error correction, byte pair encoding tokenization and sequence to sequence model. Our framework achieves an accuracy of 54.04% on our dataset, which is far better than previous rule based system (nine times of accuracy) and thus enables the related chemical information extraction into more practical use stage. The advantage of our framework is that it is trained end to end, fully data-driven and independent of external chemical knowledge. This work starts a brand new research line for the related chemical information extraction as to our best knowledge.",1567,0.997,902,1.737250554323725,"Chemical information extraction to convert chemical knowledge in text true chemical database a text processing task heavily relying chemical compound name identification standardization Once a systematic name will naturally and much simply convert the eventually required molecular formula However for many chemical substances in many other names besides their systematic names which poses this task In do the auto standardization from the non-systematic names by the spelling error correction, byte pair encoding tokenization neural sequence to sequence model Our framework trained end fully data Our standardization accuracy on the test dataset achieves which has a great improvement compared state result There named chemical substances In order uniquely every chemical substance there elaborate rules assigning on their structures These names called systematic names The rules these names defined International Union BID1 .However , besides the systematic name can also due Firstly , many chemical are so much know them which common trivial names For example , sucrose a kind we very Its systematic name much which (triolSecondly chemistry industry especially many producers always generate new names a chemical substance We call these kind names proprietary names The most famous example Aspirin Its systematic name So due the history reasons idiomatic usages a chemical substanceChemical information extraction a research that extracts useful chemical knowledge in text converts a database strongly relies the unique standard chemical names Nowadays many chemical databases such PubChem SciFinder store including chemical structures molecular formulas For these databases , it still extract chemical information chemical papers update If all the chemical substances expressed the systematic names generate other information For example nearly perfectly convert the systematic name other representations Simplified Molecular-Input LineEntry BID13 generate the structural formulas Some online systems already well developed converting automatically systematic names SMILES string with such Open Parser for Systematic IUPAC NomenclatureOPSIN BID7 developed In the following passage consider ""error 2 . In view natural language processing the error types non-systematic names summarized 1 Spelling error It means non-systematic names just have slightly differences systematic names spelling; 2 Ordering error It means the groups a non-systematic name in wrong order; 3 Common name error As mentioned many chemical substances common names or proprietary names look totally their systematic names; 4 Synonym error. It means the words the nonsystematic names different but of word In fact the error type happens For example 2-(Acetyloxy)benzoic Acid has synonyms and these three words share of word Some examples errors TAB0 . What worth several types error appear a single non-systematic name especially the ordering error The mixed types error make this task .Based these four error types propose convert automatically the non-systematic names systematic names Our framework structured followed 1 Spelling error correction It aims correct; 2 Byte pair encoding (BPE) tokenization It aims split a name small parts; 3. Sequence to sequence model It aims fix all the remaining ordering errors common name errors synonym errorsActually due its great challenge few work has the chemical name standardization To our best knowledge BID2 deserving a citation which developed an online system ChemHits to do the standardization basing several transformation rules the queries online chemical databases The work BID2 severely depends chemical knowledge limiting its application potential effectiveness some extentDifferently adopt sequence to sequence model that widely on neural machine translation The reason apply the sequence sequence model our task some similarities the machine translation problem In machine translation source language target which correspond the non-systematic names the systematic names our task Two different languages can different: 1 Vocabularies corresponds the common name error and; 2 Word order which corresponds the ordering error. Our framework trained end , fully data without using external chemical knowledgeWith achieve an accuracy 54.04%Our work will a corpus containing chemical names extracted report Chemical Journals with High Impact factors 3 . The corpus collected checked paid manual work It a parallel corpus non-systematic names systematic names chemical substances . In the following passage call a non-systematic name and the corresponding systematic name a chemical substance data pair In our corpus 384816 data pairs In FIG1 give the distribution the non-systematic names to show different In the experiment use 80% 19% as training set test set development In this work propose automatically non-systematic names systematic names . Our framework consists spelling error correction byte pair encoding tokenization sequence to sequence model Our framework achieves an accuracy 54.04% our dataset far previous rule based systemnine times of accuracy thus enables the related chemical information extraction into more practical use stage The advantage our framework trained end fully data independent external chemical knowledge This work starts a brand new research line the related chemical information extraction as to our best knowledge",0.01,0.5825288079751975
"The training of deep neural networks with Stochastic Gradient Descent (SGD) with a large learning rate or a small batch-size typically ends in flat regions of the weight space, as indicated by small eigenvalues of the Hessian of the training loss. This was found to correlate with a good final generalization performance.   In this paper we extend previous work by investigating the curvature of the loss surface along the whole training trajectory, rather than only at the endpoint. We find that initially SGD visits increasingly sharp regions, reaching a maximum sharpness determined by both the learning rate and the batch-size of SGD. At this peak value SGD starts to fail to minimize the loss along directions in the loss surface corresponding to the largest curvature (sharpest directions). To further investigate the effect of these dynamics in the training process, we study a variant of SGD using a reduced learning rate along the sharpest directions which we show can improve training speed while finding both sharper and better generalizing solution, compared to vanilla SGD. Overall, our results show that the SGD dynamics in the subspace of the sharpest directions influence the regions that SGD steers to (where larger learning rate or smaller batch size result in wider regions visited), the overall training speed, and the generalization ability of the final model. Deep Neural Networks (DNNs) are often massively over-parameterized BID29 ), yet show state-of-the-art generalization performance on a wide variety of tasks when trained with Stochastic Gradient Descent (SGD). While understanding the generalization capability of DNNs remains an open challenge, it has been hypothesized that SGD acts as an implicit regularizer, limiting the complexity of the found solution BID17 BID0 BID24 BID9 .Various links between the curvature of the final minima reached by SGD and generalization have been studied BID15 BID16 . In particular , it is a popular view that models corresponding to wide minima of the loss in the parameter space generalize better than those corresponding to sharp minima BID8 BID10 BID9 . The existence of this empirical correlation between the curvature of the final minima and generalization motivates our study.Our work aims at understanding the interaction between SGD and the sharpest directions of the loss surface, i.e. those corresponding to the largest eigenvalues of the Hessian. In contrast to studies such as those by BID10 and BID9 our analysis focuses on the whole training trajectory of SGD rather than just on the endpoint. We will show in Sec. 3.1 that the evolution of the largest eigenvalues of the Hessian follows a Outline of the phenomena discussed in the paper. Curvature along the sharpest direction(s) initially grows (A to C). In most iterations , we find that SGD crosses the minimum if restricted to the subspace of the sharpest direction(s) by taking a too large step (B and C). Finally, curvature stabilizes or decays with a peak value determined by learning rate and batch size (C, see also right). Right two: Representative example of the evolution of the top 30 (decreasing, red to blue) eigenvalues of the Hessian for a SimpleCNN model during training (with η = 0.005, note that η is close to 1 λmax = 1 160 ).consistent pattern for the different networks and datasets that we explore. Initially, SGD is in a region of broad curvature, and as the loss decreases, SGD visits regions in which the top eigenvalues of the Hessian are increasingly large, reaching a peak value with a magnitude influenced by both learning rate and batch size. After that point in training, we typically observe a decrease or stabilization of the largest eigenvalues.To further understand this phenomenon, we study the dynamics of SGD in relation to the sharpest directions in Sec. 3.2 and Sec. 3.3. Projecting to the sharpest directions 1 , we see that the regions visited in the beginning resemble bowls with curvatures such that an SGD step is typically too large, in the sense that an SGD step cannot get near the minimum of this bowl-like subspace; rather it steps from one side of the bowl to the other, see FIG0 for an illustration.Finally in Sec. 4 we study further practical consequences of our observations and investigate an SGD variant which uses a reduced and fixed learning rate along the sharpest directions. In most cases we find this variant optimizes faster and leads to a sharper region, which generalizes the same or better compared to vanilla SGD with the same (small) learning rate. While we are not proposing a practical optimizer , these results may open a new avenue for constructing effective optimizers tailored to the DNNs' loss surface in the future.On the whole this paper exposes and analyses SGD dynamics in the subspace of the sharpest directions. In particular, we argue that the SGD dynamics along the sharpest directions influence the regions that SGD steers to (where larger learning rate or smaller batch size result in wider regions visited), the training speed, and the final generalization capability. The somewhat puzzling empirical correlation between the endpoint curvature and its generalization properties reached in the training of DNNs motivated our study. Our main contribution is exposing the relation between SGD dynamics and the sharpest directions, and investigating its importance for training. SGD steers from the beginning towards increasingly sharp regions of the loss surface, up to a level dependent on the learning rate and the batch-size. Furthermore, the SGD step is large compared to the curvature along the sharpest directions, and highly aligned with them.Our experiments suggest that understanding the behavior of optimization along the sharpest directions is a promising avenue for studying generalization properties of neural networks. Additionally, results such as those showing the impact of the SGD step length on the regions visited (as characterized by their curvature) may help design novel optimizers tailor-fit to neural networks.A Additional results for Sec. 3.1",1191,0.578,687,1.7336244541484715,"The training with or typically ends flat regions the weight space indicated of This found correlate a good final generalization performance In extend investigating the loss surface along the whole training trajectory rather We find initially SGD visits increasingly sharp regions reaching determined both the learning rate At this peak value SGD starts fail minimize along directions the loss surface corresponding the largest curvaturesharpest directions To further investigate these dynamics the training process study a variant SGD using a reduced learning rate along the sharpest directions which we show while finding both sharper and better generalizing solution compared Overall the SGD dynamics the subspace the sharpest directions influence the regions SGD steerswhere larger learning rate or smaller batch size result wider regions visited the overall training speed the generalization ability Deep Neural Networks often massively over-parameterized BID29 ), yet show state performance when While understanding the generalization capability remains hypothesized SGD acts an implicit regularizer limiting the found solution BID17 BID0 BID24 BID9 .Various links the curvature the final minima reached studied . In particular , a popular view models corresponding wide minima the loss parameter generalize better sharp minima BID8 BID10 BID9 The existence this empirical correlation the final minima generalization motivatesOur work SGD the sharpest directions the loss surface those corresponding In contrast studies such BID10 our analysis focuses the whole training trajectory SGD rather on the endpoint We show in Sec that the evolution the largest eigenvalues the Hessian follows a Outline the phenomena discussed Curvature along the sharpest direction(s initially grows (A to In most iterations , find SGD crosses the minimum if restricted the subspace the sharpest direction(s taking a too large stepB and Finally, curvature stabilizes or a peak value determined learning rate and batch sizeC, right Right two: Representative example the evolution top 30 (decreasing red to blue) eigenvalues the Hessian for a SimpleCNN model during trainingwith �� note close 1 ��max = 160.consistent pattern the different networks datasets explore Initially SGD is in a region broad curvature the loss decreases visits regions increasingly reaching with influenced both learning rate and batch size After that point in training typically observe or stabilization the largest eigenvaluesTo further study SGD relation the sharpest directions Sec and Sec Projecting the sharpest directions 1 , we see the regions visited the beginning resemble bowls curvatures such an SGD step typically too in get near this bowl-like subspace; rather steps from see FIG0 forFinally in Sec 4 we study further practical consequences our observations investigate an SGD variant which uses a reduced and fixed learning rate along the sharpest directions In we find this variant optimizes faster leads a sharper region generalizes same or compared vanilla SGD with While proposing a practical optimizer , these results open constructing tailored the DNNs' loss surface inOn this exposes and analyses SGD dynamics the sharpest directions In particular argue the SGD dynamics along the sharpest directions influence the regions SGD steerswhere larger learning rate or smaller batch size result wider regions visited training speed final capability The somewhat puzzling empirical correlation the endpoint curvature its generalization properties reached the training motivated our study Our main contribution exposing the relation SGD dynamics the sharpest directions investigating training SGD steers from towards increasingly sharp regions the loss surface up dependent the batch-size Furthermore the SGD step large compared along the sharpest directions highly aligned themOur experiments understanding optimization along generalization properties Additionally results such showing the SGD step length the regions visitedas characterized design novel optimizers tailor-fit neural networksA Additional results Sec",0.01,0.5732898233143294
"We introduce a new approach to estimate continuous actions using actor-critic algorithms for reinforcement learning problems. Policy gradient methods usually predict one continuous action estimate or parameters of a presumed distribution (most commonly Gaussian) for any given state which might not be optimal as it may not capture the complete description of the target distribution. Our approach instead predicts M actions with the policy network (actor) and then uniformly sample one action during training as well as testing at each state. This allows the agent to learn a simple stochastic policy that has an easy to compute expected return. In all experiments, this facilitates better exploration of the state space during training and converges to a better policy. Reinforcement learning is a traditional branch of machine learning which focuses on learning complex tasks by assigning rewards to agents that interact with their environment. It has recently gained momentum thanks to the combination of novel algorithms for continuous control with deep learning models, sometimes even matching human performance in tasks such as playing video games and manipulating objects BID10 ; . Recent methods for continuous control problems like Deep Deterministic Policy Gradient (DDPG) , Asynchronous Advantage Actor Critic (A3C) BID11 use actor-critic architectures, where an action function is learned by mapping states to actions. DDPG works well on many tasks, but it does not model the uncertainty in actions as it produces a point estimate of the action distribution over states. The actor is forced to deterministically choose an action for every state. A3C and other stochastic policy gradient algorithms output distribution parameters (e.g. Gaussian distributions) instead of point estimate, which can be sampled for action values.As a simple example where this is sub-optimal, consider the inverted pendulum task, where a pendulum is attached to a cart and the agent needs to control the one dimensional movement of the cart to balance the pendulum upside down. A deterministic agent chooses a single action for every state. This breaks the inherent symmetry of the task. When the cart in not moving and the pendulum is hanging down, two actions are equally promising: either moving left or right. The distribution parameter estimation (e.g. A3C) might work better in this case as there are only two good options, but in cases when there are more than two good actions to select, this will not be optimal. In our approach we allow the agent to suggest multiple actions, which enables it to resolve cases like this easily.Further, we observe that a deterministic behavior of DDPG can lead to sub-optimal convergence during training. The main limitation is that, especially in the beginning of the learning procedure, the actor favors actions that lead to a good immediate reward but might end up being far from the globally optimal choice. This work is based on the intuition that if the actor is allowed to suggest, at each time step, multiple actions rather than a single one, this can render the resulting policy non-deterministic, leading to a better exploration of the entire solution space as well as a final solution of potentially higher quality. This can also eliminate the external exploration mechanisms required during training e.g. OrnsteinUhlenbeck process noise BID20 , parameter noise or differential entropy of normal distribution.Here, we introduce an algorithm, which we refer to as Multiple Action Policy Gradients (MAPG), that models a stochastic policy with several point estimates and allows to predict a pre-defined number M of actions at each time step, extending any policy gradient algorithm with little overhead. We will demonstrate the working of this algorithm by adapting DDPG Lillicrap et al. (2016) to use MAPG.Another benefit of the proposed method is that the variance of the predicted actions can give additional insights into the decision process during runtime. A low variance usually implies that the model only sees one way to act in a certain situation. A wider or even multi-modal distribution suggests that there exist several possibilities given the current state.We evaluate the proposed method on six continuous control problems of the OpenAI Gym BID0 as well as a deep driving scenario using the TORCS car simulator BID22 . For a fair evaluation we directly compare DDPG to our MAPG without changing hyper-parameters or modifying the training scheme. In all experiments, we show an improved performance using MAPG over DDPG. To verify if MAPG helps in better exploration during training, we also analyze MAPG under no external exploration policy. In this paper, we have proposed MAPG, a technique that leverages multiple action prediction to learn better policies in continuous control problems. The proposed method enables a better exploration of the state space and shows improved performance over DDPG. As indicated by exploration experiments, it can also be a used as a standalone exploration technique, although more work needs to be done in this direction. Last but not least, we conclude with interesting insights gained from the action variance. There are several interesting directions which we would like to investigate in the future. The number of actions M is a hyper-parameter in our model that needs to be selected and seems to be task specific. In general, the idea of predicting multiple action proposals can be extended to other on-or off-policy algorithms, such as NAF BID1 or TRPO. Evaluating MA-NAF and MA-TRPO will enable studying the generality of the proposed approach.",1065,0.577,616,1.728896103896104,"We introduce estimate continuous actions actor-critic algorithms reinforcement learning problems Policy gradient methods usually predict one continuous action estimate parameters a presumed distributionmost commonly Gaussian which might optimal as the complete description Our approach instead predicts M actions the policy networkactor then uniformly sample one action during training as testing at This allows the agent learn a simple stochastic policy has easy compute expected return In all experiments this facilitates better exploration the state space during training converges a better policy Reinforcement learning a traditional branch complex tasks assigning rewards agents interact It recently gained the combination novel algorithms continuous control with sometimes even matching human performance playing manipulating objects BID10 ; . Recent methods continuous control problems like Deep Deterministic Policy Gradient , Asynchronous Advantage Actor Critic BID11 use actor-critic architectures where an action function learned mapping states DDPG works many tasks model the uncertainty actions produces the action distribution states The actor forced deterministically choose an action every state A3C and other stochastic policy gradient algorithms output distribution parameters instead point estimate, sampled action valuesAs where sub the inverted pendulum task attached the agent needs control the one dimensional movement balance upside A deterministic agent chooses This breaks the inherent symmetry the task When the cart in not moving hanging two actions equally promising either moving left The distribution parameter estimation might work there cases when select In our approach allow the agent suggest multiple actions enables resolve cases like easilyFurther observe DDPG during training The main limitation, especially the learning procedure the actor favors actions a good immediate reward but might end far the globally optimal choice This work based the intuition the actor allowed suggest at each time step multiple rather render the resulting policy non a better exploration the entire solution space as of potentially higher quality This can eliminate the external exploration mechanisms required during training OrnsteinUhlenbeck process noise BID20 , parameter noise or differential entropy normal distributionHere introduce, refer Multiple Action Policy Gradients models several point estimates allows a pre-defined number M actions extending any policy gradient algorithm little overhead We demonstrate the working adapting DDPG Lillicrap et (2016 to use MAPG.Another benefit the proposed method the variance the predicted actions give additional insights during runtime A low variance usually implies only sees act A wider or even multi-modal distribution suggests exist several possibilities given.We evaluate on six continuous control problems the OpenAI Gym BID0 as a deep driving scenario the TORCS car simulator BID22 . For a fair evaluation we directly DDPG our MAPG without changing hyper modifying the training scheme In all experiments show an improved performance using MAPG over DDPG To verify MAPG helps in better exploration during training also analyze under no external exploration policy In have MAPG, multiple action prediction learn better policies continuous control problems The proposed method enables a better exploration the state space shows improved performance over DDPG As indicated exploration experiments it a used a standalone exploration technique more work Last but conclude interesting insights gained the action variance There several interesting directions which would investigate The number actions M is a hyper that needs selected seems task In general predicting multiple action proposals can extended other on-or off-policy algorithms NAF BID1 TRPO MA-NAF and will enable studying the proposed approach",0.01,0.5612424022996075
"Recently convolutional neural networks (CNNs) achieve great accuracy in visual recognition tasks. DenseNet becomes one of the most popular CNN models due to its effectiveness in feature-reuse. However, like other CNN models, DenseNets also face overfitting problem if not severer. Existing dropout method can be applied but not as effective due to the introduced nonlinear connections. In particular, the property of feature-reuse in DenseNet will be impeded, and the dropout effect will be weakened by the spatial correlation inside feature maps. To address these problems, we craft the design of a specialized dropout method from three aspects, dropout location, dropout granularity, and dropout probability. The insights attained here could potentially be applied as a general approach for boosting the accuracy of other CNN models with similar nonlinear connections. Experimental results show that DenseNets with our specialized dropout method yield better accuracy compared to vanilla DenseNet and state-of-the-art CNN models, and such accuracy boost increases with the model depth. Recent years have seen a rapid development of deep neural network in the computer vision area, especially for visual object recognition tasks. From AlexNet, the winner of ImageNet Large Scale Visual Recognition Challenge (ILSVRC) , to later VGG network BID14 and GoogLeNet , CNNs have shown significant success with its shocking improvement of accuracy.Researchers gradually realized that the depth of the network always plays an important role in the final accuracy of one model due to increased expressiveness BID2 BID3 . However, simply increasing the depth does not always help due to the induced vanishing gradient problem BID0 . ResNet BID4 has been proposed to promote the flow of information across layers without attenuation by introducing identity skip-connections, which sums together the input and the output of several convolutional layers. In 2016, Densely connected network (DenseNet) BID7 came out, which replaces the simple summation in ResNet with concatenation after realizing the summation may also impede the information flow.Despite the improved information flow, DenseNet still suffers from the overfitting problem, especially when the network goes deeper. Standard dropout BID16 has been used to combat such problem, but can not work effectively on DenseNet. The reasons are twofold: 1) Feature-reuse will be weakened by standard dropout as it could make features dropped at previous layers no longer be used at later layers. 2) Standard dropout method does not interact well with convolutional layers because of the spatial correlation inside feature maps BID19 . Since dense connectivity increases the number of feature maps tremendously -especially at deep layers -the effectiveness of standard dropout would further be reduced.In this paper, we design a specialized dropout method to resolve these problems. In particular, three aspects of dropout design are addressed: 1) Where to put dropout layers in the network? 2) What is the best dropout granularity? 3) How to assign appropriate dropout (or survival) probabilities for different layers? Meanwhile, we show that the idea to re-design the dropout method from the three aspects also applies to other CNN models like ResNet. The contributions of the paper can be summarized as follows:• First, we propose a new structure named pre-dropout to solve the possible feature-reuse obstruction when applying standard dropout method on DenseNet.• Second, we are the first to show that channel-wise dropout (compared to layer-wise and unit-wise) fit best for CNN through both detailed analysis and experimental results.• Third, we propose three distinct probability schedules, and via experiments we find out the best one for DenseNet.• Last, we provide a good insight for future practitioners, inspiring them regarding what should be considered and which is the best option when applying the dropout method on a CNN model.Experiments in our paper suggest that DenseNets with our proposed specialized dropout method outperforms other comparable DenseNet and state-of-art CNN models in terms of accuracy, and following the same idea dropout methods designed for other CNN models could also achieve consistent improvements over the standard dropout method. In this paper, first we show problems of applying standard dropout method on DenseNet. To deal with these problems, we come up with a new pre-dropout structure and adopt channel-wise dropout granularity. Specifically, we put dropout before convolutional layers to reinforce feature-reuse inside the model. Meanwhile we randomly drop some feature maps in inputs of convolutional layers to break dependence among them. Besides to further promote model generalization ability we introduce stochastic probability method to add various degrees of noise to different layers in DenseNet. Experiments show that in terms of accuracy DenseNets with our specialized dropout method outperform other CNN models.",936,0.488,526,1.779467680608365,"Recently convolutional neural networks achieve DenseNet becomes the most popular CNN models due feature-reuse However like other CNN models DenseNets also face overfitting problem if not severer Existing dropout method can but as effective due the introduced nonlinear connections In particular the property feature-reuse DenseNet will impeded the dropout effect weakened the spatial correlation inside feature maps To address craft the design a specialized dropout method from three aspects dropout location granularity probability The insights attained here could as boosting other CNN models with similar nonlinear connections Experimental results DenseNets with our specialized dropout method yield better accuracy compared vanilla DenseNet state CNN models such accuracy boost increases the model depth Recent years deep neural network in From AlexNet, the winner ImageNet Large Scale Visual Recognition Challenge , later VGG network BID14 and GoogLeNet CNNs shown its shocking improvementResearchers gradually the depth always plays one model due increased expressiveness BID2 BID3 However simply increasing the depth does due the induced vanishing gradient problem BID0 . ResNet BID4 has proposed promote the flow layers without attenuation introducing identity skip-connections sums together In 2016 Densely connected network (DenseNet) BID7 came replaces the simple summation in ResNet with after realizing may also impedeDespite especially goes deeper Standard dropout BID16 has used combat such problem can work effectively DenseNet The reasons Feature-reuse will weakened standard dropout as could make features dropped at previous layers no at 2 Standard dropout method does interact well because the spatial correlation inside feature BID19 . Since dense connectivity increases feature maps tremendously -especially at deep layers -the effectiveness standard dropout would furtherIn design resolve In particular three aspects dropout design addressed Where? 2 What the best dropout granularity 3 How assign appropriate dropout (or survival) probabilities different layers? Meanwhile we show to redesign the dropout method the three aspects also other CNN models like ResNet The contributions the paper can named predropout solve the possible feature-reuse obstruction when applying standard dropout method on are the ( layer and unit fit best CNN through both detailed analysis experimental three distinct probability schedules via experiments out a good insight for future practitioners inspiring regarding what considered and whichExperiments suggest with comparable and stateart following dropout methods designed could achieve consistent improvements In first problems applying standard dropout method on DenseNet To deal come a new pre-dropout structure adopt channel-wise dropout granularity Specifically put dropout before convolutional layers reinforce feature-reuse inside Meanwhile we randomly drop some feature maps inputs break dependence among Besides to further promote model generalization ability we introduce stochastic probability method add various degrees noise different layers DenseNet Experiments in terms accuracy DenseNets with our specialized dropout method other CNN models",0.01,0.6900943365923005
"While extremely successful in several applications, especially with low-level representations; sparse, noisy samples and structured domains (with multiple objects and interactions) are some of the open challenges in most deep models. Column Networks, a deep architecture, can succinctly capture such domain structure and interactions, but may still be prone to sub-optimal learning from sparse and noisy samples. Inspired by the success of human-advice guided learning in AI, especially in data-scarce domains, we propose Knowledge-augmented Column Networks that leverage human advice/knowledge for better learning with noisy/sparse samples. Our experiments demonstrate how our approach leads to either superior overall performance or faster convergence. The re-emergence of Deep Learning BID11 has found significant and successful applications in difficult real-world domains such as image BID17 , audio BID23 ) and video processing (Yue-Hei BID40 . Deep Learning has also been increasingly applied to structured domains, where the data is represented using richer symbolic or graph features to capture relational structure between entities and attributes in the domain. Intuitively, deep learning architectures are naturally suited to learning and reasoning over such multi-relational domains as they are able to capture increasingly complex interactions between features with deeper layers. However, the combinatorial complexity of reasoning over a large number of relations and objects has remained a significant bottleneck to overcome.Recent work in relational deep learning has sought to address this particular issue. This includes relational neural networks BID15 Šourek et al., 2015) , relational Restricted Boltzmann machines BID14 and neuro-symbolic architectures such as C-ILP BID7 . In our work, we focus upon the framework of Column Networks (CLNs) developed by BID31 . Column networks are composed of several (feedforward) mini-columns each of which represents an entity in the domain. Relationships between two entities are modeled through edges between mini-columns. These edges allow for the short-range exchange of information over successive layers of the column network; however, the true power of column networks emerges as the depth of interactions increases, which allows for the natural modeling of long-range interactions.Column networks are an attractive approach for several reasons: (1) hidden layers of a CLN share parameters, which means that making the network deeper does not introduce more parameters, (2) as the depth increases, the CLN can begin to model feature interactions of considerable complexity, which is especially attractive for relational learning, and (3) learning and inference are linear in the size of the network and the number of relations, which makes CLNs highly efficient. However, like other deep learning approaches, CLNs rely on vast amounts of data and incorporate little to no knowledge about the problem domain. While this may not be an issue for low-level applications such as image or video processing, it is a significant issue in relational domains, since the relational structure encodes rich, semantic information. This suggests that ignoring domain knowledge can considerably hinder generalization.It is well known that biasing learners is necessary in order to allow them to inductively leap from training instances to true generalization over new instances BID26 . Indeed, the inductive bias towards ""simplicity and generality"" leads to network architectures with simplifying assumptions through regularization strategies that aim to control the complexity of the neural/deep network.While deep learning does incorporate one such bias in the form of domain knowledge (for example, through parameter tying or convolution, which exploits neighborhood information), we are motivated to develop systems that can incorporate richer and more general forms of domain knowledge. This is especially germane for deep relational models as they inherently construct and reason over richer representations. Such domain-knowledge-based inductive biases have been applied to a diverse array of machine learning approaches, variously known as advice-based, knowledge-based or human-guided machine learning.One way in which a human can guide learning is by providing rules over training examples and features. The earliest such approaches combined explanation-based learning (EBL-NN, BID35 ) or symbolic domain rules with ANNs (KBANN, Towell & Shavlik (1994) ). Domain knowledge as rules over input features can also be incorporated into support vector machines (SVMs, BID2 ; BID34 BID9 ; BID21 ; BID19 ). Another natural way a human could guide learning is by expressing preferences and has been studied extensively within the preference-elicitation framework due to BID1 . We are inspired by this form of advice as they have been successful within the context of inverse reinforcement learning BID20 , imitation learning BID29 and planning BID3 .These approaches span diverse machine learning formalisms, and they all exhibit the same remarkable behavior: better generalization with fewer training examples because they effectively exploit and incorporate domain knowledge as an inductive bias. This is the prevailing motivation for our approach: to develop a framework that allows a human to guide deep learning by incorporating rules and constraints that define the domain and its aspects. Incorporation of prior knowledge into deep learning has begun to receive interest recently, for instance, the recent work on incorporating prior knowledge of color and scene information into deep learning for image classification BID5 . However, in many such approaches, the guidance is not through a human, but rather through a pre-processing algorithm to generate guidance. Our framework is much more general in that a human provides guidance during learning. Furthermore, the human providing the domain advice is not an AI/ML expert but rather a domain expert who provides rules naturally. We exploit the rich representation power of relational methods to capture, represent and incorporate such rules into relational deep learning models.We make the following contributions: (1) we propose the formalism of Knowledge-augmented Column Networks, (2) we present, inspired by previous work (such as KBANN), an approach to inject generalized domain knowledge in a CLN and develop the learning strategy that exploits this knowledge, and (3) we demonstrate, across four real problems in some of which CLNs have been previously employed, the effectiveness and efficiency of injecting domain knowledge. Specifically, our results across the domains clearly show statistically superior performance with small amounts of data. As far as we are aware, this is the first work on human-guided CLNs. We considered the problem of providing guidance for CLNs. Specifically, inspired by treating the domain experts as true domain experts and not CLN experts, we developed a formulation based on preferences. This formulation allowed for natural specification of guidance. We derived the gradients based on advice and outlined the integration with the original CLN formulation. Our experimental results across different domains clearly demonstrate the effectiveness and efficiency of the approach, specifically in knowledge-rich, data-scarce problems. Exploring other types of advice including feature importances, qualitative constraints, privileged information, etc. is a potential future direction. Scaling our approach to web-scale data is a natural extension. Finally, extending the idea to other deep models remains an interesting direction for future research.",1384,0.778,819,1.6898656898656899,"While extremely successful several applications especially low-level representations; sparse noisy samples structured domainswith multiple objects interactions some most deep models Column Networks a deep architecture, can succinctly capture such domain structure interactions may still prone from sparse noisy samples Inspired human-advice guided learning AI especially data-scarce domains propose Knowledge-augmented Column Networks that leverage human advice/knowledge for with noisy/sparse samples Our experiments demonstrate our approach leads either superior overall performance faster convergence The re Deep Learning BID11 found significant and successful applications difficult real-world domains image BID17 , ) video processingYueHei . Deep Learning has also increasingly applied structured domains represented richer symbolic or graph features to capture relational structure between attributes Intuitively deep learning architectures naturally learning reasoning over such multi-relational domains they able capture increasingly complex interactions features with deeper layers However the combinatorial complexity reasoning over relations objects remained a significant bottleneck overcomeRecent work relational deep learning sought This includes relational neural BID15 ��ourek , relational Restricted machines neuro-symbolic architectures such C-ILP BID7 . In our work upon the framework Column Networks developed BID31 . Column networks composed several (feedforward) mini each represents an entity Relationships two entities modeled edges between minicolumns These edges allow the short-range exchange over successive layers the column network; the true power column networks emerges interactions increases the natural modelingColumn networks an attractive approach a CLN share parameters making deeper does introduce more parameters as begin model feature interactions of considerable complexity which especially attractive relational learning and linear the size relations highly However like other deep learning approaches CLNs rely vast amounts incorporate little While this low-level applications image or relational domains since encodes rich, semantic information This suggests ignoring domain knowledge considerably hinder generalizationIt well biasing learners necessary allow inductively leap training instances true generalization over new instances BID26 . Indeed the inductive bias towards "" and leads network architectures simplifying assumptions through regularization strategies aim control the neural/deep networkWhile does incorporate one such bias domain knowledgefor through parameter tying, exploits neighborhood information motivated develop systems incorporate richer and more general forms This especially deep relational models as inherently construct reason over richer representations Such domain-knowledge-based inductive biases applied a diverse array variously knownOne way guide learning rules over training examples features The earliest such approaches combined explanation-based learningEBL-NN, BID35 ) or symbolic domain rules ANNsKBANN Towell & Shavlik (1994 Domain knowledge as rules over input features can incorporated support vector machines, BID2 ; BID34 BID9 ; Another natural way a human guide learning expressing preferences has been studied within the preference-elicitation framework due BID1 . We inspired this form advice as they successful within inverse reinforcement BID20 , imitation planning .These approaches span diverse machine learning formalisms exhibit the same remarkable behavior better generalization with fewer training examples because effectively exploit and incorporate domain knowledge as an inductive bias This the prevailing motivation our approach develop a human guide deep learning incorporating rules constraints define its aspects prior knowledge into deep learning has begun receive interest recently for the recent incorporating of color and scene information for image classification BID5 . However many such approaches the guidance through a human, a pre-processing algorithm to guidance Our framework much general a human provides guidance during learning Furthermore the human providing the domain advice an AI/ML expert provides rules naturally We exploit the rich representation power relational methods capture represent incorporate such rules relational deep learning modelsWe make ( propose the formalism Knowledge-augmented Column Networks present, inspiredsuch KBANN inject generalized domain knowledge a CLN and develop the learning strategy exploits across four real problems some which previously employed injecting Specifically our results across the domains clearly statistically superior performance small amounts data As far human-guided CLNs considered providing guidance. Specifically inspired treating the domain experts true domain experts a formulation preferences This formulation allowed natural specification guidance We derived the gradients based advice and outlined the integration the original CLN formulation Our experimental results across different domains clearly efficiency specifically knowledge-rich, data-scarce problems Exploring other types advice including feature importances qualitative constraints privileged information is a potential future direction Scaling our approach web-scale data. Finally extending the idea other deep models remains",0.01,0.46179633652479435
"Recent research has shown that one can train a neural network with binary weights and activations at train time by augmenting the weights with a high-precision continuous latent variable that accumulates small changes from stochastic gradient descent. However, there is a dearth of work to explain why one can effectively capture the features in data with binary weights and activations. Our main result is that the neural networks with binary weights and activations trained using the method of Courbariaux, Hubara et al. (2016) work because of the high-dimensional geometry of binary vectors. In particular, the ideal continuous vectors that extract out features in the intermediate representations of these BNNs are well-approximated by binary vectors in the sense that dot products are approximately preserved. Compared to previous research that demonstrated good classification performance with BNNs, our work explains why these BNNs work in terms of HD geometry.   Furthermore, the results and analysis used on BNNs are shown to generalize to neural networks with ternary weights and activations. Our theory serves as a foundation for understanding not only BNNs but a variety of methods that seek to compress traditional neural networks. Furthermore, a better understanding of multilayer binary neural networks serves as a starting point for generalizing BNNs to other neural network architectures such as recurrent neural networks. The rapidly decreasing cost of computation has driven many successes in the field of deep learning in recent years. Consequently, researchers are now considering applications of deep learning in resource limited hardware such as neuromorphic chips, embedded devices and smart phones , BID26 , BID2 ). A recent realization for both theoretical researchers and industry practitioners is that traditional neural networks can be compressed because they are highly over-parameterized. While there has been a large amount of experimental work dedicated to compressing neural networks (Sec. 2), we focus on the particular approach that replaces costly 32-bit floating point multiplications with cheap binary operations. Our analysis reveals a simple geometric picture based on the geometry of high dimensional binary vectors that allows us to understand the successes of the recent efforts to compress neural networks. and showed that one can efficiently train neural networks with binary weights and activations that have similar performance to their continuous counterparts. Such BNNs execute 7 times faster using a dedicated GPU kernel at test time. Furthermore, they argue that such BNNs require at least a factor of 32 fewer memory accesses at test time that should result in an even larger energy savings. There are two key ideas in their papers FIG0 . First, a continuous weight, w c , is associated with each binary weight, w b , that accumulates small changes from stochastic gradient descent. Second, the non-differentiable binarize function (θ(x) = 1 if x > 0 and −1 otherwise) is replaced with a continuous one during backpropagation. These modifications allow one to train neural networks that have binary weights and activations with stochastic gradient descent. While the work showed how to train such networks, the existence of neural networks with binary weights and activations needs to be reconciled with previous work that has sought to understand weight matrices as extracting out continuous features in data (e.g. BID30 ). Summary of contributions: Each oval corresponds to a tensor and the derivative of the cost with respect to that tensor. Rectangles correspond to transformers that specify forward and backward propagation functions. Associated with each binary weight, w b , is a continuous weight, w c , that is used to accumulate gradients. k denotes the kth layer of the network. (b) Each binarize transformer has a forward function and a backward function. The forward function simply binarizes the inputs. In the backward propagation step, one normally computes the derivative of the cost with respect to the input of a transformer via the Jacobian of the forward function and the derivative of the cost with respect to the output of that transformer (δu ≡ dC/du where C is the cost function used to train the network). Since the binarize function is non-differentiable, the straight-through estimator BID3 ), which is a smoothed version of the forward function, is used for the backward function . Neural networks with binary weights and activations have similar performance to their continuous counterparts with substantially reduced execution time and power usage. We provide an experimentally verified theory for understanding how one can get away with such a massive reduction in precision based on the geometry of HD vectors. First, we show that binarization of high-dimensional vectors preserves their direction in the sense that the angle between a random vector and its binarized version is much smaller than the angle between two random vectors (Angle Preservation Property). Second, we take the perspective of the network and show that binarization approximately preserves weight-activation dot products (Dot Product Proportionality Property). More generally, when using a network compression technique, we recommend looking at the weight activation dot product histograms as a heuristic to help localize the layers that are most responsible for performance degradation. Third, we discuss the impacts of the low effective dimensionality of the data on the first layer of the network. We recommend either using continuous weights for the first layer or a Generalized Binarization Transformation. Such a transformation may be useful for architectures like LSTMs where the update for the hidden state declares a particular set of axes to be important (e.g. by taking the pointwise multiply of the forget gates with the cell state). Finally, we show that neural networks with ternary weights and activations can also be understood with our approach. More broadly speaking, our theory is useful for analyzing a variety of neural network compression techniques that transform the weights, activations or both to reduce the execution cost without degrading performance.",1159,0.901,695,1.6676258992805755,"Recent research one can train binary weights activations train time by augmenting a high-precision continuous latent variable that accumulates small changes from However work explain one effectively capture the features data with binary weights activations Our main result neural with binary weights activations trained using the method Courbariaux Hubara et al (2016) work because the high-dimensional geometry binary vectors In particular the ideal continuous vectors that extract out features the intermediate representations these BNNs well binary vectors in dot products approximately preserved Compared previous research demonstrated good classification performance BNNs explains work terms HD geometry Furthermore and used on BNNs shown to ternary weights activations Our theory serves not only BNNs a variety methods seek compress Furthermore a better understanding multilayer binary neural networks serves BNNs The rapidly decreasing cost computation driven many successes researchers considering applications resource limited hardware neuromorphic chips embedded devices , BID26 BID2 A recent realization for both theoretical researchers industry practitioners traditional neural networks compressed because highly over While experimental work dedicated compressing neural networksSec. 2), we focus the particular approach replaces costly 32-bit floating point multiplications cheap binary operations Our analysis a simple geometric picture based high dimensional binary vectors allows understand the successes the recent efforts compress and showed one efficiently train binary weights activations that have similar performance their continuous counterparts Such BNNs execute 7 using a dedicated GPU kernel at test time Furthermore they argue such BNNs require 32 fewer memory at test time that should result an even larger energy savings There two key ideas their papers FIG0 . First a continuous weight, w c associated each binary weight small changes from Second, the non-differentiable binarize function�� if replaced a continuous one during These modifications allow one train neural networks that binary weights activations with While the work showed train such networks the existence with binary weights activations needs sought weight matrices extracting out continuous features data (e.g. BID30 Summary contributions Each oval corresponds a tensor the derivative the cost with Rectangles correspond transformers specify forward propagation functions Associated with each binary weight w b accumulate gradients k denotes the kth layer (b Each binarize transformer has a forward function The forward function simply binarizes In the backward propagation step one normally with a transformer via the Jacobian of the forward function (��u ≡ dC/du where used train the network Since the binarize function nondifferentiable the straight-through estimator BID3 ), a smoothed version the forward function the backward function . Neural networks with binary weights activations similar performance their continuous counterparts with substantially reduced execution time and power usage We provide an experimentally verified theory one get away such a massive reduction precision based the geometry HD vectors First show binarization preserves their direction in a random vector muchAngle Preservation Property Second take the perspective the network show binarization approximately preserves weight-activation dot productsDot Product Proportionality Property More generally when using a network compression technique we looking the weight activation dot product histograms a heuristic localize the layers that responsible performance degradation Third discuss the impacts the low effective dimensionality the first layer We recommend either continuous weights the first layer a Generalized Binarization Transformation Such a transformation may useful architectures LSTMs the update for the hidden state declares axes important by taking the pointwise multiply the forget gates with the cell state Finally show neural networks with ternary weights also understood with our approach More broadly speaking our theory useful analyzing neural network compression techniques transform the weights, activations or both to reduce the execution cost without",0.01,0.4051313040805589
"In recent years Convolutional Neural Networks (CNN) have been used extensively for Superresolution (SR). In this paper, we use inverse problem and sparse representation solutions to form a mathematical basis for CNN operations. We show how a single neuron is able to provide the optimum solution for inverse problem, given a low resolution image dictionary as an operator. Introducing a new concept called Representation Dictionary Duality, we show that CNN elements (filters) are trained to be representation vectors and then, during reconstruction, used as dictionaries. In the light of theoretical work, we propose a new algorithm which uses two networks with different structures that are separately trained with low and high coherency image patches and show that it performs faster compared to the state-of-the-art algorithms while not sacrificing from performance. Recent years have witnessed an increased demand for superresolution (SR) algorithms. Increased number of video devices boosted the need for displaying high quality videos online with lower bandwidth. In addition, the social media required the storage of videos and images with lowest possible size for server optimization. Other areas include 4K video displaying from Full HD broadcasts, increasing the output size for systems that have limited sized sensors, such as medical imaging, thermal cameras and surveillance systems.SR algorithms aim to generate high-resolution (HR) image from single or ensemble of lowresolution (LR) images. The observation model of a real imaging system relating a high resolution image to the low resolution observation frame can be given as DISPLAYFORM0 where H models the blurring effects, S models the downsampling operation, and n models the system noise. The solution to this problem seeks a minimal energy of an energy functional comprised of the fidelity of the estimated imagef to the observational image f .State-of-the art algorithms that are addressing SR problem can be collected under Dictionary learning based methods (DLB) and Deep learning based methods (DLM) categories. Although SR problem is an inverse problem by nature, performance of other methods such as Bayesian and Example based methods have been surpassed which is the reason why they are not included in this work. Also the SR problem has never been directly dealt with inverse problem solutions as in BID3 BID4 DLB are generally solving optimization problems with sparsity constraints such as BID20 BID21 and L 2 norm regularization as in BID19 . The main concern of DLB is creation of a compact dictionary for reconstruction of high resolution (HR) image. Although useful, DLB methods become heavy and slow algorithms as reconstruction performance increases. Recent advances on GPUs have fueled the usage of convolutional neural networks (CNNs) for SR problem. CNN based algorithms such as BID5 and BID9 have used multi-layered networks which have successfully surpassed DLB methods in terms of run speed and performance. State-of-the art algorithms also use Perceptual Loss (PL) to generate new textures from LR images BID11 . By uniting PL and generative networks, photo realistic images can be generated BID10 . PL minimization based algorithms are visually superior to MSE minimization based ones. Stability of such algorithms have been improved since they have been first proposed BID7 . Although, stability issue is not yet completely addressed for generative networksIn BID1 authors have described representation learning as a manifold learning for which a higher dimensional data is represented compactly in a lower dimensional manifold. They have discussed that the variations in the input space is captured by the representations, for which we are explaining the mechanism at work.Though CNNs are successful for SR problem experimentally, their mathematical validation is still lacking. We summarized the contributions of this work.• We show that neurons solve an Iterative Shrinkage Thresholding (IST) equation during training for which the operator is dictionary matrix constructed from LR training data. The solution yields a representation vector as the neuron filters. Contrary to the discussion in literature for which an encoder-decoder structure is needed to obtain and use representations, we claim that the filters themselves become the representations.• We describe a new concept namely Representation Dictionary Duality (RDD) and show that neuron filters act as representation vectors during training phase. Then in the testing phase, filters start acting as dictionaries upon which the HR reconstruction is made layer by layer. This is a concept which helps us analyze CNNs with sparse representation and inverse problem mathematics.• After analyzing a neuron with inverse problem and DLB solutions and discussing how the entire network operates during training, we propose a new network structure which is able to recover certain details better, faster without sacrificing overall performance.Rest of the paper organized as follows: in section 2 we refer to related literature for different areas of research. Section 3 ties previous work into our analysis of CNNs . In section 4 we propose a new network for SR problem. In section 5 we give experimentation results.2 RELATED WORK 2.1 ANALYTIC APPROACHES Solution to eq. 1 is inherently ill-conditioned since a multiplicity of solutions exist for any given LR pixel. Thus proper prior regularization for the high resolution image is crucial. The regularization of the inversion is provided with a function , reg, which promotes the priori information from the desired output, reg takes different forms ranging from L 0 norm, Tikhonov regularization to orthogonal decomposition of the estimate. Denoting the SH matrix in eq. 2 by K, the regularized solution is given byf DISPLAYFORM1 In BID4 DISPLAYFORM2 Where a class of proximity operators are defined, the special function for the case of L 1 regularization is soft thresholding function also known as shrinkage operator. DISPLAYFORM3 Notice that K T (g − Kf n−1 ) is the negative gradient of data fidelity term in the original formulation. Therefore the solution for the inverse problem using IST iterations is obtained in a gradient descent type method thresholded by Moreau proximity mapping which is also named as Proximal Landweber Iterations. BID4 have proposed the usage of non-quadratic regularization constraints that promote sparsity by the help of an orthonormal (or overcomplete) basis ϕ l of a Hilbert space. For the problem defined in eq. 2 it is proposed to use a functional φ b, p as DISPLAYFORM4 For the case when p = 1, a straightforward variational equation can be obtained in an iterative way. DISPLAYFORM5 Iterations over the set of basis functions can be carried out in one formula DISPLAYFORM6 where DISPLAYFORM7 which can be seen as a method to file the elements of x in the direction of ϕ l . Daubechies et. al. have proven that the solution obtained by iterating f is the global minimum of the solution space. The solution will reach to an optimum point if K is a bounded operator satisfying ||Kf || ≤ C||f || for any vector f and some constant C.We will use this result in proving that neurons in a CNN architecture are able to reach to the optimum solution for SR problem by solving for the exact same eq. 7. A similar work is conducted by BID8 . They have proposed a Learned IST algorithm which can be seen as a time unfolded recurrent neural network. Later BID2 have discussed that LISTA and their own algorithms that extend LISTA are not mere approximations for an iterative algorithm but themselves are full featured sparse coders.Our work diverges from theirs in showing how a convolutional neural network is able to learn image representation and reconstruction for SR problem inside network parameters. We will unite inverse problem approaches, DLM and DLB methods in a representation-dictionary duality concept. We have proven that a neuron is able to solve an inverse problem optimally. By introducing RDD we have shown that CNN layers act as sparse representation solvers. We have proposed a method that addresses the texture recovery better. Experiments have shown that RDD is valid and proposed network recovers some texture components better and faster than state of the art algorithms while not sacrificing performance and speed. In the future we plan to investigate a content-aware aggregation method which might perform better than simple averaging. We will investigate ways of jointly training or optimizing two networks and including aggregation step inside a unified network. In parallel we are investigating a better network structure for texture recovery. Also we are going to incorporate the initial upsampling step into the network by allowing the network to learn its own interpolation kernels.A VISUAL RESULTS",1685,1.27,974,1.7299794661190966,"In Superresolution In inverse problem and sparse representation solutions form CNN operations We show a single neuron provide the optimum solution inverse problem, given a low resolution image dictionary as an operator Introducing Representation Dictionary Duality show CNN elements trained representation vectors, during reconstruction used In theoretical work two networks different structures separately trained low and high coherency image patches show faster compared state while from Recent years superresolution ( algorithms Increased number video devices boosted the need displaying with lower In required the storage videos with lowest possible size server optimization Other areas displaying from Full HD broadcasts increasing systems sized sensors medical imaging thermal camerasSR algorithms aim generate single ensemble lowresolution The observation model a real imaging system relating the low resolution observation frame given DISPLAYFORM0 where H models the blurring effects S n The solution seeks a minimal energy of an energy functional comprised the fidelity the estimated imagef to addressing SR problem collected under Dictionary learning based methodsDLB Although SR problem an inverse problem by performance other methods Example based methods surpassed which Also the SR problem never directly dealt inverse problem solutions BID3 BID4 DLB are generally solving optimization problems sparsity constraints such L 2 norm regularization as . The main concern DLB creation a compact dictionary reconstruction high resolution (HR) image Although useful, DLB methods become heavy and slow algorithms as reconstruction performance increases Recent advances on GPUs fueled the usage SR problem. CNN based algorithms such BID5 used which successfully surpassed DLB methods run speed also use Perceptual Loss new textures LR images BID11 . By uniting PL and generative networks photo realistic images BID10 . PL minimization based algorithms visually superior Stability such algorithms have improved BID7 . Although, stability issue completely generative networksIn BID1 authors representation learning a manifold learning for which a higher dimensional data compactly They discussed that the variations the input space is captured the representations for explaining atThough CNNs successful SR problem experimentally their mathematical validation We summarized work.• show neurons solve Iterative Thresholding (IST equation during training which the operator dictionary matrix constructed LR training data The solution yields a representation vector as the neuron filters Contrary the discussion literature for an encoder-decoder structure needed obtain and representations claim the filters themselves become representations.• describe namely Representation Dictionary Duality neuron filters act representation vectors during training phase Then in the testing phase filters start acting dictionaries upon the HR reconstruction layer This a concept helps analyze CNNs with sparse representation inverse problem mathematics.• After a neuron and DLB solutions discussing operates during propose recover certain details better faster withoutRest organized in section refer related literature different areas Section ties previous work our analysis CNNs . In section we propose SR problem In section we give experimentation eq 1 is inherently ill since a multiplicity solutions exist any given LR pixel Thus proper prior regularization the high resolution image crucial The regularization provided with , reg promotes the priori information the desired output reg takes different forms ranging L 0 norm Tikhonov the estimate Denoting the SH matrix eq 2 by K, the regularized solution given byf DISPLAYFORM1 In Where a class proximity operators L 1 regularization soft thresholding function also shrinkage operator DISPLAYFORM3 Notice K T (g − Kf n−1 the negative gradient data fidelity term the original formulation Therefore the solution the inverse problem using IST iterations obtained a gradient descent type method thresholded Moreau proximity mapping which named Proximal Landweber Iterations BID4 have proposed the usage non-quadratic regularization constraints promote sparsity by the help an orthonormal (or overcomplete) basis �� l For the problem defined eq 2 it proposed a functional �� b, p DISPLAYFORM4 For when a straightforward variational equation DISPLAYFORM5 Iterations over basis functions can carried one formula where which seen file x the direction �� l Daubechies et. al. have proven the solution obtained iterating f the global minimum the solution space The solution will reach to an optimum point K is a bounded operator satisfying ||Kf || ≤ C||f || for f some constant C.We proving neurons a CNN architecture reach SR problem the exact same eq 7 A similar work conducted BID8 . They proposed a Learned IST algorithm seen unfolded recurrent neural network Later BID2 have discussed that LISTA their own algorithms that extend themselves full featured sparse codersOur work diverges theirs showing image representation reconstruction for SR problem inside network parameters We unite inverse problem approaches DLM and DLB methods a representation-dictionary duality concept We proven a neuron solve optimally By introducing RDD we shown CNN layers act sparse representation solvers We proposed addresses the texture recovery better Experiments RDD valid and proposed network recovers some texture components better state of while In plan investigate a content-aware aggregation method perform simple averaging We investigate ways jointly training or optimizing two networks including aggregation step inside In parallel we investigating a better network structure texture recovery Also we incorporate the initial upsampling step by allowing learn its own interpolation kernelsA VISUAL RESULTS",0.01,0.5640027140606286
"We consider the learning of algorithmic tasks by mere observation of input-output
 pairs. Rather than studying this as a black-box discrete regression problem with
 no assumption whatsoever on the input-output mapping, we concentrate on tasks
 that are amenable to the principle of divide and conquer, and study what are its
 implications in terms of learning.
 This principle creates a powerful inductive bias that we leverage with neural
 architectures that are defined recursively and dynamically, by learning two scale-
 invariant atomic operations: how to split a given input into smaller sets, and how
 to merge two partially solved tasks into a larger partial solution. Our model can be
 trained in weakly supervised environments, namely by just observing input-output
 pairs, and in even weaker environments, using a non-differentiable reward signal.
 Moreover, thanks to the dynamic aspect of our architecture, we can incorporate
 the computational complexity as a regularization term that can be optimized by
 backpropagation. We demonstrate the flexibility and efficiency of the Divide-
 and-Conquer Network on several combinatorial and geometric tasks: convex hull,
 clustering, knapsack and euclidean TSP. Thanks to the dynamic programming
 nature of our model, we show significant improvements in terms of generalization
 error and computational complexity. Algorithmic tasks can be described as discrete input-output mappings defined over variable-sized inputs, but this ""black-box"" vision hides all the fundamental questions that explain how the task can be optimally solved and generalized to arbitrary inputs. Indeed, many tasks have some degree of scale invariance or self-similarity, meaning that there is a mechanism to solve it that is somehow independent of the input size. This principle is the basis of recursive solutions and dynamic programming, and is ubiquitous in most areas of discrete mathematics, from geometry to graph theory. In the case of images and audio signals, invariance principles are also critical for success: CNNs exploit both translation invariance and scale separation with multilayer, localized convolutional operators. In our scenario of discrete algorithmic tasks, we build our model on the principle of divide and conquer, which provides us with a form of parameter sharing across scales akin to that of CNNs across space or RNNs across time.Whereas CNN and RNN models define algorithms with linear complexity, attention mechanisms BID1 generally correspond to quadratic complexity, with notable exceptions BID0 . This can result in a mismatch between the intrinsic complexity required to solve a given task and the complexity that is given to the neural network to solve it, which Figure 1: Divide and Conquer Network. The split phase is determined by a dynamic neural network S θ that splits each incoming set into two disjoint sets: {X j+1,l , X j+1,l+1 } = S θ (X j,m ), with X j,m = X j+1,l X j+1,l+1 . The merge phase is carried out by another neural network M φ that combines two partial solutions into a solution of the coarser scale: Y j,m = M φ (Y j+1,l , Y j+1,l+1 ); see Section 3 for more details. may impact its generalization performance. Our motivation is that learning cannot be 'complete' until these complexities match, and we start this quest by first focusing on problems for which the intrinsic complexity is well known and understood.Our Divide-and-Conquer Networks (DiCoNet ) contain two modules: a split phase that is applied recursively and dynamically to the input in a coarse-to-fine way to create a hierarchical partition encoded as a binary tree; and a merge phase that traces back that binary tree in a fine-to-coarse way by progressively combining partial solutions; see Figure 1 . Each of these phases is parametrized by a single neural network that is applied recursively at each node of the tree, enabling parameter sharing across different scales and leading to good sample complexity and generalisation.In this paper, we attempt to incorporate the scale-invariance prior with the desiderata to only require weak supervision. In particular, we consider two setups: learning from input-output pairs, and learning from a non-differentiable reward signal. Since our split block is inherently discrete, we resort to policy gradient to train the split parameters, while using standard backpropagation for the merge phase; see Section 5. An important benefit of our framework is that the architecture is dynamically determined, which suggests using the computational complexity as a regularization term. As shown in the experiments, computational complexity is a good proxy for generalisation error in the context of discrete algorithmic tasks. We demonstrate our model on algorithmic and geometric tasks with some degree of scale self-similarity: planar convex-hull, k-means clustering, Knapsack Problem and euclidean TSP. Our numerical results on these tasks reaffirm the fact that whenever the structure of the problem has scale invariance, exploiting it leads to improved generalization and computational complexity over non-recursive approaches. We have presented a novel neural architecture that can discover and exploit scale invariance in discrete algorithmic tasks, and can be trained with weak supervision. Our model learns how to split large inputs recursively, then learns how to solve each subproblem and finally how to merge partial solutions. The resulting parameter sharing across multiple scales yields improved generalization and sample complexity.Due to the generality of the DiCoNet , several very different problems have been tackled, some with large and others with weak scale invariance. In all cases, our inductive bias leads to better generalization and computational complexity. An interesting perspective is to relate our scale invariance with the growing paradigm of meta-learning; that is, to what extent one could supervise the generalization across problem sizes.In future work, we plan to extend the results of the TSP by increasing the number of splits J, by refining the supervised DiCoNet model with the non-differentiable TSP cost, and by exploring higher-order interactions using Graph Neural Networks defined over graph hierarchies BID17 . We also plan to experiment on other NP-hard combinatorial tasks.",1223,0.826,707,1.72984441301273,"We consider the learning algorithmic tasks by mere observation Rather studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping concentrate tasks amenable the principle divide study what are learning This principle creates a powerful inductive bias we leverage neural architectures defined by learning two scale- invariant atomic operations how split smaller sets merge two partially solved tasks Our model can trained weakly supervised environments namely by just observing in using a non-differentiable reward signal Moreover thanks the dynamic aspect our architecture incorporate the computational complexity as a regularization term optimized We demonstrate the flexibility the Divide- and-Conquer Network on several combinatorial and geometric tasks: convex hull knapsack euclidean TSP Thanks the dynamic programming nature our model show significant improvements terms generalization error computational complexity Algorithmic tasks described discrete input-output mappings defined over variable-sized inputs this ""black-box"" vision hides all the fundamental questions explain optimally solved generalized arbitrary inputs Indeed many tasks some degree scale invariance or meaning a mechanism solve it that somehow independent the input size This principle recursive solutions dynamic programming ubiquitous most areas discrete mathematics geometry graph In images audio signals invariance principles also critical success CNNs exploit both translation invariance scale separation with multilayer, localized convolutional operators In our scenario of discrete algorithmic tasks build divide provides parameter sharing across scales akin CNNs across spaceWhereas and define algorithms linear complexity attention mechanisms BID1 generally correspond notable exceptions BID0 . This can result a mismatch the intrinsic complexity required solve given Figure: Divide Conquer Network The split phase determined a dynamic neural network S �� splits each incoming set {X j+1,l , =m The merge phase carried another neural network M �� that combines two partial solutions into the coarser scale: Y j,m , see Section may impact its generalization performance Our motivation learning cannot 'complete these complexities match, start this quest first focusing problems for the intrinsic complexity well understoodOur Divide-and-Conquer NetworksDiCoNet ) contain two modules a split phase that applied dynamically in encoded; traces that binary tree finecoarse by progressively combining partial solutions; see Each these phases parametrized applied at enabling parameter sharing different scales leading good sample complexity generalisationIn attempt incorporate prior with only require weak supervision In particular consider two setups learning input-output pairs a non-differentiable reward signal Since our split block inherently discrete resort policy gradient to train the split parameters while the merge phase; see An important benefit our framework the architecture dynamically determined suggests using the computational complexity a regularization term As shown the experiments computational complexity generalisation error discrete algorithmic tasks We demonstrate our model algorithmic and geometric tasks some degree scale self-similarity: planar convex-hull, Knapsack Problem TSP Our numerical results on these tasks reaffirm whenever the structure has scale invariance exploiting computational complexity over We presented a novel neural architecture discover scale discrete algorithmic tasks can trained weak supervision Our model learns split large inputs recursively then learns solve each subproblem and finally merge partial solutions The resulting parameter sharing across multiple scales yields improved sample complexityDue the DiCoNet , several very different problems tackled some with large and others weak scale invariance In all cases our inductive bias leads better generalization computational complexity An interesting perspective relate our scale invariance the growing paradigm meta-learning; one could supervise across problem sizesIn future work extend the results the TSP by increasing splits J, by refining the supervised DiCoNet model with the non-differentiable TSP cost exploring using Graph Neural Networks defined over graph hierarchies BID17 . We also plan experiment on other NP-hard combinatorial tasks",0.01,0.5636586106112427
"Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\boldsymbol{\gamma}$ for expectation-based objectives $\mathbb{E}_{q_{\boldsymbol{\gamma}} (\boldsymbol{y})} [f (\boldsymbol{y}) ]$. Most existing methods either ($i$) suffer from high variance, seeking help from (often) complicated variance-reduction techniques; or ($ii$) they only apply to reparameterizable continuous random variables and employ a reparameterization trick. To address these limitations, we propose a General and One-sample (GO) gradient that ($i$) applies to many distributions associated with non-reparameterizable continuous {\em or} discrete random variables, and ($ii$) has the same low-variance as the reparameterization trick. We find that the GO gradient often works well in practice based on only one Monte Carlo sample (although one can of course use more samples if desired). Alongside the GO gradient, we develop a means of propagating the chain rule through distributions, yielding statistical back-propagation, coupling neural networks to common random variables. Neural networks, typically trained using back-propagation for parameter optimization, have recently demonstrated significant success across a wide range of applications. There has been interest in coupling neural networks with random variables, so as to embrace greater descriptive capacity. Recent examples of this include black-box variational inference (BBVI) BID17 BID33 BID29 BID11 BID32 BID31 Zhang et al., 2018) and generative adversarial networks (GANs) BID8 BID28 Zhao et al., 2016; BID1 BID20 . Unfortunately, efficiently backpropagating gradients through general distributions (random variables) remains a bottleneck. Most current methodology focuses on distributions with continuous random variables, for which the reparameterization trick may be readily applied BID17 BID9 .As an example, the aforementioned bottleneck greatly constrains the applicability of BBVI, by limiting variational approximations to reparameterizable distributions. This limitation excludes discrete random variables and many types of continuous ones. From the perspective of GAN, the need to employ reparameterization has constrained most applications to continuous observations. There are many forms of data that are more-naturally discrete.The fundamental problem associated with the aforementioned challenges is the need to efficiently calculate an unbiased low-variance gradient wrt parameters γ for an expectation objective of the form E qγ (y) [f (y)]1 . We are interested in general distributions q γ (y), for which the components of y may be either continuous or discrete. Typically the components of y have a hierarchical structure, and a subset of the components of y play a role in evaluating f (y).Unfortunately , classical methods for estimating gradients of E qγ (y) [f (y)] wrt γ have limitations. The REINFORCE gradient (Williams, 1992) , although generally applicable (e.g., for continuous and discrete random variables), exhibits high variance with Monte Carlo (MC) estimation of the expectation, forcing one to apply additional variance-reduction techniques. The reparameterization trick (Rep) BID38 BID17 BID33 works well, with as few as only one MC sample, but it is limited to continuous reparameterizable y. Many efforts have been devoted to improving these two formulations, as detailed in Section 6. However, none of these methods is characterized by generalization (applicable to general distributions) and efficiency (working well with as few as one MC sample).The key contributions of this work are based on the recognition that REINFORCE and Rep are seeking to solve the same objective, but in practice Rep yields lower-variance estimations, albeit for a narrower class of distributions. Recent work BID32 has made a connection between REINFORCE and Rep, recognizing that the former estimates a term the latter evaluates analytically. The high variance by which REINFORCE approximates this term manifests high variance in the gradient estimation. Extending these ideas, we make the following main contributions. (i) We propose a new General and One-sample (GO) gradient in Section 3, that principally generalizes Rep to many non-reparameterizable distributions and justifies two recent methods BID5 BID15 ; the ""One sample"" motivating the name GO is meant to highlight the low variance of the proposed method, although of course one may use more than one sample if desired. (ii) We find that the core of the GO gradient is something we term a variable-nabla, which can be interpreted as the gradient of a random variable wrt a parameter. (iii) Utilizing variablenablas to propagate the chain rule through distributions, we broaden the applicability of the GO gradient in Sections 4-5 and present statistical back-propagation, a statistical generalization of classic back-propagation BID36 . Through this generalization, we may couple neural networks to general random variables, and compute needed gradients with low variance. For expectation-based objectives, we propose a General and One-sample (GO) gradient that applies to continuous and discrete random variables. We further generalize the GO gradient to cases for which the underlying model is deep and has a marginal distribution corresponding to the latent variables of interest, and to cases for which the latent variables are hierarchical. The GO-gradient setup is demonstrated to yield the same low-variance estimation as the reparameterization trick, which is only applicable to reparameterizable continuous random variables. Alongside the GO gradient, we constitute a means of propagating the chain rule through distributions. Accordingly, we present statistical back-propagation, to flexibly integrate deep neural networks with general classes of random variables. A PROOF OF THEOREM 1We first prove (7) in the main manuscript, followed by its discrete counterpart, i.e., (8) in the main manuscript. Then, it is easy to verify Theorem 1.A.1 PROOF OF EQUATION FORMULA3 IN THE MAIN MANUSCRIPT Similar proof in one-dimension is also given in the supplemental materials of BID32 .We want to calculate DISPLAYFORM0 where y −v denotes y with y v excluded. Without loss of generality, we assume y v ∈ (−∞, ∞). DISPLAYFORM1 , and we have DISPLAYFORM2 where DISPLAYFORM3 , we then apply integration by parts (or partial integration) to get DISPLAYFORM4 With Q γ (∞) = 1 and Q γ (−∞) = 0, it's straightforward to verify that the first term is always zero for any Q γ (y v ), thus named the ""0"" term.",1354,0.689,774,1.7493540051679586,"Within many machine learning a fundamental problem concerns efficient calculation an unbiased gradient wrt parameters expectation-based objectives (} ] Most existing methods either ($i$ suffer high variance seeking help ( complicated variance-reduction techniques; they only apply reparameterizable continuous random variables employ To address these limitations a General and One-sample (GO gradient that ($ applies many distributions associated non-reparameterizable continuous {\em or has as the reparameterization trick We find the GO gradient often works practice based only one Monte Carlo samplealthough one of Alongside the GO gradient develop a means the chain rule distributions yielding coupling neural networks common random variables Neural networks typically trained using for parameter optimization recently demonstrated significant success across applications There interest coupling random variables so as embrace greater descriptive capacity Recent examples include black-box variational inferenceBBVI BID31 Zhang 2018) . Unfortunately efficiently gradients through general distributionsrandom variables remains Most current methodology focuses distributions continuous random variables for the reparameterization trick may readily BID17 BID9 .As the aforementioned bottleneck greatly BBVI by This limitation excludes discrete random variables many types continuous ones From GAN the need employ reparameterization constrained most applications continuous observations There many forms data more-naturally discreteThe fundamental problem associated the aforementioned challenges efficiently calculate an unbiased low-variance gradient wrt parameters � for an expectation objective E qγ (y [f (y)]1 We interested general distributions q �y for the components y may either continuous Typically the components y have a subset play evaluating fy).Unfortunately , classical methods estimating gradients E qγ [f wrt � have The REINFORCE gradient (Williams 1992 , although generally applicable ( for continuous and discrete random variables exhibits high variance Monte CarloMC estimation the expectation, forcing one apply The reparameterization trick (Rep) BID38 BID17 BID33 works well with as only one MC sample limited continuous reparameterizable y. Many efforts devoted these two formulations detailed Section However none characterized generalizationapplicable general distributions efficiencyworking well as few as one MC sample).The key contributions based REINFORCE Rep are seeking solve the same objective practice Rep yields albeit for distributions Recent work BID32 has made a connection REINFORCE Rep, recognizing former estimates a term the evaluates The high variance by REINFORCE approximates this term manifests high variance the gradient estimation Extending these ideas make the following main contributions (i We propose a new General and One-sample (GO) gradient Section that principally generalizes Rep to many non-reparameterizable distributions justifies two recent methods BID5 BID15 ; the ""One sample motivating the name GO meant highlight the low variance although of one if (ii We find the core the GO gradient something term a variable-nabla wrt (iii variablenablas propagate the chain rule through distributions we broaden the GO gradient Sections present, classic back-propagation BID36 . Through this generalization couple neural networks general random variables compute needed gradients with low variance For expectation-based objectives propose a General and One-sample (GO) gradient that applies continuous and discrete random variables We further generalize GO gradient cases for deep has a marginal distribution corresponding hierarchical The GO-gradient setup demonstrated to yield the same low-variance estimation the reparameterization trick only continuous random variables Alongside the GO gradient constitute a means the chain rule distributions Accordingly present to flexibly integrate deep neural networks general classes random variables THEOREM 1We first prove (7 in the main manuscript followed its discrete counterpart Then easy verify Theorem 1.A.1 PROOF EQUATION FORMULA3 IN Similar proof one-dimension is the supplemental materials BID32 .We want calculate DISPLAYFORM0 where y −v denotes y with y v excluded Without loss assume y v �� ( DISPLAYFORM1 , and we where , we then apply integration by partsor get With Q ��� ( straightforward verify the first term always zero fory v thus named",0.01,0.6133673373287405
"Quantum computers promise significant advantages over classical computers for a number of different applications. We show that the complete loss function landscape of a neural network can be represented as the quantum state output by a quantum computer. We demonstrate this explicitly for a binary neural network and, further, show how a quantum computer can train the network by manipulating this state using a well-known algorithm known as quantum amplitude amplification. We further show that with minor adaptation, this method can also represent the meta-loss landscape of a number of neural network architectures simultaneously. We search this meta-loss landscape with the same method to simultaneously train and design a binary neural network. Finding a suitable set of weights for a neural network has become one of the most studied problems of modern machine learning. It has presented a significant challenge to computer scientists for whom few successful alternatives to back-propagation are available. It can be difficult to explore very large search spaces efficiently and, worse, optimization may converge to a local minima far from global optimum BID2 . Understanding the cost function landscape is also hard, and choosing hyper-parameters and designing neural networks remains mostly a manual process. As Moore's law approaches its end, two new computing paradigms have been explored, neuromorphic and quantum computers. Quantum computing is based on quantum bits (or qbits) obeying the laws of quantum physics as opposed to the classical bits of today that are based on classical physics. Note that in physics the term classical is used to mean non-quantum and we use this terminology throughout. Quantum machine learning aims to find an advantage in applying quantum computing to machine learning. Current research into quantum machine learning falls into one of two catgeories. Some quantum algorithms promise a revolution in machine learning in theory, but contain many gaps in their implementation in practice. In contrast, others are more realistic in their method, but struggle to justify a place amongst the well-established methods of machine learning. In this paper, it is shown that a quantum computer can output a quantum state that represents the entire cost landscape for a given neural network. The method is shown to be versatile and even able to represent a meta-cost landscape of all possible hyperparameters and parameters. Applying it to the connectivities and weights of a binary neural network and simulating the quantum algorithm on a classical computer, we further show that this landscape state can be used for training and metatraining the binary neural network for a small toy problem using quantum amplitude amplification, a standard quantum algorithm. We show that quantum superposition can be used to represent many parameters of a neural network at once and efficiently encode entire loss landscapes in a quantum state using just a single run of a quantum circuit. We demonstrate this explicitly for both parameters and hyper-parameters of a BNN, and show that further processing of this state can lead to quantum advantage in training and metatraining. As a training method it possesses significant advantages as it is landscape-independent, has a quadratic speedup over a classical search of the same kind, and would be able to solve statistically neutral problems such as parity problems BID23 . It is not, however, without shortcomings. One potential criticism is the issue of over-fitting. Since our problem is so small, we chose to define a target state as one where the accuracy is 100% on the training set but this is rarely desirable in real machine learning. One solution may be to simply run the quantum algorithm and, upon finding a particular set of weights that represents an overfit, run the algorithm again but with a deselection of that particular set of weights. This can be done by simply changing the sign of the probability amplitude corresponding to that state during each iteration of the quantum amplitude amplification. A similar issue is that regular machine learning typically uses batch learning, whilst our method incorporates the entire dataset at once. This too can be fixed by altering our method to use a different batch of the data for each quantum amplitude amplification iteration. This works since no matter what batch we use, a good set of weights should still be amplified by the circuit. In fact, such an implementation is advantageous since it would allow us to use less qubits which in practical terms are limited in number in the near term. A significant limitation in our method is the requirement that the input is binary, and the poor scaling of the activation function. Both of these problems arise completely from our implementation of the sign function, which could either be improved or replaced entirely with a different binary activation function that could be implemented more efficiently on a quantum computer and would be compatible with non-binary input. There has been progress on creating effective non-linear activation functions by so-called repeat-until-success circuits BID1 ). An alternative approach would be to use floating point representations as in classical computing and the quantum equivalent of full-adders, but this would require an overhead in the number of qubits that would take us beyond the limit of classical simulation. Finally, we note that this method scales poorly compared to backpropagation and that the advantage only appears in like for like comparisons of unstructured classical/quantum searches. The cost function landscape is not unstructured and algorithms such as backpropagation take advantage of this. We conjecture that a quantum search method that applies quantum advantage to structured searches, if it exists, can be applied to the cost landscape in place of quantum amplitude amplification.Finding ways to harness quantum computers to aid classical machine learning methods in a meaningful way remains an open problem and we present the loss landscape state as a plausible candidate towards this goal. Whilst we used the example of quantum training, the most fruitful approach in the short term is to ask whether some property of the state can be used to glean useful information for classical machine learning methods. This might take the form of understanding the roughness of the landscape, identifying certain features, or even choosing an appropriate learning rate. Further work in investigating the relationship between the landscape as a quantum state and its features from a machine learning perspective would be a step forward in this direction.",1192,0.758,689,1.730043541364296,"Quantum computers promise significant advantages for We show the complete loss function landscape represented the quantum state output by We demonstrate this explicitly for a binary neural network and, further a quantum computer train manipulating this state using quantum amplitude amplification We further show with minor adaptation this method also represent the meta-loss landscape a number neural network simultaneously We search this meta-loss landscape the same method to simultaneously train design Finding a suitable set weights a neural network has It presented computer scientists for whom few successful alternatives It can explore very large search spaces efficiently, worse optimization may converge a local minima far global optimum BID2 . Understanding the cost function landscape also hard choosing hyper designing neural networks remains mostly As Moore's law approaches two new computing paradigms explored neuromorphic and quantum computers Quantum computing based qbits obeying as opposed today that based Note in physics term classical non we throughout Quantum machine learning aims find an advantage applying Current research into quantum machine learning falls two catgeories Some quantum algorithms promise a revolution in theory contain many gaps in In contrast others realistic their method struggle justify a place amongst the well-established methods machine learning In this paper it a quantum computer output represents the entire cost landscape The method shown versatile even able represent a meta-cost landscape all possible hyperparameters Applying it the connectivities weights a binary neural network and simulating the quantum algorithm on further this landscape state training metatraining for a small toy problem using quantum amplitude amplification a standard quantum algorithm We show quantum superposition represent many parameters at efficiently encode entire loss landscapes using just a single run a quantum circuit We demonstrate this explicitly for both parameters hyper- a BNN further processing this state quantum advantage training metatraining As a training method it possesses as landscapeindependent has a quadratic speedup over a classical search of would solve statistically neutral problems parity problems BID23 . It, without shortcomings One potential criticism the issue over-fitting Since our problem chose define a target state the accuracy on the training set but this rarely desirable real machine learning One solution may simply run the quantum algorithm, upon finding weights represents an overfit but a deselection This can changing the sign the probability amplitude corresponding that state during each iteration the quantum amplitude amplification A similar issue that regular machine learning typically batch learning whilst our method incorporates the entire dataset at This too fixed altering our method a different batch the data each quantum amplitude amplification iteration This works since no matter batch we a good set weights still amplified the circuit In fact such an implementation advantageous since less qubits which in practical terms limited in A significant limitation our method the input binary the poor scaling the activation function. Both arise completely our implementation the sign function could either improved entirely a different binary activation function on and would compatible non-binary input There progress creating effective non-linear activation functions by so repeatuntilsuccess circuits BID1 ). An alternative approach floating point representations in classical computing the quantum equivalent full-adders an overhead take us beyond classical simulation Finally note this method scales poorly compared the advantage only appears like for like comparisons of unstructured classical/quantum searches The cost function landscape not unstructured algorithms such take We conjecture a quantum search method applies quantum advantage structured searches if exists the cost landscape place quantum amplitude amplificationFinding ways harness quantum computers aid classical machine learning methods remains and present the loss landscape state towards Whilst used the example quantum training the most fruitful approach in ask some property glean for classical machine learning methods This might take understanding the roughness identifying certain features choosing an appropriate learning rate Further work in investigating the landscape as a quantum state its features from would step",0.01,0.5641659721558074
"Several recent works have developed methods for training classifiers that are certifiably robust against norm-bounded adversarial perturbations. These methods assume that all the adversarial transformations are equally important, which is seldom the case in real-world applications. We advocate for cost-sensitive robustness as the criteria for measuring the classifier's performance for tasks where some adversarial transformation are more important than others. We encode the potential harm of each adversarial transformation in a cost matrix, and propose a general objective function to adapt the robust training method of Wong & Kolter (2018) to optimize for cost-sensitive robustness. Our experiments on simple MNIST and CIFAR10 models with a variety of cost matrices show that the proposed approach can produce models with substantially reduced cost-sensitive robust error, while maintaining classification accuracy. Despite the exceptional performance of deep neural networks (DNNs) on various machine learning tasks such as malware detection BID24 , face recognition BID22 and autonomous driving BID2 , recent studies BID26 BID9 have shown that deep learning models are vulnerable to misclassifying inputs, known as adversarial examples, that are crafted with targeted but visually-imperceptible perturbations. While several defense mechanisms have been proposed and empirically demonstrated to be successful against existing particular attacks BID21 BID9 , new attacks BID3 BID27 BID1 are repeatedly found that circumvent such defenses. To end this arm race, recent works BID23 BID28 propose methods to certify examples to be robust against some specific norm-bounded adversarial perturbations for given inputs and to train models to optimize for certifiable robustness.However, all of the aforementioned methods aim at improving the overall robustness of the classifier. This means that the methods to improve robustness are designed to prevent seed examples in any class from being misclassified as any other class. Achieving such a goal (at least for some definitions of adversarial robustness) requires producing a perfect classifier, and has, unsurprisingly, remained elusive. Indeed, BID20 proved that if the metric probability space is concentrated, overall adversarial robustness is unattainable for any classifier with initial constant error.We argue that overall robustness may not be the appropriate criteria for measuring system performance in security-sensitive applications, since only certain kinds of adversarial misclassifications pose meaningful threats that provide value for potential adversaries. Whereas overall robustness places equal emphasis on every adversarial transformation, from a security perspective, only certain transformations matter. As a simple example, misclassifying a malicious program as benign results in more severe consequences than the reverse.In this paper, we propose a general method for adapting provable defenses against norm-bounded perturbations to take into account the potential harm of different adversarial class transformations. Inspired by cost-sensitive learning BID5 BID7 ) for non-adversarial contexts, we capture the impact of different adversarial class transformations using a cost matrix C, where each entry represents the cost of an adversary being able to take a natural example from the first class and perturb it so as to be misclassified by the model as the second class. Instead of reducing the overall robust error, our goal is to minimize the cost-weighted robust error (which we define for both binary and real-valued costs in C). The proposed method incorporates the specified cost matrix into the training objective function, which encourages stronger robustness guarantees on cost-sensitive class transformations, while maintaining the overall classification accuracy on the original inputs.Contributions. By encoding the consequences of different adversarial transformations into a cost matrix, we introduce the notion of cost-sensitive robustness (Section 3.1) as a metric to assess the expected performance of a classifier when facing adversarial examples. We propose an objective function for training a cost-sensitive robust classifier (Section 3.2). The proposed method is general in that it can incorporate any type of cost matrix, including both binary and real-valued. We demonstrate the effectiveness of the proposed cost-sensitive defense model for a variety of cost scenarios on two benchmark image classification datasets: MNIST (Section 4.1) and CIFAR10 (Section 4.2). Compared with the state-of-the-art overall robust defense model , our model achieves significant improvements in cost-sensitive robustness for different tasks, while maintaining approximately the same classification accuracy on both datasets.Notation. We use lower-case boldface letters such as x for vectors and capital boldface letters such as A to represent matrices. Let [m] be the index set {1, 2, . . . , m} and A ij be the (i, j)-th entry of matrix A. Denote the i-th natural basis vector, the all-ones vector and the identity matrix by e i , 1 and I respectively. For any vector x ∈ R d , the ∞ -norm of x is defined as DISPLAYFORM0 By focusing on overall robustness, previous robustness training methods expend a large fraction of the capacity of the network on unimportant transformations. We argue that for most scenarios, the actual harm caused by an adversarial transformation often varies depending on the seed and target class, so robust training methods should be designed to account for these differences. By incorporating a cost matrix into the training objective, we develop a general method for producing a cost-sensitive robust classifier. Our experimental results show that our cost-sensitive training method works across a variety of different types of cost matrices, so we believe it can be generalized to other cost matrix scenarios that would be found in realistic applications.There remains a large gap between the small models and limited attacker capabilities for which we can achieve certifiable robustness, and the complex models and unconstrained attacks that may be important in practice. The scalability of our techniques is limited to the toy models and simple attack norms for which certifiable robustness is currently feasible, so considerable process is needed before they could be applied to realistic scenarios. However, we hope that considering cost-sensitive robustness instead of overall robustness is a step towards achieving more realistic robustness goals.",1184,0.659,721,1.6421636615811372,"Several recent works developed methods training classifiers certifiably robust norm-bounded adversarial perturbations These methods assume all the adversarial transformations equally important which seldom We advocate cost-sensitive robustness as the criteria measuring the classifier's performance for tasks where some adversarial transformation are more We encode the potential harm each adversarial transformation a cost matrix propose a general objective function adapt the robust training method Wong & Kolter2018 optimize for cost-sensitive robustness Our experiments simple MNIST and CIFAR10 models with cost matrices the proposed approach models substantially reduced cost-sensitive robust error classification accuracy Despite the exceptional performance deep neural networks such malware detection BID24 , face recognition BID22 recent studies BID26 BID9 have vulnerable inputs known adversarial examples crafted targeted but visually-imperceptible perturbations While several defense mechanisms and empirically successful existing particular attacks BID21 BID9 , new attacks are repeatedly found that circumvent To end this arm race recent works BID23 BID28 propose methods certify examples to robust some specific norm-bounded adversarial perturbations for given inputs to train models optimize certifiable robustnessHowever all aim This means the methods to improve robustness designed prevent seed examples in any class misclassified Achieving (at some definitions adversarial robustness producing a perfect classifier has, unsurprisingly remained Indeed BID20 proved if the metric probability space concentrated overall adversarial robustness for any classifier with initial constant errorWe argue the appropriate criteria measuring system performance only certain kinds pose meaningful threats that provide value potential adversaries Whereas overall robustness places equal every adversarial transformation from only certain transformations matter As misclassifying a malicious program benign results the reverseIn propose a general method adapting provable defenses norm-bounded perturbations take different adversarial class transformations Inspired costsensitive learning BID5 BID7 ) for non-adversarial contexts capture different adversarial class transformations a cost matrix C, each entry an adversary being take a natural example perturb so misclassified Instead reducing the overall robust error our goal the cost-weighted robust errorwhich for both binary and real-valued costs C The proposed method incorporates the specified cost matrix the training objective function encourages stronger robustness guarantees cost-sensitive class transformations on the original inputsContributions. By encoding the consequences different adversarial transformations a cost matrix introduce cost-sensitive robustnessSection facing We propose an objective function training a cost-sensitive robust classifierSection The proposed method general incorporate cost matrix both binary real We demonstrate the proposed cost-sensitive defense model a variety cost scenarios on two benchmark image classification datasets MNISTSection CIFAR10 Compared state overall robust defense model , achieves cost-sensitive robustness different tasks while approximately the same classification accuracy on both datasetsNotation. We use lower-case boldface letters such x vectors capital boldface letters A represent matrices Let [m be the index set { . . . , m} and A ij be the (i, j)-th entry matrix A. Denote the i-th natural basis vector the all-ones vector by e i 1 I respectively For any vector x �� R d the �� -norm of defined DISPLAYFORM0 By focusing overall robustness previous robustness training methods expend the capacity unimportant transformations We argue for most scenarios the actual harm an adversarial transformation often varies the seed and target class so robust training methods designed By incorporating a cost matrix the training objective develop producing a cost-sensitive robust classifier Our experimental results our cost-sensitive training method across cost matrices so believe generalized other cost matrix scenarios would found realistic applicationsThere remains the small models limited attacker capabilities which achieve certifiable robustness unconstrained attacks may important practice The scalability our techniques limited the toy models simple attack norms for certifiable robustness currently feasible so considerable process they could realistic scenarios However we hope considering cost-sensitive robustness instead overall robustness achieving",0.01,0.3402557595101341
"Retinal prostheses for treating incurable blindness are designed to electrically stimulate surviving retinal neurons,  causing them to send artificial visual signals to the brain. However, electrical stimulation generally cannot precisely reproduce  normal patterns of neural activity in the retina. Therefore, an electrical stimulus must be selected that produces a neural response as close as possible to the desired response. This requires a technique for computing a distance between the desired response and the achievable response that is meaningful in terms of the visual signal being conveyed. Here we propose a method to learn such a metric on neural responses, directly from recorded light responses of a population of retinal ganglion cells (RGCs) in the primate retina. The learned metric produces a measure of similarity of RGC population responses that accurately reflects the similarity of the visual input. Using data from electrical stimulation experiments, we demonstrate that this metric may improve the performance of a prosthesis. An important application of neuroscience research is the development of electronic devices to replace the function of diseased or damaged neural circuits BID57 BID39 . Artificial vision has been a particularly challenging modality due to the richness of visual information, its diverse uses in perception and behavior, and the complexity of fabricating a device that can interface effectively with neural circuitry BID47 BID56 BID20 .The most advanced example is a retinal prosthesis: a device that replaces the function of neural circuitry in the retina lost to degenerative disease. Most of the computational work related to this application has focused on building encoding models that use the visual image to accurately predict the spiking activity of populations of retinal ganglion cells (RGCs), the output neurons of the retina that convey visual information to the brain. Leading models include linear models BID7 , probabilistic point-process models BID33 and recently proposed models employing rich nonlinearities BID30 BID2 BID41 .However, an accurate encoding model, although valuable, is insufficient. Any retinal prosthesiswhether based on electrical stimulation BID40 or optical stimulation BID6 BID3 -is limited in its ability to create arbitrary desired patterns of neural activity, due to inefficiencies or lack of specificity in the stimulation modality BID1 BID20 . Thus, a given stimulation system can only achieve a limited vocabulary of elicited spike patterns. Although a powerful and accurate encoding model might indicate that a particular spike pattern would be the natural biological response to the incident visual stimulus, the desired spike pattern might not reside within the feasible set of the stimulation device FIG0 ).Previous studies BID21 have addressed this problem by selecting the electrical stimulation which minimizes the number of unmatched spikes across cells -equivalent to the Hamming distance between two binary vectors. Even though a Hamming distance is easy to compute, this solution is not necessarily optimal. The goal of a prosthetics device should be to instead select an Real recorded spiking activity in a two populations of primate retinal ganglion cells (RGCs) demonstrating the lack of specificity from electrical stimulation. The electrodes are in blue and the stimulated electrode is shaded green. C. The target firing pattern r often lies outside the set of firing patterns achievable with the prosthesis. The goal of the learned metric is to define a distance measure to identify the nearest feasible electrical stimulationr. R denotes the set of all neural population responses.electrical stimulation pattern that produces a response as close as possible to the desired pattern of activity in terms of the elicited visual sensation ( FIG0 ). In lieu of measuring the visual sensation produced by a prosthetic, we instead posit that one may infer a distance metric based on the signal and noise properties of individual and populations of neurons BID43 BID33 BID11 . In contrast, previous approaches to spike metrics have focused on user-specified, parameteric functions BID52 BID51 or unsupervised techniques to cluster nearby spike patterns BID50 BID9 BID14 .In this work, we propose a neural response metric learned directly from the statistics and structure of firing patterns in neural populations, with the aim of using it to select optimal electrical stimulation patterns in a prosthesis device. In particular, we learn a neural response metric by applying ideas from metric learning to recordings of RGC populations in non-human primate retina. We demonstrate that the learned metric provides an intuitive, meaningful representation of the similarity between spike patterns in the RGC population, capturing the statistics of neural responses as well as similarity between visual images. Finally, we use this metric to select the optimal electrical stimulation pattern within the constraints of the electrical interface to a population of RGCs. The learned metric approach has two major potential implications for visual neuroscience. First, it provides a novel method to find ""symbols"" in the neural code of the retina that are similar in the sense that they indicate the presence of similar stimuli BID14 . Second, it has an application to retinal prosthesis technology, in which hardware constraints demand that the set of neural responses that can be generated with a device be used to effectively transmit useful visual information. For this application, a metric on responses that reflects visual stimulus similarity could be extremely useful.The present approach differs from previously proposed spike train metrics (reviewed in BID51 ). Previous approaches have employed unsupervised techniques to cluster nearby spike patterns BID14 BID34 BID15 or employed user-specified, paramteric approaches BID53 BID0 . In the case of single snapshots in time used here, the latter approach (Victor-Purpura metric) has only one degree of freedom which is a user-specified cost associated with moving spikes from one cell to another. In our proposed method, the relative importance of cell identity is learned directly from the statistics of population firing patterns.The present work is a stepping stone towards building an encoding algorithm for retinal prostheses. In this paper, we learn the metric using light evoked responses. However, we need to estimate this metric in a blind retina, which has no light evoked responses. The convolutional metric is adaptable to any RGC population by merely noting cell types and center locations. Thus a convolutional metric could be trained on multiple healthy retinas and applied to a blind retina. Preliminary results in this direction indicate that a convolutional metric trained on half of the cells in a retinal recording (training data) generalizes to the other half (validation data), yielding performance higher than a quadratic metric (and comparable to a convolutional metric) trained directly on the validation data.Additional techniques may also be helpful in extending our method to data involving many cells, temporal responses, and additional response structure. For example, using recurrent neural networks BID26 to embed responses may help compute distances between spiking patterns consisting of multiple time bins, perhaps of unequal length. Boosting BID13 may help combine multiple efficiently learned metrics for a smaller, spatially localized groups of cells. Other metrics may be developed to capture invariances learned by commonly used encoding models BID7 BID33 . Also, triplet mining techniques (i.e., choosing hard negatives), a commonly used trick in computer vision, may improve efficiency BID38 BID32 . Novel metrics could also be learned with additional structure in population responses, such as the highly structured correlated activity in RGCs Mastronarde (1983); BID17 . This noise correlation structure may be learnable using negative examples that destroy the noise correlations in data while preserving light response properties, by taking responses of different cells from different repeats of the stimulus.Note that the convolutional metric outperforms the quadratic metric at both global (ROC curves) and local (precision recall curves) scales. However, using current retinal prosthesis technologies, we might be able to resolve information only up to a particular scale. For current retinal prostheses, capturing global structure may be of greatest importance, because state-of-the-art technology has a relatively coarse vocabulary for stimulating RGCs (Humayun et al., 2012; BID58 ) (see also FIG0 ). Specifically, the ""nearest"" elicited firing pattern is ""far"" in terms of the corresponding visual stimulus ( FIG5 ) . In terms of the proposed learned metric, the nearest feasible firing pattern achievable by electrical stimulation in our experiments is at the 10th percentile of all possible firing patterns. In this context, the average closest stimulation pattern, expressed as a percentile of the learned metric distances, provides a valuable benchmark to measure the performance of a prosthesis and how that performance is affected by advances in the underlying hardware and software. In particular, the network employs knowledge of the receptive field locations and firing rates of individual cells but the network is independent of the number of cells in the retina. The latter point is achieved by embedding the responses of neurons into pathways grouped by cell type. In our experiments, we focus on 2 cell types (ON and OFF parasols), thus we employ a 2 channel pathway BID22 .The network receives as input the spiking activity of ON and OFF parasols and embeds these spike patterns as one-hot vectors placed at the spatial locations of each cell's receptive field. The resulting pattern of activations is summed across all cells in the ON and OFF populations, respectively, and passed through several convolutional layers of a network. Successive layers shrink the spatial activation size of the representation, while increasing the number of filter channels BID24 BID44 . The final embedding response vector has 1/16th number of pixels in the stimulus and represents the flattened representation of the last layer of the network.Let c denote the number of different cells. The RGC population response is a vector r ∈ {0, 1} c .• Represent responses as vectors over {+1, −1} withr = 2(r − 0.5).• Compute the scale for each cell as a function of the mean firing rate: DISPLAYFORM0 • Map each cell to its center location on a grid with spatial dimensions same as those of visual stimulus. Let M i be grid embedding on cell i. So, M i has zero for all positions except center of cell.• Perform a separable 5 × 5 convolution of stride 1 on each M i to get RF estimate of cell,M i .• Add the activation of cells of the same type to get the total activation for a given cell type.Hence, activation map for each cell type A i = ir i s iMi . Subsequent layers receive input as a two layered activation map corresponding to ON and OFF parasol cells.• The convolutional layers further combine information accross multiple cells, of different types. The details of different layers are shown in FIG6 and Normalization Batch normalization after every convolution Optimizer Adam BID23 ) (α = 0.01, β 1 = 0.9, β 2 = 0.999) Parameter updates 20,000Batch size 100 Weight initialization Xavier initialization BID16",2159,1.119,1314,1.643074581430746,"Retinal prostheses treating incurable blindness designed electrically surviving retinal neurons causing send artificial visual signals However electrical stimulation generally precisely reproduce normal patterns Therefore an electrical stimulus must selected as close This requires a technique for computing a distance the desired response the achievable response that meaningful the visual signal conveyed Here propose learn such metric on neural responses directly recorded light responses a population The learned metric produces similarity RGC population responses that accurately the visual input Using data electrical stimulation experiments demonstrate this metric improve An important application neuroscience research electronic devices replace the function BID57 BID39 . Artificial vision a particularly challenging modality due the richness diverse perception behavior fabricating a device interface effectively neural circuitry BID47 BID56 BID20 .The most advanced example: replaces the function neural circuitry lost Most the computational work related this application building encoding models the visual image accurately the spiking activity populations the output neurons convey Leading models include linear models BID7 , probabilistic point-process models recently proposed models employing rich nonlinearities BID30 BID2 BID41 .However an accurate encoding model although valuable insufficient Any retinal prosthesiswhether based electrical stimulation BID40 BID6 BID3 -is limited create arbitrary desired patterns due inefficiencies or . Thus a given stimulation system achieve a limited vocabulary elicited spike patterns Although a powerful and accurate encoding model might indicate a particular spike pattern would the natural biological response the incident visual stimulus reside the feasible set the stimulation device FIG0 ).Previous BID21 addressed selecting the electrical stimulation which unmatched spikes across cells -equivalent the Hamming distance two binary vectors Even a Hamming distance easy compute this solution necessarily The goal a prosthetics device should instead select an Real recorded spiking activity a two populations demonstrating the lack specificity from electrical stimulation The electrodes in blue the stimulated electrode shaded C. The target firing pattern r often lies outside firing achievable the prosthesis The goal the learned metric define a distance measure identify the nearest feasible electrical stimulationr R denotes the set all neural population responses.electrical stimulation pattern that produces as close terms the elicited visual sensation FIG0 In lieu measuring the visual sensation produced instead posit one infer distance metric the signal and noise properties individual and populations BID43 BID33 BID11 . In contrast previous approaches spike metrics user-specified, parameteric functions BID52 BID51 unsupervised techniques cluster nearby spike patterns a neural response metric learned directly the statistics structure firing neural populations using select optimal electrical stimulation patterns a prosthesis device In particular learn a neural response metric by applying ideas metric learning recordings RGC populations We demonstrate the learned metric provides the similarity spike patterns the RGC population capturing the statistics neural responses as similarity visual images Finally use this metric select the optimal electrical stimulation pattern within the constraints the electrical interface to a population RGCs The learned metric approach two major potential implications visual neuroscience First provides a novel method find the neural code the retina similar the sense indicate similar stimuli BID14 . Second an application retinal prosthesis technology in hardware constraints demand the set neural responses with used effectively transmit useful visual information For this application a metric on responses that reflects visual stimulus similarity could extremelyThe present approach differs previously proposed spike train metricsreviewed BID51 Previous approaches employed unsupervised techniques cluster nearby spike patterns BID14 BID34 BID15 or employed user-specified, paramteric approaches . In single snapshots time used here the latter approach (Victor-Purpura metric only one degree which a user-specified cost associated moving spikes one cell In our proposed method the relative importance cell identity learned directly the statistics population firing patternsThe present work a stepping stone building an encoding algorithm retinal prostheses In learn metric using light evoked responses However we need estimate this metric a blind retina has no light evoked responses The convolutional metric adaptable any RGC population by merely noting cell types center locations Thus a convolutional metric could trained multiple healthy retinas applied a blind retina in this direction a convolutional metric trained half a retinal recording (training data generalizes yielding performance higher aand comparable) directlyAdditional techniques extending our method data involving temporal responses additional response structure For example using recurrent neural networks BID26 embed responses may compute distances spiking patterns consisting multiple time bins perhaps of unequal length Boosting BID13 may combine multiple efficiently learned metrics a smaller, spatially localized groups Other metrics may developed capture invariances learned commonly used encoding models BID7 BID33 . Also triplet mining techniques choosing hard negatives a commonly used trick computer vision may improve efficiency BID38 BID32 . Novel metrics could also learned with additional structure population responses the highly structured correlated activity RGCs Mastronarde1983 BID17 . This noise correlation structure may learnable negative examples destroy data while light response properties by taking responses different cells different repeatsNote metric outperforms at both global (ROC curves (precision recall curves However using current retinal prosthesis technologies might resolve information only up a particular scale For current retinal prostheses capturing global structure may state a relatively coarse vocabulary stimulating RGCsHumayun BID58 ) FIG0 Specifically the ""nearest"" elicited firing pattern ""far terms the corresponding visual stimulus FIG5 In terms proposed learned metric the nearest feasible firing pattern achievable electrical stimulation our experiments at In this context the average closest stimulation pattern, expressed the learned metric distances provides a prosthesis and how advances the underlying hardware In particular the network employs knowledge the receptive field locations firing individual cells but the network independent The latter point achieved the responses neurons pathways grouped In our experiments focus 2 cell typesON and OFF parasols thus employ a 2 channel pathway BID22 .The network receives as embeds these spike patterns one-hot vectors placed the spatial locations The resulting pattern activations summed across the ON and OFF populations respectively passed a network Successive layers shrink the spatial activation size the representation filter channels BID24 BID44 . The final embedding response vector 1/16th number pixels the stimulus represents the flattened representationLet c different cells The RGC population response a vector r �� {0 c .• Represent responses as over {+1, −1} withr Compute the scale each cell the mean firing rate: DISPLAYFORM0 • Map its center location spatial dimensions same visual stimulus Let M i grid embedding on cell i. So M i has zero for all positions center cell.• Perform a separable 5 × 5 convolution stride on each M to RF estimate,M Add the activation ofHence, activation map A ir i s iMi Subsequent layers receive input a two layered activation map corresponding ON OFF parasol cells.• further combine information accross multiple cells of The details different layers shown FIG6 and Normalization Batch normalization after every convolution Optimizer Adam BID23 )α 1 Parameter updates 20,000Batch size 100 Weight initialization Xavier initialization BID16",0.01,0.34257670325439404
"We introduce a novel workflow, QCue, for providing textual stimulation during mind-mapping. Mind-mapping is a powerful tool whose intent is to allow one to externalize ideas and their relationships surrounding a central problem. The key challenge in mind-mapping is the difficulty in balancing the exploration of different aspects of the problem (breadth) with a detailed exploration of each of those aspects (depth). Our idea behind QCue is based on two mechanisms: (1) computer-generated automatic cues to stimulate the user to explore the breadth of topics based on the temporal and topological evolution of a mind-map and (2) user-elicited queries for helping the user explore the depth for a given topic. We present a two-phase study wherein the first phase provided insights that led to the development of our work-flow for stimulating the user through cues and queries. In the second phase, we present a between-subjects evaluation comparing QCue with a digital mind-mapping work-flow without computer intervention. Finally, we present an expert rater evaluation of the mind-maps created by users in conjunction with user feedback. Mind-maps are widely used for quick visual externalization of one's mental model around a central idea or problem. The underlying principle behind mind-mapping is to provide a means for associative thinking so as to foster the development of concepts that both explore different aspects around a given problem (breadth) and explore each of those aspects in a detailoriented manner (depth) [48] . The ideas in a mind-map spread out in a hierarchical/tree-like manner [35] , which allows for Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. the integration of diverse knowledge elements into a coherent pattern [8] to enable critical thinking and learning through making synaptic connections and divergent exploration [55, 74, 75, 41] . As a result, mind-maps are uniquely suitable for problem understanding/exploration prior to design conceptualization [8] . There are two main limitations in this work. First, a majority of the recruited users had little to no experience in mindmapping. While this allowed us to demonstrate the capability of QCue in guiding novices to explore problem spaces, we believe that including expert users in our future studies can help us (1) understand how differently they perform using this workflow and (2) lead to a richer discussion on how expertise can be transferred to our system toward better facilitation. Second, one of the key challenges we faced was the lack of robust methodology for determining the effect of cue-based stimulus during mind-mapping (how users may have used cues and queries without explicitly using them to add nodes). While we characterize it on the basis of the number of cues answered and the number of suggestions assimilated directly in the mind-map, we believe that a deeper qualitative study on the mind-mapping process can reveal valuable insights. We plan to conduct such an analysis as our immediate next step. Our intention in this research was to augment users' capability to discover more about a given problem during mind-mapping. For this, we introduced and investigated a new digital workflow (QCue) that provides cues to users based on the current state of the mind-map and also allows them to query suggestions. While our experiments demonstrated the potential of such mechanisms in stimulating idea exploration, the fundamental take-away is that such stimulation requires a balancing act between intervening the user's own line of thought with computer-generated cues and providing suggestions to the user's queries. Furthermore, our work shows the impact of computer-facilitated textual stimuli particularly for those with little practice in brainstorming-type tasks. We believe that QCue is only a step toward a much richer set of research directions in the domain of intelligent cognitive assistants.",848,0.505,488,1.7377049180327868,"We introduce a novel workflow QCue providing textual stimulation during Mind-mapping whose intent allow one externalize ideas their relationships surrounding a central problem The key challenge mind-mapping the difficulty balancing the exploration (breadth) a detailed explorationdepth Our idea behind QCue based two mechanisms (1) computer-generated automatic cues stimulate explore the breadth topics based the temporal and topological evolution a mind-map helping for We present wherein provided insights that our work-flow for stimulating the user through cues queries In present a between-subjects evaluation comparing QCue a digital mind-mapping work-flow without computer intervention Finally present an expert rater evaluation the mind-maps created users conjunction user feedback Mind-maps widely quick visual externalization one's mental model around a central idea The underlying principle mind-mapping provide associative thinking so foster concepts both explore aroundbreadth explore each a detailoriented mannerdepth [48 The ideas a mind-map spread out a hierarchical/tree-like manner [35 allows Permission make digital or hard copies this work is granted without fee provided copies bear this notice on Copyrights components owned than must honored Abstracting with credit permitted To copy otherwise or to post servers to lists requires prior specific permission a fee Request permissions the integration diverse knowledge elements [8 to enable critical thinking learning through making synaptic connections divergent exploration55 74 41 As mind-maps uniquely suitable problem understanding/exploration prior design conceptualization [8 There two main limitations in First a majority the recruited users had little mindmapping While this allowed demonstrate the capability QCue in guiding novices explore problem spaces believe including expert users our future studies (1 differently they perform using this workflow lead a richer discussion expertise transferred our system toward better facilitation Second one robust methodology cue-based stimulus during mind-mappinghow users may used cues queries without explicitly using to add nodes While characterize it on cues answered suggestions assimilated directly in the mind-map believe a deeper qualitative study We plan conduct such an analysis our immediate next step Our intention augment users' capability discover a given problem during mind-mapping For this, introduced and investigated a new digital workflow (QCue provides cues users based the mind-map also query suggestions While our experiments demonstrated such mechanisms stimulating idea exploration fundamental take such stimulation a balancing act intervening the user's own line computer-generated cues providing suggestions the user's queries Furthermore our work the impact computer-facilitated textual stimuli particularly those little practice brainstorming-type tasks We believe QCue only a step a much richer set research directions the domain intelligent cognitive assistants",0.01,0.5836864867859277
"The ability to detect when an input sample was not drawn from the training distribution is an important  desirable property of deep neural networks. In this paper, we show that a simple ensembling of first and second order deep feature statistics can be exploited to effectively differentiate in-distribution and out-of-distribution samples. Specifically, we observe that  the mean and standard deviation within feature maps  differs greatly between in-distribution and out-of-distribution samples. Based on this observation, we propose a simple and  efficient plug-and-play detection procedure that does not require re-training, pre-processing or changes to the model.   The proposed method outperforms the state-of-the-art by a large margin in all standard benchmarking tasks, while being much simpler to implement and execute. Notably, our method improves the true negative rate from 39.6% to 95.3% when 95% of in-distribution (CIFAR-100) are correctly detected using a DenseNet and the out-of-distribution dataset is TinyImageNet resize. The source code of our method will be made publicly available. In the past few years, deep neural networks (DNNs) BID6 have settled as the state-of-the art-techniques in many difficult tasks in a plurality of domains, such as image classification BID18 , speech recognition BID9 , and machine translation BID2 BID28 . This recent progress has been mainly due to their high accuracy and good generalization ability when dealing with realworld data. Unfortunately, DNNs are also highly confident when tested against unseen samples, even if the samples are vastly different from the ones employed during training BID12 . Moreover, several works have shown that such deep networks are easily fooled by minor perturbations to the input BID5 BID27 . Obtaining a calibrated confidence score from a deep neural network is a problem under continuous investigation BID12 ) and a major thread in artificial intelligence (AI) safety BID1 . In fact, knowing when the model is wrong or inaccurate has a direct impact in many production systems, such as self-driving cars, authentication and disease identification BID0 BID7 , to name a few. BID8 showed that despite producing significantly low classification errors, DNNs confidence scores are not faithful estimates of the true certainty. Their experiments confirmed that depth, width, weight decay, and batch normalization are the main reasons for overconfident scores. Moreover, they demonstrated that a simple and yet powerful method of temperature scaling in the softmax scores is an effective way to improve calibrate a DNNs confidence. While calibrating the classifier's output to represent a faithful likelihood from the training (in-distribution) data has effective solutions, the problem of detecting whether or not the samples are generated from a known distribution (out-of-distribution), is still an open problem BID12 .One straightforward approach to calibrate the classifier's confidence in order to detect samples whose distribution differs from the training samples distribution is to train a secondary classifier that digests both in-distribution (ID) and out-of-distribution (OOD) data so that anomalies are scored differently from ID samples, as performed in BID13 . Re-training a network, however, can be computationally intensive and may even be intractable, since the number of OOD samples is virtually infinite. Other solutions rely on training both classification and generative neural net- Table 1 : Summary comparison of the characteristics of recent related methods. Test complexity refers to the required number of passes over the network. Training data is the number of samples for which the methods were calibrated against (with all standing for the whole training set). AUROC is the area under receiver characteristic curve (detailed in Section 4). Performance shown is for DenseNet trained on CIFAR-100 and using TinyImageNet (resized) as OOD dataset. Deep neural networks trained to maximize classification performance in a given dataset are extremely adapted to said dataset. The statistics of activations throughout the network for samples from the training distribution (in-distribution) are remarkably stable. However, when a sample from a different distribution (out-of-distribution) is given to the network, its activation statistics depart greatly from those of in-distribution samples. Based on this observation, we propose a very simple yet efficient method to detect out-of-distribution samples. Our method is based on computing averages of low-order statistics at the batch normalization layers of the network, and then use them as features in a linear classifier. This procedure is much simpler and efficient than current stateof-the-art methods, and outperforms them by a large margin in the traditional ID/OOD fitting task (as proposed in previous works). We evaluated all methods in the challenging task of fitting on a single OOD dataset and testing on samples from other (unseen) datasets. In this harder scenario, our method generalizes well to unseen OOD datasets, outperforming ODIN by an even larger margin. Moreover, we show some preliminary results that even in the extreme case where no OOD samples are used for the training (unsupervised) we get reasonable performance. tuning is carried out on each pair of in-and out-of-distribution samples, which is the same procedure presented in BID22 and BID21 . For reproducibility, a grid search is employed considering T ∈ {1, 1000} and with 21 linearly spaced values between 0 and 0.004 plus [0.00005, 0.0005, 0.0011].",1106,0.633,643,1.7200622083981338,"The ability detect when an input sample was not drawn the training distribution an important desirable property In this paper a simple ensembling first and second order deep feature statistics exploited effectively differentiate indistribution samples Specifically observe within feature maps differs greatly indistributionof samples Based this observation does retraining preprocessing changes The proposed method outperforms the state by all standard benchmarking tasks while being simpler execute Notably our method improves the true negative rate from 95% indistribution (CIFAR-100 are correctly detected using a DenseNet and the out dataset TinyImageNet resize The source code our method will made publicly In deep neural networks BID6 settled as many difficult tasks a plurality image classification BID18 , This recent progress mainly their high accuracy good generalization ability when realworld data Unfortunately DNNs also highly confident when tested unseen samples even vastly employed during training BID12 . Moreover several works such deep networks easily fooled minor perturbations to the input BID5 BID27 . Obtaining a calibrated confidence score a deep neural network a problem under continuous investigation BID12 ) a major thread BID1 . In fact knowing when the model wrong inaccurate has in many production systems authentication and disease identification BID0 BID7 , to BID8 showed despite producing significantly low classification errors DNNs confidence scores are faithful estimates the true certainty. Their experiments confirmed depth, width weight decay batch normalization overconfident scores Moreover they demonstrated a simple and yet powerful method temperature scaling in the softmax scores calibrate a DNNs confidence. While calibrating the classifier's output represent a faithful likelihood from training (in-distribution has effective solutions detecting whether the samples generated a known distributionout BID12 .One straightforward approach calibrate order samples whose distribution differs the training samples distribution train digests both inIDOOD so anomalies scored differently ID samples performed Re-training a network, however computationally may even intractable since OOD samples virtually Other solutions rely training both classification generative neural net- Table : Summary comparison the characteristics recent related methods Test complexity refers passes over the network Training data the number samples for the methods calibrated against (with all standing for AUROC is the area under receiver characteristic curvedetailed Section Performance shown DenseNet trained CIFAR-100 using TinyImageNetresized OOD dataset Deep neural networks trained maximize classification performance extremely adapted said The statistics activations throughout the network for samples the training distributionin-distribution remarkably stable However when a sample from a different distributionout given the network its activation statistics depart greatly in samples Based this observation a very simple yet efficient method outdistribution samples Our method computing averages low-order statistics at the batch normalization layers use features This procedure much efficient current stateof-the-art methods outperforms them the traditional ID/OOD fitting taskas proposed previous works We evaluated all methods in the challenging task fitting on a single OOD dataset testing on samples other (unseen) datasets In this harder scenario our method generalizes well unseen OOD datasets outperforming ODIN Moreover we show some preliminary results even no OOD samples the training (unsupervised we get reasonable performance tuning is carried each pair inand outdistribution samples presented BID22 For reproducibility a grid search employed considering T �� { 1000 with 21 linearly spaced values between 0.004 plus [",0.01,0.5387344127083519
"Due to the sharp increase in the severity of the threat imposed by software vulnerabilities, the detection of vulnerabilities in binary code has become an important concern in the software industry, such as the embedded systems industry, and in the field of computer security. However, most of the work in binary code vulnerability detection has relied on handcrafted features which are manually chosen by a select few, knowledgeable domain experts. In this paper, we attempt to alleviate this severe binary vulnerability detection bottleneck by leveraging recent advances in deep learning representations and propose the Maximal Divergence Sequential Auto-Encoder. In particular, latent codes representing vulnerable and non-vulnerable binaries are encouraged to be maximally divergent, while still being able to maintain crucial information from the original binaries. We conducted extensive experiments to compare and contrast our proposed methods with the baselines, and the results show that our proposed methods outperform the baselines in all performance measures of interest. Software vulnerabilities are specific flaws or oversights in a piece of software that allow attackers to perform malicious acts including exposing or altering sensitive information, disrupting or destroying a system, or taking control of a computer system or program BID5 . Due to the ubiquity of computer software, the growth and the diversity in its development process, a great amount of computer software potentially includes software vulnerabilities. This fact makes the problem of software security vulnerability identification an important concern in the software industry and in the field of computer security. Although a great effort has been made by the security community, the severity of the threat from software vulnerabilities has gradually increased over the years. Numerous exist of examples and incidents in the past two decades in which software vulnerabilities have imposed significant damages to companies and individuals BID6 . For example, vulnerabilities in popular browser plugins have threatened the security and privacy of millions of Internet users (e.g., Adobe Flash Player (US-CERT 2015; Adobe Security Bulletin 2015) and Oracle Java (US-CERT 2013)), vulnerabilities in popular and fundamental open-source software have also threatened the security of thousands of companies and their customers around the globe (e.g., Heartbleed (Codenomicon 2014) and ShellShock (Symantec Security Response 2014).Software vulnerability detection (SVD) can be categorized into source code and binary code vulnerability detection. Source code vulnerability detection has been widely studied in a variety of works BID20 BID17 BID22 BID13 BID9 BID14 . Most of the previous work in source code vulnerability detection BID17 BID20 BID22 BID13 BID9 has been based on handcrafted features which are manually chosen by a limited number of domain experts. To mitigate the dependency on handcrafted features, the use of automatic features in SVD has been studied recently in BID4 BID14 BID15 . In particular , BID4 ; BID15 employed a Recurrent Neural Network (RNN) to transform sequences of code tokens to vectorial features, which are further fed to a separate classifier, while BID14 combined learning the vector representation and the training of the classifier in a deep network.Compared with source code vulnerability detection, binary code vulnerability detection is significantly more difficult because much of the syntactic and semantic information provided by high-level programming languages is lost during the compilation process. The existence of such syntactic and semantic information makes it easier to reason how data and inputs drive the paths of execution. Unfortunately , a software binary, such as proprietary binary code (with no access to source code) or embedded systems code, is generally all that is made available for code analysis (together perhaps with the processor architecture such as x86 etc.). The ability to detect the presence or absence of vulnerabilities in binary code, without getting access to source code, is therefore a major importance in the context of computer security. Some work has been proposed to detect vulnerabilities at the binary code level when source code is not available, notably work based on fuzzing, symbolic execution BID2 BID1 BID16 , or techniques using handcrafted features extracted from dynamic analysis BID8 BID3 BID21 . To the best of our knowledge, there has been no work studying the use of automatically extracted features for binary code vulnerability detection, though there has been some work using automatic features in conjunction with deep learning methods for malware detection, notably BID19 BID18 . It is worth noting that binary code vulnerability detection and malware detection are two different tasks. In particular, binary code vulnerability detection aims to detect specific flaws or oversights in binary code, while malware detection aims to detect if a given binary is malicious or not. The former is arguably harder in the sense that vulnerable and non-vulnerable binaries might be only slightly different, while there might be a clearer difference in general between malware and benign binaries.In addition, a significant constraint in research on binary code vulnerability detection is the lack of suitable binaries labeled as either vulnerable or non-vulnerable. Although we have some source code datasets for software vulnerability detection, to the best of our knowledge, there exists no large public binary dataset for the purpose of binary code vulnerability detection. The reason is that most source code in source code vulnerability detection datasets is not compilable due to incompleteness, and they have important pieces missing (e.g., variables, data types) and relevant libraries -making the code compilable take a large effort in fixing a vast volume of source code. This arises from the nature of the process that involves collecting and labeling source code wherein we start from security reports in CVE 1 and navigate through relevant websites to obtain code snippets of vulnerable and non-vulnerable source code.In this work, we leverage recent advances in deep learning to derive the automatic features of binary code for vulnerability detection. In particular, we view a given binary as a sequence of machine instructions and then use the theory of Variational Auto-Encoders (VAE) BID11 to develop the Maximal Divergence Sequential Auto-Encoder (MDSAE) that can work out representations of binary code in such a way that representations of vulnerable and nonvulnerable binaries are encouraged to be maximally different for vulnerability detection purposes, while still preserving crucial information inherent in the original binaries. In contrast to the original VAE wherein the data prior is kept fixed, we propose using two learnable Gaussian priors, one for each class. Based on the VAE principle, latent codes (i.e., data representations) are absorbed (or compressed) into the data prior distribution, we further propose maximizing a divergence (e.g., Wasserstein (WS) distance or Kullback-Leibler (KL) divergence) between these two priors to separate representations of vulnerable and non-vulnerable binaries. Our MDSAE can be used to produce data representations for another independent classifier (e.g., Support Vector Machine or Random Forest) or incorporated with a shallow feedforward neural network built on top of the latent codes for simultaneously training both the mechanism to generate data representations and the classifier. The former is named MDSAE-R and the latter is named MDSAE-C. We summarize our contributions in this paper as follows:• We propose a novel method named Maximal Divergence Sequential Auto-Encoder (MDSAE) that leverages recent advances in deep learning representation (namely, VAE) for binary code vulnerability detection.• One of our most significant contributions is to create a labeled dataset for use in binary code vulnerability detection. In particular, we used the source code in the published NDSS18 dataset used in BID14 and then extracted vulnerable and non-vulnerable functions. We developed a tool that can automatically detect the syntactical errors in a given piece of source code, fix them, and finally compile the fixed source code into binaries for various platforms (both Windows OS and Linux OS) and architectures (both x86 and x86-64 processors). Specifically, after preprocessing and filtering out identical functions from the NDSS18 source code dataset, we obtain 13, 000 functions of which 9, 000 are able to be fixed and compiled to binaries. By compiling the source code of these functions under the various platform and architecture options, we obtain 32, 281 binary functions including 17, 977 binaries for Windows and 14, 304 binaries for Linux.• We conducted extensive experiments on the NDSS18 binary dataset. The experimental results show that the two variants MDSAE-R and MDSAE-C outperform the baselines in all performance measures of interest. It is not surprising that MDSAE-C achieves higher predictive performances compared with MDSAE-R, but the fact that MDSAE-R achieves good predictive performances confirms our hypothesis of encouraging the separation in representations of data in different classes so that a simple linear classifier subsequently trained on these data representations can obtain good predictive results. The detection of vulnerabilities in binary code is an important problem in the software industry and in the field of computer security. In this paper, we leverage recent advances in deep learning representation to propose the Maximal Divergence Sequential Auto-Encoder for binary vulnerability detection. Specifically, latent codes representing vulnerable and non-vulnerable binaries are encouraged to be maximally different, while still being able to maintain crucial information from the original binaries. To address the issue of limited labelled public binary datasets for this problem and to facilitate research in the application of machine learning and deep learning to the domain of binary vulnerability detection, we have created a labelled binary software dataset. Furthermore, our developed tool and approach can be reused to create other high-quality binary datasets. We conducted extensive experiments to compare our proposed methods with the baselines. The experimental results show that our proposed methods outperform the baselines in all performance measures of interest.",1925,0.918,1145,1.6812227074235808,"Due the sharp increase the severity the threat imposed software vulnerabilities the detection binary code an important concern such the embedded systems industry However most binary code vulnerability detection relied handcrafted features which manually chosen a select few, knowledgeable domain experts In this paper attempt alleviate this severe binary vulnerability detection bottleneck recent advances deep learning representations propose the Maximal Divergence Sequential Auto-Encoder In particular, latent codes representing vulnerable and non-vulnerable binaries encouraged maximally divergent while still maintain crucial information from We conducted extensive experiments compare and our proposed methods the baselines, all performance measures of interest Software vulnerabilities specific flaws or oversights a piece allow perform malicious acts including exposing or altering disrupting taking program BID5 . Due computer software the growth and the diversity in its development process a great amount potentially includes software vulnerabilities This fact makes the problem software security vulnerability identification an concern and Although a great effort the security community the severity from software vulnerabilities gradually Numerous exist of examples and incidents software vulnerabilities imposed significant damages companies BID6 . For example vulnerabilities popular browser plugins threatened and ( (US-CERT 2015; Adobe Security Bulletin) Oracle Java vulnerabilities popular and fundamental open-source software companies aroundCodenomicon ShellShock (Symantec Security Response 2014).Software vulnerability detection ( can categorized source code Source code vulnerability detection has widely studied works BID20 BID17 BID22 BID13 BID9 BID14 . Most the previous work source code vulnerability detection BID17 BID20 BID22 BID13 BID9 has based handcrafted features which manually chosen a limited number domain experts To mitigate the dependency handcrafted features the use automatic features in SVD has studied recently BID4 BID14 BID15 . In particular , BID4 ; BID15 employed a Recurrent Neural Network transform sequences code tokens to vectorial features further fed a separate classifier while combined learning the vector representation the training in a deep networkCompared source code vulnerability detection significantly much provided The existence such syntactic and semantic information makes easier reason how data and inputs drive the paths execution Unfortunately , a software binary, such proprietary binary codewith no access embedded systems code generally all made code analysis (together perhaps the processor architecture such etc The ability detect vulnerabilities binary code without getting access therefore a major importance the context Some work has proposed detect vulnerabilities at the binary code level when source code notably work based fuzzing symbolic execution BID2 BID1 BID16 , techniques using handcrafted features extracted dynamic analysis To the studying automatically extracted features binary code vulnerability detection though using automatic features conjunction deep learning methods notably BID19 BID18 . It worth binary code vulnerability detection malware detection In particular binary code vulnerability detection aims specific flaws or oversights while malware detection if The former is arguably harder in vulnerable and non-vulnerable binaries might only different while there a clearer difference general between malwareIn addition a significant constraint research binary code vulnerability detection suitable binaries labeled either vulnerable Although we some source code datasets software vulnerability detection to the exists no large public binary dataset the purpose binary code vulnerability detection The reason most source code in source code vulnerability detection datasets compilable due incompleteness they important pieces ( variables data types relevant libraries -making take a large effort in fixing a vast volume This arises the nature the process that involves collecting labeling source code wherein we start security reports in CVE 1 navigate relevant websites obtain code snippets ofIn this work leverage recent advances deep learning derive the automatic features binary code for In particular we view a given binary machine instructions then use the theory Variational AutoEncoders BID11 develop the Maximal Divergence Sequential Auto-EncoderMDSAE that work out representations representations vulnerable and nonvulnerable binaries encouraged different for vulnerability detection purposes while still preserving crucial information inherent In contrast the original VAE wherein the data prior is kept fixed propose using two learnable Gaussian priors each class Based the VAE principle latent codes absorbed ( compressed prior distribution we further propose maximizing a divergence ( Wasserstein (WS distance or Kullback- these two priors separate representations vulnerable and non-vulnerable binaries Our MDSAE can produce data representations another independent classifier Support Random incorporated with a shallow feedforward neural network built the latent codes simultaneously training both the mechanism to The former is named MDSAE-R and We summarize our contributions as propose named Maximal Divergence Sequential Auto-EncoderMDSAE recent advances deep learning representation (namely, VAE for binary code vulnerability One create a labeled dataset use In particular we used the source code in the published NDSS18 dataset used BID14 then extracted vulnerable and non-vulnerable functions We developed automatically the syntactical errors a given piece fix finally compile the fixed source code binaries (both Windows OS architectures Specifically after preprocessing filtering identical functions the NDSS18 source code dataset obtain 13, 000 functions of 9 able fixed and compiled binaries By compiling these functions under the various platform and architecture options obtain 32, 281 binary functions including 17 977 binaries 14 304 binaries Linux.• We conducted extensive experiments the NDSS18 binary dataset The experimental results the two variants MDSAE-R outperform the baselines all performance measures interest It surprising MDSAE-C achieves higher predictive performances compared achieves good predictive performances confirms of encouraging the separation in representations data different classes so a simple linear classifier subsequently trained these data representations obtain The detection vulnerabilities binary code and In this paper leverage recent advances deep learning representation propose the Maximal Divergence Sequential Auto-Encoder binary vulnerability detection Specifically latent codes representing vulnerable and non-vulnerable binaries encouraged maximally different while still maintain crucial information from To address limited labelled public binary datasets for this problem and facilitate research the application the domain binary vulnerability detection a labelled binary software dataset Furthermore our developed tool and approach can reused other high-quality binary datasets We conducted extensive experiments compare our proposed methods the baselines. The experimental results our proposed methods outperform the baselines all performance measures interest",0.01,0.43977477662643494
"Modern neural architectures critically rely on attention for mapping structured inputs to sequences. In this paper we show that prevalent attention architectures do not adequately model the dependence among the attention and output tokens across a predicted sequence.
 We present an alternative architecture called  Posterior Attention Models that after a principled factorization of the full joint distribution of the attention and output variables, proposes two major changes.   First, the position where attention is marginalized is changed from the input to the output. Second, the attention propagated to the next decoding stage is a posterior attention distribution conditioned on the output. Empirically on five translation and two morphological inflection tasks the proposed posterior attention models yield better BLEU score and alignment accuracy than existing attention models. Attention is a critical module of modern neural models for sequence to sequence learning as applied to tasks like translation, grammar error correction, morphological inflection, and speech to text conversion. Attention specifies what part of the input is relevant for each output. Many variants of attention have been proposed including soft BID1 BID14 , sparse BID15 , local BID14 , hard (Xu et al., 2015; Zaremba & Sutskever, 2015) , monotonic hard (Yu et al., 2016; BID0 , hard non-monotonic (Wu et al., 2018; , and variational BID6 , The most prevalent of these is soft attention that computes attention for each output as a multinomial distribution over the input states. The multinomial probabilities serve as weights, and an attention weighted sum of input states serves as relevant context for the output and subsequent attention. Soft attention is end to end differentiable, easy to implement, and hence widely popular. Hard attention and sparse attentions are difficult to implement and not popularly used.In this paper we revisit the statistical soundness of the way soft attention and other variants capture the dependence between attention and output variables, and among multiple attention variables along the length of the sequence. Our investigation leads to a more principled model that we call the Posterior Attention Model (PAM). We start with an explicit joint distribution of all output and attention variables in a predicted sequence. We then propose a tractable approximation that retains the advantages of forward dependence and token-level decomposition and thus leads to efficient training and inference. The computations performed at each decode step has two important differences with existing models. First, at each decoding step the probability of the output token is a mixture of output probability for each attention. In contrast, existing models take a mixture of the input, and compute a single output distribution from this diffused mixed input. We show that our direct coupling of output and attention gives the benefit of hard attention without its computational challenges. Second, we introduce the notion of a posterior attention distribution, that is, the attention distribution conditioned on the current output. We show that it is both statistically sounder and more accurate to condition subsequent attention on the output corrected posterior attention, rather than the output independent prior attention as in existing models.We evaluate the posterior attention model on five translation tasks and two morphological inflection tasks. We show that posterior attention provides improved BLEU score, higher alignment accuracy, and better input coverage. We also empirically analyze the reasons behind the improved performance of the posterior attention model. We discover that the entropy of posterior attention is much lower than entropy of soft attention. This is a significant finding that challenges the current practice of computing attention distribution without considering the output token. The running time overhead of posterior attention is only 40% over existing soft-attention. We show in this paper that none of the existing attention models adequately model the dependence of the output and attention along the length of the output for general sequence prediction tasks. We propose a factorization of the joint distribution, and develop practical approximations that allows the joint distribution to decompose over output tokens, much like in existing attention. Our more principled probabilistic joint modeling of the dependency structure leads to three important differences. First, the output token distribution is obtained by aggregating predictions across all attention. Second, the concept of conditioning attention on the current output i.e. a posterior attention for inferring the next output becomes important. Our experiments show that it is sounder, more meaningful and more accurate to condition subsequent attention distribution on the posterior attention. Thirdly, via directly exposing attention coupling, we have a principled way to directly incorporate task-specific structural biases and prior knowledge into attention. We experimented with some simple biases and found boosts in related tasks. Our work opens avenues for future work in scaling these techniques to large-scale models and multi-headed attention. Another promising line is to incorporate more complex biases like phrasal structure or image segments into joint attention models.",943,0.625,546,1.7271062271062272,"Modern neural architectures critically rely attention mapping structured inputs sequences In prevalent attention architectures do adequately model among the attention and output tokens across a predicted sequence We present called Posterior Attention Models after a principled factorization the full joint distribution the attention and output variables proposes two major changes First the position where attention marginalized changed the input Second the attention propagated the next decoding stage a posterior attention distribution conditioned. on five translation and two morphological inflection tasks the proposed posterior attention models yield better BLEU score and alignment accuracy Attention is a critical module modern neural models sequence to as applied tasks translation grammar error correction morphological inflection speech to text conversion Attention specifies what part relevant Many variants attention have including soft BID1 BID14 , hard (Xu Sutskever hard (Yu BID0 hard non 2018 , The most prevalent soft attention that computes each output as The multinomial probabilities serve weights an attention weighted sum input states serves relevant context and subsequent attention Soft attention end to differentiable easy hence widely popular Hard attention sparse attentions difficult implement not popularlyIn revisit the statistical soundness the way soft attention other variants capture the dependence output variables among along Our investigation leads a more principled model the Posterior Attention Model We start an explicit joint distribution all output and attention variables a predicted sequence We then propose a tractable approximation retains forward dependence token-level decomposition leads efficient training The computations each decode step has with existing models First at each decoding step probability token a mixture output probability for each attention In contrast existing models take a mixture the input compute this diffused mixed input We show our direct coupling output attention gives the benefit hard attention without its computational challenges Second introduce a posterior attention distribution conditioned the current output We show it both statistically sounder condition subsequent attention the output corrected posterior attention independent prior as existing modelsWe evaluate five translation tasks We show posterior attention provides improved BLEU score higher alignment accuracy better input coverage We also empirically analyze the posterior attention model We discover the entropy posterior attention entropy soft attention This a significant finding challenges computing attention distribution without considering the output token The running time overhead posterior attention over existing soft-attention. We show none the existing attention models adequately the output and attention along for general sequence prediction tasks We propose the joint distribution develop allows decompose output tokens much existing attention. Our more principled probabilistic joint modeling the dependency structure leads three important differences First the output token distribution obtained predictions across all attention. Second the concept conditioning attention the current output for becomes Our experiments it sounder meaningful condition subsequent attention distribution the posterior attention. Thirdly via directly exposing attention coupling a principled way directly incorporate prior knowledge attention We experimented some simple biases boosts related tasks Our work opens avenues scaling these techniques multi-headed attention Another promising line incorporate more complex biases like phrasal structure image segments joint attention models",0.01,0.5566819534958569
"The growing interest to implement Deep Neural Networks (DNNs) on resource-bound hardware has motivated innovation of compression algorithms. Using these algorithms, DNN model sizes can be substantially reduced, with little to no accuracy degradation. This is achieved by either eliminating components from the model, or penalizing complexity during training. While both approaches demonstrate considerable compressions, the former often ignores the loss function during compression while the later produces unpredictable compressions. In this paper, we propose a technique that directly minimizes both the model complexity and the changes in the loss function. In this technique, we formulate compression as a constrained optimization problem, and then present a solution for it. We will show that using this technique, we can achieve competitive results. Deep Neural Networks have been rapidly improving in many classification tasks, even surpassing human accuracy for some problems BID12 . This high accuracy, however, is obtained by employing wider BID15 or deeper BID4 networks. Some prominent networks today even surpass 100 layers, store hundreds of millions of parameters, and require billions of operations per input sample BID4 ; BID13 . Such large networks are not well-suited for resource-bound, embedded and mobile platforms which are dominating the consumer market. This mismatch between computational requirements and available resources has motivated efforts to compress DNN models.Compression techniques exploit the redundancy inherent to neural networks that emerges due to the considerable number of parameters in them. These many parameters help learn highly informative features during training. However, they simultaneously learn multitudes of unnecessary, ineffectual ones. BID3 reduces these redundancies by pruning the network and quantizing the remaining parameters. Using these techniques, they were able to reduce the model size by more than an order of magnitude. Their success inspired other methodical approaches such as the soft weight-sharing BID14 . This method encodes model parameters using Bayesian prior and then penalizes this prior during training. As a result, it performs both pruning and quantization simultaneously and achieves superior compressions with negligible loss in accuracy.In this work, we take a similar, integrated approach with the twist that we directly minimize the complexity. Unlike soft weight-sharing, however, we encode the parameters using the k-means objective which imposes less computations. We further apply a hard constraint on the training loss to maintain sufficient accuracy. Such a constraint takes advantage of the fact that we have already obtained some information about the loss function during training. We then present a straightforward solution for this constrained optimization problem. Our solution iteratively minimizes the k-means objective, while satisfying the loss constraint. Consequently, it can compress the model progressively where the compression rate can be adjusted. Finally, we test the proposed technique on three popular datasets and show that this method can achieve state-of-the-art compression with minimal loss of accuracy.",553,0.433,319,1.7335423197492164,"The growing interest to implement Deep Neural Networks resource-bound hardware motivated innovation of compression algorithms Using these algorithms DNN model sizes substantially little This achieved either eliminating components penalizing complexity during training While both approaches demonstrate considerable compressions former often ignores the loss function during while later produces In directly both the model complexity the changes In this technique formulate compression a constrained optimization problem present We show using competitive results Deep Neural Networks have rapidly many classification tasks even human accuracy some problems BID12 . This high accuracy however obtained employing wider BID15 or Some prominent networks today even surpass 100 layers store parameters require operations input sample BID4 ; BID13 Such large networks well resource-bound, embedded and mobile platforms which dominating This mismatch computational requirements motivated efforts compress DNN modelsCompression techniques exploit the redundancy emerges parameters them These many parameters help learn highly informative features during However they simultaneously learn multitudes unnecessary, ineffectual ones BID3 reduces these redundancies pruning quantizing the remaining parameters Using reduce the model size Their success inspired other methodical approaches such the soft weight-sharing BID14 . This method encodes model parameters prior and then penalizes this prior during As performs both pruning quantization simultaneously achieves superior compressions accuracyIn take a similar, integrated approach the twist that directly minimize. Unlike soft weight-sharing however we encode the parameters which imposes less computations We further apply a hard constraint the training loss maintain sufficient accuracy Such a constraint takes advantage already obtained the loss function during training We then present a straightforward solution this constrained optimization problem Our solution iteratively minimizes satisfying the loss constraint can compress the model progressively where adjusted Finally test the proposed technique three popular datasets state compression accuracy",0.0,0.5730805520812765
"Deep neural networks are able to solve tasks across a variety of domains and modalities of data. Despite many empirical successes, we lack the ability to clearly understand and interpret the learned mechanisms that contribute to such effective behaviors and more critically, failure modes. In this work, we present a general method for visualizing an arbitrary neural network's inner mechanisms and their power and limitations. Our dataset-centric method produces visualizations of how a trained network attends to components of its inputs. The computed ""attention masks"" support improved interpretability by highlighting which input attributes are critical in determining output. We demonstrate the effectiveness of our framework on a variety of deep neural network architectures in domains from computer vision and natural language processing. The primary contribution of our approach is an interpretable visualization of attention that provides unique insights into the network's underlying decision-making process irrespective of the data modality. Machine-learning systems are ubiquitous, even in safety-critical areas. Trained models used in self-driving cars, healthcare, and environmental science must not only strive to be error free but, in the face of failures, must be amenable to rapid diagnosis and recovery. This trend toward realworld applications is largely being driven by recent advances in the area of deep learning. Deep neural networks have achieved state-of-the-art performance on fundamental domains such as image classification BID15 , language modeling BID2 BID20 , and reinforcement learning from raw pixels BID22 . Unlike traditional linear models, deep neural networks offer the significant advantage of being able to learn their own feature representation for the completion of a given task. While learning such a representation removes the need for manual feature engineering and generally boosts performance, the resulting models are often hard to interpret, making it significantly more difficult to assign credit (or blame) to the model's behaviors. The use of deep learning models in increasingly important application areas underscores the need for techniques to gain insight into their failure modes, limitations, and decision-making mechanisms.Substantial prior work investigates methods for increasing interpretability of these systems. One body of work focuses on visualizing various aspects of networks or their relationship to each datum they take as input BID33 ; BID35 . Other work investigates algorithms for eliciting an explanation from trained machine-learning systems for each decision they make BID26 ; BID0 ; BID27 . A third line of work, of which our method is most aligned, seeks to capture and understand what networks focus on and what they ignore through attention mechanisms.Attention-based approaches focus on network architectures that specifically attend to regions of their input space. These ""explicit"" attention mechanisms were developed primarily to improve network behavior, but additionally offer increased interpretability of network decision making through highlighting key attributes of the input data BID30 BID12 BID25 BID16 . Crucially, these explicit attention mechanisms act as filters on the input. As such, the filtered components of the input could be replaced with reasonably generated noise without dramatically affecting the final network output. The ability to selectively replace irrelevant components of the input space is a direct consequence of the explicit attention mechanism. The insight at the heart of the present work is that it is possible to evaluate the property of ""selective replaceability"" to better understand a network that lacks any explicit attention mechanism. An architecture without explicit attention may still depend more on specific facets of its input data when constructing its learned, internal representation, resulting in a ""latent"" attention mechanism.In this work, we propose a novel approach for indirectly measuring latent attention mechanisms in arbitrary neural networks using the notion of selective replaceability. Concretely, we learn an auxiliary, ""Latent Attention Network"" (LAN) , that consumes an input data sample and generates a corresponding mask (of the same shape) indicating the degree to which each of the input's components are replaceable with noise. We train this LAN by corrupting the inputs to a pre-trained network according to generated LAN masks and observing the resulting corrupted outputs. We define a loss function that trades off maximizing the corruption of the input while minimizing the deviation between the outputs generated by the pre-trained network using the true and corrupted inputs, independently. The resultant LAN masks must learn to identify the components of the input data that are most critical to producing the existing network's output (i.e. those regions that are given the most attention by the existing network.)We empirically demonstrate that the LAN framework can provide unique insights into the inner workings of various pre-trained networks. Specifically, we show that classifiers trained on a Translated MNIST domain learn a two-stage process of first localizing a digit within the image before determining its class. We use this interpretation to predict regions on the screen where digits are less likely to be properly classified. Additionally, we use our framework to visualize the latent attention mechanisms of classifiers on both image classification (to learn the visual features most important to the network's prediction), and natural language document classification domains (to identify the words most relevant to certain output classes). Finally, we examine techniques for generating attention masks for specific samples, illustrating the capability of our approach to highlight salient features in individual members of a dataset. As deep neural networks continue to find application to a growing collection of tasks, understanding their decision-making processes becomes increasingly important. Furthermore, as this space of tasks grows to include areas where there is a small margin for error, the ability to explore and diagnose problems within erroneous models becomes crucial.In this work, we proposed Latent Attention Networks as a framework for capturing the latent attention mechanisms of arbitrary neural networks that draws parallels between noise-based input corruption and attention. We have shown that the analysis of these attention measurements can effectively diagnose failure modes in pre-trained networks and provide unique perspectives on the mechanism by which arbitrary networks perform their designated tasks.We believe there are several interesting research directions that arise from our framework. First, there are interesting parallels between this work and the popular Generative Adversarial Networks BID9 . It may be possible to simultaneously train F and A as adversaries. Since both F and A are differentiable, one could potentially exploit this property and use A to encourage a specific attention mechanism on F , speeding up learning in challenging domains and otherwise allowing for novel interactions between deep networks. Furthermore, we explored two types of noise for input corruption: η const and η boot . It may be possible to make the process of generating noise a part of the network itself by learning a nonlinear transformation and applying it to some standard variety of noise (such as Normal or Uniform). Since our method depends on being able to sample noise that is similar to the ""background noise"" of the domain, better mechanisms for capturing noise could potentially enhance the LAN's ability to pick out regions of attention and eliminate the need for choosing a specific type of noise at design time. Doing so would allow the LAN to pick up more specific features of the input space that are relevant to the decision-making process of arbitrary classifier networks.In the following experiment subsections we describe network architectures by sequentially listing their layers using an abbreviated notation: DISPLAYFORM0 for convolutional, convolutional-transpose and fully connected layers respectively. In all network architectures, -ReLU denotes the leaky-ReLU BID18 .We now describe each experiment in greater detail.",1426,0.776,834,1.709832134292566,"Deep neural networks solve tasks across modalities of data Despite many empirical successes we lack clearly understand the learned mechanisms such effective behaviors more critically failure modes In this work an arbitrary neural network's inner mechanisms their power limitations Our dataset-centric method produces a trained network attends components The computed ""attention masks"" support improved interpretability highlighting which input attributes critical output We demonstrate our framework deep domains The primary contribution our approach an interpretable visualization attention that irrespective the data modality Machine-learning systems ubiquitous even Trained models used healthcare environmental science must not strive error, failures amenable rapid diagnosis recovery This trend toward realworld applications largely being recent advances Deep neural networks achieved state fundamental domains image classification BID15 , language modeling from raw pixels Unlike traditional linear models offer the significant advantage their own feature representation for the completion While learning such a representation removes manual feature engineering generally boosts the resulting models hard interpret making significantly assign credit ( the model's behaviors The use deep learning models increasingly important application areas underscores techniques gain their failure modes limitationsSubstantial prior investigates methods increasing interpretability these systems One body focuses visualizing various aspects networks or their relationship each datum they take as BID33 ; Other work investigates algorithms eliciting an explanation trained machine-learning systems each decision they BID26 ; BID0 ; A third line work of our method most aligned seeks capture what networks focus ignore through attention mechanismsAttention network architectures specifically attend regions their input space These ""explicit"" attention mechanisms primarily network behavior additionally offer increased interpretability network decision through highlighting key attributes the input BID30 BID12 BID25 BID16 . Crucially these explicit attention mechanisms act filters. As such the filtered components could replaced reasonably generated noise without dramatically the final network output The ability selectively replace irrelevant components the input space the explicit attention mechanism The insight at the present work evaluate the property ""selective replaceability to better a network lacks any explicit attention mechanism An architecture without explicit attention may still depend more specific facets its input data when constructing its learned, internal representation resulting a ""latent"" attention mechanismIn indirectly arbitrary neural networks the notion selective replaceability Concretely learn an auxiliary, ""Latent Attention NetworkLAN , consumes an input data sample a corresponding maskof indicating each replaceable noise We train this LAN by corrupting the inputs according generated LAN masks observing the resulting corrupted outputs We define a loss function that trades maximizing the corruption while generated using the true and corrupted inputs independently The resultant LAN masks must learn identify the input data most critical producing the existing network's output given the existing network.)We empirically demonstrate the LAN framework unique insights various pre-trained networks Specifically show classifiers trained a Translated MNIST domain learn first localizing a digit within before determining We use this interpretation predict regions on the screen digits less properly classified Additionally use our framework visualize the latent attention mechanisms classifiers on both image classificationto the visual features most the network's prediction natural language document classification domains identify certain output classes Finally examine techniques generating attention masks specific samples illustrating the capability highlight individual members As deep neural networks continue find application to a growing collection understanding becomes Furthermore as this space of tasks to areas a small margin explore diagnose problems within erroneous models crucialIn proposed Latent Attention Networks capturing the latent attention mechanisms arbitrary neural networks draws parallels noise-based input corruption attention. We shown the analysis these attention measurements effectively diagnose failure modes pre-trained networks provide unique perspectives arbitrary networks perform their designated tasksWe believe there several interesting research directions arise our framework First interesting parallels this work the popular Generative Adversarial Networks BID9 . It may possible simultaneously train F and as adversaries Since both F and differentiable one potentially exploit A encourage a specific attention mechanism on , speeding learning challenging domains otherwise allowing novel interactions deep networks Furthermore explored two types noise for input corruption �� const and �� boot It may possible the process generating noise a part the network itself by learning some standard variety ( Normal Uniform Since our method depends being sample noise that similar the domain better mechanisms capturing could potentially enhance the LAN's ability pick regions attention eliminate choosing at design time Doing the LAN pick more specific features the input space relevant arbitrary classifier networksIn the following experiment subsections network architectures by sequentially listing their layers using DISPLAYFORM0 for respectively In all network architectures -ReLU denotes leakyReLU BID18 .We now describe each experiment",0.01,0.5126690826918483
"The design of small molecules with bespoke properties is of central importance to drug discovery.   However significant challenges yet remain for computational methods, despite recent advances such as deep recurrent networks and reinforcement learning strategies for sequence generation, and it can be difficult to compare results across different works.   This work proposes 19 benchmarks selected by subject experts, expands smaller datasets previously used to approximately 1.1 million training molecules, and explores how to apply new reinforcement learning techniques effectively for molecular design.   The benchmarks here, built as OpenAI Gym environments, will be open-sourced to encourage innovation in molecular design algorithms and to enable usage by those without a background in chemistry.   Finally, this work explores recent development in reinforcement-learning methods with excellent sample complexity (the A2C and PPO algorithms) and investigates their behavior in molecular generation, demonstrating significant performance gains compared to standard reinforcement learning techniques. Novel drugs are developed using design -make -test cycles: molecules are designed, synthesized in the laboratory, and then tested for their biological effect. The insights gained from these tests then inform the design for the next iteration. The objective of de novo design methodologies is to perform this cycle with computational methods BID4 BID29 . The test phase was the first to be automated, using the broad categorization of machine learning models known as quantitative structure-activity/property relationships (QSAR/QSPR) to predict the activity of a molecule against a certain biological target, or physicochemical properties. To make virtual molecules, symbolic approaches based on graph rewriting have been used, which are domain-specific and rely on extensive hand-engineering by experts. To optimize the properties of a molecule, for example its activity against a biological target (design), global optimization approaches such as evolutionary algorithms or ant colony optimization have been used BID4 BID29 . Symbolic approaches have been highlighted as either generating unrealistic molecules that would be difficult to synthesize, or for being too conservative, and therefore not sufficiently exploring the space of tractable molecules BID29 BID2 .Recently , generative models have been proposed to learn the distribution of real druglike molecules from data, and then to generate chemical structures that are appropriate for the application domain BID36 . Interestingly , the generation of molecules is related to natural language generation (NLG) . Two classic problems of NLG -preserving coherent long-range dependencies, and syntactic and semantic correctness -directly map to molecules. Current investigations draw heavily from tools developed for language tasks, including variational autoencoders (VAE) BID12 BID18 , recurrent neural network (RNN) models BID32 BID17 BID24 , generative adversarial networks (GAN) BID15 and Monte Carlo Tree Search (MCTS) BID38 .This work seeks to consolidate the growing body of recurrent models for molecular design that employ reinforcement learning. Here, we suggest a set of 19 benchmarks of relevance to de novo design. Furthermore, an implementation of these benchmarks as an OpenAI Gym is provided to the community to spur further innovation. Finally, we demonstrate state-of-the-art performance using new techniques drawing from recent advances in reinforcement learning.Under review as a conference paper at ICLR 2018 In this work, we proposed a large, standardized dataset and a set of 19 benchmarks to evaluate models for molecule generation and design. Several RL strategies were investigated on these benchmarks. Here, the results suggest that the Hillclimb-MLE model is a surprisingly robust technique with large datasets and deep models, outperforming PPO given sufficient compute times and sample evaluations. In the space of constrained compute and sample evaluations, PPO was shown to be an effective learning algorithm, converging an order of magnitude before other reinforcement-learning algorithms for molecule generation.Nevertheless, there is still tremendous need for more efficient and effective models for molecular design, which could have a profound impact on molecular design -including drug, materials and agrochemicals discovery -and thus immediately on human well-being. With the present, easily usable benchmark, we hope to inspire the machine learning community to pick up this challenge.",805,0.39,464,1.7349137931034482,"The design small molecules bespoke properties of However significant challenges yet remain computational methods despite such deep recurrent networks reinforcement learning strategies sequence generation and it can compare results different works This work proposes 19 benchmarks selected subject experts expands smaller datasets previously approximately 1.1 million training molecules explores apply new reinforcement learning techniques effectively molecular design The benchmarks here, built as OpenAI Gym environments will open encourage innovation molecular design algorithms usage those without Finally this work explores recent development reinforcement-learning methods with excellent sample complexitythe A2C and PPO algorithms investigates their behavior molecular generation demonstrating compared Novel drugs developed design -make -test cycles: molecules, in The insights then inform for The objective de novo design methodologies perform this cycle computational methods BID4 BID29 . The test phase the automated using the broad categorization machine learning models known quantitative structure-activity/property relationships a molecule against physicochemical properties To virtual molecules symbolic approaches based graph rewriting which domain rely extensive hand-engineering by experts To optimize the properties a molecule for its activity againstdesign global optimization approaches evolutionary algorithms ant colony optimization BID4 BID29 . Symbolic approaches highlighted either generating unrealistic molecules for being conservative exploring the space tractable molecules BID29 BID2 .Recently , generative models learn the distribution real druglike molecules data, chemical structures appropriate the application domain BID36 Interestingly , the generation molecules related natural language generationNLG Two classic problems NLG -preserving coherent long-range dependencies syntactic and semantic correctness map molecules Current investigations draw heavily tools language tasks variationalVAE BID12 BID18 , recurrent models seeks consolidate recurrent models molecular design employ Here, suggest a set 19 benchmarks of relevance de novo design Furthermore an implementation these benchmarks as an OpenAI Gym provided to spur Finally demonstrate state performance using new techniques drawing recent advances reinforcement learningUnder review as a conference paper at ICLR 2018 In proposed a large, standardized dataset and 19 benchmarks models molecule generation design Several RL strategies investigated on these benchmarks Here, the results suggest the Hillclimb-MLE model a surprisingly robust technique with large datasets deep models outperforming PPO given sufficient compute times sample evaluations In the space constrained compute sample evaluations PPO was shown converging an order before other reinforcement-learning algorithms for molecule generationNevertheless tremendous need molecular design could have molecular -including drug, materials discovery thus immediately With the present, easily usable benchmark hope inspire the machine learning community pick this challenge",0.01,0.5765749456915279
"Analogical reasoning has been a principal focus of various waves of AI research. Analogy is particularly challenging for machines because it requires relational structures to be represented such that they can be flexibly applied across diverse domains of experience. Here, we study how analogical reasoning can be induced in neural networks that learn to perceive and reason about raw visual data. We find that the critical factor for inducing such a capacity is not an elaborate architecture, but rather, careful attention to the choice of data and the manner in which it is presented to the model. The most robust capacity for analogical reasoning is induced when networks learn analogies by contrasting abstract relational structures in their input domains, a training method that uses only the input data to force models to learn about important abstract features. Using this technique we demonstrate capacities for complex, visual and symbolic analogy making and generalisation in even the simplest neural network architectures. The ability to make analogies -that is, to flexibly map familiar relations from one domain of experience to another -is a fundamental ingredient of human intelligence and creativity BID10 BID14 BID16 BID20 . As noted, for instance, by BID15 , analogies gave Roman scientists a deeper understanding of sound when they leveraged knowledge of a familiar source domain (water waves in the sea) to better understand the structure of an unfamiliar target domain (acoustics). The Romans 'aligned' relational principles about water waves (periodicity, bending round corners, rebounding off solids) to phenomena observed in acoustics, in spite of the numerous perceptual and physical differences between water and sound. This flexible alignment, or mapping, of relational structure between source and target domains, independent of perceptual congruence, is a prototypical example of analogy making.It has proven particularly challenging to replicate processes of analogical thought in machines. Many classical or symbolic AI models lack the flexibility to apply predicates or operations across diverse domains, particularly those that may have never previously been observed. It is natural to consider, however, whether the strengths of modern neural network-based models can be exploited to solve difficult analogical problems, given their capacity to represent stimuli at different levels of abstraction and to enable flexible, context-dependent computation over noisy and ambiguous inputs.In this work we demonstrate that well-known neural network architectures can indeed learn to make analogies with remarkable generality and flexibility. This ability, however, is critically dependent on a method of training we call learning analogies by contrasting abstract relational structure (LABC). We show that simple architectures can be trained using this approach to apply abstract relations to never-before-seen source-target domain mappings, and even to entirely unfamiliar target domains.Our work differs from previous computational models of analogy in two important ways. First, unlike previous neural network models of analogy, we optimize a single model to perform both stimulus representation and cross-domain mapping jointly. This allows us to explore the potential benefit of interactions between perception, representation and inter-domain alignment, a question of some debate in the analogy literature BID8 The number of shapes increases as you go along the panels 2) Apply the relation from (1) to the target panels:The darkness of the lines increases as you go along the panels One shape Two shapes Three shapes These results demonstrate that LABC increases the ability of models to generalize beyond the distribution of their training data. This effect is observed for the prototypical analogical processes involving novel domain mappings and unfamiliar target domains FIG0 . Interestingly, it also results in moderate improvements to how well models extrapolate to perceptual input outside the range of their training experience (Experiment 3). Our experiments show that simple neural networks can learn to make analogies with visual and symbolic inputs, but this is critically contingent on the way in which they are trained; during training, the correct answers should be contrasted with alternative incorrect answers that are plausible at the level of relations rather than simple perceptual attributes. This is consistent with the SMT of human analogy-making, which highlights the importance of inter-domain comparison at the level of abstract relational structures. At the same time, in the visual analogy domain, our model reflects the idea of analogy as closely intertwined with perception itself. We find that models that are trained by LABC to reason better by analogy are, perhaps surprisingly, also better able to extrapolate to a wider range of input values. Thus, making better analogies seems connected to the ability of models to perceive and represent their raw experience.Recent literature has questioned whether neural networks can generalise in systematic ways to data drawn from outside the training distribution BID17 . Our results show that neural networks are not fundamentally limited in this respect. Rather, the capacity needs to be coaxed out through careful learning. The data with which these networks learn, and the manner in which they learn it, are of paramount importance. Such a lesson is not new; indeed, the task of one-shot learning was thought to be difficult, if not impossible to perform using neural networks, but was nonetheless ""solved"" using appropriate training objectives, models, and optimization innovations (e.g., BID28 BID6 ). The insights presented here may guide promising, general purpose approaches to obtain similar successes in flexible, generalisable abstract reasoning.Earlier work on analogical reasoning in AI and cognitive science employed constructed symbolic stimuli or pre-processed perceptual input (Carbonell ( BID21 show how analogies can be made via non-parametric operations on vector-spaces of text-based word representations. While the input to our visual analogy model is less naturalistic than these latter cases, this permits clear control over the semantics of training or test data when designing and evaluating hypotheses. Our study is nonetheless the only that we are aware to demonstrates such flexible, generalisable analogy making in neural networks learning end-to-end from raw perception. It is therefore a proof of principle that even very basic neural networks have the potential for strong analogical reasoning and generalization.As discussed in Sec. 5.3, in many machine-learning contexts it may not be possible to know exactly what a 'good quality' negative example looks like. The experiments there show that, in such cases, we might still achieve notable improvements in generalization via methods that learn to play the role of teacher by presenting alternatives to the main (student) model, as per BID31 . This underlines the fact that, for established learning algorithms involving negative examples such as (noise) contrastive estimation BID36 BID13 or negative sampling BID21 , the way in which negative examples are selected can be critical 3 . It may also help to explain the power of methods like self-play BID32 , in which a model is encouraged to continually challenge itself by posing increasingly difficult learning challenges.Analogies as the functions of the mind To check whether a plate is on a table we can look at the space above the table, but to find out whether a picture is on a wall or a person is on a train, the equivalent check would fail. A single on function operating in the same way on all input domains could not explain these entirely divergent outcomes of function evaluation. On the other hand, it seems implausible that our cognitive system encodes the knowledge underpinning these apparently distinct applications of the on relation in entirely independent representations. The findings of this work argue instead for a different perspective; that a single concept of on is indeed exploited in each of the three cases, but that its meaning and representation is sufficiently abstract to permit flexible interaction with, and context-dependent adaptation to, each particular domain of application. If we equate this process with analogy-making, then analogies are something like the functions of the mind. We believe that greater focus on analogy may be critical for replicating human-like cognitive processes, and ultimately human-like intelligent behaviour, in machines. It may now be time to revisit the insights from past waves of AI research on analogy, while bringing to bear the tools, perspectives and computing power of the present day. It is interesting to consider to what extent the effects reported in this work can transfer to a wider class of learning and reasoning problems beyond classical analogies. The importance of teaching concepts (to humans or models) by contrasting with negative examples is relatively established in both cognitive science BID31 BID35 and educational research BID34 BID0 . Our results underline the importance of this principle when training modern neural networks to replicate human-like cognitive processes and reasoning from raw perceptual input. In cases where expert understanding of potential data exists, for instance in the case of active learning with human interaction, it provides a recipe for achieving more robust representations leading to far greater powers of generalization. We should aspire to select as negative examples those examples that are plausible considering the most abstract principles that describe the data.A further notable property of our trained networks is the fact they can resolve analogies (even those involving with unfamiliar input domains) in a single rollout (forward pass) of a recurrent network. This propensity for fast reasoning has an interesting parallel with the fast and instinctive way in which humans can execute visual analogical reasoning BID23 BID24 .",1802,0.865,1056,1.706439393939394,"Analogical reasoning a principal focus various waves Analogy is particularly challenging machines relational structures represented such flexibly applied diverse domains experience Here study how analogical reasoning induced perceive reason raw visual data We find the critical factor inducing such a capacity an elaborate architecture careful the choice data manner The most robust capacity analogical reasoning induced networks learn analogies contrasting abstract relational structures their input domains, a training method uses force models about important abstract features Using demonstrate capacities complex, visual and symbolic analogy making generalisation even neural The ability make analogies -that flexibly map familiar relations from creativity BID10 BID14 BID16 BID20 . As noted for by BID15 , analogies gave Roman scientists sound when leveraged knowledge a familiar source domainwater waves better an unfamiliar target domain The Romans 'aligned relational principles about water wavesperiodicity bending round corners rebounding off solids phenomena observed in spite sound This flexible alignment, or mapping relational structure source and target domains independent perceptual congruence analogy makingIt proven challenging replicate processes analogical thought machines Many classical or symbolic AI models lack apply predicates operations across diverse domains may never observed It natural consider, the strengths modern neural network-based models exploited solve difficult analogical problems given their capacity represent stimuli enable over noisy and ambiguous inputsIn indeed learn make analogies remarkable generality This ability, critically dependent a method training we learning analogies by contrasting abstract relational structureLABC We show simple architectures trained this approach apply abstract relations never-before-seen source-target domain mappings even entirely unfamiliar target domainsOur work differs analogy First unlike previous neural network models analogy optimize both stimulus representation cross-domain mapping jointly This allows explore the potential benefit interactions perception representation inter-domain alignment a question of some debate the analogy literature BID8 The number shapes increases the panels 2) Apply the relation from ( the target panels:The darkness increases One shape Two shapes These results demonstrate LABC increases models beyond the distribution their training data This effect observed the prototypical analogical processes involving novel domain mappings unfamiliar target domains FIG0 . Interestingly also results moderate improvements how well models extrapolate perceptual input outside their training experienceExperiment Our experiments simple neural networks make analogies visual and symbolic inputs critically contingent; during the correct answers should contrasted alternative incorrect answers plausible at relations rather simple perceptual attributes This consistent the SMT of human analogy-making highlights inter-domain comparison at abstract relational structures At in the visual analogy domain our model reflects analogy closely intertwined perception itself We find that models trained LABC reason better by analogy, perhaps surprisingly also able extrapolate input values Thus making better analogies seems connected the ability models perceive represent their raw experienceRecent literature questioned neural networks generalise systematic ways data drawn outside the training distribution BID17 . Our results neural networks fundamentally limited Rather the capacity needs coaxed through careful learning The data with these networks learn the manner of Such a lesson indeed the task one-shot learning thought difficult using neural networks nonetheless "" using appropriate training objectives models optimization innovations (e.g., BID28 BID6 The insights presented guide promising, general purpose approaches obtain similar successes flexible, generalisable abstract reasoningEarlier work analogical reasoning employed constructed symbolic stimuli orCarbonell ( BID21 show how analogies made via vector-spaces of text-based word representations. While the input to our visual analogy model less naturalistic these latter cases this permits clear control training or when designing evaluating hypotheses Our study nonetheless only that are to demonstrates such flexible, generalisable analogy making learning end from raw perception It therefore a proof even very basic neural networks strong analogical reasoningAs discussed Sec, in many machine-learning contexts it know a 'good quality' negative example The experiments there such cases we still achieve notable improvements generalization via methods learn play teacher by presenting alternatives the main (student) model per BID31 . This underlines established learning algorithms involving negative examples such (noise contrastive estimation BID36 BID13 or the way selected critical 3 It may also explain the power methods self-play BID32 , in a model encouraged continually challenge posing increasingly difficult learning challengesAnalogies as the functions To check a plate on we the space above but a person the equivalent check fail A single on function operating on all input domains could not explain these entirely divergent outcomes of function evaluation On implausible our cognitive system encodes underpinning these apparently distinct applications the on relation in entirely independent representations The findings this work argue instead; a single concept on is indeed exploited each its meaning representation sufficiently abstract permit flexible interaction, each particular domain application If equate this process analogy-making analogies something the functions We believe greater focus analogy may critical replicating ultimately human intelligent machines It may now revisit the insights past waves AI research analogy while bringing, perspectives computing It interesting to reported transfer a wider class learning reasoning problems beyond classical analogies The importance teaching concepts (to humans or models by contrasting negative examples relatively established BID31 BID35 . Our results underline this principle training modern neural networks replicate reasoning from raw perceptual input In cases expert understanding potential data exists for active learning with human interaction provides a recipe achieving more robust representations leading far greater powers generalization We should aspire select as negative examples those examples plausible considering the most abstract principles describe the dataA further notable property our trained networks they resolve analogies (even those involving with unfamiliar input domains a single rollout (forward pass This propensity fast reasoning an interesting parallel the fast and instinctive way can execute visual analogical reasoning BID23 BID24",0.01,0.5040246783548743
"Building chatbots that can accomplish goals such as booking a flight ticket is an unsolved problem in natural language understanding. Much progress has been made to build conversation models using techniques such as sequence2sequence modeling. One challenge in applying such techniques to building goal-oriented conversation models is that maximum likelihood-based models are not optimized toward accomplishing goals. Recently, many methods have been proposed to address this issue by optimizing a reward that contains task status or outcome. However, adding the reward optimization on the fly usually provides little guidance for language construction and the conversation model soon becomes decoupled from the language model. In this paper, we propose a new setting in goal-oriented dialogue system to tighten the gap between these two aspects by enforcing model level information isolation on individual models between two agents. Language construction now becomes an important part in reward optimization since it is the only way information can be exchanged. We experimented our models using self-play and results showed that our method not only beat the baseline sequence2sequence model in rewards but can also generate human-readable meaningful conversations of comparable quality. Building chatbots that can naturally interact with human users has long been an important challenge in artificial intelligence and computer science BID15 . Recently, there is growing interest in applying end-to-end neural networks to this task with promising results BID16 BID12 BID13 . A compelling aspect of these models is that they require fewer hand-crafted rules compared to traditional models. Their success is however limited to conversations with very few turns and without any goals (also known as ""chitchat"").The goal of this work is to build goal-oriented conversational models. Here we use ""goal-oriented"" to mean that the model must accomplish a particular desired goal in the dialogue. Depending on the nature of the task, conversations can be as simple as few-round dialogues such as resetting passwords or it can involve back and forth investigations in the case of travel recommendation and IT support. Different from chitchat based conversation models, whose goal is to generate response without task restrictions, goal-oriented models will have to direct the conversations in a way that facilitates the progress of the task. For example in the case of flight booking, customers are only interested in moving the conversation forward if the flight recommendations meet their expectations. Similarly, agents are only supposed to make responses that will resolve customers' requests.Building goal-oriented conversational models presents a fresh challenge to neural network-based conversational models because their success in chitchat dialogues can not be easily transferred into the world of goal-oriented dialogues. Firstly, chitchat models trend to remember the exact settings of the context-response pairs. Due to the high variance of deep models, slight changes in the context such as cities, time or names will likely change the response completely. Although one can provide more training data to cover different combinations of these pieces of information, acquiring dialogue data for the exhaustive set of conditions is difficult or in many cases infeasible. Secondly, the fact that most chitchat models optimize the likelihood of the utterances makes it hard for them to generate responses that are less likely in general but are appropriate given the context of the task. The progress of the dialogue can easily get lost during the conversation and agents might not be able to reach to the optimal conclusion. And finally, while in most chitchat models, diversity of the responses is one of the key metrics, goal-oriented conversation models focus on robustness and reliability of the response especially in it's roles to guide the conversation.To address these problems, in this paper we propose a two-party model for goal-oriented conversation with each sub-model being responsible for its own utterances. We define the goal oriented conversation problem to be a dialogue cooperation with two agents each having access to some pieces of hidden information that is only visible to itself. One of the agents is required to come up with a series of ""action"", which correctness relies solely on the understanding of the hidden information. Although the exact form of the hidden information is not visible, it can be interpreted using natural language and be exchanged to the other party. In order to achieve this, agents need to establish a protocol to talk and complete the task correctly.The two-party architecture makes it feasible to conduct self-play between agents, which enables two conversation models to talk to itself without human supervision. Different from previous proposed self-play dialogue models such as the negotiation chatbot BID4 , our setting enforces the isolation of information between the models of the two agents, which ensure the coupling between task reward and language models. And because hidden information is not directly visible , agents will need to guide and structure the conversation in a proper way in order to acquire the key pieces of information that is required to generate the correct actions. This process can be naturally strengthened using self-play with reinforcement learning.Another benefit of the self-play model is the ability to utilize large scale un-supervised knowledge that is otherwise difficult to leverage. Training of dialogue models require lots of data but supervised conversation data are usually hard to acquire. Fortunately, it is usually easy to generate the initial conditions of the dialogue such as user restrictions available information in the database. Based on those initial settings, a rule based program is usually enough to generate action states, which constitutes a perfect reinforcement learning environment to estimate rewards. Using self-play to exchange hidden information, we can potentially leverage knowledge of a much larger scale and train a much more reliable chatbot.To validate the performance of the model we first trained a supervised model based on fully supervised dialogue utterance, action states and hidden conditions. The supervised model is then used as a bootstrap to initialize a self-play training model based on initial conditions without supervised dialogues. We evaluated both models on a held-out self-play data sets and observed 37 % performances improvements on average rewards for the agent learned from self-play. In this paper, we proposed a new approach to model goal-oriented conversations based on information isolation and action states. By leveraging supervised learning with self-plays on actions states, we expanded the coverage of the training significantly and exposed the model with unseen data. By enforcing information isolation, we tightly coupled dialogue data with action states. Results indicated self-play under those settings significantly improved the reward function compares to the supervised learning baseline. Since dialogue data is usually hard to get while action states can be acquired easily, our approach can be easily applied in those scenario where the amount of the data is a bottleneck to the performance of the system.",1269,0.705,729,1.7407407407407407,"Building chatbots accomplish goals booking a flight ticket an unsolved problem natural language understanding Much progress build conversation models using techniques sequence2sequence modeling One challenge applying such techniques building goal-oriented conversation models maximum likelihood-based models optimized toward accomplishing Recently many methods optimizing a reward that contains task status outcome However adding the reward optimization on usually provides little guidance language construction the conversation model soon In goal-oriented dialogue system tighten these two aspects by enforcing model level information isolation individual models between two agents Language construction now becomes in reward optimization since information exchanged We experimented our models self-play results our method not beat the baseline sequence2sequence model rewards can generate human-readable meaningful conversations of comparable quality Building chatbots naturally artificial intelligence and computer science BID15 . applying end neural this task with BID16 BID12 BID13 . A compelling aspect these models require fewer hand-crafted rules compared Their success however conversations very few turns without any goals (alsochitchat"").The goal build goal-oriented conversational models Here use ""goal the model accomplish the dialogue Depending conversations few-round dialogues such resetting passwords it back and forth investigations in travel recommendation IT support Different chitchat based conversation models whose goal generate response without task restrictions will direct facilitates the progress For example in flight booking customers only interested moving the conversation the flight recommendations meet Similarly agents only supposed make responses resolve customers' requestsBuilding goal-oriented conversational models presents their success chitchat dialogues not easily transferred the world Firstly chitchat models trend remember the exact settings the context-response pairs Due the high variance deep models slight changes the context such cities time or names will completely Although one provide more training data cover different combinations these pieces acquiring dialogue data the exhaustive set conditions or in Secondly most chitchat models optimize the likelihood the utterances makes generate responses less in but appropriate given The progress the dialogue can easily get during agents might reach to the optimal conclusion And finally while in most chitchat models diversity the responses one goal-oriented conversation models focus robustness reliability especially it roles to guideTo address in with each sub responsible We define the goal oriented conversation problem a dialogue cooperation with two agents each access some pieces hidden information only visible itself One the agents is required come ""action correctness relies solely the hidden information Although the exact form the hidden information visible interpreted using natural language and be exchanged In order achieve agents establish talk and complete correctlyThe two-party architecture makes feasible conduct self-play between two conversation models talk itself human supervision Different previous proposed self-play dialogue models such the negotiation chatbot BID4 our setting enforces the isolation information the models of ensure the coupling task reward language models And because hidden information directly , agents guide structure in acquire is generate This process naturally strengthened using self-play with reinforcement learningAnother benefit utilize large scale un-supervised knowledge that otherwise leverage Training of dialogue models require lots but supervised conversation data hard acquire Fortunately usually generate the initial conditions the dialogue such user restrictions available information in Based those initial settings a rule based program usually enough generate action states constitutes a perfect reinforcement learning environment to estimate rewards Using self-play exchange hidden information potentially leverage knowledge trainTo validate the model trained a supervised model based fully supervised dialogue utterance action states hidden conditions The supervised model then initialize a self-play training model based initial conditions without supervised dialogues We evaluated both models a held-out self-play data sets observed 37 % performances improvements average rewards the agent learned In proposed model goal-oriented conversations information isolation action states By leveraging supervised learning self-plays on actions states expanded the coverage the training significantly exposed with unseen data By enforcing information isolation tightly coupled dialogue data action states Results indicated self-play under those settings significantly the reward function compares the supervised learning baseline Since dialogue data usually hard while action states can acquired easily our approach can easily those scenario the amount the data a bottleneck",0.01,0.5914214963213275
"Search engine users nowadays heavily depend on query completion and correction to shape their queries.  Typically, the completion is done by database lookup which does not understand the context and cannot generalize to prefixes not in the database . In the paper, we propose to use unsupervised deep language models to complete and correct the queries given an arbitrary prefix .  We show how to address two main challenges that renders this method practical for large-scale deployment : 1) we propose a method for integrating error correction into the language model completion via a edit-distance potential and a variant of beam search that can exploit these potential functions; and 2) we show how to efficiently perform CPU-based computation to complete the queries, with error correction, in real time (generating top 10 completions within 16 ms). Experiments show that the method substantially increases hit rate over standard approaches, and is capable of handling tail queries.
 Search completion is the problem of taking a prefix of a search query from a user and generating several candidate completions. This problem has enormous potential utility and monetary value to any search provider: the more accurately an engine can find the desired completions for a user (or indeed, potentially steer the user towards high-value completions), the more quickly it can lead the user to their desired goal. This paper proposes a realtime search completion architecture based upon deep character-level language models. The basic idea is that instead of looking up possible completions from a generic database, we perform search under a deep-network-based language model to find the most likely completions of a user's current input. This allows us to integrate the power of deep language models, that has been shown to perform extremely well on complex language modeling and prediction tasks, with the desired goal of finding a good completion. Although this is a conceptually simple strategy (and one which has been considered before, as we highlight in the literature below), there are two key elements required to make this of practical use for a search engine provider, which together make up the primary technical contributions of the paper: 1) The completion must be error correcting, able to handle small errors in the user's initial input and provide completions for the most likely ""correct"" input. We propose such an approach that combines a character-level language model with an edit-distance-based potential function, combining the two using a tree-based beam search algorithm;2) The completion must be realtime, able to produce high-quality potential completions in a time that is not even perceivable to the user. We achieve this by developing an efficient tree-based version of the error-correcting beam search, exploiting CPU-based computation for single queries (due to the high levels of branching in the beam search), and through numerous optimizations to the implementation that we discuss below.We evaluate the method on the AOL search data set, a dataset consisting of over 36 million total search queries. In total, the method substantially outperforms highly optimized standard search completion algorithms in terms of its hit rate (the benefit of the deep language model and the error correction), while being fast enough to execute in real time for search engines. Experiments and code are all available online, and a real-time demo of the approach is available at http: //www.deepquerycompletion.com. In this paper, we presented a search query completion approach based upon character-level deep language models. We proposed a method for integrating the approach with an error correction framework and showed that candidate completions with error correction can be efficiently generated using beam search. We further described several optimizations that enabled the system to work in real time, including a CPU-based custom LSTM implementation. The method is able to jointly produce better completions than simple prefix lookup, while simultaneously being able to generate the candidates in real time.",752,0.349,449,1.6748329621380846,"Search engine users nowadays heavily query completion correction shape Typically the completion is database lookup which does understand generalize prefixes not . In the paper we propose unsupervised deep language models complete and correct the queries given an arbitrary prefix . We show address two main challenges renders this method practical : 1 we propose integrating error correction the language model completion via a edit-distance potential and a variant beam search exploit these potential functions; efficiently perform CPU-based computation complete the queries (generating top 10 completions within 16 ms Experiments show the method substantially hit over standard approaches capable handling tail queries Search completion the problem taking a prefix generating several candidate completions This problem enormous potential utility monetary value any search provider: more accurately an engine find the desired completions ( indeed potentially steer quickly lead This paper proposes a realtime search completion architecture upon deep character-level language models The basic idea instead looking up possible completions a generic database perform search under a deep-network-based language model This allows integrate the power deep language models that has shown perform extremely complex language modeling and prediction tasks the desired goal finding a good completion. Although this a conceptually simple strategy ( considered before highlight the literature below required of for a search engine provider together the primary technical contributions The completion must error correcting able provide completions We propose such an approach combines a character-level language model an edit-distance-based potential function combining using a tree-based beam search algorithm;2) The completion must realtime able produce high-quality potential completions that even perceivable We achieve developing an efficient tree-based version the error-correcting beam search, exploiting CPU-based computation single queriesdue the high levels branching through numerous optimizations that we discussWe evaluate the method on the AOL search data set a dataset In total the method substantially highly optimized standard search completion algorithms its hit ratethe benefit the deep language model and the error correction while being fast execute for search engines Experiments code all online the approach: //www.deepquerycompletion.com In this paper presented a search query completion approach upon character-level deep language models We proposed integrating the approach an error correction framework showed that candidate completions efficiently generated beam search We further described several optimizations enabled work a CPU-based custom LSTM implementation The method able jointly produce better completions simple prefix lookup while simultaneously being generate the candidates",0.0,0.42349426703587306
"RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse generalization properties when compared to carefully tuned stochastic gradient descent or its momentum variants. In this work, we make progress towards a deeper understanding of ADAM and RMSProp in two ways. First, we provide proofs that these adaptive gradient algorithms are guaranteed to reach criticality for smooth non-convex objectives, and we give bounds on the running time.

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

 We also report experiments on different autoencoders to demonstrate that NAG has better abilities in terms of reducing the gradient norms, and it also produces iterates which exhibit an increasing trend for the minimum eigenvalue of the Hessian of the loss function at the iterates. Many optimization questions arising in machine learning can be cast as a finite sum optimization problem of the form: min x f (x) where f (x) = 1 k k i=1 f i (x). Most neural network problems also fall under a similar structure where each function f i is typically non-convex. A well-studied algorithm to solve such problems is Stochastic Gradient Descent (SGD), which uses updates of the form: x t+1 := x t − α∇f it (x t ), where α is a step size, andf it is a function chosen randomly from {f 1 , f 2 , . . . , f k } at time t. Often in neural networks, ""momentum"" is added to the SGD update to yield a two-step update process given as: v t+1 = µv t − α∇f it (x t ) followed by x t+1 = x t + v t+1 . This algorithm is typically called the Heavy-Ball (HB) method (or sometimes classical momentum), with µ > 0 called the momentum parameter (Polyak, 1987) . In the context of neural nets, another variant of SGD that is popular is Nesterov's Accelerated Gradient (NAG), which can also be thought of as a momentum method (Sutskever et al., 2013) , and has updates of the form v t+1 = µv t − α∇f it (x t + µv t ) followed by x t+1 = x t + v t+1 (see Algorithm 1 for more details).Momentum methods like HB and NAG have been shown to have superior convergence properties compared to gradient descent in the deterministic setting both for convex and non-convex functions (Nesterov, 1983; Polyak, 1987; Zavriev & Kostyuk, 1993; Ochs, 2016; O'Neill & Wright, 2017; Jin et al., 2017) . While (to the best of our knowledge) there is no clear theoretical justification in the stochastic case of the benefits of NAG and HB over regular SGD in general (Yuan et al., 2016; Kidambi et al., 2018; Wiegerinck et al., 1994; Orr & Leen, 1994; Yang et al., 2016; Gadat et al., 2018) , unless considering specialized function classes (Loizou & Richtárik, 2017) ; in practice, these momentum methods, and in particular NAG, have been repeatedly shown to have good convergence and generalization on a range of neural net problems (Sutskever et al., 2013; Lucas et al., 2018; Kidambi et al., 2018) .The performance of NAG (as well as HB and SGD), however, are typically quite sensitive to the selection of its hyper-parameters: step size, momentum and batch size (Sutskever et al., 2013) . Thus, ""adaptive gradient"" algorithms such as RMSProp (Algorithm 2) (Tieleman & Hinton, 2012) and ADAM (Algorithm 3) (Kingma & Ba, 2014) have become very popular for optimizing deep neural networks (Melis et al., 2017; Xu et al., 2015; Denkowski & Neubig, 2017; Gregor et al., 2015; Radford et al., 2015; Bahar et al., 2017; Kiros et al., 2015) . The reason for their widespread popularity seems to be the fact that they are believed to be easier to tune than SGD, NAG or HB. Adaptive gradient methods use as their update direction a vector which is the image under a linear transformation (often called the ""diagonal pre-conditioner"") constructed out of the history of the gradients, of a linear combination of all the gradients seen till now. It is generally believed that this ""pre-conditioning"" makes these algorithms much less sensitive to the selection of its hyperparameters. A precursor to these RMSProp and ADAM was outlined in Duchi et al. (2011) .Despite their widespread use in neural net problems, adaptive gradients methods like RMSProp and ADAM lack theoretical justifications in the non-convex setting -even with exact/deterministic gradients (Bernstein et al., 2018) . Further, there are also important motivations to study the behavior of these algorithms in the deterministic setting because of usecases where the amount of noise is controlled during optimization, either by using larger batches (Martens & Grosse, 2015; De et al., 2017; Babanezhad et al., 2015) or by employing variance-reducing techniques (Johnson & Zhang, 2013; Defazio et al., 2014) .Further, works like Wilson et al. (2017) and Keskar & Socher (2017) have shown cases where SGD (no momentum) and HB (classical momentum) generalize much better than RMSProp and ADAM with stochastic gradients. Wilson et al. (2017) also show that ADAM generalizes poorly for large enough nets and that RMSProp generalizes better than ADAM on a couple of neural network tasks (most notably in the character-level language modeling task). But in general it's not clear and no heuristics are known to the best of our knowledge to decide whether these insights about relative performances (generalization or training) between algorithms hold for other models or carry over to the full-batch setting.A summary of our contributions In this work we try to shed some light on the above described open questions about adaptive gradient methods in the following two ways.• To the best of our knowledge, this work gives the first convergence guarantees for adaptive gradient based standard neural-net training heuristics. Specifically we show run-time bounds for deterministic RMSProp and ADAM to reach approximate criticality on smooth non-convex functions, as well as for stochastic RMSProp under an additional assumption. Recently, Reddi et al. (2018) have shown in the setting of online convex optimization that there are certain sequences of convex functions where ADAM and RMSprop fail to converge to asymptotically zero average regret. We contrast our findings with Theorem 3 in Reddi et al. (2018) . Their counterexample for ADAM is constructed in the stochastic optimization framework and is incomparable to our result about deterministic ADAM. Our proof of convergence to approximate critical points establishes a key conceptual point that for adaptive gradient algorithms one cannot transfer intuitions about convergence from online setups to their more common use case in offline setups.• Our second contribution is empirical investigation into adaptive gradient methods, where our goals are different from what our theoretical results are probing. We test the convergence and generalization properties of RMSProp and ADAM and we compare their performance against NAG on a variety of autoencoder experiments on MNIST data, in both full and mini-batch settings. In the full-batch setting, we demonstrate that ADAM with very high values of the momentum parameter (β 1 = 0.99) matches or outperforms carefully tuned NAG and RMSProp, in terms of getting lower training and test losses. We show that as the autoencoder size keeps increasing, RMSProp fails to generalize pretty soon. In the mini-batch experiments we see exactly the same behaviour for large enough nets. We further validate this behavior on an image classification task on CIFAR-10 using a VGG-9 convolutional neural network, the results to which we present in the Appendix E. We note that recently it has been shown by Lucas et al. (2018) , that there are problems where NAG generalizes better than ADAM even after tuning β 1 . In contrast our experiments reveal controlled setups where tuning ADAM's β 1 closer to 1 than usual practice helps close the generalization gap with NAG and HB which exists at standard values of β 1 .Remark. Much after this work was completed we came to know of a related paper ( Li & Orabona, 2018 ) which analyzes convergence rates of a modification of AdaGrad (not RMSPRop or ADAM).After the initial version of our work was made public, a few other analysis of adaptive gradient methods have also appeared like Chen et al. (2018) , Zhou et al. (2018) and Zaheer et al. (2018) . To the best of our knowledge, we present the first theoretical guarantees of convergence to criticality for the immensely popular algorithms RMSProp and ADAM in their most commonly used setting of optimizing a non-convex objective.By our experiments, we have sought to shed light on the important topic of the interplay between adaptivity and momentum in training nets. By choosing to study textbook autoencoder architectures where various parameters of the net can be changed controllably we highlight the following two aspects that (a) the value of the gradient shifting hyperparameter ξ has a significant influence on the performance of ADAM and RMSProp and (b) ADAM seems to perform particularly well (often supersedes Nesterov accelerated gradient method) when its momentum parameter β 1 is very close to 1. On VGG-9 with CIFAR-10 and for the task of training autoencoders on MNIST we have verified these conclusions across different widths and depths of nets as well as in the full-batch and the mini-batch setting (with large nets) and under compression of the input/out image size. Curiously enough, this regime of β 1 being close to 1 is currently not within the reach of our proof techniques of showing convergence for ADAM. Our experiments give strong reasons to try to advance theory in this direction in future work.Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. Now we give the proof of Theorem 3.1.Proof. We define σ t := max k=1,.. ,t ∇f i k (x k ) and we solve the recursion for v t as, DISPLAYFORM0 . This lets us write the following bounds, DISPLAYFORM1 i and this lets us get the following bounds, DISPLAYFORM2 Now we invoke the bounded gradient assumption about the f i functions and replace in the above equation the eigenvalue bounds of the pre-conditioner by worst-case estimates µ max and µ min defined as, DISPLAYFORM3 Using the L-smoothness of f between consecutive iterates x t and x t+1 we have, DISPLAYFORM4 We note that the update step of stochastic RMSProp is x t+1 = x t − α(V t ) − 1 2 g t where g t is the stochastic gradient at iterate x t . Let H t = {x 1 , x 2 , .., x t } be the set of random variables corresponding to the first t iterates. The assumptions we have about the stochastic oracle give us the following relations, DISPLAYFORM5 f . Now we can invoke these stochastic oracle's properties and take a conditional (on H t ) expectation over g t of the L−smoothness in equation to get, DISPLAYFORM6 We now separately analyze the middle term in the RHS above in Lemma A.1 below and we get, DISPLAYFORM7 We substitute the above into equation 1 and take expectations over H t to get, DISPLAYFORM8 Doing the above replacements to upperbound the RHS of equation 2 and summing the inequation over t = 1 to t = T and taking the average and replacing the LHS by a lowerbound of it, we get, DISPLAYFORM9 Replacing into the RHS above the optimal choice of, DISPLAYFORM10 Thus stochastic RMSProp with the above step-length is guaranteed is reach −criticality in number of iterations given by, T ≤ DISPLAYFORM11 Lemma A.1. At any time t, the following holds, DISPLAYFORM12 Proof. DISPLAYFORM13 Now we introduce some new variables to make the analysis easier to present. Let a pi := [∇f p (x t )] i where p indexes the training data set, p ∈ {1, . . . , k}. (conditioned on H t , a pi s are constants) This implies, DISPLAYFORM14 where the expectation is taken over the oracle call at the t th update step. Further our instantiation of the oracle is equivalent to doing the uniformly at random sampling, (g t ) i ∼ {a pi } p=1,...,k .Given that we have, DISPLAYFORM15 i +di where we have defined DISPLAYFORM16 This leads to an explicit form of the needed expectation over the t th −oracle call as, DISPLAYFORM17 Substituting the above (and the definition of the constants a pi ) back into equation 3 we have, DISPLAYFORM18 Substituting this, the above expression can be written as, DISPLAYFORM19 Note that with this substitution, the RHS of the claimed lemma becomes, DISPLAYFORM20 Therefore our claim is proved if we show that for all i, DISPLAYFORM21 To further simplify, we define DISPLAYFORM22 −µ min . We therefore need to show, DISPLAYFORM23 We first bound d i by recalling the definition of σ f (from which it follows that a 2 pi ≤ σ 2 f ), DISPLAYFORM24 The inequality follows since β 2 ∈ (0, 1]Putting this all together, we get, DISPLAYFORM25 Now our assumption that for all x, sign(∇f p (x)) = sign(∇f q (x)) for all p, q ∈ {1, . . . , k} leads to the conclusion that the term a pi a qi ≥ 0. And we had already shown in equation 5 that DISPLAYFORM26 Thus we have shown that (a i 1 k )(q i a i ) ≥ 0 and this finishes the proof.",3228,1.347,1806,1.787375415282392,"RMSProp and ADAM continue extremely popular algorithms training but their theoretical convergence properties remained Further recent work seemed these algorithms worse generalization properties when carefully tuned or its momentum variants In this work make progress ADAM RMSProp in First provide proofs these adaptive gradient algorithms guaranteed reach criticality smooth non-convex objectives give bounds Next we design experiments empirically study the convergence and generalization properties RMSProp ADAM against Nesterov's Accelerated Gradient method on common autoencoder setups on VGG-9 with Through these experiments demonstrate the interesting sensitivity that ADAM its momentum parameter \beta_1 We show at very high values the momentum parameter ADAM a carefully tuned NAG on most in getting lower training and test losses On NAG can sometimes do ADAM's \beta_1: indicating the importance tuning We also report experiments different autoencoders demonstrate NAG has better abilities terms reducing the gradient norms it produces iterates exhibit an increasing trend for the Hessian of at the iterates Many optimization questions arising cast a finite sum optimization problem of min x f (x k k f Most neural network problems also fall a similar structure where function f i typically non A well-studied algorithm updates the form x t+1 − α��f it andf chosen { . . . , f k } at time Often neural networks added the SGD update yield given as v t+1 µv − α��f it followed This algorithm typically called HeavyBall (HB (or sometimes classical momentum with µ > called the momentum parameterPolyak . In neural nets another variant SGD that popular Nesterov's Accelerated Gradient (NAG also thought a momentum methodSutskever , updates the form v t+1 = µv − α��f it followedsee Algorithm 1 like HB superior convergence properties gradient descent in the deterministic setting both 1983 Polyak 1987 Zavriev & 2016 Wright Jin While (to no clear theoretical justification in the benefits NAG and HB over regular SGD (Yuan Kidambi 2018 Wiegerinck 1994 Orr & Leen 1994 Yang Gadat , unless considering specialized function classesLoizou Richtárik ; practice these momentum methods, repeatedly good convergence on neural net problemsSutskever Lucas 2018 .The performance are typically sensitive the selection its hyper: step size momentum batch size Thus ""adaptive gradient"" algorithms such RMSProp (Algorithm 2 (Tieleman Hinton ADAM (Kingma Ba, become very optimizingMelis 2017 Xu Denkowski Neubig Gregor Radford Bahar Kiros . The reason their widespread popularity seems believed easier tune SGD NAG or HB Adaptive gradient methods use as their update direction the image underoftendiagonal preconditioner constructed out the history of a linear combination seen till It generally this ""preconditioning makes these algorithms the selection A precursor these RMSProp and ADAM was outlined Duchi (2011 .Despite their widespread use neural net problems adaptive gradients methods like RMSProp ADAM lack theoretical justifications in the non-convex setting -even exact/deterministic gradientsBernstein 2018 Further also important motivations study these algorithms the deterministic setting because usecases the amount noise controlled during optimization either using larger batchesMartens & Grosse De et Babanezhad employingJohnson Zhang Defazio .Further works Wilson (2017 and Keskar & Socher have cases SGD (no momentum HBclassical momentum generalize much RMSProp ADAM with Wilson et al (2017 also show ADAM generalizes poorly for large enough nets RMSProp generalizes on a couple neural network tasksmost the character-level language modeling task But general it and no heuristics known best to decide these insights about relative performances (generalization training between algorithms hold other models carry the full-batch settingA summary our contributions In try shed the above described open questions adaptive gradient methods the following two ways.• To the gives the first convergence guarantees based standard neural-net training heuristics Specifically we show run-time bounds deterministic RMSProp ADAM to reach approximate criticality smooth non-convex functions under an additional assumption Recently, Reddi et (2018 have shown in the setting online convex optimization there certain sequences ADAM RMSprop fail asymptotically zero average regret We contrast Theorem in Reddi (2018 . Their counterexample for ADAM constructed and incomparable our result about Our proof convergence to approximate critical points establishes for adaptive gradient algorithms one transfer intuitions convergence online setups their more common use case offline setups.• Our second contribution empirical investigation into our goals different what our theoretical results probing We test the convergence and generalization properties RMSProp ADAM and we NAG on experiments on In the full-batch setting demonstrate that ADAM with very high values the momentum parameterβ 1 matches or carefully tuned NAG and RMSProp, getting lower training and test losses We show as the autoencoder size keeps RMSProp fails generalize pretty soon In the mini-batch experiments see for large enough nets We further validate this behavior on an image classification task on the results to which We note recently it shown by Lucas et al (2018 , that there problems where NAG generalizes better ADAM even after tuning β 1 In contrast our experiments reveal controlled setups tuning ADAM β 1 closer than usual practice helps close with NAG HB which exists standard values β 1 .Remark. Much after this work we came a related paper ( Li Orabona 2018 analyzes convergence rates a modification AdaGrad (not RMSPRop or ADAM).After the initial version made a few other analysis of adaptive gradient methods have like Chen et al (2018 , Zhou (2018 and Zaheer et (2018 . To we present the first theoretical guarantees convergence criticality for the immensely popular algorithms RMSProp ADAM in their most commonly used setting optimizingBy our experiments sought shed adaptivity momentum training nets By choosing study textbook autoencoder architectures where various parameters the net can changed we highlight (a) the value gradient shifting hyperparameter �� has ADAM seems particularly (often supersedes Nesterov accelerated gradient method its momentum parameter β 1 very 1 On VGG-9 with CIFAR-10 for the task training autoencoders MNIST we verified these conclusions across different widths depths nets as the full-batch andwith large nets under compression of the input/out image size Curiously this regime β 1 being close 1 currently within our proof techniques of showing convergence for ADAM Our experiments give strong reasons try advance theory inIlya Sutskever James Martens George Dahl Geoffrey Hinton. Now give the proof Theorem 3.1.Proof We define �� t max k=1.. ,t �f k and we solve v t as, DISPLAYFORM0 This lets write the following bounds DISPLAYFORM1 i and this lets get Now invoke the bounded gradient assumption about the f i functions replace inconditioner by worst-case estimates µ max defined, Using the Lsmoothness f between consecutive iterates x t note the update step RMSProp − 1 2 g t where at Let H t = { 1 .. t be random variables corresponding the first t iterates The assumptions the stochastic oracle give the following relations DISPLAYFORM5 f . Now invoke these stochastic oracle's properties take conditional (on H t expectation over g t of the L−smoothness in equation to, DISPLAYFORM6 We separately analyze the middle term the RHS above Lemma A.1 below substitute above into take expectations Doing the above replacements to upperbound summing the inequation t = t = T and taking and replacing by a lowerbound it Replacing into the optimal choice, Thus RMSProp with the above step-length guaranteed is reach −criticality number given At, following holds Proof. DISPLAYFORM13 Now we introduce some new variables the analysis present Let a pi := [��f p (x t i where indexes the training data set p � { . . . , k}. (conditioned on H t , a pi s are constants This implies DISPLAYFORM14 where the expectation taken over the oracle call at the t th update step Further our instantiation is equivalent doing uniformly at random sampling (g t i ∼ {a pi p=1,,k .Given, DISPLAYFORM15 i +di where defined This leads an explicit form the needed expectation over t th −oracle call as, Substituting above the constants a pi back equation 3 this, can Note with the RHS the claimed lemma Therefore our claim proved if show for, To further DISPLAYFORM22 −�� min . We therefore show, DISPLAYFORM23 We first bound d i by recalling �� ffrom which 2 pi ≤ The inequality follows since β 2 ��0 1]Putting all, Now our assumption for all x, sign(��f p (x q for { . . . , k} leads term a pi a qi ≥ And we had already shown equation DISPLAYFORM26 Thus shown (a i 1 k(q a ≥ this finishes",0.02,0.7102425497757496
"Recent advances in adversarial Deep Learning (DL) have opened up a new and largely unexplored surface for malicious attacks jeopardizing the integrity of autonomous DL systems. We introduce a novel automated countermeasure called Parallel Checkpointing Learners (PCL) to thwart the potential adversarial attacks and significantly improve the reliability (safety) of a victim DL model. The proposed PCL methodology is unsupervised, meaning that no adversarial sample is leveraged to build/train parallel checkpointing learners. We formalize the goal of preventing adversarial attacks as an optimization problem to minimize the rarely observed regions in the latent feature space spanned by a DL network. To solve the aforementioned minimization problem, a set of complementary but disjoint checkpointing modules are trained and leveraged to validate the victim model execution in parallel. Each checkpointing learner explicitly characterizes the geometry of the input data and the corresponding high-level data abstractions within a particular DL layer. As such, the adversary is required to simultaneously deceive all the defender modules in order to succeed. We extensively evaluate the performance of the PCL methodology against the state-of-the-art attack scenarios, including Fast-Gradient-Sign (FGS), Jacobian Saliency Map Attack (JSMA), Deepfool, and Carlini&WagnerL2 algorithm. Extensive proof-of-concept evaluations for analyzing various data collections including MNIST, CIFAR10, and ImageNet corroborate the effectiveness of our proposed defense mechanism against adversarial samples. Security and safety consideration is a major obstacle to the wide-scale adoption of emerging learning algorithms in sensitive scenarios, such as intelligent transportation, healthcare, and video surveillance applications BID18 ; BID5 ; BID12 ). While advanced learning technologies are essential for enabling coordination and interaction between the autonomous agents and the environment, a careful analysis of their decision reliability in the face of carefully crafted adversarial samples ; ; BID22 ; BID3 ) and thwarting their vulnerabilities are still in their infancy.Consider a traffic sign classifier employed in self-driving cars. In this setting, an adversary can carefully add imperceptible perturbation to a legitimate ""stop"" sign sample and fool the DL model to classify it as a ""yield"" sign; thus, jeopardizes the safety of the vehicle as shown in BID18 ). As such, it is highly important to reject risky adversarial samples to ensure the integrity of DL models used in autonomous systems such as unmanned vehicles and drones. In this paper, we aim to answer two open questions regarding the adversarial attacks.(i ) Why are machine learning models vulnerable to adversarial samples? Our hypothesis is that the vulnerability of neural networks to adversarial samples originates from the existence of rarely explored sub-spaces in each feature map. This phenomenon is particularly caused by the limited access to the labeled data and/or inefficiency of regularization algorithms BID30 ; BID7 ). Figure 1 provides a simple illustration of the partially explored space in a twodimensional setup. We analytically and empirically back up our hypothesis by extensive evaluations on the state-of-the-art attacks, including Fast-Gradient-Sign ), Jacobian Saliency Map Attack ), Deepfool BID22 ), and Carlini&WagnerL2 BID3 ).(ii) How can we characterize and thwart the underlying space for unsupervised model assurance as well as defend against the adversaries? A line of research has shown that there is a trade-off between the robustness of a model and its accuracy BID17 ; BID25 ). Taking this into account , instead of making a single model that is both robust and accurate, we introduce a new defense mechanism called Parallel Checkpointing Learners (PCL) . In this setting, the victim model is kept as is while separate defender modules are trained to checkpoint the data abstractions and assess the reliability of the victim's prediction. Each defender module characterizes the explored sub-space in the pertinent layer by learning the probability density function (pdf) of legitimate data points and marking the complement sub-spaces as rarely observed regions. Once such characterization is obtained , the checkpointing modules 1 evaluate the input sample in parallel with the victim model and raise alarm flags for data points that lie within the rarely explored regions ( Figure 1c ). As we demonstrate in Section 4, adversarial samples created by various attack methods mostly lie within the sub-spaces marked as partially explored sectors.We consider a white-box attack model in which the attacker knows everything about the victim model including its architecture, learning algorithm, and parameters. This threat model represents the most powerful attacker that can endanger the real-world applications. We validate the security of our proposed approach for different DL benchmarks including MNIST, CIFAR10, and a subset of ImageNet data. Based on the result of our analysis, we provide new insights on the reason behind the existence of adversarial transferability. We open-source our API to ensure ease of use by the users (the link is omitted for blind review purposes) and invite the community to attempt attacks against our provided benchmarks in the form of a challenge.The explicit contribution of this paper is as follows: (i) Devising an automated end-to-end framework for unsupervised model assurance as well as defending against the adversaries. (ii) Incepting the idea of parallel checkpointing learners to validate the legitimacy of data abstractions at each intermediate DL layer. (iii) Performing extensive proof-of-concept evaluations against state-of-the-art attack methods. (iv) Providing new insights regarding the transferability of adversarial samples in between different models. Figure 1: (a) In this example, data points (denoted by green and blue squares) can be easily separated in one-dimensional space. Having extra dimensions adds ambiguity in choosing the pertinent decision boundaries. For instance, all the shown boundaries (dashed lines) are sufficient to classify the raw data with full accuracy in two-dimensional space but are not equivalent in terms of robustness to noise. (b) The rarely explored space (region specified by diagonal striped) in a learning model leaves room for adversaries to manipulate the nuisance (non-critical) variables and mislead the model by crossing the decision boundaries. (c) In PCL methodology, a set of defender (checkpoint) modules is trained to characterize the data density distribution in the space spanned by the victim model. The defender modules are then used in parallel to checkpoint the reliability of the ultimate prediction and raise an alarm flag for risky samples. Note that the remaining adversarial samples that are not detected in this experiment are crafted from legitimate samples that are inherently hard to classify even by a human observer due to the closeness of decision boundaries corresponding to such classes. For instance, in the MNIST application, such adversarial samples mostly belong to class 5 that is misclassified to class 3 or class 4 misclassified as 9. Such misclassifications are indeed the model approximation error which is well-understood to the statistical nature of the models. As such, a more precise definition of adversarial samples DISPLAYFORM0 Figure 9: Example adversarial confusion matrix (a) without PCL defense mechanism, and (b) with PCL defense and a security parameter of (1%). (c) Example adversarial samples for which accurate detection is hard due to the closeness of decision boundaries for the corresponding classes.is extremely required to distinguish malicious samples form those that simply lie near the decision boundaries.We emphasize that the PCL defenders are trained in an unsupervised setting independent of the attack strategy, meaning that no adversarial sample is used to train the defender models. This is particularly important as it corroborates the effectiveness of the proposed countermeasure in the face of generic attack scenarios including possible future adversarial DL algorithms. Nevertheless, one might question the effectiveness of the proposed approach for adaptive attack algorithms that target the defender modules. A comprehensive study of possible adaptive attack algorithms is yet to be performed if such attacks are developed in the future. We emphasize that, thus far, we have been able to significantly thwart all the existing attacks with only one checkpoint model approximating the data distribution in the second-to-last layer of the corresponding models. Our proposed PCL methodology, however, provides a rather more generic approach that can be adapted/modified against potential future attacks by training parallel disjoint models (with diverse objectives/parameters) to further strengthen the defense.Figure 10 demonstrate how using multiple checkpoints with a negative correlation in parallel can effectively reduce the number of false alarms while increasing the detection rate of adversarial samples. In this experiment, we have considered MNIST data classification using LeNet model with 4 layers and FGS attack. The checkpoints are inserted in different layers of the pertinent neural network (first layer up to the second-to-last layer). We empirically select the mixing coefficients to aggregate the confidence of the checkpoint defenders for rejecting an incoming sample. Note that, there is a trade-off between the computational complexity (e.g., runtime overhead) of the PCL defenders and the reliability of the overall system. On the one hand, a high number of validation checkpoints increases the reliability of the systems, but it also increases the computational load as each input sample should be validated by more defender networks. On the other hand, a small number of checkpoints may degrade the defense mechanism performance by treating adversarial samples as legitimate ones. We are looking into automated techniques to customize the number of checkpoint modules and their corresponding mixing coefficients based on application data and physical constraints such as real-time analysis requirement as future work. This paper proposes a novel end-to-end methodology for characterizing and thwarting adversarial DL space. We introduce the concept of parallel checkpointing learners as a viable countermeasure to significantly reduce the risk of integrity attacks. The proposed PCL methodology explicitly characterizes statistical properties of the features within different layers of a neural network by learning a set of complementary dictionaries and corresponding probability density functions. The effectiveness of the PCL approach is evaluated against the state-of-the-art attack models including FGS, JSMA, Deepfool, and Carlini&WagnerL2. Proof-of-concept experiments for analyzing various data collections including MNIST, CIFAR10, and a subset of the ImageNet dataset corroborate successful detection of adversarial samples with relatively small false-positive rates.We devise an open-source API for the proposed countermeasure and invite the community to attempt attacks against the provided benchmarks in the form of a challenge. Table 2 presents the neural network architectures for the victim models used in each benchmark. The network for MNIST is the popular LeNet-3 architecture, the CIFAR-10 architecture is taken from BID4 , and the ImageNet model is inspired by the AlexNet architecture BID14 ). Table 2 : Baseline (victim) network architectures for evaluated benchmarks. Here, 128C3(2) denotes a convolutional layer with 128 maps and 3 × 3 filters applied with a stride of 2, MP3(2) indicates a max-pooling layer over regions of size 3 × 3 and stride of 2, and 300FC is a fully-connected layer consisting of 300 neurons. All convolution and fully connected layers (except the last layer) are followed by ReLU activation. A Softmax activation is applied to the last layer of each network. We visually evaluate the perturbed examples to determine the attack parameters (e.g., perturbation level ε and n iters ) such that the perturbations cannot be recognized by a human observer. Table 3 details the parameters used for the realization of different attack algorithms. The JSMA attack for the ImageNet benchmark is computationally expensive (e.g., it took more than 20min to generate one adversarial sample on an NVIDIA TITAN Xp GPU). As such, we could not generate the adversarial samples of this attack using the JSMA library provided by (Nicolas Papernot (2017) ). Table 3 : Details of attack algorithms for each evaluated application. The FGS method ) is characterized with a single ε parameter. The JSMA attack ) has two parameters: γ specifies the maximum percentage of perturbed features and θ denotes the value added to each selected feature. The Deepfool attack BID22 ) is characterized by the number of iterative updates, which we denote by n iters in this table. For the Carlini&WagnerL2 attack BID3 ), ""C"" denotes the confidence, ""LR"" is the learning rate, ""steps"" is the number of binary search steps, and ""iterations"" stands for the maximum number of iterations.",2522,1.281,1529,1.6494440810987574,"Recent advances adversarial Deep Learning opened malicious attacks jeopardizing autonomous DL systems We introduce a novel automated countermeasure called Parallel Checkpointing Learners thwart the potential adversarial attacks and significantly the reliability (safety a victim DL model The proposed PCL methodology unsupervised no adversarial sample leveraged build/train parallel checkpointing learners We formalize the goal preventing adversarial attacks as an optimization problem minimize the rarely observed regions the latent feature space spanned a DL network To solve the aforementioned minimization problem a set complementary but disjoint checkpointing modules trained validate the victim model execution parallel Each checkpointing learner explicitly characterizes the geometry within a particular DL layer As such the adversary required simultaneously deceive all the defender modules succeed We extensively evaluate the PCL methodology against state attack scenarios Fast-Gradient-Sign ( Jacobian Saliency Map AttackJSMA Deepfool Carlini&WagnerL2 algorithm Extensive proof evaluations analyzing various data collections including CIFAR10 ImageNet corroborate our proposed defense mechanism against adversarial samples Security and safety consideration a major obstacle emerging learning algorithms sensitive scenarios intelligent transportation, healthcare, and video surveillance applications BID18 ; While advanced learning technologies essential enabling coordination interaction the autonomous agents a careful analysis their decision reliability in carefully crafted adversarial samples ; ; BID22 ) thwarting their vulnerabilities still inConsider a traffic sign classifier employed In this setting an adversary carefully add legitimate ""stop sign sample fool the DL model classify; jeopardizes as shown BID18 ). As such highly important reject risky adversarial samples to DL models used autonomous systems such unmanned vehicles In aim answer the adversarial attacks.(i ) vulnerable adversarial samples Our hypothesis the vulnerability samples originates rarely explored sub each feature map This phenomenon particularly caused the limited access the labeled data inefficiency regularization algorithms BID30 ; Figure provides the partially explored space a twodimensional setup We analytically and back extensive evaluations on state attacks Fast-Gradient-Sign ), Jacobian Saliency Map Attack Deepfool BID22 Carlini&WagnerL2 BID3 ).(ii How characterize thwart the underlying space for unsupervised model assurance as defend the adversaries A line research there a model BID17 ; BID25 Taking this , instead making a single model both robust accurate introduce a new defense mechanism Parallel Checkpointing Learners In this setting the victim model kept is while separate defender modules trained checkpoint the data abstractions assess Each defender module characterizes the explored sub the pertinent layer learning the probability density functionpdf legitimate data points marking the complement sub rarely observed regions Once such characterization obtained , checkpointing modules 1 evaluate the input sample parallel the victim model raise alarm flags data points lie the rarely explored regions Figure As demonstrate adversarial samples created various attack methods mostly lie marked partially explored sectorsWe consider knows everything the victim model including its architecture learning parameters This threat model represents endanger We validate our proposed approach for different DL benchmarks including MNIST CIFAR10 a subset ImageNet data Based the result provide new insights the reason the existence adversarial transferability We open-source ease by (the link omitted blind review purposes invite attempt attacks our provided benchmarks in a challengeThe explicit contribution this paper as ( Devising end framework unsupervised model assurance as defending the adversaries (ii Incepting the idea parallel checkpointing learners validate the legitimacy data abstractions at each intermediate DL layer (iii Performing extensive proof evaluations against state attack methods (iv new insights regarding the transferability adversarial samples between different models Figure ( In data pointsdenoted can easily separated Having extra dimensions adds ambiguity choosing the pertinent decision boundaries For instance all the shown boundaries sufficient classify with full accuracy in but equivalent terms robustness noise (b) The rarely explored space (region specified diagonal striped) a learning model leaves adversaries manipulate the nuisance (non-critical) variables mislead crossing the decision boundaries (c In PCL methodology set defender (checkpoint) modules trained characterize the data density distribution spanned the victim model The defender modules then parallel checkpoint the reliability the ultimate prediction raise an alarm flag risky samples Note the remaining adversarial samples that detected crafted legitimate samples inherently hard classify even a human observer due decision boundaries corresponding such classes For instance the MNIST application such adversarial samples mostly belong class 5 that misclassified misclassified 9 Such misclassifications indeed the model approximation error which well to the statistical nature As such a more precise definition adversarial samples DISPLAYFORM0 Figure: Example adversarial confusion matrixa without PCL defense mechanism and a security parameter (c) Example adversarial samples which accurate detection hard due the closeness decision boundaries for corresponding classes.is extremely required distinguish malicious samples form those simply lie nearWe emphasize the PCL defenders trained independent the attack strategy meaning train the defender models This particularly corroborates the effectiveness generic attack scenarios including possible future adversarial DL algorithms Nevertheless one might question for adaptive attack algorithms target the defender modules A comprehensive study possible adaptive attack algorithms yet performed if developed We emphasize, thus significantly thwart all the existing attacks with only one checkpoint model approximating the data distribution the corresponding models Our proposed PCL methodology however provides adapted/ against potential future attacks training parallel disjoint modelswith diverse objectives/parameters further strengthenFigure 10 demonstrate using multiple checkpoints a negative correlation parallel effectively false alarms while adversarial samples In this experiment considered MNIST data classification LeNet model 4 layers FGS attack The checkpoints inserted different layers the pertinent neural network up We empirically select the mixing coefficients aggregate the confidence the checkpoint defenders rejecting an incoming sample Note, there the computational complexity overhead the PCL defenders On a high number validation checkpoints increases as each input sample should more defender networks On checkpoints may degrade the defense mechanism performance treating adversarial samples legitimate ones We looking into automated techniques customize the number checkpoint modules their corresponding mixing coefficients based application data physical constraints such real-time analysis requirement as future work This paper end methodology thwarting adversarial DL space We introduce parallel checkpointing learners as significantly integrity attacks The proposed PCL methodology explicitly characterizes statistical properties the features within different layers by learning complementary dictionaries corresponding probability density functions The effectiveness the PCL approach evaluated against state attack models including FGS JSMA Deepfool Carlini&WagnerL2 Proof experiments for analyzing various data collections including CIFAR10 a subset corroborate successful detection adversarial samplesWe devise the proposed countermeasure invite attempt attacks the provided benchmarks a challenge Table 2 presents the neural network architectures the victim models each benchmark The network for MNIST the popular LeNet-3 architecture the CIFAR-10 architecture is taken BID4 , the ImageNet model inspired BID14 Table 2 : Baseline (victim) network architectures evaluated benchmarks Here 128C3(2 denotes 128 maps 3 × applied with a stride MP3(2 indicates a max-pooling layer over regions size stride and 300FC is consisting 300 neurons All convolution and fully connected layersexcept followed ReLU activation A Softmax activation applied the last layer each network We visually evaluate the perturbed examples the attack parameters level � n iters ) such recognized Table 3 details parameters the realization different attack algorithms The JSMA attack for the ImageNet benchmark computationally it took 20min one adversarial sample on an NVIDIA TITAN Xp GPU As such could generate the adversarial samples this attack using the JSMA library provided (Nicolas Papernot (2017 Table 3 : Details attack algorithms each evaluated application The FGS method ) characterized with a single �� parameter The JSMA attack ) two parameters � specifies perturbed features denotes added The Deepfool attack BID22 ) characterized the number iterative updates we denote n iters this table For the Carlini&WagnerL2 attack BID3 ), ""C denotes the confidence, ""LR ""steps binary search steps stands",0.01,0.35880562879036537
"Neural architecture search (NAS) has a great impact by automatically designing effective neural network architectures. However, the prohibitive computational demand of conventional NAS algorithms (e.g. 10 4 GPU hours) makes it difficult to directly search the architectures on large-scale tasks (e.g. ImageNet). Differentiable NAS can reduce the cost of GPU hours via a continuous representation of network architecture but suffers from the high GPU memory consumption issue (grow linearly w.r.t. candidate set size). As a result, they need to utilize proxy tasks, such as training on a smaller dataset, or learning with only a few blocks, or training just for a few epochs. These architectures optimized on proxy tasks are not guaranteed to be optimal on the target task. In this paper, we present ProxylessNAS that can directly learn the architectures for large-scale target tasks and target hardware platforms. We address the high memory consumption issue of differentiable NAS and reduce the computational cost (GPU hours and GPU memory) to the same level of regular training while still allowing a large candidate set. Experiments on CIFAR-10 and ImageNet demonstrate the effectiveness of directness and specialization. On CIFAR-10, our model achieves 2.08% test error with only 5.7M parameters, better than the previous state-of-the-art architecture AmoebaNet-B, while using 6× fewer parameters. On ImageNet, our model achieves 3.1% better top-1 accuracy than MobileNetV2, while being 1.2× faster with measured GPU latency. We also apply ProxylessNAS to specialize neural architectures for hardware with direct hardware metrics (e.g. latency) and provide insights for efficient CNN architecture design.",347,0.184,218,1.591743119266055,Neural architecture searchNAS a great impact by automatically designing However the prohibitive computational demand conventional NAS algorithms (e.g. 10 4 GPU hours directly search the architectures large-scale tasks Differentiable NAS can reduce GPU hours via a continuous representation network architecture but suffers the high GPU memory consumption issuegrow linearly candidate set size As they need utilize proxy tasks training on a smaller dataset learning with just These architectures optimized proxy tasks guaranteed the target task In ProxylessNAS that directly learn the architectures large-scale target tasks target hardware platforms We address the high memory consumption issue differentiable NAS reduce (GPU hours regular training while a large candidate set. Experiments CIFAR-10 ImageNet demonstrate directness specialization On CIFAR-10 our model achieves 2.08% test error only 5.7M parameters better state architecture AmoebaNet-B while 6× fewer parameters On ImageNet our model achieves 3.1% better top-1 accuracy MobileNetV2 while being measured GPU latency We also apply ProxylessNAS specialize neural architectures hardware with direct hardware metrics provide insights efficient CNN architecture design,0.0,0.2117886475917153
"With the recently rapid development in deep learning, deep neural networks have been widely adopted in many real-life applications. However, deep neural networks are also known to have very little control over its uncertainty for test examples, which potentially causes very harmful and annoying consequences in practical scenarios. In this paper, we are particularly interested in designing a higher-order uncertainty metric for deep neural networks and investigate its performance on the out-of-distribution detection task proposed by~\cite{hendrycks2016baseline}. Our method first assumes there exists a underlying higher-order distribution $\mathcal{P}(z)$ , which generated label-wise distribution $\mathcal{P}(y)$ over classes on the K-dimension simplex, and then approximate such higher-order distribution via parameterized posterior function $p_{\theta}(z|x)$ under variational inference framework, finally we use the entropy of learned posterior distribution $p_{\theta}(z|x)$ as uncertainty measure to detect out-of-distribution examples. However , we identify the overwhelming over-concentration issue in such a framework, which greatly hinders the detection performance. Therefore , we further design a log-smoothing function to alleviate such issue to greatly increase the robustness of the proposed entropy-based uncertainty measure. Through comprehensive experiments on various datasets and architectures, our proposed variational Dirichlet framework with entropy-based uncertainty measure is consistently observed to yield significant improvements over many baseline systems. Recently, deep neural networks BID18 have surged and replaced the traditional machine learning algorithms to demonstrate its potentials in many real-life applications like speech recognition BID10 , image classification BID11 , and machine translation BID34 BID32 , reading comprehension BID27 , etc. However, unlike the traditional machine learning algorithms like Gaussian Process, Logistic Regression, etc, deep neural networks are very limited in their capability to measure their uncertainty over the unseen test cases and tend to produce over-confident predictions. Such overconfidence issue BID1 ) is known to be harmful or offensive in real-life applications. Even worse, such models are prone to adversarial attacks and raise concerns in AI safety BID9 BID23 . Therefore, it is very essential to design a robust and accurate uncertainty metric in deep neural networks in order to better deploy them into real-world applications. Recently, An out-of-distribution detection task has been proposed in BID12 as a benchmark to promote the uncertainty research in the deep learning community. In the baseline approach, a simple method using the highest softmax score is adopted as the indicator for the model's confidence to distinguish in-from out-ofdistribution data. Later on, many follow-up algorithms BID21 BID19 BID30 BID4 have been proposed to achieve better performance on this benchmark. In ODIN BID21 , the authors follow the idea of temperature scaling and input perturbation BID25 to widen the distance between in-and out-of-distribution examples. Later on, adversarial training BID19 ) is introduced to explicitly introduce boundary examples as negative training data to help increase the model's robustness. In BID4 , the authors proposed to directly output a real value between [0, 1] as the confidence measure. The most recent paper BID30 leverages the semantic dense representation into the target labels to better separate the label space and uses the cosine similarity score as the confidence measure.These methods though achieve significant results on out-of-distribution detection tasks, they conflate different levels of uncertainty as pointed in BID22 . For example, when presented with two pictures, one is faked by mixing dog, cat and horse pictures, the other is a real but unseen dog, the model might output same belief as {cat:34%, dog:33%, horse:33%}. Under such scenario, the existing measures like maximum probability or label-level entropy BID21 BID30 BID12 will misclassify both images as from out-of-distribution because they are unable to separate the two uncertainty sources: whether the uncertainty is due to the data noise (class overlap) or whether the data is far from the manifold of training data. More specifically, they fail to distinguish between the lower-order (aleatoric) uncertainty BID5 , and higherorder (episdemic) uncertainty BID5 , which leads to their inferior performances in detecting out-domain examples. In order to resolve the issues presented by lower-order uncertainty measures, we are motivated to design an effective higher-order uncertainty measure for out-of-distribution detection. Inspired by Subjective Logic BID14 BID37 BID29 , we first view the label-wise distribution P(y ) as a K-dimensional variable z generated from a higher-order distribution P(z ) over the simplex S k , and then study the higher-order uncertainty by investigating the statistical properties of such underlying higher-order distribution. Under a Bayesian framework with data pair D = (x, y), we propose to use variational inference to approximate such ""true"" latent distribution P(z) = p(z|y ) by a parameterized Dirichlet posterior p θ (z|x), which is approximated by a deep neural network. Finally, we compute the entropy of the approximated posterior for outof-distribution detection. However, we have observed an overwhelming over-concentration problem in our experiments, which is caused by over-confidence problem of the deep neural network to greatly hinder the detection accuracy. Therefore, we further propose to smooth the Dirichlet distribution by a calibration algorithm. Combined with the input perturbation method BID21 BID16 , our proposed variational Dirichlet framework can greatly widen the distance between in-and out-of-distribution data to achieve significant results on various datasets and architectures.The contributions of this paper are described as follows:• We propose a variational Dirichlet algorithm for deep neural network classification problem and define a higher-order uncertainty measure.• We identify the over-concentration issue in our Dirichlet framework and propose a smoothing method to alleviate such problem. In this paper, we aim at finding an effective way for deep neural networks to express their uncertainty over their output distribution. Our variational Dirichlet framework is empirically demonstrated to yield better results, but its detection accuracy on a more challenging setup like CIFAR100 is still very compromised. We conjecture that better prior Dirichlet distribution or smoothing function could help further improve the performance. In the future work, we plan to apply our method to broader applications like natural language processing tasks or speech recognition tasks.• LSUN (out-of-distribution): The Large-scale Scene UNderstanding dataset (LSUN) BID38 has a test set consisting of 10,000 images from 10 different scene classes, such as bedroom, church, kitchen, and tower. We downsample LSUN's original image and create 32 × 32 images as an out-of-distribution dataset.• iSUN (out-of-distribution): The iSUN dataset BID35 ) is a subset of the SUN dataset, containing 8,925 images. All images are downsampled to 32 × 32 pixels.",1388,0.663,817,1.6988984088127295,"With the recently rapid development deep learning widely However deep neural networks also very little control its uncertainty for test examples potentially causes very harmful and annoying consequences practical scenarios In are particularly designing a higher-order uncertainty metric investigate outdistribution detection proposed by~\cite{hendrycks2016baseline Our method first assumes there exists a underlying higher-order distribution $ , generated label-wise distribution over classes on the K-dimension simplex approximate via parameterized posterior function under variational inference framework finally we the entropy learned posterior distribution uncertainty measure detect out examples However , identify the overwhelming over-concentration issue such a framework greatly the detection performance Therefore , further design alleviate such issue to greatly the proposed entropy-based uncertainty measure Through comprehensive experiments various datasets architectures our proposed variational Dirichlet framework with entropy-based uncertainty measure consistently observed yield many baseline systems Recently deep neural networks BID18 surged and replaced to demonstrate its potentials like speech recognition BID10 , BID34 BID32 reading etc However unlike the traditional machine learning like etc limited measure their uncertainty over the unseen test cases tend produce Such overconfidence issue BID1 ) known harmful or offensive real-life applications Even worse such models prone adversarial attacks raise in AI safety BID9 BID23 . Therefore very essential design a robust and accurate uncertainty metric deep neural networks in better deploy into Recently An outdistribution detection task BID12 as a benchmark promote the uncertainty research In the baseline approach a simple method using the highest softmax score adopted as the indicator to distinguish infrom out-ofdistribution data Later many follow-up algorithms BID21 BID19 BID30 BID4 have achieve this benchmark In ODIN BID21 , the authors follow the idea temperature scaling input perturbation BID25 widen inanddistribution examples Later adversarial training BID19 ) explicitly introduce boundary examples as negative training data increase In BID4 , the authors proposed directly output a real value between [ as the confidence measure The most recent paper BID30 leverages the semantic dense representation into the target labels better separate the label space uses the cosine similarity score the confidence measureThese methods though achieve out detection tasks they conflate different levels uncertainty as pointed in BID22 . For example presented two pictures faked mixing dog, horse pictures a real but unseen dog the model might output same belief {cat:34% Under such scenario the existing measures like maximum probability or label-level entropy BID21 BID30 BID12 misclassify both images from because unable separate the two uncertainty sources: whether the data noise (class overlap far the manifold training data More specifically fail the lower-order (aleatoric) uncertainty BID5 , higherorder (episdemic) uncertainty leads their inferior performances detecting out-domain examples In order resolve presented lower-order uncertainty measures motivated design out detection Inspired Subjective Logic BID14 BID37 BID29 , first view the label-wise distribution P(y ) a K-dimensional variable z generated over the simplex S k study by investigating such underlying higher-order distribution Under a Bayesian framework with data pair D = propose approximate such ""true"" latent distribution P(z ) by a parameterized Dirichlet posterior p �� Finally compute the approximated posterior for outof-distribution detection However we observed overwhelming over problem our experiments caused problem to greatly hinder Therefore further smooth a calibration algorithm Combined the input perturbation method BID21 BID16 our proposed variational Dirichlet framework greatly widen inanddistribution data to achieve significant results on various datasets architecturesThe contributions described deep neural network classification problem define identify over issue alleviate such problem In aim finding for express their uncertainty their output distribution Our variational Dirichlet framework empirically demonstrated yield its detection accuracy on a more challenging setup like CIFAR100 compromised We conjecture better prior Dirichlet distribution or smoothing function further In the future work, plan apply our method broader applications natural language processing tasks or speech recognition tasks.• LSUN (out): The Large-scale Scene UNderstanding dataset BID38 has test such bedroom church kitchen tower We downsample LSUN's original image create 32 × 32 images as outdistribution dataset.• iSUN (out): The iSUN dataset BID35 ) the SUN dataset containing 8,925 images All images downsampled 32 × 32 pixels",0.01,0.48481091079584193
"Intelligent agents can learn to represent the action spaces of other agents simply by observing them act. Such representations help agents quickly learn to predict the effects of their own actions on the environment and to plan complex action sequences. In this work, we address the problem of learning an agent’s action space purely from visual observation. We use stochastic video prediction to learn a latent variable that captures the scene's dynamics while being minimally sensitive to the scene's static content. We introduce a loss term that encourages the network to capture the composability of visual sequences and show that it leads to representations that disentangle the structure of actions. We call the full model with composable action representations Composable Learned Action Space Predictor (CLASP). We show the applicability of our method to synthetic settings and its potential to capture action spaces in complex, realistic visual settings. When used in a semi-supervised setting, our learned representations perform comparably to existing fully supervised methods on tasks such as action-conditioned video prediction and planning in the learned action space, while requiring orders of magnitude fewer action labels. Project website: https://daniilidis-group.github.io/learned_action_spaces Agents behaving in real-world environments rely on perception to judge what actions they can take and what effect these actions will have. Purely perceptual learning may play an important role in how these action representations are acquired and used. In this work, we focus on the problem of learning an agent's action space from unlabeled visual observations. To see the usefulness of this strategy, consider an infant that is first learning to walk. From around 10 months of age, infants rapidly progress from crawling, to irregular gaits with frequent falling, and finally to reliable locomotion (Adolph et al. (2012) ). But before they first attempt to walk, infants have extensive sensory exposure to adults walking. Unsupervised learning from sensory experience of this type appears to play a critical role in how humans acquire representations of actions before they can reliably reproduce the corresponding behaviour BID33 ). Infants need to relate the set of motor primitives they can generate to the action spaces exploited by adults (Dominici et al. (2011)) , and a representation acquired by observation may allow an infant to more efficiently learn to produce natural, goal-directed walking behavior.Reinforcement learning (RL) provides an alternative to the (passive) unsupervised learning approach as it implicitly discovers an agent's action space and the consequences of its actions. Recent breakthroughs in model-free and model-based RL suggest that end-to-end training can be used to learn mappings between sensory input and actions BID14 ; BID12 ; BID11 ; Finn & Levine (2017) ; BID25 ). However, these methods require active observations and the sensorimotor mappings learned in this way cannot be easily generalized to new agents with different control interfaces. Methods for sensorimotor learning from purely visual Using latent composition to recover actions from passive data. a) Two sequences starting from different initial states but changing according to the same actions. Without requiring labels, our model learns to represent the action in sequences like these identically. We train a representation z to capture the dynamics of the scene and its compositional structure: applying (z 1 and z 2 ) should have the same effect as applying the composed representation g(z 1 , z 2 ). These properties capture the fact that effector systems, such as a robot arm, use the same composable action space in many different states. b) The learned action space z recovered by our method (PCA visualization). Points are colored by the true action u: true actions can be easily decoded from z, validating that the structure of the action space has been captured.data may facilitate learning where action information is not available, such as when using video data collected from the Internet. Such methods may also be useful for imitation learning, where ground truth actions are often hard or impossible to collect other than by visual observation (Finn et al. (2017) ; BID18 ). More generally, learning from passive observations may make it easier to reuse action representations between systems with different effectors and goals. The representations learned by unsupervised methods are invariant to these choices because the model does not have access to motor commands or goals during training.In this work, we evaluate the proposal that learning what you can do before doing anything can lead to action space representations that make subsequent learning more efficient. To this end, we develop a model that learns to represent an agent's action space given only unlabeled videos of the agent. The resulting representation enables direct planning in the latent space. Given a small number of action-labeled sequences we can execute the plan by learning a simple mapping from latent action representations to the agent's controls. This representation may be analogous to those in the parietal and premotor areas of cortex, which include populations of neurons that represent the structure of actions produced both by the self and by others BID20 ; BID21 ) and that are critical for reliably producing flexible, voluntary motor control (see BID6 , Chapter 38). In the brain, representations of this kind could plausibly be learned using specialized loss functions BID13 ) whose effect is to induce the prior needed to determine the structure of actions in observation data.In contrast to most approaches to unsupervised learning of dynamics, which focus on learning the statistical structure of the environment, we focus on disentangling action information from the instantaneous state of the environment FIG0 . We base our work on recent stochastic video prediction methods (Babaeizadeh et al. (2018); Denton & Fergus (2018) ; BID10 ) and impose two properties on the latent representation. First, we train the representation to be minimal, i.e. containing minimal information about the current world state. This forces the representation to focus on dynamic properties of the sensory input. A similar objective has been used in previous work to constrain the capacity of video prediction models (Denton & Fergus (2018) ). Second, we train the representation to be composable by introducing a novel loss term that enforces that the cumulative effect of a sequence of actions can be computed from the individual actions' representations ( FIG0 . Composability encourages disentangling: as a composed representation does not have access to the static content of the intermediate frames, a representation is composable only if the individual action representations are disentangled from the static content. Taken together, these two properties lead to a representation of sensory dynamics that captures the structure of the agent's actions.We make the following three contributions. First, we introduce a method for unsupervised learning of an agent's action space by training the latent representation of a stochastic video prediction model for the desiderata of minimality and composability. Second, we show that our method learns a representation of actions that is independent of scene content and visual characteristics on (i) a simulated robot with one degree of freedom and (ii) the BAIR robot pushing dataset (Ebert et al. (2017) ). Finally, we demonstrate that the learned representation can be used for action-conditioned video prediction and planning in the learned action space, while requiring orders of magnitude fewer action-labeled videos than extant supervised methods. We have shown a way of learning the structure of an agent's action space from visual observations alone by imposing the properties of minimality and composability on a latent variable for stochastic video prediction. This strategy offers a data-efficient alternative to approaches that rely on fully supervised action-conditioned methods. The resulting representation can be used for a range of tasks, such as action-conditioned video prediction and planning in the learned latent action space. The representation is insensitive to the static scene content and visual characteristics of the environment. It captures meaningful structure in synthetic settings and achieves promising results in realistic visual settings.",1563,0.907,928,1.6842672413793103,"Intelligent agents represent the action spaces simply act Such representations help agents quickly learn predict plan complex action sequences In this work address learning an agent��s action space purely visual observation We use stochastic video prediction learn a latent variable captures while being sensitive We introduce a loss term encourages the network capture the composability visual sequences show leads representations disentangle actions We call the full model with composable action representations Composable Learned Action Space Predictor We show our method synthetic settings its potential capture action spaces complex, realistic visual settings When used our learned representations perform existing fully supervised methods on tasks action-conditioned video prediction planning in the learned action space requiring orders magnitude fewer action labels Project website https://daniilidis-group.github.io/learned_action_spaces Agents behaving rely perception judge what effect Purely perceptual learning may play how these action representations acquired In this work learning an agent's action space unlabeled visual observations To the usefulness this strategy an infant first learning From around 10 months of infants rapidly progress crawling irregular gaits with frequent falling reliable locomotion (Adolph et (2012 ). But before first attempt walk infants extensive sensory exposure adults walking Unsupervised learning from sensory experience of this type appears play how acquire representations actions before reliably reproduce the corresponding behaviour BID33 Infants need relate the set motor primitives generate the action spaces exploited adultsDominici (2011 , and a representation acquired observation may allow an infant more efficiently produce natural, goal-directed walking behaviorReinforcement learningRL provides as implicitly discovers an agent's action space the consequences Recent breakthroughs model-free and model-based RL suggest end training learn mappings sensory input actions BID14 ; BID12 Finn & Levine2017 BID25 However these methods require active observations the sensorimotor mappings learned easily generalized new agents different control interfaces Methods sensorimotor from purely Using latent composition to recover actions passive data a) Two sequences starting different initial states but changing according the same actions Without requiring labels our model learns represent the action sequences like identically We train a representation z to capture: applying (z 1 and should have the composed representation g(z These properties capture the fact effector systems a robot arm use the same composable action space in b The learned action space z recovered our method (PCA visualization Points colored the true action u: true actions can easily decoded z, validating the structure captured.data may facilitate learning where action information not using video data collected Such methods imitation learning ground truth actions hard or collect other visual observationFinn (2017 ; BID18 ). More generally learning passive observations may make reuse action representations between systems with different effectors goals The representations learned unsupervised methods invariant these choices because access motor commands goals duringIn evaluate the proposal learning what before doing action space representations make subsequent learning To this end develop learns represent an agent's action space given only unlabeled videos The resulting representation enables direct planning the latent space Given a small number action-labeled sequences we execute the plan learning a simple mapping latent action representations the agent's controls This representation may analogous cortex include populations represent actions produced both BID20 ; ) that critical reliably producing flexible, voluntary motor control Chapter 38 In the brain representations this kind could plausibly learned specialized loss functions BID13 ) whose effect induce prior needed determine actions observation dataIn most approaches of dynamics the statistical structure action information the instantaneous state FIG0 We base recent stochastic video prediction methodsBabaeizadeh (2018 Denton & Fergus ; BID10 ) and impose two properties the latent representation First train the representation minimal containing This forces the representation focus dynamic properties the sensory input A similar objective previous work video prediction modelsDenton Fergus (2018 Second train the representation composable introducing a novel loss term enforces the cumulative effect a sequence actions the individual actions' representations FIG0 Composability encourages: as a composed representation does access the static content the intermediate frames the individual action representations Taken lead a representation sensory dynamics captures the agent's actionsWe make First introduce a method an agent's action space training the latent representation a stochastic video prediction model the desiderata minimality composability Second show our method learns a representation actions independent scene content visual characteristics on ( a simulated robot with one degree the BAIR robot pushing dataset (2017 ). Finally demonstrate the learned representation can action-conditioned video prediction planning the learned action space requiring orders extant supervised methods We shown a way learning an agent's action space from visual observations alone by imposing minimality composability a latent variable for stochastic video prediction This strategy offers a data-efficient alternative approaches fully supervised action-conditioned methods The resulting representation can action-conditioned video prediction planning in the learned latent action space The representation insensitive the static scene content visual characteristics It captures meaningful structure synthetic settings achieves promising results realistic visual settings",0.01,0.447531981655805
"When autonomous agents interact in the same environment, they must often cooperate to achieve their goals. One way for agents to cooperate effectively is to form a team, make a binding agreement on a joint plan, and execute it. However, when agents are self-interested, the gains from team formation must be allocated appropriately to incentivize agreement. Various approaches for multi-agent negotiation have been proposed, but typically only work for particular negotiation protocols. More general methods usually require human input or domain-specific data, and so do not scale. To address this, we propose a framework for training agents to negotiate and form teams using deep reinforcement learning. Importantly, our method makes no assumptions about the specific negotiation protocol, and is instead completely experience driven. We evaluate our approach on both non-spatial and spatially extended team-formation negotiation environments, demonstrating that our agents beat hand-crafted bots and reach negotiation outcomes consistent with fair solutions predicted by cooperative game theory. Additionally, we investigate how the physical location of agents influences negotiation outcomes. Multiple agents inhabiting the same environment affect each other, and may gain by coordinating their actions. Indeed, many tasks are effectively intractable for any single agent, and so can only be solved by a team of collaborators. Examples include search and rescue BID27 , multirobot patrolling BID1 , security BID56 and multiplayer first-person video games BID24 . Despite the need to cooperate, stakeholders have different abilities and preferences which affect the chosen course of action. Agents must therefore negotiate to form teams that are both fairly aligned with individual interests and capable of achieving the task at hand. This problem can formalized as a team-formation negotiation task as follows BID29 BID51 . By definition, no single agent can perform the task on their own, but there may be several teams of agents who are capable of doing so, so each agent must decide who to collaborate with. The reward for accomplishing the task is awarded to the first team that solves it. Hence, agents need to interact with one another to simultaneously form a team and agree on how to share the joint reward. To solve this abstract problem, one must provide a concrete environment where agents can negotiate and reach an agreement; We must specify a negotiation protocol that encodes the allowed negotiation actions and determines the agreement reached BID46 .Team-formation negotiation tasks are natural objects of study in game theory. More precisely , cooperative game theory focuses on interactions between agents who form teams and make enforceable agreements about outcomes BID7 BID11 .1 Weighted voting games are an archetypal problem, in which every agent has a weight and a team of agents is successful if the sum of the weights of its participants exceeds a fixed threshold BID5 BID21 . Weighted voting games also offer a simple model of coalition formation in legislative bodies BID31 BID17 . Cooperative game theory seeks to predict the agreements negotiated by agents in such settings, proposing several solution concepts. Some solutions, such as the core and nucleolus BID47 , have focused on identifying stable agreements. Other solutions , known as power indices, have tried to measure the objective negotiation position of agents, quantifying their relative ability to affect the outcome of the game, or the fair share of the joint reward they should receive BID11 . The most prominent of these is the Shapley value BID49 which has been widely studied for weighted voting games BID50 BID54 . In particular, it has been used to estimate political power BID31 BID17 . In Appendix A we provide a detailed motivating example, showing how the Shapley value fairly measures power in such settings.There remains a pragmatic question for the design of multi-agent systems. How should one construct a negotiating agent that maximizes the reward obtained? Many researchers have borrowed ideas from cooperative game theory to hand-craft bots (Zlotkin & Rosenschein, 1989; BID2 BID23 , often requiring additional human data BID43 BID35 . Such bots are tailored to specific negotiation protocols, so modifying the protocol or switching to a different protocol requires manually re-writing the bot BID25 . As a result, algorithms based purely on cooperative game theory are neither generally applicable nor scalable.Moreover, negotiation and team formation in the real world is significantly more complex than in the game theoretic setting, for several reasons: (1) negotiation protocols can be arbitrarily complicated and are rarely fixed; (2) enacting a negotiation requires a temporally extended policy; (3) the idiosyncrasies of the environment affect the negotiation mechanics; (4) Players must make decisions based on incomplete information about others' policies.We propose multi-agent reinforcement learning as an alternative paradigm which may be applied to arbitrary negotiation protocols in complex environments. Here, individual agents must learn how to solve team formation tasks based on their experiences interacting with others, rather than via hand-crafted algorithms. Our RL approach is automatically applicable to Markov games BID48 Littman, 1994) , which are temporally and spatially extended, similar to recent work in the non-cooperative case BID33 Foerster et al., 2017) . In contrast to earlier work on multi-agent RL in non-cooperative games, the key novelty of our work is comparing the behaviour of negotiating RL agents with solutions from cooperative game theory.Some previous work in multi-agent (deep) reinforcement learning for negotiation has cast the problem as one of communication, rather than team formation (e.g. BID19 ; BID34 BID9 ). In particular, the environments considered involved only two agents, sidestepping the issue of coalition selection. Closer to our perspective is the work of Chalkiadakis & Boutilier (2004); BID40 , which propose a Bayesian reinforcement learning framework for team formation. However, they do not consider spatially extended environments and the computational cost of the Bayesian calculation is significant. We evaluate our approach on a team formation negotiation task using a direct negotiation protocol, showing that agents trained via independent reinforcement learning outperform hand-crafted bots based on game-theoretic principles. We analyze the reward distribution, showing a high correspondence with the Shapley value solution from cooperative game theory. We show that the slight deviation is not due to lack of neural network capacity by training a similar-sized supervised model to predict the Shapley value. We also introduce a more complicated spatial grid-world environment in which agents must move around to form teams. We show that the correspondence with the Shapley value persists in this case, and investigate how spatial perturbations influence agents' rewards. Team formation is an important problem for multi-agent systems, since many real-world tasks are impossible without the cooperation and coordination of multiple agents. Our contributions are as follows: FORMULA0 we introduced a scalable method for team-formation negotiation based on deep reinforcement learning which generalizes to new negotiation protocols and does not require human data, (2) we showed that negotiator agents derived by this method outperform simple hand-crafted bots, and produce results consistent with cooperative game theory, 3) we applied our method to spatially and temporally extended team-formation negotiation environments, where solving for the equilibrium behavior is hard, and (4) we showed that our method makes sensible predictions about the effect of spacial changes on agent behavioral and negotiation outcomes.This work opens up a new avenue of research applying deep learning to team-formation negotiation tasks. In particular, it would be interesting to analyze how team formation dynamics affect emergent language in reinforcement learning agents, naturally extending the work of BID8 and BID30 . Indeed, it has been suggested that the human ability to negotiate and form teams was critical in the evolution of language (Thomas & Kirby, 2018) . One might also consider creating tasks that interpolate between the fully cooperative game-theoretic setting and the purely non-cooperative one. Fundamentally, binding contracts are managed by dynamic institutions, whose behavior is also determined by learning. In principle, we could extend our method to this hierarchical case, perhaps along the lines of BID20",1593,0.854,940,1.6946808510638298,"When autonomous agents interact in must often cooperate One way for agents cooperate effectively form make a joint plan execute However when agents self the gains team formation must allocated appropriately incentivize agreement Various approaches for multi-agent negotiation typically work particular negotiation protocols More general methods usually human input do scale To address propose training agents negotiate form teams using deep reinforcement learning Importantly our method makes the specific negotiation protocol instead completely experience driven We evaluate our approach on both non-spatial and spatially extended team-formation negotiation environments demonstrating our agents beat hand-crafted bots reach negotiation outcomes consistent fair solutions predicted cooperative game theory Additionally investigate the physical location agents negotiation outcomes Multiple agents inhabiting affect may gain by coordinating Indeed many tasks effectively any single agent can collaborators Examples include search and rescue BID27 , multirobot patrolling security multiplayer first video Despite cooperate stakeholders different abilities preferences which the chosen course Agents must therefore negotiate to form teams both fairly aligned individual interests capable the task This problem formalized a team-formation negotiation task as BID29 BID51 By definition no single agent perform on their may several teams of decide who collaborate The reward awarded solves it Hence agents need interact one simultaneously form agree share the joint reward To solve this abstract problem one provide a concrete environment agents negotiate reach; We must specify a negotiation protocol the allowed negotiation actions determines reached BID46 .Team-formation negotiation tasks natural objects study game theory More precisely , cooperative game theory focuses interactions agents form teams make enforceable agreements about outcomes BID7 BID11 .1 Weighted voting games an archetypal problem every agent a team successful Weighted voting games also offer a simple model coalition formation legislative bodies BID31 BID17 . Cooperative game theory seeks predict the agreements negotiated agents such settings proposing several solution concepts Some solutions the core and nucleolus BID47 , focused identifying stable agreements Other solutions , known power indices tried measure the objective negotiation position agents quantifying affect the fair share the joint reward they should BID11 most prominent the Shapley value BID49 which studied weighted voting games BID50 BID54 In particular used estimate political power BID31 BID17 . In Appendix A a detailed motivating example, the Shapley value fairly measures power such settingsThere remains a pragmatic question multi-agent systems How should one construct a negotiating agent that the reward obtained Many researchers borrowed cooperative game theory hand-craft bots (Zlotkin Rosenschein 1989 BID2 BID23 , often requiring additional human data BID43 BID35 . Such bots tailored specific negotiation protocols modifying or switching requires manually re BID25 . As algorithms based purely cooperative game theory neither generally scalableMoreover negotiation team formation significantly for arbitrarily are rarely fixed enacting requires a temporally extended policy the environment affect the negotiation mechanics make incomplete information others' policiesWe multi-agent reinforcement learning which may arbitrary negotiation protocols complex environments Here individual agents must learn solve team formation tasks based interacting via Our RL approach automatically applicable Markov games BID48 Littman 1994) , temporally and extended similar recent work the non-cooperative case BID33 2017) In contrast earlier work multi-agent RL in the key novelty comparing negotiating solutions fromSome previous work multi-agent (deep) reinforcement learning for negotiation cast the problem communication team formatione.g. BID19 ; BID34 BID9 In particular, the environments considered involved only two agents sidestepping coalition selection Closer our perspective Chalkiadakis & Boutilier BID40 , propose a Bayesian reinforcement learning framework team formation However they consider spatially extended environments and the computational cost the Bayesian calculation is significant We evaluate our approach on a team formation negotiation task a direct negotiation protocol showing agents trained via independent reinforcement learning hand-crafted bots based We analyze the reward distribution, showing a high correspondence the Shapley value solution from cooperative game theory We show the slight deviation is lack neural network capacity by training a similar-sized supervised model predict the Shapley value We also introduce a more complicated spatial grid-world environment agents must move to form teams We show the correspondence with the Shapley value persists investigate how spatial perturbations influence agents' rewards Team formation an important problem multi-agent systems since impossible Our contributions as FORMULA0 we introduced a scalable method team-formation negotiation based deep reinforcement learning which generalizes new negotiation protocols does human data (2 showed negotiator agents derived by simple hand-crafted bots produce results consistent cooperative game theory 3 applied solving the equilibrium behavior hard ( makes sensible predictions spacial changes agent behavioral and negotiation outcomesThis work opens applying In particular analyze team formation dynamics emergent language in reinforcement learning agents naturally extending BID8 . Indeed the human ability negotiate form teams critical language (Thomas & Kirby 2018 One might creating tasks interpolate the fully cooperative game-theoretic setting Fundamentally binding contracts managed dynamic institutions whose behavior also learning In principle extend our method this hierarchical case perhaps along BID20",0.01,0.47406494420221784
"Neural machine translation (NMT) models learn representations containing substantial linguistic information. However, it is not clear if such information is fully distributed or if some of it can be attributed to individual neurons. We develop unsupervised methods for discovering important neurons in NMT models. Our methods rely on the intuition that different models learn similar properties, and do not require any costly external supervision. We show experimentally that translation quality depends on the discovered neurons, and find that many of them capture common linguistic phenomena. Finally, we show how to control NMT translations in predictable ways, by modifying activations of individual neurons. Neural machine translation (NMT) systems achieve state-of-the-art results by learning from large amounts of example translations, typically without additional linguistic information. Recent studies have shown that representations learned by NMT models contain a non-trivial amount of linguistic information on multiple levels: morphological BID4 BID7 , syntactic BID31 , and semantic BID16 . These studies use trained NMT models to generate feature representations for words, and use these representations to predict certain linguistic properties. This approach has two main limitations. First, it targets the whole vector representation and fails to analyze individual dimensions in the vector space. In contrast, previous work found meaningful individual neurons in computer vision BID34 BID36 Bau et al., 2017, among others) and in a few NLP tasks BID18 BID27 BID25 . Second, these methods require external supervision in the form of linguistic annotations. They are therefore limited by available annotated data and tools.In this work, we make initial progress towards addressing these limitations by developing unsupervised methods for analyzing the contribution of individual neurons to NMT models. We aim to answer the following questions:• How important are individual neurons for obtaining high-quality translations?• Do individual neurons in NMT models contain interpretable linguistic information?• Can we control MT output by intervening in the representation at the individual neuron level?To answer these questions, we develop several unsupervised methods for ranking neurons according to their importance to an NMT model. Inspired by work in machine vision BID22 , we hypothesize that different NMT models learn similar properties, and therefore similar important neurons should emerge in different models. To test this hypothesis, we map neurons between pairs of trained NMT models using several methods: correlation analysis, regression analysis, and SVCCA, a recent method combining singular vectors and canonical correlation analysis BID28 . Our mappings yield lists of candidate neurons containing shared information across models. We then evaluate whether these neurons carry important information to the NMT model by masking their activations during testing. We find that highly-shared neurons impact translation quality much more than unshared neurons, affirming our hypothesis that shared information matters.Given the list of important neurons, we then investigate what linguistic properties they capture, both qualitatively by visualizing neuron activations and quantitatively by performing supervised classification experiments. We were able to identify neurons corresponding to several linguistic phenomena, including morphological and syntactic properties.Finally, we test whether intervening in the representation at the individual neuron level can help control the translation. We demonstrate the ability to control NMT translations on three linguistic properties-tense, number, and gender-to varying degrees of success. This sets the ground for controlling NMT in desirable ways, potentially reducing system bias to properties like gender.Our work indicates that not all information is distributed in NMT models, and that many humaninterpretable grammatical and structural properties are captured by individual neurons. Moreover, modifying the activations of individual neurons allows controlling the translation output according to specified linguistic properties. The methods we develop here are task-independent and can be used for analyzing neural networks in other tasks. More broadly, our work contributes to the localist/distributed debate in artificial intelligence and cognitive science BID13 by investigating the important case of neural machine translation. Neural machine translation models learn vector representations that contain linguistic information while being trained solely on example translations. In this work, we developed unsupervised methods for finding important neurons in NMT, and evaluated how these neurons impact translation quality. We analyzed several linguistic properties that are captured by individual neurons using quantitative prediction tasks and qualitative visualizations. We also designed a protocol for controlling translations by modifying neurons that capture desired properties.Our analysis can be extended to other NMT components (e.g. the decoder) and architectures BID14 BID33 , as well as other tasks. We believe that more work should be done to analyze the spectrum of localized vs. distributed information in neural language representations. We would also like to expand the translation control experiments to other architectures and components (e.g. the decoder), and to develop more sophisticated ways to control translation output, for example by modifying representations in variational NMT architectures BID35 BID32 . Our code is publicly available as part of the NeuroX toolkit BID9 .",966,0.558,555,1.7405405405405405,"Neural machine translation learn representations containing substantial linguistic information However such information fully distributed some attributed individual neurons We develop unsupervised methods discovering important neurons NMT models Our methods rely the intuition different models learn similar properties do any costly external supervision We show experimentally translation quality depends the discovered neurons find many capture common linguistic phenomena Finally show control NMT translations predictable ways modifying activations individual neurons Neural machine translation achieve state learning large amounts example translations typically without additional linguistic information Recent studies representations learned NMT models contain linguistic information on multiple levels morphological BID4 BID7 These studies use trained NMT models generate feature representations words certain linguistic properties This approach First targets the whole vector representation fails analyze individual dimensions In contrast previous work meaningful individual neurons computer vision BID34 BID36 Bau et al. among others) a few NLP tasks . Second these methods require external supervision in linguistic annotations They therefore limited available annotated data toolsIn make initial progress addressing analyzing the contribution NMT models We aim answer important individual neurons obtaining NMT models contain control MT output intervening at develop ranking neurons according Inspired work machine vision BID22 , hypothesize different NMT models learn similar properties similar important neurons emerge To test map neurons between pairs trained NMT models several methods correlation analysis SVCCA a recent method combining singular vectors canonical correlation analysis BID28 . Our mappings yield lists candidate neurons containing shared information across models We then evaluate these neurons carry important information to the NMT model masking testing We find that highly-shared neurons impact translation quality much affirming information mattersGiven the list important neurons then what linguistic properties capture both qualitatively by performing supervised classification experiments We were identify neurons corresponding several linguistic phenomenaFinally test intervening in the representation at control We demonstrate control NMT translations on three linguistic properties- number genderto varying degrees success This sets the ground controlling NMT desirable ways potentially system bias to properties genderOur work indicates not all information distributed many humaninterpretable grammatical and structural properties captured individual neurons Moreover modifying the activations individual neurons allows controlling the translation output according specified linguistic properties The methods develop task analyzing More broadly our work contributes the localist/distributed debate artificial intelligence and cognitive science BID13 by investigating the important case neural machine translation Neural machine translation models learn vector representations contain linguistic information while being trained solely example translations In this work developed unsupervised methods finding important neurons NMT evaluated impact translation quality We analyzed several linguistic properties captured individual neurons using quantitative prediction tasks qualitative visualizations We also designed a protocol controlling translations modifying neurons capture desired propertiesOur analysis can other NMT components architectures BID14 BID33 , as other tasks We believe more work analyze the spectrum localized vs. distributed information in neural language representations We would expand the translation control experiments other architectures components develop translation output modifying representations variational NMT architectures BID35 BID32 Our code publicly as the NeuroX toolkit BID9 .",0.01,0.5909114038006147
"Recent state-of-the-art reinforcement learning algorithms are trained under the goal of excelling in one specific task. Hence, both environment and task specific knowledge are entangled into one framework. However, there are often scenarios where the environment (e.g. the physical world) is fixed while only the target task changes. Hence, borrowing the idea from hierarchical reinforcement learning, we propose a framework that disentangles task and environment specific knowledge by separating them into two units. The environment-specific unit handles how to move from one state to the target state; and the task-specific unit plans for the next target state given a specific task. The extensive results in simulators indicate that our method can efficiently separate and learn two independent units, and also adapt to a new task more efficiently than the state-of-the-art methods. Let's imagine ourselves learning how to play tennis for the first time. Even though we have never played tennis before, we already have a good understanding of agent and environment dynamics related to tennis. For example, we know how to move our arm from one position to another and that a ball will slow down and bounce back from the ground. Hence, we just need to learn the tennis specific knowledge (e.g. its game rule and a relationship between an arm control and a tennis racket). Just like this example, when we learn to complete a new task, we utilize the prior knowledge that is disentangled from the task and acquired over our lifetime. Figure 1: Our model disentangles environment-specific information (e.g. transition dynamics) and task-specific knowledge (e.g. task rewards) for training efficiency and interpretability.From a reinforcement learning perspective, this brings a very interesting question -how can agents also obtain and utilize such disentangled prior knowledge about the environment? Most of today's deep reinforcement learning (DRL) models BID14 ; BID25 are trained with entangled environment-specific knowledge (e.g. transition dynamics) and taskspecific knowledge (e.g. rewards), as described in Figure 1a However, as described earlier, humans τ τ Figure 2 : Proposed universal agent, which consists of three parts: a φ function mapping raw observation to feature space, a PATH function as an environment actor, and a τ function for future state planning.have an innate ability to obtain a good understanding about the environment dynamics, and utilize them in a newly given task. Motivated from this, we introduce a new scheme to disentangle the learning procedure of task-independent transition dynamics and task-specific rewards, as described in Figure 2 . This will help an agent to adapt to a new task more efficiently and also provides an extra interpretability.The idea of disentangling a model into two components can be related to hierarchical RL approaches BID29 ; BID17 ; BID16 . However, to the best of our knowledge, there has not been a work that separating units by the natural criteria of environment and task specific knowledge, for the goal of transfer learning.To this end, we introduce a model that consists of two major units: a PATH function and a goal generator. This is illustrated in Figure 2 . The key intuition is as the following. PATH function handles the environment specific knowledge, and a goal function handles the task specific knowledge. We design (1) PATH function to learn how to move from one state to another -a lower-level controller, which is independent from the task and only depends on the environment, and (2) the goal function τ to determine the next state given a target task -a higher-level planner. Thus, PATH function can be shared across different tasks as long as it is under the same environment (e.g. the physical world).We evaluate our method to answer the following two questions: (1) how a good PATH unit can benefit the task learning, and (2) how efficient is our model for learning a new task in the same environment. We analyze the behavior of our method on various environments including a maze world and multiple Atari 2600 games. Our study shows that a good PATH unit can be trained, and our model has a faster convergence compared to the state-of-the-art method BID15 in most of the tasks, especially on transfer learning tasks.In summary, we introduce an RL model with disentangled units for task-specific and environmentspecific knowledge. We demonstrate in multiple environments that our method learns environmentspecific knowledge, which further enables an agent adapting to a new task in the same environment. Model-based reinforcement learning Typical model-based RL frameworks aim to model the dynamics of the environment. They usually involve search-based algorithms (e.g., Monte Carlo Tree Search) as part of the policy Sutton & Barto (1998) (e.g., Alpha GO with a simulator , Scheme-networks with learned forward dynamics BID11 ). In this paper, we address the problem of representing the knowledge about the environment by learning skills (how to reach a given state). As a cognitive science motivation described in BID6 , humans also store the knowledge of movements or actions by their end-states. Most importantly, this knowledge can be easily utilized by a task-specific module (the goal generator) to exploit novel tasks.Multi-task learning and transfer learning Multi-task learning and transfer learning BID2 ; BID0 ; Taylor & Stone (2009) provide approaches to transfer knowledge among multiple agents. The methods include the decomposition of value function or task and direct multi-task learning where agents learn several tasks jointly. Contrary to them, universal agent is able to obtain the environment specific knowledge without any specific task supervision. (2015) ; BID32 , the τ function does not perform option selection but directly composes target state since a general-purpose PATH function is utilized. We do not follow typical HRL methods where once the subtask is selected, the low-level controller will be executed for multiple time steps. In universal agent, for simplicity now, τ function plans the future state at every time step. We leave its adaption to HRL frameworks as a future work. We present a new reinforcement learning scheme that disentangles the learning procedure of taskindependent transition dynamics and task-specific rewards. The main advantage of this is efficiency of task adaptation and interpretability. For this we simply introduce two major units: a PATH function and a goal generator. Our study shows that a good PATH unit can be trained, and our model outperforms the state-of-the-art method BID15 in most of tasks, especially on transfer learning tasks.The proposed framework is a novel step towards the knowledge representation learning for deep reinforcement learning (DRL). There are a variety of future research directions. For example, how PATH function can be learned (e.g., in a continual learning manner BID22 , with less requirement such as state restoration), how it can better cooperate with the goal generator (e.g., incorporating explicit future planning) and how it can be used for other tasks (e.g., learning from demonstration).",1375,0.722,798,1.7230576441102756,"Recent state reinforcement learning trained under the goal excelling Hence both environment task specific knowledge entangled into one framework However often scenarios the environment ( fixed while only target task changes Hence borrowing hierarchical reinforcement learning propose task and environment specific knowledge by separating two units The environment-specific unit handles how move from the target state; and given The extensive results in simulators indicate our method efficiently separate learn two independent units also adapt a new task more state Let imagine ourselves learning tennis for Even never played tennis already agent and environment dynamics related For example we how move our arm that a ball slow bounce Hence just learn the tennis specific knowledge (e.g. its game rule a relationship an arm control Just this example when learn complete utilize the prior knowledge disentangled acquired over Figure Our model disentangles environment-specific information task knowledge training efficiency interpretabilityFrom brings -how agents also obtain and utilize such disentangled prior knowledge Most today's deep reinforcement learning (DRL) models BID14 ; trained entangled environment-specific knowledge taskspecific knowledge as However as humans τ τ Figure : Proposed universal agent, which consists three parts a �� function mapping raw observation feature space a PATH function as an environment actor future state planning.have an innate ability obtain a good understanding about the environment dynamics utilize a newly given task Motivated from this introduce the learning procedure task-independent transition dynamics task-specific rewards Figure This will help an agent adapt more also provides an extra interpretabilityThe idea disentangling a model into related hierarchical RL approaches BID29 ; However to a work that separating units by the natural criteria environment task specific knowledge, for the goal transfer learningTo introduce consists two major units a PATH function a goal generator This illustrated . The key intuition as the following. PATH function handles specific knowledge a goal function We design (1) PATH function learn move another -a lower-level controller which independent the task only depends the goal function τ given Thus PATH function shared different tasks as under the physical world).We evaluate our method answer a good PATH unit benefit the task learning efficient our model We analyze our method on various environments including a maze world multiple Atari 2600 games Our study a good PATH unit trained, our model has a faster convergence compared state method BID15 in most transfer learning tasksIn summary introduce an RL model disentangled units task-specific and environmentspecific knowledge We demonstrate in multiple environments our method learns environmentspecific knowledge further an agent adapting Model-based reinforcement Typical model-based RL frameworks aim model They usually involve search-based algorithms ( Monte Carlo Tree Search as part the policy Sutton & Barto ( Alpha GO with a simulator , Scheme-networks learned forward dynamics BID11 In address representing the knowledge the environment learning skills (how reach As a cognitive science motivation described BID6 , humans also store the knowledge movements or by their end-states Most importantly this knowledge easily utilized a task-specific modulethe goal generator exploit novel tasksMulti-task learning transfer BID2 ; Taylor Stone provide approaches transfer knowledge among multiple agents The methods include the decomposition value function or task and direct multi-task learning where agents several tasks jointly Contrary them universal agent able obtain the environment specific knowledge without any specific task supervision (2015 ; BID32 , the τ function does perform option selection but directly composes target state since a general-purpose PATH function utilized We do follow typical HRL methods where once the subtask selected the low-level controller executed for multiple time steps In universal agent for simplicity now τ function plans the future state at We leave its adaption HRL frameworks as a future work We present a new reinforcement learning scheme the learning procedure taskindependent transition dynamics task-specific rewards The main advantage efficiency of task adaptation interpretability For this we simply introduce two major units a PATH function a goal generator Our study a good PATH unit trained, our model outperforms state method BID15 most tasks on transfer learning tasksThe proposed framework a novel step the knowledge representation learning for deep reinforcement learning There future research directions. For example how PATH function learned ( a continual learning manner BID22 , with less requirement such state restoration better cooperate the goal generator incorporating explicit future planning learning demonstration",0.01,0.5463665197267851
"Modelling 3D scenes from 2D images is a long-standing problem in computer vision with implications in, e.g., simulation and robotics. We propose pix2scene, a deep generative-based approach that implicitly models the geometric properties of a scene from images. Our method learns the depth and orientation of scene points visible in images. Our model can then predict the structure of a scene from various, previously unseen view points. It relies on a bi-directional adversarial learning mechanism to generate scene representations from a latent code, inferring the 3D representation of the underlying scene geometry. We showcase a novel differentiable renderer to train the 3D model in an end-to-end fashion, using only images. We demonstrate the generative ability of our model qualitatively on both a custom dataset and on ShapeNet. Finally, we evaluate the effectiveness of the learned 3D scene representation in supporting a 3D spatial reasoning. Understanding the 3-dimensional (3D) world from its 2-dimensional (2D) projections is a fundamental problem in computer vision with a broad range of application in robotics, simulation and design. Given that the majority natural scene data is available exclusively in the form of 2D images, the ability to directly infer knowledge about 3D structure from these images would be of great utility in scene understanding.Inferring the 3D structure from multiple images of a scene has been pursued extensively, such as in stereo or structure from motion tasks BID9 . Since most available natural image data informative about the real world comes with only a single view of a given scene, it is perhaps more important to explore the development of models which can infer the 3D structural properties from a single image. On the other hand, single image 3D recovery is an extremely challenging and heavily under constrained task. The system has to rely on prior knowledge and 2D visual cues such as textures, shadows or occlusions in order to provide hints to the 3D structure of the scene. Practically, building a machine learning model that learns to infer 3D structure from images requires either a strong inductive bias or supervision. While some have used the 3D ground truth as explicit supervision BID34 , in most cases of interest, such supervision will not be available. Consequently, our long term goal is to infer the 3D structure of realistic scenes from single images. In this paper we take a step towards this direction via a method of unsupervised learning of the 3D structure, directly from a single 2D image of each scene. Our method based on the adversarial learning framework BID6 and exploits a uniquely suitable 3D representation (i.e., surfels BID24 ) and a differentiable renderer.Most 3D reconstruction methods rely on representing 3D objects explicitly using either voxels BID26 BID36 or meshes BID14 BID31 . Explicit representations store all the rendering-relevant information from a given 3D space and are easily transferable, i.e., they can be loaded with any 3D modeling software and viewed from any angle. However, approaches using explicit representations typically scale very poorly (O(n 3 ) or require a sparse/discrete representation which can be challenging for deep learning methods. As a result, these representations have only been applied to the reconstruction of single objects. As an alternative we propose to learn an implicit 3D representation which produces only the 3D geometry which is directly relevant for a particular viewpoint. Our viewpoint-specific 3D geometry is captured Figure 1: Implicit vs explicit representations. Explicit voxel and mesh representations are viewpoint-independent and constitutes the complete scene. Our implicit surfel-based representation is viewpoint-dependent and it adapts the resolution to the viewpoint. The full scene is contained in a high-dimensional latent variable and only when the scene is to be rendered, the latent variable is serialized to surfels for a specific view.using camera facing surfels BID24 which are surface elements defined by its position, orientation and material properties. Given an image we can infer its implicit 3D representation and then recreate novel surfel representations of the underlying scene from unobserved viewpoints. In general, we note that in a 3D scene, only a small fraction of the entities are perceivable from the camera. As the camera moves, and the occluded regions become visible, our method then generates surfels for those newly unoccluded regions. Another advantage of this approach is that minimal number of primitives (surfels) are required to obtain a high-resolution image as the camera moves closer to a part of the scene. Moreover this representation fits well with image based convolutional architectures.Our model, Pix2Scene, is a deep generative-based approach for modelling the 3D structure of a scene directly from images. This model is unsupervised in the sense that it does not require 3D groundtruth or any other kind of image annotations. We base our model on Adversarially Learned Inference (ALI) approach BID5 . ALI extends the GAN BID6 framework by learning to infer the latent representation of a given image. In pix2scene the learned latent space embeds the 3D information of the underlying scene. The latent representation is mapped via a decoder network to a view-dependent 3D surface and then projected to image space by a differentiable renderer. The resulting image is then evaluated by an adversarial critic.While our long-term goal is to be able to infer the 3D structure of a real-world photograph, in this paper we experiment exclusively with synthetically-constructed scenes and adopt several simplifying assumptions. In particular, we assume that the world is piece-wise smooth and that for each input image the illumination, view and object materials are known.This work has the following main contributions, (1) we propose a novel unsupervised method for 3D understanding from a single image; (2) we propose a new implicit 3D representation based on view-space surfels; (3) we propose a surfel-based differentiable 3D renderer that can be used as a layer of a neural network; and (4) we propose 3D-IQTT a new 3D understanding evaluation benchmark. This task evaluates the model's ability to perform mental rotation by obtaining comprehensive understanding of underlying 3D structure. We also estimate the camera pose as part of the learnt latent variable for this particular task. In this paper we proposed a generative approach to learn 3D structural properties from single images in an unsupervised and implicit fashion. Our model receives an image of a scene with uniform material as input, estimates the depth of the scene points and then reconstructs the input scene. We also provided quantitative evidence that support our argument by introducing a novel IQ-task in a semi-supervised setup. We hope that this evaluation metric will be used as a standard benchmark to measure the 3D understanding capability of the models across different 3D representations. The main drawback of our current model is that it requires the knowledge of lighting and material properties. Future work will focus on tackling the more ambitious setting of learning complex materials and texture along with modelling the lighting properties of the scene.",1452,0.776,842,1.7244655581947743,"Modelling 3D scenes with implications in, simulation robotics We propose pix2scene a deep generative-based approach implicitly models the geometric properties from images Our method learns the depth orientation scene points visible images Our model can then predict the structure a scene various, previously unseen view points It relies scene representations a latent code inferring We showcase a novel differentiable renderer train an end only images We demonstrate the generative ability our model qualitatively on both a custom dataset on ShapeNet Finally evaluate the learned 3D scene representation supporting a 3D spatial reasoning. Understanding from with application robotics simulation design Given the majority natural scene data available exclusively directly infer knowledge scene understandingInferring multiple images has pursued such stereo or structure from motion tasks BID9 . Since most available natural image data informative comes only a single view perhaps more explore the development models which infer the 3D structural properties from On single image 3D recovery challenging heavily under constrained task The system to rely prior knowledge 2D visual cues such textures shadows in provide hints the 3D structure Practically building that learns infer 3D structure requires either a strong inductive bias supervision While some used the 3D ground truth explicit supervision BID34 , in of interest such supervision available our long term goal infer the 3D structure realistic scenes single images In take towards this direction via, directly each scene Our method based the adversarial learning framework BID6 and exploits a uniquely suitable 3D representation ( surfels BID24 ) differentiable rendererMost 3D reconstruction methods representing explicitly using either voxels BID26 BID36 meshes Explicit representations store all the rendering-relevant information from easily loaded with viewed However approaches using explicit representations typically scale (O(n 3 or require a sparse/discrete representation which challenging deep learning methods As these representations only applied the reconstruction single objects As an alternative we propose learn an implicit 3D representation which produces which directly relevant a particular viewpoint Our viewpoint-specific 3D geometry captured Figure Implicit vs explicit representations Explicit voxel and mesh representations viewpoint constitutes the complete scene Our implicit surfel-based representation viewpoint it adapts the resolution The full scene contained a high-dimensional latent variable and only when to rendered, serialized surfels for a specific view.using camera facing surfels BID24 which surface elements defined its position material Given an image we infer its implicit 3D representation recreate novel surfel representations the underlying scene from unobserved viewpoints In general we note in a 3D scene the entities perceivable from As the camera moves and the occluded regions our method then generates surfels those newly unoccluded regions Another advantage that minimal number primitivessurfels obtain as closer a part Moreover this representation fits image based convolutional architecturesOur model, Pix2Scene a deep generative-based approach modelling directly images This model unsupervised in 3D groundtruth image annotations We base Adversarially Learned Inference approach BID5 . ALI extends the GAN BID6 framework by learning infer the latent representation a given image In pix2scene the learned latent space embeds the 3D information The latent representation is mapped via a decoder network a view-dependent 3D surface and projected image space a differentiable renderer The resulting image then evaluated an adversarial criticWhile be infer in experiment exclusively synthetically-constructed scenes adopt several simplifying assumptions In particular assume the world piece-wise smooth for each input image the illumination, view object materials knownThis work the following main contributions ( we propose 3D understanding from; based view-space surfels a surfel-based differentiable 3D renderer 3D-IQTT a new 3D understanding evaluation benchmark This task evaluates mental rotation obtaining comprehensive understanding underlying 3D structure We also estimate the camera pose part the learnt latent variable this particular task In proposed learn 3D structural properties single images in an unsupervised and implicit fashion Our model receives an image a scene uniform material as input estimates the scene points We also provided quantitative evidence support our argument introducing a novel IQ-task a semi-supervised setup We hope this evaluation metric the 3D understanding capability the models across The main drawback our current model the knowledge lighting and material properties Future work tackling the more ambitious setting learning complex materials texture along modelling the lighting properties",0.01,0.5499537611161087
"Identifying the relations that connect words is an important step towards understanding human languages and is useful for various NLP tasks such as knowledge base completion and analogical reasoning. Simple unsupervised operators such as vector offset between two-word embeddings have shown to recover some specific relationships between those words, if any. Despite this, how to accurately learn generic relation representations from word representations remains unclear. We model relation representation as a supervised learning problem and learn parametrised operators that map pre-trained word embeddings to relation representations. We propose a method for learning relation representations using a feed-forward neural network that performs relation prediction. Our evaluations on two benchmark datasets reveal that the penultimate layer of the trained neural network-based relational predictor acts as a good representation for the relations between words. Different types of relations exist between words in a language such as Hypernym, Meronym, Synonym, etc. Representing relations between words is important for various NLP tasks such as questions answering BID43 , knowledge base completion BID35 and relational information retrieval BID7 .Two main approaches have been proposed in the literature to represent relations between words. In the first approach, a pair of words is represented by a vector derived from a statistical analysis of a text corpus BID39 . In a text corpus, a relationship between two words X and Y can be expressed using lexical patterns containing X and Y as slot variables. For example, ""X is a Y"" or ""Y such as X"" indicate that Y is a Hypernym of X BID34 . The elements of the vector representing the relation between two words correspond to the number of times those two words co-occur with a particular pattern in a corpus. Given such a relation representation, the relational similarity between the relations that exist between the two words in two word-pairs can be measured by the cosine of the angle between the corresponding vectors. We call this the holistic approach because a pair of words is treated as a whole rather than the two constituent words separately when creating a relation representation . Sparsity is a well-known problem for the holistic approach as two words have to co-occur enough in a corpus, or else no relation can be represented for rare or unseen word-pairs.In contrast, the second approach for relation representation directly computes a relation representation from pre-trained word representations (i.e. word embeddings) using some relational operators. Prediction-based word embedding learning methods BID27 BID24 represent the meaning of individual words by dense, low-dimensional real-valued vectors by optimising different language modelling objectives. Although no explicit information is provided to the word embedding learning algorithms regarding the semantic relations that exist among words, prior work BID25 has shown that the learnt word embeddings encode remarkable structural properties pertaining to semantic relations. They showed that the difference (vector offset) between two word vectors (here-onwards denoted by PairDiff) is an accurate method for solving analogical questions in the form ""a is to b as c is to ?"". For example, king − man + woman results in a vector that is closest to the queen vector. We call this approach compositional because the way in which the relation representation is composed by applying some linear algebraic relational operator on the the semantic representations of the the words that participate in a relation. This interesting property of word embeddings sparked a renewed interest in methods that compose relation representations using word embeddings and besides PairDiff, several other unsupervised methods have been proposed such as 3CosAdd and 3CosMult BID19 .Despite the initial hype, recently, multiple independent works have raised concerns about of word embeddings capturing relational structural properties BID22 BID32 BID23 BID29 . Although PairDiff performs well on the Google analogy dataset, its performance for other relation types has been poor BID3 BID41 BID18 . BID41 tested for the generalisation ability of PairDiff using different relation types and found that semantic relations are captured less accurately compared to syntactic relations. Likewise, BID18 showed that word embeddings are unable to detect paradigmatic relations such as Hypernym, Synonym and Antonyms. Methods such as PairDiff are biased towards attributional similarities between individual words than relational similarities and fails in the presence of nearest neighbours. We further discuss various limitations of the existing unsupervised relation composition methods in Section 2.2.Considering the above-mentioned limitations of the unsupervised relation composition methods, a natural question that arises is whether it is possible to learn supervised relation composition methods to overcome those limitations. In this paper, we model relation representation as learning a parametrised operator f (a, b; θ) such that we can accurately represent the relation between two given words a and b from their word representations a and b, without modifying the input word embeddings. For this purpose, we propose a Multi-class Neural Network Penultimate Layer (MnnPl), a simple and effective parametrised operator for computing relation representations from word representations. Specifically, we train a nonlinear multilayer feed-forward neural network using a labelled dataset consisting of word-pairs for different relation types, where the task is to predict the relation between two input words represented by their pre-trained word embeddings. We find that the penultimate layer of the trained neural network provides an accurate relation representation that generalises beyond the relations in the training dataset. We emphasise that our focus here is not to classify a given pair to a relation in a pre-defined set (relation classification), but rather to obtain a good representation for the relation between the two words in the pair. Our experimental results show that MnnPl significantly outperforms unsupervised relational operators including PairDiff in two standard benchmark datasets, and generalises well to unseen out-of-domain relations. We considered the problem of learning relation embeddings from word embeddings using parametrised operators that can be learnt from relation-labelled word-pairs. We experimentally showed that the penultimate layer of a feed-forward neural network trained for classifying relation types (MnnPl) can accurately represent relations between two given words. In particular, some of the disfluencies of the popular PairDiff operator can be avoided by using MnnPl, which works consistently well for both lexicographic and encyclopaedic relations. The relation representations learnt by MnnPl generalise well to previously unseen (out-of-domain) relations as well, even though the number of training instances is typically small for this purpose.Our analysis highlighted some important limitations in the evaluation protocol used in prior work for relation composition operators. Our work questions the belief that unsupervised operators such as vector offset can discover rich relational structures in the word embedding space. More importantly we show that simple supervised relational composition operators can accurately recover the relational regularities hidden inside word embedding spaces. We hope our work will inspire the NLP community to explore more sophisticated supervised operators to extract useful information from word embeddings in the future.Recently, BID31 show that accessing lexical relations such as hypernym relying only on distributional word embeddings that are trained considering 2-ways cooccurrences between words is insufficient. They illustrate the advantages of using the holistic (pattern-based) to detect such relations. Indeed, it is expected that the holistic and the compositional approaches for representing relations have complementary properties since the holistic uses lexical contexts in which the two words of interest co-occur, while the compositional uses only their embeddings BID33 . Interesting future work includes unifying the two approaches for relation representations.",1469,0.746,855,1.7181286549707602,"Identifying the relations connect words is human languages is useful various NLP tasks knowledge base completion analogical reasoning Simple unsupervised operators such vector offset between have shown recover some specific relationships those words if Despite how to accurately learn generic relation representations word representations remains We model relation representation learn parametrised operators map We propose learning relation representations performs relation prediction Our evaluations on two benchmark datasets reveal the penultimate layer the trained neural network-based relational predictor acts the relations words Different types relations words Hypernym Meronym Representing relations words is important various NLP tasks questions answering BID43 , knowledge base completion BID35 relational information .Two main approaches represent In the first approach a pair words represented derived a statistical analysis a text corpus BID39 In a text corpus a relationship X containing slot variables For example ""X is a Y such indicate a Hypernym X BID34 . The elements the vector representing two words correspond co a particular pattern a corpus Given such a relation representation the relational similarity that two word-pairs measured We call the holistic approach a pair words treated the two constituent words separately when creating a relation representation . Sparsity the holistic approach as two words co enough a corpus else no relation represented for rare or unseen word-pairsIn the second approach for relation representation directly computes pre-trained word representations some relational operators Prediction-based word learning methods BID27 BID24 represent the meaning individual words dense, low-dimensional real-valued vectors by optimising different language modelling objectives Although no explicit information the word embedding learning algorithms regarding the semantic relations exist words prior work BID25 the learnt word encode remarkable structural properties pertaining They showed the difference (vector offset two word vectorshere-onwards denoted PairDiff an accurate method solving analogical questions ""a is to as For example king − man + woman results a vector closest the queen vector We call this approach compositional because the relation representation by applying some linear algebraic relational operator on the the semantic representations the the words participate This interesting property word embeddings sparked methods compose relation representations using besides PairDiff such 3CosAdd BID19 .Despite recently multiple independent works raised of capturing relational structural properties BID22 BID32 BID23 BID29 Although PairDiff performs the Google analogy dataset for other relation types poor BID3 BID41 BID18 . BID41 tested the generalisation ability PairDiff using different relation types found semantic relations captured less compared Likewise BID18 showed word embeddings unable paradigmatic relations Hypernym Synonym Antonyms Methods such PairDiff biased attributional similarities individual words than relational similarities and fails in nearest neighbours We further various limitations the existing unsupervised relation composition methods Section a natural question that learn to overcome In model relation representation as learning a parametrised operator f such accurately two given words a from their word a without modifying For this purpose propose a Multi-class Neural Network Penultimate LayerMnnPl a simple and effective parametrised operator computing relation representations from word representations Specifically train a labelled dataset consisting different relation types where represented We find the penultimate layer the trained neural network provides an accurate relation representation that generalises beyond the relations We emphasise here classify a given pair to a relation a pre-defined set (relation classification obtain Our experimental results MnnPl significantly unsupervised relational operators including PairDiff in two standard benchmark datasets generalises well unseen outdomain relations We considered learning relation embeddings using parametrised operators that learnt relation-labelled word-pairs We experimentally showed the penultimate layer trained classifying relation typesMnnPl accurately represent relations two given words In particular some the disfluencies the popular PairDiff operator avoided MnnPl, works consistently well The relation representations learnt MnnPl generalise well to previously unseen (outdomain relations as, even the number training instances typicallyOur analysis highlighted the evaluation protocol prior work for relation composition operators Our work questions unsupervised operators such vector offset can discover rich relational structures the word More importantly we show simple supervised relational composition operators accurately recover the relational regularities hidden inside word spaces We hope our work the NLP community explore more sophisticated supervised operators extract the futureRecently BID31 show accessing lexical relations such hypernym relying only that trained considering 2-ways cooccurrences insufficient They illustrate holistic (pattern to detect such relations Indeed expected holistic and the compositional approaches for representing relations have complementary properties since holistic uses lexical contexts of interest co only their embeddings BID33 . Interesting future work includes unifying relation representations",0.01,0.5338078884555504
"Recurrent neural networks (RNNs) are important class of architectures among neural networks useful for language modeling and sequential prediction. However, optimizing RNNs is known to be harder compared to feed-forward neural networks. A number of techniques have been proposed in literature to address this problem. In this paper we propose a simple technique called fraternal dropout that takes advantage of dropout to achieve this goal. Specifically, we propose to train two identical copies of an RNN (that share parameters) with different dropout masks while minimizing the difference between their (pre-softmax) predictions. In this way our regularization encourages the representations of RNNs to be invariant to dropout mask, thus being robust. We show that our regularization term is upper bounded by the expectation-linear dropout objective which has been shown to address the gap due to the difference between the train and inference phases of dropout. We evaluate our model and achieve state-of-the-art results in sequence modeling tasks on two benchmark datasets - Penn Treebank and Wikitext-2. We also show that our approach leads to performance improvement by a significant margin in image captioning (Microsoft COCO) and semi-supervised (CIFAR-10) tasks. Recurrent neural networks (RNNs) like long short-term memory (LSTM; BID4 ) networks and gated recurrent unit (GRU; BID0 ) are popular architectures for sequence modeling tasks like language generation, translation, speech synthesis, and machine comprehension. However, they are harder to optimize compared to feed-forward networks due to challenges like variable length input sequences, repeated application of the same transition operator at each time step, and largely-dense embedding matrix that depends on the vocabulary size. Due to these optimization challenges in RNNs, the application of batch normalization and its variants (layer normalization, recurrent batch normalization, recurrent normalization propagation) have not been as successful as their counterparts in feed-forward networks , although they do considerably provide performance gains. Similarly, naive application of dropout BID23 has been shown to be ineffective in RNNs BID27 . Therefore, regularization techniques for RNNs is an active area of research.To address these challenges, BID27 proposed to apply dropout only to the nonrecurrent connections in multi-layer RNNs. Variational dropout BID2 ) uses the same dropout mask throughout a sequence during training. DropConnect BID25 applies the dropout operation on the weight matrices. Zoneout BID7 ), in a similar spirit with dropout, randomly chooses to use the previous time step hidden state instead of using the current one. Similarly as a substitute for batch normalization, layer normalization normalizes the hidden units within each sample to have zero mean and unit standard deviation. Recurrent batch normalization applies batch normalization but with unshared mini-batch statistics for each time step BID1 .In this paper we propose a simple regularization based on dropout that we call fraternal dropout, where we minimize an equally weighted sum of prediction losses from two identical copies of the same LSTM with different dropout masks, and add as a regularization the 2 difference between the predictions (pre-softmax) of the two networks. We analytically show that our regularization objective is equivalent to minimizing the variance in predictions from different i.i.d. dropout masks; thus encouraging the predictions to be invariant to dropout masks. We also discuss how our regularization is related to expectation linear dropout BID10 , Π-model BID8 and activity regularization BID16 , and empirically show that our method provides non-trivial gains over these related methods which we explain furthermore in our ablation study (Section 5). In this paper we propose a simple regularization method for RNNs called fraternal dropout that acts as a regularization by reducing the variance in model predictions across different dropout masks. We show that our model achieves state-of-the-art results on benchmark language modeling tasks along with faster convergence. We also analytically study the relationship between our regularization and expectation linear dropout BID10 . We perform a number of ablation studies to evaluate our model from different aspects and carefully compare it with related methods both qualitatively and quantitatively.",827,0.786,493,1.6774847870182557,"Recurrent neural networks important class architectures among useful language modeling sequential prediction However optimizing RNNs known harder compared A number techniques literature In called fraternal dropout that takes to achieve Specifically propose train two identical copiesthat share parameters different dropout masks while their (pre-softmax) predictions In this way our regularization encourages the representations RNNs dropout mask being robust We show our regularization term upper bounded the expectation-linear dropout objective which address due the train inference phases dropout We evaluate our model achieve state results sequence modeling tasks on two benchmark datasets - Penn Treebank Wikitext-2 We also show our approach leads performance improvement image captioning (Microsoft COCO semi (CIFAR-10 tasks Recurrent neural networks like; BID4 ) networks gated recurrent unit are popular architectures sequence modeling tasks language generation translation speech synthesis machine comprehension However they harder optimize compared feed-forward networks due challenges variable length input sequences repeated application the same transition operator at largely-dense embedding matrix that depends the vocabulary size Due these optimization challenges in RNNs the application batch normalization its variants (layer normalization recurrent normalization propagation have as feed-forward networks , although considerably provide Similarly naive application dropout BID23 has RNNs BID27 . Therefore regularization techniques is an active areaTo address BID27 proposed apply dropout only the nonrecurrent connections Variational BID2 ) uses throughout a sequence during training DropConnect BID25 applies the dropout operation the weight matrices Zoneout BID7 ), in a similar spirit with dropout randomly to the previous time step hidden state instead Similarly as a substitute batch normalization normalizes the hidden units within each sample have zero mean and unit standard deviation Recurrent batch normalization applies but with unshared mini-batch statistics step BID1 .In dropout that we fraternal dropout minimize an equally weighted sum prediction losses two identical copies with different dropout masks add as the 2 differencepresoftmax We analytically show our regularization objective equivalent minimizing predictions different i.i.d. dropout masks; encouraging the predictions We also discuss our regularization related expectation linear dropout BID10 , ��-model BID8 activity regularization BID16 empirically our method provides these related methods which explain furthermore our ablation studySection In called fraternal dropout that acts by model predictions across different dropout masks We show our model achieves state results benchmark language modeling tasks along faster convergence We also analytically study our regularization and expectation linear dropout BID10 . We perform ablation studies our model from different aspects and carefully compare related methods both qualitatively",0.01,0.43025088384376237
"We propose a novel approach for deformation-aware neural networks that learn the weighting and synthesis of dense volumetric deformation fields. Our method specifically targets the space-time representation of physical surfaces from liquid simulations. Liquids exhibit highly complex, non-linear behavior under changing simulation conditions such as different initial conditions. Our algorithm captures these complex phenomena in two stages: a first neural network computes a weighting function for a set of pre-computed deformations, while a second network directly generates a deformation field for refining the surface. Key for successful training runs in this setting is a suitable loss function that encodes the effect of the deformations, and a robust calculation of the corresponding gradients. To demonstrate the effectiveness of our approach, we showcase our method with several complex examples of flowing liquids with topology changes. Our representation makes it possible to rapidly generate the desired implicit surfaces. We have implemented a mobile application to demonstrate that real-time interactions with complex liquid effects are possible with our approach. Learning physical functions is an area of growing interest within the research community, with applications ranging from physical priors for computer vision problems BID20 , over robotic control BID35 , to fast approximations for numerical solvers Tompson et al. (2017) . While the underlying model equations for many physics problems are known, finding solutions is often prohibitively expensive for phenomena on human scales. At the same time, the availability of model equations allows for the creation of reliable ground truth data for training, if enough computational resources can be allocated.Water, and liquids in general, are ubiquitous in our world. At the same time, they represent an especially tough class of physics problems, as the constantly changing boundary conditions at the liquid-gas interface result in a complex space of surface motions and configurations. In this work we present a novel approach to capture parametrized spaces of liquid behavior that is based on space-time deformations. We represent a single 3D input surface over time as a four-dimensional signed-distance function (SDF), which we deform in both space and time with learned deformations to recover the desired physical behavior. To calculate and represent these deformations efficiently, we take a two-stage approach: First, we span the sides of the original parameter region with precomputed deformations, and infer a suitable weighting function. In a second step, we synthesize a dense deformation field for refinement. As both the parameter weighting problem and the deformation synthesis are highly non-linear problems, we demonstrate that neural networks are a particularly suitable solver to robustly find solutions.We will demonstrate that it is possible to incorporate the non-linear effects of weighted deformations into the loss functions of neural networks. In particular, we put emphasis on incorporating the influence of deformation alignment into the loss gradients. This alignment step is necessary to ensure the correct application of multiple consecutive deformations fields. The second stage of our algorithm is a generative model for deformation fields, for which we rely on a known parametrization of the inputs. Thus, in contrast to other generative models which learn to represent unknown parametrization of data sets BID31 , our models are trained with a known range and dimensionality to parameter range, which serves as input.Once trained, the models can be evaluated very efficiently to synthesize new implicit surface configurations. To demonstrate its performance, we have implemented a proof-of-concept version for mobile devices, and a demo app is available for Android devices in the Google Play store. Our approach generates liquid animations several orders of magnitude faster than a traditional simulator, and achieves effective speed up factors of more than 2000, as we will outline in Sec. 5. The central contributions of our work are:• A novel deformation-aware neural network approach to very efficiently represent large collections of space-time surfaces with complex behavior.• We show how to compute suitable loss gradient approximations for the sub-problems of parameter and deformation inference.• In addition we showcase the high performance of our approach with a mobile device implementation that generates liquid simulations interactively. We have presented a novel method to generate space-time surfaces with deformation-aware neural networks. In particular, we have demonstrated the successful inference of weighting sequences of aligned deformations, and the generation of dense deformation fields across a range of varied inputs. Our method exhibits significant improvements in terms surface reconstruction accuracy across the full parameter range. In this way, our networks can capture spaces of complex surface behavior, and Beyond liquid surfaces, our deformation networks could also find application for other types of surface data, such as those from object collections or potentially also moving characters. Likewise, it could be interesting to extend our method in order to infer deformations for input sets without an existing parametrization.",924,0.982,552,1.673913043478261,"We propose deformation-aware neural networks learn the weighting synthesis dense volumetric deformation fields Our method specifically the space-time representation physical surfaces from liquid simulations Liquids exhibit under changing simulation conditions such different initial conditions Our algorithm captures these complex phenomena two stages a first neural network while directly generates refining Key for successful training runs this setting a suitable loss function encodes the effect the deformations a robust calculation the corresponding gradients To demonstrate our approach showcase our method several complex examples flowing liquids topology changes Our representation makes rapidly generate the desired implicit surfaces We implemented a mobile application demonstrate complex liquid effects our approach Learning physical functions within applications physical priors for computer vision problems BID20 , over robotic control BID35 fast approximations numerical solvers Tompson (2017 . While the underlying model equations many physics problems known finding phenomena on human scales At the availability model equations allows reliable ground truth data training if enough computational resourcesWater, and liquids ubiquitous At they represent an especially tough class physics problems the constantly changing boundary conditions liquid result a complex space surface motions configurations In this work capture parametrized spaces of liquid behavior space-time deformations We represent a single 3D input surface over time as a four-dimensional signed-distance function deform both space learned deformations recover the desired physical behavior To calculate and represent these deformations efficiently take span the sides the original parameter region infer a suitable weighting function In a second step synthesize a dense deformation field refinement As both the parameter weighting problem the deformation synthesis highly non-linear problems demonstrate neural networks a particularly suitable solver robustly find solutionsWe will demonstrate it incorporate weighted deformations the loss functions In particular put emphasis incorporating the influence deformation alignment the loss gradients This alignment step necessary the correct application multiple consecutive deformations fields The second stage our algorithm deformation fields for rely the inputs Thus contrast other generative models which learn represent of BID31 our models trained a known range and dimensionality to parameter range serves input.Once evaluated very synthesize new implicit surface configurations To demonstrate its performance implemented proof version for mobile devices is in Our approach generates liquid animations several orders a traditional simulator achieves effective speed up factors more 2000 as we will outline Sec 5 The central contributions our work are:• A novel deformation-aware neural network approach very efficiently represent large collections space-time surfaces complex We compute suitable loss gradient approximations the subproblems parameter and In showcase a mobile device implementation generates liquid simulations interactively We presented generate space-time surfaces deformation-aware neural networks In particular demonstrated the successful inference weighting sequences aligned deformations the generation dense deformation fields across varied inputs Our method exhibits significant improvements terms surface reconstruction accuracy across the full parameter range In this way our networks capture spaces complex surface behavior Beyond liquid surfaces our deformation networks could find application surface data those object collections potentially also moving characters Likewise could interesting extend our method in order infer deformations for input sets without",0.01,0.42115039511381214
"This is an empirical paper which constructs color invariant networks and evaluates their performances on a realistic data set. The paper studies the simplest possible case of color invariance: invariance under pixel-wise permutation of the color channels. Thus the network is aware not of the specific color object, but its colorfulness. The data set introduced in the paper consists of images showing crashed cars from which ten classes were extracted. An additional annotation was done which labeled whether the car shown was red or non-red.   The networks were evaluated by their performance on the classification task. With the color annotation we altered the color ratios  in the training data and analyzed the generalization capabilities of the networks on the unaltered test data. We further split the test data in red and non-red cars and did a similar evaluation. It is shown in the paper that an pixel-wise ordering of the rgb-values of the images performs better or at least similarly for small deviations from the true color ratios. The limits of these networks are also discussed. Imagine a training set without red objects, and a test set which contains red objects. How well does a trained net perform? This is not a mere academic question. Imagine we want to separate cars, humans and free space for an autonomous driving task. If our data contained red cars but not red trousers say, it will most likely classify legs as cars. Even worse it could mix up yellow markings and yellow trouser and classify an human as free space. On the other hand we can not disregard color all together as it yields some clues for natural objects such as trees, sky, mist, snow and also some man made objects such as markings, or traffic signs. The first thing that comes to mind is to balance the color statistics of our data set. But this impossible to do in practice, and worse at training time it is unknown which colors will become fashion in say five years. What is called for is network which is invariant under color changes. In this paper we construct and analyze such a network. We compared different color invariant neural networks. It is shown in the paper that only pixel-wise ordering of the color channels shows similar results on cifar10 (and also on the crashed car data set). To test the hypothesis that ordering is invariant under color changes, a classification task has been extracted from a publicly available crashed car data set. In addition each car was labeled as red or non-red. On this data set it was shown that all three nets showed similar behavior on all cars and on all non-red cars, on the red cars the order nets performed noticeably better. Further, we excluded red cars from the training set, and showed that the weighted order nets performed better than the baseline on all three test sets. On the red cars the order showed significantly better results. Further, we fixed the ratio of red / non-red in the training sets. The order nets perform better or at least similar to the baseline net. All nets degrade noticeable while increasing the ratio red cars. As a teaser we report in the appendix there all three nets fail. No net can cope with one class of entirely red cars and all other classes set to non red.We can also view the paper as an empirical study on generalization: trained nets are tested on a statistically different test set. Most plots of accuracy over iterations on the test set showed overshooting despite of the l 2 regularization in the final layer. The curve of the weighted net in FIG2 being a typical example. We interpret this as over fitting, training should be stopped much earlier. A further empirical conclusion shows that sub-sampling the unevenly distributed test data gave similar results than deriving the accuracies for all class separately and then taking the mean. But the individual class may perform rather poor, an insight which is lost in sub-sampling.The paper introduced and evaluated a variant of color invariant nets. The constructed nets are invariant under pixel-wise permutation of the color channels. Thus the network is aware not of the specific color, but the colorfulness of the object. Further, a data set was introduced which allowed to evaluate color invariance in a realistic setting. We see that the net constructed in the paper are better or equal to the baseline if the color distribution is not to far away from the true distribution. We conclude that colorfulness is enough information for classification. The crash car data set itself calls for further experiments and insights, and remains a tough classification challenge.",885,0.868,490,1.8061224489795917,This an empirical paper constructs color invariant networks evaluates their performances paper studies the simplest possible case color invariance under pixel-wise permutation Thus the network aware not the specific color object its colorfulness The data introduced consists images showing crashed cars which ten classes An additional annotation done which labeled whether shown red non The networks evaluated their performance the classification task With the color annotation we altered the color ratios analyzed the generalization capabilities on We further split red and non-red cars did It shown an pixel-wise ordering performs or at similarly small deviations the true color ratios The limits these networks also discussed Imagine a training set without red objects which How well a trained net perform This a mere academic question Imagine we want separate cars humans free space an autonomous driving task If our data contained red cars but red trousers say will most classify legs cars Even worse it mix yellow markings yellow trouser and classify an human free space On we not disregard color all yields some clues natural objects sky mist snow also some man markings or traffic signs to balance the color statistics But impossible to in worse at training time it unknown colors fashion say What called for network which invariant under color changes construct We compared different color invariant neural networks It shown only pixel-wise ordering shows similar results cifar10 the crashed car data set To test ordering color changes extracted publicly crashed car data each car labeled red non On this data all three nets showed all cars on the order nets performed noticeably Further excluded red cars showed the weighted order nets performed On the red cars the order showed significantly better results Further fixed the ratio red / non in The order nets perform or at similar the baseline net All nets degrade noticeable while increasing the ratio red cars As a teaser report the appendix there all three nets fail No net can cope one class entirely red cars set non redWe view the paper generalization trained nets tested Most plots accuracy over iterations on showed overshooting despite of the l 2 regularization The curve the weighted net in FIG2 being We interpret over fitting training should stopped much A further empirical conclusion shows sub the unevenly distributed test data gave than deriving all class separately taking But the individual class may perform rather poor an insight lost subThe paper introduced and evaluated color invariant nets The constructed nets invariant under pixel-wise permutation Thus the network aware not the specific color the colorfulness Further data introduced evaluate color invariance We see the net constructed are better or equal if the color distribution to far We conclude colorfulness enough information classification The crash car data itself calls further experiments insights remains a tough classification challenge,0.01,0.7580083445398434
"Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially efficient with respect to shallow networks, in the sense that a shallow network must grow exponentially large in order to approximate the functions represented by a deep network of polynomial size. In this work, we extend the study of expressive efficiency to the attribute of network connectivity and in particular to the effect of ""overlaps"" in the convolutional process, i.e., when the stride of the convolution is smaller than its filter size (receptive field).
 To theoretically analyze this aspect of network's design, we focus on a well-established surrogate for ConvNets called Convolutional Arithmetic Circuits (ConvACs), and then demonstrate empirically that our results hold for standard ConvNets as well. Specifically, our analysis shows that having overlapping local receptive fields, and more broadly denser connectivity, results in an exponential increase in the expressive capacity of neural networks. Moreover, while denser connectivity can increase the expressive capacity, we show that the most common types of modern architectures already exhibit exponential increase in expressivity, without relying on fully-connected layers. One of the most fundamental attributes of deep networks, and the reason for driving its empirical success, is the ""Depth Efficiency"" result which states that deeper models are exponentially more expressive than shallower models of similar size. Formal studies of Depth Efficiency include the early work on boolean or thresholded circuits BID19 BID25 Håstad and Goldmann, 1991; Hajnal et al., 1993) , and the more recent studies covering the types of networks used in practice BID13 BID12 Eldan and Shamir, 2016; BID5 BID23 BID16 . What makes the Depth Efficiency attribute so desirable, is that it brings exponential increase in expressive power through merely a polynomial change in the model, i.e. the addition of more layers. Nevertheless, depth is merely one among many architectural attributes that define modern networks. The deep networks used in practice consist of architectural features defined by various schemes of connectivity, convolution filter defined by size and stride, pooling geometry and activation functions. Whether or not those relate to expressive efficiency, as depth has proven to be, remains an open question.In order to study the effect of network design on expressive efficiency we should first define ""efficiency"" in broader terms. Given two network architectures A and B, we say that architecture A is expressively efficient with respect to architecture B, if the following two conditions hold: (i) any function h realized by B of size r B can be realized (or approximated) by A with size r A ∈ O(r B ); (ii) there exist a function h realized by A with size r A , that cannot be realized (or approximated) by B, unless r B ∈ Ω(f (r A )) for some super-linear function f . The exact definition of the sizes r A and r B depends on the measurement we care about, e.g. the number of parameters, or the number of ""neurons"". The nature of the function f in condition (ii) determines the type of efficiency taking place -if f is exponential then architecture A is said to be exponentially efficient with respect to architecture B, and if f is polynomial so is the expressive efficiency. Additionally, we say A is completely efficient with respect to B, if condition (ii) holds not just for some specific functions (realizable by A), but for all functions other than a negligible set.In this paper we study the efficiency associated with the architectural attribute of convolutions, namely the size of convolutional filters (receptive fields) and more importantly its proportion to their stride. We say that a network architecture is of the non-overlapping type when the size of the local receptive field in each layer is equal to the stride. In that case, the sets of pixels participating in the computation of each two neurons in the same layer are completely separated. When the stride is smaller than the receptive field we say that the network architecture is of the overlapping type. In the latter case, the overlapping degree is determined by the total receptive field and stride projected back to the input layer -the implication being that for the overlapping architecture the total receptive field and stride can grow much faster than with the non-overlapping case.As several studies have shown, non-overlapping convolutional networks do have some theoretical merits. Namely, non-overlapping networks are universal BID5 , i.e. they can approximate any function given sufficient resources, and in terms of optimization, under some conditions they actually possess better convergence guaranties than overlapping networks. Despite the above, there are only few instances of strictly non-overlapping networks used in practice (e.g. BID17 ; van den BID24 ), which raises the question of why are non-overlapping architectures so uncommon? Additionally, when examining the kinds of architectures typically used in recent years, which employ a mixture of both overlapping and nonoverlapping layers, there is a trend of using ever smaller receptive fields, as well as non-overlapping layers having an ever increasing role BID10 BID20 BID21 . Hence, the most common networks used practice, though not strictly non-overlapping, are increasingly approaching the non-overlapping regime, which raises the question of why having just slightly overlapping architectures seems sufficient for most tasks?In the following sections, we will shed some light on these questions by analyzing the role of overlaps through a surrogate class of convolutional networks called Convolutional Arithmetic Circuits (ConvACs) BID5 ) -instead of non-linear activations and average/max pooling layers, they employ linear activations and product pooling. ConvACs , as a theoretical framework to study ConvNets, have been the focused of several works, showing, amongst other things, that many of the results proven on this class are typically transferable to standard ConvNets as well . Though prior works on ConvACs have only considered non-overlapping architectures, we suggest a natural extension to the overlapping case that we call Overlapping ConvACs. In our analysis, which builds on the known relation between ConvACs and tensor decompositions, we prove that overlapping architectures are in fact completely and exponentially more efficient than non-overlapping ones, and that their expressive capacity is directly related to their overlapping degree. Moreover , we prove that having even a limited amount of overlapping is sufficient for attaining this exponential separation. To further ground our theoretical results, we demonstrate our findings through experiments with standard ConvNets on the CIFAR10 image classification dataset. The common belief amongst deep learning researchers has been that depth is one of the key factors in the success of deep networks -a belief formalized through the depth efficiency conjecture. Nevertheless, depth is one of many attributes specifying the architecture of deep networks, and each could potentially be just as important. In this paper, we studied the effect overlapping receptive fields have on the expressivity of the network, and found that having them, and more broadly denser connectivity, results in an exponential gain in the expressivity that is orthogonal to the depth.Our analysis sheds light on many trends and practices in contemporary design of neural networks. Previous studies have shown that non-overlapping architectures are already universal BID5 , and even have certain advantages in terms of optimization BID0 , and yet, real-world usage of non-overlapping networks is scarce. Though there could be multiple factors involved, our results clearly suggest that the main culprit is that non-overlapping networks are significantly handicapped in terms of expressivity compared to overlapping ones, explaining why the former are so rarely used. Additionally, when examining the networks that are commonly used in practice, where the majority of the layers are of the convolutional type with very small receptive field, and only few if any fully-connected layers BID18 BID20 He et al., 2016) , we find that though they are obviously overlapping, their overlapping degree is rather low. We showed that while denser connectivity can increase the expressive capacity, even in the most common types of modern architectures already exhibit exponential increase in expressivity, without relying on fully-connected layers. This could partly explain that somewhat surprising observation, as it is probable that such networks are sufficiently expressive for most practical needs simply because they are already in the exponential regime of expressivity. Indeed, our experiments seems to suggests the same, in which we saw that further increases in the overlapping degree beyond the most limited overlapping case seems to have insignificant effects on performance -a conjecture not quite proven by our current work, but one we wish to investigate in the future.There are relatively few other works which have studied the role of receptive fields in neural networks. Several empirical works BID9 BID8 have demonstrated similar behavior, showing that the classification accuracy of networks can sharply decline as the degree of overlaps is decreased, while also showing that gains from using very large local receptive fields are insignificant compared to the increase in computational resources. Other works studying the receptive fields of neural networks have mainly focused on how to learn them from the data Jia et al., 2012) . While our analysis has no direct implications to those specific works, it does lay the ground work for potentially guiding architecture design, through quantifying the expressivity of any given architecture. Lastly, BID11 studied the effective total receptive field of different layers, a property of a similar nature to our total receptive field, where they measure the the degree to which each input pixel is affecting the output of each activation. They show that under common random initialization of the weights, the effective total receptive field has a gaussian shape and is much smaller than the maximal total receptive field. They additionally demonstrate that during training the effective total receptive field grows in size, and suggests that weights should be initialized such that the initial effective receptive field is large. Their results strengthen our theory, by showing that trained networks tend to maximize their effective receptive field, taking full potential of their expressive capacity.To conclude, we have shown both theoretically and empirically that overlapping architectures have an expressive advantage compared to non-overlapping ones. Our theoretical analysis is grounded on the framework of ConvACs, which we extend to overlapping configurations. Though are proofs are limited to this specific case, previous studies have already shown that such results could be transferred to standard ConvNets as well, using most of the same mathematical machinery. While adapting our analysis accordingly is left for future work, our experiments on standard ConvNets (see sec. 5) already suggest that the core of our results should hold in this case as well. Finally, an interesting outcome of moving from non-overlapping architectures to overlapping ones is that the depth of a network is no longer capped at log 2 (input size), as has been the case in the models investigated by Cohen et al. DISPLAYFORM0 Figure 7: The original Convolutional Arithmetic Circuits as presented by BID5 .",2218,1.026,1284,1.7274143302180685,"Expressive efficiency refers the relation two architectures A whereby any function realized B could replicated there exists functions unless its size grows significantly larger For example it known deep networks exponentially efficient with shallow networks in must grow large approximate the functions represented of polynomial size In this work extend expressive efficiency the attribute network connectivity in ""overlaps when the stride smaller its filter sizereceptive field To theoretically analyze this aspect network's design focus a well-established surrogate ConvNets called Convolutional Arithmetic CircuitsConvACs then demonstrate empirically our results hold Specifically our analysis having overlapping local receptive fields more denser connectivity results the expressive capacity Moreover while denser connectivity the expressive capacity, we show the most common types modern architectures already exhibit exponential increase without relying fully-connected layers One the most fundamental attributes deep networks driving its empirical success the ""Depth Efficiency"" result which states deeper models exponentially expressive shallower models of similar size Formal studies Depth Efficiency include the early work boolean or thresholded circuits BID19 BID25 Håstad Goldmann 1991 Hajnal) , more studies covering the types networks practice BID13 BID12 Eldan Shamir 2016 . What makes the Depth Efficiency attribute desirable, brings exponential increase expressive power through merely a polynomial change the model more layers Nevertheless depth merely among many architectural attributes modern networks The deep networks used practice consist architectural features defined various schemes connectivity convolution filter defined size stride pooling geometry and activation functions Whether relate expressive efficiency as depth has proven remainsIn order study network design we should define ""efficiency broader terms Given two network architectures A say that architecture expressively efficient with architecture B if any function h realized B of size r B can realized ( with size there exist , that unless r ��(f ( for some super-linear function The exact definition the sizes r A depends we care parameters ""neurons The nature the function f in conditionii determines efficiency taking -if exponential architecture A said exponentially with so is the expressive efficiency Additionally say A is completely efficient with B if condition (ii holds not just some specific functionsrealizable by other a negligible setIn study associated the architectural attribute convolutions namely the sizereceptive fields more importantly its proportion their stride We say a network architecture of when the size the local receptive field in each layer equal the stride. In that case the sets pixels participating each two neurons completely separated When the stride smaller the receptive field we say the network architecture of the overlapping type In the latter case the overlapping degree is determined the total receptive field stride projected back the input layer -the implication for the overlapping architecture can grow much withAs several studies do some theoretical merits Namely non-overlapping networks universal BID5 , approximate any function given sufficient resources in terms optimization under actually possess better convergence guaranties overlapping Despite the above only few instances strictly non-overlapping networks used practice BID17 ; van BID24 raises uncommon Additionally when examining the kinds architectures typically recent years which employ a mixture using ever smaller receptive fields having an ever increasing role BID10 BID20 BID21 . Hence the most common networks practice, though strictly non increasingly approaching raises why having just slightly overlapping architectures seems sufficient most tasks?In shed analyzing through a surrogate class called Convolutional Arithmetic CircuitsConvACs) BID5 ) -instead non-linear activations average/max pooling layers they employ product pooling ConvACs , as a theoretical framework to study ConvNets the focused several works showing, amongst many proven on this class typically transferable as . Though prior works ConvACs only considered suggest a natural extension the overlapping case that our analysis which builds the known relation prove overlapping architectures in completely and exponentially their expressive capacity directly their overlapping degree Moreover , we prove having even a limited amount overlapping is attaining this exponential separation To further ground our theoretical results demonstrate our findings through experiments standard ConvNets on the CIFAR10 image classification dataset The common belief amongst deep learning researchers has that depth one deep networks -a belief formalized the depth efficiency conjecture Nevertheless depth many attributes specifying the architecture deep networks each could potentially just In this paper studied overlapping receptive fields the expressivity the network having them, more denser connectivity results an exponential gain that the depthOur analysis sheds many trends practices contemporary design Previous studies non-overlapping architectures already universal BID5 , even have certain advantages optimization BID0 yet real-world usage scarce Though could multiple factors our results clearly the main culprit that non-overlapping networks significantly handicapped expressivity compared overlapping ones explaining former so rarely Additionally when examining the networks commonly practice where the layers of the convolutional type with very small receptive field only few if fully BID18 BID20 He et) , though they obviously overlapping their overlapping degree rather We showed while denser connectivity the expressive capacity, even the most common types modern architectures already exhibit exponential increase without relying fully-connected layers This could partly that somewhat surprising observation probable such networks sufficiently expressive most practical needs simply already in the exponential regime expressivity Indeed our experiments seems suggests the same, in which saw further increases the overlapping degree beyond the most limited overlapping case seems insignificant effects performance -a conjecture not quite proven wishThere relatively few other works which studied receptive fields Several empirical works BID9 BID8 have demonstrated similar behavior showing the classification accuracy networks can sharply decline overlaps decreased while also gains using very large local receptive fields insignificant the increase computational resources Other works studying the receptive fields neural networks mainly how learn them Jia) . While our analysis no direct implications to those specific works lay potentially guiding architecture design through quantifying the expressivity any given architecture Lastly BID11 studied the effective total receptive field different layers a property a similar nature where they the the degree each input pixel affecting each activation They show under common random initialization the weights the effective total receptive field has a gaussian shape much They additionally demonstrate during training the effective total receptive field grows suggests weights initialized such large Their results strengthen our theory, by trained networks tend maximize their effective receptive field taking full potential of their expressive capacityTo conclude both theoretically overlapping architectures have an expressive advantage compared Our theoretical analysis grounded the framework ConvACs extend overlapping configurations Though are proofs are limited this specific case previous studies already such results could transferred standard ConvNets as using most the same mathematical machinery While adapting our analysis accordingly is left for our experiments on standard ConvNetssee sec 5) already suggest the core our results hold in as Finally an interesting outcome moving non-overlapping architectures overlapping ones the depth a network no capped log (input size has the models investigated DISPLAYFORM0 Figure 7 The original Convolutional Arithmetic Circuits as presented BID5 .",0.01,0.557466973155185
"We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data points on the nondifferentiability of the ReLU divides the parameter space into at most 2^M regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, O(M) (in)equality tests, and one (or a few) nonconvex QP. For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast. In the bad case, we have to solve a few more inequality constrained QPs, but we prove that the time complexity is exponential only in the number of inequality constraints. Our experiments show that either benign case or bad case with very few inequality constraints occurs, implying that our algorithm is efficient in most cases. Empirical success of deep neural networks has sparked great interest in the theory of deep models. From an optimization viewpoint, the biggest mystery is that deep neural networks are successfully trained by gradient-based algorithms despite their nonconvexity. On the other hand, it has been known that training neural networks to global optimality is NP-hard BID2 . It is also known that even checking local optimality of nonconvex problems can be NP-hard (Murty & Kabadi, 1987) . Bridging this gap between theory and practice is a very active area of research, and there have been many attempts to understand why optimization works well for neural networks, by studying the loss surface BID1 Yu & Chen, 1995; Kawaguchi, 2016; Soudry & Carmon, 2016; Nguyen & Hein, 2017; Safran & Shamir, 2018; Laurent & Brecht, 2018; Yun et al., 2019; Zhou & Liang, 2018; Wu et al., 2018; Shamir, 2018) and the role of (stochastic) gradientbased methods (Tian, 2017; BID4 Zhong et al., 2017; Soltanolkotabi, 2017; Li & Yuan, 2017; Zhang et al., 2018; BID5 Wang et al., 2018; Li & Liang, 2018; BID9 BID11 BID7 BID0 Zou et al., 2018; Zhou et al., 2019) .One of the most important beneficial features of convex optimization is the existence of an optimality test (e.g., norm of the gradient is smaller than a certain threshold) for termination, which gives us a certificate of (approximate) optimality. In contrast, many practitioners in deep learning rely on running first-order methods for a fixed number of epochs, without good termination criteria for the optimization problem. This means that the solutions that we obtain at the end of training are not necessarily global or even local minima. Yun et al. (2018; 2019) showed efficient and simple global optimality tests for deep linear neural networks, but such optimality tests cannot be extended to general nonlinear neural networks, mainly due to nonlinearity in activation functions.Besides nonlinearity, in case of ReLU networks significant additional challenges in the analysis arise due to nondifferentiability, and obtaining a precise understanding of the nondifferentiable points is still elusive. ReLU activation function h(t) = max{t, 0} is nondifferentiable at t = 0. This means that, for example, the function f (w, b) := (h(w T x + b) − 1) 2 is nondifferentiable for any (w, b) satisfying w T x+b = 0. See FIG2 for an illustration of how the empirical risk of a ReLU network looks like. Although the plotted function does not exactly match the definition of empirical risk we study in this paper, the figures help us understand that the empirical risk is continuous but piecewise differentiable, with affine hyperplanes on which the function is nondifferentiable.Such nondifferentiable points lie in a set of measure zero, so one may be tempted to overlook them as ""non-generic."" However, when studying critical points we cannot do so, as they are precisely such ""non-generic"" points. For example , Laurent & Brecht (2018) study one-hidden-layer ReLU networks with hinge loss and note that except for piecewise constant regions, local minima always occur on nonsmooth boundaries. Probably due to difficulty in analysis, there have not been other works that handle such nonsmooth points of losses and prove results that work for all points. Some theorems (Soudry & Carmon, 2016; Nguyen & Hein, 2018) hold ""almost surely""; some assume differentiability or make statements only for differentiable points (Nguyen & Hein, 2017; Yun et al., 2019) ; others analyze population risk, in which case the nondifferentiability disappears after taking expectation (Tian, 2017; BID4 BID10 Safran & Shamir, 2018; Wu et al., 2018 ). We provided a theoretical algorithm that tests second-order stationarity and escapes saddle points, for any points (including nondifferentiable ones) of empirical risk of shallow ReLU-like networks. Despite difficulty raised by boundary data points dividing the parameter space into 2 M regions, we reduced the computation to d h convex QPs, O(M ) equality/inequality tests, and one (or a few more) nonconvex QP. In benign cases, the last QP is equality constrained, which can be efficiently solved with projected gradient descent. In worse cases, the QP has a few (say L) inequality constraints, but it can be solved efficiently when L is small. We also provided empirical evidences that L is usually either zero or very small, suggesting that the test can be done efficiently in most cases. A limitation of this work is that in practice, exact nondifferentiable points are impossible to reach, so the algorithm must be extended to apply the nonsmooth analysis for points that are ""close"" to nondifferentiable ones. Also, current algorithm only tests for exact SOSP, while it is desirable to check approximate second-order stationarity. These extensions must be done in order to implement a robust numerial version of the algorithm, but they require significant amount of additional work; thus, we leave practical/robust implementation as future work. Also, extending the test to deeper neural networks is an interesting future direction. Algorithm 2 SOSP-CHECK DISPLAYFORM0",1434,0.676,845,1.6970414201183432,"We provide a theoretical algorithm checking local optimality escaping saddles at nondifferentiable points empirical risks of two-layer ReLU networks Our algorithm receives any parameter value: local minimum, second-order stationary point a strict descent direction The presence M data points the nondifferentiability the ReLU divides the parameter space at most 2^M regions makes analysis By exploiting polyhedral geometry reduce the total computation downQP each hidden node O(M (in)equality tests one (or a For the last QP show our specific problem can efficiently spite nonconvexity In the benign case we solve one equality constrained QP, prove projected gradient descent solves exponentially fast In the bad case we solve a few more inequality constrained QPs prove the time complexity exponential only the number inequality constraints Our experiments either benign case or bad case with very few inequality constraints occurs implying our algorithm efficient Empirical success of deep neural networks sparked the theory deep models From an optimization viewpoint the biggest mystery deep neural networks successfully by gradient-based algorithms despite On has known training neural networks global optimality NPhard BID2 . It also even checking local optimality of nonconvex problems NP (Murty Kabadi 1987 . Bridging theory a very active area there understand optimization works well by the loss surface BID1 Yu & Chen 1995 Kawaguchi 2016 Soudry Carmon Nguyen Hein Safran Shamir Laurent Brecht Yun Zhou Liang Shamir) the role ( gradientbased methodsTian BID4 Zhong Soltanolkotabi Li Yuan Liang BID9 BID11 BID7 BID0 Zou Zhou 2019 .One convex optimization the existence an optimality test norm of is smaller termination gives a certificate In contrast many practitioners in deep learning rely running first-order methods a fixed number without good termination criteria the optimization problem This means the solutions obtain at training global or even local minima Yun et (2018; 2019 showed efficient and simple global optimality tests deep linear neural networks but extended mainly activation functionsBesides in case ReLU significant additional challenges in arise nondifferentiability and obtaining a precise understanding the nondifferentiable points still elusive ReLU activation function h(t max{t 0 is nondifferentiable at t This means, function f (w := T x + − 2 nondifferentiable for ( satisfying = See FIG2 for how the empirical risk a ReLU network looks Although the plotted function does exactly empirical risk we study the figures help that continuous but piecewise differentiable affine hyperplanes on which nondifferentiableSuch nondifferentiable points lie measure zero so one overlook ""nongeneric when studying critical points we do For example , Laurent & Brecht2018 study one-hidden-layer ReLU networks hinge loss note except piecewise constant regions local minima always occur on nonsmooth boundaries Probably due difficulty analysis there have not other works handle such nonsmooth points losses prove results work for all points Some theorems (Soudry & Carmon 2016 Nguyen Hein 2018 hold ""almost surely""; assume differentiability or make statements only for differentiable points Yun 2019 ; analyze population risk in the nondifferentiability disappears after taking expectationTian BID4 BID10 Safran & Shamir We provided a theoretical algorithm tests second-order stationarity escapes saddle points for any points (including nondifferentiable ones empirical risk of shallow ReLU-like networks Despite difficulty raised boundary data points dividing the parameter space 2 M regions reduced the computation d h convex QPs O(M ) equality/inequality tests one (or a In benign cases the last QP equality constrained can efficiently solved projected gradient descent In worse cases the QP has few (say L) inequality constraints solved efficiently when L small We also provided empirical evidences L is usually either zero very suggesting the test done efficiently A limitation in practice exact nondifferentiable points impossible reach the algorithm extended apply the nonsmooth analysis for points ""close Also current algorithm only tests exact SOSP while desirable check approximate second-order stationarity These extensions must done implement a robust numerial version require significant amount additional work; thus leave practical/robust implementation future work Also extending the test deeper neural networks an interesting future direction Algorithm 2 SOSP-CHECK DISPLAYFORM0",0.01,0.4800794667557886
"We present a new technique for learning visual-semantic embeddings for cross-modal retrieval.   Inspired by the use of hard negatives in structured prediction, and ranking loss functions used in retrieval, we introduce a simple change to common loss functions used to learn multi-modal embeddings.   That, combined with fine-tuning and the use of augmented data, yields significant gains in retrieval performance.   We showcase our approach, dubbed VSE++, on the MS-COCO and Flickr30K datasets, using ablation studies and comparisons with existing methods.   On MS-COCO our approach outperforms state-of-the-art methods by 8.8% in caption retrieval, and 11.3% in image retrieval (based on R@1). Joint embeddings enable a wide range of tasks in image, video and language understanding. Examples include shape-image embeddings BID18 ) for shape inference, bilingual word embeddings BID33 ), human pose-image embeddings for 3D pose inference BID17 ), fine-grained recognition BID22 ), zero-shot learning BID7 ), and modality conversion via synthesis BID23 a) ). Such embeddings entail mappings from two (or more) domains into a common vector space in which semantically associated inputs (e.g., text and images) are mapped to similar locations. The embedding space thus represents the underlying structure of the domains, where locations and often direction are semantically meaningful.In this paper we focus on learning visual-semantic embeddings, central to tasks such as imagecaption retrieval and generation BID13 ; BID11 , and visual questionanswering BID20 . One approach to visual question-answering, for example, is to first describe an image by a set of captions, and then to find the nearest caption in response to a question BID0 ; BID32 ). In the case of image synthesis from text, one approach is to invert the mapping from a joint visual-semantic embedding to the image space BID23 a) ).Here we focus on visual-semantic embeddings for the generic task of cross-modal retrieval; i.e. the retrieval of images given captions, or of captions from a query image. As is common in information retrieval, we measure performance by R@K, i.e., recall at K -the fraction of queries for which the correct item is retrieved in the closest K points to the query in the embedding space (K is usually a small integer, often 1). More generally, retrieval is a natural way to assess the quality of joint embeddings for image and language data for use in subsequent tasks BID9 ).To this end, the problem is one of ranking, for which the correct target(s) should be closer to the query than other items in the corpus, not unlike learning to rank problems (e.g., BID16 ), and max-margin structured prediction BID2 ; . The formulation and model architecture in this paper are most closely related to those of BID13 , learned with a triplet ranking loss. In contrast to that work, we advocate a novel loss, the use of augmented data, and fine-tuning, that together produce a significant increase in caption retrieval performance over the baseline ranking loss on well-known benchmark datasets. We outperform the best reported result on MS-COCO by almost 9%. We also demonstrate that the benefit from a more powerful image encoder, and fine-tuning the image encoder, is amplified with the use of our stronger loss function. To ensure reproducibility , our code will be made publicly available. We refer to our model as VSE++.Finally, we note that our formulation complements other recent articles that propose new model architectures or similarity functions for this problem. BID28 propose an embedding network to fully replace the similarity function used for the ranking loss. An attention mechanism on both image and caption is used by BID21 , where the authors sequentially and selectively focus on a subset of words and image regions to compute the similarity. In BID10 , the authors use a multi-modal context-modulated attention mechanism to compute the similarity between an image and a caption. Our proposed loss function and triplet sampling could be extended and applied to other such approaches. This paper focused on learning visual-semantic embeddings for cross-modal, image-caption retrieval. Inspired by structured prediction, we proposed a new loss based on violations incurred by relatively hard negatives compared to current methods that used expected errors BID13 BID27 ). We performed experiments on the MS-COCO and Flickr30K datasets and showed that our proposed loss significntly improves performance on these datasets. We observed that the improved loss can better guide a more powerful image encoder, ResNet152, and also guide better when fine-tuning an image encoder. With all modifications, our VSE++ model achieves state-of-the-art performance on the MS-COCO dataset, and is slightly below the best recent model on the Flickr30K dataset. Our proposed loss function can be used to train more sophisticated models that have been using a similar ranking loss for training.",986,0.558,562,1.7544483985765125,"We present learning Inspired hard negatives structured prediction and ranking loss functions used retrieval introduce common loss functions used learn That, combined augmented data yields significant gains retrieval performance We showcase our approach, dubbed VSE++ on the MS-COCO and Flickr30K datasets ablation studies comparisons existing methods On MS-COCO our approach outperforms state methods caption retrievalbased R@1 Joint embeddings enable tasks image, language understanding Examples include shape-image embeddings BID18 ) shape inference bilingual word human pose zero-shot learning modality conversion via synthesis a ). Such embeddings entail mappings in semantically associated inputs text similar locations The embedding space thus represents the domains locations often direction semantically meaningfulIn learning central tasks imagecaption retrieval generation BID13 ; BID11 visual questionanswering One approach visual question for first describe find response a question BID0 ; BID32 In image synthesis from text one approach invert the mapping from joint visual- embedding the image space BID23 a) ).Here focus the generic task; given captions a query image As is information retrieval measure performance R@K at K -the fraction queries for the correct item the closest K points in the embedding space is usually often More generally retrieval assess joint embeddings image and language data for subsequent tasks BID9 ).To this the problem one ranking for correct target(s closer the query other items not unlike learning rank problems max-margin structured prediction BID2 ; . The formulation and model architecture in most BID13 , learned with a triplet ranking loss In contrast that work advocate a novel loss, the use augmented data, that together produce caption retrieval performance over the baseline ranking loss on well-known benchmark datasets We outperform the best reported result MS-COCO We also demonstrate the benefit a more powerful image encoder fine amplified our stronger loss function To ensure , our code made We refer our model VSE++.Finally note our formulation complements other recent articles propose new model architectures or similarity functions this problem BID28 propose an embedding network fully replace the similarity function used the ranking loss An attention mechanism on both image caption BID21 , where the authors sequentially and focus words image regions compute In BID10 , the authors use a multi-modal context-modulated attention mechanism compute Our proposed loss function and triplet sampling could extended and applied other such approaches This paper focused learning cross-modal, image-caption retrieval Inspired structured prediction proposed a new loss based violations incurred relatively hard negatives compared current methods that used expected errors BID13 BID27 ). We performed experiments the MS-COCO and Flickr30K datasets showed our proposed loss significntly improves We observed the improved loss can better guide a more powerful image encoder ResNet152 guide better when fine With all modifications our VSE++ model achieves state the MS-COCO dataset slightly below the best recent model on the Flickr30K dataset Our proposed loss function can train more sophisticated models have using a similar ranking loss for training",0.01,0.6263474041452248
"We present DANTE, a novel method for training neural networks, in particular autoencoders, using the alternating minimization principle. DANTE provides a distinct perspective in lieu of traditional gradient-based backpropagation techniques commonly used to train deep networks. It utilizes an adaptation of quasi-convex optimization techniques to cast autoencoder training as a bi-quasi-convex optimization problem. We show that for autoencoder configurations with both differentiable (e.g. sigmoid) and non-differentiable (e.g. ReLU) activation functions, we can perform the alternations very effectively. DANTE effortlessly extends to networks with multiple hidden layers and varying network configurations. In experiments on standard datasets, autoencoders trained using the proposed method were found to be very promising when compared to those trained using traditional backpropagation techniques, both in terms of training speed, as well as feature extraction and reconstruction performance. For much of the recent march of deep learning, gradient-based backpropagation methods, e.g. Stochastic Gradient Descent (SGD) and its variants, have been the mainstay of practitioners. The use of these methods, especially on vast amounts of data, has led to unprecedented progress in several areas of artificial intelligence. On one hand, the intense focus on these techniques has led to an intimate understanding of hardware requirements and code optimizations needed to execute these routines on large datasets in a scalable manner. Today, myriad off-the-shelf and highly optimized packages exist that can churn reasonably large datasets on GPU architectures with relatively mild human involvement and little bootstrap effort.However, this surge of success of backpropagation-based methods in recent years has somewhat overshadowed the need to continue to look for options beyond backprogagation to train deep networks. Despite several advancements in deep learning with respect to novel architectures such as encoderdecoder networks and generative adversarial models, the reliance on backpropagation methods remains. While reinforcement learning methods are becoming increasingly popular, their scope is limited to a particular family of settings such as agent-based systems or reward-based learning. Recent efforts have studied the limitations of SGD-based backpropagation, including parallelization of SGDbased techniques that are inherently serial BID14 ); vanishing gradients, especially for certain activation functions BID7 ); convergence of stochastic techniques to local optima BID0 ); and many more. For a well-referenced recent critique of gradient-based methods, we point the reader to BID14 .From another perspective, there has been marked progress in recent years in the area of non-convex optimization (beyond deep learning), which has resulted in scalable methods such as iterated hard thresholding BID2 ) and alternating minimization BID9 ) as methods of choice for solving large-scale sparse recovery, matrix completion, and tensor factorization tasks. Several of these methods not only scale well to large problems, but also offer provably accurate solutions. In this work, we investigate a non-backpropagation strategy to train neural networks, leveraging recent advances in quasi-convex optimization. Our method is called DANTE (Deep AlterNations for Training autoEncoders), and it offers an alternating minimization-based technique for training neural networks -in particular, autoencoders.DANTE is based on a simple but useful observation that the problem of training a single hidden-layer autoencoder can be cast as a bi-quasiconvex optimization problem (described in Section 3.1). This observation allows us to use an alternating optimization strategy to train the autoencoder, where each step involves relatively simple quasi-convex problems. DANTE then uses efficient solvers for quasiconvex problems including normalized gradient descent BID11 ) and stochastic normalized gradient descent BID6 ) to train autoencoder networks. The key contributions of this work are summarized below:• We show that viewing each layer of a neural network as applying an ensemble of generalized linear transformations, allows the problem of training the network to be cast as a bi-quasiconvex optimization problem (exact statement later).• We exploit this intuition by employing an alternating minimization strategy, DANTE, that reduces the problem of training the layers to quasi-convex optimization problems.• We utilize the state-of-the-art Stochastic Normalized Gradient Descent (SNGD) technique BID6 ) for quasi-convex optimization to provide an efficient implementation of DANTE for networks with sigmoidal activation functions. However, a limitation of SNGD is its inability to handle non-differentiable link functions such as the ReLU.• To overcome this limitation, we introduce the generalized ReLU, a variant of the popular ReLU activation function and show how SNGD may be applied with the generalized ReLU function. This presents an augmentation in the state-of-the-art in quasi-convex optimization and may be of independent interest. This allows DANTE to train AEs with both differentiable and non-differentiable activation functions, including ReLUs and sigmoid.• We show that SNGD offers provably more rapid convergence with the generalized ReLU function than it does even for the sigmoidal activation. This is corroborated in experiments as well. A key advantage of our approach is that these theoretical results can be used to set learning rates and batch sizes without finetuning/cross-validation.• We also show DANTE can be easily extended to train deep AEs with multiple hidden layers.• We empirically validate DANTE with both the generalized ReLU and sigmoid activations and establish that DANTE provides competitive test errors, reconstructions and classification performance (with the learned representations), when compared to an identical network trained using standard mini-batch SGD-based backpropagation. In this work, we presented a novel methodology, Deep AlterNations for Training autoEncoders (DANTE), to efficiently train autoencoders using alternating minimization, thus providing an effective alternative to backpropagation. We formulated the task of training each layer of an autoencoder as a Strictly Locally Quasi-Convex (SLQC) problem, and leveraged recent results to use Stochastic Normalized Gradient Descent (SNGD) as an effective method to train each layer of the autoencoder. While recent work was restricted to using sigmoidal activation functions, we introduced a new generalized ReLU activation function, and showed that a GLM with this activation function also satisfies the SLQC property, thus allowing us to expand the applicability of the proposed method to autoencoders with both sigmoid and ReLU family of activation functions. In particular, we extended the definitions of local quasi-convexity to use subgradients in order to prove that the GLM with generalized ReLU activation is , DISPLAYFORM0 , w * − SLQC, which improves the convergence bound for SLQC in the GLM with the generalized ReLU (as compared to a GLM with sigmoid). We also showed how DANTE can be extended to train multi-layer autoencoders. We empirically validated DANTE with both sigmoidal and ReLU activations on standard datasets as well as in a multi-layer setting, and observed that it provides a competitive alternative to standard backprop-SGD, as evidenced in the experimental results.Future Work and Extensions. DANTE can not only be used to train autoencoders, but can be extended to train standard multi-layer neural networks too. One could use DANTE to train a neural network layer-wise in a round robin fashion, and then finetune end-to-end using backprop-SGD. In case of autoencoders with tied weights, one could use DANTE to learn the weights of the required layers, and then finetune end-to-end using a method such as SGD. Our future work will involve a more careful study of the proposed method for deeper autoencoders, including the settings mentioned above, as well as in studying performance bounds for the end-to-end alternating minimization strategy for the proposed method.",1589,0.726,953,1.6673662119622246,"We present DANTE training, particular autoencoders using the alternating minimization principle DANTE provides a distinct perspective in lieu traditional gradient-based backpropagation techniques commonly train deep networks It utilizes an adaptation quasi-convex optimization techniques cast autoencoder training as We show for autoencoder configurations both differentiable (e.g. sigmoid perform the alternations very DANTE effortlessly extends to networks multiple hidden layers varying network configurations In experiments standard datasets trained using the proposed method very promising when both training speed feature extraction reconstruction performance For much the recent march deep learning, gradient-based backpropagation methods, its variants practitioners The use these methods, on vast amounts unprecedented progress several areas artificial intelligence On the intense focus these techniques an intimate understanding hardware requirements code optimizations needed execute these routines large datasets in Today myriad off and highly optimized packages exist churn reasonably large datasets on GPU with relatively mild human involvement and little bootstrap effortHowever this surge success of backpropagation-based methods somewhat continue look options beyond backprogagation train deep networks Despite several advancements deep learning with respect novel architectures such encoderdecoder networks the reliance remains. While reinforcement learning methods their scope a particular family settings such agent-based systems Recent efforts studied the limitations SGD-based backpropagation parallelization SGDbased techniques that inherently serial BID14 ); vanishing gradients especially certain activation functions BID7 convergence local optima BID0 many For a well-referenced recent critique gradient-based methods we point BID14 .From another perspective there has markedbeyond deep learning resulted scalable methods such iterated hard thresholding BID2 ) alternating ) methods solving large-scale sparse recovery, matrix completion tensor factorization tasks Several these methods not scale large problems offer provably accurate solutions In this work investigate a non-backpropagation strategy train, leveraging quasi-convex optimization Our method called DANTE (Deep AlterNations for Training autoEncoders offers an alternating minimization-based technique a simple but useful observation the problem cast a bi-quasiconvex optimization problemdescribed Section This observation allows use an alternating optimization strategy train, where involves relatively simple quasi-convex problems DANTE then uses efficient solvers for quasiconvex problems including normalized gradient descent BID11 ) train The key contributions this work below:• We show viewing each layer applying an ensemble generalized linear transformations allows the problem training cast a bi-quasiconvex optimization problemexact statement later).• exploit this intuition employing an alternating minimization strategy DANTE reduces the layers quasi utilize state Normalized BID6 ) to provide networks sigmoidal activation functions However a limitation SNGD its inability handle non-differentiable link functions such the ReLU.• To introduce the generalized ReLU, a variant the popular ReLU activation function and show may applied with This presents an augmentation in- in quasi-convex optimization may independent interest This allows DANTE train AEs both differentiable and non-differentiable activation functions including ReLUs sigmoid.• We show SNGD offers provably more rapid convergence the generalized ReLU function it even for This corroborated experiments as A key advantage our approach these theoretical results set learning rates batch without finetuning/crossvalidation.• also show DANTE can easily train deep AEs multiple hidden layers.• empirically validate both the generalized ReLU sigmoid activations establish provides competitive test errors, reconstructions classification performance (with the learned representations when an identical network trained standard mini-batch SGD-based backpropagation In this work presented, Deep AlterNations for Training autoEncodersDANTE efficiently alternating minimization thus We formulated the task training each layer as Strictly Locally Quasi ( problem leveraged recent results use Stochastic Normalized Gradient Descent While recent work was restricted using sigmoidal activation functions introduced a new generalized ReLU activation function and showed a GLM with also satisfies the SLQC property thus expand the proposed method with both sigmoid ReLU family In particular extended the definitions local quasiconvexity use subgradients order prove the GLM with generalized ReLU activation , DISPLAYFORM0 w * − SLQC, which improves the convergence bound (as compared We also showed DANTE extended train multi-layer autoencoders We empirically validated DANTE with both sigmoidal and ReLU activations standard datasets as a multi-layer setting observed it provides a competitive alternative standard backprop-SGD, evidenced inFuture Work and Extensions. DANTE can not only train autoencoders extended standard multi-layer neural networks too One could use DANTE train a neural network layer- finetune end using backprop-SGD In case of autoencoders with tied weights one could DANTE learn the required layers finetune end using a method such SGD Our future work a more careful study the proposed method deeper autoencoders the settings mentioned in studying performance bounds end alternating minimization strategy for",0.01,0.4044696436092791
"We develop new algorithms for estimating heterogeneous treatment effects, combining recent developments in transfer learning for neural networks with insights from the causal inference literature. By taking advantage of transfer learning, we are able to efficiently use different data sources that are related to the same underlying causal mechanisms. We compare our algorithms with those in the extant literature using extensive simulation studies based on large-scale voter persuasion experiments and the MNIST database. Our methods can perform an order of magnitude better than existing benchmarks while using a fraction of the data. The rise of massive datasets that provide fine-grained information about human beings and their behavior provides unprecedented opportunities for evaluating the effectiveness of treatments. Researchers want to exploit these large and heterogeneous datasets, and they often seek to estimate how well a given treatment works for individuals conditioning on their observed covariates. This problem is important in medicine (where it is sometimes called personalized medicine) (Henderson et al., 2016; Powers et al., 2018) , digital experiments (Taddy et al., 2016) , economics (Athey and Imbens, 2016) , political science (Green and Kern, 2012) , statistics (Tian et al., 2014) , and many other fields. Although a large number of articles are being written on this topic, many outstanding questions remain. We present the first paper that applies transfer learning to this problem.In the simplest case, treatment effects are estimated by splitting a training set into a treatment and a control group. The treatment group receives the treatment, while the control group does not. The outcomes in those groups are then used to construct an estimator for the Conditional Average Treatment Effect (CATE), which is defined as the expected outcome under treatment minus the expected outcome under control given a particular feature vector (Athey and Imbens, 2015) . This is a challenging task because, for every unit, we either observe its outcome under treatment or control, but never both. Assumptions, such as the random assignment of treatment and additional regularity conditions, are needed to make progress. Even with these assumptions, the resulting estimates are often noisy and unstable because the CATE is a vector parameter. Recent research has shown that it is important to use estimators which consider both treatment groups simultaneously (Künzel et al., 2017; Wager and Athey, 2017; Nie and Wager, 2017; Hill, 2011) . Unfortunately, these recent advances are often still insufficient to train robust CATE estimators because of the large sample sizes required when the number of covariates is not small.In this paper, we show how these difficulties in estimating the CATE can sometimes be overcome through the use of transfer learning. In particular, we provide several strategies for utilizing ancillary datasets that are related to the causal mechanism under investigation. Examples of such datasets include observations from: experiments in different locations on different populations, different treatment arms, different outcomes, and non-experimental observational studies. We show that, by transferring information from these ancillary datasets, CATE estimators can converge to better solutions with fewer samples. This is particularly important for CATE estimation, as the cost of collecting additional data is quite high and often requires real-world data collection. Our contributions are as follows:1. We introduce the new problem of transfer learning for estimating heterogeneous treatment effects.2. MLRW Transfer for CATE Estimation adapts the idea of meta-learning regression weights (MLRW) to CATE estimation. By using a learned initialization, regression problems can be optimized much more quickly than with random initializations. Though a variety of MLRW algorithms exist, it is not immediately obvious how one should use these methods for CATE estimation. The principal difficulty is that CATE estimation requires the simultaneous estimation of outcomes under both treatment and control, but we only observe one of the outcomes for any individual unit. Most MLRW transfer methods optimize on a per-task basis to estimate a single quantity. We show that one can overcome this problem with clever use of the Reptile algorithm (Nichol et al., 2018) .3. We provide several additional methods for transfer learning for CATE estimation: warm start, frozen-features, multi-head, and joint training.4. We apply our methods to difficult data problems and show that they perform better than existing benchmarks. We reanalyze a set of large field experiments that evaluate the effect of a mailer on voter turnout in the 2014 U.S. midterm elections (Gerber et al., 2017) . This includes 17 experiments with 1.96 million individuals in total. We also simulate several randomized controlled trials using image data of handwritten digits found in the MNIST database (LeCun, 1998) . We show that our methods, MLRW in particular, obtain better than state-of-the-art performance in estimating CATE, and that they require far fewer observations than extant methods.",1007,0.555,591,1.7038917089678511,"We develop new algorithms estimating heterogeneous treatment effects combining recent developments transfer learning for insights the causal inference literature By taking transfer learning efficiently use different data sources that related the same underlying causal mechanisms We compare our algorithms in the extant literature using extensive simulation studies based large-scale voter persuasion experiments the MNIST database Our methods can perform an order existing benchmarks while using a fraction The rise massive datasets provide human beings provides unprecedented opportunities evaluating treatments Researchers want exploit these large and heterogeneous datasets often seek estimate individuals conditioning on their observed covariates This problem important in medicine (where sometimes personalized medicine (Henderson 2016 Powers 2018 , digital experimentsTaddy economicsAthey ImbensGreen Kern statisticsTian Although articles being many outstanding questions We present that applies transfer learning this problemIn treatment effects estimated splitting a training a treatment The treatment group receives while does The outcomes in those groups then construct the Conditional Average Treatment Effect defined under treatment minus given a particular feature vectorAthey Imbens 2015) . This a challenging task because, every unit either observe its outcome under treatment control never both Assumptions, such the random assignment treatment and additional regularity conditions needed progress Even these assumptions the resulting estimates often noisy unstable because the CATE is a vector parameter Recent research it use estimators which consider both treatment groups simultaneouslyKünzel 2017 Wager Athey Nie and Hill 2011 . Unfortunately these recent advances often still insufficient train robust CATE estimators because when the number not smallIn these difficulties can sometimes transfer learning In particular provide several strategies utilizing ancillary datasets related the causal mechanism under Examples such datasets observations: experiments different locations different populations different treatment arms different outcomes We show, by transferring information these ancillary datasets CATE estimators converge better solutions with fewer samples This particularly CATE estimation the cost collecting quite often Our contributions as We introduce the new problem transfer learning estimating heterogeneous treatment effects.2. MLRW Transfer for CATE Estimation adapts the idea meta-learning regression weights By using a learned initialization regression problems optimized much random initializations Though a variety MLRW algorithms immediately one these methods for CATE estimation The principal difficulty CATE estimation requires the simultaneous estimation outcomes under both treatment, we only observe any individual unit Most MLRW transfer methods optimize ontask to estimate a single quantity We show one can overcome this problem clever use the Reptile algorithm (Nichol et 2018 .3 We provide several additional methods transfer learning CATE estimation: warm start frozen-features multihead joint training.4. We apply difficult data problems show perform existing benchmarks We reanalyze a set large field experiments evaluate a mailer voter turnout (Gerber 2017) . This includes 17 experiments 1.96 million individuals total We also simulate several randomized controlled trials image data of handwritten digits foundLeCun 1998 . We show our methods, MLRW in obtain than state performance estimating CATE, they require far fewer observations extant methods",0.01,0.4975334008845372
"Neuronal assemblies, loosely defined as subsets of neurons with reoccurring spatio-temporally coordinated activation patterns, or ""motifs"", are thought to be building blocks of neural representations and information processing. We here propose LeMoNADe, a new exploratory data analysis method that facilitates hunting for motifs in calcium imaging videos, the dominant microscopic functional imaging modality in neurophysiology. Our nonparametric method extracts motifs directly from videos, bypassing the difficult intermediate step of spike extraction. Our technique augments variational autoencoders with a discrete stochastic node, and we show in detail how a differentiable reparametrization and relaxation can be used. An evaluation on simulated data, with available ground truth, reveals excellent quantitative performance. In real video data acquired from brain slices, with no ground truth available, LeMoNADe uncovers nontrivial candidate motifs that can help generate hypotheses for more focused biological investigations. Seventy years after being postulated by Hebb (1949) , the existence and importance of reoccurring spatio-temporally coordinated neuronal activation patterns (motifs), also known as neuronal assemblies, is still fiercely debated BID12 Singer, 1993; BID17 Ikegaya et al., 2004; Cossart & Sansonetti, 2004; BID4 BID13 BID20 Stevenson & Kording, 2011; BID0 Carrillo-Reid et al., 2015) . Calcium imaging, a microscopic video technique that enables the concurrent observation of hundreds of neurons in vitro and in vivo (Denk et al., 1990; Helmchen & Denk, 2005; Flusberg et al., 2008) , is best suited to witness such motifs if they indeed exist. We have presented a novel approach for the detection of neuronal assemblies that directly operates on the calcium imaging data, making the cumbersome extraction of individual cells and discrete spike times from the raw data dispensable. The motifs are extracted as short, repeating image sequences. This provides them in a very intuitive way and additionally returns information about the spatial distribution of the cells within an assembly.The proposed method's performance in identifying motifs is equivalent to that of a state-of-the-art method that requires the previous extraction of individual cells. Moreover, we were able to identify repeating firing patterns in two datasets from hippocampal slice cultures, proving that the method is capable of handling real calcium imaging conditions.For future work, a post-processing step as used in BID21 or a group sparsity regularization similar to the ones used in BID2 or BID10 could be added to determine a plausible number of motifs automatically. Moreover, additional latent dimensions could be introduced to capture artefacts and background fluctuations and hence automatically separate them from the actual motifs. The method is expected to, in principle, also work on other functional imaging modalities. We will investigate the possibility of detecting motifs using LeMoNADe on recordings from human fMRI or voltage-sensitive dyes in the future.",599,0.29,380,1.5763157894736841,"Neuronal assemblies loosely subsets with reoccurring spatio-temporally coordinated activation patterns or building neural representations We here propose LeMoNADe a new exploratory data analysis method facilitates hunting motifs calcium imaging videos the dominant microscopic functional imaging modality neurophysiology Our nonparametric method extracts motifs directly videos bypassing the difficult intermediate step spike extraction Our technique augments variational autoencoders a discrete stochastic node show in a differentiable reparametrization and relaxation. An evaluation on simulated data, with available ground truth reveals excellent quantitative performance In real video data acquired brain slices with no ground truth available LeMoNADe nontrivial candidate motifs generate hypotheses more focused biological investigations being postulated Hebb , the existence and importance reoccurring spatio-temporally coordinated neuronal activation patterns (motifs also neuronal assemblies fiercely BID12 Singer 1993; BID17 Ikegaya Cossart & Sansonetti BID4 BID13 BID20 Stevenson Kording 2011 Calcium imaging a microscopic video technique enables the concurrent observation hundreds neurons vitro (Denk 1990 Helmchen & 2005 Flusberg , best witness such motifs if indeed We presented neuronal assemblies directly operates the calcium imaging data making the cumbersome extraction individual cells discrete spike times from dispensable The motifs extracted as short, repeating image sequences This provides them in additionally returns information the spatial distribution the cells an assemblyThe proposed method's performance identifying motifs equivalent state method requires the previous extraction Moreover we were identify repeating firing two datasets hippocampal slice cultures proving the method handling real calcium imaging conditionsFor future work as used BID21 or a group sparsity regularization similar the ones added determine a plausible number motifs automatically Moreover additional latent dimensions could introduced capture artefacts background fluctuations and hence automatically separate the actual motifs The method expected, also other functional imaging modalities We will investigate detecting motifs using LeMoNADe on recordings human fMRI or voltage-sensitive dyes the future",0.0,0.17248116671112965
"A noisy and diverse demonstration set may hinder the performances of an agent aiming to acquire certain skills via imitation learning. However, state-of-the-art imitation learning algorithms often assume the optimality of the given demonstration set.
 In this paper, we address such optimal assumption by learning only from the most suitable demonstrations in a given set. Suitability of a demonstration is estimated by whether imitating it produce desirable outcomes for achieving the goals of the tasks. For more efficient demonstration suitability assessments, the learning agent should be capable of imitating a demonstration as quick as possible, which shares similar spirit with fast adaptation in the meta-learning regime. Our framework, thus built on top of Model-Agnostic Meta-Learning, evaluates how desirable the imitated outcomes are, after adaptation to each demonstration in the set. The resulting assessments hence enable us to select suitable demonstration subsets for acquiring better imitated skills. The videos related to our experiments are available at: https://sites.google.com/view/deepdj Imagine that you intend to learn how to make a free throw in basketball, which requires you to throw the ball into the basket from a fixed position. Without the proper knowledge, one may observe professional players perform a free throw on YouTube by obtaining numerous exemplary videos. However, learning from every demonstration videos might lead to worse performance, as they may contain unsuitable or even irrelevant content.The challenge of learning from noisy demonstration sets is as well crucial in the robot imitation learning regime, as demonstrations which are not aligned with achieving the intended goal deteriorate the learning process. The assumptions of optimality (or at least sub-optimality) of the demonstrations are often made in state-of-the-art imitation learning algorithms (Ross & Bagnell, 2010; Ross et al., 2011; BID10 Sermanet et al., 2018) . As a result, they are vulnerable to demonstrations that are potentially detrimental to the learning outcomes in the given set. To address assumptions of optimality, in this paper, we aim for a generic framework capable of learning from a noisy demonstration set, via evaluating the suitability of imitated skills judged by task specific heuristics.Prior works have handled deteriorated imitated outcomes due to noisy demonstration sets by utilizing expected Q-values provided in the demonstrations to avoid learning from bad demonstrated actions BID14 BID17 BID5 . However, these works require demonstrations to have a rich representation such as incorporating the aforementioned Q-values, which may neither be available in other cases nor directly applicable to the agent training environment. Our framework, on the other hand, does not require demonstrations to contain specific information, and hence is able to cope with any forms of expert demonstrations. To be specific, we propose to first assess which demonstrations in the given set might be more suitable by learning from them, and then train the agent imitating only a selected subset.In order to achieve selectively learning from suitable demonstrations, we examine if the learning outcomes are favorable after imitating each demonstration in a set. Typically in robot learning regime, we are able to receive designed feedbacks in the target training environment to evaluate how well the agent performs. Thus, in each task, we predefine specific heuristics for assessing if the agent exhibits imitation learning outcomes desirable for reaching the goals of the tasks.The key challenges for the feasibility of assessing learned outcomes from each demonstration are the efficiency and generalization ability. A framework should be capable of producing these assessable outcomes as quick as possible, and generalizing to unseen demonstrations. To this end, we propose a framework with the demonstration suitability assessor leveraging meta-learning, where we train adaptive parameters via meta-imitation-learning. The meta-imitation-learned parameters can thus: (1) produce assessable imitated outcomes at testing time quicker than both imitation learning from scratch and fine-tune a pretrained initialization BID3 , and (2) adapt to imitating newly sampled unseen demonstrations. Overall, the imitated outcomes after adaptation will be judged by task heuristics to indicate the suitability of certain demonstrations. We then train agents using imitation learning from the selected suitable demonstration subsets for obtaining better policies. We demonstrate two empirical approaches to utilize the resulting suitability assessments. One composes new subsets of demonstrations from the top ranked, the other iteratively fine-tunes the meta-learned parameters by strengthening or weakening certain demonstrations in a set according to current suitability judgments, producing a selected suitable subset at convergence.In some cases, the distribution of demonstration sets can be imbalanced or multi-modal. To prevent over-fitting to certain subsets of such demonstration distributions, we augment the meta-imitationtraining with a regularization objective-maximization of mutual information between the demonstration and the induced behavioral differences from imitating it. This additional regularization term aims to make the meta-trained parameters more responsive to the demonstrations being imitated, and as a result, help differentiate better the adapted behaviors from a noisy and diverse set.We test our framework on four different simulation sports environments in MuJuCo. Our results, both qualitative and quantitative, show that the proposed method outperforms various baselines, including vanilla MAML and fine-tuning a pretrained initialization, on learning better policies from noisy demonstration sets. We propose a framework to tackle the challenging problem -learning a good policy through imitation learning from a noisy demonstration set. Our framework, built on top of MAML with a mutual information maximized regularization, learns a set of adaptive parameters from the given noisy set. The agent should exhibit significant learning outcomes after fast adaptation to certain demonstrations where these outcomes can be evaluated via predefined task heuristics. By being a learning framework, the system learns to discover the most suitable demonstrations for the agent from the expert rather than selecting based on hand crafted judging rules. For future research direction, we hope this work can serve as the first trial to lure more advanced research on tackling imitation learning from noisy demonstration sets. For evaluating the suitability of certain demonstrations, we require a task dependent knowledge to judge from the imitation learning outcomes after the adaptation to a particular demonstration. We hereby describe the task heuristics for each environment in the following:• Free Throw: The minimum distance between the basketball and the fixed basket.• Penalty Save: The minimum distance between the agent and the incoming shot in an episode.• Handstand: The height of two feet of a humanoid if both two hands are touching the ground without letting the head to hit the ground. We accumulate this heuristics score when the aforementioned body pose condition is satisfied.• Martial Arts: The minimum distance between right foot and the target if the head of the humanoid is higher than a pelvis.Setups of our simulation environments are listed in",1319,0.636,783,1.6845466155810984,"A noisy and diverse demonstration set may hinder the performances an agent aiming acquire certain skills via imitation learning However state imitation learning often assume the optimality the given demonstration set In address such optimal assumption learning only from the most suitable demonstrations Suitability a demonstration estimated whether imitating it produce desirable outcomes achieving the tasks For more efficient demonstration suitability assessments the learning agent capable imitating as quick shares similar spirit fast adaptation the meta-learning regime Our framework thus built Model-Agnostic Meta-Learning evaluates desirable the imitated outcomes after adaptation each demonstration The resulting assessments hence enable select suitable demonstration subsets acquiring better imitated skills The videos related our experiments Imagine intend learn a free throw throw Without one observe professional players perform a free throw YouTube by obtaining numerous exemplary videos However learning every demonstration videos might worse performanceThe challenge noisy demonstration sets as crucial the robot imitation learning regime demonstrations which aligned achieving deteriorate The assumptions optimality at least sub of the demonstrations state imitation learningRoss BID10 Sermanet 2018 . As vulnerable demonstrations potentially detrimental the learning outcomes the given set To address assumptions optimality in aim for capable learning a noisy demonstration set via evaluating imitated skills judged task specific heuristicsPrior works handled deteriorated imitated outcomes due by utilizing expected Q-values provided the demonstrations avoid learning bad demonstrated actions BID14 BID17 BID5 . However these works require demonstrations have a rich representation such incorporating the aforementioned Q-values neither other cases directly the agent training environment Our framework on demonstrations contain hence able cope any forms expert demonstrations To specific propose first assess which demonstrations the given set might by learning train agent imitating only a selected subsetIn selectively learning suitable demonstrations examine if favorable after Typically robot learning regime able receive designed feedbacks the target training environment evaluate Thus each task predefine assessing if exhibits imitation learning outcomes desirable reachingThe key challenges the feasibility assessing learned each demonstration the efficiency and generalization ability. A framework should capable these assessable outcomes quick generalizing unseen demonstrations To propose with the demonstration suitability assessor leveraging meta-learning where train adaptive parameters via The meta-imitation-learned parameters can thus: produce assessable imitated outcomes at testing time quicker both imitation from scratch a pretrained initialization BID3 , adapt newly sampled unseen demonstrations Overall the imitated outcomes after adaptation will judged task heuristics indicate certain demonstrations We then train agents imitation from the selected suitable demonstration subsets obtaining better policies We demonstrate two empirical approaches utilize the resulting suitability assessments One composes new subsets demonstrations ranked by strengthening or certain demonstrations according current suitability judgments producing a selected suitable subset at convergenceIn demonstration sets imbalanced multi To prevent overfitting to certain subsets such demonstration distributions augment the meta-imitationtraining a regularization objective-maximization mutual information the demonstration the induced behavioral differences from imitating it This additional regularization term aims the meta-trained parameters responsive the demonstrations being imitated as help differentiate better the adapted behaviors a noisy and diverse setWe test our framework four different simulation sports environments MuJuCo, both qualitative various baselines vanilla MAML fine a pretrained initialization on learning better policies noisy demonstration sets We propose tackle -learning a good policy through imitation learning from a noisy demonstration set Our framework MAML with a mutual information maximized regularization learns adaptive parameters the given noisy set The agent should exhibit significant learning outcomes fast adaptation certain demonstrations where these outcomes via By being a learning framework the system discover the most suitable demonstrations the agent from the expert rather selecting based hand crafted judging rules For future research direction hope this work the first trial lure more advanced research tackling imitation from noisy demonstration sets For evaluating certain demonstrations require a task dependent knowledge to judge from the imitation learning outcomes after the adaptation We hereby describe the task heuristics each environment the following:• Free Throw The minimum distance Penalty Save the agent in an episode.• Handstand two feet a humanoid if both two hands without letting to hit We accumulate this heuristics score when the aforementioned body pose condition satisfied.• Martial Arts The minimum distance right foot if the humanoid higher a pelvisSetups our simulation environments listed",0.01,0.44824380257641216
"We introduce causal implicit generative models (CiGMs): models that allow sampling from not only the true observational but also the true interventional distributions. We show that adversarial training can be used to learn a CiGM, if the generator architecture is structured based on a given causal graph. We consider the application of conditional and interventional sampling of face images with binary feature labels, such as mustache, young. We preserve the dependency structure between the labels with a given causal graph. We devise a two-stage procedure for learning a CiGM over the labels and the image. First we train a CiGM over the binary labels using a  Wasserstein GAN where the generator neural network is consistent with the causal graph between the labels. Later, we combine this with a conditional GAN to generate images conditioned on the binary labels. We propose two new conditional GAN architectures: CausalGAN and CausalBEGAN. We show that the optimal generator of the CausalGAN, given the labels, samples from the image distributions conditioned on these labels. The conditional GAN combined with a trained CiGM for the labels is then a CiGM over the labels and the generated image. We show that the proposed architectures can be used to sample from observational and interventional image distributions, even for interventions which do not naturally occur in the dataset. An implicit generative model BID7 ) is a mechanism that can sample from a probability distribution without an explicit parameterization of the likelihood. Generative adversarial networks (GANs) arguably provide one of the most successful ways to train implicit generative models. GANs are neural generative models that can be trained using backpropagation to sample from very high dimensional nonparametric distributions (Goodfellow et al. (2014) ). A generator network models the sampling process through feedforward computation given a noise vector. The generator output is constrained and refined through feedback by a competitive adversary network, called the discriminator, that attempts to distinguish between the generated and real samples. The objective of the generator is to maximize the loss of the discriminator (convince the discriminator that it outputs samples from the real data distribution). GANs have shown tremendous success in generating samples from distributions such as image and video BID20 ).An extension of GANs is to enable sampling from the class conditional data distributions by feeding class labels to the generator alongside the noise vectors. Various neural network architectures have been proposed for solving this problem BID6 ; BID10 ; Antipov et al. Figure 1: Observational and interventional samples from CausalBEGAN. Our architecture can be used to sample not only from the joint distribution (conditioned on a label) but also from the interventional distribution, e.g., under the intervention do(M ustache = 1). The two distributions are clearly different since P(M ale = 1|M ustache = 1) = 1 and P(Bald = 1|M ale = 0) = 0 in the data distribution P.(2017)). However, these architectures do not capture the dependence between the labels. Therefore, they do not have a mechanism to sample images given a subset of the labels, since they cannot sample the remaining labels. In this paper, we are interested in extending the previous work on conditional image generation by i) capturing the dependence between labels and ii) capturing the causal effect between labels. We can think of conditional image generation as a causal process: Labels determine the image distribution. The generator is a non-deterministic mapping from labels to images. This is consistent with the causal graph ""Labels cause the Image"", denoted by L → I, where L is the random vector for labels and I is the image random variable. Using a finer model, we can also include the causal graph between the labels, if available.As an example, consider the causal graph between Gender (G) and Mustache (M ) labels. The causal relation is clearly Gender causes Mustache , denoted by the graph G → M . Conditioning on Gender = male, we expect to see males with or without mustaches, based on the fraction of males with mustaches in the population. When we condition on Mustache = 1, we expect to sample from males only since the population does not contain females with mustaches. In addition to sampling from conditional distributions , causal models allow us to sample from various different distributions called interventional distributions. An intervention is an experiment that fixes the value of a variable in a causal graph. This affects the distributions of the descendants of the intervened variable in the graph. But unlike conditioning, it does not affect the distribution of its ancestors. For the same causal graph, intervening on Mustache = 1 would not change the distribution of Gender. Accordingly, the label combination (Gender = female, Mustache = 1) would appear as often as Gender = female after the intervention. Please see Figure 1 for some of our conditional and interventional samples, which illustrate this concept on the Bald and Mustache variables.In this work we propose causal implicit generative models (CiGM): mechanisms that can sample not only from the correct joint probability distributions but also from the correct conditional and interventional probability distributions. Our objective is not to learn the causal graph: we assume that the true causal graph is given to us. We show that when the generator structure inherits its neural connections from the causal graph, GANs can be used to train causal implicit generative models. We use Wasserstein GAN (WGAN) (Arjovsky et al. (2017) ) to train a CiGM for binary image labels, as the first step of a two-step procedure for training a CiGM for the images and image labels. For the second step, we propose two novel conditional GANs called CausalGAN and CausalBEGAN. We show that the optimal generator of CausalGAN can sample from the true conditional distributions (see Theorem 1).We show that combining CausalGAN with a CiGM on the labels yields a CiGM on the labels and the image, which is formalized in Corollary 1 in Section 5. Our contributions are as follows:• We observe that adversarial training can be used after structuring the generator architecture based on the causal graph to train a CiGM. We empirically show that WGAN can be used to learn a CiGM that outputs essentially discrete 1 labels, creating a CiGM for binary labels.• We consider the problem of conditional and interventional sampling of images given a causal graph over binary labels. We propose a two-stage procedure to train a CiGM over the binary labels and the image. As part of this procedure, we propose a novel conditional GAN architecture and loss function. We show that the global optimal generator provably samples from the class conditional distributions.• We propose a natural but nontrivial extension of BEGAN to accept labels: using the same motivations for margins as in BEGAN (Berthelot et al. (2017) ), we arrive at a ""margin of margins"" term. We show empirically that this model, which we call CausalBEGAN, produces high quality images that capture the image labels.• We evaluate our CiGM training framework on the labeled CelebA data BID2 ).We empirically show that CausalGAN and CausalBEGAN can produce label-consistent images even for label combinations realized under interventions that never occur during training, e.g., ""woman with mustache"" 2 . We proposed a novel generative model with label inputs. In addition to being able to create samples conditioned on labels, our generative model can also sample from the interventional distributions. Our theoretical analysis provides provable guarantees about correct sampling under such interventions.Top: Intervene Narrow Eyes=1, Bottom: Condition Narrow Eyes=1Figure 7: Intervening/Conditioning on Narrow Eyes label in CelebA Causal Graph with CausalBEGAN. Since Smiling → Narrow Eyes in CelebA Causal Graph, we do not expect do(Narrow Eyes = 1) to affect the probability of Smiling = 1, i.e., P(Smiling = 1|do(Narrow Eyes = 1)) = P(Smiling = 1) = 0.48. However on the bottom row, conditioning on Narrow Eyes = 1 increases the proportion of smiling images (From 0.48 to 0.59 in the dataset), although 10 images may not be enough to show this difference statistically. As a rare artifact, in the dark image in the third column the generator appears to rule out the possibility of Narrow Eyes = 0 instead of demonstrating Narrow Eyes = 1.Causality leads to generative models that are more creative since they can produce samples that are different from their training samples in multiple ways. We have illustrated this point for two models (CausalGAN and CausalBEGAN).",1798,0.99,1027,1.750730282375852,"We introduce causal implicit generative models sampling not true observational but We show adversarial training learn a CiGM if the generator architecture structured based a given causal graph We consider the application conditional and interventional sampling of face images binary feature labels mustache young. We preserve the dependency structure the labels with a given causal graph We devise learning a CiGM over the labels the image First we train a CiGM over the binary labels using a Wasserstein GAN where the generator neural network consistent the causal graph between Later combine a conditional GAN images conditioned the binary labels We propose two new conditional GAN architectures CausalGAN We show optimal generator the CausalGAN, given the labels samples from the image distributions conditioned The conditional GAN combined a trained CiGM for the labels then a CiGM over the generated image We show the proposed architectures can sample from observational and interventional image distributions even interventions naturally An implicit generative model BID7 ) sample without Generative adversarial networks arguably one train implicit generative models GANs neural generative models sample from very high dimensional nonparametric distributionsGoodfellow (2014 ). A generator network models the sampling process through feedforward computation given a noise vector The generator output constrained and refined feedback by a competitive adversary network called attempts distinguish The objective the generator maximize the loss the discriminatorconvince outputs samples the real data distribution GANs shown generating samples distributions such image BID20 ).An extension enable sampling the class conditional data distributions feeding class labels the generator alongside the noise vectors Various neural network architectures solving BID6 ; Antipov et Figure interventional samples CausalBEGAN Our architecture can sample not from the joint distributionconditioned on a label under the intervention do(M ustache = The two distributions clearly since P(M ale = 1|M ustache in the data distribution P.(2017 However these architectures capture the dependence the labels Therefore they do a mechanism sample images given a subset the labels since In are extending conditional image generation i) capturing the dependence labels ii We think conditional image generation Labels determine the image distribution The generator labels images This consistent the causal graph ""Labels cause the Image denoted L → I the random vector for Using a finer model also include the causal graph between the labels if availableAs GenderG Mustache (M ) labels The causal relation is clearly Gender causes Mustache , denoted the graph G → M Conditioning on Gender = male we expect males or mustaches based the fraction When condition on Mustache = 1 expect sample males since the population does with mustaches In addition sampling conditional distributions , causal models allow sample various different distributions called interventional distributions An intervention an experiment fixes the value a causal graph This affects the distributions the descendants the intervened variable But unlike conditioning the distribution its ancestors For the same causal graph intervening Mustache = change Gender Accordingly the label combination (Gender = female 1 would often Gender after the intervention Please see Figure some our conditional and interventional samples illustrate this concept on the Bald and Mustache variablesIn propose causal implicit generative models (CiGM): mechanisms sample not the correct joint probability distributions Our objective not learn the causal graph: assume given to We show when the generator structure inherits its neural connections the causal graph GANs train causal implicit generative models We use Wasserstein GANWGAN (Arjovsky et al (2017 ) to train a CiGM for binary image labels the images and For the second step propose two novel conditional GANs called CausalGAN We show the optimal generator CausalGAN sample the true conditional distributions Theorem 1).We combining a CiGM on the labels yields the image, formalized in Our contributions as observe adversarial training after structuring the generator architecture based the causal graph to train a CiGM We empirically WGAN learn a CiGM that outputs essentially discrete 1 labels creating binary labels.• consider conditional and interventional sampling images given a causal graph over We propose train a CiGM over the binary labels the image As this procedure propose a novel conditional GAN architecture and loss function We show the global optimal generator provably samples the class conditional distributions.• propose BEGAN accept labels: using the same motivations margins (2017 ), we arrive ""margin margins term We show empirically this model, CausalBEGAN produces high quality images the image labels.• evaluate our CiGM training framework the labeled CelebA data BID2 ).We and label-consistent images even label combinations realized under interventions never occur during ""woman mustache 2 We proposed with label inputs In addition create samples conditioned labels our generative model sample from the interventional distributions Our theoretical analysis provides provable guarantees correct sampling under such interventionsTop: Intervene Narrow Eyes=1 Bottom Condition Narrow 7 on in CelebA Causal Graph with CausalBEGAN Since Smiling → Narrow Eyes in CelebA Causal Graph do expect do(Narrow = affect = However on the bottom row conditioning on Narrow Eyes = 1 increases smiling imagesFrom the dataset although 10 images may statistically As a rare artifact in the dark image in the generator rule Narrow Eyes = 0 instead demonstrating leads generative models creative since produce samples different their training samples We illustrated for two modelsCausalGAN",0.01,0.6168739707360593
"Self-normalizing discriminative models approximate the normalized probability of a class without having to compute the partition function. This property is useful to computationally-intensive neural network classifiers, as the cost of computing the partition function grows linearly with the number of classes and may become prohibitive. In particular, since neural language models may deal with up to millions of classes, their self-normalization properties received notable attention. Several
 recent studies empirically found that language models, trained using Noise Contrastive Estimation (NCE), exhibit self-normalization, but could not explain why. In this study, we provide a theoretical justification to this property by viewing
 NCE as a low-rank matrix approximation. Our empirical investigation compares NCE to the alternative explicit approach for self-normalizing language models. It also uncovers a surprising negative correlation between self-normalization and
 perplexity, as well as some regularity in the observed errors that may potentially be used for improving self-normalization algorithms in the future. The ability of statistical language models (LMs) to estimate the probability of a word given a context of preceding words, plays an important role in many NLP tasks, such as speech recognition and machine translation. Recurrent Neural Network (RNN) language models have recently become the preferred method of choice, having outperformed traditional n-gram LMs across a range of tasks BID8 ). Unfortunately however, they suffer from scalability issues incurred by the computation of the softmax normalization term, which is required to guarantee proper probability predictions. The cost of this computation is linearly proportional to the size of the word vocabulary and has a significant impact on both training and testing. 1 Several methods have been proposed to cope with this scaling issue by replacing the softmax with a more computationally efficient component at train time. These include importance sampling BID1 ), hierarchical softmax BID13 , BlackOut BID7 ) and Noise Contrastive Estimation (NCE) BID5 ). NCE has been applied to train neural LMs with large vocabularies BID14 ) and more recently was also successfully used to train LSTM-RNN LMs BID17 ; BID3 ; BID19 ), achieving near state-of-the-art performance on language modeling tasks BID8 ; BID2 ). All the above works focused on solving the run-time complexity problem at train time. However, at test time the assumption was that one still needs to explicitly compute the softmax normalization term to obtain a normalized score fit as an estimate for the probability of a word.Self-normalization was recently proposed as means to address the high run-time complexity associated with predicting normalized probabilities at test time. A self-normalized discriminative model is trained to produce near-normalized scores in the sense that the sum over the scores of all classes is approximately one. If this approximation is close enough, the assumption is that the costly exact normalization can be waived at test time without significantly sacrificing prediction accuracy BID4 ). Two main approaches were proposed to train self-normalizing models. Explicit selfnormalization is based on using softmax for training and explicitly encouraging the normalization term of the softmax to be as close to one as possible, thus making its computation redundant at test time BID4 ; BID0 ; BID2 ). The alternative approach is based on NCE. The original formulation of NCE included a normalization term Z. However, the first work that applied NCE to LM BID14 ) discovered, empirically, that fixing Z to a constant did not affect the performance. More recent studies BID17 ; BID19 ; BID3 ; BID15 ) empirically found that models trained using NCE with a fixed Z, exhibit self-normalization, but they could not explain this behavior. To the best of our knowledge, the only theoretical analysis of self-normalization was proposed by BID0 . This analysis shows that a model trained explicitly to be self-normalizing only on a subset of the training instances, can potentially be self-normalizing on other similar instances as well. However, their analysis cannot explain how NCE can be self-normalizing without explicitly imposing self-normalization on any of its training instances.The main contribution of this study is providing a theoretical justification to the self-normalization property of NCE, which was empirically observed in prior work. We do so by showing that NCE's unnormalized objective can be viewed as finding the best low-rank approximation of the normalized conditional probabilities matrix, without having to explicitly estimate the partition function. While the said self-normalizing property of NCE is more general, we focus the empirical contribution of the paper on language modeling. We investigate the self-normalization performance of NCE as well as that of the alternative explicit self-normalization approach over two datasets. Our results suggest, somewhat surprisingly, that models that achieve better perplexities tend to have worse selfnormalization properties. We also observe that given a context, the sum of the self-normalized scores is negatively correlated with the entropy of the respective normalized distribution. We provided theoretical justification to the empirical observation that NCE is self-normalizing. Our empirical investigation shows that it performs reasonably well, but not as good as a language model that is explicitly trained to self-normalize. Accordingly, we believe that an interesting future research direction could be to augment NCE's training objective with some explicit self-normalization component. In addition, we revealed unexpected correlations between self-normalization and perplexity performance, as well as between the partition function of self-normalized predictions and the entropy of the respective distribution. We hope that these insights would be useful in improving self-normalizing models in future work.",1117,0.617,662,1.6873111782477341,"Self-normalizing discriminative models approximate the normalized probability a class without having compute This property useful computationally-intensive neural network classifiers the cost the partition function grows classes may In particular since neural language models may deal up to millions classes their self-normalization properties received notable attention Several recent studies empirically found language models trained using Noise Contrastive Estimation exhibit self-normalization could In provide to this property viewing NCE as a low-rank matrix approximation Our empirical investigation compares NCE to the alternative explicit approach self-normalizing language models It also a surprising negative correlation self-normalization perplexity some regularity the observed errors that potentially used improving in The ability statistical language modelsLMs a word given preceding words plays choice, having traditional n-gram LMs across BID8 ). Unfortunately however they suffer scalability issues incurred the computation the softmax normalization term required guarantee proper probability predictions The cost this computation linearly the word vocabulary has both training testing 1 Several methods cope this scaling issue by replacing the softmax at train time These include importance sampling BID1 ), hierarchical softmax BID13 BlackOut BID7 ) Noise Contrastive Estimation NCE has applied train neural LMs BID14 ) more was also successfully ; achieving near state language modeling tasks All the above works focused solving at train time However at test time the assumption one still explicitly compute the softmax normalization term normalized score fit as a wordSelf-normalization recently means address predicting normalized probabilities at A self-normalized discriminative model trained produce the sum over all classes approximately one If this approximation close the assumption the costly exact normalization can waived test time without significantly sacrificing prediction accuracy BID4 Two main approaches train self-normalizing models Explicit selfnormalization based using softmax for training explicitly encouraging the normalization term of to as one thus its computation redundant at test time BID4 ; BID0 ; The alternative approach based NCE. The original formulation NCE included a normalization term Z. However the first work applied NCE to LM BID14 ) discovered, empirically fixing Z to did More recent studies BID17 ; ) empirically found that models trained using NCE with a fixed Z, exhibit self-normalization could To the only theoretical analysis self-normalization proposed BID0 . This analysis a model trained explicitly be selfnormalizing only on the training instances can potentially self other similar instances However their analysis NCE can selfnormalizing without explicitly imposing any its training instancesThe main contribution providing observed We do so showing NCE's unnormalized objective can viewed finding the best low-rank approximation the normalized conditional probabilities matrix without explicitly estimate the partition function While the said self-normalizing property NCE more general we focus the empirical contribution the paper language modeling We investigate the self-normalization performance NCE as that the alternative explicit self-normalization approach over two datasets Our results, somewhat that models achieve better perplexities tend worse selfnormalization properties We also observe given a context the sum the self-normalized scores negatively the entropy the respective normalized distribution We provided theoretical justification the empirical observation NCE selfnormalizing Our empirical investigation it performs reasonably a language model explicitly trained selfnormalize Accordingly believe an interesting future research direction could augment NCE's training objective some explicit self-normalization component In addition revealed unexpected correlations self-normalization and perplexity performance the partition function the entropy the respective distribution We hope these insights would improving self-normalizing models future work",0.01,0.4552876653591799
"Learning word representations from large available corpora relies on the distributional hypothesis that words present in similar contexts tend to have similar meanings. Recent work has shown that word representations learnt in this manner lack sentiment information which, fortunately, can be leveraged using external knowledge. Our work addresses the question: can affect lexica improve the word representations learnt from a corpus? In this work, we propose techniques to incorporate affect lexica, which capture fine-grained information about a word's psycholinguistic and emotional orientation, into the training process of Word2Vec SkipGram, Word2Vec CBOW and GloVe methods using a joint learning approach. We use affect scores from Warriner's affect lexicon to regularize the vector representations learnt from an unlabelled corpus. Our proposed method outperforms previously proposed methods on standard tasks for word similarity detection, outlier detection and sentiment detection. We also demonstrate the usefulness of our approach for a new task related to the prediction of formality, frustration and politeness in corporate communication. In natural language research, words, sentences and paragraphs are considered in context through vector space representations, rather than as atomic units with no relational information among them. Although n-gram based methods trained on large volumes of data have been found to outperform more complex approaches both on computational cost and accuracy, the techniques do not scale well in cases where the corpus size is limited(for example, for labeled speech or affect corpora with a size of a few millions of words). Recent work has attempted to improve the performance of word distributions for downstream tasks such as sentiment analysis BID27 and knowledge base completion BID16 using lexical knowledge to enrich word embeddings, by performing methods such as regularization or introducing a loss term in the learning objective.Sentiment relationships between words can be considered transitive, where 'good' < 'better' < 'best' implies that 'good' < 'best'. However, word representations based on traditional approaches such as Word2Vec BID19 and GloVe BID23 are agnostic to the associated sentiments, emotions, or more generally affects BID4 . Furthermore, although words such as delighted and disappointed share similar vector representations given their similar contexts, these words are associated with opposite reactions (or sentiments) as well as have a fairly different interpreted meaning. The challenge in using syntactic relational information for sentiment detection, is that sentiment relations are transitive and symmetric (i.e., if 'delighted' is the opposite of 'disappointed', then 'disappointed' is the opposite of 'delighted'.) Ignoring the bipolar nature of words could lead to spurious results, especially in predictive tasks related to synonyms and antonyms and sentiment analysis. On the other hand, incorporating affect-related information would make word distributions homogeneous and suitable for speech and text generation tasks that aim at capturing author or reader reactions. Furthermore, by using a small sentiment lexicon, it is possible to develop an automatic way to rate words based on their vector space representations. This could help reduce the time and cost required to gather word ratings, as well as eliminate the implicit biases that may be introduced in annotations, such as the high correlation between high valence ratings with high arousal reported by BID27 .We present an approach to build affect-enriched word representations. In other words, we enhance word distributions by incorporating reactions and affect dimensions. The output of this work produces word distributions that capture human reactions by modeling the affect information in the words. The affective word representations distinguish between semantically similar words that have varying affective interpretations. Affect is represented as a weighted relational information between two words, following the approach used by existing work. BID27 identify words of opposite polarity by performing signed spectral clustering on pre-trained embeddings. We present an approach to incorporate external affect and reaction signals in the pre-training step, using the hand-annotated affect lexica to learn from. Our experiments are based on using the state-of-the-art Warriner's affect lexicon BID30 as the input. The proposed approach builds on the intuition that relationships between synonyms and antonyms can be characterized using semantic dictionaries and the relationship can then be deterministically captured into the training loss functions.We evaluate the proposed enriched word distributions on standard natural language tasks. We predict formality, frustration and politeness on a labeled dataset and show improved results using the enriched word embeddings. Further, we outperform the state-of-the-art for sentiment prediction on standard datasets. The key contributions of this paper include:• Algorithm to incorporate affect sensors in the cost functions of distributional word representations (including Word2Vec SkipGram, Word2Vec CBOW, and GloVe) during training using semantic and external affect signals.• Establish the utility of affect enriched word-embeddings for linguistic tasks such as Sentiment and Formality prediction in text data. Our method out performs the state-of-the-art with an 20% improvement in accuracy for the outlier detection methods. Detailed results are reported in table 1.• Introduce a workflow to incorporate affective and reaction signals to word representations during pre-training. We show the generalizability of the workflow through experiments on 3 existing embeddings; Word2Vec-CBOW, Word2Vec-SkipGram, and GloVe.Section 2 covers the prior art in both pre-training and post-training approaches for distributional word representations. Section 3 presents the proposed approach and detailed experiments are discussed in section 4. We conclude with a discussion on the learnings and the observations through this process 5. We find reasonable improvements by our proposed approaches in all the task-based evaluations. SkipGram based methods perform poorly in word similarity prediction and outlier detection, but do well on sentiment and affect prediction. This difference in performance on downstream tasks, has been discussed before in BID9 and BID6 , who point out various issues with word similarity based evaluations such as task subjectivity, low inter annotator agreements and low correlations between the performance of word vectors on word similarity and NLP tasks like text classification, parsing and sentiment analysis. Performance differences can also be attributed to corpus size, which are examined in the Appendix section. Table 3 : Performance of proposed approaches on affect prediction task: (a) In terms of Mean Square Error (MSE) values for affect prediction on a labeled email corpus, (b) Comparison with prior work. The baseline model refers to the corpus only approach, with λ = 0. λ is set to 2 for all other approaches: using Valence list(+V), Arousal(+A), Dominance(+D) and average strength(+VAD).(a ) The results suggest that different embeddings perform well for different tasks. In word similarity tasks, the +V model performs well in GloVe setting but the +A model seems to perform the best for CBOW. Similar results are observed in sentiment prediction: for binary sentiment prediction, arousal scores give the best performance with CBOW embeddings but dominance and valence give the best performance with skip-gram and GloVe embeddings respectively. This suggests that the most flexible method could be an ensemble implementation that considers all these inputs before predicting a final class. Also note that given the vocabulary of our ukWaC corpus as 569, 574 words, our affect lexica with 13, 915 words is relatively small. We plan to take this work forward by further analysis in the future. At the least, we expect superior word embeddings with better quality and larger affect lexica. This work proposes methods to incorporate information from an affect lexicon into Word2Vec and GloVe training process. In a nutshell, we first use WordNet to identify word pairs in the affect lexicon which are semantically related. We define the strength of this relationship using available affect scores. Finally, we modify the training objectives to incorporate this information. In order to evaluate our embeddings, we compare them with baseline approaches where the training completely ignores the affect information. Our embeddings show improvements over baselines on not only Word Similarity benchmarks but also on a more complex, Outlier Detection task. We also do this comparison extrinsically and show that our modified embeddings perform better over prior work in predicting sentiment and predicting formality, frustration and politeness in emails. Among models using Valence, Arousal or Dominance score lists, there is no clear winner but overall addition of valence scores does a reasonable job in almost all of the cases.1. Choosing an appropriate value for hyper-parameter λ:In order to choose a suitable value for λ, we take a 100 MB sample of ukWaC corpus. The sample has close to 20 million tokens, with a vocabulary size of 27,978 words, eliminating all the words having the frequency count of less than 20. We choose a smaller corpus for tuning as it is more manageable with respect to space and time resources.We train a Word2Vec SkipGram model on the above 100MB sample and Valence affect lists by using all the λ value from the set (0, 0.5, 1, 2, 10, 100, 1000) one by one.To pick the most suitable value, we compare the results on word similarity task on the Rubenstein-Goodenough(RG) dataset BID26 . The results are given in FIG2 . Since λ = 2.0 performs the best, we fix this value for all our experiments.",1896,0.964,1137,1.6675461741424802,"Learning word representations large available corpora relies the distributional hypothesis present similar contexts Recent work that word representations learnt this manner lack sentiment information which fortunately using external knowledge Our work addresses can affect lexica improve the word representations learnt In this work propose techniques incorporate affect lexica capture the training process Word2Vec SkipGram Word2Vec CBOW GloVe methods using a joint learning approach We use affect scores Warriner's affect lexicon regularize the vector representations learnt an unlabelled corpus Our proposed method outperforms previously standard tasks for word similarity detection, outlier detection and sentiment detection We also demonstrate our approach a new task related the prediction formality frustration politeness corporate communication In natural language research words, paragraphs in through vector space representations rather atomic units with no relational information among Although n-gram based methods trained large volumes found more complex approaches both computational cost accuracy do scale cases limited(for example labeled speech affect corpora with a size Recent work attempted improve word distributions downstream tasks sentiment analysis BID27 knowledge base completion BID16 lexical knowledge to enrich by performing methods or introducing a loss term the learning objectiveSentiment relationships considered transitive 'good <betterbest implies However word representations based traditional approaches Word2Vec BID19 agnostic the associated sentiments emotions more affects BID4 . Furthermore although words delighted and disappointed share similar vector representations given their similar contexts associated opposite reactionsor sentiments have a fairly different interpreted meaning The challenge using syntactic relational information sentiment detection is sentiment relations transitive if 'delighted the opposite Ignoring the bipolar nature words could predictive tasks related synonyms and sentiment analysis On incorporating affect-related information would word distributions homogeneous suitable speech text generation tasks aim capturing author or reader reactions Furthermore by a small sentiment lexicon develop an automatic way rate words their vector space representations This could help reduce required gather word ratings eliminate the implicit biases introduced annotations the high correlation high valence ratings with high arousal reported BID27 .We present build affect-enriched word representations In enhance word distributions incorporating reactions affect dimensions The output this work produces word distributions capture human reactions by modeling the affect information The affective word representations distinguish varying affective interpretations Affect is represented a weighted relational information between following existing work BID27 identify words opposite polarity by performing signed spectral clustering We present incorporate external affect reaction signals the pre-training step handannotated affect lexica learn. Our experiments using state Warriner's affect lexicon BID30 The proposed approach builds the intuition relationships synonyms characterized semantic dictionaries the relationship can captured the training loss functionsWe evaluate the proposed enriched word distributions standard natural language tasks We predict formality frustration politeness a labeled dataset show improved results using Further outperform state for sentiment prediction standard datasets The key contributions include:• Algorithm to incorporate affect sensors the cost functions distributional word representationsincluding Word2Vec SkipGram GloVe during training using semantic and external affect signals.• Establish the utility affect enriched word-embeddings linguistic tasks Sentiment and Formality prediction text data Our method out performs the state with an 20% improvement the outlier detection methods Detailed results reported table 1.• Introduce a workflow incorporate affective and reaction signals word representations during pretraining We show the generalizability the workflow through experiments 3 existing embeddings; Word2Vec-CBOW GloVeSection covers the prior art for distributional word representations Section presents and detailed experiments are We conclude the learnings the observations through this process 5 We find reasonable improvements by our proposed approaches all the task-based evaluations SkipGram based methods perform poorly word similarity prediction outlier detection do sentiment and affect This difference performance on downstream tasks has BID9 , who point various issues word similarity based evaluations such task subjectivity low inter annotator agreements low correlations like text classification parsing sentiment Performance differences can corpus size are examined the Appendix section Table 3 : Performance proposed approaches on affect prediction task In terms affect on a labeled email corpus The baseline model refers corpus only approach �� λ is set 2 for all other approaches using Valence list(+V average strength(+VAD).(a ) The results suggest different embeddings perform In word similarity tasks the +V model performs GloVe setting seems the CBOW Similar results sentiment prediction for binary sentiment prediction arousal scores give CBOW embeddings dominance skip-gram and GloVe embeddings respectively This suggests the most flexible method could an ensemble implementation considers all these inputs before predicting a final class Also note given the vocabulary our ukWaC corpus as 569 574 words our affect lexica with 13 relatively We plan this work further analysis At least expect superior word embeddings with larger affect lexica This work proposes methods incorporate information an affect lexicon Word2Vec GloVe training process In first use WordNet identify word pairs the affect lexicon which semantically We define the strength using available affect scores Finally modify the training objectives incorporate In evaluate our embeddings compare baseline approaches where completely ignores the affect information Our embeddings show improvements baselines on not only Word Similarity benchmarks a more complex, Outlier Detection task We also do this comparison extrinsically show our modified embeddings over prior work predicting sentiment predicting formality frustration politeness emails Among models using Valence or Dominance score lists but overall addition does a reasonable job almost all. hyper-parameter ��:In choose take a 100 MB sample ukWaC corpus The sample has close to 20 million tokens a vocabulary size 27,978 words eliminating having the frequency count less We choose a smaller corpus tuning as manageable with respectWe train a Word2Vec SkipGram model the above 100MB sample Valence affect lists by all the �� value0 10 oneTo pick compare on word similarity task on RubensteinGoodenough(RG BID26 . The results given FIG2 Since �� = performs best fix this value all our experiments",0.01,0.40492817143326615
"Different kinds of representation learning techniques on graph have shown significant effect in downstream machine learning tasks. Recently, in order to inductively learn representations for graph structures that is unobservable during training, a general framework with sampling and aggregating (GraphSAGE) was proposed by Hamilton and Ying and had been proved more efficient than transductive methods on fileds like transfer learning or evolving dataset. However, GraphSAGE is uncapable of selective neighbor sampling and lack of memory of known nodes that've been trained. To address these problems, we present an unsupervised method that samples neighborhood information attended by co-occurring structures and optimizes a trainable global bias as a representation expectation for each node in the given graph. Experiments show that our approach outperforms the state-of-the-art inductive and unsupervised methods for representation learning on graphs. Graphs and networks, e.g., social network analysis BID7 , molecule screening BID4 , knowledge base reasoning BID19 , and biological proteinprotein networks BID24 ), emerge in many real-world applications. Learning low-dimensional vector embeddings of nodes in large graphs has been proved effective for a wide variety of prediction and graph analysis tasks BID5 ; BID18 ). The high-level idea of node embedding is to explore high-dimensional information about the neighborhood of a node with a dense vector embedding, which can be fed to off-the-shelf machine learning approaches to tasks such as node classification and link prediction BID14 ).Whereas previous approaches BID14 ; BID5 ; BID18 ) can transductively learn embeddings on graphs, without re-training they cannot generalize to new nodes that are newly added to graphs. It is ubiquitous in real-world evolving networks, e.g., new users joining in a social friendship circle such as facebook. To address the problem , BID8 propose an approach, namely GraphSAGE, to leverage node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen nodes. Despite the success of GraphSAGE, it randomly and uniformly samples neighbors of nodes, which suggests it is difficult to explore the most useful neighbor nodes. It could be helpful if we can take advantage of the most relevant neighbors and ignore irrelevant neighbors of the target node. Besides, GraphSAGE only focuses on training parameters of the hierarchical aggregator functions, but lose sight of preserving the memory of the training nodes, which means when training is finished, those nodes that have been trained over and over again would still be treated like unseen nodes, which causes a huge waste.To address the first issue, inspired by GAT BID20 ), a supervised approach that assigns different weights to all neighbors of each node in each aggregating layer, we introduce a bi-attention architecture BID16 ) to perform selective neighbor sampling in unsupervised learning scenarios. In unsupervised representation learning, when encoding embeddings of a positive 1 node pair before calculating their proximity loss BID7 ), we assume that neighbor nodes positive to both of the pair should have larger chance to be selected, since they are statistically more relevant to the current positive pair than other neighbors. For example, when embedding words like ""mouse"", in FIG0 , it's more reasonable to choose ""keyboard"" rather than ""cat"" as sampled neighbor while maximizing co-occrrence probability between ""mouse"" and ""PC"", because ""keyboard"" also tends to co-occurr with ""PC"", which means its imformation should be more relevant. We thus stack a bi-attention architecture BID16 ) on representations aggregated from both side in a positive node pair. In this way, we learn the most relevant representations for each positive node pair corresponding to their most relevant neighbors, and simply use a fixed-size uniform sampling which allows us to efficiently generate node embeddings in batches.To address the second issue, we combine the idea behind transductive approaches and inductive approaches, by intuitively applying an additive global embedding bias to each node's aggregated embedding. The global embedding biases are trainable as well as parameters of aggregator functions and can be considered as a memorable global identification of each node in training sets. When the training is completed, we generate the embedding for each node by calculating an average of multiple embedding outputs corresponding to different sampled neighbors with respect to different positive nodes. In this way, nodes that tend to co-occur in short random-walks will have more similar embeddings based on our bi-attention mechanism.Based on the above-mentioned two techniques, we propose a novel approach, called BIGSAGE (which stands for the BI-attention architeture, global BIas and the original framework GraphSAGE,) to explore most relevant neighbors and preserve previously learnt knowledge of nodes by utilizing bi-attention architecture and introducing global bias, respectively. In this paper, we proposed BIGSAGE, an unsupervised and inductive network embedding approach which is able to preserve local proximity wisely as well as learn and memorize global identities for seen nodes while generalizing to unseen nodes or networks. We apply a bi-attention architeture upon hierarchical aggregating layers to directly capture the most relevant representations of co-occurring nodes. We also present an efficient way of combining inductive and transductive approaches by allowing trainable global embedding bias to be retrieved in all layers within the hierarchical aggregating framework. Experiments demenstrate the superiority of BIGSAGE over the state-of-art baselines on unsupervised and inductive tasks.",1080,0.455,632,1.7088607594936709,"Different kinds representation learning techniques on graph have shown significant effect downstream machine learning tasks Recently in order inductively learn representations graph structures that is during training a general framework with sampling aggregating (GraphSAGE Hamilton Ying had proved more efficient transductive methods on fileds like transfer learning evolving dataset However GraphSAGE uncapable of selective neighbor sampling lack memory known nodes that've trained To address present samples neighborhood information attended optimizes a trainable global bias as a representation expectation the given graph Experiments our approach outperforms state inductive and representation on graphs Graphs networks BID7 , molecule screening knowledge base reasoning biological proteinprotein networks emerge Learning low-dimensional vector embeddings nodes large graphs proved effective prediction graph BID5 ; The high-level idea node embedding explore the neighborhood with a dense vector fed off machine approaches tasks node classification and link prediction BID14 ).Whereas BID14 ; ) can transductively learn on graphs without re they newly graphs It ubiquitous real-world evolving networks new users joining in a social friendship circle such facebook To address , BID8 propose, namely GraphSAGE leverage node feature information efficiently previously unseen nodes Despite GraphSAGE randomly and uniformly samples neighbors nodes suggests difficult explore the most useful neighbor nodes It could helpful take the most relevant neighbors ignore irrelevant neighbors of the target node Besides GraphSAGE only focuses training parameters of the hierarchical aggregator functions lose sight preserving the training nodes when finished those that over would treated unseen nodes causes.To inspired GAT BID20 ), supervised approach assigns all neighbors each aggregating layer a bi-attention architecture BID16 ) perform selective neighbor sampling In unsupervised representation learning when encoding a positive 1 node pair before calculating their proximity loss BID7 ), assume neighbor positive both should larger chance selected statistically relevant For example embedding wordsmouse in FIG0 , more reasonable choose ""cat sampled neighbor while maximizing co-occrrence probability between also tends cooccurr its imformation should relevant We thus stack a bi-attention architecture BID16 ) representations aggregated both side in a positive node pair In this way learn the most relevant representations each positive node pair corresponding their most relevant neighbors simply a fixed-size uniform sampling which efficiently generate batchesTo address combine behind transductive approaches intuitively applying an additive global embedding bias's aggregated The global embedding biases trainable as parameters aggregator functions considered a memorable global identification each node training sets When the training generate the embedding for each node calculating multiple embedding outputs corresponding different sampled neighbors with different positive nodes In this way nodes tend co short random-walks more similar embeddings based our bi-attention mechanismBased propose, BIGSAGE the BI-attention architeture global BIas and the original framework GraphSAGE,) explore most relevant neighbors preserve previously learnt knowledge nodes by utilizing introducing global bias, respectively In proposed BIGSAGE embedding approach which preserve local proximity wisely as learn global identities seen nodes while generalizing or We apply a bi-attention architeture upon hierarchical aggregating layers directly capture the most relevant representations We also present combining inductive and transductive approaches by allowing trainable global embedding bias retrieved all layers within the hierarchical aggregating framework Experiments demenstrate BIGSAGE stateart baselines on unsupervised and inductive tasks",0.01,0.5101941050483203
"Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both positive and negative edges while constraining the dimension of the embedding vectors. We argue that the generalization performance of these methods is not due to the dimensionality constraint as commonly believed, but rather the small norm of embedding vectors. Both theoretical and empirical evidence are provided to support this argument: (a) we prove that the generalization error of these methods can be bounded by limiting the norm of vectors, regardless of the embedding dimension; (b) we show that the generalization performance of linear graph embedding methods is correlated with the norm of embedding vectors, which is small due to the early stopping of SGD and the vanishing gradients. We performed extensive experiments to validate our analysis and showcased the importance of proper norm regularization in practice. Graphs have long been considered as one of the most fundamental structures that can naturally represent interactions between numerous real-life objects (e.g., the Web, social networks, proteinprotein interaction networks). Graph embedding, whose goal is to learn distributed representations for nodes while preserving the structure of the given graph, is a fundamental problem in network analysis that underpins many applications. A handful of graph embedding techniques have been proposed in recent years BID10 BID15 BID2 , along with impressive results in applications like link prediction, text classification BID14 , and gene function prediction BID18 .Linear graph embedding methods preserve graph structures by converting the inner products of the node embeddings into probability distributions with a softmax function BID10 BID15 BID2 . Since the exact softmax objective is computationally expensive to optimize, the negative sampling technique BID8 is often used in these methods: instead of optimizing the softmax objective function, we try to maximize the probability of positive instances while minimizing the probability of some randomly sampled negative instances. It has been shown that by using this negative sampling technique, these graph embedding methods are essentially computing a factorization of the adjacency (or proximity) matrix of graph BID7 . Hence, it is commonly believed that the key to the generalization performance of these methods is the dimensionality constraint.However, in this paper we argue that the key factor to the good generalization of these embedding methods is not the dimensionality constraint, but rather the small norm of embedding vectors. We provide both theoretical and empirical evidence to support this argument:• Theoretically, we analyze the generalization error of two linear graph embedding hypothesis spaces (restricting embedding dimension/norm), and show that only the norm-restricted hypothesis class can theoretically guarantee good generalization in typical parameter settings.• Empirically , we show that the success of existing linear graph embedding methods BID10 BID15 BID2 are due to the early stopping of stochastic gradient descent (SGD), which implicitly restricts the norm of embedding vectors. Furthermore, with prolonged SGD execution and no proper norm regularization, the embedding vectors can severely overfit the training data. So far, we have seen many pieces of evidence supporting our argument, suggesting that the generalization of embedding vectors in linear graph embedding is determined by the vector norm. Intuitively, it means that these embedding methods are trying to embed the vertices onto a small sphere centered around the origin point. The radius of the sphere controls the model capacity, and choosing proper embedding dimension allows us to control the trade-off between the expressive power of the model and the computation efficiency.Note that the connection between norm regularization and generalization performance is actually very intuitive. To see this, let us consider the semantic meaning of embedding vectors: the probability of any particular edge (u, v) being positive is equal to DISPLAYFORM0 As we can see, this probability value is determined by three factors: DISPLAYFORM1 , the cosine similarity between x u and x v , evaluates the degree of agreement between the directions of x u and x v .• ||x u || 2 and ||x v || 2 on the other hand, reflects the degree of confidence we have regarding the embedding vectors of u and v.Therefore, by restricting the norm of embedding vectors, we are limiting the confidence level that we have regarding the embedding vectors, which is indeed intuitively helpful for preventing overfitting.It is worth noting that our results in this paper do not invalidate the analysis of BID7 , but rather clarifies on some key points: as pointed out by BID7 , linear graph embedding methods are indeed approximating the factorization of PMI matrices. However , as we have seen in this paper, the embedding vectors are primarily constrained by their norm instead of embedding dimension, which implies that the resulting factorization is not really a standard low-rank one, but rather a low-norm factorization: DISPLAYFORM2 The low-norm factorization represents an interesting alternative to the standard low-rank factorization, and our current understanding of such factorization is still very limited. Given the empirical success of linear graph embedding methods, it would be really helpful if we can have a more in-depth analysis of such factorization, to deepen our understanding and potentially inspire new algorithms. We have shown that the generalization of linear graph embedding methods are not determined by the dimensionality constraint but rather the norm of embedding vectors. We proved that limiting the norm of embedding vectors would lead to good generalization, and showed that the generalization of existing linear graph embedding methods is due to the early stopping of SGD and vanishing gradients. We experimentally investigated the impact embedding dimension choice, and demonstrated that such choice only matters when there is no norm regularization. In most cases, the best generalization performance is obtained by choosing the optimal value for the norm regularization coefficient, and in such case the impact of embedding dimension case is negligible. Our findings combined with the analysis of BID7 suggest that linear graph embedding methods are probably computing a low-norm factorization of the PMI matrix, which is an interesting alternative to the standard low-rank factorization and calls for further study.",1207,0.477,734,1.6444141689373297,"Learning distributed representations for nodes graphs a crucial primitive network analysis with a wide spectrum Linear graph embedding methods learn such representations optimizing the likelihood both positive and negative edges while constraining the dimension We argue the generalization performance these methods due the dimensionality constraint as commonly small norm of embedding vectors Both theoretical and empirical evidence are provided this argument: we prove the generalization error these methods can bounded limiting the norm vectors regardless the embedding dimension the generalization performance linear graph embedding methods correlated which small due the early stopping SGD the vanishing gradients We performed extensive experiments validate our analysis showcased the importance proper norm regularization practice Graphs have that naturally represent interactions numerous real-life objects ( the Web, social networks proteinprotein interaction networks Graph embedding, whose goal learn distributed representations for nodes while preserving the given graph a fundamental problem network analysis that underpins A handful graph embedding techniques proposed BID10 BID15 , along impressive results applications link prediction text classification BID14 gene function prediction BID18 .Linear graph embedding methods preserve graph structures converting the inner products the node embeddings probability distributions with a softmax function Since the exact softmax objective computationally optimize the negative sampling technique BID8 often these methods: instead optimizing try maximize positive instances while some randomly sampled negative instances It has shown by this negative sampling technique these graph embedding methods essentially computing a factorization the adjacency (or proximity) matrix graph BID7 . Hence commonly the key the generalization performance these methods the dimensionality constraintHowever argue the key factor the good generalization these embedding methods not small norm of embedding vectors We provide both theoretical and empirical evidence this argument:• Theoretically analyze the generalization error two linear graph embedding hypothesis spacesrestricting embedding dimension/norm show only the norm-restricted hypothesis class can theoretically guarantee good generalization in typical parameter , the success existing linear graph embedding methods BID10 BID15 BID2 are due the early stopping implicitly restricts of Furthermore with prolonged SGD execution no proper norm regularization the embedding vectors severely overfit So many pieces supporting our argument suggesting the generalization embedding vectors linear graph determined the vector norm Intuitively means these embedding methods trying embed the vertices onto a small sphere centered The radius controls the model capacity choosing proper embedding dimension control the expressive power the computation efficiencyNote the connection norm regularization and generalization performance actually intuitive To see this, let consider the semantic meaning embedding vectors the probability any particular edge (u positive equal DISPLAYFORM0 As this probability value determined three factors the cosine similarity x u evaluates the degree agreement the directions x v .• ||x 2 and on reflects confidence we regarding uTherefore by restricting the norm of are limiting the confidence level that, indeed intuitively helpful preventingIt our results in invalidate the analysis BID7 , clarifies on as pointed linear graph embedding methods indeed approximating the factorization PMI matrices However , as this paper the embedding vectors primarily constrained their norm instead embedding dimension implies the resulting factorization really standard lowrank one: DISPLAYFORM2 represents an interesting alternative our current understanding still Given the empirical success linear graph embedding methods really can have in analysis such factorization to deepen and potentially inspire new algorithms We shown the generalization linear graph embedding methods are determined the dimensionality constraint but the norm of embedding vectors We proved limiting the norm embedding vectors would good generalization showed existing linear graph embedding methods due the early stopping SGD and vanishing gradients We experimentally investigated embedding dimension choice, and demonstrated such choice only matters there no norm regularization In most cases the best generalization performance obtained choosing the optimal value the norm regularization coefficient in such case the impact embedding dimension case negligible Our findings combined the analysis BID7 suggest linear graph embedding methods probably computing a low-norm factorization the PMI matrix an interesting alternative and calls further study",0.01,0.34598985452629816
"Momentum-based acceleration of stochastic gradient descent (SGD) is widely used in deep learning. We propose the quasi-hyperbolic momentum algorithm (QHM) as an extremely simple alteration of momentum SGD, averaging a plain SGD step with a momentum step. We describe numerous connections to and identities with other algorithms, and we characterize the set of two-state optimization algorithms that QHM can recover. Finally, we propose a QH variant of Adam called QHAdam, and we empirically demonstrate that our algorithms lead to significantly improved training in a variety of settings, including a new state-of-the-art result on WMT16 EN-DE. We hope that these empirical results, combined with the conceptual and practical simplicity of QHM and QHAdam, will spur interest from both practitioners and researchers. Code is immediately available. Stochastic gradient descent (SGD) serves as the optimizer of choice for many recent advances in deep learning across domains (Krizhevsky et al., 2012; He et al., 2016a; . SGD for deep learning is typically augmented with either the ""heavy ball"" momentum technique of Polyak (1964) or the accelerated gradient of Nesterov (1983) . In the deterministic setting, these methods provably yield faster convergence in fairly general settings. In the stochastic setting, these methods lose many theoretical advantages. However, due to its implicit gradient averaging, momentum can confer the benefit of variance reduction, applying less noisy parameter updates than plain SGD. Recent work has explicitly shown the use of momentum as a variance reducer (Roux et al., 2018) .Algorithms Starting with gradient variance reduction as an informal and speculative motivation, we introduce the quasi-hyperbolic momentum (QHM) optimization algorithm in Section 3. Put as simply as possible, QHM's update rule is a weighted average of momentum's and plain SGD's update rule. We later propose a similar variant of Adam (QHAdam) in Section 5.Connecting the dots QHM is simple yet expressive. In Section 4, we connect QHM with plain SGD, momentum, Nesterov's accelerated gradient, PID control algorithms (Recht, 2018; , synthesized Nesterov variants (Lessard et al., 2016) , noise-robust momentum (Cyrus et al., 2018) , Triple Momentum (Scoy et al., 2018) , and least-squares acceleration of SGD (Kidambi et al., 2018) . Such connections yield reciprocal benefits -these algorithms aid in analyzing QHM, and conversely QHM recovers many of these algorithms in a more efficient and conceptually simpler manner. We then characterize the set of optimization algorithms that QHM recovers. Theoretical convergence results We note that various convergence results follow simply via these connections. In the deterministic (full-batch) case, since QHM recovers Triple Momentum, QHM also recovers the global linear convergence rate of 1 − 1/ √ κ for strongly convex, smooth loss functions.6 For first-order methods, this is the fastest known global convergence rate for such functions. In the stochastic (minibatch) case, QHM's recovery of AccSGD gives QHM the same convergence results as in Kidambi et al. (2018) 's least-squares regression setting, of O( √ κ · log κ · log 1 ) iterations for -approximation of the minimal loss.Unifying two-state optimization algorithms These connections demonstrate that many two-state optimization algorithms are functionally similar or equivalent to each other. However, they are often implemented inefficiently and their parameterizations can be inaccessible to practitioners. QHM yields a highly accessible and efficient version of these algorithms. Polyak, 1964) subfamily better recovered by QHM with ν = 1 NAG (Nesterov, 1983) subfamily same recovered by QHM with ν = β PID (Recht, 2018) parent worse QHM's β restricts PID's k P /k D PID bijective worse degenerate; either ""PI"" or ""PD"" SNV (Lessard et al., 2016) bijective worse used in handling multiplicative noise Robust M. (Cyrus et al., 2018) subfamily worse SNV w/ convergence guarantees Triple M. (Scoy et al., 2018) subfamily worse ""fastest"" for str. convex, smooth L(·) AccSGD (Kidambi et al., 2018) subfamily worse acceleration for least-squares SGD * ""subfamily"" means that QHM recovers the algorithm but not vice-versa. ""parent"" means that the algorithm recovers QHM but not vice-versa. ""bijective"" means that the algorithms recover each other. † Efficiency (compute and/or memory) vs. QHM.In Appendix D, we characterize the set of two-state optimization algorithms recoverable by QHM. Our hope here is to provide future work with a routine conversion to QHM so that they may leverage the accessibility and efficiency benefits, as well as the many connections to other algorithms.Many-state optimization algorithms Going beyond a single momentum buffer, it is possible to recover many-state algorithms by linearly combining many momentum buffers (with different discount factors) in the update rule. However, we found in preliminary experiments that using multiple momentum buffers yields negligible value over using a single slow-decaying momentum buffer and setting an appropriate immediate discount -that is, using QHM with high β and appropriate ν.We note that the Aggregated Momentum (AggMo) algorithm (Lucas et al., 2018) precisely performs this linear combination of multiple momentum buffers. While AggMo takes a simple average of the buffers, an extended variant of AggMo allows for other linear combinations. This extended AggMo can be viewed as a many-state generalization of two-state algorithms (including QHM), recovering them when two buffers are used. Appendix H provides a supplemental discussion and empirical comparison of QHM and AggMo, corroborating our preliminary experiments' findings. QHM and QHAdam are computationally cheap, intuitive to interpret, and simple to implement. They can serve as excellent replacements for momentum/NAG and Adam in a variety of settings. In particular, they enable the use of high exponential discount factors (i.e. β) through the use of immediate discounting (i.e. ν). QHM recovers numerous other algorithms in an efficient and accessible manner. Parameter sweep experiments and case studies demonstrate that the QH algorithms can handily outpace their vanilla counterparts. We hope that practitioners and researchers will find these algorithms both practically useful and interesting as a subject of further study. The recommended vanilla Adam setting of β 2 = 0.999 in Kingma & Ba (2015) makes the right-hand side of (19) to be large, and various work has employed Adam with a significantly lower β 2 ; e.g. 0.98 BID12 BID15 . 26 Decreasing β 2 is undesirable, often slowing down training. 27 Moving from Adam to QHAdam, an alternative solution is to decrease ν 2 to be below 1. This decreases the right-hand side of (18), up to a point, and thus imposes a tighter constraint on the magnitudes of updates than the vanilla Adam setting of ν 2 = 1. Fig. 3 shows an example of this phenomenon using a fixed ν 1 , β 1 , and β 2 .Figure 3: Bound from (18), fixing ν 1 = 0.8, β 1 = 0.95, and β 2 = 0.98, and varying ν 2 . 26 We performed experiments on these models indicating that increasing β2 far beyond 0.98 led to training explosion. We suspect that these instability issues are especially prevalent in settings with rare inputs or labels, such as machine translation. 27 In proposing the AdamNC algorithm, Reddi et al. (2018) suggests that β2 should be high to capture a sufficiently long history of past gradients. To recap, we take the optimal AggMo parameterization from an extensive sweep, we convert that parameterization by hand to one for QHM, and we find that the latter outperforms the former on this autoencoder task.These results indicate that using multiple momentum buffers with an arbitrary weighting scheme (i.e. AggMo with K > 2) provides negligible benefit over using a single slow-decaying momentum buffer with an appropriate weight (i.e. QHM with high β and appropriate ν). Lucas et al. (2018) offer an interpretation of AggMo as passive damping for physical systems. In this interpretation, fast-decaying momentum buffers ""dampen"" the oscillations of slow-decaying momentum buffers by providing velocity in an opposite direction.",1804,0.945,1055,1.709952606635071,"Momentum-based acceleration widely We propose the quasi-hyperbolic momentum algorithmQHM an extremely simple alteration momentum SGD averaging a plain SGD step We describe numerous connections and identities other algorithms characterize the set two-state optimization QHM can recover Finally propose a QH variant Adam called QHAdam empirically our algorithms lead significantly improved training in settings new state result on WMT16 EN-DE We hope these empirical results QHM QHAdam spur interest Code is immediately Stochastic gradient descent serves choice many recent advances across domains ( He . SGD for deep learning typically augmented either the ""heavy ball"" momentum technique Polyak1964 the accelerated gradient of Nesterov . In the deterministic setting these methods provably faster convergence fairly general settings In the stochastic setting these methods lose many theoretical advantages However due its implicit gradient averaging momentum confer variance reduction applying less noisy parameter updates than plain SGD Recent work explicitly momentum a variance reducer (Roux 2018 .Algorithms Starting gradient variance reduction as an informal and speculative motivation (QHM optimization Section Put as QHM's update rule a weighted average momentum's and plain SGD's update rule We later propose a similar variant Adam (QHAdam Section 5.Connecting the dots QHM simple yet expressive In Section connect QHM plain SGD momentum Nesterov's accelerated gradient PID control algorithmsRecht 2018 , synthesized Nesterov variantsLessard noise-robust momentumCyrus Triple Momentum (Scoy ofKidambi Such connections yield reciprocal benefits -these algorithms aid analyzing QHM QHM recovers many these algorithms We then characterize optimization QHM recovers Theoretical convergence results We note various convergence results follow simply via these connections In the deterministic (full-batch) case since QHM recovers Triple Momentum the global linear convergence rate 1 − 1/ �� �� for strongly smooth loss functions.6 In the stochastic (minibatch) case QHM's recovery AccSGD gives the same convergence results Kidambi (2018) 's least-squares regression setting of O( �� �� · log · iterations -approximation the minimal lossUnifying two-state optimization algorithms These connections demonstrate functionally or However they often implemented inefficiently their parameterizations inaccessible practitioners QHM yields a highly accessible and efficient version these algorithms Polyak, 1964 subfamily better recovered QHM with �� 1 NAG (Nesterov 1983 same recovered β PIDRecht 2018 parent worse QHM's β restricts PID's k P /k D PID bijective worse degenerate; either ""PI SNVLessard used handling multiplicative noise Robust M. 2018 subfamily worse SNV w/ convergence guarantees Triple M. (Scoy et 2018 subfamily worse ""fastest for str. convex smooth L(· AccSGD (Kidambi et 2018 subfamily worse acceleration for * "" means QHM recovers the algorithm but viceparent the algorithm recovers QHM but vicebijective the algorithms recover each † Efficiency (compute and/or memory QHM.In Appendix characterize two-state optimization recoverable Our hope here future work a routine conversion QHM so they leverage, many connections other algorithmsMany-state optimization Going beyond a single momentum buffer recover linearlywith different discount factors the update rule However we found in preliminary experiments using multiple momentum buffers yields negligible value over using and setting an appropriate immediate discount -that QHM with high β appropriate �.We Aggregated (AggMo (Lucas 2018 precisely performs this linear combination While AggMo takes a simple average the buffers an extended variant allows other linear combinations This extended AggMo can viewed a many-state generalization two-state algorithmsincluding QHM recovering them when two buffers Appendix H provides a supplemental discussion empirical comparison QHM AggMo corroborating our preliminary experiments' findings QHM and QHAdam computationally cheap intuitive interpret They can serve excellent replacements momentum/NAG Adam in settings In particular they enable high exponential discount factors β through immediate discounting QHM recovers numerous other algorithms Parameter sweep experiments case demonstrate the QH algorithms handily outpace their vanilla counterparts We hope practitioners these algorithms both practically a subject The recommended vanilla Adam setting of β 2 = in Kingma & Ba (2015 makes (19 to large various work has employed Adam with significantly ; e.g. 0.98 BID12 BID15 . 26 Decreasing β 2 is undesirable often slowing training 27 Moving from Adam QHAdam an alternative solution decrease � 2 be below This decreases (18 up thus imposes updates than the vanilla Adam setting of �� 2 Fig 3 shows this phenomenon using a fixed �� 1 β .Figure Bound from (18 fixing varying 26 We performed experiments these models indicating increasing β2 far beyond led training explosion We suspect these instability issues especially settings rare inputs labels machine translation 27 In proposing the AdamNC algorithm Reddi et al (2018 suggests β2 should high to capture a sufficiently long history past gradients To recap take the optimal AggMo parameterization an extensive sweep we convert by hand one for QHM find latter onThese results using multiple momentum buffers with K > provides negligible benefit high β and appropriate �� Lucas et al (2018 offer an interpretation AggMo as passive damping physical systems In this interpretation fast-decaying momentum buffers "" providing velocity in",0.01,0.5129760356359667
"Reinforcement Learning (RL) can model complex behavior policies for goal-directed sequential decision making tasks. A hallmark of RL algorithms is Temporal Difference (TD) learning: value function for the current state is moved towards a bootstrapped target that is estimated using the next state's value function. lambda-returns define the target of the RL agent as a weighted combination of rewards estimated by using multiple many-step look-aheads. Although mathematically tractable, the use of  exponentially decaying weighting of n-step returns based targets in lambda-returns is a rather ad-hoc design choice. Our major contribution  is that we propose a generalization of lambda-returns called Confidence-based Autodidactic Returns (CAR), wherein the RL agent learns the weighting of the n-step returns in an end-to-end manner. In contrast to lambda-returns wherein the RL agent is restricted to use an exponentially decaying weighting scheme, CAR allows the agent to learn to decide how much it wants to weigh the n-step returns based targets. Our experiments, in addition to showing the efficacy of CAR, also empirically demonstrate that using sophisticated weighted mixtures of multi-step returns (like CAR and lambda-returns) considerably outperforms the use of n-step returns. We perform our experiments on the  Asynchronous Advantage Actor Critic (A3C) algorithm in the Atari 2600 domain. Reinforcement Learning (RL) BID21 ) is often used to solve goal-directed sequential decision making tasks wherein conventional Machine Learning methods such as supervised learning are not suitable. Goal-directed sequential decision making tasks are modeled as Markov Decision Process (MDP) BID11 . Traditionally, tabular methods were extensively used for solving MDPs wherein value function or policy estimates were maintained for every state. Such methods become infeasible when the underlying state space of the problem is exponentially large or continuous. Traditional RL methods have also used linear function approximators in conjunction with hand-crafted state spaces for learning policies and value functions. This need for hand-crafted task-specific features has limited the applicability of RL, traditionally.Recent advances in representation learning in the form of deep neural networks provide us with an effective way to achieve generalization BID1 BID6 . Deep neural networks can learn hierarchically compositional representations that enable RL algorithms to generalize over large state spaces. The use of deep neural networks in conjunction with RL objectives has shown remarkable results such as learning to solve the Atari 2600 tasks from raw pixels BID0 BID8 BID16 BID4 , learning to solve complex simulated physics tasks BID24 BID13 BID7 and showing super-human performance on the ancient board game of Go . Building accurate and powerful (in terms of generalization capabilities) state and action value function BID21 estimators is important for successful RL solutions. This is because many practical RL solutions (Q-Learning (Watkins & Dayan, 1992) , SARSA (Rummery & Niranjan, 1994) and Actor-Critic Methods BID5 ) use Temporal Difference (TD) Learning BID20 . In TD learning, a n-step return is used as an estimate of the value function by means of bootstrapping from the n th state's value function estimate. On the other hand, in Monte Carlo learning, the cumulative reward obtained in the entire trajectory following a particular state is used as an estimate for the value function of that state. The ability to build better estimates of the value functions directly results in better policy estimates as well as faster learning. λ-returns (LR) BID21 are very effective in this regard. They are effective for faster propagation of delayed rewards and also result in more reliable learning. LR provide a trade-off between using complete trajectories (Monte Carlo) and bootstrapping from n-step returns (TD learning). They model the TD target using a mixture of n-step returns, wherein the weights of successively longer returns are exponentially decayed. With the advent of deep RL, the use of multi-step returns has gained a lot of popularity BID9 . However, it is to be noted that the use of exponentially decaying weighting for various n-step returns seems to be an ad-hoc design choice made by LR. In this paper, we start off by extensively benchmarking λ-returns (our experiments only use truncated λ-returns due to the nature of the DRL algorithm (A3C) that we work with and we then propose a generalization called the Confidence-based Autodidactic Returns (CAR), In CAR, the DRL agent learns in an end-to-end manner, the weights to assign to the various n-step return based targets. Also in CAR, it's important to note that the weights assigned to various n-step returns change based on the different states from which bootstrapping is done. In this sense, CAR weights are dynamic and using them represents a significant level of sophistication as compared to the usage of λ-returns.In summary, our contributions are:1. To alleviate the need for some ad-hoc choice of weights as in the case of λ-returns, we propose a generalization called Autodidactic Returns and further present a novel derivative of it called Confidence-based Autodidactic Returns (CAR) in the DRL setting.2. We empirically demonstrate that using sophisticated mixtures of multi-step return methods like λ-returns and Confidence-based Autodidactic Returns leads to considerable improvement in the performance of a DRL agent.3. We analyze how the weights learned by CAR are different from that of λ-returns, what the weights signify and how they result in better estimates for the value function. We propose a straightforward way to incorporate λ-returns into the A3C algorithm and carry out a large-scale benchmarking of the resulting algorithm LRA3C. We go on to propose a natural generalization of λ-returns called Confidence-based Autodidactic returns (CAR). In CAR, the agent learns to assign weights dynamically to the various n-step returns from which it can bootstrap. Our experiments demonstrate the efficacy of sophisticated mixture of multi-steps returns with at least one of CARA3C or LRA3C out-performing A3C in 18 out of 22 tasks. In 9 of the tasks CARA3C performs the best whereas in 9 of them LRA3C is the best. CAR gives the agent the freedom to learn and decide how much it wants to weigh each of its n-step returns.The concept of Autodidactic Returns is about the generic idea of giving the DRL agent the ability to model confidence in its own predictions. We demonstrate that this can lead to better Under review as a conference paper at ICLR 2018 TD-targets, in turn leading to improved performances. We have proposed only one way of modeling the autodidactic weights wherein we use the confidence values that are predicted alongside the value function estimates. There are multiple other ways in which these n-step return weights can be modeled. We believe these ways of modeling weighted returns can lead to even better generalization in terms how the agent perceives it's TD-target. Modeling and bootstrapping off TD-targets is fundamental to RL. We believe that our proposed idea of CAR can be combined with any DRL algorithm BID8 BID4 BID16 wherein the TD-target is modeled in terms of n-step returns.",1469,0.751,899,1.6340378197997776,"Reinforcement LearningRL can model complex behavior policies goal-directed sequential decision tasks A hallmark RL algorithms Temporal DifferenceTD: value function for is moved towards that estimated using lambda-returns define the target the RL agent a weighted combination rewards estimated using multiple many-step look-aheads Although mathematically the use exponentially decaying weighting of n-step returns based targets lambda-returns Our major contribution propose lambda-returns called Confidence-based Autodidactic ReturnsCAR wherein the RL agent the weighting the n-step returns end In contrast lambda-returns wherein the RL agent restricted use an exponentially decaying weighting scheme CAR allows learn decide weigh the n-step returns based targets Our experiments, showing CAR empirically using sophisticated weighted mixtures multi-step returnslike CAR lambda-returns considerably We perform our experiments Asynchronous Advantage Actor Critic the Atari 2600 domain Reinforcement Learning (RL) BID21 ) often goal-directed sequential decision wherein conventional Machine Learning methods Goal-directed sequential decision making tasks modeled Markov Decision ProcessMDP) BID11 . tabular methods extensively solving MDPs wherein value function or policy estimates maintained every state Such methods become the underlying state space exponentially continuous Traditional RL methods also used linear function approximators conjunction hand-crafted state spaces learning policies value functions This need hand-crafted task-specific features limited RL, traditionally.Recent advances representation learning provide achieve generalization BID1 BID6 . Deep neural networks hierarchically compositional representations enable RL algorithms large state spaces The use conjunction RL objectives such learning solve the Atari 2600 tasks from raw pixels BID0 BID8 BID16 BID4 , complex simulated physics tasks and showing the ancient board game Go Building accurate powerful (in generalization capabilities state and action value function BID21 estimators successful RL solutions This because many practical RL solutionsQ-Learning (Watkins Dayan 1992 , SARSA (Rummery Niranjan Actor-Critic Methods BID5 ) Temporal Difference Learning BID20 In TD learning a n-step return the value function by means the n th state's value function estimate On Monte Carlo learning, the cumulative reward obtained the entire trajectory following a particular state used the value function The ability build better estimates the value functions directly results better policy estimates as faster learning λ-returns (LR) BID21 are very effective They effective faster propagation delayed rewards also result more reliable learning LR provide using complete trajectoriesMonte Carlo from n-step returnsTD learning They model the TD target using a mixture n-step returns wherein the weights successively longer returns exponentially decayed With deep RL the use multi-step returns gained popularity BID9 . However to exponentially decaying weighting various n-step returns seems made LR In start extensively benchmarking ��-returnsour experiments only due the DRL algorithm (A3C work and propose called the Confidence-based Autodidactic ReturnsCAR In CAR the DRL agent learns in end the weights to assign the various n-step return based targets Also CAR, it important the weights assigned various nstep returns change the different states from bootstrapping In this sense CAR weights dynamic using represents sophistication as the usage ��-returnsIn summary our contributions To alleviate some ad-hoc choice weights as in ��-returns propose called Autodidactic Returns further present a novel derivativeCAR the DRL setting.2 empirically using sophisticated mixtures multi-step return methods like leads considerable improvement analyze the weights learned what signify result better estimates the value function We propose incorporate ��-returns the A3C algorithm carry the resulting algorithm LRA3C. We go propose a natural generalization ��-returns called Confidence-based Autodidactic returnsCAR In CAR the agent learns assign weights dynamically the various n-step returns from which bootstrap. Our experiments demonstrate sophisticated mixture multi-steps returns at of CARA3C or LRA3C out-performing A3C 18 out 22 tasks In 9 of the tasks CARA3C performs the whereas LRA3C CAR gives the agent learn decide weigh each its n-step returnsThe concept Autodidactic Returns about the generic idea giving the DRL agent model confidence We demonstrate this can Under review as a conference paper at ICLR 2018 TD-targets turn improved performances We proposed only one way modeling the autodidactic weights wherein the confidence values that predicted alongside the value function estimates There multiple other ways these n-step return weights modeled We believe these ways modeling weighted returns terms how the agent it TD-target Modeling off TD-targets fundamental RL We believe our proposed idea CAR can combined any DRL algorithm BID8 BID4 BID16 wherein the TD-target modeled n-step returns",0.01,0.3195518285798824
"Current end-to-end deep learning driving models have two problems: (1) Poor
 generalization ability of unobserved driving environment when diversity of train-
 ing driving dataset is limited (2) Lack of accident explanation ability when driving
 models don’t work as expected. To tackle these two problems, rooted on the be-
 lieve that knowledge of associated easy task is benificial for addressing difficult
 task, we proposed a new driving model which is composed of perception module
 for see and think and driving module for behave, and trained it with multi-task
 perception-related basic knowledge and driving knowledge stepwisely.  Specifi-
 cally segmentation map and depth map (pixel level understanding of images) were
 considered as what & where and how far knowledge for tackling easier driving-
 related perception problems before generating final control commands for difficult
 driving task. The results of experiments demonstrated the effectiveness of multi-
 task perception knowledge for better generalization and accident explanation abil-
 ity. With our method the average sucess rate of finishing most difficult navigation
 tasks in untrained city of CoRL test surpassed current benchmark method for 15
 percent in trained weather and 20 percent in untrained weathers. Observing progressive improvement in various fields of pattern recognition with end-to-end deep learning based methods BID13 BID8 , self-driving researchers try to revolutionize autonomous car field with the help of end-to-end deep learning techniques BID3 BID4 . Impressive results have been acquired by mapping camera images directly to driving control commands BID3 with simple structure similar to ones for image classfication task BID19 . Further researches were conducted to improve the performance of deep learning based autonomous driving system, for example, Conditional Imitation Learning approach has been proposed to solve the ambigious action problem.However, two crutial problems failed to be spotted: (1) Poor generalization ability of unobserved driving environment given limited diversity of training scenerios. For example, though addressed the driving direction selection problem, it showed poor generalization ability in unseen test town which has different map and building structure than training town's. This generalization problem is extremely important since collected driving dataset always has limitation of diversity (2) Current end-to-end autonomous approaches lack of accident explanation ability when these models behave unexpectedly. Although saliency map based visualization methods BID20 BID23 BID21 BID2 have been proposed to dig into the 'black box', the only information these methods could bring is the possible attention of the model instead of the perception process of the model.We proposed a new driving approach to solve the two aforementioned problems by using multi-task basic perception knowledge. We argue that when end-to-end model is trained to address a specific difficult task, it's better to train the model with some basic knowledge to solve relevant easier tasks before BID17 ). An analogy for this can be observed when human beings learn a difficult knowledge. For example, to solve a complex integration problem, compared with students without basic math knowledge, students who know about basic knowledge of math are able to learn the core of intergration more quickly and solve other similar integration problems instead of memorizing the solution of the specific problem.Our proposed model consists of two modules: perception module and driving module as in FIG0 . The perception module is used for learning easier driving-related perception knowledge, which we refer as ability of pixel level understanding of input including what & where and how far knowledge. We trained perception module with segmentation map and depth map first, while the former serves as what & where knowledge and the latter serves as how far knowledge. By visualizing inferenced segmentation and depth results whether perception process works well or not could be inferred. After the perception module was trained to have ability of pixel level understanding of its image input, we freezed the perception module weights and trained driving module with driving dataset. This decomposition of end-to-end driving network strucuture is considered to be mediated perception approach BID25 . With our proposed driving structure and stepwise training strategy, the generalization and accident explanation problems were addressed to a certain extent. In this paper we propose a new driving system for better generalization and accident explanation ability by enabling it to do simpler driving-related perception task before generating commands for diffult driving task. Through multiple experiments we empirically proved the effectiveness of the multi basic perception knowledge for better generalization ability of unobserved town when diversity of training dataset is limited. Besides our proposed model has self-explanation ability by visualizing the predicted segmentation and depth maps from the perception module to determine the cause of driving problems when they happen. One interesting result we acquired by comparing different train strategies is that the generalization ability of driving origins from basic knowledge and lies in weights of the perception module which should not be modified during training with driving dataset. We hope our work could movitivate other researches to use multi-task target related perception knowledge for better performance in robot learning. In future we will investigate more effective network structures.",987,0.483,590,1.6728813559322033,"Current end deep driving models two problems unobserved driving environment when diversity train- ing driving dataset Lack accident explanation ability don��t work To tackle rooted the be- lieve knowledge associated easy task benificial addressing difficult task proposed composed perception module for see think driving behave trained it stepwisely Specifi- cally segmentation map depth mappixel level understanding images considered what & and far knowledge for tackling easier driving- related perception problems before generating final control commands difficult driving task The results experiments demonstrated multi- task perception knowledge better generalization and accident explanation abil- ity With our method the average sucess rate finishing most difficult navigation tasks untrained city of CoRL test surpassed current benchmark method 15 percent trained weather Observing progressive improvement various fields pattern recognition with end deep based methods BID13 BID8 , self-driving researchers try autonomous car field Impressive results acquired mapping camera images directly driving control commands BID3 with simple structure similar ones image classfication task Further researches improve deep learning based autonomous driving system for Conditional Imitation Learning approach has the ambigious action problemHowever two crutial problems failed spotted unobserved driving environment given limited diversity training scenerios For though addressed the driving direction selection problem showed poor generalization ability unseen test town which different map building structure training town's This generalization problem extremely since collected driving dataset always limitation diversity2 Current end autonomous approaches lack of accident explanation ability when these models behave unexpectedly Although saliency map based visualization methods BID20 BID23 BID21 have dig bring the possible attention instead the perception processWe proposed a new driving approach solve multi-task basic perception knowledge We argue when end model trained address a specific difficult task's to relevant easier tasks before BID17 ). An analogy can observed learn a difficult knowledge For to solve compared students without basic knowledge intergration solve insteadOur proposed model consists perception module driving as in FIG0 The perception module learning easier driving-related perception knowledge we refer as ability of pixel level understanding input including what & far knowledge We trained perception module segmentation map first while former serves what & knowledge the how far knowledge By visualizing inferenced segmentation and depth results whether perception process works could inferred After the perception module trained have ability of pixel level understanding its image input freezed trained driving module driving dataset This decomposition end driving network strucuture considered mediated perception approach BID25 With our proposed driving structure stepwise training strategy the generalization accident explanation problems better generalization accident explanation ability enabling it do simpler driving-related perception task before generating commands diffult driving task Through multiple experiments empirically proved the multi basic perception knowledge better generalization ability unobserved town when diversity training dataset Besides our proposed model has self-explanation ability by the predicted segmentation and depth maps the perception module driving problems when One interesting result we acquired by different train strategies generalization ability driving origins basic knowledge lies weights the perception module which should modified with driving dataset We hope our work could movitivate other researches use multi-task target related perception knowledge robot learning future we investigate more effective network structures",0.01,0.41852174588953395
"Recently there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework – a generic methodology allowing contemporary graph embedding methods to scale to large graphs. MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique to maintain the backbone structure of the graph. It then applies existing embedding methods on the coarsest graph and refines the embeddings to the original graph through a novel graph convolution neural network that it learns. The proposed MILE framework is agnostic to the underlying graph embedding techniques and can be applied to many existing graph embedding methods without modifying them. We employ our framework on several popular graph embedding techniques and conduct embedding for real-world graphs. Experimental results on five large-scale datasets demonstrate that MILE significantly boosts the speed (order of magnitude) of graph embedding while also often generating embeddings of better quality for the task of node classification. MILE can comfortably scale to a graph with 9 million nodes and 40 million edges, on which existing methods run out of memory or take too long to compute on a modern workstation. In recent years, graph embedding has attracted much interest due to its broad applicability for various tasks BID17 BID10 . However, such methods rarely scale to large datasets (e.g., graphs with over 1 million nodes) since they are computationally expensive and often memory intensive. For example, random-walkbased embedding techniques require a large amount of CPU time to generate a sufficient number of walks and train the embedding model. As another example, embedding methods based on matrix factorization, including GraRep BID1 and NetMF BID18 , requires constructing an enormous objective matrix (usually much denser than adjacency matrix), on which matrix factorization is performed. Even a medium-size graph with 100K nodes can easily require hundreds of GB of memory using those methods. On the other hand, many graph datasets in the real world tend to be large-scale with millions or even billions of nodes. To the best of our knowledge, none of the existing efforts examines how to scale up graph embedding in a generic way. We make the first attempt to close this gap. We are also interested in the related question of whether the quality of such embeddings can be improved along the way. Specifically, we ask: 1) Can we scale up the existing embedding techniques in an agnostic manner so that they can be directly applied to larger datasets?2 ) Can the quality of such embedding methods be strengthened by incorporating the holistic view of the graph?To tackle these problems, we propose a MultI-Level Embedding (MILE) framework for graph embedding. Our approach relies on a three-step process: first, we repeatedly coarsen the original graph into smaller ones by employing a hybrid matching strategy; second, we compute the embeddings on the coarsest graph using an existing embedding techniquesand third, we propose a novel refinement model based on learning a graph convolution network to refine the embeddings from the coarsest graph to the original graph -learning a graph convolution network allows us to compute a refinement procedure that levers the dependencies inherent to the graph structure and the embedding method of choice. To summarize, we find that:• MILE is generalizable : Our MILE framework is agnostic to the underlying graph embedding techniques and treats them as black boxes.• MILE is scalable : MILE can significantly improve the scalability of the embedding methods (up to 30-fold), by reducing the running time and memory consumption.• MILE generates high-quality embeddings : In many cases, we find that the quality of embeddings improves by levering MILE (in some cases is in excess of 10%). In this work, we propose a novel multi-level embedding (MILE) framework to scale up graph embedding techniques, without modifying them. Our framework incorporates existing embedding techniques as black boxes, and significantly improves the scalability of extant methods by reducing both the running time and memory consumption. Additionally, MILE also provides a lift in the quality of node embeddings in most of the cases. A fundamental contribution of MILE is its ability to learn a refinement strategy that depends on both the underlying graph properties and the embedding method in use. In the future, we plan to generalize MILE for information-rich graphs and employing MILE for more applications.",895,0.456,499,1.7935871743486973,"Recently there designing graph embedding methods Few, can scale a large-sized graph millions due In this paper relax this limitation the MultI-Level Embedding (MILE) framework – a generic methodology allowing contemporary graph embedding methods scale large graphs MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique maintain the backbone structure It then applies existing embedding methods the coarsest graph refines the original graph through a novel graph convolution neural network it learns The proposed MILE framework agnostic the underlying graph embedding techniques can without modifying them We employ our framework on several popular graph embedding techniques conduct embedding for Experimental results on five large-scale datasets demonstrate MILE significantly boosts the speed (order graph embedding while often generating embeddings better quality for the task of node classification MILE can comfortably scale a graph with 9 million nodes 40 million edges on which existing methods run out or take compute on a modern workstation In graph embedding attracted due for various tasks BID17 BID10 . However such methods rarely scale large datasets graphs with since memory For example random-walkbased embedding techniques require generate walks train As another example embedding methods based matrix factorization, including GraRep BID1 NetMF BID18 requires constructing an enormous objective matrixusually much denser on Even a medium-size graph with 100K nodes easily require hundreds GB using those methods On many graph datasets in tend with millions To none the existing efforts examines scale graph embedding a generic way We make the first attempt close We also interested the related question the quality such embeddings along Specifically ask 1 Can scale the existing embedding techniques an agnostic manner directly ) the quality strengthened incorporating the holistic view the graph?To tackle a MultI-Level Embedding (MILE) framework graph Our approach relies first repeatedly coarsen the original graph into smaller ones by employing a hybrid matching strategy compute on existing techniquesand propose a novel refinement model learning a graph convolution network refine from -learning allows compute a refinement procedure levers the dependencies inherent choice To summarize find that:• MILE is generalizable : Our MILE framework agnostic the underlying graph embedding techniques treats them scalable significantlyup 30- by memory generates In improves levering (in is in In this work propose scale graph embedding techniques without modifying them Our framework incorporates existing embedding techniques as black boxes significantly extant methods Additionally MILE also a lift in the quality node embeddings most A fundamental contribution MILE learn a refinement strategy depends both the underlying graph properties the embedding method use In the future plan generalize MILE for information-rich graphs employing more applications",0.01,0.7260695661175114
"Anomaly detection discovers regular patterns in unlabeled data and identifies the non-conforming data points, which in some cases are the result of malicious attacks by adversaries. Learners such as One-Class Support Vector Machines (OCSVMs) have been successfully in anomaly detection, yet their performance may degrade significantly in the presence of sophisticated adversaries, who target the algorithm itself by compromising the integrity of the training data. With the rise in the use of machine learning in mission critical day-to-day activities where errors may have significant consequences, it is imperative that machine learning systems are made secure. To address this, we propose a defense mechanism that is based on a contraction of the data, and we test its effectiveness using OCSVMs. The proposed approach introduces a layer of uncertainty on top of the OCSVM learner, making it infeasible for the adversary to guess the specific configuration of the learner. We theoretically analyze the effects of adversarial perturbations on the separating margin of OCSVMs and provide empirical evidence on several benchmark datasets, which show that by carefully contracting the data in low dimensional spaces, we can successfully identify adversarial samples that would not have been identifiable in the original dimensional space. The numerical results show that the proposed method improves OCSVMs performance significantly (2-7%) Anomaly detection refers to the problem of discovering patterns in data and identifying data points that do not conform to the learned patterns. These non-conforming data points are often referred to as anomalies or outliers. Anomaly detection has numerous applications in a variety of domains such as network intrusion detection, credit card fraud detection, and spam filtering. It is an important problem since the presence of anomalies may indicate malicious attacks that could disrupt mission critical operations. Many machine learning methods, such as One-Class Support Vector Machines (OCSVM) BID14 , have been proven to be effective in anomaly detection applications. Although they are designed to withstand the effects of random noise in data, when adversaries deliberately alter the input data and compromise their integrity, the performance of these learning algorithms may degrade significantly.Anomaly detection systems are often deployed in environments where the data naturally evolves. In such situations, the models need to be retrained periodically, in contrast to many conventional machine learning applications, where the current and future data is assumed to have identical properties. This periodic training may allow adversaries to gradually inject malicious data to diminish the decision making capabilities of the learning algorithms BID8 . The aim of the adversaries may be to avoid the detection of attacks or to decrease the performance of the learning system BID8 . To achieve these aims, adversaries can undermine learning algorithms in several ways. For instance, they may manipulate the training data if it is gathered from the real operation of a system (e.g., spam filtering, firewall, anti-virus, etc.) and force the learning algorithm to learn a distorted representation that is favorable to them.A sophisticated adversary has the capacity to conduct an attack in numerous ways. Hence, it is not feasible to provide a general analysis that covers the whole range of attacks, across different machine learning algorithms. In this work, we explore the following key question: Is it possible to make OCSVMs more resistant against adversarial attacks which target the integrity of the training data through distortions? . If an adversary can maliciously perturb the input data used by a learning algorithm, they can force the learner to learn a model that is favorable to them. It has become imperative to secure machine learning systems against such adversaries due to the recent increase of automation in many day to day applications. In the context of image recognition, the perturbations caused by an adversary are usually imperceptible to humans, but they can force a learned model to mis-classify the perturbed images with high confidence. As BID5 have shown, with the emergence of self driving vehicles, an adversary could alter a ""S-T-O-P"" road sign in such a way that a vehicle (learning system) would reliably classify it as a ""Speed Limit 45"" sign. Such perturbations could be imperceptible to humans and could result in the loss of human lives.Our goal is to utilize a nonlinear data projection based algorithm to increase the attack resistance of OCSVMs against an adversarial opponent under realistic assumptions. The theory of nonlinear random projections facilitates large-scale, data-oriented, multi-agent decisions by reducing the number of optimization parameters and variables. Recent work in the literature shows that nonlinear random projections improve the training and evaluation times of kernel machines, without significantly compromising the accuracy of the trained models BID13 BID4 . In this paper, we show that under adversarial conditions, selective nonlinear random projections can be leveraged to increase the attack resistance of OCSVMs as well.A dataset X ∈ R n×d that is projected using a carefully chosen projection matrix A ∈ R d×r comprised of random elements that are normally distributed, would have its pairwise Euclidean distances preserved with high probability in the projected space XA BID9 . Therefore, the properties of the original data distribution would be present in the projected dataset with only minor perturbations. Note that here r is the dimension to which the data is nonlinearly projected and r < d. Since the elements of A are drawn randomly, the learner obtains an additional layer of security as it becomes virtually impossible for the adversary to guess the projection mechanism used by the learner due to the search space becoming unbounded.More formally, let w * pd 2 be the length of the weight vector of the OCSVM in the transformed space, after solving the corresponding optimization problem that includes the distortion made by the adversary and the nonlinear random projection. Let w * p 2 be the length of the weight vector in the transformed space, where there is no adversary present. Since the learner cannot distinguish between the original data and the distorted data, the learner would not have the ability to explicitly calculate w * p 2 . Therefore, for reasonable values of r and small distortions D, we prove in this paper that w * p 2 is bounded above: DISPLAYFORM0 The main contributions of this work are summarized as follows. We derive analytically an upper bound on the length of the weight vector of a OCSVM trained on an undistorted dataset that has been nonlinearly transformed to a lower dimensional space. In addition, the resistance added by nonlinear data transformations against an adversarial opponent is studied through numerical experiments on several benchmark datasets. We believe that our proposed approach can (i) increase the attack resistance of OCSVMs under adversarial conditions, and (ii) give the learner a significant advantage from a security perspective by adding a layer of unpredictability through the randomness of the data transformation in a selective direction. The experimental evaluation presented in the following section demonstrates the effectiveness of our proposed defense mechanism on three benchmark datasets: MNIST, CIFAR-10, and SVHN. We compare the performance of OCSVMs in conjunction with nonlinear random projections, when an active adversary is conducting a directed attack by maliciously distorting the data. We observe that the f-scores across the dimensions decrease between train C |test D and train D |test D . This indicates that a OCSVM trained on clean data can identify adversarial samples better than a OCSVM trained on distorted data. Consequently this shows that OCSVMs are not immune to integrity attacks by design, and by carefully crafting adversarial data points, adversaries can manipulate OCSVMs to learn models that are favorable to them.A comparison between f-scores of train D |test C and train D |test D shows that, as the dimension is reduced from the original dimension, the f-scores increase, but as we reduce the dimension further, the f-scores begin to decrease. The increase in f-score confirms that by projecting data to a lower dimensional space using a carefully selected direction, we can identify adversarial samples that would not have been identifiable in the original feature space. This is confirmed by the graphs in the second row, which show the false positive rate of the OCSVMs under integrity attacks (i.e., number of anomalies that are undetected). We find that there is a significant improvement in detecting adversarial samples under the proposed approach (e.g., 23% on CIFAR-10 and 31% on MNIST).When the dimensions are reduced below a certain dataset dependent threshold the OCSVM performance starts to decline (e.g., SVHN 1,500 vs 463). We postulate that the explanation of this effect is the reduction in distance between classes (in this case perturbed anomalies and normal data points) with the dimension. As we reduce the dimension of the transformation, we are able to reduce the effects of the adversarial datapoints. But at the same time, there is a significant loss of useful information due to the dimensionality reduction. Due to the interplay between these two factors, the performance of OCSVMs reduces as we decrease the dimension beyond a certain threshold. Finally, TAB2 shows the effectiveness of the bound derived in Theorem 1. The results show the consistency of the upper bound, which becomes tighter under dimension reduction.In summary, the above experiments demonstrate that, (i) OCSVMs are vulnerable to adversarial attacks on integrity, (ii) by projecting a distorted dataset to a lower dimension in an appropriate direction we can increase the robustness of the learned model w.r.t. integrity attacks, (iii) the performance, in terms of f-score, starts to decline when the dimensionality is reduced beyond a certain threshold, and (iv) the performance in the projected spaces, when there are no attacks on integrity, is comparable to that in the original dimensional space, but with less computational burden. This paper presents a theoretical and experimental investigation based on a unique combination of unsupervised anomaly detection, using OCSVMs and random projections for dimensionality reduction in the presence of a sophisticated adversary. Our numerical analysis focuses on two main aspects: the performance of OCSVMs in lower dimensional spaces under adversarial conditions and the impact of nonlinear random projections on the robustness of OCSVMs w.r.t. adversarial perturbations. The results suggest that OCSVMs can be significantly affected if an adversary has access to the data on which they are trained. For each dataset, with very high probability, there is at least one dimensionality and projection direction that results in a OCSVM that is able to identify adversarial samples that would not have been identifiable by a OCSVM in the original dimensional space. Due to the layer of uncertainty added by the randomness of the projection, our approach makes the learning system more secure by making it virtually impossible for an adversary to guess the underlying details of the learner. Therefore, our approach can be utilized to make a learning system secure by, (i) reducing the impact of possible adversarial perturbations by contracting, and moving the normal data cloud away from the origin in the projected space, and (ii) making the search space of the adversary unbounded by adding a layer of randomness.Since data contraction is at the core of our proposed approach, for our future work we would like to investigate whether our approach will still hold if used with other learning algorithms. One major question that arises from this work is how to optimally select the number of dimensions to transform the data to. We are currently exploring the possibility of using the intrinsic dimensionality of datasets to address this problem. Since there is a clear information asymmetry between the adversary and learner (due to the randomness), this problem provides a good foundation to explore game-theoretical formulations of anomaly detection and adversarial learning problems under dimensionality reduction techniques. We also plan to study ""boiling frog"" type of attacks, where the adversary gradually injects malicious data over time.A PROOFS Definition 1. Let X ∈ R n×d be the matrix that contains the training data. Similarly, define D ∈ R n×d as the matrix that contains the distortions made by the Adversary. Let A ∈ R d×r be the projection matrix where each element is an i.i.d. N (0, 1) random variable. Define b as a 1 × r row vector where each element is drawn uniformly from [0, 2π] . Using these variables, we define C ∈ R n×r , where the element at row i column j takes the following form.C i,j = cos DISPLAYFORM0 C i,j = cos DISPLAYFORM1 Similarly, we define the matrices C X , C D , S X , S D as follows, Proof: (of Theorem 1) Letα be the vector achieving the optimal solution in the projected space when adversarial distortions are present. Then, the solution for the primal problem in the projected space with adversarial distortions, defined as wSince the optimization problem is a minimization problem, as shown in (2), the optimal solution for the OCSVM without any distortion (i.e., α * ) would give a value less than or equal to the value given byα. Thus, DISPLAYFORM2 Define w * p as the primal solution optimization in the projected space, if there were no adversarial perturbations present, therefore DISPLAYFORM3 B RESULTS",2699,1.223,1579,1.7093096896770108,"Anomaly detection discovers regular patterns in the result malicious attacks by adversaries Learners such One-Class Support Vector Machines successfully in anomaly detection yet may degrade sophisticated adversaries who target the algorithm itself by compromising With machine learning mission day where errors may significant consequences made secure To address propose a defense mechanism a contraction the data we test using OCSVMs The proposed approach introduces a layer uncertainty the OCSVM learner making guess the specific configuration We theoretically analyze adversarial perturbations the separating margin OCSVMs provide several benchmark datasets by carefully contracting in low dimensional spaces successfully identify adversarial samples would identifiable the original dimensional space The numerical results the proposed method improves OCSVMs performance27 Anomaly detection refers the problem discovering patterns do conform the learned patterns These non-conforming data points often anomalies Anomaly detection has numerous applications domains network intrusion detection spam filtering It an important problem since the presence anomalies may malicious attacks that disrupt mission critical operations Many machine learning methods One-Class Support Vector Machines (OCSVM) BID14 , proven anomaly detection applications Although they designed withstand random noise in data when adversaries deliberately alter and compromise the performance these learning algorithms degradeAnomaly detection systems environments naturally In such situations the models need retrained periodically in contrast many conventional machine learning applications assumed identical properties This periodic training may allow adversaries gradually inject malicious data to diminish the decision the learning BID8 . The aim the adversaries may avoid attacks or decrease the performance the learning system BID8 . To achieve these aims adversaries can undermine learning algorithms For instance they manipulate the training data if gathered the real operation spam firewall anti force the learning learn a distorted representation that favorableA sophisticated adversary has conduct numerous ways Hence feasible provide a general analysis that covers attacks across different machine learning In this work explore the following key question make OCSVMs resistant against which target the training data through distortions . If an adversary maliciously perturb the input data used a learning algorithm they force a model favorable It imperative secure machine learning systems against such adversaries due automation many day applications In the context image recognition the perturbations caused an adversary are usually force a learned model mis- the perturbed images with high confidence As BID5 have shown with the emergence self driving vehicles an adversary could alter a ""S-T-O-P"" road sign (learning system reliably classify a ""Speed Limit 45"" sign Such perturbations could resultOur goal utilize a nonlinear data projection based algorithm increase the attack resistance OCSVMs against an adversarial opponent under realistic assumptions The theory nonlinear random projections facilitates reducing optimization parameters variables Recent work nonlinear random projections improve the training and evaluation times kernel machines without significantly compromising BID13 BID4 . In this paper under adversarial conditions selective nonlinear random projections leveraged increase the attack resistance OCSVMs as.A dataset X �� R n×d that projected using comprised random elements that normally, would its pairwise preserved with high probability the projected space XA BID9 . Therefore the properties the original data distribution would present the projected dataset with Note here r is the dimension to nonlinearly projected r < d. Since the elements A are drawn randomly the learner obtains an additional layer security as becomes virtually guess the projection mechanism used due the search space becomingMore formally let w * pd 2 the weight vector the OCSVM in the transformed space after solving that includes the distortion made the adversary and the nonlinear random projection Let w * p 2 be the weight vector the transformed space there adversary present Since the learner distinguish the original data would explicitly calculate w * p 2 Therefore for reasonable values r small distortions D prove in w * p 2 bounded above: DISPLAYFORM0 The main contributions summarized as We derive analytically an upper the weight vector a OCSVM trained that nonlinearly a lower dimensional space In addition the resistance added nonlinear data transformations against an adversarial opponent studied through numerical experiments on several benchmark datasets We believe our proposed approach can (i increase the attack resistance OCSVMs under give the learner from by adding through the randomness the data transformation in a selective direction The experimental evaluation presented demonstrates our proposed defense mechanism on three benchmark datasets MNIST SVHN We compare OCSVMs conjunction nonlinear random projections when an active adversary conducting by maliciously distorting We observe the f-scores across the dimensions decrease between train C |test D This indicates a OCSVM trained clean data identify adversarial samples better distorted data Consequently this shows OCSVMs immune integrity attacks by design by carefully crafting adversarial data points adversaries manipulate learn models favorableA comparison f-scores train D |test C train shows, the dimension reduced we reduce further begin The increase f-score confirms by projecting data a lower dimensional space using a carefully selected direction identify adversarial samples would identifiable the original feature space This confirmed the graphs the false positive rate the OCSVMs under integrity attacks anomalies We find there detecting adversarial samples under the proposed approach 23 on 31 MNIST).When the dimensions reduced below a certain dataset dependent threshold the OCSVM performance starts decline SVHN 1,500 463 We postulate the explanation this effect the reduction distance classesin perturbed anomalies and normal data points with the dimension. As reduce the dimension the transformation the effects the adversarial datapoints But at a significant loss useful information due the dimensionality reduction Due the performance OCSVMs reduces as we decrease the dimension beyond Finally TAB2 shows the effectiveness bound derived in Theorem The results show the consistency the upper bound, becomes tighter under dimension reductionIn summary the above experiments (i) OCSVMs vulnerable adversarial attacks integrity by projecting a distorted dataset in an appropriate direction we the learned model w.r.t integrity attacks the performance, in f-score starts the dimensionality beyond in the projected spaces, there comparable the original dimensional space less computational burden This paper based a unique combination unsupervised anomaly detection using OCSVMs and random projections for dimensionality reduction the presence a sophisticated adversary Our numerical analysis focuses two main aspects the performance OCSVMs lower dimensional spaces under nonlinear random projections adversarial perturbations The results suggest OCSVMs significantly affected if an adversary trained For each dataset with very high probability and projection direction results a OCSVM able identify adversarial samples would identifiable the original dimensional space Due the layer uncertainty added the randomness the projection our approach makes the learning system secure virtually guess the underlying details Therefore our approach can utilized make a learning system secure, ( reducing possible adversarial perturbations contracting, moving the normal data cloud away in the projected space making the search space of unbounded addingSince data contraction at for our future work investigate still hold if used other learning algorithms One major question optimally select dimensions transform We exploring the intrinsic dimensionality datasets address Since there a clear information asymmetry the adversary learnerdue this problem provides game-theoretical formulations anomaly detection under dimensionality reduction techniques We also plan study ""boiling frog"" type attacks where the adversary gradually injects malicious data overA PROOFS Definition 1 Let X �� R n×d that the training data Similarly define D �� R n×d the matrix that the distortions made Let A �� R d×r be the projection matrix where N (0 random variable Define b as a 1 × r row vector where each element drawn uniformly [ 2π . Using these variables define C �� R n×r the element at row i column j takesC i,j cos DISPLAYFORM0 C i Similarly the matrices C X C D S X as, Proof (of Theorem 1) Letα achieving the optimal solution the projected space when adversarial distortions Then the solution for the primal problem in the projected space with adversarial distortions defined wSince the optimization problem as shown ( the OCSVM without any distortion * ) would give less or byα Thus DISPLAYFORM2 Define w * p as the primal solution optimization in the projected space if there were present therefore B RESULTS",0.02,0.5113379397128957
"In this paper, we present a layer-wise learning of stochastic neural networks (SNNs) in an information-theoretic perspective. In each layer of an SNN, the compression and the relevance are defined to quantify the amount of information that the layer contains about the input space and the target space, respectively. We jointly optimize the compression and the relevance of all parameters in an SNN to better exploit the neural network's representation. Previously, the Information Bottleneck (IB) framework (\cite{Tishby99}) extracts relevant information for a target variable. Here, we propose Parametric Information Bottleneck (PIB) for a neural network by utilizing (only) its model parameters explicitly to approximate the compression and the relevance. We show that, as compared to the maximum likelihood estimate (MLE) principle, PIBs : (i) improve the generalization of neural networks in classification tasks, (ii) push the representation of neural networks closer to the optimal information-theoretical representation in a faster manner.   Deep neural networks (DNNs) have demonstrated competitive performance in several learning tasks including image recognition (e.g., BID14 , ), natural language translation (e.g., , ) and game playing (e.g., BID22 ). Specifically in supervised learning contexts, a common practice to achieve good performance is to train DNNs with the maximum likelihood estimate (MLE) principle along with various techniques such as data-specific design of network architecture (e.g., convolutional neural network architecture), regularizations (e.g., early stopping, weight decay, dropout BID25 ), and batch normalization BID12 )), and optimizations (e.g., BID13 ). The learning principle in DNNs has therefore attributed to the MLE principle as a standard one for guiding the learning toward a beneficial direction. However, the MLE principle is very generic that is not specially tailored for neural networks. Thus, a reasonable question is does the MLE principle effectively and sufficiently exploit a neural network's representative power and is there any better alternative? As an attempt to address this important question, this work investigates the learning of DNNs from the information-theoretic perspective.An alternative principle is the Information Bottleneck (IB) framework BID29 ) which extracts relevant information in an input variable X about a target variable Y . More specifically, the IB framework constructs a bottleneck variable Z = Z(X) that is compressed version of X but preserves as much relevant information in X about Y as possible. In this information-theoretic perspective, I(Z, X) 1 , the mutual information of Z and X, captures the compression of Z about X and I(Z, Y ) represents the relevance of Z to Y . The optimal representation Z is determined via the minimization of the following Lagrangian: DISPLAYFORM0 where β is the positive Lagrangian multiplier that controls the trade-off between the complexity of the representation, I(Z, X), and the amount of relevant information in Z, I(Z, Y ). The exact solution to the minimization problem above is found BID29 ) with the implicit selfconsistent equations: DISPLAYFORM1 p(z) = p(z|x)p(x)dx p(y|z) = p(y|x)p(x|z)dx (2) where Z(x; β) is the normalization function, and D KL [. .] is the Kullback -Leibler (KL) divergence BID15 ). Unfortunately, the self-consistent equations are highly non-linear and still non-analytic for most practical cases of interest. Furthermore, the general IB framework assumes that the joint distribution p(X, Y ) is known and does not specify concrete models.On the other hand, the goal of the MLE principle is to match the model distribution p model as close to the empirical data distributionp D as possible (e.g., see Appendix I.B). The MLE principle treats the neural network model p(x x x; θ θ θ) as a whole without explicitly considering the contribution of its internal structures (e.g., hidden layers and hidden neurons). As a result, a neural network with redundant information in hidden layers may have a good distribution match in a training set but show a poor generalization in test sets. In the MLE principle, we only need empirical samples of the joint distribution to maximize the likelihood function of the model given the data. The MLE principle is proved to be mathematically equivalent to the IB principle for the multinomial mixture model for clustering problem when the input distribution X is uniform or has a large sample size BID24 ). However in general the two principles are not obviously related.In this work, we leverage neural networks and the IB principle by viewing neural networks as a set of encoders that sequentially modify the original data space. We then propose a new generalized IB-based objective that takes into account the compression and relevance of all layers in the network as an explicit goal for guiding the encodings in a beneficial manner. Since the objective is designed to optimize all parameters of neural networks and is mainly motivated by the IB principle for deep learning BID28 ), we name this method the Parametric Information Bottleneck (PIB). Because the generalized IB objective in PIB is intractable, we approximate it using variational methods and Monte Carlo estimation. We propose re-using the existing neural network architecture as variational decoders for each hidden layers. The approximate generalized IB objective in turn presents interesting connections with the MLE principle. We show that our PIBs have a better generalization and better exploit the neural network's representation by pushing it closer to the information-theoretical optimal representation as compared to the MLE principle. In this paper we introduced an information-theoretic learning framework to better exploit a neural network's representation. We have also proposed an approximation that fully utilizes all parameters in a neural network and does not resort to any extra models. Our learning framework offers a principled way of interpreting and learning all layers of neural networks and encourages a more Figure 4 : Samples drawn from the prediction of the lower half of the MNIST test data digits based on the upper half for PIB (left, after 60 epochs) and SFNN (right, after 200 epochs). The leftmost column is the original MNIST test digit followed by the masked out digits and nine samples. The rightmost column is obtained by averaging over all generated samples of bottlenecks drawn from the prediction. The figures illustrate the capability of modeling structured output space using PIB and SFNN. informative yet compressed representation, which is supported by qualitative empirical results. One limitation is that we consider here fully-connected feed-forward architecture with binary hidden layers. Since we used generated samples to estimate mutual information, we can potentially extend the learning framework to larger and more complicated neural network architectures. This work is our first step toward exploiting expressive power of large neural networks using informationtheoretic perspective that is not yet fully utilized.",1385,0.694,811,1.7077681874229347,"In a layer-wise learning of In each layer an SNN the compression the relevance defined to quantify about We jointly optimize the compression the relevance all parameters an SNN better exploit Previously the Information Bottleneck (IB) framework\cite{Tishby99 extracts relevant information for a target variable Here propose Parametric Information Bottleneck by utilizing (only its model parameters explicitly approximate the compression the relevance. We show, compared the maximum likelihood estimate PIBs : improve neural networks classification tasks push the representation a faster manner Deep neural networks demonstrated competitive performance BID14 , natural language translation , game playing Specifically in supervised learning contexts a common practice to achieve DNNs the maximum likelihood estimate along various techniques data-specific design of network architecture regularizations weight decay dropout BID25 batch normalization BID12 )), optimizations The learning principle DNNs therefore attributed the MLE principle as standard one guiding toward a beneficial direction However the MLE principle very generic that specially tailored neural networks Thus a reasonable question does the MLE principle effectively and sufficiently exploit a neural network's representative power is any better alternative As an attempt address this important question this work investigates the learning DNNsAn alternative principle the Information BottleneckIB) framework BID29 ) extracts in an input variable X about More specifically the IB framework constructs a bottleneck variable Z = Z(X compressed version but preserves as much relevant information in X about Y In this information-theoretic perspective, I(Z, X 1 , the mutual information captures the compression Z about ) represents the relevance The optimal representation Z determined via DISPLAYFORM0 where β positive multiplier that controls the complexity the representation, I(Z, X relevant information ). The exact solution above found BID29 ) with the implicit selfconsistent equations DISPLAYFORM1 p(z (2 where; β D KL [. .] is the Kullback -Leibler (KL divergence BID15 ). Unfortunately the self-consistent equations highly non still non for most practical cases interest Furthermore the general IB framework assumes the joint distribution p(X ) known does specify concrete modelsOn the goal the MLE principle match the model distribution p model as close distributionp D see Appendix I.B The MLE principle treats the neural network model p(x x x; �� �� �� without explicitly considering the contribution its internal structures hidden neurons As a neural network redundant information in hidden layers a good distribution match but show In the MLE principle only empirical samples the joint distribution maximize the likelihood function given The MLE principle proved equivalent the IB principle for the multinomial mixture model for clustering problem when the input distribution X uniform or has BID24 However in general the two principles obviouslyIn this work leverage neural networks the IB principle by viewing sequentially modify the original data space We then propose a new generalized IB-based objective takes the compression relevance all layers an explicit goal guiding a beneficial manner Since the objective designed optimize all parameters neural networks is mainly motivated the IB principle for BID28 name the Parametric Information Bottleneck Because the generalized IB objective in PIB approximate variational methods Monte Carlo estimation We propose reusing variational decoders each hidden layers The approximate generalized IB objective turn presents interesting connections the MLE principle We show our PIBs a better generalization and exploit the neural network's representation by pushing closer the information-theoretical optimal representation as the MLE principle In introduced better exploit We also proposed an approximation that fully utilizes all parameters does resort any extra models Our learning framework offers a principled way interpreting learning all layers encourages a more Figure : Samples drawn the prediction the lower half the MNIST test data digits based for PIBleft after 60 epochs SFNN The leftmost column the original MNIST test digit followed the masked out digits nine samples The rightmost column obtained averaging over all generated samples drawn the prediction. The figures illustrate the capability modeling structured output space PIB SFNN informative yet compressed representation supported qualitative empirical results One limitation consider here fully-connected feed-forward architecture with binary hidden layers Since we used generated samples estimate mutual information potentially extend the learning framework larger and more complicated neural network This work our first step exploiting expressive power large neural networks informationtheoretic perspective that yet utilized",0.01,0.5074103274044169
"The maximum mean discrepancy (MMD) between two probability measures P
 and Q is a metric that is zero if and only if all moments of the two measures
 are equal, making it an appealing statistic for two-sample tests. Given i.i.d. samples
 from P and Q, Gretton et al. (2012) show that we can construct an unbiased
 estimator for the square of the MMD between the two distributions. If P is a
 distribution of interest and Q is the distribution implied by a generative neural
 network with stochastic inputs, we can use this estimator to train our neural network.
 However, in practice we do not always have i.i.d. samples from our target
 of interest. Data sets often exhibit biases—for example, under-representation of
 certain demographics—and if we ignore this fact our machine learning algorithms
 will propagate these biases. Alternatively, it may be useful to assume our data has
 been gathered via a biased sample selection mechanism in order to manipulate
 properties of the estimating distribution Q.
 In this paper, we construct an estimator for the MMD between P and Q when we
 only have access to P via some biased sample selection mechanism, and suggest
 methods for estimating this sample selection mechanism when it is not already
 known. We show that this estimator can be used to train generative neural networks
 on a biased data sample, to give a simulator that reverses the effect of that
 bias. Neural networks with stochastic input layers can be trained to approximately sample from an arbitrary probability distribution P based on samples from P BID7 . Generating simulations from complex distributions has applications in a large number of fields: We can automatically generate illustrations for text BID21 or streams of video BID20 ; we can simulate novel molecular fingerprints to aid scientific exploration BID11 ; and, we can synthesize medical time-series data that can be shared without violating patient privacy BID6 .In this paper, we consider the setting of a feedforward neural network (referred to as the generator) that maps random noise inputs z ∈ R d to some observation space X . The weights of the neural network are trained to minimize some loss function between the resulting simulations and exemplars of real data. The general form of the resulting distribution Q over simulations G(z) is determined by the architecture of the generator-which governs the form of the mapping G-and by the loss function used to train the generator. Generative adversarial networks BID7 use dynamically varying, adversarially learned loss functions specified in terms of the output of a classifier. Other generative networks use a loss function defined using a distributional distance or divergence between the simulation distribution Q and a target distribution P BID0 BID15 BID22 , requiring the generator to mimic the variance in a collection of data points rather than simply converge to a single mode. In particular, the maximum mean discrepancy BID8 has demonstrated good performance as a loss function in this setting BID18 BID19 , since it reduces to zero if and only if all moments of two distributions are equal, requiring the generator to reproduce the full range of variation found in the data.These approaches, like most machine learning methods, assume our data is a representative sample from the distribution of interest. If this assumption is correct, minimizing the distributional distance between the simulations and the data is equivalent to learning a distribution that is indistinguishable under an appropriate two-sample test from our target distribution. However, we run into problems if our data is not in fact a representative sample from our target distribution-for instance, if our data gathering mechanism is susceptible to sample selection bias. The problem of machine learning algorithms replicating and even magnifying human biases is gathering increasing awareness BID2 BID23 , and if we believe our dataset suffers from such biases-for example, if our audio dataset contains primarily male speakers or our image dataset contains primarily white faces -we will typically want to take steps to correct this bias.Even if our data is representative of the underlying distribution, we might want to generate samples from a modified version of this distribution. For example, we might want to alter the demographics of characters in a scene to fit a story-line. In this setting, we can treat our desired modified distribution as our target distribution, and treat our data as if they were sampled from this distribution subject to an appropriately biased sample selection mechanism.If we know the form of our sample selection bias, we can reformulate our loss function to penalize the generator based on the difference between simulated data and the unbiased distribution of interest, which we will refer to as our target distribution. After a review of relevant background information in Section 2, we show in Section 3 that, given a function that describes how our observed data deviates from this target distribution, we can construct an estimator of the MMD between the generator and the target distribution.In practice, we will not know the function linking the target distribution and the empirical data distribution. However, we can approximate this function based on user-provided examples of data points that are over-and under-represented. In Section 4, we discuss ways to estimate this function, and in Section 5 we discuss related work in survey sampling statistics and bias reduction. We demonstrate the efficacy and applicability of our approach in Section 6. We have presented an asymptotically unbiased estimator for the MMD between two distributions P and Q, for use when we only have access to P via a biased sampling mechanism. This mechanism can be specified by a known or estimated thinning function T (x), where samples are then assumed to come from a distribution T (x)P(x)/Z. We show that this estimator can be used to manipulate the distribution of simulations learned by a generative network, in order to correct for sampling bias or to explicitly change the distribution according to a user-specified function.When the thinning function is unknown, it can be estimated from labeled data. We demonstrate this in an interpretable experiment using partially labeled images, where we jointly estimate the thinning function alongside the generator weights. An obvious next step is to explore the use of more sophisticated thinning functions appropriate for complex, multimodal settings.",1230,0.552,706,1.7422096317280453,"The maximum mean discrepancy two probability measures P a metric zero all moments making appealing statistic Given i.i.d samples P and Q Gretton (2012 show we construct the square the MMD between If P is a distribution interest Q implied a generative neural network with train However practice we always i.i.d samples from our target of interest Data sets often exhibit biases— certain demographics if ignore this fact our machine learning algorithms propagate Alternatively it assume our data gathered a biased sample selection mechanism in manipulate properties the estimating distribution Q. In this paper construct the MMD between P Q when only access via some biased sample selection mechanism suggest methods when it already We show this estimator train a biased data sample to give a simulator reverses that bias Neural networks with stochastic input layers trained approximately sample from an arbitrary probability distribution P based samples P BID7 Generating simulations from complex distributions has applications: We automatically illustrations text BID21 streams ; novel molecular fingerprints to aid scientific exploration BID11 medical time-series data that shared without violating .In consider the settingreferred the generator maps random noise inputs z �� R d some observation space X The weights the neural network trained minimize some loss function between the resulting simulations exemplars real data The general form the resulting distribution Q over simulations G(z determined the architecture the generator-which governs the mapping G-and by used train Generative adversarial networks BID7 use dynamically varying, adversarially learned loss functions specified terms the output Other generative networks use a loss function defined using a distributional distance or divergence between the simulation distribution Q a target distribution P BID0 BID15 BID22 , requiring the generator mimic the variance a collection rather simply converge a single mode In particular the maximum mean discrepancy BID8 has demonstrated good performance as a loss function this setting BID18 BID19 , since reduces to and all moments two distributions requiring the generator reproduce variation foundThese approaches like most machine learning methods assume our data from interest If this assumption minimizing the distributional distance the simulations equivalent learning that indistinguishable under an appropriate two-sample test from our target distribution However we run if in fact from our target distribution-for our data gathering mechanism susceptible sample selection bias The problem machine learning algorithms replicating and even magnifying human biases gathering increasing awareness BID2 BID23 , if believe our dataset suffers-for our audio dataset primarily male speakers -we typically want takeEven representative the underlying distribution generate samples a modified version For example we might alter the demographics characters fit In this setting treat our desired modified distribution our target distribution treat our data they sampled this distribution subject an appropriately biased sample selection mechanismIf know the form our sample selection bias reformulate our loss function penalize the generator based simulated data interest After a review relevant background information in Section show in given a function describes how our observed data deviates this target distribution construct the MMD between the generatorIn practice will not know linking the empirical data distribution However we approximate this function based user-provided examples data points overand under In Section ways estimate this function in related work survey sampling statistics bias reduction We demonstrate our approach Section We presented an asymptotically unbiased estimator the MMD between two distributions P for use when only access P via a biased sampling mechanism This mechanism can specified a known or estimated thinning function Tx samples then assumed come a distribution T We show this estimator manipulate simulations learned a generative network correct sampling bias or explicitly change accordingWhen the thinning function unknown estimated labeled data We demonstrate this an interpretable experiment partially labeled images jointly estimate the thinning function alongside the generator weights An obvious next step explore more sophisticated thinning functions appropriate complex, multimodal settings",0.01,0.5951641015016287
"We propose Bayesian Deep Q-Network  (BDQN), a  practical Thompson sampling based Reinforcement Learning (RL) Algorithm. Thompson sampling allows for targeted exploration in high dimensions through posterior sampling but is usually computationally expensive. We address this limitation by introducing uncertainty only at the output layer of the network through a Bayesian Linear Regression (BLR) model, which can be trained with fast closed-form updates and its samples can be drawn efficiently through the Gaussian distribution. We apply our method to a wide range of Atari Arcade Learning Environments. Since BDQN carries out more efficient exploration, it is able to reach higher rewards substantially faster than a key baseline, DDQN. Designing algorithms that achieve an optimal trade-off between exploration and exploitation is one of the primary goal of reinforcement learning (RL). However, targeted exploration in high dimensional spaces is a challenging problem in RL. Recent advances in deep RL mostly deploy simple exploration strategies such as ε-greedy, where the agent chooses the optimistic action, the action with highest promising return, with probability (1 − ε), otherwise, uniformly at random picks one of the available actions. Due to this uniform sampling, the ε-greedy method scales poorly with the dimensionality of state and action spaces. Recent work has considered scaling exploration strategies to large domains BID12 . Several of these papers have focused on employing optimism-under-uncertainty approaches, which essentially rely on computing confidence bounds over different actions, and acting optimistically with respect to that uncertainty.An alternative to optimism-under-uncertainty (Brafman & Tennenholtz, 2003) is Thompson Sampling (TS) BID57 , one of the oldest heuristics for multi arm bandits. TS is a Bayesian approach where one starts with a prior distribution over the belief and compute the posterior beliefs based on the collected data through the interaction with the environment and then maximizes the expected return under the sampled belief. The TS based posterior sampling can provide more targeted exploration since it can trade off uncertainty with the expected return of actions. In contrast, the ε-greedy strategy is indifferent to uncertainty of the actions and the expected rewards of sub-optimistic ones (set of actions excluding the optimistic action).There has been relatively little work on scaling Thompson Sampling to large state spaces. The primary difficulty in implementing Thompson sampling is the difficulty of sampling from general posterior distributions. Prior efforts in this space have generally required extremely expensive computations (e.g. BID21 BID52 )We derive a practical Thompson sampling framework, termed as Bayesian deep Q-networks (BDQN), where we approximate the posterior distribution on the set of Q-functions and sample from this approximated posterior. BDQN is computationally efficient since it incorporates uncertainty only at the output layer, in the form of a Bayesian linear regression model. Due to linearity and by choosing a Gaussian prior, we derive a closed-form analytical update to the approximated posterior distribution over Q functions. We can also draw samples efficiently from the Gaussian distribution. As addressed in BID32 , one of the major benefits of function approximation methods in deep RL is that the estimation of the Q-value, given a state-action pair, can generalize well to other state-action pairs, even if they are visited rarely. We expect this to hold in BDQN as well, but additionally, we also expect the uncertainty of state-action pairs to generalize well.We test BDQN on a wide range of Arcade Learning Environment Atari games BID13 BID15 ) against a strong baseline DDQN BID58 . Aside from simplicity and popularity of DDQN, BDQN and DDQN share the same architecture, and follow same target objective. These are the main reasons we choose DDQN for our comparisons.In table. 1 we see significant gains for BDQN over DDQN. BDQN is able to learn significantly faster and reach higher returns due to more efficient exploration. The evidence of this is further seen from the fact that we are able to train BDQN with much higher learning rates compared to DDQN. This suggests that BDQN is able to learn faster and reach better scores.These promising results suggest that BDQN can further benefit from additional modifications that were done to DQN, e.g. Prioritized Experience Replay , Dueling approach , A3C BID33 , safe exploration BID30 , and etc. This is because BDQN only changes that exploration strategy of DQN, and can easily accommodate additional improvements to DQN.",885,0.476,504,1.755952380952381,"We propose Bayesian Deep Q-Network a practical Thompson sampling based Reinforcement Thompson sampling allows targeted exploration in high dimensions through posterior sampling but usually computationally We address this limitation uncertainty only the output layer through trained fast closed-form updates its samples drawn efficiently We apply our method Atari Arcade Learning Environments Since BDQN carries out more efficient exploration able reach higher rewards substantially a key baseline DDQN Designing algorithms achieve exploration reinforcement learning However targeted exploration in high dimensional spaces RL Recent advances deep RL mostly deploy simple exploration strategies ��-greedy chooses the optimistic action the action with highest promising return with probability ( otherwise uniformly at random picks one Due this uniform sampling the ��-greedy method scales poorly the dimensionality state and action spaces Recent work considered scaling exploration strategies large domains BID12 . Several these papers focused employing optimism-under essentially computing confidence bounds over different actions acting optimistically that uncertaintyAn alternative (Brafman Tennenholtz Thompson Sampling (TS) BID57 one multi arm bandits TS is a Bayesian approach where one starts the belief and compute through the interaction maximizes under the sampled belief The TS based posterior sampling can more targeted exploration since trade uncertainty actions In contrast the ��-greedy strategy indifferent uncertainty of the actions the expected rewards sub-optimistic onesset excluding the optimistic action).There has scaling Thompson Sampling large state spaces The primary difficulty implementing Thompson sampling general posterior distributions Prior efforts in this space generally required extremely expensive computationse.g. BID21 BID52 )We derive a practical Thompson sampling framework termed as Bayesian deep Q-networks where approximate on sample from approximated BDQN computationally since incorporates uncertainty only in Due linearity by choosing prior derive a closed-form analytical update to over Q functions We draw samples efficiently As addressed BID32 , one function approximation methods deep RL the estimation, given a state-action pair generalize well visited rarely We expect hold in BDQN additionally also the uncertainty state-action pairs generalizeWe test Arcade Learning Environment Atari games BID13 BID15 ) against a strong baseline DDQN BID58 Aside simplicity popularity of DDQN BDQN share follow same target objective These choose DDQN our comparisonsIn table. 1 we see significant gains BDQN over BDQN able learn significantly reach higher returns due more efficient exploration The evidence further seen we train BDQN with compared This suggests BDQN able learn faster reach better scoresThese promising results further benefit additional modifications were done e.g. Prioritized Experience Replay , Dueling approach A3C BID33 safe exploration etc This because BDQN only changes that exploration strategy of can easily accommodate additional improvements",0.01,0.630179419100491
"In this work, we propose the polynomial convolutional neural network (PolyCNN), as a new design of a weight-learning efficient variant of the traditional CNN. The biggest advantage of the PolyCNN is that at each convolutional layer, only one convolutional filter is needed for learning the weights, which we call the seed filter, and all the other convolutional filters are the polynomial transformations of the seed filter, which is termed as an early fan-out. Alternatively, we can also perform late fan-out on the seed filter response to create the number of response maps needed to be input into the next layer. Both early and late fan-out allow the PolyCNN to learn only one convolutional filter at each layer, which can dramatically reduce the model complexity by saving 10x to 50x parameters during learning. While being efficient during both training and testing, the PolyCNN does not suffer performance due to the non-linear polynomial expansion which translates to richer representational power within the convolutional layers. By allowing direct control over model complexity, PolyCNN provides a flexible trade-off between performance and efficiency. We have verified the on-par performance between the proposed PolyCNN and the standard CNN on several visual datasets, such as MNIST, CIFAR-10, SVHN, and ImageNet. Applications of deep convolutional neural networks (CNNs) have been overwhelmingly successful in all aspect of perception tasks, ranging from computer vision to speech recognition and understanding, from biomedical data analysis to quantum physics. In the past couple of years, we have seen the evolution of many successful CNN architectures such as AlexNet BID13 , VGG BID25 , Inception , and ResNet BID8 a) . However, training these networks end-to-end with fully learnable convolutional filters (as is standard practice) is still very computationally expensive and is prone to over-fitting due to the large number of parameters. To alleviate this issue, we have come to think about this question: can we arrive at a more efficient CNN in terms of learnable parameters, without sacrificing the high CNN performance?In this paper, we present an alternative approach to reducing the computational complexity of CNNs while performing as well as standard CNNs. We introduce the polynomial convolutional neural networks (PolyCNN). The core idea behind the PolyCNN is that at each convolutional layer, only one convolutional filter is needed for learning the weights, which we call the seed filter, and all the other convolutional filters are the polynomial transformations of the seed filter, which is termed as an early fan-out. Alternatively , we could also perform late fan-out on the seed filter response to create the number of response maps desired to be input into the next layer. Both early and late fan-out allow the PolyCNN to learn only one convolutional filter at each layer, which can dramatically reduce the model complexity. Parameter savings of at least 10×, 26×, 50×, etc. can be realized during the learning stage depending on the spatial dimensions of the convolutional filters (3 × 3, 5 × 5, 7 × 7 etc. sized filters respectively). While being efficient during both training and testing, the PolyCNN does not suffer performance due to the non-linear polynomial expansion which translates to richer representational power within the convolutional layers. We have verified the on-par performance between the proposed PolyCNN and the standard CNN on several visual datasets, such as MNIST, CIFAR-10, SVHN, and ImageNet. DISPLAYFORM0 PolyCNN Module (Late Fan-Out, Single-Seed) PolyCNN Module (Early Fan-Out, Single-Seed) x l x l+1PolyCNN Module (Early Fan-Out, Multi-Seed) x l x l+1PolyCNN Module (Late Fan-Out, Multi-Seed) (e) ( We have shown the effectiveness of the proposed PolyCNN. Not only can it achieve on-par performance with the state-of-the-art, but also enjoy a significant utility savings. The PyTorch implementation of the PolyCNN will be made publicly available. Inspired by the polynomial correlation filter, in this paper, we have proposed the PolyCNN as an alternative to the standard convolutional neural networks. The PolyCNN module enjoys significant savings in the number of parameters to be learned at training, at least 10× to 50×. PolyCNN have much lower model complexity compared to traditional CNN with standard convolutional layers. The proposed PolyCNN demonstrates performance on par with the state-of-the-art architectures on several image recognition datasets.",910,0.449,524,1.7366412213740459,"In this work proposePolyCNN as a new design of a weight-learning efficient variant The biggest advantage the PolyCNN at each convolutional layer learning the weights we the seed filter the polynomial transformations termed as an early fan-out Alternatively we also perform late fan-out on the seed filter response create the number response maps needed be input the next layer Both early and late fan-out allow the PolyCNN learn only one convolutional filter at each layer dramatically the model complexity by saving 10x to 50x parameters during learning While being efficient during both training testing the PolyCNN does suffer performance due the non-linear polynomial expansion which translates richer representational power within By allowing direct control model complexity PolyCNN provides We verified onpar between the proposed PolyCNN the standard CNN on several visual datasets such MNIST SVHN Applications of overwhelmingly all aspect perception tasks ranging understanding, from biomedical data analysis quantum physics In the evolution many successful CNN architectures such AlexNet BID13 , VGG BID25 Inception ResNet BID8 a) . However training these networks end- with fully learnable convolutional filtersas is still is prone over due To alleviate come think can arrive a more efficient CNN in learnable parameters without the high CNN performance?In reducing while performing as standard introducePolyCNN The core idea the PolyCNN at each convolutional layer only one convolutional filter learning the weights we the seed filter the polynomial transformations termed as an early fan-out Alternatively , we perform late fan-out on the seed filter response create the number response maps desired to input the next layer Both early and late fan-out allow the PolyCNN learn only one convolutional filter at each layer dramatically the model complexity Parameter savings of at 10×, 26× etc can realized during the learning stage depending the spatial dimensions the convolutional filters3 ×, etc sized filters respectively While being efficient during both training testing the PolyCNN does suffer performance due the non-linear polynomial expansion which translates richer representational power within We verified onpar between the proposed PolyCNN the standard CNN on several visual datasets such MNIST SVHN DISPLAYFORM0 PolyCNN ModuleLate Fan-Out, SingleSeed x l x l+1PolyCNN Module Multi (e We shown the effectiveness the proposed PolyCNN. Not can achieve onpar the state also enjoy a significant utility savings The PyTorch implementation the PolyCNN will made publicly Inspired the polynomial correlation filter in have proposed the PolyCNN as The PolyCNN module enjoys significant savings the number parameters to learned at training at least 10× to PolyCNN have much lower model complexity compared traditional CNN with standard convolutional layers The proposed PolyCNN demonstrates performance on par state architectures on several image recognition datasets",0.01,0.5809762811548224
"Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches. However, selecting kernels is non-trivial in practice. Although kernel selection for the two-sample test has been studied, the insufficient samples in change point detection problem hinder the success of those developed kernel selection algorithms. In this paper, we propose KL-CPD, a novel kernel learning framework for time series CPD that optimizes a lower bound of test power via an auxiliary generative model. With deep kernel parameterization, KL-CPD endows kernel two-sample test with the data-driven kernel to detect different types of change-points in real-world applications. The proposed approach significantly outperformed other state-of-the-art methods in our comparative evaluation of benchmark datasets and simulation studies. Detecting changes in the temporal evolution of a system (biological, physical, mechanical, etc.) in time series analysis has attracted considerable attention in machine learning and data mining for decades BID3 BID7 . This task, commonly referred to as change-point detection (CPD) or anomaly detection in the literature, aims to predict significant changing points in a temporal sequence of observations. CPD has a broad range of real-world applications such as medical diagnostics BID12 , industrial quality control BID4 , financial market analysis BID31 , video anomaly detection ) and more.Figure 1: A sliding window over the time series input with two intervals: the past and the current, where w l , w r are the size of the past and current interval, respectively. X (l) , Xconsists of the data in the past and current interval, respectively.As shown in Fig. 1 , we focus on the retrospective CPD BID36 BID23 , which allows a flexible time window to react on the change-points. Retrospective CPD not only enjoys more robust detection BID9 ) but embraces many applications such as climate change detection BID32 , genetic sequence analysis BID37 , networks intrusion detection BID41 , to name just a few. Various methods have been developed BID17 , and many of them are parametric with strong assumptions on the distributions BID3 BID16 , including auto-regressive models BID40 and state-space models BID20 for tracking changes in the mean, the variance, and the spectrum.Ideally, the detection algorithm should be free of distributional assumptions to have robust performance as neither true data distributions nor anomaly types are known a priori. Thus the parametric assumptions in many works are unavoidably a limiting factor in practice. As an alternative, nonparametric and kernel approaches are free of distributional assumptions and hence enjoy the advantage to produce more robust performance over a broader class of data distributions.Kernel two-sample test has been applied to time series CPD with some success. For example, BID18 presented a test statistic based upon the maximum kernel fisher discriminant ratio for hypothesis testing and BID23 proposed a computational efficient test statistic based on maximum mean discrepancy with block sampling techniques. The performance of kernel methods, nevertheless, relies heavily on the choice of kernels. BID13 BID14 conducted kernel selection for RBF kernel bandwidths via median heuristic. While this is certainly straightforward, it has no guarantees of optimality regarding to the statistical test power of hypothesis testing. BID15 show explicitly optimizing the test power leads to better kernel choice for hypothesis testing under mild conditions. Kernel selection by optimizing the test power, however, is not directly applicable for time series CPD due to insufficient samples, as we discuss in Section 3.In this paper, we propose KL-CPD, a kernel learning framework for time series CPD. Our main contributions are three folds.• In Section 3, we first observe the inaptness of existing kernel learning approaches in a simulated example. We then propose to optimize a lower bound of the test power via an auxiliary generative model, which aims at serving as a surrogate of the abnormal events.• In Section 4, we present a deep kernel parametrization of our framework, which endows a data-driven kernel for the kernel two-sample test. KL-CPD induces composition kernels by combining RNNs and RBF kernels that are suitable for the time series applications.• In Section 5, we conduct extensive benchmark evaluation showing the outstanding performance of KL-CPD in real-world CPD applications. With simulation-based analysis in Section 6, in addition, we can see the proposed method not only boosts the kernel power but also evades the performance degradation as data dimensionality of time series increases.Finally, our experiment code and datasets are available at https://github.com/ OctoberChang/klcpd_code. We propose KL-CPD, a new kernel learning framework for two-sample test by optimizing a lower bound of test power with a auxiliary generator, to resolve the issue of insufficient samples in changepoints detection. The deep kernel parametrization of KL-CPD combines the latent space of RNNs with RBF kernels that effectively detect a variety of change-points from different real-world applications. Extensive evaluation of our new approach along with strong baseline methods on benchmark datasets shows the outstanding performance of the proposed method in retrospective CPD. With simulation analysis in addition we can see that the new method not only boosts the kernel power but also evades the performance degradation as data dimensionality increases.A CONNECTION TO MMD GAN Although our proposed method KL-CPD has a similar objective function as appeared in MMD GAN BID22 , we would like to point out the underlying interpretation and motivations are radically different, as summarized below.The first difference is the interpretation of inner maximization problem max k M k (P, G). MMD GANs BID22 treat whole maximization problem max k M k (P, G) as a new probabilistic distance, which can also be viewed as an extension of integral probability metric (IPM). The properties of the distance is also studied in BID22 ; . A follow-up work by combining BID29 push max k M k (P, G) further to be a scaled distance with gradient norm. However, the maximization problem (4) of this paper defines the lower bound of the test power, which also takes the variance of the empirical estimate into account, instead of the distance.Regarding the goals, MMD GAN aims to learn a generative model that approximates the underlying data distribution P of interests. All the works BID11 BID24 BID34 BID22 use MMD or max k M k (P, G) to define distance, then try to optimize G to be as closed to P as possible. However, that is not the goal of this paper, where G is just an auxiliary generative model which needs to satisfies Eq. (3). Instead, we aim to find the most powerful k for conducting hypothesis test. In practice, we still optimize G toward P because we usually have no prior knowledge (sufficient samples) about Q, and we want to ensure the lower bound still hold for many possible Q (e.g. Q can be also similar to P). However, even with this reason, we still adopt early stopping to prevent the auxiliary G from being exactly the same as P.",1461,0.7,879,1.6621160409556315,"Detecting the emergence abrupt property changes time series Kernel two-sample test has studied this task which makes fewer assumptions the distributions traditional parametric approaches However selecting kernels non Although kernel selection for the two-sample test studied the insufficient samples change point detection problem hinder those developed kernel selection algorithms In KL-CPD a novel kernel learning framework time series CPD a lower bound test power via an auxiliary generative model With deep kernel parameterization KL-CPD endows kernel two-sample test the data-driven kernel to change-points The proposed approach significantly outperformed state our comparative evaluation benchmark datasets simulation studies Detecting changes the temporal evolution a system ( physical mechanical attracted machine learning BID3 BID7 . This task, commonly change-point detection anomaly detection in aims predict significant changing points observations CPD such medical diagnostics BID12 , financial market analysis ) moreFigure A sliding window over the time series input with two intervals w l , the size X (l , Xconsists the past current interval respectivelyAs 1 , we focus the retrospective CPD BID36 BID23 , allows a flexible time window react on the change-points Retrospective CPD not enjoys more robust detection BID9 ) embraces many applications climate change detection BID32 genetic sequence analysis to Various methods BID17 , many parametric with strong assumptions BID3 BID16 including auto-regressive models for tracking the spectrumIdeally the detection algorithm free distributional assumptions to have robust performance as neither true data distributions anomaly types a Thus the parametric assumptions many works unavoidably practice As an alternative, nonparametric and kernel approaches free distributional assumptions hence enjoy to produce over a broader class data distributionsKernel two-sample test CPD some success For example BID18 presented a test statistic based upon the maximum kernel fisher discriminant ratio hypothesis testing proposed maximum mean discrepancy with block sampling techniques The performance kernel methods nevertheless relies kernels BID13 BID14 conducted kernel selection RBF kernel bandwidths via median heuristic While this straightforward no guarantees optimality regarding to the statistical test power hypothesis testing BID15 show explicitly optimizing the test power leads better kernel choice hypothesis testing under mild conditions Kernel selection by optimizing the test power however directly applicable time series CPD due insufficient samples discuss KL-CPD a kernel learning framework Our main contributions three folds.• In Section first observe the inaptness existing kernel learning approaches a simulated example We then propose optimize a lower bound the test power via an auxiliary generative model aims serving abnormal events.• Section our framework endows for the kernel two-sample test KL-CPD induces composition kernels combining RBF kernels that suitable the time series applications.• In Section conduct extensive benchmark evaluation showing With simulation-based analysis in Section in, see the proposed method not boosts the kernel power evades as data dimensionality timeFinally our experiment code and datasets We propose KL-CPD a new kernel learning framework two-sample test by optimizing a lower bound test power a auxiliary generator resolve insufficient samples changepoints detection The deep kernel parametrization KL-CPD combines the latent space RBF kernels effectively detect a variety change-points Extensive evaluation our new approach along strong baseline methods on benchmark datasets the outstanding performance retrospective CPD With simulation analysis addition we the new method not boosts the kernel power evades as data dimensionalityA CONNECTION MMD GAN Although our proposed method KL-CPD a similar objective function appeared MMD GAN BID22 would the underlying interpretation motivations are radically summarized inner maximization problem max k M kP, G MMD GANs BID22 treat whole maximization problem max k M kP, G as, also viewed integral probability metric The properties the distance is also studied BID22 ; . A follow-up work combining BID29 push max k M kP, G further be a scaled distance with gradient norm. However, the maximization problem (4 this defines lower the test power also takes the variance the empirical estimate instead the distanceRegarding the goals MMD GAN aims learn the underlying data distribution P of interests All the works BID11 BID24 BID34 BID22 use MMD or max k M kP, G to define distance then try optimize G closed P However that where G is just an auxiliary generative model needs satisfies Eq Instead aim find the most powerful k for conducting hypothesis test In practice still optimize G toward P because usually (sufficient samples Q lower still hold many possible Q ( can also similar However even this reason adopt early stopping to the auxiliary G from exactly P.",0.01,0.39109266915946095
"Theories in cognitive psychology postulate that humans use similarity as a basis
 for object categorization. However, work in image classification generally as-
 sumes disjoint and equally dissimilar classes to achieve super-human levels of
 performance on certain datasets. In our work, we adapt notions of similarity using
 weak labels over multiple hierarchical levels to boost classification performance.
 Instead of pitting clustering directly against classification, we use a warm-start
 based evaluation to explicitly provide value to a clustering representation by its
 ability to aid classification. We evaluate on CIFAR10 and a fine-grained classifi-
 cation dataset to show improvements in performance with the procedural addition
 of intermediate losses and weak labels based on multiple hierarchy levels. Further-
 more, we show that pretraining AlexNet on hierarchical weak labels in conjunc-
 tion with intermediate losses outperforms a classification baseline by over 17% on
 a subset of Birdsnap dataset. Finally, we show improvement over AlexNet trained
 using ImageNet pre-trained weights as initializations which further supports our 
 claim of the importance of similarity. Similarity is one of the bases of object categorization in humans BID14 . Theories of perceptual categorization in cognitive psychology postulate that humans construct categories by grouping similar stimuli to construct one or several prototypes. New instances are then labeled as the category that they are most similar to. For instance, when one categorizes a specific animal as a dog, they are saying that it is more similar to previously observed dogs than it is to all other objects. This view of categorization better explains the often fuzzy boundaries between real-life classes, where a new object may be equally similar to multiple prototypes. For example, while a dolphin is technically a mammal, its visual appearance is similar to fish, resulting in a lot of people misclassifying it.While research in cognitive psychology on object categorization might indicate that similarity should play a central role in object classification in humans, image classification in computer vision seems to do pretty well without using it. The task is commonly interpreted as one of classifying an image into one of multiple classes that are assumed to be disjoint and equally dissimilar. The use of softmax-based loss functions assumes that the classes are disjoint, while the use of one-hot labels assumes that classes are equally dissimilar. Despite those strong assumptions, which seem to violate human notions of categories, image classification has shown remarkable progress, achieving superhuman performance on multiple datasets BID6 BID3 . Far from being an anomaly, state-of-the-art models across image classification benchmark datasets use losses, such as cross-entropy loss, that make the explicit assumption of disjoint classes. However, BID4 notes that the predictions of ensembles of image classification models produces soft labels that ""define a rich similarity structure over the data"" despite the predictions of individual models not capturing this structure.Can similarity-based metrics improve classification performance in convolutional neural networks? Previous work has tried to answer this question in different problems such as metric learning BID0 , clustering BID16 , and hierarchical classification BID11 . We focus on applications of similarity in the context of convolutional neural networks such as BID5 who use a contrastive loss to perform end-to-end clustering using weak labels. While they show impressive performance on MNIST BID10 and CIFAR-10 (Krizhevsky & Hinton, 2009) , their method does not scale well to more complex datasets. BID13 propose a new loss function, magnet loss, to learn a representational space where distance corresponds to similarity. They show that clustering in this space allows them to achieve state-of-the-art performance on multiple fine-grained classification datasets.1 However, they initialize their model with pre-trained weights on ImageNet BID15 , so it is not clear whether their model is learning a good representation, or if it is finding a good mapping between already learned representations and the labels. BID20 pose the problem as one of hierarchical classification and propose a loss based on an ultra-metric tree representation of a hierarchy over the labels. While their loss has interesting properties, it only outperforms classification losses for datasets with a small number of instances per class. In this work, we use a contrastive loss to improve the classification performance of randomly initialized convolutional neural networks on a fine-grained classification task.What measures of similarity should we teach our model? We represent the relations between our classes in a hierarchy where the labels are all leaf nodes. Therefore, there are two kinds of similarities that we want our model to capture. The first is intra-class similarity-all cats are similar to each other and they are dissimilar to other animals. The second is inter-class similarity-dogs and cats are more similar to each other than they are to non-living objects. For a more complex hierarchy, our model should learn similarity at different levels of the class hierarchy. BID20 use their hierarchical loss function to learn those similarities, however, they observe that reducing the similarity between two classes across all levels of the hierarchy to a single value biases the model towards correct classification at the higher levels of the hierarchy resulting in poor classification performance. BID13 also observe that applying classification losses to the final layer reduces the entire representation of each class to a single scalar value which destroys intra-and inter-class variation. However, these are the same variations that we want our model to capture. We overcome those limitations by explicitly training the model to capture different grains of similarity at different levels of the network through applying an intermediate pairwise contrastive loss at those levels. In this manner, we can use hierarchical information, such as species of birds having the same coarse-grained category of bird while having different fine-grained labels. Despite being able to encode different levels of similarity, a contrastive loss does not require an explicit hierarchy; we only need weak labels for pairs of instances.How can we evaluate the representations learned by a clustering algorithm? Previous work has always tried to compete against classification using metrics biased towards the latter task. While some researchers have used hierarchical metrics BID20 or qualitative measures BID13 to evaluate the quality of their representations, their primary evaluation criteria has consistently been the classification accuracy of their model. We propose another way to evaluate the clustering representations by using the clustering model as a ""warm start"" from which they can train on classification. The intuition is that if the clustering model learned a representations that captures similarity in a space, it would be be at an advantage when it is fine-tuned for classification.We propose the use of a contrastive loss at different layers of a convolutional neural network to learn a notion of similarity across a set of labels. We also propose the use of the accuracy of a model pre-trained for clustering and fine-tuned for classification as an evaluation metric for clustering algorithms. In this work, we argue that similarity-based losses can be applied as a warm start to boost the performance of image classification models. We show that applying a pairwise contrastive loss to intermediate layers of the network results in better clustering performance, as well as better finetuned classification performance. Furthermore, we demonstrate how the pairwise loss can be used to train a model using weak hierarchical labels.We find that training with hierarchical labels results in the highest performance beating models with more parameters and approaches the performance of models pre-trained with ImageNet weights. This is a very significant finding since ImageNet contains multiple bird classes, so a model pretrained with ImageNet has seen many more birds than a model pre-trained with pairwise constraints on Birdsnap34. Nevertheless, it only outperforms a cluster-based warm-start model by just 10%. Regardless, we also show that applying our approach to ImageNet weights still results in a boost of 1.27%. This supports our claim that similarity-based metrics can improve classification performance, but it suggests that the gains we expect decrease if we start of with a good representational space.We hope to expand this in future work in multiple ways. We plan on extending our approach to the entire Birdsnap dataset, as well as to other fine-grained classification datasets. We also hope to perform more extensive analysis of the quality of the embedding spaces learned as it is obvious that the use of the Hungarian algorithm does not accurately reflect the performance of the clustering model.",1652,0.865,939,1.7593184238551651,"Theories in cognitive psychology postulate humans use similarity object categorization However work image classification generally as- sumes disjoint and equally dissimilar classes to achieve super-human levels on certain datasets In our work adapt notions similarity using weak labels over multiple hierarchical levels boost classification performance Instead pitting clustering directly classification a warm-start based evaluation explicitly provide value its ability aid We evaluate on CIFAR10 a fine classifi- show improvements the procedural addition intermediate losses weak labels based multiple hierarchy levels Further- more show pretraining AlexNet on hierarchical weak labels conjunc- tion intermediate losses outperforms a classification baseline over 17% a subset Birdsnap dataset Finally show improvement AlexNet trained using ImageNet pre as initializations which further supports similarity Similarity one the bases object categorization humans BID14 . Theories perceptual categorization postulate humans construct grouping similar stimuli construct one or several prototypes New instances then labeled the category that For instance one categorizes a specific animal saying more similar previously observed dogs all other objects This view categorization better the often fuzzy boundaries real-life classes where a new object equally similar multiple prototypes For example while a dolphin technically its visual appearance similar fish resulting peopleWhile research cognitive psychology on object categorization might indicate that similarity should play image classification computer vision seems do pretty without using it The task commonly interpreted one classifying an image multiple classes that assumed equally The use softmax-based loss functions assumes the classes while one-hot labels classes equally Despite those strong assumptions which seem violate human notions categories image classification shown achieving superhuman performance multiple datasets BID6 BID3 . Far anomaly state models across image classification benchmark datasets use losses such that make the explicit assumption disjoint classes However BID4 notes the predictions ensembles image classification models produces soft labels ""define a rich similarity structure over despite the predictions not capturingCan similarity-based metrics improve Previous work tried answer different problems such metric learning BID0 , We focus applications similarity such BID5 who a contrastive loss to perform end using weak labels While they show impressive performance MNIST BID10 (Krizhevsky Hinton , their method scale BID13 propose a new loss function magnet loss learn a representational space where distance corresponds similarity They show clustering this space allows them achieve state datasets.1 However initialize on ImageNet BID15 , learning a good representation, finding already learned representations the labels BID20 pose the problem as one hierarchical classification propose a loss based an ultra-metric tree representation over the labels While their loss has interesting properties only outperforms classification losses datasets instances per class In this work a contrastive loss to improve the classification performance onWhat measures similarity should teach We represent the relations our classes a hierarchy where the labels all leaf nodes Therefore there similarities want our model capture first is intra-class similarity-all cats similar dissimilar The second is inter-class similarity-dogs cats more For a more complex hierarchy our model learn similarity at BID20 use their hierarchical loss function learn those similarities however observe reducing two classes across all levels to biases correct classification at resulting BID13 also observe applying classification losses the final layer reduces the entire representation each class which destroys However these the same variations want our model capture We overcome those limitations explicitly training the model capture different grains similarity at the network through applying an intermediate pairwise contrastive loss at In this manner use hierarchical information, species having the same coarse-grained category bird while Despite able encode different levels similarity a contrastive loss does require an explicit hierarchy; we weak labels pairs instancesHow evaluate the representations learned Previous work always tried compete classification using metrics biased the latter task While some researchers used hierarchical metrics BID20 or qualitative measures their representations their primary evaluation criteria consistently the classification accuracy We propose another way evaluate the clustering representations by a ""warm start from they train classification The intuition the clustering model learned a representations captures similarity a space be at fine classificationWe propose a contrastive loss at different layers a notion across labels We also propose the accuracy a model pre clustering fine classification as an evaluation metric In this work argue similarity-based losses as a warm start boost image classification models We show applying a pairwise contrastive loss intermediate layers finetuned classification performance Furthermore demonstrate how the pairwise loss can train using weak hierarchical labelsWe training with the highest performance beating models more parameters approaches the performance pre ImageNet weights This a very significant finding since ImageNet contains multiple bird classes a model pretrained has seen pre pairwise constraints Birdsnap34 Nevertheless only outperforms a cluster-based warm-start model Regardless also show applying our approach ImageNet weights still results a boost This supports our claim similarity-based metrics classification performance suggests gains decrease start of a good representational spaceWe hope expand in multiple ways We plan extending our approach the entire Birdsnap dataset We also hope perform the quality the embedding spaces learned as it obvious the Hungarian algorithm accurately",0.01,0.6387558006794892
"Deep reinforcement learning algorithms that estimate state and state-action value functions have been shown to be effective in a variety of challenging domains, including learning control strategies from raw image pixels. However, algorithms that estimate state and state-action value functions typically assume a fully observed state and must compensate for partial or non-Markovian observations by using finite-length frame-history observations or recurrent networks. In this work, we propose a new deep reinforcement learning algorithm based on counterfactual regret minimization that iteratively updates an approximation to a cumulative clipped advantage function and is robust to partially observed state. We demonstrate that on several partially observed reinforcement learning tasks, this new class of algorithms can substantially outperform strong baseline methods: on Pong with single-frame observations, and on the challenging Doom (ViZDoom) and Minecraft (Malmö) first-person navigation benchmarks. Many reinforcement learning problems of practical interest have the property of partial observability, where observations of state are generally non-Markovian. Despite the importance of partial observation in the real world, value function-based methods such as Q-learning (Mnih et al., 2013; BID6 generally assume a Markovian observation space. On the other hand, Monte Carlo policy gradient methods do not assume Markovian observations, but many practical policy gradient methods such as A3C (Mnih et al., 2016) introduce the Markov assumption when using a critic or state-dependent baseline in order to improve sample efficiency.Consider deep reinforcement learning methods that learn a state or state-action value function. One common workaround for the problem of partial observation is to learn value functions on the space of finite-length frame-history observations, under the assumption that frame-histories of sufficient length will give the environment the approximate appearance of full observability. When learning to play Atari 2600 games from images, deep Q-learning algorithms (Mnih et al., 2013; BID6 concatenate the last 4 observed frames of the video screen buffer as input to a state-action value convolutional network. Not all non-Markovian tasks are amenable to finite-length frame-histories; recurrent value functions can incorporate longer and potentially infinite histories BID12 BID8 , but at the cost of solving a harder optimization problem. Can we develop methods that learn a variant of the value function that is more robust to partial observability?Our contribution is a new model-free deep reinforcement learning algorithm based on the principle of regret minimization which does not require access to a Markovian state. Our method learns a policy by estimating a cumulative clipped advantage function, which is an approximation to a type of regret that is central to two partial information game-solving algorithms from which we draw our primary inspiration: counterfactual regret minimization (CFR) BID35 and CFR+ BID28 . Hence we call our algorithm ""advantage-based regret minimization"" (ARM).We evaluate our approach on three visual reinforcement learning domains: Pong with varying framehistory lengths BID2 , and the first-person games Doom BID16 and Minecraft BID15 . Doom and Minecraft exhibit a first-person viewpoint in a 3-dimensional environment and should appear non-Markovian even with frame-history observations. We find that our method offers substantial improvement over prior methods in these partially observ-able environments: on both Doom and Minecraft, our method can learn well-performing policies within about 1 million simulator steps using only visual input frame-history observations. In this paper, we presented a novel deep reinforcement learning algorithm based on counterfactual regret minimization (CFR). We call our method advantage-based regret minimization (ARM). Similarly to prior methods that learn state or state-action value functions, our method learns a cumulative clipped advantage function of observation and action. However, in contrast to these prior methods, ARM is well suited to partially observed or non-Markovian environments, making it an appealing choice in a number of difficult domains. When compared to baseline methods, including deep Q-learning and TRPO, on non-Markovian tasks such as the challenging ViZDoom and Malmö firstperson navigation benchmarks, ARM achieves substantially better results. This illustrates the value of ARM for partially observable problems. In future work, we plan to further explore applications of ARM to more complex tasks, including continuous action spaces.6 APPENDIX 6.1 EXPERIMENTAL DETAILS 6.1.1 PONG (ARCADE LEARNING ENVIRONMENT)We use the preprocessing and convolutional network model of (Mnih et al., 2013) . Specifically, we view every 4th emulator frame, convert the raw frames to grayscale, and perform downsampling to generate a single observed frame. The input observation of the convnet is a concatenation of the most recent frames (either 4 frames or 1 frame). The convnet consists of an 8 × 8 convolution with stride 4 and 16 filters followed by ReLU, a 4 × 4 convolution with stride 2 and 32 filters followed by ReLU, a linear map with 256 filters followed by ReLU, and a linear map with |A| filters where |A| is the action space cardinality (|A| = 6 for Pong).We used Adam with a constant learning rate of α = 10 −4 , a minibatch size of 32, and the moment decay rates set to their defaults β 1 = 0.9 and β 2 = 0.999. Our results on each method are averaged across 3 random seeds.We ran ARM with the hyperparameters: sampling batch size of 12500, 4000/3000 minibatches of Adam for the first/subsequent sampling iterations respectively, and target update step size τ = 0.01. Double DQN uses the tuned hyperparameters . Note that our choice of ARM hyperparameters yields an equivalent number of minibatch gradient updates per sample as used by DQN and double DQN, i.e. 1 minibatch gradient update per 4 simulator steps.",1204,0.519,740,1.627027027027027,"Deep reinforcement learning algorithms estimate state and state-action value functions challenging domains learning control strategies from raw image pixels However, algorithms estimate state and state-action value functions typically a fully observed state must compensate partial or non-Markovian observations finite-length frame-history observations recurrent networks In this work propose deep reinforcement counterfactual regret minimization iteratively an approximation a cumulative clipped advantage function is robust to partially observed state We demonstrate on several partially observed reinforcement learning tasks this new class algorithms substantially strong baseline methods: on Pong with single-frame observations the challenging Doom (ViZDoom and first navigation benchmarks Many reinforcement learning problems of practical interest the property partial observability observations state generally nonMarkovian Despite partial observation value function- methods Q-learningMnih et al BID6 generally assume a Markovian observation space. On Monte Carlo policy gradient methods do assume Markovian observations many practical policy gradient methods such A3CMnih et al 2016 introduce the Markov assumption when a critic or state-dependent baseline in improve sample efficiencyConsider deep reinforcement learning methods learn a state or state-action value function One common workaround partial observation learn value functions on the space finite-length frame-history observations under sufficient length give the environment the approximate appearance When learning from images deep Q-learning algorithms (Mnih BID6 concatenate the last 4 observed frames the video screen buffer as a state-action value convolutional network. Not all non-Markovian tasks amenable finite-length frame-histories recurrent value functions incorporate longer and potentially infinite BID12 BID8 , at solving a harder optimization problem Can develop methods learn a variant robust partial observability?Our contribution model-free deep reinforcement regret minimization which does access a Markovian state Our method learns a policy estimating a cumulative clipped advantage function a type regret central two partial information game-solving algorithms from draw our primary inspirationCFR) BID35 CFR+ Hence we call our algorithm ""advantage-based regret minimizationARM).We evaluate three visual reinforcement learning domains Pong with varying framehistory lengths BID2 , and first games Doom BID16 Doom and Minecraft exhibit and should appear nonMarkovian even with frame-history observations We find our method offers substantial improvement these partially observ-able environments on both Doom learn well-performing policies within about 1 million simulator steps using only visual input frame-history observations In presented counterfactual regret minimization We call our method advantage-based regret minimizationARM Similarly prior methods that learn state or state-action value functions our method a cumulative clipped advantage function of observation action However contrast these prior methods ARM well partially observed or non-Markovian environments making appealing difficult domains When compared baseline methods including deep Q-learning TRPO on non-Markovian tasks challenging ViZDoom and Malmö firstperson navigation benchmarks ARM achieves This illustrates ARM partially observable problems In future work further applications ARM continuous action spaces.6 (ARCADE LEARNING ENVIRONMENT)We use (Mnih et al . Specifically view every 4th emulator frame convert perform generate a single observed frame The input observation the convneteither 4 frames The convnet consists an 8 × 8 convolution with stride 4 and 16 filters followed ReLU a linear map 256 filters |A| filters where the action space cardinality 6 for Pong).We used Adam with a constant learning rate α 10 −4 32 the moment decay rates set their defaults β 1 Our results on each method averaged 3 random seedsWe ran ARM the hyperparameters sampling batch size 12500 4000/3000 minibatches of Adam for the first/subsequent sampling iterations respectively target update step size τ Double DQN uses the tuned hyperparameters . Note our choice ARM hyperparameters yields minibatch gradient updates sample as used DQN double DQN 4 simulator steps",0.01,0.30168894455643214
"Recent deep multi-task learning (MTL) has been witnessed its success in alleviating data scarcity of some task by utilizing domain-specific knowledge from related tasks. Nonetheless, several major issues of deep MTL, including the effectiveness of sharing mechanisms, the efficiency of model complexity and the flexibility of network architectures, still remain largely unaddressed. To this end, we propose a novel generalized latent-subspace based knowledge sharing mechanism for linking task-specific models, namely tensor ring multi-task learning (TRMTL). TRMTL has a highly compact representation, and it is very effective in transferring task-invariant knowledge while being super flexible in learning task-specific features, successfully mitigating the dilemma of both negative-transfer in lower layers and under-transfer in higher layers. Under our TRMTL, it is feasible for each task to have heterogenous input data dimensionality or distinct feature sizes at different hidden layers. Experiments on a variety of datasets demonstrate our model is capable of significantly improving each single task’s performance, particularly favourable in scenarios where some of the tasks have insufficient data. Multi-task learning (MTL) (Caruana, 1997; BID15 is an approach for boosting the overall performance in each individual task by learning multiple related tasks simultaneously. In the deep learning context, jointly fitting sufficiently flexible deep neural networks (DNNs) to data of multiple tasks can be seen as adding an inductive bias to the deep models, which could be beneficial to learn feature representations preferable by all tasks. Recently, the deep MTL has gained much popularity and been successfully explored in an abroad range of applications, such as computer vision BID32 BID16 , natural language processing BID14 , speech recognition BID5 and so on.However, a number of key challenges posed by the issues of ineffectiveness, inefficiency and inflexibility in deep MTL are left largely unaddressed. One major challenge is how to seek effective information sharing mechanisms across related tasks, which is equivalent to designing better parameter sharing patterns in the deep networks. Some previous work BID32 BID30 tried to solve this problem by means of hard parameter sharing BID21 , where the bottom layers are all shared except with one branch per task at the top layers. Although being simple and robust to over-fitting BID0 , this kind of architecture can be harmful when learning high-level task-specific features, since it focuses only on common low-level features of all tasks. Moreover, these common features may be polluted by some noxious tasks, leading to the negative transfer in low-level features among tasks BID31 ). An alternative line of work mitigate this issue to some extent by following the soft parameter sharing strategy BID21 , under which one separate DNN is learned for each task with its own set of parameters, and the individual DNNs are implicitly linked by imposing constraints on the aligned weights. The deep MTL models of this type include using 2 norm regularization BID4 , trace norm regularization BID29 and tensor norm priors BID12 BID13 .The lack of efficiency in model complexity gives rise to another great challenge for current deep MTL. The above soft-sharing based deep models (one set of parameters per task) typically involve enormous number of trainable parameters and require extremely large storage and memory. It is thus usually infeasible to deploy those deep MTL models on resource-constrained devices such as mobile The overall sharing mechanisms of MRN, two variants of DMTRL (for the setting of CNN) and our TRMTL w.r.t. two tasks. The shared portion is depicted in yellow. The circles, squares and thin rectangles represent tensor cores, matrices and vectors, respectively. MRN : original weights are totally shared at the lower layers and the relatedness between tasks at the top layers is modeled by tensor normal priors. DMTRL (TT or Tucker): all layer-wise weights must be equal-sized so as to be stacked and decomposed into factors. For each task, almost all the factors are shard at each layer except the very last 1D vector. Such pattern of sharing is identical at all layers. TRMTL: layer-wise weights are separately encoded into TR-formats for different tasks, and a subset of latent cores are selected to be tied across two tasks. The portions of sharing can be different from layer to layer. phones and wearable computers . BID28 alleviated the issue by integrating tensor factorization with deep MTL and proposed deep multi-task representation learning (DMTRL). Specifically, they first stack up the layer-wise weights from all tasks and then decompose them into low-rank factors, yielding a succinct deep MTL model with fewer parameters. Despite the compactness of the model, DMTRL turns out to be rather restricted on sharing knowledge effectively. This is because, as shown in FIG0 , DMTRL (TT or Tucker) shares almost all fractions of layer-wise weights as common factors, leaving only a tiny portion of weights to encode the task-specific information. Even worse, such pattern of sharing must be identical across all hidden layers, which is vulnerable to the negative transfer of the features. As an effect, the common factors become highly dominant at each layer and greatly suppress model's capability in expressing task-specific variations.The last challenge arises from the flexibility of architecture in deep MTL. Most of deep MTL models force tasks to have the equal-sized layer-wise weights or input dimensionality. This restriction makes little sense for the case of loosely-related tasks, since individual tasks' features (input data) can be quite different and the sizes of layer-wise features (input data) may vary a lot from task to task.In this work, we provide a generalized latent-subspace based solution to addressing aforementioned difficulties of deep MTL, from all aspects of effectiveness, efficiency and flexibility. Regarding the effectiveness, we propose to share different portions of weights as common knowledge at distinct layers, so that each individual task can better convey its private knowledge. As for the efficiency, our proposal shares knowledge in the latent subspace instead of original space by utilizing a general tensor ring (TR) representation with a sequence of latent cores BID21 . One motivation of TR for MTL is it generalizes other chain structured tensor networks , especially tensor train (TT) BID18 , in terms of model expressivity power, as TR can be formulated as a sum of TT networks. On the other hand, TR is able to approximate tensors using lower overall ranks than TT does , thus yielding a more compact and sparselyconnected model with significantly less parameters for deep MTL. Adopting TR-format with much lower ranks could bring more benefits to deep MTL if we tensorize a layer-wise weight of each task into a higher-order weight tensor, since the weight can be decomposed into a relatively larger number but smaller-sized cores. This in turn facilitates the sharing of cores at a finer granularity and further enhances the effectiveness of sharing. Additionally, BID34 In this paper, we have introduced a novel knowledge sharing mechanism for connecting task-specific models in deep MTL, namely TRMTL. The proposed approach models each task separately in the form of TR representation using a sequence latent cores. Next, TRMTL shares the common knowledge by ting any subset of layer-wise TR cores among all tasks, leaving the rest TR cores for private knowledge. TRMTL is highly compact yet super flexible to learn both task-specific and task-invariant features. TRMTL is empirically verified on various datasets and achieves the stateof-the-art results in helping the individual tasks to improve their overall performance. Table 4 : Performance comparison of STL, MRN, DMTRL and our TRMTL on CIFAR-10 with unbalanced training samples, e.g., '5% vs 5% vs 5%' means 5% of training samples are available for the respective task A, task B and task C. TR-ranks R = 10 for TRMTL.",1587,0.814,938,1.6918976545842217,"Recent deep multi-task learningMTL witnessed its success data scarcity of some task by utilizing from related tasks Nonetheless several major issues of deep MTL sharing mechanisms model complexity still largely To propose a novel generalized latent-subspace based knowledge sharing mechanism linking namely tensor ring multi-task learning TRMTL has a highly compact representation effective transferring task-invariant knowledge while super learning successfully mitigating the dilemma both negative-transfer in lower layers Under our TRMTL it feasible each task heterogenous input data dimensionality or distinct feature sizes at different hidden layers Experiments datasets demonstrate our model significantly each single task��s performance favourable scenarios some insufficient data Multitask learning (Caruana BID15 is boosting learning In the deep learning context jointly fitting sufficiently flexible deep neural networks data of multiple tasks adding the deep models beneficial learn feature representations preferable by all tasks Recently the deep MTL gained been successfully explored an abroad range BID32 BID16 , natural soHowever key challenges posed the issues ineffectiveness left largely One major challenge seek effective information sharing mechanisms related tasks equivalent designing better parameter sharing patterns the deep networks Some previous work BID32 BID30 tried means hard parameter sharing BID21 , where the bottom layers except with one branch per task at Although being simple robust to over-fitting BID0 , this kind architecture harmful learning since focuses all tasks Moreover these common features polluted some noxious tasks leading the negative transfer in low-level features among tasks BID31 An alternative line mitigate to following the soft parameter sharing strategy BID21 , under one separate DNN learned with implicitly imposing constraints the aligned weights The deep MTL models this type include using 2 norm regularization BID4 , trace .The lack efficiency model complexity gives another great challenge. The above soft-sharing based deep modelsone set parameters task typically enormous number trainable parameters extremely large storage It thus usually deploy those deep MTL models The overall sharing mechanisms MRN two variants DMTRLfor the setting CNN our TRMTL w.r.t two tasks The shared portion depicted yellow The circles squares thin rectangles tensor cores MRN : original weights totally shared at the lower layers the relatedness tasks at modeled tensor normal priors DMTRLTT or Tucker): all layer-wise weights must- so stacked decomposed factors For each task almost all the factors shard at each layer except the very last 1D vector Such pattern sharing identical at all layers TRMTL layer-wise weights separately encoded TR-formats different tasks a subset latent cores selected tied across The portions sharing can different layer phones wearable computers . BID28 alleviated integrating tensor factorization deep MTL proposed deep multi-task representation learningDMTRL Specifically first stack the layer-wise weights all tasks low-rank factors yielding a succinct deep MTL model fewer parameters Despite the compactness DMTRL turns rather restricted sharing knowledge effectively This because shown FIG0 DMTRLTT or Tucker shares almost all fractions layer-wise weights common factors leaving encode Even worse such pattern sharing must identical all hidden layers vulnerable the negative transfer the features As an effect the common factors become highly dominant at each layer greatly suppress model's capability in expressing task-specific variationsThe last challenge arises the flexibility architecture deep MTL Most deep MTL models force tasks have the equal-sized layer-wise weights or input dimensionality This restriction makes loosely-related tasks individual tasks' featuresinput data quite the sizes layer-wise featuresIn provide a generalized latent-subspace based solution addressing aforementioned difficulties deep MTL from all aspects effectiveness flexibility Regarding the effectiveness, we propose share different portions weights common knowledge at distinct layers each individual task better convey its private knowledge As for the efficiency our proposal shares knowledge in the latent subspace instead original space by utilizing a general tensor ring (TR) representation latent cores BID21 . One motivation TR for MTL it generalizes other chain structured tensor networks , especially tensor train (TT) BID18 terms model expressivity power TR can formulated TT networks On TR able approximate tensors lower overall ranks TT does , yielding a more compact and sparselyconnected model significantly less parameters deep MTL TR-format with much lower ranks could bring deep MTL if tensorize a layer-wise weight each task into since but smaller-sized cores This in facilitates cores at further sharing Additionally BID34 In this paper connecting task-specific models deep MTL namely TRMTL proposed approach models each task separately TR representation using a sequence latent cores Next TRMTL shares the common knowledge by ting any subset layer-wise TR cores among all tasks leaving the rest TR cores private knowledge TRMTL highly compact yet super learn TRMTL empirically verified on various datasets achieves stateof helping the individual tasks Table 4 : Performance comparison STL MRN DMTRL our TRMTL on unbalanced training samples '5 means available the respective task A task B TR-ranks R = 10 for TRMTL",0.01,0.46697360410114536
"Neural Processes (NPs) (Garnelo et al., 2018) approach regression by learning to map a context set of observed input-output pairs to a distribution over regression functions. Each function models the distribution of the output given an input, conditioned on the context. NPs have the benefit of fitting observed data efficiently with linear complexity in the number of context input-output pairs, and can learn a wide family of conditional distributions; they learn predictive distributions conditioned on context sets of arbitrary size. Nonetheless, we show that NPs suffer a fundamental drawback of underfitting, giving inaccurate predictions at the inputs of the observed data they condition on. We address this issue by incorporating attention into NPs, allowing each input location to attend to the relevant context points for the prediction. We show that this greatly improves the accuracy of predictions, results in noticeably faster training, and expands the range of functions that can be modelled. Regression tasks are usually cast as modelling the distribution of a vector-valued output y given a vector-valued input x via a deterministic function, such as a neural network, taking x as an input. In this setting, the model is trained on a dataset of input-output pairs, and predictions of the outputs are independent of each other given the inputs. An alternative approach to regression involves using the training data to compute a distribution over functions that map inputs to outputs, and using draws from that distribution to make predictions on test inputs. This approach allows for reasoning about multiple functions consistent with the data, and can capture the co-variability in outputs given inputs. In the Bayesian machine learning literature, non-parametric models such as Gaussian Processes (GPs) are popular choices of this approach.Neural Processes (NPs) BID9 BID12 offer an efficient method to modelling a distribution over regression functions, with prediction complexity linear in the context set size. Once trained, they can predict the distribution of an arbitrary target output conditioned on a set of context inputoutput pairs of an arbitrary size. This flexibility of NPs enables them to model data that can be interpreted as being generated from a stochastic process. It is important to note however that NPs and GPs have different training regimes. NPs are trained on samples from multiple realisations of a stochastic process (i.e. trained on many different functions), whereas GPs are usually trained on observations from one realisation of the stochastic process (a single function). Hence a direct comparison between the two is usually not plausible.Despite their many appealing properties, one substantial weakness of NPs is that they tend to underfit the context set. This manifests in the 1D curve fitting example on the left half of FIG0 as inaccurate predictive means and overestimated variances at the input locations of the context set. The right half of the figure shows this phenomenon when predicting the bottom half of a face image from its top half: although the prediction is globally coherent, the model's reconstruction of the top-half is far from perfect. In an NP, the encoder aggregates the context set to a fixed-length latent summary via a permutation invariant function, and the decoder maps the latent and target input to the target output. We hypothesise that the underfitting behaviour is because the mean-aggregation step in the encoder acts as a bottleneck: since taking the mean across context representations gives the same weight to each context point, it is difficult for the decoder to learn which context points provide relevant information for a given target prediction. In theory, increasing the dimensionality of the representation could address this issue, but we show in Section 4 that in practice, this is not sufficient.To address this issue, we draw inspiration from GPs, which also define a family of conditional distributions for regression. In GPs, the kernel can be interpreted as a measure of similarity among two points in the input domain, and shows which context points (x i , y i ) are relevant for a given query x * . Hence when x * is close to some x i , its y-value prediction y * is necessarily close to y i (assuming small likelihood noise), and there is no risk of underfitting. We implement a similar mechanism in NPs using differentiable attention that learns to attend to the contexts relevant to the given target, while preserving the permutation invariance in the contexts. We evaluate the resulting Attentive Neural Processes (ANPs) on 1D function regression and on 2D image regression. Our results show that ANPs greatly improve upon NPs in terms of reconstruction of contexts as well as speed of training, both against iterations and wall clock time. We also demonstrate that ANPs show enhanced expressiveness relative to the NP and is able to model a wider range of functions. We have proposed ANPs, which augment NPs with attention to resolve the fundamental problem of underfitting. We have shown that this greatly improves the accuracy of predictions in terms of context and target NLL, results in faster training, and expands the range of functions that can be modelled. There is a wide scope of future work for ANPs. Regarding model architecture, one way of incorporating cross-attention into the latent path and modelling the dependencies across the resulting local latents is to also have a global latent, much like the setup of the Neural Statistician but translated to the regression setting. An interesting further application would be to train ANPs on text data, enabling them to fill in the blanks in a stochastic manner. For the image application, the Image Transformer (ImT) BID21 has some interesting connections with ANPs: its local self-attention used to predict consecutive pixel blocks from previous blocks has parallels with how our model attends to context pixels to predict target pixels. Replacing the MLP in the decoder of the ANP with self-attention across the target pixels, we have a model that closely resembles an ImT defined on arbitrary orderings of pixels. This is in contrast to the original ImT, which presumes a fixed ordering and is trained autoregressively. We plan to equip ANPs with self-attention in the decoder, and see how far their expressiveness can be extended. In this setup, however, the targets will affect each other's predictions, so the ordering and grouping of the targets will become important.",1260,0.633,728,1.7307692307692308,"Neural Processes (Garnelo et al., 2018) approach regression learning map context set observed input-output pairs over regression functions Each function models the distribution given conditioned NPs the benefit fitting observed data efficiently linear complexity in the number context input-output pairs can learn a wide family conditional distributions; learn predictive distributions conditioned context sets arbitrary size Nonetheless we show NPs suffer a fundamental drawback underfitting giving inaccurate predictions at the inputs they condition We address incorporating attention into NPs allowing each input location attend the relevant context points the prediction We show this greatly predictions results noticeably faster training expands functions Regression tasks usually cast modelling the distribution a vector-valued output y given via taking x In this setting the model trained predictions independent given An alternative approach regression involves the training data compute functions map inputs draws from make on test inputs This approach reasoning multiple functions consistent capture the co outputs given inputs In the Bayesian machine learning literature such popular choices of this approachNeural Processes BID9 BID12 offer modelling a distribution regression functions prediction complexity linear the context set size Once trained predict the distribution an arbitrary target output conditioned context inputoutput pairs of This flexibility NPs enables model data interpreted generated It however NPs NPs trained on samples multiple realisations trained many different functions whereas usually observationsa single function Hence a direct comparison usually plausibleDespite their many appealing properties one substantial weakness NPs underfit the context set This manifests the 1D curve fitting example on FIG0 as inaccurate predictive means overestimated variances at the input locations the context set The right half this phenomenon when predicting a face image from although the prediction globally coherent the model's reconstruction far In an NP, the encoder aggregates the context set to a fixed-length latent summary via maps and target input We hypothesise the underfitting behaviour because the mean-aggregation step the encoder acts: since taking across context representations gives each context point difficult learn provide relevant information a given target prediction In theory increasing the dimensionality the representation could address we show Section sufficientTo draw inspiration GPs also define a family conditional distributions regression In GPs the kernel interpreted a measure similarity two points the input domain shows which context points (x i relevant x * . Hence when x * close some x i its y-value prediction y necessarily closeassuming small likelihood noise there underfitting We implement NPs differentiable attention that learns attend contexts relevant preserving. We evaluate the resulting Attentive Neural Processes on 1D function regression on 2D image regression Our results ANPs greatly upon NPs reconstruction contexts as speed training both against iterations wall clock time We also demonstrate ANPs show enhanced expressiveness relative the NP is able model functions We proposed ANPs augment NPs attention resolve the fundamental problem underfitting We shown this greatly predictions terms context target NLL, results faster training expands functions There a wide scope future work ANPs Regarding model architecture one way incorporating crossattention into the latent path and modelling the dependencies across the resulting local latents also a global latent, much the setup the Neural Statistician but translated regression setting An interesting further application would train ANPs text data enabling fill For the image application the Image Transformer (ImT) BID21 has some interesting connections ANPs its local self-attention used predict consecutive pixel blocks previous blocks has parallels how our model attends context pixels to target pixels Replacing the MLP in the decoder of the ANP with self-attention across pixels a model closely an ImT defined arbitrary orderings This in contrast the original ImT, presumes a fixed ordering trained autoregressively We plan equip ANPs self-attention in the decoder see far their expressiveness In this setup however the targets affect each other's predictions the ordering and grouping become",0.01,0.5660149650012073
"Deconvolutional layers have been widely used in a variety of deep
 models for up-sampling, including encoder-decoder networks for
 semantic segmentation and deep generative models for unsupervised
 learning. One of the key limitations of deconvolutional operations
 is that they result in the so-called checkerboard problem. This is
 caused by the fact that no direct relationship exists among adjacent
 pixels on the output feature map. To address this problem, we
 propose the pixel deconvolutional layer (PixelDCL) to establish
 direct relationships among adjacent pixels on the up-sampled feature
 map. Our method is based on a fresh interpretation of the regular
 deconvolution operation. The resulting PixelDCL can be used to
 replace any deconvolutional layer in a plug-and-play manner without
 compromising the fully trainable capabilities of original models.
 The proposed PixelDCL may result in slight decrease in efficiency,
 but this can be overcome by an implementation trick. Experimental
 results on semantic segmentation demonstrate that PixelDCL can
 consider spatial features such as edges and shapes and yields more
 accurate segmentation outputs than deconvolutional layers. When used
 in image generation tasks, our PixelDCL can largely overcome the
 checkerboard problem suffered by regular deconvolution operations. Deep learning methods have shown great promise in a variety of artificial intelligence tasks such as image classification BID9 BID26 , semantic segmentation BID16 BID24 BID23 , and natural image generation BID3 BID8 . Some key network layers, such as convolutional layers BID11 , pooling layers, fully connected layers and deconvolutional layers, have been frequently used to create deep models for different tasks. Deconvolutional layers, also known as transposed convolutional layers BID28 , are initially proposed in BID29 . They have been primarily used in deep models that require up-sampling of feature maps, such as generative models BID19 BID15 BID22 and encoder-decoder architectures BID23 BID16 . Although deconvolutional layers are capable of producing larger feature maps from smaller ones, they suffer from the problem of checkerboard artifacts BID17 . This greatly limits deep model's capabilities in generating photo-realistic images and producing smooth outputs on semantic segmentation. To date, very little efforts have been devoted to improving the deconvolution operation.In this work, we propose a simple, efficient, yet effective method, known as the pixel deconvolutional layer (PixelDCL), to address the checkerboard problem suffered by deconvolution operations. Our method is motivated from a fresh interpretation of deconvolution operations, which clearly pinpoints the root of checkerboard artifacts. That is, the up-sampled feature map generated by deconvolution can be considered as the result of periodical shuffling of multiple intermediate feature maps computed from the input feature map by independent convolutions. As a result, adjacent pixels on the output feature map are not directly related, leading to the checkerboard artifacts. To overcome this problem, we propose the pixel deconvolutional operation to be used in PixelDCL. In this new layer, the intermediate feature maps are generated sequentially so that feature maps generated in a later stage are required to depend on previously generated ones. In this way, direct relationships among adjacent pixels on the output feature map have been established. Sequential generation of intermediate feature maps in PixelDCL may result in slight decrease in computational efficiency, but we show Figure 1 : Comparison of semantic segmentation results. The first and second rows are images and ground true labels, respectively. The third and fourth rows are the results of using regular deconvolution and our proposed pixel deconvolution PixelDCL, respectively. that this can be largely overcome by an implementation trick. Experimental results on semantic segmentation (samples in Figure 1) and image generation tasks demonstrate that the proposed PixelDCL can effectively overcome the checkerboard problem and improve predictive and generative performance.Our work is related to the pixel recurrent neural networks (PixelRNNs) and PixelCNNs BID21 , which are generative models that consider the relationship among units on the same feature map. They belong to a more general class of autoregressive methods for probability density estimation BID2 BID10 . By using masked convolutions in training, the training time of PixelRNNs and PixelCNNs is comparable to that of other generative models such as generative adversarial networks (GANs) BID3 BID20 and variational autoencoders (VAEs) BID8 BID6 . However, the prediction time of PixelRNNs or PixelCNNs is very slow since it has to generate images pixel by pixel. In contrast, our PixelDCL can be used to replace any deconvolutional layer in a plug-and-play manner, and the slight decrease in efficiency can be largely overcome by an implementation trick. In this work, we propose pixel deconvolutional layers that can solve the checkerboard problem in deconvolutional layers. The checkerboard problem is caused by the fact that there is no direct relationship among intermediate feature maps generated in deconvolutional layers. PixelDCL proposed here try to add direct dependencies among these generated intermediate feature maps. PixelDCL generates intermediate feature maps sequentially so that the intermediate feature maps generated in a later stage are required to depend on previously generated ones. The establishment of dependencies in PixelDCL can ensure adjacent pixels on output feature maps are directly related. Experimental results on semantic segmentation and image generation tasks show that PixelDCL is effective in overcoming the checkerboard artifacts. Results on semantic segmentation also show that PixelDCL is able to consider local spatial features such as edges and shapes, leading to better segmentation results. In the future, we plan to employ our PixelDCL in a broader class of models, such as the generative adversarial networks (GANs).",1181,0.634,706,1.6728045325779037,"Deconvolutional layers have widely deep models semantic segmentation One the key limitations deconvolutional operations result This caused no direct relationship among adjacent pixels the output feature map To address propose the pixel deconvolutional layerPixelDCL establish direct relationships the up-sampled feature map Our method a fresh interpretation the regular deconvolution operation The resulting PixelDCL can replace any deconvolutional layer without compromising the fully trainable capabilities original models The proposed PixelDCL may result slight decrease efficiency can an implementation trick Experimental results on semantic segmentation demonstrate PixelDCL consider spatial features such edges shapes yields more accurate segmentation outputs When used image generation tasks our PixelDCL can largely overcome suffered regular deconvolution operations Deep learning methods shown image classification BID9 BID26 , semantic natural image generation Some key network layers convolutional layers BID11 , pooling fully connected layers frequently deep models different tasks Deconvolutional layers also BID28 initially proposed BID29 They primarily deep models that require up-sampling feature maps generative models BID19 BID15 BID22 architectures . Although deconvolutional layers capable producing larger feature maps from smaller ones suffer checkerboard artifacts BID17 . This greatly limits deep model's capabilities generating producing smooth outputs on semantic segmentation To date very little efforts devoted the deconvolution operationIn this work, known the pixel deconvolutional layerPixelDCL address suffered Our method motivated from a fresh interpretation deconvolution operations clearly pinpoints checkerboard artifacts That the up-sampled feature map generated deconvolution can considered the result periodical shuffling multiple intermediate feature maps computed by independent convolutions As adjacent pixels the output feature map directly related, leading the checkerboard artifacts To overcome propose the pixel deconvolutional operation PixelDCL In this new layer the intermediate feature maps generated so feature maps generated a later stage required depend previously generated ones In this way direct relationships among adjacent pixels on the output feature map have established Sequential generation intermediate feature maps PixelDCL may result slight decrease computational efficiency we show Figure : Comparison semantic segmentation results The first and second rows images and ground true labels The third and fourth rows the results using regular deconvolution our proposed pixel deconvolution PixelDCL, that this can largely overcome an implementation trick Experimental results on semantic segmentationsamples in image generation tasks demonstrate the proposed PixelDCL can effectively overcome improve predictive and generative performanceOur work related the pixel recurrent neural networks PixelCNNs BID21 , consider the relationship among units on the same feature map They belong a more general class autoregressive methods for probability density estimation BID2 BID10 . By using masked convolutions training the training time PixelRNNs and PixelCNNs comparableGANs) BID3 BID20 . However the prediction time PixelRNNs or PixelCNNs slow since generate images pixel In contrast our PixelDCL can replace any deconvolutional layer the slight decrease efficiency largely overcome an implementation trick In this work propose pixel deconvolutional layers solve The checkerboard problem caused no direct relationship among intermediate feature maps generated deconvolutional layers PixelDCL proposed here try add direct dependencies among these generated intermediate feature maps PixelDCL generates intermediate feature maps sequentially so generated a later stage required depend previously generated ones The establishment dependencies PixelDCL ensure adjacent pixels on output feature maps directly related Experimental results on semantic segmentation image generation tasks PixelDCL effective overcoming the checkerboard artifacts Results on semantic segmentation also PixelDCL consider local spatial features edges shapes leading In the future plan employ our PixelDCL in a broader class models the generative adversarial networks",0.01,0.41832600673240466
"In this paper, the preparation of a neural network for pruning and few-bit quantization is formulated as a variational inference problem. To this end, a quantizing prior that leads to a multi-modal, sparse posterior distribution over weights, is introduced and a differentiable Kullback-Leibler divergence approximation for this prior is derived. After training with Variational Network Quantization, weights can be replaced by deterministic quantization values with small to negligible loss of task accuracy (including pruning by setting weights to 0). The method does not require fine-tuning after quantization. Results are shown for ternary quantization on LeNet-5 (MNIST) and DenseNet (CIFAR-10). Parameters of a trained neural network commonly exhibit high degrees of redundancy BID4 which implies an over-parametrization of the network. Network compression methods implicitly or explicitly aim at the systematic reduction of redundancy in neural network models while at the same time retaining a high level of task accuracy. Besides architectural approaches, such as SqueezeNet BID25 or MobileNets (Howard et al., 2017) , many compression methods perform some form of pruning or quantization. Pruning is the removal of irrelevant units (weights, neurons or convolutional filters) BID31 . Relevance of weights is often determined by the absolute value (""magnitude based pruning"" BID15 ), but more sophisticated methods have been known for decades, e.g., based on second-order derivatives (Optimal Brain Damage (LeCun et al., 1990) and Optimal Brain Surgeon BID18 ) or ARD (automatic relevance determination, a Bayesian framework for determining the relevance of weights, BID35 BID39 BID27 ). Quantization is the reduction of the bit-precision of weights, activations or even gradients, which is particularly desirable from a hardware perspective BID46 . Methods range from fixed bit-width computation (e.g., 12-bit fixed point) to aggressive quantization such as binarization of weights and activations BID41 BID52 . Few-bit quantization (2 to 6 bits) is often performed by k-means clustering of trained weights with subsequent fine-tuning of the cluster centers . Pruning and quantization methods have been shown to work well in conjunction . In so-called ""ternary"" networks, weights can have one out of three possible values (negative, zero or positive) which also allows for simultaneous pruning and few-bit quantization BID33 BID53 ).This work is closely related to some recent Bayesian methods for network compression BID34 BID40 that learn a posterior distribution over network weights under a sparsity-inducing prior. The posterior distribution over network parameters allows identifying redundancies through three means: weights with (1) an expected value very close to zero and (2) weights with a large variance can be pruned as they do not contribute much to the overall computation. (3) the posterior variance over non-pruned parameters can be used to determine the required bit-precision (quantization noise can be made as large as implied by the posterior uncertainty). Additionally , Bayesian inference over modelparameters is known to automatically reduce parameter redundancy by penalizing overly complex models BID36 .In this paper we present Variational Network Quantization (VNQ), a Bayesian network compression method for simultaneous pruning and few-bit quantization of weights. We extend previous Bayesian pruning methods by introducing a multi-modal quantizing prior that penalizes weights of low variance unless they lie close to one of the target values for quantization. As a result, weights are either drawn to one of the quantization target values or they are assigned large variance values-see Fig. 1 . After training, our method yields a Bayesian neural network with a multi-modal posterior over weights (typically with one mode fixed at 0), which is the basis for subsequent pruning and quantization. Additionally, posterior uncertainties can also be interesting for network introspection and analysis, as well as for obtaining uncertainty estimates over network predictions BID9 BID8 BID5 . After pruning and hard quantization, and without the need for additional fine-tuning, our method yields a deterministic feed-forward neural network with heavily quantized weights. Our method is applicable to pre-trained networks but can also be used for training from scratch. Target values for quantization can either be manually fixed or they can be learned during training. We demonstrate our method for the case of ternary quantization on LeNet-5 (MNIST) and DenseNet (CIFAR-10). Figure 1: Distribution of weights (means θ and log-variance log σ 2 ) before and after VNQ training of LeNet-5 on MNIST (validation accuracy before: 99.2% vs. after 195 epochs: 99.3%). Top row: scatter plot of weights (blue dots) per layer. Means were initialized from pre-trained deterministic network, variances with log σ 2 = −8. Bottom row: corresponding density 1 . Red shaded areas show the funnel-shaped "" basins of attraction"" induced by the quantizing prior. Positive and negative target values for ternary quantization have been learned per layer. After training, weights with small expected absolute value or large variance (log α ij ≥ log T α = 2 corresponding to the funnel marked by the red dotted line) are pruned and remaining weights are quantized without loss in accuracy. A potential shortcoming of our method is the KL divergence approximation (Sec. 3.3) . While the approximation is reasonably good on the relevant range of θ-and σ-values, there is still room for improvement which could have the benefit that weights are drawn even more tightly onto the quantization levels, resulting in lower accuracy loss after quantization and pruning. Since our functional approximation to the KL divergence only needs to be computed once and an arbitrary amount of ground-truth data can be produced, it should be possible to improve upon the approximation presented here at least by some brute-force function approximation, e.g., a neural network, polynomial or kernel regression. The main difficulty is that the resulting approximation must be differentiable and must not introduce significant computational overhead since the approximation is evaluated once for each network parameter in each gradient step. We have also experimented with a naive Monte-Carlo approximation of the KL divergence term. This has the disadvantage that local reparameterization (where pre-activations are sampled directly) can no longer be used, since weight samples are required for the MC approximation. To keep computational complexity comparable, we used a single sample for the MC approximation. In our LeNet-5 on MNIST experiment the MC approximation achieves comparable accuracy with higher pruning rates compared to our functional KL approximation. However, with DenseNet on CIFAR-10 and the MC approximation validation accuracy plunges catastrophically after pruning and quantization. See Sec. A.3 in the Appendix for more details. Compared to similar methods that only consider network pruning, our pruning rates are significantly lower. This does not seem to be a particular problem of our method since other papers on network ternarization report similar or even lower sparsity levels BID53 roughly achieve between 30% and 50% sparsity). The reason for this might be that heavily quantized networks have a much lower capacity compared to full-precision networks. This limited capacity might require that the network compensates by effectively using more weights such that the pruning rates become significantly lower. Similar trends have also been observed with binary networks, where drops in accuracy could be prevented by increasing the number of neurons (with binary weights) per layer. Principled experiments to test the trade-off between low bit-precision and sparsity rates would be an interesting direction for future work. One starting point could be to test our method with more quantization levels (e.g., 5, 7 or 9) and investigate how this affects the pruning rate.",1579,0.881,915,1.7256830601092896,"In the preparation pruning and few-bit quantization formulated To this end a quantizing prior that leads multi sparse posterior distribution weights introduced and a differentiable Kullback-Leibler divergence approximation derived After training Variational Network Quantization weights replaced deterministic quantization values with small to negligible loss task accuracyincluding pruning by setting The method does after quantization Results are shown ternary quantization on LeNet-5MNIST DenseNet Parameters of a trained neural network commonly exhibit high degrees redundancy BID4 which implies Network compression methods implicitly or aim the systematic reduction redundancy neural network models while retaining task accuracy Besides architectural approaches such SqueezeNet BID25 or MobileNetsHoward et al. 2017 many compression methods perform pruning Pruning the removal irrelevant unitsweights neurons BID31 . Relevance weights is determined ("" based pruning"" BID15 more sophisticated methods known decades based second-order derivativesOptimal Brain DamageLeCun et ARDautomatic relevance determination a Bayesian framework BID35 BID39 BID27 Quantization the reduction weights activations even gradients particularly desirable from BID46 . Methods range fixed bit-width computation aggressive quantization such weights activations BID41 BID52 . Few-bit quantization often performed trained weights the cluster centers . Pruning and quantization methods shown work conjunction . In so-called ""ternary"" networks weights havenegative zero also allows simultaneous pruning few-bit quantization BID33 BID53 ).This work closely some recent Bayesian methods network compression that learn under sparsityinducing prior The posterior distribution over network parameters allows identifying redundancies through three means weights with ( very weights can pruned as they do contribute the overall computation (3) the posterior variance over non-pruned parameters can the required bit-precisionquantization noise can made large implied Additionally , Bayesian inference over modelparameters known automatically parameter redundancy penalizing overly complex models BID36 .In Variational Network Quantization simultaneous pruning few-bit quantization weights We extend previous Bayesian pruning methods introducing prior penalizes weights low variance unless lie close one As weights either drawn the quantization target values assigned large variance-see Fig 1 . After training our method yields multi posterior over weightstypically with one mode fixed 0 subsequent pruning quantization Additionally posterior uncertainties interesting network introspection analysis obtaining uncertainty estimates over network predictions BID9 . After pruning hard quantization and without our method heavily quantized weights Our method applicable pre-trained networks but from scratch Target values quantization can either manually fixed they learned during We demonstrate our method the case ternary quantization on LeNet-5MNIST DenseNet Figure Distribution weights (means � log-variance log � 2 before VNQ training of LeNet-5 onvalidation accuracy before: after 195 epochs Top row: scatter plot weightsblue dots per layer Means were initialized pre-trained deterministic network, variances with log �� 2 −8 Bottom row corresponding density 1 . Red shaded areas the funnel-shaped "" basins attraction induced quantizing prior Positive and negative target values ternary quantization have learned per layer After training weights with small expected absolute value or large variancelog α ij ≥ log T α corresponding the funnel marked pruned remaining weights quantized without loss accuracy A potential shortcoming our method the KL divergence approximationSec) . While the approximation reasonably on the relevant range which have the benefit that weights drawn even onto the quantization levels resulting lower accuracy loss after pruning Since our functional approximation the KL divergence only needs an arbitrary amount ground-truth data produced improve presented at some brute-force function approximation polynomial or kernel regression The main difficulty the resulting approximation must differentiable must introduce significant computational overhead since evaluated once each network parameter each gradient step We also experimented a naive Monte-Carlo approximation the KL divergence term This has the disadvantage local reparameterizationwhere preactivations sampled directly no weight samples required the MC approximation To keep computational complexity comparable used a single sample the MC approximation In our LeNet-5 on MNIST experiment the MC approximation achieves comparable accuracy higher pruning rates compared our functional KL approximation However with DenseNet on CIFAR-10 the MC approximation validation accuracy plunges after pruning quantization. See Sec A.3 in the Appendix for more details Compared similar methods that only consider network pruning our pruning rates This does seem of our method since other papers network ternarization report BID53 roughly achieve The reason might heavily quantized networks compared This limited capacity might require the network compensates by effectively using more weights such the pruning rates become significantly Similar trends binary networks drops accuracy could prevented neuronswith binary weights layer Principled experiments to low bit-precision and sparsity rates would One starting point could test our method more quantization levels 5 investigate",0.01,0.5530558490257451
"Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model compression or pruning. However, most of the previous work took heuristic approaches. This work proposes a progressive weight pruning approach based on ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed method reaches extremely high pruning rate by using partial prunings with moderate pruning rates. Therefore, it resolves the accuracy degradation and long convergence time problems when pursuing extremely high pruning ratios. It achieves up to 34× pruning rate for ImageNet dataset and 167× pruning rate for MNIST dataset, significantly higher than those reached by the literature work. Under the same number of epochs, the proposed method also achieves faster convergence and higher compression rates. The codes and pruned DNN models are released in the anonymous link bit.ly/2zxdlss. Deep neural networks (DNNs) have achieved human-level performance in many application domains such as image classification BID17 , object recognition BID18 BID9 , natural language processing , etc. At the same time, the networks are growing deeper and bigger for higher classification/recognition performance (i.e., accuracy) BID25 . However, the very large DNN model size increases the computation time of the inference phase. To make matters worse, the large model size hinders DNN' deployments on edge computing, which provides the ubiquitous application scenarios of DNNs besides cloud computing applications.As a result, extensive research efforts have been devoted to DNN model compression, in which DNN weight pruning is a representative technique. BID7 is the first work to present the DNN weight pruning method, which prunes the weights with small magnitudes and retrains the network model, heuristically and iteratively. After that, more sophisticated heuristics have been proposed for DNN weight pruning, e.g., incorporating both weight pruning and growing BID6 , L 1 regularization BID27 , and genetic algorithms BID3 . Other improvement directions of weight pruning include trading-off between accuracy and compression rate, e.g., energy-aware pruning BID29 , incorporating regularity, e.g., channel pruning BID10 , and structured sparsity learning BID27 .While the weight pruning technique explores the redundancy in the number of weights of a network model, there are other sources of redundancy in a DNN model. For example , the weight quantization BID19 BID22 BID34 BID20 BID23 BID13 BID1 and clustering BID8 techniques explore the redundancy in the number of bits for weight representation. The activation pruning technique BID15 BID24 leverages the redundancy in the intermediate results. While our work focuses on weight pruning as the major DNN model compression technique, it is orthogonal to the other model compression techniques and might be integrated under a single ADMM-based framework for achieving more compact network models.The majority of prior work on DNN weight pruning take heuristic approaches to reduce the number of weights as much as possible, while preserving the expressive power of the DNN model. Then one may ask , how can we push for the utmost sparsity of the DNN model without hurting accuracy? and what is the maximum compression rate we can achieve by weight pruning? Towards this end , BID32 took a tentative step by proposing an optimization-based approach that leverages ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with nonconvex optimization problems with potentially combinatorial constraints. This direct ADMM-based weight pruning technique can be perceived as a smart DNN regularization where the regularization target is dynamically changed in each ADMM iteration. As a result it achieves higher compression (pruning) rate than heuristic methods.Inspired by BID32 , in this paper we propose a progressive weight pruning approach that incorporates both an ADMM-based algorithm and masked retraining, and takes a progressive means targeting at extremely high compression (pruning) rates with negligible accuracy loss. The contributions of this work are summarized as follows:• We make a key observation that when pursuing extremely high compression rates (say 150× for LeNet-5 or 30× for AlexNet), the direct ADMM-based weight pruning approach BID32 cannot produce exactly sparse models upon convergence, in that many weights to be pruned are close to zero but not exactly zero. Certain accuracy degradation will result from this phenomenon if we simply set these weights to zero.• We propose and implement the progressive weight pruning paradigm that reaches an extremely high compression rate through multiple partial prunings with progressive pruning rates. This progressive approach, motivated by dynamic programming, helps to mitigate the long convergence time by direct ADMM pruning.• Extensive experiments are performed by comparing with many state-of-the-art weight pruning approaches and the highest compression rates in the literature are achieved by our progressive weight pruning framework, while the loss of accuracy is kept negligible. Our method achieves up to 34× pruning rate for the ImageNet data set and 167× pruning rate for the MNIST data set, with virtually no accuracy loss. Under the same number of epochs, the proposed method achieves notably better convergence and higher compression rates than prior iterative pruning and direct ADMM pruning methods.We provide codes (both Caffe and TensorFlow versions) and pruned DNN models (both for the ImageNet and MNIST data sets) in the link: bit.ly/2zxdlss. For other types of DNN models, we have tested the proposed method on the facial recognition application on two representative DNN models BID16 BID12 . We demonstrate over 10× weight pruning rate with 0.2% and 0.4% accuracy loss, respectively, compared with the original DNN models.In summary, the experimental results demonstrate that our framework applies to a broad set of representative DNN models and consistently outperforms the prior work. It also applies to the DNN models that consist of mainly convolutional layers, which are different with weight pruning using prior methods. These promising results will significantly contribute to the energy-efficient implementation of DNNs in mobile and embedded systems, and on various hardware platforms.Finally, some recent work have focused on the simultaneous weight pruning and weight quantization, as both will contribute to the model storage compression of DNNs. Weight pruning and quantization can be unified under the ADMM framework, and we demonstrate the comparison results in TAB8 using the LeNet-5 model as illustrative example. As can be observed in the table, we can simultaneously achieve 167× weight reduction and use 2-bit for fully-connected layer weight quantization and 3-bit for convolutional layer weight quantization. The overall accuracy is 99.0%. When we focus on the weight data storage, the compression rate is unprecendented 1,910× compared with the original DNN model with floating point representation. When indices (required in weight pruning) are accounted for, the overall compression rate is 623×, which is still much higher than the prior work. It is interesting to observe that the amount of storage for indices is even higher than that for actual weight data. This work proposes a progressive weight pruning approach based on ADMM, a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed method reaches extremely high pruning rates by using partial prunings, with moderate pruning rates in each partial pruning step. Therefore, it resolves the accuracy degradation and long convergence time problems when pursuing extremely high pruning ratios. It achieves up to 34× pruning rate for the ImageNet data set and 167× pruning rate for the MNIST data set, significantly higher than those reached by work in the existing literature. Under the same number of epochs, the proposed method also achieves better convergence and higher compression rates.",1600,0.754,957,1.6718913270637408,"Deep neural networks although achieving very large model size that on edge computing devices Extensive research work have DNN model compression or However most the previous work took heuristic approaches This work proposes a progressive weight pruning approach ADMMAlternating Direction Method Multipliers a powerful technique deal potentially combinatorial constraints Motivated dynamic programming the proposed method reaches extremely high pruning rate partial prunings with moderate pruning rates Therefore resolves the accuracy degradation long convergence time problems when pursuing extremely high pruning ratios It achieves up to 34× pruning rate ImageNet dataset and 167× pruning rate significantly those reached the literature work Under the same number epochs the proposed method also achieves faster convergence The codes pruned DNN models released the anonymous link bit.ly/2zxdlss Deep neural networks achieved image classification BID17 , , etc At the networks growing deeper bigger for higher classification/recognition performance BID25 . However the very large DNN model size increases the inference phase To the large model size hinders DNN' deployments edge computing provides the ubiquitous application scenarios besidesAs extensive research efforts devoted DNN model compression in DNN weight pruning a representative technique BID7 is the first work present the DNN weight pruning method with small magnitudes retrains the network model heuristically After that more sophisticated heuristics DNN weight pruning incorporating growing BID6 , L 1 regularization BID27 genetic algorithms Other improvement directions of weight pruning trading-off accuracy compression rate energy-aware pruning BID29 , incorporating regularity channel structured sparsity learning .While explores the redundancy in weights a network model other sources For example , the weight quantization BID19 BID22 BID34 and clustering BID8 techniques explore the redundancy bits for weight representation The activation pruning BID15 BID24 leverages the redundancy the intermediate results While our work focuses weight pruning as the major DNN model compression technique orthogonal might integrated under a single ADMM-based framework achieving more compact network modelsThe majority prior work take heuristic approaches reduce weights as much preserving Then one may , push for the utmost sparsity the DNN model hurting accuracy and what the maximum compression rate we weight pruning , BID32 took by proposing ADMMAlternating Direction Method Multipliers deal potentially combinatorial constraints This direct ADMM-based weight pruning technique perceived a smart DNN regularization where dynamically changed As it achieves higher compression (pruning) rate heuristic methodsInspired BID32 , in a progressive weight pruning approach incorporates both an ADMM-based algorithm masked retraining takes a progressive means targeting at with negligible accuracy loss The contributions this work summarized We make a key observation when pursuing extremely high compression ratessay 150× for LeNet-5 AlexNet the direct ADMM-based weight pruning approach BID32 exactly sparse models upon convergence in many weights to close but Certain accuracy degradation will this phenomenon if we simply set these weights zero.• We propose and implement the progressive weight pruning paradigm reaches an extremely high compression rate through multiple partial prunings with progressive pruning rates This progressive approach motivated dynamic programming helps mitigate the long convergence time by direct ADMM pruning.• Extensive experiments comparing with many state weight pruning the highest compression rates are while accuracy kept negligible Our method achieves up to 34× pruning rate the ImageNet data 167× virtually no accuracy loss Under the same number epochs the proposed method achieves notably better convergence prior iterative pruning direct ADMM pruning methodsWe provide codes ( pruned DNN models for the link: bit.ly/2zxdlss For other types DNN models we tested the proposed method the facial recognition application on BID16 BID12 . We demonstrate over 10× weight pruning rate and compared the original DNN modelsIn summary our framework applies consistently It also applies the DNN models consist mainly convolutional layers different with weight pruning using prior methods These promising results significantly contribute the energy-efficient implementation DNNs on various hardware platformsFinally have focused the simultaneous weight pruning weight quantization both will contribute the model storage compression unified under the ADMM framework we demonstrate the comparison results TAB8 using the LeNet-5 model illustrative example As can observed simultaneously achieve 167× weight reduction use 2-bit for fully-connected layer weight quantization The overall accuracy When focus the weight data storage the compression rate unprecendented 1,910× compared the original DNN model floating point representation When indices (required weight pruning accounted the overall compression rate 623×, still the prior work It interesting observe storage for indices even actual weight data This work proposes a progressive weight pruning approach ADMM a powerful technique deal potentially combinatorial constraints Motivated dynamic programming the proposed method reaches extremely high pruning rates partial prunings with Therefore resolves the accuracy degradation long convergence time problems when pursuing extremely high pruning ratios It achieves up to 34× pruning rate the ImageNet data 167× significantly those reached work the existing literature Under the same number epochs the proposed method also achieves better convergence higher compression rates",0.01,0.41599923931567667
"In this paper, we present a new deep learning architecture for addressing the problem of supervised learning with sparse and irregularly sampled multivariate time series. The architecture is based on the use of a semi-parametric interpolation network followed by the application of a prediction network. The interpolation network allows for information to be shared across multiple dimensions of a multivariate time series during the interpolation stage, while any standard deep learning model can be used for the prediction network. This work is motivated by the analysis of physiological time series data in electronic health records, which are sparse, irregularly sampled, and multivariate. We investigate the performance of this architecture on both classification and regression tasks, showing that our approach outperforms a range of baseline and recently proposed models.
 Over the last several years, there has been significant progress in developing specialized models and architectures that can accommodate sparse and irregularly sampled time series as input BID25 BID20 BID21 BID12 BID4 ). An irregularly sampled time series is a sequence of samples with irregular intervals between their observation times. Irregularly sampled data are considered to be sparse when the intervals between successive observations are often large. Of particular interest in the supervised learning setting are methods that perform end-to-end learning directly using multivariate sparse and irregularly sampled time series as input without the need for a separate interpolation or imputation step.In this work, we present a new model architecture for supervised learning with multivariate sparse and irregularly sampled data: Interpolation-Prediction Networks. The architecture is based on the use of several semi-parametric interpolation layers organized into an interpolation network, followed by the application of a prediction network that can leverage any standard deep learning model. In this work, we use GRU networks BID6 as the prediction network.The interpolation network allows for information contained in each input time series to contribute to the interpolation of all other time series in the model. The parameters of the interpolation and prediction networks are learned end-to-end via a composite objective function consisting of supervised and unsupervised components. The interpolation network serves the same purpose as the multivariate Gaussian process used in the work of BID12 , but remove the restrictions associated with the need for a positive definite covariance matrix.Our approach also allows us to compute an explicit multi-timescale representation of the input time series, which we use to isolate information about transients (short duration events) from broader trends. Similar to the work of BID21 and BID4 , our architecture also explicitly leverages a separate information channel related to patterns of observation times. However, our representation uses a semi-parametric intensity function representation of this information that is more closely related to the work of Lasko (2014) on modeling medical event point processes.Our architecture thus produces three output time series for each input time series: a smooth interpolation modeling broad trends in the input, a short time-scale interpolation modeling transients, and an intensity function modeling local observation frequencies.This work is motivated by problems in the analysis of electronic health records (EHRs) BID25 BID21 BID12 BID4 ). It remains rare for hospital systems to capture dense physiological data streams. Instead, it is common for the physiological time series data in electronic health records to be both sparse and irregularly sampled. The additional issue of the lack of alignment in the observation times across physiological variables is also very common.We evaluate the proposed architecture on two datasets for both classification and regression tasks. Our approach outperforms a variety of simple baseline models as well as the basic and advanced GRU models introduced by BID4 across several metrics. We also compare our model with to the Gaussian process adapter BID19 and multi-task Gaussian process RNN classifier BID12 . Further, we perform full ablation testing of the information channels our architecture can produce to assess their impact on classification and regression performance. In this paper, we have presented a new framework for dealing with the problem of supervised learning in the presence of sparse and irregularly sampled time series. The proposed framework is fully modular. It uses an interpolation network to accommodate the complexity that results from using sparse and irregularly sampled data as supervised learning inputs, followed by the application of a prediction network that operates over the regularly spaced and fully observed, multi-channel output provided by the interpolation network. The proposed approach also addresses some difficulties with prior approaches including the complexity of the Gaussian process interpolation layers used in BID19 BID12 , and the lack of modularity in the approach of BID4 . Our framework also introduces novel elements including the use of semi-parametric, feed-forward interpolation layers, and the decomposition of an irregularly sampled input time series into multi-ple distinct information channels. Our results show statistically significant improvements for both classification and regression tasks over a range of baseline and state-of-the-art methods.Ruslan This data set contains sparse and irregularly sampled physiological signals, medications, diagnostic codes, inhospital mortality, length of stay and more. We focus on predicting in-hospital mortality and length of stay using the first 48 hours of data. We extracted 12 standard physiological variables from each of the 53,211 records obtained after removing hospital admission records with length of stay less than 48 hours. TAB2 shows the features, sampling rates (per hour) and their missingness information computed using the union of all time stamps that exist in any dimension of the input time series. In our experiments, each admission record corresponds to one data case (s n , y n ). Each data case n consists of a sparse and irregularly sampled time series s n with D = 12 dimensions. Each dimension d of s n corresponds to one of the 12 vital sign time series mentioned above. In the case of classification, y n is a binary indicator where y n = 1 indicates that the patient died at any point within the hospital stay following the first 48 hours and y n = 0 indicates that the patient was discharged at any point after the first 48 hours. There are 4310 (8.1%) patients with a y n = 1 mortality label. The complete data set is D = {(s n , y n )|n = 1, ..., N }, and there are N = 53, 211 data cases. The goal in the classification task is to learn a classification function g of the form y n ← g(s n ) whereŷ n is a discrete value.In the case of regression, y n is a real-valued regression target corresponding to the length of stay. Since the data set includes some very long stay durations, we let y n represent the log of the length of stay in days for all models. We convert back from the log number of days to the number of days when reporting results. The complete data set is again D = {(s n , y n )|n = 1, ..., N } with N = 53, 211 data cases (we again require 48 hours worth of data). The goal in the regression task is to learn a regression function g of the formŷ n ← g(s n ) whereŷ n is a continuous value.",1415,0.708,859,1.6472642607683352,"In this paper a new deep learning architecture addressing sparse irregularly sampled multivariate time series The architecture based the use a semi-parametric interpolation network followed a prediction network The interpolation network allows information shared multiple dimensions during while any standard deep learning model the prediction network This work motivated the analysis physiological time series data electronic health records sparse irregularly sampled multivariate We investigate this architecture both classification regression tasks showing our approach a range baseline and recently proposed models Over specialized models architectures accommodate sparse irregularly sampled time series as input BID25 BID20 ). An irregularly sampled time series samples irregular intervals their observation times Irregularly sampled data considered sparse when the intervals successive observations often Of the supervised learning setting methods perform end directly multivariate sparse and irregularly sampled time series as without imputation stepIn a new model architecture: Interpolation-Prediction Networks The architecture based the use several semi-parametric interpolation layers organized an interpolation network followed a prediction network leverage any standard deep learning model In this work GRU networks BID6 as the prediction networkThe interpolation network allows information contained each input time series contribute The parameters the interpolation and prediction networks learned end via a composite objective function consisting The interpolation network serves used the work BID12 , remove the restrictions associated the need a positive definite covariance matrixOur approach also compute an explicit multi-timescale representation isolate information transientsshort duration events broader trends Similar the work BID21 our architecture also explicitly a separate information channel related patterns observation times However our representation uses a semi-parametric intensity function representation this information closely the work Lasko2014 on modeling medical event point processesOur architecture thus produces three output time series a smooth interpolation modeling broad trends local observation frequenciesThis work motivated problems electronic health records BID25 BID21 BID12 BID4 ). It remains rare hospital systems capture dense physiological data streams Instead common the physiological time series data in electronic health records both sparse irregularly sampled The additional issue the lack alignment the observation times across physiological variables also veryWe evaluate the proposed architecture on two datasets for both classification and regression tasks Our approach outperforms a variety simple baseline models as the basic and advanced GRU models introduced BID4 across several metrics We also compare our model to the Gaussian process adapter BID19 RNN classifier BID12 Further perform full ablation testing the information channels our architecture produce assess their impact classification and regression performance In this paper have presented dealing supervised learning the presence sparse and irregularly sampled time series The proposed framework fully modular It uses an interpolation network accommodate the complexity that results sparse irregularly as supervised learning inputs followed the application operates the regularly spaced and fully observed, multi-channel output provided The proposed approach also addresses some difficulties prior approaches including the complexity the Gaussian process interpolation layers BID19 BID12 , modularity of Our framework also introduces novel elements including semi-parametric, feed-forward interpolation layers an irregularly sampled input time series multi-ple distinct information channels Our results statistically significant improvements both classification regression tasks baseline stateRuslan This data sparse irregularly physiological signals medications diagnostic codes inhospital mortality length more We focus predicting inhospital length using the first 48 hours data We extracted 12 standard physiological variables each the 53,211 records obtained after removing hospital admission records with length TAB2 shows the features, sampling rates (per hour their missingness information computed the union all time stamps that exist any dimension In our experiments each admission record corresponds one data case (s n y Each data case n consists a sparse irregularly sampled time series s n with D = 12 dimensions Each dimension d of s n corresponds the 12 vital sign time series mentioned In classification y n is a binary indicator where indicates the patient died at the hospital stay following and There 4310 ( patients a y n = 1 mortality label The complete data D = {(s n y|n = ... N there N 53 211 data cases The goal in the classification task learn a classification function g of y n ���In regression y a real-valued regression target corresponding stay Since the data includes some very long stay durations let y n represent the log for all models We convert back from the log number days when reporting results The complete data again D = {(s n y|n = ... N with N 53 211 data caseswe again require 48 hours worth The goal in the regression task learn regression g of the form�� n � n��",0.01,0.3532516381053698
"We introduce an analytic distance function for moderately sized point sets of known cardinality that is shown to have very desirable properties, both as a loss function as well as a regularizer for machine learning applications. We compare our novel construction to other point set distance functions and show proof of concept experiments for training neural networks end-to-end on point set prediction tasks such as object detection. Parametric machine learning models, like artificial neural networks, are routinely trained by empirical risk minimization. If we aim to predict an output y ∈ Y from an input x ∈ X , we collect a training set D of (x, y) pairs and train a parametrized prediction function h θ : X → Y by minimizing DISPLAYFORM0 Here, L : Y × Y → R is a loss function that assigns a scalar loss value to the predictionŷ = h θ (x) for the true value y. Classical machine learning problems allow for standard choices for the loss function. E.g., for regression problems, where y,ŷ ∈ R, it is common to use the squared loss L(ŷ, y) = (ŷ − y) 2 .Assume , however, that we want to train a machine learning system which-given some inputpredicts a set of points. In particular , the ordering of the points is neither semantically meaningful nor in any way consistent across data instances. As an example , one may consider an object detection task such as finding the positions of the black stones on an image of a real-world game of Nine Men's Morris. What should the loss function be in such a case?Naively, we might just impose an arbitrary ordering to the sets and treat them as ordered tuples. However, this conceals an important property of the task, the permutation invariance, from our machine learning system. This property might in fact be crucial to learn such a task efficiently. Instead, we would like our loss function to define a meaningful distance between two sets, which requires such a loss to be permutation-invariant. We discussed a novel point set loss function, which is analytic everywhere, vis-a-vis two other simple alternatives with matching computational complexity for point set prediction tasks as alternatives to more involved approaches BID3 BID2 . Proof of concept experiments showed that end-to-end training with such simple loss functions is a viable approach for point set prediction tasks, such as object detection. We expect that simple constructions such as the ""holographic"" point set distance introduced here may turn out useful not only for point set predictions, but also as a regularizer, for example to encourage (unsupervised) clustering to align its clusters with the clusters found by an earlier version of the model. We will need the following Lemma, which states that the roots of a complex polynomial continuously depend on its coefficients. DISPLAYFORM0 k=0 c k u k be a monic complex polynomial and factor it as F (u) = (u − a 1 )(u − a 2 ) · · · (u − a N ) with a k ∈ C some ordering of the roots. Then, for every ε > 0 there exists δ > 0 such that every polynomial DISPLAYFORM1 Proof. This is a reformulation of the well-known continuity result, a proof of which can be found, for example, inĆurgus & Mascioni (2006) . One notes that, to first order in a small shift in the coefficients of a polynomial, the shift of the zeros can be found by a single step of Newton-Raphson iteration, except at higher-degree zeros (where the derivative of the polynomial in the denominator also has a zero).We can now prove the Proposition. DISPLAYFORM2 We already observed that L(Ẑ, Z) 2 = 0 if and only ifẐ = σ(Z) for some σ ∈ S N . Now assume L(Ẑ , Z) 2 = 0. To see thatẐ can not be a local minimum, we need to show that for any ε > 0 there DISPLAYFORM3 To construct such a Z , we define the polynomial Q λ : C → C, DISPLAYFORM4 which linearly interpolates between PẐ and P Z . Note that Q λ is monic for λ ∈ [0, 1] and Q 0 = PẐ. Let Z λ be some ordering of the roots of Q λ . Then DISPLAYFORM5 Since we assumed L(Ẑ, Z) > 0, this means that L(Z λ , Z) < L(Ẑ, Z) for any λ > 0. It remains to show that for any ε > 0 there is λ ε > 0 and a permutation σ such that d(Ẑ, σ(Z λε )) < ε. However, since the coefficients of Q λ continuously depend on λ, this follows as a simple consequence of Lemma 1.",998,0.492,576,1.7326388888888888,"We introduce an analytic distance function moderately sized point sets known cardinality that shown very desirable properties both as machine learning applications We compare our novel construction other point set distance functions proof training end on point set prediction tasks such object detection Parametric machine learning models routinely trained empirical risk minimization If we aim predict an output y �� Y from collect a training set D of ( pairs train h �� : X by minimizing DISPLAYFORM0 Here L : assigns a scalar loss value the prediction�� = h �� the true value Classical machine learning problems allow standard choices the loss function for regression problems where y,�� �� R it common the squared loss L y 2 .Assume , however train which-given some inputpredicts points In particular , the ordering the points neither semantically in across data instances As , one may an object detection task finding the positions the black stones Nine Men's Morris What should the loss function such a case?Naively just impose an arbitrary ordering to the sets treat ordered tuples However conceals an important property the task the permutation invariance from our machine learning system This property might in crucial learn such a task efficiently Instead would our loss function define a meaningful distance two sets, requires such a loss permutation We discussed a novel point set loss function analytic everywhere visvis two other simple alternatives with matching computational complexity for point set prediction tasks as alternatives more involved approaches BID3 BID2 . Proof concept experiments showed end training such simple loss functions point set prediction tasks object detection We expect simple constructions the ""holographic"" point set distance introduced may turn useful not point set predictions as, example encourage ( to align its clusters the clusters found an earlier version We will need the following Lemma, states the roots continuously depend DISPLAYFORM0 k=0 c k u k be a monic complex polynomial and factor it Fu − a 1 · · with some ordering the roots Then for every �� > there such every DISPLAYFORM1 Proof. This a reformulation the well-known continuity result a proof which,��urgus & Mascioni2006 One notes to first order in a small shift the coefficients the shift can found a single step Newton-Raphson iteration except at higher-degree zeros the derivative in also a zero).We prove the Proposition. DISPLAYFORM2 We already observed L(�, Z 2 if andZ for some �� �� S N Now assume L(� , Z 2 To see that��� can not a local minimum show for any �� > there DISPLAYFORM3 To construct such a Z , define the polynomial Q �� : C → C, which linearly P��� P Z Note Q �� monic for [ 0 P��. Let Z �� some ordering the roots Then DISPLAYFORM5 Since assumed L(���, Z > for It remains show for any �� > there such d(�(Z ��ε However since the coefficients Q �� continuously depend follows as Lemma",0.01,0.5707786896237296
"We introduce a hierarchical model for efficient placement of computational graphs onto hardware devices, especially in heterogeneous environments with a mixture of CPUs, GPUs, and other computational devices. Our method learns to assign graph operations to groups and to allocate those groups to available devices. The grouping and device allocations are learned jointly. The proposed method is trained with policy gradient and requires no human intervention. Experiments with widely-used
 computer vision and natural language models show that our algorithm can find optimized, non-trivial placements for TensorFlow computational graphs with over 80,000 operations. In addition, our approach outperforms placements by human
 experts as well as a previous state-of-the-art placement method based on deep reinforcement learning. Our method achieves runtime reductions of up to 60.6% per training step when applied to models such as Neural Machine Translation. Deep neural networks have been successfully applied to many practical problems, such as image classification BID20 BID19 BID32 BID29 , speech recognition BID9 , and machine translation BID28 BID1 BID36 . These successes have lead to a surge in demand for the computational resources needed to train and infer with neural networks. A common approach to addressing this demand is to use a distributed environment with a combination of CPUs and GPUs. In this environment, it is typical for a machine learning practitioner to explicitly place the operations of their neural network onto particular computing devices for model parallelism and data parallelism. For example, one might distribute the computation of the first layer in a translation network onto the first GPU and the computation of the second layer onto the second GPU BID28 BID36 . Although these decisions can be made by a human practitioner, such an approach does not scale well or produce optimal results, especially in the case of more complicated networks BID31 a) . Given the growing diversity of hardware devices (e.g., Google TPUs, Intel Nervana, etc.) and recent trends toward automated neural architecture search BID38 BID27 BID2 , where new models are generated, trained and evaluated in an entirely end-to-end fashion, it seems natural to move toward more automated solutions for efficiently distributing computation.Device placement can be framed as the problem of learning to partition a graph across available devices. Given that graph partitioning is a well-studied subject in computer science BID8 BID16 BID26 , traditional graph partitioning methods represent a natural baseline for automated device placement. We ran experiments using Scotch BID26 , a well-established open source library for graph partitioning, which includes optimizations such as k-way Fiduccia-Mattheyses BID8 , Multilevel methods BID3 BID11 BID15 , the Band Method BID5 , the Diffusion Method BID23 , and Dual Recursive Bipartitioning Mapping BID25 . The objective was to balance the computational load across a set of connected processing nodes, while colocating neighboring nodes to minimize communication cost. Despite its promise, this approach yielded disappointing results, likely due to the non-stationarity of the cost function. We target a distributed environment where we use a shared cluster of CPUs and GPUs, and our CPUs may also serve other jobs at the same time. Thus, while cost-based models such as BID21 provide a strong baseline for memory optimizations, since memory usage is deterministic, they cannot be directly applied to environments with dynamic costs.Using deep networks and reinforcement learning for combinatorial optimization has already been proposed BID33 BID4 BID22 . Recent work BID22 ) uses a recurrent neural network (RNN) policy network to predict the placement of operations in a computational graph, optimizing for speed of computation using policy gradient methods. While this approach outperforms traditional graph partitioning heuristics and human expert placements, it is prohibitively expensive for the RNN policy to learn when the number of operations is large. This method is therefore limited to small graphs (with fewer than 1000 nodes) and requires human experts to manually partition the graph into collocation groups as a pre-processing step in order to scale to larger graphs. We refer to the method in BID22 as ColocRL.In this paper, we propose a more flexible approach which learns to optimize device placement for training neural networks that have tens of thousands of operations with no need for manual grouping. Our method consists of a two-level hierarchical network, in which the first model groups the operations of the graph (the Grouper) and the second model places those groups onto devices (the Placer). The Grouper is a feed forward network which reads in information about each operation and its context within the graph, in order to predict the group to which that operation should be assigned. The Placer is a sequence-to-sequence model BID28 that reads in the embedding of the group and predicts the device placement for that group. The entire two-level network is trained jointly using reinforcement learning to optimize for speed of computation and for feasibility (e.g., having sufficient memory available on each device for the computation assigned). Unlike the previous work, our method is end-to-end and does not require human experts to manually group operations as a pre-processing step, making it a fully automated solution to optimizing device placement.Our main result is that our model effectively handles very large graphs and finds non-trivial placements on multiple devices for models such as Inception-V3 BID31 , ResNet BID10 , Language Modeling BID14 , and Neural Machine Translation BID36 . The placements found by our model outperform TensorFlow's default placements BID0 , the Scotch algorithm's placements, and human expert placements, as well as those of ColocRL BID22 ). Our results demonstrate that the proposed approach learns the properties of the environment, including the complex tradeoff between computation and communication in hardware. For example, on a Neural Machine Translation model, our method achieves a 60.6% reduction in training time per iteration. In this paper, we present a hierarchical method for efficiently placing the operations of a computational graph onto devices. Our approach consists of a hierarchical model that first assigns the operations to groups and then places those groups onto devices. We use a policy gradient method to optimize the parameters of the planner. The proposed method enables us to scale to computational graphs containing over 80,000 operations. Unlike previous work, our method is end-to-end and requires no manual effort. On a range of tasks including image classification, language modeling, and machine translation, our method surpasses placements designed by human experts as well as those of previous state-of-the-art deep RL methods. Our approach finds highly granular parallelism within the graph, enabling us to outperform prior methods by up to 60.6%.",1316,0.657,764,1.7225130890052356,"We introduce a hierarchical model efficient placement computational graphs onto hardware devices especially a mixture CPUs Our method learns assign graph operations groups allocate available devices The grouping and device allocations learned jointly The proposed method trained policy gradient requires Experiments widely-used computer vision natural language models our algorithm find optimized, non-trivial placements TensorFlow computational graphs with over 80,000 operations In addition our approach outperforms placements human experts as a previous state placement method based deep reinforcement learning Our method achieves runtime reductions training step when models such Neural Machine Translation Deep neural networks successfully many practical problems BID20 BID19 , speech machine These successes lead the computational resources train infer with neural networks A common approach addressing this demand a distributed environment a combination CPUs it typical a machine learning practitioner explicitly place the operations onto particular computing devices for model parallelism For example one distribute the computation the first layer a translation network onto the first GPU the second GPU BID28 BID36 Although these decisions can a human practitioner scale or produce more complicated networks BID31 a . Given the growing diversity hardware devices Intel Nervana recent trends toward automated neural architecture search BID38 BID27 , where new models generated trained evaluated entirely end natural move efficiently distributing computationDevice placement framed the problem learning partition across available devices Given that graph partitioning computer science BID8 BID16 BID26 , represent a natural baseline automated device placement We ran experiments Scotch BID26 , graph partitioning includes optimizations such k-way Fiduccia-Mattheyses BID8 Multilevel methods the Band Method Diffusion Dual Recursive The objective balance the computational load across connected processing nodes while colocating neighboring nodes communication cost Despite its promise this approach yielded likely nonstationarity the cost function We target a distributed environment use a shared cluster CPUs our CPUs may also serve other jobs at Thus while cost-based models such BID21 provide memory optimizations since deterministic directly environments dynamic costsUsing deep networks for has already BID33 BID4 BID22 . Recent work BID22 ) usesRNN) policy network the placement operations a computational graph optimizing speed of using policy gradient methods While this approach outperforms traditional graph partitioning heuristics and human expert placements the RNN policy learn when the number operations This method therefore limited small graphswith fewer than 1000 nodes requires human experts manually partition collocation groups as in scale We refer the method in BID22 ColocRL.In propose which learns optimize device placement training that operations with no need manual grouping Our method consists a two-level hierarchical network in the first model groups the operations the graphthe Grouper places those groups onto devicesthe Placer The Grouper a feed forward network which reads in information each operation its context within in predict the group to The Placer sequence-to model BID28 reads in the embedding of the group and predicts the device placement The entire two-level network trained jointly using reinforcement learning optimize for speed computation for feasibility ( having sufficient memory on assigned Unlike the previous work our method end human experts manually group operations as making fully solution optimizing device placementOur main result effectively handles very large graphs finds for models such Inception-V3 BID31 , ResNet BID10 Language Modeling BID14 The placements found our model outperform TensorFlow default placements BID0 , the Scotch algorithm's placements human expert placements ColocRL BID22 Our results demonstrate the proposed approach learns the properties the environment the complex tradeoff computation communication in hardware For example on a Neural Machine Translation model our method achieves per iteration In this paper a hierarchical method efficiently placing the operations a computational graph devices Our approach consists a hierarchical model first assigns the operations groups places onto devices We use a policy gradient method optimize the parameters the planner The proposed method enables us scale to computational graphs containing Unlike previous work our method end On a range tasks image classification language modeling our method surpasses placements designed human experts as previous state deep RL methods Our approach finds highly granular parallelism within the graph enabling outperform prior methods",0.01,0.5449790411632314
"Motion is an important signal for agents in dynamic environments, but learning to represent motion from unlabeled video is a difficult and underconstrained problem. We propose a model of motion based on elementary group properties of transformations and use it to train a representation of image motion. While most methods of estimating motion are based on pixel-level constraints, we use these group properties to constrain the abstract representation of motion itself. We demonstrate that a deep neural network trained using this method captures motion in both synthetic 2D sequences and real-world sequences of vehicle motion, without requiring any labels. Networks trained to respect these constraints implicitly identify the image characteristic of motion in different sequence types. In the context of vehicle motion, this method extracts information useful for localization, tracking, and odometry. Our results demonstrate that this representation is useful for learning motion in the general setting where explicit labels are difficult to obtain. Motion perception is a key component of biological and computer vision. By understanding how a stream of images reflects the motion of the world around it, an agent can better judge how to act. For example, a fly can use visual motion cues to dodge an approaching hand and to distinguish this threat from a looming landing surface BID21 ). Motion is an important cue for understanding actions and predicting 3D scene structure, and it has been extensively studied from computational, ethological, and biological perspectives BID10 ).In computer vision, the problem of motion representation has typically been approached from either a local or global perspective. Local representations of motion are exemplified by optical flow. Flow represents image motion as the 2D displacement of individual pixels of an image, giving rich low-level detail while foregoing a compact representation of the underlying scene motion. In contrast , global representations such as those used in visual odometry attempt to compactly explain the movement of the whole scene. Such representations typically rely on a rigid world assumption, thus limiting their applicability to more general settings.Image transformations due to motion form a subspace of all continuous image transformations. Smooth changes in the motion subspace correspond to sequences of images with realistic motion. We wish to characterize this subspace. The motion subspace differs from other image transformation subspaces, such as changes in the space of images of human faces. Smooth changes in this space also form a subspace of image transformations, but one containing transformations that do not occur in natural image sequences, such as the face of one person transforming into the face of another. A representation that characterizes motion should be sensitive to the distinction between image transformations that are realistic (produced by image motion) vs. those that are unrealistic (not produced by image motion).To be useful for understanding and acting on scene motion, a representation should capture the motion of the observer and all relevant scene content. Supervised training of such a representation is challenging: explicit motion labels are difficult to obtain, especially for nonrigid scenes where it can be unclear how the structure and motion of the scene should be decomposed. We propose a framework for learning global, nonrigid motion representations without labels. While most methods of representing motion rely on pixel-level reconstruction or correspondence to guide learning, our method constrains the representation itself by directly addressing the properties of the latent motion space.Motion has several properties that we use to operationalize to what extent a model characterizes it.(1) A model of motion can be read out to estimate metric properties of the motion in the scene, such as the camera translation and rotation. (2) A model of motion should represent the same motion identically regardless of the image content. For example, the motion of an object moving to the right should be represented the same whether the object is a cat or a dog. (3) A model of motion should distinguish sequences produced by natural motion from sequences with image transitions not produced by natural motion, such as cuts.Here, we present a general model of visual motion and describe how the group properties of visual motion can be used to constrain learning in this model (Figure 1) . We enforce the group properties of associativity and invertibility during training using a metric learning approach BID3 ) on recomposed sequences. We describe how this technique can be used to train a deep neural network to represent the motion in image sequences of arbitrary length in a low-dimensional, global fashion. We present evidence that the learned representation captures the global structure of motion in both 2D and 3D settings without labels, hard-coded assumptions about the scene, or explicit feature matching. DISPLAYFORM0 Figure 1: (a) A graphical model describing the relationship between the latent scene structure {S t }, motion {M t }, and the observed images of a sequence. We describe a method for learning a representation M of the motion space M from observed image sequences {I t }. (b) By recomposing sequences of images to satisfy the group properties of associativity and invertibility, we construct pairs of image sequences with equivalent motion. We use these properties to learn an approximate group homomorphism Φ ∈ M between motion in the world and in an embedding. We have presented a new model of motion and a method for learning motion representations. We have shown that enforcing group properties of motion is sufficient to learn a representation of image motion. These results suggest that this representation is able to generalize between scenes with disparate content and motion to learn a motion state representation useful for navigation, prediction, and other behavioral tasks relying on motion. Because of the wide availability of unlabeled video sequences in many settings, we expect our framework to be useful for generating better global motion representations in a variety of real-world tasks.",1121,0.627,651,1.7219662058371736,"Motion is an important signal agents dynamic environments learning represent from unlabeled video We propose motion based elementary group properties transformations use train a representation image motion While most methods estimating motion pixel-level constraints these group properties the abstract representation itself We demonstrate trained using this method captures motion both synthetic 2D sequences vehicle motion any labels Networks trained respect these constraints implicitly identify the image characteristic motion different sequence types In vehicle motion this method extracts useful localization tracking odometry Our results demonstrate this representation useful learning motion the general setting explicit labels difficult Motion perception biological and computer vision By understanding a stream images reflects an agent judge act For example a fly can use visual motion cues dodge an approaching hand distinguish this threat a looming landing surface BID21 ). Motion is an important cue understanding actions predicting 3D scene structure extensively from computational, ethological, and biological perspectives BID10 ).In computer vision the problem motion representation typically approached Local representations motion exemplified optical flow Flow represents image motion the 2D displacement individual pixels giving rich low-level detail while foregoing a compact representation the underlying scene motion In contrast , global representations such visual odometry attempt compactly explain the whole scene Such representations typically rely a rigid world assumption thus limiting more general settingsImage transformations due motion form all continuous image transformations Smooth changes the motion subspace correspond sequences images realistic motion We wish characterize this subspace The motion subspace differs other image transformation subspaces changes human faces Smooth changes this space also form image transformations one containing transformations natural image sequences the face transforming A representation that characterizes motion should sensitive the distinction image transformations realisticproduced image motion those unrealistic (not produced image motion).To useful understanding acting scene motion a representation capture all relevant scene content Supervised training such a representation challenging: explicit motion labels obtain nonrigid scenes unclear the structure motion decomposed We propose learning global, nonrigid motion representations without labels While most methods representing motion rely pixel-level reconstruction or correspondence guide learning our method itself directly addressing the latent motion spaceMotion has operationalize to what extent a model characterizes it.(1 read out estimate metric properties in the camera translation (2) A model motion should represent identically regardless the image content For example the motion moving to should represented the whether a cat (3) A model motion should distinguish sequences produced natural motion with image transitions not cutsHere visual motion the group properties learning () We enforce the group properties associativity invertibility during training using a metric learning approach BID3 ) on recomposed sequences We describe this technique train represent the motion image sequences arbitrary length We present the learned representation captures the global structure motion without labels hard-coded assumptions the scene explicit feature matching DISPLAYFORM0 Figure describing the latent scene structure {S t motion { the observed images a sequence. We describe learning a representation M the motion space M observed image sequences {I t. (b By recomposing sequences images satisfy the group properties associativity we construct pairs equivalent motion We use these properties learn an approximate group homomorphism �� �� M between motion in an embedding. We presented motion a method learning motion representations We shown enforcing group properties of motion sufficient learn a representation image motion These results this representation able generalize between scenes disparate content motion to learn a motion state representation useful navigation prediction other behavioral tasks relying Because unlabeled video sequences many settings expect our framework useful generating better global motion representations",0.01,0.5435856308996393
"This paper introduces the concept of continuous convolution to neural networks and deep learning applications in general. Rather than directly using discretized information, input data is first projected into a high-dimensional Reproducing Kernel Hilbert Space (RKHS), where it can be modeled as a continuous function using a series of kernel bases. We then proceed to derive a closed-form solution to the continuous convolution operation between two arbitrary functions operating in different RKHS. Within this framework, convolutional filters also take the form of continuous functions, and the training procedure involves learning the RKHS to which each of these filters is projected, alongside their weight parameters. This results in much more expressive filters, that do not require spatial discretization and benefit from properties such as adaptive support and non-stationarity. Experiments on image classification are performed, using classical datasets, with results indicating that the proposed continuous convolutional neural network is able to achieve competitive accuracy rates with far fewer parameters and a faster convergence rate. In recent years, convolutional neural networks (CNNs) have become widely popular as a deep learning tool for addressing various sorts of problems, most predominantly in computer vision, such as image classification BID22 BID17 , object detection BID30 and semantic segmentation BID8 . The introduction of convolutional filters produces many desirable effects, including: translational invariance, since the same patterns are detected in the entire image; spatial connectivity, as neighboring information is taken into consideration during the convolution process; and shared weights, which results in significantly fewer training parameters and smaller memory footprint.Even though the convolution operation is continuous in nature BID19 , a common assumption in most computational tasks is data discretization, since that is usually how information is obtained and stored: 2D images are divided into pixels, 3D point clouds are divided into voxels, and so forth. Because of that, the exact convolution formulation is often substituted by a discrete approximation BID4 , calculated by sliding the filter over the input data and calculating the dot product of overlapping areas. While much simpler to compute, it requires substantially more computational power, especially for larger datasets and filter sizes BID28 . The fast Fourier transform has been shown to significantly increase performance in convolutional neural network calculations BID18 BID32 , however these improvements are mostly circumstantial, with the added cost of performing such transforms, and do not address memory requirements.To the best of our knowledge, all versions of CNNs currently available in the literature use this discrete approximation to convolution, as a way to simplify calculations at the expense of a potentially more descriptive model. In BID24 a sparse network was used to dramatically decrease computational times by exploiting redundancies, and in BID11 spatial sparseness was exploited to achieve state-of-the-art results in various image classification datasets. Similarly, BID31 used octrees to efficiently partition the space during convolution, thus focusing memory allocation and computation to denser regions. A quantized version was proposed in BID40 to improve performance on mobile devices, with simultaneous computational acceleration and model compression. A lookup-based network is described in BID0 , that encodes convolution as a series of lookups to a dictionary that is trained to cover the observed weight space. This paper takes a different approach and introduces the concept of continuous convolution to neural networks and deep learning applications in general. This is achieved by projecting information into a Reproducing Kernel Hilbert Space (RKHS) BID33 , in which point evaluation takes the form of a continuous linear functional. We employ the Hilbert Maps framework, initially described in BID29 , to reconstruct discrete input data as a continuous function, based on the methodology proposed in BID12 . Within this framework, we derive a closed-form solution to the continuous convolution between two functions that takes place directly in this high-dimensional space, where arbitrarily complex patterns are represented using a series of simple kernels, that can be efficiently convolved to produce a third RKHS modeling activation values. Optimizing this neural network involves learning not only weight parameters, but also the RKHS that defines each convolutional filter, which results is much more descriptive feature maps that can be used for both discriminative and generative tasks. The use of high-dimensional projection, including infinite-layer neural networks BID15 ; BID9 , has been extensively studied in recent times, as a way to combine kernel-based learning with deep learning applications. Note that, while works such as BID26 and BID25 take a similar approach of projecting input data into a RKHS, using the kernel trick, it still relies on discretized image patches, whereas ours operates solely on data already projected to these highdimensional spaces. Also, in these works extra kernel parameters are predetermined and remain fixed during the training process, while ours jointly learns these parameters alongside traditional weight values, thus increasing the degrees of freedom in the resulting feature maps.The proposed technique, entitled Continuous Convolutional Neural Networks (CCNNs), was evaluated in an image classification context, using standard computer vision benchmarks, and achieved competitive accuracy results with substantially smaller network sizes. We also demonstrate its applicability to unsupervised learning, by describing a convolutional auto-encoder that is able to produce latent feature representations in the form of continuous functions, which are then used as initial filters for classification using labeled data. This paper introduced a novel technique for data representation that takes place in a highdimensional Reproducing Kernel Hilbert Space (RKHS), where arbitrarily complex functions can be approximated in a continuous fashion using a series of simple kernels. We show how these kernels can be efficiently convolved to produce approximations of convolution results between two functions in different RKHS, and how this can be applied in an image classification scenario, via the introduction of a novel deep learning architecture entitled Continuous Convolutional Neural Networks (CCNN). Experimental tests using standard benchmark datasets show that this proposed architecture is able to achieve competitive results with much smaller network sizes, by focusing instead on more descriptive individual filters that are used to extract more complex patterns. Although promising, there are still several potential improvements that are left for future work, such as: RKHS sparsification, so only a subset of clusters are used for feature vector calculation, which would greatly improve computational speed and memory requirements; different learning rates and optimization strategies for each class of parameter (cluster location, length-scale and weight), to improve convergence rates; and the use of different kernels for feature vector representation, as a way to encode different properties in the resulting feature maps.",1288,0.541,776,1.6597938144329898,"This paper introduces continuous convolution to deep learning applications Rather directly using discretized information input data first projected a high-dimensional Reproducing Kernel Hilbert SpaceRKHS modeled using kernel bases We then proceed derive a closed-form solution the continuous convolution operation between two arbitrary functions operating different RKHS Within this framework convolutional filters also take continuous functions the training procedure involves learning the RKHS to which projected alongside their weight parameters This results much more expressive filters that do spatial discretization benefit properties adaptive support non Experiments image classification performed, classical datasets results indicating the proposed continuous convolutional neural network achieve competitive accuracy rates with far fewer parameters In convolutional neural networks widely addressing various sorts most predominantly such BID22 BID17 , semantic The introduction convolutional filters produces many desirable effects translational invariance since the same patterns detected the entire image; spatial connectivity neighboring information taken during shared weights results significantly fewer training parameters smaller memory footprintEven continuous in BID19 , a common assumption most computational tasks data discretization since that usually how information obtained: 2D images divided pixels 3D point clouds divided Because that the exact convolution formulation often substituted a discrete approximation BID4 , calculated sliding the filter calculating overlapping areas While much simpler compute requires especially larger datasets filter sizes BID28 . The fast Fourier transform shown significantly performance BID18 BID32 , however these improvements mostly the added cost performing such transforms, do address memory requirementsTo the all versions CNNs currently the literature use this discrete approximation, as simplify calculations at a potentially more descriptive model In BID24 a sparse network dramatically computational times exploiting redundancies BID11 spatial sparseness exploited achieve state results various image classification datasets Similarly BID31 used octrees efficiently partition during convolution thus focusing memory allocation computation to denser regions A quantized version was proposed BID40 to performance simultaneous computational acceleration model compression A lookup-based network described BID0 , that encodes convolution as lookups to a dictionary that trained cover the observed weight space This paper takes introduces continuous convolution to deep learning applications This achieved projecting information a Reproducing Kernel Hilbert SpaceRKHS BID33 , in point evaluation takes the form a continuous linear functional. We employ the Hilbert Maps framework initially described BID29 , reconstruct discrete input data as based the methodology proposed Within this framework derive a closed-form solution the continuous convolution between takes place directly arbitrarily complex patterns simple kernels that efficiently a third RKHS modeling activation values Optimizing this neural network involves not only weight parameters the RKHS that defines each convolutional filter results is much more descriptive feature maps that generative tasks The use high-dimensional projection, including infinitelayer neural BID15 ; extensively recent times combine kernel-based learning Note, while works such BID26 take of projecting input data a RKHS using the kernel trick still relies discretized image patches whereas ours operates solely data already projected these highdimensional spaces Also in these works extra kernel parameters predetermined remain fixed during the training process while ours jointly learns alongside traditional weight values thus the degrees the resulting feature mapsThe proposed technique, entitled evaluated an image classification context standard computer vision benchmarks achieved competitive accuracy results substantially smaller network sizes We also demonstrate its applicability by describing a convolutional auto-encoder produce latent feature representations continuous functions initial filters classification using labeled data This paper introduced data representation takes place a highdimensional Reproducing Kernel Hilbert Space arbitrarily complex functions simple kernels We show these kernels efficiently convolved convolution results between two functions in different RKHS, an image classification scenario, via the introduction a novel deep learning architecture entitled Experimental tests using standard benchmark datasets show this proposed architecture able competitive results much smaller network sizes by focusing instead more descriptive individual filters used extract more complex patterns Although promising there several potential improvements left future work RKHS sparsification so only a subset clusters used feature vector calculation which greatly computational speed and memory requirements; different learning rates optimization each class parameter (cluster location length-scale weight to convergence rates the different kernels feature vector representation encode different properties the resulting feature maps",0.01,0.3851758400083613
"Convolutional Neural Networks (CNNs) are commonly thought to recognise objects by learning increasingly complex representations of object shapes. Some recent studies suggest a more important role of image textures. We here put these conflicting hypotheses to a quantitative test by evaluating CNNs and human observers on images with a texture-shape cue conflict. We show that ImageNet-trained CNNs are strongly biased towards recognising textures rather than shapes, which is in stark contrast to human behavioural evidence and reveals fundamentally different classification strategies. We then demonstrate that the same standard architecture (ResNet-50) that learns a texture-based representation on ImageNet is able to learn a shape-based representation instead when trained on 'Stylized-ImageNet', a stylized version of ImageNet. This provides a much better fit for human behavioural performance in our well-controlled psychophysical lab setting (nine experiments totalling 48,560 psychophysical trials across 97 observers) and comes with a number of unexpected emergent benefits such as improved object detection performance and previously unseen robustness towards a wide range of image distortions, highlighting advantages of a shape-based representation. How are Convolutional Neural Networks (CNNs) able to reach impressive performance on complex perceptual tasks such as object recognition (Krizhevsky et al., 2012) and semantic segmentation (Long et al., 2015) ? One widely accepted intuition is that CNNs combine low-level features (e.g. edges) to increasingly complex shapes (such as wheels, car windows) until the object (e.g. car) can be readily classified. As Kriegeskorte (2015) puts it, ""the network acquires complex knowledge about the kinds of shapes associated with each category. [...] High-level units appear to learn representations of shapes occurring in natural images"" (p. 429). This notion also appears in other explanations, such as in LeCun et al. (2015) : Intermediate CNN layers recognise ""parts of familiar objects, and subsequent layers [...] detect objects as combinations of these parts"" (p. 436). We term this explanation the shape hypothesis.This hypothesis is supported by a number of empirical findings. Visualisation techniques like Deconvolutional Networks (Zeiler & Fergus, 2014) often highlight object parts in high-level CNN features. 1 Moreover, CNNs have been proposed as computational models of human shape perception by Kubilius et al. (2016) , who conducted an impressive number of experiments comparing human and CNN shape representations and concluded that CNNs ""implicitly learn representations of shape that reflect human shape perception"" (p. 15). Ritter et al. (2017) discovered that CNNs develop a so-called ""shape bias"" just like children, i.e. that object shape is more important than colour for object classification (although see BID15 for contrary evidence). Furthermore, CNNs are currently the most predictive models for human ventral stream object recognition (e.g. BID2 BID2 ; and it is well-known that object shape is the single most important cue for human object recognition (Landau et al., 1988) , much more than other cues like size or texture (which may explain the ease at which humans recognise line drawings or millennia-old cave paintings).On the other hand, some rather disconnected findings point to an important role of object textures for CNN object recognition. CNNs can still classify texturised images perfectly well, even if the global shape structure is completely destroyed BID1 . Conversely , standard CNNs are bad at recognising object sketches where object shapes are preserved yet all texture cues are missing BID0 . Additionally , two studies suggest that local information such as textures may actually be sufficient to ""solve"" ImageNet object recognition: BID6 discovered that a linear classifier on top of a CNN's texture representation (Gram matrix) achieves hardly any classification performance loss compared to original network performance. More recently , BID1 demonstrated that CNNs with explicitly constrained receptive field sizes throughout all layers are able to reach surprisingly high accuracies on ImageNet, even though this effectively limits a model to recognising small local patches rather than integrating object parts for shape recognition. Taken together , it seems that local textures indeed provide sufficient information about object classes-ImageNet object recognition could, in principle, be achieved through texture recognition alone. In the light of these findings, we believe that it is time to consider a second explanation, which we term the texture hypothesis: in contrast to the common assumption, object textures are more important than global object shapes for CNN object recognition.Resolving these two contradictory hypotheses is important both for the deep learning community (to increase our understanding of neural network decisions) as well as for the human vision and neuroscience communities (where CNNs are being used as computational models of human object recognition and shape perception). In this work we aim to shed light on this debate with a number of carefully designed yet relatively straightforward experiments. Utilising style transfer BID7 , we created images with a texture-shape cue conflict such as the cat shape with elephant texture depicted in Figure 1c . This enables us to quantify texture and shape biases in both humans and CNNs. To this end, we perform nine comprehensive and careful psychophysical experiments comparing humans against CNNs on exactly the same images, totalling 48,560 psychophysical trials across 97 observers. These experiments provide behavioural evidence in favour of the texture hypothesis: A cat with an elephant texture is an elephant to CNNs, and still a cat to humans. Beyond quantifying existing biases, we subsequently present results for our two other main contributions: changing biases, and discovering emergent benefits of changed biases. We show that the texture bias in standard CNNs can be overcome and changed towards a shape bias if trained on a suitable data set. Remarkably, networks with a higher shape bias are inherently more robust to many different image distortions (for some even reaching or surpassing human performance, despite never being trained on any of them) and reach higher performance on classification and object recognition tasks. DISPLAYFORM0 As noted in the Introduction, there seems to be a large discrepancy between the common assumption that CNNs use increasingly complex shape features to recognise objects and recent empirical findings which suggest a crucial role of object textures instead. In order to explicitly probe this question, we utilised style transfer BID7 to generate images with conflicting shape and texture information. On the basis of extensive experiments on both CNNs and human observers in a controlled psychophysical lab setting, we provide evidence that unlike humans, ImageNet-trained CNNs tend to classify objects according to local textures instead of global object shapes. In combination with previous work which showed that changing other major object dimensions such as colour BID10 and object size relative to the context (Eckstein et al., 2017) do not have a strong detrimental impact on CNN recognition performance, this highlights the special role that local cues such as textures seem to play in CNN object recognition.Intriguingly, this offers an explanation for a number of rather disconnected findings: CNNs match texture appearance for humans (Wallis et al., 2017) , and their predictive power for neural responses along the human ventral stream appears to be largely due to human-like texture representations, but not human-like contour representations (Laskar et al., 2018; Long & Konkle, 2018) . Furthermore, texture-based generative modelling approaches such as style transfer BID7 , single image super-resolution BID12 as well as static and dynamic texture synthesis BID6 BID5 all produce excellent results using standard CNNs, while CNNbased shape transfer seems to be very difficult BID11 . CNNs can still recognise images with scrambled shapes BID1 ), but they have much more difficulties recognising objects with missing texture information BID0 Yu et al., 2017) . Our hypothesis might also explain why an image segmentation model trained on a database of synthetic texture images transfers to natural images and videos (Ustyuzhaninov et al., 2018) . Beyond that, our results show marked behavioural differences between ImageNet-trained CNNs and human observers. While both human and machine vision systems achieve similarly high accuracies on standard images BID10 , our findings suggest that the underlying classification strategies might actually be very different. This is problematic, since CNNs are being used as computational models for human object recognition (e.g. BID2 BID2 .In order to reduce the texture bias of CNNs we introduced Stylized-ImageNet (SIN), a data set that removes local cues through style transfer and thereby forces networks to go beyond texture recognition. Using this data set, we demonstrated that a ResNet-50 architecture can indeed learn to recognise objects based on object shape, revealing that the texture bias in current CNNs is not by design but induced by ImageNet training data. This indicates that standard ImageNet-trained models may be taking a ""shortcut"" by focusing on local textures, which could be seen as a version of Occam's razor: If textures are sufficient, why should a CNN learn much else? While texture classification may be easier than shape recognition, we found that shape-based features trained on SIN generalise well to natural images.Our results indicate that a more shape-based representation can be beneficial for recognition tasks that rely on pre-trained ImageNet CNNs. Furthermore , while ImageNet-trained CNNs generalise poorly towards a wide range of image distortions (e.g. BID3 BID9 , our ResNet-50 trained on Stylized-ImageNet often reaches or even surpasses human-level robustness (without ever being trained on the specific image degradations). This is exciting because BID10 showed that networks trained on specific distortions in general do not acquire robustness against other unseen image manipulations. This emergent behaviour highlights the usefulness of a shape-based representation: While local textures are easily distorted by all sorts of noise (including those in the real world, such as rain and snow), the object shape remains relatively stable. Furthermore, this finding offers a compellingly simple explanation for the incredible robustness of humans when coping with distortions: a shape-based representation. In summary, we provided evidence that machine recognition today overly relies on object textures rather than global object shapes as commonly assumed. We demonstrated the advantages of a shapebased representation for robust inference (using our Stylized-ImageNet data set 5 to induce such a representation in neural networks). We envision our findings as well as our openly available model weights, code and behavioural data set (49K trials across 97 observers) 6 to achieve three goals: Firstly, an improved understanding of CNN representations and biases. Secondly, a step towards more plausible models of human visual object recognition. Thirdly, a useful starting point for future undertakings where domain knowledge suggests that a shape-based representation may be more beneficial than a texture-based one. We would like to thank Dan Hendrycks for providing the results of We followed the paradigm of Geirhos et al. (2018) for maximal comparability. A trial consisted of 300 ms presentation of a fixation square and a 200 ms presentation of the stimulus image, which was followed by a full-contrast pink noise mask (1/f spectral shape) of the same size lasting for 200 ms. Participants had to choose one of 16 entry-level categories by clicking on a response screen shown for 1500 ms. On this screen, icons of all 16 categories were arranged in a 4 × 4 grid. The experiments were not self-paced and therefore one trial always lasted 2200 ms (300 ms + 200 ms + 200 ms + 1500 ms = 2200 ms). The necessary time to complete an experiment with 1280 stimuli was 47 minutes, for 160 stimuli six minutes, and for 48 stimuli two minutes. In the experiments with 1280 trials, observers were given the possibility of taking a brief break after every block of 256 trials (five blocks in total).As preparation, participants were shown the response screen prior to an experiment and were asked to name all 16 categories in order to get an overview over the possible stimuli categories and to make sure that all categories were clear from the beginning. They were instructed to click on the category they believed was presented. Responses through clicking on a response screen could be changed within the 1500 ms response interval, only the last entered response was counted as the answer. Prior to the real experiment a practice session was performed for the participants to get used to the time course of the experiment and the position of category items on the response screen. This screen was shown for an additional 300 ms in order to provide feedback and indicate whether the entered answer was incorrect. In that case , a short low beep sound occurred and the correct category was highlighted by setting its background to white. The practice session consisted of 320 trials. After 160 trials the participants had the chance to take a short break. In the break, their performance of the first block was shown on the screen along the percentage of trials where no answer was entered. After the practice blocks, observers were shown an example image of the manipulation (not used in the experiment) to minimise surprise. Images used in the practice session were natural images from 16-class-ImageNet BID10 , hence there was no overlap with images or manipulations used in the experiments.",2682,1.311,1601,1.6752029981261711," commonly thought recognise learning increasingly complex representations object shapes Some recent studies image textures We here put these conflicting hypotheses a quantitative test evaluating CNNs human observers images with a texture-shape cue conflict We show ImageNet-trained CNNs strongly recognising textures rather shapes in human behavioural evidence reveals fundamentally different classification strategies We then demonstrate the same standard architecture (ResNet-50 learns a texture-based representation on instead when trained 'Stylized-ImageNet This provides human behavioural performance our well-controlled psychophysical lab settingnine experiments totalling 48,560 psychophysical trials across 97 observers comes unexpected emergent benefits such improved object detection performance previously unseen robustness towards image distortions highlighting advantages a shape-based representation How are reach impressive performance ( semantic segmentation One widely accepted intuition CNNs combine to increasingly complex shapessuch wheels car windows until ( readily classified As Kriegeskorte (2015 putsthe network acquires complex knowledge the kinds shapes associated each category [ High-level units appear learn representations shapes occurring natural images"" 429). This notion also other explanations in LeCun et (2015 : Intermediate CNN layers recognise ""parts familiar objects subsequent layers detect objects combinations 436). We term this explanation the shape hypothesisThis hypothesis Visualisation techniques likeZeiler & Fergus often highlight object parts high CNN features 1 Moreover CNNs proposed computational models human shape perception Kubilius et al (2016 , who conducted an impressive number comparing human and CNN shape representations concluded "" learn representations shape that reflect 15 Ritter et al (2017 discovered CNNs develop just children colour for object classificationalthough see BID15 contrary evidence Furthermore CNNs are currently the most predictive models human ventral stream object recognition ; and it well that object shapeLandau 1988) much size texturewhich the ease recognise line drawings millennia-old cave paintings).On some rather disconnected findings point object textures CNN object recognition CNNs can still classify texturised images perfectly the global shape structure completely destroyed BID1 . Conversely , standard CNNs bad recognising object sketches where object shapes preserved yet all texture cues BID0 Additionally , two studies local information such textures actually sufficient "" ImageNet object recognition: BID6 discovered a linear classifier top a CNN's texture representation (Gram matrix achieves hardly any classification performance loss original network performance More recently , BID1 demonstrated CNNs with explicitly constrained receptive field sizes throughout all layers reach ImageNet this effectively a model recognising small local patches rather integrating object parts for shape recognition Taken , local textures indeed sufficient information object classes-ImageNet object recognition could, achieved alone In the light a second explanation term the texture hypothesis in contrast object textures important global object shapes for CNN object recognitionResolving both (to increase neural network decisions the human vision and neuroscience communitieswhere CNNs being computational models shape perception In this work aim shed this debate with carefully designed yet relatively straightforward experiments Utilising style transfer BID7 , created images a texture-shape cue conflict such the cat shape with elephant texture depicted This enables quantify texture biases both humans CNNs To perform nine comprehensive and careful psychophysical experiments comparing humans against on totalling 48,560 psychophysical trials across 97 observers These experiments provide behavioural evidence in the texture hypothesis: A cat an elephant texture an elephant to CNNs still a cat humans Beyond quantifying existing biases subsequently present for our two other main contributions changing biases discovering emergent benefits changed biases We show the texture bias standard CNNs and changed towards a shape bias if trained networks a higher shape bias inherently robust many different image distortions some even reaching or human performance despite never trained reach classification and object recognition tasks DISPLAYFORM0 As noted seems the common assumption CNNs use increasingly complex shape features recognise objects recent empirical findings a crucial role object textures instead In order explicitly probe utilised style transfer BID7 generate images conflicting shape On extensive experiments both CNNs human observers a controlled psychophysical lab setting provide unlike humans ImageNet-trained CNNs tend classify objects local textures instead global object shapes In combination previous work which changing other major object dimensions such colour BID10 object size relative the contextEckstein 2017 do CNN recognition performance highlights local cues textures seemIntriguingly offers rather disconnected findings CNNs match texture appearance for humans (Wallis , their predictive power neural responses along the human ventral stream appears largely human-like texture representations human Long & Konkle Furthermore texture-based generative modelling approaches such style transfer BID7 , single image super-resolution BID12 as static texture synthesis all produce standard CNNs CNNbased shape transfer seems very difficult BID11 CNNs can still recognise images with scrambled shapes BID1 ), much more difficulties objects missing texture information BID0 Yu et) . Our hypothesis might also an image segmentation model trained a database synthetic texture transfers natural images videosUstyuzhaninov 2018 . Beyond our results marked behavioural differences ImageNet-trained CNNs human observers While both human and machine vision systems achieve standard images BID10 , the underlying classification strategies might actually very This problematic CNNs being computational models human object recognition BID2 BID2 .In order reduce the texture bias introduced Stylized-ImageNet removes local cues through style transfer thereby forces networks go texture recognition Using this data set demonstrated a ResNet-50 architecture indeed learn recognise objects based object shape revealing the texture bias current CNNs by induced ImageNet training data This indicates standard ImageNet-trained models may taking by focusing local textures seen a version Occam's razor If textures sufficient why a CNN learn much else While texture classification easier shape recognition shape-based features trained SIN generalise well natural imagesOur results beneficial recognition tasks pre-trained ImageNet CNNs Furthermore , while generalise poorly towards image distortionse.g. BID3 BID9 our ResNet-50 trained Stylized-ImageNet often reaches or even (without ever the specific image degradations This exciting because BID10 showed networks trained specific distortions general do acquire robustness against other unseen image manipulations This emergent behaviour highlights the usefulness a shape-based representation: While local textures easily distorted all sorts noise those rain the object shape remains relatively Furthermore this finding offers the incredible robustness humans when coping distortions: a shape-based representation. In summary provided machine recognition today overly object textures global object shapes as commonly We demonstrated the advantages a shapebased representation robust inference (using our Stylized-ImageNet data 5 to induce We envision our findings well our openly available model weights code behavioural data set (49K trials across 97 observers 6 achieve three goals CNN representations biases Secondly, a step towards more plausible models human visual object recognition Thirdly, a useful starting point future undertakings where domain knowledge suggests a shape-based representation beneficial texture We would Dan Hendrycks the results We followed the paradigm Geirhos et (2018 for maximal comparability A trial consisted 300 ms presentation a fixation square a full-contrast pink noise mask (1/f spectral shape of lasting Participants had 16 entry-level categories by clicking a response screen shown for 1500 ms On this screen icons all 16 categories were arranged The experiments not selfpaced therefore one trial always 2200 ms + The necessary time complete an experiment 1280 stimuli 47 minutes for 160 stimuli six In the experiments 1280 trials observers the possibility taking every block 256 trialsfive blocks total).As preparation shown the response screen prior name all 16 categories get over the possible stimuli categories clear from They instructed click the category they believed presented Responses through clicking a response screen could changed within the 1500 ms response interval only the last entered response Prior the real experiment a practice session performed get the time course the position category items the response screen This screen was shown an additional 300 ms provide feedback indicate the entered answer In that case , a short low beep sound occurred the correct category highlighted setting its background The practice session consisted 320 trials After 160 trials the participants take In the break their performance of the first block shown along the percentage trials no answer entered After the practice blocks observers shown an example image the manipulation (not used minimise surprise Images used the practice session natural images 16-class-ImageNet BID10 , hence there or manipulations",0.02,0.42443708622251103
"In this work, we exploited different strategies to provide prior knowledge to commonly used generative modeling approaches aiming to obtain speaker-dependent low dimensional representations from short-duration segments of speech data, making use of available information of speaker identities. Namely, convolutional variational autoencoders are employed, and statistics of its learned posterior distribution are used as low dimensional representations of fixed length short-duration utterances. In order to enforce speaker dependency in the latent layer, we introduced a variation of the commonly used prior within the variational autoencoders framework, i.e. the model is simultaneously trained for reconstruction of inputs along with a discriminative task performed on top of latent layers outputs. The effectiveness of both triplet loss minimization and speaker recognition are evaluated as implicit priors on the challenging cross-language NIST SRE 2016 setting and compared against fully supervised and unsupervised baselines.",176,0.076,102,1.7254901960784315,In this work exploited different strategies provide prior knowledge commonly aiming obtain speaker-dependent low dimensional representations from short-duration segments making available information of speaker identities Namely employed statistics its learned posterior distribution low dimensional representations fixed length short-duration utterances In enforce speaker dependency the latent layer introduced a variation commonly prior within is simultaneously trained reconstruction inputs along performed top latent layers outputs The effectiveness both triplet loss minimization speaker recognition evaluated as implicit priors challenging cross NIST SRE 2016 setting compared fully supervised and unsupervised baselines,0.0,0.552564448419967
"The importance-weighted autoencoder (IWAE) approach of Burda et al. defines a sequence of increasingly tighter bounds on the marginal likelihood of latent variable models. Recently, Cremer et al. reinterpreted the IWAE bounds as ordinary variational evidence lower bounds (ELBO) applied to increasingly accurate variational distributions. In this work, we provide yet another perspective on the IWAE bounds. We interpret each IWAE bound as a biased estimator of the true marginal likelihood where for the bound defined on $K$ samples we show the bias to be of order O(1/K). In our theoretical analysis of the IWAE objective we derive asymptotic bias and variance expressions. Based on this analysis we develop jackknife variational inference (JVI),
 a family of bias-reduced estimators reducing the bias to $O(K^{-(m+1)})$ for any given m < K while retaining computational efficiency. Finally, we demonstrate that JVI leads to improved evidence estimates in variational autoencoders. We also report first results on applying JVI to learning variational autoencoders.

 Our implementation is available at https://github.com/Microsoft/jackknife-variational-inference Variational autoencoders (VAE) are a class of expressive probabilistic deep learning models useful for generative modeling, representation learning, and probabilistic regression. Originally proposed in BID8 and BID22 , VAEs consist of a probabilistic model as well as an approximate method for maximum likelihood estimation. In the generative case, the model is defined as DISPLAYFORM0 where z is a latent variable, typically a high dimensional vector; the corresponding prior distribution p(z) is fixed and typically defined as a standard multivariate Normal distribution N (0, I). To achieve an expressive marginal distribution p(x), we define p θ (x|z) through a neural network, making the model (1) a deep probabilistic model.Maximum likelihood estimation of the parameters θ in (1) is intractable, but BID8 and BID22 propose to instead maximize the evidence lower-bound (ELBO), log p(x) ≥ E z∼qω(z|x) log p θ (x|z) p(z) q ω (z|x)=: L E .Here , q ω (z|x) is an auxiliary inference network, parametrized by ω. Simultaneous optimization of (2) over both θ and ω performs approximate maximum likelihood estimation in the model p(x) of FORMULA0 and forms the standard VAE estimation method. 1 The implementation is available at https://github.com/Microsoft/ jackknife-variational-inferenceIn practice L E is estimated using Monte Carlo: we draw K samples z i ∼ q ω (z|x), then use the unbiased estimatorL E of L E ,L DISPLAYFORM1 The VAE approach is empirically very successful but are there fundamental limitations? One limitation is the quality of the model p θ (x|z): this model needs to be expressive enough to model the true distribution over x. Another limitation is that L E is only a lower-bound to the true likelihood. Is this bound tight? It can be shown, BID8 , that when q(z|x) = p(z|x) we have L E = log p(x), hence (2) becomes exact. Therefore, we should attempt to choose an expressive class of distributions q(z|x) and indeed recent work has extensively investigated richer variational families. We discuss these methods in Section 7 but now review the importance weighted autoencoder (IWAE) method we build upon. In summary we proposed to leverage classic higher-order bias removal schemes for evidence estimation. Our approach is simple to implement, computationally efficient, and clearly improves over existing evidence approximations based on variational inference. More generally our jackknife variational inference debiasing formula can also be used to debias log-evidence estimates coming from annealed importance sampling.However, one surprising finding from our work is that using our debiased estimates for training VAE models did not improve over the IWAE training objective and this is surprising because apriori a better evidence estimate should allow for improved model learning.One possible extension to our work is to study the use of other resampling methods for bias reduction; promising candidates are the iterated bootstrap, the Bayesian bootstrap, and the debiasing lemma. These methods could offer further improvements on bias reduction or reduced variance, however, the key challenge is to overcome computational requirements of these methods or, alternatively, to derive key quantities analytically. 6 Application of the debiasing lemma in particular requires the careful construction of a truncation distribution and often produces estimators of high variance.While variance reduction plays a key role in certain areas of machine learning, our hope is that our work shows that bias reduction techniques are also widely applicable. DISPLAYFORM0 Note that only Y K is random in (28), all other quantities are constant. Therefore, by taking the expectation on the left and right side of FORMULA1 we obtain DISPLAYFORM1 The right hand side of FORMULA1 is expressed in terms of the central moments for i ≥ 2, DISPLAYFORM2 of Y K , whereas we are interested in an expression using the central moments i ≥ 2, DISPLAYFORM3 we denote the shared first non-central moment. Because Y K is a sample mean we can use existing results that relate γ i to µ i . In particular (Angelova, 2012, Theorem 1) gives the relations DISPLAYFORM4 DISPLAYFORM5 Expanding FORMULA1 to order five and using the relations FORMULA2 to FORMULA2 gives DISPLAYFORM6 Regrouping the terms by order of K produces the result (8).",1168,0.55,670,1.7432835820895523,"The importance-weighted autoencoderIWAE defines increasingly tighter bounds the marginal likelihood latent variable models Recently, Cremer et al reinterpreted the IWAE bounds ordinary variational evidence lower boundsELBO applied increasingly accurate variational distributions In this work provide yet another perspective the IWAE bounds We interpret each IWAE bound a biased estimator the true marginal likelihood where for bound defined on $ samples show to of In our theoretical analysis the IWAE objective we derive variance expressions Based this analysis develop jackknife variational inferenceJVI a family reducing $O(K^{-(m+1)})$ m < while computational efficiency Finally demonstrate JVI leads improved evidence estimates We also report first results applying JVI learning Our implementation availableVAE useful representation learning Originally proposed BID8 , VAEs consist as an approximate method In the generative case defined DISPLAYFORM0 where z typically a high dimensional vector; the corresponding prior distribution p(z fixed typically defined a standard multivariate Normal distribution N0 I To achieve an expressive marginal distribution p(x p �� through making (1 deepMaximum likelihood estimation BID8 and propose instead maximize the evidence lower-bound (ELBO log ≥ E z�qω(z|x log: L E .Here , q an auxiliary inference network Simultaneous optimization (2 over performs approximate maximum likelihood estimation the model p(x FORMULA0 forms the standard VAE estimation method 1 The implementation available https://github.com/Microsoft/ jackknife-variational-inferenceIn practice L E is estimated using Monte Carlo: we draw K samples z i ∼ q ��z|x the unbiased estimatorL E ofL DISPLAYFORM1 The VAE approach empirically very successful but are fundamental limitations One limitation p ��x|z needs expressive model the true distribution Another limitation L E lowerbound to the true likelihood Is bound tight It can shown BID8 , q(z|x we L E hence ( becomes exact Therefore attempt choose an expressive class distributions q(z|x indeed recent work extensively richer variational families We discuss these methods Section but now review weightedIWAE we build upon In summary we proposed leverage classic higher-order bias removal schemes evidence estimation Our approach to computationally clearly improves over existing evidence approximations based More generally our jackknife variational inference debiasing formula also debias log-evidence estimates coming annealed importance samplingHowever one surprising finding using training VAE models did improve over the IWAE training objective and this surprising apriori a better evidence estimate should allow improved model learningOne possible extension study bias reduction; promising candidates the iterated bootstrap These methods could offer further improvements bias reduction or reduced variance however overcome computational requirements or, derive key quantities 6 Application the debiasing lemma particular requires the careful construction a truncation distribution often produces estimators high varianceWhile variance reduction plays certain areas our hope shows bias reduction techniques widely DISPLAYFORM0 Note only Y K is random (28 all other quantities constant Therefore by taking the expectation on FORMULA1 we obtain DISPLAYFORM1 The right hand side expressed the central moments for i ≥ of Y K whereas we an expression using i we denote the shared first non-central moment Because Y K is a sample mean we existing results that relate �� i µ In particular (Angelova 2012 Theorem gives the relations DISPLAYFORM4 Expanding FORMULA1 order five and using gives Regrouping the terms by K produces8)",0.01,0.5979004326665012
"In this paper, we consider the problem of autonomous lane changing for self driving vehicles in a multi-lane, multi-agent setting. We present a framework that demonstrates a more structured and data efficient alternative to end-to-end complete policy learning on problems where the high-level policy is hard to formulate using traditional optimization or rule based methods but well designed low-level controllers are available. Our framework uses deep reinforcement learning solely to obtain a high-level policy for tactical decision making, while still maintaining a tight integration with the low-level controller, thus getting the best of both worlds. We accomplish this with Q-masking, a technique with which we are able to incorporate prior knowledge, constraints, and information from a low-level controller, directly in to the learning process thereby simplifying the reward function and making learning faster and data efficient. We provide preliminary results in a simulator and show our approach to be more efficient than a greedy baseline, and more successful and safer than human driving. In recent years, there has been a growing interest in self driving vehicles. Building such autonomous systems has been an active area of research BID23 BID27 BID3 for its high potential in leading to road networks that are much more safer and efficient. One of the fundamental skills a self driving vehicle must possess is an ability to perform lane change maneuvers, which is especially critical on a multi-lane highway in the presence fast moving traffic (as shown in FIG0 . A bad decision at best leads to congestion and at worst leads to accidents BID8 . Reasoning about interactions with other agents and forming an efficient long term strategy while maintaining safety makes this problem challenging and complex.Prior work on lane changing consists of a diverse set of approaches with early work considering vision based control BID21 . Other methods track trajectories BID14 BID19 , use fuzzy control BID6 , model predictive control BID5 , generate a steering command with adaptive control BID15 , consider planning BID23 BID26 , and mixed logic programming BID4 . However majority of the prior work considers the problem only from a local perspective, i.e. changing between adjacent lanes while avoiding the few neighboring vehicles. There is no notion of a goal, like reaching an exit, which would require reasoning about long term decisions on a strategic level when present on a multi-lane highway among traffic. Formulating a control or optimization based problem to handle such a scenario is not straight forward, would require a lot of hand design and tuning, may work only on a subset of cases, and would generally be intractable. The primary roadblock is that there is no abstraction of what the overall ideal policy should look like, only the ideal outcome is know: reaching the exit safely and efficiently (in least amount of time).Reinforcement learning provides a way to learn arbitrary policies giving specific goals. In recent years learning based methods have been used to address similar or related problems, like learning from human driving BID22 , inverse reinforcement learning BID18 , end-to-end methods that map perception inputs (mainly images) directly to control commands BID13 BID9 BID0 BID25 , and methods that understand the scene via learning to make driving decisions BID2 BID17 . Along these lines deep reinforcement learning has had great success in learning policies from raw sensor information BID12 .In this work, we investigate the use and place of deep reinforcement learning in solving the autonomous lane changing problem. In general learning a full policy than can reason about tactical decisions while at same time address continuous control and collision avoidance can be exceedingly difficult with large notorious to train networks. Thus, an ideal approach would strike the right balance by learning the hard to specify high-level tactical policy while relying on established optimization or rule based method for low-level control.We propose a framework that uses deep Q-learning to learn a high-level tactical decision making policy, and also introduce, Q-masking, a novel technique that forces the agent to explore and learn only a subspace of Q-values. This subspace is directly governed by a low-level module that consists of prior knowledge about the system, constraints of the problem, and information from the lowlevel controller. Not only does Q-masking provide the tight integration between the two paradigms: learning high-level policy and using low-level control, but also heavily simplifies the reward function and makes learning faster and data efficient. By relying on a controller for low-level decisions, we are also able to completely eliminate collisions during training or testing, which makes it a possibility to perform training directly on real systems. We present preliminary benchmarks and show that our framework can outperform a greedy baseline in terms of efficiency and humans driving in the simulator in terms of safety and success, while also generalizing to several unseen scenarios without any extra training. We proposed a framework that leverages the strengths of deep reinforcement learning for high-level tactical decision making, and traditional optimization or rule-based methods for low-level control, by striking the right balance between both domains. At the heart of this framework lies, Q-masking, that provides an interface between the two levels. Using Q-masking we are able to incorporate prior knowledge, constraints about the system and information from the lower-level controller, directly in to the training of the network, simplifying the reward function and making learning faster and more data efficient, while completely eliminating collisions during training or testing. We applied our framework on the problem of autonomous lane changing for self driving cars, where the neural network learned a high-level tactical decision making policy. We presented preliminary results and benchmarked our approach against a greedy baseline and humans driving in the simulator and showed that our approach is able to outperform them both on different metrics with a more efficient and much safer policy. Finally, we demonstrated zero shot generalizations on several unseen scenarios.",1138,0.534,614,1.8534201954397393,"In consider autonomous lane changing We present demonstrates a more structured and data efficient alternative end complete policy learning on problems where hard formulate using traditional optimization or rule based but well designed low-level controllers are Our framework uses deep reinforcement solely obtain thus getting We accomplish Q-masking with incorporate prior knowledge constraints information directly to thereby the reward function data efficient We provide preliminary results in a simulator show our approach be a greedy baseline successful and safer human driving In self driving vehicles Building such autonomous systems an active area research BID23 BID27 BID3 for its high potential leading road networks much safer One the fundamental skills a self driving vehicle perform lane change maneuvers especially fast moving traffic (as FIG0 . A bad decision at best leads congestion at accidents BID8 . Reasoning interactions other agents forming an efficient long term strategy while safety makes this problem challenging complexPrior work lane changing consists early work considering vision based control BID21 . Other methods track trajectories BID14 BID19 , use fuzzy control BID6 model predictive control generate a steering command with consider planning mixed logic programming However majority the prior work considers only from changing between adjacent lanes while avoiding the few neighboring vehicles There no notion a goal like reaching an exit reasoning long term decisions on when present on among traffic Formulating a control or optimization based problem to handle straight would hand design tuning may work generally The primary roadblock no abstraction the overall ideal policy only the ideal outcome is know: reaching the exit safely (in least amount time).Reinforcement learning provides arbitrary policies giving specific goals In learning based methods address similar or related problems like learning human driving BID22 , inverse end methods that map perception inputsmainly images directly control commands methods understand the scene via learning to make driving decisions Along deep reinforcement learning had learning policies from raw sensor information BID12 .In investigate and place solving the autonomous lane changing problem In general learning a full policy than can reason tactical decisions while at address continuous control and collision avoidance exceedingly with large notorious to train networks Thus an ideal approach strike by learning hard to specify high-level tactical policy while relying established optimization or rule based method forWe uses deep Q-learning policy also introduce, Q-masking forces explore only a subspace Q-values This subspace directly governed consists prior knowledge constraints information the lowlevel controller Not Q-masking provide the tight integration: learning high-level policy using heavily the reward function faster data efficient By relying a controller low-level decisions completely collisions during training or possibility perform training directly real systems We present preliminary benchmarks show our framework a greedy baseline efficiency humans driving in the simulator in safety success generalizing several unseen scenarios without any extra training We proposed traditional optimization or by striking both domains At this framework, Q-masking that provides Using Q-masking we incorporate prior knowledge constraints about information the lower-level controller directly to the training of the reward function learning data completely collisions during or We applied our framework autonomous lane changing where the neural network learned a high-level tactical decision policy We presented and benchmarked against a greedy baseline humans driving in the simulator and showed able them both different metrics with a more efficient and much safer policy Finally demonstrated zero shot generalizations several unseen scenarios",0.01,0.8785188469857325
"Despite the recent successes in robotic locomotion control, the design of robot relies heavily on human engineering. Automatic robot design has been a long studied subject, but the recent progress has been slowed due to the large combinatorial search space and the difficulty in evaluating the found candidates. To address the two challenges, we formulate automatic robot design as a graph search problem and perform evolution search in graph space. We propose Neural Graph Evolution (NGE), which performs selection on current candidates and evolves new ones iteratively. Different from previous approaches, NGE uses graph neural networks to parameterize the control policies, which reduces evaluation cost on new candidates with the help of skill transfer from previously evaluated designs. In addition, NGE applies Graph Mutation with Uncertainty (GM-UC) by incorporating model uncertainty, which reduces the search space by balancing exploration and exploitation. We show that NGE significantly outperforms previous methods by an order of magnitude. As shown in experiments, NGE is the first algorithm that can automatically discover kinematically preferred robotic graph structures, such as a fish with two symmetrical flat side-fins and a tail, or a cheetah with athletic front and back legs. Instead of using thousands of cores for weeks, NGE efficiently solves searching problem within a day on a single 64 CPU-core Amazon EC2
 machine.
 The goal of robot design is to find an optimal body structure and its means of locomotion to best achieve a given objective in an environment. Robot design often relies on careful human-engineering and expert knowledge. The field of automatic robot design aims to search for these structures automatically. This has been a long-studied subject, however, with limited success. There are two major challenges: 1) the search space of all possible designs is large and combinatorial, and 2) the evaluation of each design requires learning or testing a separate optimal controller that is often expensive to obtain.In BID28 , the authors evolved creatures with 3D-blocks. Recently, soft robots have been studied in BID13 , which were evolved by adding small cells connected to the old ones. In BID3 , the 3D voxels were treated as the minimum element of the robot. Most evolutionary robots BID8 BID24 require heavy engineering of the initial structures, evolving rules and careful human-guidance. Due to the combinatorial nature of the problem, evolutionary, genetic or random structure search have been the de facto algorithms of automatic robot design in the pioneering works BID28 BID31 BID20 BID16 BID17 BID34 BID2 . In terms of the underlying algorithm, most of these works have a similar population-based optimization loop to the one used in BID28 . None of these algorithms are able to evolve kinematically reasonable structures, as a result of large search space and the inefficient evaluation of candidates.Similar in vein to automatic robot design, automatic neural architecture search also faces a large combinatorial search space and difficulty in evaluation. There have been several approaches to tackle these problems. Bayesian optimization approaches BID29 primarily focus on fine-tuning the number of hidden units and layers from a predefined set. Reinforcement learning BID38 and genetic algorithms BID19 are studied to evolve recurrent neural networks (RNNs) and convolutional neural networks (CNNs) from scratch in order to maximize the validation accuracy. These approaches are computationally expensive because a large number of candidate networks have to be trained from grounds up. BID25 and BID30 propose weight sharing among all possible candidates in the search space to effectively amortize the inner loop training time and thus speed up the architecture search. A typical neural architecture search on ImageNet BID15 ) takes 1.5 days using 200 GPUs BID19 .In this paper, we propose an efficient search method for automatic robot design, Neural Graph Evolution (NGE), that co-evolves both, the robot design and the control policy. Unlike the recent reinforcement learning work, where the control policies are learnt on specific robots carefully designed by human experts BID21 BID0 BID11 , NGE aims to adapt the robot design along with policy learning to maximize the agent's performance. NGE formulates automatic robot design as a graph search problem. It uses a graph as the main backbone of rich design representation and graph neural networks (GNN) as the controller. This is key in order to achieve efficiency of candidate structure evaluation during evolutionary graph search. Similar to previous algorithms like BID28 , NGE iteratively evolves new graphs and removes graphs based on the performance guided by the learnt GNN controller. The specific contributions of this paper are as follows:• We formulate the automatic robot design as a graph search problem.• We utilize graph neural networks (GNNs) to share the weights between the controllers, which greatly reduces the computation time needed to evaluate each new robot design.• To balance exploration and exploitation during the search, we developed a mutation scheme that incorporates model uncertainty of the graphs.We show that NGE automatically discovers robot designs that are comparable to the ones designed by human experts in MuJoCo , while random graph search or naive evolutionary structure search BID28 fail to discover meaningful results on these tasks. In this paper, we introduced NGE, an efficient graph search algorithm for automatic robot design that co-evolves the robot design graph and its controllers. NGE greatly reduces evaluation cost by transferring the learned GNN-based control policy from previous generations, and better explores the search space by incorporating model uncertainties. Our experiments show that the search over the robotic body structures is challenging, where both random graph search and evolutionary strategy fail to discover meaning robot designs. NGE significantly outperforms the naive approaches in both the final performance and computation time by an order of magnitude, and is the first algorithm that can discovers graphs similar to carefully hand-engineered design. We believe this work is an important step towards automated robot design, and may show itself useful to other graph search problems. A DETAILS OF NERVENET++ Similar to NerveNet, we parse the agent into a graph, where each node in the graph corresponds to the physical body part of the agents. For example, the fish in FIG0 can be parsed into a graph of five nodes, namely the torso (0), left-fin (1), right-fin (2), and tail-fin bodies (3, 4). By replacing MLP with NerveNet, the learnt policy has much better performance in terms of robustness and the transfer learning ability. We here propose minor but effective modifications to BID37 , and refer to this model as NerveNet++.In the original NerveNet, at every timestep, several propagation steps need to be performed such that every node is able to receive global information before producing the control signal. This is time and memory consuming, with the minimum number of propagation steps constrained by the depth of the graph.Since the episode of each game usually lasts for several hundred timesteps, it is computationally expensive and ineffective to build the full back-propagation graph. Inspired by BID22 , we employ the truncated graph back-propagation to optimize the policy. NerveNet++ is suitable for an evolutionary search or population-based optimization, as it brings speed-up in wall-clock time, and decreases the amount of memory usage.Therefore in NerveNet++, we propose a propagation model with the memory state, where each node updates its hidden state by absorbing the input feature and a message with time. The number of propagation steps is no longer constrained by the depth of the graph, and in back-propagation, we save memory and time consumption with truncated computation graph. The memory state h t+1,τ u depends on the previous actions, observations, and states. Therefore, the full back-propagation graph will be the same length as the episode length, which is very computationally intensive. The intuition from the authors in BID22 is that, for the RL agents, the dependency of the agents on timesteps that are far-away from the current timestep is limited. Thus, negligible accuracy of the gradient estimator will be lost if we truncate the back-propagation graph. We define a back-propagation length Γ, and optimize the following objective function instead: DISPLAYFORM0 DISPLAYFORM1 Essentially this optimization means that we only back-propagate up to Γ timesteps, namely at the places where κ = 0, we treat the hidden state as input to the network and stop the gradient. To optimize the objective function , we follow same optimization procedure as in BID37 , which is a variant of PPO Schulman et al. (2017) , where a surrogate loss J ppo (θ) is optimized. We refer the readers to these papers for algorithm details.",1745,0.911,1020,1.7107843137254901,"Despite the recent successes robotic locomotion control the design robot relies human engineering Automatic robot design a long studied subject slowed the large combinatorial search space evaluating the found candidates To address the two challenges formulate automatic robot design as a graph search problem perform evolution search graph space We propose Neural Graph Evolution performs selection current candidates evolves iteratively Different previous approaches NGE uses graph parameterize the control policies reduces evaluation cost on new candidates with skill transfer from previously evaluated designs In addition NGE applies Graph Mutation withGM-UC by incorporating model uncertainty the search space balancing exploration exploitation We show NGE significantly previous methods As shown experiments NGE the first algorithm automatically discover kinematically preferred robotic graph structures a fish with two symmetrical flat side-fins athletic front and back legs Instead thousands cores weeks NGE efficiently solves searching problem within on The goal robot design find its means best in Robot design often relies careful human-engineering and expert knowledge The field automatic robot design aims search these structures automatically This has however limited success There: the search space all possible designs the evaluation learning or testing a separate optimal controller often expensive obtainIn BID28 , the authors evolved creatures 3D-blocks Recently soft robots studied BID13 , were evolved adding small cells connected the old ones In BID3 , treated the minimum element the robot Most evolutionary robots BID8 BID24 require heavy engineering of the initial structures evolving rules careful human-guidance Due evolutionary, genetic or random structure search have the de facto algorithms automatic robot design the pioneering works . In terms the underlying algorithm most these works a similar population-based optimization loop BID28 . None these algorithms able evolve kinematically reasonable structures large search space the inefficient evaluation candidatesSimilar in vein automatic robot design automatic neural architecture search also faces difficulty evaluation There several approaches tackle Bayesian optimization approaches BID29 primarily fine hidden units layers from Reinforcement learning BID38 and genetic algorithms studied evolve maximize the validation accuracy These approaches computationally candidate networks from grounds up BID25 and propose weight sharing among all possible candidates the search space effectively amortize the inner loop training time speed the architecture search A typical neural architecture search on ImageNet BID15 ) takes using 200 GPUs BID19 .In automatic robot design Neural Graph Evolution co both, the control policy Unlike the recent reinforcement learning work the control policies learnt specific robots carefully designed BID21 BID0 BID11 , NGE aims adapt along policy learning maximize NGE formulates automatic robot design as a graph search problem It uses a graph as the main backbone rich design representation graph neural networks the controller This key order achieve efficiency candidate structure evaluation during evolutionary graph search Similar previous algorithms like BID28 , NGE iteratively evolves new graphs removes graphs based the performance guided the learnt GNN controller The specific contributions this paper as We formulate the automatic robot design a graph search utilize graph neural networks share the weights the controllers greatly evaluate To balance exploration exploitation during developed a mutation scheme incorporates model uncertainty of the graphsWe show NGE automatically discovers comparable designed human experts MuJoCo , while random graph or naive evolutionary structure search BID28 fail meaningful results on these tasks In introduced NGE automatic robot design co the robot design graph its controllers NGE greatly evaluation cost transferring the learned GNN-based control policy previous generations better explores the search space incorporating model uncertainties Our experiments the search over the robotic body structures challenging where both random graph search evolutionary strategy fail discover meaning robot designs NGE significantly the naive approaches both the final performance computation time by discovers graphs similar carefully hand-engineered design We believe this work automated robot design may show itself useful other graph search problems DETAILS NERVENET++ Similar to NerveNet we parse the agent into corresponds the physical body part the agents For example the fish FIG0 can parsed five nodes namely the torso0 left-fin tail-fin bodies By replacing MLP NerveNet the learnt policy much better performance robustness the transfer learning ability We here propose minor but effective modifications BID37 , refer this model NerveNet++.In at every timestep several propagation steps need such global information before producing the control signal This time and memory consuming with the minimum number propagation steps constrained the depthSince the episode each game usually several hundred timesteps computationally ineffective build Inspired BID22 , employ the truncated graph back-propagation optimize the policy NerveNet++ suitable an evolutionary search or population-based optimization brings speed-up wall-clock time decreasesTherefore in propose a propagation model the memory state, where updates absorbing the input feature a message with time The number propagation steps no constrained in save memory and time consumption with truncated computation graph memory state h t+1,τ u depends the previous actions observations states Therefore the full back-propagation graph the episode length very computationally The intuition from in BID22 the RL agents the dependency timesteps that far- limited Thus negligible accuracy the gradient estimator will lost We define a back-propagation length ��, optimize the following objective function instead DISPLAYFORM0 Essentially this optimization means only back up �� timesteps namely the places �� = treat the hidden state input stop the gradient To optimize the objective function , follow same optimization procedure BID37 a variant PPO Schulman (2017 , where a surrogate loss J ppo optimized We refer the readers these papers algorithm details",0.01,0.5150951522293687
"Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks only, which is in contrast with advances in generative models for images and text. Is it possible to transfer this progress to the domain of graphs? We propose to sidestep hurdles associated with linearization of such discrete structures by having a decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. Our method is formulated as a variational autoencoder. We evaluate on the challenging task of conditional molecule generation. Deep learning on graphs has very recently become a popular research topic, with useful applications across fields such as chemistry BID5 , medicine (Ktena et al.) , or computer vision (Simonovsky & Komodakis, 2017) . Past work has concentrated on learning graph embedding tasks so far, i.e. encoding an input graph into a vector representation. This is in stark contrast with fastpaced advances in generative models for images and text, which have seen massive rise in quality of generated samples. Hence, it is an intriguing question how one can transfer this progress to the domain of graphs, i.e. their decoding from a vector representation. Moreover, the desire for such a method has been mentioned in the past by BID7 .However , learning to generate graphs is a difficult problem for methods based on gradient optimization, as graphs are discrete structures. Incremental construction involves discrete decisions, which are not differentiable. Unlike sequence (text) generation, graphs can have arbitrary connectivity and there is no clear best way how to linearize their construction in a sequence of steps.In this work, we propose to sidestep these hurdles by having the decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. In a probabilistic graph, the existence of nodes and edges, as well as their attributes, are modeled as independent random variables. The method is formulated in the framework of variational autoencoders (VAE) by BID12 .We demonstrate our method , coined GraphVAE, in cheminformatics on the task of molecule generation. Molecular datasets are a challenging but convenient testbed for our generative model, as they easily allow for both qualitative and quantitative tests of decoded samples. While our method is applicable for generating smaller graphs only and its performance leaves space for improvement, we believe our work is an important initial step towards powerful and efficient graph decoders. In this work we addressed the problem of generating graphs from a continuous embedding in the context of variational autoencoders. We evaluated our method on two molecular datasets of different maximum graph size. While we achieved to learn embedding of reasonable quality on small molecules, our decoder had a hard time capturing complex chemical interactions for larger molecules. Nevertheless, we believe our method is an important initial step towards more powerful decoders and will spark interesting in the community.There are many avenues to follow for future work. Besides the obvious desire to improve the current method (for example, by incorporating a more powerful prior distribution or adding a recurrent mechanism for correcting mistakes), we would like to extend it beyond a proof of concept by applying it to real problems in chemistry, such as optimization of certain properties or predicting chemical reactions. An advantage of a graph-based decoder compared to SMILES-based decoder is the possibility to predict detailed attributes of atoms and bonds in addition to the base structure, which might be useful in these tasks. Our autoencoder can also be used to pre-train graph encoders for fine-tuning on small datasets BID6 .",712,0.413,403,1.7667493796526055,"Deep learning on graphs with However past work concentrated learning graph embedding tasks only in advances generative models images Is transfer this progress the domain graphs We propose hurdles associated linearization such discrete structures having a decoder output a predefined maximum size directly at once Our method formulated as We evaluate on the challenging task conditional molecule generation Deep learning on graphs very recently useful applications across chemistry BID5 , medicine (Ktena orSimonovsky Komodakis 2017 Past work concentrated learning graph embedding tasks so far encoding an input graph This in fastpaced advances generative models images seen massive rise quality of generated samples Hence an intriguing question how one transfer this progress the domain graphs their decoding from a vector representation Moreover the desire such a method mentioned BID7 .However , learning generate graphs methods based gradient optimization graphs discrete structures Incremental construction involves discrete decisions differentiable Unlike sequence (text) generation graphs arbitrary connectivity there how linearize their construction in stepsIn sidestep these hurdles having the decoder output a predefined maximum size directly at once In a probabilistic graph the existence nodes, their attributes modeled independent random variables The method formulatedVAE by BID12 .We demonstrate , coined GraphVAE cheminformatics on the task molecule generation Molecular datasets challenging but convenient testbed our generative model easily decoded samples While our method applicable generating smaller graphs only and its performance leaves space improvement our work powerful and efficient graph decoders In this work addressed generating graphs continuous embedding in We evaluated our method on two molecular datasets different maximum graph size While achieved to learn embedding reasonable quality on small molecules our decoder had capturing complex chemical interactions for Nevertheless we our method more powerful decoders will spark interesting in the communityThere many avenues follow future work Besides the obvious desire the current method (for incorporating a more powerful prior distribution or adding a recurrent mechanism correcting mistakes extend a proof by applying chemistry optimization certain properties predicting An advantage a graph-based decoder compared SMILES-based decoder predict detailed attributes atoms bonds addition the base structure might these tasks Our autoencoder also pre-train graph encoders on small datasets BID6 .",0.0,0.6576892231747296
"Long Short-Term Memory (LSTM) is one of the most widely used recurrent structures in sequence modeling. Its goal is to use gates to control the information flow (e.g., whether to skip some information/transformation or not) in the recurrent computations, although its practical implementation based on soft gates only partially achieves this goal and is easy to overfit. In this paper, we propose a new way for LSTM training, which pushes the values of the gates towards 0 or 1. By doing so, we can (1) better control the information flow: the gates are mostly open or closed, instead of in a middle state; and (2) avoid overfitting to certain extent: the gates operate at their flat regions, which is shown to correspond to better generalization ability. However, learning towards discrete values of the gates is generally difficult. To tackle this challenge, we leverage the recently developed Gumbel-Softmax trick from the field of variational methods, and make the model trainable with standard backpropagation. Experimental results on language modeling and machine translation show that (1) the values of the gates generated by our method are more reasonable and intuitively interpretable, and (2) our proposed method generalizes better and achieves better accuracy on test sets in all tasks. Moreover, the learnt models are not sensitive to low-precision approximation and low-rank approximation of the gate parameters due to the flat loss surface. Recurrent neural networks (RNN) BID10 are widely used in sequence modeling tasks, such as language modeling BID19 BID17 , speech recognition BID44 , time series prediction BID40 , machine translation BID2 , image captioning BID35 BID41 , and image generation BID34 .To address the long-term dependency and gradient vanishing problem of conventional RNN, long short-term memory (LSTM) BID7 BID12 was proposed, which introduces gate functions to control the information in a recurrent unit: a forget gate function to determine how much previous information should be excluded for the current step, an input gate function to find relevant signals to be absorbed into the hidden context, and an output gate function for prediction and decision making. For ease of optimization, in practical implementation, one usually uses element-wise sigmoid function to mimic the gates, whose outputs are soft values between 0 and 1. By using such gates, LSTM usually performs much better than conventional RNN. However , the benefits come with the cost of introducing many more parameters in the gates, which makes the training of a LSTM model inefficient and easy to overfit BID20 BID42 BID30 .In this paper, we explore a new way to train LSTM by pushing the values of the gates to the boundary of their ranges (0, 1)1 . Pushing the values of the gates to 0/1 has certain advantages. First, it well aligns with the original purpose of the development of gates: to get the information in or skip by ""opening"" or ""closing"" the gates during the recurrent computation. Second , training LSTM 1 The output of a gate function is usually a vector. For simplicity , in the paper, we say ""pushing the output of the gate function to 0/1"" when meaning ""pushing each dimension of the output vector of the gate function to either 0 or 1"". We also say that each dimension of the output vector of the gate function is a gate, and say a gate is open/closed if its value is close to 1/0. towards binary-valued gates can make the learnt model generalize better. According to BID11 BID9 BID18 BID4 , a model lying in a flat region of the loss surface is likely to generalize well, since any small perturbation to the model makes little fluctuation to the loss. Training LSTM towards binary-valued gates means seeking a set of parameters to make the values of the gates approaching zero or one, namely residing in the flat region of the sigmoid function. Simple deductions show that this also corresponds to the flat region of the overall loss surface.Technically, pushing the outputs of the gates towards such discrete values is challenging. A straightforward approach is to sharpen the sigmoid function by a smaller temperature. However, this is equivalent to rescaling the input and cannot guarantee the values of the learnt gates to be close to 0 or 1. To tackle this challenge, in this paper, we leverage the Gumbel-Softmax trick that BID15 and BID23 recently develop for variantional methods. The trick aims to generate approximated samples for categorical latent variables in a stochastic computational graph, e.g., variational autoencoder, brings convenience to using reparametrization tricks, and thus leads to efficient learning. Specifically, during training, we apply the Gumbel-Softmax trick to the gates to approximate the values sampled from the Bernoulli distribution given by the parameters, and train the LSTM model with standard backpropagation methods. We call this method Gumbel-Gate LSTM (G 2 -LSTM). We conduct three experiments on two tasks (language modeling and machine translation) to verify our proposed method. We have the following observations from experimental results:• Our model generalizes well: In all tasks, we achieve superior performance to baseline algorithms on the test sets, and the gap between training and test is effectively reduced.• Our model is not sensitive due to its flat loss surface : We apply several model compression algorithms to the parameters in the gates, including low-precision approximation and lowrank approximation, and all results show that our learnt models are better.• The gates in our learnt model are meaningful and intuitively interpretable after visualization. Furthermore, our model can automatically learn the boundaries inside the sentences.The organization of the paper is as follows. We introduce related work in Section 2 and propose our learning algorithm in Section 3. Experiments are reported in Section 4 and future work is discussed in the last section.2 RELATED WORK In this paper, we have designed a new training algorithm for LSTM by leveraging the recently developed Gumbel-Softmax trick. Our training algorithm can push the values of the input and forget gates to 0 or 1, leading to robust LSTM models. Experiments on language modeling and machine translation have demonstrated the effectiveness of the proposed training algorithm.We will explore following directions in the future. First, we have only tested with shallow LSTM models in this paper. We will apply our algorithm to deeper models (e.g., 8+ layers) and test on larger datasets. Second, we have considered the tasks of language modeling and machine translation. We will study more applications such as question answering and text summarization. Third, we are cleaning and refactoring the code and will release the training code to public soon.",1378,0.703,800,1.7225,"Long Short-Term Memory the most widely used recurrent structures sequence modeling Its goal use gates ( whether skip some information/transformation the recurrent computations although its practical implementation based soft gates only partially and easy overfit In LSTM training pushes the values the gates towards 0 By doing (1 better control: the gates mostly or instead in a middle state avoid overfitting to certain extent operate their flat regions shown correspond better generalization ability However learning towards discrete values the gates generally To tackle leverage the recently developed Gumbel-Softmax trick the field variational methods make the model trainable Experimental results on language modeling machine translation the gates generated our method more reasonable intuitively our proposed method generalizes better and achieves test sets in all tasks Moreover the learnt models sensitive low-precision approximation low-rank approximation the gate parameters due the flat loss surface Recurrent neural networks BID10 widely sequence modeling tasks language modeling BID19 BID17 speech machine translation image captioning generation .To address and gradient vanishing problem conventional RNN long short-term memory introduces gate functions control the information a recurrent unit: a forget gate function to determine should excluded for find relevant signals absorbed the hidden context prediction and decision making For ease optimization in practical implementation one usually element-wise sigmoid function mimic the gates whose outputs soft values between By using such gates LSTM usually performs much conventional RNN However , the benefits come introducing many more parameters the gates makes the training a LSTM model inefficient easy overfit BID20 BID42 .In explore by pushing their ranges0 1)1 Pushing the values the gates 0/1 has certain advantages First well aligns the original purpose the development gates get or skip by ""opening during the recurrent computation Second , training LSTM 1 The output a gate function usually For simplicity , in the paper saypushing the output the gate function 0/1 when meaning each dimension of either We also say each dimension the output vector the gate function a gate, say a gate open/ if close towards binary-valued gates can make the learnt model generalize better According BID11 BID9 BID18 BID4 , a model lying a flat region the loss surface likely generalize well, makes little fluctuation to Training LSTM towards binary-valued gates means seeking parameters make the values approaching zero namely residing the flat region Simple deductions show this also corresponds the flat region the overall loss surfaceTechnically pushing the outputs the gates towards such discrete values challenging A straightforward approach sharpen the sigmoid function a smaller temperature However equivalent rescaling the input cannot guarantee the values the learnt gates close 0 To tackle in leverage the Gumbel-Softmax trick BID15 recently develop variantional methods The trick aims generate approximated samples categorical latent variables brings convenience using thus leads efficient learning Specifically during training we apply the Gumbel-Softmax trick the gates approximate the values sampled given the parameters, train We call this method Gumbel-Gate LSTM 2 We conduct three experiments two taskslanguage modeling and machine translation verify our proposed method We the following observations experimental results:• Our model generalizes well: In all tasks achieve to baseline algorithms on the gap training effectively sensitive due its flat loss surface : apply several model compression algorithms the parameters the gates including low-precision approximation lowrank approximation all results our learnt models The gates in our learnt model meaningful intuitively after visualization Furthermore our model can automatically learn the boundaries inside the sentencesThe organization the paper as We introduce related work Section and propose our learning algorithm Experiments reported Section 4 and future work the last section.2 RELATED WORK In designed by leveraging the recently developed Gumbel-Softmax trick Our training algorithm push the values forget gates 0 leading robust LSTM models Experiments language modeling machine translation the proposed training algorithmWe will following directions First only tested with shallow LSTM models in We will apply our algorithm deeper models ( 8+ layers test on Second considered the tasks language modeling and machine translation We will study more applications such question answering text summarization Third cleaning and will release the training code public soon",0.01,0.5449456915278784
"We present a personalized recommender system using neural network for recommending
 products, such as eBooks, audio-books, Mobile Apps, Video and Music.
 It produces recommendations based on customer’s implicit feedback history such
 as purchases, listens or watches. Our key contribution is to formulate recommendation
 problem as a model that encodes historical behavior to predict the future
 behavior using soft data split, combining predictor and auto-encoder models. We
 introduce convolutional layer for learning the importance (time decay) of the purchases
 depending on their purchase date and demonstrate that the shape of the time
 decay function can be well approximated by a parametrical function. We present
 offline experimental results showing that neural networks with two hidden layers
 can capture seasonality changes, and at the same time outperform other modeling
 techniques, including our recommender in production. Most importantly, we
 demonstrate that our model can be scaled to all digital categories, and we observe
 significant improvements in an online A/B test. We also discuss key enhancements
 to the neural network model and describe our production pipeline. Finally
 we open-sourced our deep learning library which supports multi-gpu model parallel
 training. This is an important feature in building neural network based recommenders
 with large dimensionality of input and output data. Recently, deep learning based recommender systems gained significant attention by outperforming conventional approaches BID36 . It shows promising results on products like videos BID6 , mobile apps BID5 , music BID31 etc.In the papers mentioned above, we noticed that NN based recommenders are different for each product category (videos, music, mobile apps), requiring unique feature extraction methods and NN topologies. All of these challenges makes it harder to scale over different product categories. In this paper we are exploring effectiveness of a multilayer neural network (NN) for personalized recommendations of products which were never purchased before by a customer. The simplicity of this approach allows us to scale it on various categories of Amazon catalog in production. We focus on improving accuracy of the neural network based personalized recommender.It is noticed in BID6 ) that accuracy of NN depends on how the problem is formulated. They found that NN performs better when it is trained to predict the user's next purchase, rather than a set of randomly held-out purchases. We use the same idea, but on top of this, we propose to train NN model to predict not only future purchase, but all future purchases in the certain time (for example in the next week).Capturing temporal popularity (trendiness) also called seasonal changes of consumption pattern is a challenging and important problem in recommender systems BID33 , which can impact the accuracy of the model over time. In BID33 BID19 authors propose methods to capture seasonality changes using sequence modeling. Another approach BID29 ) models both long-term static and short-term temporal user preferences. In both cases they use different versions of recurrent neural networks. In this paper we propose to combine predictor model (which can captures short term preferences and recommend products which are currently popular) with auto-encoder model (which can capture static customer preferences and recommend products which were popular at any time in the past) using feed forward NN. These models are combined by training them jointly. We re-train NN model every day to learn new popular products and changes in customer preferences. Even though our model is simpler then RNN, we show that it captures seasonality changes well.Improving NN based recommender is important problem, for example in BID6 authors observed that adding features and depth significantly improves precision on holdout data from YouTube catalog. In BID5 authors show that wide and deep NN with multiple features can improve performance of the neural network on mobile apps. So both methods BID5 and BID6 ) require different production pipelines for different data sets: video and mobile apps. In this paper we use only purchase history and focus on improvements of NN accuracy by applying different splits of the training data. It simplifies the production pipeline and allows us to reuse it on all digital categories: video, eBooks, audio-books, mobile apps, and music.Another way of improving recommender system is time decay, which was introduced by BID35 for collaborative filtering. We also apply it on input data for the neural network based recommender and observe positive impact on accuracy metrics. Our contribution is to use convolutional layer BID20 for estimating the shape of time decay function. Convolutional layers are used in existing recommender systems, but it is applied for different purposes, for example in BID15 convolutional layer is used for learning local relation between adjacent songs, in BID37 BID18 it is used for text feature extraction and in BID31 it is used for extracting features from audio signal.There can be millions of products in the catalog and it is a hard problem to run NN based recommender in production with such amount of items BID6 . Both BID6 and BID5 are splitting the problem into candidate generation and ranking. Candidate generation retrieves a small subset of products from a large corpus. These candidates should be relevant to customer interest. Ranking does a fine-level scoring of the candidates and in addition to consumption history it can use more features (context, impression, etc) . Another way of scaling this problem is to learn similarity between products using DSSM approach BID8 which is relying on content features. In this paper we focused on training end-to-end one neural network which is using only purchases events. On one hand it simplifies the production pipeline, because there is no splitting into candidate generation and ranking models and there is no special feature extraction step. But on the other hand we have to deal with large dimensionality of input features and labels. To solve this problem we use multi-GPU model parallelization, implemented by our team in DSSTNE library (10). It allows us to re-train large NN models every day and produce fresh recommendations for our customers.In this paper, we are focused on modeling consumption patterns in digital products (For example, recommending movies to customers based on the movies already purchased). Depending on the domain, we also exclude movies that were already purchased by the customer while computing offline metrics as well as recommending online. We present different methods of splitting the training data and observed that it can improve NN based recommender accuracy metrics. Techniques like the one presented here feed into recommendation technology deployed at Amazon.The rest of the paper is organized as follows. Section 2 introduces offline metrics used for algorithm evaluation . Section 3 details our NN model development procedure, including how different methods are compared. Section 4 provides extensive offline evaluation results, in conjunction with model property exploration. Section 5 presents how to run NN model in production and describes on-line A/B test. Finally, section 6 presents our conclusions. We described a personalized neural network based recommender system which was launched in production on categories like eBooks, Audible, Apps and Video. We are currently working on expand-ing it to non-digital categories. We showed that splitting customer purchases into a history period (input) and a future period (output) in our models led to good results, and some of our production models use this approach (with soft split which combines the auto-encoder model with the future predictor model). We have applied time decay learnt by convolutional layer, or defined by parametrical function to consumption event. It captures the importance of recent activity, and combined with soft split, it leads to significant improvements in offline metrics. We demonstrated that two layer neural networks are outperforming other NN based approaches which are more complicated than our method, both on public dataset (MovieLens) and company's internal datasets. Because of simplicity of the NN model we can scale it on all digital categories. We observed significant KPI improvements during online A/B tests in production. Finally we open sourced our deep learning library which supports multi gpu model parallel training and allows us to train large models in timely manner.There are around 6200 products (movies) purchased (rated) by these customers in the above period of time. Distribution of customers sorted by number of purchases is shown on FIG0 , where H(c) number of purchases made by customer c, c customer index. It shows that 90 percent of the customers have less than 400 purchases. Distribution of products in data X and Y are shown on FIG0 (a), where P X(p), P Y (p) number of purchases of product p in the input (X) and output (Y ) training data accordingly, p product index. Both of these distributions have long tail: 90 percent of purchases are covered by 1000 products. During evaluation we feed XY data to the models and produce output scoresŶ . These scores are sorted and the top K products are returned as recommendations. Before sorting, all previous purchases (products belonging to data XY ) of the selected customer are removed from the recommendations, so that only new products are recommended. These recommendations are compared with future purchases (data Z) for accuracy calculation. We get testing input data XY and testing output data Z by selecting customers who has at least two purchases in period of time dx . . . dyz and at least one purchase in period of time dyz . . . dz. There are 921 customers who satisfy these conditions. Purchases belonging to dates dx . . . dyz assigned to testing input data XY , and belonging to dyz . . . dz assigned to testing output data Z. Accuracy metrics of predictor, soft split and fastXML models are presented on FIG0 . Predictor model has the same PCC@K with soft split and lower precision@K. Both of these models have higher accuracy metrics than fastXML. We observe similar difference in precision between predictor model and fastXML on Figure. 3, but fastXML has higher PCC@K. These results can be used only as an approximation of a performance on real implicit feedbacks (purchase history), because in this section we were using ratings converted to implicit feedbacks.",1995,1.515,1143,1.7454068241469816,"We present a personalized recommender system for recommending products such audio-books Mobile Apps Video It produces recommendations customer��s implicit feedback history such purchases listens watches Our key contribution formulate recommendation problem as encodes historical behavior to using soft data split combining predictor and auto-encoder models We introduce convolutional layer for learning the importance (time decay the purchases depending demonstrate the shape well a parametrical function We present offline experimental results two hidden layers capture seasonality changes at other modeling techniques our recommender in production Most demonstrate our model scaled all digital categories observe We also discuss key enhancements describe our production pipeline Finally we which supports multi-gpu model parallel training This an important feature building neural network based recommenders with large dimensionality Recently deep learning based recommender systems gained BID36 . It shows promising results products videos BID6 , mobileIn the papers mentioned noticed NN based recommenders differentvideos requiring unique feature extraction methods All these challenges makes scale over different product categories In are effectiveness personalized recommendations products which were never purchased by The simplicity scale it on various categories Amazon catalog in production We focus improving accuracy based personalized recommenderIt noticed BID6 ) that accuracy NN depends the problem formulated They found NN performs trained predict a set randomly held-out purchases We use the same idea on top propose train NN model not only future purchase the certain time ( the next week).Capturing temporal popularitytrendiness also called seasonal changes consumption pattern recommender systems BID33 impact over In BID33 BID19 authors propose methods capture seasonality changes using sequence modeling Another approach BID29 ) models In they use recurrent neural networks In combine predictor modelwhich captures short term preferences recommend products which currently auto-encoder model static customer preferences were using feed forward NN These models combined training jointly We retrain NN model every learn new popular products changes Even our model simpler then RNN show captures seasonality changes wellImproving NN based recommender important problem BID6 authors observed adding features depth significantly precision on holdout data from YouTube catalog In BID5 authors show wide and deep NN with multiple features improve on mobile apps So both methods BID5 ) require different production pipelines: video and mobile apps In only purchase history focus improvements NN accuracy applying different splits It simplifies reuse it all digital categories eBooks audio-books musicAnother way improving recommender system time decay was BID35 collaborative filtering We also apply it input data based recommender observe positive impact accuracy metrics Our contribution use convolutional layer BID20 estimating time decay function Convolutional layers existing recommender systems applied for BID15 convolutional layer is learning local relation adjacent songs it text feature extraction extracting features audio signalThere can millions products run in such amount items BID6 . Both BID6 splitting candidate generation ranking Candidate generation retrieves products These candidates relevant customer interest Ranking does a fine-level scoring the candidates in addition consumption history use more featurescontext impression . Another way scaling learn similarity products DSSM approach BID8 which relying content features In focused training end one neural which using only purchases events On simplifies because no splitting candidate generation ranking models no special feature extraction step But on we large dimensionality input features labels To solve multi-GPU model parallelization implemented our team DSSTNE library10 It allows retrain large NN models every produce fresh recommendationsIn focused modeling consumption patterns digital productsFor recommending movies already Depending the domain also exclude movies already purchased while computing offline metrics as recommending online. We present different methods splitting observed that improve NN based recommender accuracy metrics Techniques like presented feed recommendation technology deployed AmazonThe rest organized Section introduces offline metrics used algorithm evaluation . Section details our NN model development procedure how different methods compared Section provides extensive offline evaluation results in model property exploration Section presents how run NN model production describes on A Finally section presents our conclusions We described a personalized neural network based recommender system which launched production categories eBooks Apps Video We expand-ing it non-digital categories We showed splitting customer purchases a history period (input future in our models led some our production models usewith soft split which combines the auto-encoder model the future predictor model We applied time decay learnt convolutional layer, or defined parametrical function consumption event It captures recent activity combined soft split leads significant improvements offline metrics We demonstrated two layer neural networks outperforming other NN based approaches which complicated both public datasetMovieLens company's internal datasets Because simplicity the NN model scale on all digital categories We observed significant KPI improvements online A/B tests production Finally open sourced which supports multi gpu model parallel training allows large models timely mannerThere around 6200 products (movies purchased (rated these customers the above period Distribution customers sorted number purchases is FIG0 where H(c) number made customer c c customer index It shows 90 percent the customers less than 400 purchases Distribution products data X FIG0 ( P X(p ( number purchases product p the input ( ) training accordingly p product index Both these distributions long tail: 90 percent purchases covered 1000 products During evaluation we feed XY data the models produce output scores�� . These scores sorted and the top K products returned recommendations Before sorting all previous purchases (products belonging data XY ) the recommendations recommended These recommendations compared future purchases (data Z) accuracy calculation We get testing input data XY testing by selecting customers has period dx . . . dyz and at least one purchase period dyz . . . dz. There 921 customers satisfy these conditions Purchases belonging dates dx . . . dyz assigned testing input data XY , belonging . . dz assigned testing output data Z. Accuracy metrics predictor, soft split fastXML models FIG0 Predictor model has the same PCC@K with soft split lower precision@K. Both higher accuracy metrics fastXML We observe similar difference precision predictor model fastXML on Figure. 3 but fastXML has higher PCC@K. These results can only a performance on real implicit feedbackspurchase history this section were ratings converted",0.01,0.6033102668828236
"Deep Learning (DL) algorithms based on Generative Adversarial Network (GAN) have demonstrated great potentials in computer vision tasks such as image restoration. Despite the rapid development of image restoration algorithms using DL and GANs, image restoration for specific scenarios, such as medical image enhancement and super-resolved identity recognition, are still facing challenges. How to ensure visually realistic restoration while avoiding hallucination or mode- collapse? How to make sure the visually plausible results do not contain hallucinated features jeopardizing downstream tasks such as pathology identification and subject identification?
 Here we propose to resolve these challenges by coupling the GAN based image restoration framework with another task-specific network. With medical imaging restoration as an example, the proposed model conducts additional pathology recognition/classification task to ensure the preservation of detailed structures that are important to this task. Validated on multiple medical datasets, we demonstrate the proposed method leads to improved deep learning based image restoration while preserving the detailed structure and diagnostic features. Additionally, the trained task network show potentials to achieve super-human level performance in identifying pathology and diagnosis.
 Further validation on super-resolved identity recognition tasks also show that the proposed method can be generalized for diverse image restoration tasks. Image restoration is an essential computer vision task and a widely applied technique. Recently there are increasing interests and significant progresses in this area enabling more realistic image super-resolution BID6 ; BID17 ; ; BID2 ; BID43 BID39 , in-painting BID35 ; BID38 ; BID37 ; BID31 and denoising BID35 ; BID41 a) . With the development of image restoration technologies, various applications can be applied in different verticals to reach the unfulfilled needs.Among all the image restoration applications, restoration in medical imaging is one of the most challenging tasks. Image restoration in medical imaging is important and attractive, since it enables imaging in more desirable conditions, e.g. imaging with faster protocols BID29 , cheaper devices and lower radiation BID26 , etc. However, medical image restoration requires a tougher evaluation than restoring natural images. It does not only require sharper and visually realistic restoration, but also requires accurate image completion without altering any pathological features or affecting any diagnostic qualities/properties. Therefore medical image restoration can be a benchmark task for related image restoration techniques.Within this decade, image restoration technique has been rapidly growing by incorporating various prior information into solving the ill-posed inverse imaging task. The prior information evolves from using sparse representation assumption BID23 , enforcing low-rank analysis BID7 to more recently using deep learning based priors BID33 or models BID42 . However there are still several challenges and limitations for existing algorithms: 1) Pixel-wise losses for deep learning do not consider non-local structural information which leads to blurred and not visually plausible restoration BID17 .2) Generative Adversarial Network (GAN) BID11 based methods significantly improve the results to generate visually realistic restoration BID17 . However GANs ensure the consistency to a learned distribution but do not necessarily guarantee the visually plausible solution exactly matches the corresponding ground truth.3) It is still possible that hallucination or mode-collapses may happen while minimizing loss function designed in improved GAN frameworks BID10 , BID0 .4) The discriminator network regularizes on general image distribution and visual quality , but it does not consider what are the key characteristic features such as pathologies, contrasts and image identification that the model needs to preserve for restoring an image.These challenges are critical for vertical applications such as medical imaging and surveillance where not only the visual property but also the fidelity of the recovered details matters for key purposes of pathology or recognizing faces.To solve the problems and challenges for realistic and accurate image restoration, we propose the task-GAN which extends GAN based image restoration framework and includes 3 networks: a Generator, a Discriminator and a Task-specific Network. The new task-specific network predicts the pathology recognition or face identity from both the ground truth images and the restored images. It helps to regularize the training of generator and complement the adversarial loss of GAN to ensure the output images better approximate the ground truth images. Task-GAN both achieves realistic visual quality and preserves the important task-specific features/properties, which are related to the end goal for medical imaging restoration and super-resolution face restoration.The contribution of this work are:• We propose a Task Generative Adversarial Network framework (Task-GAN) to ensure both visually plausible and more accurate (medical/face) image restoration.• A Task Network and a task-driven loss are introduced to ensure the preservation of visual details important to the downstream tasks, and more importantly it regularizes the image restoration to be more accurate both quantitatively and qualitatively.• The method is validated on two in-vivo clinical medical imaging datasets across different modalities, including Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET). Additionally , the generalization of the proposed method is further evaluated on a super-resolution face restoration dataset.• Both quantitative and qualitative evaluations were conducted, including rigorous evaluation by human experts (radiologists) to ensure the image restoration quality and preservation of important visual features.• Results demonstrate the superiority of the proposed method in image restoration and also show the potential of applying the trained task network for super-human level automatic classification/diagnosis.• Theory behind the method is further discussed. More justification on how the proposed method improves GAN to approximate one-to-one mapping.The way of how the proposed Task-GAN improves the image restoration may lead to better model design for other applications. Results on in-vivo medical imaging datasets demonstrate the superior performance of the proposed algorithm on improved image restoration. The proposed task-GAN achieves this by coupling adversarial training with the training of the task-specific network. Detailed contribution of the task-GAN is explained in the figure 4.In comparison, the task of the image restoration is to learn a non-linear mapping from low-quality images in the measurement domain to its corresponding high-quality images in a different highquality domain containing visually realistic images. Shown in figure 4(a ), in addition, the recognition of image is a space separation of features/labels along different dimensions that can be orthogonal to the quality dimensions.In comparison, as is shown in FIG4 ( b), conventional learning strategy learns the image restoration task by regression, which may fail to generate realistic restoration. The learning is usually based on the minimization of an averaged distance penalty which ensures robustness but lead to unrealistic restoration such as blurring. Additionally, the averaged solution is also likely to be away from the distribution of visually plausible solutions that falls out of the high-quality image space as is shown in the figure.GAN-based approach on one hand overcomes this by further enforcing an adversarial loss with a Discriminator network which ensures to generate realistic restoration following the distribution of the target high-quality images. As the figure 4(c ) shows, the solution is no longer an simple average but pushed into the space of visually realistic high-quality images. However , on the other hand, the discriminator only regularizes the output samples to follow the distribution but ignores the inter-sample relationship. For example , it cannot avoid hallucinations or mode-collapse, where the restored images may be over-similar or undesirably add/remove important visual features. As is shown in the figure, the restored image can have a different label as the ground-truth which fails the purpose of image restoration. We can picture the hallucinations or mode-collapse as a ""shrinking"" of solution space.To avoid the possible mode-collapse and ensure a 1-to-1 mapping, various improved GAN models and cost functions have been proposed. For example, Cycle- GAN Zhu et al. (2017) incorporate a cyclic relationship to improve the mapping. However, cyclic relationship does not necessarily lead to exact mappings. The inter-sample relationship as well as the important feature labels can be swapped while still satisfying the cyclic relationship. The illustrating image can be found in the appendix. For example, in the figure, one task label is altered while the cyclic loss is not affected. This may lead to mode-collapse, or specifically a failed image restoration leading to misclassified pathology/normality for medical imaging applications. The consequences of the restoration errors can be huge for medical imaging applications since they can directly lead to mis-diagnosis or overdiagnosis. We can picture the mislabeling or mode-collapse as a ""twisting"" of solution space. This ""twisting"" maintains well within visually-plausible space, however severely changes the positioning around the decision boundary of task-label space. More details of the reasoning and visualization will be place in the appendix.Differently, task-GAN here regularizes both the inter-sample relationship and the sample-label relationship. As is shown in figure 4(d), accurate mapping can be generated with the mixed loss regularization:1 ) pixel-level supervision so the restored image is closer to the ground truth,2) Adversarial loss regularization so that the restored image is within the high-quality space consisting of visually realistic images 3) the task-specific loss that ensure the restored image still preserve the important feature of interests, aka the same labels. In other words, the combination regularization enforce the solution to fall onto the intersection of the manifold preserving pixel-level similarity, distribution consistency and important visual labels. In the view of inter-sample relationship, the task regularization stop the inter-sample relationship to any visual plausible but destructive ""shrinking"" or ""twisting"" around the boundary of task-label space, which ensures more accurate mappings. In this paper, we proposed an improved design of GAN, Task-GAN, which includes a new taskspecific network and corresponding task-specific loss for training GAN based image restoration. Task-GAN is demonstrated to boost the performance of image restoration while preserving important features. Medical imaging applications are used as primary examples, which is one of the most challenging restoration applications since it requires not only realistic restoration, but also high-fidelity as well as accurate classification for subtle diagnostic features. Super-resolution face restoration is used to show the proposed method generalize to natural image applications such as super-resolving face images, where face identity need to be preserved.The proposed method is demonstrated to achieve superior performance compared with GAN on both image quality metrics and task-specific feature preservation (e.g. pathological features, face identity features, etc.). Based on visual inspection from human experts (clinicians/radiologists), anatomical and diagnostic features are preserved better and fewer artifacts are introduced. The trained task network also shows potentials for super-human level diagnosis tasks.Task-GAN further extends the regularization of adversarial training. The mixed loss balances between content similarity, distribution consistency and preserving important features for the given tasks. It results in more accurate image restoration with better visual similarity and avoids modecollapse and hallucinations. Intuitively, task-GAN enforces the solution fall into proper manifold, prevents any alternation (""shrinking"" and ""twisting"") of the restoration from the correct solution space, and preserves both inter-sample relationship and feature-of-interest.In the future, we will explore further improvements in the design of networks and task formulation. The proposed technique is also valuable to other challenging restoration applications that require realistic restoration and preserving distinguishable details for down-stream tasks.",2247,1.118,1315,1.708745247148289,"Deep ( algorithms based demonstrated image restoration Despite image restoration algorithms using DL and GANs for specific scenarios medical image enhancement super-resolved identity recognition facing How ensure visually realistic restoration while avoiding hallucination mode- collapse? How the visually plausible results do contain hallucinated features jeopardizing downstream tasks pathology identification subject identification Here propose resolve these challenges coupling the GAN based image restoration framework another task-specific network With medical imaging restoration as an example the proposed model conducts additional pathology recognition/classification task detailed structures this task Validated multiple medical datasets demonstrate the proposed method leads improved deep learning based image restoration while diagnostic features Additionally the trained task network show potentials achieve identifying pathology diagnosis Further validation on super-resolved identity recognition tasks also show generalized diverse image restoration tasks Image restoration an essential computer vision task a widely applied technique Recently there increasing interests significant progresses enabling more realistic image super-resolution BID6 ; BID17 ; and denoising a . With image restoration technologies various applications different verticals reach the unfulfilled needsAmong restoration medical imaging Image restoration medical imaging important attractive since more desirable conditions imaging faster protocols BID29 , cheaper devices lower radiation BID26 etc However medical image restoration requires a tougher evaluation restoring natural images It does only sharper and visually realistic restoration accurate image completion without altering any pathological features affecting any diagnostic qualities/properties Therefore medical image restoration a benchmark task related image restoration techniquesWithin this decade rapidly by incorporating various prior information solving the ill-posed inverse imaging task The prior information evolves using sparse representation assumption BID23 , enforcing low-rank analysis more recently or models However there several challenges existing algorithms: 1) Pixel-wise losses for do consider non-local structural information which leads blurred and not visually plausible restoration BID17 .2 Generative Network based methods significantly to generate visually realistic restoration However GANs ensure the consistency to a learned distribution but the visually plausible solution exactly matches the corresponding ground) still hallucination mode-collapses happen while minimizing loss function designed in improved GAN frameworks BID10 , The discriminator network regularizes on general image distribution visual quality , consider what are such pathologies contrasts image identification preserve restoringThese challenges critical vertical applications surveillance the recovered details matters key purposes pathology recognizing facesTo and challenges for the task-GAN which extends includes 3 networks a Generator The new task-specific network predicts the pathology recognition or face identity from both the ground truth images the restored images It helps regularize the training generator complement the adversarial loss GAN ensure the output images better approximate the ground truth images Task-GAN both achieves realistic visual quality preserves related for medical imaging restoration and super-resolution face restorationThe contribution are:• We a Task Generative Adversarial Network framework ensure both visually plausible and more accurate (medical/face) image A Task Network and are visual details important the downstream tasks more it regularizes both validated across Additionally , the generalization further evaluated on a super-resolution face restoration dataset.•, rigorous evaluation human experts the image restoration quality preservation important visual Results demonstrate also applying the trained task network super-human level automatic classification/diagnosis.• Theory behind further More justification on the proposed method improves GAN to approximateThe way how the proposed Task-GAN improves the image restoration may lead better model design other applications Results on in-vivo medical imaging datasets demonstrate the proposed algorithm improved image restoration The proposed task-GAN achieves coupling adversarial training Detailed contribution the task-GAN is explained 4.In comparison the image restoration to learn the measurement domain a different highquality domain containing visually realistic images Shown in addition, the recognition image is a space separation features/labels along that the quality dimensionsIn comparison as FIG4 b conventional learning strategy learns the image restoration task regression may fail realistic restoration The learning is usually based the minimization an averaged distance penalty which ensures robustness but lead unrealistic restoration such Additionally the averaged solution also likely away visually plausible solutions falls out as isGAN-based approach on overcomes further enforcing an adversarial loss with a Discriminator network ensures to generate realistic restoration following As the figure 4(c ) the solution no an simple average pushed visually realistic high-quality images However , on the discriminator only regularizes the output samples follow but ignores For example , avoid hallucinations mode-collapse where the restored images oversimilar undesirably add/ As is shown the restored image have a different label the ground-truth which fails the purpose We picture the hallucinations or mode-collapse solution spaceTo avoid ensure various improved GAN models cost functions For example Cycle- GAN Zhu et (2017 incorporate a cyclic relationship improve the mapping. However cyclic relationship does exact mappings The inter-sample relationship as the important feature labels swapped while satisfying The illustrating image can For example the figure one task label altered while the cyclic loss affected This may lead mode-collapse specifically a failed image restoration leading misclassified pathology/normality for medical imaging applications The consequences the restoration errors medical imaging applications since directly lead We picture the mislabeling or mode-collapse solution space This ""twisting"" maintains well visually-plausible space however severely changes the positioning around the decision boundary task-label space More details the reasoning visualization placeDifferently task-GAN here regularizes both the inter-sample relationship As is shown figure accurate mapping generated mixed loss regularization:1 ) pixel supervision so the restored image closer the ground truth,2 within consisting visually realistic images 3 the task-specific loss that ensure still preserve the important feature interests aka the same labels In the combination regularization enforce the solution fall onto the intersection the manifold preserving pixel-level similarity distribution consistency important visual labels In the view inter-sample relationship the task regularization stop to any visual plausible but destructive ""shrinking around task-label space ensures more accurate mappings In proposed GAN, Task-GAN includes a new taskspecific network corresponding task-specific loss for training GAN based image restoration Task-GAN demonstrated boost image restoration while Medical imaging applications used primary examples one the most challenging restoration applications since not only realistic restoration as accurate classification for subtle diagnostic features Super-resolution face restoration used show the proposed method generalize natural image applications where face identity needThe proposed method demonstrated superior performance compared GAN on both image quality metrics task feature preservation face identity features Based visual inspection from human experts ( anatomical and diagnostic features preserved better and fewer artifacts introduced The trained task network also shows potentials super-human level diagnosis tasksTaskGAN further extends The mixed loss balances content similarity distribution consistency preserving important features for the given tasks It results more accurate image restoration better visual similarity avoids modecollapse hallucinations Intuitively task-GAN enforces the solution fall proper manifold prevents any alternation (""shrinking the restoration from preserves both inter-sample relationship featureofinterestIn further improvements networks and task formulation The proposed technique also valuable other challenging restoration applications realistic restoration preserving distinguishable details down-stream tasks",0.01,0.5098997897410906
"Unsupervised anomaly detection on multi- or high-dimensional data is of great importance in both fundamental machine learning research and industrial applications, for which density estimation lies at the core. Although previous approaches based on dimensionality reduction followed by density estimation have made fruitful progress, they mainly suffer from decoupled model learning with inconsistent optimization goals and incapability of preserving essential information in the low-dimensional space. In this paper, we present a Deep Autoencoding Gaussian Mixture Model (DAGMM) for unsupervised anomaly detection. Our model utilizes a deep autoencoder to generate a low-dimensional representation and reconstruction error for each input data point, which is further fed into a Gaussian Mixture Model (GMM). Instead of using decoupled two-stage training and the standard Expectation-Maximization (EM) algorithm, DAGMM jointly optimizes the parameters of the deep autoencoder and the mixture model simultaneously in an end-to-end fashion, leveraging a separate estimation network to facilitate the parameter learning of the mixture model. The joint optimization, which well balances autoencoding reconstruction, density estimation of latent representation, and regularization, helps the autoencoder escape from less attractive local optima and further reduce reconstruction errors, avoiding the need of pre-training. Experimental results on several public benchmark datasets show that, DAGMM significantly outperforms state-of-the-art anomaly detection techniques, and achieves up to 14% improvement based on the standard F1 score. Unsupervised anomaly detection is a fundamental problem in machine learning, with critical applications in many areas, such as cybersecurity BID18 ), complex system management BID14 ), medical care BID10 ), and so on. At the core of anomaly detection is density estimation: given a lot of input samples, anomalies are those ones residing in low probability density areas.Although fruitful progress has been made in the last several years, conducting robust anomaly detection on multi-or high-dimensional data without human supervision remains a challenging task. Especially, when the dimensionality of input data becomes higher, it is more difficult to perform density estimation in the original feature space, as any input sample could be a rare event with low probability to observe BID3 ). To address this issue caused by the curse of dimensionality, two-step approaches are widely adopted BID2 ), in which dimensionality reduction is first conducted, and then density estimation is performed in the latent low-dimensional space. However, these approaches could easily lead to suboptimal performance, because dimensionality reduction in the first step is unaware of the subsequent density estimation task, and the key information for anomaly detection could be removed in the first place. Therefore, it is desirable to combine the force of dimensionality reduction and density estimation, although a joint optimization accounting for these two components is usually computationally difficult. Several recent works BID29 ; BID26 ; BID24 ) explored this direction by utilizing the strong modeling capacity of deep networks, but the resulting performance is limited either by a reduced low-dimensional space that is unable to preserve essential information of input samples, an over-simplified density estimation model without enough capacity, or a training strategy that does not fit density estimation tasks.Figure 1: Low-dimensional representations for samples from a private cybersecurity dataset: (1) each sample denotes a network flow that originally has 20 dimensions, (2) red/blue points are abnormal/normal samples, (3) the horizontal axis denotes the reduced 1-dimensional space learned by a deep autoencoder, and (4) the vertical axis denotes the reconstruction error induced by the 1-dimensional representation.In this paper, we propose Deep Autoencoding Gaussian Mixture Model (DAGMM), a deep learning framework that addresses the aforementioned challenges in unsupervised anomaly detection from several aspects.First, DAGMM preserves the key information of an input sample in a low-dimensional space that includes features from both the reduced dimensions discovered by dimensionality reduction and the induced reconstruction error. From the example shown in Figure 1 , we can see that anomalies differ from normal samples in two aspects: (1) anomalies can be significantly deviated in the reduced dimensions where their features are correlated in a different way; and (2) anomalies are harder to reconstruct, compared with normal samples. Unlike existing methods that only involve one of the aspects BID32 ; BID29 ) with sub-optimal performance, DAGMM utilizes a sub-network called compression network to perform dimensionality reduction by an autoencoder, which prepares a low-dimensional representation for an input sample by concatenating reduced low-dimensional features from encoding and the reconstruction error from decoding.Second, DAGMM leverages a Gaussian Mixture Model (GMM) over the learned low-dimensional space to deal with density estimation tasks for input data with complex structures, which are yet rather difficult for simple models used in existing works BID29 ). While GMM has strong capability, it also introduces new challenges in model learning. As GMM is usually learned by alternating algorithms such as Expectation-Maximization (EM) (Huber (2011)), it is hard to perform joint optimization of dimensionality reduction and density estimation favoring GMM learning, which is often degenerated into a conventional two-step approach. To address this training challenge, DAGMM utilizes a sub-network called estimation network that takes the low-dimensional input from the compression network and outputs mixture membership prediction for each sample. With the predicted sample membership, we can directly estimate the parameters of GMM, facilitating the evaluation of the energy/likelihood of input samples. By simultaneously minimizing reconstruction error from compression network and sample energy from estimation network, we can jointly train a dimensionality reduction component that directly helps the targeted density estimation task.Finally, DAGMM is friendly to end-to-end training. Usually, it is hard to learn deep autoencoders by end-to-end training, as they can be easily stuck in less attractive local optima, so pre-training is widely adopted BID22 ; BID26 ; BID24 ). However, pre-training limits the potential to adjust the dimensionality reduction behavior because it is hard to make any significant change to a well-trained autoencoder via fine-tuning. Our empirical study demonstrates that, DAGMM is well-learned by the end-to-end training, as the regularization introduced by the estimation network greatly helps the autoencoder in the compression network escape from less attractive local optima.Experiments on several public benchmark datasets demonstrate that, DAGMM has superior performance over state-of-the-art techniques, with up to 14% improvement of F1 score for anomaly detection. Moreover, we observe that the reconstruction error from the autoencoder in DAGMM by the end-to-end training is as low as the one made by its pre-trained counterpart, while the reconstruction error from an autoencoder without the regularization from the estimation network stays high. In addition, the end-to-end trained DAGMM significantly outperforms all the baseline methods that rely on pre-trained autoencoders. In this paper, we propose the Deep Autoencoding Gaussian Mixture Model (DAGMM) for unsupervised anomaly detection. DAGMM consists of two major components: compression network and estimation network, where the compression network projects samples into a low-dimensional space that preserves the key information for anomaly detection, and the estimation network evaluates sample energy in the low-dimensional space under the framework of Gaussian Mixture Modeling. DAGMM is friendly to end-to-end training: (1) the estimation network predicts sample mixture membership so that the parameters in GMM can be estimated without alternating procedures; and (2) the regularization introduced by the estimation network helps the compression network escape from less attractive local optima and achieve low reconstruction error by end-to-end training. Compared with the pre-training strategy, the end-to-end training could be more beneficial for density estimation tasks, as we can have more freedom to adjust dimensionality reduction processes to favor the subsequent density estimation tasks. In the experimental study, DAGMM demonstrates superior performance over state-of-the-art techniques on public benchmark datasets with up to 14% improvement on the standard F 1 score, and suggests a promising direction for unsupervised anomaly detection on multior high-dimensional data.A BASELINE CONFIGURATION OC-SVM. Unlike other baselines that only need decision thresholds in the testing phase, OC-SVM needs parameter ν be set in the training phase. Although ν intuitively means anomaly ratio in training data, it is non-trivial to set a reasonable ν in the case where training data are all normal samples and anomaly ratio in the testing phase could be arbitrary. In this study, we simply perform exhaustive search to find the optimal ν that renders the highest F 1 score on individual datasets. In particular, ν is set to be 0.1, 0.02, 0.04, and 0.1 for KDDCUP, Thyroid, Arrhythmia, and KDDCUP-Rev, respectively.DSEBM. We use the network structure for the encoding in DAGMM as guidelines to set up DSEBM instances. For KDDCUP and KDDCUP-Rev, it is configured as FC FORMULA0",1815,0.75,1057,1.717123935666982,"Unsupervised anomaly detection on multi- or high-dimensional data of both fundamental machine learning research and industrial applications for density estimation lies Although previous approaches based dimensionality reduction followed by density estimation made fruitful progress mainly suffer decoupled model learning with inconsistent optimization goals incapability preserving essential information In this paper a Deep Autoencoding Gaussian Mixture Model unsupervised anomaly detection Our model utilizes a deep autoencoder a low-dimensional representation and reconstruction error further fed Instead using decoupled two-stage training the standard Expectation-Maximization (EM) algorithm DAGMM jointly the deep autoencoder the mixture model simultaneously in an end leveraging a separate estimation network facilitate the parameter learning The joint optimization, well balances autoencoding reconstruction density estimation of latent representation regularization helps the escape less attractive local optima further reconstruction errors avoiding pretraining Experimental results on several public benchmark datasets, DAGMM significantly state anomaly achieves based the standard F1 score Unsupervised anomaly detection with critical applications cybersecurity BID18 ), complex system management BID14 so At anomaly detection density estimation: given a lot input samples anomalies those ones residing low probability density areasAlthough fruitful progress conducting on multi-or high-dimensional data without human supervision Especially, the dimensionality input data higher perform density estimation the original feature space any input sample a rare event with low probability to observe BID3 ). To address caused the curse dimensionality two-step approaches widely BID2 ), in dimensionality reduction first conducted, density estimation the latent low-dimensional space However these approaches could easily because dimensionality reduction unaware the subsequent density estimation task the key information anomaly detection could removed Therefore desirable combine the force dimensionality reduction density estimation although a joint optimization accounting usually computationally Several recent works BID29 ; ) explored this direction utilizing the strong modeling capacity deep networks the resulting performance limited either a reduced low-dimensional space that unable preserve essential information of input samples without enough capacity a training strategy fit density estimation tasksFigure samples a private cybersecurity dataset: each sample denotes a network flow that originally has 20 dimensions2) red/blue points abnormal/normal samples the horizontal axis denotes learned the reconstruction error inducedIn Deep Autoencoding Gaussian Mixture Model addresses the aforementioned challenges unsupervised anomaly detection from several aspectsFirst preserves includes features both the reduced dimensions discovered dimensionality reduction From the example shown , anomalies differ normal samples two aspects can significantly deviated in the reduced dimensions where their features correlated in harder reconstruct compared Unlike existing methods that only involve one of the aspects BID32 ; BID29 ) with DAGMM utilizesnetwork called compression network perform dimensionality reduction by prepares an input sample by reduced low-dimensional features encoding the reconstruction error fromSecond over the learned low-dimensional space deal density estimation tasks for with complex structures yet rather simple models used existing works BID29 While GMM strong capability introduces model learning As GMM is usually learned alternating algorithms such Expectation-Maximization (Huber (2011 hard perform joint optimization dimensionality reduction density estimation favoring GMM learning, degenerated To address this training challenge DAGMM utilizes a sub-network called estimation network takes the low-dimensional input the compression network outputs mixture membership prediction With the predicted sample membership, directly estimate the parameters GMM facilitating the energy/likelihood input samples By simultaneously minimizing reconstruction error from compression network sample energy from estimation network jointly train a dimensionality reduction component directly helps the targeted density estimation taskFinally DAGMM friendly end training Usually hard learn deep autoencoders by end training easily stuck less attractive local optima pre widely adopted BID22 ; BID26 However, pre-training limits the potential to adjust the dimensionality reduction behavior because hard make via Our empirical study demonstrates, DAGMM welllearned endto training, the regularization introduced the estimation network greatly helps in compression network escape less attractive local optimaExperiments on several public benchmark datasets demonstrate state techniques of F1 score anomaly detection Moreover we observe the reconstruction error from in DAGMM by end training as low the made its pre-trained counterpart while without the regularization from the estimation network stays high In addition end trained DAGMM significantly all the baseline methods that rely In this paper the Deep Autoencoding Gaussian Mixture Model DAGMM consists compression network and estimation network where projects samples preserves for anomaly detection evaluates sample energy under the framework DAGMM is friendly end training: ( the estimation network predicts sample mixture membership so the parameters in GMM estimated without alternating procedures introduced helps compression network escape less attractive local optima achieve low reconstruction error by end Compared the pre-training strategy end could density estimation tasks we have more freedom dimensionality reduction processes favor the subsequent density estimation tasks In the experimental study DAGMM demonstrates superior performance over state techniques on public benchmark datasets with up to 14% improvement the standard F 1 score suggests a promising direction unsupervised anomaly detection on multior high-dimensional dataA BASELINE CONFIGURATION OC-SVM. Unlike other baselines that only need decision thresholds in the testing phase OC-SVM needs parameter �� be Although �� intuitively anomaly ratio in training data non set in all normal samples anomaly ratio the testing phase could arbitrary In simply perform exhaustive search the optimal �� that renders the highest F 1 score on individual datasets In particular, �� set KDDCUP, Thyroid KDDCUP-Rev,DSEBM. We use the network structure the encoding in DAGMM as guidelines set DSEBM instances For KDDCUP and, configured FC FORMULA0",0.01,0.5312479519431966
"Generalization from limited examples, usually studied under the umbrella of meta-learning, equips learning techniques with the ability to adapt quickly in dynamical environments and proves to be an essential aspect of lifelong learning. In this paper, we introduce the Projective Subspace Networks (PSN), a deep learning paradigm that learns non-linear embeddings from limited supervision. In contrast to previous studies, the embedding in PSN deems samples of a given class to form an affine subspace. We will show that such modeling leads to robust solutions, yielding competitive results on supervised and semi-supervised few-shot classification. Moreover, our PSN approach has the ability of end-to-end learning. In contrast to previous works, our projective subspace can be thought of as a richer representation capturing higher-order information datapoints for modeling new concepts.",162,0.102,94,1.7234042553191489,Generalization from limited examples usually studied meta-learning equips learning techniques adapt quickly dynamical environments proves lifelong learning In the Projective Subspace Networks learns limited supervision In contrast embedding in PSN deems samples a given class form an affine subspace We will show such modeling leads robust solutions yielding competitive results on supervised and semi-supervised few-shot classification Moreover our PSN approach of end learning In contrast previous works our projective subspace can thought a richer representation capturing for modeling new concepts,0.0,0.5472496546340663
"This paper investigates whether learning contingency-awareness and controllable aspects of an environment can lead to better exploration in reinforcement learning. To investigate this question, we consider an instantiation of this hypothesis evaluated on the Arcade Learning Element (ALE). In this study, we develop an attentive dynamics model (ADM) that discovers controllable elements of the observations, which are often associated with the location of the character in Atari games. The ADM is trained in a self-supervised fashion to predict the actions taken by the agent. The learned contingency information is used as a part of the state representation for exploration purposes. We demonstrate that combining actor-critic algorithm with count-based exploration using our representation achieves impressive results on a set of notoriously challenging Atari games due to sparse rewards. For example, we report a state-of-the-art score of >11,000 points on Montezuma's Revenge without using expert demonstrations, explicit high-level information (e.g., RAM states), or supervisory data. Our experiments confirm that contingency-awareness is indeed an extremely powerful concept for tackling exploration problems in reinforcement learning and opens up interesting research questions for further investigations. The success of reinforcement learning (RL) algorithms in complex environments hinges on the way they balance exploration and exploitation. There has been a surge of recent interest in developing effective exploration strategies for problems with high-dimensional state spaces and sparse rewards BID8 Oudeyer & Kaplan, 2009; Houthooft et al., 2016; Bellemare et al., 2016; Osband et al., 2016; Pathak et al., 2017; BID5 BID16 . Deep neural networks have seen great success as expressive function approximators within RL and as powerful representation learning methods for many domains. In addition, there have been recent studies on using neural network representations for exploration BID13 Martin et al., 2017; Pathak et al., 2017) . For example, count-based exploration with neural density estimation (Bellemare et al., 2016; BID13 Ostrovski et al., 2017) presents one of the state-of-the-art techniques on the most challenging Atari games with sparse rewards.Despite the success of recent exploration methods, it is still an open question on how to construct an optimal representation for exploration. For example, the concept of visual similarity is used for learning density models as a basis for calculating pseudo-counts (Bellemare et al., 2016; Ostrovski et al., 2017) . However, as BID13 noted, the ideal way to represent states should be based on what is relevant to solving the MDP, rather than only relying on visual similarity. In addition, there remains another question on whether the representations used for recent exploration works are easily interpretable. To address these questions, we investigate whether we can learn a complementary, more intuitive, and interpretable high-level abstraction that can be very effective in exploration by using the ideas of contingency awareness and controllable dynamics.The key idea that we focus on in this work is the notion of contingency awareness BID14 Bellemare et al., 2012) -the agent's understanding of the environmental dynamics and recognizing that some aspects of the dynamics are under the agent's control. Intuitively speaking, this can represent the segmentation mask of the agent operating in the 2D or 3D environments (yet one can think of more abstract and general state spaces). In this study, we investigate the concept of contingency awareness based on self-localization, i.e., the awareness of where the agent is located in the abstract state space. We are interested in discovering parts of the world that are directly dependent on the agent's immediate action, which often reveal the agent's approximate location.For further motivation on the problem, we note that contingency awareness is a very important concept in neuroscience and psychology. In other words, being self-aware of one's location is an important property within many observed intelligent organisms and systems. For example, recent breakthroughs in neuroscience, such as the Nobel Prize winning work on the grid cells (Moser et al., 2015; BID4 , show that organisms that perform very well in spatially-challenging tasks are self-aware of their location. This allows rats to navigate, remember paths to previously visited places and important sub-goals, and find shortcuts. In addition, the notion of contingency awareness has been shown as an important factor in developmental psychology BID14 BID2 . We can think of self-localization (and more broadly self-awareness) as a principled and fundamental direction towards intelligent agents.Based on these discussions, we hypothesize that contingency awareness can be a powerful mechanism for tackling exploration problems in reinforcement learning. We consider an instantiation of this hypothesis evaluated on the Arcade Learning Element (ALE). For example, in the context of 2D Atari games, contingency-awareness roughly corresponds to understanding the notion of controllable entities (e.g., the player's avatar), which Bellemare et al. (2012) refer to as contingent regions. More concretely, as shown in FIG0 , in the game FREEWAY, only the chicken sprite is under the agent's control and not the multiple moving cars; therefore the chicken's location should be an informative element for exploration (Bellemare et al., 2012; Pathak et al., 2017) .In this study, we also investigate whether contingency awareness can be learned without any external annotations or supervision. For this, we provide an instantiation of an algorithm for automatically learning such information and using it for improving exploration on a 2D ALE environment (Bellemare et al., 2013) . Concretely , we employ an attentive dynamics model (ADM) to predict the agent's action chosen between consecutive states. It allows us to approximate the agent's position in 2D environments, but unlike other approaches such as (Bellemare et al., 2012) , it does not require any additional supervision to do so. The ADM learns in an online and self-supervised fashion with pure observations as the agent's policy is updated and does not require hand-crafted features, an environment simulator, or supervision labels for training.In experimental evaluation, our methods significantly improve the performance of A2C on hardexploration Atari games in comparison with competitive methods such as density-based exploration (Bellemare et al., 2016; Ostrovski et al., 2017) and SimHash BID13 . We report very strong results on sparse-reward Atari games, including the state-of-the-art performance on the notoriously difficult MONTEZUMA'S REVENGE, when combining our proposed exploration strategy with PPO , without using expert demonstrations, explicit high-level information (e.g., RAM states), or resetting the environment to an arbitrary state.We summarize our contributions as follows:• We demonstrate the importance of learning contingency awareness for efficient exploration in challenging sparse-reward RL problems.• We develop a novel instance of attentive dynamics model using contingency and controllable dynamics to provide robust localization abilities across the most challenging Atari environments.• We achieve a strong performance on difficult sparse-reward Atari games, including the state-ofthe-art score on the notoriously challenging MONTEZUMA'S REVENGE.Overall, we believe that our experiments confirm the hypothesis that contingency awareness is an extremely powerful concept for tackling exploration problems in reinforcement learning, which opens up interesting research questions for further investigations. This paper investigates whether discovering controllable dynamics via an attentive dynamics model (ADM) can help exploration in challenging sparse-reward environments. We demonstrate the effectiveness of this approach by achieving significant improvements on notoriously difficult video games. That being said, we acknowledge that our approach has certain limitations. Our currently presented instance of state abstraction method mainly focuses on controllable dynamics and employs a simple clustering scheme to abstract away uncontrollable elements of the scene. In more general setting, one can imagine using attentive (forward or inverse) dynamics models to learn an effective and compact abstraction of the controllable and uncontrollable dynamics as well, but we leave this to future work.Key elements of the current ADM method include the use of spatial attention and modelling of the dynamics. These ideas can be generalized by a set of attention-based dynamics models (ADM) operating in forward, inverse, or combined mode. Such models could use attention over a lowerdimensional embedding that corresponds to an intrinsic manifold structure from the environment (i.e., intuitively speaking, this also corresponds to being self-aware of (e.g., locating) where the agent is in the abstract state space). Our experiments with the inverse dynamics model suggest that the mechanism does not have to be perfectly precise, allowing for some error in practice. We speculate that mapping to such subspace could be obtained by techniques of embedding learning.We note that RL environments with different visual characteristics may require different forms of attention-based techniques and properties of the model (e.g., partial observability). Even though this paper focuses on 2D video games, we believe that the presented high-level ideas of learning contingency-awareness (with attention and dynamics models) are more general and could be applicable to more complex 3D environments with some extension. We leave this as future work. We proposed a method of providing contingency-awareness through an attentive dynamics model (ADM). It enables approximate self-localization for an RL agent in 2D environments (as a specific perspective). The agent is able to estimate its position in the space and therefore benefits from a compact and informative representation of the world. This idea combined with a variant of countbased exploration achieves strong results in various sparse-reward Atari games. Furthermore, we report state-of-the-art results of >11,000 points on the infamously challenging MONTEZUMA'S REVENGE without using expert demonstrations or supervision. Though in this work we focus mostly on 2D environments in the form of sparse-reward Atari games, we view our presented high-level concept and approach as a stepping stone towards more universal algorithms capable of similar abilities in various RL environments. DISPLAYFORM0 Perform actor-critic using on-policy samples in E θ A2C ← θ A2C − η∇ θA2C L",2025,0.952,1232,1.6436688311688312,"This paper learning contingency-awareness and controllable aspects an environment better exploration in To investigate consider an instantiation this hypothesis evaluated on the Arcade Learning ElementALE In develop an attentive dynamics model ( discovers controllable elements the observations often associated the location the character Atari games The ADM trained a self-supervised fashion predict taken the agent The learned contingency information the state representation for exploration purposes We demonstrate combining actor-critic algorithm count-based exploration using our representation achieves on a set notoriously challenging Atari games due sparse rewards For example we report state score >11,000 points Montezuma's Revenge without expert demonstrations explicit high-level informatione.g., RAM states supervisory data Our experiments confirm contingency-awareness indeed an extremely powerful concept tackling exploration problems reinforcement learning opens interesting research questions further investigations The success reinforcement learningRL algorithms complex environments hinges balance exploration exploitation There has recent interest developing effective exploration strategies problems high-dimensional state spaces sparse rewards BID8 Oudeyer & Kaplan 2009 Houthooft 2016 Bellemare Osband Pathak BID5 BID16 . Deep neural networks seen as expressive function approximators within RL and as powerful representation learning methods many domains In addition recent studies using neural network representations exploration BID13 Martin; Pathak . For example, count-based exploration with neural density estimation 2016 BID13 Ostrovski presents one state on the most challenging Atari games with sparse rewardsDespite recent exploration methods on construct an optimal representation exploration For example the concept visual similarity used for learning density models as calculating pseudocounts 2016 . However as BID13 noted the ideal way represent states should based what relevant solving the MDP only relying visual similarity In addition remains another question on whether the representations used recent exploration works easily To address these questions investigate we learn a complementary, more intuitive, and interpretable high-level abstraction very exploration by using the ideas contingency awareness controllable dynamicsThe key idea that focus BID14 Bellemare et al) -the agent's understanding the environmental dynamics recognizing some aspects the dynamics under Intuitively speaking can represent the segmentation mask the agent operatingyet one think more abstract and general state spaces In investigate the concept contingency awareness based self-localization where the agent the abstract state space We interested discovering parts directly dependent the agent's immediate action which often revealFor further motivation note contingency awareness neuroscience psychology In being self of one's location an important property within many observed intelligent organisms and systems For example recent breakthroughs neuroscience the grid cells (Moser BID4 , show organisms perform very spatially-challenging tasks self. This allows rats navigate, remember paths to previously important sub find shortcuts In addition the notion contingency awareness shown as developmental psychology BID14 BID2 . We can think self-localization (and a principled and fundamental direction intelligent agentsBased these discussions contingency awareness tackling exploration problems reinforcement learning We consider an instantiation this hypothesis evaluated on the Arcade Learning ElementALE For example 2D Atari games contingency-awareness roughly understanding the notion controllable entities Bellemare et (2012 refer as contingent regions More concretely as shown FIG0 , in the game FREEWAY only the chicken sprite under multiple moving cars; should an informative element exploration (Bellemare et al Pathak 2017 .In study also investigate contingency awareness learned without any external annotations supervision For this, provide an instantiation an algorithm automatically learning such information and using improving exploration on a 2D ALE environment (Bellemare et al) . Concretely , employ an attentive dynamics model the agent's action chosen between consecutive states It allows approximate the agent's position 2D environments unlike such (Bellemare et al , any additional supervision do The ADM learns in an online and self-supervised fashion with pure observations as the agent's policy updated does hand-crafted features an environment simulator supervision labels for trainingIn experimental evaluation our methods significantly A2C on hardexploration Atari games in comparison competitive methods density-based explorationBellemare et al 2016 SimHash BID13 . We report very strong results sparse-reward Atari games state performance on the notoriously difficult MONTEZUMA'S REVENGE when combining our proposed exploration strategy PPO , without expert demonstrations explicit high-level information ( resettingWe summarize our contributions the importance learning contingency awareness efficient exploration challenging sparse-reward RL problems.• develop a novel instance attentive dynamics model contingency and controllable dynamics provide robust localization abilities across most Atari achieve the state-ofthe-art score our experiments confirm an extremely powerful concept tackling exploration problems reinforcement learning opens interesting research questions further investigations This paper discovering controllable dynamics via an attentive dynamics model exploration in challenging sparse-reward environments We demonstrate this approach achieving significant improvements on notoriously difficult video games That being acknowledge our approach Our currently presented instance state abstraction method mainly focuses controllable dynamics employs abstract away uncontrollable elements In more general setting one imagine using attentive (forward or inverse) dynamics models learn an effective and compact abstraction as, we leaveKey elements the current ADM method spatial attention modelling These ideas can generalized by a set attention-based dynamics models operating forward, inverse combined Such models could use attention over a lowerdimensional embedding that corresponds an intrinsic manifold structure from the environment intuitively speaking also being self ( locating where the agent the abstract state space Our experiments the inverse dynamics model suggest the mechanism does perfectly precise allowing some error practice We speculate mapping to such subspace obtained techniques embedding learning.We note RL environments with different visual characteristics attention-based techniques properties the model Even this paper focuses 2D video games believe the presented high-level ideas learning contingency-awarenesswith attention and dynamics models more general could applicable with some extension We leave as future work We proposed providing contingency-awareness through an attentive dynamics model It enables approximate self-localization an RL agent 2D environmentsas a specific perspective The agent is able estimate its position therefore benefits a compact and informative representation This idea combined a variant countbased exploration achieves strong results various sparse-reward Atari games Furthermore we report state results >11,000 points the infamously challenging MONTEZUMA'S REVENGE without using expert demonstrations supervision Though in this work focus mostly 2D environments in sparse-reward Atari games view our presented high-level concept more universal algorithms capable similar abilities various RL environments DISPLAYFORM0 Perform actor-critic using onpolicy samples E �� A2C �� �� A2C − ���� ��A2C L",0.01,0.3440907993768243
"Disentangling factors of variation has always been a challenging problem in representation learning. Existing algorithms suffer from many limitations, such as unpredictable disentangling factors, bad quality of generated images from encodings, lack of identity information, etc. In this paper, we proposed a supervised algorithm called DNA-GAN trying to disentangle different attributes of images. The latent representations of images are DNA-like, in which each individual piece represents an independent factor of variation. By annihilating the recessive piece and swapping a certain piece of two latent representations, we obtain another two different representations which could be decoded into images. In order to obtain realistic images and also disentangled representations, we introduced the discriminator for adversarial training. Experiments on Multi-PIE and CelebA datasets demonstrate the effectiveness of our method and the advantage of overcoming limitations existing in other methods. The success of machine learning algorithms depends on data representation, because different representations can entangle different explanatory factors of variation behind the data. Although prior knowledge can help us design representations, the vast demand of AI algorithms in various domains cannot be met, since feature engineering is labor-intensive and needs domain expert knowledge. Therefore, algorithms that can automatically learn good representations of data will definitely make it easier for people to extract useful information when building classifiers or predictors.Of all criteria of learning good representations as discussed in BID1 , disentangling factors of variation is an important one that helps separate various explanatory factors. For example, given a human-face image, we can obtain various information about the person, including gender, hair style, facial expression, with/without eyeglasses and so on. All of these information are entangled in a single image, which renders the difficulty of training a single classifier to handle different facial attributes. If we could obtain a disentangled representation of the face image, we may build up only one classifier for multiple attributes.In this paper, we propose a supervised method called DNA-GAN to obtain disentangled representations of images. The idea of DNA-GAN is motivated by the DNA double helix structure, in which different kinds of traits are encoded in different DNA pieces. We make a similar assumption that different visual attributes in an image are controlled by different pieces of encodings in its latent representations. In DNA-GAN, an encoder is used to encode an image to the attribute-relevant part and the attribute-irrelevant part, where different pieces in the attribute-relevant part encode information of different attributes, and the attribute-irrelevant part encodes other information. For example, given a facial image, we are trying to obtain a latent representation that each individual part controls different attributes, such as hairstyles, genders, expressions and so on. Though annihilating recessive pieces and swapping certain pieces, we can obtain novel crossbreeds that can be decoded into new images. By the adversarial discriminator loss and the reconstruction loss, DNA-GAN can reconstruct the input images and generate new images with new attributes. Each attribute is disentangled from others gradually though iterative training. Finally, we are able to obtain disentangled representations in the latent representations.The summary of contributions of our work is as follows:1. We propose a supervised algorithm called DNA-GAN, that is able to disentangle multiple attributes as demonstrated by the experiments of interpolating multiple attributes on Multi-PIE BID5 and CelebA BID12 datasets.2. We introduce the annihilating operation that prevents from trivial solutions: the attributerelevant part encodes information of the whole image instead of a certain attribute.3. We employ iterative training to address the problem of unbalanced multi-attribute image data, which was theoretically proved to be more efficient than random image pairs. In this paper, we propose a supervised algorithm called DNA-GAN that can learn disentangled representations from multi-attribute images. The latent representations of images are DNA-like, consisting of attribute-relevant and attribute-irrelevant parts. By the annihilating operation and attribute hybridization, we are able to create new latent representations which could be decoded into novel images with designed attributes. The iterative training strategy effectively overcomes the difficulty of training on unbalanced datasets and helps disentangle multiple attributes in the latent space.The experimental results not only demonstrate that DNA-GAN is effective in learning disentangled representations and image editing, but also point out its potential in interpretable deep learning, image understanding and transfer learning.There also exist some limitations of our model. Without strong guidance on the attribute-irrelevant parts, some background information is encoded into the attribute-relevant part. As we can see in FIG3 , the background color gets changed when swapping attributes. Besides, our model may fail when several attributes are highly correlated with each other. For example, Male and Mustache are statistically dependent, which are hard to disentangle in the latent representations. These are left as our future work.",975,0.539,580,1.6810344827586208,"Disentangling factors variation has always representation learning Existing algorithms suffer unpredictable disentangling factors bad quality generated images from lack identity information In proposed a supervised algorithm called DNA-GAN trying different attributes images The latent representations images DNAlike in each individual piece an independent factor variation By annihilating the recessive piece and swapping a certain piece two latent representations obtain another two different representations which could decoded images In order obtain realistic images also disentangled representations introduced the discriminator for adversarial training Experiments Multi-PIE and CelebA datasets demonstrate our method the advantage overcoming existing The success machine learning algorithms depends data representation because different representations entangle different explanatory factors of variation behind Although prior knowledge can design representations the vast demand AI algorithms various domains met since feature engineering labor needs domain expert knowledge Therefore algorithms automatically learn good representations definitely make extract when building classifiersOf all criteria learning as discussed BID1 , factors variation helps separate various explanatory factors For example given a human-face image obtain various information gender hair style with/ All these information entangled renders the difficulty training handle different facial attributes If we obtain a disentangled representation the face image may build only one classifier multiple attributesIn a supervised method called DNA-GAN images The idea DNA-GAN motivated in different kinds traits We make a similar assumption different visual attributes in controlled different pieces encodings its latent representations In DNA-GAN an encoder an image to the attribute-relevant part and different pieces of For example given a facial image are trying obtain a latent representation that each individual part controls different attributes hairstyles genders expressions Though annihilating recessive pieces and swapping certain pieces we obtain novel crossbreeds decoded new images By the adversarial discriminator loss and the reconstruction loss DNA-GAN can reconstruct the input images generate new attributes Each attribute disentangled others gradually though iterative training Finally obtain disentangled representations in the latent representationsThe summary contributions We propose a supervised algorithm called DNA-GAN able multiple attributes as demonstrated interpolating Multi-PIE BID5 CelebA BID12 datasets.2. introduce the annihilating operation prevents from trivial solutions: the attributerelevant part encodes information of the whole image instead employ iterative training address unbalanced multi-attribute image data was theoretically proved more random image pairs In a supervised algorithm called DNA-GAN learn disentangled representations multi-attribute images The latent representations images DNAlike consisting attribute-relevant and attribute-irrelevant parts By the annihilating operation and attribute hybridization new latent representations which could decoded novel images with designed attributes The iterative training strategy effectively overcomes on unbalanced datasets helps multiple attributes the latent spaceThe experimental results not DNA-GAN learning representations image editing point interpretable deep learning, image understanding transfer learningThere also Without strong guidance the attribute-irrelevant parts some background information encoded As can FIG3 gets swapping attributes Besides our model may fail when several attributes highly For example Male Mustache statistically dependent which are hard the latent representations These left as our future work",0.01,0.439295196717355
"Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach to representation learning is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning. Representation learning BID0 is part of the foundation of deep learning; powerful deep neural network models appear to derive their performance from sequentially representing data in more-and-more refined structures, tailored to the training task.However, representation learning has a broader impact than just model performance. Transferable representations are leveraged efficiently for new tasks BID22 , representations are used for human interpretation of machine learning models BID18 , and meaningfully structured (disentangled) representations can be used for model control (e.g. semisupervised learning as in , topic modelling as in BID1 ).Consequently , it is often preferable to have interpretable data representations within a model, in the sense that the information contained in the representation is easily understood and the representation can be used to control the output of the model (e.g. to generate data of a given class or with a particular characteristic). Unfortunately , there is often a tension between optimal model performance and cleanly disentangled or controllable representations.To overcome this, some practitioners have proposed modifying their model's objective functions by inserting parameters in front of particular terms BID2 BID11 , while others have sought to modify the associated generative models BID20 . Further still , attempts have been made to build the symmetries of the data directly into the neural network architecture in order to force the learning of latent variables that transform meaningfully under those symmetries BID27 . The diversity and marginal success of these approaches point to the importance and difficulty of learning meaningful representations in deep generative modelling.In this work we present an approach to probabilistic modelling of data comprised of a finite number of distinct classes, each described by a smooth manifold of instantiations of that class. For convenience , we call our approach EQUIVAE for Equivariant Variational Autoencoder. EQUIVAE is a probabilistic model with 2 latent variables: an invariant latent that represents the global class information, and an equivariant latent that smoothly interpolates between all of the members of that class. The EQUIVAE approach is general in that the symmetry group of the manifold must not be specified (as in for example BID6 ; BID8 ), and it can be used for any number of classes and any dimensionality of both underlying representations. The price that must be paid for this level of model control and flexibility is that some labelled data is needed in order to provide the concept of class invariance versus equivariance to the model. The endeavor to model the content and the style of data separately is certainly not new to this work BID29 . BID25 and BID24 go further, disentangling the continuous sources of variation in their representations using a clamping technique that exposes specific latent components to a single source of variation in the data during training. In the same vein, other approaches have used penalty terms in the objective function that encourage the learning of disentangled representations BID5 BID4 . EQUIVAE does not require any modification to the training algorithm, nor additional penalty terms in the objective function in order to bifurcate the information stored in the two latent variables. This is due to the way in which multiple data points are used to reconstruct a single data point from the same-class manifold, which we consider the primary novel aspect of our approach. In particular, our invariant representation takes as input multiple data points that come from the same class, but are different from the data point to be reconstructed. This invariant representation thus directly learns to encode the information common to the overall class, but not the individual data point, simply due to the information flowing through it.Of further note, we deliberately use a deterministic latent for the invariant representation, and a stochastic latent for the smooth equivariant representation (an idea also employed by BID30 ). This choice is why we do not need to explicitly force the equivariant latent to not contain any class-level information: it is available and easier to access from the deterministic latent.EQUIVAE is also comparable to BID28 , where the authors leverage labelled data explicitly in their generative model in order to force the VAE latent to learn the non-class information BID19 do similarly using adversarial training). The primary difference between those works and ours is that EQUIVAE provides a non-trivial representation of the global information instead of simply using the integer-valued label. Furthermore, this invariant representation can be deterministically evaluated directly on unlabelled data. Practitioners can reuse this embedding on unlabelled data in downstream tasks, along with the equivariant encoder if needed. The invariant representation provides more information than a simple prediction of the class-label distribution.The encoding procedure for the invariant representation in EQUIVAE is partially inspired by BID7 , who use images from various, known coordinates in a scene in order to reconstruct a new image of that scene at new, known coordinates. In contrast, we do not have access to the exact coordinates of the class instance , which in our case corresponds to the unknown, non-trivial manifold structure of the class; we must infer these manifold coordinates in an unsupervised way. BID9 similarly explore the simultaneous usage of multiple data points in generative modelling in order to better capture modelling uncertainty. We have introduced a technique for jointly learning invariant and equivariant representations of data comprised of discrete classes of continuous values. The invariant representation encodes global information about the given class manifold which is ensured by the procedure of reconstructing a data point through complementary samples from the same class. The equivariant representation is a stochastic VAE latent that learns the smooth set of transformations that cover the instances of data on that class manifold. We showed that the invariant latents are so widely separated that a 99.18% accuracy can be achieved on MNIST (87.70% on SVHN) with a simple 0-parameter distance metric based on the invariant embedding. The equivariant latent learns to cover the manifold for each class of data with qualitatively excellent samples and interpolations for each class. Finally, we showed that semi-supervised learning based on such latent variable models is competitive with similar approaches in the literature with essentially no hyperparameter tuning.",1401,0.623,828,1.6920289855072463,"Representations learnt through deep neural networks tend informative opaque learn to encode We introduce an approach learns represent two separate deep representations the class from belongs the symmetry transformation defining within the class manifold in varies naturally symmetry transformations This approach representation learning conceptually transparent easy in- generally comprised discrete classes continuous distributions objects images topics language individuals behavioural data We demonstrate qualitatively compelling representation learning competitive quantitative performance, versus comparable modelling approaches with little fine tuning Representation learning BID0 is part the foundation deep learning; powerful deep neural network models appear derive their performance sequentially representing data more-and-more refined structures tailoredHowever a broader impact just model performance Transferable representations leveraged efficiently new tasks BID22 , representations human interpretation machine meaningfully structured (disentangled can model control semisupervised as , topic modelling.Consequently , often preferable interpretable data representations within contained control generate data of with Unfortunately , often optimal model performance cleanly disentangled or controllable representationsTo overcome some practitioners modifying their model's objective functions inserting front particular terms BID2 BID11 while sought the associated generative models Further still , attempts build the symmetries directly in force latent variables that transform meaningfully under those symmetries BID27 The diversity marginal success these approaches point and difficulty learning meaningful representations deep generative modellingIn data comprised distinct classes described a smooth manifold instantiations For convenience , call our approach EQUIVAE for Equivariant Variational Autoencoder EQUIVAE is 2 latent variables an invariant latent that represents the global class information smoothly all the members The EQUIVAE approach general the symmetry group the manifold must specified (as for BID6 ; classes and any dimensionality both underlying representations The price that must this level model control and flexibility that some labelled data needed the concept class invariance versus equivariance to The endeavor model the content the style data separately certainly this work BID29 . BID25 and go further disentangling the continuous sources variation their representations using a clamping technique exposes specific latent components during training In other approaches used penalty terms the objective function that encourage the learning disentangled representations BID5 BID4 . EQUIVAE does require any modification the training algorithm additional penalty terms in the objective function in the information stored the two latent variables This due multiple data points used reconstruct the same-class manifold we consider the primary novel aspect In particular our invariant representation takes as input multiple data points come to reconstructed This invariant representation thus directly learns encode common the overall class not the individual data point simply due flowingOf further deliberately a deterministic latent for the smooth equivariant representation (an idea also employed BID30 This choice why do need explicitly force the equivariant latent to not contain: available and easier the deterministic latentEQUIVAE is comparable BID28 , the authors leverage labelled explicitly in force the VAE latent learn BID19 do similarly using adversarial training). The primary difference those works ours EQUIVAE provides the global information instead the integer-valued label Furthermore this invariant representation evaluated directly unlabelled data Practitioners reuse embedding on unlabelled data downstream tasks along the equivariant encoder if The invariant representation provides more information a simple prediction the class-label distributionThe encoding procedure in EQUIVAE partially inspired BID7 , who use images various, known coordinates a scene in at new, known coordinates In contrast we do access the exact coordinates the class instance , in corresponds the unknown, non-trivial manifold structure; must infer these manifold coordinates in BID9 similarly explore the simultaneous usage multiple data points generative modelling better capture modelling uncertainty We introduced a technique jointly learning invariant and equivariant representations data comprised discrete classes continuous values The invariant representation encodes global information the given class manifold which ensured the procedure reconstructing a data point through complementary samples The equivariant representation a stochastic VAE latent that learns the smooth set transformations cover the instances data on that class manifold We showed the invariant latents so widely separated a 99.18% accuracy can on MNIST87.70% SVHN a simple 0-parameter distance metric based The equivariant latent learns cover the manifold for each class data with qualitatively excellent samples interpolations for Finally showed based such latent variable models competitive similar approaches with essentially no hyperparameter tuning",0.01,0.4673082237544034
"Convolutional neural networks (CNNs) have been successfully applied to many recognition and learning tasks using a universal recipe;  training a deep model on a very large dataset of supervised examples. However, this approach is rather restrictive in practice since collecting a large set of labeled images is very expensive. One way to ease this problem is coming up with smart ways for choosing images to be labelled from a  very large collection (i.e. active learning).

 Our empirical study suggests that many of the active learning heuristics in the literature are not effective when applied to CNNs when applied in batch setting. Inspired by these limitations, we define the problem of active learning as core-set selection, i.e. choosing set of points such that a model learned over the selected subset is competitive for the remaining data points. We further present a theoretical result characterizing the performance of any selected subset using the geometry of the datapoints. As an active learning algorithm, we choose the subset which is expected to yield best result according to our characterization. Our experiments show that the proposed method significantly outperforms existing approaches in image classification experiments by a large margin.
 Deep convolutional neural networks (CNNs) have shown unprecedented success in many areas of research in computer vision and pattern recognition, such as image classification, object detection, and scene segmentation. Although CNNs are universally successful in many tasks, they have a major drawback; they need a very large amount of labeled data to be able to learn their large number of parameters. More importantly, it is almost always better to have more data since the accuracy of CNNs is often not saturated with increasing dataset size. Hence, there is a constant desire to collect more and more data. Although this a desired behavior from an algorithmic perspective (higher representative power is typically better), labeling a dataset is a time consuming and an expensive task. These practical considerations raise a critical question: ""what is the optimal way to choose data points to label such that the highest accuracy can be obtained given a fixed labeling budget."" Active learning is one of the common paradigms to address this question.The goal of active learning is to find effective ways to choose data points to label, from a pool of unlabeled data points, in order to maximize the accuracy. Although it is not possible to obtain a universally good active learning strategy BID4 , there exist many heuristics BID38 which have been proven to be effective in practice. Active learning is typically an iterative process in which a model is learned at each iteration and a set of points is chosen to be labelled from a pool of unlabelled points using these aforementioned heuristics. We experiment with many of these heuristics in this paper and find them not effective when applied to CNNs. We argue that the main factor behind this ineffectiveness is the correlation caused via batch acquisition/sampling. In the classical setting, the active learning algorithms typically choose a single point at each iteration; however, this is not feasible for CNNs since i) a single point is likely to have no statistically significant impact on the accuracy due to the local optimization methods, and ii) each iteration requires a full training until convergence which makes it intractable to query labels one-by-one. Hence, it is necessary to query labels for a large subset at each iteration and it results in correlated samples even for moderately small subset sizes.In order to tailor an active learning method for the batch sampling case, we decided to define the active learning as core-set selection problem. Core-set selection problem aims to find a small subset given a large labeled dataset such that a model learned over the small subset is competitive over the whole dataset. Since we have no labels available, we perform the core-set selection without using the labels. In order to attack the unlabeled core-set problem for CNNs, we provide a rigorous bound between an average loss over any given subset of the dataset and the remaining data points via the geometry of the data points. As an active learning algorithm, we try to choose a subset such that this bound is minimized. Moreover, minimization of this bound turns out to be equivalent to the k-Center problem (Wolf, 2011) and we adopt an efficient approximate solution to this combinatorial optimization problem. We further study the behavior of our proposed algorithm empirically for the problem of image classification using three different datasets. Our empirical analysis demonstrates state-of-the-art performance by a large margin. We study the active learning problem for CNNs. Our empirical analysis showed that classical uncertainty based methods have limited applicability to the CNNs due to the correlations caused by batch sampling. We re-formulate the active learning problem as core-set selection and study the core-set problem for CNNs. We further validated our algorithm using an extensive empirical study. Empirical results on three datasets showed state-of-the-art performance by a large margin.A PROOF FOR LEMMA 1Proof. We will start with showing that softmax function defined over C class is , i = 1, 2, ..., C For brevity, we will denote f i (x) as f i . The Jacobian matrix will be, DISPLAYFORM0 Now, Frobenius norm of above matrix will be, DISPLAYFORM1 It is straightforward to show that f i = 1 C is the optimal solution for J * F = max . If we assume, i |w i,j | ≤ α ∀i, j, d, for any convolutional or fully connected layer, we can state: DISPLAYFORM2 On the other hand, using |a − b| ≤ | max(0, a) − max(0, a)| and the fact that max pool layer can be written as a convolutional layer such that only one weight is 1 and others are 0, we can state for ReLU and max-pool layers, DISPLAYFORM3 Combining with the Lipschitz constant of soft-max layer, B PROOF FOR THEOREM 1 DISPLAYFORM4 Before starting our proof, we state the Claim 1 from BID1 . Fix some p, p ∈ [0, 1] and y ∈ {0, 1}. Then, p y∼p (y = y ) ≤ p y∼p (y = y ) + |p − p |",1262,0.603,716,1.7625698324022345," successfully many recognition a universal recipe; training a deep model supervised examples However this approach rather restrictive since collecting a large set labeled images One way ease coming smart ways choosing images labelled from a very large collection (i.e. active learning Our empirical study suggests many the active learning heuristics effective CNNs when batch setting Inspired these limitations define the problem active learning core-set selection choosing set points such a model learned over the selected subset competitive We further present a theoretical result characterizing any selected subset using the geometry As an active learning algorithm choose the subset which expected yield best result according our characterization Our experiments the proposed method significantly image classification experiments Deep convolutional neural networks shown unprecedented success scene segmentation Although CNNs universally successful many tasks; need labeled data learn their large number parameters More importantly almost more data since the accuracy CNNs saturated increasing dataset size Hence there a constant desire collect Although this a desired behavior from (higher representative power typically better labeling a dataset time These practical considerations raise ""what choose data points label such that the highest accuracy given a fixed labeling budget Active learning one to addressThe goal find effective ways choose from a pool in Although obtain a universally good active learning strategy BID4 , exist many heuristics BID38 proven practice Active learning typically a model at points chosen labelled from a pool unlabelled points using these aforementioned heuristics We experiment many this paper them not effective CNNs argue the main factor the correlation caused via batch acquisition/sampling In the classical setting the active learning algorithms typically choose at each iteration; feasible CNNs since i) likely no statistically significant impact due the local optimization methods requires a full training until convergence which makes query labels one Hence necessary query labels a large subset at each iteration and it results correlated samples even for moderately small subset sizesIn tailor an active learning method the batch sampling case decided define as core-set selection problem Core-set selection problem aims find given a large labeled dataset such a model learned over competitive over Since we no labels available perform the core-set selection without using In order attack the unlabeled core-set problem for CNNs provide a rigorous bound between an average loss over any given subset the remaining data points via the geometry As an active learning algorithm try choose such this bound minimized Moreover minimization this bound turns equivalent the k-Center problemWolf 2011 we adopt an efficient approximate solution We further study our proposed algorithm empirically for the problem image classification three different datasets Our empirical analysis demonstrates state performance by a large margin We study the active learning problem for CNNs Our empirical analysis showed classical uncertainty based methods limited due the correlations caused batch sampling We reformulate the active learning problem core-set selection study CNNs further validated our algorithm an extensive empirical study Empirical results on three datasets showed state performance by a large marginA PROOF FOR LEMMA 1Proof. We will start showing that softmax function defined over C class , i = ... C For denote f i ( The Jacobian matrix will, DISPLAYFORM0 Now Frobenius norm of above matrix It straightforward show f i 1 C the optimal solution J * F max . If we assume, i |w ij | ≤ α ��i j d for any convolutional or fully connected layer state DISPLAYFORM2 On using |a − b| ≤ | max(0 a and the fact max pool layer can written such only one weight 1 and others for ReLU max-pool layers Combining with the Lipschitz constant soft-max layer B PROOF FOR Before starting our proof state the Claim 1 from BID1 . Fix some p, p � [0 and { Then p y�y = y ) ≤ |p",0.01,0.6470401039917907
"Recurrent neural networks are known for their notorious exploding and vanishing gradient problem (EVGP). This problem becomes more evident in tasks where the information needed to correctly solve them exist over long time scales, because EVGP prevents important gradient components from being back-propagated adequately over a large number of steps. We introduce a simple stochastic algorithm (\textit{h}-detach) that is specific to LSTM optimization and targeted towards addressing this problem. Specifically, we show that when the LSTM weights are large, the gradient components through the linear path (cell state) in the LSTM computational graph get suppressed. Based on the hypothesis that these components carry information about long term dependencies (which we show empirically), their suppression can prevent LSTMs from capturing them. Our algorithm\footnote{Our code is available at https://github.com/bhargav104/h-detach. } prevents gradients flowing through this path from getting suppressed, thus allowing the LSTM to capture such dependencies better. We show significant improvements over vanilla LSTM gradient based training in terms of convergence speed, robustness to seed and learning rate, and generalization using our modification of LSTM gradient on various benchmark datasets. Recurrent Neural Networks (RNNs) BID25 ; BID4 ) are a class of neural network architectures used for modeling sequential data. Compared to feed-forward networks, the loss landscape of recurrent neural networks are much harder to optimize. Among others, this difficulty may be attributed to the exploding and vanishing gradient problem BID8 BID2 BID24 which is more severe for recurrent networks and arises due to the highly ill-conditioned nature of their loss surface. This problem becomes more evident in tasks where training data has dependencies that exist over long time scales.Due to the aforementioned optimization difficulty, variants of RNN architectures have been proposed that aim at addressing these problems. The most popular among such architectures that are used in a wide number of applications include long short term memory (LSTM, BID9 ) and gated recurrent unit (GRU, Chung et al. (2014) ) networks, which is a variant of LSTM with forget gates BID5 . These architectures mitigate such difficulties by introducing a linear temporal path that allows gradients to flow more freely across time steps. BID0 on the other hand try to address this problem by parameterizing a recurrent neural network to have unitary transition matrices based on the idea that unitary matrices have unit singular values which prevents gradients from exploding/vanishing.Among the aforementioned RNN architectures, LSTMs are arguably most widely used (for instance they have more representational power compared with GRUs BID31 ) and it remains a hard problem to optimize them on tasks that involve long term dependencies. Examples of such tasks are copying problem BID2 BID24 , and sequential MNIST (Le Figure 1 : The computational graph of a typical LSTM. Here we have omitted the inputs x i for convenience. The top horizontal path through the cell state units c t s is the linear temporal path which allows gradients to flow more freely over long durations. The dotted blue crosses along the computational paths denote the stochastic process of blocking the flow of gradients though the h t states (see Eq 2) during the back-propagation phase of LSTM. We call this approach h-detach. et al., 2015) , which are designed in such a way that the only way to produce the correct output is for the model to retain information over long time scales.The goal of this paper is to introduce a simple trick that is specific to LSTM optimization and improves its training on tasks that involve long term dependencies. To achieve this goal, we write out the full back-propagation gradient equation for LSTM parameters and split the composition of this gradient into its components resulting from different paths in the unrolled network. We then show that when LSTM weights are large in magnitude, the gradients through the linear temporal path (cell state) get suppressed (recall that this path was designed to allow smooth gradient flow over many time steps). We show empirical evidence that this path carries information about long term dependencies (see section 3.5) and hence gradients from this path getting suppressed is problematic for such tasks. To fix this problem, we introduce a simple stochastic algorithm that in expectation scales the individual gradient components, which prevents the gradients through the linear temporal path from being suppressed. In essence, the algorithm stochastically prevents gradient from flowing through the h-state of the LSTM (see figure 1) , hence we call it h-detach. Using this method, we show improvements in convergence/generalization over vanilla LSTM optimization on the copying task, transfer copying task, sequential and permuted MNIST, and image captioning. In section 3.5 we showed that LSTMs trained with h-detach are stable even without gradient clipping. We caution that while this is true, in general the gradient magnitude depends on the value of detaching probability used in h-detach. Hence for the general case, we do not recommend removing gradient clipping.When training stacked LSTMs, there are two ways in which h-detach can be used: 1) detaching the hidden state of all LSTMs simultaneously for a given time step t depending on the stochastic variable ξ t ) stochastically detaching the hidden state of each LSTM separately. We leave this for future work.h-detach stochastically blocks the gradient from flowing through the hidden states of LSTM. In corollary 1, we showed that in expectation, this is equivalent to dampening the gradient components from paths other than the cell state path. We especially chose this strategy because of its ease of implementation in current auto-differentiation libraries. Another approach to dampen these gradient components would be to directly multiply these components with a dampening factor. This feature is currently unavailable in these libraries but may be an interesting direction to look into. A downside of using this strategy though is that it will not reduce the amount of computation similar to h-detach (although it will not increase the amount of computation compared with vanilla LSTM either). Regularizing the recurrent weight matrices to have small norm can also potentially prevent the gradient components from the cell state path from being suppressed but it may also restrict the representational power of the model.Given the superficial similarity of h-detach with dropout, we outline the difference between the two methods. Dropout randomly masks the hidden units of a network during the forward pass (and can be seen as a variant of the stochastic delta rule BID6 ). Therefore, a common view of dropout is training an ensemble of networks BID30 . On the other hand, our method does not mask the hidden units during the forward pass. It instead randomly blocks the gradient component through the h-states of the LSTM only during the backward pass and does not change the output of the network during forward pass. More specifically, our theoretical analysis shows the precise behavior of our method: the effect of h-detach is that it changes the update direction used for descent which prevents the gradients through the cell state path from being suppressed.We would also like to point out that even though we show improvements on the image captioning task, it does not fit the profile of a task involving long term dependencies that we focus on. We believe the reason why our method leads to improvements on this task is that the gradient components from the cell state path are important for this task and our theoretical analysis shows that h-detach prevents these components from getting suppressed compared with the gradient components from the other paths. On the same note, we also tried our method on language modeling tasks but did not notice any benefit. We proposed a simple stochastic algorithm called h-detach aimed at improving LSTM performance on tasks that involve long term dependencies. We provided a theoretical understanding of the method using a novel analysis of the back-propagation equations of the LSTM architecture. We note that our method reduces the amount of computation needed during training compared to vanilla LSTM training. Finally, we empirically showed that h-detach is robust to initialization, makes the convergence of LSTM faster, and/or improves generalization compared to vanilla LSTM (and other existing methods) on various benchmark datasets. . The next T − 1 entries are set to a 8 , which constitutes a delay. The next single entry is a 9 , which represents a delimiter, which should indicate to the algorithm that it is now required to reproduce the initial 10 input tokens as output. The remaining 10 input entries are set to a 8 . The target sequence consists of T + 10 repeated entries of a 8 , followed by the first 10 entries of the input sequence in exactly the same order. DISPLAYFORM0 Here denotes the element-wise product, also called the Hadamard product. σ denotes the sigmoid activation function. DISPLAYFORM1 For any ∈ {f, g, o, i}, define E (w) to be a matrix of size dim(h t ) × dim([h t ; x t ]). We set all the elements of this matrix to 0s if if w is not an element of W . Further, if w = (W ) kl , then (E (w)) kl = 1 and (E (w)) k l = 0 for all (k , l ) = (k, l). DISPLAYFORM2 Lemma 1 Let us assume w is an entry of the matrix DISPLAYFORM3 Proof By chain rule of total differentiation, DISPLAYFORM4 We note that, DISPLAYFORM5 DISPLAYFORM6 Recall that h t = o t tanh(c t ), and thus DISPLAYFORM7 Using the previous Lemma as well as the above notation, we get DISPLAYFORM8 DISPLAYFORM9 Then, z t = (A t + B t )z t−1In other words, where all the symbols used to define A t and B t are defined in notation 1.Proof By Corollary 2, we get DISPLAYFORM10 Similarly by Corollary 3, we get DISPLAYFORM11 Thus we have DISPLAYFORM12 Applying this formula recursively proves the claim.Note: Since A t has 0 n 's in the second column of the block matrix representation, it ignores the contribution of z t coming from h t−1 , whereas B t (having non-zero block matrices only in the second column of the block matrix representation) only takes into account the contribution coming from h t−1 . Hence A t captures the contribution of the gradient coming from the cell state c t−1 . T andz t be the analogue of z t when applying h-detach with probability p during back-propagation. Then, z t = (A t + ξ t B t )(A t−1 + ξ t−1 B t−1 ) . . . (A 2 + ξ 2 B 2 )z 1 where ξ t , ξ t−1 , . . . , ξ 2 are i.i.d. Bernoulli random variables with probability p of being 1, A t and B t and are same as defined in theorem 1.Proof Replacing DISPLAYFORM13 Iterating this formula gives, z t = (A t + ξ t B t )(A t−1 + ξ t−1 B t−1 ) . . . (A 3 + ξ 3 B 3 )z 2Corollary 4 E[z t ] = (A t + pB t )(A t−1 + pB t−1 ) . . . (A 3 + pB 3 )z 2It suffices to take the expectation both sides, and use independence of ξ t 's.",2372,1.278,1305,1.817624521072797,"Recurrent neural networks known their notorious exploding and vanishing gradient problemEVGP This problem becomes evident tasks the information correctly solve them exist over because EVGP prevents important gradient components back adequately over steps We introduce simple (\textit{h}-detach specific LSTM optimization targeted addressing Specifically show when the LSTM weights large the gradient components throughcell state in get suppressed Based the hypothesis these components carry information long term dependencieswhich show their suppression prevent capturing them Our algorithm\footnote{Our code available } prevents gradients flowing this path getting suppressed thus capture such dependencies better We show significant improvements vanilla LSTM gradient based training terms convergence speed to seed learning using our modification on various benchmark datasets Recurrent BID25 ; ) sequential data Compared feed-forward networks the loss landscape are harder optimize Among others this difficulty the exploding and vanishing gradient problem BID8 which more severe recurrent networks arises their loss surface This problem becomes evident tasks training data dependencies exist overDue the aforementioned optimization difficulty variants RNN architectures aim addressing most among such architectures that include long short term memory, BID9 ) gated recurrent unit Chung (2014 ) networks which a variant with forget gates BID5 . These architectures mitigate such difficulties introducing a linear temporal path gradients flow more time steps BID0 on try address parameterizing have unitary transition matrices based the idea unit singular values prevents gradients exploding/vanishingAmong the aforementioned RNN architectures arguably most they more representational power compared GRUs BID31 ) it remains optimize on tasks long term dependencies Examples such tasks copying problem BID2 BID24 , sequential MNIST (Le Figure : The computational graph. Here omitted the inputs x i convenience The top horizontal path through the cell state units c t s the linear temporal path which allows gradients flow more over long durations The dotted blue crosses along the computational paths denote blocking gradients though h t states Eq 2) during We call this approach h-detach et al which designed in produce the correct output retain information overThe goal introduce a simple trick specific LSTM optimization improves its training on tasks long term dependencies To achieve write out the full back-propagation gradient equation LSTM parameters split the composition resulting different paths the unrolled network We then show when LSTM weights large in magnitude through the linear temporal pathcell state get suppressedrecall this path designed allow smooth gradient flow many time steps We show empirical evidence this path carries information long term dependenciessee section hence gradients from getting suppressed is problematic such tasks To fix introduce in expectation scales the individual gradient components prevents through the linear temporal path suppressed In essence the algorithm prevents gradient from flowing the h-state , hence call hdetach Using show improvements convergence/generalization over vanilla LSTM optimization on the copying task transfer copying task sequential and permuted MNIST image captioning In section we showed LSTMs trained hdetach stable without gradient clipping We caution while true in the gradient magnitude depends detaching probability used h-detach Hence for the general case do removing gradient clippingWhen training stacked in h-detach the hidden state simultaneously for a given time step t depending ) stochastically We leave for future work.h-detach stochastically blocks the gradient flowing the hidden states In corollary 1 showed expectation this equivalent dampening the gradient components from paths other the cell state path We especially chose this strategy implementation in current auto-differentiation libraries Another approach dampen these gradient components directly multiply This feature these libraries but an interesting direction A downside this strategy though reduce computation similar hdetachalthough compared vanilla LSTM either Regularizing the recurrent weight matrices have small norm can potentially prevent the gradient components the cell state path suppressed but restrictGiven the superficial similarity hdetach with dropout outline Dropout randomly masks the hidden units a network during the forward passand can seen a variant rule BID6 Therefore a common view dropout training an ensemble networks BID30 . On our method mask the hidden units during the forward pass It instead randomly blocks the gradient component through the h-states only during the backward pass does during More specifically our theoretical analysis the precise behavior our method: h-detach that changes the update direction used descent which prevents through the cell state path suppressedWe would even show improvements the image captioning task fit a task involving long term dependencies that focus We believe the reason our method leads improvements on this task the gradient components from the cell state path important our theoretical analysis h-detach prevents getting suppressed compared On tried our method language modeling tasks but did notice We proposed called h-detach aimed tasks long term dependencies We provided a theoretical understanding the method using a novel analysis the LSTM architecture We note our method reduces computation during training compared vanilla LSTM training Finally empirically showed h-detach robust initialization makes the convergence faster improves comparedand other existing methods various benchmark datasets . The next T − 1 entries set 8 , constitutes a delay The next single entry 9 , represents a delimiter should indicate to the algorithm now required reproduce the initial 10 input tokens output The remaining 10 input entries set 8 . The target sequence consists T + 10 repeated entries 8 , followed in DISPLAYFORM0 Here denotes the element-wise product also the Hadamard product σ denotes the sigmoid activation function DISPLAYFORM1 For any �� {f o define Ew to size dim(h t ; We set all the elements this matrix 0s if if w W Further w = ) klE ( and k l , = DISPLAYFORM2 Lemma 1 Let us assume w is an entry of the matrix DISPLAYFORM3 Proof By chain rule total differentiation We note, Recall h t = o t tanh(c t thus Using as well notation Then zz where all the symbols used defined notation 1.Proof, Similarly by Thus Applying proves the claimNote Since has 0 n 's the block matrix representation ignores the contribution coming , whereas (having non block only in only coming Hence A t captures the contribution the gradient coming the cell state c T andz t be the analogue z t when applying h-detach with probability p during Then z t =A� B( . . (A 2 + �� Bz where t , . . . , �� 2 are Bernoulli random variables of being A t and B t and are same defined theorem 1.Proof Replacing DISPLAYFORM13 Iterating this formula gives, z t t B . . (A 3 + �� 3 Bz 2Corollary 4 E[z tA t + pB t . . . (A 3 + pB 3 )z 2It suffices take the expectation both sides use independence �� t '",0.02,0.787314613672326
"Convolutional Neural Networks (CNNs) significantly improve the state-of-the-art for many applications, especially in computer vision. However, CNNs still suffer from a tendency to confidently classify out-distribution samples from unknown classes into pre-defined known classes. Further, they are also vulnerable to adversarial examples. We are relating these two issues through the tendency of CNNs to over-generalize for areas of the input space not covered well by the training set. We show that a CNN augmented with an extra output class can act as a simple yet effective end-to-end model for controlling over-generalization. As an appropriate training set for the extra class, we introduce two resources that are computationally efficient to obtain: a representative natural out-distribution set and interpolated in-distribution samples. To help select a representative natural out-distribution set among available ones, we propose a simple measurement to assess an out-distribution set's fitness. We also demonstrate that training such an augmented CNN with representative out-distribution natural datasets and some interpolated samples allows it to better handle a wide range of unseen out-distribution samples and black-box adversarial examples without training it on any adversaries. Finally, we show that generation of white-box adversarial attacks using our proposed augmented CNN can become harder, as the attack algorithms have to get around the rejection regions when generating actual adversaries. Convolutional Neural Networks (CNNs) have allowed for significant improvements over the stateof-the-art in the last few years for various applications, and in particular for computer vision. Notwithstanding these successes, challenging issues remain with these models. In the following work, we specifically look at two concerns. First, CNNs are vulnerable to different types of adversarial examples BID26 BID13 BID3 . These adversarial examples are created by deliberately modifying clean samples with imperceptible perturbations, with the aim of misleading CNNs into classifying them to a wrong class with high confidence. Second, CNNs are not able to handle instances coming from outside the task domain on which they are trained -the so-called out-distribution samples BID18 BID15 . In other words, although these examples are semantically and statistically different from the (in-distribution) samples relevant to a given task, the neural network trained on the task assigns such out-of-concept samples with high-confidence to the pre-defined in-distribution classes. Due to the susceptibility of CNNs to both adversaries and out-distribution samples, deploying them for real-world applications, in particular for security-sensitive ones, is a serious concern. These two issues have been treated separately in the past, with two distinct family of approaches. For instance, on the one hand, to handle out-distribution samples, some researchers have proposed threshold-based post-processing approaches with the aim of firstly calibrating the predictive confidence scores provided by either a single pre-trained CNN BID18 BID10 BID17 or an ensemble of CNNs BID15 , and then detecting out-distribution samples according to an optimal threshold. However, it is difficult to define an optimal and stable threshold for rejecting a wide range of out-distribution samples without increasing the false negative rate (i.e., rejecting in-distribution samples). On the other hand, researchers regarded adversarial examples as a distinct issue from the out-distribution problem and attempted to either correctly classify all adversaries through adversarial training of CNNs BID27 BID7 or reject all of them by training a separate detector BID5 BID20 . The performance of these approaches at properly handling adversarial instances mostly depends on having access to a diverse set of training adversaries, which is not only computationally expensive but also handling some possible future adversaries, which have not been discovered yet, most likely is difficult.It is known that deep neural networks (e.g. CNNs) are prone to over-generalization in the input space by partitioning it entirely into a set of pre-defined classes for a given in-distribution set (task), regardless of the fact that in-distribution samples may only be relevant to a small portion of the input space BID18 BID25 BID0 . In this paper, we highlight that the two aforementioned issues of CNNs can be alleviated simultaneously through control of over-generalization. To this end, we propose that an augmented CNN, a regular (naive) CNN with an extra class dubbed as dustbin, can be a simple yet effective solution, if it is trained on appropriate training samples for the dustbin class. Furthermore, we introduce here a computationally-efficient answer to the following key question: how to acquire such an appropriate set to effectively reduced the over-generalized regions induced by naive CNN. We note that our motivation for employing an augmented CNN is different from the threshold-based post-processing approaches that attempt to calibrate the predictive confidence scores of a pre-trained naive CNN without impacting its feature space. Our motivation in fact is to learn a more expressive feature space, where along with learning the sub-manifolds corresponding to in-distribution classes, a distinct extra sub-manifold for the dustbin class can be obtained such that the samples drawn from many over-generalized regions including a wide-range of out-distribution samples and various types of adversaries are mapped to this ""dustbin"" sub-manifold.As a training source for the extra class (dustbin), one can consider using synthetically generated out-distribution samples BID17 BID11 or adversarial examples BID8 . However, using such generated samples is not only computationally expensive but also barely able to effectively reduce over-generalization compared to naive CNNs (see Sec. 3). Instead of such synthetic samples, there are plenty of cost-effective training sources available for the extra dustbin class, namely natural out-distribution datasets. By natural out-distribution sets we mean the sets containing some realistic (not synthetically generated) samples that are semantically and statistically different from those in the in-distribution set. A representative natural out-distribution set for a given in-distribution task should be able to adequately cover the over-generalized regions. To recognize such a representative natural set, we propose a simple measurement to assess its fitness for a given in-distribution set. In addition to the selected set, we generate some artificial out-distribution samples through a straightforward and computationally efficient procedure, namely by interpolating some pair of in-distribution samples. We believe a properly trained augmented CNN can be utilized as a threshold-free baseline for identifying concurrently a broad range of unseen out-distribution samples and different types of strong adversarial attacks.The main contributions of the paper are summarized as:• By limiting the over-generalization regions induced by naive CNNs, we are able to drastically reduce the risk of misclassifying both adversaries and samples from a broad range of (unseen) out-distribution sets. To this end, we demonstrate that an augmented CNN can act as a simple yet effective solution.• We introduce a measurement to select a representative natural out-distribution set among those available for training effective augmented CNNs, instead of synthesizing some dustbin samples using hard-to-train generators.• Based on extensive experiments on a range of different image classification tasks, we demonstrate that properly trained augmented CNNs can significantly reduce the misclassification rates for both 1 ) unseen out-distribution sets, and 2) for various types of strong black-box adversarial examples, even though they are never trained on any specific types of adversaries.• For the generation of white-box adversaries using our proposed augmented CNN, the adversarial attack algorithms frequently encounter dustbin regions rather than regions from other classes when distorting a clean samples, making the adversaries generation process more difficult. In this paper we bridge two issues of CNNs that were previously thought of as unrelated: susceptibility of naive CNNs to various types of adversarial examples and incorrect high confidence prediction for out-distribution samples. We argue these two issues are connected through over-generalization. We propose augmented CNNs as a simple yet effective solution for controlling over-generalization, when they are trained on an appropriate set of dustbin samples. Through empirical evidence, we define an indicator for selecting an ""appropriate"" natural out-distribution set as training samples for dustbin class from among those available and show such selection plays a vital role for training effective augmented CNNs. Through extensive experiments on several augmented CNNs in different settings, we demonstrate that reducing over-generalization can significantly reduce the misclassification error rates of CNNs on adversaries and out-distribution samples, simultaneously, while their accuracy rates on in-distribution samples are maintained. Indeed, reducing over-generalization by such an end-to-end learning model (e.g., augmented CNNs) leads to learning more expressive feature space where these two categories of hostile samples (i.e., adversaries and out-distribution samples) are disentangled from in-distribution samples.",1771,0.771,1035,1.711111111111111," significantly the state for many applications However CNNs still suffer confidently classify out-distribution samples unknown classes into pre-defined known classes Further they vulnerable adversarial examples We relating through the tendency CNNs over for areas the input space not well the training set We show a CNN augmented with an extra output class act simple yet end model controlling over-generalization As an appropriate training set the extra class introduce two resources computationally obtain a representative natural out-distribution set interpolated in samples To select a representative natural out-distribution set among available ones propose a simple measurement We also demonstrate training such an augmented CNN with representative out-distribution natural datasets and some interpolated samples allows it better handle unseen out-distribution samples black-box adversarial examples without training any adversaries Finally show generation white-box adversarial attacks using our proposed augmented CNN can become harder as the attack algorithms get around the rejection regions when generating actual adversaries allowed for various applications Notwithstanding these successes challenging issues with these models In the following work specifically look two concerns First CNNs are vulnerable different types adversarial examples BID26 BID13 BID3 . These adversarial examples created deliberately modifying clean samples with misleading CNNs classifying to a wrong class with high confidence Second CNNs are able handle instances coming the task domain on trained -the so-called out-distribution samples BID18 BID15 . In although these examples semantically and statistically (indistribution samples relevant the neural network trained assigns such outconcept samples with predefined in classes Due the susceptibility CNNs both adversaries out-distribution samples deploying them in security-sensitive ones These two issues treated separately two distinct family of approaches For instance on to handle out-distribution samples some researchers proposed threshold-based post-processing approaches with firstly calibrating the predictive confidence scores provided either a single pre-trained CNN BID18 BID10 BID17 , detecting according an optimal threshold However difficult define an optimal and stable threshold rejecting out-distribution samples without increasing rejecting in On researchers regarded adversarial examples a distinct issue the out-distribution problem and attempted either correctly all adversaries through of CNNs BID27 BID7 reject training a separate detector . The performance these approaches at properly handling adversarial instances mostly having access training adversaries only computationally handling some possible future adversaries have discovered most is difficultIt known prone the input space by partitioning entirely indistribution settask regardless in samples only relevant BID18 BID25 BID0 . In highlight that the two aforementioned issues CNNs can simultaneously control To this end propose an augmented CNN, a regular (naive) CNN an extra class dubbed as dustbin can a simple yet effective solution, if trained appropriate training samples Furthermore introduce here a computationally-efficient answer acquire such an appropriate set to effectively reduced the over-generalized regions induced naive CNN We note our motivation employing an augmented CNN different the threshold-based post-processing approaches attempt calibrate the predictive confidence scores a pre-trained naive CNN without impacting its feature space Our motivation fact learn a more expressive feature space along learning the submanifolds corresponding indistribution classes a distinct extra sub for the dustbin class obtained such the samples drawn many over-generalized regions including various types adversaries mapped this ""As a training source the extra class ( one consider using BID17 BID11 or adversarial examples . However using such generated samples only barely able effectively reduce compared naive CNNs Sec 3 Instead such synthetic samples there plenty cost-effective training sources the extra dustbin class namely natural out-distribution datasets By natural out-distribution sets we mean the sets containing some realistic (not synthetically generated) samples semantically and statistically in A representative natural out-distribution set given in task should adequately cover the over-generalized regions To recognize such a representative natural set propose a simple measurement assess its fitness in set In addition the selected set generate some artificial out-distribution samples through namely by some pair in We believe a properly trained augmented CNN utilized a threshold-free baseline identifying concurrently a broad range unseen out-distribution samples different types strong adversarial attacksThe main contributions the paper By limiting over regions induced naive CNNs drastically both adversaries samples from To this end demonstrate an augmented CNN act simple yet solution.• introduce a measurement select a representative natural out-distribution set among those available training effective augmented CNNs instead synthesizing some dustbin samples using hardtrain Based extensive experiments different image classification tasks significantly both 1 ) for various types strong black-box adversarial examples even never any specific types For the generation white-box adversaries using the adversarial attack algorithms frequently encounter dustbin regions rather regions from other classes when distorting a clean samples the adversaries generation process In bridge two issues CNNs that were thought unrelated susceptibility naive CNNs various types adversarial examples incorrect high confidence prediction for out-distribution samples We argue these two issues connected through over-generalization We propose augmented CNNs controlling when they trained dustbin samples Through empirical evidence define an indicator selecting an ""appropriate"" natural out-distribution set training samples dustbin class from among those available and show such selection plays training effective augmented CNNs Through extensive experiments reducing on adversaries simultaneously, their accuracy rates on in maintained Indeed reducing over-generalization by such end learning (e.g., augmented CNNs leads learning more expressive feature space where these two categories hostile samples out-distribution samples in",0.01,0.5159278032558264
"Modern deep artificial neural networks have achieved impressive results through models with very large capacity---compared to the number of training examples---that control overfitting with the help of different forms of regularization. Regularization can be implicit, as is the case of stochastic gradient descent or parameter sharing in convolutional layers, or explicit. Most common explicit regularization techniques, such as dropout and weight decay, reduce the effective capacity of the model and typically require the use of deeper and wider architectures to compensate for the reduced capacity. Although these techniques have been proven successful in terms of results, they seem to waste capacity. In contrast, data augmentation techniques reduce the generalization error by increasing the number of training examples and without reducing the effective capacity. In this paper we systematically analyze the effect of data augmentation on some popular architectures and conclude that data augmentation alone---without any other explicit regularization techniques---can achieve the same performance or higher as regularized models, especially when training with fewer examples. Regularization plays a central role in machine learning. Loosely defined, regularization is any modification applied to a learning algorithm that helps prevent overfitting and improve generalization. Whereas in simple machine learning algorithms the sources of regularization can be easily identified as explicit terms in the objective function, in modern deep neural networks the sources of regularization are multiple and some of them are not explicit, but implicit.Although the terms explicit and implicit regularization have been used recently in the literature (Neyshabur et al., 2014; Zhang et al., 2017) , their distinction is rather subjective. We propose the following definitions:• Explicit regularization techniques are those specifically and solely designed to constrain the effective capacity of a given model in order to reduce overfitting. Furthermore, explicit regularizers are not a structural or essential part of the network architecture, the data or the learning algorithm and can typically be added or removed easily.• Implicit regularization is the reduction of the generalization error or overfitting provided by characteristics of the network architecture, the training data or the learning algorithm, which are not specifically designed to constrain the effective capacity of the given model.Examples of explicit regularizers are weight decay BID14 , which penalizes large parameters; dropout (Srivastava et al., 2014) , which randomly removes a fraction of the neural connections during training; or stochastic depth BID18 , which drops whole layers instead. Implicit regularization effects are provided by the popular stochastic gradient descent (SGD) algorithm, which tends to converge to solutions with small norm (Zhang et al., 2017) ; convolutional layers, which impose parameter sharing based on prior knowledge about the data; batch normalization BID19 , whose main goal is reducing the the internal covariate shift, but also implicitly regularizes the model due to the noise in the batch estimates for mean and variance.Driven by the efficient use and development of GPUs, much research efforts have been devoted to finding ways of training deeper and wider networks of larger capacity (Simonyan & Zisserman, 2014; BID17 Zagoruyko & Komodakis, 2016) , Ironically, their effective capacity is eventually reduced in practice by the use of weight decay and dropout, among other explicit regularizers. It is known , for instance, that the gain in generalization provided by dropout comes at the cost of using larger models and training for longer BID11 . Hence, it seems that with such an approach deep networks are wasting capacity BID4 . As a matter of fact, unlike traditional machine learning models, deep neural networks seem not to need explicit regularizers to generalize well, as recently suggested by Zhang et al. (2017) .One popular technique that also improves generalization is data augmentation. Importantly , it differs from explicit regularizers mainly in that it does not reduce the effective capacity of the model. Data augmentation is a very old practice in machine learning (Simard et al., 1992) and it has been identified as a critical component of many models BID3 BID22 BID24 . However, although some authors have reported the impact of data augmentation on the performance of their models and, in some cases, a comparison of different amount of augmentation BID13 ) the literature lacks, to our knowledge, a systematic analysis of the impact of data augmentation on deep neural networks compared to the most popular regularization techniques. In this work, we have presented a systematic analysis of the role of data augmentation in deep neural networks for object recognition, focusing on the comparison with popular techniques of explicit regularization. We have built upon the work by Zhang et al. (2017) , where the authors concluded that explicit regularization is not necessary, although it improves generalization performance. Here, we have shown that it is not only unnecessary, but also that the generalization gain provided by explicit regularization can be achieved by data augmentation alone.The importance of these results lies in the fact that explicit regularization is the standard tool to enable the generalization of most machine learning methods. However, according to Zhang et al. (2017) , explicit regularization plays a different role in deep learning, not explained by statistical learning theory (Vapnik & Chervonenkis, 1971) . We argue instead that the theory still holds in deep learning, but one has to properly consider the crucial role of implicit regularization. Explicit regularization is no longer necessary because its contribution is already provided by the many elements that implicitly regularize the models: SGD, convolutional layers or data augmentation, among others.Whereas explicit regularizers, such as weight decay and dropout, succeed in mitigating overfitting by blindly reducing the effective capacity of a model, implicit regularization operates more effectively at capturing important characteristics of the data (Neyshabur et al., 2014) . For instance, convolutional layers successfully reduce the capacity of a model by imposing a parameter sharing strategy that incorporates some essential prior domain knowledge, as well as data augmentation by transforming the training examples in a meaningful and plausible way.In this regard it is worth highlighting some of the advantages of data augmentation: Not only does it not reduce the effective capacity of the model, but it increases the number of training examples, which, according to statistical learning theories, reduces the generalization error. Furthermore, if the transformations are such that they reflect plausible variations of the real objects, it increases the robustness of the model and it can be regarded as a data-dependent prior, similarly to unsupervised pre-training BID7 . Besides, unlike explicit regularization techniques, data augmentation does not increase the computational complexity because it can be performed in parallel to the gradient updates on the CPU, making it a computationally free operation. Finally, in Section 2.4 we have shown how data augmentation transparently adapts to architectures of different depth, whereas explicitly regularized models need manual adjustment of the regularization parameters.Deep neural networks can especially benefit from data augmentation because they do not rely on precomputed features and because the large number of parameters allows them to shatter the augmented training set. Actually, if data augmentation is included for training, we might have to reconsider whether deep learning operates in an overparameterization regime, since the model capacity should take into account the amount of training data, which is exponentially increased by augmentation.Some argue that despite these advantages, data augmentation is a highly limited approach because it depends on some prior expert knowledge and it cannot be applied to all domains. However, we argue instead that expert knowledge should not be disregarded but exploited. A single data augmentation scheme can be designed for a broad family of data, e.g. natural images, and effectively applied to a broad set of tasks, e.g. object recognition, segmentation, localization, etc. Besides, some recent works show that it is possible to learn the data augmentation strategies (Lemley et al., 2017; Ratner et al., 2017) and future research will probably yield even better results in different domains.Finally, it is important to note that, due to computational limitations, we have performed a systematic analysis only on CIFAR-10 and CIFAR-100, which consist of very small images. These data sets do not allow performing more agressive data augmentation since the low resolution images can easily show distortions that hinder the recognition of the object. However, some previous works BID13 Springenberg et al., 2014) have shown impressive results by performing heavier data augmentation on higher resolution versions on CIFAR-10. We plan to extend this analysis to higher resolution data sets such as ImageNet and one could expect even more benefits from data augmentation compared to explicit regularization techniques.",1755,0.725,1041,1.685878962536023,"Modern deep artificial neural networks achieved impressive results through models with very large capacity--- training examples---that control overfitting with the help different forms regularization Regularization can implicit is of or parameter sharing explicit. Most common explicit regularization techniques, dropout weight decay reduce the effective capacity the model typically deeper and wider architectures compensate Although these techniques proven successful terms results seem waste capacity In contrast data augmentation techniques reduce the generalization error increasing training examples without the effective capacity In this paper systematically analyze data augmentation some popular architectures conclude alone---without any other explicit regularization techniques achieve or higher as regularized models especially training fewer examples Regularization plays machine learning Loosely defined regularization any modification applied a learning helps prevent improve Whereas in simple machine learning the sources regularization can as explicit terms the objective function modern deep neural multiple and some implicitAlthough the terms explicit regularization recently (Neyshabur et al Zhang 2017 , their distinction rather subjective We propose the following definitions:• Explicit regularization techniques those specifically and solely constrain the effective capacity a given model reduce Furthermore explicit regularizers a structural or essential part the network architecture the data or the learning algorithm and can typically added easily.• the reduction the generalization error or provided characteristics specifically constrain the effective capacity the given modelExamples weight decay BID14 , which penalizes large parameters; dropout (Srivastava randomly removes a fraction the neural connections during stochastic depth BID18 drops whole layers instead. Implicit regularization effects provided the popular stochastic gradient descent tends converge solutions small norm (Zhang et al 2017 ; convolutional layers, impose parameter sharing based prior knowledge; batch normalization BID19 , whose main goal reducing the the internal covariate shift implicitly due the noise the batch estimates for meanDriven the efficient use and development GPUs much research efforts finding training deeper and wider networks larger capacitySimonyan Zisserman BID17 Zagoruyko Komodakis Ironically their effective capacity eventually in practice weight decay dropout among other explicit regularizers It known , for the gain generalization provided dropout comes using larger models training for longer BID11 . Hence with such an approach deep networks wasting capacity BID4 . As a matter unlike traditional machine learning models seem not need explicit regularizers generalize well recently suggested (2017) .One popular technique that also improves generalization data augmentation Importantly , it differs explicit regularizers mainly reduce the effective capacity Data augmentation a very old practice (Simard 1992 identified many models BID3 BID22 . However although some authors reported the impact data augmentation and, a comparison different amount augmentation BID13 ) the literature lacks, to deep neural networks compared the most popular regularization techniques In this work have presented data augmentation deep neural networks for focusing the comparison with popular techniques explicit regularization We built upon by Zhang et al (2017 , where concluded explicit regularization although improves Here, shown it unnecessary that the generalization gain provided explicit regularization achieved data augmentation aloneThe importance these results the standard tool enable most machine learning methods However according Zhang et al (2017 , explicit regularization plays deep learning not explained statistical learning theoryVapnik Chervonenkis 1971 We argue instead the theory still deep learning one has properly the crucial role implicit regularization Explicit regularization no because its contribution already provided the many elements implicitly the models: SGD convolutional layers or data augmentation amongWhereas, weight decay dropout succeed mitigating overfitting blindly reducing the effective capacity operates more at capturing important characteristics (Neyshabur et al) . For instance convolutional layers successfully reduce the capacity a model imposing a parameter sharing strategy incorporates some essential prior domain knowledge as data augmentation by transforming the training examples in a meaningful and plausible wayIn this regard it highlighting: Not not reduce the effective capacity increases, according statistical learning theories reduces Furthermore if the transformations such reflect plausible variations the real objects increases it regarded datadependent prior similarly unsupervised pre-training BID7 . Besides unlike explicit regularization techniques data augmentation does increase because can to the gradient updates on the CPU making computationally free operation Finally in Section we shown data augmentation transparently adapts architectures different depth whereas explicitly regularized models need manual adjustment the regularization parametersDeep neural networks especially do because the large number parameters allows shatter the augmented training set Actually if data augmentation included for training might reconsider whether deep learning operates an overparameterization regime the model capacity should take which exponentially increased augmentationSome argue despite these advantages a highly limited approach because depends some prior expert knowledge it However we argue instead that expert knowledge should but exploited A single data augmentation scheme designed a broad family data, e.g. natural images and effectively applied tasks object segmentation localization Besides some recent works show it learn the data augmentation strategies (Lemley 2017 Ratner future research probably yield in different domainsFinally, due computational limitations performed CIFAR-10 consist very small images These data sets do allow performing more agressive data augmentation since the low resolution images easily show distortions that hinder the recognition However some previous works BID13 Springenberg et al) impressive results by performing heavier data augmentation higher resolution versions on CIFAR-10 We plan extend this analysis higher resolution data sets such ImageNet one could even more benefits data augmentation compared explicit regularization techniques",0.01,0.4516385055588367
"Text editing on mobile devices can be a tedious process. To perform various editing operations, a user must repeatedly move his or her fingers between the text input area and the keyboard, making multiple round trips and breaking the flow of typing. In this work, we present Gedit, a system of on-keyboard gestures for convenient mobile text editing. Our design includes a ring gesture and flicks for cursor control, bezel gestures for mode switching, and four gesture shortcuts for copy, paste, cut, and undo. Variations of our gestures exist for one and two hands. We conducted an experiment to compare Gedit with the de facto touch+widget based editing interactions. Our results showed that Gedit’s gestures were easy to learn, 24% and 17% faster than the de facto interactions for one- and two-handed use, respectively, and preferred by participants. Text entry is a fundamental input task on almost all computers, including touch-based mobile devices like smartphones and tablets. However, while touch-based text entry has garnered much attention, touch-based text editing has garnered less. Text editing, the process of correcting text, moving and replacing the cursor, selecting character ranges, and performing operations like copy-and-paste, still largely borrows from desktop mouse interactions, leading to certain inefficient editing processes on touch-based mobile devices. Modeless editing operations [18] such as copy, paste, and cut are often handled in a touch+widget [7] manner: to copy text, one must touch exactly on the text to be selected, long-press to trigger ""selection mode,"" drag the selection endpoints to adjust the selection range, and then select ""copy."" However, the cursor is positioned using tap gestures, which are error prone because of the fat finger problem [20] , especially when text characters are small [1] . Also, users must press long enough to exceed a time threshold to trigger selection mode, and later select ""copy"" in a popup menu to complete the operation. These extra steps significantly slow text editing on mobile touch screens. Moreover, if an editing operation must happen during the text entry process, one must lift one's finger from the keyboard area to directly interact with the text input area, introducing unnecessary round-trips [5, 10, 12] and breaking the flow of typing. Previous work has demonstrated the feasibility of gesture shortcuts. Fuccella et al. [7] designed multiple gestures on the keyboard area for different editing operations. For example, one can perform a swipe gesture to move the cursor, or a ""C"" gesture to copy text. They further introduced a gesture to initiate editing mode to avoid conflict with gesture typing [8] . Building upon their work, we improve the cursormoving and edit-initiating gestures and provide a gestureonly system, Gedit, for most text editing operations on mobile devices. For example, one of Gedit's designs, the ring gesture, is shown in Figure 1 . Our work distinguishes itself from Fuccella et al. [7] and other prior work in four important respects: (1) instead of discrete cursor control (e.g., one swipe gesture yields one cursor movement action), we provide a ring gesture for continuous, reversible cursor control. A significant advantage is that a user can move the cursor over a long range without clutching; (2) rather than using a single tap, we use bezel gestures [17] to enter editing mode, which we show is more distinguishable than a key-press [4] ; (3) we added undo functionality to the gesture set, as undo is heavily used in text editing; and (4) we provide text editing gestures in both one-and two-handed modes, a significant design achievement given the constraints of one-handed use. In our design of Gedit, we were careful to ensure that it remains compatible with gesture typing [13, 22] . And because Gedit respects current interaction techniques, it is deployable on today's mobile systems without causing interference. To evaluate Gedit, we conducted a text editing experiment. Our results show that compared to the de facto touch+widget method of text editing described above, Gedit was faster and preferred, especially for one-handed use. Our goal was to evaluate Gedit on its editing efficiency and users' subjective preferences. The results showed that our gesture interactions sped up the text editing process compared to the de facto editing approach of tapping keys and tapping the text input area to position the cursor (touch+widget). Participants especially appreciated the capability that Gedit's gestures offered for one-handed use. Participants generally enjoyed the Gedit gestures. The major reasons were having a feeling of precise control, convenience, and speed. Many participants also mentioned that the editing gestures such as copy and paste were faster than pointing and holding, and also less tedious to perform. Participants had split preferences on the one-vs. two-handed versions of Gedit. Four participants preferred two-handed Gedit because ""it is more intuitive just like the shortcuts"" (P13), and ""the gestures in double-hand mode are easier to perform"" (P14). Four participants preferred one-handed Gedit because ""it is faster, as I don't need to enter the editing mode with another finger"" (P7). As for different gestures, we noticed that participants usually used the ring gesture to fix typos, while using the flick gestures to select whole words. In this paper, we presented Gedit, a system of on-keyboard gestures for text editing: ring and flick gestures for cursor control and text selection, bezel gestures for mode switching, and letter-like gestures for editing commands. The gestures can be performed in both one-and two-handed modes. Through our formal study, we demonstrated that Gedit sped up the editing process and reduced text entry time, was perceived to require less workload, and was preferred to the de facto method of tapping keys and tapping text input areas.",1188,0.725,702,1.6923076923076923,"Text editing on To perform various editing operations repeatedly move the text input area making multiple round trips and breaking the flow typing In this work Gedit onkeyboard gestures convenient mobile text editing Our design includes a ring gesture flicks for cursor control bezel gestures mode switching four gesture shortcuts copy cut undo Variations our gestures exist one and two hands We conducted Gedit the de facto touch+widget based editing interactions Our results Gedit��s gestures easy 24 and 17 the de facto interactions for preferred participants Text entry is a fundamental input task on almost all computers However while touch-based text entry garnered garnered. Text editing the process correcting moving replacing the cursor selecting character ranges performing operations like copy still largely borrows desktop mouse interactions leading certain inefficient editing processes on Modeless editing operations [18 such copy cut often handled a touch+widget [7 manner: to one touch exactly on selected long-press trigger ""selection mode drag the selection endpoints adjust However positioned using tap gestures error because the fat finger problem , especially text characters small Also users must press long exceed a time threshold trigger selection mode later select ""copy in complete These extra steps significantly slow text editing mobile touch screens Moreover if an editing operation must happen during the text entry process one lift one's finger directly interact introducing unnecessary round-trips [5 10 breaking typing Previous work demonstrated gesture shortcuts Fuccella et [7 designed multiple gestures the keyboard area different editing operations For example one perform a swipe gesture ""C copy text They further introduced a gesture initiate editing mode avoid conflict gesture typing [8 Building upon we improve the cursormoving and edit-initiating gestures provide a gestureonly system Gedit most text operations on For example one Gedit's designs the ring gesture shown Figure . Our work distinguishes Fuccella [7 and other prior four important respects instead discrete cursor control one swipe gesture yields one cursor movement action provide a ring gesture continuous, reversible cursor control A significant advantage a user move clutching; ( rather we bezel gestures [17 enter editing mode we show is more distinguishable4 ; added undo functionality the gesture set as undo heavily provide text editing gestures both one-and two-handed modes a significant design achievement given In our design Gedit were careful remains compatible gesture typing [13, 22 And because Gedit respects current interaction techniques deployable today's mobile systems without causing interference To evaluate Gedit a text editing experiment Our results compared the de facto touch+widget method text editing described Gedit was faster preferred, especially Our goal evaluate Gedit on its editing efficiency users' subjective preferences The results showed our gesture interactions sped the text editing process compared the de facto editing approach tapping keys the text input area position (touch+widget Participants especially appreciated the capability that Gedit's gestures offered Participants generally enjoyed the Gedit gestures The major reasons were having a feeling precise control convenience speed Many participants also mentioned the editing gestures such copy faster pointing holding, also less tedious Participants had split preferences the one-vs. two-handed versions Gedit Four participants preferred two-handed Gedit because "" just the shortcutsP13the gestures in double-hand mode perform Four participants preferred one-handed Gedit because "" faster as I enter with another finger (P7 As for different gestures noticed participants usually the ring gesture fix typos using the flick gestures select whole words In this paper presented Gedit onkeyboard gestures: ring and flick cursor control text selection bezel mode switching letterlike editing commands The gestures can performed Through our formal study demonstrated Gedit sped reduced text entry time was perceived require less workload preferred the de facto method tapping keys tapping text input areas",0.01,0.4680183441950279
"Deep learning achieves remarkable generalization capability with overwhelming number of model parameters. Theoretical understanding of deep learning generalization receives recent attention yet remains not fully explored. This paper attempts to provide an alternative understanding from the perspective of maximum entropy. We first derive two feature conditions that softmax regression strictly apply maximum entropy principle. DNN is then regarded as approximating the feature conditions with multilayer feature learning, and proved to be a recursive solution towards maximum entropy principle. The connection between DNN and maximum entropy well explains why typical designs such as shortcut and regularization improves model generalization, and provides instructions for future model development. Deep learning has achieved significant success in various application areas. Its success has been widely ascribed to the remarkable generalization ability. Recent study shows that with very limited training data, a 12-layer fully connected neural network still generalizes well while kernel ridge regression easily overfits with polynomial kernels of more than 6 orders (Wu et al., 2017) . Classical statistical learning theories like Vapnik-Chervonenkis (VC) dimension (Maass, 1994) and Rademacher complexity (Neyshabur et al., 2015) evaluate generalization based on the complexity of the target function class. It is suggested that the models with good generalization capability are expected to have low function complexity. However, most successful deep neural networks already have over 100 hidden layers, e.g., ResNet BID2 and DenseNet BID3 for image recognition. The number of model parameters in these cases is even larger than the number of training samples. Statistical learning theory cannot well explain the generalization capability of deep learning models (Zhang et al., 2017) .Maximum Entropy (ME) is a general principle for designing machine learning models. Models fulfilling the principle of ME make least hypothesis beyond the stated prior data, and thus lead to least biased estimate possible on the given information BID5 . Appropriate feature functions are critical in applying ME principle and largely decide the model generalization capability BID1 . Different selections of feature functions lead to different instantiations of maximum entropy models (Malouf, 2002; Yusuke & Jun'ichi, 2002) . The most simple and wellknown instantiation is that ME principle invents identical formulation of softmax regression by selecting certain feature functions and treating data as conditionally independent (Manning & Klein, 2003) . It is obvious that softmax regression has no guaranty of generalization, indicating that inappropriate feature functions and data hypothesis violates ME principle and undermines the model performance. It remains not fully studied how to select feature functions to maximally fulfill ME principle and guarantee the generalization capability of ME models. Maximum entropy provides a potential but not-ready way to understand deep learning generalization. This paper is motivated to improve the theory behind applying ME principle and use it to understand deep learning generalization. We research on the feature conditions to equivalently apply ME principle, and indicates that deep neural networks (DNN) is essentially a recursive solution to approximate the feature conditions and thus maximally fulfill ME principle.• In Section 2, we first revisit the relation between generalization and ME principle, and conclude that models well fulfilling ME principle requires least data hypothesis so to possess good generalization capability. One general guideline for feature function selection is to transfer the hypothesis on input data to the constrain on model features 1 . This demonstrates the role of feature learning in designing ME models.• Section 3 addresses what features to learn. Specifically, we derive two feature conditions to make softmax regression strictly equivalent to the original ME model (denoted as Maximum Entropy Equivalence Theorem). That is, if the utilized features meet the two conditions, simple softmax regression model can fulfill ME principle and guarantee generalization. These two conditions actually specify the goal of feature learning.• Section 4 resolves how to meet the feature conditions and connects DNN with ME. Based on Maximum Entropy Equivalence Theorem, viewing the output supervision layer as softmax regression, the DNN hidden layers before the output layer can be regarded as learning features to meet the feature conditions. Since the feature conditions are difficult to be directly satisfied, they are optimized and recursively decomposed to a sequence of manageable problems. It is proved that, standard DNN uses the composition of multilayer non-linear functions to realize the recursive decomposition and uses back propagation to solve the corresponding optimization problem.• Section 5 employs the above ME interpretation to explain some generalization-related observations of DNN. Specifically, from the perspective of ME, we provide an alternative way to understand the connection between deep learning and Information Bottleneck (Shwartz-Ziv & Tishby, 2017) . Theoretical explanations on typical generalization design of DNN, e.g., shortcut, regularization , are also provided at last.The contributions are summarized in three-fold:1. We derive the feature conditions that softmax regression strictly apply maximum entropy principle . This helps understanding the relation between generalization and ME models, and provides theoretical guidelines for feature learning in these models.2. We introduce a recursive decomposition solution for applying ME principle. It is proved that DNN maximally fulfills maximum entropy principle by multilayer feature learning and softmax regression, which guarantees the model generalization performance.3. Based on the ME understanding of DNN, we provide explanations to the information bottleneck phenomenon in DNN and typical DNN designs for generalization improvement. This paper regards DNN as a solution to recursively decomposing the original maximum entropy problem. From the perspective of maximum entropy, we ascribe the remarkable generalization capability of DNN to the introduction of least extra data hypothesis. The future work goes in two directions: (1) first efforts will be payed to identifying connections with other generalization theories and explaining more DNN observations like the role of ReLu activation and redundant features; (2) the second direction is to improve and exploit the new theory to provide instructions for future model development of traditional machine learning as well as deep learning methods.",1219,0.667,714,1.707282913165266,"Deep learning achieves remarkable generalization capability overwhelming number model parameters Theoretical understanding deep learning generalization receives yet not This paper attempts from maximum entropy We first derive two feature conditions softmax regression strictly apply maximum entropy principle DNN then regarded approximating the feature conditions with multilayer feature learning proved a recursive solution towards maximum entropy principle The connection DNN maximum entropy well explains typical designs such shortcut regularization improves model generalization provides instructions future model development Deep learning achieved various application areas Its success widely the remarkable generalization ability. Recent study with very limited training data a 12-layer fully connected neural network still generalizes while kernel ridge regression easily overfits with polynomial kernels (Wu Classical statistical learning theories like Vapnik-Chervonenkis (VC) dimensionMaass Rademacher complexityNeyshabur et al 2015 evaluate the target function class It suggested the models with good generalization capability expected low function complexity However most successful deep neural networks already over 100 hidden layers ResNet BID2 for The number model parameters these cases even training samples Statistical learning theory well the generalization capability 2017 .Maximum EntropyME designing Models fulfilling ME make least hypothesis beyond the stated prior data lead least biased estimate possible on BID5 . Appropriate feature functions critical applying ME principle largely decide the model generalization capability BID1 Different selections feature functions lead maximum entropy modelsMalouf Yusuke Jun'ichi The most simple and wellknown instantiation ME principle invents identical formulation softmax regression by selecting certain feature functions treating data conditionally independentManning Klein It obvious softmax regression no guaranty generalization indicating inappropriate feature functions data hypothesis violates ME principle undermines the model performance It remains not fully studied select feature functions maximally fulfill ME principle guarantee the generalization capability Maximum entropy provides a potential but not-ready way understand This paper motivated improve behind applying ME principle use We research on the feature conditions to equivalently apply ME principle indicates is essentially a recursive solution approximate maximally fulfill ME principle.• Section first revisit conclude well fulfilling requires least data hypothesis so to possess One general guideline feature function selection transfer the hypothesis on input data model features 1 This demonstrates feature learning designing ME models.• Section addresses what Specifically derive two feature conditions softmax regression strictly equivalent the original ME modeldenoted That the utilized features meet simple softmax regression model fulfill ME principle guarantee These two conditions actually specify feature learning.• Section resolves meet the feature conditions connects DNN with ME Based Maximum Entropy Equivalence Theorem viewing the output supervision layer softmax regression the DNN hidden before can regarded learning features to meet Since the feature conditions difficult be directly satisfied they optimized decomposed a sequence manageable problems It proved standard DNN uses the composition realize uses back propagation problem.• Section employs the above ME interpretation some generalization-related observations Specifically from ME provide deep learning Information Bottleneck (Shwartz-Ziv & Tishby . Theoretical explanations on typical generalization design DNN, shortcut , lastThe contributions three- We derive the feature conditions softmax regression strictly apply maximum entropy principle . This helps understanding generalization ME models theoretical guidelines feature learning We introduce a recursive decomposition solution applying principle It proved DNN maximally fulfills maximum entropy principle multilayer feature learning and softmax regression guarantees the model generalization performance.3 Based the ME understanding provide explanations the information bottleneck phenomenon typical DNN designs This paper regards DNN the original maximum entropy problem From maximum entropy the remarkable generalization capability DNN least extra data hypothesis The future work goes payed identifying connections other generalization theories explaining more DNN observations like the role ReLu activation redundant features improve exploit instructions of as",0.01,0.5061738912316073
"As people learn to navigate the world, autonomic nervous system (e.g., ``fight or flight) responses provide intrinsic feedback about the potential consequence of action choices (e.g., becoming nervous when close to a cliff edge or driving fast around a bend.) Physiological changes are correlated with these biological preparations to protect one-self from danger. We present a novel approach to reinforcement learning that leverages a task-independent intrinsic reward function trained on peripheral pulse measurements that are correlated with human autonomic nervous system responses. Our hypothesis is that such reward functions can circumvent the challenges associated with sparse and skewed rewards in reinforcement learning settings and can help improve sample efficiency. We test this in a simulated driving environment and show that it can increase the speed of learning and reduce the number of collisions during the learning stage. The human autonomic nervous system (ANS) is composed of two branches. One of these, the sympathetic nervous system (SNS), is ""hard-wired"" to respond to potentially dangerous situations often reducing, or by-passing, the need for conscious processing. The ability to make rapid decisions and respond to immediate threats is one way of protecting oneself from danger. Whether one is in the African savanna or driving in Boston traffic.The SNS regulates a range of visceral functions from the cardiovascular system to the adrenal system BID9 . The anticipatory response in humans to a threatening situation is for the heart rate to increase, heart rate variability to decrease, blood to be diverted from the extremities and the sweat glands to dilate. This is the body's ""fight or flight"" response.While the primary role of these anticipatory responses is to help one prepare for action, they also play a part in our appraisal of a situation. The combination of sensory inputs, physiological responses and cognitive evaluation form emotions that influence how humans learn, plan and make decisions BID14 . Intrinsic motivation refers to being moved to act based on the way it makes one feel. For example, it is generally undesirable to be in a situation that causes fear and thus we might choose to take actions that help avoid these types of contexts in future. This is contrasted with extrinsic motivation that involves explicit goals BID4 .Driving is an everyday example of a task in which we commonly rely on both intrinsic and extrinsic motivations and experience significant physiological changes. When traveling in a car at highspeed one may experience a heightened state of arousal. This automatic response is correlated with the body's reaction to the greater threats posed by the situation (e.g., the need to adjust steering more rapidly to avoid a pedestrian that might step into the road). Visceral responses are likely to preempt accidents or other events (e.g., a person will become nervous before losing control and hitting someone). Therefore, these signals potentially offer an advantage as a reward mechanism compared to extrinsic rewards based on events that occur in the environment, such as a collision. This paper provides a reinforcement learning (RL) framework that incorporates reward functions for achieving task-specific goals and also minimizes a cost trained on physiological responses to the environment that are correlated with stress. We ask if such a reward function with extrinsic and intrinsic components is useful in a reinforcement learning setting. We test our approach by training a model on real visceral human responses in a driving task.The key challenges of applying RL in the real-world include the amount of training data required and the high-cost associated with failure cases. For example, when using RL in autonomous driving, rewards are often sparse and skewed. Furthermore, bad actions can lead to states that are both catastrophic and expensive to recover from. While much of the work in RL focuses on mechanisms that are task or goal dependent, it is clear that humans also consider the feedback from the body's nervous system for action selection. For example, increased arousal can help signal imminent danger or failure to achieve a goal. Such mechanisms in an RL agent could help reduce the sample complexity as the rewards are continually available and could signal success or failure before the end of the episode. Furthermore, these visceral signals provide a warning mechanism that in turn could lead to safer explorations.Our work is most closely related to that in intrinsically motivated learning BID4 BID26 BID7 BID17 that uses a combination of intrinsic and extrinsic rewards and shows benefits compared to using extrinsic rewards alone. The key distinction in our work is that we specifically aim to build intrinsic reward mechanisms that are visceral and trained on signals correlated with human affective responses. Our approach could also be considered a form of imitation learning BID20 BID19 BID8 BID2 as we use the signal from a human expert for training. However, a difference is that our signal is an implicit response from the driver versus an explicit instruction or action which might commonly be the case in imitation learning.The structural credit assignment problem, or generalization problem, aims to address the challenge posed by large parameter spaces in RL and the need to give the agent the ability to guess, or have some intuition about new situations based on experience BID13 . A significant advantage of our proposed method is the reduced sparsity of the reward signal. This makes learning more practical in a large parameter space. We conduct experiments to provide empirical evidence that this can help reduce the number of epochs required in learning. In a sense, the physiological response could be considered as an informed guess about new scenarios before the explicit outcome is known. The challenge with traditional search-based structured prediction is the assumptions that must be made in the search algorithms that are required BID5 . By training a classifier using a loss based on the human physiological response this problem can potentially be simplified.The core contributions of this paper are to: (1) present a novel approach to learning in which the reward function is augmented with a model learned directly from human nervous system responses, (2) show how this model can be incorporated into a reinforcement learning paradigm and (3) report the results of experiments that show the model can improve both safety (reducing the number of mistakes) and efficiency (reducing the sample complexity) of learning.In summary, we argue that a function trained on physiological responses could be used as an intrinsic reward or value function for artificially intelligent systems, or perhaps more aptly artificially emotionally intelligent systems. We hypothesize that incorporating intrinsic rewards with extrinsic rewards in an RL framework (as shown in FIG0 will both improve learning efficiency as well as reduce catastrophic failure cases that occur during the training. Heightened arousal is an key part of the ""fight or flight"" response we experience when faced with risks to our safety. We have presented a novel reinforcement learning paradigm using an intrinsic reward function trained on peripheral physiological responses and extrinsic rewards based on mission goals. First, we trained a neural architecture to predict a driver's peripheral blood flow modulation based on the first-person video from the vehicle. This architecture acted as the reward in our reinforcement learning step. A major advantage of training a reward on a signal correlated with the sympathetic nervous system responses is that the rewards are non-sparse -the negative reward starts to show up much before the car collides. This leads to efficiency in training and with proper design can lead to policies that are also aligned with the desired mission. While emotions are important for decision-making BID12 , they can also detrimentally effect decisions in certain contexts. Future work will consider how to balance intrinsic and extrinsic rewards and include extensions to representations that include multiple intrinsic drives (such as hunger, fear and pain).We must emphasize that in this work we were not attempting to mimic biological processes or model them explicitly. We were using a prediction of the peripheral blood volume pulse as an indicator of situations that are correlated with high arousal.",1523,0.816,868,1.7546082949308757,"As people learn navigate autonomic nervous system ``fight) responses provide intrinsic feedback the potential consequence action choices becoming nervous when close a cliff edge driving fast around Physiological changes correlated these biological preparations to protect one-self We present reinforcement learning a task-independent intrinsic reward function trained peripheral pulse measurements that correlated Our hypothesis such reward functions circumvent the challenges sparse and skewed rewards reinforcement learning settings can help sample efficiency We test this in a simulated driving environment show increase learning collisions during The human autonomic nervous systemANS two branches One these, the sympathetic nervous system ""hard potentially dangerous situations often reducing, conscious processing The ability make rapid decisions respond oneself danger Whether one the African savanna driving Boston traffic.The SNS regulates visceral functions from BID9 . The anticipatory response in humans a threatening situation for the heart rate to diverted the sweat glands This the body's ""fight or flight"" responseWhile the primary role these anticipatory responses one prepare action our appraisal The combination sensory inputs physiological responses cognitive evaluation form emotions learn plan make BID14 . Intrinsic motivation refers being moved act based it makes one For example it generally undesirable be causes fear thus we take actions help these types contexts in future This contrasted extrinsic motivation involves explicit goals BID4 .Driving an everyday example a task commonly rely and experience significant physiological changes When traveling at highspeed one a heightened state This automatic response correlated the greater threats adjust steering more a pedestrian that step Visceral responses likely preempt accidents ( will become nervous before losing hitting Therefore these signals potentially offer as a reward mechanism compared based events a collision This paper a reinforcement learning incorporates reward functions achieving also a cost trained physiological responses the environment that correlated stress We ask if such a reward function with extrinsic and intrinsic components useful a reinforcement learning setting We test our approach training a model real visceral human responses a driving taskThe key challenges applying RL include the amount training data associated failure cases For example using RL in autonomous driving rewards often sparse skewed Furthermore bad actions states both catastrophic expensive recover While much RL focuses mechanisms task or goal dependent humans consider the feedback from for action selection For example increased arousal signal imminent danger failure achieve Such mechanisms in an RL agent help reduce the sample complexity as the rewards continually available could signal success before the episode Furthermore these visceral signals provide a warning mechanism in safer explorationsOur work most closely that in intrinsically motivated learning BID4 BID26 BID7 BID17 that uses shows benefits compared using The key distinction our work specifically aim build intrinsic reward mechanisms visceral trained signals correlated human affective responses Our approach could imitation learning BID20 BID19 BID8 BID2 as use the signal a human expert for training However a difference our signal an implicit response from versus an explicit instruction or action which might commonly imitation learningThe structural credit assignment problem or generalization problem aims large parameter spaces RL give the agent guess, have some intuition new situations based experience BID13 . A significant advantage our proposed method the reduced sparsity the reward signal This makes learning practical in a large parameter space We conduct experiments provide this can help reduce epochs required learning In a sense the physiological response could an informed guess new scenarios before the explicit outcome The challenge with traditional search-based structured prediction the assumptions must required BID5 . By training a classifier using a loss based the human physiological response this problem potentially simplifiedThe core contributions: present learning in which the reward function augmented learned directly incorporated report experiments improve both safety ( mistakes efficiency the sample complexityIn argue a function trained an intrinsic reward or value function artificially intelligent systems or perhaps more aptly artificially emotionally intelligent systems We hypothesize incorporating intrinsic rewards with an RL framework (as shown FIG0 will both efficiency as catastrophic failure cases that. Heightened arousal an key part we faced risks We presented a novel reinforcement learning paradigm using an intrinsic reward function trained peripheral physiological responses based mission goals First trained a neural architecture a driver's peripheral blood flow modulation based from This architecture acted the reward in our reinforcement learning step A major advantage training a reward on a signal correlated the sympathetic nervous system responses non-sparse -the negative reward starts show much before the car collides This leads efficiency training with proper design can lead policies also aligned the desired mission While emotions important decision-making BID12 , they detrimentally effect decisions certain contexts Future work consider balance include extensions representations include multiple intrinsic drives hunger fear pain).We must emphasize in were mimic biological processes model them explicitly We were using a prediction the peripheral blood volume pulse situations correlated high arousal",0.01,0.6267548060078022
"Deep convolutional neural networks (CNNs) are known to be robust against label noise on extensive datasets. However, at the same time, CNNs are capable of memorizing all labels even if they are random, which means they can memorize corrupted labels. Are CNNs robust or fragile to label noise? Much of researches focusing on such memorization uses class-independent label noise to simulate label corruption, but this setting is simple and unrealistic. In this paper, we investigate the behavior of CNNs under class-dependently simulated label noise, which is generated based on the conceptual distance between classes of a large dataset (i.e., ImageNet-1k). Contrary to previous knowledge, we reveal CNNs are more robust to such class-dependent label noise than class-independent label noise. We also demonstrate the networks under class-dependent noise situations learn similar representation to the no noise situation, compared to class-independent noise situations. Deep convolutional neural networks (CNNs) excel in supervised image classification tasks BID17 ). Representation learned from such tasks can be transfer to other tasks, including object detection BID31 ; ; BID30 ) and semantic segmentation BID2 ; Badrinarayanan et al.) . Furthermore, if the training dataset is sufficiently larger, CNNs can improve the performance in classification, or learn better transferable representation, even if some labels are corrupted BID20 ; BID36 ; BID22 ).However , recent CNNs have far more parameters than their training samples. Therefore , the networks can memorize all the training data even if all labels are randomly replaced with the wrong ones ; ). This capability may degrade CNNs' performance under the label-corrupted situation, thus learning methods against label noise have been studied.Are CNNs robust or fragile to label noise? To investigate this question, we need to adopt noisy labels in controlled experiments. In previous work , both natural and synthetic noise have been used to research label corrupted situations. Natural noise appears in generally every dataset, and it comes from, for instance, annotators' mislabeling BID3 or their varieties BID6 ). Some researchers have been proposed robust training methods under this type of noise BID19 ; BID15 ; BID38 ). However, natural noise is uncontrollable, in other words, the relationship between the magnitude of noise and CNNs' performance has been unknown.On the other hand, synthetic noise simulates natural one by stochastically replacing ground truth labels with others. Class-independent uniform label permutation is a common setting BID15 ; BID10 ), yet some researchers use class-dependent label permutation, which is considered as more realistic situation BID26 ; BID8 ; BID27 ; BID9 ). Previous research has mainly adopted MNIST (10 classes, 60,000 training samples, BID18 ) or CIFAR-10/100 (10 and 100 classes, 50,000 training samples, BID17 ), and these datasets lack pre-defined conceptual relationships between classes. This limitation results in simplified noise simulation on such datasets, although synthetic noise enables researchers to research the relationship between the noise magnitude and the performance of networks.To investigate whether CNNs are robust or fragile to label corruption, we propose to use simulated noise considering possible mislabeling on ImageNet-1k (Russakovsky et al. (2015) ) to complement the disadvantages. Exploiting ImageNet-1k's conceptual hierarchy , we can divide its 1,000 labels into some clusters. We use these clusters to generate class-conditional label noise. We train several networks on the training dataset with and without corrupted labels. Then we evaluate the performance of the networks on the original validation set, the robustness of the networks against adversarial perturbation BID37 ; BID28 ), and their learned representation using transfer learning, canonical correlation analysis BID29 ; BID25 ).In this paper, we show the performance of CNNs trained on such synthesized noise considering possible mislabeling is better than uniformly synthesized noise, which is contrary to previous research BID8 ; BID27 ). Besides, models trained on class-dependent label noise are more robust to adversarial perturbation than ones trained on class-independent label noise. We also demonstrate CNNs trained under class-conditionally noisy conditions learn similar features to ones trained under the clean condition. As a result, even when 80% of labels are class-dependently corrupted, CNNs can learn useful representation for transfer learning. Meanwhile, we demonstrate class-independent noise leads models to learn different representation from ones trained with data with clean labels or label noise considering conceptual hierarchy. These differences can be attributed to the property of categorical cross entropy loss, which is a well-used loss function for image recognition tasks. We believe using class-independent noise is not a suitable protocol to investigate the CNNs' tolerance in practical situations. Why does class-dependent noise affect less than class-independent noise? We think there are two reasons: class-dependent noise is more informative, and it avoids the loss value getting too large.When class-dependent noise swaps a ground truth label with a wrong one, it is still a similar class to the original. Thus, the network can learn ""which cluster the sample belongs to"". This idea is related to the soft label BID12 ), though in our case, the label is ""hard"". Contrary to this, class-independent noise conveys no information.The other reason results from the property of categorical cross entropy loss. When the label of sample x is i, the loss value can be written as − log[f (x)] i , where f (x) is the corresponding softmax output. Therefore, when a CNN predicts x as i with weaker confidence, the penalty gets larger. Since the wrong label corrupted by class-dependent noise belongs to the same cluster as the ground truth, [f (x)] i is relatively large (c.f. Figure 2 (b) ). However, in the case of classindependent noise, the wrong label has nothing to do with the ground truth, and if the ground truth and the corrupted label are irrelevant, [f (x)] i should be small. Thus, the loss value gets larger, which leads the network to a worse solution.Also, our finding can be applicable to the quality control of annotation of data. Our results show class-dependent noise is more favorable than class-independent noise. Inexperienced but honest annotators will yield class-dependent noise, while lazy and malicious annotators may randomly annotate the labels and will yield class-independent noise. Therefore, according to our results, the administrators of the annotation need to exclude such workers. In this paper, we investigated the relationship between label noise, the performance and representation of CNNs in image classification tasks. We used ImageNet-1k with simulated noise which includes class-independent noise and class-dependent noise considering conceptual similarity. We examined such noise considering possible mislabeling causes less performance decrease and more robustness against adversarial perturbation compared to class-independent noise. Besides, we investigated the internal representation of CNNs trained with and without label corruption. Experiments showed networks trained on class-independently noisy data learn different representation from ones trained on clean or class-conditionally noisy data.Some previous research on label-noise-tolerant learning methods has used class-independent noise. However, as we revealed in this research, this noise setting is so artificial and straightforward that such methods may not be effective against real noise. Meanwhile, our results suggest plain CNNs themselves can be robust against real noise. This property should be good news for practitioners. Nevertheless, it is also shown noise considering possible mislabeling still somewhat degrades the performance of networks. Thus, how to avoid the effect of label noise is still a remaining problem.",1523,0.894,863,1.7647740440324449," known robust against label noise on extensive datasets However at CNNs capable memorizing all labels even random corrupted labels Are CNNs robust fragile to label noise Much researches focusing such memorization uses class-independent label noise simulate label corruption this setting simple unrealistic In CNNs under class-dependently simulated label noise generated based the conceptual distance classes Contrary previous knowledge we reveal CNNs more robust such class-dependent label noise We also demonstrate the networks under class-dependent noise situations learn similar representation the no noise situation compared excel supervised image classification tasks BID17 ). Representation learned such tasks transfer to object detection BID31 ; ; ) semantic Badrinarayanan.) Furthermore the training dataset sufficiently larger CNNs improve classification learn better transferable representation even some labels corrupted BID20 ; BID36 ).However , recent CNNs far more parameters their training samples Therefore , the networks memorize even all labels randomly replaced ; This capability degrade CNNs' performance under the label-corrupted situation thus learning methods against label noise have studiedAre robust fragile To investigate need adopt noisy labels controlled experiments In previous work , both natural and synthetic noise research label corrupted situations Natural noise appears generally every dataset comes, annotators' BID3 or their varieties ). Some researchers proposed robust training methods under this type noise BID19 ; BID15 However natural noise uncontrollable in the relationship CNNs' performance unknownOn synthetic simulates one by stochastically replacing ground truth labels others Class-independent uniform label permutation setting BID15 ; yet some researchers use considered more realistic situation Previous research mainly adopted MNIST10 classes 60,000 training samples BID18 ) these datasets lack pre-defined conceptual relationships This limitation results simplified noise simulation on such datasets synthetic noise enables researchers research networksTo CNNs robust or fragile label corruption propose considering on ImageNet-1k (Russakovsky (2015 ) to complement the disadvantages. Exploiting ImageNet-1k's conceptual hierarchy , we divide its 1,000 labels some clusters We use these clusters class-conditional label noise We train several networks the training dataset and corrupted labels Then evaluate the networks the original validation set BID37 ; their learned representation using transfer learning canonical correlation analysis.In CNNs trained such synthesized noise considering possible mislabeling is better uniformly synthesized noise contrary Besides models trained class-dependent label noise robust ones We also demonstrate CNNs trained under class-conditionally noisy conditions learn similar features ones the clean condition As even 80% labels classdependently corrupted CNNs learn useful representation transfer learning Meanwhile we demonstrate class-independent noise leads models learn different representation from ones trained data with clean labels or label noise considering conceptual hierarchy These differences the property categorical cross entropy loss image recognition tasks We believe using class-independent noise a suitable protocol investigate the CNNs' tolerance in practical situations Why class-dependent noise less We think: class-dependent noise informative avoids the loss value getting tooWhen swaps a ground truth label still a similar class to Thus the network learn ""which cluster the sample This idea related the soft label BID12 ), thoughhard Contrary this class-independent noise conveysThe other reason results the property categorical cross entropy loss When the label sample x i the loss value can − log[f i the corresponding softmax output Therefore a CNN predicts x as i with weaker confidence the penalty gets Since the wrong label corrupted by class-dependent noise belongs the same cluster the ground truth [f ( i relatively However classindependent noise the wrong label nothing the ground truth if and the corrupted label irrelevant [f ( i should small Thus the loss value gets the network a worse solutionAlso our finding can applicable the quality control annotation of Our results class-dependent noise favorable Inexperienced but honest annotators yield class-dependent noise randomly annotate the labels will Therefore according our results the administrators the annotation need exclude such workers In investigated label noise the performance and representation CNNs. We used ImageNet-1k with simulated noise which includes considering conceptual similarity We examined such noise considering possible mislabeling causes less performance decrease against compared class-independent noise Besides investigated the internal representation CNNs trained with and label corruption Experiments showed networks trained class-independently noisy data learn different representation from onesSome previous research However revealed this research this noise setting so artificial straightforward such methods against real noise Meanwhile our results plain CNNs themselves robust against real noise This property should good news practitioners Nevertheless also shown noise considering possible mislabeling still somewhat degrades networks Thus how avoid the effect label noise still a remaining problem",0.01,0.6526562415656503
"Efficient audio synthesis is an inherently difficult machine learning task, as human perception is sensitive to both global structure and fine-scale waveform coherence. Autoregressive models, such as WaveNet, model local structure at the expense of global latent structure and slow iterative sampling, while Generative Adversarial Networks (GANs), have global latent conditioning and efficient parallel sampling, but struggle to generate locally-coherent audio waveforms. Herein, we demonstrate that GANs can in fact generate high-fidelity and locally-coherent audio by modeling log magnitudes and instantaneous frequencies  with sufficient frequency resolution in the spectral domain. Through extensive empirical investigations on the NSynth dataset, we demonstrate that GANs are able to outperform strong WaveNet baselines on automated and human evaluation metrics, and efficiently generate audio several orders of magnitude faster than their autoregressive counterparts.
 Neural audio synthesis, training generative models to efficiently produce audio with both highfidelity and global structure, is a challenging open problem as it requires modeling temporal scales over at least five orders of magnitude (∼0.1ms to ∼100s). Large advances in the state-of-the art have been pioneered almost exclusively by autoregressive models, such as WaveNet, which solve the scale problem by focusing on the finest scale possible (a single audio sample) and rely upon external conditioning signals for global structure BID32 . This comes at the cost of slow sampling speed, since they rely on inefficient ancestral sampling to generate waveforms one audio sample at a time. Due to their high quality, a lot of research has gone into speeding up generation, but the methods introduce significant overhead such as training a secondary student network or writing highly customized low-level kernels BID33 BID25 . Furthermore, since these large models operate at a fine timescale, their autoencoder variants are restricted to only modeling local latent structure due to memory constraints BID9 .On the other end of the spectrum, Generative Adversarial Networks (GANs) BID11 have seen great recent success at generating high resolution images BID2 BID19 BID16 BID22 . Typical GANs achieve both efficient parallel sampling and global latent control by conditioning a stack of transposed convolutions on a latent vector, The potential for audio GANs extends further, as adversarial costs have unlocked intriguing domain transformations for images that could possibly have analogues in audio BID35 BID15 . However , attempts to adapt image GAN architectures to generate waveforms in a straightforward manner ) fail to reach the same level of perceptual fidelity as their image counterparts.Figure 1: Frame-based estimation of audio waveforms. Much of sound is made up of locallycoherent waves with a local periodicity, pictured as the red-yellow sinusoid with black dots at the start of each cycle. Frame-based techniques, whether they be transposed convolutions or STFTs, have a given frame size and stride, here depicted as equal with boundaries at the dotted lines. The alignment between the two (phase, indicated by the solid black line and yellow boxes), precesses in time since the periodicity of the audio and the output stride are not exactly the same. Transposed convolutional filters thus have the difficult task of covering all the necessary frequencies and all possible phase alignments to preserve phase coherence. For an STFT, we can unwrap the phase over the 2π boundary (orange boxes) and take its derivative to get the instantaneous radial frequency (red boxes), which expresses the constant relationship between audio frequency and frame frequency. The spectra are shown for an example trumpet note from the NSynth dataset. By carefully controlling the audio representation used for generative modeling, we have demonstrated high-quality audio generation with GANs on the NSynth dataset, exceeding the fidelity of a strong WaveNet baseline while generating samples tens of thousands of times faster. While this is a major advance for audio generation with GANs, this study focused on a specific controlled dataset, and further work is needed to validate and expand it to a broader class of signals including speech and other types of natural sound. This work also opens up possible avenues for domain transfer and other exciting applications of adversarial losses to audio. Issues of mode collapse and diversity common to GANs exist for audio as well, and we leave it to further work to consider combining adversarial losses with encoders or more straightforward regression losses to better capture the full data distribution.A MEASURING DIVERSITY ACROSS GENERATED EXAMPLES Table 3 , including adding a pitch classifier to the end of the discriminator as in AC-GAN. All models were trained with the ADAM optimizer BID18 . We sweep over learning rates (2e-4, 4e-4, 8e-4) and weights of the auxiliary classifier loss (0.1, 1.0, 10), and find that for all variants (spectral representation, progressive/no progressive, frequency resolution) a learning rate of 8e-4 and classifier loss of 10 perform the best.As in the original progressive GAN paper, both networks use box upscaling/downscaling and the generators use pixel normalization, DISPLAYFORM0 where n, h, w, and c refer to the batch, height, width, and channel dimensions respectively, x is the activations, and C is the total number of channels. The discriminator also appends the standard deviation of the minibatch activations as a scalar channel near the end of the convolutional stack as seen in Table 3 .Since we find it helpful to use a Tanh output nonlinearity for the generator, we normalize real data before passing to the discriminator. We measure the maximum range over 100 examples and independently shift and scale the log-magnitudes and phases to [-0.8, 0 .8] to allow for outliers and use more of the linear regime of the Tanh nonlinearity.We train each GAN variant for 4.5 days on a single V100 GPU, with a batch size of 8. For nonprogressive models, this equates to training on ∼5M examples. For progressive models , we train on 1.6M examples per a stage (7 stages), 800k during alpha blending and 800k after blending. At the last stage we continue training until the 4.5 days completes. Because the earlier stages train faster, the progressive models train on ∼11M examples.For the WaveNet baseline, we also adapt the open source Tensorflow implementation 11 . The decoder is composed of 30 layers of dilated convolution, each of 512 channels and receptive field of 3, and each with a 1x1 convolution skip connection to the output. The layers are divided into 3 stacks of 10, with dilation in each stack increasing from 2 0 to 2 9 , and then repeating. We replace the audio encoder stack with a conditioning stack operating on a one-hot pitch conditioning signal distributed in time (3 seconds on, 1 second off). The conditioning stack is 5 layers of dilated convolution, increasing to 2 5 , and then 3 layers of regular convolution, all with 512 channels. This conditioning signal is then passed through a 1x1 convolution for each layer of the decoder and added to the output of each layer, as in other implementations of WaveNet conditioning. For the 8-bit model we use mulaw encoding of the audio and a categorical loss, while for the 16-bit model we use a quantized mixture of 10 logistics BID29 . WaveNets converged to 150k iterations in 2 days with 32 V100 GPUs trained with synchronous SGD with batch size 1 per GPU, for a total batch size of 32.",1558,0.686,940,1.6574468085106382,"Efficient audio synthesis an inherently difficult machine learning task human perception sensitive both global structure fine-scale waveform coherence Autoregressive models WaveNet, model local structure at global latent structure slow iterative sampling while have global latent conditioning efficient parallel sampling struggle locally-coherent audio waveforms Herein, demonstrate GANs in generate modeling log magnitudes instantaneous frequencies sufficient frequency resolution Through extensive empirical investigations on the NSynth dataset demonstrate GANs able strong WaveNet baselines automated and human evaluation metrics efficiently audio several orders Neural audio synthesis training generative models to efficiently produce audio with both highfidelity global structure a challenging open problem as modeling temporal scales over at least five orders Large advances have pioneered almost autoregressive models WaveNet solve the scale problem focusing the finest scale possible (a single audio) rely external conditioning signals global structure BID32 . This comes slow sampling speed since they rely inefficient ancestral sampling waveforms one audio sample Due a lot research speeding generation the methods introduce significant overhead such training a secondary student network writing highly customized low-level kernels BID33 BID25 . Furthermore since these large models operate a fine timescale their autoencoder variants restricted modeling local latent structure due memory constraints BID9 .On end Generative BID11 seen great recent success at Typical GANs achieve both efficient parallel sampling and global latent control conditioning a stack transposed convolutions The potential extends further adversarial costs have unlocked intriguing domain transformations images possibly analogues audio BID35 BID15 . However , attempts adapt image GAN architectures generate waveforms ) fail reach perceptual fidelityFigure Frame-based estimation Much sound locallycoherent waves with a local periodicity pictured as the red-yellow sinusoid with black dots Frame-based techniques whether transposed convolutions STFTs a given frame size stride here depicted equal with boundaries at the dotted lines The alignment the two (phase, indicated yellow boxes precesses time since the periodicity the audio the output stride Transposed convolutional filters thus covering all possible phase alignments preserve phase coherence For an STFT, can unwrap the phase over the 2π boundaryorange boxes take its derivative to the instantaneous radial frequency expresses the constant relationship audio frequency frame frequency The spectra shown an example trumpet note the NSynth dataset By carefully controlling the audio representation used generative modeling high-quality audio generation GANs on the NSynth dataset exceeding a strong WaveNet baseline while generating samples tens of thousands While this a major advance audio generation with GANs this study focused a specific controlled dataset further work a broader class signals including speech natural sound This work also opens possible avenues domain transfer other exciting applications adversarial losses audio Issues mode collapse diversity common GANs exist audio as leave further work consider combining adversarial losses encoders or more straightforward regression losses better capture the full data distributionA MEASURING DIVERSITY , including adding a pitch as in AC-GAN All models trained the ADAM optimizer BID18 . We sweep over learning rates (2e-4 weights the auxiliary classifier loss 10 find for all variantsspectral representation progressive/no progressive, frequency resolution and performAs in the original progressive GAN paper both networks use box upscaling/downscaling the generators pixel normalization DISPLAYFORM0 where n, h w c refer the batch, height channel dimensions x C The discriminator also appends the standard deviation the minibatch activations as a scalar channel near as seen Table .Since find it helpful a Tanh output nonlinearity the generator normalize real data before passing We measure the maximum range over 100 examples independently shift and the log-magnitudes phases [ .8 allow use more of the linear regime the Tanh nonlinearityWe train each GAN variant a single V100 GPU For nonprogressive models equates training on ∼5M examples For progressive models , train on 1.6M examples a stage7 stages 800k during alpha blending At the last stage we continue training until the 4.5 days completes Because the earlier stages train faster the progressive models train on ∼11M examplesFor the WaveNet baseline also adapt 11 . The decoder composed 30 layers dilated convolution, 512 channels receptive field 3 and with a 1x1 convolution skip connection The layers divided 3 stacks with dilation in increasing 0 9 , then repeating We replace the audio encoder stack a conditioning stack operating a one-hot pitch conditioning signal distributed time3 seconds on, The conditioning stack 5 layers dilated convolution, increasing 5 , all 512 channels This conditioning signal then for added other implementations WaveNet conditioning For the 8-bit model mulaw encoding a categorical loss, while a quantized mixture 10 logistics BID29 . WaveNets converged 150k iterations 32 V100 GPUs trained synchronous SGD with batch size 1 per for 32",0.01,0.37919587512389513
"In this work we propose a novel approach for learning graph representation of the data using gradients obtained via backpropagation. Next we build a neural network architecture compatible with our optimization approach and motivated by graph filtering in the vertex domain. We demonstrate that the learned graph has richer structure than often used nearest neighbors graphs constructed based on features similarity. Our experiments demonstrate that we can improve prediction quality for several convolution on graphs architectures, while others appeared to be insensitive to the input graph. Recently we have seen a rise in deep learning models, which can account for non-linearities and fit a wide range of functions. Multilayer perceptron (MLP), a general purpose neural network, is a powerful predictor, but requires too many parameters to be estimated and often faces the problem of over-fitting, i.e. learns to almost exactly match training data and unable to generalize when it comes to testing.While MLPs treat all features equally, which partially is the cause of excessive number of parameters, Convolutional Neural Networks (CNNs) have significantly fewer parameters and demonstrate groundbreaking results when it comes to object recognition in images BID11 . The parameter reduction is due to utilizing convolutional operation: a window is sliding through the image and applying same linear transformation of the pixels. The number of parameters then is proportional to the size of the window rather than polynomial of the number of data features as in the case of the MLPs.Indeed images posses a specific structure, which can be encoded as a lattice graph, that makes the sliding window procedure meaningful, but inapplicable outside of the image domain. In recent years there have been multiple works (cf. Bronstein et al. (2017) for an overview) on generalizing convolution operation to a general domain, where graph is not a lattice. Citing BID3 -""classification performance critically depends on the quality of the graph"", nonetheless the problem of learning the graph useful for prediction has not been addressed so far and the graph was either known or pre-estimated only based on feature similarity in all of the prior work.There are two major challenges when estimating the graph inside the neural network architecture. First is the architecture itself -majority of the neural networks rely on gradient optimization methods, but the graph is often used in such ways that it is not possible to obtain its gradient. In Section 3 we define a novel neural network architecture which is differentiable with respect to the graph adjacency matrix and built upon graph filtering in the vertex domain, extending the linear polynomial filters of BID20 . Second problem is the series of constraints that are often imposed on the graph and therefore its adjacency. In Section 2 we show how the three common graph properties, undirected sparse edges with positive weights, can be enforced by only utilizing the gradient obtained through backpropagation, therefore allowing us to utilize any of the modern deep learning libraries for graph estimation. In Section 4 we discuss other graph based neural networks and evaluate them from the perspective of graph estimation. In Section 5 we analyze graph estimation and interpretation for text categorization and time series forecasting. We conclude with a discussion in Section 6 2 GRAPH OPTIMIZATION BASED ON BACKPROPAGATION In this section we provide an optimization procedure for learning adjacency matrix of a graph with various properties of interest, assuming that we can obtain its derivative via backpropagation. In a subsequent section we will present novel neural network architecture that will allow us to get the derivative and utilize the graph in meaningful way.Let data X ∈ R N ×D with N observation, D features and response Y ∈ R (or Y ∈ N for classification). Graph G among data features can be encoded as its adjacency matrix A ∈ R D×D . Our goal is to estimate functionŶ := f W (X, A), where W are weight parameters, that minimize some loss L := L(Ŷ , Y ). We assume that we are able to evaluate partial derivative ∂L ∂A . In the most general case, when edges of G can be directed, have negative weights and G can be fully connected, we perform the update A := A − γG ∂L ∂A , where G(·) depends on the optimizer (e.g., identity function for vanilla gradient descent) and γ is the step size. Nonetheless, in the majority of the applications, G is desired to have some (or all) of the following properties:• Undirected graph, in which case A is restricted to be symmetric.• Have Positive edge weights, in which case A ∈ R D×D + .• Be Sparsely connected, in which case A should contain small proportion of non-zero entries.First two properties are necessary for the existence of the graph Laplacian, crucial for the vast amount of neural networks on graphs architectures (e.g., BID2 ; BID8 ; BID3 ). Third property greatly reduces computational complexity, helps to avoid overfitting and improves interpretability of the learned graph. We proceed to present the Undirected Positive Sparse UPS optimizer, that can deliver each of the three properties and can be easily implemented as part of modern deep learning libraries.Remark When node classification is of interest, our approach can be applied to graph between observations (e.g. social networks), then A ∈ R N ×N .",1071,0.506,593,1.806070826306914,"In this work propose learning graph representation gradients obtained via Next we build compatible our optimization approach motivated graph filtering in the vertex domain We demonstrate the learned graph has richer structure often nearest constructed based features similarity Our experiments demonstrate we improve prediction quality several convolution on graphs architectures while others appeared insensitive the input graph Recently deep learning models account non fit functions Multilayer perceptron a powerful predictor, requires estimated often faces over- learns almost exactly training data unable when testingWhile treat all features which partially is the cause excessive number demonstrate groundbreaking results object images BID11 . The parameter reduction due utilizing convolutional operation: a window sliding applying same linear transformation The number parameters then proportional rather of data features as the MLPsIndeed images posses a specific structure encoded that makes the sliding window procedure meaningful outside In multiple works (cf Bronstein et (2017 for an overview) on generalizing convolution operation a general domain where graph not Citing BID3 -""classification performance critically depends the graph nonetheless the problem learning useful prediction so was either known pre based feature similarity in allThere when estimating inside First is the architecture itself -majority the neural networks rely gradient optimization methods the graph often such ways obtain its gradient In Section we define a novel neural network architecture which differentiable the graph adjacency matrix built graph filtering in the vertex domain extending the linear polynomial filters BID20 . Second problem the series constraints often the graph In Section we show the three common graph properties undirected sparse edges with positive weights enforced only utilizing the gradient obtained through therefore utilize any the modern deep learning libraries graph estimation In Section we other graph based neural networks evaluate from graph estimation In Section we analyze graph estimation interpretation text categorization time series forecasting We conclude in Section 2 GRAPH OPTIMIZATION BASED BACKPROPAGATION In provide an optimization procedure learning adjacency matrix of a graph various properties interest assuming its derivative via In a subsequent section present novel neural network architecture get the derivative and utilize the graph meaningful wayLet data X �� R N ×D with N observation D features response Y (or for classification Graph G among data features can encoded its adjacency matrix A �� R D×D Our goal estimate function�� := f WX A are weight parameters that minimize some loss L :� , Y We assume able evaluate partial derivative ��L ��A In the most general case when edges G can directed have negative weights G fully connected we perform the update A := − �GL(· depends vanilla gradient descent Nonetheless in the majority the applications G is desired some ( the following properties:• Undirected graph, in A restricted be Have Positive edge weights A �� R D×D + .• Be Sparsely connected should contain small proportionFirst two properties necessary the existence crucial the vast amount neural networks on graphs architectures BID2 ; Third property greatly computational complexity helps interpretability the learned graph We proceed present the Undirected Positive Sparse UPS optimizer that deliver each and can part modern deep learning librariesRemark When node classification of our approach graph between observations then A �� R N ×N .",0.01,0.7578768145053792
"The use of AR in an industrial context could help for the training of new operators. To be able to use an AR guidance system, we need a tool to quickly create a 3D representation of the assembly line and of its AR annotations. This tool should be very easy to use by an operator who is not an AR or VR specialist: typically the manager of the assembly line. This is why we proposed WAAT, a 3D authoring tool allowing user to quickly create 3D models of the workstations, and also test the AR guidance placement. WAAT makes on-site authoring possible, which should really help to have an accurate 3D representation of the assembly line. The verification of AR guidance should also be very useful to make sure everything is visible and doesn't interfere with technical tasks. In addition to these features, our future work will be directed in the deployment of WAAT into a real boiler assembly line to assess the usability of this solution. In a context of constant industrial evolution and a need of more industrial agility to answer the increasingly unpredictable customer requests, having well trained assembly line operators is extremely important. This operator training problematic is well known by the XXX company, a boiler manufacturer for which this training problem is very important during each winter, when boiler orders rise a lot, as many new operators must be hired for a few months. After meetings and interviews with the XXX company, it appears that the training of these operators requires time and human resources. Currently, the training is done in 3 days with one experienced operator showing three trainees how to perform the technical gestures at their workstation. During these training days, none of the workers actually works on the assembly line and no boiler is built. After that, it takes 2 weeks for the operator in training to perform the technical tasks in the required time. Furthermore, only 1/3 of the new operators accept the job at the end of the training. To improve the training of these new operators, we want to propose an AR-based operator training system, allowing the operators to train directly on the assembly line without the need of an experimented operator. This tool could also be used by experimented operator to train on a new position of the assembly line or on a different assembly line. AR can be used in many different ways in the industrial context. It can be use to make expert remote guidance, create new products in collaborative engineering, or realize digital inspection of new prototypes [3] . AR is also used to test the ergonomics of the workstations and the reachability of some equipment. Testing new layout for the plant is also one of the AR use [1] . These different use are interesting, but the most interesting feature of AR and the most used is the assembly assistance, for training use or not [12, 15] . To use our AR-based operator training system we need to be able to create quickly and easily a 3D representation of the assembly line, and to be able to place anchors and markers (the details will be given in section 3.2.1) for the AR guidance elements. Furthermore, this tool must be very easy to use because the operators are not used to this technology. Indeed, the final users of the authoring tool will be the line managers, who are not used to use AR devices, or don't even know what AR is. That is why we need to adapt the interactions to the line manager, to ease the use of the tool. The remaining of this paper is organized as follows: in section 2 we explain the industrial constraints for the use of this authoring tool. Section 3 contains the related work, justifying the choices made in section 4 which describes WAAT, our authoring tool. Finally, section 5 concludes this paper and discusses about future developments. So we created WAAT, a 3D authoring tool allowing untrained users to create 3D models of the assembly line in a boiler factory. WAAT allow fast creation and AR comparison of the 3D and the real model. In case of a mismatch, the user can move the 3D components to match the real workstation. He can test the AR guidance used to train assembly line operators to make sure everything is fully visible and doesn't interfere in the realization of the technical tasks. Every modification made in desktop and AR is saved in a file on a server so there is no need to change on multiple platform. WAAT needs to be tested with 3D elements corresponding to the factory's workstations to find the most suitable level of details the 3D objects need to have, and the level of fidelity in the positioning of the 3D objects. We also have to test this tool with real operators from the factory to test the usability and the intuitiveness of WAAT. To adapt the interactions used to move/rotate/resize the 3D objects to our users, adding accessories such as a controller will be explored. We will also test new AR systems to test their usability and native interactions to see if we can use them, or if we can adapt them to our users. The immersive mode of WAAT will allow us to visualize the augmented environment and test the placement of the operator guidance, even if it's not the focus right now. We will be able to simulate the AR test of the scenes without the need to be in the plant all the time.",1087,0.649,624,1.7419871794871795,"The use AR in an industrial context could help for the training new operators To able an AR guidance system quickly the assembly line of its AR annotations This tool should very by an operator an AR or VR specialist: typically the manager the assembly line This why proposed WAAT authoring allowing user quickly test the AR guidance placement WAAT makes on authoring possible which should really have an accurate 3D representation the assembly line The verification AR guidance should also very useful make everything visible does technical tasks In addition these features our future work directed in the deployment WAAT into a real boiler assembly line assess the usability In a context constant industrial evolution a need of more industrial agility answer the increasingly unpredictable customer requests having well trained assembly line operators extremely This operator training problematic is well by the XXX company a boiler manufacturer for this training problem very important during each winter boiler orders rise a many new operators must After meetings interviews the XXX company it the training these operators requires time human resources Currently the training 3 days one experienced operator showing three trainees how the technical gestures at their workstation During these training days none actually works and no boiler After that takes 2 weeks the operator in training perform the technical tasks Furthermore only the new operators accept the job at To improve the training these new operators want propose an AR-based operator training system allowing directly an experimented operator This tool could experimented operator train on a new position the assembly line on AR can in the industrial context It can use expert remote guidance create new products in collaborative engineering realize digital inspection new prototypes [ AR is also used test the reachability some equipment Testing new layout the plant is also one the AR use [ These different use are interesting AR and the most used the assembly assistance for training use or not [12 To use our AR-based operator training system create the assembly line place anchors markers (the details will given section the AR guidance elements Furthermore this tool must very easy because the operators used this technology Indeed the final users the authoring tool the line managers used use AR devices do That adapt the interactions the line manager ease remaining of this paper organized in section explain the industrial constraints this authoring tool Section contains the related work justifying the choices which describes WAAT our authoring tool Finally section concludes this paper about future developments So we created WAAT allowing untrained users the assembly line a boiler factory WAAT allow fast creation and AR comparison and the real model In case of a mismatch the user move the 3D components match the real workstation He can test the AR guidance used train assembly line operators everything fully visible does in the realization the technical tasks Every modification made desktop AR saved so change on multiple platform WAAT needs tested with 3D elements corresponding the factory's workstations find details the 3D objects fidelity in the positioning We also test this tool real operators from the factory test the usability the intuitiveness WAAT To adapt the interactions used move/resize our users adding accessories will explored We will test new AR systems their usability native interactions to see use, adapt The immersive mode WAAT us visualize the augmented environment test the placement the operator guidance even the focus right We will able simulate the AR test the scenes without be the plant all",0.01,0.5945973127363428
"Generative adversarial network (GAN) is one of the best known unsupervised learning techniques these days due to its superior ability to learn data distributions. In spite of its great success in applications, GAN is known to be notoriously hard to train. The tremendous amount of time it takes to run the training algorithm and its sensitivity to hyper-parameter tuning have been haunting researchers in this area. To resolve these issues, we need to first understand how GANs work. Herein, we take a step toward this direction by examining the dynamics of GANs. We relate a large class of GANs including the Wasserstein GANs to max-min optimization problems with the coupling term being linear over the discriminator. By developing new primal-dual optimization tools, we show that, with a proper stepsize choice, the widely used first-order iterative algorithm in training GANs would in fact converge to a stationary solution with a sublinear rate. The same framework also applies to multi-task learning and distributional robust learning problems. We verify our analysis on numerical examples with both synthetic and real data sets. We hope our analysis shed light on future studies on the theoretical properties of relevant machine learning problems. Since it was first invented by Ian Goodfellow in his seminal work BID8 , generative adversarial networks (GANs) have been considered as one of the greatest discoveries in machine learning community. It is an extremely powerful tool to estimate data distributions and generate realistic samples. To train its implicit generative model, GAN uses a discriminator since traditional Bayesian methods that require analytic density functions are no longer applicable. This novel approach inspired by zero sum game theory leads to a significant performance boost; GANs are able to generate samples in a fidelity level that is way beyond traditional Bayesian methods. During the last few years, there have been numerous research articles in this area aiming at improving its performance (Radford et al., 2015; Zhao et al., 2016; Nowozin et al., 2016; Mao et al., 2017) . GANs have now become one of most recognized unsupervised learning techniques and have been widely used in a variety of domains such as image generation (Nguyen et al., 2017) , image super resolution BID16 , imitation learning BID12 .Despite the great progress of GANs, many essential problems remain unsolved. Why is GAN so hard to train? How to tune the hyper-parameters to reduce instability in GAN training? How to eliminate mode collapse and fake images that show up frequently in training ? Comparing with many other machine learning techniques, the properties of GANs are far from being well understood. It is quite likely that the theoretical foundation of GANs will become a longstanding problem. The theoretical difficulty of GANs mainly lies in the following several aspects. First, it is a non-convex optimization problem with a complicated landscape. It is unclear how to solve such optimization problems efficiently. The first-order method widely used in the literature via updating the generator and discriminator along descent/ascent direction does not seem to converge all the time. Although some techniques were proposed to stabilize the training performance of the network, e.g., spectral normalization Miyato et al. (2018) , in fact, there is no evidence that these algorithms guarantee even local optimality. Second, even if there were an efficient algorithm to solve this optimization problem, we do not know how well they generalize. After all, the optimization formulation is based only on the samples generated by the underlying distribution but our goal is to recover this underlying distribution. Of course, this is a problem faced by all machine learning techniques. Last, there are no reliable ways to evaluate the quality of trained models. There are a number of works in this topic (Salimans et al., 2016; BID11 , but human eyes inspection remains the primary approach to judge a GAN model.In the present work, we focus on the first problem and analyze the dynamics of GANs from an optimization point of view. More precisely, we study the convergence properties of the first-order method in GAN training. Our contributions can be summarized as follows. 1) We formulate a large class of GAN problems as a primal-dual optimization problem with a coupling term that is linear over discriminator (see Section 2 for the exact formulation); 2) We prove that the simple primal-dual first-order algorithm converges to a stationary solution with a sublinear convergent rate O(1/t).There have been a number of papers that study the dynamics of GANs from an optimization viewpoint. These works can be roughly divided into three categories. In the first category, the authors focus on high level idea using nonparametric models. This includes the original GAN paper BID8 , the Wasserstein GAN papers ; and many other works proposing new GAN structures. In the second category, the authors consider the unrolled dynamics (Metz et al., 2016) , that is, the discriminator remains optimal or almost optimal during the optimization processes. This is considerably different to the first-order iterative algorithm widely used in GAN training. Recent works BID11 ; BID17 Sanjabi et al. (2018) provide global convergence analysis for this algorithm.The last category is on the first-order primal-dual algorithm, in which both the discriminator and the generator update via (stochastic) gradient descent. However, most of the convergence analysis are local BID4 Mescheder et al., 2017; Nagarajan & Kolter, 2017; BID18 . Other related work including the following: In Qian et al. (2018) the authors consider a gradient descent/ascent algorithm for a special min-max problem arising from robust learning (min problem is unconstrained, max problem has simplex constraints); In Yadav et al. (2018) the GANs are treated as convex-concave primal-dual optimization problems. This formulation is considerably different to our setup where GANs, as they should be, are formulated as nonconvex saddle point problems. In BID5 , the authors investigated the properties of the optimal solutions, which is also different from our work focusing on convergence analysis of the first-order primal-dual algorithm. In Zhao et al. (2018) , some unified framework covering several generative models, e.g., VAE, infoGAN, were proposed in the Lagrangian framework. However, the dual variable in their problem is a Lagrangian multiplier, while in our problem, it is the discriminator of GAN. Besides, the focus of their paper is not the optimization algorithm . In BID2 , the authors related a class of GANs to constrained convex optimization problems. More specifically, such GANs can be viewed as Lagrangian forms of these convex optimization problems. The optimization variables in their formulation are the probability density of the generator and the function values of the discriminator. Many issues like nonconvexity do not show up. This is essentially a nonparametric model, which doesn't apply to cases when the discriminator and the generator are represented by parametric models. On the other hand, our analysis is carried out on the parametric models directly and we have to deal with the nonconvexity of neural networks. In BID9 a primal-dual algorithm has been studied for a non-convex linearly constrained problem (which can be reformulated into a min-max problem, with the max problem being linear and unconstrained, and with linear coupling between variables); In BID10 , BID3 and the references therein, first-order methods have been developed for convex-concave saddle point problems. Compared to these works, our considered problem is more general, allowing non-convexity and non-smoothness in the objective, non-convex coupling between variables, and can further include constraints. Moreover, we provide global convergence rate analysis, which is much stronger than the local analysis mentioned above.It turns out that the primal-dual framework we study in this paper can also be applied to the distributional robust machine learning problems (Namkoong & Duchi, 2016 ) and the multi-task learning problems (Qian et al., 2018) . In multi-task learning, the goal is to train a single neural network that would work for several different machine learning tasks. Similarly, in distributional robust learning, the purpose is to have a single model that would work for a set of data distributions. In both problems, an adversarial layer is utilized to improve the worst case performance , which leads to a primal-dual optimization structure that falls into the scope of problems we consider.The rest of the paper is structured as follows. In Section 2 we introduce GAN and its primal-dual formulation. We provide details of the algorithms with proof sketches in Section 3. The full proofs are relegated to the appendix. We highlight our theoretical results in Section 4 via several numerical examples, with both synthetic and real datasets. In this work, we presented a convergence result for a first-order algorithm on a class of non-convex max-min optimization problems that arise in many machine learning applications such as generative adversarial networks and multi-task learning. To the best of our knowledge, this is the first convergence result for this type of primal-dual algorithms.Our results allow us to analyze GANs with neural network generator as well as general multi-task non-convex supervised learning problems. A critical assumption we made is that the inner maximization loop is a strictly convex problem. For applications in GANs, our assumptions require the discriminator to be a linear combination of predefined basis functions. Extending this to the most general cases where the discriminator is a neural network requires further investigations and will be a future research topic.",1955,1.171,1182,1.6539763113367174,"Generative adversarial network these due data distributions In spite applications GAN known notoriously train The tremendous amount time run the training algorithm its sensitivity hyper-parameter tuning have haunting researchers To resolve first GANs Herein, take toward this direction examining GANs relate a large class including max-min optimization problems with the coupling term being linear over the discriminator By developing new primal-dual optimization tools show, a proper stepsize choice widely first iterative in training GANs would in converge a stationary solution a sublinear rate The same framework also multi-task learning distributional robust learning problems We verify our analysis numerical examples We hope our analysis shed future studies the theoretical properties relevant machine learning problems Since invented Ian Goodfellow his seminal work BID8 , generative adversarial networks considered one machine learning community It an extremely powerful tool estimate data distributions generate realistic samples To train its implicit generative model GAN uses since traditional Bayesian methods that require analytic density functions no applicable This novel approach inspired zero sum game theory leads a significant performance boost; GANs able generate samples a fidelity level way traditional Bayesian methods During numerous research articles in aiming its performance (Radford Zhao Nowozin Mao . GANs have now most recognized unsupervised learning techniques image generation (Nguyen 2017 , super resolution BID16 imitation learning .Despite many essential problems Why GAN so hard train How tune the hyper reduce instability GAN training? How eliminate mode collapse fake images that show frequently training ? Comparing with many other machine learning techniques the properties GANs far well It quite the theoretical foundation GANs become a longstanding problem The theoretical difficulty GANs mainly the following several aspects First a non-convex optimization problem with a complicated landscape It unclear to solve such optimization problems efficiently The first-order method widely the literature via updating the generator discriminator along descent/ascent direction does seem converge Although some techniques proposed stabilize the training performance the network spectral normalization Miyato (2018 , in fact there these algorithms guarantee even local optimality Second even an efficient algorithm solve do they generalize After all the optimization formulation only the samples generated the underlying distribution but our goal recover this underlying distribution Of faced all machine learning techniques Last, there are no reliable ways evaluate trained models There works this topic (Salimans et 2016 BID11 , but human eyes inspection remains judge a GAN model.In focus the first problem and analyze the dynamics from an optimization point More precisely study the convergence properties the first-order method GAN training Our contributions can summarized 1 We formulate a large class GAN problems as a primal-dual optimization problem a coupling term linear over discriminator ( the exact formulation 2 prove a stationary solution a sublinear convergent rate O(1t).There have study from These works roughly In the first category the authors focus high level idea using This includes the original GAN paper BID8 , the Wasserstein GAN papers ; proposing In the second category the authors consider the unrolled dynamics (Metz et al 2016 , that the discriminator remains optimal or almost during the optimization processes This considerably the first-order iterative algorithm widely GAN training Recent works BID11 ; BID17 Sanjabi et (2018 provide global convergence analysis this algorithmThe last category on the first-order primal-dual algorithm in update via However most the convergence analysis are local BID4 Mescheder et 2017 & Kolter BID18 . Other related work including In Qian (2018 the authors consider a gradient descent/ascent algorithm a special min-max problem arising robust learningmin problem is has simplex constraints In Yadav (2018 the GANs treated convex-concave primal-dual optimization problems This formulation considerably our setup where GANs, as they should formulated nonconvex saddle point problems In BID5 , the authors investigated the properties the optimal solutions is also different our work focusing convergence analysis the first-order primal-dual algorithm In Zhao (2018 , some unified framework covering several generative models VAE infoGAN were the Lagrangian framework However the dual variable in their problem multiplier while our problem the discriminator GAN Besides the focus their paper the optimization algorithm . In BID2 , the authors related a class GANs constrained convex optimization problems More specifically such GANs viewed Lagrangian forms these convex optimization problems The optimization variables their formulation the probability density the generator the function values Many issues like nonconvexity do show. This essentially a nonparametric model does apply cases when and the generator represented On our analysis is carried the parametric models directly deal neural networks In BID9 a primal-dual algorithm studied a non-convex linearly constrained problemwhich reformulated the max problem linear unconstrained linear coupling variables In , the references therein first-order methods convex-concave saddle point problems Compared these works our considered problem more general allowing nonconvexity the objective variables can further include constraints. Moreover we provide global convergence rate analysis much stronger the local analysis mentionedIt turns the primal-dual framework we study the distributional robust machine learning problems (Namkoong Duchi ) multitask learningQian 2018) . In multi-task learning train would work Similarly distributional robust learning the purpose have would work data distributions In both problems an adversarial layer utilized improve the worst case performance , leads a primal-dual optimization structure falls the scope problems we considerThe rest structured In Section we introduce GAN and its primal-dual formulation We provide details the algorithms with proof sketches in Section The full proofs relegated We highlight our theoretical results Section via several numerical examples both synthetic and real datasets In this work presented a convergence result on a class non-convex max-min optimization problems arise such To the first convergence result primal-dual algorithmsOur results allow analyze GANs neural network generator as general multi-task non-convex supervised learning problems A critical assumption we the inner maximization loop a strictly convex problem For applications in GANs our assumptions require the discriminator a linear combination predefined basis functions Extending this the most general cases where the discriminator a neural network requires further investigations will a future research topic",0.01,0.3703533532392927
"Social dilemmas, where mutual cooperation can lead to high payoffs but participants face incentives to cheat, are ubiquitous in multi-agent interaction. We wish to construct agents that cooperate with pure cooperators, avoid exploitation by pure defectors, and incentivize cooperation from the rest. However, often the actions taken by a partner are (partially) unobserved or the consequences of individual actions are hard to predict. We show that in a large class of games good strategies can be constructed by conditioning one's behavior solely on outcomes (ie. one's past rewards). We call this consequentialist conditional cooperation. We show how to construct such strategies using deep reinforcement learning techniques and demonstrate, both analytically and experimentally, that they are effective in social dilemmas beyond simple matrix games. We also show the limitations of relying purely on consequences and discuss the need for understanding both the consequences of and the intentions behind an action. Deep reinforcement learning (RL) is concerned with constructing agents that start as blank slates and can learn to behave in optimal ways in complex environments.1 A recent stream of research has taken a particular interest in social dilemmas, situations where individuals have incentives to act in ways that undermine socially optimal outcomes (Leibo et al., 2017; Perolat et al., 2017; Lerer & Peysakhovich, 2017; Kleiman-Weiner et al., 2016) . In this paper we consider RL-based strategies for social dilemmas in which information about a partner's actions or the underlying environment is only partially observed.The simplest social dilemma is the Prisoner's Dilemma (PD) in which two players choose between one of two actions: cooperate or defect. Mutual cooperation yields the highest payoffs, but no matter what one's partner is doing, one can get a higher reward by defecting. A well studied strategy for maintaining cooperation when the PD is repeated is tit-for-tat (TFT, Axelrod (2006) ). TFT behaves by copying the prior behavior of their partner, rewarding cooperation today with cooperation tomorrow. Thus, if an agent commits to TFT it makes cooperation the best strategy for the agent's partner. TFT has proven to be a heavily studied strategy because it has intuitive appeal: 1) it is easily explainable, 2) it begins cooperating, 3) it rewards a cooperative partner, 4) it avoids being exploited, 5) it is forgiving.In Markov games cooperation and defection are not single actions, but rather temporally extended policies. Recent work has considered expanding TFT to more complex Markov games either as a heuristic, by learning cooperative and selfish policies and switching between them as needed (Lerer & Peysakhovich, 2017) , or as an outcome of an end-to-end procedure (Foerster et al., 2017c) . TFT is * Both authors contributed equally to this paper. Author ordering was determined at random. 1 This approach has been applied to domains including: single agent decision problems (Mnih et al., 2015) , board and card-based zero-sum games BID15 BID13 Heinrich & Silver, 2016) , video games (Kempka et al., 2016; BID17 Ontanón et al., 2013; BID16 Foerster et al., 2017a) , multi-agent coordination problems (Lowe et al., 2017; Foerster et al., 2017b; BID7 BID14 Peysakhovich & Lerer, 2017) , and the emergence of language (Lazaridou et al., 2017; Das et al., 2017; Evtimova et al., 2017; Havrylov & Titov, 2017; Jorge et al., 2016) .an example of a conditionally cooperative strategy -that is, it cooperates when a certain condition is fulfilled (ie. the partner's last period action was cooperative). TFT , however, has a weakness -it requires perfect observability of a partner's behavior and perfect understanding of each action's future consequences.Our main contribution is to use RL methods to construct conditionally cooperative strategies for games with imperfect information. When information is imperfect, the agent must use what they can observe to try to estimate whether a partner is acting cooperatively (or not) and determine how to respond. We show that when the game is ergodic, observed rewards can be used as a summary statistic -if the current total (or time averaged) reward is above a time-dependent threshold (where the threshold values are computed using RL and a form of self play) the agent cooperates, otherwise the agent does not 2 . We call this consequentialist conditional cooperation (CCC). We show analytically that this strategy cooperates with cooperators, avoids exploitation, and guarantees a good payoff to the CCC agent in the long run.We study CCC agents in a partially observed Markov game which we call Fishery. In Fishery two agents live on different sides of a lake in which fish appear. The game has partial information because agents cannot observe what happens across the lake. Fish spawn randomly , starting young and swim to the other side and become mature. Agents can catch fish on their side of the lake. Catching any fish yields payoff but mature fish are worth more. Therefore, cooperative strategies are those which leave young fish for one's partner. However, there is always a temptation to defect and catch both young and mature fish. We show that CCC agents cooperate with cooperators, avoid exploitation, and get high payoffs when matched with themselves.Second, we show that CCC is an efficient strategy for more complex games where implementing conditional cooperation by fully modeling the effect of an action on future rewards (eg. amTFT (Lerer & Peysakhovich, 2017) ) is computationally demanding. We compare the performance of CCC to amTFT in the Pong Player's Dilemma (PPD). This game is a modification of standard Atari pong such that when an agent scores they gain a reward of 1 but the partner receives a reward of −2. Cooperative payoffs are achieved when both agents try hard not to score but selfish agents are again tempted to defect and try to score points even though this decreases total social reward. We see that CCC is a successful, robust, and simple strategy in this game.However, this does not mean CCC completely dominates forward looking strategies like amTFT. We consider a version of the Pong Players' Dilemma where when a player scores, instead of their partner losing 2 points deterministically they lose 2/p points with probability p. Here the expected rewards of non-cooperation are the same as in the PPD and so expected-future-reward based methods (eg. amTFT) will act identically. However, when p is low it may take a long time for consequentialist agents to detect a defector. Empirically we see that in short risky PPD games CCC agents can be exploited by defectors but that amTFT agents cannot. We close by discussing limitations and progress towards agents that can effectively use both intention and outcome information effectively in navigating the world. In this work we have introduced consequentialist conditionally cooperative strategies and shown that they are useful heuristics in social dilemmas, even in those where information is imperfect either due to the structure of the game or due to the fact that we cannot perfectly forecast a partner's future actions. We have shown that using one's own reward stream as a summary statistic for whether to cooperate (or not) in a given period is guaranteed to work in the limit as long as the underlying game is ergodic. Note that this sometimes (but not always) gives good finite time guarantees. In particular, 4 For simplicity for this experiment we use theπ C andπ D strategies trained in the standard PPD for the risky PPD, this is because the risky PPD is the same (in expectation) as the PPD. the time scale for a CCC agent to detect exploitation is related to the mixing time of the POMG and the stochasticity of rewards; if these are large, then correspondingly long games are required for CCC to perform well.We have also compared consequentialist and forward-looking models. As another simple example of the difference between the two we can consider the random Dictator Game (rDG) introduced by Cushman et al. (2009) . In the rDG, individuals are paired, one (the Dictator) is given an amount of money to split with a Partner, and chooses between one of two dice, a 'fair' die which yields a 50 − 50 split with a high probability and an unfair split with a low probability and an 'unfair' die which yields a 50 − 50 split with low probability. Consequentialist conditional cooperators would label a partner a defector if an unfair outcome came up (regardless of die choice) whereas intention-based cooperators would look at the choice of die, not the actual outcome.For RL trained agents, conditioning purely on intentions (eg. amTFT) has advantages in that it is forward looking and doesn't require ergodicity assumptions but it is an expensive strategy that is complex (or impossible) to implement for POMDPs and requires very precise estimates of potential outcomes. CCC is simple, works in POMDPs and requires only information about payoff rates (rather than actual policies), however it may take a long time to converge. Each has unique advantages and disadvantages. Therefore constructing agents that can solve social dilemmas will require combining consequentialist and intention-based signals.Interestingly, experimental evidence shows that while humans combine both intentions and outcomes, we often rely much more heavily on consequences than 'optimal' behavior would demand. For example, experimental subjects rely heavily on the outcome of the die throw rather than die choice in the rDG (Cushman et al., 2009) . This is evidence for the notion that rather than acting optimally in each situation, humans have social heuristics which are tuned to work across many environments BID6 Hauser et al., 2014; Ouss & Peysakhovich, 2015; BID1 Mao et al., 2017; Niella et al., 2016) . There is much discussion of hybrid environments that include both artificial agents and humans (eg. BID11 Crandall et al. (2017) ). Constructing artificial agents that can do well in such environments will require going beyond the kinds of optimality theorems and experiments highlighted in this and related work.In addition, we have defined cooperative policies as those which maximize the sum of the rewards. This seems like a natural focal point in symmetric games like the ones we have studied but it is well known that human social preferences take into account factors such as inequity (Fehr & Schmidt, 1999) and social norms BID8 . To be successful, AI researchers will have to understand human social heuristics and construct agents that are in tune with human moral and social intuitions BID4 BID6 6 TECHNICAL APPENDIX 6.1 PROOF OF MAIN THEOREM We will use this basic property of almost sure convergence. If a sequence of random variables X n converges to X almost surely then DISPLAYFORM0 The intuition behind the proof is as follows: first, we show that if the CCC agent's partner plays π C then for any R s > 0 there exists a time t s at which the CCC agent's total payoff exceeds the threshold t s T by at least R s with high probability. Intuitively this is because the rate T is lower than ρ CC which is weakly lower than the rate guaranteed to a CCC agent whose partner behaves according to π C always.Second, we will show that for sufficiently large R s , if the CCC agent's total payoff exceeds the threshold by R s then the CCC agent also only plays π C from that point on with high probability.Together this implies that if the partner plays according to π C then with high probability the CCC agent behaves according to π D only a finite amount of times and thus the rates of payoffs for both agents converge to ρ CC .",2484,1.219,1441,1.7238029146426093,"Social dilemmas where mutual cooperation high payoffs but participants face incentives ubiquitous multi-agent interaction We wish construct agents cooperate pure cooperators avoid exploitation pure defectors incentivize from the rest However often the actions a partner (partially unobserved the consequences hard We show in a large class games good strategies constructed conditioning solely outcomesie one's past rewards). We call this consequentialist conditional cooperation We show construct such strategies deep reinforcement learning techniques demonstrate, both beyond simple matrix games We also show the limitations relying purely consequences discuss understanding and the intentions an action Deep reinforcement learningRL concerned constructing agents start as blank slates can learn behave optimal ways complex environments.1 A recent stream taken social dilemmas situations individuals incentives undermine socially optimal outcomesLeibo et al 2017 Perolat Lerer Peysakhovich Kleiman-Weiner) . In this paper consider RL-based strategies information or the underlying environment only partially observedThe simplest social dilemma two players cooperate defect Mutual cooperation yields no matter one's partner one get defecting A well studied strategy maintaining cooperation when the PD repeated tit (, Axelrod (2006 TFT behaves by copying the prior behavior their partner rewarding cooperation today cooperation Thus an agent commits to TFT it makes cooperation the best TFT has proven a heavily studied strategy because intuitive appeal: 1 easily begins cooperating rewards a cooperative partner avoids being exploited forgivingIn Markov games cooperation defection not single actions temporally extended policies Recent work considered expanding TFT more complex Markov games either a heuristic by learning cooperative and selfish policies switchingLerer Peysakhovich 2017 , an outcome an end procedure 2017c TFT * Both authors contributed equally Author ordering was determined at random 1 This approach domains including single agent decision problemsMnih et al 2015 board BID15 BID13 Heinrich & Silver) video gamesKempka; BID17 Ontanón 2013 Foerster 2017aLowe Peysakhovich Lerer the emergence languageLazaridou Das et al Evtimova Havrylov Titov Jorge .an example a conditionally cooperative strategy -that when a certain condition fulfilledie the partner's last period action cooperative). TFT , however a weakness -it requires perfect observability a partner's behavior perfect understanding each action's future consequencesOur main contribution use RL methods construct conditionally cooperative strategies games imperfect information When information imperfect the agent use what they observe try estimate whether a partner acting cooperatively ( determine We show when the game ergodic observed rewards used a summary statistic -if the current total (or time averaged) reward abovewhere the threshold values computed RL and a form self play agent cooperates, otherwise 2 . We call this consequentialist conditional cooperationCCC We show analytically this strategy cooperates cooperators avoids exploitation guarantees a good payoff the CCC agentWe study a partially observed Markov game which we Fishery In Fishery two agents live which fish appear. The game partial information because agents observe what across the lake Fish spawn randomly , starting young swim and become mature Agents can catch fish their side Catching any fish yields payoff but mature fish worth Therefore cooperative strategies those leave young fish for one's partner However always defect catch both young and mature fish We show CCC agents cooperate cooperators avoid exploitation get high payoffs matched themselvesSecond is an efficient strategy more complex games implementing conditional cooperation by fully modeling future rewards (eg amTFT (Lerer & Peysakhovich 2017 ) computationally demanding We compare CCC to amTFT the Pong Player's Dilemma This game a modification standard Atari pong such that when an agent scores they gain but the partner receives −2 Cooperative payoffs achieved both agents try hard not score but selfish agents again tempted defect try points even this decreases total social reward We see CCC successful, robust simple strategy this gameHowever completely dominates forward looking strategies amTFT We consider a version the Pong Players' Dilemma where instead their partner losing deterministically they 2/p points with probability p. Here the expected rewards noncooperation the the PPD and so expected-future-reward based methodseg amTFT) will act identically. However when p is low take consequentialist agents detect a defector Empirically we in short risky PPD games CCC agents exploited defectors but amTFT agents We close discussing limitations progress agents effectively use both intention outcome effectively navigating In this work introduced consequentialist conditionally cooperative strategies shown useful heuristics even those information imperfect either the structure we perfectly forecast We shown using one's own reward stream a summary statistic for whether to cooperate ( a given period guaranteed work the limit as the underlying game ergodic Note sometimes ( gives good finite time guarantees In particular 4 For simplicity for this experiment use theπ C andπ D strategies trained the standard PPD for the risky PPD this (in expectation. the time scale a CCC agent detect exploitation related the mixing time the POMG rewards; if these large correspondingly long games required performWe compared consequentialist and forward-looking models As another simple example we the random Dictator Game introduced Cushman et al (2009 . In the rDG individuals paired, one (the Dictator given an amount split a Partner chooses two dice a 'fair' die which yields a 50 − 50 split and an unfair split and Consequentialist conditional cooperators would label a partner defector an unfair outcome came ( die choice whereas look dieFor RL trained agents conditioning purely intentionseg amTFT) has advantages forward does ergodicity assumptions but an expensive strategy complex (or impossible for POMDPs requires very precise estimates potential outcomes CCC is simple works POMDPs requires only information payoff ratesrather actual policies however may take converge Each has unique advantages Therefore constructing agents solve will combining consequentialist and intention-based signalsInterestingly experimental evidence while humans combine both intentions outcomes often rely much consequences ' would demand For example experimental subjects rely the outcome the die throw rather die choice the rDGCushman . This evidence rather acting optimally each situation humans social heuristics tuned work across BID6 Hauser; Ouss & Peysakhovich BID1 Mao Niella . There much discussion hybrid environments include both artificial agents humanseg BID11 Crandall et al (2017 ). Constructing artificial agents do well such environments going the kinds optimality theorems and experiments highlighted this and related workIn defined cooperative policies maximize the sum. This seems a natural focal point in symmetric games the ones studied but well human social preferences take into inequityFehr & Schmidt social norms BID8 . To successful AI researchers human social heuristics construct agents in BID4 BID6 6 TECHNICAL APPENDIX MAIN THEOREM We this basic property almost sure convergence. If a sequence random variables X n converges X almost surely DISPLAYFORM0 The intuition the proof as first show the CCC agent's partner plays �� C for R s > there at exceeds the threshold t s T by with high probability Intuitively this because the rate T lower �� CC which weakly lower guaranteed a CCC agent whose partner behaves according �� C alwaysSecond will show for sufficiently R s if exceeds by R also only plays from withTogether the partner plays according with behaves only a finite amount thus the rates payoffs both agents converge",0.02,0.5482654035644181
"In distributed training, the communication cost due to the transmission of gradients
 or the parameters of the deep model is a major bottleneck in scaling up the number
 of processing nodes. To address this issue, we propose dithered quantization for
 the transmission of the stochastic gradients and show that training with Dithered
 Quantized Stochastic Gradients (DQSG) is similar to the training with unquantized
 SGs perturbed by an independent bounded uniform noise, in contrast to the other
 quantization methods where the perturbation depends on the gradients and hence,
 complicating the convergence analysis. We study the convergence of training
 algorithms using DQSG and the trade off between the number of quantization
 levels and the training time. Next, we observe that there is a correlation among the
 SGs computed by workers that can be utilized to further reduce the communication
 overhead without any performance loss. Hence, we develop a simple yet effective
 quantization scheme, nested dithered quantized SG (NDQSG), that can reduce the
 communication significantly without requiring the workers communicating extra
 information to each other. We prove that although NDQSG requires significantly
 less bits, it can achieve the same quantization variance bound as DQSG. Our
 simulation results confirm the effectiveness of training using DQSG and NDQSG
 in reducing the communication bits or the convergence time compared to the
 existing methods without sacrificing the accuracy of the trained model. In recent years, the size of deep learning problems has increased significantly both in terms of the number of available training samples as well as the complexity of the model. Hence, training deep models on a single processing node is unappealing or nearly impossible. As such, large-scale distributed machine learning in which the training samples are distributed among different repository or processing units (referred to as workers) has started to be a viable approach for tackling the memory, storage and computational constraints.The requirement to exchange the gradients or the parameters of the model incurs significant communication overhead which is a major bottleneck in distributed training algorithms. In recent years, there has been a great amount of effort on reducing the communication overhead. The majority of existing methods can be categorized into two groups: The first group mitigates the communication bottleneck by reducing the overall transmission rate via sparsification, quantization and/or compression of the gradients. For example, BID15 reduces the communication overhead significantly by one-bit quantization of the stochastic gradients (SG). However, the reduced accuracy of gradient may impair the convergence rate. Using different quantization levels or adaptive quantizers, one can alleviate such issues by decreasing the error in the quantized gradients in the expense of increased communication bits BID4 . Moreover, applying entropy coding algorithms such as Huffman coding on the quantized values can further reduce the communication bit-rate BID13 ; BID17 . BID0 introduced QSGD which uses probabilistic (stochastic) quantization of SGs instead of ordinary fixed (deterministic) quantization methods. They investigated its convergence guarantee and the trade-off between the quantization precision and variance of QSG. Terngrad BID18 probabilistically quantizes the gradients into {−1, 0, +1} and it is shown that the convergence rate can be improved by layer-wise quantization and gradient clipping.The second group of works attempts to attenuate the communication bottleneck by relaxing the synchronization between workers. Each worker may continue its own computations while some others are still communicating and exchanging parameters. Carefully scheduling and managing the asynchronous parameter exchange can lead to a better utilization of both the communication bandwidth and the computational power of the distributed system. Examples of such approaches include DownpourSGD BID3 , Hogwild! Niu et al. (2011 ), Hogwild++ Zhang et al. (2016 and Stale Synchronous Parallel model of computation BID7 .Our Contributions. Our work in this paper falls within the first line of research, i.e. reducing the communication overhead by quantizing and compressing the gradients. We first introduce using dithered quantization in the distributed computations of the stochastic gradient and show that stochastic quantizer of BID0 and ternarization of BID18 can be considered as special cases of our proposed method, although the reconstruction algorithms are slightly different. The convergence of dithered quantized stochastic gradient descent algorithm is analyzed and its convergence speed w.r.t. the number of workers and quantization precision is investigated. Next , we observe that in a typical distributed system, the stochastic gradients computed by the workers are correlated. However , the existing communication methods ignore that correlation. We tap into the question of how that correlation can be exploited to further reduce the communication without sacrificing the precision or convergence of the learning algorithm. We model the correlation between the stochastic gradients computed by each worker and propose a nested quantization scheme to reduce the communication bits without increasing the variance of the quantization error or reducing the convergence speed of the distributed training algorithm.",998,0.545,560,1.7821428571428573,"In distributed training the communication cost due gradients the parameters the deep model a major bottleneck scaling processing nodes To address propose dithered quantization the transmission show training similar perturbed an independent bounded uniform noise where depends hence, complicating the convergence analysis We study the convergence training algorithms using DQSG the trade quantization levels Next observe among the SGs computed workers that can utilized further the communication without any performance loss Hence develop a simple yet effective quantization scheme nested dithered quantized SG (NDQSG reduce the communication significantly without the workers communicating extra information We prove although NDQSG requires significantly less bits achieve the same quantization variance bound Our simulation results confirm training using DQSG the communication bits or the convergence time compared the existing methods without sacrificing In the size deep learning problems both available training samples as Hence training deep models a single processing node unappealing or nearly As such, large-scale distributed machine learning in which the training samples different repository or processing units workers started tackling the memory, computational constraintsThe requirement exchange the gradients or the parameters incurs significant communication In effort reducing the communication overhead The majority existing methods can categorized mitigates the communication bottleneck via sparsification quantization compression the gradients For example BID15 reduces the communication overhead significantly one-bit quantizationSG However the reduced accuracy gradient may impair the convergence rate Using different quantization levels or adaptive quantizers one alleviate such issues decreasing the expense increased communication bits BID4 Moreover applying entropy coding algorithms such coding on the quantized values further the communication bit-rate BID13 ; BID17 . BID0 introduced QSGD which uses SGs instead They investigated its convergence guarantee the quantization precision variance QSG Terngrad BID18 probabilistically quantizes into { it improved gradient clippingThe second group works attempts attenuate the communication bottleneck relaxing the synchronization workers Each worker may continue its own computations some others still communicating exchanging parameters Carefully scheduling the asynchronous parameter exchange lead a better utilization both the communication Examples such approaches DownpourSGD BID3 , Hogwild! Niu et al (2011 ), Hogwild++ Zhang et al (2016 and Stale Synchronous Parallel model computation BID7 .Our Contributions Our work this paper falls reducing the communication overhead by quantizing compressing We first introduce using dithered quantization the distributed computations and show of BID0 ternarization considered special cases our proposed method although the reconstruction algorithms slightly The convergence dithered quantized stochastic gradient descent algorithm is analyzed its convergence speed w.r.t the number workers quantization precision Next , observe a typical distributed system computed the workers correlated However , the existing communication methods ignore that correlation We tap the question that correlation exploited further reduce the communication without the precision or convergence the learning algorithm We model the correlation computed each worker propose a nested quantization scheme reduce the communication bits without or reducing the convergence speed",0.01,0.6969104513637466
"Deep neural networks have been shown to perform well in many classical machine learning problems, especially in image classification tasks. However, researchers have found that neural networks can be easily fooled, and they are surprisingly sensitive to small perturbations imperceptible to humans.   Carefully crafted input images (adversarial examples) can force a well-trained neural network to provide arbitrary outputs.   Including adversarial examples during training is a popular defense mechanism against adversarial attacks. In this paper we propose a new defensive mechanism under the generative adversarial network~(GAN) framework. We model the adversarial noise using a generative network, trained jointly with a classification discriminative network as a minimax game. We show empirically that our adversarial network approach works well against black box attacks, with performance on par with state-of-art methods such as ensemble adversarial training and adversarial training with projected gradient descent.
 Deep neural networks have been successfully applied to a variety of tasks, including image classification BID12 , speech recognition BID8 , and human-level playing of video games through deep reinforcement learning BID20 . However, BID29 showed that convolutional neural networks (CNN) are extremely sensitive to carefully crafted small perturbations added to the input images. Since then, many adversarial examples generating methods have been proposed, including Jacobian based saliency map attack (JSMA) BID23 , projected gradient descent (PGD) attack , and C&W's attack BID3 . In general, there are two types of attack models: white box attack and black box attack. Attackers in white box attack model have complete knowledge of the target network, including network's architecture and parameters. Whereas in black box attacks, attackers only have partial or no information on the target network BID25 .Various defensive methods have been proposed to mitigate the effect of the adversarial examples. Adversarial training which augments the training set with adversarial examples shows good defensive performance in terms of white box attacks BID13 . Apart from adversarial training, there are many other defensive approaches including defensive distillation BID24 , using randomization at inference time BID33 , and thermometer encoding BID2 , etc.In this paper, we propose a defensive method based on generative adversarial network (GAN) BID6 . Instead of using the generative network to generate samples that can fool the discriminative network as real data, we train the generative network to generate (additive) adversarial noise that can fool the discriminative network into misclassifying the input image. This allows flexible modeling of the adversarial noise by the generative network, which can take in the original image or a random vector or even the class label to create different types of noise. The discriminative networks used in our approach are just the usual neural networks designed for their specific classification tasks. The purpose of the discriminative network is to classify both clean and adversarial example with correct label, while the generative network aims to generate powerful perturbations to fool the discriminative network. This approach is simple and it directly uses the minimax game concept employed by GAN. Our main contributions include:• We show that our adversarial network approach can produce neural networks that are robust towards black box attacks. In the experiments they show similar, and in some cases better, performance when compared to state-of-art defense methods such as ensemble adversarial training BID30 and adversarial training with projected gradient descent . To our best knowledge we are also the first to study the joint training of a generative attack network and a discriminative network.• We study the effectiveness of different generative networks in attacking a trained discriminative network, and show that a variety of generative networks, including those taking in random noise or labels as inputs, can be effective in attacks. We also show that training against these generative networks can provide robustness against different attacks.The rest of the paper is organized as follows. In Section 2, related works including multiple attack and defense methods are discussed. Section 3 presents our defensive method in details. Experimental results are shown in Section 4, with conclusions of the paper in Section 5. In the experiments above we see that adversarial PGD training usually works best on white box attacks, but there is a tradeoff between accuracies on clean data against accuracies on adversarial examples due to finite model capacity. We can try to use models with larger capacity, but there is always a tradeoff between the two, especially for larger perturbations . There are some recent works that indicate training for standard accuracy and training for adversarial accuracy (e.g., with PGD) are two fairly different problems . Examples generated from PGD are particularly difficult to train against. This makes adversarial PGD training disadvantaged in many black box attack situations, when compared with models trained with weaker adversaries, e.g., ensemble adversarial training and our adversarial networks method.We have also observed in the experiments that for black box attacks, the most effective adversarial examples are usually those constructed from models trained using the same method but with different random seed. This suggests hiding the knowledge of the training method from the attacker could be an important factor in defending against black box attacks. Defending against black box attacks is closely related to the question of the transferability of adversarial examples. Although there are some previous works exploring this question BID15 , the underlying factors affecting transferability are still not well understood.In our experimentation with the architectures of the discriminative and generative networks, the choice of architectures of G φ does not seem to have a big effect on the quality of solution. The dynamics of training, such as the step size used and the number of iterations to run for each network during gradient descent/ascent, seem to have a bigger effect on the saddle point solution quality than the network architecture. It would be interesting to find classes of generative network architectures that lead to substantially different saddle points when trained against a particular discriminative network architecture. Also, recent works have shown that there are connected flat regions in the minima of neural network loss landscapes BID5 BID4 . We believe that the same might hold true for GANs, and it would be interesting to explore how the training dynamics can lead to different GAN solutions that might have different robustness properties.Our approach can be extended with multiple discriminative networks playing against multiple generative networks. It can also be combined with ensemble adversarial training, where some adversarial examples come from static pre-trained models, while some other come from dynamically adjusting generative networks. We have proposed an adversarial network approach to learning discriminative neural networks that are robust to adversarial noise, especially under black box attacks. For future work we are interested in extending the experiments to ImageNet, and exploring the choice of architectures of the discriminative and generative networks and their interaction. generative networks used in this paper. G0 and G1 are encoder-decoder networks, while G2 and G3 are decoder networks using a random vector and a one-hot encoding of the label respectively. The generative networks are parameterized by a factor k determining the number of filters used (width of network). As default we use k = 64, and k = 16 for networks using labels as inputs.EXTRA RESULTS ON CIFAR100 AND WIDE RESNET ON CIFAR10The discriminative and generative networks in our CIFAR100 experiment have the same network architecture as the CIFAR10 experiment, except that the output layer dimension of the D network is 100 other than 10 in CIFAR10. We use learning rate of 0.1 for the first 100k iterations, and 0.01 for another 100k iterations. The batch size is 64 and weight decay is 1E-5. TAB8 gives the results on CIFAR10 using a wider version of Resnet (Model D2), by multiplying the number of filters in each convolutional layer by a factor of 10. Some of the previous works in the literature use models of larger capacity for training adversarially robust models, so we perform experiments on these large capacity models here. First the accuracies increase across the board with larger capacity models. The accuracy gap on clean data between adversarial PGD and standard training still exists, but now there is also a small accuracy gap between our adversarial network approach and standard training. For the rest of the white box and black accuracies the story is similar, the models are weakest against attacks trained with the same method but with a different random seed. Our adversarial network approach has very good performance across different attacks, even as it is not always the winner for each individual attack. TAB10 gives the results of Wide ResNet on CIFAR100, and the results are qualitatively similar.",1752,0.923,1038,1.6878612716763006,"Deep neural networks many classical machine learning problems especially However researchers neural networks easily fooled surprisingly imperceptible Carefully crafted input images (adversarial examples force provide arbitrary outputs Including adversarial examples during training a popular defense mechanism In this paper a new defensive mechanism under the generative adversarial network~(GAN) framework We model the adversarial noise using a generative network trained jointly as a minimax game We show empirically our adversarial network approach against black box attacks with performance on par stateart methods ensemble adversarial training projected gradient descent Deep neural networks successfully image classification BID12 , human-level playing through deep reinforcement However BID29 showed extremely carefully crafted small perturbations added Since many adversarial examples generating methods proposed Jacobian based saliency map attackJSMA BID23 , projected gradient descent , C&W's attack BID3 In general attack models white box attack Attackers white box attack model have complete knowledge the target network network's architecture parameters Whereas in black box attacks only partial or no information BID25 .Various defensive methods the adversarial examples Adversarial training which augments set with adversarial examples shows good defensive performance terms white box attacks BID13 . Apart adversarial training many other defensive approaches including defensive distillation BID24 , using randomization at inference time BID33 thermometer encoding etcIn Instead using the generative network samples fool as real data train (additive) adversarial noise that into This allows flexible modeling the adversarial noise by the generative network take in the original image even the class label to different types The discriminative networks used our approach just the usual neural networks designed their specific classification tasks The purpose the discriminative network classify both clean and adversarial example with correct label while aims generate powerful perturbations fool This approach simple it directly uses the minimax game concept employed GAN Our main contributions include:• We show our adversarial network approach produce neural networks towards black box attacks In the experiments they show similar, and in better performance compared stateart defense methods ensemble adversarial training BID30 with projected gradient descent . To our best knowledge we also study the joint training a generative attack network network.• study attacking show a variety taking in random noise labels as attacks We also show training against these generative networks provide robustness different attacksThe rest organized In Section, related works including multiple attack and defense methods Section presents our defensive method details Experimental results are shown Section with conclusions of in In the experiments above see adversarial PGD training usually works white box attacks there accuracies on clean data against accuracies due finite model capacity We can try use models larger capacity two . There some recent works indicate training standard accuracy training adversarial accuracy with PGD two fairly different problems . Examples generated PGD particularly difficult train against This makes adversarial PGD training disadvantaged many black box attack situations when compared models weaker adversaries ensemble and our adversarial networks methodWe observed in the experiments for usually constructed models the same method different random seed This suggests hiding the knowledge the training method could defending black box attacks Defending black box attacks closely the question the transferability adversarial examples Although some previous works exploring BID15 , the underlying factors affecting transferabilityIn our experimentation the architectures the discriminative and generative networks the choice of G �� does solution The dynamics training such the step size used iterations to run for each network during gradient descent/ascent seem the saddle point solution quality the network architecture It would interesting find classes generative network architectures lead substantially different saddle points when trained Also recent works that there are connected flat regions the minima neural network loss landscapes BID5 BID4 . We believe same might hold GANs it interesting explore the training dynamics lead different GAN solutions that might different robustness propertiesOur approach can with multiple discriminative networks playing against multiple generative networks It can combined ensemble adversarial training some adversarial examples come static pre-trained models other come dynamically adjusting generative networks We proposed an adversarial network approach learning discriminative neural networks that robust especially under black box attacks For future work we interested extending the experiments ImageNet exploring the choice architectures of and generative networks used this paper G0 and encoder-decoder networks while using a random vector and a one-hot encoding the label respectively The generative networks parameterized a factor k determining filters used (width network As default we k = 64 networks using labels asEXTRA RESULTS ON CIFAR100 AND WIDE RESNET ON CIFAR10The discriminative and generative networks in the same network architecture the output layer dimension the D network 100 other 10 in We use learning rate of the first 100k iterations The batch size 64 and weight decay 1E-5 TAB8 gives the results on CIFAR10 using a wider version ResnetModel D2 by multiplying filters Some the previous works the literature use models larger capacity training adversarially robust models so perform experiments here First the accuracies increase across larger capacity models The accuracy gap on clean data between adversarial PGD standard training still now also our adversarial network approach For the white box and black accuracies the story similar the models weakest against attacks trained the same method a different random seed Our adversarial network approach very good performance across different attacks even as the winner for TAB10 gives the results Wide ResNet on CIFAR100 qualitatively",0.01,0.45668925508448716
"Deep learning has become the state of the art approach in many machine learning problems such as classification. It has recently been shown that deep learning is highly vulnerable to adversarial perturbations. Taking the camera systems of self-driving cars as an example, small adversarial perturbations can cause the system to  make errors in important tasks, such as classifying traffic signs or detecting pedestrians. Hence, in order to use deep learning without safety concerns a proper defense strategy is required. We propose to use ensemble methods as a defense strategy against adversarial perturbations. We find that an attack leading one model to misclassify does not imply the same for other networks performing the same task. This makes ensemble methods an attractive defense strategy against adversarial attacks. We empirically show for the MNIST and the CIFAR-10 data sets that ensemble methods not only improve the accuracy of neural networks on test data but also increase their robustness against adversarial perturbations. In recent years, deep neural networks (DNNs) led to significant improvements in many areas ranging from computer vision BID14 BID17 to speech recognition . Some applications that can be solved with DNNs are sensitive from the security perspective, for example camera systems of self driving cars for detecting traffic signs or pedestrians BID21 BID24 . Recently, it has been shown that DNNs can be highly vulnerable to adversaries BID25 BID5 BID20 . The adversary produces some kind of noise on the input of the system to mislead its output behavior, producing undesirable outcomes or misclassification. Adversarial perturbations are carefully chosen in order to be hard, if not impossible, to be detected by the human eye (see FIG1 ). Attacks occur after the training of the DNN is completed. Furthermore, it has been shown that the exact structure of the DNN does not need to be known in order to mislead the system as one can send inputs to the unknown system in order to record its outputs to train a new DNN that imitates its behavior BID21 . Hence, in this manuscript it is assumed that the DNN and all its parameters are fully known to the adversary.There are many methods on how to attack neural networks appearing in the literature. Some of the most well-known ones are the Fast Gradient Sign Method BID5 and its iterative extension BID15 , DeepFool BID19 , Jacobian-Based Saliency Map Attack BID22 , and the L-BFGS Attack BID25 . This shows the need of building neural networks that are themselves robust against any kind of adversarial perturbations.Novel methods on defending against adversarial attacks are appearing more and more frequently in the literature. Some of those defense methods are to train the network with different kinds of adversarially perturbated training data BID5 BID22 , the use of distillation to reduce the effectiveness of the perturbation BID23 or to apply denoising autoencoders to preprocess the data used by the DNN BID7 . It also has been noted that adversarial attacks can be detected BID18 BID4 , but FIG1 : The first line shows original and correctly classified MNIST test data images. In the second line are the corresponding adversarial BIM attacks on a single classifier ( = 0.2, α = 0.025, n = 8) which predicts (from left to right): 6, 8, 1, 5, 9, 3, 0, 2, 2, and 4. Analogously, the third line corresponds to correctly predicted examples of the CIFAR-10 test data set. In the bottom line are the corresponding adversarial BIM attacks on a single classifier ( = 0.02, α = 0.0025, n = 8) which predicts (from left to right): deer, cat, deer, ship, bird, deer, deer, frog, automobile, and automobile. these detection systems are again vulnerable to adversarial attacks. To our knowledge, there is no method that can reliably defend or detect all kinds of adversarial attacks.In this manuscript, ensemble methods are used to obtain a classification system that is more robust against adversarial perturbations. The term ensemble method refers to constructing a set of classifiers used to classify new data points by the weighted or unweighted average of their predictions. Many ensemble methods have been introduced in the literature such as Bayesian averaging, Bagging BID1 and boosting BID3 . These methods frequently win machine learning competitions, for example the Netflix prize BID12 . Initial results on using ensembles of classifiers in adversarial context can be found in BID0 BID9 . However, to the best of our knowledge this is the first manuscript that empirically evaluates the robustness of ensemble methods to adversarial perturbations.One advantage of using ensemble methods as defense against adversarial perturbations is that they also increase the accuracy on unperturbed test data. This is not the case in general for other defense methods (see TAB4 ). However, in most applications a perturbated input can be considered as exception. Hence, it is desirable to obtain a state of the art result on unperturbed test data while making the model more robust against adversarial attacks. Another advantage is that ensemble methods can easily be combined with other defense mechanisms to improve the robustness against adversarial perturbations further (see TAB4 ). However, the advantages come at a cost of an increase of computational complexity and memory requirements which are proportional to the number of classifiers in the ensemble. This paper is organized as follows: In section 2, some methods for producing adversarial perturbations are briefly introduced. Section 3 describes the defense strategy proposed in this manuscript. In section 4, the previous methods are tested on the MNIST and CIFAR-10 data sets and are compared to other defense strategies appearing in the literature. Finally, in section 5 the conclusions are presented. With the rise of deep learning as the state-of-the-art approach for many classification tasks, researchers noted that neural networks are highly vulnerable to adversarial perturbations. This is particularly problematic when neural networks are used in security sensitive applications such as autonomous driving. Hence, with the development of more efficient attack methods against neural networks it is desirable to obtain neural networks that are themselves robust against adversarial attacks.In this manuscript, it is shown that several ensemble methods such as random initialization or Bagging do not only increase the accuracy on the test data, but also make the classifiers considerably more robust against certain adversarial attacks. We consider ensemble methods as sole defense methods, but more robust classifiers can be obtained by combining ensemble methods with other defense mechanisms such as adversarial training. Although only having tested simple attack scenarios, it can be expected that ensemble methods may improve the robustness against other adversarial attacks.",1356,0.719,758,1.7889182058047493,"Deep learning the state many machine learning problems such classification It recently shown deep learning highly vulnerable Taking the camera systems as small adversarial perturbations make errors important tasks classifying traffic signs detecting Hence in use deep learning without safety concerns a proper defense strategy We propose ensemble methods as a defense strategy We find an attack leading one model does imply for other networks performing This makes ensemble methods an defense adversarial attacks We empirically show for the MNIST and ensemble methods not improve neural networks on test data against In deep neural networks led ranging BID14 BID17 . Some applications can solved DNNs sensitive from for camera systems of self driving for detecting traffic signs pedestrians BID21 BID24 . Recently it shown DNNs highly vulnerable adversaries BID25 BID5 BID20 . The adversary produces some kind noise on to mislead its output behavior producing undesirable outcomes or Adversarial perturbations carefully chosen be hard, if be (see FIG1 Attacks occur after the training the DNN is Furthermore the exact structure the DNN does need mislead as one send inputs the unknown system in record its outputs to train that imitates its behavior BID21 . Hence in this manuscript it assumed the DNN and all its parameters fully known the adversaryThere many methods on attack neural networks appearing Some the Fast Gradient Sign Method BID5 its iterative extension BID15 , DeepFool BID19 Jacobian-Based Saliency Map Attack BID22 the L-BFGS Attack BID25 This shows the need of building neural networks themselves robust againstNovel methods on defending appearing more Some those defense methods to train the network with different kinds adversarially perturbated training data BID5 BID22 , the use distillation reduce the effectiveness or apply preprocess used It also has noted adversarial attacks can detected BID18 BID4 , FIG1 : The first line original and correctly classified MNIST test data images In the second line are the corresponding adversarial BIM attacks a single classifier = α which predicts (from left 6 1 0 and Analogously third line corresponds correctly predicted examples CIFAR-10 test data In the bottom line are the corresponding adversarial BIM attacks a single classifier = 0.02 α predicts (from left deer cat deer ship bird deer frog automobile and automobile these detection systems again vulnerable To our knowledge reliably defend or detect all kinds adversarial attacksIn this manuscript ensemble methods obtain a classification system more The term ensemble method constructing classifiers used new data points their predictions Many ensemble methods introduced such Bayesian averaging Bagging BID1 boosting . These methods frequently win machine learning competitions for Netflix prize BID12 . Initial results on using ensembles classifiers adversarial context can BID0 BID9 . However to this empirically evaluates ensemble methodsOne advantage using as defense also increase on unperturbed test data This not general for other defense methods ( TAB4 However in most applications a perturbated input can considered exception Hence desirable obtain a state the art result on unperturbed test data while making the model more against Another advantage ensemble methods easily other defense mechanisms against further ( TAB4 However the advantages come of an increase computational complexity and memory requirements which proportional classifiers the ensemble This paper organized In section some methods producing adversarial perturbations briefly Section describes the defense strategy proposed this manuscript In section the previous methods tested the MNIST and CIFAR-10 data sets compared other defense strategies appearing Finally in section the conclusions With deep learning as state approach many classification tasks researchers noted highly vulnerable This particularly problematic neural networks security sensitive applications Hence with the development more efficient attack methods against neural networks it desirable obtain neural networks themselves robustIn this manuscript it several ensemble methods such random initialization or Bagging do only increase on the test data make the classifiers considerably We consider ensemble methods as sole defense methods more robust classifiers obtained other defense mechanisms adversarial training Although only having tested simple attack scenarios can expected ensemble methods may improve against",0.01,0.7141734444786227
"In this paper, we propose the Associative Conversation Model that generates visual information from textual information and uses it for generating sentences in order to utilize visual information in a dialogue system without image input. In research on Neural Machine Translation, there are studies that generate translated sentences using both images and sentences, and these studies show that visual information improves translation performance. However, it is not possible to use sentence generation algorithms using images for the dialogue systems since many text-based dialogue systems only accept text input. Our approach generates (associates) visual information from input text and generates response text using context vector  fusing associative visual information and sentence textual information. A comparative experiment between our proposed model and a model without association showed that our proposed model is generating useful sentences by associating visual information related to sentences. Furthermore, analysis experiment of visual association showed that our proposed model generates (associates) visual information effective for sentence generation. As a model that can extract knowledge from conversations, the encoder-decoder model has been proposed BID12 BID14 . It consists of an encoder that encodes the input information into a context vector and a decoder that generates sentences using the context. BID14 showed that it is possible to extract knowledge and to conduct conversation by learning pairs of dialogues with the model. For example, BID14 reported that when asked who is Skywalker, their conversation model (NCM) responded ""he is a hero."" NCM has a problem that it is not possible to respond properly to the input texts that require visual information. For example, BID14 reported that when asked how many legs a spider have, NCM responded ""three, i think."" Further, the image or video may contain more detailed information than texts. Consider, for example, a scene in a news program including a closed caption ""one marathon runner won the marathon competition "" and showing an image with the marathon runner with the gold medal. Here, in the video, more detailed information such as the gold medal that does not exist directly in the text is presented. We thought that if such detailed visual information could be extracted from the image, more specific and useful texts could be generated, including ""gold medals"" which can not be obtained with text alone. In recent years, studies have been reported in which translated sentences are generated by adding image features to the context vector encoded by the encoder-decoder model BID1 BID3 BID7 BID8 BID13 . These studies showed that visual information works effectively for generating translation.Meanwhile, visual information is not considered in many text-based dialogue systems, because what is given to the input is only the utterance text. How can the visual information be used without accepting visual information as the input to the dialogue system? Based on the discussion above, we propose an Associative Conversation Model that associates the input text with the visual information and generates the response using both the text and the asso- Figure 1 : Generating a response by visual association. The textual information is used to estimate the corresponding visual information, and a response text is generated using the vector obtained by fusing the textual and visual information. ciated visual information. In our proposed method, we attempted to generate response texts using visual information without inputting images. The contribution of this research is as follows:• We made it possible to generate visual information related to sentence textual information through end-to-end learning of dialogue.• We made it possible to generate sentences using visual information without directly inputting visual information by association. • Our proposed model can generate response texts including useful information compared with a model without association by associating visual information related to input text. Our method is useful for constructing the text-based dialogue systems that automatically extract information from the text and the video data (e.g., TV news) to generate sentences. In a study applying a sentence generation algorithm of translation sentence to a conversation model, there was a problem that it was not possible to respond well to an input text which requires visual information. However, it is not possible to use sentence generation algorithms using images for the dialogue systems since many text-based dialogue systems only accept text input. Based on the discussion above, we propose an Associative Conversation Model that associates the input text with the visual information and generates the response using both the text and the associated visual infor-mation. Comparative experiments with models that do not use association show that association of visual information related to input texts produces response texts that contain valuable information compared to models without association. Analysis of association also showed that our proposed method can generate visual information related to sentence textual information through end-to-end learning of dialogue. Our method is useful for constructing the text-based dialogue systems that automatically extract information from the text and the video data (e.g., TV news) to generate sentences.",950,0.54,521,1.8234165067178503,"In the Associative Conversation Model generates visual information textual information uses generating sentences order utilize a dialogue system without image input In research Neural Machine Translation there studies generate translated sentences both images visual information improves However possible use sentence generation algorithms using images for the dialogue systems since only accept Our approach generates ( input text generates response text context vector fusing associative visual information and sentence textual information A comparative experiment between our proposed model without association showed generating useful sentences by visual information related sentences Furthermore analysis experiment of visual association showed our proposed model generates ( effective sentence generation As a model that extract knowledge conversations proposed BID12 BID14 . It consists a context vector generates sentences BID14 showed it extract knowledge to conduct conversation learning pairs dialogues the model For example BID14 reported when asked who Skywalker their conversation model (NCM respondedhe a problem respond properly the input texts require visual information For example BID14 reported when asked how many legs a spider have NCM respondedthree i Further the image or may texts Consider, a scene a news program including ""one marathon runner won the marathon competition "" showing with with Here in, more detailed information such the gold medal that does exist directly We thought such detailed visual information more specific and useful texts generated ""gold medals not text In studies reported translated sentences generated adding image features the context vector encoded These studies showed visual information works effectively generating translationMeanwhile considered many text-based dialogue systems what given the input only the utterance text How the visual information without accepting the dialogue system Based the discussion propose an Associative Conversation Model associates the input text generates the response using the asso- Figure : Generating visual association The textual information used estimate the corresponding visual information a response text the vector obtained fusing ciated visual information In our proposed method attempted generate response texts visual information without inputting images The contribution this research as made it generate visual information related sentence textual information through end learning dialogue.• sentences without directly by association • Our proposed model can generate response texts including useful information compared association by associating visual information related input text Our method useful constructing the text-based dialogue systems automatically extract the video data ( sentences In applying a sentence generation of translation sentence a conversation model there it respond well an input text which requires visual information However possible use sentence generation algorithms using images for the dialogue systems since only accept Based the discussion propose an Associative Conversation Model associates the input text generates the response using Comparative experiments models do association show association of visual information related input texts produces response texts contain valuable information compared without Analysis association also our proposed method can generate visual information related sentence textual information through end learning dialogue Our method useful constructing the text-based dialogue systems automatically extract the video data ( sentences",0.01,0.802072084217627
"Feedforward convolutional neural network has achieved a great success in many computer vision tasks. While it validly imitates the hierarchical structure of biological visual system, it still lacks one essential architectural feature: contextual recurrent connections with feedback, which widely exists in biological visual system. In this work, we designed a Contextual Recurrent Convolutional Network with this feature embedded in a standard CNN structure. We found that such feedback connections could enable lower layers to ``rethink"" about their representations given the top-down contextual information. We carefully studied the components of this network, and showed its robustness and superiority over feedforward baselines in such tasks as noise image classification, partially occluded object recognition and fine-grained image classification. We believed this work could be an important step to help bridge the gap between computer vision models and real biological visual system. It has been long established that the primate's ventral visual system has a hierarchical structure BID5 including early (V1, V2), intermediate (V4), and higher (IT) visual areas. Modern deep convolutional neural networks (CNNs) for image recognition BID10 BID18 trained on large image data sets like ImageNet (Russakovsky et al., 2015) imitate this hierarchical structure with multiple layers. There is a hierarchical correspondence between internal feature representations of a deep CNN's different layers and neural representations of different visual areas BID3 BID25 ; lower visual areas (V1, V2) are best explained by a deep CNN's internal representations from lower layers (Cadena et al., 2017; Khaligh-Razavi & Kriegeskorte, 2014) and higher areas (IT, V4) are best explained by its higher layers (Khaligh-Razavi & Kriegeskorte, 2014; BID24 . Deep CNNs explain neuron responses in ventral visual system better than any other model class BID25 BID9 , and this success indicates that deep CNNs share some similarities with the ventral visual system, in terms of architecture and internal feature representations BID25 .However , there is one key structural component that is missing in the standard feedforward deep CNNs: contextual feedback recurrent connections between neurons in different areas BID5 . These connections greatly contribute to the complexity of the visual system, and may be essential for the success of the visual systems in reality; for example, there are evidences that recurrent connections are crucial for object recognition under noise, clutter, and occlusion BID14 BID19 BID15 .In this paper, we explored a variety of model with different recurrent architectures, contextual modules, and information flows to understand the computational advantages of feedback circuits. We are interested in understanding what and how top-down and bottom-up contextual information can be combined to improve in performance in visual tasks. We investigated VGG16 BID18 , a standard CNN that coarsely approximate the ventral visual hierarchical stream, and its recurrent variants for comparison. To introduce feedback recurrent connections, we divided VGG16's layers into stages and selectively added feedback connections from the groups' highest layers to their lowest layers. At the end of each feedback connection, there is a contextual module (Section 3.2) that refines the bottom-up input with gated contextual information. We tested and compared several networks with such contextual modules against VGG16 in several standard image classification task, as well as visual tasks in which refinement under feedback guidance is more likely to produce some beneficial effects, such as object recognition under degraded conditions (noise, clutter and occlusion) and fine-grained recognition. We found that our network could outperform all the baseline feedforward networks and surpassed them by a large margin in finegrained and occlusion tasks. We also studied the internal feature representations of our network to illustrate the effectiveness of the structure. While much future work has to be done , our work can still be an important step to bridge the gap between biological visual systems and state-of-the-art computer vision models. In this paper, we proposed a novel Contextual Recurrent Convolutional Network. Based on the recurrent connections between layers in the hierarchy of a feedforward deep convolutional neural network, the new network can show some robust properties in some computer vision tasks compared with its feedforward baseline. Moreover, the network shares many common properties with biological visual system. We hope this work will not only shed light on the effectiveness of recurrent connections in robust learning and general computer vision tasks, but also give people some inspirations to bridge the gap between computer vision models and real biological visual system.",913,0.443,557,1.6391382405745063,"Feedforward convolutional neural network has achieved many computer vision tasks While validly imitates the hierarchical structure biological visual system still one essential architectural feature contextual recurrent connections with feedback, widely exists In this work designed a Contextual Recurrent Convolutional Network this feature embedded a standard CNN structure We found such feedback connections could enable lower layers ``rethink about their representations given the top-down contextual information We carefully studied the components this network showed its robustness superiority feedforward baselines such tasks noise image classification partially occluded object recognition We believed this work help bridge computer vision models real biological visual system It long the primate's ventral visual system BID5 including early (V1 higherIT Modern deep convolutional neural networks for image recognition BID10 BID18 trained large image data sets like ImageNetRussakovsky imitate this hierarchical structure There a hierarchical correspondence internal feature representations a deep CNN's different layers neural representations different visual areas BID3 BID25 ; lower visual areasV1 best explained from lower layersCadena 2017 Khaligh-Razavi & Kriegeskorte higher areasIT its higher layers BID24 . Deep CNNs explain neuron responses ventral visual system better any other model class BID25 BID9 , and this success indicates share in architecture internal feature representations BID25 .However , one key structural component the standard feedforward deep CNNs contextual feedback recurrent connections different areas BID5 These connections greatly contribute may essential the success reality; there evidences recurrent connections crucial object recognition under noise clutter BID14 BID19 .In explored model with different recurrent architectures contextual modules information flows the computational advantages feedback circuits We interested understanding and combined improve in performance visual tasks We investigated VGG16 BID18 , a standard CNN that coarsely approximate the ventral visual hierarchical stream its recurrent variants for comparison To introduce feedback recurrent connections divided VGG16's layers stages selectively added feedback connections from the groups' highest layers At each feedback connection there a contextual module (Section refines the bottom-up input with gated contextual information We tested and compared several networks such contextual modules against VGG16 in several standard image classification task as visual tasks refinement under feedback guidance more some beneficial effects object recognition under degraded conditionsnoise clutter. We found our network could all the baseline feedforward networks surpassed finegrained and occlusion tasks We also studied the internal feature representations our network illustrate the structure While much future work , our work can still bridge biological visual systems state computer models In this paper proposed a novel Contextual Recurrent Convolutional Network. Based the recurrent connections layers the hierarchy the new network show some robust properties some computer vision tasks compared its feedforward baseline Moreover the network shares many common properties biological visual system We hope this work not shed the effectiveness recurrent connections robust learning general computer vision tasks give people some inspirations bridge computer vision models real biological visual system.",0.01,0.3325472525958217
"Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance. Deep learning has dramatically advanced the state of the art in a number of domains, and now surpasses human-level performance for certain tasks such as recognizing the contents of an image BID10 and playing Go (Silver et al., 2017) . But, despite their unprecedented discriminative power, deep networks are prone to make mistakes. Sometimes, the consequences of mistakes are minor -misidentifying a food dish or a species of flower (Liu et al., 2016) may not be life threatening. But deep networks can already be found in settings where errors carry serious repercussions such as autonomous vehicles BID2 and high frequency trading. In medicine, we can soon expect automated systems to screen for skin cancer BID4 , breast cancer (Shen, 2017) , and to diagnose biopsies BID3 . As autonomous systems based on deep learning are increasingly deployed in settings with the potential to cause physical or economic harm, we need to develop a better understanding of when we can be confident in the estimates produced by deep networks, and when we should be less certain.Standard deep learning techniques used for supervised learning lack methods to account for uncertainty in the model, although sometimes the classification network's output vector is mistakenly understood to represent the model's uncertainty. The lack of a confidence measure can be especially problematic when the network encounters conditions it was not exposed to during training. For example, if a network trained to recognize dog breeds is given an image of a cat, it may predict it to belong to a breed of small dog with high probability. When exposed to data outside of the distribution it was trained on, the network is forced to extrapolate, which can lead to unpredictable behavior. In such cases, if the network can provide information about its uncertainty in addition to its point estimate, disaster may be avoided. This work focuses on estimating such predictive uncertainties in deep networks (Figure 1 ).The Bayesian approach provides a solid theoretical framework for modeling uncertainty BID7 , which has prompted several attempts to extend neural networks (NN) into a Bayesian setting. Most notably, Bayesian neural networks (BNNs) have been studied since the 1990's (Neal, 2012) . Although they are simple to formulate, BNNs require substantially more computational resources than their non-Bayesian counterparts, and inference is difficult. Importantly , BNNs do 2 RELATED WORK Bayesian models provide a natural framework for modeling uncertainty, and several approaches have been developed to adapt NNs to Bayesian reasoning. A common approach is to place a prior distribution (often a Gaussian) over each weight. For infinite weights , the resulting model corresponds to a Gaussian process (Neal, 1995) , and for a finite number of weights it corresponds to a Bayesian neural network (MacKay, 1992) . Although simple to formulate, inference in BNNs is difficult BID5 . Therefore, focus has shifted to techniques to approximate the posterior distribution, leading to approximate BNNs. Methods based on variational inference (VI) typically rely on a fully factorized approximate distribution (Kingma & Welling, 2014; Hinton & Van Camp, 1993) but these methods do not scale easily. To alleviate these difficulties , BID9 proposed a model using sampling methods to estimate a factorized posterior. Another approach, probabilistic backpropagation (PBP), also estimates a factorized posterior based on expectation propagation (Hernández-Lobato & Adams, 2015) .Deep Gaussian Processes (DGPs) formulate GPs as Bayesian models capable of working on large datasets with the aid of a number of strategies to address scaling and complexity requirements BID1 . The authors compare DGP with a number of state-of-the-art approximate BNNs, showing superior performance in terms of RMSE and uncertainty quality 2 . Another recent approach to Bayesian learning , Bayesian hypernetworks, use a neural network to learn a distribution of paramaters over another neural network (Krueger et al., 2017) . Although these recent techniques address some of the difficulties with approximate BNNs, they all require modifications to the architecture or the way networks are trained, as well as specialized knowledge from practitioners.Recently, BID5 showed that a network trained with dropout implicitly performs the VI objective. Therefore any network trained with dropout can be treated as an approx. Bayesian model by making multiple predictions as forward passes through the network while sampling different dropout masks for each prediction. An estimate of the posterior can be obtained by computing the mean and variance of the predictions. This technique, referred to here as MCDO, has been empirically demonstrated to be competitive with other approx. BNN methods and DGPs in terms of RMSE and uncertainty quality (Li & Gal, 2017) . However, as the name implies, MCDO depends on dropout . While once ubiquitous in training deep learning models , dropout has largely been replaced by batch normalization in modern networks, limiting its usefulness. The results presented in TAB2 and Appendix 6.6 indicate that MCBN generates meaningful uncertainty estimates which correlate with actual errors in the model's prediction. We show statistically significant improvements over CUBN in the majority of the datasets, both in terms of CRPS and PLL. The visualizations in FIG0 and in Appendix 6.6 show clear correlations between the estimated model uncertainty and actual errors produced by the network. We perform the same experiments using MCDO, and find that MCBN generally performs on par with MCDO. Looking closer, in terms of CRPS, MCBN performs better than MCDO in more cases than not. However, care must be used when comparing different models. The learned network parameters are different, leading to different predictive means which can confound direct comparison.The results on the Yacht Hydrodynamics dataset seem contradictory. The CRPS score for MCBN is extremely negative, while the PLL score is extremely positive. The opposite trend is observed for MCDO. To add to the puzzle, the visualization in FIG0 depicts an extremely promising uncertainty estimation that models the predictive errors with high fidelity. We hypothesize that this strange behavior is due to the small size of the data set, which only contains 60 test samples, or due to the Gaussian assumption of CRPS. There is also a large variability in the model's accuracy on this dataset, which further confounds the measurements for such limited data.One might criticize the overall quality of the uncertainty estimates of MCBN and MCDO based on the magnitude of the CRPS and PLL scores in TAB2 . The scores rarely exceed 10% improvement over the lower bound. However, we caution that these measures should be taken in context. The upper bound is very difficult to achieve in practice (it is optimized for each test sample individually), and the lower bound is a quite reasonable estimate for uncertainty. We have further compared against the recent work of Louizos & Welling (2017) , and find comparable results to their MNF-based variational technique specifically targeted to increase the flexibility of the approximate posterior.Our approximation of the implied prior in Appendix 6.5 also provides a new interpretation of the empirical evidence that significantly lower λ should be used in batch normalized networks (Ioffe & Szegedy, 2015) . From a VA perspective, too strong a regularization for a given dataset size could be seen as constraining the prior distribution of BN units' means, effectively narrowing the approximate posterior.In this work, we have shown that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. We show evidence that the uncertainty estimates from MCBN correlate with actual errors in the model's prediction, and are useful for practical tasks such as regression or semantic image segmentation. Our experiments show that MCBN yields an improvement over the baseline of optimized constant uncertainty on par with MCDO and MNF. Finally, we make contributions to the evaluation of uncertainty quality by suggesting new evaluation metrics based on useful baselines and upper bounds, and proposing a new visualization tool which gives an intuitive visual explanation of uncertainty quality. Finally, it should be noted that, over the past few years, batch normalization has become an integral part of most-if-not-all cutting edge deep networks which signifies the relevance of our work for estimating model uncertainty.",1889,1.079,1085,1.7410138248847926,"Deep neural networks led dramatically The techniques driving these advances lack a formal method account model uncertainty While the Bayesian approach learning provides handle uncertainty inference in difficult In provide Bayesian learning relies a regularization technique found nearly every modern network batch normalization We show training a deep network batch normalization equivalent approximate inference this finding allows make useful estimates the model uncertainty Using our approach it make meaningful uncertainty estimates conventional architectures without modifying the training procedure Our approach thoroughly validated empirical experiments different tasks using various measures showing it outperform baselines on a majority datasets with Deep learning dramatically the state domains surpasses for recognizing the contents BID10 playing Go (Silver et) . But despite their unprecedented discriminative power deep networks prone make Sometimes the consequences mistakes minor -misidentifying a food dish a species flower (Liu 2016 life But deep networks already settings errors carry serious repercussions such autonomous vehicles BID2 high frequency trading In medicine soon expect automated systems screen skin cancer BID4 , (Shen 2017 and to As autonomous systems based settings cause when be the estimates produced deep networks lessStandard used supervised learning lack methods account uncertainty although sometimes the classification network's output vector mistakenly understood The lack a confidence measure can especially the network encounters conditions it was exposed training For example a network trained recognize dog breeds given predict it belong small dog high probability When exposed data outside the distribution it was trained is forced, unpredictable behavior In such cases if the network can information its uncertainty addition its point estimate disaster may This work focuses estimating such predictive uncertainties deep networksFigure ).The modeling uncertainty BID7 prompted extend neural networksNN into Most notably Bayesian neural networks since the 1990's (Neal 2012 . Although they simple formulate BNNs require inference difficult Importantly , BNNs 2 RELATED WORK Bayesian models provide modeling uncertainty several approaches adapt NNs A common approach place a prior distributionoften a Gaussian each weight For infinite weights , the resulting model corresponds (Neal ,MacKay Although simple formulate inference in BNNs difficult BID5 . Therefore focus has techniques approximate the posterior distribution leading approximate BNNs Methods basedVI typically rely a fully factorized approximate distributionKingma & Welling 2014 Hinton Van Camp 1993 but scale easily To alleviate these difficulties , BID9 proposed using sampling methods a factorized posterior. Another approachPBP also estimates a factorized posterior based expectation propagation & Adams 2015 .Deep Gaussian Processes capable working the aid strategies address scaling and complexity requirements BID1 . The authors compare DGP state approximate BNNs showing superior performance terms RMSE uncertainty quality 2 Another recent approach Bayesian learning , Bayesian hypernetworks use a distribution paramaters another neural networkKrueger 2017 Although these recent techniques address approximate BNNs all modifications or networks trained specialized knowledge from practitionersRecently BID5 showed trained dropout implicitly performs the VI objective Therefore any network trained with dropout can treated an approx Bayesian model by making multiple predictions as forward passes while sampling different dropout masks An estimate the posterior can computing This technique, referred here MCDO empirically competitive other approx. BNN methods DGPs terms RMSE uncertainty quality (Li Gal, 2017 . However as the name MCDO depends dropout . While once ubiquitous training deep learning models , dropout has largely batch normalization modern networks limiting The results presented TAB2 and Appendix 6.6 indicate MCBN generates meaningful uncertainty estimates which correlate actual errors We show statistically significant improvements over CUBN the majority the datasets both CRPS PLL The visualizations FIG0 and in Appendix 6.6 clear correlations the estimated model uncertainty actual errors produced the network We perform MCDO find MCBN generally on par Looking closer in terms CRPS MCBN performs MCDO more cases not However care used comparing different models The learned network parameters different leading different predictive means which confound direct comparisonThe results on the Yacht Hydrodynamics dataset seem contradictory The CRPS score MCBN extremely negative while The opposite trend observed MCDO To add the puzzle the visualization in FIG0 an extremely promising uncertainty estimation that models the predictive errors with high fidelity We hypothesize this strange behavior only 60 test samples or the Gaussian assumption CRPS There also a large variability the model's accuracy on this dataset further the measurements for such limited dataOne might criticize of MCBN MCDO based the CRPS and PLL scores TAB2 . The scores rarely exceed 10% improvement lower However we caution these measures context. The upper bound very difficult (it optimized each test sample individually a quite reasonable estimate uncertainty We further compared against the recent work Louizos & Welling2017 , find comparable results their MNF-based variational technique specifically targeted increase the flexibility the approximate posterior.Our approximation implied prior Appendix also significantly lower �� should batch normalized networksIoffe Szegedy From a VA perspective too strong regularization for a given dataset size seen constraining the prior distribution BN units' means effectively narrowing the approximate posterior.In training a deep network batch normalization equivalent approximate inference Using our approach it make meaningful uncertainty estimates conventional architectures without modifying the training procedure We show evidence the uncertainty estimates MCBN correlate actual errors useful practical tasks regression or semantic image segmentation Our experiments MCBN yields an improvement optimized constant uncertainty on par MCDO MNF Finally make contributions the evaluation uncertainty quality suggesting new evaluation metrics based useful baselines upper bounds proposing a new visualization tool which gives Finally should, over batch normalization most-if- cutting deep networks which signifies the relevance our work estimating model uncertainty",0.01,0.5921172907274612
"Data-parallel neural network training is network-intensive, so gradient dropping was designed to exchange only large gradients.   However, gradient dropping has been shown to slow convergence.   We propose to improve convergence by having each node combine its locally computed gradient with the sparse global gradient exchanged over the network. We empirically confirm with machine translation tasks that gradient dropping with local gradients approaches convergence 48% faster than non-compressed multi-node training and 28% faster compared to vanilla gradient dropping. We also show that gradient dropping with a local gradient update does not reduce the model's final quality. Training a neural network can be slow, especially with a large model or dataset BID12 BID18 . Distributed training is becoming essential to speed up the process. In data-parallel training, multiple workers optimize the same parameters based on different parts of the training data then exchange parameters.Data-parallel training is network intensive because workers send and fetch gradients that have the same size as the model. Several techniques have been proposed to reduce the traffic in dataparallelism training by using quantization to compress the gradient sent BID13 BID1 or selecting sparse matrices BID17 BID5 BID0 BID10 .Gradient dropping, and its extension Deep Gradient Compression BID10 , is a recent approach that compresses the network by sending a small fraction (about 1%) of the largest gradients (by absolute value). This technique is based on the observation that the gradient values are skewed, as most are close to zero. An issue with gradient compression is that gradients are compressed so much that it slows the model's convergence rate and can reduce the model's final quality BID0 .In vanilla gradient dropping, all nodes update with the same sparse gradient exchanged over the network, while other parameters are unchanged. However, each node has computed a local gradient on its own data. Can we exploit this dense local gradient alongside the sparse global gradient to improve convergence? We propose and evaluate three ways to combine them. We significantly reduce convergence damage caused by compressing the gradient through gradient dropping in data-parallelism training. We utilize a locally-computed gradient to predict and reconstruct the dense gradient. Our experiments show that we can improve the training time up to 45% faster compared to a non-compressed multi-node system and 3x faster compared to a single-node system. Local gradient update is also empirically shown to negate the quality loss caused by gradient dropping.",481,0.308,277,1.736462093862816,"Data-parallel neural network training network-intensive, so gradient dropping was designed exchange only large gradients However gradient dropping slow convergence We propose improve convergence having combine its locally computed gradient the sparse global gradient exchanged We empirically confirm with machine translation tasks gradient dropping with approaches convergence 48% non-compressed multi-node training and 28 compared vanilla gradient dropping We also show gradient dropping with a local gradient update the model's final quality Training a neural network slow a large model dataset BID12 BID18 . Distributed training becoming essential speed In data-parallel training multiple workers optimize the same parameters based different parts then exchange parameters network intensive workers send fetch gradients have Several techniques the traffic dataparallelism training quantization compress the gradient sent BID13 BID1 or selecting sparse .Gradient dropping its extension Deep Gradient Compression BID10 by sending ( the largest gradientsby absolute value This technique the gradient values skewed most are close An issue gradient compression slows the model's convergence rate reduce BID0 .In vanilla gradient dropping all nodes update exchanged other parameters unchanged However each node computed a local gradient Can exploit this dense local gradient alongside convergence We propose and evaluate three ways combine them We significantly convergence damage compressing the gradient through gradient dropping data-parallelism training We utilize a locally-computed gradient predict and reconstruct the dense gradient Our experiments we improve the training time up 45 compared Local gradient update also empirically shown negate the quality loss gradient dropping",0.0,0.5805198799941795
"We establish the relation between Distributional RL and the Upper Confidence Bound (UCB) approach to exploration.
     In this paper we show that the density of the Q function estimated by Distributional RL can be successfully used for the estimation of UCB. This approach does not require counting and, therefore, generalizes well to the Deep RL. We also point to the asymmetry of the empirical densities estimated by the Distributional RL algorithms like QR-DQN. This observation leads to the reexamination of the variance's performance in the UCB type approach to exploration. We introduce truncated variance as an alternative estimator of the UCB and a novel algorithm based on it. We empirically show that newly introduced algorithm achieves better performance in multi-armed bandits setting. Finally, we extend this approach to high-dimensional setting and test it on the Atari 2600 games. New approach achieves better performance compared to QR-DQN in 26 of games, 13 ties out of 49 games. Exploration is a long standing problem in Reinforcement Learning (RL). It's been the main focus of the multi-armed bandits literature. Here the algorithms are easier to design and analyze. However, these solutions are quite unfeasible for high dimensional Deep RL setting, where the complication comes from the presence of the function approximator.The multi-armed bandit can be represented by a slot machine with several arms. Each arms' expected reward is unknown to the gambler. Her/his goal is to maximize cumulative reward by pulling bandit's arms. If the true expected rewards are known, then the best strategy is to pull the arm with the highest value. However, gambler only observes stochastic reward after the arm is pulled. One possible solution described by BID18 is to initialize values of arms' estimated means optimistically and then improve the estimates by pulling the same arm again. Arm with a lower true mean will get its estimate decreased over time. Eventually, the best arm will be discovered. The drawback is that the set of the arms has to be enumerated and every arm has to be pulled infinitely many times. In the RL setting an arm corresponds to a state-action pair, which implies that both assumptions are too strong for the Deep RL.Another line of reasoning is Upper Confidence Bound (UCB) type algorithms, e.g. UCB-1, introduce by BID10 . The essence of the approach is nicely summarized by BID0 : 'optimism in the face of uncertainty principle'. The idea is statistically intuitive: pull the arm which has the highest upper confidence bound, hoping for a better mean. Estimation of the arm's UCB is performed via Hoeffdings Inequality 1 which is entirely based on counting the number of times the arm was pulled. UCB extends to the tree search case in the form of UCT developed by BID10 . Although this idea was successfully applied to the problem when perfect model is accessible, i.e. AlphaGo by BID17 , it does not generalize in a straightforward fashion to the general Deep RL setting without perfect model. The main obstacle is the requirement of counting of the state-action pairs. Another popular variation is UCB-V introduced by BID0 . It estimates UCB via the empirical variance, which again involves counting. Therefore, the requirement of counting prevents UCB ideas from successful generalization to the high dimensional setting of Deep RL.The generalization of exploration ideas from multi-armed bandits to Deep RL is challenging. Therefore, one the most popular exploration approaches in Deep RL is the annealed epsilon greedy approach popularized by BID13 . However, epsilon greedy approach is not very efficient, especially in Deep RL. It does not take into account the underlying structure of the environment. Therefore, researchers have been looking for other more efficient ways of exploration in Deep RL setting. For example the idea of parametric noise was explored by BID4 . Posterior sampling for reinforcement learning BID15 ) in Deep RL setting was developed by BID16 . Uncertainty Bellman Equation proposed by BID14 , generalizes Bellman equation to the uncertainty measure. The closest UCB type approach was developed by BID2 . In order to avoid counting authors estimate UCB based on the empirical distribution of the Q function produced by Bootstrapped DQN BID16 ). The approach reduces to estimating an ensemble of randomly initialized Q functions. According to the averaged human normalized learning curve the performance improvement was insignificant. Currently, there is a much better approach to estimating empirical distributions of Q function, i.e. distributional RL , ). The results in the distributional RL are both theoretically sound and achieve state of the art performance in Deep RL environments, like Atari 2600. However, we should note that Distributional RL does not use the whole distribution, but only the mean.Another important characteristic of Distributional RL is that both C51 ) and Quantile Regression DQN (QR-DQN) ) are non parametric in the sense that the estimated distribution is not assumed to belong to any specific parametric family. Hence, it is not assumed to be symmetric or even unimodal 2 . We argue that in the case of asymmetric distributions, variance might become less sensitive in estimating UCB. This problem seems to be overseen by the existing literature. However, this issue might become more important in a more general setting, when symmetric assumption is not simply relaxed but is a very rare case. We empirically show in the Section 4 that symmetry is in fact rare in Distributional RL.In this paper we build upon generic UCB idea. We generalize it to the asymmetric distributions and high-dimensional setting. In order to extend UCB approach to asymmetric distributions, we introduce truncated variability measure and show empirically that it achieves higher performance than variance in bandits setting. Extension of this measure to rich visual environments provided by Atari 2600 platform is based on recent advances in Distributional RL. Recent advancements in RL, namely Distributional RL, not only established new theoretically sound principles but also achieved state-of-the-art performance in challenging high dimensional environments like Atari 2600. The by-product of the Distributional RL is the empirical PDF for the Q function which is not directly used except for the mean computation. UCB on the other hand is a very attractive exploration algorithm in the multi-armed bandits setting, which does not generalize in a straightforward fashion to Deep RL.In this paper we established the connection between the UCB idea and Distributional RL. We also pointed to the asymmetry of the PDFs estimated by Distributional RL, which is not a rare exception but rather the only case. We introduced truncated variability measure as an alternative to the variance and empirically showed that it can be successfully applied to multi-armed bandits and rich visual environments like Atari 2600. It is highly likely that DQN-QUCB+ might be improved through schedule tuning. DQN-QUCB+ might be combined with other advancements in Deep RL, e.g. Rainbow by BID6 , to yield better results.",1406,0.984,845,1.663905325443787,"We establish Distributional RL the Upper Confidence Bound (UCB) approach exploration In the density the Q function estimated Distributional RL successfully UCB This approach does counting, generalizes well the Deep RL We also point the empirical densities estimated the Distributional RL algorithms like QR-DQN This observation leads the variance's performance the UCB type approach exploration We introduce truncated variance as the UCB and a novel algorithm We empirically newly introduced algorithm achieves multi-armed bandits setting Finally extend this approach high-dimensional setting test New approach achieves compared QR-DQN in 26 of games 13 ties Exploration a long standing problem Reinforcement Learning It the main focus the multi-armed bandits literature Here the algorithms easier design analyze However these solutions quite high dimensional Deep RL setting the complication the function approximatorThe multi-armed bandit represented a slot machine several arms Each arms' expected reward unknown to Her/his goal maximize cumulative reward pulling bandit's arms If the true expected rewards known pull the arm with However gambler only observes stochastic reward after the arm pulled One possible solution described BID18 initialize values arms' estimated means optimistically improve pulling again Arm with a lower true mean will its estimate decreased over Eventually the best arm will discovered The drawback the set the arms enumerated every arm pulled infinitely many In the RL setting an arm corresponds a state-action pair implies both assumptions too the Deep RL.Another line Upper Confidence Bound (UCB) type algorithms introduce by BID10 . The essence the approach nicely BID0 : 'optimism uncertainty principle The idea statistically intuitive pull the arm which the highest upper confidence hoping Estimation the arm's UCB is performed via Hoeffdings Inequality 1 which entirely counting times pulled UCB extends to the tree search case the form UCT developed BID10 . Although this idea successfully when perfect model accessible AlphaGo by BID17 , generalize general Deep RL setting without perfect model The main obstacle counting of the state-action pairs Another popular variation UCB-V introduced BID0 . It estimates UCB via the empirical variance again involves counting. Therefore the requirement counting prevents UCB ideas successful generalization the high dimensional setting Deep RL.The generalization exploration ideas multi-armed bandits challenging Therefore one the most popular exploration approaches Deep RL the annealed epsilon greedy approach popularized BID13 . However epsilon greedy approach very Deep RL It does into the underlying structure Therefore researchers exploration Deep RL setting For example the idea parametric noise explored BID4 . Posterior sampling for reinforcement BID15 ) in Deep RL setting was developed Uncertainty Bellman Equation proposed BID14 , generalizes the uncertainty measure The closest UCB type approach developed BID2 . In counting authors estimate UCB based the empirical distribution the Q function produced Bootstrapped DQN BID16 The approach reduces to estimating an ensemble randomly initialized Q functions According the averaged human normalized learning the performance improvement insignificant Currently estimating empirical distributions Q function , ). The results in the distributional RL are both theoretically achieve state Deep RL environments like Atari However we should Distributional RL the whole distribution meanAnother important characteristic both C51 ) Quantile Regression DQN ) non parametric assumed belong Hence assumed symmetric 2 . We argue in asymmetric distributions variance might become estimating UCB This problem seems overseen the existing literature However this issue might become symmetric assumption simply relaxed a very rare case We empirically in the Section that symmetry in rare Distributional RL.In build generic UCB idea We generalize it the asymmetric distributions high-dimensional setting In extend UCB approach asymmetric distributions introduce truncated variability measure show achieves higher performance variance bandits setting Extension this measure rich visual environments provided Atari 2600 platform based recent advances Distributional RL Recent advancements RL, namely Distributional RL not established new theoretically sound principles achieved state challenging high dimensional environments Atari the Distributional RL the empirical PDF for the Q function not except the mean computation UCB on a very attractive exploration algorithm multiarmed bandits setting does generalize Deep RL.In established Distributional RL We also pointed the PDFs estimated Distributional RL a rare exception but We introduced truncated variability measure as and empirically successfully multi-armed bandits rich visual environments like Atari It highly DQN-QUCB+ might improved through schedule tuning DQN-QUCB+ might combined other advancements Deep RL Rainbow by BID6 , yield",0.01,0.39565160883046496
"Good representations facilitate transfer learning and few-shot learning. Motivated by theories of language and communication that explain why communities with large number of speakers have, on average, simpler languages with more regularity, we cast the representation learning problem in terms of learning to communicate. Our starting  point sees traditional autoencoders as  a single encoder with a fixed decoder partner that must learn to communicate. Generalizing from there, we introduce community-based autoencoders in which multiple encoders and decoders collectively learn representations by being randomly paired up on successive training iterations. Our experiments show that increasing community sizes reduce idiosyncrasies in the learned codes, resulting in more invariant representations with increased reusability and structure. The importance of representation learning lies in two dimensions. First and foremost, representation learning is a crucial building block of a neural model being trained to perform well on a particular task, i.e., representation learning that induces the ""right"" manifold structure can lead to models that generalize better, and even extrapolate. Another property of representation learning, and arguably the most important one, is that it can facilitate transfer of knowledge across different tasks , essential for transfer learning and few-shot learning among others BID0 . With this second point in mind, we can define good representations as the ones that are reusable, induce the abstractions that capture the ""right"" type of invariances and can allow for generalizing very quickly to a new task. Significant efforts have been made to learn representations with these properties; one frequently explored direction involves trying to learn disentangled representations BID12 BID6 BID5 BID17 ), while others focus on general regularization methods BID15 BID18 . In this work, we take a different approach to representation learning, inspired by successful abstraction mechanisms found in nature, to wit human language and communication.Human languages and their properties are greatly affected by the size of their linguistic community BID11 BID19 BID16 BID9 . Small linguistic communities of speakers tend to develop more structurally complex languages, while larger communities give rise to simpler languages (Dryer & Haspelmath, 2013) . Moreover, we even observe structural simplification as the effective number of speakers grows, as in the example of English language BID10 . A similar relation between number of speakers and linguistic complexity can also be observed during linguistic communication. Speakers, aiming at maximizing communication effectiveness, adapt and shape their conceptualizations to account for the needs of their specific partners, a phenomenon often termed in dialogue research as partner specificity BID2 ). As such, speakers form conceptual pacts with their listeners BID1 , and in some extreme cases, these pacts are so ad-hoc and idiosyncratic that overhearers cannot follow the discussion BID13 )! But how are all these linguistic situations related to representation learning? We start by drawing an analogy between language and representations induced by the traditional and extensively used framework of autonencoders (AE). In the traditional AE set-up, there is a fixed pair of a single encoder and a single decoder that are trained to maximize a reconstruction loss. However, encoders and decoders co-adapt to one another, yielding idiosyncratic representations. The encoders spend repre-sentational capacity modeling any kind of information about the data that could allow the decoder to successfully reconstruct the input; as long as the encoder and the decoder agree on a representation protocol, this information need not be abstract or systematic. This has a negative impact on the reusability of the representations, something that afterall is a key objective of representation learning. Evidence of this co-adaption is found in the above-mentioned efforts targeting generalization. The human language analogy of the traditional AE setup would be an extreme version of the conceptual pact experiments from BID13 , where two people never communicate with anybody else: the resulting language would be very hard to understand for any outsider.In this work we test whether removing this co-adaptation between encoders and decoders can yield better generalization, much as dropout removes co-adaptation between activations and thereby yields better generalization in general neural networks. We hypothesize that machines that communicate not with a specific partner but with a multitude of partners, will shape the representations they communicate to be simpler in nature. We introduce a simple framework that we term communitybased autoencoders (CbAEs), in which there exist multiple encoders and decoders, and at every training iteration one of each is randomly sampled to perform a traditional autoencoder (AE) training step. Given that the identity of the decoder is not revealed to the encoder during the encoding of the input, the induced representation should be such that all decoders can use it to successfully reconstruct the input. A similar argument holds for the decoder, which at reconstruction time does not have access to the identity of the encoder. We conjecture that this process will reduce the level of idiosyncrasy, resulting in representations that are invariant to the diverse encoders and decoders.We apply CbAEs to two standard computer vision datasets and probe their representations along two axes; their reusability and their structural properties. We find that in contrast to representations induced within a traditional AE framework 1) the CbAE-induced representations encode abstract information that is more easily extracted and re-used for a different task 2) CbAE representations provide an interface that is easier to learn for new users 3) and the underlying topology of the CbAE representations is more aligned to human perceptual data that are disentangled and structured. We have presented Community-based AutoEncoders, a framework in which multiple encoders and decoders collectively learn representations by being randomly paired up on successive training iterations, encouraging a similar lack of co-adaptation that dropout does at the activation level, at model level. Analogous to the structural simplicity found in languages with many speakers, we find that the latent representations induced in this scheme are easier to use and more structured. This result is philosophically interesting in that it suggests that the community size effects found in human languages are general properties of any representation learning system, opening avenues to potential synergies between representation learning linguistics.The price for obtaining these representations is the increase in computational requirements, which is linear in the community size. Due to the reusability of the resulting representations, this cost may be amortized over a number of applications trained on top of the encoders. Furthermore, the community-based training procedure is highly parallelizable, since only the latents and corresponding backpropagated errors need to be sent between the encoders and decoders.",1316,0.671,770,1.709090909090909,"Good representations facilitate transfer learning few-shot learning Motivated theories language communication explain communities with large number, simpler cast the representation learning problem learning to Our starting point sees traditional autoencoders a single encoder a fixed decoder partner must learn communicate Generalizing there introduce community-based autoencoders which collectively learn representations by being randomly paired successive training iterations Our experiments increasing community sizes reduce idiosyncrasies the learned codes resulting more invariant representations with increased reusability structure The importance representation learning lies two dimensions First and representation learning a neural model being that induces the ""right"" manifold structure can models generalize even extrapolate. Another property representation learning facilitate transfer different tasks , essential transfer learning few-shot learning among others BID0 . With this second point define good representations the ones reusable induce the abstractions capture invariances can allow generalizing very a new task Significant efforts learn representations with these properties; one frequently explored direction involves trying BID12 BID6 BID5 BID17 ), while general regularization methods . In this work take representation learning inspired successful abstraction mechanisms found nature wit human language communicationHuman languages their properties greatly the size their linguistic community BID11 BID19 BID16 BID9 . Small linguistic communities speakers tend develop give (Dryer Haspelmath 2013) . Moreover we even observe structural simplification as the effective number speakers in English language BID10 . A similar relation number speakers linguistic complexity during linguistic communication Speakers, aiming maximizing communication effectiveness adapt shape their conceptualizations account their specific partners a phenomenon often in dialogue research partner specificity BID2 As such speakers form conceptual pacts BID1 , in some extreme cases so ad overhearers follow the discussion BID13 )! But how all these linguistic situations representation learning We start drawing language representations induced the traditional and extensively used framework autonencodersAE In the traditional AE set-up a fixed pair a single encoder trained maximize a reconstruction loss However encoders coadapt one yielding idiosyncratic representations The encoders spend repre-sentational capacity modeling any kind information allow successfully reconstruct; as and agree a representation protocol need abstract systematic This has a negative impact the representations something afterall a key objective representation learning Evidence this coadaption the above-mentioned efforts targeting generalization The human language analogy the traditional AE setup would an extreme version the conceptual pact experiments from BID13 , never anybody: the resulting language very hard for any outsiderIn test removing this coadaptation encoders yield much dropout removes co activations thereby yields We hypothesize machines communicate not a specific partner shape the representations they communicate be simpler in nature We introduce we term communitybased autoencodersCbAEs there exist at every training iteration each randomly sampled perform (AE) training step Given the identity the decoder revealed during the induced representation should such use successfully reconstruct A similar argument holds the decoder at reconstruction time does access the identity We conjecture this process reduce idiosyncrasy resulting representations the diverse encodersWe apply CbAEs two standard computer vision datasets probe their representations along; their reusability structural We find in contrast representations induced within a traditional AE framework 1) the CbAE-induced representations encode abstract information more extracted reused for a different task provide an interface easier for the underlying topology aligned human perceptual data that disentangled and structured We presented Community-based AutoEncoders in collectively learn representations by being randomly paired up successive training iterations encouraging a similar lack co that dropout does at the activation level at model level Analogous the structural simplicity found languages many speakers we the latent representations induced this scheme easier use structured This result philosophically interesting in the community size effects found human languages general properties any representation learning system opening avenues potential synergies representation learning linguisticsThe price obtaining these representations the increase computational requirements linear Due the reusability the resulting representations this cost applications trained top Furthermore the community-based training procedure highly parallelizable since only the latents corresponding backpropagated errors need sent between",0.01,0.5107805060013604
"Humans are experts at high-fidelity imitation -- closely mimicking a demonstration, often in one attempt. Humans use this ability to quickly solve a  task instance, and to bootstrap learning of new tasks. Achieving these abilities in autonomous agents is an open problem. In this paper, we introduce an off-policy RL algorithm (MetaMimic) to narrow this gap. MetaMimic can learn both (i) policies for high-fidelity one-shot imitation of diverse novel skills, and (ii) policies that enable the agent to solve tasks more efficiently than the demonstrators. MetaMimic relies on the principle of storing all experiences in a memory and replaying these to learn massive deep neural network policies by off-policy RL. This paper introduces, to the best of our knowledge, the largest existing neural networks for deep RL and shows that larger networks with normalization are needed to achieve one-shot high-fidelity imitation on a challenging manipulation task.
 The results also show that both types of policy can be learned from vision, in spite of the task rewards being sparse, and without access to demonstrator actions. One-shot imitation is a powerful way to show agents how to solve a task. For instance, one or a few demonstrations are typically enough to teach people how to solve a new manufacturing task. In this paper, we introduce an AI agent that when provided with a novel demonstration is able to (i) mimic the demonstration with high-fidelity, or (ii) forego high-fidelity imitation to solve the intended task more efficiently. Both types of imitation can be useful in different domains.Motor control is a notoriously difficult problem, and we are often deceived by how simple a manipulation task might appear to be. Tying shoe-laces, a behaviour many of us learn by imitation, might appear to be simple. Yet, tying shoe-laces is something most 6 year olds struggle with, long after object recognition, walking, speech, often translation, and sometimes even reading comprehension. This long process of learning that eventually results in our ability to rapidly imitate many behaviours provides inspiration for the work in this paper.We refer to high-fidelity imitation as the act of closely mimicking a demonstration trajectory, even when some actions may be accidental or irrelevant to the task. This is sometimes called over-imitation BID28 . It is known that humans over-imitate more than other primates BID18 and that this may be useful for rapidly acquiring new skills BID24 . For AI agents however, learning to closely imitate even one single demonstration from raw sensory input can be difficult. Many recent works focus on using expensive reinforcement learning (RL) methods to solve this problem BID46 BID27 BID37 BID3 . In contrast, high-fidelity imitation in humans is often cheap: in one-shot we can closely mimic a demonstration. Inspired by this, we introduce a meta-learning approach (MetaMimic - FIG0 ) to learn high-fidelity one-shot imitation policies by off-policy RL. These policies, when deployed, require a single demonstration as input in order to mimic the new skill being demonstrated.AI agents could acquire a large and diverse set of skills by high-fidelity imitation with RL. However, representing many behaviours requires the adoption of a model with very high capacity, such as a very large deep neural network. Unfortunately, showing that RL methods can be used to train massive deep neural networks has been an open question because of the variance inherent to these methods. Indeed, traditional deep RL neural networks tend to be small, to the point that researchers have recently questioned their contribution BID42 . In this paper, we show that it is possible to train massive high-fidelity imitation policy π(ot,gt) with off-policy RL. This policy, represented with a massive deep neural network, enables the robot arm to mimic any demonstration in one-shot. In addition to producing an imitation policy that generalizes well, MetaMimic populates its replay memory with all its rich experiences, including not only the demonstration videos, but also its past observations, actions and rewards. By harnessing these augmented experiences, a task policy π(ot) can be trained to solve difficult sparse-reward control tasks.deep networks by off-policy RL to represent many behaviours. Moreover, we show that bigger networks generalize better. These results therefore provide important evidence that RL is indeed a scalable and viable framework for the design of AI agents. Specifically this paper makes the following contributions 1 :• It introduces the MetaMimic algorithm and shows that it is capable of one-shot high-fidelity imitation from video in a complex manipulation domain.• It shows that MetaMimic can harness video demonstrations and enrich them with actions and rewards so as to learn uncoditional policies capable of solving manipulation tasks more efficiently than teleoperating humans. By retaining and taking advantage of all its experiences, MetaMimic also substantially outperforms the state-of-the-art D4PG RL agent, when D4PG uses only the current task experiences.• The experiments provide ablations showing that larger networks (to the best of our knowledge, the largest networks ever used in deep RL) lead to improved generalization in high-fidelity imitation. The ablations also highlight the important value of instance normalization.• The experiments show that increasing the number of demonstrations during training leads to better generalization on one-shot high-fidelity imitation tasks. In this paper, we introduced MetaMimic, a method to 1) train a high-fidelity one-shot imitation policy, and to 2) efficiently train a task policy. MetaMimic employs the largest neural network trained via RL, and works from vision, without the need of expert actions. The one-shot imitation policy can generalize to unseen trajectories and can mimic them closely. Bootstrapping on imitation experiences, the task policy can quickly outperform the demonstrator, and is competitive with methods that receive privileged information.The framework presented in this paper can be extended in a number of ways. First, it would be exciting to combine this work with existing methods for learning third-person imitation rewards BID45 BID3 . This would bring us a step closer to how humans imitate: By watching other agents act in the environment. Second, it would be exciting to extend MetaMimic to imitate demonstrations of a variety of tasks. This may allow it to generalize to demonstrations of unseen tasks.To improve the ease of application of MetaMimic to robotic tasks, it would be desirable to address the question of how to relax the initialization constraints for high-fidelity imitation; specifically not having to set the initial agent observation to be close to the initial demonstration observation.",1329,0.766,765,1.7372549019607844,"Humans experts high-fidelity imitation -- closely a demonstration often one attempt Humans use quickly solve a task instance bootstrap learning of these abilities autonomous agents an open problem In an off-policy RL algorithm (MetaMimic narrow MetaMimic can learn both (i) policies high-fidelity one-shot imitation diverse novel skills the agent solve tasks the demonstrators MetaMimic relies storing all experiences these learn massive deep neural network policies by off-policy RL This paper introduces, the largest existing neural networks deep RL shows larger networks normalization needed one-shot high-fidelity imitation on a challenging manipulation task The results also both types policy learned vision in spite the task rewards sparse without access demonstrator actions One-shot imitation agents solve For instance one or a few demonstrations typically enough teach solve a new manufacturing task In an AI agent when provided a novel demonstration is mimic solve more Both types imitation can useful different domainsMotor control deceived how a manipulation task Tying shoe-laces a behaviour many learn imitation might appear simple Yet tying shoe-laces something most 6 year olds struggle long object recognition, walking speech often translation sometimes comprehension This long process learning that eventually results our ability rapidly imitate many behaviours provides inspiration inWe refer closely a demonstration trajectory even some actions accidental irrelevant This sometimes over BID28 . It known humans overimitate more BID18 useful rapidly acquiring For AI agents however learning closely imitate even one single demonstration from raw sensory input Many recent works focus using expensive reinforcement learning BID46 BID27 BID37 BID3 . In contrast high-fidelity imitation in humans cheap: in one-shot we closely a demonstration. Inspired introduce a meta-learning approach (MetaMimic - FIG0 ) high-fidelity one-shot imitation policies off-policy RL These policies when deployed require a single demonstration as input mimic the new skill being demonstratedAI agents could acquire with RL However representing many behaviours requires the adoption with very high capacity Unfortunately showing RL methods train because the variance inherent Indeed traditional deep RL neural networks tend small to researchers recently questioned their contribution BID42 . In it train massive high-fidelity imitation policy ��otgt off-policy RL This policy, represented with a massive deep neural network enables the robot arm mimic any demonstration one-shot In producing an imitation policy generalizes well MetaMimic populates its replay memory all its rich experiences not only the demonstration videos its past observations actions rewards By harnessing these augmented experiences a task policy ��(ot trained solve difficult sparse-reward control tasks.deep networks by off-policy RL to represent many behaviours Moreover show bigger networks generalize These results therefore RL indeed a scalable and viable framework AI agents Specifically this paper makes 1 :• It introduces from video in a complex manipulation harness video demonstrations enrich actions rewards so learn uncoditional policies capable solving manipulation tasks more teleoperating humans By retaining and taking all its experiences MetaMimic also substantially state D4PG RL agent when only the current task experiences.• The experiments provide ablations showing larger networks (to best ever deep RL lead The ablations also highlight the important value instance normalization.• The experiments increasing demonstrations during training leads on one-shot high-fidelity imitation tasks In introduced MetaMimic 1 train a high-fidelity one-shot imitation policy to efficiently a task policy MetaMimic employs trained via RL works from vision without expert actions The one-shot imitation policy can generalize unseen trajectories mimic them closely Bootstrapping imitation experiences the task policy quickly outperform the demonstrator competitive methods receive privileged informationThe framework presented First exciting combine this work existing methods learning third-person imitation rewards BID45 BID3 . This would bring step how humans imitate: By watching other agents act the environment Second exciting extend MetaMimic imitate demonstrations a variety tasks This may allow it generalize demonstrations unseen tasksTo improve application MetaMimic robotic tasks address relax the initialization constraints; specifically not having set the initial agent observation close the initial demonstration observation",0.01,0.5825398853724453
"Normalization methods are a central building block in the deep learning toolbox. They accelerate and stabilize training, while decreasing the dependence on manually tuned learning rate schedules. When learning from multi-modal distributions, the effectiveness of batch normalization (BN), arguably the most prominent normalization method, is reduced. As a remedy, we propose a more flexible approach: by extending the normalization to more than a single mean and variance, we detect modes of data on-the-fly, jointly normalizing samples that share common features. We demonstrate that our method outperforms BN and other widely used normalization techniques in several experiments, including single and multi-task datasets. A challenge in optimizing deep learning models is the change in input distributions at each layer, complicating the training process. Normalization methods, such as batch normalization (BN, BID15 aim to overcome this issue -often referred to as internal covariate shift BID38 . 1 When applied successfully in practice, BN enables the training of very deep networks, shortens training times by supporting larger learning rates, and reduces sensitivity to parameter initializations. As a result, BN has become an integral element of many state-of-the-art machine learning techniques BID12 BID39 .It can be difficult to standardize the activations in a neural network exposed to heterogeneous or multi-modal data. When training a deep neural network on images that come from a diverse set of visual domains, each with significantly different statistics, BN is not effective at normalizing the activations with a single mean and variance . In this paper we relax the assumption that the entire mini-batch should be normalized with the same mean and variance.Our new normalization method, mode normalization (MN), first assigns samples in a mini-batch to different modes via a gating network, and then normalizes each sample with estimators for its corresponding mode FIG0 ). We further show that MN can be incorporated into other normalization techniques such as group normalization (GN, BID45 ) by learning which filters should be grouped together. The proposed methods can easily be implemented as layers in standard deep learning libraries, and their parameters are learned jointly with the other parameters of the network in an end-to-end manner. We evaluate MN on multiple classification tasks where it achieved a consistent improvement over currently available normalization approaches. Stabilizing the training process of deep neural networks is a challenging problem. Several normalization approaches that aim to tackle this issue have recently emerged, enabling training with higher learning rates, faster model convergence, and allowing for more complex network architectures.Here, we showed that normalization approaches can be extended to allow the network to jointly normalize its features within multiple modes. We further demonstrated that accounting for modality in intermediate feature distributions results in a consistent improvement in classification performance for various deep learning architectures. As part of future work, we plan to explore customized, layer-wise mode numbers in MN, and automatically determining them, e.g. by using concepts from sparse regularization. A ADDITIONAL MULTI-TASK RESULTS TAB5 are additional results for jointly training on MNIST, CIFAR10, SVHN, and Fashion-MNIST. The same network is used as in previous multi-task experiments, for hyperparameters see Section 4. In these additional experiments, we varied the batch size to N = {256, 512}. For larger batch sizes, increasing K to values larger than two increases performance, while for a smaller batch size of N = 128 (c.f. TAB0 , errors incurred by finite estimation prevent this benefit from appearing.",695,0.419,393,1.7684478371501273,"Normalization methods a central building block They accelerate stabilize training while decreasing the dependence manually tuned learning rate schedules When learning from multi-modal distributions the effectiveness batch normalizationBN reduced As a remedy propose by extending more a single mean variance detect modes data on- jointly normalizing samples that share We demonstrate our method BN and several experiments A challenge optimizing the change input distributions at complicating Normalization methodsBN, BID15 aim overcome -often internal covariate shift BID38 . 1 When applied successfully practice BN enables the training very deep networks shortens supporting larger learning rates sensitivity parameter initializations As BN an integral element many state machine BID12 BID39 .It standardize the activations exposed When training a deep neural network images that come visual domains each with significantly different statistics BN not effective normalizing with a single mean and . In relax the entire minibatch should normalizedOur new normalization method mode normalizationMN first assigns samples via a gating network estimators FIG0 We further show MN can incorporated other normalization techniques group normalizationGN, BID45 ) by learning which filters should grouped The proposed methods can easily layers standard deep learning libraries their parameters learned jointly in end We evaluate MN on multiple classification tasks where it achieved a consistent improvement currently available normalization approaches Stabilizing the training process of deep neural networks Several normalization approaches that aim tackle recently enabling training with higher learning rates faster model convergence allowingHere showed extended the network jointly its features within multiple modes We further demonstrated accounting modality intermediate feature distributions results classification performance various deep learning As future work explore customized, layer-wise mode numbers MN, automatically determining them, concepts sparse regularization A ADDITIONAL MULTI-TASK RESULTS TAB5 are additional results jointly training on MNIST CIFAR10 SVHN Fashion-MNIST The same network used previous multi-task experiments for hyperparameters see Section In these additional experiments varied N = {256 For larger batch sizes increasing K to values larger two increases performance N = 128 (c.f TAB0 , errors incurred finite estimation prevent this benefit appearing.",0.0,0.6620167436535711
"Multilingual machine translation, which translates multiple languages with a single model, has attracted much attention due to its efficiency of offline training and online serving. However, traditional multilingual translation usually yields inferior accuracy compared with the counterpart using individual models for each language pair, due to language diversity and model capacity limitations. In this paper, we propose a distillation-based approach to boost the accuracy of multilingual machine translation. Specifically, individual models are first trained and regarded as teachers, and then the multilingual model is trained to fit the training data and match the outputs of individual models simultaneously through knowledge distillation. Experiments on IWSLT, WMT and Ted talk translation datasets demonstrate the effectiveness of our method. Particularly, we show that one model is enough to handle multiple languages (up to 44 languages in our experiment), with comparable or even better accuracy than individual models. Neural Machine Translation (NMT) has witnessed rapid development in recent years BID1 BID26 BID36 BID8 BID34 BID32 BID31 BID12 , including advanced model structures BID8 BID34 and human parity achievements . While conventional NMT can well handle single pair translation, training a separate model for each language pair is resource consuming, considering there are thousands of languages in the world 1 . Therefore, multilingual NMT BID17 BID5 BID13 ) is developed which handles multiple language pairs in one model, greatly reducing the offline training and online serving cost.Previous works on multilingual NMT mainly focus on model architecture design through parameter sharing, e.g., sharing encoder, decoder or attention module BID5 or sharing the entire models BID17 BID13 . They achieve comparable accuracy with individual models (each language pair with a separate model) when the languages are similar to each other and the number of language pairs is small (e.g., two or three). However, when handling more language pairs (dozens or even hundreds), the translation accuracy of multilingual model is usually inferior to individual models, due to language diversity.It is challenging to train a multilingual translation model supporting dozens of language pairs while achieving comparable accuracy as individual models. Observing that individual models are usually of higher accuracy than the multilingual model in conventional model training, we propose to transfer the knowledge from individual models to the multilingual model with knowledge distillation, which has been studied for model compression and knowledge transfer and well matches our setting of multilingual translation. It usually starts by training a big/deep teacher model (or ensemble of multiple models), and then train a small/shallow student model to mimic the behaviors of the teacher model, such as its hidden representation BID39 BID29 , its output probabilities BID16 BID6 or directly training on the sentences generated by the teacher model in neural machine translation BID19 ). The student model can (nearly) match the accuracy of the cumbersome teacher model (or the ensemble of multiple models) with knowledge distillation.In this paper, we propose a new method based on knowledge distillation for multilingual translation to eliminate the accuracy gap between the multilingual model and individual models. In our method, multiple individual models serve as teachers, each handling a separate language pair, while the student handles all the language pairs in a single model, which is different from the conventional knowledge distillation where the teacher and student models usually handle the same task. We first train the individual models for each translation pair and then we train the multilingual model by matching with the outputs of all the individual models and the ground-truth translation simultaneously. After some iterations of training, the multilingual model may get higher translation accuracy than the individual models on some language pairs. Then we remove the distillation loss and keep training the multilingual model on these languages pairs with the original log-likelihood loss of the ground-truth translation.We conduct experiments on three translation datasets: IWSLT with 12 language pairs, WMT with 6 language pairs and Ted talk with 44 language pairs. Our proposed method boosts the translation accuracy of the baseline multilingual model and achieve similar (or even better) accuracy as individual models for most language pairs. Specifically, the multilingual model with only 1/44 parameters can match or surpass the accuracy of individual models on the Ted talk datasets. Selective Distillation Considering that distillation from a bad teacher model is likely to hurt the student model and thus result in inferior accuracy, we selectively use distillation in the training process, as shown in Line 15-19 in Algorithm 1. When the accuracy of multilingual model surpasses the individual model for the accuracy threshold τ on a certain language pair, we remove the distillation loss and just train the model with original negative log-likelihood loss for this pair. Note that in one iteration, one language may not uses the distillation loss; it is very likely in later iterations that this language will be distilled again since the multilingual model may become worse than the teacher model for this language. Therefore, we call this mechanism as selective distillation. We also verify the effectiveness of the selective distillation in experiment part (Section 4.3).Top-K Distillation It is burdensome to load all the teacher models in the GPU memory for distillation considering there are dozens or even hundreds of language pairs in the multilingual setting. Alternatively , we first generate the output probability distribution of each teacher model for the sentence pairs offline, and then just load the top-K probabilities of the distribution into memory and normalize them so that they sum to 1 for distillation. This can reduce the memory cost again from the scale of |V | (the vocabulary size) to K. We also study in Section 4.3 that top-K distribution can result in comparable or better distillation accuracy than the full distribution. In this work, we have proposed a distillation-based approach to boost the accuracy of multilingual NMT, which is usually of lower accuracy than the individual models in previous works. Experiments on three translation datasets with up to 44 languages demonstrate the multilingual model based on our proposed method can nearly match or even outperform the individual models, with just 1/N model parameters (N is up to 44 in our experiments).In the future, we will conduct more deep analyses about how distillation helps the multilingual model training. We will apply our method to larger datasets and more languages pairs (hundreds or even thousands), to study the upper limit of our proposed method.",1261,0.588,712,1.771067415730337,"Multilingual machine translation with attracted due of offline training online serving However traditional multilingual translation usually yields inferior accuracy compared the counterpart using individual models for due language diversity model capacity limitations In boost multilingual machine translation Specifically individual models first trained regarded teachers the multilingual model fit match simultaneously through knowledge distillation Experiments IWSLT WMT Ted talk translation datasets demonstrate our method Particularly show one model enough handle multiple languages our experiment comparable or even better accuracy individual models Neural Machine Translation witnessed , including advanced model structures and human parity achievements . While conventional NMT can well handle single pair translation training a separate model each language pair resource consuming considering there thousands 1 . Therefore multilingual NMT BID17 BID5 BID13 ) developed which handles multiple language pairs one model greatly the offline training online serving costPrevious works mainly model architecture design through parameter sharing sharing encoder attention module BID5 sharing the entire models They achieve comparable accuracy individual modelseach language pair with the languages similar two However handling more language pairsdozens the translation accuracy multilingual model inferior individual models due language diversityIt challenging train supporting dozens while achieving as Observing that individual models usually of higher accuracy the multilingual model in conventional model training propose transfer with knowledge distillation has studied model compression knowledge transfer and well matches our setting It usually starts training a big/deep teacher model ensemble train mimic such its hidden representation BID39 BID29 , its output probabilities directly training on the sentences generated neural machine translation The student model can (nearly match the accuracy the cumbersome teacher model the ensemble knowledge distillationIn based multilingual translation to eliminate individual models In our method multiple individual models serve teachers each handling a separate language pair while handles different the conventional knowledge distillation where usually handle We first train the individual models each translation pair by matching with the outputs simultaneously After some iterations training the multilingual model may get higher translation accuracy on some language pairs Then remove the distillation loss keep training the multilingual model on these languages pairs with the original log-likelihood loss the ground-truth translationWe conduct experiments three translation datasets IWSLT with WMT Ted talk Our proposed method boosts the translation accuracy the baseline multilingual model achieve individual models most language pairs Specifically the multilingual model with only 1/44 parameters match or individual models on the Ted talk datasets Selective Distillation Considering from a bad teacher model likely hurt thus result inferior accuracy selectively Line 1519 Algorithm When the accuracy multilingual model surpasses the individual model for the accuracy threshold τ on a certain language pair remove the distillation loss just train original negative log-likelihood loss this pair Note one iteration one language uses the distillation loss; very in distilled again since the multilingual model worse the teacher model Therefore call this mechanism as selective distillation We also verify the effectiveness the selective distillation in experiment partSection 4.3).Top-K Distillation It burdensome load all the teacher models the GPU memory considering there dozens language pairs the multilingual setting Alternatively , first generate the output probability distribution each teacher model the sentence pairs offline just load the top-K probabilities memory so sum distillation This can reduce again from the scale |V | (the vocabulary size K. We also study in Section that top-K distribution can result comparable or better distillation accuracy the full distribution In this work proposed boost multilingual NMT, usually of the individual models previous works Experiments three translation datasets with up to 44 languages demonstrate the multilingual model based our proposed method can nearly or the individual models just 1/N model parametersN is up our experiments).In future conduct more deep analyses about distillation helps We apply our method larger datasets more languages pairshundreds study the upper limit our proposed method",0.01,0.6686911997222877
"What makes humans so good at solving seemingly complex video games?   Unlike computers, humans bring in a great deal of prior knowledge about the world, enabling efficient decision making. This paper investigates the role of human priors for solving video games. Given a sample game, we conduct a series of ablation studies to quantify the importance of various priors. We do this by modifying the video game environment to systematically mask different types of visual information that could be used by humans as priors. We find that removal of some prior knowledge causes a drastic degradation in the speed with which human players solve the game, e.g. from 2 minutes to over 20 minutes. Furthermore, our results indicate that general priors, such as the importance of objects and visual consistency, are critical for efficient game-play. While deep Reinforcement Learning (RL) methods have shown impressive performance on a variety of video games BID17 , they remain woefully inefficient compared to human players, taking millions of action inputs to solve even the simplest Atari games. Much research is currently focused on improving sample efficiency of RL algorithms BID19 BID9 . However, there is an orthogonal issue that is often overlooked: RL agents attack each problem tabula rasa, whereas humans come in with a wealth of prior knowledge about the world, from physics to semantics to affordances.Consider the following motivating example: you are tasked with playing an unfamiliar computer game shown in FIG0 (a) . No manual or instructions are provided; you don't even know which game sprite is controlled by you. Indeed, the only feedback you are ever given is ""terminal"", i.e. once you successfully finish the game. Would you be able to successfully finish this game? How long would it take? We recruited forty human subjects to play this game and found that subjects finished it quite easily, taking just under 1 minute of game-play or 3000 action inputs. This is not overly surprising as one could easily guess that the game's goal is to move the robot sprite towards the princess by stepping on the brick-like objects and using ladders to reach the higher platforms while avoiding the angry pink and the fire objects. Now consider a second scenario in which this same simple game is re-rendered with new textures, getting rid of semantic and affordance BID8 cues, as shown in FIG0 (b) . How would human performance change? We recruited another forty subjects to play this game and found that, on average, it took the players more than twice the time (2 minutes) and action inputs ( 6500) to complete the game. The second game is clearly much harder for humans, likely because it is now more difficult to guess the game structure and goal, as well as to spot obstacles.For comparison, we can also examine how modern RL algorithms perform on these games. This is not so simple, as most standard RL approaches expect very dense rewards (e.g. continuously updated game-score BID17 ), whereas we provide only a terminal reward, to mimic how most humans play video games. In such sparse reward scenarios, standard methods like A3C BID18 are too sample-inefficient and were too slow to finish the games. Hence, we used a curiosity-based RL algorithm specifically tailored to sparse-reward settings BID20 , which was able to solve both games. Unlike humans, RL did not show much difference between the The same game modified by re-rendering the textures. Despite the two games being structurally the same, human players took twice as long to finish the second game as the first one. In comparison, the performance of an RL agent was approximately the same for the two games. two games, taking about 4 million action inputs to solve each one. This should not be surprising: since RL did not have any prior knowledge about the world, both these games carried roughly the same amount of information from the perspective of the agent.This simple motivating experiment highlights the importance of prior knowledge that humans draw upon to quickly solve tasks given to them BID13 BID24 . Developmental psychologists have begun documenting the prior knowledge that children draw upon in learning about the world BID23 BID4 . However, these studies have not explicitly quantified the relative importance of the various priors for problem-solving.In this work, we systematically quantify the importance of different types of priors humans bring to bear while solving one particular kind of problem -video games. We chose video games as the task for our investigation because it is relatively easy to methodically change the game to include or mask different kinds of knowledge and run large-scale human studies. Furthermore, video games, such as ATARI, are a popular choice in the reinforcement learning community.The paper consists of a series of ablation studies on a specially-designed game environment, systematically masking out various types of visual information that could be used by humans as priors. The full game (unlike the motivating example above) was designed to be sufficiently complex and difficult for humans to easily measure changes in performance between different testing conditions. We find that removal of some prior knowledge causes a drastic degradation in the performance of human players from 1 minute to over 20 minutes. Another key finding of our investigation is that while specific knowledge, such as ""ladders are to be climbed"", ""keys are used to open doors"", ""jumping on spikes is dangerous"", is important for humans to quickly solve games, more general priors about the importance of objects and visual consistency are even more critical. While there is no doubt that the performance of deep RL algorithms is impressive, there is much to be learned from human cognition if our goal is to enable RL agents to solve sparse reward tasks with human-like efficiency. Humans have the amazing ability to use their past knowledge (i.e., priors) to solve new tasks quickly. Success in such scenarios critically depends on the agent's ability to explore its environment and then promptly learn from its successes BID6 BID5 . In this vein, our results demonstrate the importance of prior knowledge in helping humans explore efficiently in these sparse reward environments BID11 BID7 .However , being equipped with strong prior knowledge can sometimes lead to constrained exploration that might not be optimal in all environments BID14 BID3 . For instance , consider the game shown in FIG6 consisting of a robot and a princess object. The game environment also includes rewards in hidden locations (shown as dashed yellow boxes only for illustration). When tasked to play this game, human participants (n=30) immediately assume that princess is the goal and do not explore the free space containing hidden rewards. They directly reach the princess and thereby terminate the game with sub-optimal rewards. In contrast, a random agent (30 seeds) ends up obtaining almost four times more reward than human players as shown in FIG6 . Thus, while incorporating prior knowledge in RL agents has many potential benefits, future work should also consider challenges regarding under-constrained exploration in certain kinds of settings.While our paper primarily investigated object priors (and physics priors to some extent), humans also possess rich prior knowledge about the world in the form of intuitive psychology and also bring in various priors about general video game playing such as that moving up and to the right in games is generally correlated with progress, games have goals, etc. Studying the importance of such priors will be an interesting future direction of research.Building RL algorithms that require fewer interactions to reach the goal (i.e., sample efficient algorithms) is an active area of research, and further progress is inevitable. In addition to developing better optimization methods, we believe that instead of always initializing learning from scratch, either incorporating prior knowledge directly or constructing mechanisms for condensing experience into reusable knowledge (i.e., learning priors through continual learning) might be critical for building RL agents with human-like efficiency. Our work takes first steps toward quantifying the importance of various priors that humans employ in solving video games and in understanding how prior knowledge makes humans good at such complex tasks. We believe that our results will inspire researchers to think about different mechanisms of incorporating prior knowledge in the design of RL agents. We also hope that our experimental platform of video games, available in open-source, will fuel more detailed studies investigating human priors and a benchmark for quantifying the efficacy of different mechanisms of incorporating prior knowledge into RL agents.",1658,0.862,950,1.7452631578947368,"What makes humans solving seemingly complex video games Unlike computers humans bring in prior knowledge enabling This paper human priors for solving video games Given a sample game conduct ablation studies quantify various priors We do modifying the video game environment systematically mask different types visual information humans as priors We find removal some prior knowledge causes a drastic degradation the speed human players solve from 2 minutes Furthermore our results general priors, the importance objects visual consistency critical efficient game-play While deep ReinforcementRL methods shown video games BID17 , they remain inefficient compared human players taking millions action inputs solve even the simplest Atari games Much research improving sample efficiency RL algorithms BID19 BID9 . However an orthogonal issue RL agents attack each problem tabula rasa humans come a wealth from physics semantics affordancesConsider motivating you tasked playing shown FIG0 No manual instructions; do even which game sprite controlled Indeed the only feedback are everterminal once successfully finish Would successfully finish How long We recruited forty human subjects play found subjects finished it quite taking of or 3000 action inputs This overly one guess move the robot sprite towards the princess by stepping the brick-like objects ladders while the angry pink the fire objects Now consider a second scenario this same simple game rerendered getting semantic and affordance BID8 cues as shown FIG0 (b How would human performance change We recruited another forty subjects play found it the players more twice ( action inputs 6500 The second game clearly much humans likely now guess goal spot obstaclesFor comparison examine modern RL algorithms these games This so most standard RL approaches expect very dense rewards (e.g. continuously updated game-score BID17 whereas we provide only a terminal reward to mimic how most humans play In such sparse reward scenarios standard methods A3C BID18 too sampleinefficient were finish the games Hence used a curiosity-based RL algorithm specifically sparse-reward settings BID20 , solve both games Unlike humans RL did show much difference the The same game modified re the textures Despite the two games structurally the human players took twice finish In comparison the performance an RL agent was approximately the two games two games taking about 4 million action inputs solve This should since RL did both these games carried from the agentThis simple motivating experiment highlights that humans draw quickly solve tasks given to BID13 BID24 . Developmental psychologists begun documenting the prior knowledge draw learning BID23 BID4 . However these studies explicitly the various priorsIn systematically quantify humans bring bear while one particular kind problem -video games We chose video games the task relatively methodically change include or mask different kinds knowledge run large-scale human studies Furthermore video games ATARI a popular choice in the reinforcement learning communityThe paper consists ablation studies a specially-designed game environment systematically masking out various types visual information humans as priors The full game (unlike the motivating example designed sufficiently difficult humans easily measure changes between We find removal some prior knowledge causes a drastic degradation human players from 1 minute Another key finding while specific knowledge, ""ladders to ""keys used openjumping on spikes dangerous is important humans quickly solve games more general priors about objects visual consistency even While the performance deep RL algorithms impressive human cognition if our goal enable RL agents solve sparse reward tasks Humans the amazing ability use their past knowledge new tasks quickly Success such scenarios critically explore then promptly learn BID6 BID5 . In this vein our results prior knowledge helping humans explore efficiently in these sparse reward BID11 BID7 .However , being equipped sometimes constrained exploration that optimal For instance , consider the game shown FIG6 consisting a robot princess object The game environment also rewards in hidden locations (shown dashed yellow boxes only for illustration When tasked to play human participants (n=30 immediately assume princess the goal do explore the free space containing hidden rewards They directly reach the princess thereby terminate with In contrast a random agent30 seeds ends obtaining almost four times more reward human players as shown FIG6 Thus while incorporating prior knowledge RL agents has future work also challenges regarding under-constrained exploration certain kinds settingsWhile our paper primarily investigated object priorsand physics priors to humans rich prior knowledge intuitive psychology also bring in various priors about general video game playing such that moving up to games generally correlated progress games goals etc Studying the importance such priors will an interesting future directionBuilding RL algorithms require fewer interactions reach (i.e., sample efficient algorithms further progress inevitable In addition developing better optimization methods instead always initializing learning either incorporating prior knowledge directly constructing mechanisms condensing experience reusable knowledge priors through continual learning might critical RL agents Our work takes first steps various priors that humans employ solving video games in understanding prior knowledge makes humans good such complex tasks We believe our results inspire researchers think different mechanisms incorporating prior knowledge RL agents We also hope our experimental platform of video games available fuel more detailed studies investigating human priors a benchmark different mechanisms incorporating prior knowledge RL agents",0.01,0.602944217894483
"Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions.
 In particular, we propose the use of $k$-determinantal point processes in  hyperparameter optimization via random search. Compared to conventional uniform random search where hyperparameter settings are sampled independently, a $k$-DPP promotes diversity.   We describe an approach that transforms hyperparameter search spaces for efficient use with a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from $k$-DPPs defined over spaces with a mixture of discrete and continuous dimensions. Our experiments show significant benefits over uniform random search  in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel. Hyperparameter values-regularization strength, model family choices like depth of a neural network or which nonlinear functions to use, procedural elements like dropout rates, stochastic gradient descent step sizes, and data preprocessing choices-can make the difference between a successful application of machine learning and a wasted effort. To search among many hyperparameter values requires repeated execution of often-expensive learning algorithms, creating a major obstacle for practitioners and researchers alike.In general, on request/iteration k, a hyperparameter searcher suggests a hyperparameter configuration x k , a worker trains a model using x k , and returns a validation loss of y k computed on a hold out set. In this work we say a hyperparameter searcher is open loop if x k depends only on {x i } k−1 i=1 ; examples include choosing x k uniformly at random BID4 , or x k coming from a low-discrepancy sequence (c.f., BID12 ). We say a searcher is closed loop if x k depends on both the past configurations and validation losses {(x i , y i )} k−1 i=1 ; examples include Bayesian optimization BID19 and recent reinforcement learning methods BID25 . Note that open loop methods can draw an infinite sequence of configurations before training a single model, whereas closed loop methods rely on validation loss feedback in order to make suggestions.While sophisticated closed loop selection methods have been shown to empirically identify good hyperparameter configurations faster (i.e., with fewer iterations) than open loop methods like random search, two trends have rekindled interest in embarrassingly parallel open loop methods: 1) modern deep learning models can take days or weeks to train with no signs of efficiency breakthroughs, and 2) the rise of cloud resources available to anyone that charge not by the number of machines, but by the number of CPU-hours used so that 10 machines for 100 hours costs the same as 1000 machines for 1 hour. This paper explores the landscape of open loop methods, identifying tradeoffs that are rarely considered, if at all acknowledged. While random search is arguably the most popular open loop method and chooses each x k independently of {x i } k−1 i=1 , it is by no means the only choice. In many ways uniform random search is the least interesting of the methods we will discuss because we will advocate for methods where x k depends on {x i } k−1 i=1 to promote diversity. In particular, we will focus on drawing {x i } k i=1 from a k-determinantal point process (DPP) BID16 . DPPs support real, integer, and categorical dimensions-any of which may have a tree structure-and have computationally efficient methods of drawing samples.Experimentally, we explore the use of our diversity-promoting open-loop hyperparameter optimization method based on k-DPP random search. We find that it significantly outperforms uniform random search in cases where the hyperparameter values have a large effect on performance.Open source implementations of both our hyperparameter optimization algorithm (as an extension to the hyperopt package BID5 ) and the MCMC algorithm introduced in Algorithm 2 will be released upon publication. We have explored open loop hyperparameter optimization built on sampling from k-DPPs. We described how to construct k-DPPs over hyperparameter search spaces, and showed that sampling from these retains the attractive parallelization capabilities of random search. Our experiments demonstrate that, under a limited computation budget, on a number of realistic hyperparameter optimization problems, these approaches perform better than sampling uniformly at random. As we increase the difficulty of our hyperparameter optimization problem (i.e., as values which lead to good model Average best-found model accuracy by iteration when training a convolutional neural network on the ""Stable"" search space (defined in Section 5.2), averaged across 50 trials of hyperparameter optimization, with k = 20. Discretizing the space reduces the accuracy found for both uniform sampling and k-DPP-RBF, but in both cases k-DPP-RBF finds better optima than uniform sampling.evaluations become more scarce) the improvement over sampling uniformly at random increases. An open-source implementation of our method is available.",1046,0.451,617,1.6952998379254458,"Driven parallelizable hyperparameter optimization methods studies \emph{open loop} search methods: sequences predetermined generated before a single configuration evaluated Examples include grid search uniform random search low discrepancy sequences other sampling distributions In particular propose $k$-determinantal point processes via random search Compared conventional uniform random search where hyperparameter settings sampled independently a $k$-DPP promotes diversity We describe transforms hyperparameter search spaces for efficient use a $k$-DPP. In addition introduce a novel Metropolis-Hastings algorithm sample $k$-DPPs defined over spaces a mixture Our experiments significant benefits over uniform random search realistic scenarios a limited budget supervised learners whether serial Hyperparameter values-regularization strength model family choices like depth which nonlinear functions procedural elements dropout rates data choicescan make To search among many hyperparameter values requires repeated execution oftenexpensive learning creating a major obstacle practitionersIn general on request/iteration k, searcher suggests x k a worker trains using returns a validation loss computed a hold out set In this work say a hyperparameter searcher open loop if x k depends {x i } k−1 ; examples choosing uniformly random BID4 x coming We say a searcher closed loop x k depends both the past configurations validation losses {( i k−1 i=1 ; examples Bayesian optimization BID19 recent reinforcement methods Note open loop methods draw configurations before training whereas rely validation loss feedback in suggestionsWhile sophisticated closed loop selection methods empirically identify good hyperparameter configurations faster like random search two trends rekindled embarrassingly parallel open loop methods take days no signs efficiency breakthroughs cloud resources available anyone that charge not by machines CPU-hours used so that 10 machines for 100 hours costs the 1000 machines This paper the landscape open loop methods identifying tradeoffs rarely if acknowledged While random search arguably the most popular open loop method and chooses each x k independently {x i } k−1 i=1 by In uniform random search least because advocate methods where x k depends {x i } k−1 to promote diversity In particular drawing {x i k i=1 from a k-determinantal point processDPP) BID16 . DPPs support real, integer categorical dimensions-any a tree structure have computationally efficient methods drawing samplesExperimentally explore our diversity-promoting open-loop hyperparameter optimization method based k-DPP random search We find it significantly uniform random search cases performanceOpen source implementationsas an extension the hyperopt package BID5 ) introduced Algorithm will upon We explored open loop hyperparameter optimization built sampling kDPPs described over hyperparameter search spaces sampling these retains the attractive parallelization capabilities random search Our experiments demonstrate a limited computation budget on realistic hyperparameter optimization problems these approaches sampling uniformly As increase our hyperparameter optimization problem as values which lead good model Average best-found model accuracy by iteration when training on the ""Stable"" search space (defined averaged across 50 trials with k Discretizing the space reduces found for both uniform sampling k-DPP-RBF in finds better optima than uniform sampling.evaluations become scarce) the improvement sampling uniformly at random increases our method is",0.01,0.4756420683420243
"In inductive transfer learning, fine-tuning pre-trained convolutional networks substantially outperforms training from scratch.
 When using fine-tuning, the underlying assumption is that the pre-trained model extracts generic features, which are at least partially relevant for solving the target task, but would be difficult to extract from the limited amount of data available on the target task.
 However, besides the initialization with the pre-trained model and the early stopping, there is no mechanism in fine-tuning for retaining the features learned on the source task.
 In this paper, we investigate several regularization schemes that explicitly promote the similarity of the final solution with the initial model.
 We eventually recommend a simple $L^2$ penalty using the pre-trained model as a reference, and we show that this approach behaves much better than the standard scheme using weight decay on a partially frozen network. It is now well known that modern convolutional neural networks (e.g. BID14 BID25 BID11 BID28 ) can achieve remarkable performance on large-scale image databases, e.g. ImageNet BID3 ) and Places 365 BID37 ), but it is really dissatisfying to see the vast amounts of data, computing time and power consumption that are necessary to train deep networks. Fortunately, such convolutional networks, once trained on a large database, can be refined to solve related but different visual tasks by means of transfer learning, using fine-tuning BID34 BID25 .Some form of knowledge is believed to be extracted by learning from the large-scale database of the source task and this knowledge is then transferred to the target task by initializing the network with the pre-trained parameters. However , after fine-tuning, some of the parameters may be quite different from their initial values, resulting in possible losses of general knowledge that may be relevant for the targeted problem. In particular , during fine-tuning, L 2 regularization drives the parameters towards the origin and thereby encourages large deviations between the parameters and their initial values.In order to help preserve the acquired knowledge embedded in the initial network, we consider using other parameter regularization methods during fine-tuning. We argue that the standard L 2 regularization, which drives the parameters towards the origin, is not adequate in the framework of transfer learning where the initial values provide a more sensible reference point than the origin. This simple modification keeps the original control of overfitting, by constraining the effective search space around the initial solution, while encouraging committing to the acquired knowledge. We show that it has noticeable effects in inductive transfer learning scenarios.This paper aims at improving transfer learning by requiring less labeled training data. A form of transfer learning is thus considered, where some pieces of knowledge, acquired when solving a previous learning problem, have to be conveyed to another learning problem. Under this setting, we explore several parameter regularization methods that can explicitly retain the knowledge acquired on the source problem. We investigate variants of L 2 penalties using the pre-trained model as reference, which we name L 2 -SP because the pre-trained parameters represent the starting point (-SP) of the fine-tuning process. In addition, we evaluate other regularizers based on the Lasso and Group-Lasso penalties, which can freeze some individual parameters or groups of parameters to the pre-trained parameters. Fisher information is also taken into account when we test L 2 -SP and Group-Lasso-SP approaches.Our experiments indicate that all tested parameter regularization methods using the pre-trained parameters as a reference get an edge over the standard L 2 weight decay approach. We also analyze the effect of L 2 -SP with theoretical arguments and experimental evidence to recommend using L 2 -SP for transfer learning tasks. Among all -SP methods, L 2 -SP and L 2 -SP-Fisher always reach a better accuracy on the target task. We expected L 2 -SP-Fisher to outperform L 2 -SP, since Fisher information helps in continual learning, but there is no significant difference between the two options. Since L 2 -SP is simpler than L 2 -SP-Fisher, we recommend the former, and we focus on the analysis of L 2 -SP, although most of the analysis and the discussion would also apply to L 2 -SP-Fisher. We proposed simple regularization techniques for inductive transfer learning, to encode an explicit bias towards the solution learned on the source task. Most of the regularizers evaluated here have been already used for other purposes, but we demonstrate their relevance for inductive transfer learning with deep convolutional networks.We show that a simple L 2 penalty using the starting point as a reference, L 2 -SP, is useful, even if early stopping is used. This penalty is much more effective than the standard L 2 penalty that is commonly used in fine-tuning. It is also more effective and simpler to implement than the strategy consisting in freezing the first layers of a network. We provide theoretical hints and strong experimental evidence showing that L 2 -SP retains the memory of the features learned on the source database.Besides, we tested the effect of more elaborate penalties, based on L 1 or Group-L 1 norms, or based on Fisher information. None of the L 1 or Group-L 1 options seem to be valuable in the context of inductive transfer learning that we considered here, and using the Fisher information with L 2 -SP does not improve accuracy on the target task. Different approaches, which implement an implicit bias at the functional level, alike BID16 ), remain to be tested: being based on a different principle, their value should be assessed in the framework of inductive transfer learning.",1138,0.517,650,1.7507692307692309,"In inductive transfer learning substantially from scratch When using the underlying assumption extracts generic features at relevant solving would extract the limited amount However besides the initialization with the early stopping for retaining learned on the source task In several regularization schemes explicitly promote the similarity the final solution We eventually recommend a simple $L^2$ penalty using show behaves the standard scheme using weight decay on a partially frozen network Ite.g. BID14 BID25 BID11 BID28 achieve ) Places 365 really dissatisfying the vast amounts, computing time power consumption necessary train deep networks Fortunately such convolutional networks once trained refined solve related but different visual tasks by means transfer learning using fine-tuning BID34 BID25 .Some form knowledge believed extracted the source task initializing However , after some may quite resulting possible losses general knowledge that relevant the targeted problem In particular , during L 2 regularization drives the parameters towards the origin thereby encourages large deviationsIn help preserve the acquired knowledge embedded the initial network consider using other parameter regularization methods during We argue the standard L 2 regularization, drives the parameters towards the origin transfer learning where provide a more sensible reference point This simple modification keeps the original control of overfitting by constraining the effective search space around the initial solution while encouraging committing the acquired knowledge We show it has noticeable effects inductive transfer learning scenariosThis paper aims improving transfer requiring less labeled training data A form transfer learning thus considered, some pieces acquired when solving conveyed Under this setting explore several parameter regularization methods explicitly retain the knowledge acquired on the source problem We investigate variants L 2 penalties using the pre-trained model as reference name -SP because represent ( In addition evaluate other regularizers the Lasso and Group-Lasso penalties freeze some individual parameters groups to the pre-trained parameters Fisher information is also taken into we test L 2 -SP and Group-Lasso-SP approachesOur experiments indicate all tested parameter regularization methods using as get an edge the standard L 2 weight decay approach We also analyze L 2 -SP with theoretical arguments recommend using transfer learning tasks Among all -SP methods L 2 -SP and-Fisher always reach a better accuracy the target task We expected L 2 -SP-Fisher, since Fisher information helps in continual learning there Since L 2 -SP simpler-Fisher recommend former focus the analysis although most and the discussion would also We proposed simple regularization techniques inductive transfer learning to encode an explicit bias towards the solution learned on the source task Most the regularizers evaluated already used demonstrate their relevance inductive transfer learning withWe a simple L 2 penalty using the starting point L 2 -SP useful, early stopping used This penalty much the standard L 2 penalty commonly fine-tuning It more effective simpler implement the strategy consisting in freezing the first layers We provide theoretical hints strong experimental evidence showing L 2 -SP retains the memory the features learned on the source databaseBesides tested more elaborate penalties based L or Group-L 1 norms or based Fisher information None the L 1 or Group-L 1 options seem valuable inductive transfer learning that considered using the Fisher information with L -SP does improve accuracy on the target task Different approaches which implement an implicit bias at alike BID16 ), remain: being based a different principle their value the framework inductive transfer learning",0.01,0.6169732078204204
"Artificial neural networks have opened up a world of possibilities in data science and artificial intelligence, but neural networks are cumbersome tools that grow with the complexity of the learning problem. We make contributions to this issue by considering a modified version of the fully connected layer we call a block diagonal inner product layer. These modified layers have weight matrices that are block diagonal, turning a single fully connected layer into a set of densely connected neuron groups. This idea is a natural extension of group, or depthwise separable, convolutional layers applied to the fully connected layers. Block diagonal inner product layers can be achieved by either initializing a purely block diagonal weight matrix or by iteratively pruning off diagonal block entries. This method condenses network storage and speeds up the run time without significant adverse effect on the testing accuracy, thus offering a new approach to improve network computation efficiency. Today, it is well known that larger neural networks can better represent complex data and hence achieve higher accuracy than smaller networks BID14 BID35 BID34 . While larger networks are more capable than their smaller counterparts, their size consumes significant storage and computational resources and memory bandwidth. Ideally, efforts to reduce memory requirements would also lessen computational demand, but often these competing interests force a trade-off. The fully connected layers are unwieldy, yet they continue to be present in the most successful networks BID21 BID43 BID35 . Our work addresses both memory and computational demand without compromise. Focusing our attention on the inner product layers, we decrease network memory footprint and improve network computational demand.While larger network architectures achieve higher accuracy, there are a variety of methods to condense them without much harm to the network accuracy. One such technique that has gained popularity is pruning BID30 BID7 , but traditional pruning has disadvantages related to network runtime. Most existing pruning processes significantly slow down network training, and the final trained network is usually slower to execute BID7 . Sparse format operations require additional overhead that can greatly slow down performance unless one prunes nearly all weight entries, which can damage network accuracy.Localized memory access patterns can be computed faster than non-localized lookups. By implementing block diagonal inner product layers in place of fully connected layers, we condense neural networks in a structured manner that speeds up the final runtime and does little harm to the final accuracy. Block diagonal inner product layers can be implemented by either initializing a purely block diagonal weight matrix or by initializing a fully connected layer and focusing pruning efforts off the diagonal blocks to coax the dense weight matrix into structured sparsity. The first method also reduces the gradient computation time and hence the overall training time. The latter method can improve accuracy and supports the robustness of networks to shaping. That is, pruning can be used as a mapping between architectures-in particular, a mapping to more convenient architectures. Depending on how many iterations the pruning process takes, this method may also speed up training. We have converted a single fully connected layer into a group of smaller inner product learners whose combined efforts form a stronger learner, in essence boosting the layer. These methods also bring artificial neural networks closer to the architecture of biological mammalian brains, which have more local connectivity BID11 ). We have shown that block diagonal inner product layers can reduce network size, training time and final execution time without significant harm to the network performance.While traditional iterative pruning can reduce storage, the random indices of the surviving weights make sparse computation inefficient, slowing down the training and final execution time of the network. Our block diagonal methods address this inefficiency by confining dense regions to blocks along the diagonal. Without pruning, block diagonal method 1 allows for faster training time. Method 2 preserves the learning with focused, structured pruning that reduces computation for speedup during execution. In our experiments, method 2 saw higher accuracy than the purely block diagonal method for the more complex learning problem, CIFAR10; however, the increase in accuracy came in exchange for slightly more time to train the network. There is great deal of flexibility in our block diagonal methods that can be tuned to an individual problem. These methods may also make larger network architectures more feasible to train and use since they convert a fully connected layer into a collection of smaller inner product learners working jointly to form a stronger learner. In particular, GPU memory constraints become less constricting.There is a lot of room for additional speedup with block diagonal layers. Dependency between layers poses a noteworthy bottleneck in network parallelization. With structured sparsity like ours, one no longer needs a full barrier between layers. Additional speedup would be seen in software optimized to support weight matrices with organized sparse form, such as blocks, rather than being optimized for dense matrices. For example, for many small blocks, one can reach up to 6 fold speedup with specialized batched matrix multiplication BID16 . Hardware has been developing to better support sparse operations. Block format may be especially suitable for training on evolving architectures such as neuromorphic systems. These systems, which are far more efficient than GPUs at simulating mammalian brains, have a pronounced 2-D structure and are ill-suited to large dense matrix calculations BID28 BID0 .",1020,0.627,613,1.66394779771615," opened cumbersome tools grow We make contributions this issue considering a modified version the fully connected layer we a block diagonal inner product layer These modified layers weight matrices block diagonal turning a single fully connected layer densely connected neuron groups This idea group, depthwise separable, convolutional layers applied the fully connected layers Block diagonal inner product layers can achieved either initializing a purely block diagonal weight matrix iteratively pruning off diagonal block entries This method condenses network storage speeds without significant adverse effect the testing accuracy thus offering improve network computation efficiency Today well larger neural networks better represent hence achieve BID14 BID35 BID34 While larger networks capable consumes significant storage memory Ideally efforts memory requirements also lessen computational demand often these competing interests force The fully connected layers yet continue present the most successful networks BID21 BID43 BID35 . Our work addresses both memory computational demand without compromise Focusing the inner product layers decrease network memory footprint network computational demandWhile larger network achieve higher accuracy methods condense them without much harm the network accuracy One such technique pruning BID30 BID7 , but disadvantages related network runtime Most existing pruning processes significantly slow network training the final trained network execute BID7 . Sparse format operations require additional overhead greatly slow unless one prunes nearly all weight entries damage network accuracyLocalized memory access patterns computed faster By implementing block diagonal inner product layers place fully connected layers condense neural networks speeds the final runtime does little harm Block diagonal inner product layers can implemented either a purely block diagonal weight matrix and focusing pruning efforts off coax structured sparsity The first method also reduces the gradient computation time The latter method can improve supports networks to shaping That pruning can a mapping architectures- particular more convenient architectures Depending also speed training We converted a single fully connected layer smaller inner product learners whose combined efforts form, in essence boosting the layer These methods also bring artificial neural networks closer the architecture biological mammalian brains more local connectivity BID11 We shown that block diagonal inner product layers reduce network size training time final execution time without significant harmWhile traditional iterative pruning storage the random indices the surviving weights make sparse computation slowing Our block diagonal methods address this inefficiency confining dense regions blocks along Without pruning block diagonal method 1 allows faster training time Method 2 preserves the learning with focused structured pruning reduces computation for speedup during execution In our experiments method 2 saw higher accuracy the purely block diagonal method the more complex learning problem CIFAR10; came exchange There great deal flexibility our block diagonal methods tuned an individual problem These methods make larger network architectures train since convert a fully connected layer smaller inner product learners working jointly form In particular GPU memory constraints become less constrictingThere additional speedup block diagonal layers between layers poses a noteworthy bottleneck network parallelization With structured sparsity like ours one no a full barrier layers Additional speedup would seen software optimized weight matrices organized sparse form blocks rather being optimized For example for many small blocks one reach up to 6 fold speedup specialized batched matrix multiplication BID16 Hardware has developing better sparse operations Block format may especially suitable training on evolving architectures These systems far GPUs mammalian brains a pronounced 2-D structure ill large dense matrix calculations BID28 BID0 .",0.01,0.3957598244488731
"One of the challenges in the study of generative adversarial networks is the instability of its training. 
 In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator.
 Our new normalization technique is computationally light and easy to incorporate into existing implementations. 
 We tested the efficacy of spectral normalization on CIFAR10, STL-10, and ILSVRC2012 dataset, and we experimentally confirmed that spectrally normalized GANs (SN-GANs) is capable of generating images of better or equal quality relative to the previous training stabilization techniques. Generative adversarial networks (GANs) BID11 have been enjoying considerable success as a framework of generative models in recent years, and it has been applied to numerous types of tasks and datasets BID15 . In a nutshell, GANs are a framework to produce a model distribution that mimics a given target distribution, and it consists of a generator that produces the model distribution and a discriminator that distinguishes the model distribution from the target. The concept is to consecutively train the model distribution and the discriminator in turn, with the goal of reducing the difference between the model distribution and the target distribution measured by the best discriminator possible at each step of the training. GANs have been drawing attention in the machine learning community not only for its ability to learn highly structured probability distribution but also for its theoretically interesting aspects. For example, BID26 BID37 BID24 revealed that the training of the discriminator amounts to the training of a good estimator for the density ratio between the model distribution and the target. This is a perspective that opens the door to the methods of implicit models BID24 BID36 that can be used to carry out variational optimization without the direct knowledge of the density function.A persisting challenge in the training of GANs is the performance control of the discriminator. In high dimensional spaces, the density ratio estimation by the discriminator is often inaccurate and unstable during the training, and generator networks fail to learn the multimodal structure of the target distribution. Even worse, when the support of the model distribution and the support of the target distribution are disjoint, there exists a discriminator that can perfectly distinguish the model distribution from the target . Once such discriminator is produced in this situation, the training of the generator comes to complete stop, because the derivative of the so-produced discriminator with respect to the input turns out to be 0. This motivates us to introduce some form of restriction to the choice of the discriminator.In this paper, we propose a novel weight normalization method called spectral normalization that can stabilize the training of discriminator networks. Our normalization enjoys following favorable properties.• Lipschitz constant is the only hyper-parameter to be tuned, and the algorithm does not require intensive tuning of the only hyper-parameter for satisfactory performance.• Implementation is simple and the additional computational cost is small.In fact, our normalization method also functioned well even without tuning Lipschitz constant, which is the only hyper parameter. In this study, we provide explanations of the effectiveness of spectral normalization for GANs against other regularization techniques, such as weight normalization BID31 , weight clipping , and gradient penalty BID12 . We also show that, in the absence of complimentary regularization techniques (e.g., batch normalization, weight decay and feature matching on the discriminator), spectral normalization can improve the sheer quality of the generated images better than weight normalization and gradient penalty. This paper proposes spectral normalization as a stabilizer of training of GANs. When we apply spectral normalization to the GANs on image generation tasks, the generated examples are more diverse than the conventional weight normalization and achieve better or comparative inception scores relative to previous studies. The method imposes global regularization on the discriminator as opposed to local regularization introduced by WGAN-GP, and can possibly used in combinations. In the future work, we would like to further investigate where our methods stand amongst other methods on more theoretical basis, and experiment our algorithm on larger and more complex datasets.",796,0.363,478,1.6652719665271967,"One the study generative adversarial networks the instability its training In this paper a novel weight normalization technique called spectral normalization stabilize the training the discriminator Our new normalization technique computationally light incorporate existing implementations We tested spectral normalization CIFAR10, STL-10 ILSVRC2012 dataset experimentally spectrally normalized GANsSN-GANs is capable images better or equal quality relative the previous training stabilization techniques Generative adversarial networks BID11 have enjoying as of generative models it applied numerous types tasks and datasets BID15 . In a nutshell GANs a framework produce a model distribution mimics a given target distribution it consists a generator distinguishes The concept consecutively train the model distribution the discriminator in turn reducing measured possible at GANs have drawing the machine learning community not highly structured probability distribution its theoretically interesting aspects For example BID26 BID37 BID24 revealed the training the discriminator amounts the training a good estimator the density ratio between the model distribution This a perspective opens the methods implicit models BID24 BID36 that carry variational optimization without the direct knowledge the density functionA persisting challenge the training GANs the performance control In high dimensional spaces the density ratio estimation by the discriminator inaccurate unstable during, generator networks fail learn the multimodal structure the target distribution Even worse when the support the model distribution and disjoint exists a discriminator perfectly distinguish the model distribution . Once such discriminator produced this situation the training the generator comes complete stop because the derivative the so-produced discriminator with turns 0 This motivates introduce some form restriction the choice the discriminatorIn a novel weight normalization method called spectral normalization stabilize the training Our normalization enjoys following favorable properties.• Lipschitz constant the only hyper tuned the algorithm does require intensive tuning the only hyper for satisfactory Implementation simple the additional computational costIn also functioned even tuning In provide explanations the effectiveness spectral normalization GANs against other regularization techniques weight normalization BID31 , weight clipping , gradient penalty BID12 We also show, complimentary regularization techniques weight decay feature matching on the discriminator spectral normalization improve the sheer quality better and gradient penalty This paper proposes spectral normalization as a stabilizer training of GANs When on image generation tasks the generated examples more diverse the conventional weight normalization and achieve better or comparative inception scores relative previous studies The method imposes global regularization the discriminator as opposed introduced WGAN-GP can possibly used combinations In the future work, would further investigate where our methods stand amongst on more theoretical basis experiment our algorithm",0.0,0.3991336902392201
"Humans acquire complex skills by exploiting previously learned skills and making transitions between them. To empower machines with this ability, we propose a method that can learn transition policies which effectively connect primitive skills to perform sequential tasks without handcrafted rewards. To efficiently train our transition policies, we introduce proximity predictors which induce rewards gauging proximity to suitable initial states for the next skill. The proposed method is evaluated on a set of complex continuous control tasks in bipedal locomotion and robotic arm manipulation which traditional policy gradient methods struggle at. We demonstrate that transition policies enable us to effectively compose complex skills with existing primitive skills. The proposed induced rewards computed using the proximity predictor further improve training efficiency by providing more dense information than the sparse rewards from the environments. We make our environments, primitive skills, and code public for further research at https://youngwoon.github.io/transition .",169,0.112,94,1.797872340425532, acquire exploiting transitions To empower machines propose learn transition policies which effectively connect primitive skills perform sequential tasks handcrafted rewards To efficiently train our transition policies introduce proximity predictors induce rewards gauging proximity suitable initial states the next skill The proposed method evaluated complex continuous control tasks robotic arm manipulation which traditional policy gradient methods struggle at demonstrate transition policies enable compose complex skills existing primitive skills The proposed induced rewards computed the proximity predictor further improve more dense information rewards the environments make our environments primitive skills code public further research at,0.0,0.736987792790711
"Gated recurrent units (GRUs) were inspired by the common gated recurrent unit, long short-term memory (LSTM), as a means of capturing temporal structure with less complex memory unit architecture. Despite their incredible success in tasks such as natural and artificial language processing, speech, video, and polyphonic music, very little is understood about the specific dynamic features representable in a GRU network. As a result, it is difficult to know a priori how successful a GRU-RNN will perform on a given data set. In this paper, we develop a new theoretical framework to analyze one and two dimensional GRUs as a continuous dynamical system, and classify the dynamical features obtainable with such system.
 We found rich repertoire that includes stable limit cycles over time (nonlinear oscillations), multi-stable state transitions with various topologies, and homoclinic orbits. In addition, we show that any finite dimensional GRU cannot precisely replicate the dynamics of a ring attractor, or more generally, any continuous attractor, and is limited to finitely many isolated fixed points in theory. These findings were then experimentally verified in two dimensions by means of time series prediction. Recurrent neural networks (RNNs) have been widely used to capture and utilize sequential structure in natural and artificial languages, speech, video, and various other forms of time series. The recurrent information flow within RNN implies that the data seen in the past has influence on the current state of the RNN, forming a mechanism for having memory through (nonlinear) temporal traces. Unfortunately, training vanilla RNNs (which allow input data to directly interact with the hidden state) to capture long-range dependences within a sequence is challenging due to the vanishing gradient problem BID8 . Several special RNN architectures have been proposed to mitigate this issue, notably the long short-term memory (LSTM; BID9 ) which explicitly guards against unwanted corruption of the information stored in the hidden state until necessary. Recently, a simplification of the LSTM called the gated recurrent unit (GRU; BID1 ) has become wildly popular in the machine learning community thanks to its performance in machine translation BID0 , speech BID16 , music BID2 , video BID4 , and extracting nonlinear dynamics underlying neural data BID15 . As a variant of the vanilla LSTM, GRUs incorporate the use of forget gates, but lack an output gate BID5 . While this feature reduces the number of required parameters, LSTM has been shown to outperform GRU on neural machine translation BID0 . In addition, certain mechanistic tasks, specifically unbounded counting, come easy to LSTM networks but not to GRU networks BID18 . Despite these empirical findings, we lack systematic understanding of the internal time evolution of GRU's memory structure and its capability to represent nonlinear temporal dynamics.In general, a RNN can be written as h t+1 = f (h t , x t ) where x t is the current input in a sequence indexed by t, f is a point-wise nonlinear function, and h t represents the hidden memory state that carries all information responsible for future output. In the absence of input, the hidden state h t can evolve over time on its own: DISPLAYFORM0 where f (·) := f (·, 0) for notational simplicity. In other words, we can consider the temporal evolution of memory stored within RNN as a trajectory of a dynamical system defined by (1). Then we can use dynamical systems theory to investigate the fundamental limits in the expressive power of RNNs in terms of their temporal features. We develop a novel theoretical framework to study the dynamical features fundamentally attainable, in particular, given the particular form of GRU. We then validate the theory by training GRUs to predict time series with prescribed dynamics. Our analysis shows the rich but limited classes of dynamics the GRU can approximate in one, two, and arbitrary dimensions. We developed a new theoretical framework to analyze GRUs as a continuous dynamical system, and showed that two GRUs can exhibit a variety of expressive dynamic features, such as limit cycles, homoclinic orbits, and a substantial catalog of stability structures and bifurcations. However, we also showed that finitely many GRUs cannot exhibit the dynamics of an arbitrary continuous attractor. These claims were then experimentally verified in two dimensions. We believe these findings also unlock new avenues of research on the trainability of recurrent neural networks. Although we have analyzed GRUs only in 1-and 2-dimensions in near exhaustive, we believe that the insights extends to higher-dimensions. We leave rigorous analysis of higher-dimensional GRUs as future work.A CONTINUOUS TIME SYSTEM DERIVATION We begin with the fully gated GRU as a discrete time system, where the input vector x t has been set equal to zero, as depicted in FORMULA0 - FORMULA0 , where is the Hadamard product, and σ is the sigmoid function. DISPLAYFORM0 We recognize that (15) is a forward Euler discretization of a continuous time dynamical system. This allows us to consider the underlying continuous time dynamics on the basis of the discretization. The following steps are a walk through of the derivation:Since z t is a bounded function on R ∀t, there exists a functionz t , such that z t +z t = 1 at each time step (due to the symmetry of z t ,z t is the result of vertically flipping z t about 0.5, the midpoint of its range). As such, we can rewrite (15) withz t as depicted in FORMULA0 . DISPLAYFORM1 Let h(t) ≡ h t−1 . As a result, we can sayz t ≡z(t) and r t ≡ r(t), as depicted in FORMULA7 . DISPLAYFORM2 Dividing both sides of the equation by ∆t yields (24). DISPLAYFORM3 If we take the limit as ∆t → 0, we get the analogous continuous time system to (13) -(15), DISPLAYFORM4 whereḣ ≡",1243,0.621,730,1.7027397260273973,"Gated recurrent units inspired long short-term memory capturing temporal structure with less complex memory unit architecture Despite their incredible success tasks natural and artificial language processing speech, video polyphonic music very understood the specific dynamic features representable a GRU network As a priori successful a GRU-RNN perform In develop analyze one and two dimensional GRUs classify obtainable such system We found rich repertoire that stable limit cycles over multi-stable state transitions with various topologies homoclinic orbits In addition show any finite dimensional GRU precisely replicate a ring attractor more continuous is limited finitely many isolated fixed points theory These findings then experimentally two dimensions means time series prediction Recurrent neural networks widely capture utilize sequential structure natural and artificial languages speech video time series The recurrent information flow within RNN implies seen has influence forming a mechanism having memory through (nonlinear) temporal traces Unfortunately training vanilla RNNs ( allow input data directly the hidden state to capture long-range dependences within a sequence challenging the vanishing gradient problem BID8 . Several special RNN architectures mitigate notably long short; BID9 ) which explicitly guards unwanted corruption the information the hidden state until necessary Recently a simplification called the gated recurrent unit; BID1 ) become wildly thanks its performance machine translation BID0 speech BID16 extracting nonlinear dynamics underlying neural data As a variant the vanilla LSTM GRUs incorporate forget gates lack an output gate BID5 . While this feature reduces required parameters LSTM has shown GRU on neural machine translation BID0 . In addition certain mechanistic tasks specifically unbounded counting come easy LSTM networks but GRU networks BID18 . Despite these empirical findings lack systematic understanding the internal time evolution GRU's memory structure its capability represent nonlinear temporal dynamicsIn general a RNN written h t+1 = f (h t , x t in indexed represents that carries all information responsible future output In input the hidden state h t can evolve on: DISPLAYFORM0 where f (· for notational simplicity In consider the temporal evolution memory stored RNN as a trajectory a dynamical system defined ( Then use dynamical systems theory investigate the fundamental limits in the expressive power in their temporal features We develop fundamentally attainable, given the particular form GRU We then validate training GRUs time series prescribed dynamics Our analysis the rich but limited classes dynamics the GRU approximate one, arbitrary dimensions We developed GRUs as showed exhibit expressive dynamic features limit cycles homoclinic orbits a substantial catalog stability structures and However we showed finitely many GRUs exhibit the dynamics an arbitrary continuous attractor These claims then experimentally two dimensions We believe these findings also unlock the trainability recurrent neural networks Although we analyzed GRUs only 1-and 2-dimensions near exhaustive, we believe the insights extends We leave rigorous analysis higher-dimensional GRUs as future workA CONTINUOUS TIME SYSTEM We begin the fully gated GRU as the input vector x t has set equal zero as depicted FORMULA0 - FORMULA0 , is the Hadamard product DISPLAYFORM0 We recognize (15 a forward Euler discretization a continuous time dynamical system This allows consider the underlying continuous time dynamics on. The following steps a walk:Since z t a bounded function on R ��t there exists such +z at each timeduez t the result vertically flipping about, the midpoint its range As such rewrite (15 withz t as depicted FORMULA0 DISPLAYFORM1 Let h(t ≡ As sayz t ≡z(t and as depicted FORMULA7 DISPLAYFORM2 Dividing both sides ��t yields (24 DISPLAYFORM3 If we take the limit as ��t → the analogous continuous time system to (13 -(15 DISPLAYFORM4�� ≡",0.01,0.4945982495643753
"Stacked hourglass network has become an important model for Human pose estimation. The estimation of human body posture depends on the global information of the keypoints type and the local information of the keypoints location. The consistent processing of inputs and constraints makes it difficult to form differentiated and determined collaboration mechanisms for each stacked hourglass network. In this paper, we propose a Multi-Scale Stacked Hourglass (MSSH) network to high-light the differentiation capabilities of each Hourglass network for human pose estimation.   The pre-processing network forms feature maps of different scales,and dispatch them to various locations of the stack hourglass network, where the small-scale features reach the front of stacked hourglass network, and large-scale features reach the rear of stacked hourglass network.    And a new loss function is proposed for multi-scale stacked hourglass network.   Different keypoints have different weight coefficients of loss function at different scales, and the keypoints weight coefficients are dynamically adjusted from the top-level hourglass network to the bottom-level hourglass network.   Experimental results show that the pro-posed method is competitive with respect to the comparison algorithm on MPII and LSP datasets. Human pose estimation need locate the body keypoints (head, shoulder, elbow, wrist, knee, ankle, etc.) from the input image, and it is basic method for some advanced vision task BID4 , such as human motion recognition, human-computer interaction, and human reidentification et al. We focus on single-person pose estimation problems in a single RGB image. Due to the high flexibility of the human body and limbs, diverse viewpoint, camera projection transformation and occlusion, it still is a difficult task to accurately determine body keypoints from a single image.In recent years, the deep convolutional neural network (DCNN) has made significant progress in the human pose estimation; especially the stacked hourglass network BID7 has achieved good results and has attracted much attention. The human pose estimation involves two kinds of information: the type and location of body keypoints. The type of body keypoints needs to be determined in a larger receptive field, and the location of body keypoints needs to be based on the specific pixel position, which are respectively equivalent to global information and local information. The hourglass network uses a convolution layer and a deconvolution layer to form an hourglass structure, and establish crossover channels between convolution and deconvolution layers on different scales. Using the hourglass network for human pose estimation, the hourglass structure extracts global information through information compression, and the crossover channels compensates for local information loss in information compression. The stacked hourglass network continuously improves the human pose estimation by enhancing the context constraints among body keypoints through the stacked structure.The stacked hourglass network theoretically increases the stacked depth to expand the receptive field and form a stronger context constraints among body keypoints. However, in practical applications, simply increasing the stacked depth is difficult to effectively improve the accuracy of human pose estimation. The main reason is that the consistent processing of inputs and constraints makes it difficult to form differentiated and determined collaboration mechanisms for each stacked hourglass network, to make up the information loss caused by the functional consistency of hourglass networks. Inspired by multi-scale information fusion from the single hourglass network, we propose a Multi-Scale Stacked Hourglass (MSSH) network. A pre-processing network consisting primarily of residual networks is designed to generate multi-scale features, and features of each scale are sent to different stacked hourglass networks. Each hourglass network has different inputs: the output of the pre-level hourglass network, and the received feature. Small-scale feature input makes the hourglass network tend to focus on global information, such as the type and context constraints of body keypoints, and large-scale feature input makes the hourglass network more likely to focus on local information, such as the location of body keypoints. The input of entire stacking hourglass network has changed from small-scale feature to large-scale feature, and it is a top-down route of body keypoints estimation. The iterative relationship between the loss functions of different scales of the MSSH network is established, so that the pre-level detection results affect the weight of the next keypoint loss function, and the optimization process of network model training is controlled by adaptive weighted loss function. The iterative relationship of the adjacent network loss function is established on the MSSH network, so that the weight of the loss function on pre-level hourglass network affects the weight of the loss function on the current hourglass network. The optimization process of the model training is controlled by the adaptive weighted loss function.The main contributions of this paper can be summarized as follows:• In a multi-scale stacked hourglass network, the pre-processing network generates features of different scales and dispatchs them to every hourglass network, where the small-scale features reaches the front of stacked hourglass network and the large-scale features reaches the rear of stacked hourglass network. From global information to local information, each hourglass network can form a differentiated function, which is conducive to the formation of collaborative processing.• A new loss function of the MSSH network is proposed. The weighting coefficient of the loss function in hourglass network is defined. The weight coefficient and the loss function of the pre-level hourglass network are used to adjust the weight coefficient of the current hourglass network, and the convergence process of the model training is optimized by the adaptive weighted loss function.The remainder of this paper is organized as follows. Section 2 briefly reviews recent work on human pose estimation. Section 3 details the structure of the MSSH network. Section 4 describes the new loss function for MSSH network networks. Section 5 describes the implementation details and experimental results. Section 6 summarizes our paper.",1152,0.589,709,1.624823695345557,"Stacked hourglass network has an important model Human pose estimation The estimation human body posture depends the global information of the keypoints type The consistent processing inputs constraints makes form differentiated and determined collaboration mechanisms each stacked hourglass network In this paper a Multi-Scale Stacked Hourglass (MSSH) network high-light the differentiation capabilities each Hourglass network for human pose estimation The pre-processing network forms feature maps different scalesand dispatch them various locations of the stack hourglass network where the small-scale features reach the front stacked hourglass network And a new loss function proposed multi-scale stacked hourglass network Different keypoints have different weight coefficients of loss function at dynamically the top-level hourglass network Experimental results the pro-posed method competitive respect the comparison algorithm on MPII and LSP datasets Human pose estimation need locate the body keypointshead shoulder elbow wrist knee from the input image it basic method some advanced vision task BID4 , such human motion recognition human reidentification et We focus single-person pose estimation problems a single RGB image Due the high flexibility limbs diverse viewpoint, camera projection transformation it still accurately body keypoints fromIn made the human pose estimation; especially the stacked hourglass network BID7 achieved good results attracted The human pose estimation involves two kinds information the type location body keypoints The type body keypoints needs determined a larger receptive field the location based the specific pixel position are respectively equivalent global information The hourglass network uses a convolution layer and form an hourglass structure establish crossover channels on different scales Using the hourglass network for human pose estimation the hourglass structure extracts global information through information compression the crossover channels compensates information compression The stacked hourglass network continuously improves the human pose estimation enhancing the context constraints among body keypoints through the stacked structure theoretically increases the stacked depth expand the receptive field form a stronger context constraints However in practical applications simply increasing the stacked depth difficult effectively improve human pose estimation The main reason the consistent processing inputs constraints makes form differentiated and determined collaboration mechanisms each stacked hourglass network to make up the information loss caused the functional consistency hourglass networks Inspired multi-scale information fusion from the single hourglass network propose A pre-processing network consisting primarily residual networks designed generate multi-scale features features each scale sent different stacked hourglass networks Each hourglass network different inputs: the pre-level hourglass network the received feature Small-scale feature input makes the hourglass network tend focus global information such the type and context constraints body keypoints likely The input entire stacking hourglass network has changed small-scale feature a top-down route body keypoints estimation The iterative relationship the loss functions different scales the MSSH network established so the pre-level detection results affect the weight the next keypoint loss function the optimization process network model training controlled adaptive weighted The iterative relationship the adjacent network loss function established on the MSSH network so the weight pre-level hourglass network affects The optimization process the model training controlled the adaptive weightedThe main contributions this paper can In a multi-scale stacked hourglass network the pre-processing network generates features different scales dispatchs every hourglass network reaches the front From global information to local information each hourglass network can form a differentiated function conducive the formation collaborative processing.• A new loss function of the MSSH network proposed The weighting coefficient the loss function hourglass network defined. The weight coefficient and the loss function the pre-level hourglass network used adjust the convergence process the model training optimized the adaptive weightedThe remainder organized Section briefly reviews recent work human pose estimation Section details the structure the MSSH network Section describes the new loss function MSSH network networks Section describes the implementation details experimental results Section 6 summarizes our paper",0.01,0.2960750490146514
"We present a new unsupervised method for learning general-purpose sentence embeddings.
 Unlike existing methods which rely on local contexts, such as words
 inside the sentence or immediately neighboring sentences, our method selects, for
 each target sentence, influential sentences in the entire document based on a document
 structure. We identify a dependency structure of sentences using metadata
 or text styles. Furthermore, we propose a novel out-of-vocabulary word handling
 technique to model many domain-specific terms, which were mostly discarded by
 existing sentence embedding methods. We validate our model on several tasks
 showing 30% precision improvement in coreference resolution in a technical domain,
 and 7.5% accuracy increase in paraphrase detection compared to baselines. Distributed representations are ever more leveraged to understand text BID20 b; BID16 BID23 . Recently, BID12 proposed a neural network model, SKIP-THOUGHT, that embeds a sentence without supervision by training the network to predict the next sentence for a given sentence. However, unlike human reading with broader context and structure in mind, the existing approaches focus on a small continuous context of neighboring sentences. These approaches work well on less structured text like movie transcripts, but do not work well on structured documents like encylopedic articles and technical reports.To better support semantic understanding of such technical documents, we propose a new unsupervised sentence embedding framework to learn general-purpose sentence representations by leveraging long-distance dependencies between sentences in a document. We observe that understanding a sentence often requires understanding of not only the immediate context but more comprehensive context, including the document title, previous paragraphs or even related articles as shown in Figure 1. For instance, all the sentences in the document can be related to the title of the document (1(a )). The first sentence of each item in a list structure can be influenced by the sentence introducing the list (1(b)) . Moreover , html documents can contain hyperlinks to provide more information about a certain term (1(c)). With the contexts obtained from document structure, we can connect ransomware with payment (1(a)) and the four hashes with Locky (1(b)). In this paper, we presented a novel sentence embedding technique exploiting diverse types of structural contexts and domain-specific OOV words. Our method is unsupervised and applicationindependent, and it can be applied to various NLP applications. We evaluated the method on several NLP tasks including coreference resolution, paraphrase detection and sentence prediction. The results show that our model consistently outperforms the existing approaches confirming that considering the structural context generates better quality sentence representations.",514,0.302,295,1.7423728813559323,"We present learning Unlike existing methods which local contexts such words inside immediately neighboring sentences our selects, influential sentences based a document structure We identify a dependency structure sentences using metadata or text styles Furthermore propose out-of-vocabulary word handling model were mostly discarded existing sentence embedding methods We validate our model several tasks showing 30% precision improvement coreference resolution a technical domain paraphrase detection compared baselines Distributed representations ever leveraged understand text BID20 b; . Recently BID12 proposed a neural network model, SKIP-THOUGHT a sentence without supervision by training for However unlike human reading with broader context structure in the existing approaches focus a small continuous context neighboring sentences These approaches on less structured text like movie transcripts do encylopedic articles technical reportsTo better support semantic understanding such technical documents propose learn general-purpose sentence representations by leveraging long-distance dependencies We observe understanding a sentence often more comprehensive context the document title previous paragraphs or even related articles as shown For instance all the sentences can related1(a ) The first sentence each item a list structure influenced the sentence introducing (1(b Moreover , html documents provide a certain term1(c With the contexts obtained document structure connect ransomware payment (1(a the four hashes with Locky In presented a novel sentence technique exploiting diverse types structural contexts domain-specific OOV words Our method unsupervised applicationindependent various NLP applications We evaluated the method on several NLP tasks including coreference resolution paraphrase sentence The results our model consistently the existing approaches confirming considering the structural context generates better quality sentence representations",0.0,0.595580047210529
"Neural network training relies on our ability to find ````````""good"" minimizers of highly non-convex loss functions. It is well known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce minimizers that generalize better. However, the reasons for these differences, and their effect on the underlying loss landscape, is not well understood.

 In this paper, we explore the structure of neural loss functions, and the effect of loss landscapes on generalization, using a range of visualization methods. First, we introduce a simple ``""filter normalization"" method that helps us visualize loss function curvature, and make meaningful side-by-side comparisons between loss functions. Then, using a variety of visualizations, we explore how network architecture effects the loss landscape, and how training parameters affect the shape of minimizers. Training neural networks requires minimizing a high-dimensional non-convex loss function -a task that is hard in theory, but sometimes easy in practice. Despite the NP-hardness of training general neural loss functions BID0 , simple gradient methods often find global minimizers (parameter configurations with zero or near-zero training loss), even when data and labels are randomized before training BID39 . However, this good behavior is not universal; the trainability of neural nets is highly dependent on network architecture design choices, the choice of optimizer, variable initialization, and a variety of other considerations. Unfortunately, the effect of each of these choices on the structure of the underlying loss surface is unclear. Because of the prohibitive cost of loss function evaluations (which requires looping over all the data points in the training set), studies in this field have remained predominantly theoretical.Our goal is to use high-resolution visualizations to provide an empirical characterization of neural loss functions, and to explore how different network architecture choices affect the loss landscape. Furthermore, we explore how the non-convex structure of neural loss functions relates to their trainability, and how the geometry of neural minimizers (i.e., their sharpness/flatness, and their surrounding landscape), affects their generalization properties.To do this in a meaningful way, we propose a simple ""filter normalization"" scheme that enables us to do side-by-side comparisons of different minima found by different methods. We then use visualizations to explore sharpness/flatness of minimizers found by different methods, as well as the effect of network architecture choices (use of skip connections, number of filters, network depth) on the loss landscape. Out goal is to understand how differences in loss function geometry effect the generalization of neural nets. In this paper, we presented a new, more accurate visualization technique that provided insights into the consequences of a variety of choices facing the neural network practitioner, including network architecture, optimizer selection, and batch size.Neural networks have advanced dramatically in recent years, largely on the back of anecdotal knowledge and theoretical results with complex assumptions. For progress to continue to be made, a more general understanding of the structure of neural networks is needed. Our hope is that effective visualization, when coupled with continued advances in theory, can result in faster training, simpler models, and better generalization. Figure 4 , the first row uses zero weight decay and the second row uses 5e-4 weight decay.Generalization error for each plot is shown in TAB2 10 TEST AND TRAINING DATA FOR VARIOUS NETWORKS FIG0 , the first row uses zero weight decay and the second row sets weight decay to 5e-4.",719,0.333,439,1.6378132118451025,"Neural network training relies our ability find ```````""good"" minimizers of highly non-convex loss functions It well certain network architecture designs produce loss functions train easier, well-chosen training parametersbatch size learning rate optimizer produce minimizers generalize better However the reasons these differences, the underlying loss landscape is In this paper explore the structure neural loss functions the effect loss landscapes generalization, using a range visualization methods First introduce a simple ``""filter normalization"" method helps visualize loss function curvature make meaningful side Then using a variety visualizations explore network architecture effects the loss landscape training parameters minimizers Training neural networks requires minimizing a high-dimensional non-convex loss function -a task hard in theory sometimes easy Despite the NP-hardness training general neural loss functions BID0 , simple gradient methods often find global minimizersparameter configurations with even data and labels randomized before BID39 However this good behavior universal; the trainability neural nets highly network architecture design choices the choice optimizer variable initialization a variety Unfortunately the effect each the structure the underlying loss surface Because loss function evaluationswhich requires looping studies in remained predominantlyOur goal use provide an empirical characterization neural loss functions explore how different network architecture choices the loss landscape Furthermore we explore the non-convex structure neural loss functions relates their trainability how the geometry neural minimizers, their surrounding landscape affects their generalization propertiesTo do in propose a simple ""filter normalization"" scheme enables do side different minima found by different methods We then use visualizations explore sharpness/flatness minimizers found by different methods as network architecture choicesuse skip connections number filters network depth the loss landscape Out goal understand differences loss function geometry effect the generalization neural nets In this paper presented a new, more accurate visualization technique provided insights the consequences a variety choices facing the neural network practitioner network architecture optimizer selection batch sizeNeural networks advanced dramatically largely on anecdotal knowledge theoretical results with complex assumptions For progress to continue a more general understanding neural networks Our hope that effective visualization, when continued advances theory result faster training simpler models Figure , the first row uses zero weight decay 5e-4 weight decayGeneralization error each plot TAB2 10 TEST AND TRAINING DATA FOR VARIOUS NETWORKS FIG0 , sets",0.0,0.32917119580905213
"Deep models are state-of-the-art for many computer vision tasks including image classification and object detection. However, it has been shown that deep models are vulnerable to adversarial examples. We highlight how one-hot encoding directly contributes to this vulnerability and propose breaking away from this widely-used, but highly-vulnerable mapping. We demonstrate that by leveraging a different output encoding, multi-way encoding, we can make models more robust. Our approach makes it more difficult for adversaries to find useful gradients for generating adversarial attacks. We present state-of-the-art robustness results for black-box, white-box attacks, and achieve higher clean accuracy on four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN when combined with adversarial training. The strength of our approach is also presented in the form of an attack for model watermarking, raising challenges in detecting stolen models. Deep learning models are vulnerable to adversarial examples BID19 ]. Evidence shows that adversarial examples are transferable BID14 ; BID11 ]. This weakness can be exploited even if the adversary does not know the target model under attack, posing severe concerns about the security of the models. This is because an adversary can use a substitute model for generating adversarial examples for the target model, also known as black-box attacks.Black-box attacks such as BID4 rely on perturbing input by adding an amount dependent upon the gradient of the loss function with respect to the input of a substitute model. An example adversarial attack is x adv = x + sign(∇ x Loss(f (x)), where f (x) is the model used to generate the attack. This added ""noise"" can fool a model although it may not be visually evident to a human. The assumption of such gradient-based approaches is that the gradients with respect to the input, of the substitute and target models, are correlated.Our key observation is that the setup of conventional deep classification frameworks aids in the correlation of such gradients. Typically, a cross-entropy loss, a soft-max layer, and a one-hot vector encoding for a target label are used when training deep models. These conventions make a model more vulnerable to black-box attacks. This setting constrains the encoding length, and the number of possible non-zero gradient directions at the encoding layer. This makes it easier for an adversary to pick a harmful gradient direction and perform an attack.We aim to increase the adversarial robustness of deep models. Our multi-way encoding representation relaxes the one-hot encoding to a real number encoding, and embeds the encoding in a space that has dimension higher than the number of classes. These encoding methods lead to an increased number of possible gradient directions, as illustrated in Figure 1 . This makes it more difficult for an adversary to pick a harmful direction that would cause a misclassification of a correctly classified point, generating a targeted or untargeted attack. Untargeted attacks aim to misclassify a point, while targeted attacks aim to misclassify a point to a specific target class. Multi-way encoding also helps improve a model's robustness in cases where the adversary has full knowledge of the target model under attack: a white-box attack. The benefits of multi-way encoding are demonstrated in experiments with four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN.We also demonstrate the strength of our approach by introducing an attack for the recent model watermarking algorithm of BID24 , which deliberately trains a model to misclassify (a) (b) (c) Figure 1 : Demonstration of the benefit of relaxing and increasing the encoding dimensionality, for a binary classification problem at the final encoding layer. C i is the codebook encoding for class i, axis s i represents the output activation of neuron i in the output encoding layer, where i = 1, . . . , l and l is the encoding dimensionality. The depicted points are correctly classified points of the green and blue classes. The arrows depict the possible non-zero perturbation directions sign( ∂Loss ∂si ). (a) 2D 1of K softmax-crossentropy setup: Only two non-zero gradient directions exist for a 1of K encoding. Of these two directions, only one is an adversarial direction, depicted in red. (b) 2D multi-way encoding: Four non-zero perturbation directions exist. The fraction of directions that now move a point to the adversarial class (red) drops. (c) 3D multi-way encoding: A higher dimensional encoding results in a significantly lower fraction of gradient perturbations whose direction would move an input from the green ground-truth class to the blue class, or vice versa. certain watermarked images. We interpret such watermarked images as adversarial examples. We demonstrate that the multi-way encoding reduces the transferability of the watermarked images, making it more challenging to detect stolen models.We summarize our contributions as follows:1. We show that the traditional 1of K mapping is a source of vulnerability to adversarial gradients. 2. We propose a novel solution using multi-way encoding to alleviate the vulnerability caused by the 1of K mapping. 3. We empirically show that the proposed approach improves model robustness against both black-box and white-box attacks. 4. We also show how to apply our encoding framework in attacking the recently proposed model watermarking scheme of BID24 .",1090,0.716,640,1.703125,"Deep models state for including However shown deep models vulnerable adversarial examples We highlight how one-hot encoding directly contributes this vulnerability propose breaking away We demonstrate by leveraging a different output encoding multi-way encoding models Our approach makes more adversaries useful gradients generating We present state robustness results black-box, white-box attacks achieve higher clean accuracy four benchmark datasets MNIST SVHN when combined The strength our approach also presented an attack for model watermarking raising challenges detecting stolen models Deep learning models vulnerable adversarial examples BID19 ]. Evidence adversarial examples transferable BID14 ; ]. This weakness even the target model under posing severe concerns the models This because an adversary a substitute model generating adversarial examples also such BID4 rely perturbing input by adding an amount dependent the gradient with of An example adversarial attack x adv sign�� Loss(f where the model used This added ""noise fool a model although visually evident The assumption such gradient-based approaches with, of the substitute and target models correlatedOur key observation the setup conventional deep classification frameworks aids the correlation Typically a cross-entropy loss, a soft-max layer a one-hot vector encoding for a target label when training deep models These conventions make a model more vulnerable This setting constrains the encoding length possible non-zero gradient directions at This makes an adversary pick a harmful gradient direction performWe aim increase deep models Our multi-way encoding representation relaxes the one-hot encoding to a real number encoding embeds dimension higher classes These encoding methods lead possible gradient directions This makes an adversary pick a harmful direction that a correctly classified point generating Untargeted attacks aim misclassify a point while to Multi-way encoding also a model's robustness cases the adversary full knowledge under: The benefits multi-way encoding demonstrated experiments four benchmark datasets MNIST SVHN.We introducing an attack for the recent model watermarking of BID24 , deliberately trains ( (b : Demonstration relaxing and increasing the encoding dimensionality for a binary classification problem at the final encoding layer C i is the codebook encoding class i axis s i represents the output activation neuron i the output encoding layer = . . . , l and is the encoding dimensionality The depicted points correctly classified points the green and blue classes The arrows depict the possible non-zero perturbation directions sign( ��Loss ��si (a 2D 1of K softmax-crossentropy setup Only two non-zero gradient directions exist a 1of K encoding Of these two directions only an adversarial direction depicted red (b 2D multiway encoding: Four non-zero perturbation directions exist The fraction directions now move a point to the adversarial classred drops (c) 3D multi-way encoding: A higher dimensional encoding results gradient perturbations whose direction would move an input the green ground-truth class certain watermarked images We interpret such watermarked images adversarial examples We demonstrate the multi-way encoding reduces the transferability the watermarked images making challenging stolen modelsWe summarize our contributions as We show the traditional 1of K mapping a source vulnerability adversarial gradients 2 We propose using multi-way encoding alleviate caused the 1of K mapping 3 We empirically the proposed approach improves model against 4 We also show apply our encoding framework attacking the recently proposed model watermarking scheme BID24 .",0.01,0.4955798937967658
"Existing approaches to neural machine translation condition each output word on previously generated outputs. We introduce a model that avoids this autoregressive property and produces its outputs in parallel, allowing an order of magnitude lower latency during inference. Through knowledge distillation, the use of input token fertilities as a latent variable, and policy gradient fine-tuning, we achieve this at a cost of as little as 2.0 BLEU points relative to the autoregressive Transformer network used as a teacher. We demonstrate substantial cumulative improvements associated with each of the three aspects of our training strategy, and validate our approach on IWSLT 2016 English–German and two WMT language pairs. By sampling fertilities in parallel at inference time, our non-autoregressive model achieves near-state-of-the-art performance of 29.8 BLEU on WMT 2016 English–Romanian. Neural network based models outperform traditional statistical models for machine translation (MT) BID0 BID9 . However, state-of-the-art neural models are much slower than statistical MT approaches at inference time BID16 . Both model families use autoregressive decoders that operate one step at a time: they generate each token conditioned on the sequence of tokens previously generated. This process is not parallelizable, and, in the case of neural MT models, it is particularly slow because a computationally intensive neural network is used to generate each token.While several recently proposed models avoid recurrence at train time by leveraging convolutions BID6 BID4 or self-attention BID14 as more-parallelizable alternatives to recurrent neural networks (RNNs), use of autoregressive decoding makes it impossible to take full advantage of parallelism during inference.We introduce a non-autoregressive translation model based on the Transformer network BID14 . We modify the encoder of the original Transformer network by adding a module that predicts fertilities, sequences of numbers that form an important component of many traditional machine translation models BID1 . These fertilities are supervised during training and provide the decoder at inference time with a globally consistent plan on which to condition its simultaneously computed outputs.",414,0.199,228,1.8157894736842106,"Existing approaches neural machine translation condition each output word on previously generated outputs We introduce avoids this autoregressive property produces its outputs an order during inference Through knowledge distillation use input token fertilities as a latent variable policy gradient fine-tuning achieve this at relative the autoregressive Transformer network used a teacher We demonstrate substantial cumulative improvements associated each our training strategy validate on IWSLT 2016 English– two WMT language pairs By sampling fertilities parallel at inference time achieves nearstate 29.8 BLEU WMT 2016 English–Romanian Neural network based models outperform machine translation (MT) BID0 BID9 . However state neural models much slower statistical MT approaches at inference time BID16 Both model families use operate one step: generate each token conditioned previously This process parallelizable, neural MT models particularly slow each tokenWhile several recently proposed models avoid recurrence at train time leveraging BID6 BID4 as use makes impossible take during inferenceWe introduce . We modify the original Transformer network predicts fertilities sequences form many traditional machine translation models BID1 . These fertilities supervised during training provide the decoder at inference time a globally consistent plan on condition its simultaneously computed outputs",0.0,0.7826390741517085
"While neural networks have achieved high accuracy on standard image classification benchmarks, their accuracy drops to nearly zero in the presence of small adversarial perturbations to test inputs. Defenses based on regularization and adversarial training have been proposed, but often followed by new, stronger attacks that defeat these defenses. Can we somehow end this arms race? In this work, we study this problem for neural networks with one hidden layer. We first propose a method based on a semidefinite relaxation that outputs a certificate that for a given network and test input, no attack can force the error to exceed a certain value. Second, as this certificate is differentiable, we jointly optimize it with the network parameters, providing an adaptive regularizer that encourages robustness against all attacks. On MNIST, our approach produces a network and a certificate that no that perturbs each pixel by at most $\epsilon = 0.1$ can cause more than $35\%$ test error.
 Despite the impressive (and sometimes even superhuman) accuracies of machine learning on diverse tasks such as object recognition BID18 , speech recognition BID55 , and playing Go BID46 , classifiers still fail catastrophically in the presence of small imperceptible but adversarial perturbations BID50 BID17 BID25 . In addition to being an intriguing phenonemon, the existence of such ""adversarial examples"" exposes a serious vulnerability in current ML systems BID13 BID45 . While formally defining an ""imperceptible"" perturbation is difficult, a commonly-used proxy is perturbations that are bounded in ∞ -norm BID17 BID31 BID53 ; we focus on this attack model in this paper, as even for this proxy it is not known how to construct high-performing image classifiers that are robust to perturbations.While a proposed defense (classifier) is often empirically shown to be successful against the set of attacks known at the time, new stronger attacks are subsequently discovered that render the defense useless. For example, defensive distillation BID42 and adversarial training against the Fast Gradient Sign Method BID17 were two defenses that were later shown to be ineffective against stronger attacks BID53 . In order to break this arms race between attackers and defenders, we need to come up with defenses that are successful against all attacks within a certain class.However, even computing the worst-case error for a given network against all adversarial perturbations in an ∞ -ball is computationally intractable. One common approximation is to replace the worst-case loss with the loss from a given heuristic attack strategy, such as the Fast Gradient Sign Method BID17 or more powerful iterative methods BID7 BID31 . Adversarial training minimizes the loss with respect to these heuristics. However, this essentially minimizes a lower bound on the worst-case loss, which is problematic since points where the bound is loose have disproportionately lower objective values, which could lure and mislead an optimizer. Indeed, while adversarial training often provides robustness against a specific attack, it often fails to generalize to new attacks, as described above. Another approach is to compute the worst-case perturbation exactly using discrete optimization BID21 (b) Figure 1 : Illustration of the margin function f (x) for a simple two-layer network. (a) Contours of f (x) in an ∞ ball around x. Sharp curvature near x renders a linear approximation highly inaccurate, and f (A fgsm (x)) obtained by maximising this approximation is much smaller than f (A opt (x)).(b ) Vector field for ∇f (x) with length of arrows proportional to ∇f (x) 1 . In our approach, we bound f (A opt (x)) by bounding the maximum of ∇f (x) 1 over the neighborhood (green arrow).In general, this could be very different from ∇f (x) 1 at just the point x (red arrow).et al., 2017) . Currently , these approaches can take up to several hours or longer to compute the loss for a single example even for small networks with a few hundred hidden units. Training a network would require performing this computation in the inner loop, which is infeasible.In this paper, we introduce an approach that avoids both the inaccuracy of lower bounds and the intractability of exact computation, by computing an upper bound on the worst-case loss for neural networks with one hidden layer, based on a semidefinite relaxation that can be computed efficiently. This upper bound serves as a certificate of robustness against all attacks for a given network and input. Minimizing an upper bound is safer than minimizing a lower bound, because points where the bound is loose have disproportionately higher objective values, which the optimizer will tend to avoid. Furthermore , our certificate of robustness, by virtue of being differentiable, is trainable-it can be optimized at training time jointly with the network, acting as a regularizer that encourages robustness against all ∞ attacks.In summary, we are the first (along with the concurrent work of BID24 ) to demonstrate a certifiable, trainable, and scalable method for defending against adversarial examples on two-layer networks. We train a network on MNIST whose test error on clean data is 4.2%, and which comes with a certificate that no attack can misclassify more than 35% of the test examples using ∞ perturbations of size = 0.1.Notation. For a vector z ∈ R n , we use z i to denote the i th coordinate of z. For a matrix Z ∈ R m×n , Z i denotes the i th row. For any activation function σ : R → R (e.g., sigmoid, ReLU) and a vector z ∈ R n , σ(z) is a vector in R n with σ(z) i = σ(z i ) (non-linearity is applied element-wise). We use B (z) to denote the ∞ ball of radius around z ∈ R d : B (z) = {z | |z i − z i | ≤ for i = 1, 2, . . . d}. Finally, we denote the vector of all zeros by 0 and the vector of all ones by 1. In this work, we proposed a method for producing certificates of robustness for neural networks, and for training against these certificates to obtain networks that are provably robust against adversaries.Related work. In parallel and independent work, BID24 also provide provably robust networks against ∞ perturbations by using convex relaxations. While our approach uses a single semidefinite program to compute an upper bound on the adversarial loss, Kolter & Wong (2017) use separate linear programs for every data point, and apply their method to networks of depth up to four. In theory, neither bound is strictly tighter than the other, and our experiments TAB2 suggest that the two bounds are complementary. Combining the approaches seems to be a promising future direction. BID21 and the follow-up BID10 also provide certificates of robustness for neural networks against ∞ perturbations. That work uses SMT solvers, which are a tool from the formal verification literature. The SMT solver can answer the binary question ""Is there an adversarial example within distance of the input x?"", and is correct whenever it terminates. The main drawback of SMT and similar formal verification methods is that they are slow-they have worst-case exponential-time scaling in the size of the network; moreover, to use them during training would require a separate search for each gradient step. BID20 use SMT solvers and are able to analyze state-of-the-art networks on MNIST, but they make various approximations such that their numbers are not true upper bounds. BID2 provide tractable certificates but require to be small enough to ensure that the entire ∞ ball around an input lies within the same linear region. For the networks and values of that we consider in our paper, we found that this condition did not hold. Recently, Hein & Andriushchenko (2017) proposed a bound for guaranteeing robustness to p -norm perturbations, based on the maximum p p−1 -norm of the gradient in the -ball around the inputs. BID19 show how to efficiently compute this bound for p = 2, as opposed to our work which focuses on ∞ and requires different techniques to achieve scalability. BID31 perform adversarial training against PGD on the MNIST and CIFAR-10 datasets, obtaining networks that they suggest are ""secure against first-order adversaries"". However, this is based on an empirical observation that PGD is nearly-optimal among gradient-based attacks, and does not correspond to any formal robustness guarantee.Finally, the notion of a certificate appears in the theory of convex optimization, but means something different in that context; specifically, it corresponds to a proof that a point is near the optimum of a convex function, whereas here our certificates provide upper bounds on non-convex functions. Additionally, while robust optimization BID3 provides a tool for optimizing objectives with robustness constraints, applying it directly would involve the same intractable optimization for A opt that we deal with here.Other approaches to verification. While they have not been explored in the context of neural networks, there are approaches in the control theory literature for verifying robustness of dynamical systems, based on Lyapunov functions (Lyapunov, 1892; BID29 . We can think of the activations in a neural network as the evolution of a time-varying dynamical system, and attempt to prove stability around a trajectory of this system BID51 BID52 . Such methods typically use sum-of-squares verification BID38 BID43 and are restricted to relatively low-dimensional dynamical systems, but could plausibly scale to larger settings. Another approach is to construct families of networks that are provably robust a priori, which would remove the need to verify robustness of the learned model; to our knowledge this has not been done for any expressive model families.Adversarial examples and secure ML. There has been a great deal of recent work on the security of ML systems; we provide only a sampling here, and refer the reader to BID0 , BID4 , BID41 , and BID14 for some recent surveys.Adversarial examples for neural networks were first discovered by BID50 , and since then a number of attacks and defenses have been proposed. We have already discussed gradientbased methods as well as defenses based on adversarial training. There are also other attacks based on, e.g., saliency maps BID40 , KL divergence BID33 , and elastic net optimization BID11 ; many of these attacks are collated in the cleverhans repository . For defense, rather than making networks robust to adversaries, some work has focused on simply detecting adversarial examples. However, BID7 recently showed that essentially all known detection methods can be subverted by strong attacks.As explained in BID0 , there are a number of different attack models beyond the testtime attacks considered here, based on different attacker goals and capabilities. For instance, one can consider data poisoning attacks, where an attacker modifies the training set in an effort to affect test-time performance. BID35 , BID26 , and BID5 have demonstrated poisoning attacks against real-world systems.Other types of certificates. Certificates of performance for machine learning systems are desirable in a number of settings. This includes verifying safety properties of air traffic control systems BID21 and self-driving cars (O' Kelly et al., 2016; , as well as security applications such as robustness to training time attacks BID48 . More broadly, certificates of performance are likely necessary for deploying machine learning systems in critical infrastructure such as internet packet routing BID54 BID47 . In robotics, certificates of stability are routinely used both for safety verification BID30 BID32 and controller synthesis BID1 BID51 .In traditional verification work, Rice's theorem BID44 ) is a strong impossibility result essentially stating that most properties of most programs are undecidable. Similarly, we should expect that verifying robustness for arbitrary neural networks is hard. However, the results in this work suggest that it is possible to learn neural networks that are amenable to verification, in the same way that it is possible to write programs that can be formally verified. Optimistically, given expressive enough certification methods and model families, as well as strong enough specifications of robustness, one could even hope to train vector representations of natural images with strong robustness properties, thus finally closing the chapter on adversarial vulnerabilities in the visual domain.",2523,1.233,1444,1.747229916897507,"While neural networks achieved high accuracy on standard image benchmarks drops nearly test inputs Defenses based regularization adversarial training often followed new, stronger attacks defeat Can somehow end In this work study this problem neural networks one hidden layer We first propose based a semidefinite relaxation that outputs a certificate for and test input no attack force the error exceed Second as this certificate differentiable jointly optimize the network parameters providing an adaptive regularizer encourages against all attacks On MNIST our approach produces a network and a certificate no that perturbs each pixel at most $\epsilon = can cause more than $35\%$ test error Despite impressive (and sometimes even superhuman) accuracies machine on diverse tasks object recognition BID18 , speech recognition BID55 playing Go classifiers small imperceptible but BID50 BID17 BID25 In addition an intriguing phenonemon the existence such ""adversarial examples exposes current ML systems BID13 BID45 . While formally defining a commonly-used proxy bounded �� -norm BID17 BID31 BID53 ; we focus this attack model even for this proxy known construct high-performing image classifiersWhile a proposed defense (classifier often empirically shown successful the set attacks known at new stronger attacks subsequently render For example defensive distillation BID42 adversarial training against the Fast Gradient Sign Method BID17 two defenses later stronger attacks BID53 . In order break this arms race attackers come defenses successful withinHowever even computing the worst-case error against an �� -ball is One common approximation replace from a given heuristic attack strategy the Fast Gradient Sign Method BID17 more powerful iterative methods BID7 BID31 Adversarial training minimizes with these heuristics However essentially minimizes a lower bound problematic points where bound loose have disproportionately lower objective values lure and mislead an optimizer Indeed while adversarial training often robustness against generalize described Another approach compute exactly using discrete optimization BID21 (b) Figure : Illustration the margin function f (x (a) Contours f (x an �� ball around Sharp curvature near x renders a linear approximation highly f (A fgsm ( obtained maximising this approximation muchx)).(b ) Vector field for ��f with length of arrows proportional � 1 In our approach bound f (A opt ( bounding the maximum � 1 over the neighborhoodgreen arrow).In general could very different at just the point 2017) . Currently , these approaches take or compute the loss for even small networks a few hundred hidden units Training a network would performing this computation the inner loopIn both the inaccuracy lower bounds exact computation computing neural networks one hidden layer based a semidefinite relaxation that efficiently This upper bound serves a certificate robustness against all attacks for input Minimizing an upper bound safer points where loose have disproportionately higher objective values the optimizer tend Furthermore , our certificate robustness, by differentiable trainable-it optimized at training time jointly acting that encourages against all �� attacksIn are the (along the concurrent work BID24 defending adversarial examples on We train a network on MNIST whose test error on clean data comes a certificate no attack misclassify more than 35% the test examples using �� perturbations size = 0.1.Notation. For a vector z �� R n use z i i th For a matrix Z �� R m×n Z i denotes i th row For any activation function �� : R → R( in inon applied element We use B (z the �� ball radius around z �� R d : B { | |z i ≤ for . . . d}. Finally denote the vector 0 In this work proposed producing certificates robustness neural networks for training against obtain networks provably adversariesRelated work. In parallel and independent work BID24 also provide provably robust networks against �� perturbations convex relaxations While our approach uses a single semidefinite program the adversarial loss Kolter & Wong2017 separate linear programs every data point apply networks depth up four In theory neither bound strictly tighter our experiments TAB2 suggest the two bounds complementary Combining the approaches seems a promising future direction BID21 and also certificates robustness neural networks against �� perturbations That work uses SMT solvers a tool from the formal verification literature The SMT solver answer the binary question an adversarial example within distance x correct whenever terminates The main drawback SMT and similar formal verification methods slow-they have worst-case exponential-time scaling in the size; moreover to during training would a separate search each gradient step BID20 use SMT solvers are analyze state networks MNIST but make such their numbers true upper bounds BID2 provide tractable certificates but to small ensure the entire �� ball around an input lies the same linear region For the networks values that we consider our paper found this condition did Recently Hein & Andriushchenko2017 bound for guaranteeing robustness p -norm perturbations based the maximum p p−1 -norm of the gradient the -ball around the inputs BID19 show efficiently compute this bound for p as our work which focuses �� requires different techniques scalability BID31 perform adversarial training against PGD on the MNIST and CIFAR-10 datasets obtaining networks they suggest ""secure against first-order adversaries However based PGD nearly- among gradient-based attacks does correspond any formal robustness guaranteeFinally the notion a certificate appears the theory convex optimization means something that context; specifically corresponds near the optimum here our certificates provide upper bounds Additionally while robust optimization BID3 provides a tool objectives with robustness constraints applying directly would involve for A opt that dealOther approaches verification. While they explored neural networks approaches the control theory literature verifying robustness dynamical systems based Lyapunov functions 1892 BID29 . We think the activations the evolution attempt prove stability around a trajectory BID51 BID52 Such methods typically sum verification BID38 BID43 restricted could scale larger settings Another approach construct families networks provably robust a remove verify robustness the learned model; to our knowledge any expressive model familiesAdversarial examples and secure ML. There recent work the security ML systems; provide only a sampling here refer BID0 , some recent surveysAdversarial examples neural networks were discovered BID50 since attacks defenses We already gradientbased methods as defenses based adversarial training There also other attacks based, saliency maps BID40 , KL divergence elastic net optimization many collated the cleverhans repository For defense rather making networks robust adversaries some work simply detecting adversarial examples However BID7 recently showed essentially all known detection methods subverted strong attacksAs explained BID0 , different attack models beyond the testtime attacks considered based different attacker goals capabilities For instance one consider data poisoning attacks the training set affect test-time performance BID35 , demonstrated poisoning attacks real-world systemsOther types certificates. Certificates performance desirable settings This includes verifying safety properties air traffic control systems BID21O' Kelly , as security applications robustness training time attacks BID48 . More broadly certificates performance likely necessary deploying critical infrastructure such internet packet routing BID54 BID47 . In robotics certificates stability routinely both safety verification BID30 BID32 controller synthesis BID51 .In traditional verification work Rice theorem BID44 ) a strong impossibility result essentially stating most properties most programs Similarly verifying robustness for arbitrary neural networks hard However in this work learn amenable verification write programs formally Optimistically given expressive enough certification methods model families as strong enough specifications of one even hope train vector representations natural images strong robustness properties thus finally closing the chapter adversarial vulnerabilities",0.02,0.6079553470359846
"We formulate an information-based optimization problem for supervised classification. For invertible neural networks, the control of these information terms is passed down to the latent features and parameter matrix in the last fully connected layer, given that mutual information is invariant under invertible map.   We propose an objective function and prove that it solves the optimization problem. Our framework allows us to learn latent features in an more interpretable form while improving the classification performance. We perform extensive quantitative and qualitative experiments in comparison with the existing state-of-the-art classification models. Quantities of information are nonlinear measures capable of describing complex relationship between unstructured data and they form the basis of the probabilistic algorithms in the literature of machine learning. Information theoretic methods are also reported to be effective on improving deep generative models BID6 ; Kim & Mnih (2018) ) and deep learning models for classification (Grandvalet & Bengio (2004) ; Pereyra et al. (2017) ). Information Bottleneck (IB) problem BID12 ) is formulated as: DISPLAYFORM0 where the solution random variable T is interpreted as a minimal sufficient representation of signal X for label Y and the mutual information is defined as DISPLAYFORM1 p(x, y) log p(x, y) p(x)p(y ) dydx .The term I(X; T ) has its origins in Lossy Compression and Rate-Distortion Theory (Cover & BID7 , conveying an simple idea of ""keep only what is relevant"".However, Saxe et al. (2018) argued that the mutual information I(X; T ) between signal X and feature T in intermediate layer is infinite, as the transformation from X to continuous random variable T is deterministic. In addition they showed experimentally that layers equipped with ReLU actually do not compress too much information, which is supported by many recent work on the invertibility of the neural network BID8 ; Jacobsen et al. (2018) ). This motivates us to consider a different problem with similar principle idea: we would like to establish a theoretically valid objective that allows the neural network to extract only the relevant information for classification from the data.We focus on the discrete prediction random variable Y inferred by the probabilistic model P( Y |X) and introduce the following information optimization problem for supervised classification:maximize I(Y ; Y ) subject to I(X; Y ) − I(Y ; Y ) < τ , for some τ > 0 .The intuition behind this objective lies in twofold:Information perspective: A good classification model should be robust against irrelevant features of X, and prevent over-fitting in the learning process. In optimization problem (3) we maximize the relevant information I(Y ; Y ), while constraining the irrelevant information I(X; Y ) − I(Y ; Y )that X has about Y . Although I(X; Y ) − I(Y ; Y ) converges to zero as I(Y ; Y ) approaching its maximum (see FIG0 ), in practice it's never attained due to the limited capacity of the models or over-fitting. Our proposed constrain addresses the problem of over-fitting: if two models achieve the similar classification accuracy, this constraint prefers the one that does not overfit to spurious factors of variation in X (e.g., pixel-level artifact/noise in the image that accidentally correlates to the labels in the training data).Prediction confidence perspective : A good classification model should not be certain about its decision which is in fact wrong. However, modern neural networks are too confident in their predictions (Guo et al., 2017; Szegedy et al., 2015; Pereyra et al., 2017) . To be more precise, high capacity neural networks mostly assign labels of data with prediction confidence near 0 or 1. In particular, they assign 0 probability to some correct labels and therefore do not have enough flexibility to correct themselves from making the wrong prediction. We propose to compress the irrelevant information I(X; Y ) − I(Y ; Y ), where minimizing I(X; Y ) decreases the confidence on all predictions but maximizing I(Y ; Y ) increases the confidence on the correct predictions. Therefore the overall effect reduces the certainty on the false prediction of Y (see FIG0 ).To solve this optimization problem, we first present some insights on the dynamics of deep neural network, which can be decomposed into two stages: (i) Transformation stage: samples {X k } k=1:n of the high dimensional unstructured signal X are transformed under the deep invertible (information preserving) feature map F to become (almost) linearly separable; (ii) Classification stage: the weight matrix w in the last fully connected layer together with the Softmax function, takes structured features {F (X k )} k=1:n as input and gives predictions.Invertibility of F allows neural networks to pass the control of I(X; Y ) = I(F (X); Y ) towards F (X) and w in the last layer, where F (X) can be interpreted as transformed signal that preserves information about the original signal X and the inference model becomes conceptually linear with classifier w (see FIG0 ). In Section 2 we derive objective function (7) and prove that it solves the optimization problem (3). We show the classification performance is improved in Section 4.1 and the features F (X) are sculpted into a form with more interpretability entry-wise in Section 4.2. . The optimal solution is obtained when the smaller disks coincide , which is typically not achieved in practice. In particular, the trained model may be extremely confident in its prediction (when H( Y ) lies inside of H(X)), but predicts the wrong label (having large grey area). Our optimization problem explicitly prohibits the growth of grey area throughout the training. (R) Logic chart of our formulation: our proposed optimization problem only involves F (X) and w, allowing us to have control over the latent feature F (X) directly.The invertibility property has been empirically demonstrated for complex non-linear deep neural networks that are widely used in practice. We will discuss the literature in Section 3. In addition, we prove in Proposition C.1 that a lower bound of classification error is minimized if neural network is invertible.Our contribution: Our contribution lies in the following: (i) we formulated a novel information optimization problem for supervised classification; (ii) we propose a simple objective function that improves supervised deep learning with better performance and interpretability; (iii) we formally justify the use of 1 , 2 regularization from an information perspective. Different from the naive regularization on w, our regularization on w T F (X) is novel and effective. We give an interpretation of the deep learning dynamics by decomposing it into an signal transformation stage and feature classification stage, where we emphasis importance of the classifier w in the last fully connected layer given that the feature map F is invertible. Then we take the advantage of the fact that mutual information quantities are invariance under invertible mapping to attack our proposed information optimization problem for supervised classification in deep learning. Our theory justifies the use of direct regularization terms on w, F (X) for neural networks with invertibility property. Our regularization improves the performance of neural networks by a noticeable margin and is capable of encouraging the interpretability of the entries of features learned in the last layer.A PROOF OF PROPOSITION 2.1 Proposition 2.1 establishes a connection between I(X, Y ) and the absolute value of the logits |w T F (X)| for the binary case. Intuitively, decreasing the confidence of the model on its predictions will decrease the mutual information I(X; Y ).Proposition 2.1. I(X; Y ) = I(F (X); Y ) is well estimated by its empirical version (Montecarlo approximation) with high probability, which shares the same unique (global) minimum with DISPLAYFORM0 The mutual information I(X; Y ) is given as DISPLAYFORM1 Apply the assumption (II), the marginal distribution of Y is uniformly distributed: DISPLAYFORM2 Substituting FORMULA16 into FORMULA15 yields DISPLAYFORM3 According to the Hoeffding's inequality for bounded random variables [Proposition 2.2.6, Vershynin FORMULA0 ], let M, m denote upper and lower bounds of the integrand of (10) correspondingly, we have DISPLAYFORM4 Equivalently, with probability at least 1 − δ, DISPLAYFORM5 Here n k=1 y∈C p( y|x k ) log(2p( y|x k ))/n is a Monte carlo estimation of RHS of I(X; Y ). Recall that , for the binary case p( y|x) = p( y|F (x)) can expressed as DISPLAYFORM6 Then we have DISPLAYFORM7 which is bounded by [0, log(2)].Take M = log(2 ), m = 0, we have DISPLAYFORM8 hold with probability at least 1 − δ.The conclusion follows from the fact that n k=1 y∈C p( y|x k ) log(2p( y|x k ))/n has a unique global minimum at w T F (x k ) = 0 for each x k .",1894,0.715,1090,1.7376146788990825,"We formulate an information-based optimization problem supervised classification For invertible neural networks the control these information terms passed the latent features parameter matrix in the last fully connected layer given mutual information under invertible map We propose an objective function and prove solves Our framework learn latent features an more interpretable form while improving the classification performance We perform comparison state classification Quantities information nonlinear measures capable complex relationship they form of Information theoretic methods also reported on improving deep generative models BID6 ; Kim & Mnih (2018 ) deep learning models classificationGrandvalet Bengio2004 Pereyra (2017 ). Information Bottleneck (IB) problem BID12 ) is formulated: DISPLAYFORM0 where the solution random variable T interpreted a minimal sufficient representation signal X label Y the mutual information defined p(x log ) dydx .The term I(X; T ) has its origins Lossy Compression and Rate-Distortion TheoryCover & BID7 , conveying an simple idea ""keep only whatHowever, Saxe et al (2018 argued the mutual information I(X; T ) between signal X feature T in intermediate layer infinite the transformation continuous random variable T In addition they showed experimentally layers equipped ReLU actually do compress too much information supported many recent work the invertibility BID8 ; Jacobsen (2018 ). This motivates consider a different problem with similar principle idea would establish a theoretically valid objective allows the neural network extract classification fromWe focus the discrete prediction random variable Y inferred P Y |X introduce the following information optimization problem supervised classificationmaximize I(Y ; subject < τ , for some τ > 0 .The intuition this objective lies twofoldInformation perspective A good classification model robust irrelevant features X prevent over In optimization problem (3 maximize the relevant information I(Y ; while constrainingthat X about Although I(X; Y ) − ; converges as approaching FIG0 in's never attained due the limited capacity the models or over Our proposed constrain addresses the problem overfitting: if two models achieve the similar classification accuracy this constraint prefers does spurious factors variation X in that accidentally correlates the labels the training data).Prediction confidence perspective : A good classification model certain its decision which in wrong However modern neural networks too confident (Guo 2017 Szegedy Pereyra . To more high capacity neural networks mostly assign labels of data with prediction confidence near or In particular they assign 0 probability some correct labels therefore enough flexibility correct themselves from making We propose compress the irrelevant information I(X; ) ; where minimizing decreases the confidence on all predictions but maximizing Therefore the overall effect reduces the certainty on the false prediction Y ( FIG0 ).To solve present some insights deep neural network, samples {X k k=1:n of the high dimensional unstructured signal X are under the deep invertible (information preserving) feature map F to becomealmost the weight matrix w in the last fully connected layer together the Softmax function takes structured features as gives predictionsInvertibility of F allows pass the control I(X; ) = towards w can interpreted transformed signal that preserves the inference model becomes conceptually linear classifier w In Section we derive objective function7 prove solves3 We show the classification performance is improved Section the features F (X sculpted a form more interpretability entrywise . The optimal solution obtained the smaller disks coincide , typically achieved In particular the trained model may extremely confident (when H( Y lies inside predicts the wrong labelhaving large grey area Our optimization problem explicitly prohibits the growth grey area throughout (R Logic chart our formulation our proposed optimization problem only F (X w allowing have control directlyThe invertibility property has that widely practice We discuss the literature Section In addition prove in Proposition C.1 a lower bound classification error minimized neural network invertibleOur contribution: Our contribution lies ( formulated a novel information optimization problem supervised classification; propose a simple objective function improves supervised deep learning interpretability formally justify 1 , 2 regularization from an information perspective Different the naive regularization on w, on w T FX novel effective We give an interpretation the deep learning dynamics by an signal transformation stage feature emphasis importance the classifier w the last fully connected layer given F Then take the advantage mutual information quantities invariance under invertible mapping to attack our proposed information optimization problem for supervised classification in Our theory justifies direct regularization terms on w, FX for neural networks invertibility property Our regularization improves a noticeable margin capable encouraging the interpretability the entries features learned the last layerA PROOF OF Proposition establishes a connection I(X ) the absolute value the logits |w T F (X)| the binary case Intuitively decreasing the confidence the model on decrease the mutual information I(X; ).Proposition ( is well estimated its empirical versionMontecarlo approximation high probability shares the same unique (global) minimum with DISPLAYFORM0 The mutual information I(X given ApplyII the marginal distribution Y uniformly: FORMULA16 into According the Hoeffding's inequality for bounded random variables [Proposition Vershynin FORMULA0 let M, m denote the integrand (10 correspondingly we with probability Here n k=1 y�C p( y|x k log(2p/n a Monte carlo estimation RHS Recall , for the binary case p y|x y|F ( can expressed DISPLAYFORM6 Then bounded [ log(2)].Take M m 0 we hold with probability at − � conclusion follows n k=1 y�C p log(2p/n has a unique global minimum at w T F",0.01,0.5834565654015728
"Powerful generative models, particularly in Natural Language Modelling, are commonly trained by maximizing a variational lower bound on the data log likelihood. These models often suffer from poor use of their latent variable, with ad-hoc annealing factors used to encourage retention of information in the latent variable. We discuss an alternative and general approach to latent variable modelling, based on an objective that encourages a perfect reconstruction by tying a stochastic autoencoder with a variational autoencoder (VAE). This ensures by design that the latent variable captures information about the observations, whilst retaining the ability to generate well. Interestingly, although our model is fundamentally different to a VAE, the lower bound attained is identical to the standard VAE bound but with the addition of a simple pre-factor; thus, providing a formal interpretation of the commonly used, ad-hoc pre-factors in training VAEs. Generative latent variable models are probabilistic models of observed data x of the form p(x, z) = p(x|z)p(z), where z is the latent variable. These models are widespread in machine learning and statistics. They are useful both because of their ability to generate new data and because the posterior p(z|x) provides insight into the low dimensional representation z corresponding to the high dimensional observation x. These latent z values are then often used in downstream tasks, such as topic modelling BID2 , multi-modal language modeling BID8 , and image captioning BID9 BID10 .Latent variable models, particularly in the form of Variational Autoencoders (VAEs) BID7 BID11 , have been successfully employed in natural language modelling tasks using varied architectures for both the encoder and the decoder BID0 BID2 BID12 BID16 BID13 . However , an architecture that is able to effectively capture meaningful semantic information into its latent variables is yet to be discovered.A VAE approach to language modelling was given by BID0 , the graphical model for which is shown in FIG0 (a). This forms a generative model p(x|z)p(z) of sentence x, based on latent variable z. Since the integral p(x) = p(x|z)p(z)dz is typically intractable, a common approach is to maximize the Evidence Lower Bound (ELBO) on the log likelihood, log p(x) ≥ log p(x|z) q(z|x) − D KL [q(z|x)||p(z)]where · q(z|x) is the expectation with respect to the variational distribution q(z|x), and D KL [·||·] represents the Kullback-Leibler (KL) divergence. Summing over all datapoints x gives a lower bound on the likelihood of the full dataset.In language modelling, typically both the generative model (decoder) p(x|z), and variational distribution (encoder) q(z|x), are parameterised using an LSTM recurrent neural networksee for example BID0 . This autoregressive generative model is so powerful that the maximum ELBO is achieved without making appreciable use of the latent variable in the model. Indeed, if trained using the SGVB algorithm BID7 , the model learns to ignore the latent representation and effectively relies solely on the decoder to generate good sentences. This is evidenced by the KL term in the objective function converging to zero, indicating that the approximate posterior distribution of the latent variable is trivially converging to its prior distribution.The dependency between what is represented by latent variables, and the capacity of the decoding distribution (i.e., its ability to model the data without using the latent) is a general phenomenon. BID16 used a lower capacity dilated CNN decoder to generate sentences, preventing the KL term going to zero. BID3 ; BID4 have discussed this in the context of image processing. A clear explanation of this phenomenon in terms of Bit-Back Coding is given in BID1 .A mechanism to avoid the model ignoring the latent entirely, while allowing a high capacity decoder is discussed in BID0 and uses an alternative training procedure called ""KL annealing"" -slowly turning on the KL term in the ELBO during training. KL annealing allows the model to use its latent variable to some degree by forcing the model into a local maximum of its objective function. Modifying the training procedure in this way to preferentially obtain local maxima suggests that the objective function used in BID0 may not be ideal for modelling language in such a way as to create a model that leverages its latent variables. We have seen that AutoGen successfully improves the fidelity of reconstructions from the latent variable as compared to VAEs. It does so in a principled way, by explicitly modelling both generation of the data and high-fidelity reconstruction. This is especially useful when the generative model is powerful, such as the autoregressive LSTM in BID0 .Other work toward enabling latent variables in VAE models to learn meaningful representations has focused on managing the structure of the representation, such as ensuring disentanglement. A detailed discussion of disentanglement in the context of VAEs is given by BID4 and its references. An example of disentangling representations in the context of image generation is BID3 , where the authors restrict the decoding model to describe only local information in the image (e.g., texture, shading), allowing their latents to describe global information (e.g., object geometry, overall color).Demanding high-fidelity reconstructions from latent variables in a model (e.g., AutoGen) is in tension with demanding specific information to be stored in the latent variables (e.g., disentanglement). This can be seen very clearly by comparing our work to BID4 , where the authors introduce an ad-hoc factor of β in front of the KL-divergence term of the VAE objective function, the ELBO. They find that β > 1 is required to improve the disentanglement of their latent representations.Interestingly, β > 1 corresponds analytically to −1 < m < 0 in Equation 9, since the overall normalization of the objective function does not impact the location of its extrema. That is, Equation 9 is equivalent to the β-VAE objective function with β = (1 + m) −1 .Since m in AutoGen represents the number of times a high-fidelity reconstruction is demanded (in addition to a single generation from the prior), β-VAE with β > 1 is analytically equivalent to demanding a negative number of high-fidelity reconstructions. As an analytic function of m, with larger m corresponding to higher-fidelity reconstructions, negative m would correspond to a deprecation of the reconstruction quality. This is indeed what the authors in BID4 find and discuss. They view β-VAE as a technique to trade off more disentangled representations at the cost of lower-fidelity reconstructions, in contrast to our view of AutoGen as a technique to trade off higher-fidelity reconstructions at the cost of slightly inferior generation from the prior.In connecting to β-VAE, we have considered AutoGen with m as a real number. Practically, m could take positive real values, and can be seen as a hyperparameter that requires taskspecific tuning. From our results, we expect m ≈ 1 to be a useful ballpark value, with smaller m improving generation from the prior, and larger m improving reconstruction fidelity. The advantage of tuning m as described is that it has a principled interpretation at integer values; namely that of demanding m exact reconstructions from the latent, as derived in Section 2.In this light, KL annealing amounts to starting with m = ∞ at the beginning, and smoothly reducing m down to 0 during training. Thus, it is equivalent to optimizing the AutoGen lower bound given in Equation 9 with varying m during training. However, AutoGen should never require KL annealing.Scaling of the ELBO is common in multimodal generation, where the reconstruction terms are typically of different orders of magnitude BID14 BID15 . AutoGen can be adapted to provide a bound on a meaningful objective function in multimodal generation with well-scaled terms, by requiring a larger number of reconstructions for one data modality than the other. Autogen thus has broader applications in generative modelling, which the authors leave to future work. In this paper, we introduced AutoGen: a novel modelling approach to improve the descriptiveness of latent variables in generative models, by combining the log likelihood of m high-fidelity reconstructions via a stochastic autoencoder, with the log likelihood of a VAE. This approach is theoretically principled in that it retains a bound on a meaningful objective, and computationally amounts to a simple factor of (1 + m) in front of the reconstruction term in the standard ELBO. We find that the most natural version of AutoGen (with m = 1) provides significantly better reconstructions than the VAE approach to language modelling, and only minimally deprecates generation from the prior.",1811,0.771,1001,1.809190809190809,"Powerful generative models particularly Natural Language Modelling commonly trained maximizing a variational lower the data log likelihood These models often suffer poor use their latent variable with ad-hoc annealing factors used encourage retention information We discuss an alternative and general approach latent variable modelling an objective that encourages a perfect reconstruction by tyingVAE This ensures by design the latent variable captures information the observations whilst generate well. Interestingly although our model fundamentally a VAE lower bound attained identical standard bound but a simple prefactor; thus providing a formal interpretation training VAEs Generative latent variable models observed data x of z These models widespread machine learning statistics They useful both because generate posterior p(z|x provides insight the low dimensional representation z corresponding x. These latent z values then often downstream tasks topic modelling BID2 image .Latent variable models particularly successfully varied architectures both the encoder However , an architecture able effectively capture meaningful semantic information into its latent variables yetA VAE approach language modelling was given BID0 the graphical model which shown FIG0 ( This forms a generative model p(x|z)p(z of sentence x based latent variable Since the integral p(x = typically intractable a common approach maximize Evidence LowerELBO on the log likelihood log ≥ − D KL [ the expectation with·|| represents Kullback ( divergence Summing over x gives lower the full datasetIn language modelling typicallydecoder) p(x|z variational distribution parameterised networksee BID0 . This autoregressive generative model so the maximum ELBO is achieved without making appreciable use Indeed trained using the SGVB algorithm BID7 , learns ignore the latent representation effectively relies solely good sentences This evidenced the KL term in the objective function converging zero indicating the approximate posterior distribution trivially converging its prior distributionThe dependency what represented the capacity the decoding distribution model without using) a general phenomenon BID16 used a lower capacity dilated CNN decoder sentences preventing the KL term going zero BID3 ; have discussed image processing A clear explanation in Bit-Back Coding BID1 .A mechanism avoid the model ignoring the latent entirely while a high capacity decoder is uses an alternative training procedure ""KL annealing -slowly turning the KL term the ELBO during KL annealing allows the model use its latent variable some degree by forcing a local maximum its objective function Modifying the training procedure to obtain local maxima suggests the objective function used BID0 may ideal modelling language create leverages its latent variables We AutoGen successfully improves the fidelity reconstructions the latent variable as VAEs explicitly modelling both generation This especially useful the generative model powerful in BID0 .Other work toward enabling latent variables VAE models to learn meaningful representations managing the structure ensuring A detailed discussion disentanglement VAEs by BID4 its references An example disentangling representations image generation BID3 , the authors restrict the decoding model describe only local information texture shading allowing their latents describe object geometry overall color).Demanding high-fidelity reconstructions from latent variables AutoGen in tension demanding specific information to stored This can very our work BID4 , introduce β in front the KL-divergence term of the VAE objective function the ELBO. They find β > required improve their latent representationsInterestingly corresponds analytically < m in Equation 9 since the overall normalization the objective function does impact the location its extrema That Equation 9 equivalent β-VAE objective function with m .Since m in AutoGen represents times a high-fidelity reconstruction demandedin addition a single generation from prior with > demanding a negative number As an analytic function m with larger corresponding negative would the reconstruction quality This indeed the authors in BID4 find and discuss They view β-VAE a technique trade more disentangled representations at in our view AutoGen slightly inferior generation from priorIn connecting to considered AutoGen with m as a real number Practically m could take positive real values can seen requires taskspecific tuning From our results expect m � a useful ballpark value smaller m improving generation from prior, reconstruction fidelity The advantage tuning m as described a principled interpretation at integer values; namely that of demanding m exact reconstructions the latent, as derived in Section 2.In light KL annealing amounts starting m at smoothly reducing m down during training Thus equivalent optimizing the AutoGen lower given in 9 with varying m during training However AutoGen should never require KL annealingScaling the ELBO common multimodal generation the reconstruction terms typically of different orders magnitude BID14 BID15 . AutoGen can adapted provide a bound on a meaningful objective function multimodal generation with well-scaled terms by requiring reconstructions one data modality Autogen thus has broader applications generative modelling the authors leave In introduced AutoGen: a novel modelling approach improve the descriptiveness latent variables combining the log likelihood m high-fidelity reconstructions via a VAE This approach theoretically principled retains a bound on a meaningful objective computationally amounts a simple factor of ( m front the reconstruction term in the standard ELBO We find the most natural version AutoGen (with m = provides significantly better reconstructions the VAE approach to language modelling only generation from prior",0.01,0.7658262567748448
"This paper studies the problem of domain division which aims to segment instances drawn from different probabilistic distributions. This problem exists in many previous recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL), where the testing instances come from either seen or unseen/novel classes with different probabilistic distributions. Previous works only calibrate the confident prediction of classifiers of seen classes (WSVM Scheirer et al. (2014)) or taking unseen classes as outliers Socher et al. (2013). In contrast, this paper proposes a probabilistic way of directly estimating and fine-tuning the decision boundary between seen and unseen classes. In particular, we propose a domain division algorithm to split the testing instances into known, unknown and uncertain domains, and then conduct recognition tasks in each domain. Two statistical tools, namely, bootstrapping and KolmogorovSmirnov (K-S) Test, for the first time, are introduced to uncover and fine-tune the decision boundary of each domain. Critically, the uncertain domain is newly introduced in our framework to adopt those instances whose domain labels cannot be predicted confidently. Extensive experiments demonstrate that our approach achieved the state-of-the-art performance on OSL and G-ZSL benchmarks. This paper discusses the problem of learning to separate two domains which include the instances sampled from different distributions. This is a typical and general research topic that can be potentially used in various recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL). Particularly, OSL can break the constraints of the closed set in supervised learning, and aim at recognizing the testing instances from one of the seen classes (i.e., known domain), and the novel class (i.e., unknown domain). The novel classes include the testing instances which have different distributions from that of the seen ones. In contrast, G-ZSL targets at distinguishing the labels of instances from the seen and unseen classes. Only the seen classes have the training instances, but unseen classes do not. Note that OSL does not explicitly give the class labels for those instances categorized as the novel class, but G-ZSL requires predicting the class labels of unseen classes. To address G-ZSL, semantic attributes or vectors are introduced as the intermediate representations; each (seen/unseen) class has one semantic prototype that contains class level information. Specifically, a reasonable solution of OSL and G-ZSL is via dividing the known and unknown domains. For training classes, the predictors are constructed to map visual features to the class label space (OSL), (or semantic space (G-ZSL)). Testing is performed on each separated domain to identify seen classes and the novel class (OSL), or both seen and unseen classes (G-ZSL).The key question of OSL and ZSL is how to deal with the newly introduced novel class/unseen classes efficiently in the testing time. This is different from the conventional Zero-Shot Learning (ZSL) task which assumes that, in the testing stage, seen classes would not be misclassified as unseens, and vice versa; ZSL only uses the unseen classes for testing. Unfortunately , the predictors learned on training classes will inevitably make OSL or G-ZSL approaches tend to be biased towards the seen classes, and thus leading to very poor classification results for the novel class (OSL) or unseen classes (G-ZSL) BID39 ; . We show an example in Fig. 1 . On aPY dataset (described in Sec. 6.1) BID10 ), t-SNE van der Maaten & Hinton (2008 is The initial boundary of the known domain is estimated by bootstrapping. We can further divide an uncertain domain by K-S Test. Then we can recognize instances in each domain. (b) The distribution of pairwise intraclass and interclass distances: We compute the empirical density of the pairwise distance in aPY dataset (described in Sec. 6.1). There is a large overlapping of the distribution of the intraclass and interclass distances.employed to visualize the distributions of the testing instances of the ResNet-101 features in BID39 (Fig. 1 (a) ), and semantic features learned by SAE Kodirov et al. (2017) (Fig. 1 (b) ). We categorize the SAE prediction as known or unknown domain labels and compare with the groundtruth in Fig. 1(c) . We show that a large portion of unseen instances being predicted as one of the known classes.A natural recipe for addressing this problem is to learn to separate domains by the distributions of instances; and different classifiers can be directly applied in each domain. However, there are still two key problems. First , visual features alone are not discriminative enough to help to distinguish the seen and unseen/novel classes. As Fig. 2 (a) , bicycle and motorbike, respectively , are one of the seen and unseen classes 1 in aPY dataset (described in Sec. 6.1). We can observe that there is a large overlapping region between their t-SNE visualized feature distributions. That is, the visual features may not be representative enough to differentiate these two classes; the instances of motorbike (circled as the uncertain domain) may be taken as the bicycle, or vice versa; Second, the predictors trained on seen classes may be not trustworthy. A not well-trained predictor may negatively affect the recognition algorithms. Third and even worse, the performance of classifiers in each domain is still very sensitive to the results of domain separation: should the domain of one testing instance be wrongly divided, it would never be correctly categorized by the classifiers.To tackle the aforementioned issues, our key insight (see Fig. 2(a) ) is to introduce a novel domain -uncertain domain that accounts for the overlapping regions of testing instances from seen or novel/unseen classes. Thus, the visual or semantic space can be learned to be divided into known, unknown and uncertain domains. The recognition algorithms will be directly employed in each domain . Nonetheless, how to divide the domains based on known information is also a non-trivial task. Though the supervised classifiers can learn the patterns of known classes, not all classes encountered during testing are known.Formally, we propose exploiting the distribution information of seen and novel/unseen classes to efficiently learn to divide the domains from a probabilistic perspective. Our domain separation algorithm has two steps: the initial division of domains by bootstrapping, and fine-tuning by the Kolmogorov-Smirnov test. Specifically, according to extreme value theory BID30 , the maximum/minimum confidence scores predicted by the classifier of each class can be taken as an extreme value distribution. Since we do not have the prior knowledge of the underlying data distributions of each class; bootstrapping is introduced here as an asymptotically consistent method in estimating an initial boundary of known classes. Nevertheless, the initial boundary estimated by bootstrapping is too relaxed to include novel testing instances as is illustrated in Fig. 2(b) . To finetune the boundary, we exploit the K-S Test to validate whether the learned predictors are trustworthy in a specific region. The uncertain domain introduced thus accounts for those testing instances whose labels are hard to be judged. Recognition models can be conducted in each domain. This paper learns to divide the instances into known, unknown and uncertain domains for the recognition tasks from a probabilistic perspective. The domain division procedure consists of bootstrapping and K-S Test steps. The bootstrapping is used to set an initial threshold for each class; we further employ the K-S test to fine-tune the boundary. Such a domain division algorithm can be used for OSL and G-ZSL tasks, and achieves remarkable results.",1592,1.041,953,1.670514165792235,"This paper studies domain division which aims segment instances drawn This problem many previous recognition tasks Open Set Learning Generalized Zero-Shot Learning the testing instances come either seen or unseen/novel classes with Previous works only calibrate the con���dent prediction classi���ers of seen classesWSVM Scheirer (2014 or taking unseen classes as outliers Socher et (2013 In contrast this paper directly ��ne- the decision boundary seen and unseen classes In particular propose a domain division split the testing instances known, unknown and uncertain domains conduct recognition tasks Two statistical tools namely Test for the ���rst time introduced uncover ���ne-tune the decision boundary Critically the uncertain domain newly introduced our framework adopt those instances whose domain labels predicted con���dently Extensive experiments demonstrate our approach achieved state on OSL G-ZSL benchmarks This paper learning separate two domains which include the instances sampled different distributions This a typical and general research topic potentially various recognition tasks Open Set Learning Generalized Zero-Shot Learning Particularly OSL break the constraints the closed set supervised learning aim recognizing the testing instances from one the seen classes the novel class The novel classes include the testing instances which different distributions that the seen ones In contrast G-ZSL targets at distinguishing the labels instances the seen and unseen classes Only the seen classes the training instances unseen classes Note OSL explicitly give the class labels those instances categorized the novel class G-ZSL requires predicting unseen classes To address G-ZSL semantic attributes or vectors introduced the intermediate representations; each (seen/unseen) class one semantic prototype class level information Specifically a reasonable solution of OSL G-ZSL via dividing For training classes the predictors constructed map visual features the class label spaceOSL (or semantic (G-ZSL Testing performed each separated domain seen classes the novel class (OSL both seenG-ZSL).The key question deal efficiently the testing time This different the conventional Zero-Shot Learning (ZSL) task which assumes, the testing stage seen classes would misclassified unseens, vice; the unseen classes Unfortunately , the predictors learned on training classes inevitably make OSL or G-ZSL approaches tend biased the seen classes leading very poor classification results the novel class unseen classes BID39 ; . We show in Fig 1 . On aPY datasetdescribed Sec BID10 ), t-SNE van der Maaten & Hinton is The initial boundary the known domain is estimated. We further divide an uncertain domain K-S Test Then recognize instances each domain (b distribution pairwise intraclass and interclass distances: We the empirical density aPY datasetdescribed Sec There a large overlapping the distribution interclass distances.employed visualize the testing instances the ResNet-101 features BID39 1 (a ), semantic features learned SAE Kodirov et (2017) (Fig 1 (b ). We categorize the SAE prediction known or unknown domain labels compare with the groundtruth in Fig 1(c . We show unseen instances being predicted one the known classes.A natural recipe addressing learn separate domains the distributions instances; different classifiers directly However First , visual features alone discriminative enough help the seen and unseen/novel classes As Fig 2 (a) , bicycle respectively are one the seen and unseen classes 1 in aPY datasetdescribed Sec We observe a large overlapping region their t-SNE visualized feature distributions That the visual features may representative differentiate; the instances motorbike ( as the uncertain domain taken the bicycle vice Second the predictors trained seen classes trustworthy A not well-trained predictor may negatively the recognition algorithms Third even worse the performance classifiers each domain still sensitive domain separation: should one testing instance wrongly never correctly categorizedTo tackle our key ( Fig 2(a ) introduce a novel domain -uncertain domain accounts the overlapping regions testing instances from seen Thus the visual or semantic space learned divided known, unknown and uncertain domains The recognition algorithms will directly employed each domain . Nonetheless how divide the domains based known information also Though the supervised classifiers learn the patterns known classes encounteredFormally propose exploiting the distribution information efficiently to divide the domains from Our domain separation bootstrapping by Specifically according extreme value theory BID30 , the maximum/minimum confidence scores predicted of taken Since do the prior knowledge the underlying data distributions; introduced estimating an initial boundary known classes Nevertheless the initial boundary estimated relaxed include novel testing instances as is illustrated 2(b . To finetune the boundary exploit the K-S Test validate the learned predictors trustworthy The uncertain domain introduced thus accounts those testing instances whose labels hard be judged Recognition models conducted each domain This paper learns to divide the instances known, unknown and uncertain domains the recognition tasks from The domain division procedure consists bootstrapping and K-S Test steps The bootstrapping is used set an initial threshold each class; further employ Such a domain division algorithm OSL and G-ZSL tasks achieves",0.01,0.41249035339194656
"Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average potential over the posterior distribution of weights along with an entropic regularization term. This potential is however not the original loss function in general. So SGD does perform variational inference, but for a different loss than the one used to compute the gradients. Even more surprisingly, SGD does not even converge in the classical sense: we show that the most likely trajectories of SGD for deep networks do not behave like Brownian motion around critical points. Instead, they resemble closed loops with deterministic components. We prove that such out-of-equilibrium behavior is a consequence of highly non-isotropic gradient noise in SGD; the covariance matrix of mini-batch gradients for deep networks has a rank as small as 1% of its dimension. We provide extensive empirical validation of these claims, proven in the appendix. Our first result is to show precisely in what sense stochastic gradient descent (SGD) implicitly performs variational inference, as is often claimed informally in the literature. For a loss function f (x) with weights x ∈ R d , if ρ ss is the steady-state distribution over the weights estimated by SGD, DISPLAYFORM0 where H(ρ) is the entropy of the distribution ρ and η and b are the learning rate and batch-size, respectively. The potential Φ(x), which we characterize explicitly, is related but not necessarily equal to f (x). It is only a function of the architecture and the dataset. This implies that SGD implicitly performs variational inference with a uniform prior, albeit of a different loss than the one used to compute back-propagation gradients.We next prove that the implicit potential Φ(x) is equal to our chosen loss f (x) if and only if the noise in mini-batch gradients is isotropic. This condition, however, is not satisfied for deep networks. Empirically, we find gradient noise to be highly non-isotropic with the rank of its covariance matrix being about 1% of its dimension. Thus, SGD on deep networks implicitly discovers locations where ∇Φ(x) = 0, these are not the locations where ∇ f (x) = 0. This is our second main result: the most likely locations of SGD are not the local minima, nor the saddle points, of the original loss. The deviation of these critical points, which we compute explicitly scales linearly with η/b and is typically large in practice.When mini-batch noise is non-isotropic, SGD does not even converge in the classical sense. We prove that, instead of undergoing Brownian motion in the vicinity of a critical point, trajectories have a deterministic component that causes SGD to traverse closed loops in the weight space. We detect such loops using a Fourier analysis of SGD trajectories. We also show through an example that SGD with non-isotropic noise can even converge to stable limit cycles around saddle points. The continuous-time point-of-view used in this paper gives access to general principles that govern SGD, such analyses are increasingly becoming popular BID61 BID9 . However, in practice, deep networks are trained for only a few epochs with discrete-time updates. Closing this gap is an important future direction. A promising avenue towards this is that for typical conditions in practice such as small mini-batches or large learning rates, SGD converges to the steady-state distribution quickly BID48 . Let F(ρ) be as defined in (11). In non-equilibrium thermodynamics, it is assumed that the local entropy production is a product of the force −∇ δ F δ ρ from (A8) and the probability current −J(x,t) from (FP). This assumption in this form was first introduced by BID46 based on the works of BID41 BID40 . See Frank (2005, Sec. 4 .5) for a mathematical treatment and Jaynes (1980) for further discussion. The rate of entropy (S i ) increase is given by DISPLAYFORM0 This can now be written using (A8) again as DISPLAYFORM1 The first term in the above expression is non-negative, in order to ensure that DISPLAYFORM2 where the second equality again follows by integration by parts. It can be shown (Frank, 2005, Sec. 4.5.5 ) that the condition in Assumption 4, viz., ∇ · j(x) = 0, is sufficient to make the above integral vanish and therefore for the entropy generation to be non-negative.C SOME PROPERTIES OF THE FORCE jThe Fokker-Planck equation (FP) can be written in terms of the probability current as DISPLAYFORM3 Since we have ρ ss ∝ e −β Φ(x) , from the observation (7), we also have that DISPLAYFORM4 and consequently, DISPLAYFORM5 In other words, the conservative force is non-zero only if detailed balance is broken, i.e., J ss = 0. We also have DISPLAYFORM6 which shows using Assumption 4 and ρ ss (x) > 0 for all x ∈ Ω that j(x) is always orthogonal to the gradient of the potential DISPLAYFORM7 Using the definition of j(x) in (8), we have detailed balance when DISPLAYFORM8",1093,0.599,621,1.7600644122383253,"Stochastic gradient descent widely believed perform implicit regularization when used train the precise manner occurs thus elusive We prove SGD minimizes an average potential over the posterior distribution weights along an entropic regularization term This potential however the original loss function general So SGD does perform variational inference for a different loss than Even more surprisingly SGD does even converge the classical sense we show for deep networks do behave Brownian motion around critical points Instead resemble closed loops deterministic components We prove such outequilibrium behavior highly non-isotropic gradient noise SGD; mini-batch gradients for deep networks a rank its dimension We provide extensive empirical validation proven the appendix Our first result to precisely in implicitly performs is claimed informally For a loss function f (x with weights x �� R d if �� ss estimated SGD DISPLAYFORM0 where H(ρ and b are batch-size The potential ��( characterize explicitly related but f (x It only a function the architecture the dataset This implies SGD implicitly performs variational inference uniform prior albeit of a different loss thanWe next prove the implicit potential �� equal our chosen loss f (x the noise mini-batch gradients This condition, however satisfied for deep networks find gradient noise to highly nonisotropic with the rank its covariance matrix its dimension Thus SGD on deep networks implicitly discovers locations �� these f This our second main result: the most likely locations SGD are not the local minima nor the saddle points of the original loss The deviation these critical points compute explicitly scales ��/b typically large practiceWhen mini-batch noise non SGD does even converge We prove, instead undergoing Brownian motion the vicinity trajectories have causes SGD traverse closed loops the weight space We detect such loops using SGD trajectories We also show through SGD with non-isotropic noise even converge stable limit cycles around saddle points continuous-time point used gives access general principles SGD such analyses increasingly popular BID61 BID9 . However practice deep networks trained with discrete-time updates Closing this gap an important future direction A promising avenue towards this that for typical conditions practice such small minibatches large learning rates SGD converges the steady-state distribution quickly BID48 . Let F(ρ as defined11 In non-equilibrium thermodynamics assumed the local entropy production −�� � fromA8 probability current −J(x,tFP This assumption in this form BID46 based the works . See Frank (2005 Sec 4 .5) for a mathematical treatment and Jaynes1980 further discussion rate entropy (S i increase given DISPLAYFORM0 This now using (A8 again The first term non in ensure where the second equality again follows by integration by parts It can shown (Frank, 2005 Sec ) that the condition in Assumption, viz �� · j(x sufficient the above integral vanish therefore for the entropy generation nonC SOME PROPERTIES jThe Fokker-Planck equationFP probability current as DISPLAYFORM3 Since � ss � e −β �( from (7 also consequently In the conservative force non only detailed balance broken J ss We also DISPLAYFORM6 shows using Assumption 4 and �� ssx > for� that j(x always the gradient the potential DISPLAYFORM7 Using the definition ( detailed balance when",0.01,0.6406565135379587
"The current dominant paradigm for imitation learning relies on strong supervision of expert actions to learn both 'what' and 'how' to imitate. We pursue an alternative paradigm wherein an agent first explores the world without any expert supervision and then distills its experience into a goal-conditioned skill policy with a novel forward consistency loss. In our framework, the role of the expert is only to communicate the goals (i.e., what to imitate) during inference. The learned policy is then employed to mimic the expert (i.e., how to imitate) after seeing just a sequence of images demonstrating the desired task. Our method is 'zero-shot' in the sense that the agent never has access to expert actions during training or for the task demonstration at inference. We evaluate our zero-shot imitator in two real-world settings: complex rope manipulation with a Baxter robot and navigation in previously unseen office environments with a TurtleBot. Through further experiments in VizDoom simulation, we provide evidence that better mechanisms for exploration lead to learning a more capable policy which in turn improves end task performance. Videos, models, and more details are available at https://pathak22.github.io/zeroshot-imitation/.",235,0.137,145,1.6206896551724137,The current dominant paradigm imitation learning strong supervision expert actions both 'what We pursue an alternative paradigm wherein first explores without any expert supervision a goal-conditioned skill policy with a novel forward consistency loss our framework the expert only communicate ( imitate during inference The learned policy then employed mimic the expert ( how imitate after seeing just a sequence images demonstrating Our method 'zero-shot the agent never access expert actions during training for the task demonstration at inference We evaluate our zero-shot imitator complex rope manipulation a Baxter robot navigation previously unseen office environments a TurtleBot Through further experiments VizDoom simulation provide evidence better mechanisms exploration lead learning a more capable policy which in end task performance Videos models more details https://pathak22.github.io/zeroshot-imitation/.,0.0,0.2855418778662804
"Distributional Semantics Models(DSM) derive word space from linguistic items
 in context. Meaning is obtained by defining a distance measure between vectors
 corresponding to lexical entities. Such vectors present several problems. This
 work concentrates on quality of word embeddings, improvement of word embedding
 vectors, applicability of a novel similarity metric used ‘on top’ of the
 word embeddings. In this paper we provide comparison between two methods
 for post process improvements to the baseline DSM vectors. The counter-fitting
 method which enforces antonymy and synonymy constraints into the Paragram
 vector space representations recently showed improvement in the vectors’ capability
 for judging semantic similarity. The second method is our novel RESM
 method applied to GloVe baseline vectors. By applying the hubness reduction
 method, implementing relational knowledge into the model by retrofitting synonyms
 and providing a new ranking similarity definition RESM that gives maximum
 weight to the top vector component values we equal the results for the ESL
 and TOEFL sets in comparison with our calculations using the Paragram and Paragram
 + Counter-fitting methods. For SIMLEX-999 gold standard since we cannot
 use the RESM the results using GloVe and PPDB are significantly worse compared
 to Paragram. Apparently, counter-fitting corrects hubness. The Paragram
 or our cosine retrofitting method are state-of-the-art results for the SIMLEX-999
 gold standard. They are 0.2 better for SIMLEX-999 than word2vec with sense
 de-conflation (that was announced to be state-of the-art method for less reliable
 gold standards). Apparently relational knowledge and counter-fitting is more important
 for judging semantic similarity than sense determination for words. It is to
 be mentioned, though that Paragram hyperparameters are fitted to SIMLEX-999
 results. The lesson is that many corrections to word embeddings are necessary
 and methods with more parameters and hyperparameters perform better.
 Distributional language models are frequently used to measure word similarity in natural language. This is a basis for many semantic tasks. The DSM often consists of a set of vectors; each vector corresponds to a character string, which represents a word. BID14 and BID19 implemented the most commonly used word embedding (WE) algorithms. Vector components in language models created by these algorithms are latent. Similarity between words is defined as a function of vectors corresponding to given words. The cosine measure is the most frequently used similarity function, although many other functional forms were attempted. BID25 highlights the fact that the cosine can be outperformed by ranking based functions.As pointed out by many works, e.g. , evidence suggests that distributional models are far from perfect.Vector space word representations obtained from purely distributional information of words in large unlabeled corpora are not enough to best the state-of-the-art results in query answering benchmarks, because they suffer from several types of weaknesses: 3. Appearance of hubness that distorts distances between vectors, 4. Inability of distinguishing from antonyms. 5. In case of retrofitting distortion vector space -loss of information contained in the original vectorsIn this paper we use the existing word embedding model but with several post process enhancement techniques. We address three of these problems. In particular, we define a novel similarity measure, dedicated for language models.Similarity is a function, which is monotonically opposite to distance. As the distance between two given entities gets shorter, entities are more similar. This holds for language models. Similarity between words is equal to similarity between their corresponding vectors. There are various definitions of distance. The most common Euclidean distance is defined as follows: DISPLAYFORM0 Similarity based on the Euclidean definition is inverse to the distance: DISPLAYFORM1 Angular definition of distance is defined with cosine function: DISPLAYFORM2 We define angular similarity as: DISPLAYFORM3 Both Euclidean and Cosine definitions of distance could be looked at as the analysis of vector components. Simple operations, like addition and multiplication work really well in low dimensional spaces. We believe, that applying those metrics in spaces of higher order is not ideal, hence we compare cosine similarity to a measure of distance dedicated for high dimensional spaces.In this paper we restrict ourselves to three gold standards: TOEFL, ESL and SIMLEX-999. The first two are small but reliably annotated (and therefore confidence in their performance can be assumed 100%). Other used benchmarks suffer from several drawbacks. Both WS- 353 Finkelstein et al. (2001) and MEN Bruni et al. (2012) do not measure the ability of models to reflect similarity. Moreover, as pointed out by , for WS-353, RG Rubenstein & Goodenough (1965) and MEN, state-of-the-art models have reached the average performance of a human annotator on these evaluations. This work compares the state-of-the-art word embedding methods for three most reliable gold standards: TOEFL, ESL and SIMLEX-999. For TOEFL and ESL the GloVe, PPDB baseline with retrofitting, our novel RESM similarity measure and hubness reduction we are able to equal the Paragram results. For SIMLEX-999 Paragram with Counter-fitting results are clearly better than the Glove based methods using the PPDB 1.0. However, we propose the cosine retrofitting that basically achieves the Paragram with Counter-fitting results. The Paragram with Counter-fitting method contains several hyperparameters which is one source of its success. Its effects can be seen in TAB0 at https://arxiv.org/pdf/1506.03487.pdf. The Spearman ρ values for SIMLEX-999 are 0.667 for Paragram300 fitted to WS353, and 0.685 for Paragram300 fitted to SIMLEX-999. The difference is even larger for WS353. Then the Spearman ρ values for WS-353 are 0. 769 for Paragram300 fitted toWS353, and 0.720 for Paragram300 fitted to SIMLEX-999. Still the best word embedding based methods are not able to achieve the performance of other dedicated methods for TOEFL and ESL. The work of BID13 employed 2 fitting constants (and it is not clear that they were the same for all questions) for answering the TOEFL test where only 50 questions are used. Techniques introduced in the paper are lightweight and easy to implement, yet they provide a significant performance boost to the language model. Since the single word embedding is a basic element of any semantic task one can expect a significant improvement of results for these tasks. In particular, SemEval-2017 International Workshop on Semantic Evaluation run (among others) the following tasks(se2):1. Task 1: Semantic Textual Similarity 2. Task 2: Multilingual and Cross-lingual Semantic Word Similarity 3. Task 3: Community Question Answering in the category Semantic comparison for words and texts. Another immediate application would be information retrieval (IR). Expanding queries by adding potentially relevant terms is a common practice in improving relevance in IR systems. There are many methods of query expansion. Relevance feedback takes the documents on top of a ranking list and adds terms appearing in these document to a new query. In this work we use the idea to add synonyms and other similar terms to query terms before the pseudo-relevance feedback. This type of expansion can be divided into two categories. The first category involves the use of ontologies or lexicons (relational knowledge). The second category is word embedding (WE). Here closed words for expansion have to be very precise, otherwise a query drift may occur, and precision and accuracy of retrieval may deteriorate. There are several avenues to further improve the similarity results.1. Use the multi-language version of the methods (e.g. Recski et al. FORMULA0 2. Use PPDB 2.0 to design the Paragram vectors BID18 3. Apply the multi-sense methods (knowledge graps) with state-of-the-art relational enriched vectors 4. Recalibrate annotation results using state-of-the-art results.",1653,1.116,1000,1.653,"Distributional Semantics Models(DSM) derive word space linguistic items context Meaning is obtained defining a distance measure vectors corresponding lexical entities Such vectors present This work concentrates quality improvement applicability a novel similarity metric used ��on top�� In comparison post process improvements the baseline DSM vectors The counter-fitting method which enforces antonymy synonymy constraints into the Paragram vector space representations recently showed improvement the vectors�� capability judging semantic similarity The second method our novel RESM method applied GloVe baseline vectors By applying the hubness reduction method implementing relational knowledge into by retrofitting synonyms providing a new ranking similarity definition RESM that gives maximum weight the top vector component values we equal the ESL and TOEFL sets comparison our calculations the Paragram and Paragram + Counter-fitting methods For SIMLEX-999 gold standard since we the RESM the results using GloVe and PPDB significantly compared Paragram Apparently, counter-fitting corrects hubness The Paragram or our cosine retrofitting method are state results the SIMLEX-999 gold standard They 0.2 better for SIMLEX-999 word2vec with sense deconflationthat was announced to state the-art method less reliable gold standards Apparently relational knowledge counterfitting judging semantic similarity sense determination for words It to mentioned Paragram hyperparameters fitted SIMLEX-999 results The lesson many corrections necessary methods with more parameters perform Distributional language models frequently word similarity This a basis many semantic tasks The DSM often consists vectors; BID14 and implemented (WE Vector components language models created these algorithms latent Similarity words defined vectors corresponding given words The cosine measure the most frequently used similarity function many other functional forms were attempted BID25 highlights the cosine can outperformed ranking based functionsAs pointed many works , evidence distributional models farVector space word representations obtained purely distributional information of words enough best state results query answering benchmarks suffer several types weaknesses 3 Appearance hubness that distances vectors 4 Inability distinguishing from 5 In case retrofitting distortion vector space -loss information contained the original vectorsIn this paper the existing word but several post process enhancement techniques We address three In particular define a novel similarity measure dedicated language modelsSimilarity, opposite distance As the distance two given entities gets entities similar This holds for language models Similarity words equal their corresponding vectors There various definitions distance The most common Euclidean distance defined DISPLAYFORM0 Similarity based inverse Angular definition with We angular similarity could looked the analysis vector components Simple operations addition multiplication work really low dimensional spaces We believe, applying those metrics spaces higher order ideal hence compare cosine similarity distance dedicated forIn restrict three gold standards TOEFL ESL SIMLEX-999 first are small reliably annotated ( therefore confidence in their performance assumed 100 Other used benchmarks suffer several drawbacks Both WS- 353 Finkelstein et (2001 and MEN Bruni et al (2012 do measure models reflect similarity Moreover pointed , for WS-353 RG Rubenstein & Goodenough1965 MEN state models reached the average performance a human annotator on these evaluations This work compares state word methods three most reliable gold standards TOEFL ESL SIMLEX-999 For TOEFL ESL the GloVe, PPDB baseline with retrofitting our novel RESM similarity measure hubness reduction we equal Paragram results For SIMLEX-999 Paragram with Counter-fitting results are clearly better the Glove based methods using the PPDB However propose the cosine retrofitting that basically achieves The Paragram with Counter-fitting method contains several hyperparameters is one source its success Its effects TAB0 at The Spearman �� values SIMLEX-999 Paragram300 fitted WS353 The difference even WS353 Then the Spearman �� values WS-353 0 769 for Paragram300 fitted toWS353 0.720 SIMLEX-999 Still the best word embedding based methods not able achieve other dedicated methods for TOEFL ESL The work BID13 employed 2 fitting constantsand it all questions answering where only 50 questions Techniques introduced the paper lightweight the language model Since the single word embedding a basic element any semantic task one expect results In particular, SemEval-2017 International Workshop Semantic Evaluation run (among the tasks(se2):1 Task 1 Semantic Textual Similarity 2 Task 2 Multilingual and Cross-lingual Semantic Word Similarity 3 Task 3 Community Question in the category Semantic comparison for words texts Another immediate application information retrieval Expanding queries potentially relevant terms improving relevance IR systems There query expansion Relevance feedback takes the documents on top a ranking list terms appearing these document to a new query In to add synonyms query terms before the pseudo-relevance feedback This type expansion divided The first category involves ontologiesrelational knowledge The second category wordWE Here closed words expansion have to very precise otherwise a query drift precision and retrieval There several avenues further the similarity results.1 Use Recski et al FORMULA0 2 Use PPDB design Paragram vectors BID18 3 Apply the multi-sense methodsknowledge graps state relational enriched vectors 4 Recalibrate annotation results state results",0.01,0.36786579773111294
"Recurrent neural networks have achieved excellent performance in many applications. However, on portable devices with limited resources, the models are often too large to deploy. For applications on the server with large scale concurrent requests, the latency during inference can also be very critical for costly computing resources. In this work, we address these problems by quantizing the network, both weights and activations, into multiple binary codes {-1,+1}. We formulate the quantization as an optimization problem. Under the key observation that once the quantization coefficients are fixed the binary codes can be derived efficiently by binary search tree, alternating minimization is then applied.   We test the quantization for two well-known RNNs, i.e., long short term memory (LSTM) and gated recurrent unit (GRU), on the language models. Compared with the full-precision counter part, by 2-bit quantization we can achieve ~16x memory saving and  ~6x real inference acceleration on CPUs, with only a reasonable loss in the accuracy. By 3-bit quantization, we can achieve almost no loss in the accuracy or even surpass the original model, with ~10.5x memory saving and ~3x real inference acceleration. Both results beat the exiting quantization works with large margins.   We extend our alternating quantization to image classification tasks. In both RNNs and feedforward neural networks, the method also achieves  excellent performance. Recurrent neural networks (RNNs) are specific type of neural networks which are designed to model the sequence data. In last decades, various RNN architectures have been proposed, such as LongShort-Term Memory (LSTM) BID9 and Gated Recurrent Units BID0 . They have enabled the RNNs to achieve state-of-art performance in many applications, e.g., language models (Mikolov et al., 2010) , neural machine translation BID21 , automatic speech recognition BID5 , image captions BID23 , etc. However, the models often build on high dimensional input/output,e.g., large vocabulary in language models, or very deep inner recurrent networks, making the models have too many parameters to deploy on portable devices with limited resources. In addition, RNNs can only be executed sequentially with dependence on current hidden states. This causes large latency during inference. For applications in the server with large scale concurrent requests, e.g., on-line machine translation and speech recognition, large latency leads to limited requests processed per machine to meet the stringent response time requirements. Thus much more costly computing resources are in demand for RNN based models.To alleviate the above problems, several techniques can be employed, i.e., low rank approximation (Sainath et al., 2013; BID14 BID16 BID22 , sparsity BID19 BID7 , and quantization. All of them are build on the redundancy of current networks and can be combined. In this work, we mainly focus on quantization based methods. More precisely, we are to quantize all parameters into multiple binary codes {−1, +1}.The idea of quantizing both weights and activations is firstly proposed by BID11 . It has shown that even 1-bit binarization can achieve reasonably good performance in some visual classification tasks. Compared with the full precision counterpart, binary weights reduce the memory by a factor of 32. And the costly arithmetic operations between weights and activations can then be replaced by cheap XNOR and bitcount operations BID11 , which potentially leads to much acceleration. Rastegari et al. (2016) further incorporate a real coefficient to compensate for the binarization error. They apply the method to the challenging ImageNet dataset and achieve better performance than pure binarization in BID11 . However, it is still of large gap compared with the full precision networks. To bridge this gap, some recent works BID12 BID29 further employ quantization with more bits and achieve plausible performance. Meanwhile, quite an amount of works, e.g., BID3 BID30 BID6 , quantize the weights only. Although much memory saving can be achieved, the acceleration is very limited in modern computing devices (Rastegari et al., 2016) .Among all existing quantization works, most of them focus on convolutional neural networks (CNNs) while pay less attention to RNNs. As mentioned earlier, the latter is also very demanding. Recently, BID10 showed that binarized LSTM with preconditioned coefficients can achieve promising performance in some easy tasks such as predicting the next character. However, for RNNs with large input/output , e.g., large vocabulary in language models, it is still very challenging for quantization. Both works of BID12 and BID28 test the effectiveness of their multi-bit quantized RNNs to predict the next word. Although using up to 4-bits, the results with quantization still have noticeable gap with those with full precision. This motivates us to find a better method to quantize RNNs . The main contribution of this work is as follows:(a) We formulate the multi-bit quantization as an optimization problem . The binary codes {−1, +1} are learned instead of rule-based. For the first time, we observe that the codes can be optimally derived by the binary search tree once the coefficients are knowns in advance, see, e.g., Algorithm 1. Thus the whole optimization is eased by removing the discrete unknowns , which are very difficult to handle. (b) We propose to use alternating minimization to tackle the quantization problem. By separating the binary codes and real coefficients into two parts, we can solve the subproblem efficiently when one part is fixed. With proper initialization, we only need two alternating cycles to get high precision approximation, which is effective enough to even quantize the activations on-line. (c) We systematically evaluate the effectiveness of our alternating quantization on language models.Two well-known RNN structures, i.e., LSTM and GRU, are tested with different quantization bits. Compared with the full-precision counterpart, by 2-bit quantization we can achieve ∼16× memory saving and ∼6× real inference acceleration on CPUs, with a reasonable loss on the accuracy. By 3-bit quantization, we can achieve almost no loss in accuracy or even surpass the original model with ∼10.5× memory saving and ∼3× real inference acceleration. Both results beat the exiting quantization works with large margins. To illustrate that our alternating quantization is very general to extend, we apply it to image classification tasks. In both RNNs and feedforward neural networks, the technique still achieves very plausible performance. In this work, we address the limitations of RNNs, i.e., large memory and high latency, by quantization. We formulate the quantization by minimizing the approximation error. Under the key observation that some parameters can be singled out when others fixed, a simple yet effective alternating method is proposed. We apply it to quantize LSTM and GRU on language models. By 2-bit weights and activations, we achieve only a reasonably accuracy loss compared with full precision one, with ∼16× reduction in memory and ∼6× real acceleration on CPUs. By 3-bit quantization, we can attain compatible or even better result than the full precision one, with ∼10.5× reduction in memory and ∼3× real acceleration. Both beat existing works with a large margin. We also apply our alternating quantization to image classification tasks. In both RNNs and feedforward neural networks, the method can still achieve very plausible performance. In this section, we discuss the implementation of the binary multiplication kernel in CPUs. The binary multiplication is divided into two steps: Entry-wise XNOR operation (corresponding to entry-wise product in the full precision multiplication) and bit count operation for accumulation (corresponding to compute the sum of all multiplied entries in the full precision multiplication). We test it on Intel Xeon E5-2682 v4 @ 2.50 GHz CPU. For the XNOR operation, we use the Single instruction, multiple data (SIMD) _mm256 _xor _ps, which can execute 256 bit simultaneously. For the bit count operation, we use the function _popcnt64 (Note that this step can further be accelerated by the up-coming instruction _mm512 _popcnt_epi64 , which can execute 512 bits simultaneously. Similarly, the XNOR operation can also be further accelerated by the up-coming _mm512 _xor _ps instruction to execute 512 bits simultaneously). We compare with the much optimized Intel Math Kernel Library (MKL) on full precision matrix vector multiplication and execute all codes in the single-thread mode. We conduct two scales of experiments: a matrix of size 4096 × 1024 multiplying a vector of size 1024 and a matrix of size 42000 × 1024 multiplying a vector of size 1024, which respectively correspond to the hidden state product W h h t−1 and the softmax layer W s h t for Text8 dataset during inference with batch size of 1 (See Eq. (6)). The results are shown in TAB6 . We can see that our alternating quantization step only accounts for a small portion of the total executing time, especially for the larger scale matrix vector multiplication. Compared with the full precision one, the binary multiplication can roughly achieve 6× acceleration with 2-bit quantization and 3× acceleration with 3-bit quantization. Note that this is only a simple test on CPU. Our alternating quantization method can also be extended to GPU, ASIC, and FPGA.",1973,1.152,1155,1.7082251082251083,"Recurrent neural networks achieved However on portable devices limited resources the models deploy For applications on with large scale concurrent requests the latency during inference also critical costly computing resources In this work address these problems quantizing, both weights into multiple binary codes { We formulate the quantization as Under the key observation once the quantization coefficients fixed the binary codes derived efficiently binary search tree alternating minimization is then We test the quantization for gated recurrent unit the language models Compared the full-precision counter part by 2-bit quantization ~16x memory saving ~6x real inference acceleration CPUs only a reasonable loss By 3-bit quantization achieve almost no loss even surpass ~10.5x memory saving ~3x real inference acceleration Both results beat the exiting quantization works with large margins We extend our alternating quantization image classification tasks In both RNNs feedforward neural networks the method also achieves Recurrent neural networks specific type model the sequence data In last decades various RNN architectures proposed LongShort-Term Memory (LSTM) BID9 Gated Recurrent Units BID0 . They enabled the RNNs achieve stateart language models (Mikolov , neural machine translation BID21 etc However the models often build high dimensional input/output, large vocabulary in language models very deep inner recurrent networks making have deploy portable devices with In addition RNNs only executed with dependence current hidden states This causes large latency during inference For applications the server with large scale concurrent requests on-line machine translation speech recognition large latency leads limited requests processed per machine to meet Thus much more costly computing resources in RNN based modelsTo alleviate several techniquesSainath BID14 BID16 BID22 , sparsity quantization. All build the redundancy current networks can combined In this work mainly quantization based methods More precisely quantize all parameters into multiple binary codes {−1 +1}.The idea both weights activations firstly proposed BID11 . It shown even 1-bit binarization achieve some visual classification tasks Compared the full precision counterpart binary weights reduce by 32 And the costly arithmetic operations between weights activations then replaced cheap XNOR and bitcount operations BID11 , potentially leads much acceleration Rastegari et al (2016 further incorporate a real coefficient compensate the binarization error They apply the challenging ImageNet dataset achieve pure binarization BID11 . However of large gap the full precision networks To bridge some recent works BID12 BID29 further employ quantization with more bits achieve plausible performance Meanwhile quite an amount works, BID3 BID30 BID6 , quantize the weights only Although much memory saving the acceleration modern computing devicesRastegari et 2016 .Among existing quantization works most while pay latter also demanding Recently BID10 showed binarized LSTM with achieve promising performance some easy tasks predicting the next character However for RNNs , large vocabulary in language models still challenging quantization Both works BID12 test their multi-bit quantized RNNs the next word Although using up to 4-bits, the results with quantization still noticeable gap full precision This motivates find quantize RNNs . The main contribution as follows:(a We formulate the multi-bit quantization as . The binary codes {−1 learned instead rule For observe the codes can optimally derived the binary search tree once the coefficients knowns in see, Algorithm Thus the whole optimization eased removing the discrete unknowns , very handle (b We propose alternating minimization tackle By separating the binary codes real coefficients solve efficiently when fixed With proper initialization only two alternating cycles high precision approximation effective enough even quantize the activations- (c We systematically evaluate our alternating quantization on language modelsTwo well-known RNN structures GRU tested different quantization bits Compared the full-precision counterpart by 2-bit quantization ∼16× memory saving real inference acceleration CPUs a reasonable loss on the accuracy By 3-bit quantization achieve almost no loss even surpass with ∼10.5× memory saving ∼3× real inference acceleration Both results beat the exiting quantization works with large margins To illustrate our alternating quantization very general to extend, apply image In both RNNs feedforward neural networks the technique still achieves very plausible performance In this work address RNNs quantization We formulate the quantization by minimizing Under the key observation some parameters singled when others fixed a simple yet effective alternating method proposed We apply it quantize GRU on language models By 2-bit weights activations achieve only a reasonably accuracy loss compared full precision one ∼16× reduction memory real acceleration on CPUs By attain compatible or result Both beat existing works We also apply our alternating quantization image classification tasks In both RNNs feedforward neural networks the method can still achieve very plausible performance In the binary multiplication kernel CPUs is divided: Entry-wise XNOR operation in the full precision multiplication bit count operation for accumulation compute all multiplied entries We test it For the XNOR operation the Single instruction multiple data ( _mm256 _ _ps, execute 256 bit simultaneously For the bit count operation _popcnt64Note this step further accelerated the up-coming instruction _mm512 _ execute 512 bits simultaneously Similarly the XNOR operation further accelerated the up-coming _mm512 _ _ps instruction to execute 512 bits simultaneously). We compare with the much optimized Intel Math Kernel Library full precision matrix vector multiplication execute all codes We conduct two scales experiments a matrix size 4096 multiplying a vector and 42000 1024, respectively correspond the hidden state product W h h t−1 the softmax layer for Text8 dataset during inference batch sizeSee Eq ( The results shown TAB6 . We our alternating quantization step only accounts especially the larger scale matrix vector multiplication Compared full precision one the binary multiplication can roughly achieve 6× acceleration Note on CPU Our alternating quantization method extended GPU ASIC",0.01,0.5085745214637326
"The goal of this paper is to demonstrate a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for linear layers in a neural network and test this implementation on the CIFAR-10 dataset. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA-layers with 3900 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers.
 The curse of dimensionality is a major bottleneck in machine learning, stemming from the exponential growth of variables with the number of modes in a data set BID0 ). Typically state-of-the-art convolutional neural networks have millions or billions of parameters. However, previous work has demonstrated that representations stored in the network parameters can be highly compressed without significant reduction in network performance BID15 , BID3 , BID5 ). Determining the best network architecture for a given task remains an open problem.Descriptions of quantum mechanical systems raise a similar challenge; representing n d-dimensional particles requires a rank-n tensor whose memory cost scales as d n . Indeed, it was the promise of harnessing this that led Richard Feynman BID2 ) to suggest the possibility of quantum computation. In the absence of a quantum computer, however, one must use compressed representations of quantum states.A level of compression can be achieved by factorizing the tensorial description of the quantum wavefunction. Many such factorizations are possible, the optimal structure of the factorization being determined by the structure of correlations in the quantum system being studied. A revolution in quantum mechanics was made by realizing that the best way to characterize the distribution of correlations and information in a state is by a quantity known as entanglement -loosely the mutual quantum information between partitions of a quantum system BID1 ).This has led to many successful applications of tensorial approaches to problems in solid state physics and quantum chemistry over the past 25 years BID16 , BID7 ). Intriguing ideas have also emerged over the past few years attempting to bridge the successes of neural networks in machine learning with those of tensorial methods in quantum physics, both at a fundamental level BID10 , BID13 ), and as a practical tool for network design BID9 ). Recent work has suggested that entanglement itself is a useful quantifier of the performance of neural networks BID9 , BID11 The simplest factorization employed in quantum systems is known as the matrix product state BID16 ). In essence, it expresses the locality of information in certain quantum states. It has already been adopted to replace expensive linear layers in neural networks -in which context it has been independently termed tensor trains BID17 ). This led to substantial compression of neural networks with only a small reduction in the accuracy BID15 , BID3 ).Here we use a different tensor factorization -known as the Multi-scale Entanglement Renormalization Ansatz (MERA) -that encodes information in a hierarchical manner BID24 ). MERA works through a process of coarse graining or renormalization. There have been a number of papers looking at the relationship between renormalization and deep learning. MERA is a concrete realization of such a renormalization procedure BID25 ) and so possesses a multi-scale structure that one might anticipate in complex data. A number of works have utilized tree tensor network models that possess a similar hierarchical structure. However, they do not include the disentangler tensors that are essential if each layer of the MERA is to capture correlations on different length scales BID11 ).In this work we employ MERA as a replacement for linear layers in a neural network used to classify the CIFAR-10 dataset. Our results show that this performs better than the tensor train decomposition of the same linear layer, and gives better accuracy for the same level of compression and better compression for the same level of accuracy. In Section 2 we introduce factorizations of fully connected linear layers, starting with the tensor train factorization followed by a tree-like factorization and finally the MERA factorization. In Section 3 we discuss how this is employed as a replacement for a fully connected linear layer in deep learning networks. Section 4 gives our main results and we note connections with the existing literature in Section 5. Finally, in Section 6 we discuss some potential developments of the work. In this report we have replaced the linear layers of the standard neural network with tensorial MERA layers. The first step in achieving this involves expressing a linear layer as a tensor. This can be accomplished by taking a matrix W and reshaping it to be a higher dimensional array. For example, suppose W is d n by d n dimensional with components W AB . It can be transformed into a rank 2n tensor by mapping A to n elements A → i 1 , i 2 , ..., i n and B to another n elements B → j 1 , j 2 , ..., j n . In this case each of the elements of the new tensor will be of size d. FIG0 gives a graphical representation of this rank 2n tensor W i1,i2,... ,in j1,j2,...,jn . It is important to note that in this representation, the lines represent the indices of the tensors rather than weights. FIG0 We have shown that replacing the fully connected layers of a deep neural network with layers based upon the multi-scale entanglement renormalization ansatz can generate significant efficiency gains with only small reduction in accuracy. When applied to the CIFAR-10 data we found the fully connected layers can be replaced with MERA layers with 3900 times less parameters with a reduction in the accuracy of less than 1%. The model significantly outperformed compact fully connected layers with 70 − 100 times as many parameters. Moreover, it outperformed a similar replacement of the fully connected layers with tensor trains, both in terms of accuracy for a given compression and compression for a given accuracy.An added advantage -not explored here -is that a factorized layer can potentially handle much larger input data sets, thus enabling entirely new types of computation. Correlations across these large inputs can be handled much more efficiently by MERA than by tensor trains. Moreover, a compressed network may provide a convenient way to avoid over-fitting of large data sets. The compression achieved by networks with these factorized layers comes at a cost. They can take longer to train than networks containing the large fully connected layers due to the number of tensor contractions required to apply the factorized layer.Our results suggest several immediate directions for future inquiry. Firstly, there are some questions about how to improve the existing model. For example, before the MERA layer is used the input is reshaped into a rank-12 tensor. There isn't a well defined method for how to perform this reshaping optimally and some experimentation is necessary. The best way to initialize the MERA layers is also still an open question.The results presented here are a promising first step for using MERA in a more fundamental way. Since MERA can be viewed as a coarse graining procedure (as explained in Section 2), and image data is often well represented in a hierarchical manner, one possibility would be to simply train a two-dimensional MERA directly on an image dataset, with no reference to a neural network. In BID22 a similar idea was explored with matrix product states being trained directly on MNIST. An alternative possibility would be the replacement of just the convolutional layers of the network with a two-dimensional MERA. Both of these approaches would be closer in spirit to the fundamental ideas about the relationships between quantum physics and machine learning proposed in BID10 and BID13 .Additionally , there has been some work using entanglement measures to explore how correlations are distributed in deep neural networks, and then utilizing these in order to optimize the design of networks BID11 , BID9 ). It would be intriguing to explore such ideas using MERA, for example by using the concrete MERA model explored in this paper, or one of the more ambitious possibilities mentioned above.We end by noting two facts: any variational approximation to a quantum wavefunction can be used to construct a replacement for linear layers of a network. There are many examples and each may have its sphere of useful application. Moreover, quantum computers of the type being developed currently by several groups are precisely described by a type of tensor network (a finite-depth circuit -and one that may very soon be too large to manipulate classically) and could be used as direct replacement for linear layers in a hybrid quantum/classical neural computation scheme.",1755,0.925,1045,1.6794258373205742,"The goal tensorizing upon an efficient way approximating scale invariant quantum states the Multi-scale Entanglement Renormalization AnsatzMERA We employ MERA as a replacement linear layers test this implementation proposed method outperforms factorization using tensor trains providing greater compression the same level compression We demonstrate MERA-layers 3900 times fewer parameters a reduction accuracy the equivalent fully connected layers The curse dimensionality a major bottleneck machine learning stemming variables with the number modes a data BID0 ). Typically state convolutional millions parameters However previous work representations stored the network parameters highly compressed without significant reduction BID15 , BID3 Determining the best network architecture remainsDescriptions quantum mechanical systems raise a similar challenge; representing n d-dimensional particles requires a rank-n tensor whose memory cost scales as Indeed the promise harnessing this that BID2 ) suggest quantum computation In a quantum computer however one use compressed representationsA level factorizing the tensorial description Many such factorizations possible the optimal structure being correlations the quantum system being A revolution quantum mechanics made realizing characterize the distribution correlations and information a quantity entanglement -loosely the mutual quantum information partitions BID1 ).This has many successful applications tensorial approaches problems over BID16 Intriguing ideas also over attempting bridge the successes neural networks machine tensorial methods quantum physics both BID10 , ), as network design BID9 Recent work entanglement itself a useful quantifier the performance neural networks BID9 , The simplest factorization employed quantum systems known the matrix product state BID16 In essence expresses the locality information certain quantum states It already adopted to replace expensive linear layers neural networks -in which context it independently termed tensor trains BID17 This led substantial compression neural networks with the accuracy BID15 , BID3 ).Here use a different tensor factorization -known the Multi-scale Entanglement Renormalization AnsatzMERA information BID24 MERA works through coarse graining or renormalization There papers looking renormalization deep learning MERA is a concrete realization such a renormalization procedure BID25 ) so possesses a multi-scale structure one anticipate complex data A number works utilized tree tensor network models possess However they include the disentangler tensors essential if each layer the MERA capture correlations on different length scales BID11 ).In employ as a replacement linear layers used classify the CIFAR-10 dataset Our results this performs the tensor train decomposition the same linear layer gives the same level compression better compression accuracy In Section we introduce factorizations fully connected linear layers starting the tensor train factorization followed and finally the MERA factorization In Section we this employed a replacement a fully connected linear layer deep learning networks Section gives our main results note connections the existing literature Section Finally in Section we some potential developments of the work In this report have replaced the linear layers tensorial MERA layers The first step achieving involves expressing a linear layer as This can accomplished taking a matrix W For example suppose W is d n by dimensional with components W AB It can transformed a rank 2n tensor by mapping A n elements A → i 1 i ... and B another n elements B j In each the new tensor will of size d. FIG0 gives this rank 2n tensor W i1,i2 ,in j1,j2, . It important this representation the lines represent the indices the tensors rather weights FIG0 We replacing the fully connected layers layers based upon the multi-scale entanglement renormalization ansatz can generate only small reduction accuracy When applied the CIFAR-10 data we the fully connected layers can replaced MERA layers 3900 times less parameters with the accuracy The model significantly compact fully connected layers 70 − 100 times Moreover outperformed a similar replacement the fully connected layers with tensor trains both accuracy for a given compression compression forAn added advantage -not explored a factorized layer potentially handle thus entirely new types computation Correlations across these large inputs handled much MERA tensor trains Moreover a compressed network avoid over-fitting The compression achieved networks these factorized layers comes They can take longer train networks containing the large fully connected layers due tensor contractions apply the factorized layerOur results several immediate directions future inquiry Firstly there improve the existing model For example before the MERA layer the input reshaped a rank-12 tensor There is a well defined method how perform this reshaping optimally and some experimentation initialize the MERA layers also stillThe results presented a promising first step using Since MERA can viewed a coarse graining procedureas explained and image data often well a hierarchical manner one possibility simply train directly no reference In BID22 a similar idea explored matrix product states being trained directly MNIST An alternative possibility the replacement just the convolutional layers a two-dimensional MERA Both would closer spirit the fundamental ideas about the relationships quantum physics proposed BID10 .Additionally , has using entanglement measures explore correlations then utilizing in order optimize networks BID11 It would intriguing explore such ideas using MERA for by the concrete MERA model explored one mentionedWe end two facts any variational approximation a quantum wavefunction construct a replacement linear layers a network There and each may its sphere useful application Moreover quantum computers of being currently by several groups precisely described a type tensor networka finite-depth circuit -and one may very soon too manipulate classically could direct replacement linear layers a hybrid quantum/classical neural computation scheme",0.01,0.435196509475255
"Deep learning models have outperformed traditional methods in many fields such
 as natural language processing and computer vision. However, despite their
 tremendous success, the methods of designing optimal Convolutional Neural Networks
 (CNNs) are still based on heuristics or grid search. The resulting networks
 obtained using these techniques are often overparametrized with huge computational
 and memory requirements. This paper focuses on a structured, explainable
 approach towards optimal model design that maximizes accuracy while keeping
 computational costs tractable. We propose a single-shot analysis of a trained CNN
 that uses Principal Component Analysis (PCA) to determine the number of filters
 that are doing significant transformations per layer, without the need for retraining.
 It can be interpreted as identifying the dimensionality of the hypothesis space
 under consideration. The proposed technique also helps estimate an optimal number
 of layers by looking at the expansion of dimensions as the model gets deeper.
 This analysis can be used to design an optimal structure of a given network on
 a dataset, or help to adapt a predesigned network on a new dataset. We demonstrate
 these techniques by optimizing VGG and AlexNet networks on CIFAR-10,
 CIFAR-100 and ImageNet datasets. This analysis has only been done on activation outputs for convolutional layers before the application of non-linearities such as ReLU. Non-linearities introduce more dimensions, but those are not a function of the number of filters in a layer. Hence we recommend not to perform ReLU in-place while performing this analysis. The number of samples to be taken into account for PCA are recommended to be around 2 orders of magnitudes more than the number of filters we are trying to find redundancy in. This is particularly of importance in the later layers where the activation map sizes are small. We need to collect these activations over many batches to make sure we have enough data to run PCA analysis on. While the percentage variance one would like to retain depends on the application and acceptable error tolerance, empirically we have found that preserving 99.9% puts us at a sweet spot for most cases with less than half a percentage point in accuracy degradation and a considerable gain in computational cost. This analysis comes in handy in three cases: While designing new network for new data; while adapting given network for new data; and while optimizing current network for faster runtimes or reduced power consumption during training or inference in hardware implementations. Another benefit of this analysis is that not only does it deliver an optimal point, but enables an interpretable, graceful exploration of accuracy-energy trade-off with negligible overhead of compute cost and time. This method is orthogonal to other model compression techniques.",538,0.31,294,1.8299319727891157,"Deep learning models outperformed However despite the methods designing based or grid search The resulting networks obtained using these techniques often overparametrized huge computational and memory requirements This paper focuses a structured, explainable approach towards optimal model design accuracy while keeping computational costs tractable We propose a single-shot analysis a trained CNN that filters doing significant transformations per layer without retraining It can interpreted identifying the dimensionality the hypothesis space under The proposed technique also helps estimate an optimal number layers the expansion dimensions the model gets This analysis can design an optimal structure a given network on help adapt a predesigned network on We demonstrate these techniques optimizing VGG and AlexNet networks This analysis only activation outputs before the application non such ReLU Nonlinearities introduce more dimensions those a function filters Hence we recommend not perform ReLU in-place while this analysis The number samples to into PCA are recommended around 2 orders magnitudes more filters we trying find redundancy This particularly of the later layers the activation map sizes We need collect these activations over many batches run PCA analysis While the percentage variance one like retain depends the application and acceptable error tolerance empirically preserving puts most cases with in accuracy degradation and a considerable gain computational cost This analysis comes handy three cases While designing new network for new data; adapting given network optimizing faster runtimes or during training inference in hardware implementations Another benefit this analysis not deliver an optimal point, enables an interpretable, graceful exploration accuracy-energy trade-off with negligible overhead of compute cost This method other model compression techniques",0.0,0.8186729193246214
"Recent work has introduced attacks that extract the architecture information of deep neural networks (DNN), as this knowledge enhances an adversary’s capability to conduct attacks on black-box networks. This paper presents the first in-depth security analysis of DNN fingerprinting attacks that exploit cache side-channels.   First, we define the threat model for these attacks:  our adversary does not need the ability to query the victim model; instead, she runs a co-located process on the host machine victim ’s deep learning  (DL) system is running and passively monitors the accesses of the target functions in the shared framework.   Second, we introduce DeepRecon, an attack that reconstructs the architecture of the victim network by using the internal information extracted via Flush+Reload, a cache side-channel technique. Once the attacker observes function invocations that map directly to architecture attributes of the victim network, the attacker can reconstruct the victim’s entire network architecture.   In our evaluation, we demonstrate that an attacker can accurately reconstruct two complex networks (VGG19 and ResNet50) having only observed one forward propagation. Based on the extracted architecture attributes, we also demonstrate that an attacker can build a meta-model that accurately fingerprints the architecture and family of the pre-trained model in a transfer learning setting. From this meta-model,  we evaluate the importance of the observed attributes in the fingerprinting process. Third, we propose and evaluate new framework-level defense techniques that obfuscate our attacker’s observations. Our empirical security analysis represents a step toward understanding the DNNs’ vulnerability to cache side-channel attacks. Deep neural networks (DNNs) have become an essential tool in various applications, such as face recognition, speech recognition, malware detection, and autonomous driving or aviation BID18 BID1 BID2 BID3 BID21 . A DNN's performance depends widely on the network architecture-the number and types of layers, how the layers are connected, and the activation functions-and, unfortunately, there is no universal architecture that performs well on all tasks. Consequently, researchers and practitioners have devoted substantial efforts to design various DNN architectures to provide high performance for different learning tasks.Owing to their critical role, DNN architectures represent attractive targets for adversaries who aim to mount DNN fingerprinting attacks. In such an attack, the adversary probes a DNN model, considered confidential, until she infers enough attributes of the network to distinguish it among other candidate architectures. In addition to revealing valuable and secret information to the adversary, DNN fingerprinting can enable further attacks on black-box models. While the prior work on adversarial machine learning often assumes a white-box setting, where the adversary knows the DNN model under attack, these attacks are usually unrealistic in practice BID22 . In consequence, researchers have started focusing on a black-box setting, where model architecture is unknown to the adversary. However, in this setting, the adversary often makes some assumptions about the victim model in order to craft successful adversarial examples . Instead of approxi-mating, the adversary can start by conducting a DNN fingerprinting attack to infer the information required about the model, then use this information to craft adversarial examples that can evade the model. This can also enable model extraction attacks BID25 BID12 BID27 and membership inference or model inversion attacks BID19 BID15 .Because of the large number and types of architectural attributes, and the subtle effect that each attribute has on the model's inferences, DNN fingerprinting is challenging when using the typical methods employed in the adversarial machine learning literature. For example , BID27 propose a hyperparameter stealing attack that requires knowledge of the training dataset, the ML algorithm, and the learned model parameters, yet is unable to extract the model architecture. demonstrate a fingerprinting attack against transfer learning; however, they rely on the assumption that the teacher model and learning parameters are known to the attacker. To overcome these challenges, recent work has started to investigate attacks that utilize information leaked by architectural side-channels on the hardware where the DNN model runs. BID8 extract the network architecture of a model running on a hardware accelerator by monitoring off-chip memory addresses. BID30 reduce the search space from 10 35 to 16 candidates within a given network architecture by exploiting cache side-channels.In this paper, we ask the question: how vulnerable are DNNs to side-channel attacks, and what information do adversaries need for architecture fingerprinting? We perform, to the best of our knowledge, the first security analysis of DNNs operating in the presence of cache side-channel attacks. Specifically , we define the threat model for these attacks, including the adversary's capabilities and limitations. We then introduce DeepRecon, an efficient attack that reconstructs a black-box DNN architecture by exploiting the Flush+Reload BID32 technique, and we further evaluate the importance of specific architectural attributes in the success of fingerprinting. Finally, we propose and evaluate new framework-level defenses against these attacks.Our attack works by targeting lines of code corresponding to the execution of specific network architecture attributes of a deep learning (DL) framework. Specifically, these lines of code correspond to instructions to execute functions that are mapped into the instruction cache when the functions are invoked. Once these lines of code are identified, our attack flushes them from the instruction cache shared by the attacker and the victim. The attacker waits for the victim's process to run and then measures the time it takes to re-access those same lines of code. If the victim's DNN model has accessed any of these particular functions, the corresponding lines of code will be present in the instruction cache when the attacker tries to re-access them. Therefore, the access time to call these functions will be measurably faster than if the victim had not loaded them back into the shared instruction cache. On the other hand, if the victim DNN model did not access these particular functions, the corresponding lines will not be present in the cache when accessed by the attacker, and thus the access time will be measurably slower. We show that from this seemingly small amount of information that is leaked to the attacker, much of the victim's DNN architecture can be extracted with no query access required. To launch this attack, we only assume that: 1) an attacker and a victim are co-located in the same machine, and 2) they use the same shared DL framework.In evaluations, we demonstrate that, by learning whether or not specific functions were invoked during inference, we can extract 8 architecture attributes across 13 neural network architectures with high accuracy. Based on the extracted attributes , we demonstrate how an attacker can reconstruct the architectures of two common networks, VGG16 BID20 and ResNet50 BID6 as proof of concept. We also demonstrate a useful example of DeepRecon through model fingerprinting in a transfer learning attack. Finally, we propose countermeasures to obfuscate an attacker from extracting the correct attributes and sequences using observation attacks like DeepRecon and show that these defenses significantly increase the errors in the extracted attributes and can be implemented in various DL frameworks without hardware or operating system support. This paper conducts the first in-depth security analysis of DNN fingerprinting attacks that exploit cache side-channels. We first define the realistic threat model for these attacks: our attacker does not require the ability to query the victim model; she runs a co-located process on the machine where the victims DL system is running and passively monitors the accesses of target functions in a shared framework. We also present DeepRecon, an attack that reconstructs the architecture of a victim network using the architecture attributes extracted via the Flush+Reload technique. Based on the extracted attributes, we further demonstrate that an attacker can build a meta-model that precisely fingerprints the architecture and family of the pre-trained model in a transfer learning setting. With the meta-model, we identified the essential attributes for these attacks. DISPLAYFORM0 Recon.Steps Details VGG16 Recon.(1 ) Block 1 . Block 2. Block 3. Block 4. Block 5. DISPLAYFORM1 (Note that C,P ,F indicate the Convolutional, P ooling, F ully connected layers, and the subscripts mean the activation functions (R: ReLU, and So: Softmax). ) Table 7 : Reconstruction Process of VGG16 Architecture. We list the computation sequences captured by our attack above and the reconstruction process at the bottom.We describe the reconstruction process of VGG16 in Table 7 . The upper table indicates the sequences that our attacker captured, and the bottom shows the actual reconstruction steps. Our attacker identifies the basic building blocks by splitting the sequence with pooling layers. Then, the attacker counts the number of convolutional layers in each block. In VGG16, we found the first two ConvNet blocks have two convolutional layers, and the next three ConvNet blocks have three convolutional layers in each. Additionally, the attacker estimates the number of fully connected layers attached at the end. Once the attacker recovers all the blocks, our attacker can identify the victim architecture as being VGG16 with the ConvNet configuration 'C' or 'D'.B OBFUSCATED RE SNE T50 ARCHITECTURE In Sec. 5.2, we construct the obfuscated ResNet50 architecture by using the unraveled view of the first three blocks in ResNet50 as shown in FIG3 . The upper architecture depicts the block connections in the original ResNet50. In this network, the blocks are computed sequentially, e.g., Residual Block → Identity Block → Identity Block. However , in our unraveled architecture at the bottom, there are individual 8 paths that can be computed independently. We use this architecture to compute the blocks as follows: Residual Block 1, 2 → Identity Block 1 → Residual Block 3, 4 → Identity Block 2 → Identity Block 3. This makes our attacker have difficulty in estimating the architecture attributes and computation sequences of ResNet50.",2021,1.108,1199,1.6855713094245204,"Recent work introduced attacks extract the architecture information as this knowledge enhances an adversary��s capability conduct This paper DNN fingerprinting attacks cache side-channels First define the threat model these attacks our adversary does query the victim model she runs the host machine victim ��s deep learning (DL) system is passively monitors the target functions Second introduce DeepRecon an attack reconstructs the architecture the victim network the internal information extracted via Flush+Reload a cache side-channel technique Once the attacker observes function invocations map directly architecture attributes reconstruct the victim��s entire network architecture In our evaluation demonstrate an attacker accurately reconstruct two complex networksVGG19 ResNet50 having only observed one forward propagation Based the extracted architecture attributes also demonstrate an attacker build a meta-model accurately fingerprints family the pre-trained model a transfer learning setting From this meta-model evaluate the observed attributes the fingerprinting process Third propose and evaluate new framework-level defense techniques obfuscate our attacker��s observations Our empirical security analysis represents the DNNs�� vulnerability cache side-channel attacks Deep neural networks various applications malware detection or aviation BID18 BID1 . A DNN's performance depends widely-the number layers how the layers the activation functions- unfortunately performs researchers and devoted design various DNN architectures different learning tasksOwing represent attractive targets adversaries aim mount In such an attack the adversary probes a DNN model considered confidential until she infers enough attributes distinguish among other candidate architectures In addition revealing valuable and secret information the adversary DNN fingerprinting enable further attacks black-box models While the prior work adversarial machine learning often assumes a white-box setting where the DNN model under attack these attacks unrealistic BID22 . In consequence researchers started focusing a black-box setting model architecture unknown the adversary However this setting the adversary often makes some assumptions the victim model in craft successful adversarial examples . Instead approxi-mating the adversary start conducting a DNN fingerprinting attack infer required about craft adversarial examples evade This can enable model extraction attacks BID25 BID12 BID27 and membership inference or model inversion attacks and types architectural attributes and the subtle effect DNN fingerprinting challenging when the typical methods employed For example , BID27 propose stealing requires knowledge the training dataset ML the learned model parameters yet unable extract the model architecture demonstrate a fingerprinting attack transfer learning; however they rely the teacher model and learning parameters known To overcome recent work started attacks utilize information leaked architectural side-channels on the hardware where the DNN model runs BID8 extract the network architecture a model running by monitoring off addresses BID30 reduce the search space from 35 16 candidates within a given network architecture exploiting cache side-channelsIn ask vulnerable adversaries for architecture fingerprinting We perform, to the first security analysis DNNs operating cache side-channel attacks Specifically , define the threat model these attacks including limitations We then introduce DeepRecon an efficient attack reconstructs a black-box DNN architecture exploiting the Flush+Reload BID32 technique we further evaluate specific architectural attributes the success fingerprinting Finally propose and evaluate new framework-level defensesOur attack works targeting lines corresponding specific network architecture attributes Specifically, these lines code correspond instructions functions mapped when Once these lines identified our attack flushes the instruction cache shared The attacker waits measures reaccess those same lines If the victim's DNN model accessed these particular functions the corresponding lines present when re Therefore the access time call these functions will if the victim loaded back the shared instruction cache On the victim DNN model did access these particular functions the corresponding lines when accessed We show from this seemingly small amount leaked the attacker much the victim's DNN architecture extracted no query access To launch this attack only assume: and co use the same shared DL frameworkIn evaluations demonstrate learning whether not specific functions invoked inference extract 8 architecture attributes across 13 neural network Based the extracted attributes , demonstrate an attacker reconstruct the architectures two common networks VGG16 BID20 ResNet50 BID6 as proof We also demonstrate a useful example DeepRecon through model fingerprinting a transfer learning attack Finally propose countermeasures obfuscate an attacker from extracting the correct attributes sequences using observation attacks like DeepRecon show these defenses significantly the errors the extracted attributes can various DL frameworks without This paper conducts DNN fingerprinting attacks cache side-channels We first define the realistic threat model these attacks our attacker does require query the victim model she runs where the victims DL system passively target functions a shared framework We also present DeepRecon an attack reconstructs the architecture a victim network the architecture attributes extracted via the Flush+Reload technique Based the extracted attributes further demonstrate an attacker build precisely fingerprints the architecture family the pre-trained model a transfer learning setting With the meta-model, identified the essential attributes these attacks DISPLAYFORM0 Recon.Steps Details VGG16 Recon.(1 ) Block 1 . Block 2 Block 3 Block 4 Block 5 DISPLAYFORM1Note C,P , indicate the Convolutional, P ooling F ully connected layers the subscripts mean the activation functionsR: ReLU and So: Softmax ) Table 7 : Reconstruction Process VGG16 Architecture We list the computation sequences captured our attack above the reconstruction process atWe describe VGG16 Table 7 The upper table indicates the sequences our attacker captured the actual reconstruction steps Our attacker identifies by splitting with pooling layers Then the attacker counts convolutional layers each block In VGG16 found the first two ConvNet blocks have in Additionally the attacker estimates fully connected layers attached. Once the attacker recovers all the blocks our attacker identify the victim architecture VGG16 with the ConvNet configuration 'CB OBFUSCATED RE SNE T50 ARCHITECTURE In Sec, we construct the obfuscated ResNet50 architecture the unraveled view shown FIG3 The upper architecture depicts the block connections the original ResNet50 In this network the blocks computed Residual → Identity However , our unraveled architecture at individual 8 paths computed independently We use this architecture compute the blocks as follows Residual Block 1 → Identity Block This makes our attacker have difficulty estimating the architecture attributes computation sequences ResNet50",0.01,0.4508546324608346
"Learning with a primary objective, such as softmax cross entropy for classification and sequence generation, has been the norm for training deep neural networks for years. Although being a widely-adopted approach, using cross entropy as the primary objective exploits mostly the information from the ground-truth class for maximizing data likelihood, and largely ignores information from the complement (incorrect) classes. We argue that, in addition to the primary objective, training also using a complement objective that leverages information from the complement classes can be effective in improving model performance. This motivates us to study a new training paradigm that maximizes the likelihood of the ground-truth class while neutralizing the probabilities of the complement classes. We conduct extensive experiments on multiple tasks ranging from computer vision to natural language understanding. The experimental results confirm that, compared to the conventional training with just one primary objective, training also with the complement objective further improves the performance of the state-of-the-art models across all tasks. In addition to the accuracy improvement, we also show that models trained with both primary and complement objectives are more robust to single-step adversarial attacks.
 Statistical learning algorithms work by optimizing towards a training objective. A dominant principle for training is to optimize likelihood BID16 , which measures the probability of data given the model under a specific set of parameters. The popularity of deep neural networks has given rise to the use of cross entropy BID13 as its primary training objective, since minimizing cross entropy is essentially equivalent to maximizing likelihood for disjoint classes. Cross entropy has become the standard training objective for many tasks including classification BID12 and sequence generation .Let y i ∈ {0, 1} K be the label of the i th sample in one-hot encoded representation andŷ i ∈ [0, 1] K be the predicted probabilities, the cross entropy H(y,ŷ) is defined as: DISPLAYFORM0 whereŷ ig represents the predicted probability of the ground-truth class for the i th sample. Training with cross entropy as the primary objective aims at findingθ = arg min θ H(y,ŷ), wherê y = h θ (x), h θ is a neural network and x is a sample. Although training using the cross entropy as The model is ResNet-110, and the ""embedding"" is the vector representation before taking the softmax operation. The embedding representation of each sample is projected to two dimensions using t-SNE for visualization purpose. Compared to ( a), the cluster of each class in (b) is ""narrower "" in terms of intra-cluster distance. Also, the clusters in (b) seem to have clean and separable boundaries, leading to more accurate and robust classification results.the primary objective has achieved tremendous success, we have observed one limitation: it exploits mostly the information from the ground-truth class as Eq(1) shows; the information from complement classes (i.e., incorrect classes) has been largely ignored, since the predicted probabilities other thanŷ ig are zeroed out due to the dot product calculation with the one-hot encoded y i . Therefore, for classes other than the ground truth, the model behavior is not explicitly optimized -their predicted probabilities are indirectly minimized whenŷ ig is maximized since the probabilities sum up to 1. One way to utilize the information from the complement classes is to neutralize their predicted probabilities. To this end, we propose Complement Objective Training (COT), a new training paradigm that achieves this optimization goal without compromising the model's primary objective. FIG1 illustrates the comparison between FIG1 : the predicted probabilityŷ from the model trained with just cross entropy as the primary objective, and FIG1 :ŷ from the model trained with both primary and complement objectives. Training with the complement objective finds the parameters θ that evenly suppress complement classes without compromising the primary objective (i.e., maximizingŷ g ), making the model more confident of the ground-truth class. Complement objective training requires a function that complements the primary objective. In this paper, we propose ""complement entropy"" (defined in Section 2) to complement the softmax cross entropy for neutralizing the effects of complement classes. The neural net parameters θ are then updated by alternating iteratively between (a) minimizing cross entropy to increaseŷ g , and (b) maximizing complement entropy to neutralizeŷ j =g . Experimental results (in Section 3) confirm that COT improves the accuracies of the state-of-the-art methods for both (a) the image classification tasks on ImageNet-2012 , Tiny ImageNet, CIFAR-10, CIFAR-100, and SVHN, and (b) language understanding tasks on machine translation and speech recognition. Furthermore, experimental results also show that models trained by COT are more robust to adversarial attacks. In this paper, we study Complement Objective Training (COT), a new training paradigm that optimizes the complement objective in addition to the primary objective. We propose complement entropy as the complement objective for neutralizing the effects of complement (incorrect) classes.Models trained using COT demonstrate superior performance compared to the baseline models. We also find that COT makes the models robust to single-step adversarial attacks.COT can be extended in several ways: first, in this paper, the complement objective is chosen to be the complement entropy. Non-entropy-based complement objectives should also be considered for future studies, which is left as a straight-line future work. Secondly, the exploration of COT on broader applications remains as an open research question. One example would be applying COT on generative models such as Generative Adversarial Networks . Another example would be using COT on object detection and segmentation. Finally, in this work, we show using complement objective help defend single-step adversarial attacks; the behavior of COT on more advanced adversarial attacks deserves further investigation and is left as another future work.A ITERATIVE FAST GRADIENT SIGN METHOD TAB9 shows the performance of the models on the CIFAR-10 dataset under I-FGSM transfer attacks. Generally, the models trained using COT have lower classification error under I-FGSM transfer attacks. The number of iteration is set to 10 in the experiment.",1240,0.63,731,1.6963064295485637,"Learning with a primary objective softmax cross entropy for classification and sequence generation has training Although being a widely-adopted approach using cross entropy the primary objective exploits mostly the information from the ground-truth class for maximizing data likelihood largely the complement (incorrect) classes We argue training also using a complement objective leverages information the complement classes can model performance This motivates study a new training paradigm the ground-truth class while neutralizing the probabilities the complement classes We conduct extensive experiments multiple tasks ranging The experimental results confirm, the conventional training with just one primary objective training also with the complement objective further state models across In addition the accuracy improvement show models trained both primary and complement objectives robust single-step adversarial attacks Statistical learning algorithms work optimizing towards a training objective A dominant principle training optimize likelihood BID16 , measures data given under The popularity deep neural networks given cross entropy BID13 as its primary training objective since minimizing essentially equivalent likelihood for Cross entropy has the standard training objective including classification BID12 sequence generation .Let y i �� {} K the label i th sample one-hot encoded representation and�� i �� [ the predicted probabilities, the cross H(y� DISPLAYFORM0 where�� ig represents the ground-truth class for Training cross entropy as aims at finding� arg min H(y�� wherê y � is and x Although training using the cross entropy as The model ResNet-110 and ""embedding the vector representation before taking the softmax operation. The embedding representation each sample projected two dimensions t-SNE visualization purpose Compared ( a the cluster each class "" "" Also the clusters (b seem clean and separable boundaries leading results.the primary objective has achieved tremendous success we observed one limitation exploits mostly the information the ground-truth class as Eq(1 shows; complement classes largely the predicted probabilities other�� ig are zeroed due the dot product calculation with the one-hot encoded y i Therefore for classes other the ground truth the model behavior not explicitly optimized -their predicted probabilities indirectly minimized when�� ig is since sum One way utilize the complement classes neutralize their predicted probabilities To this end propose Complement Objective Training achieves this optimization goal without FIG1 illustrates the comparison FIG1 : the predicted probability�� from trained just cross entropy the primary objective� both primary and complement objectives Training the complement objective finds the parameters � that evenly suppress complement classes without compromising maximizing� g making confident the ground-truth class Complement objective training requires a function complements In ""complement entropydefined complement the softmax cross entropy for neutralizing complement classes neural parameters � are then updated alternating iteratively between ( minimizing cross entropy to increase�� g complement entropy neutralize =g Experimental results ( Section COT improves the accuracies state methods both ( the image classification tasks on ImageNet-2012 , Tiny ImageNet SVHN understanding machine translation Furthermore experimental results also models trained by COT In study Complement Objective Training the complement objective addition We propose complement entropy the complement objective neutralizing complement (incorrect) classesModels trained using COT demonstrate superior performance compared the baseline models We also find COT makes the models robust single-step adversarial attacksCOT extended first in the complement objective chosen the complement entropy Non-entropy-based complement objectives should is left a straight-line future work Secondly the exploration COT on broader applications remains as One example would applying COT on generative models such . Another example would using COT on object detection segmentation Finally this work using complement objective help defend single-step adversarial attacks; the behavior COT on deserves left another future workA ITERATIVE FAST SIGN METHOD TAB9 shows the models under I-FGSM transfer attacks Generally the models trained using COT have lower classification error under I-FGSM transfer attacks The number iteration is set the experiment",0.01,0.4782067753595557
"We present a new method for uncertainty estimation and out-of-distribution detection in neural networks with softmax output. We extend softmax layer with an additional constant input. The corresponding additional output is able to represent the uncertainty of the network. The proposed method requires neither additional parameters nor multiple forward passes nor input preprocessing nor out-of-distribution datasets. We show that our method performs comparably to more computationally expensive methods and outperforms baselines on our experiments from image recognition and sentiment analysis domains. The applications of computational learning systems might cause intrusive effects if we assume that predictions are always as accurate as during the experimental phase. Examples include misclassified traffic signs BID5 and an image tagger that classified two African Americans as gorillas BID3 . This is often caused by overconfidence of models that has been observed in the case of deep neural networks BID8 . Such malfunctions can be prevented if we estimate correctly the uncertainty of the machine learning system. Beside AI safety, uncertainty is useful in the active learning setting in which data collection process is expensive or time consuming BID12 BID32 .While uncertainty estimation in neural networks is an active field of research, the current methods are rarely adopted. It is desirable to develop a method that does not create an additional computational overhead. Such a method could be used in environments that focus on quick training and/or inference. If such a method is simple, the ease of implementation should encourage practitioners to develop danger-aware systems in their work.We suggest a method that measures uncertainty of the neural networks with a softmax output layer. We replace this layer with Inhibited Softmax layer BID33 , and we show that it can be used to express the uncertainty of the model. In our experiments the method outperforms baselines and performs comparably with more computationally expensive methods on the out-of-distribution detection task.We contribute with:• The mathematical explanation why the additional Inhibited Softmax output can be interpreted as an uncertainty measure.• The additions to the Inhibited Softmax that improve its uncertainty approximation properties.• The benchmarks comparing Inhibited Softmax, baseline and contemporary methods for measuring uncertainty in neural networks.The modern Bayesian Neural Networks BID0 BID11 BID25 BID27 BID37 BID9 Zhang et al., 2018; BID15 aim to confront this issue by inferring distribution over the models' weights. This approach has been inspired by Bayesian approaches suggested as early as the nineties BID2 BID29 . A very popular regularisation mean -dropout -also can be a source of approximate Bayesian inference BID7 . Such technique, called Monte Carlo dropout BID6 , belongs to the Bayesian Neural Networks class and has been since used in the real-life scenarios (e.g. Leibig et al., 2017) . In the Bayesian Neural Networks the uncertainty is modelled by computing the predictive entropy or mutual information over the probabilities coming from stochastic predictions BID34 .Other methods to measure uncertainty of neural networks include a non-Bayesian ensemble BID19 , a student network that approximates the Monte Carlo posterior predictive distribution BID16 , modelling Markov chain Monte Carlo samples with a GAN BID38 , Monte Carlo Batch Normalization BID35 and the nearest neighbour analysis of penultimate layer embedding BID28 .The concept of uncertainty is not always considered as a homogeneous whole. Some of the authors distinguish two types of uncertainties that influence predictions of machine learning models BID14 : epistemic uncertainty and aleatoric uncertainty. Epistemic uncertainty represents the lack of knowledge about the source probability distribution of the data. This uncertainty can be reduced by increasing the size of the training data. Aleatoric uncertainty arises from homoscedastic , heteroscedastic and label noises and cannot be reduced by the model. We will follow another source BID27 ) that defines the third type: distributional uncertainty. It appears when the test distribution differs from the training distribution, i.e. when new observations have different nature then the ones the model was trained on.A popular benchmark for assessing the ability of the models to capture the distributional uncertainty is distinguishing the original test set from out-of-distribution dataset BID10 . There are works that focus only on this type of uncertainty BID22 . ODIN BID24 does not require changing already existing network and relies on gradient-based input preprocessing. Another work BID4 ) is close to the functionality of our method , as it only adds a single densely connected layer and uses a single forward pass for a sample.Bayesian neural networks are more computationally demanding as they usually require multiple stochastic passes and/or additional parameters to capture the priors specification.To the best of our knowledge, our method is the first that improves upon the baseline, and meets all the following criteria:• No additional learnable parameters required.• Only single forward pass needed.• No additional out-of-distribution or adversarial observations required.• No input preprocessing.The technique we use, Inhibited Softmax, has been successfully used for the prediction of background class in the task of extraction the objects out of aerial imagery BID33 . The original work does not mention other possible applications of this softmax modification. We presented a new method for uncertainty estimation -Inhibited Softmax. The method can be easily applied to various multilayer neural network architectures and does not require additional parameters, multiple stochastic forward passes or OOD examples.The results show that the method outperforms baseline and performs comparably to the other methods. The method does not deteriorate predictive performance of the classifier.The predictive performance from IMDB/Movie Reviews experiment suggests that even if the observation comes from another probability distribution and the uncertainty measure is able to detect it, the network can still serve as a useful classifier.The improvement of the baseline on the sentiment task after adding suggested regularisation indicates it might be worth to apply such measures to other uncertainty estimation methods.",1157,0.565,677,1.7090103397341212,"We present uncertainty estimation out detection softmax output We extend softmax layer with an additional constant input The corresponding additional output able represent the uncertainty the network The proposed method requires neither additional parameters multiple forward passes nor input preprocessing nor outdistribution datasets We show our method performs comparably baselines on our experiments from image recognition sentiment analysis domains The applications computational learning systems might cause intrusive effects if predictions as during Examples include misclassified traffic signs BID5 an image tagger classified two African Americans . This often caused overconfidence of models has observed BID8 . Such malfunctions estimate correctly the uncertainty the machine learning system Beside AI safety uncertainty useful active learning setting in data collection process expensive BID12 BID32 .While uncertainty estimation an active field rarely adopted It desirable develop create an additional computational overhead Such a method environments focus quick training inference If such a method simple the ease encourage practitioners develop danger-aware systemsWe suggest measures uncertainty the neural networks with a softmax output layer We replace this layer Inhibited Softmax layer BID33 , show express the uncertainty In our experiments the method outperforms baselines performs on out detectionWe contribute with:• The mathematical explanation why the additional Inhibited Softmax output interpreted an uncertainty The additions that improve its uncertainty approximation The benchmarks comparing measuringThe modern Bayesian Neural BID0 2018; aim confront inferring distribution over the models' weights This approach inspired suggested as early BID2 BID29 . A very popular regularisation mean -dropout -also can a source approximate Bayesian inference BID7 . Such technique Monte Carlo dropout BID6 , belongs since used ( Leibig 2017 . In the Bayesian Neural Networks the uncertainty modelled computing the predictive entropy or mutual information over coming BID34 .Other of a student network modelling samples a GAN BID38 , Monte Carlo Batch Normalization BID35 the nearest neighbour analysis penultimate layer embedding concept always considered a homogeneous whole Some distinguish uncertainties that influence predictions machine learning models BID14 : aleatoric uncertainty Epistemic uncertainty represents the lack knowledge the source probability distribution This uncertainty reduced increasing the training data Aleatoric uncertainty arises homoscedastic , heteroscedastic and label noises reduced the model We follow another source BID27 ) defines the third type distributional uncertainty It appears when the test distribution differs new observations different nature then the ones the model.A popular benchmark assessing capture the distributional uncertainty distinguishing the original test set out dataset BID10 . There works focus only this type uncertainty BID22 . ODIN BID24 does changing already existing network and relies gradient-based input preprocessing Another work BID4 ) close the functionality our method , as only adds a single densely connected layer uses a single forward pass a sampleBayesian neural networks more as usually additional parameters capture the priors specificationTo the that improves the baseline, meets No additional learnable parameters single outdistribution adversarial observationsThe technique Inhibited Softmax background class in the task extraction the objects out aerial imagery BID33 The original work does mention other possible applications this softmax modification We presented uncertainty estimation -Inhibited Softmax The method can easily various multilayer neural network does additional parameters, multiple stochastic forward passes OOD examplesThe results baseline performs The method does deteriorate predictive performanceThe predictive performance from IMDB/Movie Reviews experiment suggests even the observation comes another probability distribution and the uncertainty measure able the network serveThe improvement the baseline on the sentiment task after adding suggested regularisation indicates it might apply such measures other uncertainty estimation methods",0.01,0.5105752223590114
"When deep learning is applied to sensitive data sets, many privacy-related implementation issues arise. These issues are especially evident in the healthcare, finance, law and government industries. Homomorphic encryption could allow a server to make inferences on inputs encrypted by a client, but to our best knowledge, there has been no complete implementation of common deep learning operations, for arbitrary model depths, using homomorphic encryption. This paper demonstrates a novel approach, efficiently implementing many deep learning functions with bootstrapped homomorphic encryption. As part of our implementation, we demonstrate Single and Multi-Layer Neural Networks, for the Wisconsin Breast Cancer dataset, as well as a Convolutional Neural Network for MNIST. Our results give promising directions for privacy-preserving representation learning, and the return of data control to users.

 The healthcare, finance, law and government industries often require complete privacy and confidentiality between various stakeholders and partners. With the advent of highly effective AI using deep learning, many real-world tasks can be made more effective and efficient in these industries. However deep learning approaches are seldom performed with privacy preservation in mind, let alone with the encryption of information throughout the entire process.As a result, current deep learning implementations often cannot be used for these confidential applications. Homomorphic Encryption (HE) BID28 offers an opportunity to address the privacy preservation gap, for data processing in general and deep learning in particular. HE can be used to perform computation on encrypted information BID26 , without ever having access to the plaintext information.Our work combines the paradigms of deep learning and homomorphic encryption, allowing improved privacy for existing server-side models , and thus enabling many novel, intelligent, privacy-guaranteeing services.Figure 1: General overview of our privacy-preserving method for deep learning. Encrypted inputs are fed into our hybrid model on the server-side, and this produces encrypted outputs. Our work shows that with the proposed Hybrid Homomorphic Encryption system, almost any production deep learning model can be converted, such that it can process encrypted inputs. Our design also makes it feasible to implement new or bespoke functionality, as the deep learning paradigm evolves.Depending on the value of the problem and the size of the model, this system is already viable for production use. New and updated HE libraries appear frequently, and our code should adapt to any library which implements homomorphic logic gates. Therefore our software could potentially receive ""free"" performance gains, as the HE paradigm evolves.",483,0.271,302,1.599337748344371,"When deep learning sensitive data sets many privacy-related implementation issues These issues especially evident the healthcare, finance, law and government industries Homomorphic encryption could a server make inferences on inputs encrypted to our best knowledge common deep learning operations for arbitrary model depths using This paper demonstrates, efficiently implementing many deep learning functions bootstrapped homomorphic encryption As our implementation demonstrate Single and Multi-Layer Neural Networks for the Wisconsin Breast Cancer dataset MNIST Our results give promising directions privacy-preserving representation learning the return data control users The healthcare, finance, law and government industries often require complete privacy between various stakeholders partners With highly effective AI using made effective efficient these industries However deep learning approaches seldom performed privacy preservation let the encryption throughoutAs current deep learning implementations these confidential applications Homomorphic EncryptionHE BID28 offers an opportunity address the privacy preservation gap for data processing deep learning HE can used perform computation encrypted information BID26 , without ever accessOur work combines homomorphic encryption allowing improved privacy existing server-side models , thus enabling many novel, intelligent, privacy-guaranteeing servicesFigure General overview our privacy-preserving method Encrypted inputs fed our hybrid model on this produces Our work shows with the proposed Hybrid Homomorphic Encryption system almost any production deep learning model converted, such process encrypted inputs Our design also makes feasible implement new or bespoke functionality the deep learning paradigm evolvesDepending size this system already viable production use New and updated HE libraries appear frequently our code should adapt any library which implements homomorphic logic gates Therefore our software could potentially receive ""free"" performance gains the HE paradigm evolves",0.0,0.23113909522644946
"In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct machine-checkable proofs in a step-by-step manner. Hence, they provide an opportunity to explore theorem proving with human supervision. We use GamePad to synthesize proofs for a simple algebraic rewrite problem and train baseline models for a formalization of the Feit-Thompson theorem. We address position evaluation (i.e., predict the number of proof steps left) and tactic prediction (i.e., predict the next proof step) tasks, which arise naturally in tactic-based theorem proving. Theorem proving is a challenging AI task that involves symbolic reasoning (e.g., SMT solvers BID2 ) and intuition guided search. Recent work BID7 Loos et al., 2017; has shown the promise of applying deep learning techniques in this domain, primarily on tasks useful for automated theorem provers (e.g., premise selection) which operate with little to no human supervision. In this work, we aim to move closer to learning on proofs constructed with human supervision.We look at theorem proving in the realm of formal proofs. A formal proof is systematically derived in a formal system, which makes it possible to algorithmically (i.e., with a computer) check these proofs for correctness. Thus, formal proofs provide perfect learning signal-theorem statements and proofs are unambiguous. Human mathematicians usually do not write proofs in this style, and instead, construct and communicate proofs in natural language. Although the form and level of detail involved in each kind of proof differ, the logical content is similar in both contexts.Our work focuses on interactive theorem provers (ITPs), which are software tools that enable human users to construct formal proofs. ITPs have at least two features that make them compelling environments for exploring the application of learning techniques to theorem proving. First and foremost, ITPs provide full-fledged programmable environments. Consequently, any machine learning infrastructure built for an ITP can be reused across any problem domain crafted to study an aspect of learning and theorem proving. Second, the proofs are constructed by humans, and thus, have the constraint that they must be relatively human-understandable. Hence, ITPs provide access to large amounts of supervised data (i.e., expert-constructed proofs of theorems that are mathematically interesting). For example, ITPs have been used to build and check the proofs of large mathematical theorems such as the Feit-Thompson theorem BID6 and provide provable guarantees on complex pieces of software such as the CompCert C compiler BID13 .We introduce a system called GamePad 1 that exposes parts of the Coq ITP to enable machine learning tasks and explore a few use cases. We focus on the Coq proof assistant for two reasons. First , Figure 1 : A proof script in Coq (left) and the resulting proof states, proof steps, and the complete proof tree (right). A proof state consists of a context (pink rectangles) and a goal (white rectangles). The initial proof state has as its goal the statement we are trying to prove and an empty context. The arrows indicate what tactic the prover used. The final states of the proof are indicated by the red circles and can be transitioned to only when the goal in the previous state is trivially true.Coq is a mature system with an active developer community that has been used to formalize nontrivial theorems, including Feit-Thompson and CompCert. Second, Coq supports the extraction of verified software. Consequently , one can prove that a program is correct and then run the verified program. The ease of extraction makes Coq a popular choice for program verification.Our contributions are the following. First, we introduce GamePad, which provides a structured Python representation of Coq proofs (Section 3), including all the proof states encountered in a proof, the steps taken, and expression abstract syntax trees (ASTs). The tool also enables lightweight interaction with Coq so that it can be used to dynamically build proofs (e.g., used as an environment for reinforcement learning). Tasks that can leverage this structured representation (Section 4) include position evaluation (i.e., predict the number of proof steps left) and tactic prediction (i.e., predict the next proof step to take). We also discuss how we can use the structured representation to embed proof states into R D (Section 5) . Second, we demonstrate the synthesis of Coq proof scripts that makes use of a tactic prediction model for a hand-crafted algebraic rewriting problem (Section 6). Third and finally, we apply baseline models for position evaluation and tactic prediction to the FeitThompson formalization using data extracted by GamePad (Section 7).The code for GamePad, as well as the associated data sets, models and results, are open source on GitHub at https://github.com/ml4tp/gamepad. In this work, we look at theorem proving problem through the lens of a system that enables learning with proofs constructed with human supervision. We highlight three key aspects of the problem at this level. The first concerns obtaining inputs to a learning algorithm that approximate the level of abstraction faced by a human prover. For this, we use an ITP, as it retains aspects of human supervision. GamePad preserves the structure of the proofs (e.g., annotations regarding implicit arguments) so they can be used for building models. The second involves building models that employ the game-like structure of ITP proofs. Here, we experiment with tactic prediction for toy and real world data sets. Finally, as a consequence of theorem proving at a higher-level (compared to SMT solvers), we will need to be careful to distinguish the syntax from the semantics of terms. Our current approach is to provide structured representations of terms so that more semantic structure can be exploited. While our results are preliminary, our hope is that GamePad provides an accessible starting point to explore the application of machine learning in the context of interactive theorem proving.",1238,0.72,741,1.670715249662618,"In this paper introduce called GamePad that explore the application theorem the Coq proof assistant Interactive theorem provers such Coq enable users construct machine-checkable proofs step Hence they provide explore theorem proving human supervision We use GamePad synthesize proofs a simple algebraic rewrite problem and train baseline models a formalization the Feit-Thompson theorem We address position evaluation ( predict the number proof steps left arise naturally tactic-based theorem proving Theorem proving is a challenging AI task symbolic reasoning SMT solvers BID2 ) intuition guided search Recent work BID7 Loos et; has the promise applying this domain primarily on tasks useful automated theorem provers which operate little to In this work aim move closer learning on proofs constructed human supervisionWe look theorem proving the realm A formal proof systematically derived makes algorithmically ( with check these proofs Thus formal proofs provide perfect learning signal-theorem statements proofs unambiguous Human mathematicians usually write proofs instead construct and communicate Although the form and level detail involved each kind proof differ the logical content similar contextsOur work focuses interactive theorem provers software tools enable human users construct ITPs at least two features compelling environments exploring the application learning techniques to theorem proving First and ITPs provide full-fledged programmable environments any machine learning infrastructure built an ITP can reused any problem domain crafted to study an aspect learning and theorem proving Second the proofs constructed humans thus have the constraint relatively humanunderstandable Hence ITPs provide access large amounts supervised data (i.e., expert-constructed proofs that mathematically interesting For example ITPs build and check the proofs large mathematical theorems such the Feit-Thompson theorem BID6 provide provable guarantees complex pieces software the CompCert C compiler .We introduce GamePad 1 exposes parts the Coq ITP enable machine learning tasks explore We focus the Coq proof assistant two reasons First , Figure : A proof script in Coqleft the resulting proof states proof steps the complete proof tree A proof state consists a contextpink rectangles a goal The initial proof state as the statement we and an empty context The arrows indicate what tactic the prover The final states the proof indicated can transitioned only when the goal in triviallyCoq a mature system an active developer community used formalize Feit-Thompson CompCert Second Coq supports the extraction verified software , one prove a program correct and then run the verified program The ease extraction makes Coq popular program verificationOur contributions the following First introduce GamePad provides a structured Python representation Coq proofsSection all the proof states encountered the steps expression abstract syntax treesASTs The tool also enables lightweight interaction Coq so dynamically build proofs ( used an environment reinforcement learning Tasks leverage this structured representation (Section position evaluation predict proof steps left tactic prediction take We also discuss the structured representation embed proof states R D (Section . Second demonstrate the synthesis Coq proof scripts makes a tactic prediction model for a hand-crafted algebraic rewriting problemSection Third and finally apply baseline models position evaluation and tactic prediction the FeitThompson formalization using data extracted by GamePadSection 7).The code, models results open source In this work look theorem problem through a system enables learning with proofs constructed human supervision We highlight at this level The first concerns obtaining inputs a learning algorithm approximate abstraction faced a human prover For this, use an ITP, as retains aspects human supervision GamePad preserves the structure the proofs ( regarding implicit arguments building models second involves building models employ the game-like structure ITP proofs Here, experiment tactic prediction toy real world data sets Finally as a consequence theorem proving atcompared SMT solvers will be the syntax terms Our current approach provide structured representations terms so more semantic structure exploited While our results our hope GamePad provides an accessible starting point the application interactive theorem proving",0.01,0.4130026974266467
"Deep neural networks are usually huge, which significantly limits the deployment on low-end devices. In recent years, many
 weight-quantized models have  been proposed. They have small storage and fast inference, but training can still be time-consuming. This can be improved with distributed learning. To reduce the high communication cost due to worker-server synchronization, recently gradient quantization has also been proposed to train deep networks with full-precision weights. 
 In this paper, we theoretically study how the combination of both weight and gradient quantization affects convergence.
 We show  that (i) weight-quantized models converge to an error related to the weight quantization resolution and weight dimension; (ii) quantizing gradients slows convergence by a factor related to the gradient quantization resolution and dimension; and (iii) clipping the gradient before quantization renders this factor dimension-free, thus allowing the use of fewer bits for gradient quantization. Empirical experiments confirm the theoretical convergence results, and demonstrate that quantized networks can speed up training and have comparable performance as full-precision networks. Deep neural networks are usually huge. The high demand in time and space can significantly limit deployment on low-end devices. To alleviate this problem, many approaches have been recently proposed to compress deep networks. One direction is network quantization, which represents each network weight with a small number of bits. Besides significantly reducing the model size, it also accelerates network training and inference. Many weight quantization methods aim at approximating the full-precision weights in each iteration BID3 BID20 BID23 BID15 BID19 BID8 . Recently, loss-aware quantization minimizes the loss directly w.r.t. the quantized weights BID11 BID10 BID14 , and often achieves better performance than approximation-based methods.Distributed learning can further speed up training of weight-quantized networks BID6 . A key challenge is on reducing the expensive communication cost incurred during synchronization of the gradients and model parameters BID17 . Recently, algorithms that sparsify BID0 BID28 or quantize the gradients BID26 BID29 BID2 have been proposed.In this paper, we consider quantization of both the weights and gradients in a distributed environment. Quantizing both weights and gradients has been explored in the DoReFa-Net BID32 , QNN BID12 , WAGE BID30 and ZipML . We differ from them in two aspects. First, existing methods mainly consider learning on a single machine, and gradient quantization is used to reduce the computations in backpropagation. On the other hand, we consider a distributed environment, and use gradient quantization to reduce communication cost and accelerate distributed learning of weight-quantized networks. Second, while DoReFa-Net, QNN and WAGE show impressive empirical results on the quantized network, theoretical guarantees are not provided. ZipML provides convergence analysis, but is limited to stochastic weight quantization, square loss with the linear model, and requires the stochastic gradients to be unbiased. This can be restrictive as most state-of-the-art weight quantization methods BID23 BID20 BID15 BID8 BID11 BID10 ) are deterministic, and the resultant stochastic gradients are biased.In this paper, we relax the restrictions on the loss function, and study in an online learning setting how the gradient precision affects convergence of weight-quantized networks in a distributed environment. The main findings are:1. With either full-precision or quantized gradients, the average regret of loss-aware weight quantization does not converge to zero, but to an error related to the weight quantization resolution ∆ w and dimension d. The smaller the ∆ w or d, the smaller is the error (Theorems 1 and 2). 2. With either full-precision or quantized gradients, the average regret converges with a O(1/ √ T ) rate to the error, where T is the number of iterations. However, gradient quantization slows convergence (relative to using full-precision gradients) by a factor related to gradient quantization resolution ∆ g and d. The larger the ∆ g or d, the slower is the convergence FIG0 ). This can be problematic when (i) the weight quantized model has a large d (e.g., deep networks); and (ii) the communication cost is a bottleneck in the distributed setting, which favors a small number of bits for the gradients, and thus a large ∆ g . 3. For gradients following the normal distribution, gradient clipping renders the speed degradation mentioned above dimension-free. However, an additional error is incurred. The convergence speedup and error are related to how aggressive clipping is performed. More aggressive clipping results in faster convergence, but a larger error (Theorem 3). 4. Empirical results show that quantizing gradients significantly reduce communication cost, and gradient clipping makes speed degradation caused by gradient quantization negligible. With quantized clipped gradients, distributed training of weight-quantized networks is much faster, while comparable accuracy with the use of full-precision gradients is maintained (Section 4).Notations . For a vector x, √ x is the element-wise square root, x 2 is the element-wise square, Diag(x) returns a diagonal matrix with x on the diagonal, and x y is the element-wise multiplication of vectors x and y. For a matrix Q, x 2 Q = x Qx. For a matrix X, √ X is the element-wise square root, and diag(X) returns a vector extracted from the diagonal elements of X. In this paper, we studied loss-aware weight-quantized networks with quantized gradient for efficient communication in a distributed environment. Convergence analysis is provided for weight-quantized models with full-precision, quantized and quantized clipped gradients. Empirical experiments confirm the theoretical results, and demonstrate that quantized networks can speed up training and have comparable performance as full-precision networks.",1186,0.716,682,1.7390029325513197,"Deep neural networks usually huge which significantly the deployment on In many weight-quantized models They small storage and fast inference training can still time This can improved distributed learning To reduce the high communication cost due worker-server synchronization recently gradient quantization also train deep networks full-precision weights In theoretically study the combination both weight gradient quantization affects convergence We show (i) weight-quantized models converge an error related the weight quantization resolution weight dimension; slows convergence related dimension clipping the gradient before renders this factor dimension- fewer bits Empirical experiments confirm the theoretical convergence results demonstrate quantized networks speed training have as Deep neural networks usually huge The high demand time can significantly limit deployment on To alleviate many approaches recently compress deep networks One direction network quantization represents each network weight with Besides significantly the model size network training inference Many weight quantization methods aim the full-precision weights each iteration BID3 BID20 . Recently loss-aware quantization minimizes directly w.r.t BID11 BID10 BID14 often achieves approximation-based methodsDistributed learning can further speed training weight-quantized networks BID6 A key challenge on reducing the expensive communication cost incurred synchronization the gradients model parameters BID17 . Recently algorithms sparsify BID0 BID28 or quantize the gradients haveIn consider quantization both the weights a distributed environment Quantizing both weights gradients has explored the DoReFa-Net BID32 , QNN BID12 WAGE BID30 ZipML . We differ them two aspects First existing methods mainly consider learning on gradient quantization reduce On consider a distributed environment use gradient quantization reduce communication cost accelerate distributed learning of weight-quantized networks Second while DoReFa-Net, QNN WAGE show impressive empirical results the quantized network theoretical guarantees provided ZipML provides convergence analysis but limited stochastic weight quantization square loss with the linear model requires unbiased This can restrictive most stateof weight quantization ) deterministic biasedIn relax study in an online learning setting the gradient precision affects convergence weight-quantized networks The main findings are:1 With either full-precision or quantized gradients the average regret loss-aware weight quantization does converge to related the weight quantization resolution �� w and dimension smaller � w or d the errorTheorems 2 With either full-precision or quantized gradients average regret converges a O(1/ �� T ) rate to However gradient quantization slows convergence (relative using related gradient quantization resolution �� g and d. larger � g or d slower is FIG0 This can problematic ( the weight quantized model a large d the communication cost a bottleneck the distributed setting favors bits the gradients � g 3 For gradients following gradient clipping renders the speed degradation mentioned dimensionfree However an additional error incurred The convergence speedup error are related how aggressive clipping performed More aggressive clipping results faster convergence a larger error (Theorem 4 quantizing gradients significantly reduce communication cost gradient clipping makes speed degradation caused gradient quantization negligible With quantized clipped gradients distributed training weight-quantized networks much while comparable accuracy the use maintained (Section 4).Notations . For vector x � is, x 2 returns a diagonal matrix on y vectors For a matrix Q x 2 Q x Qx is, diag(X returns extracted In studied loss-aware weight-quantized networks quantized gradient for efficient communication Convergence analysis provided weight-quantized models full-precision quantized clipped gradients Empirical experiments confirm the theoretical results demonstrate quantized networks speed training have comparable performance as",0.01,0.5869937137368407
"Sequential learning, also called lifelong learning, studies the problem of learning tasks in a sequence with access restricted to only the data of the current task. In this paper we look at a scenario with fixed model capacity, and postulate that the learning process should not be selfish, i.e. it should account for future tasks to be added and thus leave enough capacity for them. To achieve Selfless Sequential Learning we study different regularization strategies and activation functions. We find that
 imposing sparsity at the level of the representation (i.e. neuron activations) is more beneficial for sequential learning than encouraging parameter sparsity. In particular, we propose a novel regularizer, that encourages representation sparsity by means of neural inhibition. It results in few active neurons which in turn leaves more free neurons to be utilized by upcoming tasks. As neural inhibition over an entire layer can be too drastic, especially for complex tasks requiring strong representations,
 our regularizer only inhibits other neurons in a local neighbourhood, inspired by lateral inhibition processes in the brain. We combine our novel regularizer with state-of-the-art lifelong learning methods that penalize changes to important previously learned parts of the network. We show that our new regularizer leads to increased sparsity which translates in consistent performance improvement on diverse datasets. Sequential learning, also referred to as continual, incremental, or lifelong learning (LLL), studies the problem of learning a sequence of tasks, one at a time, without access to the training data of previous or future tasks. When learning a new task, a key challenge in this context is how to avoid catastrophic interference with the tasks learned previously BID11 BID25 . Some methods exploit an additional episodic memory to store a small amount of previous tasks data to regularize future task learning (e.g. BID28 ). Others store previous tasks models and at test time, select one model or merge the models BID1 BID23 . In contrast, in this work we are interested in the challenging situation of learning a sequence of tasks without access to any previous or future task data and restricted to a fixed model capacity, as also studied in ; ; BID8 ; BID31 ; BID38 . This scenario not only has many practical benefits, including privacy and scalability, but also resembles more closely how the mammalian brain learns tasks over time.The mammalian brain is composed of billions of neurons. Yet at any given time, information is represented by only a few active neurons resulting in a sparsity of 90-95% BID24 . In neural biology, lateral inhibition describes the process where an activated neuron reduces the activity of its weaker neighbors. This creates a powerful decorrelated and compact representation with minimum interference between different input patterns in the brain BID49 . This is in stark contrast with artificial neural networks, which typically learn dense representations that are highly entangled BID3 . Such an entangled representation is quite sensitive to changes in the case. First layer indicates input patterns. Learning the first task utilizes parts indicated in red. Task 2 has different input patterns and uses parts shown in green. Orange indicates changed neurons activations as a result of the second task. In (a), when an example from the first task is encountered again, the activations of the first layer will not be affected by the changes, however, the second and later layer activations are changed. Such interference is largely reduced when imposing sparsity on the representation (b).input patterns, in that it responds differently to input patterns with only small variations. BID11 suggests that an overlapped internal representation plays a crucial role in catastrophic forgetting and reducing this overlap would result in a reduced interference. BID5 show that when the amount of overfitting in a neural network is reduced, the representation correlation is also reduced. As such , learning a disentangled representation is more powerful and less vulnerable to catastrophic interference. However , if the learned disentangled representation at a given task is not sparse, only little capacity is left for the learning of new tasks. This would in turn result in either an underfitting to the new tasks or again a forgetting of previous tasks. In contrast , a sparse and decorrelated representation would lead to a powerful representation and at the same time enough free neurons that can be changed without interference with the neural activations learned for the previous tasks.In general, sparsity in neural networks can be thought of either in terms of the network parameters or in terms of the representation (i.e., the activations). In this paper we postulate, and confirm experimentally, that a sparse and decorrelated representation is preferable over parameter sparsity in a sequential learning scenario. There are two arguments for this: first, a sparse representation is less sensitive to new and different patterns (such as data from new tasks) and second, the training procedure of the new tasks can use the free neurons leading to less interference with the previous tasks, hence reducing forgetting. In contrast, when the effective parameters are spread among different neurons, changing the ineffective ones would change the function of their corresponding neurons and hence interfere with previous tasks (see also FIG0 ). Based on these observations, we propose a new regularizer that exhibits a behavior similar to the lateral inhibition in biological neurons. The main idea of our regularizer is to penalize neurons that are active at the same time. This leads to more sparsity and a decorrelated representation. However, complex tasks may actually require multiple active neurons in a layer at the same time to learn a strong representation. Therefore, our regularizer , Sparse coding through Local Neural Inhibition and Discounting (SLNID), only penalizes neurons locally. Furthermore, we don't want inhibition to affect previously learned tasks, even if later tasks use neurons from earlier tasks. An important component of SLNID is thus to discount inhibition from/to neurons which have high neuron importance -a new concept that we introduce in analogy to parameter importance BID50 . When combined with a state-of-the-art important parameters preservation method , our proposed regularizer leads to sparse and decorrelated representations which improves the lifelong learning performance.Our contribution is threefold. First, we direct attention to Selfless Sequential Learning and study a diverse set of representation based regularizers, parameter based regularizers, as well as sparsity inducing activation functions to this end. These have not been studied extensively in the lifelong learning literature before. Second, we propose a novel regularizer, SLNID, which is inspired by lateral inhibition in the brain. Third, we show that our proposed regularizer consistently outperforms alternatives on three diverse datasets (Permuted MNIST, CIFAR, Tiny Imagenet) and we compare to and outperform state-of-the-art LLL approaches on an 8-task object classification challenge. SLNID can be applied to different regularization based LLL approaches, and we show experiments with MAS and EWC .In the following, we first discuss related approaches to LLL and different regularization criteria from a LLL perspective (Section 2). We proceed by introducing Selfless Sequential Learning and detailing our novel regularizer (Section 3). Section 4 describes our experimental evaluation, while Section 5 concludes the paper. In this paper we study the problem of sequential learning using a network with fixed capacity -a prerequisite for a scalable and computationally efficient solution. A key insight of our approach is that in the context of sequential learning (as opposed to other contexts where sparsity is imposed, such as network compression or avoiding overfitting), sparsity should be imposed at the level of the representation rather than at the level of the network parameters. Inspired by lateral inhibition in the mammalian brain, we impose sparsity by means of a new regularizer that decorrelates nearby active neurons. We integrate this in a model which learns selflessly a new task by leaving capacity for future tasks and at the same time avoids forgetting previous tasks by taking into account neurons importance.",1573,0.899,919,1.7116430903155604,"Sequential learning also lifelong learning studies tasks with access restricted In look fixed model capacity postulate the learning process selfish account future tasks to added thus leave enough capacity them To achieve Selfless Sequential Learning study different regularization strategies activation functions We find imposing sparsity at the representation sequential learning encouraging parameter sparsity In particular propose a novel regularizer encourages representation sparsity means neural inhibition It results few active neurons which leaves utilized upcoming tasks As neural inhibition over an entire layer can too drastic especially requiring strong representations our regularizer only inhibits other neurons a local neighbourhood inspired lateral inhibition processes We combine our novel regularizer state lifelong methods penalize changes important previously learned parts the network We show our new regularizer leads increased sparsity which translates in consistent performance improvement on diverse datasets Sequential learning also continual, incremental, or lifelong learningLLL studies the problem tasks one access of When learning a key challenge this context avoid catastrophic interference learned previously BID11 BID25 . Some methods exploit an additional episodic memory to previous tasks data to regularize future task learninge.g. BID28 Others store previous tasks models at test time select merge BID1 BID23 . In contrast this work the challenging situation learning a sequence tasks without access any previous or future task data restricted a fixed model capacity also studied ; ; BID8 ; This scenario not including privacy resembles more closely the mammalian brain learns tasks overThe mammalian brain billions Yet at information represented only a few active neurons resulting a sparsity BID24 . In neural biology lateral inhibition describes where reduces its weaker neighbors This creates a powerful decorrelated and compact representation with minimum interference different input patterns the brain BID49 . This in artificial neural networks typically learn dense representations highly entangled BID3 . Such an entangled representation quite sensitive the case First layer indicates input patterns Learning the first task utilizes parts indicated Task 2 has different input patterns uses parts shown green Orange indicates changed neurons activations as the second task In ( when an example from the first task encountered again the activations will not, however changed Such interference largely reduced imposing sparsity the representation (b).input patterns that responds differently with only small variations BID11 suggests an overlapped internal representation plays catastrophic forgetting reducing this overlap would result a reduced interference. BID5 show when the amount overfitting the representation correlation also As such , learning a disentangled representation more powerful vulnerable catastrophic interference However , the learned disentangled representation at a given task sparse only little capacity This would in either an underfitting to the new tasks again a forgetting In contrast , a sparse and decorrelated representation would lead a powerful representation at enough free neurons that changed interference learned forIn general sparsity either the network parameters In postulate, and confirm a sparse decorrelated representation preferable parameter sparsity a sequential learning scenario There two arguments a sparse representation less sensitive new and different patterns data from new tasks the training procedure of use the free neurons leading less interference hence forgetting In contrast the effective parameters spread among different neurons changing the ineffective ones would interfere previous tasks FIG0 Based these observations a new regularizer exhibits the lateral inhibition in biological neurons The main idea our regularizer penalize neurons This leads more sparsity a decorrelated representation However complex tasks actually multiple active neurons a layer at learn a strong representation Therefore our regularizer , Sparse coding through Local Neural Inhibition DiscountingSLNID only neurons locally Furthermore do inhibition affect previously learned tasks even later tasks use neurons An important component SLNID thus discount inhibition from/ neurons which high neuron importance -a new concept introduce analogy parameter importance BID50 When combined state important parameters preservation , our proposed regularizer leads sparse decorrelated representations which improves the lifelong learning performanceOur contribution threefold First direct attention Selfless Sequential Learning study a diverse set representation based regularizers parameter based regularizers as sparsity inducing activation functions to this end These have studied the lifelong learning literature before Second propose a novel regularizer SLNID inspired lateral inhibition Third show our proposed regularizer consistently alternatives on three diverse datasetsPermuted MNIST Tiny Imagenet compare to and state LLL approaches an 8-task object classification challenge SLNID can applied different regularization based LLL approaches show experiments MAS EWC .In first related approaches different regularization criteria fromSection We proceed introducing Selfless Sequential Learning detailing our novel regularizerSection Section describes our experimental evaluation, while concludes In study the problem sequential learning fixed capacity -a prerequisite A key insight sequential learning other contexts sparsity imposed network compression avoiding imposed rather the network parameters Inspired lateral inhibition impose sparsity by means a new regularizer decorrelates nearby active neurons We integrate this in a model learns selflessly a new task leaving capacity at avoids forgetting by taking account neurons importance",0.01,0.5172832395295816
"A Synaptic Neural Network (SynaNN) consists of synapses and neurons. Inspired by the synapse research of neuroscience, we built a synapse model with a nonlinear synapse function of excitatory and inhibitory channel probabilities. Introduced the concept of surprisal space and constructed a commutative diagram, we proved that the inhibitory probability function -log(1-exp(-x)) in surprisal space is the topologically conjugate function of the inhibitory complementary probability 1-x in probability space. Furthermore, we found that the derivative of the synapse over the parameter in the surprisal space is equal to the negative Bose-Einstein distribution. In addition, we constructed a fully connected synapse graph (tensor) as a synapse block of a synaptic neural network. Moreover, we proved the gradient formula of a cross-entropy loss function over parameters, so synapse learning can work with the gradient descent and backpropagation algorithms. In the proof-of-concept experiment, we performed an MNIST training and testing on the MLP model with synapse network as hidden layers. Synapses play an important role in biological neural networks BID11 ). They are joint points of neurons' connection with the capability of learning and memory in neural networks. Based on the analysis of excitatory and inhibitory channels of synapses BID11 ), we proposed a probability model BID6 for probability introduction) of the synapse together with a non-linear function of excitatory and inhibitory probabilities BID17 (synapse function)). Inspired by the concept of surprisal from (Jones (1979)(self-information), BID15 , BID2 (surprisal analysis), BID16 (surprisal theory in language)) or negative logarithmic space BID21 ), we proposed the concept of surprisal space and represented the synapse function as the addition of the excitatory function and inhibitory function in the surprisal space. By applying a commutative diagram, we figured out the fine structure of inhibitory function and proved that it was the topologically conjugate function of an inhibitory function. Moreover, we discovered (rediscovered) that the derivative of the inhibitory function over parameter was equal to the negative Bose-Einstein distribution BID22 ). Furthermore, we constructed a fully connected synapse graph and figured out its synapse tensor expression. From synapse tensor and a cross-entropy loss function, we found and proved its gradient formula that was the basis for gradient descent learning and using backpropagation algorithm. In surprisal space, the parameter (weight) updating for learning was the addition of the value of the negative Bose-Einstein distribution. Finally, we designed the program to implement a Multiple Layer Perceptrons (MLP) BID20 ) for MNIST BID14 ) and tested it to achieve the near equal accuracy of standard MLP in the same setting. In this paper, we presented and analyzed a Synaptic Neural Network (SynaNN). We found the fine structure of synapse and the construction of synapse network as well as the BE distribution in the gradient descent learning. In surprisal space, the input of a neuron is the addition of the identity function and the sum of topologically conjugate functions of inhibitory synapses which is the sum of bits of information. The formula of surprisal synapse function is defined as LS(u, v; θ, γ) = (θ + u) + (I • F • I −1 )(γ + v))The non-linear synaptic neural network may be implemented by physical or chemical components.Instead of using a simple linear synapse function, more synapse functions maybe found in the researches and applications of neural network.",732,0.366,450,1.6266666666666667,"A Synaptic Neural Network (SynaNN consists Inspired the synapse research neuroscience built of inhibitory channel probabilities Introduced the concept surprisal space constructed a commutative diagram we proved inhibitory probability -log(1 in the topologically conjugate function the inhibitory complementary probability 1 Furthermore the derivative the synapse over the parameter in the surprisal space equal the negative Bose-Einstein distribution In addition constructed a fully connected synapse graphtensor as of a synaptic neural network Moreover we proved the gradient formula over parameters, so synapse learning work the gradient descent and In proof experiment performed an MNIST training and the MLP model synapse network as hidden layers Synapses play biological neural networks BID11 ). They joint points neurons' connection the capability learning neural networks Based the analysis excitatory BID11 ), proposed a probability model BID6 probability introduction) together BID17 (synapse function Inspired surprisal from (Jones (1979)(self-information BID15 , (surprisal analysis theory in language or negative space BID21 proposed and represented the synapse function the addition By applying a commutative diagram figured the fine structure inhibitory function proved the topologically conjugate function Moreover we discovered (rediscovered the derivative the inhibitory function over parameter was equal the negative Bose-Einstein distribution BID22 ). Furthermore constructed a fully connected synapse graph and figured its synapse tensor expression From synapse tensor and a cross-entropy loss function found and proved its gradient formula that was gradient learning using In surprisal space the parameter (weight updating for learning was the addition the negative Bose-Einstein distribution Finally designed the program implement a Multiple Layer PerceptronsMLP) BID20 ) MNIST BID14 ) tested to achieve the near equal accuracy in the same setting In this paper presented and a Synaptic Neural NetworkSynaNN We found the fine structure synapse and the construction as the BE distribution the gradient descent learning In surprisal space the input a neuron the addition the identity function and topologically conjugate functions inhibitory synapses which bits The formula surprisal synapse function defined LS(u;I • F −1(γ + v))The non-linear synaptic neural network may implemented physical or chemical componentsInstead more synapse functions maybe found the researches and applications",0.0,0.30077077801914903
"Many types of relations in physical, biological, social and information systems can be modeled as homogeneous or heterogeneous concept graphs. Hence, learning from and with graph embeddings has drawn a great deal of research interest recently, but only ad hoc solutions have been obtained this far. In this paper, we conjecture that the one-shot supervised learning mechanism is a bottleneck in improving the performance of the graph embedding learning algorithms, and propose to extend this by introducing a multi-shot unsupervised learning framework. Empirical results on several real-world data set show that the proposed model consistently and significantly outperforms existing state-of-the-art approaches on knowledge base completion and graph based multi-label classification tasks. Recent studies have highlighted the importance of learning distributed representations for symbolic data in a wide variety of artificial intelligence tasks BID2 . Research on word embeddings BID14 has led to breakthroughs in many related areas, such as machine translation BID0 , question answering BID28 , and visual-semantic alignments BID10 . However, learning to predict for large-scale knowledge graphs (KGs) is still a challenging problem left, this is largely due to the diversity of the ontologies, and the semantic richness of the concepts, which makes it really hard to generate proper and universally applicable graph embeddings, simply based on word-level embeddings BID4 .Being able to generate reasonable and accurate distributed representations for large-scale knowledge graphs would be particularly valuable, in that it may help predict unobserved facts from limited concepts, uncover gaps in our knowledge, suggest new downstream applications, which clearly reflects the central concerns of the artificial intelligence BID18 BID9 . Therefore , massive attention has been devoted to the potential of embedding entities and relationships of multi-relational data in low-dimensional vector spaces in recent years BID26 .In this paper , we consider the problem of developing simple and efficient model for learning neural representation of generalized knowledge graphs, including the multi-relational heterogeneous graphs, and more specifically defined homogeneous graphs (such as social and biological networks).Following the pioneer work of BID17 and BID3 , almost all of the stateof-the-art approaches try to model the graph embedding learning problem as supervised binary classification problems, their objective functions are usually one-shot (single purpose) . We argue that prior research in this area might have been affected and biased by "" established priors"", which prevents the formulation of a methodology that is objective enough to cope with the highly sparse knowledge graphs. We propose to handle the embedded learning problem of knowledge graphs with an unsupervised neural network model, called the Graph Embedding Network (GEN). The proposed model consists of three simple multi-layer perceptron (MLP) cells, each cell operates in response to a different ""query"" with regard to the input fact, which will be trained sequentially. The formulation of the model is inspired by the neural sequence-to-sequence (seq2seq) model BID23 , except that we attempt to use the MLP cells to mimic the sequence learning capability of the recurrent neural network (RNN), to model the semantic structure of the knowledge graphs.The major contribution of this paper is that: (1) we propose GEN, a novel and efficient multishot framework for embedding learning in generalized knowledge graphs. (2) We show how GEN is in accordance with established principles in cognitive science, providing flexibility in learning representations that works on graphs conforming to different domains. Representation learning of knowledge graphs is a key concern for artificial intelligence and cognitive science. Many types of relations in physical, biological, social and information systems can be modeled with concept (knowledge) graphs. In this paper, we present an efficient scalable framework for learning conceptual embeddings of entities and relations in generalized knowledge graphs, including the homogeneous and heterogeneous graphs. We give evidence that the proposed model learns good representations of all these graphs for knowledge inference and supervised learning. For future work, we plan to investigate more thoroughly the efficacy of the proposed modeling framework, with respect to the decomposition of the semantic information conveyed by the linked concepts into elementary information, i.e. the four Q&A pairs. Also, we seek to enhance the quality of scientific investigations and theoretical conceptualizations on graph embedding learning in the context of semantic interoperability, for there is usually no possibility to interpret the embedded information meaningfully and accurately in order to produce useful results as defined by existing algorithms.",861,0.364,514,1.6750972762645915,"Many types relations physical, biological, social and information systems modeled homogeneous or heterogeneous concept graphs Hence learning and with graph embeddings has drawn research interest recently only ad hoc solutions obtained this In this paper conjecture the one-shot supervised learning mechanism a bottleneck improving the graph learning propose to extend Empirical results on several real data set show the proposed model consistently and existing state on knowledge base completion graph based multi-label classification tasks Recent studies highlighted learning distributed representations symbolic data artificial intelligence tasks BID2 . Research word embeddings BID14 has led many related areas machine translation BID0 , question visual-semantic alignments However learning predict for large-scale knowledge graphs (KGs still left, this largely the diversity the ontologies the semantic richness really generate proper and universally applicable graph embeddings simply based BID4 .Being reasonable and accurate distributed representations would particularly in may predict unobserved facts limited concepts uncover gaps suggest new downstream applications which clearly reflects the central concerns the artificial intelligence BID18 BID9 Therefore , massive attention embedding entities relationships of multi-relational data in BID26 .In consider developing simple and efficient model learning neural representation generalized knowledge graphs more specifically defined homogeneous graphssuch social and biological networks).Following the pioneer work BID17 almost all try model the graph embedding learning problem supervised binary classification problems their objective functions usually one-shot (single purpose . We argue prior research might affected and biased "" established priors prevents the formulation a methodology objective cope the highly sparse knowledge graphs We propose handle the embedded learning problem knowledge graphs calledGEN The proposed model consists three simple multi-layer perceptron (MLP) cells each cell operates response a different ""query with regard the input fact will trained sequentially The formulation the model inspired neural sequence-toseq2seq BID23 , except we attempt the MLP cells mimic the sequence learning capability to model the semantic structure the knowledge graphsThe major contribution: propose GEN, and efficient multishot framework generalized knowledge graphs (2 We show GEN is in accordance established principles cognitive science providing flexibility learning representations works graphs conforming different domains Representation learning of knowledge graphs a key concern Many types relations physical, biological, social and information systems modeled concept (knowledge) graphs In this paper an efficient scalable framework learning conceptual embeddings entities relations generalized knowledge graphs We give evidence the proposed model learns good representations all these graphs for knowledge inference supervised For future work plan investigate more thoroughly the proposed modeling framework with respect the decomposition the semantic information conveyed the linked concepts into elementary information four Q&A pairs Also we seek enhance scientific investigations theoretical conceptualizations on graph embedding learning semantic interoperability for there usually no possibility interpret meaningfully order produce as defined existing algorithms",0.01,0.4241677162078273
"We introduce and study minimax curriculum learning (MCL), a new method for adaptively selecting a sequence of training subsets for a succession of stages in machine learning. The subsets are encouraged to be small and diverse early on, and then larger, harder, and allowably more homogeneous in later stages. At each stage, model weights and training sets are chosen by solving a joint continuous-discrete minimax optimization, whose objective is composed of a continuous loss (reflecting training set hardness) and a discrete submodular promoter of diversity for the chosen subset. MCL repeatedly solves a sequence of such optimizations with a schedule of increasing training set size and decreasing pressure on diversity encouragement. We reduce MCL to the minimization of a surrogate function handled by submodular maximization and continuous gradient methods. We show that MCL achieves better performance and, with a clustering trick, uses fewer labeled samples for both shallow and deep models while achieving the same performance. Our method involves repeatedly solving constrained submodular maximization of an only slowly varying function on the same ground set. Therefore, we develop a heuristic method that utilizes the previous submodular maximization solution as a warm start for the current submodular maximization process to reduce computation while still yielding a guarantee. Inspired by the human interaction between teacher and student, recent studies BID28 BID2 BID56 ) support that learning algorithms can be improved by updating a model on a designed sequence of training sets, i.e., a curriculum. This problem is addressed in curriculum learning (CL) BID6 , where the sequence is designed by a human expert or heuristic before training begins. Instead of relying on a teacher to provide the curriculum, self-paced learning (SPL) BID31 BID58 BID57 BID59 chooses the curriculum during the training process. It does so by letting the student (i.e., the algorithm) determine which samples to learn from based on their hardness. Given a training set D = {(x 1 , y 1 ), . . . , (x n , y n )} of n samples and loss function L(y i , f (x i , w)), where x i ∈ R m represents the feature vector for the i th sample, y i is its label, and f (x i , w) is the predicted label provided by a model with weight w, SPL performs the following: DISPLAYFORM0 SPL jointly learns the model weights w and sample weights ν, which end up being 0-1 indicators of selected samples, and it does so via alternating minimization. Fixing w, minimization w.r.t. ν selects samples with loss L(y i , f (x i , w)) < λ, where λ is a ""hardness parameter"" as it corresponds to the hardness as measure by the current loss (since with large λ, samples with greater loss are allowed in). Self-paced curriculum learning BID27 introduces a blending of ""teacher mode"" in CL and ""student mode"" in SPL, where the teacher can define a region of ν by attaching a linear constraint a T ν ≤ c to Eq. (1). SPL with diversity (SPLD) BID26 , adds to Eq. (1) a negative group sparse regularization term −γ ν 2,1 −γ b j=1 ν (j) 2 , where the samples are divided into b groups beforehand and ν (j) is the weight vector for the j th group. Samples coming from different groups are thus preferred, to the extent that γ > 0 is large. CL, SPL, and SPLD can be seen as a form of continuation scheme BID1 ) that handles a hard task by solving a sequence of tasks moving from easy to hard; the solution to each task is the warm start for the next slightly harder task. That is, each task, in the present case, is determined by the training data subset and other training hyperparameters, and the resulting parameters at the end of a training round are used as the initial parameters for the next training round. Such continuation schemes can reduce the impact of local minima within neural networks BID7 BID5 . With SPL, after each round of alternating minimization to optimize Eq. (1), λ is increased so that the next round selects samples that have a larger loss, a process BID28 BID59 BID2 ) that can both help avoid local minima and reduce generalization error. In SPLD, γ is also increased between training rounds, increasingly preferring diversity. In each case, each round results in a fully trained model for the currently selected training samples.Selection of training samples has been studied in other settings as well, often with a different motivation. In active learning (AL) BID53 and experimental design BID43 , the learner can actively query labels of samples from an unlabeled pool during the training process, and the goal is to reduce annotation costs. The aim is to achieve the same or better performance using fewer labeled samples by ruling out uninformative ones. Diversity modeling was introduced to AL in BID62 . It uses submodular maximization to select diverse training batches from the most uncertain samples. However, changing the diversity during the learning process has not been investigated as far as we know. In boosting BID51 BID19 , the goal is to learn an ensemble of weak classifiers sequentially; it does this by assigning weights to all samples, with larger weights given to samples having larger loss measured by an aggregation of previously trained models. Both active learning and boosting favor samples that are difficult to predict, since they are the most informative to learn. For example, uncertainty sampling BID13 BID52 BID14 BID15 selects samples that are most uncertain, while query by committee BID54 BID14 BID0 selects the ones that multiple models most disagree on. With machine teaching BID28 BID66 BID49 BID65 , a separate teacher helps the training procedure find a good model.The SPL approach starts with a smaller set of easy samples and gradually increases the difficulty of the chosen samples as measured by the sample loss of the model produced by previous round's training. One of the difficulties of this approach is the following: since for any given value of λ the relatively easiest samples are chosen, there is a good chance that the process can repeatedly select a similar training set over multiple rounds and therefore can learn slowly. This is precisely the problem that SPLD address -by concomitantly increasing the desired diversity over rounds, the sample selection procedure chooses from an increasingly diverse set of different groups, as measured by ν 2,1 . Therefore, in SPLD, early stages train on easier not necessarily diverse samples and later stages train on harder more diverse samples.There are several challenges remaining with SPLD, however. One is that in early stages, it is still possible to repeatedly select a similar training set over multiple rounds since diversity might not increase dramatically between successive rounds. Potentially more problematically, it is not clear that having a large diversity selection weight in late stages is desirable. For example, with a reasonably trained model, it might be best to select primarily the hardest samples in the part of the space near the difficult regions of the decision boundaries. With a high diversity weight, samples in these difficult decision boundary regions might be avoided in favor of other samples perhaps already well learnt and having a large margin only because they are diverse, thereby leading to wasted effort. At such point, it would be beneficial to choose points having small margin from the same region but that might not have the greatest diversity, especially when using only a simple notion of diversity such as the group sparse norm v 2,1 . Also, it is possible that late stages of learning can select outliers only because they are both hard and diverse. Lastly, the SPL/SPLD min-min optimization involves minimizing a lower bound of the loss, while normally one would, if anything, wish to minimize the loss directly or at least an upper bound.Motivated by these issues, we introduce a new form of CL that chooses the hardest diverse samples in early rounds of training and then actually decreases, rather than increases, diversity as training rounds proceed. Our contention is that diversity is more important during the early phases of training when only relatively few samples are selected. Later rounds of training will naturally have more diversity opportunity simply because the size of the selected samples is much larger. Also, to avoid successive rounds selecting similar sets of samples, our approach selects the hardest, rather than the easiest, samples at each round. Hence, if a set of samples is learnt well during one training round, those samples will tend to be ill-favored in the next round because they become easier. We also measure hardness via the loss function, but the selection is always based on the hardest and most diverse samples of a given size k, where the degree of diversity is controlled by a parameter λ, and where diversity is measured by an arbitrary non-monotone submodular function. In fact, for binary variables the group sparse norm is also submodular where ν 2,1 = b j=1|C j ∩ A| = F (A) where A is the set for which ν is the characteristic vector, and C j is the set of samples in the j th group. Our approach allows the full expressive class of submodular functions to be used to measure diversity since the selection phases is based on submodular optimization.Evidence for the naturalness of such hardness and diversity adjustment in a curriculum can also be found in human education. For example, courses in primary school usually cover a broad, small, and relatively easy range of topics, in order to expose the young learner to a diversity of knowledge early on. In college and graduate school, by contrast, students focus on advanced deeper knowledge within their majors. As another example, studies of bilingualism BID8 BID35 BID39 BID29 show that learning multiple languages in childhood is beneficial for future brain development, but early-age multi-lingual learning is usually not advanced or concentrated linguistically for any of the languages involved. Still other studies argue that difficulty can be desired at early human learning stages BID10 BID38 ).",2034,0.996,1156,1.759515570934256,"We introduce and study minimax curriculum learning ( adaptively selecting a sequence training subsets a succession stages machine learning The subsets encouraged be small diverse early then larger harder allowably in At each stage model weights training sets chosen solving a joint continuous-discrete minimax optimization, whose objective composed a continuous loss (reflecting training set hardness a discrete submodular promoter diversity for the chosen subset MCL repeatedly solves a sequence such optimizations a schedule increasing training set size decreasing pressure diversity encouragement We reduce MCL the minimization a surrogate function handled submodular maximization continuous gradient methods We show MCL achieves, a clustering trick uses fewer labeled samples both shallow and deep models while achieving Our method involves repeatedly solving constrained submodular maximization an only slowly varying function on the same ground set Therefore develop utilizes the previous submodular maximization solution a warm start to reduce computation while a guarantee Inspired the human interaction teacher recent studies BID28 BID2 BID56 ) support algorithms improved updating a model on a designed sequence training sets This problem addressed curriculum learning (CL) BID6 , where the sequence designed by a human expert or heuristic before training Instead relying a teacher selfpaced BID31 BID58 BID57 BID59 chooses during It does so letting the student ( samples learn their hardness Given training set D = {( 1 . . . , (x n} of n samples loss function L(y i f ( w � m represents i th its label the predicted label provided weight w SPL performs DISPLAYFORM0 SPL jointly learns weights w sample weights �� end 0-1 indicators selected samples it does via alternating minimization Fixing w, minimization �� selects samples loss L(y i f ( < a ""hardness parameter as corresponds as measure the current losssince with samples allowed in Self-paced curriculum learning BID27 introduces a blending ""teacher mode in CL SPL define a region �� by attaching a linear constraint a T �� ≤ c to Eq SPL with diversity (SPLD BID26 , adds Eq sparse regularization term −γ � j=1 � (j 2 the samples divided b groups beforehand and �� the j th group Samples coming different groups thus preferred to �� > large CL, SPL SPLD can seen continuation scheme BID1 ) handles a hard task solving tasks moving easy; the warm start That each task determined the training data subset other training hyperparameters at a training round Such continuation schemes reduce local minima within neural networks BID7 BID5 . With SPL after each round alternating minimization to optimize Eq �� increased so selects samples a process BID28 BID59 BID2 ) both help avoid local minima In SPLD �� also increased between training rounds increasingly preferring diversity In each case each round results a fully trained model the currently selected training samplesSelection has studied other settings often a different motivation In active learningAL) BID53 experimental design actively query labels samples during the goal reduce annotation costs The aim achieve using fewer labeled samples by ruling Diversity modeling was AL in BID62 . It uses submodular maximization select diverse training batches the most uncertain samples However changing the diversity during investigated far In boosting BID51 BID19 , learn an ensemble weak classifiers sequentially; does assigning all samples given having larger loss measured an aggregation previously trained models Both active learning boosting favor samples difficult since the informative For example uncertainty sampling BID13 BID52 BID14 BID15 selects samples most uncertain query by the ones multiple models most disagree With machine teaching BID28 BID66 BID49 BID65 , a separate teacher helps the training procedure findThe SPL approach starts easy samples the chosen samples measured the sample loss of produced previous round's training One following since for the relatively easiest samples chosen repeatedly select a similar training over multiple rounds therefore can learn slowly This precisely SPLD address -by concomitantly increasing the desired diversity over rounds the sample selection procedure chooses from different groups measured �� 2,1 Therefore SPLD early stages train on easier not necessarily diverse samples later stagesThere several challenges remaining One is in early stages still repeatedly select a similar training since diversity might increase dramatically between Potentially problematically having a large diversity selection weight late stages desirable For example with a reasonably trained model best select primarily the hardest samples the part near the difficult regions the decision boundaries With a high diversity weight samples in these difficult decision boundary regions might avoided other samples perhaps already well learnt having only because diverse thereby leading wasted effort At such point beneficial choose points having small margin from the same region but that might the greatest diversity using only a simple notion diversity such the group sparse norm v 2,1 Also late stages learning select outliers only both hard diverse Lastly the SPL/SPLD min-min optimization involves minimizing a lower bound, normally one, anything wishMotivated these issues introduce CL that chooses the hardest diverse samples early rounds training actually decreases, diversity training rounds Our contention diversity during training when only relatively few samples selected Later rounds training naturally have more diversity opportunity simply the selected samples Also to successive rounds selecting similar sets samples our approach selects hardest rather at Hence a set samples learnt well during one training round those samples tend illfavored because become easier. We also measure hardness via the loss function the selection always the hardest and most diverse samples a given size k the degree diversity controlled diversity In fact for binary variables the group sparse norm also submodular where �� 2,1 = b j=1|C j �� A| = F (A for the characteristic vector samples j th Our approach allows the full expressive class submodular functions measure diversity since the selection phases isEvidence the naturalness such hardness and diversity adjustment a curriculum also human education For example courses primary school usually in expose early In by focus advanced deeper knowledge within As another example studies bilingualism BID8 BID35 show learning beneficial usually advanced or concentrated linguistically for Still other studies argue difficulty can desired early human learning BID10 BID38 ).",0.01,0.63925811411586
"Progress in probabilistic generative models has accelerated, developing richer models with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference. However, there has been limited progress in models that capture causal relationships, for example, how individual genetic factors cause major human diseases. In this work, we focus on two challenges in particular: How do we build richer causal models, which can capture highly nonlinear relationships and interactions between multiple causes? How do we adjust for latent confounders, which are variables influencing both cause and effect and which prevent learning of causal relationships? To address these challenges, we synthesize ideas from causality and modern probabilistic modeling. For the first, we describe implicit causal models, a class of causal models that leverages neural architectures with an implicit density. For the second, we describe an implicit causal model that adjusts for confounders by sharing strength across examples. In experiments, we scale Bayesian inference on up to a billion genetic measurements. We achieve state of the art accuracy for identifying causal factors: we significantly outperform the second best result by an absolute difference of 15-45.3%. Probabilistic models provide a language for specifying rich and flexible generative processes BID5 Murphy, 2012) . Recent advances expand this language with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference BID9 BID15 . However, there has been limited progress in models that capture high-dimensional causal relationships (Pearl, 2000; BID13 Imbens & Rubin, 2015) . Unlike models which learn statistical relationships, causal models let us manipulate the generative process and make counterfactual statements, that is, what would have happened if the distributions changed.As the running example in this work, consider genome-wide association studies (GWAS) BID19 BID7 Kang et al., 2010) . The goal of GWAS is to understand how genetic factors, i.e., single nucleotide polymorphisms (SNPs), cause traits to appear in individuals. Understanding this causation both lets us predict whether an individual has a genetic predisposition to a disease and also understand how to cure the disease by targeting the individual SNPs that cause it.With this example in mind, we focus on two challenges to combining modern probabilistic models and causality. The first is to develop richer, more expressive causal models. Probabilistic causal models represent variables as deterministic functions of noise and other variables, and existing work usually focuses on additive noise models (Hoyer et al., 2009 ) such as linear mixed models (Kang et al., 2010) . These models apply simple nonlinearities such as polynomials, hand-engineered low order interactions between inputs, and assume additive interaction with, e.g., Gaussian noise. In GWAS, strong evidence suggests that susceptibility to common diseases is influenced by epistasis (the interaction between multiple genes) (Culverhouse et al., 2002; McKinney et al., 2006) . We would like to capture and discover such interactions. This requires models with nonlinear, learnable interactions among the inputs and the noise.The second challenge is how to address latent population-based confounders. In GWAS, both latent population structure, i.e., subgroups in the population with ancestry differences, and relatedness among sample individuals produce spurious correlations among SNPs to the trait of interest. Existing methods correct for this correlation in two stages BID19 BID7 Kang et al., 2010) : first, estimate the confounder given data; then, run standard causal inferences given the estimated confounder. These methods are effective in some settings, but they are difficult to understand as principled causal models, and they cannot easily accommodate complex latent structure.To address these challenges, we synthesize ideas from causality and modern probabilistic modeling. For the first challenge, we develop implicit causal models, a class of causal models that leverages neural architectures with an implicit density. With GWAS, implicit causal models generalize previous methods to capture important nonlinearities, such as gene-gene and gene-population interaction. Building on this, for the second challenge, we describe an implicit causal model that adjusts for population-confounders by sharing strength across examples (genes). We derive conditions that prove the model consistently estimates the causal relationship. This theoretically justifies existing methods and generalizes them to more complex latent variable models of the confounder.In experiments, we scale Bayesian inference on implicit causal models on up to a billion genetic measurements. Validating these results are not possible for observational data (Pearl, 2000) , so we first perform an extensive simulation study of 11 configurations of 100,000 SNPs and 940 to 5,000 individuals. We achieve state of the art accuracy for identifying causal factors: we significantly outperform existing genetics methods by an absolute difference of 15-45.3%. In a real-world GWAS, we also show our model discovers real causal relationships-identifying similar SNPs as previous state of the art-while being more principled as a causal model. We described implicit causal models, a rich class of models that can capture high-dimensional, nonlinear causal relationships. With genome-wide association studies, implicit causal models generalize previous successful methods to capture important nonlinearities, such as gene-gene and gene-population interaction. In addition, we described an implicit causal model that adjusts for confounders by sharing strength across examples. Our model achieves state-of-the-art accuracy, significantly outperforming existing genetics methods by 15-45.3%.There are several limitations to learning true causal associations. For example , alleles at different loci typically exhibit linkage disequilibrium, which is a local non-random association influenced by factors such as the rate of recombination, mutation, and genetic drift. The implicit causal model might be extended with variables shared across subsets of SNPs to model the recombination process. Another limitation involves the data, where granularity of sequenced loci may lose signal or attribute causation to a region involving multiple SNPs. Better technology, and accounting for mishaps in the sequencing process in the model, can help.While we focused on GWAS applications in this paper, we also believe implicit causal models have significant potential in other sciences: for example, to design new dynamical theories in high energy physics; and to accurately model structural equations of discrete choices in economics. We're excited about applications to these new domains, leveraging modern probabilistic modeling and causality to drive new scientific understanding.",1317,0.709,746,1.7654155495978552,"Progress accelerated developing richer models neural architectures implicit densities with scalable algorithms their Bayesian inference However limited progress models capture causal relationships for how individual genetic factors cause major human diseases In this work two challenges particular How richer causal models capture highly nonlinear relationships interactions multiple causes How adjust latent confounders variables influencing both cause and prevent learning To address synthesize ideas causality modern probabilistic modeling For, describe implicit causal models a class leverages neural architectures with an implicit density For, describe an implicit causal model adjusts sharing strength examples In experiments we scale Bayesian inference up to a billion genetic measurements We achieve state identifying causal factors: we significantly the second best result Probabilistic models provide a language specifying rich and flexible generative processes BID5 Murphy 2012) . Recent advances expand this language with neural architectures implicit densities with scalable algorithms their Bayesian inference BID9 BID15 . However limited progress models capture high-dimensional causal relationships (Pearl BID13 Imbens & Rubin 2015 . Unlike models which learn statistical relationships causal models let manipulate make that what the distributions changedAs the running example in consider BID19 BID7 Kang et al) . The goal GWAS cause traits appear Understanding this causation both lets predict understand cure by targeting the individual SNPsWith this example focus two challenges combining modern probabilistic models causality first is to develop richer, more expressive causal models Probabilistic causal models represent variables as deterministic functions noise other variables existing work usually additive noise modelsHoyer ) such) . These models apply simple nonlinearities such hand-engineered low order interactions inputs assume additive interaction, In GWAS strong evidence susceptibility common diseases epistasisthe interaction multiple genes (Culverhouse McKinney . We would capture discover such interactions This requires models nonlinear, learnable interactions among the inputs the noiseThe second challenge address latent population-based confounders In GWAS both latent population structure, subgroups in ancestry differences relatedness among sample individuals produce spurious correlations among to the trait Existing methods correct this correlation in two stages BID19 BID7 Kang et) : first estimate given data; run standard causal inferences given These methods effective some settings difficult understand as principled causal models easily accommodate complex latent structureTo ideas causality modern probabilistic modeling For the first challenge develop implicit causal models a class leverages neural architectures with an implicit density With GWAS implicit causal models generalize previous methods capture Building this for the second challenge describe an implicit causal model adjusts population-confounders sharing strength across examplesgenes We derive conditions prove the model consistently estimates. This theoretically justifies existing methods generalizes more complex latent variable models the confounderIn experiments scale implicit causal models on up to a billion genetic measurements Validating these results are observational dataPearl , first perform an extensive simulation study 11 configurations 940 to 5,000 individuals We achieve state identifying causal factors: we significantly existing genetics methods an absolute difference In a real-world GWAS also show our model discovers real causal-identifying similar SNPs previous state-while being more principled as We described implicit causal models a rich class capture With implicit causal models generalize previous successful methods capture In addition described an implicit causal model adjusts sharing strength examples Our model achieves state accuracy significantly existing genetics methods 1545.3%.There learning true causal associations For example , alleles at typically exhibit influenced factors the rate mutation The implicit causal model might extended with variables shared subsets to model Another limitation involves the data, where granularity sequenced loci lose signal or attribute causation a region involving Better technology accounting mishaps in the modelWhile focused GWAS applications believe implicit causal models other sciences: to design new dynamical theories high energy physics; accurately structural equations discrete choices economics We applications these new domains leveraging modern probabilistic modeling causality drive new scientific understanding",0.01,0.654290741384253
"Few-shot learning trains image classifiers over datasets with few examples per category. 
 It poses challenges for the optimization algorithms, which typically require many examples to fine-tune the model parameters for new categories. 
 Distance-learning-based approaches avoid the optimization issue by embedding the images into a metric space and applying the nearest neighbor classifier for new categories. In this paper, we propose to exploit the object-level relation to learn the image relation feature, which is converted into a distance directly.
 For a new category, even though its images are not seen by the model, some objects may appear in the training images. Hence, object-level relation is useful for inferring the relation of images from unseen categories. Consequently, our model generalizes well for new categories without fine-tuning.
 Experimental results on benchmark datasets show that our approach outperforms state-of-the-art methods. Real-world data typically follows power-law distributions, where the majority of the data categories have only a small number of examples. For instance, to train an image classifier for food images, one would probably crawl few images for some local dishes. Similarly, there are few images for new products, e.g. new toys. However, state-of-the-art image classifiers, i.e. deep convolutional neural networks (ConvNets) BID7 , are hungry for data. The benchmark datasets for ConvNets, including CIFAR10 and ImageNet BID0 , usually have more than 1000 images per category. Fine-tuning ConvNets BID18 by transferring the knowledge (i.e. parameters) learned from a big dataset could alleviate the gap, but still fails to resolve the issue. This is because the widely used gradient-based optimization algorithms need many iterations over plenty of examples to adapt the ConvNets (with a large number of parameters) for new categories.Two types of approaches have been proposed towards addressing the above issue. They are referred as few-shot image classification, which trains classifiers over datasets with few (e.g. less than 20) examples per category. The first set of approaches BID12 ; ; BID2 are based on meta-learning. They train a meta learner to guide the optimization of the classifier for the new categories. They improve the optimization by providing a good initialization BID2 , an adaptive learning rate or even replacing the gradient-based optimization method BID12 . The second set of approaches ; BID17 ; BID13 ; BID15 ; BID16 are based on embedding learning. They learn an embedding function to project the images into a space and then classify images from new categories through the nearest neighbour search. No fine-tuning is required as the nearest neighbour classifier is non-parametric. The embedding functions are vital to the classification accuracy, which must be general enough to extract good embedding features for evaluating the distance/similarity between images belonging to the unseen categories.In this paper, we propose a new few-short learning approach. It is motivated by the observation that human beings are pretty good at few-shot learning. Take the Segway in FIG0 as an example BID6 ) although the Segway could be new to us, we are familiar with its components, e.g. wheels, which are similar to those of the motors or electric scooters. Hence, we know Segway is a traffic tool for riding. Moreover, we are able to analyze the image by decomposing it. For example, we are aware of the relationship between Segway and rider. This kind of relationship-awareness helps in recognition when we see a different rider with another Segway. However, existing methods take each image as a whole without exploiting the object-level information including relation.Based on the above observation, we design our learning model with two parts, namely the relation extraction network and the distance learning network. We draw inspiration from the relation network BID14 . In particular, we compare the objects from two images instead of a single image as BID14 in order to extract the relation between images. The relation is converted into a similarity score. We expect the object relationship to play a crucial role in determining the image relation for distinguishing images from different categories. The training is conducted in episodes, each of which is constructed in the same way as in the test, i.e. with few examples for each category. After training, we extract the relation feature vectors among the query image (to be classified) and each labelled image from the test dataset. Nearest neighbour classifier is then applied with the similarity score calculated from the relation feature vector. Extensive experiments on benchmark datasets confirm the superiority of our approach in terms of classification accuracy against existing work. In this paper, we exploit the object-level relation to infer the image relation. In particular, we consider each 'pixel' on the feature map as an object in the input image, and use the values across all channels as the object feature. In fact, one 'pixel' corresponds to one patch of the original image. Small patches may not contain any objects, while in big patches, there could be multiple objects. In the extreme case where the feature map size is 1x1, the corresponding patch is the whole image. Our model is then equivalent to LearningToCompare Sung et al. (2017) . In fact, we capture object pairs from different locations, whereas LearningToCompare is restricted to element-wise match at the same spatial location. The effectiveness of our approach from the experimental study confirms that the relation extracted from multiple local patches is useful for determining the image relation. Particularly, we do one more set of comparison against Learning2Compare since it has similar architecture as our model. We change the input image size of Learning2Compare to 224x224, i.e. , the same as our model. The accuracy for 5-way 1-shot and 5-way 5-shot is 50.16% and 65.98% respectively. In addition, we compare effect of the feature map size of our model. We vary the feature map size as 1x1, 3x3, 5x5, 7x7 and 9x9. The corresponding accuracy of 5-way 5-shot classification is 64.55%, 67.78%, 69.68%, 69.82%, 70.90%. The improvement becomes marginal for bigger sizes. We can see that with the increasing of objects number (feature map size), the performance improves. It indicates that the objects-level relation does make a difference.The basic idea behind our model is to aggregate the local information for global reasoning. In this paper, we consider the spatial local information. However, the framework is extensible for other local information. For example, if we treat different feature maps as different aspects (or features) of the image, in Figure 2 , we can compare (combine) these feature maps from two images to get c × c local relation features, each of size w × h + w × h. Similarly, we can compare the features of different attributes of each class with the feature maps to do zero-shot learning. It compares the local text information with local image information. ConvNets have shown great success for image classification with many examples per category. However, few-shot learning is challenging because the training algorithms of ConvNets, i.e. gradient based optimization algorithms, require many iterations to fine-tune the parameters over a lot of examples for new image classes. In this paper, we avoid the fine-tuning step by training a model that is general to learn the relation of images from unseen categories. We observe that the object-level relation persists across training and test images, although the relation of images from test datasets is unseen. Therefore, we propose to exploit object-level relation to infer the image relation. In particular, object features are compared (combined) and transformed to extract the image relation feature, which is applied directly for similarity learning. Using the learned similarity from the relation feature, our approach outperforms existing algorithms for few-shot image classification tasks.",1595,1.067,882,1.808390022675737,"Few-shot learning trains image classifiers over datasets few examples per category It poses challenges optimization algorithms typically many examples for new categories Distance-learning-based approaches avoid the optimization issue the images a metric space applying the nearest neighbor classifier new categories In exploit the object-level relation learn the image relation feature converted directly. For a new category even its images seen the model some objects Hence object-level relation useful images unseen categories our model generalizes well new categories without Experimental results benchmark datasets our approach state typically follows power-law distributions the data categories examples For instance to train an image classifier food images probably crawl few images some local dishes Similarly few images for new products However state image classifiersConvNets) BID7 , hungry The benchmark datasets ConvNets including CIFAR10 ImageNet BID0 , usually category Fine-tuning ConvNets BID18 by transferring the knowledge learned a big dataset could alleviate the gap, still fails resolve This because the widely used gradient-based optimization algorithms need many iterations over plenty examples adapt the ConvNets (with parameters new categoriesTwo types approaches towards addressing They referred as few-shot image classification trains classifiers over datasets per category The first set approaches BID12 ; ; are meta-learning They train a meta learner guide the optimization the new categories They improve the optimization by providing a good initialization BID2 , an adaptive learning rate or replacing method BID12 The second set approaches ; BID17 ; are embedding learning They learn an embedding function project classify images new categories through the nearest neighbour search No fine-tuning as the nearest neighbour classifier non The embedding functions vital the classification accuracy must general extract good embedding features evaluating the distance/similarity images belonging the unseen categoriesIn a new few-short learning approach. It motivated the observation pretty few-shot learning Take the Segway in FIG0 as BID6 ) although new familiar its components which similar the motors or Hence Segway a traffic tool riding Moreover able analyze the image by decomposing. For example aware the relationship Segway rider This kind relationship-awareness helps in recognition when a different rider with another Segway However existing methods take each image without exploiting including relation.Based design our learning model namely the relation extraction network We draw the relation network BID14 . In particular compare the objects two images instead as BID14 in extract The relation converted a similarity score We expect the object relationship play the image relation distinguishing different categories The training conducted episodes constructed in the test few examples for After training extract the relation feature vectors among the query imageto classified each labelled image from Nearest neighbour classifier then the similarity score calculated the relation feature vector Extensive experiments benchmark datasets confirm terms against existing work In exploit the object-level relation infer the image relation In particular consider each 'pixel on the feature map across all channels object feature In fact one 'pixel corresponds one patch Small patches may contain any objects while in could In the extreme case the feature map size the corresponding patch the whole image Our model then equivalent LearningToCompare Sung et al (2017 . In fact capture object pairs whereas LearningToCompare restricted element-wise match at The effectiveness our approach from the experimental study confirms the relation extracted multiple local patches useful the image relation Particularly do one more set comparison against Learning2Compare since similar architecture our model We change the input image size Learning2Compare , same our model The accuracy for 50.16% In addition compare effect the feature map size our model We vary the feature map size as The corresponding accuracy 5-way 5-shot classification The improvement becomes marginal bigger sizes We with increasing of objects number (feature map size improves It indicates the objects-level relation makeThe basic idea our model aggregate the local information for global reasoning In consider the spatial local information. However the framework extensible for other local information For example treat different feature maps different aspects ( features the image in Figure compare (combine from c × c local relation features each size w × h + Similarly compare the features different attributes the feature maps do zero-shot learning It compares the local text information ConvNets have shown for image classification many examples per category However few-shot learning challenging because the training algorithms of ConvNets gradient based optimization over a lot examples for new image classes In avoid training general to learn the relation images unseen categories We observe the object-level relation persists training and test images images from test datasets unseen Therefore exploit object-level relation infer the image relation In particular object features compared (combined transformed extract the image relation feature applied directly for similarity learning Using the learned similarity from the relation feature our approach existing algorithms few-shot image classification tasks",0.01,0.7637859230907751
"Word embeddings are widely used in machine learning based natural language processing systems. It is common to use pre-trained word embeddings which provide benefits such as reduced training time and improved overall performance. There has been a recent interest in applying natural language processing techniques to programming languages. However, none of this recent work uses pre-trained embeddings on code tokens. Using extreme summarization as the downstream task, we show that using pre-trained embeddings on code tokens provides the same benefits as it does to natural languages, achieving: over 1.9x speedup, 5\% improvement in test loss, 4\% improvement in F1 scores, and resistance to over-fitting. We also show that the choice of language used for the embeddings does not have to match that of the task to achieve these benefits and that even embeddings pre-trained on human languages provide these benefits to programming languages.    One of the initial steps in a machine learning natural language processing (NLP) pipeline is converting the one-hot encoded R V tokens into dense R D representations, with V being the size of the vocabulary, D the embedding dimensions and V << D. This conversion is usually done with a single layer neural network, commonly called an embedding layer.The parameters of the embedding layer can either be initialized randomly or initialized via ""pretrained"" parameters obtained from a model such as word2vec BID22 a) , GloVe BID25 or a language model BID17 BID11 BID26 .It is common to use pre-trained parameters (most frequently the GloVe embeddings), which act as a form of transfer learning BID23 similar to that of using pre-trained parameters for the convolutional kernels in a machine learning computer vision task BID12 BID14 . These parameters in the embedding layer are then fine-tuned whilst training on the desired downstream task.The use of these pre-trained embeddings over random initialization allows machine learning models to: train faster, achieve improved overall performance BID13 , increase the stability of their training, and reduce the amount of over-fitting BID23 .Recently there has been an increased interest in applying NLP techniques to programming languages and software engineering applications BID30 BID3 , the most common of which involves predicting the names of methods or variables using surrounding source code BID27 BID0 BID4 BID6 a) .Remarkably , none of this work takes advantage of pre-trained embeddings created on source code. From the example below in table 1, we can see how semantic knowledge (provided by the pre-trained code embeddings) of the method body would help us predict the method name, i.e. knowing how pi and radius are used to calculate an area and how height and width are used to calculate an aspect ratio.float getSurfaceArea (int radius) { return 4 * Math.PI * radius * radius; } float getAspectRatio (int height, int width) { return height / width; } Table 1 : Examples showing how the semantics of the variable names within a method can be used to reason about the name of the method body This semantic knowledge is available to us as even though computers do not need to understand the semantic meaning of a method or variable name, they are mainly chosen to be understood by other human programmers BID10 .In this paper , we detail experiments using pre-trained code embeddings on the downstream task of predicting a method name from a method body. This task is known as extreme summarization BID2 as a method name can be thought of as a summary of the method body. Our experiments are focused on answering the following research questions:1. Do pre-trained code embeddings reduce training time?2. Do pre-trained code embeddings improve performance?3. Do pre-trained code embeddings increase stability of training?4. Do pre-trained code embeddings reduce over-fitting?5. How does the choice of corpora used for the pre-trained code embeddings affect all of the above?To answer RQ5, we gather a corpus of C, Java and Python code and train embeddings for each corpus separately, as well as comparing them with embeddings trained on natural language. We then test each of these on the same downstream task, extreme summarization, which is in Java. We also release the pre-trained code embeddings . We refer back to our research questions.Do pre-trained code embeddings reduce training time? Yes, tables 3 and 4 show we get an average of 1.93x speedup. This is correlated with the amount of overlap between the task vocabulary and the embedding vocabulary, shown in figure 2a.Do pre-trained code embeddings improve performance? Yes, tables 3 and 4 show we get an average of 5% relative validation loss improvement. Again, this is correlated with the amount of overlap between the vocabularies, shown in figure 2b.Do pre-trained code embeddings increase stability of training? Although this is difficult to quantify due to how over-fitting interacts with the variance of the validation loss curves, from figures 1a and 1c we can see a clear increase in the variance of the validation loss curves using random embeddings compared to those using pre-trained embeddings.Do pre-trained code embeddings reduce over-fitting? Yes, tables 6 and 7 show that the random embeddings over-fit more than the pre-trained embeddings on every project. However, this does not seem to have a correlation with the amount of vocabulary overlap and further work is needed to determine the cause of this.How does the choice of corpora used for the pre-trained code embeddings affect all of the above? Intuitively, it would seem the best pre-trained embeddings would be those that are trained on the same language as that of the downstream task, but this is not the case. We hypothesize through the examples shown in tables 1 and 5 that the differing syntax between the languages is not as important as sensible semantic method and variable names within the dataset. This semantic information is also contained in human languages, which explains why the English embeddings also receive comparable performance.",1189,0.558,680,1.7485294117647059,"Word embeddings widely machine learning based It common use pre-trained word embeddings which provide benefits There has a recent interest applying However none this recent work uses pre-trained embeddings on code tokens Using extreme summarization as the downstream task show using pre-trained embeddings on code tokens provides it to natural languages achieving: over 5\% improvement test loss F1 scores resistance over We also show the choice language used the embeddings does match the task to achieve these benefits and even embeddings pretrained human languages provide to programming languages One the initial steps converting the one-hot encoded R V tokens dense R D representations with V the vocabulary D the embedding dimensions << D. This conversion usually a single layer neural network commonlyThe parameters either initialized randomly initialized via ""pretrained"" parameters obtained such word2vec BID22 a) , GloVe BID25 or a language model common ( act a form transfer learning BID23 similar using the convolutional kernels machine computer vision task BID12 BID14 These parameters in the embedding layer then fine whilst training on the desired downstream taskThe use over random initialization allows machine learning models: train faster achieve improved overall performance BID13 , increase the stability their training over-fitting BID23 .Recently there applying NLP techniques programming software engineering applications BID30 BID3 the most involves predicting the names methods or variables using surrounding source code a) .Remarkably , none takes created From the example below in table how semantic knowledge (provided the pre-trained code embeddings of the method body would help predict knowing pi and radius used an area and how height an aspect ratio.float getSurfaceArea (int radius 4int height height } Table : Examples showing the semantics the variable names within reason the name This semantic knowledge available even computers need or mainly chosen understood other human programmers BID10 .In , detail experiments on the downstream task predicting from This task known extreme summarization BID2 as a method name can thought the method body Our experiments focused answering Do pre-trained code embeddings reduce training time?2 Do pre-trained code embeddings improve performance?3 Do pre-trained code embeddings increase stability training?4 Do pre-trained code embeddings reduce overfitting?5 How the choice corpora used the pre-trained code embeddings all the above?To answer RQ5 gather a corpus C, Java and train separately comparing trained natural language. We then test each on the same downstream task extreme summarization in Java We also release the pre-trained code embeddings . We refer back our research questionsDo pre-trained code embeddings reduce Yes tables 3 and 4 show we get an average 1.93x speedup This correlated overlap the task vocabulary the embedding vocabulary shownDo pre-trained code embeddings improve Yes tables 3 and 4 show we get an average 5% relative validation loss improvement Again correlated overlap shown figure 2bDo pre-trained code embeddings increase stability training Although this difficult quantify due how over-fitting interacts the variance the validation loss curves from figures 1a using random embeddings compared thoseDo pre-trained code embeddings reduce over Yes tables 6 and 7 show the random embeddings over-fit more on every project However this does seem a correlation vocabulary overlap and further workHow the choice corpora used the pre-trained code embeddings all above Intuitively the best pre-trained embeddings trained that the downstream task We hypothesize through the examples shown tables 5 the differing syntax between as sensible semantic method and variable names within the dataset This semantic information also contained human languages explains the English embeddings also receive comparable performance",0.01,0.6112663457852369
"Recently, Approximate Policy Iteration (API) algorithms have achieved super-human proficiency in two-player zero-sum games such as Go, Chess, and Shogi without human data. These API algorithms iterate between two policies: a slow policy (tree search), and a fast policy (a neural network). In these two-player games, a reward is always received at the end of the game. However, the Rubik’s Cube has only a single solved state, and episodes are not guaranteed to terminate. This poses a major problem for these API algorithms since they rely on the reward received at the end of the game. We introduce Autodidactic Iteration: an API algorithm that overcomes the problem of sparse rewards by training on a distribution of states that allows the reward to propagate from the goal state to states farther away. Autodidactic Iteration is able to learn how to solve the Rubik’s Cube and the 15-puzzle without relying on human data. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves — less than or equal to solvers that employ human domain knowledge. The Rubik's Cube is a classic combination game that poses unique and interesting challenges for AI and machine learning. Although the state space is astronomically large (4.2 × 10 19 different states for the 3x3x3 cube), only a single state is considered solved. Furthermore, unlike the game of Go or Chess, the Rubik's Cube is a single-player game and a sequence of random moves, no matter how long, is unlikely to end in the solved state. Developing reinforcement learning algorithms to deal with this property of the Rubik's Cube might provide insight into other sparse-reward environments. While methods for solving the Rubik's Cube have been developed, only relatively recently have methods been derived that can compute the minimal number of moves required to solve the cube from any given starting configuration BID22 . In addition, the Rubik's Cube and its solutions are deeply rooted in group theory, raising interesting and broader questions about the applicability of machine learning methods to complex symbolic systems, including mathematics. Finally, the classical 3x3x3 Rubik's Cube is only one representative of a much larger family of possible combination puzzles, broadly sharing the characteristics described above and including: (1) Rubik's Cubes with longer edges (e.g. 4x4x4); (2) Rubik's Cubes in higher dimensions (e.g. 2x2x2x2); as well as (3) Rubik's cube on non-cubic geometries (Pyriminix, etc) and their combinations. As the length of the sides and dimensions are increased, the complexity of the underlying combinatorial problems rapidly increases and, for instance, God's numbers for the 4x4x4 cube is not known. In short, for all these reasons, the Rubik's Cube and its variations pose interesting challenges for machine learning. Here we develop deep reinforcement learning methods, in particular a new form of Approximate Policy Iteration (API), for addressing these challenges.Figure 1: An illustration of DeepCube. The training and solving process is split up into ADI and MCTS. First, we iteratively train a DNN by estimating the true value of the input states using breadth-first search. Then, using the DNN to guide exploration, we solve cubes using Monte Carlo Tree Search. See methods section for more details.Approximate Policy Iteration BID5 BID2 BID13 BID25 BID18 ) is a core Reinforcement Learning (RL) algorithm. Recently, a new type of API algorithm, called Dual Policy Iteration BID33 , has achieved success in two player zero-sum games such as Go, Chess, Shogi and Hex BID0 BID28 BID9 . AlphaZero BID30 and ExIt BID0 are examples of Dual Policy Iteration. These algorithms update the policy in a more sophisticated way than traditional API methods by using two policies: a fast policy (usually a neural network) and a slow policy (usually tree search). The fast policy is trained via supervised learning on data generated from gameplay from the slow policy. The slow policy then uses the fast policy to guide the tree search. In this way, the fast policy is used to improve the slow policy, and the slow policy generates better data to train the fast policy.This work is the first to solve the Rubik's Cube with reinforcement learning. Although DPI works for two-player games, our work is the first DPI algorithm to succeed in an environment with a high number of states and a small number of reward states. A number of these ""needle in a haystack"" environments such as generating meaningful sentences or code are seen as long-term goals for the field of AI. There is no clear way to apply current DPI algorithms such as AlphaZero or ExIt to sparse-reward environments such as the Rubik's Cube. This is because a randomly initialized policy will be unlikely to encounter the single reward state. This will cause the value function to be biased or divergent and the fast policy will not converge to the optimal policy. In our work we overcome this problem by training the fast policy on a distribution of states that propagate the reward signal to from the goal state to the further states.Our algorithm, called Autodidactic Iteration (ADI), trains a neural network value and policy function through an iterative process. These neural networks are the ""fast policy"" of DPI described earlier.In each iteration, the inputs to the neural network are created by starting from the goal state and randomly taking actions. The targets seek to estimate the optimal value function by performing a breadth-first search from each input state and using the current network to estimate the value of each of the leaves in the tree. Updated value estimates for the root nodes are obtained by recursively backing up the values for each node using a max operator. The policy network is similarly trained by constructing targets from the move that maximizes the value. After the network is trained, it is combined with MCTS to effectively solve the Rubik's Cube. We call the resulting solver DeepCube. DeepCube is based on similar principles as AlphaZero and ExIt, however, these methods receive their reward when the game reaches a terminal state, which is guaranteed to occur given enough play time. On the other hand, one is not guaranteed to find a terminal state in the Rubik's Cube environment and therefore may only encounter rewards of -1, which does not provide enough information to solve the problem. DeepCube addresses this by selecting a state distribution for the training set that allows the reward to be propagated from the terminal state to other states. In addition, while AlphaZero and ExIt make use advanced tree-search algorithms to update the policy, DeepCube is able to find success using the faster and simpler depth-1 BFS.The depth-1 BFS used to improve the policy can also be viewed as doing on-policy temporal difference learning BID34 , specifically TD(0) with function approximation. In this case, the TD(0) algorithm uses a deterministic greedy policy where each episode is one step long. Off-policy methods are often used to train a deterministic policy by using a stochastic behavior policy to facilitate exploration. An alternative approach, called exploring starts, instead changes the distribution of starting states and can also be used to train a deterministic policy in an on-policy fashion BID35 . We use a similar approach to exploring starts by ensuring exploration through the selection of the starting state distribution. The Rubik's Cube can be thought of as a classical planning problem. While traditional planning algorithms, such as Dijkstra's algorithm, would require an infeasible amount of memory to work on environments a state space as large as the Rubik's Cube, we show that Dual Policy Iteration can find a solution path in such an environment. For future work, we look to apply Autodidactic Iteration to a variety of other problems with similar characteristics such as robotic manipulation, two-player games, and path finding. Léon Bottou defines reasoning as ""algebraically manipulating previously acquired knowledge in order to answer a new question"" BID6 . Many machine learning algorithms do not reason about problems but instead use pattern recognition to perform tasks that are intuitive to humans, such as object recognition. By combining neural networks with symbolic AI, we are able to create algorithms which are able to distill complex environments into knowledge and then reason about that knowledge to solve a problem. DeepCube is able to teach itself how to reason in order to solve a complex environment with only one positive reward state using pure reinforcement learning.A KNOWLEDGE LEARNED DeepCube discovered a notable amount of Rubik's Cube knowledge during its training process, including the knowledge of how to use complex permutation groups and strategies similar to the best human ""speed-cubers"". For example, DeepCube heavily uses one particular pattern that commonly appears when examining normal subgroups of the cube: aba −1 . That is, the sequences of moves that perform some action a, performs a different action b, and then reverses the first action with a −1 . An intelligent agent should use these conjugations often because it is necessary for manipulating specific cubelets while not affecting the position of other cubelets.We examine all of the solutions paths that DeepCube generated for the 640 fully scrambled cubes by moving a sliding window across the solutions strings to gather all triplets. We then compute the frequency of each triplet and separate them into two categories: matching the conjugation pattern aba −1 and not matching it. We find that the top 14 most used triplets were, in fact, the aba −1 conjugation. We also compare the distribution of frequencies for the two types of triplets. In Figure 6 , we plot the distribution of frequencies for each of the categories. We notice that conjugations appear consistently more often than the other types of triplets.We also examine the strategies that DeepCube learned. Often, the solver first prioritizes completing a 2x2x2 corner of the cube. This will occur approximately at the half way point in the solution. Then, it uses these conjugations to match adjacent edge and corner cubelets in the correct orientation, and it returns to either the same 2x2x2 corner or to an adjacent one. Once each pair of corner-edge pieces is complete, the solver then places them into their final positions and completes the cube. An example of this strategy is presented in FIG3 . This mirrors a strategy that advanced human ""speed-cubers"" employ when solving the cube, where they prioritize matching together corner and edge cubelets before placing them in their correct locations. Each layer is fully connected. We use elu activation on all layers except for the outputs. A combined value and policy network results in more efficient training compared to separate networks. (Silver et al., 2017b) .We used a feed forward network as the architecture for f θ as shown in Figure 7 . The outputs of the network are a 1 dimensional scalar v, representing the value, and a 12 dimensional vector p, representing the probability of selecting each of the possible moves. The network was then trained using ADI for 2,000,000 iterations. The network witnessed approximately 8 billion cubes, including repeats, and it trained for a period of 44 hours. Our training machine was a 32-core Intel Xeon E5-2620 server with three NVIDIA Titan XP GPUs.During play, the neural network prediction is the major bottleneck for performance. In order to counteract this, we implemented a parallel version of MCTS that had 32 independent workers that shared a single MCTS search tree. Each of the workers queue their prediction requests, and the neural network batches all requests and processes them simultaneously. This parallelization sped up the solver 20x compared to a single core implementation.",2408,1.338,1352,1.7810650887573964,"Recently Approximate Policy Iteration algorithms achieved super-human proficiency two-player zero-sum games such Go Chess Shogi without human data These API algorithms iterate between two policies a slow policytree searcha neural network In these two-player games a reward always received However the Rubik��s Cube only a single solved state episodes guaranteed terminate This poses these API algorithms since the reward received at We introduce Autodidactic Iteration: an API algorithm overcomes sparse rewards training on a distribution states allows the reward propagate states farther Autodidactic Iteration is able learn solve the Rubik��s Cube the 15-puzzle without human data Our algorithm able solve 100% randomly scrambled cubes while achieving a median solve length 30 moves — less or solvers employ human domain knowledge a classic combination game poses Although the state space4.2 × 10 19 different states for considered solved Furthermore unlike the game of Go or Chess a sequence no, unlikely end the solved state Developing reinforcement learning deal this property might provide insight other sparse-reward environments While methods solving only relatively methods derived compute the minimal number moves from any given starting configuration BID22 . In addition and its solutions deeply group theory raising interesting and broader questions machine learning methods complex symbolic systems mathematics Finally only one representative possible combination puzzles broadly sharing described including: Rubik longer edges in higher dimensions as onPyriminix etc) their combinations As the length the sides dimensions are increased the complexity the underlying combinatorial problems rapidly, instance God's numbers for not known In short for and its variations pose interesting challenges Here develop deep reinforcement learning methods in particular a new form Approximate Policy IterationAPI addressing these challengesFigure An illustration DeepCube The training and solving process split ADI MCTS First iteratively train a DNN by estimating the input states using breadth-first search Then using the DNN to guide exploration solve cubes using Monte Carlo Tree Search See methods sectionApproximate Policy Iteration BID5 ) is core ReinforcementRL Recently API algorithm Dual Policy Iteration BID33 , achieved success two player zero-sum games such Go Chess Shogi Hex BID0 BID28 BID9 AlphaZero BID30 and ExIt BID0 examples Dual Policy Iteration These algorithms update the policy traditional API methods by two policies a fast policyusually a neural networkusually tree search The fast policy trained via supervised learning data generated gameplay from the slow policy The slow policy then uses guide the tree search In this way the fast policy used improve generates better data to trainThis work the solve with reinforcement learning Although DPI works two-player games our work the first DPI algorithm succeed an environment states reward states A number these ""needle such generating meaningful sentences code seen the field AI There apply current DPI algorithms such AlphaZero ExIt to sparse-reward environments This because a randomly initialized policy unlikely encounter the single reward state This will cause the value function biased or divergent and the fast policy converge In our work overcome training the fast policy on a distribution states propagate the reward signal from the further statesOur algorithm, Autodidactic Iteration trains a neural network value and policy function through These neural networks the ""fast policy DPI describedIn each iteration the inputs created starting the goal state and randomly taking actions The targets seek estimate the optimal value function by performing from each input state the current network the leaves Updated value estimates the root nodes obtained backing a max operator The policy network similarly trained constructing targets from the move that maximizes. After the network is trained combined MCTS effectively solve We call the resulting solver DeepCube DeepCube based similar principles AlphaZero ExIt however these methods receive their reward reaches a terminal state guaranteed given On one is guaranteed a terminal state the Rubik's Cube environment and therefore may only encounter rewards -1 does provide solve DeepCube addresses selecting a state distribution the training set that allows the reward the terminal state In addition while AlphaZero ExIt make advanced tree-search algorithms update the policy DeepCube able find success faster used improve viewed doing onpolicy temporal difference learning BID34 , specifically TD(0 function approximation In the TD(0 algorithm uses a deterministic greedy policy each episode one long Off-policy methods train a deterministic policy by a stochastic behavior policy facilitate exploration An alternative approach exploring starts instead changes starting states can also train a deterministic policy on-policy BID35 . We use exploring starts ensuring exploration through the selection the starting state distribution can thought a classical planning problem While traditional planning algorithms, would work environments a state space as we show Dual Policy Iteration find a solution path For future work look apply Autodidactic Iteration other problems with similar characteristics such robotic manipulation two-player games path finding Léon Bottou defines reasoningalgebraically manipulating previously acquired knowledge answer"" BID6 . Many machine learning algorithms do reason problems but pattern recognition perform intuitive By combining neural networks symbolic AI algorithms distill complex environments knowledge then reason DeepCube able teach itself reason a complex environment only one positive reward state using pure reinforcement learningA KNOWLEDGE LEARNED DeepCube discovered a notable amount complex permutation groups strategies similar the best human ""speed-cubers For example DeepCube heavily one particular pattern commonly when examining normal subgroups the cube aba −1 That the sequences moves perform a, performs with a −1 . An intelligent agent should use these conjugations often because necessary manipulating specific cubelets while not the positionWe examine all the solutions paths DeepCube generated the 640 fully scrambled cubes by moving a sliding window across the solutions strings gather all triplets We then compute each triplet separate matching aba −1 not We find the top 14 most used triplets, aba −1 We also compare frequencies for triplets In Figure , frequencies We notice conjugations appear consistently more tripletsWe examine the strategies DeepCube learned. Often, the solver first prioritizes completing This will occur approximately at the solution Then uses these conjugations match adjacent edge and corner cubelets returns one Once each pair corner-edge pieces complete places their final positions completes An example this strategy presented FIG3 This mirrors a strategy advanced human ""speed-cubers employ solving the cube, prioritize matching together corner and edge cubelets before placing their correct locations Each layer fully connected We use elu activation on all layers except the outputs A combined value and policy network results more efficient training compared separate networks (Silver et .We a feed forward network as the architecture f �� as 7 The outputs the network a 1 dimensional scalar v, representing, selecting each the possible moves The network then trained using ADI for The network witnessed approximately 8 billion cubes, including repeats and trained for 44 hours Our training machine three NVIDIA Titan XP GPUsDuring play the neural network prediction is the major bottleneck performance In order counteract implemented a parallel version MCTS had 32 independent workers shared Each the workers queue their prediction requests batches processes simultaneously This parallelization sped the solver 20x compared a single core implementation",0.02,0.6941643922092875
"Answering compositional questions requiring multi-step reasoning is challenging for current models. We introduce an end-to-end differentiable model for interpreting questions, which is inspired by formal approaches to semantics. Each span of text is represented by a denotation in a knowledge graph, together with a vector that captures ungrounded aspects of meaning. Learned composition modules recursively combine constituents, culminating in a grounding for the complete sentence which is an answer to the question. For example, to interpret ‘not green’, the model will represent ‘green’ as a set of entities, ‘not’ as a trainable ungrounded vector, and then use this vector to parametrize a composition function to perform a complement operation. For each sentence, we build a parse chart subsuming all possible parses, allowing the model to jointly learn both the composition operators and output structure by gradient descent. We show the model can learn to represent a variety of challenging semantic operators, such as quantifiers, negation, disjunctions and composed relations on a synthetic question answering task. The model also generalizes well to longer sentences than seen in its training data, in contrast to LSTM and RelNet baselines. We will release our code. Compositionality is a mechanism by which the meanings of complex expressions are systematically determined from the meanings of their parts, and has been widely assumed in the study of both natural languages BID10 , as well as programming and logical languages, as a means for allowing speakers to generalize to understanding an infinite number of sentences. Popular neural network approaches to question answering use a restricted form of compositionality, typically encoding a sentence word-by-word from left-to-right, and finally executing the complete sentence encoding against a knowledge source BID13 . Such models can fail to generalize from training sentences in surprising ways. Inspired by linguistic theories of compositional semantics, we instead build a latent tree of interpretable expressions over a sentence, recursively combining constituents using a small set of neural modules. When tested on longer questions than are found in the training data, we find that our model achieves higher performance than baselines using LSTMs and RelNets.Our approach resembles Montague semantics, in which a tree of interpretable expressions is built over the sentence, with nodes combined by a small set of composition functions. However, both the structure of the sentence and the neural modules that handle composition are learned by end-to-end gradient descent. To achieve this, we define the parametric form of small set of neural modules, and then build a parse chart over each sentence subsuming all possible trees. Each node in the chart represents a span of text with a distribution over groundings (in terms of booleans and knowledge base nodes and edges), as well as a vector representing aspects of the meaning that have not yet been grounded. The representation for a node is built by taking a weighted sum over different ways of building the node (similarly to BID9 ).Typical neural network approaches to grounded question answering first encode a question from left-to-right with a recurrent neural network (RNNs), and then evaluate the encoding against an encoding of the knowledge source (for example, a knowledge base or image) BID14 . In contrast to classical approaches to compositionality, constituents of complex expressions are not given explicit interpretations in isolation. For example , in Which cubes are large or green?, an RNN encoder will not explicitly build an interpretation for the expression large or green. We show that A correct parse for a question given the knowledge graph on the right, using our model. We show the type for each node, and its denotation in terms of the knowledge graph. The words or and not are represented by vectors, which parameterize composition modules. The denotation for the complete question represents the answer to the question. Nodes here have types E for sets of entities, R for relations, V for ungrounded vectors, EV for a combination of entities and a vector, and φ for semantically vacuous nodes. While we show only one parse tree here, our model builds a parse chart subsuming all trees. such approaches can generalize poorly when tested on more complex sentences than they were trained on. In contrast, our approach imposes strong independence assumptions that give a linguistically motivated inductive bias. In particular, it enforces that phrases are interpreted independently of surrounding words, allowing the model to generalize naturally to interpreting phrases in different contexts. In the previous example, large or green will be represented as a particular set of entities in a knowledge graph, and be intersected with the set of entities represented by the cubes node.Another perspective on our work is as a method for learning the layouts of Neural Module Networks (NMNs) BID1 . Work on NMNs has focused on how to construct the structure of the network, variously using rules, parsers and reinforcement learning BID0 BID3 . Our end-to-end differentiable model jointly learns structures and modules by gradient descent.",993,0.553,587,1.6916524701873936," compositional questions requiring multi-step reasoning challenging current models We introduce end differentiable interpreting questions, inspired formal approaches semantics Each span text a denotation a knowledge graph together captures ungrounded aspects meaning Learned composition modules combine constituents culminating a grounding the complete sentence which an answer. For example to interpret ��not green�� the model will represent entities a trainable ungrounded vector then a composition function perform a complement operation For each sentence build a parse chart subsuming allowing the model jointly learn both the composition operators output structure by gradient descent We show the model can learn represent challenging semantic operators composed relations on a synthetic question answering The model also generalizes well longer sentences than seen its training data in LSTM and RelNet baselines We release our code. Compositionality a mechanism the meanings complex expressions systematically from has widely assumed BID10 , as programming and logical allowing speakers understanding sentences Popular neural network approaches question answering use a restricted form compositionality typically encoding a sentence word- from left finally executing against a knowledge source BID13 . Such models fail generalize training sentences surprising ways Inspired linguistic theories compositional semantics instead build a latent tree interpretable expressions over a sentence combining constituents using neural modules When tested longer questions than are found the training data our model achieves baselines using RelNetsOur approach resembles Montague semantics a tree interpretable expressions built the sentence nodes combined composition functions However both the structure the sentence the neural modules handle composition learned end gradient To achieve define small set neural modules build a parse chart over each sentence subsuming all possible trees Each node the chart a span text a distribution groundings terms booleans knowledge base nodes and edges a vector aspects grounded The representation for a node built taking a weighted sum over different ways buildingsimilarly BID9 ).Typical neural network approaches grounded question first encode from left evaluate the encoding against the knowledge sourcefor image BID14 In contrast classical approaches compositionality constituents complex expressions given explicit interpretations isolation For example , Which cubes large green an RNN encoder not explicitly build an interpretation the expression large We show that A correct parse a question given the knowledge graph on using our model We show the type for its denotation the knowledge graph The words or and not represented vectors parameterize composition modules The denotation for the complete question represents Nodes here have types E for sets entities relations V ungrounded vectors EV a combination �� semantically vacuous nodes While show only one parse tree here our model builds a parse chart subsuming such approaches generalize poorly tested more complex sentences were trained In contrast our approach imposes strong independence assumptions give a linguistically motivated inductive bias In particular enforces phrases interpreted independently surrounding words allowing the model naturally interpreting phrases In large or green will represented a particular set entities a knowledge graph be intersected the cubes nodeAnother perspective our work as learning the layouts Neural Module Networks BID1 . Work NMNs focused how construct variously rules reinforcement BID0 BID3 . Our end differentiable model jointly learns structures modules gradient descent",0.01,0.46634889579969296
"Deep learning software demands reliability and performance. However, many of the existing deep learning frameworks are software libraries that act as an unsafe DSL in Python and a computation graph interpreter. We present DLVM, a design and implementation of a compiler infrastructure with a linear algebra intermediate representation, algorithmic differentiation by adjoint code generation, domain- specific optimizations and a code generator targeting GPU via LLVM. Designed as a modern compiler infrastructure inspired by LLVM, DLVM is more modular and more generic than existing deep learning compiler frameworks, and supports tensor DSLs with high expressivity. With our prototypical staged DSL embedded in Swift, we argue that the DLVM system enables a form of modular, safe and performant frameworks for deep learning. Within the deep learning community, most current approaches to neural networks make use of high-level frameworks with a tensor domain-specific language (DSL) such as Torch BID3 , TensorFlow BID0 , PyTorch (PyTorch Development Team, 2016) , and MXNet BID1 . Traditionally, developers would build a computation graph (or dynamically generate graph nodes) using a DSL and let the framework interpret the computation graph on parallel architectures such as NVIDIA GPUs. While using hand-tuned GPU subroutines usually yields the best performance for complex operators, advanced compiler techniques can be applied to simplify computation, merge high-level operators based on shaping conditions, and fuse compatible elementwise operators to a single kernel to minimize the latency between kernel launches. Recent projects, the TensorFlow XLA compiler and the NNVM compiler BID13 including TVM BID2 , have begun to apply compiler techniques to deep learning systems, targeting LLVM BID10 and various back-ends to achieve good performance. However, their design and implementation have not entirely followed established best practices in widely-used compiler frameworks in the industry.Moreover, some frameworks use operator-overloading algorithmic differentiation (AD) to compute gradients, leaving the gradient computation unoptimizable. The other approach to AD, source code transformation, can produce more efficient code. While frameworks such as TensorFlow already perform AD as a graph transformation and apply various optimizations, their AD transformation is not designed as a transformation pass in the pipeline of their compiler framework, but as part of the DSL library. Making AD part of the compiler framework would greatly simplify the development of DSLs, achieving separation of concerns. We introduce DLVM, a new compiler infrastructure for deep learning systems that addresses shortcomings of existing deep learning frameworks. Our solution includes (1) a domain-specific intermediate representation specifically designed for tensor computation, (2) principled use of modern compiler optimization techniques to substantially simplify neural network computation, including algebra simplification, AD checkpointing, compute kernel fusion, and various traditional compiler optimizations, (3) code generation through a mature compiler infrastructure that allows for transparent targeting of various hardware, and (4) an embedded DSL that supports static analysis, type safety, and natural expression of tensor computation, and has a just-in-time (JIT) compiler targeting DLVM for AD, optimizations, and code generation. The deep learning research community has a rich variety of available frameworks. While two existing projects have attempted a compilers approach to deep learning frameworks, and have respectively achieved good integration with existing systems (TensorFlow XLA) and good performance (NNVM + TVM), their design philosophies have not entirely followed established best practices in optimizing compiler design. While well intentioned, the remaining vast majority of other frameworks have failed to observe that the problem of front-end DSLs, algorithmic differentiation, and converting a neural network into efficient executable code is, at its core, a compilers problem. As a result, important issues of extensibility and optimization have been addressed in less than optimal fashion in such frameworks. Nevertheless, several such frameworks have achieved wide adoption. We believe that the principled application of optimizing compiler techniques will lead to substantial improvements in the tools available to deep learning researchers. DLVM and its associated front-end DSLs have a major role to play in this future. Our existing implementation supports reverse-mode AD in the core language, and utilizes LLVM to target NVIDIA GPUs. In our ongoing work, we plan to substantially increase the number of supported hardware architectures by utilizing HPVM as an additional back-end, and explore more advanced AD techniques such as mixing forward and reverse modes.",863,0.408,527,1.637571157495256,"Deep learning software demands reliability However many the existing deep learning frameworks software libraries act an unsafe DSL in Python a computation graph interpreter We present DLVM a design a compiler infrastructure with a linear algebra intermediate representation algorithmic differentiation by adjoint code generation domain- specific optimizations a code generator targeting GPU via Designed as a modern compiler infrastructure inspired DLVM more modular generic existing deep compiler frameworks supports tensor DSLs high expressivity With our prototypical staged DSL embedded Swift argue the DLVM system enables a form modular, safe and performant frameworks Within the deep learning community most current approaches make with a tensor domain-specific language such Torch BID3 , 2016 MXNet developers would a computation graph ( dynamically generate a DSL let interpret on parallel architectures NVIDIA GPUs While using hand-tuned GPU subroutines usually yields complex operators advanced compiler techniques simplify, merge based shaping conditions fuse compatible elementwise operators a single kernel to minimize the latency between kernel launches Recent projects, the TensorFlow XLA compiler the NNVM compiler BID13 including TVM BID2 , begun apply compiler techniques targeting LLVM BID10 various back-ends to achieve However their design implementation entirely followed established best practices widely-used compiler frameworks inMoreover use operator-overloading algorithmic differentiationAD compute gradients leaving gradient computation unoptimizable The other approach AD, source code transformation can produce While frameworks already perform AD as a graph transformation and apply various optimizations their AD transformation designed a transformation pass in the pipeline their compiler framework part the DSL library Making AD part the compiler framework would greatly DSLs achieving separation We introduce DLVM a new compiler infrastructure deep learning systems addresses shortcomings Our solution includes (1) a domain-specific intermediate representation specifically tensor computation2) principled use modern compiler optimization techniques substantially neural network computation including algebra simplification AD checkpointing compute kernel fusion various traditional compiler optimizations through a mature compiler infrastructure transparent targeting various hardware static analysis type safety natural expression of has just targeting DLVM for AD optimizations The deep learning research community a rich variety available frameworks While two existing projects attempted a compilers deep learning frameworks and have respectively achieved good integrationTensorFlow XLA goodNNVM + TVM their design philosophies entirely followed established best practices optimizing compiler design While well the remaining vast majority other frameworks observe that, algorithmic differentiation converting a neural network efficient executable code, a compilers problem As important issues extensibility optimization less optimal fashion such frameworks Nevertheless several such frameworks achieved We believe the principled application optimizing compiler techniques will the tools deep learning researchers DLVM and this future Our existing implementation supports reverse-mode AD in the core language utilizes LLVM target NVIDIA GPUs our ongoing work plan substantially supported hardware architectures utilizing HPVM, explore more advanced AD techniques mixing forward",0.01,0.328554462592306
"In this work, we focus on the problem of grounding language by training an agent
 to follow a set of natural language instructions and navigate to a target object
 in a 2D grid environment. The agent receives visual information through raw
 pixels and a natural language instruction telling what task needs to be achieved.
 Other than these two sources of information, our model does not have any prior
 information of both the visual and textual modalities and is end-to-end trainable.
 We develop an attention mechanism for multi-modal fusion of visual and textual
 modalities that allows the agent to learn to complete the navigation tasks and also
 achieve language grounding. Our experimental results show that our attention
 mechanism outperforms the existing multi-modal fusion mechanisms proposed in
 order to solve the above mentioned navigation task. We demonstrate through the
 visualization of attention weights that our model learns to correlate attributes of
 the object referred in the instruction with visual representations and also show
 that the learnt textual representations are semantically meaningful as they follow
 vector arithmetic and are also consistent enough to induce translation between instructions
 in different natural languages. We also show that our model generalizes
 effectively to unseen scenarios and exhibit zero-shot generalization capabilities.
 In order to simulate the above described challenges, we introduce a new 2D environment
 for an agent to jointly learn visual and textual modalities Figure 1: The agent (blue in color) should learn to read the instruction and navigate to green apple.Understanding of natural language instructions is an important aspect of an Artificial Intelligence (AI) system. In order to successfully accomplish tasks specified by natural language instructions, an agent has to extract representations of language that are semantically meaningful and ground it in perceptual elements and actions in the environment.Humans have the ability to understand the true essence of the words and thus they can easily decipher sentences even if it contains some new combination of words. It is not unreasonable to expect the same from an AI agent. The information extracted by agent from the language should be such that it corresponds to the true meaning of the word so that it enables the agent to generalize to even unseen combinations of words. For instance, when given sufficient information about the words such as 'green' and 'bag', it should automatically figure out as to what 'green bag' essentially means.Consider a task in which an agent has to learn to navigate to a target object in a 2D grid environment as shown in figure 1. The environment consists of many objects with different attributes (in our case: green apple, red apple, blue sofa, green sofa, an orange fruit, red car) and multiple obstacles. The agent receives visual information through raw pixels and an instruction telling what task needs to be achieved. The challenges that the agent has to tackle here are manyfold: a) the agent has to develop the capability to recognize various objects, b) have some memory of objects seen in previous states while exploring the environment as the objects may occlude each other and/or may not be present in the agent's field of view c) ground the instruction in visual elements and actions in the environment and d) learn a policy to navigate to the target object by avoiding the obstacles and other non-target objects.We tackle this problem by proposing an end-to-end trainable architecture that creates a combined representation of the image observed by the agent and the instruction it receives. Our model does not have any prior information of both the visual and textual modalities. We develop an attention mechanism for multimodal fusion of visual and textual modalities. Our experimental results show that our attention mechanism outperforms the existing multimodal fusion mechanisms proposed in order to solve the above mentioned task. We demonstrate through the visualization of attention weights that our model learns to correlate attributes of the object referred in the instruction with visual representations and also show that the learnt textual representations are semantically meaningful as they follow vector arithmetic and are also consistent enough to induce translation between instructions in different natural languages. We also show that our model generalizes effectively to unseen scenarios and exhibit zero-shot (ZS) generalization capabilities. In order to simulate the above described challenges, we introduce a new 2D environment for an agent to jointly learn visual and textual modalities. Our 2D environment is also thread compatible. Finally, in order to enable the reproducibility of our research through participation in BID21 and foster further research in this direction, we open source our environment as well as the code and models that we developed. In the paper we presented an attention based simple architecture to achieve grounding of natural language sentences via reinforcement learning. We show that retaining just the representation obtained after multimodal fusion phase (i.e. multiple attention maps) and discarding the visual features helps the agent achieve its goals. We justify this claim by visualization of the attention maps which reveal that they contain sufficient information needed for the agent to find the optimal policy. Through vector arithmetic, we also show that the embeddings learnt by the agent indeed make sense. In order to encourage the research in this direction we have also open sourced our environment as well as the code and models developed.Our environment is capable of supporting rich set of natural language instructions and it's highly flexible. As a future work, we would like to increase the complexity of both the types of sentences generated as well as the environment dynamics by introducing moving objects. We also plan to take forward our approach to a 3D environment to test how well does it extend there. To test if our attention mechanism could scale to 3D environments, we applied our fusion mechanism to the Vizdoom based environment and compared our results with who have recently open sourced their code Chaplot. We replaced their fusion mechanism with our attention based fusion mechanism and the results for the easy, medium and also hard scenario are shown in FIG11 . We have also compared our accuracy values with the results mentioned by the authors in their paper, in table 3, whereby we show significant performance improvement during the test phase including for the zeros shot instructions. The experiments are still running for the hard difficulty case but the results show that our approach converges much faster than the original fusion mechanism used by them. We see that our mechanism thus scales to both 2D as well as 3D environments outperforming other baselines in both the scenarios. The experiments were conducted on the same set of hardware thus ensuring a fair comparison between the plots.The plot shown here differs from the one shown in the paper ) because of a possible difference in hardwares used. We will update the plots as soon as all the experiments have been completed.",1311,0.652,741,1.7692307692307692,"In this work grounding language by training an agent follow navigate The agent receives visual information through raw pixels a natural language instruction telling what task needs achieved Other these two sources our model both the visual and textual modalities and end trainable We develop an attention mechanism multi-modal fusion visual and textual modalities the agent learn complete the navigation tasks also achieve language grounding Our experimental results our attention mechanism outperforms the existing multi-modal fusion mechanisms proposed order solve the above mentioned navigation task We demonstrate through the visualization attention weights our model learns correlate attributes referred in the instruction visual representations and also show the learnt textual representations semantically follow vector arithmetic also enough induce translation between instructions We also show our model generalizes effectively unseen scenarios exhibit zero-shot generalization capabilities In simulate the above described challenges introduce an agent jointly learn visual and textual modalities Figureblue in color should the instruction navigate green appleUnderstanding of natural language instructions an Artificial In successfully accomplish tasks specified natural language instructions an agent extract representations language semantically ground it perceptual elements actions inHumans the true essence thus they easily decipher sentences even contains some new combination It unreasonable same an AI agent The information extracted agent from the language should such corresponds so enables generalize even unseen combinations For instance given sufficient information the words suchgreenbag automatically figure as essentiallyConsider a task an agent learn navigate to as The environment consists many objects within: green apple blue sofa an orange fruit multiple obstacles The agent receives visual information through raw pixels an instruction telling what task needs achieved The challenges the agent tackle here manyfold a develop recognize various objects b have some memory seen previous states while exploring as the objects may occlude each may c ground the instruction visual elements actions learn a policy navigate by avoidingWe tackle proposing creates a combined representation the image observed Our model does any prior information both the visual and textual modalities We develop an attention mechanism multimodal fusion visual and textual modalities Our experimental results our attention mechanism outperforms the existing multimodal fusion mechanisms proposed order solve the above mentioned task We demonstrate through the visualization attention weights our model learns correlate attributes referred in the instruction visual representations and also show the learnt textual representations semantically follow vector arithmetic also enough induce translation between instructions We also show our model generalizes effectively unseen scenarios exhibit zero-shot (ZS) generalization capabilities In simulate the above described challenges introduce an agent jointly learn visual and textual modalities Our 2D environment also thread compatible Finally enable through participation BID21 foster this direction open our environment as models developed In the paper presented an attention based simple architecture achieve grounding natural language sentences via We show retaining just the representation obtained after multimodal fusion phasei.e. multiple attention maps discarding the visual features helps the agent We justify visualization the attention maps which reveal they contain sufficient information needed the agent find the optimal policy Through vector arithmetic also show learnt the agent indeed make In encourage the research this direction also open our environment as models developedOur environment capable rich set natural language instructions it highly As a future work, increase both the types sentences generated as the environment dynamics by moving objects We also plan take forward our approach a 3D environment test how does extend there To test our attention mechanism could scale 3D environments applied our fusion mechanism the Vizdoom based environment compared who have recently open their code Chaplot We replaced their fusion mechanism our attention based fusion mechanism for the easy, medium and also hard scenario FIG11 We also compared our accuracy values mentioned by table whereby significant performance improvement during including for the zeros shot instructions The experiments running for the hard difficulty case our approach converges much faster the original fusion mechanism used them We see our mechanism thus scales both 2D as outperforming other baselines both the scenarios The experiments the same set hardware thus ensuring the plotsThe plot shown differs ) hardwares We update the plots all the experiments",0.01,0.6640115858073861
"Current end-to-end machine reading and question answering (Q\&A) models are primarily based on recurrent neural networks (RNNs) with attention. Despite their success, these models are often slow for both training and inference due to the sequential nature of RNNs. We propose a new Q\&A architecture called QANet, which does not require recurrent networks:  Its encoder consists exclusively of convolution and self-attention, where convolution models local interactions and self-attention models global interactions. On the SQuAD dataset, our model is 3x to 13x faster in training and 4x to 9x faster in inference, while achieving equivalent accuracy to recurrent models. The speed-up gain allows us to train the model with much more data. We hence combine our model with data generated by backtranslation from a neural machine translation model. 
 On the SQuAD dataset, our single model, trained with augmented data, achieves 84.6 F1 score on the test set, which is significantly better than the best published F1 score of 81.8. There is growing interest in the tasks of machine reading comprehension and automated question answering. Over the past few years, significant progress has been made with end-to-end models showing promising results on many challenging datasets. The most successful models generally employ two key ingredients: (1) a recurrent model to process sequential inputs, and (2) an attention component to cope with long term interactions. A successful combination of these two ingredients is the Bidirectional Attention Flow (BiDAF) model by BID33 , which achieve strong results on the SQuAD dataset BID31 . A weakness of these models is that they are often slow for both training and inference due to their recurrent nature, especially for long texts. The expensive training not only leads to high turnaround time for experimentation and limits researchers from rapid iteration but also prevents the models from being used for larger dataset. Meanwhile the slow inference prevents the machine comprehension systems from being deployed in real-time applications.In this paper, aiming to make the machine comprehension fast, we propose to remove the recurrent nature of these models. We instead exclusively use convolutions and self-attentions as the building blocks of encoders that separately encodes the query and context. Then we learn the interactions between context and question by standard attentions BID45 BID33 BID2 . The resulting representation is encoded again with our recurrency-free encoder before finally decoding to the probability of each position being the start or end of the answer span. We call this architecture QANet, which is shown in Figure 1 .The key motivation behind the design of our model is the following: convolution captures the local structure of the text, while the self-attention learns the global interaction between each pair of words. The additional context-query attention is a standard module to construct the query-aware context vector for each position in the context paragraph, which is used in the subsequent modeling layers. The feed-forward nature of our architecture speeds up the model significantly. In our experiments on the SQuAD dataset, our model is 3x to 13x faster in training and 4x to 9x faster in inference. As a simple comparison, our model can achieve the same accuracy (77.0 F1 score) as BiDAF model BID33 within 3 hours training that otherwise should have taken 15 hours. The speed-up gain also allows us to train the model with more iterations to achieve better results than competitive models. For instance, if we allow our model to train for 18 hours, it achieves an F1 score of 82.7 on the dev set, which is much better than BID33 , and is on par with best published results.As our model is fast, we can train it with much more data than other models. To further improve the model, we propose a complementary data augmentation technique to enhance the training data. This technique paraphrases the examples by translating the original sentences from English to another language and then back to English, which not only enhances the number of training instances but also diversifies the phrasing.On the SQuAD dataset, QANet trained with the augmented data achieves 84.6 F1 score on the test set, which is significantly better than the best published result of 81.8 by . 2 We also conduct ablation test to justify the usefulness of each component of our model. In summary , the contribution of this paper are as follows:• We propose an efficient reading comprehension model that exclusively built upon convolutions and self-attentions. To the best of our knowledge, we are the first to do so. This combination maintains good accuracy, while achieving up to 13x speedup in training and 9x per training iteration, compared to the RNN counterparts. The speedup gain makes our model the most promising candidate for scaling up to larger datasets.• To improve our result on SQuAD, we propose a novel data augmentation technique to enrich the training data by paraphrasing. It allows the model to achieve higher accuracy that is better than the state-of-the-art. In this paper, we propose a fast and accurate end-to-end model, QANet, for machine reading comprehension. Our core innovation is to completely remove the recurrent networks in the encoder. The resulting model is fully feedforward, composed entirely of separable convolutions, attention, linear layers, and layer normalization, which is suitable for parallel computation. The resulting model is both fast and accurate: It surpasses the best published results on SQuAD dataset while up to 13/9 times faster than a competitive recurrent models for a training/inference iteration. Additionally, we find that we are able to achieve significant gains by utilizing data augmentation consisting of translating context and passage pairs to and from another language as a way of paraphrasing the questions and contexts.",1179,0.602,698,1.689111747851003,"Current end machine reading question (Q\&A models primarily attention. Despite their success these models slow for both training inference due the sequential nature We propose a new Q\&A architecture called QANet does recurrent networks: Its encoder consists exclusively and self-attention where models local interactions On the SQuAD dataset our model 3x to in training inference achieving equivalent accuracy recurrent models The speed-up gain allows train the model We hence combine our model generated backtranslation a neural machine translation model On the SQuAD dataset our single model, trained augmented data achieves 84.6 F1 score There is growing interest the tasks machine reading comprehension automated question Over significant progress with end models showing on many challenging datasets The most successful models generally employ two key ingredients process sequential inputs cope long term interactions A successful combination the Bidirectional Attention Flow (BiDAF) model by BID33 , achieve strong results the SQuAD dataset BID31 A weakness these models slow for both training inference due their recurrent nature especially long texts The expensive training not leads high turnaround time experimentation limits researchers from rapid iteration but prevents the models larger dataset Meanwhile the slow inference prevents the machine comprehension systems deployedIn aiming make fast propose remove the recurrent nature these models We instead exclusively convolutions self-attentions encoders separately encodes the query context Then learn the interactions context question by standard attentions BID45 BID33 . The resulting representation encoded again our recurrency-free encoder before finally the probability each position the start or the answer span We call this architecture QANet shown .The key motivation our model convolution captures the local structure the text the self-attention learns the global interaction each pair The additional context-query attention a standard module construct the query-aware context vector each position the context paragraph the subsequent modeling layers The feed-forward nature our architecture speeds the model significantly In our experiments on the SQuAD dataset our model is 3x to in training inference As a simple comparison our model can achieve (77.0 F1 score BiDAF model BID33 within 3 hours training that otherwise should The speed-up gain also allows train the model more iterations achieve than competitive models For instance allow our model train 18 hours achieves on the dev set much BID33 , on best published resultsAs fast train To further the model propose a complementary data augmentation technique This technique paraphrases the examples by translating back not enhances the number training instances diversifiesOn the SQuAD dataset QANet trained with the augmented data achieves 84.6 F1 score the best published result by . 2 We also conduct ablation test justify the usefulness each component our model In summary , the contribution are as We an efficient reading comprehension model exclusively built convolutions self-attentions To we do This combination maintains good accuracy while achieving up 13x speedup training per training iteration compared the RNN counterparts The speedup gain makes our model the promising candidate scaling larger datasets.• To improve our result on SQuAD propose enrich paraphrasing. It allows the model achieve higher accuracy that better the state In this paper fast accurate end model, QANet machine reading comprehension Our core innovation completely the recurrent networks the encoder The resulting model fully feedforward composed entirely separable convolutions attention, linear layers layer normalization suitable parallel computation The resulting model both fast accurate: surpasses the best published results SQuAD dataset while up 13/9 times a competitive recurrent models for a training/inference iteration Additionally find we achieve significant gains utilizing data augmentation consisting translating context passage pairs and as the questions contexts",0.01,0.4598753585119932
"Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined to fail, because the space-varying distortions introduced by such a projection will make translational weight sharing ineffective.

 In this paper we introduce the building blocks for constructing spherical CNNs. We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm. We demonstrate the computational efficiency, numerical accuracy, and effectiveness of spherical CNNs applied to 3D model recognition and atomization energy regression. Figure 1: Any planar projection of a spherical signal will result in distortions. Rotation of a spherical signal cannot be emulated by translation of its planar projection.Convolutional networks are able to detect local patterns regardless of their position in the image. Like patterns in a planar image, patterns on the sphere can move around, but in this case the ""move"" is a 3D rotation instead of a translation. In analogy to the planar CNN, we would like to build a network that can detect patterns regardless of how they are rotated over the sphere.As shown in Figure 1 , there is no good way to use translational convolution or cross-correlation 1 to analyze spherical signals. The most obvious approach, then, is to change the definition of crosscorrelation by replacing filter translations by rotations. Doing so, we run into a subtle but important difference between the plane and the sphere: whereas the space of moves for the plane (2D translations) is itself isomorphic to the plane, the space of moves for the sphere (3D rotations) is a different, three-dimensional manifold called SO(3) 2 . It follows that the result of a spherical correlation (the output feature map) is to be considered a signal on SO(3), not a signal on the sphere, S 2 . For this reason, we deploy SO(3) group correlation in the higher layers of a spherical CNN BID4 .The implementation of a spherical CNN (S 2 -CNN) involves two major challenges. Whereas a square grid of pixels has discrete translation symmetries, no perfectly symmetrical grids for the sphere exist. This means that there is no simple way to define the rotation of a spherical filter by one pixel. Instead, in order to rotate a filter we would need to perform some kind of interpolation. The other challenge is computational efficiency; SO(3) is a three-dimensional manifold, so a naive implementation of SO(3) correlation is O(n 6 ).We address both of these problems using techniques from non-commutative harmonic analysis BID3 BID11 . This field presents us with a far-reaching generalization of the Fourier transform, which is applicable to signals on the sphere as well as the rotation group. It is known that the SO(3) correlation satisfies a Fourier theorem with respect to the SO(3) Fourier transform, and the same is true for our definition of S 2 correlation. Hence, the S 2 and SO(3) correlation can be implemented efficiently using generalized FFT algorithms.Because we are the first to use cross-correlation on a continuous group inside a multi-layer neural network, we rigorously evaluate the degree to which the mathematical properties predicted by the continuous theory hold in practice for our discretized implementation.Furthermore, we demonstrate the utility of spherical CNNs for rotation invariant classification and regression problems by experiments on three datasets. First, we show that spherical CNNs are much better at rotation invariant classification of Spherical MNIST images than planar CNNs. Second, we use the CNN for classifying 3D shapes. In a third experiment we use the model for molecular energy regression, an important problem in computational chemistry. In this paper we have presented the theory of Spherical CNNs and evaluated them on two important learning problems. We have defined S 2 and SO(3) cross-correlations, analyzed their properties, and implemented a Generalized FFT-based correlation algorithm. Our numerical results confirm the stability and accuracy of this algorithm, even for deep networks. Furthermore, we have shown that Spherical CNNs can effectively generalize across rotations, and achieve near state-of-the-art results on competitive 3D Model Recognition and Molecular Energy Regression challenges, without excessive feature engineering and task-tuning.For intrinsically volumetric tasks like 3D model recognition, we believe that further improvements can be attained by generalizing further beyond SO(3) to the roto-translation group SE(3). The development of Spherical CNNs is an important first step in this direction. Another interesting generalization is the development of a Steerable CNN for the sphere , which would make it possible to analyze vector fields such as global wind directions, as well as other sections of vector bundles over the sphere.Perhaps the most exciting future application of the Spherical CNN is in omnidirectional vision. Although very little omnidirectional image data is currently available in public repositories, the increasing prevalence of omnidirectional sensors in drones, robots, and autonomous cars makes this a very compelling application of our work. We use the ZYZ Euler parameterization for SO(3). An element R ∈ SO(3) is written as DISPLAYFORM0 where α ∈ [0, 2π], β ∈ [0, π] and γ ∈ [0, 2π], and Z resp. Y are rotations around the Z and Y axes.Using this parameterization, the normalized Haar measure is DISPLAYFORM1 We have SO(3) dR = 1. The Haar measure BID23 BID3 ) is sometimes called the invariant measure because it has the property that SO(3) f (R R)dR = SO FORMULA2 f (R)dR (this is analogous to the more familiar property DISPLAYFORM2 f (x)dx for functions on the line). This invariance property allows us to do many useful substitutions.We have a related parameterization for the sphere. An element x ∈ S 2 is written DISPLAYFORM3 where n is the north pole.This parameterization makes explicit the fact that the sphere is a quotient S 2 = SO(3)/ SO(2), where H = SO(2) is the subgroup of rotations around the Z axis. Elements of this subgroup H leave the north pole invariant, and have the form Z(γ). The point x(α, β) ∈ S 2 is associated with the coset representativex = R(α, β, 0) ∈ SO(3). This element represents the cosetxH = {R(α, β, γ)|γ DISPLAYFORM4 The normalized Haar measure for the sphere is DISPLAYFORM5 The normalized Haar measure for SO(2) is DISPLAYFORM6 So we have dR = dx dh, again reflecting the quotient structure.We can think of a function on S 2 as a γ-invariant function on SO(3). Given a function f : S 2 → C we associate the functionf (α, β, γ) = f (α, β). When using normalized Haar measures, we have: DISPLAYFORM7 This will allow us to define the Fourier transform on S 2 from the Fourier transform on SO(3), by viewing a function on S 2 as a γ-invariant function on SO(3) and taking its SO(3)-Fourier transform.",1594,0.75,973,1.6382322713257964," the method learning problems involving 2D planar images However a number problems of recent interest created models analyze spherical images Examples include omnidirectional vision for drones robots molecular regression problems global weather and A naive application a planar projection the spherical signal destined the space-varying distortions introduced make translational weight sharing ineffective In this paper introduce the building blocks constructing spherical CNNs propose a definition the spherical cross that both expressive rotationequivariant The spherical correlation satisfies a generalized Fourier theorem allows compute it efficiently generalized ( Fast We demonstrate the computational efficiency, numerical accuracy effectiveness spherical CNNs applied 3D model recognition atomization energy regression Figure Any planar projection a spherical signal will result distortions Rotation a spherical signal cannot emulated translation its planar projectionConvolutional networks able detect local patterns regardless Like patterns a planar image patterns on the sphere move in the ""move a 3D rotation instead a translation In analogy the planar CNN we would build detect patterns regardless rotated over the sphereAs shown there use translational convolution or cross 1 analyze spherical signals The most obvious approach, change crosscorrelation by replacing filter translations rotations Doing we run the plane the sphere whereas moves for (2D translations itself isomorphic a different, three-dimensional manifold called SO(3 2 . It follows the result a spherical correlation (the output feature map to a signal on SO(3 the sphere S 2 For this reason deploy SO(3) group correlation the higher layers a spherical CNN BID4 .The implementation ( 2 -CNN involves Whereas a square grid pixels has discrete translation symmetries no perfectly symmetrical grids for the sphere exist This means there define the rotation a spherical filter by one pixel Instead in order rotate a filter we would perform interpolation The other challenge computational efficiency; SO(3 a naive implementation SO(3) correlation 6 ).We address both techniques non-commutative harmonic analysis BID3 BID11 . This field presents us a far-reaching generalization applicable signals on the sphere as the rotation group It known the SO(3) correlation satisfies a Fourier theorem with same our definition S 2 correlation Hence the S 2 and SO(3) correlation can implemented efficiently generalized FFT algorithmsBecause we the cross on a continuous group inside rigorously evaluate the mathematical properties predicted the continuous theory hold practice for our discretized implementationFurthermore spherical CNNs rotation invariant classification regression problems by experiments three datasets First show spherical CNNs much rotation invariant classification of Spherical MNIST images use for classifying 3D shapes In a third experiment we use the model for molecular energy regression an important problem computational chemistry In this paper have presented the theory Spherical CNNs evaluated them two important learning problems We defined S 2 and SO(3) cross analyzed their properties implemented a Generalized FFT-based correlation algorithm Our numerical results confirm the stability accuracy this algorithm even deep networks Furthermore we shown Spherical CNNs effectively generalize across rotations achieve near state on competitive 3D Model Recognition Molecular Energy Regression challenges without excessive feature engineering task-tuningFor intrinsically volumetric tasks believe further improvements can attained generalizing further beyond SO(3 the roto-translation group SE(3 The development Spherical CNNs Another interesting generalization the development a Steerable CNN for the sphere , make analyze vector fields such global wind directions as other sections vector bundles over the spherePerhaps the most exciting future application omnidirectional vision Although very little omnidirectional image data currently in public repositories the increasing prevalence drones robots autonomous cars makes compelling application our work We use the ZYZ Euler parameterization for SO(3 An element R �� SO(3 written DISPLAYFORM0 where α [ 2π � Z resp Y are rotations around the Z and Y axesUsing this parameterization the normalized Haar measure DISPLAYFORM1 We SO(3 dR The Haar measure BID23 BID3 ) sometimes the invariant measure has SO(3) f (R R)dR SO FORMULA2 (this analogous the more familiar property DISPLAYFORM2 fx)dx for functions on the line This invariance property do many useful substitutionsWe a related parameterization for the sphere An element x �� S 2 written DISPLAYFORM3 where n the north poleThis parameterization makes explicit the sphere a quotient S = SO(3)/ is the subgroup rotations around Elements this subgroup H leave north pole invariant have Z(γ point x(α �� S 2 associated the coset representativex = 0 �� SO(3 This element represents the cosetxH = {R(α)|γ DISPLAYFORM4 The normalized Haar measure for the sphere SO(2 So dR dx dh, again reflecting the quotient structureWe think a function on S 2 SO(3 Given a function f : S 2 → C we associate the functionfα = When using normalized Haar measures have: DISPLAYFORM7 This will define on S 2 from SO(3 by viewing a function taking",0.01,0.3302389225476967
"We propose a novel method that makes use of deep neural networks and gradient decent to perform automated design on complex real world engineering tasks. Our approach works by training a neural network to mimic the fitness function of a design optimization task and then, using the differential nature of the neural network, perform gradient decent to maximize the fitness. We demonstrate this methods effectiveness by designing an optimized heat sink and both 2D and 3D airfoils that maximize the lift drag ratio under steady state flow conditions. We highlight that our method has two distinct benefits over other automated design approaches. First, evaluating the neural networks prediction of fitness can be orders of magnitude faster then simulating the system of interest. Second, using gradient decent allows the design space to be searched much more efficiently then other gradient free methods. These two strengths work together to overcome some of the current shortcomings of automated design. Automated Design is the process by which an object is designed by a computer to meet or maximize some measurable objective. This is typically performed by modeling the system and then exploring the space of designs to maximize some desired property whether that be an automotive car styling with low drag or power and cost efficient magnetic bearings BID1 BID4 . A notable historic example of this is the 2006 NASA ST5 spacecraft antenna designed by an evolutionary algorithm to create the best radiation pattern (Hornby et al.) . More recently, an extremely compact broadband on-chip wavelength demultiplexer was design to split electromagnetic waves with different frequencies BID17 . While there have been some significant successes in this field the dream of true automated is still far from realized. The main challenges present are heavy computational requirements for accurately modeling the physical system under investigation and often exponentially large search spaces. These two problems negatively complement each other making the computation requirements intractable for even simple problems.Our approach works to solve the current problems of automated design in two ways. First, we learn a computationally efficient representation of the physical system on a neural network. This trained network can be used to evaluate the quality or fitness of the design several orders of magnitude faster. Second, we use the differentiable nature of the trained network to get a gradient on the parameter space when performing optimization. This allows significantly more efficient optimization requiring far fewer iterations then other gradient free methods such as genetic algorithms or simulated annealing. These two strengths of our method overcome the present difficulties with automated design and greatly accelerate optimization.The first problem tackled in this work is designing a simple heat sink to maximize the cooling of a heat source. The setup of our simulation is meant to mimic the conditions seen with an aluminum heat sink on a computer processor. We keep this optimization problem relatively simple and use this only as a first test and introduction to the method. Our second test is on the significantly more difficult task of designing both 2D and 3D airfoils with high lift drag ratios under steady state flow conditions. This problem is of tremendous importance in many engineering areas such as aeronautical, aerospace and automotive engineering. Because this is a particularly challenging problem and often times unintuitive for designers, there has been considerable work using automated design to produce optimized designs. We center much of the discussion in this paper around this problem because of its difficulty and view this as a true test our method. While we only look at these two problems in this work, we emphasize that the ideas behind our method are applicable to a wide variety of automated design problems and present the method with this in mind.As we will go into more detail in later sections, in order to perform our airfoil optimization we need a network that predicts the steady state flow from an objects geometry. This problem has previously been tackled in BID5 where they use a relatively simple network architecture. We found that better perform could be obtained using some of the modern network architecture developments and so, in addition to presenting our novel method of design optimization, we also present this superior network for predicting steady state fluid flow with a neural network. In this work we have presented a novel method for automated design and shown its effectiveness on a variety of tasks. Our method makes use of neural networks and gradient descent to provide powerful and fast optimization. There are many directions for future work such as applying this method to new domains like structural optimization and problems related to electromagnetism. One area of particular interest is design optimization on airfoils in turbulent time dependent flows. Another interesting area to explore is hybrid approaches where the neural network method is used to generate a rough design and then fine tuned with a high fidelity simulation. DISPLAYFORM0 The parameters present are n 1 , n 2 , A i s, and h. We also add the parameter θ that determines the angle of attack. In this work we fixed n 1 to 0.5 and n 2 to 1.0 as this will produce a rounded head on the airfoil. We also fix h to zero making the tail the same height as the head. Thus the trainable parameters are the 42 values corresponding to the A i s for the upper and lower surface. A illustration showing the parameterization can be found in FIG7 . The 3D airfoil has similar parameterization.S(φ, y) = φ n1 (1 − φ) This tells the height of the airfoil at a point (x, y). The trainable parameters here are n 1 , n 2 , A i s, B j s, h, s, and l. Again, n 1 , n 2 , and h are fixed to the values in the 2D case. We also have 2 parameters for the angle θ and ψ that determine the rotation in the x and y direction. We keep ψ at zero and only vary θ at the desired angles during the optimization. The parameters s and l correspond to the sweep present in the wing. This leaves the A i s and B j s for optimization. We split the remaining 39 parameters equally so that 13 values are used for B i s and the remaining 26 are split between the A i s for the upper and lower surface. For a much more in depth look at this parameterization, see BID13 .",1238,0.764,706,1.753541076487252,"We propose makes gradient decent to perform automated design on complex real world engineering tasks Our approach works training mimic the fitness function a design optimization task, the differential nature perform gradient decent to maximize We demonstrate this methods effectiveness designing an optimized heat sink both 2D maximize the lift drag ratio under steady state flow conditions We highlight that our method over other automated design approaches First evaluating the neural networks prediction fitness can orders then simulating the system interest Second using gradient decent allows the design space searched much then other gradient free methods These two strengths work overcome some automated design Automated Design maximize some measurable objective This typically performed modeling exploring the space designs maximize some desired property whether an automotive car styling with low drag power cost efficient magnetic bearings BID1 BID4 . A notable historic example the 2006 NASA ST5 spacecraft antenna designed an evolutionary algorithm create the best radiation pattern (Hornby . More recently an extremely compact broadband onchip wavelength design split with BID17 . While the dream true automated is The main challenges present heavy computational requirements accurately modeling under investigation often exponentially large search spaces These two problems negatively complement making the computation requirements even simple problemsOur approach works to automated design First learn a computationally efficient representation on This trained network evaluate or fitness the design several orders Second use the differentiable nature the trained network get a gradient when performing optimization This allows significantly more efficient optimization requiring far fewer iterations then other gradient free methods genetic algorithms simulated annealing These two strengths our method overcome automated design greatly accelerate optimizationThe first problem tackled designing a simple heat sink maximize The setup our simulation meant mimic seen with an aluminum heat sink on a computer processor We keep this optimization problem relatively use this only and introduction Our second test the significantly more difficult task designing both 2D high lift drag ratios under steady state flow conditions This problem of tremendous importance many engineering areas Because a particularly challenging problem and often unintuitive designers has using automated design produce optimized designs We center much around this problem because view this a true test our method While only look these two problems this work emphasize the ideas our method applicable automated design problems present the method this inAs go in perform our airfoil optimization a network predicts from an objects geometry This problem previously tackled BID5 where use a relatively simple network architecture We found better perform could obtained using some the modern network architecture developments so presenting our novel method design optimization this superior network for predicting steady state fluid flow with In this work presented automated design shown its effectiveness Our method makes neural networks provide powerful and fast optimization There many directions future work such applying this method new domains like structural optimization problems related One area design optimization on airfoils turbulent time dependent flows Another interesting area hybrid approaches where the neural network method a rough design fine tuned with DISPLAYFORM0 The parameters present n 1 A i s, h. We also add the parameter �� that In this work fixed n 1 as this produce a rounded head on We also fix h to zero making the tail Thus the trainable parameters the 42 values corresponding the A i for A illustration the parameterization can FIG7 The 3D airfoil similar parameterization.S(�� y� n1 This tells the height The trainable parameters here n 1 A i s, h Again n 1 h fixed We also 2 parameters the angle �� and �� in We keep � at zero only vary �� the desired angles during the optimization The parameters s l correspond the sweep present the wing This leaves A i s and for optimization We split the remaining 39 parameters equally so 13 values B i s 26 split for For much this parameterization BID13 .",0.01,0.6240356271782366
"Methods that align distributions by minimizing an adversarial distance between them have recently achieved impressive results. However, these approaches are difficult to optimize with gradient descent and they often do not converge well without careful hyperparameter tuning and proper initialization. We investigate whether turning the adversarial min-max problem into an optimization problem by replacing the maximization part with its dual improves the quality of the resulting alignment and explore its connections to Maximum Mean Discrepancy. Our empirical results suggest that using the dual formulation for the restricted family of linear discriminators results in a more stable convergence to a desirable solution when compared with the performance of a primal min-max GAN-like objective and an MMD objective under the same restrictions. We test our hypothesis on the problem of aligning two synthetic point clouds on a plane and on a real-image domain adaptation problem on digits. In both cases, the dual formulation yields an iterative procedure that gives more stable and monotonic improvement over time. Adversarial methods have recently become a popular choice for learning distributions of highdimensional data. The key idea is to learn a parametric representation of a distribution by aligning it with the empirical distribution of interest according to a distance given by a discriminative model. At the same time, the discriminative model is trained to differentiate between true and artificially obtained samples. Generative Adversarial Networks (GANs) that use neural networks to both discriminate samples and parameterize a learned distribution, have achieved particularly impressive results in many applications such as generative modeling of images BID9 BID4 BID26 , image super-resolution BID15 , and image-to-image translation BID13 . Adversarial matching of empirical distributions has also shown promise for aligning train and test data distributions n scenarios involving domain shift BID6 BID30 .However , GANs and related models have proved to be extremely difficult to optimize. It has been widely reported that training GANs is a tricky process that often diverges and requires very careful parameter initialization and tuning. Arjovsky and Bottou have recently identified several theoretical problems with loss functions used by GANs, and have analyzed how they contribute to instability and saturation during training.In this paper, we focus on one of the major barriers to stable optimization of adversarial methods, namely their min-max nature. Adversarial methods seek to match the generated and real distributions by minimizing some notion of statistical distance between the two, which is often defined as a maximal difference between values of certain test (witness) functions that could differentiate these distributions. More specifically in the case of GANs, the distance is usually considered to be equal to the likelihood of the best neural network classifier that discriminates between the distributions, assigning ""real or generated?"" labels to the input points. This way, in order to align these distributions one has to minimize this maximum likelihood w.r.t. the parameters of the learned or aligned distribution.Unfortunately, solving min-max problems using gradient descent is inherently very difficult. Below we use a simple example to demonstrate that different flavors of gradient descent are very unstable when it comes to solving problems of this kind.To address this issue, we explore the possibility of replacing the maximization part of the adversarial alignment problem with a dual minimization problem for linear and kernelized linear discriminators. The resulting dual problem turns out to be much easier to solve via gradient descent. Moreover, we make connections between our formulation and existing objectives such as the Maximum Mean Discrepancy (MMD) BID11 . We show that it is strongly related to the iteratively reweighted empirical estimator of MMD.We first evaluate how well our dual method can handle a point alignment problem on a lowdimensional synthetic dataset. Then, we compare its performance with the analogous primal method on a real-image domain adaptation problem using the Street View House Numbers (SVHN) and MNIST domain adaptation dataset pair. Here the goal is to align the feature distributions produced by the network on the two datasets so that a classifier trained to label digits on SVHN does not loose accuracy on MNIST due to the domain shift. In both cases, we show that our proposed dual formulation of the adversarial distance often shows improvement over time, whereas using the primal formulation results in drifting objective values and often does not converge to a solution.Our contributions can be summarized as follows:• we explore the dual formulation of the adversarial alignment objective for linear and kernelized linear discriminators and how they relate to the Maximum Mean Discrepancy; • we demonstrate experimentally on both synthetic and real datasets that the resulting objective leads to more stable convergence and better alignment quality; • we apply this idea to a domain adaptation scenario and show that the stability of reaching high target classification accuracy is also positively impacted by the dual formulation. While exact dual exists only in the logistic discriminator case, when one can use the duality and solve the inner problem in closed form, we want to stress that our paper presents a more general framework for alignment that can be extended to other classes of functions. More specifically, one can rewrite the quadratic form in kernel logistic regression (3) as a Frobenius inner product of a kernel matrix Q with a symmetric rank 1 alignment matrix S (outer product of alpha with itself). DISPLAYFORM0 The kernel matrix specifies distances between points and S chooses pairs that minimize the total distance. This way the problem reduces to ""maximizing the maximum agreement between the alignment and similarity matrices"" that in turn might be seen as replacing ""adversity"" in the original problem with ""cooperation"" in the dual maximization problem. In our paper, S is a rank 1 matrix, but we could choose different alignment matrix parameterizations and a corresponding regularizer that would correspond to having a neural network discriminator in the adversarial problem or a Wasserstein distance in Earth Mover's Distance form. The resulting problem is not dual to minimization of any existing adversarial distances, but exploits same underlying principle of ""iteratively-reweighted alignment matrix fitting"" discussed in this paper.We assert that in order to understand the basic properties of the resulting formulation, an in-depth discussion of the well-studied logistic case is no less important than the discussion involving complicated deep models, which deserves a paper of its own. This paper proposes a more stable ""cooperative"" problem reformulation rather than a new adversarial objective as many recent papers do. We presented an adversarial objective that does not lead to a min-max problem. We proposed using the dual of the discriminator objective to improve the stability of distribution alignment, showed its connection to MMD, and presented quantitative results for alignment of toy datasets and unsupervised domain adaptation results on real-image classification datasets. Our results suggest that the proposed dual optimization objective is indeed better suited for learning with gradient descent than the saddle point objective that naturally arises from the original primal formulation of adversarial alignment. Further attempts to use duality to reformulate other notions of statistical distances in adversarial settings as computationally feasible minimization problems may be promising. Bottom row: Evolution of target test accuracy over epochs. Our Dual objective (third column) clearly performs well under the majority of the learning rates. WGAN often performs better than MMD and ADDA, but experiences significant oscillations. Different validation heuristics, such as considering only runs that resulted in a significant drop in distance, did not significantly change these trends (Section 9.3). The proportion of runs that outperformed the source baseline after 40 epochs were: 52.3% for Dual, 21.5% for WGAN, 17.1% for MMD and 6.9% for ADDA.",1522,0.705,912,1.668859649122807,"Methods that align distributions by minimizing an adversarial distance achieved However these approaches difficult optimize gradient descent converge without proper initialization We investigate turning the adversarial min-max problem replacing its dual improves the resulting alignment explore its connections Maximum Mean Discrepancy Our empirical results using the dual formulation the restricted family linear discriminators results a desirable solution when the performance a primal min-max GAN-like objective and an MMD objective under We test on the problem aligning two synthetic point clouds a real-image domain adaptation problem on digits In the dual formulation yields an iterative procedure gives more stable and monotonic improvement Adversarial methods recently learning distributions highdimensional data The key idea learn a parametric representation a distribution aligning interest according a distance given At the discriminative model trained differentiate true and artificially obtained samples that both discriminate samples parameterize a learned distribution achieved many applications generative modeling images BID9 BID4 BID26 , image super- translation Adversarial matching empirical distributions has also shown aligning train and n scenarios involving domain shift BID6 BID30 .However , GANs related models proved extremely optimize It widely training GANs often diverges and very careful parameter initialization Arjovsky Bottou have recently identified several theoretical problems loss functions used GANs analyzed contribute instability saturation during trainingIn focus stable optimization adversarial methods Adversarial methods seek match the generated and real distributions by minimizing some notion statistical distance, defined a maximal difference values certain test (witness) functions could differentiate these distributions More specifically in GANs the distance usually considered equal the likelihood the best neural network classifier that the distributions assigning ""real or generated?"" labels This way in align these distributions one has minimize this maximum likelihood w.r.t the parameters the learned or aligned distributionUnfortunately solving inherently Below we use different flavors gradient descent very unstable it solvingTo address explore replacing the maximization part the adversarial alignment problem linear kernelized linear discriminators The resulting dual problem turns via Moreover make connections our formulation existing objectives such the Maximum Mean Discrepancy (MMD) BID11 . We show it strongly related iteratively reweighted empirical estimator MMD.We evaluate our dual method a point alignment problem on a lowdimensional synthetic dataset Then compare the analogous primal method on a real-image domain adaptation problem using the Street View House Numbers MNIST domain adaptation dataset pair Here the goal align the feature distributions produced the network on so a classifier trained label digits SVHN does loose due the domain shift In we show our proposed dual formulation the adversarial distance often shows improvement using the primal formulation results drifting objective values often convergeOur contributions can we explore the adversarial alignment objective linear kernelized linear discriminators how the Maximum Mean Discrepancy; experimentally on the resulting objective leads better alignment quality apply this idea a domain adaptation scenario the stability reaching high target classification accuracy positively impacted While exact dual exists only the logistic discriminator case when can and solve the inner problem closed form want stress our paper presents alignment that functions More specifically one rewrite kernel logistic regression3 a Frobenius inner product a kernel matrix Q with a symmetric rank 1 alignment matrix S (outer product alpha with itself DISPLAYFORM0 The kernel matrix specifies distances points S chooses pairs minimize This way the problem reduces "" the maximum agreement the alignment similarity matrices that in might seen replacingadversity the dual maximization problem In our paper S is a rank 1 matrix but could choose different alignment matrix parameterizations a corresponding regularizer correspond having a neural network discriminator the adversarial problem or a Wasserstein distance in Earth Mover's Distance form The resulting problem dual to minimization any existing adversarial distances exploits same underlying principle ""iteratively-reweighted alignment matrix fitting discussedWe assert understand the resulting formulation no less involving complicated deep models deserves This paper a more stable ""cooperative"" problem reformulation rather a new adversarial objective as many recent papers We presented an adversarial objective does lead a min-max problem We proposed using the dual of the discriminator objective improve distribution alignment showed its connection MMD presented quantitative results alignment toy datasets unsupervised domain adaptation results on real-image classification datasets Our results the proposed dual optimization objective indeed better learning with saddle point objective that naturally the original primal formulation adversarial alignment Further attempts use duality reformulate other notions statistical distances adversarial settings as computationally feasible minimization problems may promising Bottom row Evolution target test accuracy over epochs Our Dual objective (third column clearly performs under the majority the learning rates WGAN often performs better MMD ADDA experiences significant oscillations Different validation heuristics considering only runs resulted distance did these trendsSection The proportion runs outperformed the source baseline after 40 epochs were: Dual WGAN MMD ADDA",0.01,0.4082747902824887
"There are many applications scenarios for which the computational
  performance and memory footprint of the prediction phase of Deep
  Neural Networks (DNNs) need to be optimized. Binary Deep Neural
  Networks (BDNNs) have been shown to be an effective way of achieving
  this objective. In this paper, we show how Convolutional Neural
  Networks (CNNs) can be implemented using binary
  representations. Espresso is a compact, yet powerful
  library written in C/CUDA that features all the functionalities
  required for the forward propagation of CNNs, in a binary file less
  than 400KB, without any external dependencies. Although it is mainly
  designed to take advantage of massive GPU parallelism, Espresso also
  provides an equivalent CPU implementation for CNNs. Espresso
  provides special convolutional and dense layers for BCNNs,
  leveraging bit-packing and bit-wise computations
  for efficient execution. These techniques provide a speed-up of
  matrix-multiplication routines, and at the same time, reduce memory
  usage when storing parameters and activations. We experimentally
  show that Espresso is significantly faster than existing
  implementations of optimized binary neural networks (~ 2
  orders of magnitude). Espresso is released under the Apache 2.0
  license and is available at http://github.com/organization/project. Convolutional Neural Networks have revolutionized computer vision, pushing the task of object recognition beyond human capabilities BID18 BID25 BID27 . Deep Neural Networks (DNN), have also been successfully applied in other fields, such as speech recognition BID9 and automated translation BID1 BID26 . Despite achieving impressive classification accuracy results, DNNs require too much memory and power to be used effectively on embedded or low-power devices. Many networks consume a considerable amount of memory. Memory remains a very limited resource on mobile platforms making harder the usage of trained DNNs 1 . Even when memory is not an issue, DNNs remain very computationally intensive, and can quickly drain the battery. Reducing the computational load does not only improve energy efficiency, but can also enable further applications. For example, when processing real-time object classification on mobile, being able to perform faster predictions frees up computational resources that can be spent on tasks such as speech recognition and analysis. Therefore, there is a substantial interest in reducing the computational and memory requirements of DNNs.Efficient deep neural networks One way to achieve this target is to use specialized hardware for DNNs. Another strategy is to reduce the network's memory footprint and associated computation, hence increasing its efficiency. Such solutions are preferable as they can be implemented in software without requiring specialized hardware. In our research we follow the software approach, and focus our attention to quantized networks. In this case, the parameters are stored as ""small"" integers (typically less than 8-bit) instead of single precision floating point numbers (32-bit). In particular, we consider the binary deep neural networks (BDNN) proposed by where parameters and activations are 1-bit integers: {−1, +1}. At the expense of a relatively small decrease in accuracy, BDNNs can considerably reduce memory usage, and result in faster execution time (i.e. forward propagation). Further, note that potential hardware implementation of BDNNs would also be cheaper due to the reduced number of required FPUs. While these results are highly promising, currently only proof-of-concept implementations of BinaryNets have been published . Therefore, the availability of a flexible end-to-end framework, with particular emphasis placed on computational efficiency, can enable further research on BDNNs, as well as its application to practical scenarios.Contributions With Espresso we provide an optimized framework for BDNNs capable of achieving state-of-the-art run-time performance with minimal memory footprint while being numerical equivalent to their non-optimized binary counterpart. Espresso provides a complete optimized framework for BDNNs supporting both the dense and the convolutional layer. Current state-ofthe-art optimized BDNNs implementations are limited to the fully connected layer, with the serious drawback of not being able to run optimized state-of-art convolutional BDNNs (BCNNs). While our work is a necessary stepping stone towards optimization of training routines, in this paper we focus on the optimization of forward-propagation (i.e. testing), rather than back-propagation (i.e. training). Espresso is designed to have no external dependencies. This not only results in a highly optimized implementation of BDNNs, but also substantially simplifies its deployment in practical applications, such as those executing on mobile or embedded devices. In this paper we presented Espresso, a highly optimized forward-propagation framework for both traditional DNNs as well as BCNNs, that supports heterogeneous deployment on CPU and GPU. While BinaryNet and Nervana/neon BDNN implementations are limited to MLP networks, our framework also supports the popular CNN while simultaneously outperforming state-of-the-art implementations of MLP networks. Espresso is highly-efficient, light-weight and self-contained. Computation on the GPU side is done though specifically designed CUDA kernels, which, combined with a more careful handling of memory allocation and bit-packing, allows us to obtain considerable performance improvements. In future work we would like to add training capabilities, and perform additional performance comparisons on larger standard datasets.",1085,0.585,634,1.7113564668769716,"There many applications scenarios which computational performance and memory the prediction phase Deep Neural Networks need Binary Deep Neural Networks shown achieving this objective In this paper implemented binary representations Espresso compact yet powerful library written C/CUDA features the forward propagation CNNs in a binary file less than 400KB without Although mainly designed take massive GPU parallelism Espresso also an equivalent CPU implementation CNNs provides special and dense layers BCNNs leveraging bit-packing and bit-wise computations efficient execution These techniques provide a speed-up matrix-multiplication routines at reduce when storing parameters and activations We experimentally show Espresso significantly faster existing implementations optimized binary neural networks (~ 2 orders Espresso released under at have revolutionized pushing the task object recognition beyond human capabilities BID18 BID25 BID27 . Deep Neural Networks have also successfully speech recognition BID9 automated translation BID1 BID26 . Despite achieving impressive classification accuracy results DNNs require too much memory power on embedded or low-power devices Many networks consume memory Memory remains on mobile platforms making harder the usage trained DNNs 1 . Even when memory not DNNs remain very computationally can quickly drain Reducing the computational load does only energy efficiency can enable further applications For example when processing real-time object classification on mobile being perform faster predictions frees tasks speech recognition analysis Therefore there a substantial interest reducing the computational and memory requirements DNNsEfficient deep neural One way this target specialized hardware Another strategy reduce associated computation, hence Such solutions preferable as can software specialized hardware In our research follow the software approach, focus to quantized networks In the parameters stored ""small"" integers instead In particular we consider the binary deep neural networksBDNN proposed where parameters and activations 1-bit integers: {−1 At the expense a relatively small decrease accuracy BDNNs considerably memory usage result faster execution time (i.e. forward propagation Further, note potential hardware implementation BDNNs would also cheaper due required FPUs While these results highly currently proof BinaryNets . Therefore the availability flexible end framework, with particular emphasis placed computational efficiency enable further research BDNNs as its application practical scenariosContributions With Espresso we provide an optimized framework capable achieving state run with minimal memory footprint while being numerical equivalent their non-optimized binary counterpart Espresso provides a complete optimized framework BDNNs supporting both the dense the convolutional layer Current state-ofthe-art optimized BDNNs implementations limited the fully connected layer the serious drawback not run optimized stateart convolutional BDNNs ( While our work a necessary stepping stone optimization training routines in this paper forward-propagation (i.e. testing rather Espresso designed have no external dependencies This not results a highly optimized implementation BDNNs substantially its deployment practical applications those executing In this paper presented Espresso, a highly optimized forward-propagation framework both traditional DNNs as BCNNs supports heterogeneous deployment on CPU While BinaryNet and Nervana/neon BDNN implementations limited MLP networks our framework also the popular CNN while simultaneously outperforming state implementations Espresso highly-efficient light self Computation on the GPU side done though specifically designed CUDA kernels, combined a more careful handling memory allocation bit-packing allows obtain considerable performance improvements In future work would add training capabilities, and perform additional performance comparisons on larger standard datasets",0.01,0.5165529481905173
"Optimal selection of a subset of items from a given set is a hard problem that requires combinatorial optimization. In this paper, we propose a subset selection algorithm that is trainable with gradient based methods yet achieves near optimal performance via submodular optimization. We focus on the task of identifying a relevant set of sentences for claim verification in the context of the FEVER task. Conventional methods for this task look at sentences on their individual merit and thus do not optimize the informativeness of sentences as a set. We show that our proposed method which builds on the idea of unfolding a greedy algorithm into a computational graph allows both interpretability and gradient based training. The proposed differentiable greedy network (DGN) outperforms discrete optimization algorithms as well as other baseline methods in terms of precision and recall. In this paper, we develop a subset selection algorithm that is differentiable and discrete, which can be trained on supervised data and can model complex dependencies between elements in a straightforward and comprehensible way. This is of particular interest in natural language processing tasks such as fact extraction, fact verification, and question answering where the proposed optimization scheme can be used for evidence retrieval.Conventional evidence retrieval methods that look at lexical or semantic similarity typically treat sentences or documents independently, potentially missing dependencies between them and therefore select redundant evidence. One way to address this shortcoming is by adding a diversity promoting submodular objective function BID28 BID17 BID18 BID6 BID13 . Submodularity is a property of set functions that can be expressed by the notion of diminishing returns that allows near-optimal solutions to be found in polynomial time for NP-hard problems.A submodular set function is a function that maps sets to scalar values and has the property that the incremental value of the function computed with an additional element to an input set never increases as the input set grows. Submodular functions are defined by this natural diminishing returns property, which makes them well suited for tasks such as claim verification. With respect to a claim, the amount of relevant information in a set of sentences has diminishing returns as the set grows, meaning that the amount of additional information in an additional piece of evidence shrinks as the set of selected evidence grows. Thus, any relevancy-measuring function that is learned from data would potentially benefit from a diminishing returns constraint as it would discount redundancy in favor of diverse but relevant evidence. Claim verification often requires complicated induction from multiple sentences, so promoting diversity among selected sentences is important to capture all facets of the claim. The resulting submodular optimization model can then handle dependencies between sentences and features, and despite making the sentence selection problem more difficult computationally, a near-optimal solution can be found efficiently using a simple forward greedy algorithm.The main contribution of this paper is a new optimization scheme which integrates continuous gradient-based and discrete submodular frameworks derived by unfolding a greedy optimization algorithm: the Differentiable Greedy Network (DGN). By unfolding a greedy algorithm into a computational graph, we can combine the advantages in interpretability and representation learning. Deep unfolding is a technique that transforms inference algorithms into computational graphs, thereby allowing the original model parameters to be trained discriminatively on labeled data while still exactly corresponding to the original model parameters BID9 . We show that making a greedy algorithm differentiable and adding trainable parameters leads to promising improvements in recall@k of 10%-18% and precision@k of 5%-27% for a sentence selection task, where k = 1, 3, 5, 7 is the number of selected evidence sentences, on the Fact Extraction and Verification (FEVER) dataset BID27 and, with fewer parameters, performs very similarly to a conventional deep network. As the DGN is bootstrapping a greedy algorithm, it can be easily extended to work on other information retrieval tasks such as question answering as well as other problems that rely on greedy approaches. While more sophisticated neural architectures can deliver better performance, we focus on showing the power of our new optimization scheme on a simpler model.In Section 2, we discuss related work in the domains of information retrieval, submodularity, and deep unfolding. In Section 3, we define submodularity and present the proposed Differentiable Greedy Network (DGN). Section 4 contains experiments and results for baseline models and DGN applied to sentence selection for the FEVER dataset as well as an ablation study. We draw conclusions in Section 5. Also, the attached Appendix 6 contains an additional example demonstrating the utility of promoting diversity. In this paper, we have shown that unfolding a greedy algorithm into a computational graph, allowing us to retain the interpretability and unsupervised initialization of a conventional greedy sentence selection approach while benefiting from supervised learning techniques. The proposed differentiable greedy network (DGN) outperforms conventional discrete optimization algorithms in terms of both recall and precision. Furthermore, as sentence retrieval is often part of a larger pipeline as in the FEVER shared task, using a differentiable greedy network serves as a step towards an end-end trainable system.",1011,0.487,621,1.6280193236714975,"Optimal selection a subset items that In a subset selection algorithm trainable gradient based methods yet achieves near via submodular optimization We focus the task identifying a relevant set sentences claim verification the FEVER task Conventional methods this task look sentences on their individual merit thus optimize the informativeness as a set We show our proposed method which builds unfolding a greedy algorithm into a computational graph allows both interpretability gradient based training The proposed differentiable greedy networkDGN outperforms discrete optimization algorithms as other baseline methods precision recall In develop a subset selection algorithm differentiable and discrete trained supervised data model complex dependencies elements This of natural language processing tasks such fact extraction fact verification question where the proposed optimization scheme evidence retrievalConventional evidence retrieval methods that look lexical or semantic similarity typically treat sentences or documents independently potentially missing dependencies therefore select redundant evidence One way address adding a diversity promoting submodular objective function BID28 BID17 BID18 BID6 BID13 Submodularity set functions expressed the notion diminishing that allows near-optimal solutions be for maps sets the incremental value computed with an additional element to an input never increases Submodular functions this natural diminishing returns property makes well tasks claim verification With respect a claim, the amount relevant information a set sentences has diminishing as meaning an additional piece of selected evidence Thus any relevancy-measuring function learned data would potentially benefit a diminishing returns constraint as discount redundancy favor diverse but relevant evidence Claim verification often complicated induction from multiple sentences promoting diversity among selected sentences capture all facets The resulting submodular optimization model then handle dependencies sentences features despite making the sentence selection problem computationally efficiently a simple forward greedy algorithmThe main contribution a new optimization scheme integrates continuous gradient-based and discrete submodular frameworks derived by unfolding a greedy optimization: the Differentiable Greedy Network By unfolding a greedy algorithm into a computational graph combine the advantages in interpretability representation learning Deep unfolding is a technique transforms inference algorithms computational graphs thereby the original model parameters trained discriminatively labeled data while exactly corresponding the original model parameters BID9 . We show making a greedy algorithm differentiable and adding trainable parameters leads promising improvements recall@k of 10%-18% a sentence selection task where k 3 is selected evidence sentences on the Fact ExtractionFEVER dataset BID27 and, fewer parameters performs very similarly a conventional deep network As the DGN is bootstrapping a greedy algorithm easily extended work other information retrieval tasks question as problems rely greedy approaches While more sophisticated neural architectures deliver focus showing our new optimization schemeIn Section related work the domains submodularity deep unfolding In Section define submodularity present the proposed Differentiable Greedy Network Section contains experiments baseline models DGN applied sentence selection the FEVER dataset as an ablation study We draw conclusions in Section Also the attached Appendix 6 contains demonstrating promoting diversity In have unfolding a greedy algorithm into a computational graph allowing retain the interpretability unsupervised initialization a conventional greedy sentence selection approach while benefiting supervised learning techniques The proposed differentiable greedy networkDGN outperforms conventional discrete optimization both recall precision Furthermore as sentence retrieval part a larger pipeline as in the FEVER shared task using a differentiable greedy network serves an end-end trainable system",0.01,0.3042172292243129
"The joint optimization of representation learning and clustering in the embedding space has experienced a breakthrough in recent years. In spite of the advance, clustering with representation learning has been limited to flat-level categories, which oftentimes involves cohesive clustering with a focus on instance relations. To overcome the limitations of flat clustering, we introduce hierarchically clustered representation learning (HCRL), which simultaneously optimizes representation learning and hierarchical clustering in the embedding space. Specifically, we place a nonparametric Bayesian prior on embeddings to handle dynamic mixture hierarchies under the variational autoencoder framework, and to adopt the generative process of a hierarchical-versioned Gaussian mixture model. Compared with a few prior works focusing on unifying representation learning and hierarchical clustering, HCRL is the first model to consider a generation of deep embeddings from every component of the hierarchy, not just leaf components. This generation process enables more meaningful separations and mergers of clusters via branches in a hierarchy. In addition to obtaining hierarchically clustered embeddings, we can reconstruct data by the various abstraction levels, infer the intrinsic hierarchical structure, and learn the level-proportion features. We conducted evaluations with image and text domains, and our quantitative analyses showed competent likelihoods and the best accuracies compared with the baselines. Clustering is one of the most traditional and frequently used machine learning tasks. Clustering models are designed to represent intrinsic data structures, such as latent Dirichlet allocation BID2 . The recent development of representation learning has contributed to generalizing model feature engineering, which also enhances data representation BID1 . Therefore, representation learning has been merged into the clustering models, e.g., variational deep embedding (VaDE) (Jiang et al., 2017) . Besides merging representation learning and clustering, another critical line of research is structuring the clustering result, e.g., hierarchical clustering. This paper introduces a unified model enabling nonparametric Bayesian hierarchical clustering with neural-network-based representation learning.Autoencoder (Rumelhart et al., 1985) is a typical neural network for unsupervised representation learning and achieves a non-linear mapping from a high-dimensional input space to a lowdimensional embedding space by minimizing reconstruction errors. To turn the low-dimensional embeddings into random variables, a variational autoencoder (VAE) (Kingma & Welling, 2014) places a Gaussian prior on the embeddings. The autoencoder, whether it is probabilistic or not, has a limitation in reflecting the intrinsic hierarchical structure of data. For instance, VAE assuming a single Gaussian prior needs to be expanded to suggest an elaborate clustering structure.Due to the limitations of modeling the cluster structure with autoencoders, prior works combine the autoencoder and the clustering algorithm. While some early cases pipeline just two models, e.g., Huang et al. (2014) , a typical merging approach is to model an additional loss, such as a clustering loss, in the autoencoders (Xie et al., 2016; Guo et al., 2017; Yang et al., 2017; Nalisnick et al., 2016; BID4 Jiang et al., 2017) . These suggestions exhibit gains from unifying the encoding and the clustering, yet they remain at the parametric and flat-structured clustering. A more recent development releases the previous constraints by using the nonparametric Bayesian approach. Figure 1: Example of hierarchically clustered embeddings on MNIST with three levels of hierarchy, the reconstructed digits from the hierarchical Gaussian mixture components, and the extracted level proportion features. We marked the mean of a Gaussian mixture component with the colored square, and the digit written inside the square refers to the unique index of the mixture component.For example, the infinite mixture of VAEs (IMVAE) BID0 explores the infinite space for VAE mixtures by looking for an adequate embedding space through sampling, such as the Chinese restaurant process (CRP). Whereas IMVAE remains at the flat-structured clustering, VAEnested CRP (VAE-nCRP) (Goyal et al., 2017) captures a more complex structure, i.e., a hierarchical structure of the data, by adopting the nested Chinese restaurant process (nCRP) prior (Griffiths et al., 2004) into the cluster assignment of the Gaussian mixture model. This paper proposes hierarchically clustered representation learning (HCRL) that is a joint model of 1) nonparametric Bayesian hierarchical clustering, and 2) representation learning with neural networks. HCRL extends a previous work on merging flat clustering and representation learning, i.e., VaDE, by incorporating inter-cluster relation modelings. Unlike a previous work of VAE-nCRP, HCRL learns the full spectrum of hierarchical clusterings, such as the level assignment and the level proportion of generating a component hierarchy. These level assignments and proportions were not modeled in VAE-nCRP, so each data instance cannot be analyzed from the perspective of generalization and specialization in a hierarchy. On the contrary, by adding level assignment and proportion modeling, a data instance can be generated from an internal component of the hierarchy, which is limited to the leaf component in VAE-nCRP. Hierarchical mixture density estimation (Vasconcelos & Lippman, 1999) , where all internal and leaf components are directly modeled to generate data, is a flexible framework for hierarchical mixture modeling, such as hierarchical topic modeling (Mimno et al., 2007; Griffiths et al., 2004) , with regard to the learning of the internal components.Specifically, HCRL jointly optimizes soft-divisive hierarchical clustering in an embedding space from VAE via two mechanisms. First, HCRL includes a hierarchical-versioned Gaussian mixture model (HGMM) with a mixture of hierarchically organized Gaussian distributions. Then, HCRL sets the prior of embeddings by adopting the generative processes of HGMM. Second, to handle a dynamic hierarchy structure dealing with the clusters of unequal sizes, we explore the infinite hierarchy space by exploiting an nCRP prior. These mechanisms are fused as a unified objective function; this is done rather than concatenating the two distinct models of clustering and autoencoding. The quantitative evaluations focus on density estimation quality and hierarchical clustering accuracy, which shows that HCRL has competent likelihoods and the best accuracies compared with the baselines. When we observe our results qualitatively, we visualize 1) the hierarchical clusterings, 2) the embeddings under the hierarchy modeling, and 3) the reconstructed images from each Gaussian mixture component, as shown in FIG3 . These experiments were conducted by crossing the data domains of texts and images, so our benchmark datasets include MNIST, CIFAR-100, RCV1 v2, and 20Newsgroups. In this paper, we have introduced a hierarchically clustered representation learning framework for the hierarchical mixture density estimation on deep embeddings. HCRL aims at encoding the relations among clusters as well as among instances to preserve the internal hierarchical structure of data. The main differentiated features of HCRL are 1) the crucial assumption regarding the internal mixture components for having the ability to generate data directly, and 2) the unbalanced autoencoding neural architecture for the level proportion modeling as the encoding structure, and the probabilistic model as the decoding structure. From the modeling and the evaluation, we found that HCRL enables the improvements due to the high flexibility modeling compared with the baselines.",1523,0.727,940,1.6202127659574468,"The joint optimization representation learning the embedding space experienced a breakthrough In spite the advance, clustering with representation learning limited flat-level categories oftentimes involves cohesive a focus instance relations To overcome flat clustering introduce hierarchically clustered representation learningHCRL simultaneously the embedding space Specifically place a nonparametric Bayesian prior embeddings handle dynamic mixture hierarchies under adopt a hierarchical-versioned Gaussian mixture model Compared a few prior works focusing unifying representation learning hierarchical clustering HCRL the first model consider a generation from every component not just leaf components This generation process enables more meaningful separations mergers clusters via branches In addition obtaining hierarchically clustered embeddings reconstruct data the various abstraction levels infer the intrinsic hierarchical structure learn the level-proportion features We conducted evaluations with image text domains our quantitative analyses competent likelihoods the best accuracies compared Clustering the most traditional and frequently used machine learning tasks Clustering models designed represent intrinsic data structures latent Dirichlet allocation BID2 . The recent development representation learning contributed generalizing model feature engineering also enhances data representation BID1 . Therefore representation learning has merged the clustering models variational deep embeddingVaDEJiang 2017 . Besides merging representation learning clustering another critical line structuring the clustering result hierarchical This paper introduces a unified model enabling nonparametric Bayesian hierarchical neural-network-based representation learningAutoencoder (Rumelhart 1985 achieves from by minimizing reconstruction errors To turn the low-dimensional embeddings random variablesVAE (Kingma & Welling 2014 places prior The autoencoder, whether probabilistic a limitation reflecting the intrinsic hierarchical structure data For instance VAE assuming a single Gaussian prior needs expanded suggest an elaborate clustering structureDue modeling with prior works combine While some early cases pipeline just two models Huang (2014 , a typical merging approach model an additional loss,Xie Yang Nalisnick BID4 Jiang These suggestions exhibit gains unifying the encoding the clustering, yet remain at the parametric and flat-structured clustering A more recent development releases the previous constraints by Figure Example hierarchically clustered embeddings on MNIST with three levels hierarchy the reconstructed digits from the hierarchical Gaussian mixture components the extracted level proportion features We marked the mean a Gaussian mixture component the colored square the digit written inside refers the unique indexFor the infinite mixture VAEs (IMVAE) BID0 explores the infinite space for VAE mixtures by looking an adequate embedding space through sampling such the Chinese restaurant process Whereas IMVAE remains at the flat-structured clustering, VAEnested CRPVAEnCRP (Goyal 2017 captures the data by adopting the nested Chinese restaurant process prior 2004 into the cluster assignment of the Gaussian mixture model This paper proposes hierarchically clustered representation learningHCRL a joint model representation neural networks HCRL extends a previous work merging flat clustering and representation learning i.e., VaDE incorporating inter-cluster relation modelings Unlike a previous work VAE-nCRP HCRL learns hierarchical clusterings the level assignment the level proportion generating a component hierarchy These level assignments and proportions not modeled VAE-nCRP each data instance analyzed from generalization specialization in a hierarchy On by adding level assignment proportion modeling a data instance generated an internal component the hierarchy limited the leaf component in VAE-nCRP Hierarchical mixture density estimationVasconcelos Lippman , where all internal and leaf components directly modeled to generate data a flexible framework hierarchical mixture modeling such hierarchical topic modelingMimno Griffiths regard the learningSpecifically HCRL jointly soft-divisive hierarchical clustering an embedding space from VAE via two mechanisms First HCRL includes a hierarchical-versioned Gaussian mixture model a mixture hierarchically organized Gaussian distributions Then HCRL sets prior of embeddings by adopting the generative processes HGMM Second to handle a dynamic hierarchy structure dealing the clusters unequal sizes explore the infinite hierarchy space exploiting an nCRP prior These mechanisms fused as a unified objective function; this done rather the two distinct models clustering The quantitative evaluations focus density estimation quality hierarchical clustering accuracy shows that HCRL has competent likelihoods the best accuracies compared the baselines When observe our results qualitatively visualize 1 the hierarchical clusterings under the hierarchy modeling from each Gaussian mixture component FIG3 These experiments crossing the data domains texts so our benchmark datasets include MNIST, CIFAR-100 RCV1 v2 20Newsgroups In this paper have introduced a hierarchically clustered representation learning framework the hierarchical mixture density estimation on HCRL aims encoding the relations clusters as instances to preserve data The main differentiated features HCRL 1 the crucial assumption regarding the internal mixture components for having generate data directly the level proportion modeling as the encoding structure, From the modeling the evaluation, HCRL enables the improvements due the high flexibility modeling compared the baselines",0.01,0.284326806045573
"We introduce a novel geometric perspective and unsupervised model augmentation framework for transforming traditional deep (convolutional) neural networks into adversarially robust classifiers. Class-conditional probability densities based on Bayesian nonparametric mixtures of factor analyzers (BNP-MFA) over the input space are used to design soft decision labels for feature to label isometry. Classconditional distributions over features are also learned using BNP-MFA to develop plug-in maximum a posterior (MAP) classifiers to replace the traditional multinomial logistic softmax classification layers. This novel unsupervised augmented framework, which we call geometrically robust networks (GRN), is applied to CIFAR-10, CIFAR-100, and to Radio-ML (a time series dataset for radio modulation recognition). We demonstrate the robustness of GRN models to adversarial attacks from fast gradient sign method, Carlini-Wagner, and projected gradient descent. DeepConvNets are already prevalent in speech, vision, self-driving cars, biometrics, and robotics. However, they possess discontinuities that are easy targets for attacks as evidenced in dozens of papers (see BID7 BID15 and references therein). Adversarial images can be made to be robust to translation, scale, and rotation BID0 . Adversarial attacks have also been applied to deep reinforcement learning BID9 BID10 and speech recognition BID3 . In this work we will also consider attacks on automatic modulation recognition using deep convolutional networks BID17 . Previous work in creating adversarially robust deep neural network classifiers includes robust optimization with saddle point formulations BID13 , adversarial training (see e.g., BID11 ), ensemble adversarial training BID24 , defensive distillation BID19 , and use of detector-reformer networks BID14 . Defensive distillation has been found to be an insufficient defense BID1 and MagNet of BID14 was also shown to be defeatable in BID4 . A summary of the attacks and defenses from the NIPS 2017 competition on adversarial attack and defense can be found in .In this paper we propose a statistical geometric model augmentation approach to designing robust neural networks. We argue that signal representations involving projections onto lower-dimensional subspaces lower mean square error distortion. We implement a statistical union of subspaces learned using a mixture of factor analyzers to create the auxiliary signal space structural information that neural networks can use to improve robustness. We use the geometry of the input space to create unsupervised soft probabilistic decision labels to replace traditional hard one-hot encoded label vectors. We also use the geometry of the feature space (after soft-decision supervised training) to create accurate class-conditional probability density estimates for MAP classifiers (to replace neural network classification layers). We call this unsupervised geometric augmentation framework geometrically robust networks (GRN). The main contributions of this paper are:1. Geometric analysis of problems with current neural networks.2. A novel soft decision label coding framework using unsupervised statistical-geometric union of subspace learning.3. Maximum a posteriori classification framework based on class-conditional feature vector density estimation.The rest of this paper is organized as follows. In Section 2 we analyze neural networks from a geometric vantage point and recommend solution pathways for overcoming adversarial brittleness. In Section 3 we describe the full details of the proposed geometrically robust network design framework. We give experimental results on two datasets and three attacks in Section 4 and conclude in Section 5. We have demonstrated that geometrical statistically augmented neural network models can achieve state-of-the-art robustness on CIFAR-10 under three different adversarial attack methods. We hope that this work will be the start of further investigation into the idea of using geometrically centered unsupervised learning methods to assist in making deep learning models robust, not only to adversarial noise but to all types of noise. There is more work that could be done to understand the best way to engineer soft decision labels given auxiliary data models. We need to also understand if the training algorithms themselves can be directly manipulated to incorporate outside structural data models.A main selling point of Bayesian nonparametrics has been that the complexity of the model can grow as more data is observed. However, the current training algorithm for the BNP-MFA model is Gibbs sampling, which fails to scale to massive data sets. Stochastic variational inference BID8 has been introduced as one such way to perform variational inference for massive or streaming data sets. We are currently working to cast the BNP-MFA into a stochastic variational framework so that the GRN model can be extended to very large (or even streaming) datasets. Figure 4: Network specification and performance results for proposed geometrically robust networks applied to the Radio-ML dataset (modulation recognition over 11 modulation formats).",952,0.514,613,1.5530179445350734,"We introduce a novel geometric perspective and unsupervised model augmentation framework transforming adversarially robust classifiers Class-conditional probability densities based factor analyzersBNP-MFA over the input space design soft decision labels feature to label isometry Classconditional distributions over features learned BNP-MFA to develop plug-in maximum a posterior (MAP) classifiers to replace the traditional multinomial logistic softmax classification layers This novel unsupervised augmented framework we geometrically robust networks applied CIFAR-10 to Radio-MLa time series dataset radio modulation recognition We demonstrate GRN models adversarial attacks from fast gradient sign method Carlini-Wagner projected DeepConvNets already prevalent speech vision robotics However they possess discontinuities easy targets attacks as evidenced dozens papers ( BID7 BID15 references Adversarial images made be robust translation scale rotation BID0 . Adversarial attacks also applied deep reinforcement BID9 BID10 and speech recognition BID3 . In this work also attacks automatic modulation recognition BID17 . Previous work creating adversarially robust deep neural network classifiers includes robust optimization with saddle point formulations BID13 , adversarial training ensemble defensive distillation BID19 use detector-reformer networks Defensive distillation has found an insufficient defense BID1 and MagNet of BID14 was defeatable . A summary the attacks defenses from the NIPS 2017 competition on adversarial attack can .In propose a statistical geometric model augmentation approach designing robust neural networks We argue that signal representations involving projections onto lower mean square error distortion We implement a statistical union subspaces learned using a mixture factor analyzers the auxiliary signal space structural information neural networks improve We use the geometry the input space unsupervised soft probabilistic decision labels to replace traditional hard one-hot encoded label vectors We also use the geometry the feature spaceafter soft-decision supervised training accurate class-conditional probability density estimates MAP classifiersto replace neural network classification layers We call this unsupervised geometric augmentation framework geometrically robust networks The main contributions Geometric analysis problems current neural networks.2 A novel soft decision label coding framework using unsupervised statistical-geometric union Maximum class-conditional feature vector density estimationThe rest organized In Section we analyze neural networks a geometric vantage point recommend solution pathways overcoming adversarial brittleness In Section we describe the full details the proposed geometrically robust network design framework We give experimental results two datasets three attacks Section conclude in We demonstrated geometrical statistically augmented neural network models achieve state under three different adversarial attack methods We hope this work further investigation assist making robust not adversarial noise noise There more work understand engineer soft decision labels given auxiliary data models We need also if the training algorithms themselves directly incorporate outside structural data modelsA main selling point Bayesian nonparametrics has the complexity grow observed However the current training algorithm the BNP-MFA model Gibbs sampling fails scale Stochastic variational inference BID8 has introduced one such way massive or streaming data sets We cast the BNP-MFA into a stochastic variational framework so the GRN model extended very large (or even streaming) datasets Figure Network specification performance results proposed geometrically robust networks applied the Radio-ML datasetmodulation recognition over 11 modulation formats",0.01,0.11312030473382449
"Reinforcement learning in environments with large state-action spaces is challenging, as exploration can be highly inefficient. Even if the dynamics are simple, the optimal policy can be combinatorially hard to discover. In this work, we propose a hierarchical approach to structured exploration to improve the sample efficiency of on-policy exploration in large state-action spaces. The key idea is to model a stochastic policy as a hierarchical latent variable model, which can learn low-dimensional structure in the state-action space, and to define exploration by sampling from the low-dimensional latent space. This approach enables lower sample complexity, while preserving policy expressivity. In order to make learning tractable, we derive a joint learning and exploration strategy by combining hierarchical variational inference with actor-critic learning. The benefits of our learning approach are that 1) it is principled, 2) simple to implement, 3) easily scalable to settings with many actions and 4) easily composable with existing deep learning approaches. We demonstrate the effectiveness of our approach on learning a deep centralized multi-agent policy, as multi-agent environments naturally have an exponentially large state-action space. In this setting, the latent hierarchy implements a form of multi-agent coordination during exploration and execution (MACE). We demonstrate empirically that MACE can more efficiently learn optimal policies in challenging multi-agent games with a large number (~20) of agents, compared to conventional baselines. Moreover, we show that our hierarchical structure leads to meaningful agent coordination. Reinforcement learning in environments with large state-action spaces is challenging, as exploration can be highly inefficient in high-dimensional spaces. Hence, even if the environment dynamics are simple, the optimal policy can be combinatorially hard to discover. However, for many large-scale environments, the high-dimensional state-action space has (often hidden or implicit) low-dimensional structure which can be exploited. Many natural examples are in collaborative multi-agent problems, whose state-action space is exponentially large in the number of agents, but have a low-dimensional coordination structure. Consider a simple variant of the Hare-Hunters problem (see FIG0 . In this game, N = 2 identical hunters need to capture M = 2 identical static prey within T time-steps, and exactly H = 1 hunter is needed to capture each prey. T is set such that no hunter can capture both preys. There are two equivalent solutions: hunter 1 captures prey 1 and hunter 2 captures prey 2, or vice versa. There are also two suboptimal choices: both hunters choose the same prey. Hence, the hunters must coordinate over a (large) number of time-steps to maximize their reward. This implies the solution space has low-dimensional structure that can be used to accelerate training.In this work, we propose a principled approach to structured exploration to improve sample complexity in large state-action spaces, by learning deep hierarchical policies with a latent structure. As a highlevel intuition, consider a tabular multi-agent policy, which maps discrete (joint) states to action probabilities. For N agents with S states and A actions each, this policy has O((S · A) N ) weights. However, the low-dimensional coordination structure can be captured by a factorized, low-rank matrix, where the factorization can be learned and, for instance, only has O(N K(S + A)) weights. Similarly, our approach both 1) learns a low-dimensional factorization of the policy distribution and 2) defines exploration by also sampling from the low-dimensional latent space. For instance, in the multi-agent setting, we can learn a centralized multi-agent policy with a latent structure that encodes coordination between agents and biases exploration towards policies that encode ""good"" coordination.The key ideas of our approach are: 1) to utilize a shared stochastic latent variable model that defines the structured exploration policy, and 2) to employ a principled variational method to learn the posterior distribution over the latents jointly with the optimal policy. Our approach has several desirable properties. First we do not incorporate any form of prior domain knowledge, but rather discover the coordination structure purely from empirical experience during learning. Second, our variational learning method enables fully differentiable end-to-end training of the entire policy class. Finally, by utilizing a hierarchical policy class, our approach can easily scale to large action spaces (e.g. a large number of coordinating agents). Our approach can also be seen as a deep hierarchical generalization of Thompson sampling, which is a historically popular way to capture correlations between actions (e.g. in the bandit setting BID2 ).To summarize, our contributions in this work are as follows:• We introduce a structured probabilistic policy class that uses a hierarchy of stochastic latent variables.• We propose an efficient and principled algorithm using variational methods to train the policy end-to-end.• To validate our learning framework, we introduce several synthetic multi-agent environments that explicitly require team coordination, and feature competitive pressures that are characteristic of many coordinated decision problems.• We empirically verify that our approach improves sample complexity on coordination games with a large number (N ∼ 20) of agents.• We show that learned latent structures correlate with meaningful coordination patterns. In a sense, we studied the simplest setting that can benefit from structured exploration, in order to isolate the contribution of our work. Our hierarchical model and variational approach are a simple way to implement multi-agent coordination, and easily combine with existing actor-critic methods. Moving forward, there are many ways to expand on our work. Firstly, for complex (partial-information) environments, instead of using reactive policies with simple priors P ∼ N (0, 1), memoryfull policies with flexible priors ) may be needed. Secondly, our approach is complementary to richer forms of communication between agents. Our hierarchical structure can be interpreted as a broadcast channel, where agents are passive receivers of the message λ. Richer communication protocols could be encoded by policies with more complex inter-agent structure. It would be interesting to investigate how to learn these richer structures. We show details on how to derive a tractable learning method to the multi-agent reinforcement learning problem with a centralized controller: DISPLAYFORM0 Instead of directly optimizing (16), we cast it as a probabilistic inference problem, as in BID17 Vlassis et al. (2009) , and optimize a lower bound.To do so, we assume that the total reward R i for each i to be non-negative and bounded. Hence, we can view the total reward R(τ ) as a random variable, whose unnormalized distribution is defined as DISPLAYFORM1 We can then rewrite (16) as a maximum likelihood problem: DISPLAYFORM2 Hence, the RL objective is equivalent to a maximal likelihood problem: DISPLAYFORM3 where the probability of a rollout τ features a marginalization over the latent variables λ t : DISPLAYFORM4 DISPLAYFORM5 Here, we used the hierarchical decomposition for the policy: DISPLAYFORM6 DISPLAYFORM7 This policy distribution is intractable to learn exactly, as it involves margalization over λ t and an unknown flexible distribution P (a i t |λ t , s t ). Hence the maximization in Equation FORMULA17 is hard. Hence, we follow the variational approach and get a lower bound on the log-likelihood log P (R, τ ; θ) in Equation (19) . For this, we use an approximate variational distribution Q R (λ 0:T |τ ; φ) and Jensen's inequality BID12 : DISPLAYFORM8 DISPLAYFORM9 where in the last line we used (20) . By inspecting the quotient in (26), we see that the optimal Q R is a factorized distribution weighted by the total reward R: DISPLAYFORM10 P (s t+1 |s t , a t )Q(λ t |s t ; φ).We see that (26) simplifies to:dλ 0:T Q R (λ 0:T |τ ; φ) log P (R|τ )P (s 0 ) T t=0 P (s t+1 |s t , a t )P (a t , λ t |s t ; θ) P (R|τ )P (s 0 ) T t=0 P (s t+1 |s t , a t )Q(λ t |s t ; φ) (28) = dλ 0:T Q R (λ 0:T |τ ; φ) log T t=0 P (a t , λ t |s t ; θ) Q(λ t |s t , φ)= dλ 0:T Q R (λ 0:T |τ ; φ) T t=0 log P (a t , λ t |s t ; θ) Q(λ t |s t , φ)= dλ 0:T Q R (λ 0:T |τ ; φ) T t=0 log P (a t |λ t , s t ; θ)P (λ t |s t ) Q(λ t |s t , φ)= dλ 0:T Q R (λ 0:T |τ ; φ) DISPLAYFORM11 log P (a t |λ t , s t ; θ) + log P (λ t |s t ) Q(λ t |s t , φ)ELBO(Q R ,θ,φ).The right-hand side in Equation FORMULA30 is called the evidence lower bound (ELBO), which we can maximize as a proxy for (16). The standard choice is to use maximum-entropy standard-normal priors: P (λ t |s t ) = N (0, 1). We can then optimize (32) using e.g. stochastic gradient ascent.",1969,0.902,1152,1.7092013888888888,"Reinforcement learning environments large state-action spaces challenging exploration highly inefficient Even the dynamics simple the optimal policy can combinatorially hard discover In this work propose a hierarchical approach structured exploration to improve the sample efficiency onpolicy large state-action spaces The key idea model a stochastic policy as a hierarchical latent variable model learn low-dimensional structure the state-action space to define exploration by sampling from This approach enables lower sample complexity while preserving policy expressivity In order learning tractable derive a joint learning and exploration strategy by hierarchical variational inference actor-critic learning The benefits our learning approach 1 principled easily settings with many actions easily composable existing deep learning approaches We demonstrate our approach on learning a deep centralized multi-agent policy, as multi-agent environments naturally an exponentially large state-action space In this setting the latent hierarchy implements a form multi-agent coordination during exploration execution (MACE We demonstrate empirically MACE more learn optimal policies challenging multi-agent games ( compared conventional baselines Moreover we show our hierarchical structure leads meaningful agent coordination Reinforcement learning environments large state-action spaces challenging exploration highly inefficient Hence even the environment dynamics simple the optimal policy can combinatorially hard discover However for many large-scale environments the high-dimensional state-action space has (often hidden implicit low structure which. Many natural examples in collaborative multi-agent problems whose state-action space exponentially large in the number have a low-dimensional coordination structure Consider a simple variant the Hare-Hunters problem FIG0 . In this game N = 2 identical hunters need capture M = 2 identical static prey within T time-steps exactly H = 1 hunter is each prey T is set such no hunter capture both preys There two equivalent solutions hunter 1 captures 1 or vice There also two suboptimal choices both hunters choose the same prey Hence the hunters must coordinate over a (large) number time-steps maximize their reward This implies the solution space low-dimensional structure that accelerate trainingIn propose a principled approach structured exploration to improve sample complexity large state-action spaces learning deep hierarchical policies with a latent structure As a highlevel intuition consider a tabular multi-agent policy maps discrete (joint) states action probabilities For N agents with S states A actions each, this policy has O((S · A) N ) weights However the low-dimensional coordination structure can captured a factorized, low-rank matrix can learned, only has O(N K(S + A weights Similarly our approach both 1 learns a low-dimensional factorization the policy distribution defines exploration by also sampling from For instance the multi-agent setting learn a centralized multi-agent policy with a latent structure encodes coordination biases exploration towards policies encode "" coordinationThe key ideas to utilize a shared stochastic latent variable model defines the structured exploration policy employ a principled variational method learn the posterior distribution over the latents jointly with Our approach has several desirable properties First we do incorporate any form prior domain knowledge discover the coordination structure purely empirical experience during learning Second our variational learning method enables fully differentiable end training the entire policy class Finally by utilizing a hierarchical policy class our approach easily scale large action spaces ( coordinating Our approach can a deep hierarchical generalization Thompson sampling a historically popular way capture correlations actions in the bandit setting BID2 ).To summarize our contributions in as introduce a structured probabilistic policy class uses a hierarchy propose an efficient and principled algorithm using train end To validate our learning framework several synthetic multi-agent environments explicitly require team coordination feature competitive pressures characteristic many coordinated decision problems.• empirically verify improves sample complexity on coordination games (N ∼ 20 learned latent structures correlate meaningful coordination patterns In a sense we studied the simplest setting that benefit structured exploration in isolate the contribution our work Our hierarchical model and variational approach implement multi-agent coordination easily combine with existing actor-critic methods Moving there expand on Firstly for complex (partial-information) environments instead reactive policies with simple priors P ∼ N0 memoryfull policies ) may needed Secondly our approach complementary richer forms communication between agents Our hierarchical structure can interpreted a broadcast channel agents passive receivers the message �� Richer communication protocols could encoded policies with more complex inter-agent structure It would interesting investigate to learn these richer structures We show details derive a tractable learning method to the multi-agent reinforcement learning problem with a centralized controller: DISPLAYFORM0 Instead directly optimizing (16 cast as BID17 Vlassis (2009 , and optimize a lower.To do assume total reward R i for i to non and bounded. Hence view the total reward R(τ ) whose unnormalized distribution defined DISPLAYFORM1 We rewrite (16 a maximum likelihood problem Hence the RL objective equivalent where a rollout τ features a marginalization over the latent variables �� t : Here used the hierarchical decomposition for the policy: intractable learn exactly involves margalization an unknown flexible distribution Pa i t |λ t , s t Hence the maximization in Equation FORMULA17 is hard Hence follow the variational approach get lower the log-likelihood log PR, τ ; �) Equation19 For this, use an approximate variational distribution Q Rλ 0:T |τ ;) Jensen's inequality BID12 : DISPLAYFORM8 where in used (20 . By inspecting the quotient in (26 see the optimal Q R a factorized distribution weighted the total reward R: DISPLAYFORM10 P (s t+1 |s t , a t )Q(λ t |s t ; �).Wedλ 0:T Q R:T |τ ; log PR|τP 0 ) T t=0 P� P (28 = , �)= T logPλ ) DISPLAYFORM11 log +ELBO(Q ,) in Equation FORMULA30 called the evidence lower maximize as a proxy (16 The standard choice maximum-entropy standard-normal priors: P (λ t |s t N0 We can then optimize (32 using stochastic gradient ascent",0.01,0.5110619988199642
"Much attention has been devoted recently to the generalization puzzle in deep learning: large, deep networks can generalize well, but existing theories bounding generalization error are exceedingly loose, and thus cannot explain this striking performance. Furthermore, a major hope is that knowledge may transfer across tasks, so that multi-task learning can improve generalization on individual tasks. However we lack analytic theories that can quantitatively predict how the degree of knowledge transfer depends on the relationship between the tasks. We develop an analytic theory of the nonlinear dynamics of generalization in deep linear networks, both within and across tasks. In particular, our theory provides analytic solutions to the training and testing error of deep networks as a function of training time, number of examples, network size and initialization, and the task structure and SNR. Our theory reveals that deep networks progressively learn the most important task structure first, so that generalization error at the early stopping time primarily depends on task structure and is independent of network size. This suggests any tight bound on generalization error must take into account task structure, and explains observations about real data being learned faster than random data. Intriguingly our theory also reveals the existence of a learning algorithm that proveably out-performs neural network training through gradient descent. Finally, for transfer learning, our theory reveals that knowledge transfer depends sensitively, but computably, on the SNRs and input feature alignments of pairs of tasks. Many deep learning practitioners closely monitor both training and test errors, hoping to achieve both a small training error and a small generalization error, or gap between testing and training errors. Training is usually stopped early, before overfitting sets in and increases the test error. This procedure often results in large networks that generalize well on structured tasks, raising an important generalization puzzle BID23 : many existing theories that upper bound generalization error BID4 BID14 BID7 BID8 BID15 BID3 Arora et al., 2018, e.g ) in terms of various measures of network complexity yield very loose bounds. Therefore they cannot explain the impressive generalization capabilities of deep nets.In the absence of any such tight and computable theory of deep network generalization error, we develop an analytic theory of generalization error for deep linear networks. Such networks exhibit highly nonlinear learning dynamics BID19 b) including many prominent phenomena like learning plateaus, saddle points, and sudden drops in training error. Moreover, theory developed for the learning dynamics of deep linear networks directly inspired better initialization schemes for nonlinear networks BID21 BID16 . Here we show that deep linear networks also provide a good theoretical model for generalization dynamics. In particular we develop an analytic theory for both the training and test error of a deep linear network as a function of training time, number of training examples, network architecture, initialization, and task structure and SNR. Our theory matches simulations and reveals that deep networks with small weight initialization learn the most important aspects of a task first. Thus the optimal test error at the early stopping time depends largely on task structure and SNR, and not on network architecture, as long as the architecture is expressive enough to attain small training error. Thus our exact analysis of generalization dynamics reveals the important lesson that any theory that seeks to upper bound generalization error based only on network architecture, and not on task structure, is likely to yield exceedingly loose upper bounds. Intriguingly our theory also reveals a non-gradient-descent learning algorithm that proveably out-performs neural network training through gradient descent.We also apply our theory to multi-task learning, which enables knowledge transfer from one task to another, thereby further lowering generalization error BID6 Luong et al., 2016, e.g.) . Moreover, knowledge transfer across tasks may be key to human generalization capabilities BID10 . We provide an analytic theory for how much knowledge is transferred between pairs of tasks, and we find that it displays a sensitive but computable dependence on the relationship between pairs of tasks, in particular, their SNRs and feature space alignments.We note that a related prior work BID0 ) studied generalization in shallow and deep linear networks, but that work was limited to networks with a single output, thereby precluding the possibility of addressing the issue of transfer learning. Moreover, analyzing networks with a single output also precludes the possibility of addressing interesting tasks that require higher dimensional outputs, for example in language (Dong et al., 2015, e.g.) , generative models (Goodfellow et al., 2014, e.g ), and reinforcement learning Silver et al., 2016, e.g ).",921,0.434,541,1.7024029574861368,"Much attention devoted recently the generalization puzzle deep learning well existing theories bounding generalization error exceedingly loose thus this striking performance Furthermore a major hope knowledge may transfer across tasks improve generalization on However we lack analytic theories quantitatively the degree knowledge transfer depends the tasks We develop an analytic theory generalization deep linear networks both tasks In particular our theory provides analytic solutions the training and testing error deep networks as number examples network initialization the task structure SNR Our theory reveals deep networks progressively learn the most important task structure first generalization error at the early stopping time primarily depends task structure is independent This suggests any tight bound generalization error must take account task structure explains observations real data being learned faster random data our theory also reveals a learning algorithm proveably through gradient descent Finally for transfer learning our theory reveals knowledge transfer depends sensitively, computably the SNRs input feature alignments pairs tasks Many deep learning practitioners closely both training and test errors hoping achieve both a small training error gap Training usually stopped before overfitting sets in and increases the test error This procedure often large networks generalize well on structured tasks raising an important generalization puzzle BID23 : many existing theories that upper generalization error BID14 Arora et 2018 ) in terms various measures network complexity yield very loose bounds Therefore they explain the impressive generalization capabilities deep netsIn any such tight and computable theory deep network generalization error develop Such networks exhibit highly nonlinear learning dynamics BID19 b) including many prominent phenomena like learning plateaus saddle points sudden drops training error Moreover theory developed the learning dynamics deep linear networks directly inspired better initialization schemes BID21 BID16 . Here show deep linear networks also generalization dynamics In particular we develop an analytic theory both the training and test error a deep linear network as number network architecture initialization task structure and SNR Our theory matches simulations reveals deep networks small weight initialization learn first Thus the optimal test error at the early stopping time depends largely task structure SNR network architecture long the architecture expressive attain small training error Thus our exact analysis generalization dynamics reveals the important lesson any theory seeks upper based only network architecture task structure yield exceedingly loose upper bounds our theory also reveals a non-gradient-descent learning proveably out neural throughWe also apply enables knowledge transfer thereby further lowering BID6 Luong,) . Moreover knowledge transfer across tasks key human generalization capabilities BID10 . We provide an analytic theory how much knowledge transferred pairs tasks find displays a sensitive but computable dependence pairs in particular, their SNRs and feature space alignmentsWe note a related prior work BID0 ) studied generalization shallow and deep linear networks that work networks thereby addressing transfer learning Moreover analyzing networks a single output also addressing interesting tasks higher dimensional outputs language ( ,Goodfellow ), reinforcement Silver et",0.01,0.493740192909404
"We conduct a mathematical analysis on the Batch normalization (BN) effect on gradient backpropagation in residual network training in this work, which is believed to play a critical role in addressing the gradient vanishing/explosion problem. Specifically, by analyzing the mean and variance behavior of the input and the gradient in the forward and backward passes through the BN and residual branches, respectively, we show that they work together to confine the gradient variance to a certain range across residual blocks in backpropagation. As a result, the gradient vanishing/explosion problem is avoided. Furthermore, we use the same analysis to discuss the tradeoff between depth and width of a residual network and demonstrate that shallower yet wider resnets have stronger learning performance than deeper yet thinner resnets. Convolutional neural networks (CNNs) BID10 BID1 BID8 aim at learning a feature hierarchy where higher level features are formed by the composition of lower level features. The deep neural networks act as stacked networks with each layer depending on its previous layer's output. The stochastic gradient descent (SGD) method BID12 has proved to be an effective way in training deep networks. The training proceeds in steps with SGD, where a mini-batch from a given dataset is fed at each training step. However, one factor that slows down the stochastic-gradient-based learning of neural networks is the internal covariate shift. It is defined as the change in the distribution of network activations due to the change in network parameters during the training.To improve training efficiency, BID7 introduced a batch normalization (BN) procedure to reduce the internal covariate shift. The BN changes the distribution of each input element at each layer. Let x = (x 1 , x 2 , · · · , x K ), be a K-dimensional input to a layer. The BN first normalizes each dimension of x as DISPLAYFORM0 and then provide the following new input to the layer DISPLAYFORM1 where k = 1, · · · , K and γ k and β k are parameters to be determined. BID7 offered a complete analysis on the BN effect along the forward pass. However, there was little discussion on the BN effect on the backpropagated gradient along the backward pass. This was stated as an open research problem in BID7 . Here, to address this problem, we conduct a mathematical analysis on gradient propagation in batch normalized networks.The number of layers is an important parameter in the neural network design. The training of deep networks has been largely addressed by normalized initialization BID12 BID3 BID11 and intermediate normalization layers BID7 . These techniques enable networks consisting of tens of layers to converge using the SGD in backpropagation. On the other hand, it is observed that the accuracy of conventional CNNs gets saturated and then degrades rapidly as the network layer increases. Such degradation is not caused by over-fitting since adding more layers to a suitably deep model often results in higher training errors BID13 . To address this issue, BID6 introduced the concept of residual branches. A residual network is a stack of residual blocks, where each residual block fits a residual mapping rather than the direct input-output mapping. A similar network, called the highway network, was introduced by BID13 . Being inspired by the LSTM model BID2 , the highway network has additional gates in the shortcut branches of each block.There are two major contributions in this work. First, we propose a mathematical model to analyze the BN effect on gradient propogation in the training of residual networks. It is shown that residual networks perform better than conventional neural networks because residual branches and BN help maintain the gradient variation within a range throughout the training process, thus stabilizing gradient-based-learning of the network. They act as a check on the gradients passing through the network during backpropagation so as to avoid gradient vanishing or explosion. Second, we provide insights into wide residual networks based on the same mathematical analysis. The wide residual network was recently introduced by BID16 . As the gradient goes through the residual network, the network may not learn anything useful since there is no mechanism to force the gradient flow to go through residual block weights during the training. In other words, it might be possible that there are only a few blocks that learn useful representations while a large number of blocks share very little information with small contributions to the ultimate goal. We will show that residual blocks that stay dormant are the chains of blocks at the end of each scale of the residual network.The rest of this paper is organized as follows. Related previous work is reviewed in Sec. 2. Next, we derive a mathematical model for gradient propagation through a layer defined as a combination of batch normalization, convolution layer and ReLU in Sec. 3. Then, we apply this mathematical model to a resnet block in Sec. 4. Afterwards, we use this model to show that the dormant residual blocks are those at the far-end of a scale in deep residual networks in Sec. 5. Concluding remarks and future research directions are given in Sec. 6. We can draw two major conclusions from the analysis conducted above. First, it is proper to relate the above variance analysis to the gradient vanishing and explosion problem. The gradients go through a BN sub-layer in one residual block before moving to the next residual block. As proved in Sec. 3, the gradient mean is zero when it goes through a BN sub-layer and it still stays at zero after passing through a residual block. Thus, if it is normally distributed, the probability of the gradient values between ± 3 standard deviations is 99.7%. A smaller variance would mean lower gradient values. In contrast, a higher variance implies a higher likelihood of discriminatory gradients. Thus, we take the gradient variance across a batch as a measure for stability of gradient backpropagation.Second, recall that the number of filters in each convolution layer of a scale increases by k times with respect to its previous scale. Typically, k = 1 or 2. Without loss of generality, we can assume the following: the variance of weights is about equal across layers, c 1 /c 2 ≈ 1, and k = 2. Then, Eq. (20) can be simplified to DISPLAYFORM0 We see from above that the change in the gradient variance from one residual block to its next is little. This is especially true when the L value is high. This point will be further discussed in the next section.",1300,0.876,750,1.7333333333333334,"We conduct on the Batch normalization (BN) effect gradient backpropagation residual network training in this work believed play addressing the gradient vanishing/explosion problem Specifically by analyzing the mean and variance behavior the input the gradient in forward passes through the BN and residual branches respectively they work confine across residual blocks As the gradient vanishing/explosion problem avoided Furthermore use discuss depth width a residual network demonstrate shallower yet wider resnets stronger learning performance BID10 BID1 BID8 aim learning a feature hierarchy where higher level features formed the composition The deep neural networks act stacked depending its previous layer's output The stochastic gradient descent BID12 proved in training deep networks The training proceeds in steps with SGD minibatch from a given dataset fed at However one factor slows the stochastic-gradient-based learning the internal covariate shift It defined the change network activations due network parameters duringTo improve BID7 introduced a batch normalization the internal covariate shift The BN changes the distribution each input element at Let x 1 · · · , x K be a K-dimensional input a layer The BN first normalizes each dimension x as DISPLAYFORM0 provide the following new input the layer where k · · , K and �� k and parameters determined BID7 offered a complete analysis the BN effect along the forward pass However little discussion the BN effect the backpropagated gradient along the backward pass This was stated an open research problem BID7 . Here to address conduct gradient propagation batch normalized networksThe number layers The training deep networks largely addressed normalized initialization BID12 BID3 BID11 intermediate normalization layers . These techniques enable networks consisting tens layers converge using the SGD in On observed the accuracy conventional CNNs gets saturated then layer Such degradation caused overfitting since adding a suitably deep model often higher training errors BID13 . To address BID6 introduced residual branches A residual network a stack residual blocks where fits a residual mapping rather the direct input-output mapping A similar network, the highway network introduced BID13 . Being inspired the LSTM model BID2 , the highway network additional gates the shortcut branchesThere two major contributions First propose analyze the BN effect gradient propogation the training residual networks It shown residual networks perform residual branches BN help maintain the gradient variation a range throughout gradient-based-learning of They act the gradients passing during so gradient vanishing or explosion Second provide insights wide residual networks based the same mathematical analysis The wide residual network was recently introduced BID16 . As the gradient goes through the residual network may learn useful since force go residual block weights during In might learn useful representations while share small contributions the ultimate goal We will show residual blocks that stay dormant the chains blocks at each scale of the residual networkThe rest organized Related previous work is reviewed Sec 2 Next derive gradient propagation through a layer defined a combination batch normalization convolution layer ReLU in Sec 3 Then we apply a resnet block Sec 4 Afterwards use this model the dormant residual blocks those at a scale deep residual networks in Sec 5 Concluding remarks and future research directions are Sec 6 We can draw conducted above First proper relate the above variance analysis the gradient vanishing and explosion problem The gradients go a BN sublayer one residual block before As proved Sec 3, the gradient mean is zero when goes a BN sublayer still passing a residual block Thus normally distributed the gradient values between ± 3 standard deviations A smaller variance would lower gradient values In contrast a higher variance implies discriminatory gradients Thus take the gradient variance across a batch as for stabilitySecond recall number filters each convolution layer of a scale increases k times with its previous scale Typically, k = Without loss assume the variance weights about equal across layers c 1 � k Then Eq20 can simplified DISPLAYFORM0 We from above the change the gradient variance one residual block its little. This especially the L value high This point further",0.01,0.5725480730549525
"To study how mental object representations are related to behavior, we estimated sparse, non-negative representations of objects using human behavioral judgments on images representative of 1,854 object categories. These representations predicted a latent similarity structure between objects, which captured most of the explainable variance in human behavioral judgments. Individual dimensions in the low-dimensional embedding were found to be highly reproducible and interpretable as conveying degrees of taxonomic membership, functionality, and perceptual attributes. We further demonstrated the predictive power of the embeddings for explaining other forms of human behavior, including categorization, typicality judgments, and feature ratings, suggesting that the dimensions reflect human conceptual representations of objects beyond the specific task. A central goal in understanding the human mind is to determine how object concepts are represented and how they relate to human behavior. Given the near-infinite number of tasks or contexts of usage, this might appear to be an impossible prospect. Take the example of picking a tomato in a grocery store. A person may recognize it by its color, shape, size, or texture; they may also know many of the more conceptual dimensions of a tomato, such as it being a fruit, or functional ones such as being a salad item. In most cases, however, only a few of these aspects might matter, depending on task context (e.g. as a grocery item or as a projectile in an audience that is not pleased with a presentation). Thus, to understand how we interact meaningfully with the objects around us, we need to tackle three problems simultaneously: (1) determine the object concept, the cognitive representation of behaviorally-relevant dimensions that distinguish an object from other objects. (2) determine which object concept representations are integrated into our perceptual decisions. (3) characterize the influence of the context -determined by the surrounding objects -on those decisions.There have been many attempts to represent object concepts in terms of semantic features, a vector of variables indicating the presence of different aspects of their meaning. These representations have been used to model phenomena such as judgments of typicality or similarity between concepts, or reaction times in various semantic tasks, with the goal of drawing conclusions about mental representations of those concepts (see BID13 for an extensive review of this literature). These features have usually been binary properties, postulated by researchers. A landmark study BID9 departed from this approach by instead asking hundreds of subjects to name binary properties of 541 objects, yielding 2,526 such semantic features. These corresponded to different types of information, e.g. for the concept ""hammer"" subjects might list taxonomic (""is a tool""), functional (""is used to hammer nails""), perceptual (""heavy""), among others. The results revealed that concepts for objects in the same basic level category shared many features; at the same time, there were also features that distinguished even very similar concepts. This effort was later replicated and extended by BID4 , generating 5,929 semantic features for 638 objects.The main issues with features produced in either study are the lack of degree (they can only be present or absent, albeit with varying naming frequencies), the extreme specificity of some features, and the omission of many features shared by the majority of concepts. A separate concern is the fact that, absent a specific context of use for each object, subjects will not likely think of many valid properties (e.g. that a tomato can be thrown). A different approach is to postulate the existence of certain semantic features and ask subjects to judge the degree to which features are salient for each concept, instead of assuming binary features. BID3 did this for 65 features corresponding to types of information for which there is evidence of brain representation (in their terminology: sensory, motor, spatial, temporal, affective, social, cognitive, etc) . This requires experts to specify the features in advance, and not all features can be judged easily by salience. In all three approaches outlined above, there is also no clear way of determining which features are critical to semantic behavior.Here we introduce an approach that uses only information from behavioral judgments about the grouping of object images in the context of other objects to estimate representations of object concepts. We demonstrate that this approach can predict human behavior in face of new combinations of objects and that it also allows prediction of results in other behavioral tasks. We show that individual dimensions in the low-dimensional embedding represent complex combinations of the information in the binary features in BID4 and, furthermore, are interpretable as conveying taxonomic, functional, or perceptual information. Finally, we will discuss the way in which this representation suggests a simple, effective model of judgments of semantic similarity in context. In this paper, we show that human behavioral judgments are well-explained by a strikingly lowdimensional semantic representation of concrete concepts. This representation, which embeds each object in a 49-dimensional vector, allows prediction of subject behavior in face of new combinations of concepts not encountered before, as well as prediction of other behavioral or human-annotated data, such as typicality ratings or similarity judgments. Moreover, the representation is readily interpretable, as positive, sparse dimensions make it easy to identify which concepts load on each dimension. Further, we demonstrate that the value of each dimension in this space can be explained in terms of elementary features elicited directly from human subjects in publicly available norms. Given this converging evidence, we conclude that dimensions represent distinct types of information, from taxonomic (indicators of category membership) to functional or perceptual.As the representations were estimated solely from behavioral data, this suggests a simple model of decision making in the triplet task. This can be viewed in terms of the distinction discussed in Navarro & Lee (2004) for judging concept similarity from semantic feature vectors. They distinguish a dimensional approach for representing stimuli (each feature is a continuous value, each concept is a point in a high-dimensional space, and similarity corresponds to proximity in the space), and a featural approach (each feature is binary, or discrete, and similarity is a function of the number of features that are common to both concepts, or that distinguish them). More refined schemes use modified distance metrics (dimensional) or combine commonality and distinctiveness (featural).The use of sparsity and positivity in the SPoSE representation, and the vector dot product for computing concept similarity, blends the featural and dimensional approaches when making decisions about a triplet of concepts. First , if any two concepts share a semantic category, and the other one does not, the two concepts will likely be grouped together. Because of sparsity, the dot product between concepts will be driven primarily by the number of features are shared between the two concepts in the same category, versus the different one. Second, if any three concepts share a semantic category, they also share most, if not all of their non-zero features. The decision becomes a function of the values of the features shared between them, and hence dimensional rather than featural. Third, if all concepts belong to different categories, there may be very few features in common between any two of them. The results will likely be determined by which of those few features takes a higher value. Results might be idiosyncratic, e.g. two objects grouped because their pictures are both very red, while the alternative grouping would be because they are both string-like, and the former feature is more salient. This is another reason why our features are unbounded: their scale can reflect their importance in decision making. This is akin to learning a distance metric in dimensional approaches.Our object representations capture the information that is necessary to explain subject behavior in the triplet task. Obviously, subjects have a lot more information about each concept that is not necessary or relevant for task performance. A promising direction for further work is to sample additional triplets so as to obtain more fine-grained, within-category distinctions. Beyond this, we have also considered the possibility of there being information influencing behavior that might be too infrequent to be estimated from this type of data, or elicited from human subjects. Yet another possible extension is to consider different types of similarity judgments BID19 , e.g. resulting from asking subjects to group objects based on a specific attribute (size, color, etc.). One avenue for trying to identify this type of information is to predict synset vectors from SPoSE vectors and/or semantic features elicited from subjects, and represent the residuals in terms of a dictionary of new sparse, positive concept features. These could then be used as a complement to SPoSE dimensions.",1712,0.88,1029,1.663751214771623,"To study how mental object representations behavior estimated sparse using human behavioral judgments on images representative 1,854 object categories These representations predicted a latent similarity structure objects captured most the explainable variance human behavioral judgments Individual dimensions in the low-dimensional embedding were found highly interpretable as conveying degrees taxonomic membership functionality perceptual attributes We further demonstrated the embeddings explaining other forms categorization typicality judgments feature ratings suggesting the dimensions reflect human conceptual representations objects beyond the specific task A central goal understanding determine object concepts represented Given tasks or contexts of usage might appear an impossible prospect Take the example picking a tomato A person recognize it they know many the more conceptual dimensions a tomato it being functional ones a salad item In most cases however only these aspects might matter depending task context as a grocery item a projectile an audience that pleased a presentation Thus to interact meaningfully the objects around tackle simultaneously determine the object concept the cognitive representation behaviorally-relevant dimensions that distinguish. (2 determine which object concept representations integrated our perceptual decisions (3 characterize the influence the context -determined the surrounding objects those decisionsThere have represent object concepts semantic features a vector variables indicating different aspects their meaning These representations have used model phenomena judgments typicality similarity concepts reaction times various semantic tasks with drawing mental representations ( BID13 for These features usually binary properties postulated researchers A landmark study BID9 departed this approach instead asking hundreds subjects name binary properties 541 objects yielding 2,526 such semantic features These corresponded different types information for the concept ""hammer"" subjects might list taxonomic (""is a tool functional used hammer nails perceptualheavy among The results revealed concepts objects the same basic level category shared many features; at features distinguished even very similar concepts This effort later replicated extended BID4 , generating 5,929 semantic features 638 objectsThe main issues features produced either study degree (they can present or albeit varying naming frequencies the extreme specificity the omission shared concepts A separate concern, absent a specific context use for each object subjects likely think many valid properties ( that a tomato thrown A different approach postulate certain semantic features and ask subjects judge features salient for each concept instead binary features BID3 did this for 65 features corresponding types information for which evidence brain representationin their terminology spatial) . This requires experts specify the features advance not all features judged easily salience In all three approaches outlined also which features critical semantic behaviorHere introduce only information behavioral judgments about the grouping object images other objects representations object concepts We demonstrate this approach predict human behavior face new combinations objects that allows prediction results other behavioral tasks We show individual dimensions in the low-dimensional embedding represent complex combinations the information the binary features BID4, furthermore are interpretable conveying taxonomic, functional, or perceptual information Finally will discuss this representation suggests a simple, effective model judgments semantic similarity context In this paper human behavioral judgments wellexplained a strikingly lowdimensional semantic representation concrete concepts This representation, embeds each object a 49-dimensional vector prediction subject behavior face of new combinations concepts not encountered prediction other behavioral or human-annotated data typicality ratings similarity judgments Moreover the representation is readily interpretable positive sparse dimensions make which concepts load on Further demonstrate the value each dimension this space explained elementary features elicited directly human subjects publicly available norms Given this converging evidence dimensions represent distinct types from taxonomic (indicators category membership functional or perceptualAs the representations were estimated solely behavioral data this suggests a simple model decision making the triplet task This can viewed terms the distinction discussed Navarro Lee judging concept similarity from semantic feature vectors They distinguish a dimensional approach for representing stimuli (each feature a continuous value each concept similarity corresponds proximity in featural binary or discrete similarity common both concepts that distinguish More refined schemes use modified distance metricsdimensional) combine commonality distinctiveness (featural).The use sparsity positivity the SPoSE representation, the vector dot product for computing concept similarity blends the featural and dimensional approaches when making decisions a triplet concepts First , if any two concepts share a semantic category and likely grouped Because sparsity the dot product between concepts will driven primarily features are shared in versus different one Second if any three concepts share a semantic category also most, their non-zero features The decision becomes a function the values the features shared hence dimensional rather featural Third if all concepts belong different categories very few features any The results will likely determined which those few features takes a higher value Results might idiosyncratic two objects grouped because their pictures both very red the alternative grouping because string the former feature more salient This another reason our features unbounded their scale can reflect their importance decision making This akin learning a distance metric dimensional approachesOur object representations capture explain subject behavior the triplet task Obviously subjects each concept not necessary or relevant task performance A promising direction further work sample additional triplets so obtain fine, withincategory distinctions Beyond this also considered there information influencing behavior too infrequent estimated this type elicited human subjects Yet another possible extension consider different types similarity judgments BID19 , resulting asking subjects group objects a specific attributesize One avenue trying identify this type information predict synset vectors SPoSE vectors semantic features elicited subjects, represent the residuals a dictionary new sparse, positive concept features These could then a complement SPoSE dimensions",0.01,0.39525894837780645
"We frame Question Answering (QA) as a Reinforcement Learning task, an approach that we call Active Question Answering. 

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

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

We also analyze the language that the agent has learned while interacting with the question answering system. We find that successful question reformulations look quite different from natural language paraphrases. The agent is able to discover non-trivial reformulation strategies that resemble classic information retrieval techniques such as term re-weighting (tf-idf) and stemming. Web and social media have become primary sources of information. Users' expectations and information seeking activities co-evolve with the increasing sophistication of these resources. Beyond navigation, document retrieval, and simple factual question answering, users seek direct answers to complex and compositional questions. Such search sessions may require multiple iterations, critical assessment, and synthesis BID19 .The productivity of natural language yields a myriad of ways to formulate a question BID3 . In the face of complex information needs, humans overcome uncertainty by reformulating questions, issuing multiple searches, and aggregating responses. Inspired by humans' ability to ask the right questions, we present an agent that learns to carry out this process for the user. The agent sits between the user and a backend QA system that we refer to as 'the environment'. We call the agent AQA, as it implements an active question answering strategy. AQA aims to maximize the chance of getting the correct answer by sending a reformulated question to the environment. The agent seeks to find the best answer by asking many questions and aggregating the returned evidence. The internals of the environment are not available to the agent, so it must learn to probe a black-box optimally using only question strings. The key component of the AQA agent is a sequence-to-sequence model trained with reinforcement learning (RL) using a reward based on the answer returned by the environment. The second component to AQA combines the evidence from interacting with the environment using a convolutional neural network to select an answer.We evaluate on a dataset of Jeopardy! questions, SearchQA BID7 . These questions are hard to answer by design because they use convoluted language, e.g., Travel doesn't seem to be an issue for this sorcerer & onetime surgeon; astral projection & teleportation are no prob (answer: Doctor Strange). Thus SearchQA tests the ability of AQA to reformulate questions such that the QA system has the best chance of returning the correct answer. AQA improves over the performance of a deep network built for QA, BiDAF BID28 , which has produced state-of-the-art results on multiple tasks, by 11.4% absolute F1, a 32% relative F1 improvement. Additionally, AQA outperforms other competitive heuristic query reformulation benchmarks.AQA defines an instance of machine-machine communication. One side of the conversation, the AQA agent, is trying to adapt its language to improve the response from the other side, the QA environment. To shed some light on this process we perform a qualitative analysis of the language generated by the AQA agent. By evaluating on MSCOCO , we find that the agent's question reformulations diverge significantly from natural language paraphrases. Remarkably, though, the agent is able to learn non-trivial and transparent policies. In particular, the agent is able to discover classic IR query operations such as term re-weighting, resembling tf-idf, and morphological simplification/stemming. A possible reason being that current machine comprehension tasks involve the ranking of short textual snippets, thus incentivizing relevance, more than deep language understanding.2 RELATED WORK Lin & Pantel (2001) learned patterns of question variants by comparing dependency parsing trees. BID6 showed that MT-based paraphrases can be useful in principle by providing significant headroom in oracle-based estimations of QA performance. Recently, BID1 used paraphrasing to augment the training of a semantic parser by expanding through the paraphrases as a latent representation. Bilingual corpora and MT have been used to generate paraphrases by pivoting through a second language. Recent work uses neural translation models and multiple pivots BID18 . In contrast, our approach does not use pivoting and is, to our knowledge, the first direct neural paraphrasing system. BID27 propose phrase-based paraphrasing for query expansion. In contrast with this line of work, our goal is to generate full question reformulations while optimizing directly the end-to-end target performance metrics.Reinforcement learning is gaining traction in natural language understanding across many problems. For example, BID20 use RL to learn control policies for multi-user dungeon games where the state of the game is summarized by a textual description, and BID14 use RL for dialogue generation. Policy gradient methods have been investigated recently for MT and other sequence-to-sequence problems. They alleviate limitations inherent to the word-level optimization of the cross-entropy loss, allowing the use of sequence-level reward functions, like BLEU. Reward functions based on language models and reconstruction errors are used to bootstrap MT with fewer resources BID33 . RL training can also prevent exposure bias; an inconsistency between training and inference time stemming from the fact that the model never sees its own mistakes during training BID26 . We also use policy gradient to optimize our agent, however, we use end-to-end question answering quality as the reward.Uses of policy gradient for QA include , who train a semantic parser to query a knowledge base, and BID29 who propose query reduction networks that transform a query to answer questions that involve multi-hop common sense reasoning. The work of BID21 is most related to ours. They identify a document containing an answer to a question by following links on a graph. Evaluating on a set of questions from the game Jeopardy!, they learn to walk the Wikipedia graph until they reach the predicted answer. In a follow-up, BID22 improve document retrieval with an approach inspired by relevance feedback in combination with RL. They reformulate a query by adding terms from documents retrieved from a search engine for the original query. Our work differs in that we generate complete sequence reformulations rather than adding single terms, and we target question-answering rather than document retrieval.Active QA is also related to recent research on fact-checking: BID32 propose to perturb database queries in order to estimate the support of quantitative claims. In Active QA questions are perturbed semantically with a similar purpose, although directly at the surface natural language form. Figure 1 shows the Active Question Answering (AQA) agent-environment setup. The AQA model interacts with a black-box environment. AQA queries it with many versions of a question , and finally returns the best of the answers found. An episode starts with an original question q 0 . The agent then Figure 1 : The AQA agent-environment setup. In the downward pass the agent reformulates the question and sends variants to the QA system. In the upward pass the final answer is selected. Recently, BID13 trained chatbots that negotiate via language utterances in order to complete a task. They report that the agent's language diverges from human language if there is no incentive for fluency in the reward function. Our findings seem related. The fact that the questions reformulated by AQA do not resemble natural language is not due to the keyword-like SearchQA input questions, because Base-NMT is capable of producing more fluent questions from the same input. AQA learns to re-weight terms by focusing on informative (lower document frequency), query-specific (high query clarity), terms while increasing term frequency (TF) via duplication. At the same time it learns to modify surface forms in ways akin to stemming and morphological analysis.Some of the techniques seem to adapt to the specific properties of current deep QA architectures such as character-based modeling and attention. Sometimes AQA learns to generate semantically nonsensical, novel, surface term variants; e.g., it might transform the adjective dense to densey. The only justification for this is that such forms can be still exploited by the character-based BiDAF question encoder. Finally, repetitions can directly increase the chances of alignment in the attention components.We hypothesize that, while there is no incentive for the model to use human language due to the nature of the task, AQA learns to ask BiDAF questions by optimizing a language that increases the likelihood of BiDAF ranking better the candidate answers. BID10 argue that reading comprehension systems are not capable of significant language understanding and fail easily in adversarial settings. We speculate that current machine comprehension tasks involve mostly pattern matching and relevance modeling. As a consequence deep QA systems might implement sophisticated ranking systems trained to sort snippets of text from the context. As such, they resemble document retrieval systems which incentivizes the (re-)discovery of IR techniques, such as tf-idf re-weighting and stemming, that have been successful for decades BID0 . We propose a new framework to improve question answering. We call it active question answering (AQA), as it aims to improve answering by systematically perturbing input questions. We investigated a first system of this kind that has three components: a question reformulator, a black box QA system, and a candidate answer aggregator. The reformulator and aggregator form a trainable agent that seeks to elicit the best answers from the QA system. Importantly, the agent may only query the environment with natural language questions. Experimental results prove that the approach is highly effective and that the agent is able to learn non-trivial and somewhat interpretable reformulation policies.For future work, we will continue developing active question answering, investigating the sequential, iterative aspects of information seeking tasks, framed as end-to-end RL problems, thus, closing the loop between the reformulator and the selector.",2069,1.267,1213,1.7056883759274526,"We frame Question Answering We propose an agent sits a black box QA system learns reformulate questions elicit The agent probes, potentially many, natural language reformulations an initial question aggregates the returned evidence yield The reformulation system trained end maximize answer quality using policy gradient We evaluate on SearchQA a dataset complex questions extracted The agent outperforms state base model playing the environment other benchmarks We also analyze the agent while the question answering system We find successful question reformulations look quite The agent able discover resemble classic information retrieval techniques term reweightingtfidf stemming Web and primary sources Users' expectations information seeking activities coevolve these resources Beyond navigation document retrieval simple factual question answering users seek Such search sessions require multiple iterations critical assessment synthesis BID19 .The productivity natural yields myriad ways formulate BID3 In complex information needs humans overcome uncertainty reformulating questions issuing multiple searches responses Inspired humans' ability ask present an agent carry for the user The agent sits between the user a backend QA system we referthe environment We call the agent AQA implements an active question answering strategy AQA aims maximize sending a reformulated question the environment The agent seeks find by aggregating the returned evidence The internals the environment available the agent learn probe a black-box optimally only question strings The key component the AQA agent sequence-to model trainedRL a reward based the answer returned the environment The second component AQA combines the evidence interacting using select an answerWe evaluate on SearchQA BID7 . These questions hard by design because use convoluted language Travel does seem this sorcerer & onetime surgeon astral projection no prob (answer Doctor Strange Thus SearchQA tests AQA reformulate questions such returning AQA improves over the performance a deep network built BiDAF BID28 , produced state results by 11.4% absolute F1 Additionally AQA outperforms other competitive heuristic query reformulation benchmarks defines an instance machine-machine communication One side the AQA agent trying adapt improve the QA environment To shed perform generated the AQA agent By evaluating on MSCOCO , the agent's question reformulations diverge though the agent learn In particular the agent able discover classic IR query operations term re resembling tfidf morphological simplification/stemming A possible reason being current machine comprehension tasks the ranking short textual snippets thus relevance more deep language RELATED WORK Lin & Pantel ( learned patterns question variants dependency parsing trees BID6 showed MT-based paraphrases useful principle by significant headroom oracle-based estimations QA performance Recently BID1 used paraphrasing augment the training a semantic parser expanding through as a latent representation Bilingual corpora MT have generate paraphrases by pivoting through Recent work uses neural translation models multiple pivots BID18 . In contrast our approach does pivoting, the first direct neural paraphrasing system BID27 propose phrase-based paraphrasing query expansion contrast this line our goal generate full question reformulations while optimizing directly end target metricsReinforcement learning gaining natural language understanding across many problems For BID20 use RL learn control policies multi-user dungeon games where the state summarized dialogue generation Policy gradient methods investigated recently MT other sequenceto problems They alleviate limitations inherent the word-level optimization, allowing sequence-level reward functions like BLEU Reward functions based language models reconstruction errors MT with fewer resources BID33 . RL training can prevent exposure bias; an inconsistency inference time stemming never sees its own mistakes during BID26 . We also use policy gradient optimize our agent, however end question answering quality the rewardUses include , who train a semantic parser BID29 who propose query reduction networks transform answer involve multi-hop common sense reasoning The work BID21 most related ours They identify a document an answer by following links on a set questions from they learn to walk the Wikipedia graph until In BID22 improve document retrieval inspired relevance feedback combination RL They reformulate a query terms from documents retrieved for Our work differs generate complete sequence reformulations rather adding single terms target question document retrievalActive QA related recent research: BID32 propose perturb database queries estimate the support quantitative claims In Active QA questions are perturbed semantically with a similar purpose although directly at the surface natural language form Figure the Active Question Answering (AQA) agent-environment setup The AQA model interacts AQA queries it many versions , finally best of found An episode starts an original question q 0 . The agent then Figure : The AQA agent-environment setup In the downward pass the agent reformulates sends variants the upward pass the final answer selected Recently BID13 trained chatbots negotiate via language utterances complete They report agent language diverges if there no incentive fluency the reward function Our findings seem related The fact the questions reformulated AQA do resemble natural language the keyword-like SearchQA input questions because Base-NMT capable more fluent questions from AQA learns reweight terms focusing informative (lower document frequency query-specific (high query clarity terms while increasing term frequencyTF via duplication At it learns modify surface forms akin stemming and morphological analysisSome seem adapt current deep QA architectures character-based modeling attention. Sometimes AQA learns generate semantically nonsensical, novel, surface term variants; it transform the adjective dense densey The only justification such forms can still exploited the character-based BiDAF question encoder Finally repetitions directly alignment the attention componentsWe no incentive the model use human language due AQA learns ask BiDAF optimizing increases ranking better the candidate answers BID10 argue reading comprehension systems capable significant language understanding fail easily adversarial settings We speculate current machine comprehension tasks mostly pattern matching relevance modeling As deep QA systems might implement sophisticated ranking systems trained sort snippets As such they resemble document retrieval systems which incentivizes IR techniques tfidf re stemming successful BID0 . We propose question We call active question answering aims improve answering systematically perturbing input questions We investigated a first system three components a question reformulator a candidate answer aggregator The reformulator aggregator form a trainable agent seeks elicit the QA system Importantly the agent query natural language questions Experimental results prove the approach the agent learn non-trivial and somewhat interpretable reformulation policiesFor future work developing active question answering investigating the sequential, iterative aspects information seeking tasks framed end RL problems thus, closing the reformulator the selector",0.01,0.5021111504441685
"Most deep latent factor models choose simple priors for simplicity, tractability
 or not knowing what prior to use. Recent studies show that the choice of
 the prior may have a profound effect on the expressiveness of the model,
 especially when its generative network has limited capacity. In this paper, we propose to learn a proper prior from data for adversarial autoencoders
 (AAEs). We introduce the notion of code generators to transform manually selected
 simple priors into ones that can better characterize the data distribution. Experimental results show that the proposed model can generate better image quality and learn better disentangled representations than
 AAEs in both supervised and unsupervised settings. Lastly, we present its
 ability to do cross-domain translation in a  text-to-image synthesis task. Deep latent factor models, such as variational autoencoders (VAEs) and adversarial autoencoders (AAEs), are becoming increasingly popular in various tasks, such as image generation BID6 , unsupervised clustering BID2 BID7 , and cross-domain translation BID10 . These models involve specifying a prior distribution over latent variables and defining a deep generative network (i.e., the decoder) that maps latent variables to data space in stochastic or deterministic fashion. Training such deep models usually requires learning a recognition network (i.e., the encoder) regularized by the prior.Traditionally, a simple prior, such as the standard normal distribution BID5 , is used for tractability, simplicity, or not knowing what prior to use. It is hoped that this simple prior will be transformed somewhere in the deep generative network into a form suitable for characterizing the data distribution. While this might hold true when the generative network has enough capacity, applying the standard normal prior often results in over-regularized models with only few active latent dimensions BID0 .Some recent works BID4 BID3 BID9 suggest that the choice of the prior may have a profound impact on the expressiveness of the model. As an example, in learning the VAE with a simple encoder and decoder, BID4 conjecture that multimodal priors can achieve a higher variational lower bound on the data loglikelihood than is possible with the standard normal prior. BID9 confirm the truth of this conjecture by showing that their multimodal prior, a mixture of the variational posteriors, consistently outperforms simple priors on a number of datasets in terms of maximizing the data log-likelihood. Taking one step further, BID3 learn a tree-structured nonparametric Bayesian prior for capturing the hierarchy of semantics presented in the data. All these priors are learned under the VAE framework following the principle of maximum likelihood.Along a similar line of thinking, we propose in this paper the notion of code generators for learning a prior from data for AAE. The objective is to learn a code generator network to transform a simple prior into one that, together with the generative network, can better characterize the data distribution. To this end, we generalize the framework of AAE in several significant ways:• We replace the simple prior with a learned prior by training the code generator to output latent variables that will minimize an adversarial loss in data space. • We employ a learned similarity metric BID6 in place of the default squared error in data space for training the autoencoder.• We maximize the mutual information between part of the code generator input and the decoder output for supervised and unsupervised training using a variational technique introduced in InfoGAN BID1 .Extensive experiments confirm its effectiveness of generating better quality images and learning better disentangled representations than AAE in both supervised and unsupervised settings, particularly on complicated datasets. In addition, to the best of our knowledge, this is one of the first few works that attempt to introduce a learned prior for AAE.The remainder of this paper is organized as follows: Section 2 reviews the background and related works. Section 3 presents the implementation details and the training process of the proposed code generator. Section 4 compares its performance with AAE in image generation and disentanglement tasks. Lastly, we conclude this paper with remarks on future work. In this paper, we propose to learn a proper prior from data for AAE. Built on the foundation of AAE, we introduce a code generator to transform the manually selected simple prior into one that can better fit the data distribution. We develop a training process that allows to learn both the autoencoder and the code generator simultaneously. We demonstrate its superior performance over AAE in image generation and learning disentangled representations in supervised and unsupervised settings. We also show its ability to do cross-domain translation. Mode collapse and training instability are two major issues to be further investigated in future work. Figure 14: Generated images in accordance with the varying color attribute in the text description ""The flower is pink in color and has petals that are rounded in shape and ruffled."" From left to right, the color attribute is set to pink, red, yellow, orange, purple, blue, white, green, and black, respectively. Note that there is no green or black flower in the dataset. Input latent code ∈ R code size 3 x 3 conv. 64 RELU stride 2 pad 1 4 x 4 upconv. 512 BN. RELU stride 1 3 x 3 residual blcok 64 4 x 4 up sampling residual block 256 stride 2 3 x 3 down sampling residual blcok 128 stride 2 4 x 4 up sampling residual block 128 stride 2 3 x 3 down sampling residual blcok 256 stride 2 4 x 4 up sampling residual block 64 stride 2 3 x 3 down sampling residual block 512 stride 2 3 x 3 conv. image channels Tanh 4 x 4 avg. pooling stride 1 FC. 2 x code size BN. RELU FC. code size Linear Input feature map FC. 2 x noise size BN. RELU 3 x 3 conv. out channels RELU stride 2 pad 1 FC. latent code size BN. Linear 3 x 3 conv. out channels RELU stride 1 pad 1 skip connection output = input + residual RELU Table 4",1283,0.726,740,1.7337837837837837,"Most deep latent factor models choose simple priors simplicity tractability not knowing prior to use Recent studies the choice prior may the expressiveness the model its generative network limited In learn proper prior from data forAAEs We introduce the notion code generators transform manually selected simple priors ones better characterize the data distribution Experimental results the proposed model generate better image quality learn better disentangled representations AAEs Lastly present its ability do cross-domain translation textimage synthesis task Deep latent factor modelsVAEs becoming various tasks image generation BID6 , cross-domain translation These models involve specifying a prior distribution latent variables defining a deep generative network data space Training such deep models usually learning a recognition network regularized the prior.Traditionally simple prior, the standard normal distribution BID5 tractability simplicity or not knowing prior use It hoped simple prior will transformed somewhere the deep generative network into characterizing the data distribution While this might hold when the generative network enough capacity applying the standard normal prior often results over-regularized models only few active latent dimensions BID0 .Some recent works suggest the choice prior the expressiveness As in learning the VAE with a simple encoder BID4 conjecture that multimodal priors achieve higher variational lower the data loglikelihood than is normal prior BID9 confirm the truth this conjecture showing their multimodal prior, a mixture the variational posteriors consistently simple priors datasets maximizing Taking one BID3 learn a tree-structured nonparametric prior capturing the hierarchy semantics presented All these priors learned under the VAE framework following maximum likelihoodAlong propose in code generators learning a prior from for AAE The objective learn a code generator network transform simple prior, together the generative network better characterize the data distribution To this end generalize the framework AAE in several significant ways:• replace simple prior learned by training the code generator output latent variables minimize an adversarial loss data space • We employ a learned similarity metric BID6 in place the default squared error data space training maximize the mutual information part the code generator input introduced InfoGAN BID1 .Extensive experiments confirm its effectiveness of generating better quality images learning better disentangled representations than AAE in particularly on complicated datasets In addition to best the first few works attempt introduce learned prior for AAE.The remainder organized Section reviews related works Section presents the training process the proposed code generator Section compares its performance AAE in image generation and disentanglement tasks Lastly conclude this paper remarks future work In learn proper prior from data for AAE. Built AAE introduce a code generator transform manually selected simple prior into one better fit the data distribution We develop a training process to learn both the autoencoder simultaneously We demonstrate its superior performance over AAE in image generation learning disentangled representations We also show its ability do cross-domain translation Mode collapse training instability to further Figure 14 Generated images in accordance the varying color attribute in the text description ""The flower pink petals rounded From set red Note no green or black flower the dataset Input latent code �� R code size 3 x conv 64 RELU stride 2 pad 1 4 x 4 upconv 512 BN. RELU stride 1 3 x 3 residual blcok 64 4 up sampling residual block 256 stride stride. image channels Tanh 4 x 4 avg pooling stride 1 FC. 2 x code size BN. RELU FC. code size Linear Input feature map FC. 2 x noise size BN. RELU 3 x conv. out channels RELU stride 2 pad 1 FC. latent code size BN. Linear 3 x 3 conv. out channels RELU stride 1 pad 1 skip connection output = input + residual RELU Table 4",0.01,0.5736957812265561
"In the past few years, various advancements have been made in generative models owing to the formulation of Generative Adversarial Networks (GANs). GANs have been shown to perform exceedingly well on a wide variety of tasks pertaining to image generation and style transfer. In the field of Natural Language Processing, word embeddings such as word2vec and GLoVe are state-of-the-art methods for applying neural network models on textual data. Attempts have been made for utilizing GANs with word embeddings for text generation. This work presents an approach to text generation using Skip-Thought sentence embeddings in conjunction with GANs based on gradient penalty functions and f-measures. The results of using sentence embeddings with GANs for generating text conditioned on input information are comparable to the approaches where word embeddings are used. Numerous efforts have been made in the field of natural language text generation for tasks such as sentiment analysis BID35 ) and machine translation BID7 BID24 ). Early techniques for generating text conditioned on some input information were template or rule-based engines, or probabilistic models such as n-gram. In recent times, state-of-the-art results on these tasks have been achieved by recurrent BID23 BID20 ) and convolutional neural network models trained for likelihood maximization. This work proposes an approach for text generation using Generative Adversarial Networks with Skip-Thought vectors.GANs BID9 ) are a class of neural networks that explicitly train a generator to produce high-quality samples by pitting against an adversarial discriminative model. GANs output differentiable values and hence the task of discrete text generation has to use vectors as differentiable inputs. This is achieved by training the GAN with sentence embedding vectors produced by SkipThought ), a neural network model for learning fixed length representations of sentences. 4.1 CONDITIONAL GENERATION OF SENTENCES.GANs can be conditioned on data attributes to generate samples BID21 ; Radford et al.) . In this experiment, both the generator and discriminator are conditioned on Skip-Thought encoded vectors ). The encoder converts 70000 sentences from the BookCorpus dataset collected in with a training/test/validation split of 5/1/1 into vectors used as real samples for discriminator. The decoded sentences are used to evaluate model performance under corpus level BLEU-2, BLEU-3 and BLEU-4 metrics (Papineni et al.) , once using only test set as reference and then entire corpus as reference. TAB0 compares these results for different architectures that have been experimented with in this paper.",506,0.281,280,1.8071428571428572,"In various advancements generative models owing the formulation GANs shown perform exceedingly pertaining image generation and style transfer In the field such word2vec GLoVe state applying on Attempts for utilizing GANs word embeddings text generation This work presents text generation Skip-Thought sentence embeddings conjunction GANs based gradient penalty functions f-measures The results using sentence embeddings with GANs generating text conditioned input information comparable the approaches where Numerous efforts natural language text generation tasks sentiment analysis BID35 ) Early techniques generating text conditioned some input information template or rule-based engines or such n. In recent times stateof results on these tasks achieved recurrent BID23 BID20 ) trained for likelihood maximization This work proposes text generation with Skip-Thought vectorsGANs BID9 ) explicitly train a generator by pitting against GANs output differentiable values and hence the task discrete text generation use vectors This achieved training the GAN with sentence embedding vectors produced SkipThought ) fixed length representations SENTENCES.GANs can conditioned data attributes generate samples BID21 ; Radford.) . In this experiment both the generator discriminator conditioned Skip-Thought encoded vectors ). The encoder converts 70000 sentences the BookCorpus dataset collected with a training/test/validation split vectors used real samples discriminator. The decoded sentences used evaluate model performance under corpus level BLEU-2Papineni et al , once using only test set as reference then entire corpus TAB0 compares these results for different architectures that experimented",0.0,0.7606082548877628
"The novel \emph{Unbiased Online Recurrent Optimization} (UORO) algorithm allows for online learning of general recurrent computational graphs such as recurrent network models. It works in a streaming fashion and avoids backtracking through past activations and inputs. UORO is computationally as costly as \emph{Truncated Backpropagation Through Time} (truncated BPTT), a widespread algorithm for online learning of recurrent networks \cite{jaeger2002tutorial}.  UORO is a modification of \emph{NoBackTrack} \cite{DBLP:journals/corr/OllivierC15} that bypasses the need for model sparsity and makes implementation easy in current deep learning frameworks, even for complex models.   Like NoBackTrack, UORO provides unbiased gradient estimates; unbiasedness is the core hypothesis in stochastic gradient descent theory, without which convergence to a local optimum is not guaranteed. On the contrary, truncated BPTT does not provide this property, leading to possible divergence.   On synthetic tasks where truncated BPTT is shown to diverge, UORO converges. For instance, when a parameter has a positive short-term but negative long-term influence, truncated BPTT diverges unless the truncation span is very significantly longer than the intrinsic temporal range of the interactions, while UORO performs well thanks to the unbiasedness of its gradients.
 We introduced UORO, an algorithm for training recurrent neural networks in a streaming, memoryless fashion. UORO is easy to implement, and requires as little computation time as truncated BPTT, at the cost of noise injection. Importantly, contrary to most other approaches, UORO scalably provides unbiasedness of gradient estimates. Unbiasedness is of paramount importance in the current theory of stochastic gradient descent. Furthermore, UORO is experimentally shown to benefit from its unbiasedness, converging even in cases where truncated BPTT fails to reliably achieve good results or diverges pathologically.",408,0.217,255,1.6,"The novel \emph{Unbiased Online Recurrent Optimization allows online learning general recurrent computational graphs such It works a streaming fashion avoids backtracking through past activations inputs UORO computationally as costly \emph{Truncated Backpropagation Through a widespread algorithm online learning \cite{jaeger2002tutorial UORO a modification \emph{NoBackTrack} \cite{DBLP:journalscorr/OllivierC15 model sparsity makes implementation current deep even Like NoBackTrack UORO provides unbiased gradient estimates; unbiasedness the core hypothesis without which convergence guaranteed On truncated BPTT does this property leading possible divergence On synthetic tasks where truncated BPTT shown diverge, UORO converges For instance a parameter truncated BPTT diverges unless the truncation span very significantly the intrinsic temporal range the interactions while UORO performs thanks the unbiasedness We introduced UORO training a streaming, memoryless fashion UORO easy requires as little computation time truncated BPTT at noise injection Importantly contrary most other approaches UORO scalably provides unbiasedness gradient estimates Unbiasedness of the current theory Furthermore UORO experimentally shown benefit its unbiasedness converging even truncated BPTT fails reliably achieve or diverges pathologically",0.0,0.2328264542601983
"We present a deep learning-based method for super-resolving coarse (low-resolution) labels assigned to groups of image pixels into pixel-level (high-resolution) labels, given the joint distribution between those low- and high-resolution labels. This method involves a novel loss function that minimizes the distance between a distribution determined by a set of model outputs and the corresponding distribution given by low-resolution labels over the same set of outputs. This setup does not require that the high-resolution classes match the low-resolution classes and can be used in high-resolution semantic segmentation tasks where high-resolution labeled data is not available. Furthermore, our proposed method is able to utilize both data with low-resolution labels and any available high-resolution labels, which we show improves performance compared to a network trained only with the same amount of high-resolution data.
 We test our proposed algorithm in a challenging land cover mapping task to super-resolve labels at a 30m resolution to a separate set of labels at a 1m resolution. We compare our algorithm with models that are trained on high-resolution data and show that 1) we can achieve similar performance using only low-resolution data; and 2) we can achieve better performance when we incorporate a small amount of high-resolution data in our training. We also test our approach on a medical imaging problem, resolving low-resolution probability maps into high-resolution segmentation of lymphocytes with accuracy equal to that of fully supervised models. Semantic image segmentation is the task of labeling each pixel in an input image X = {x ij } as belonging to one of L fine-scale application classes, Y = {y ij }, y ∈ {1, . . . , L}. In weakly supervised segmentation, instances in the training set only contain partial observations of the target ground truth labels, e.g., summary of class labels instead of pixel-level labels. We aim to solve a variant of this problem where coarse-scale, low-resolution accessory classes, Z = {z k }; z ∈ {1, . . . , N }, are defined for sets of pixels in the input images, where we are given the joint distribution P (Y, Z) between the accessory class labels and the application labels. Specifically, a training image X is divided into K sets B k , each with an accessory class label z k , and our models are trained to produce the high-resolution application labels y ij . For example, in Figure 1 , a high-resolution aerial image is shown alongside the low-resolution ground truth land cover map (defined over accessory classes) and the target high-resolution version (defined over application classes). We aim to derive the high-resolution land cover map based on the aerial image and low-resolution ground truth.Compared to other weakly supervised image segmentation techniques, the formulation of the problem we aim to solve is more general: it applies both to existing weakly supervised image segmentation problems, as well as to other problems with different characteristics of weak labels. The more general formulation is necessary for tasks such as land cover mapping from aerial imagery and lymphocyte segmentation from pathology imagery. In these applications, coarse labels do not necessarily match the fine-scale labels, as shown in Figure 1 . The distinction between the fine-scale application and coarse-scale accessory classes is necessary for situations in which the ground-truth information that is known about an image does not match with the application classes that we aim to Figure 1 : An Illustration of land cover data and label super-resolution. Our method takes an input image (x) with low-resolution labels (z) and outputs a set of super-resolved label predictions (y), utilizing the statistical descriptions between low-resolution and high-resolution labels (Appendix B) e.g., one low-resolution class designates areas of low-intensity development, with 20% to 49% of impervious surfaces (such as houses or roads).label the image with, but instead suggests a distribution over the application labels. State-of-the-art methods for weakly supervised semantic segmentation exploit the structure of weak labels in ways that are not applicable in our examples: we cannot create bounding boxes around land cover object instances BID7 ; Papandreou et al. FORMULA0 ) -we consider data that is generally given at scales much larger than the objects being segmented and does not carry foreground-background morphology -nor use coarse approximations of ground-truth segmentation (Krähenbühl & Koltun (2011); BID13 ). Other work attempts to match a class ""density function"" to weak labels (Lempitsky & Zisserman (2010) ), but it mainly targets localization and enumeration of small foreground objects with known sizes. Existing Weak supervision approaches also often involve expensive steps in inference, such as CRFs or iterative evaluation BID3 ), which are impractical on large datasets. At the same time, thorough analyses of training algorithms only exist for models that are not sufficiently expressive for the applications we consider (Yu et al. (2013) ). While our formulation of the problem allows us to specifically address the previously mentioned land cover mapping and lymphocyte segmentation, it can also be applied to more traditional segmentation tasks such as foreground/background segmentation as we explore in Appendix. F.Our proposed method is illustrated in FIG0 . Briefly, a standard segmentation network will output probabilistic estimates of the application labels. Our methodology summarizes these estimates over the sets B k , which results in an estimated distribution of application labels for each set. These distributions can then be compared to the expected distribution from the accessory (low-resolution) labels using standard distribution distance metrics. This extension is fully differentiable and can thus be used to train image segmentation neural networks end-to-end from pairs of images and coarse labels.Land cover mapping from aerial imagery is an important application in need of such methodology. Land cover maps are essential in many sustainability-related applications such as conservation planning, monitoring habitat loss, and informing land management. In Section 3.1 we describe land cover mapping in detail and show how our method creates high-resolution land cover maps solely from high-resolution imagery low-resolution labels, at an accuracy similar to that of models trained on high-resolution labels. We further show how to train models with a combination of low-and highresolution labels that outperform the high-res models in transfer learning tasks. As low-resolution labels are much easier to collect, and indeed exist over a much wider geographic area in our land cover mapping application, the ability to combine low-and high-resolution labels is an important feature of our proposed methods.In a second example (Section 3.2), we segment tumor infiltrating lymphocytes from high-resolution (gigapixel) pathology images. Understanding the spatial distribution of immune cells, such as lymphocytes in pathology images, is fundamental for immunology and the treatment of cancer BID10 ; Thorsson et al. (2018) ). Here, coarse labels are probabilities of lymphocyte infiltration (having two or more lymphocytes) on 100×100 pixel regions, given by an automatic classifier (Saltz FORMULA0 ). Our super-resolution model trained on coarse labels performs the same as a lymphocyte classifier trained with high-resolution (cell-level) supervision (Hou et al. (2018) ).To summarize, as our first contribution, we propose a label super-resolution network which utilizes the distribution of high-resolution labels suggested by given low-resolution labels, based on visual cues in the input images, to derive high-resolution label predictions consistent to the input image. Our second contribution is that we evaluate our method extensively on the application of land cover segmentation and conclude that when there are not enough representative high-resolution training data, our method is much more robust than a model trained on high-resolution training data only, since our method utilizes more training data with weak labels. We show the generality of our method on the lymphocyte segmentation task and the task of segmenting foreground given object bounding boxes (in Appendix F). We proposed a label super-resolution network which is capable of deriving high-resolution labels, given low-resolution labels that do not necessarily match the targeting high-resolution labels in a one-to-one manner -we only assume that the joint distribution between the low-resolution and highresolution classes is known. In particular, we train a network to predict high-resolution labels, minimizing the distance/divergence between two distributions: distribution of predicted high-resolution labels and expected distribution suggested by the low-resolution labels. We applied our method in two real-world applications where high res labels are very expensive to obtain compared to low res labels, and achieved similar or better results compared to the conventional fully supervised methods trained on high-resolution labels. We also show how combining low and high res labels leads to better generalization to out-of-sample test sets.Although the main assumption of the model is that the joint distribution over coarse and fine labels is known, the model is in fact robust to errors in estimates of these distributions, as we discuss in Appendix F. There we show that these joint distributions can be acquired or inferred in a variety of ways, thus making label super-resolution widely applicable, including beyond computer vision.",1805,0.917,1037,1.7405978784956606,"We present super-resolving coarse (low-resolution labels assigned groups image pixels into given the joint distribution This method involves a novel loss function a distribution determined model outputs given low-resolution labels over This setup does that the high-resolution classes match and can high-resolution semantic segmentation tasks where labeled Furthermore our proposed method able utilize both data with low-resolution labels show improves compared a network trained only We test our proposed algorithm a challenging land cover mapping task to super-resolve labels at a 30m resolution to a separate set labels We compare our algorithm models trained show 1 achieve using incorporate We also test our approach a medical imaging problem resolving low-resolution probability maps into lymphocytes with accuracy equal fully supervised models Semantic image segmentation the task labeling an input image X = {x ij } as belonging L fine-scale application classes Y y �1 . . . , L}. In weakly supervised segmentation instances in the training only partial observations the target ground truth labels, summary class labels instead pixel-level labels We aim solve a variant where coarsescale, low accessory classes, Z = {z k z �� . . . , N }, are defined for sets pixels the input images we given the joint distribution PY between the accessory class labels the application labels Specifically a training image X divided K sets B k each an accessory class label z k our models trained produce the high-resolution application labels y ij For example Figure alongside the low-resolution ground truth land cover mapdefined over accessory classes application classes We aim derive the high-resolution land cover map based the aerial image low-resolution ground truth.Compared other weakly supervised image segmentation techniques the formulation the problem we aim general: applies both different characteristics weak labels The more general formulation necessary tasks land cover mapping from lymphocyte segmentation pathology imagery In these applications coarse labels do match shown The distinction the fine-scale application coarse-scale accessory classes necessary situations the ground-truth information known an image does the application classes we aim Figure : An Illustration land cover data label super- Our method takes an input imagex with low-resolution labels super-resolved label predictions utilizing the statistical descriptions between one low-resolution class designates areas low-intensity development with 20% to 49% impervious surfacessuch houses roads).label the image, but instead suggests a distribution over the application labels State methods weakly supervised semantic segmentation exploit the structure weak labels ways applicable our examples: we create around land cover object instances BID7 ; Papandreou et FORMULA0 ) -we consider data that generally given at scales much the objects being segmented does carry foreground morphology -nor use coarse approximations ground-truth segmentationKrähenbühl Koltun ( BID13 Other work attempts match a class ""density function weak labelsLempitsky Zisserman ( mainly targets localization enumeration small foreground objects known sizes Existing Weak supervision approaches also often involve expensive steps inference CRFs iterative evaluation BID3 ), impractical on At thorough analyses training algorithms only exist models sufficiently expressive the applications we consider (Yu (2013 ). While our formulation allows specifically the previously mentioned land cover mapping and lymphocyte segmentation can more traditional segmentation tasks foreground/background segmentation as explore Appendix F.Our proposed method illustrated FIG0 a standard segmentation network will output the application labels Our methodology summarizes these estimates over the sets B k which results application labels These distributions can then compared from accessory (low-resolution labels using standard distribution distance metrics This extension fully differentiable thus train image segmentation neural networks end from pairs coarse labelsLand cover mapping from aerial imagery need such methodology Land cover maps essential many sustainability-related applications conservation planning monitoring habitat loss informing In Section we land cover mapping detail our method creates solely high-resolution imagery low-resolution labels at an accuracy similar models trained We further show train models a combination low-and highresolution labels transfer learning tasks As low-resolution labels much collect indeed exist over in our land cover mapping application combine our proposed methodsIn a second example (Section segment tumor infiltrating Understanding the spatial distribution immune cells such in pathology images fundamental cancer BID10 ; Thorsson (2018 ). Here coarse labels probabilities lymphocyte infiltrationhaving on 100×100 pixel regions given an automatic classifierSaltz FORMULA0 Our super-resolution model trained coarse labels performs a lymphocyte classifier trained with high-resolution (cell-level) supervision (Hou (2018 ).To summarize as our first contribution a label super-resolution network which utilizes the distribution high-resolution labels suggested given based visual cues derive consistent to Our second contribution that evaluate our method extensively on land cover segmentation conclude when there not enough representative high-resolution training data much a model trained only, since utilizes with weak labels We show the generality our method on the lymphocyte segmentation task the task segmenting foreground given object bounding boxesin Appendix F We proposed a label super-resolution network which deriving given that necessarily -we only assume the joint distribution known In particular train a network predict high-resolution labels minimizing the distance/divergence two distributions: distribution expected distribution suggested We applied our method high res labels very compared achieved compared the conventional fully supervised methods trained We also show combining low and high res labels leads to out test setsAlthough the main assumption the joint distribution over coarse and fine labels known in robust errors estimates these distributions discuss There we show these joint distributions acquired or inferred thus label superresolution widely including beyond computer vision",0.01,0.591057495872603
"We propose a novel framework for combining datasets via alignment of their associated intrinsic dimensions. Our approach assumes that the two datasets are sampled from a common latent space, i.e., they measure equivalent systems. Thus, we expect there to exist a natural (albeit unknown) alignment of the data manifolds associated with the intrinsic geometry of these datasets, which are perturbed by measurement artifacts in the sampling process. Importantly, we do not assume any individual correspondence (partial or complete) between data points. Instead, we rely on our assumption that a subset of data features have correspondence across datasets. We leverage this assumption to estimate relations between intrinsic manifold dimensions, which are given by diffusion map coordinates over each of the datasets. We compute a correlation matrix between diffusion coordinates of the datasets by considering graph (or manifold) Fourier coefficients of corresponding data features. We then orthogonalize this correlation matrix to form an isometric transformation between the diffusion maps of the datasets. Finally, we apply this transformation to the diffusion coordinates and construct a unified diffusion geometry of the datasets together. We show that this approach successfully corrects misalignment artifacts, and allows for integrated data. In biology and other natural science settings we often have the problem that data are measured from the same system but with different sensors or in different days where sensors are calibrated differently. This is often termed batch effect in biology and can include, for example, drastic variations between subjects, experimental settings, or even times of day when an experiment is conducted. In such settings it is important to globally and locally align the datasets such that they can be combined for effective further analysis. Otherwise, measurement artifacts may dominate downstream analysis. For instance, clustering the data will group samples by measurement time or sensor used rather than by biological or meaningful differences between datapoints.Recent works regard the two datasets as views of the same system and construct a multiview diffusion geometry but all of them require at least partial bijection, if not full one, between views BID11 BID12 BID24 Tuia & Camps-Valls, 2016) . Other work directly attempt to match data points directly in ambient space, or by local data geometry and these can be very sensitive to differences in sampling density rather than data geometry BID10 . Here, we present a principled approach called harmonic alignment to for correct this type of effect based on the manifold assumption.The manifold assumption holds that high dimensional data originates from an intrinsically low dimensional smoothly varying space that is mapped via nonlinear functions to observable high dimensional measurements. Thus, we assume that the datasets are from transformed versions of the same low dimensional manifold. We learn the manifolds separately from the two datasets using diffusion geometric approaches and then find an isometric transformation to map from one manifold to the other. Note that we are not aligning points to points. Indeed there may be sampling differences and density differences in the data. However, our manifold learning approach uses an anisotropic kernel that detects the geometry of the data to align rather than point-by-point matching which is done in other methods.Our method involves first embedding each dataset separately into diffusion components, and then finding an isometric transformation that aligns these diffusion representations. To find such transformation, we utilize the duality between diffusion coordinates and geometric harmonics that act as generalized Fourier harmonics in the graph space. The diffusion components are eigenvectors of a Markov-normalized data diffusion operator, whose eigenvalues indicate frequency of the eigenvector. We attempt to find a transformation from one set of eigenvectors to another, via feature correspondences in the data.While datapoint correspondences may be difficult or impossible to obtain since many biological measurements are destructive, feature correspondences are often available. For instance single-cell measurements of cells from the same device, thus containing counts for the same genes, albeit affected by batch differences. Thus when corresponding features are transformed via the graph Fourier transform (GFT) into diffusion coordinates, the representations should be similar, with potentially small frequency-proximal perturbations. For instance, slowly varying features across the manifold should be load to low-frequency eigenvectors of the Markov matrix. This insight allows us to create a correlation matrix between the eigenvectors of one dataset to another based on correlation between feature loadings to the eigenvectors. However, since we know that eigenvectors represent frequency harmonics, we need not compute the entire correlation matrix but rather only the near-diagonal values. This implies that the two manifolds must be perturbed such that low and high frequency eigenvector space are similar. We then find a linear transformation between that maps the eigenvectors of one space into those of the other that maximizes these correlations by orthogonalizing this matrix. This transformation allows us to align the two datasets with each other. Finally, given an aligned representation, we build a robust unified diffusion geometry that is invariant batch effects and sample-specific artifacts and low-pass filter this geometry to denoise the unified manifold. Thus, in addition to aligning the manifolds our method denoises the manifolds as well.We demonstrate the results of our method on artificial manifolds created from rotated MNIST digits, corrupted MNIST digits, as well as on single-cell biological data measuring peripheral blood cells. In each case our method successfully aligns the manifolds such that they have appropriate neighbors within and across the two datasets. We show an application to transfer learning where a lazy classifier trained on one dataset is applied to the other dataset after alignment. Further, comparisons with recently developed methods such as the MNN-based method of BID10 show significant improvements in performance and denoising ability. We presented a novel method for aligning or batch-normalizing two datasets that involves learning and aligning their intrinsic manifold dimensions. Our method leverages the fact that common or corresponding features in the two datasets should have similar harmonics on the graph of the data. Our harmonic alignment method finds an isometric transformation that maximizes the similarity of frequency harmonics of common features. Results show that our method successfully aligns artifi- cially misaligned as well as biological data containing batch effect. Our method has the advantages that it aligns manifold geometry and not density (and thus is insensitive to sampling differences in data) and further our method denoises the datasets to obtain alignments of significant manifold dimensions rather than noise. Future applications of harmonic alignment can include integration of data from different measurement types performed on the same system, where features have known correlations.",1276,0.735,747,1.7081659973226238,"We propose combining datasets via alignment their associated intrinsic dimensions Our approach assumes the two datasets sampled a common latent space they measure equivalent systems Thus expect there exist a natural (albeit unknown) alignment the data manifolds associated the intrinsic geometry these datasets perturbed measurement artifacts Importantly assume any individual correspondence (partial data points Instead rely our assumption a subset data features correspondence across datasets We leverage this assumption relations intrinsic manifold dimensions given diffusion map coordinates over each We compute diffusion coordinates the datasets considering graph (or manifold corresponding data features We then orthogonalize this correlation matrix form an isometric transformation between the diffusion maps the datasets Finally apply this transformation the diffusion coordinates construct a unified diffusion geometry the datasets together We show this approach successfully misalignment artifacts allows integrated data. In biology other natural science settings data measured but in different days where sensors calibrated This often termed batch effect can include,, drastic variations subjects experimental settings even times In such settings globally and align the datasets such effective further analysis Otherwise measurement artifacts dominate downstream analysis For instance clustering will group samples measurement time sensor used rather biological or meaningful differencesRecent works regard views construct a multiview diffusion geometry but all require at least partial bijection if one between views BID11 BID12 BID24 Tuia & Camps-Valls) . Other work directly attempt match data points directly ambient space local data geometry these sensitive differences sampling density rather data geometry BID10 . Here called harmonic alignment for correct this type effect based the manifold assumptionThe manifold assumption that high dimensional data originates an intrinsically low dimensional smoothly varying space mapped via observable high dimensional measurements Thus assume the datasets from transformed versions the same low dimensional manifold We learn the manifolds separately the two datasets using diffusion geometric approaches find an isometric transformation map from manifold Note aligning points points Indeed there may sampling and density differences However our manifold learning approach uses detects align rather point- matching which done other methodsOur method involves first each dataset separately diffusion components finding an isometric transformation these diffusion representations To such transformation utilize between diffusion coordinates geometric harmonics act generalized Fourier harmonics The diffusion components a Markov-normalized data diffusion operator indicate frequency We attempt find a transformation one set via feature correspondencesWhile datapoint correspondences difficult since many biological measurements destructive available For instance single-cell measurements cells the same device thus containing counts albeit affected batch differences Thus when corresponding features transformed via the graph Fourier transform diffusion coordinates the representations should similar potentially small frequency-proximal perturbations For instance slowly varying features across the manifold should load to the Markov matrix This insight allows create a correlation matrix one dataset to based correlation feature loadings to However since we eigenvectors represent frequency harmonics compute the entire correlation matrix but This implies the two manifolds perturbed such that low and high frequency eigenvector space similar We then find a linear transformation that maps one space that maximizes these correlations this matrix This transformation align Finally given an aligned representation build a robust unified diffusion geometry invariant batch effects sample-specific artifacts and this geometry denoise the unified manifold Thus addition aligning the manifolds our method denoisesWe demonstrate created rotated MNIST digits as single-cell biological data measuring peripheral blood cells In our method successfully aligns such appropriate neighbors within and the two datasets We show an application transfer learning where a lazy classifier trained after alignment Further comparisons recently developed methods BID10 show performance and denoising ability We presented aligning or batch-normalizing two datasets involves learning their intrinsic manifold dimensions Our method leverages common or corresponding features should similar harmonics on Our harmonic alignment method finds an isometric transformation common features Results show our method successfully aligns artifi- misaligned as biological data containing batch effect Our method aligns manifold geometry not density insensitive sampling differences data further our method denoises the datasets obtain alignments significant manifold dimensions rather noise Future applications harmonic alignment integration data different measurement types performed where features have known correlations",0.01,0.508423912077629
"Reinforcement learning (RL) has proven to be a powerful paradigm for deriving complex behaviors from simple reward signals in a wide range of environments. When applying RL to continuous control agents in simulated physics environments, the body is usually considered to be part of the environment. However, during evolution the physical body of biological organisms and their controlling brains are co-evolved, thus exploring a much larger space of actuator/controller configurations. Put differently, the intelligence does not reside only in the agent's mind, but also in the design of their body. 
 We propose a method for uncovering strong agents, consisting of a good combination of a body and policy, based on combining RL with an evolutionary procedure. Given the resulting agent, we also propose an approach for identifying the body changes that contributed the most to the agent performance. We use the Shapley value from cooperative game theory to find the fair contribution of individual components, taking into account synergies between components. 
 We evaluate our methods in an environment similar to the the recently proposed Robo-Sumo task, where agents in a 3D environment with simulated physics compete in tipping over their opponent or pushing them out of the arena. Our results show that the proposed methods are indeed capable of generating strong agents, significantly outperforming baselines that focus on optimizing the agent policy alone. 

 A video is available at: www.youtube.com/watch?v=eei6Rgom3YY Reinforcement Learning (RL) uses a simple reward signal to derive complex agent policies, with recent progress on representing the policy using deep neural networks leading to strong results in game playing BID29 Silver et al., 2016) , robotics BID22 BID23 and dialog systems BID24 . Such algorithms were designed for stationary environments, but having multiple learning agents interact yields a non-stationary environment (Littman, 1994; BID2 . Various approaches were proposed for continuous control, required for locomotion in an physics simulator environment BID16 BID31 BID0 . Although very successful, such approaches consider the body of the agent to be fixed, simply a part of the environment. However, during evolution the physical body of biological organisms is constantly changing; thus, the controlling brain and physical body are jointly optimized, exploring a larger space of actuator-controller configurations.The interaction of evolution with learning by individual animals over their lifetime can result in superior performance (Simpson, 1953) . Researchers refer to how individual learning can enhance evolution at the species level as the ""Baldwin Effect"" (Weber & Depew, 2003) , where learning guides evolution by smoothing the fitness landscape. In learning agents, the physical shape of the body plays a double role. First, a good body has the capability of effectively exerting many forces in the environment. Second, a well-configured body is easier to learn to control, by making it simpler to identify good policies for exerting the forces. Consider a physical task which requires exerting certain forces at the right time, such as locomotion. Some bodies can exert the required forces, while others cannot. Further, some bodies exert the required forces only under a small set of exactly correct policies, whereas others have a wide range of policies under which they exert the required forces (at least approximately). In other words, some bodies have a wide ""basin of attraction"" where a learner can find a policy that exerts at least a part of the required forces; once discovering a policy in this wide basin, the learner can optimize the policy to exert the required forces.This indicates that the intelligence of agents resides not only in their mind (the controller), but also in the design of their body. Our contribution is proposing a method for uncovering strong agents, consisting of a good combination of a body and policy. This stands in contrast to the traditional paradigm, which takes the body as a given (i.e. a fixed part of the environment), as shown in FIG0 . Our technique combines RL with an evolutionary procedure. We also show how to identify the body changes that contributed the most to agent performance, taking into account synergies between them. We demonstrate our method in an environment similar to the Robo-Sumo task (AlShedivat et al., 2017) , where agents in a 3D environment with simulated physics compete in pushing the opponent out of the arena or tipping it over. This environment is based on the MuJoCo physics simulator (Todorov et al., 2012) , allowing us to easily modify the agent's body. Our results show that the proposed methods are indeed capable of generating superior agents, significantly outperforming baselines that focus on optimizing the agent policy alone.Related Work Evolving virtual creatures (EVCs) work uses genetic algorithms to evolve the structure and controllers of virtual creatures in physically simulated environments, without learning (Sims, 1994) . EVCs have a genetically defined morphology and control system that are co-evolved to perform locomotion tasks (Sims, 1994; BID7 BID4 , with some methods using a voxel-based ""soft-body"" BID4 BID17 BID28 . Most such attempts have yielded relatively simple behaviors and morphologies BID7 BID3 . One approach to enable continually increasing complex behavior is using a curriculum BID6 . Researchers hypothesized that embodied cognition, where a controller expresses its behavior through a body, may cause morphological changes to have an immediate detrimental impact on a behavior BID3 . For example, a mutation generating longer legs may harm performance with a controller optimized for shorter legs. This results in pressure to converge on a body design early in evolution, to give the controller a stable platform to optimize. This interdependence can be mitigated by giving the controller time to adapt to morphological changes, so bodies that are easier to learn to control would have an evolutionary advantage, and learning would smooth the fitness landscape; this may speed up body evolution, with the extent of learning required for new bodies decreasing over time (Simpson, 1953; Weber & Depew, 2003) .Scenarios where learning is used only in the evaluation phase of evolved agents are referred to as Baldwinian evolution (Weber & Depew, 2003) , where the results of learning are discarded when an offspring is generated. This is in contrast to ""Lamarkian evolution"" (Whitley et al., 1994; BID20 , where the result of learning is passed on to offspring. Typically the adaption stage uses a genetic algorithm operating to evolve the controller BID3 BID20 . In contrast , we use an RL algorithm to learn to control an evolving body. RL has achieved complex behaviours in continuous control tasks with fixed morphology BID16 BID31 BID0 , and has the potential to adapt to morphological changes. Our experiments evaluate the potential of evolving the bodies of a population of learning agents. We leverage Population Based Training BID18 (PBT), originally proposed to evolve parameters of the controller. To our knowledge, this is the first attempt at evolving the body of continuously controlled RL agents in a physically simulated environment.Preliminaries We apply multi-agent reinforcement learning in partially-observable Markov games (i.e. partially-observable stochastic games) BID34 Littman, 1994; BID13 . In every state, agents take actions given partial observations of the true world state, and each obtains an individual reward. Agents learn an appropriate behavior policy from past interactions. In our case, given the physics simulator state, agents observe an egocentric view consisting of the positions and velocities of their and their opponent's bodies (end effectors and joints) and distances from the edges of the pitch. Our agents have actuated hinges (one at the ""knee"" and one at the ""hip"" of every limb). The full specification for our environment (observations and actions) are given in the Appendix, and are similar to other simulated physics locomotion tasks BID16 . Every agent has its own experience in the environment, and independently learns a policy, attempting to maximize its long term γ-discounted utility, so learning is decentralized BID2 .Our analysis of the relative importance of the body changes uses cooperative game theory. We view the set of body changes as a ""team "" of players, and quantify the impact of individual components, taking into account synergies between them. Game theory studies players who can form teams, looking for fair ways of estimating the impact of individual players in a team. A cooperative game consists of a set A of n players, and a characteristic function v : 2 A → R which maps any team C ⊆ A of players to a real value, showing the performance of the team as a whole. In our case, A consists of all changes to body components resulting in the final body configuration. The marginal contribution of a player i in a team C that includes it (i.e. i ∈ C) is the change in performance resulting from excluding i: DISPLAYFORM0 We define a similar concept for permutations. Denote by π a permutation of the players ( i.e. π : {1, 2, . . . , n} → {1, 2, . . . , n} where π is a bijection), and by Π the set of all player permutations. We refer to the players occurring before i in the permutation π as the predecessors of i in π, and denote by S π (i) the predecessors of i in π, i.e. S π (i) = {j|π(j) < π(i)}. The marginal contribution of a player i in a permutation is the change in performance between i's predecessors and including i, and the performance of i's predecessors alone: BID35 ) is considered a fair allocation of the overall reward achieved by a team to the individual players in a team, reflecting the contribution of each individual player to the team's success BID12 Straffin, 1988) . It is the unique value exhibiting various fairness axioms BID9 BID11 , taking into account synergies between agents (see Section 8 in the Appendix for a detailed discussion and examples of how the Shapley value captures such synergies between body components). The Shapley value is the marginal contribution of a player , averaged across all player permutations, given by the vector DISPLAYFORM1 DISPLAYFORM2 We proposed a framework for jointly optimizing agent body and policy, combining continuous control RL agents with an evolutionary procedure for modifying agent bodies. Our analysis shows that this technique can achieve stronger agents than obtained by optimizing the controller alone. We also used game theoretic solutions to identify the most influential body changes. Several questions remain open. First, can we augment our procedure to also modify the neural network architecture of the controller, similarly to recent neural architecture optimizers BID27 ? Second, can we use similar game theoretic methods to guide the evolutionary process? Finally, How can we ensure the diversity of agents' bodies so as to improve the final performance? Darrell Whitley, V Scott Gordon, and Keith Mathias. Lamarckian evolution, the baldwin effect and function optimization. In International Conference on Parallel Problem Solving from Nature, pp. 5-15. Springer, 1994.",2263,1.266,1296,1.746141975308642,"Reinforcement learningRL proven deriving complex behaviors simple reward signals in When applying RL continuous control agents simulated physics environments the body usually considered part However during evolution the physical body biological organisms and their controlling brains co thus exploring a much larger space actuator/controller configurations Put differently the intelligence does reside only the design their body We propose uncovering strong agents consisting a good combination a body policy based combining RL an evolutionary procedure Given the resulting agent also propose the body changes contributed the the agent performance We use the Shapley value from cooperative game theory find the fair contribution individual components taking We evaluate our methods an environment similar the the recently proposed Robo-Sumo task agents in with simulated physics compete tipping over their opponent or pushing Our results the proposed methods indeed capable strong agents significantly outperforming baselines focus optimizing the agent policy alone A video is at Reinforcement LearningRL uses a simple reward signal derive complex agent policies with recent progress representing the policy using leading strong results game playing BID29 Silver et) , robotics dialog systems . Such algorithms stationary environments having multiple learning agents interact yieldsLittman BID2 . Various approaches continuous control required locomotion an physics simulator environment BID16 BID31 BID0 . Although very successful such approaches consider the body the agent fixed simply a part However during evolution the physical body biological organisms constantly; thus the controlling brain jointly optimized exploring a larger space actuator-controller configurationsThe interaction evolution learning by individual animals over superior performanceSimpson 1953 . Researchers refer how individual learning enhance evolution atWeber Depew , guides the fitness landscape In learning agents the physical shape plays First a good body has effectively many forces Second a well-configured body easier learn control by simpler identify good policies exerting the forces Consider a physical task which certain forces Some bodies exert the required forces Further some bodies exert the required forces only under a small set exactly correct policies under (at approximately In some bodies a wide ""basin attraction where a learner a policy exerts the required forces; once discovering in this wide basin optimize exertThis indicates the intelligence agents residesthe controller the design Our contribution proposing uncovering strong agents consisting a good combination a body policy This stands the traditional paradigm takes FIG0 . Our technique combines RL with an evolutionary procedure We also show identify the body changes contributed the agent taking them We demonstrate our method an environment similar the Robo-Sumo taskAlShedivat et 2017 , agents in with simulated physics compete pushing or tipping it This environment based the MuJoCo physics simulatorTodorov , allowing easily modify the agent's body Our results the proposed methods indeed capable superior agents significantly outperforming baselines focus optimizing the agent policy aloneRelated Work Evolving virtual creaturesEVCs work uses genetic algorithms evolve the structure controllers physically simulated environments without learning (Sims 1994 . EVCs a genetically defined morphology and control system co perform locomotion tasksSims BID7 BID4 , with some methods using . Most such attempts yielded relatively simple behaviors morphologies BID7 BID3 . One approach enable continually complex behavior using a curriculum BID6 . Researchers hypothesized embodied cognition where a controller expresses cause have an immediate detrimental impact BID3 For example a mutation generating longer legs harm performance with a controller optimized This results pressure converge a body design early evolution give the controller optimize This interdependence can giving the controller time adapt bodies easier learn would learning smooth the fitness landscape; speed body evolution with the extent required decreasing (Simpson 1953 Weber Depew 2003) .Scenarios used only the evaluation phase evolved agents referred Baldwinian evolution discarded an offspring generated This in contrast ""Lamarkian evolutionWhitley BID20 , where the result learning passed. Typically the adaption stage uses a genetic algorithm operating to evolve the controller BID3 BID20 . In contrast , use an RL algorithm learn control an evolving body RL has achieved complex behaviours continuous control tasks fixed morphology BID16 BID31 BID0 , adapt Our experiments evaluate evolving the bodies a population learning agents We leverage Population Based Training BID18 originally proposed evolve parameters the controller To our knowledge evolving the body continuously controlled RL agentsPreliminaries We apply partially-observable Markov games BID34 Littman 1994 BID13 . In every state agents take actions given partial observations the true world state each obtains an individual reward Agents learn an appropriate behavior policy past interactions In our case given the physics simulator state agents observe an egocentric view consisting the positionsend effectors joints distances the pitch Our agents actuated hinges (one at every limb The full specification our environment ( actions given similar other simulated physics locomotion tasks BID16 . Every agent the environment independently learns a policy attempting maximize its long term ��-discounted utility learning decentralized BID2 .Our analysis the body changes uses cooperative game theory We view the set body changes a ""team "" players quantify individual components taking Game theory studies players can form teams looking fair ways estimating A cooperative game consists a set A n players a characteristic function v : 2 A → R which maps any team C ��� A a real value showing as In our case A consists all changes body components resulting the final body configuration The marginal contribution a player i in a team C that includes it � the change performance resulting excluding: DISPLAYFORM0 We permutations Denote by �� a permutation the players : { . . . , n} → . . . , n} where ��), by �� the set all player permutations We refer the players occurring before i in the permutation �� the predecessors denote {j|π(j < The marginal contribution a player i in performance i's predecessors including, alone: BID35 ) considered a fair allocation the overall reward achieved reflecting the team's success BID12 Straffin 1988 . It the unique value exhibiting various fairness BID9 BID11 , taking account synergies agents in and examples the Shapley value captures between body components The Shapley value the marginal contribution a player , averaged given the vector DISPLAYFORM1 DISPLAYFORM2 We proposed jointly optimizing agent body policy combining continuous control RL agents an evolutionary procedure modifying Our analysis this technique achieve stronger agents obtained optimizing the controller alone We also used game theoretic solutions identify the most influential body changes Several questions open First can augment our procedure also modify the controller similarly recent neural architecture optimizers BID27 ? Second can similar game theoretic methods guide Finally How can ensure the diversity agents' bodies so improve the final performance Darrell Whitley V Scott Gordon Keith Mathias Lamarckian evolution the baldwin effect function optimization In International Conference Parallel Problem from Nature pp 515 Springer 1994",0.01,0.6051833674530597
"Many practical reinforcement learning problems contain catastrophic states that the optimal policy visits infrequently or never. Even on toy problems, deep reinforcement learners periodically revisit these states, once they are forgotten under a new policy. In this paper, we introduce intrinsic fear, a learned reward shaping that accelerates deep reinforcement learning and guards oscillating policies against periodic catastrophes. Our approach incorporates a second model trained via supervised learning to predict the probability of imminent catastrophe. This score acts as a penalty on the Q-learning objective. Our theoretical analysis demonstrates that the perturbed objective yields the same average return under strong assumptions and an $\epsilon$-close average return under weaker assumptions. Our analysis also shows robustness to classification errors. Equipped with intrinsic fear, our DQNs solve the toy environments and improve on the Atari games Seaquest, Asteroids, and Freeway. Following success on Atari games BID20 and the board game Go BID28 , many researchers have begun exploring practical applications of deep reinforcement learning (DRL). Some investigated applications include robotics BID15 , dialogue systems BID6 BID17 , energy management BID23 , and self-driving cars BID26 . Amid this push to apply DRL, we might ask, can we trust these agents in the wild? Agents acting in real-world environments might possess the ability to cause catastrophic outcomes. Consider a self-driving car that might hit pedestrians or a domestic robot that might injure a child. We might hope to prevent DRL agents from ever making catastrophic mistakes. But doing so requires extensive prior knowledge of the environment in order to constrain the exploration of policy space BID7 .Many conflicting definitions of safety and catastrophe exist, a problem that invites further philosophical consideration. In this paper, we introduce a specific but plausible notion of avoidable catastrophes. These are states that prior knowledge dictates an optimal policy should never visit. For example , we might believe that an optimal self-driving algorithm would never hit a pedestrian. Moreover, we assume that an optimal policy never even comes near an avoidable catastrophe state. We define proximity in trajectory space, and not by the geometry of feature space. We denote states proximal to avoidable catastrophes as danger states. While we don't assume prior knowledge of which states are dangerous, we do assume the existence of a catastrophe detector. After encountering a catastrophic state, an agent can realize this and take action to avoid dangerous states in the future.Given this definition, we address two challenges: First, can we expect DRL agents, after experiencing some number of catastrophic failures, to avoid perpetually making the same mistakes? Second, can we use our prior knowledge that catastrophes should be kept at a distance to accelerate learning of a DRL agent? Our experiments show that even on toy problems, the deep Q-network (DQN), a basic algorithm behind many of today's state-of-the-art DRL systems, struggles on both counts. Even in toy environments , DQNs may encounter thousands of catastrophes before learning to avoid them and are susceptible to repeating old errors. We call this latter problem the Sisyphean curse.This poses a formidable obstacle to using DQNs in the real world. How can we hand over responsibility for consequential actions (control of a car, say) to a DRL agent if it may be doomed to periodically remake every kind of mistake, however grave, so long as it continues to learn? Imagine a self-driving car that had to periodically hit a few pedestrians in order to remember that is undesirable. In the tabular setting, an RL agent never forgets the learned dynamics of its environment, even as its policy evolves. Moreover, if the Markovian assumption holds, eventual convergence to a globally optimal policy is guaranteed. Unfortunately, the tabular approach becomes infeasible in high-dimensional, continuous state spaces.The trouble for DQNs owes to the use of function approximation BID22 . When training a DQN, we successively update a neural network based on experiences. These experiences might be sampled in an online fashion, from a trailing window (experience replay buffer), or uniformly from all past experiences. Regardless of which mode we use to train the network , eventually, states that a learned policy never encounters will come to form an infinitesimally small region of the training distribution. At such times, our networks are subject to the classic problem of catastrophic interference BID19 BID18 . Nothing prevents the DQN's policy from drifting back towards a policy that revisits long-forgotten catastrophic mistakes.More formally, we characterize the problem as unfolding in the following steps: (i) Training under distribution D, our agent produces a safe policy π s that avoids catastrophes (ii) Collecting data generated under π s yields a new distribution of transitions D (iii) Training under D , the agent produces π d , a policy that once again experiences avoidable catastrophes. To illustrate the brittleness of modern DRL algorithms, we introduce a simple pathological problem called Adventure Seeker. This problem consists of a one-dimensional continuous state, two actions , simple dynamics, and a clear analytic solution. Nevertheless, the DQN fails. We then show that similar dynamics exist in the classic RL environment Cart-Pole .In this paper, to combat these problems, we propose intrinsic fear. In this approach, we train a supervised fear model that predicts which states are likely to lead to a catastrophe within k r steps. The output of the fear model (a probability), scaled by a fear factor penalizes the Q-learning target. Our approach draws inspiration from intrinsic motivation BID5 . However, instead of perturbing the reward function to encourage the discovery of novel states, we perturb it to discourage revisiting catastrophic states.We validate the approach both empirically and theoretically. Our experiments address both our Adventure Seeker problem and Cartpole as well as the Atari games Seaquest and Asteroids, and Freeway. For these environments, we label each loss of a life as a catastrophic state. On the toy environments, the intrinsic fear agent learns to avoid death indefinitely , achieving unbounded reward per episode. On Seaquest and Asteroids, the intrinsic fear agent improves markedly and on Freeway the improvement is dramatic. Theoretically, we demonstrate the following: First, we prove that when the reward is bounded and the optimal policy rarely visits the catastrophic states, the policy learned on the altered value function has return similar to the optimal policy on the original value function. Second we prove that the method is robust to noise in the danger model. Our experiments demonstrate that DQNs are susceptible to periodically repeating mistakes, however bad, raising questions about their real-world utility when harm can come of actions. While it's easy to visualize these problems on toy examples, similar dynamics are embedded in more complex domains. Consider a domestic robot acting as a barber. The robot might receive positive feedback for giving a closer shave. This reward encourages closer contact at a steeper angle. Of course, the shape of this reward function belies the catastrophe lurking just past the optimal shave. Similar dynamics might be imagines in a vehicle that is rewarded for traveling faster but could risk an accident with excessive speed. Our results with the intrinsic fear model suggest that with only a small amount of prior knowledge (the ability to recognize catastrophe states after the fact), we can simultaneously accelerate learning and avoid catastrophic states. This work represents a first step towards combating some issues relating to safety in RL stemming from catastrophic forgetting.",1476,0.949,835,1.7676646706586827,"Many practical reinforcement learning problems contain catastrophic states the optimal policy visits infrequently Even on toy problems deep reinforcement learners periodically revisit these states once forgotten under a new policy In intrinsic fear a learned reward shaping that guards oscillating policies Our approach incorporates a second model trained via imminent catastrophe This score acts a penalty the Q-learning objective Our theoretical analysis demonstrates perturbed objective yields under strong assumptions Our analysis also robustness classification errors Equipped intrinsic fear our DQNs solve the toy environments improve on the Atari games Seaquest Freeway Following success Atari games BID20 Go BID28 many researchers practical applications Some investigated applications include robotics BID15 , dialogue systems Amid this push apply DRL might ask these agents the wild Agents acting might possess cause catastrophic outcomes Consider might hit pedestrians a domestic robot injure We might hope prevent DRL agents ever catastrophic mistakes But doing extensive prior knowledge constrain the exploration policy space BID7 .Many conflicting definitions safety catastrophe exist a problem invites In a specific but plausible notion These states prior knowledge dictates an optimal policy should never visit For example , might believe an optimal self-driving algorithm never hit Moreover assume an optimal policy never even near an avoidable catastrophe state We define proximity trajectory space not feature space We denote states proximal avoidable catastrophes danger states While assume prior knowledge which states dangerous a catastrophe detector After encountering a catastrophic state an agent can realize this dangerous statesGiven this definition address can expect DRL agents, after some number perpetually making Second can that catastrophes should kept accelerate learning a DRL agent Our experiments even on toy problems the deep Q-network a basic algorithm behind state DRL struggles on both counts Even toy environments , DQNs encounter thousands learning avoid and are susceptible repeating old errors We call this latter problemThis poses using DQNs How hand responsibility consequential actions (control say a DRL agent may doomed periodically remake every kind mistake however grave so learn Imagine had periodically hit remember is undesirable In the tabular setting an RL agent never the learned dynamics its policy Moreover the Markovian assumption eventual convergence a globally optimal policy guaranteed Unfortunately the tabular approach becomes high-dimensional, continuous state spacesThe trouble for DQNs owes function approximation BID22 When training a DQN successively update experiences These experiences might sampled an online fashion from a trailing window (experience replay buffer uniformly Regardless which mode we train the network , eventually states a learned policy never encounters will come form the training distribution At such times our networks subject the classic problem catastrophic interference BID19 BID18 . Nothing prevents the DQN's policy drifting revisits long-forgotten catastrophic mistakesMore formally characterize unfolding ( Training under distribution D, our agent produces a safe policy �� s avoidsii Collecting generated , once experiences To illustrate modern DRL algorithms introduce a simple pathological problem called Adventure Seeker This problem consists two actions , simple dynamics a clear analytic solution Nevertheless the DQN fails We then show similar dynamics the classic RL environment Cart-Pole .In to combat intrinsic fear. In this approach train a supervised fear model states a catastrophe within k r steps The output the fear modela probability scaled penalizes the Q-learning target Our approach draws intrinsic motivation BID5 . However instead the reward function encourage novel states perturb revisiting catastrophic statesWe validate both Our experiments address both our Adventure Seeker problem Cartpole as the Atari games Seaquest Freeway For these environments label each loss a life a catastrophic state On the toy environments the intrinsic fear agent learns death indefinitely , achieving unbounded reward per episode On Seaquest and Asteroids the intrinsic fear agent improves markedly on Freeway the improvement dramatic demonstrate First prove when the reward bounded the optimal policy rarely visits the catastrophic states learned on the altered value function return similar Second we prove the method robust noise the danger model Our experiments demonstrate DQNs susceptible periodically repeating mistakes however bad raising when harm of actions While visualize these problems toy examples similar dynamics embedded Consider a domestic robot acting The robot might receive giving a closer shave This reward encourages closer contact at a steeper angle Of the shape this reward function belies the catastrophe lurking just past the optimal shave Similar dynamics might imagines a vehicle rewarded traveling could risk Our results with the intrinsic fear model with ability catastrophe states after simultaneously accelerate learning avoid catastrophic states This work represents combating some issues relating safety RL stemming catastrophic forgetting",0.01,0.6600213042416259
"Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere S^2 or a unit ball B^3---entails unique challenges. In this work, we propose a novel `""volumetric convolution"" operation that can effectively convolve arbitrary functions in B^3. We develop a theoretical framework for ""volumetric convolution"" based on Zernike polynomials and efficiently implement it as a differentiable and an easily pluggable layer for deep networks. Furthermore, our formulation leads to derivation of a  novel formula to measure the symmetry of a function in B^3 around an arbitrary axis, that is useful in 3D shape analysis tasks. We demonstrate the efficacy of proposed volumetric convolution operation on a possible use-case i.e., 3D object recognition task. Convolution-based deep neural networks have performed exceedingly well on 2D representation learning tasks BID11 BID7 . The convolution layers perform parameter sharing to learn repetitive features across the spatial domain while having lower computational cost by using local neuron connectivity. However, most state-of-the-art convolutional networks can only work on Euclidean geometries and their extension to other topological spaces e.g., spheres, is an open research problem. Remarkably, the adaptation of convolutional networks to spherical domain can advance key application areas such as robotics, geoscience and medical imaging. Some recent efforts have been reported in the literature that aim to extend convolutional networks to spherical signals. Initial progress was made by BID1 , who performed conventional planar convolution with a careful padding on a spherical-polar representation and its cube-sphere transformation BID17 . A recent pioneering contribution by used harmonic analysis to perform efficient convolution on the surface of the sphere (S 2 ) to achieve rotational equivariance. These works, however, do not systematically consider radial information in a 3D shape and the feature representations are learned at specified radii. Specifically, estimated similarity between spherical surface and convolutional filter in S 2 , where the kernel can be translated in S 2 . Furthermore, BID23 recently solved the more general problem of SE(3) equivariance by modeling 3D data as dense vector fields in 3D Euclidean space. In this work however, we focus on B 3 to achieve the equivariance to SO(3).In this paper, we propose a novel approach to perform volumetric convolutions inside unit ball (B 3 ) that explicitly learns representations across the radial axis. Although we derive generic formulas to convolve functions in B 3 , we experiment on one possible use case in this work, i.e., 3D shape recognition. In comparison to closely related spherical convolution approaches, modeling and convolving 3D shapes in B 3 entails two key advantages: 'volumetric convolution' can capture both 2D texture and 3D shape features and can handle non-polar 3D shapes. We develop the theory of volumetric convolution using orthogonal Zernike polynomials BID3 , and use careful approximations to efficiently implement it using low computational-cost matrix multiplications. Our experimental results demonstrate significant boost over spherical convolution and that confirm the high discriminative ability of features learned through volumetric convolution.Furthermore, we derive an explicit formula based on Zernike Polynomials to measure the axial symmetry of a function in B 3 , around an arbitrary axis. While this formula can be useful in many function analysis tasks, here we demonstrate one particular use-case with relevance to 3D shape recognition. Specifically, we use the the derived formula to propose a hand-crafted descriptor that accurately encodes the axial symmetry of a 3D shape. Moreover, we decompose the implementation of both volumetric convolution and axial symmetry measurement into differentiable steps, which enables them to be integrated to any end-to-end architecture.Finally, we propose an experimental architecture to demonstrate the practical usefulness of proposed operations. We use a capsule network after the convolution layer as it allows us to directly compare feature discriminability of spherical convolution and volumetric convolution without any bias. In other words, the optimum deep architecture for spherical convolution may not be the same for volumetric convolution. Capsules, however, do not deteriorate extracted features and the final accuracy only depends on the richness of input shape features. Therefore, a fair comparison between spherical and volumetric convolutions can be done by simply replacing the convolution layer.It is worth pointing out that the proposed experimental architecture is only a one possible example out of many possible architectures, and is primarily focused on three factors: 1) Capture useful features with a relatively shallow network compared to state-of-the-art. 2) Show richness of computed features through clear improvements over spherical convolution. 3) Demonstrate the usefulness of the volumetric convolution and axial symmetry feature layers as fully differentiable and easily pluggable layers, which can be used as building blocks for end-to-end deep architectures.The main contributions of this work include:• Development of the theory for volumetric convolution that can efficiently model functions in B 3 .• Implementation of the proposed volumetric convolution as a fully differentiable module that can be plugged into any end-to-end deep learning framework.• The first approach to perform volumetric convolution on 3D objects that can simultaneously model 2D (appearance) and 3D (shape) features.• A novel formula to measure the axial symmetry of a function defined in B 3 , around an arbitrary axis using Zernike polynomials.• An experimental end-to-end trainable framework that combines hand-crafted feature representation with automatically learned representations to obtain rich 3D shape descriptors.The rest of the paper is structured as follows. In Sec. 2 we introduce the overall problem and our proposed solution . Sec. 3 presents an overview of 3D Zernike polynomials. Then, in Sec. 4 and Sec. 5 we derive the proposed volumetric convolution and axial symmetry measurement formula respectively. Sec. 6.2 presents our experimental architecture, and in Sec. 7 we show the effectiveness of the derived operators through extensive experiments. Finally, we conclude the paper in Sec. 8. In this work, we derive a novel 'volumetric convolution' using 3D Zernike polynomials, which can learn feature representations in B 3 . We develop the underlying theoretical foundations for volumetric convolution and demonstrate how it can be efficiently computed and implemented using low-cost matrix multiplications. Furthermore, we propose a novel, fully differentiable method to measure the axial symmetry of a function in B 3 around an arbitrary axis, using 3D Zernike polynomials. Finally, using these operations as building tools, we propose an experimental architecture, that gives competitive results to state-of-the-art with a relatively shallow network, in 3D object recognition task. An immediate extension to this work would be to explore weight sharing along the radius of the sphere.Let f (θ, φ, r) and g(θ, φ, r) be the object function and kernel function (symmetric around north pole) respectively. Then volumetric convolution is defined as, f * g(θ, φ) =< f, τ (θ,φ) g >Applying the rotation η (α,β,γ) to f , we get, η (α,β,γ) (f ) * g(θ, φ) =< η (α,β,γ) (f ), τ (θ,φ) g >By the result 33, we have, DISPLAYFORM0 However, since η α,β,γ (g) = τ α,β (g) we get, η (α,β,γ) (f ) * g(θ, φ) =< f, τ (θ−α,φ−β,) g >We know that, f * g(θ, φ) =< f, τ (θ,φ) g >= η (α,β,γ) (f ) * g(θ, φ) = (f * g)(θ − α, φ − β)η (α,β,γ) (f ) * g(θ, φ) = τ (α,β) (f * g) (Hence, we achieve equivariance over 3D rotations.",1705,0.821,1043,1.6347075743048898,"Convolution an efficient technique obtain abstract feature representations using hierarchical layers in deep networks Although performing convolution fairly its extension--- a sphere S^2 unit ball B^3---entails unique In this work propose a novel `""volumetric convolution"" operation effectively arbitrary functions B^3 We develop a theoretical framework ""volumetric convolution based Zernike polynomials efficiently implement as a differentiable and an easily pluggable layer deep networks Furthermore our formulation leads derivation a novel formula to measure the symmetry a function B^3 around an arbitrary axis that useful 3D shape analysis tasks We demonstrate the efficacy proposed volumetric convolution operation a possible use-case i.e., 3D object recognition task Convolution-based deep neural networks performed exceedingly 2D representation learning tasks BID11 BID7 . The convolution layers perform parameter sharing to learn repetitive features across the spatial domain while having lower computational cost by using local neuron connectivity However most stateof convolutional work and their extension spheres is an open research problem Remarkably the adaptation convolutional networks spherical domain can advance key application areas robotics geoscience medical imaging Some recent efforts reported the literature that aim extend convolutional networks spherical signals Initial progress was BID1 , performed conventional planar convolution a careful padding on a spherical-polar representation and its cube-sphere transformation BID17 A recent pioneering contribution used harmonic analysis perform efficient convolution on the surface the sphere (S 2 to achieve rotational equivariance These works, systematically consider radial information a 3D shape the feature representations learned at specified radii Specifically, estimated similarity spherical surface convolutional filter in S 2 , the kernel can translated in Furthermore BID23 recently solved the more general problem SE(3) equivariance modeling 3D data as dense vector fields in In this work however focus B 3 to achieve the equivariance to SO(3).In propose perform volumetric convolutions inside unit ball ( that explicitly learns representations across the radial axis Although we derive generic formulas to convolve functions B 3 experiment on one possible use case in this work In comparison closely related spherical convolution approaches modeling and convolving 3D shapes B 3 entails two key advantages ' can capture both 2D texture handle We develop the theory volumetric convolution orthogonal Zernike polynomials BID3 , use careful approximations efficiently implement low computational-cost matrix multiplications Our experimental results demonstrate significant boost over spherical convolution and that confirm the high discriminative ability features learned throughFurthermore derive an explicit formula based Zernike Polynomials measure the axial symmetry a function B 3 around an arbitrary axis While this formula can useful many function analysis tasks here demonstrate with relevance 3D shape recognition Specifically use the the derived formula propose a hand-crafted descriptor accurately encodes the axial symmetry Moreover we decompose the implementation both volumetric convolution axial symmetry measurement differentiable steps enables them integrated to any end architectureFinally propose an experimental architecture demonstrate the practical usefulness proposed operations We use a capsule network after the convolution layer as directly compare feature discriminability spherical convolution and without any bias In the optimum deep architecture spherical convolution may Capsules, however do deteriorate extracted features the final accuracy only the richness input shape features Therefore a fair comparison spherical and volumetric convolutions done simply replacing.It worth the proposed experimental architecture only a one possible example out primarily focused three factors Capture useful features with a relatively shallow network compared state. 2) Show richness computed features through clear improvements spherical convolution 3) Demonstrate the usefulness the volumetric convolution and axial symmetry feature layers as fully differentiable and easily pluggable layers, building end deep architecturesThe main contributions Development the theory for that efficiently model functions B 3 as plugged end learning The first approach perform simultaneously model (appearanceshape A novel formula measure a function defined around an arbitrary axis using Zernike combines hand-crafted feature representation automatically learned representations obtain rich 3D shape descriptorsThe rest structured In Sec 2 we introduce the overall problem and . Sec 3 presents 3D Zernike polynomials Then Sec 4 and Sec 5 we derive the proposed volumetric convolution and axial symmetry measurement formula respectively Sec 6.2 presents our experimental architecture and in Sec 7 we show the effectiveness the derived operators through extensive experiments Finally conclude the paper in Sec 8 In this work derive a novel 'volumetric convolution using 3D Zernike polynomials learn feature representations B 3 We develop the underlying theoretical foundations volumetric convolution demonstrate efficiently computed low-cost matrix multiplications Furthermore we propose a novel, fully differentiable method the axial symmetry a function B 3 around an arbitrary axis 3D Zernike polynomials Finally using these operations as building tools propose an experimental architecture, gives competitive results state with a relatively shallow network in 3D object recognition task An immediate extension this work would explore weight sharing along the radius the sphereLet f (�� r and the object function and kernel function (symmetric around north pole respectively Then volumetric convolution defined, f * g(�� � =< f, τ (� g >Applying the rotation ��α , (f ) *By the result 33 DISPLAYFORM0 However since α (g τ α we−β,)We know >= � ( τ))Hence achieve equivariance over 3D rotations",0.01,0.32125830421492085
"Learning in environments with large state and action spaces, and sparse rewards, can hinder a Reinforcement Learning (RL) agent’s learning through trial-and-error. For instance, following natural language instructions on the Web (such as booking a flight ticket) leads to RL settings where input vocabulary and number of actionable elements on a page can grow very large. Even though recent approaches improve the success rate on relatively simple environments with the help of human demonstrations to guide the exploration, they still fail in environments where the set of possible instructions can reach millions. We approach the aforementioned problems from a different perspective and propose guided RL approaches that can generate unbounded amount of experience for an agent to learn from. Instead of learning from a complicated instruction with a large vocabulary, we decompose it into multiple sub-instructions and schedule a curriculum in which an agent is tasked with a gradually increasing subset of these relatively easier sub-instructions. In addition, when the expert demonstrations are not available, we propose a novel meta-learning framework that generates new instruction following tasks and trains the agent more effectively. We train DQN, deep reinforcement learning agent, with Q-value function approximated with a novel QWeb neural network architecture on these smaller, synthetic instructions. We evaluate the ability of our agent to generalize to new instructions onWorld of Bits benchmark, on forms with up to 100 elements, supporting 14 million possible instructions. The QWeb agent outperforms the baseline without using any human demonstration achieving 100% success rate on several difficult environments. We study the problem of training reinforcement learning agents to navigate the Web (navigator agent) by following certain instructions, such as book a flight ticket or interact with a social media web site, that require learning through large state and action spaces with sparse and delayed rewards. In a typical web environment, an agent might need to carefully navigate through a large number of web elements to follow highly dynamic instructions formulated from large vocabularies. For example, in the case of an instruction ""Book a flight from WTK to LON on 21-Oct-2016"", the agent needs to fill out the origin and destination drop downs with the correct airport codes, select a date, hit submit button, and select the cheapest flight among all the options. Note the difficulty of the task: The agent can fill-out the first three fields in any order. The options for selection are numerous, among all possible airport / date combination only one is correct. The form can only be submitted once all the three fields are filled in. At that point the web environment / web page changes, and flight selection becomes possible. Then the agent can select and book a flight. Reaching the true objective in these tasks through trial-and-error is cumbersome, and reinforcement learning with the sparse reward results in the majority of the episodes generating no signal at all. The problem is exacerbated when learning from large set of instructions where visiting each option could be infeasible. As an example, in the flight-booking environment the number of possible instructions / tasks can grow to more than 14 millions, with more than 1700 vocabulary words and approximately 100 web elements at each episode.A common remedy for these problems is guiding the exploration towards more valuable states by learning from human demonstrations and using pretrained word embeddings. Previous work BID7 ; BID11 ) has shown that the success rate of an agent on Web navigation tasks (Miniwob BID11 )) can be improved via human demonstrations and pretrained word embeddings; however, they indeed use separate demonstrations for each environment and as the complexity of an environment increases, these methods fail to generate any successful episode (such as flight booking and social media interaction environments). But in environments with large state and action spaces, gathering the human demonstrations does not scale, as the training needs large number of human demonstrations for each environment.In this work, we present two methods for reinforcement learning in large state and action spaces with sparse rewards for the web navigation. First, when expert demonstrations or an instructionfollowing policy (ORACLE) are available, we develop curriculum-DQN, a curriculum learning that guides the exploration by starting with an easier instruction following task and gradually increasing the difficulty over a number of training steps. Curriculum-DQN decomposes an instruction into multiple sub-instructions and assigns the web navigation agent (navigator) with an easier task of solving only a subset of these sub-instructions ( FIG0 ). An expert instruction-following policy (ORACLE) places the agent and goal closer to each other.Second, when demonstrations and ORACLE policies are not available, we present a novel metalearning framework that trains a generative model for expert instruction-following demonstrations using an arbitrary web navigation policy without instructions. The key insight here is that we can treat an arbitrary navigation policy (e. g. random policy) as if it was an expert instruction-following policy for some hidden instruction. If we recover the underlying instruction, we can autonomously generate new expert demonstrations, and use them to improve the training of the navigator. Intuitively, generating an instruction from a policy is easier than following an instruction, as the navigator does not need to interact with a dynamic web page and take complicated actions. Motivated by these observations, we develop an instructor agent, a meta-trainer, that trains the navigator by generating new expert demonstrations.In addition to the two trainers, curriculum-DQN and instructor meta-trainer, the paper introduces two novel neural network architectures for encoding web navigation Q-value functions, QWeb and INET, combining self-attention, LSTMs, and shallow encoding. QWeb serves as Q-value function for the learned instruction-following policy, trained with either curriculum-DQN or instructor agent. The INET is Q-value function for the instructor agent. We test the performance of our approaches on a set of Miniwob and Miniwob++ tasks BID7 ). We show that both approaches improve upon a strong baseline and outperform previous state-of-the-art.While we focus on the Web navigation, the methods presented here, automated curriculum generation with attention-equipped DQN, might be of interest to the larger task planning community working to solve goal-oriented tasks in large discrete state and action Markov Decision Processes. In this work, we presented two approaches for training DQN agents in difficult web navigation environments with sparse rewards and large state and action spaces, one in presence of expert demonstrations and the other without the demonstrations. In both cases, we use dense, potential-based rewards to augment the training. When an expert demonstrations are available, curriculum learning decomposes a difficult instruction into multiple sub-instructions and tasks the agent with incrementally larger subset of these sub-instructions; ultimately uncovering the original instruction. When expert demonstrations are not available, we introduced a meta-trainer that generates goal state and instruction pairs with dense reward signals for the QWeb to train more efficiently. Our models outperform previous state-of-the-art models on challenging environments without using any human demonstration. The evaluations also indicate that having a high-quality expert demonstrations is important, as the policies trained from curriculum over demonstrations outperform policies that generate nonperfect demonstrations. In future work, we plan to apply our models on a broader set of navigation tasks with large discrete state and actions, and will experiment with other signals to utilize in the meta-trainer, such as supervised pre-training using behavioral cloning, scheduling a curriculum from the episodes generated by meta-trainer, using meta-trainer as off-policy learning, etc. ACKNOWLEDGMENTSWe thank Amir Fayazi for his help with integrating the Miniwob benchmarks into our ecosystem. We are grateful to Pranav Khaitan and the Deep Dialogue team at Google Research for discussions, as well as to the anonymous reviewers for their valuable feedback.",1541,0.78,933,1.6516613076098607,"Learning in environments large state and action spaces sparse rewards hinder a Reinforcement Learning (RL) agent��s learning through trial For instance following natural language instructions booking leads RL settings where input vocabulary number actionable elements on grow very Even recent approaches improve on relatively simple environments human demonstrations to guide environments the set possible instructions reach millions We approach the aforementioned problems propose guided RL approaches generate unbounded amount experience an agent to Instead learning a complicated instruction with decompose multiple sub schedule a curriculum an agent tasked a gradually increasing subset these relatively easier sub In when the expert demonstrations not propose a novel meta-learning framework generates new instruction following tasks trains more We train DQN deep reinforcement learning agent Q-value function approximated a novel QWeb neural network architecture on these smaller, synthetic instructions We evaluate our agent generalize new instructions onWorld of Bits benchmark on forms with supporting 14 million possible instructions The QWeb agent outperforms the baseline without any human demonstration achieving several difficult environments We study the problem training reinforcement learning agents navigate the Web (navigator agent following certain instructions book a flight ticket interact learning through large state and action spaces with sparse delayed rewards In a typical web environment an agent carefully navigate web elements follow highly dynamic instructions formulated For example an instruction ""Book a flight WTK LON on the agent needs fill the origin and destination drop downs select hit submit button among Note the difficulty the task The agent fill- The options selection numerous among all possible airport / date combination only one correct The form can submitted all the three fields At the web environment / web page changes flight selection possible Then the agent can select and book Reaching the true objective in these tasks through cumbersome reinforcement learning with sparse reward results the majority the episodes generating no signal The problem exacerbated learning from large set instructions where visiting each option could As the flight-booking environment the number possible instructions / tasks grow more than 14 millions more than 1700 vocabulary words approximately 100 web elements at each episodeA common remedy guiding the exploration towards more valuable states learning human demonstrations Previous work BID7 ; ) has an agent on Web navigation tasksMiniwob BID11 )) via human demonstrations pretrained word; they indeed use separate demonstrations each environment as the complexity generate any successful episodesuch flight booking social media interaction environments But environments large state and action spaces gathering the human demonstrations does scale the training needs large number human demonstrations forIn reinforcement learning sparse rewards the web navigation First when expert demonstrations or an instructionfollowing policy (ORACLE available develop curriculum-DQN learning that the exploration by starting an easier instruction following task over Curriculum-DQN decomposes an instruction multiple sub assigns the web navigation agent with an easier task solving only a subset FIG0 An expert instruction-following policy (ORACLE places the agent goal closerSecond demonstrations not we present a novel metalearning framework trains a generative model using an arbitrary web navigation policy without instructions The key insight treat an arbitrary navigation policy g. random policy) as an expert instruction-following policy for some hidden instruction If recover the underlying instruction autonomously generate new expert demonstrations the navigator Intuitively generating an instruction a policy easier following the navigator interact take complicated actions Motivated these observations develop an instructor agent that trains the navigator generating new expert demonstrationsIn the two trainers curriculum-DQN the paper two novel neural network encoding web navigation Q-value functions QWeb INET combining self-attention LSTMs shallow encoding QWeb serves Q-value function the learned instruction-following policy trained with either curriculum-DQN instructor agent The INET Q-value function the instructor agent We test our approaches Miniwob and tasks BID7 ). We show both approaches improve upon a strong baseline and previous state.While focus the Web navigation the methods, automated curriculum generation with attention-equipped DQN might the larger task planning community working solve goal-oriented tasks large discrete state and action Markov Decision Processes In this work presented training DQN agents difficult web navigation environments sparse rewards large state and action spaces one presence expert demonstrations without the demonstrations In we use dense, potential-based rewards augment the training When an expert demonstrations are available curriculum learning decomposes a difficult instruction multiple sub tasks the agent with incrementally larger subset; ultimately uncovering When expert demonstrations introduced a meta-trainer generates goal state instruction pairs dense reward signals the QWeb to train more Our models outperform previous state challenging environments without any human demonstration The evaluations also having a high-quality expert demonstrations the policies trained from curriculum over demonstrations outperform policies generate nonperfect demonstrations In future work apply our models on navigation tasks with large discrete state and actions experiment other signals utilize supervised pre-training using behavioral cloning scheduling a curriculum from the episodes generated using off-policy learning Amir Fayazi integrating the Miniwob benchmarks our ecosystem We grateful Pranav Khaitan the Deep Dialogue team Google Research discussions as",0.01,0.36445492713726546
"Labeled text classification datasets are typically only available in a few select languages. In order to train a model for e.g news categorization in a language $L_t$ without a suitable text classification dataset there are two options. The first option is to create a new labeled dataset by hand, and the second option is to transfer label information from an existing labeled dataset in a source language $L_s$ to the target language $L_t$. In this paper we propose a method for sharing label information across languages by means of a language independent text encoder. The encoder will give almost identical representations to multilingual versions of the same text. This means that labeled data in one language can be used to train a classifier that works for the rest of the languages. The encoder is trained independently of any concrete classification task and can therefore subsequently be used for any classification task.   We show that it is possible to obtain good performance even in the case where only a comparable corpus of texts is available. Automatic systems that can classify documents quickly and precisely are useful for a wide range of practical applications. For example, organizations may be interested in using sentiment analysis of opinion posts such as tweets that mention their products and services. By classifying the sentiment of each post (e.g. positive, neutral, or negative), the organization can for example learn which parts of a product should be improved.Creating a suitable, large labeled dataset for training a classification model requires a lot of effort and available public datasets are typically only available in the most common languages. In order to train a classification model for a languages L t without a suitable text classification dataset there are two options: The first option is of course to create a new labeled dataset from scratch, and the second option is to use the label information in existing labeled datasets in a language L s and then transfer this label information to L t . The first option usually requires a great amount of work and is typically not a viable solution. The second option is called cross-language text classification (CLTC) BID20 .In this article we present a method for performing CLTC by means of a universal encoder. The method consists of two steps. In the first step, a universal encoder is trained to give similar representations to texts that describe the same topic, even if the texts are in different languages. In the second step, a classification module uses the language-independent representations from the universal encoder as inputs and is trained to predict which category each document belongs to. Compared to previous work, this method has several advantages: The method presented in this article is conceptually similar in spirit to Google's zero-shot machine translation model BID6 , which is used in the Google translate API. That model also uses a shared vocabulary and a language independent encoder. It does, however , require a large corpus of aligned sentences for training. Additionally, translating a text is a much harder problem than merely extracting discriminative features since it requires encoding of e.g. syntactic information that is not necessary for text classification. Therefore such a model is much more complex than it needs to be, and a more parsimonious model is therefore preferable. We will compare our zero-shot classification model with an equivalent model based on the zero-shot translation model in section 3.The rest of the article is organized as follows: We present our CLTC model in section 2. Experiments, data and results are presented in section 3. In section 4 we review previous approaches to cross-lingual text classification. In section 5 we will take a look at some possible improvements and future directions for the method. Finally, we conclude the article in section 6. In this article we have shown how to create a language independent representation using only a corpus of comparable texts. The language independent representation can subsequently be used for zero-shot classification.We show that it is possible to obtain very good performance even when only a comparable corpus of texts is available.The unsupervised classifier of course does not perform better than a supervised classifier trained on the same number of samples. It is, however, equal in performance to a native language supervised classifier trained on about hundred thousand samples. This means that if the number of native samples is limited and a large comparable corpus is available, the performance of our zero-shot classification can be better than that of a monolingual classifier.Our results show that even though it is possible to obtain good results using several languages at once, the best performance is obtained by using only two languages. Our results furthermore show that it is necessary to use a very large embedding size in order to obtain the best possible performance.",914,0.525,528,1.731060606060606,"Labeled text classification datasets typically only a few select languages In order train a model e.g news categorization in a language $L_t$ without a suitable text classification dataset there The first option create a new labeled dataset by hand transfer label information in a source language $L_s$ In this paper sharing label information across languages by means a language independent text encoder The encoder will give almost identical representations multilingual versions This means labeled data in one language train works The encoder trained independently any concrete classification task therefore subsequently We show it obtain good performance even the case where only a comparable corpus texts Automatic systems that classify documents quickly precisely useful practical applications For example organizations interested using sentiment analysis of opinion posts such tweets mention their products By classifying the sentiment each post ( positive the organization for learn parts a product should improvedCreating a suitable, large labeled dataset training a classification model requires available public datasets typically only the most common languages In order train a classification model a languages L t without a suitable text classification dataset there of create a new labeled dataset from the label information existing labeled datasets in s and transfer The first option usually requires a great amount is typically The second option called cross-language text classificationCLTC BID20 .In article present performing by means a universal encoder The method consists In the first step a universal encoder trained give similar representations texts describe even in In the second step a classification module uses the language-independent representations from the universal encoder as inputs is trained predict which category each document Compared previous work this method The method presented conceptually in spirit Google's zero-shot machine translation model BID6 , the Google translate API That model also uses a shared vocabulary a language independent encoder It does, , require a large corpus aligned sentences for training Additionally translating a text merely extracting discriminative features since encoding that necessary text classification Therefore such a model much complex needs therefore preferable We will compare our zero-shot classification model an equivalent model based the zero-shot translation model in section 3.The rest organized We present our CLTC model section Experiments, data section In section we review previous approaches cross-lingual text classification In section we take some possible improvements future directions the method Finally conclude in section 6 In have shown a language independent representation using only a corpus comparable texts The language independent representation can subsequently zero-shot classificationWe show it obtain very good performance even only a comparable corpus textsThe unsupervised classifier of course perform better trained samples It, equal in performance a native language supervised classifier trained about hundred thousand samples This means the number native samples limited and a large comparable corpus the performance our zero-shot classification can betterOur results even it obtain several languages at the best performance Our results furthermore it necessary use a very large embedding size obtain",0.01,0.5667573636436779
"Syntax is a powerful abstraction for language understanding. Many downstream tasks require segmenting input text into meaningful constituent chunks (e.g., noun phrases or entities); more generally, models for learning semantic representations of text benefit from integrating syntax in the form of parse trees (e.g., tree-LSTMs). Supervised parsers have traditionally been used to obtain these trees, but lately interest has increased in unsupervised methods that induce syntactic representations directly from unlabeled text. To this end, we propose the deep inside-outside recursive autoencoder (DIORA), a fully-unsupervised method for discovering syntax that simultaneously learns representations for constituents within the induced tree. Unlike many prior approaches, DIORA does not rely on supervision from auxiliary downstream tasks and is thus not constrained to particular domains. Furthermore, competing approaches do not learn explicit phrase representations along with tree structures, which limits their applicability to phrase-based tasks. Extensive experiments on unsupervised parsing, segmentation, and phrase clustering demonstrate the efficacy of our method. DIORA achieves the state of the art in unsupervised parsing (46.9 F1) on the benchmark WSJ dataset. Syntax in the form of parse trees is an essential component of many natural language processing tasks. Constituent spans taken from a parse tree are useful for tasks such as relation extraction BID0 and semantic role labeling BID1 , while the full parse itself can be used to build higher-quality systems for machine translation BID2 ) and text classification BID3 . Supervised parsers trained on datasets such as the Penn Treebank BID4 are traditionally used to obtain these trees; however, these datasets are generally small and restricted to the newswire domain. For out-of-domain applications, it is generally infeasible to create new treebanks, as syntactic annotation is expensive and time-consuming.Motivated by these limitations, we propose a method that extracts both shallow parses (i.e., noun phrases or entities) and full syntactic trees from any domain or language automatically without any training data. In addition to just producing the parse, we want our model to build representations for internal constituents that obey syntactic and semantic regularities, as we can then easily inject these representations into downstream tasks. Our model extends existing work on latent tree chart parsers BID5 BID6 BID7 BID8 , which build up representations for all internal nodes in the tree (cells in the chart) generated by a soft weighting over all possible sub-trees (Section 2).In previous work, the representation at the root node is used as a sentence encoding and trained to optimize some downstream task, typically natural language inference. Unfortunately , this method requires sentence level annotations to train the model. Worse still, analysis on the trees learned by these models show that they are actually quite poor at capturing syntax that in any way resembles linguistic theory BID9 . To address these issues, we incorporate the inside-outside algorithm BID10 BID11 ) into a latent tree chart parser. The bottom-up inside step is equivalent to the forward-pass of previous latent tree chart parsers BID7 . However, these inside representations are encoded by looking only within the current subtree, completely ignoring outside context. Thus, we perform an additional top-down outside calculation for each node in the tree incorporating external context into sub-tree representations. Finally, we train This news raised hopes for further interest-rate cuts .This news raised hopes for further interest-rate cuts .Figure 1: Example parse trees. Top PRPN-LM prediction, bottom DIORA prediction. DIORA correctly chunks the span 'raised hopes for further interest-rate cuts'. the outside representations of leaves to reconstruct the initial input, which results in a completely unsupervised autoencoder-like objective.Recently, BID12 proposed Parsing-Reading-Predict Networks (PRPN), an RNN based language model with an additional module for inferring syntactic distance. After training, this syntax module can be decomposed to recover a parse BID13 ) via a complex mechanism that involves modeling a distribution over possible syntactic structures with a stick-breaking process. Like DIORA, this model can be trained in a completely unsupervised manner. However, it has no mechanism of explicitly modeling phrases, and span representations can only be generated by post-hoc heuristics. Additionally, finding the most probable tree in DIORA is much simpler than in PRPN, as we can just run the CKY algorithm.To probe different properties of our model, we run experiments on unsupervised parsing, segmentation, and phrase representations. DIORA sets the state-of-the-art for unsupervised parsing on the WSJ dataset, has a greater recall on a more constituent types than PRPN, and demonstrates strong clustering of phrase representations. Latent tree models have been shown to perform particularly poorly on attachments at the beginning and end of the sequence BID9 . To address this, we incorporate a post-processing heuristic (+PP in Table 2 ). We see that PRPN-UP and DIORA benefit much more than PRPN-LM from this heuristic. This is consistent with qualitative analysis showing that DIORA and PRPN-UP incorrectly attach trailing punctuation much more than PRPN-LM. This heuristic simply attaches trailing punctuation to the root of the tree, regardless of its predicted attachment. We find this to be extremely effective, increasing our state-of-the-art WSJ parsing results by by over 3 absolute F1 points.On the MultiNLI dataset, PRPN-LM is the top performing model without using the PP heuristic and DIORA outperforms PRPN-UP. Afterwards, PRPN-UP surpasses DIORA. However, it is worth noting that this is not actually a gold standard evaluation and instead evaluates the ability to replicate the output of a trained parser . Table 2 : Unsupervised Parsing. † indicates trained to optimize NLI task.We use the max unlabeled binary F1 across runs for PRPN-UP 2 , PRPN-LM, and DIORA. F1 was calculated using the parse trees provided by BID13 and all results in the upper portion of the table were copied from BID13 . +PP refers to post-processing heuristic to remove trailing punctuation explained in Section 3.1. In Table 2 we see the breakdown of constituent recall across the 10 most common types. We see that PRPN-UP has the highest recall for the most common type noun-phrase, but drops in every other category. DIORA achieves the highest recall across the most types and is the only model to perform effectively on verb-phrases. However, DIORA performs poorly relative to PRPN at prepositional phrases. Table 3 : Segment recall from WSJ seperated by phrase type. The 10 most frequent phrase types are shown. Highest value in each row is bolded. In this work we presented DIORA, a completely unsupervised method for inducing syntactic trees and segmentations over text. We showed that an auto encoder language modeling objective on top of inside-outside representations of latent tree chart parsers allows us to effectively learn syntactic Third-quarter shipments slipped 7 % from the year-ago period and 17 % from this year 's second quarter Third-quarter shipments slipped 7 % from the year-ago period and 17 % from this year 's second quarter Mr. Hoelzer did n't return phone calls seeking comment on the judge 's decision Mr. Hoelzer did n't return phone calls seeking comment on the judge 's decisionThe earthquake caused many streets to buckle and crack making them impassibleThe earthquake caused many streets to buckle and crack making them impassible Figure 3 : Pairs of example parses for the same sentence from two different models. For each pair, the top is the output of PRPN-LM and bottom was produced by DIORA. Bolden token pairs or spans indicate a parse error by PRPN that was correctly attached by DIORA. Some punctuation was removed for clarity of printed trees. structure of language. In experiments on unsupervised parsing, chunking, and phrase representations we show our model is comparable to or outperforms current baselines, achieving the state-of-the-art performance on unsupervised parsing for the WSJ dataset. .Future work can improve the current method by training larger models over much larger corpora including other domains and languages. While the current model seems to focus primarily on syntax, extra unsupervised objectives or light supervision could be injected into the learning procedure to encourage a more thorough capturing of semantics.",1699,0.929,978,1.7372188139059306,"Syntax is language understanding Many downstream tasks segmenting input text meaningful constituent chunks entities more models learning text benefit integrating syntax in parse trees Supervised parsers have traditionally obtain these trees lately interest induce syntactic representations directly To this end propose the deep inside-outside recursive autoencoderDIORA discovering syntax that simultaneously representations constituents within the induced tree Unlike many prior approaches DIORA supervision auxiliary downstream tasks thus constrained particular domains Furthermore competing approaches do learn explicit phrase representations along tree structures limits phrase-based tasks Extensive experiments unsupervised parsing phrase demonstrate our method DIORA achieves the state parsing (46.9 F1 on the benchmark WSJ dataset Syntax in parse trees Constituent spans taken a parse tree are useful tasks relation extraction BID0 semantic role labeling while the full parse itself build higher-quality systems machine translation ) text Supervised parsers trained datasets the Penn Treebank BID4 traditionally obtain these trees; generally small restricted the newswire domain For outdomain applications generally new treebanks syntactic annotation expensiveMotivated extracts both shallow parses noun phrases entities any domain or automatically without any training data In addition just producing the parse want our model build representations internal constituents obey then easily inject downstream tasks Our model extends existing work latent tree chart build representations all internal nodes (cells generated a soft weighting over all possible subSection 2).In previous work the representation at a sentence encoding trained optimize some downstream task typically natural language inference Unfortunately , requires sentence level annotations train Worse analysis the trees learned these models show actually poor capturing syntax in linguistic theory BID9 . To address incorporate the inside-outside algorithm BID10 BID11 ) a latent tree chart parser The bottom-up inside step equivalent the forward-pass of previous latent tree chart parsers BID7 . However these inside representations encoded looking only within completely outside context Thus perform an additional top-down outside calculation incorporating external context into sub-tree representations Finally train This news raised hopes further interest-rate cuts .This news .Figure 1: Example parse trees Top PRPN-LM prediction bottom DIORA prediction DIORA correctly chunks the span 'raised hopes further interest-rate cuts the outside representations leaves to reconstruct the initial input resultsRecently BID12 proposed Parsing-Reading-Predict Networks an RNN based language model an additional module After training this syntax module decomposed recover a parse BID13 ) via a complex mechanism involves modeling a distribution possible syntactic structures with a stick-breaking process Like DIORA this model can trained However no mechanism explicitly modeling phrases span representations generated Additionally finding the most probable tree DIORA much in PRPN run the CKY algorithmTo probe different properties our model experiments unsupervised parsing phrase representations DIORA sets the state unsupervised parsing on the WSJ dataset has a greater recall on a more constituent types PRPN demonstrates phrase representations Latent tree models perform particularly attachments at BID9 . To address incorporate (+PP in Table We see PRPN-UP DIORA benefit much from this heuristic This consistent qualitative analysis showing DIORA PRPN-UP incorrectly attach trailing punctuation much This heuristic simply attaches trailing regardless its predicted attachment We find extremely effective increasing state WSJ parsing results by over 3 absolute F1 pointsOn the MultiNLI dataset PRPN-LM without the PP heuristic DIORA Afterwards PRPN-UP surpasses DIORA However actually a gold standard evaluation and instead evaluates replicate a trained parser . Table 2 : Unsupervised Parsing. † indicates trained to optimize NLI taskWe the max unlabeled binary F1 across runs PRPN-UP 2 DIORA F1 calculated the parse trees BID13 all results the upper portion copied . +PP refers post-processing heuristic to remove trailing punctuation explained In Table the breakdown constituent recall across We see PRPN-UP the highest recall for the most common type noun-phrase drops in DIORA achieves the highest recall across the most types and is perform effectively verb-phrases However DIORA performs poorly relative PRPN at prepositional phrases Table 3 : Segment recall from WSJ seperated phrase type The 10 most frequent phrase types shown Highest value each row bolded In this work presented DIORA inducing syntactic trees segmentations over text We showed an auto encoder language modeling objective on top inside-outside representations latent tree chart parsers allows effectively learn syntactic Third-quarter shipments slipped 7 % 17 Third-quarter shipments Mr. Hoelzer did n't return the judge 's decision caused many streets buckle crack making them Figure : Pairs example parses For each pair the output PRPN-LM bottom was produced DIORA Bolden token pairs or spans indicate a parse error by PRPN that correctly attached DIORA Some punctuation was removed of printed trees structure language In experiments unsupervised parsing chunking phrase representations we our model comparable or current baselines achieving state on for the WSJ dataset .Future work can improve training larger models over much larger corpora including other domains languages While the current model seems focus syntax extra unsupervised objectives or light supervision could injected the learning procedure encourage a more thorough capturing semantics",0.01,0.5824479361793397
"Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is unrolled. But because the training procedure must be unrolled thousands of times, the meta-objective must be defined with an orders-of-magnitude shorter time horizon than is typical for neural net training. We show that such short-horizon meta-objectives cause a serious bias towards small step sizes, an effect we term short-horizon bias. We introduce a toy problem, a noisy quadratic cost function, on which we analyze short-horizon bias by deriving and comparing the optimal schedules for short and long time horizons. We then run meta-optimization experiments (both offline and online) on standard benchmark datasets, showing that meta-optimization chooses too small a learning rate by multiple orders of magnitude, even when run with a moderately long time horizon (100 steps) typical of work in the area. We believe short-horizon bias is a fundamental problem that needs to be addressed if meta-optimization is to scale to practical neural net training regimes. The learning rate is one of the most important and frustrating hyperparameters to tune in deep learning. Too small a value causes slow progress, while too large a value causes fluctuations or even divergence. While a fixed learning rate often works well for simpler problems, good performance on the ImageNet BID23 benchmark requires a carefully tuned schedule. A variety of decay schedules have been proposed for different architectures, including polynomial, exponential, staircase, etc. Learning rate decay is also required to achieve convergence guarantee for stochastic gradient methods under certain conditions BID2 . Clever learning rate heuristics have resulted in large improvements in training efficiency BID5 BID28 . A related hyperparameter is momentum; typically fixed to a reasonable value such as 0.9, careful tuning can also give significant performance gains BID29 . While optimizers such as Adam BID8 are often described as adapting coordinate-specific learning rates, in fact they also have global learning rate and momentum hyperparameters analogously to SGD, and tuning at least the learning rate can be important to good performance.In light of this, it is not surprising that there have been many attempts to adapt learning rates, either online during optimization BID26 BID25 , or offline by fitting a learning rate schedule BID16 . More ambitiously, others have attempted to learn an optimizer BID1 BID12 BID4 BID14 BID32 BID20 . All of these approaches are forms of meta-optimization, where one defines a meta-objective (typically the expected loss after some number of optimization steps) and tunes the hyperparameters to minimize this meta-objective. But because gradient-based meta-optimization can require thousands of updates, each of which unrolls the entire base-level optimization procedure, the meta-optimization is thousands of times more expensive than the baselevel optimization. Therefore, the meta-objective must be defined with a much smaller time horizon (e.g. hundreds of updates) than we are ordinarily interested in for large-scale optimization. The hope is that the learned hyperparameters or optimizer will generalize well to much longer time horizons. Unfortunately, we show that this is not achieved in this paper. This is because of a strong tradeoff between short-term and long-term performance, which we refer to as short-horizon bias. In this work, we investigate the short-horizon bias both mathematically and empirically. First, we analyze a quadratic cost function with noisy gradients based on BID25 . We consider this a good proxy for neural net training because secondorder optimization algorithms have been shown to train neural networks in orders-of-magnitude fewer iterations BID17 , suggesting that much of the difficulty of SGD training can be explained by quadratic approximations to the cost. In our noisy quadratic problem, the dynamics of SGD with momentum can be analyzed exactly, allowing us to derive the greedy-optimal (i.e. 1-step horizon) learning rate and momentum in closed form, as well as to (locally) minimize the long-horizon loss using gradient descent. We analyze the differences between the short-horizon and long-horizon schedules.Interestingly, when the noisy quadratic problem is either deterministic or spherical, greedy schedules are optimal. However, when the problem is both stochastic and badly conditioned (as is most neural net training), the greedy schedules decay the learning rate far too quickly, leading to slow convergence towards the optimum. This is because reducing the learning rate dampens the fluctuations along high curvature directions, giving it a large immediate reduction in loss. But this comes at the expense of long-run performance, because the optimizer fails to make progress along low curvature directions. This phenomenon is illustrated in FIG0 , a noisy quadratic problem in 2 dimensions, in which two learning rate schedule are compared: a small fixed learning rate (blue), versus a larger fixed learning rate (red) followed by exponential decay (yellow). The latter schedule initially has higher loss, but it makes more progress towards the optimum, such that it achieves an even smaller loss once the learning rate is decayed. Figure 2 shows this effect quantitatively for a noisy quadratic problem in 1000 dimensions (defined in Section 2.3). The solid lines show the loss after various numbers of steps of lookahead with a fixed learning rate; if this is used as the meta-objective, it favors small learning rates. The dashed curves show the loss if the same trajectories are followed by 50 steps with an exponentially decayed learning rate; these curves favor higher learning rates, and bear little obvious relationship to the solid ones. This illustrates the difficulty of selecting learning rates based on short-horizon information. In this paper, we analyzed the problem of short-horizon bias in meta-optimization. We presented a noisy quadratic toy problem which we analyzed mathematically, and observed that the optimal learning rate schedule differs greatly from a greedy schedule that minimizes training loss one step ahead. While the greedy schedule tends to decay the learning rate drastically to reduce the loss on high curvature directions, the optimal schedule keeps a high learning rate in order to make steady progress on low curvature directions, and eventually achieves far lower loss. We showed that this bias stems from the combination of stochasticity and ill-conditioning: when the problem is either deterministic or spherical, the greedy learning rate schedule is globally optimal; however, when the problem is both stochastic and ill-conditioned (as is most neural net training), the greedy schedule performs poorly. We empirially verified the short-horizon bias in the context of neural net training by applying gradient based meta-optimization, both offline and online. We found the same pathological behaviors as in the noisy quadratic problem -a fast learning rate decay and poor long-run performance.While our results suggest that meta-optimization should not be applied blindly, our noisy quadratic analysis also provides grounds for optimism: by removing ill-conditioning (by using a good preconditioner) and/or stochasticity (with large batch sizes or variance reduction techniques), it may be possible to enter the regime where short-horizon meta-optimization works well. It remains to be seen whether this is achievable with existing optimization algorithms.We calculate the mean of the parameter θ (t+1) , DISPLAYFORM0 Let's assume the following initial conditions: DISPLAYFORM1 Then Eq.(10) and Eq.(11) describes how E θ (t) , E v (t) changes over time t.",1505,0.742,867,1.7358708189158016,"Careful tuning the learning rate or even schedules thereof crucial effective neural net training There much recent interest gradient-based meta-optimization where one tunes even learns minimize the expected loss when the training procedure unrolled But because the training procedure must unrolled thousands the meta-objective must defined with orders shorter time neural net training We show such short-horizon meta-objectives cause a serious bias small step sizes an effect term We introduce a toy problem a noisy quadratic cost function on analyze short-horizon bias by deriving and comparing the optimal schedules We then run meta-optimization experiments (both offline standard benchmark datasets showing chooses too small a learning rate by multiple orders even run a moderately long time horizon100 steps typical work We believe short-horizon bias if meta-optimization scale practical neural net training regimes The learning rate one tune deep learning Too small a value causes slow progress while fluctuations or even divergence While a fixed learning rate often works simpler problems good performance the ImageNet BID23 benchmark requires a carefully tuned schedule A variety decay schedules different architectures staircase etc Learning rate decay also required achieve convergence guarantee under BID2 . Clever learning rate heuristics have resulted large improvements training efficiency BID5 BID28 . A related hyperparameter momentum; typically fixed such careful tuning also give significant BID29 . While optimizers such Adam BID8 described adapting coordinate-specific learning rates in also global learning rate momentum hyperparameters analogously SGD tuning can important good performanceIn light there adapt either online during optimization BID26 BID25 by fitting BID16 More ambitiously others attempted learn an optimizer BID1 . All these approaches forms definestypically the expected loss after some number tunes minimize But because gradient-based meta-optimization can require thousands updates each unrolls the entire base-level optimization procedure thousands the baselevel optimization Therefore the meta-objective must a much smaller time horizon updates we ordinarily for The hope the learned hyperparameters or optimizer generalize well much longer time horizons Unfortunately show achieved this paper This because a strong tradeoff refer as short-horizon bias In this work investigate the short-horizon bias both mathematically First analyze noisy gradients based BID25 . We consider good proxy neural net training because secondorder optimization algorithms train orders- fewer iterations BID17 , suggesting much SGD training to the cost. In our noisy quadratic problem the dynamics SGD with momentum can analyzed exactly allowing derive the greedy-optimal (i.e. 1-step horizon learning momentum closed form (locally minimize using We analyzeInterestingly when the noisy quadratic problem either deterministic spherical greedy schedules optimal However when the problem both stochastic badly conditioned most neural net training the greedy schedules decay the learning rate far slow convergence towards This because reducing the learning rate dampens the fluctuations along high curvature directions giving a large immediate reduction loss But this comes long-run performance because the optimizer fails make progress along low curvature directions This phenomenon illustrated FIG0 , a noisy quadratic problem 2 dimensions two learning rate schedule are compared:blue versus followed The latter schedule initially has higher loss, makes more progress optimum, such achieves once the learning rate decayed Figure this effect quantitatively for a noisy quadratic problem 1000 dimensionsdefined Section The solid lines show the loss after various numbers steps of lookahead with a fixed learning rate; if this used the meta-objective favors The dashed curves show the loss if the same trajectories 50 steps with an exponentially decayed learning rate; favor bear little obvious relationship the solid ones This illustrates selecting learning rates short-horizon information In this paper analyzed the problem short-horizon bias meta-optimization We presented a noisy quadratic toy problem which analyzed mathematically observed the optimal learning rate schedule differs greatly a greedy schedule that training loss one While the greedy schedule tends decay the learning rate drastically to reduce the loss on high curvature directions keeps in order make steady progress eventually achieves far lower loss We showed this bias stems the combination ill-conditioning: the problem either spherical the greedy learning rate schedule globally; however both most neural net training performs We empirially verified the short-horizon bias the context neural net training applying gradient based, both offline We found the same pathological behaviors the noisy quadratic problem -a fast learning rate decayWhile meta-optimization should blindly also provides grounds optimism: by removing ill-conditioning (bywith large batch sizes or variance reduction techniques enter the regime works It remains achievable existing optimization algorithmsWe calculatet+1 , DISPLAYFORM0 Let the following initial conditions Then Eq.(10 describes E � , v changes t.",0.01,0.579013363378036
"Mainstream captioning models often follow a sequential structure to generate cap-
 tions, leading to issues such as introduction of irrelevant semantics, lack of diversity
 in the generated captions, and inadequate generalization performance. In this paper,
 we present an alternative paradigm for image captioning, which factorizes the
 captioning procedure into two stages: (1) extracting an explicit semantic represen-
 tation from the given image; and (2) constructing the caption based on a recursive
 compositional procedure in a bottom-up manner. Compared to conventional ones,
 our paradigm better preserves the semantic content through an explicit factorization
 of semantics and syntax. By using the compositional generation procedure, caption
 construction follows a recursive structure, which naturally fits the properties of
 human language. Moreover, the proposed compositional procedure requires less
 data to train, generalizes better, and yields more diverse captions. Image captioning, the task to generate short descriptions for given images, has received increasing attention in recent years. State-of-the-art models BID0 BID1 BID2 BID3 mostly adopt the encoder-decoder paradigm BID2 , where the content of the given image is first encoded via a convolutional network into a feature vector, which is then decoded into a caption via a recurrent network. In particular, the words in the caption are produced in a sequential manner -the choice of each word depends on both the preceding word and the image feature. Despite its simplicity and the effectiveness shown on various benchmarks BID4 BID5 , the sequential model has a fundamental problem. Specifically, it could not reflect the inherent hierarchical structures of natural languages BID6 BID7 in image captioning and other generation tasks, although it could implicitly capture such structures in tasks taking the complete sentences as input, e.g. parsing BID8 , and classification BID9 .As a result, sequential models have several significant drawbacks. First , they rely excessively on n-gram statistics rather than hierarchical dependencies among words in a caption. Second , such models usually favor the frequent n-grams BID10 in the training set, which, as shown in Figure 1 , may lead to captions that are only correct syntactically but not semantically, containing semantic concepts that are irrelevant to the conditioned image. Third , the entanglement of syntactic rules and semantics obscures the dependency structure and makes sequential models difficult to generalize.To tackle these issues, we propose a new paradigm for image captioning, where the extraction of semantics (i.e. what to say) and the construction of syntactically correct captions (i.e. how to say) are decomposed into two stages. Specifically , it derives an explicit representation of the semantic content of the given image, which comprises a set of noun-phrases, e.g. a white cat, a cloudy sky or two men. With these noun-phrases as the basis, it then proceeds to construct the caption through recursive composition until a complete caption is obtained. In particular , at each step of the composition, a higher-level phrase is formed by joining two selected sub-phrases via a connecting phrase. It is Preprint . Work in progress.a large building with a clock tower a building with a clock on the side of it a building with a clock on the side of it Figure 1 : This figure shows three test images in MS-COCO BID4 with captions generated by the neural image captioner BID2 , which contain n-gram building with a clock that appeared frequently in the training set but is not semantically correct for these images.noteworthy that the compositional procedure described above is not a hand-crafted algorithm. Instead, it consists of two parametric modular nets, a connecting module for phrase composition and an evaluation module for deciding the completeness of phrases.The proposed paradigm has several key advantages compared to conventional captioning models: BID0 The factorization of semantics and syntax not only better preserves the semantic content of the given image but also makes caption generation easy to interpret and control. (2) The recursive composition procedure naturally reflects the inherent structures of natural language and allows the hierarchical dependencies among words and phrases to be captured. Through a series of ablative studies, we show that the proposed paradigm can effectively increase the diversity of the generated captions while preserving semantic correctness. It also generalizes better to new data and can maintain reasonably good performance when the number of available training data is small. In this paper, we propose a novel paradigm for image captioning. While the typical existing approaches encode images using feature vectors and generate captions sequentially, the proposed method generates captions in a compositional manner. In particular, our approach factorizes the captioning procedure into two stages. In the first stage, an explicit representation of the input image, consisting of noun-phrases, is extracted. In the second stage, a recursive compositional procedure is applied to assemble extracted noun-phrases into a caption. As a result, caption generation follows a hierarchical structure, which naturally fits the properties of human language. On two datasets, the proposed compositional procedure is shown to preserve semantics more effectively, require less data to train, generalize better across datasets, and yield more diverse captions.",1035,0.501,595,1.7394957983193278,"Mainstream captioning models often follow a sequential structure generate cap- tions leading issues introduction irrelevant semantics lack diversity the generated captions inadequate generalization performance In an alternative paradigm image captioning factorizes two stages extracting an explicit semantic represen- tation constructing based a recursive compositional procedure in Compared conventional ones our paradigm better preserves the semantic content through an explicit factorization semantics syntax By using the compositional generation procedure caption construction follows naturally fits human language Moreover the proposed compositional procedure requires less data train generalizes better yields more diverse captions Image captioning, the task to generate short descriptions given images received. State models BID0 mostly adopt , where the content the given image first via into a feature vector a caption via In particular the words in produced -the choice depends both the preceding word the image feature Despite its simplicity the effectiveness shown on various benchmarks BID4 , the sequential model a fundamental problem Specifically could not reflect the inherent hierarchical structures natural languages BID6 BID7 in image other generation tasks although implicitly capture tasks taking the complete sentences parsing , classification .As sequential models have several significant drawbacks First , they rely excessively n-gram statistics rather hierarchical dependencies among words a caption Second , such models usually favor the frequent n-grams BID10 in the training set, may captions only correct but containing semantic concepts irrelevant the conditioned image Third , the entanglement syntactic rules obscures the dependency structure makes sequential modelsTo tackle image captioning the extraction semantics ( what to decomposed two stages Specifically , derives an explicit representation the given image comprises a cloudy sky two men With these noun-phrases as then proceeds construct the caption through recursive composition until a complete caption obtained In particular , at each step the composition a higher-level phrase formed joining two selected sub via a connecting phrase It Preprint . Work progress.a large building a building on Figure : This figure three test images in MS-COCO BID4 with captions generated the neural image captioner BID2 , contain n-gram building with that appeared frequently but semantically correct these images.noteworthy that the compositional procedure described a hand-crafted algorithm Instead consists two parametric modular nets a connecting module phrase composition deciding phrasesThe proposed paradigm has compared conventional captioning models BID0 The factorization semantics syntax not better preserves the given image caption generation interpret control (2) The recursive composition procedure naturally reflects the inherent structures natural language allows the hierarchical dependencies among words captured Through ablative studies show the proposed paradigm can effectively increase the diversity the generated captions while semantic correctness It also generalizes better new data can maintain reasonably good performance the number available training data In image captioning While the typical existing approaches encode images feature vectors generate sequentially generates In particular our approach factorizes the captioning procedure In an explicit representation the input image consisting noun-phrases extracted In the second stage a recursive compositional procedure assemble extracted noun-phrases a caption As caption generation follows naturally fits the properties human language On two datasets the proposed compositional procedure preserve semantics more require train generalize across yield more diverse captions",0.01,0.5882494924110125
"While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss. The practical successes of deep learning in various fields such as image processing BID34 BID18 BID21 , biomedicine BID9 BID29 BID28 , and language translation BID2 BID41 still outpace our theoretical understanding. While hyperparameter adjustment strategies exist BID3 , formal measures for assessing the generalization capabilities of deep neural networks have yet to be identified BID44 . Previous approaches for improving theoretical and practical comprehension focus on interrogating networks with input data. These methods include i) feature visualization of deep convolutional neural networks BID43 BID36 , ii) sensitivity and relevance analysis of features BID25 , iii) a descriptive analysis of the training process based on information theory BID39 BID33 BID32 BID1 , and iv) a statistical analysis of interactions of the learned weights BID40 . Additionally, BID27 develop a measure of expressivity of a neural network and use it to explore the empirical success of batch normalization, as well as for the definition of a new regularization method. They note that one key challenge remains, namely to provide meaningful insights while maintaining theoretical generality. This paper presents a method for elucidating neural networks in light of both aspects.We develop neural persistence, a novel measure for characterizing neural network structural complexity. In doing so, we adopt a new perspective that integrates both network weights and connectivity while not relying on interrogating networks through input data. Neural persistence builds on computational techniques from algebraic topology, specifically topological data analysis (TDA), which was already shown to be beneficial for feature extraction in deep learning BID19 and describing the complexity of GAN sample spaces BID23 . More precisely, we rephrase deep networks with fully-connected layers into the language of algebraic topology and develop a measure for assessing the structural complexity of i) individual layers, and ii) the entire network. In this work, we present the following contributions: -We introduce neural persistence, a novel measure for characterizing the structural complexity of neural networks that can be efficiently computed. -We prove its theoretical properties, such as upper and lower bounds, thereby arriving at a normalization for comparing neural networks of varying sizes. -We demonstrate the practical utility of neural persistence in two scenarios: i) it correctly captures the benefits of dropout and batch normalization during the training process, and ii) it can be easily used as a competitive early stopping criterion that does not require validation data. In this work, we presented neural persistence, a novel topological measure of the structural complexity of deep neural networks. We showed that this measure captures topological information that pertains to deep learning performance. Being rooted in a rich body of research, our measure is theoretically well-defined and, in contrast to previous work, generally applicable as well as computationally efficient. We showed that our measure correctly identifies networks that employ best practices such as dropout and batch normalization. Moreover, we developed an early stopping criterion that exhibits competitive performance while not relying on a separate validation data set. Thus, by saving valuable data for training, we managed to boost accuracy, which can be crucial for enabling deep learning in regimes of smaller sample sizes. Following Theorem 2, we also experimented with using the p-norm of all weights of the neural network as a proxy for neural persistence. However, this did not yield an early stopping measure because it was never triggered, thereby suggesting that neural persistence captures salient information that would otherwise be hidden among all the weights of a network. We extended our framework to convolutional neural networks (see Section A.4) by deriving a closed-form approximation, and observed that an early stopping criterion based on neural persistence for convolutional layers will require additional work. Furthermore, we conjecture that assessing dissimilarities of networks by means of persistence diagrams (making use of higher-dimensional topological features), for example, will lead to further insights regarding their generalization and learning abilities. Another interesting avenue for future research would concern the analysis of the 'function space' learned by a neural network. On a more general level, neural persistence demonstrates the great potential of topological data analysis in machine learning.",937,0.512,527,1.777988614800759,"While many approaches make neural networks fathomable they restricted interrogating with Measures for characterizing monitoring structural properties, however In this work propose neural persistence a complexity measure based topological data analysis on weighted stratified graphs To demonstrate our approach show neural persistence reflects best practices developed such dropout batch normalization Moreover we derive a neural persistence-based stopping criterion shortens while achieving as early stopping based validation loss The practical successes deep learning image BID34 BID18 BID21 , language translation still outpace While hyperparameter adjustment strategies exist BID3 , formal measures assessing the generalization capabilities identified BID44 Previous approaches for improving theoretical and practical comprehension focus interrogating networks These methods include i feature visualization BID43 BID36 , ii sensitivity relevance features a descriptive analysis the training process based information theory interactions the learned weights Additionally BID27 develop a measure expressivity use explore the empirical success batch normalization as for the definition a new regularization method They note one key challenge remains to provide meaningful insights while theoretical generality This paper neural networks light both aspects.We develop neural persistence, a novel measure In doing adopt integrates both network weights connectivity while not relying interrogating networks through input data Neural persistence builds computational techniques specifically topological data analysis was already shown beneficial feature extraction deep learning BID19 describing the complexity GAN sample spaces BID23 . More precisely rephrase deep networks fully-connected layers into the language develop a measure assessing i) individual In this work the following contributions -We neural persistence a novel measure characterizing the structural complexity that efficiently computed -We prove its theoretical properties such upper and lower bounds thereby arriving a normalization comparing neural networks -We demonstrate neural persistence two scenarios i it correctly captures the benefits dropout batch normalization during easily a competitive early stopping criterion that does validation data In this work presented neural persistence a novel topological measure We showed this measure captures topological information pertains deep learning performance Being rooted a rich body our measure theoretically well, contrast previous work generally applicable as computationally We showed our measure correctly identifies networks employ best practices dropout batch normalization Moreover we developed an early stopping criterion exhibits competitive performance while not relying separate validation data Thus by saving valuable data training managed boost accuracy which crucial enabling regimes smaller sample sizes Following Theorem also experimented using the p-norm all weights neural persistence However did yield an early stopping measure because never triggered thereby suggesting neural persistence captures salient information among all the weights We extended our frameworksee deriving a closed-form approximation, observed an early stopping criterion based neural persistence for will require additional work Furthermore conjecture assessing dissimilarities networks persistence diagramsmaking higher-dimensional topological features for further insights regarding their generalization learning abilities Another interesting avenue would concern the analysis the 'function space learned On neural persistence demonstrates topological data analysis",0.01,0.6863258068638218
"Deep neural networks (DNNs) are vulnerable to adversarial examples, which are carefully crafted instances aiming to cause prediction errors for DNNs. Recent research on adversarial examples has examined local neighborhoods in the input space of DNN models. However, previous work has limited what regions to consider, focusing either on low-dimensional subspaces or small balls. In this paper, we argue that information from larger neighborhoods, such as from more directions and from greater distances, will better characterize the relationship between adversarial examples and the DNN models. First, we introduce an attack, OPTMARGIN, which generates adversarial examples robust to small perturbations. These examples successfully evade a defense that only considers a small ball around an input instance. Second, we analyze a larger neighborhood around input instances by looking at properties of surrounding decision boundaries, namely the distances to the boundaries and the adjacent classes. We find that the boundaries around these adversarial examples do not resemble the boundaries around benign examples. Finally, we show that, under scrutiny of the surrounding decision boundaries, our OPTMARGIN examples do not convincingly mimic benign examples. Although our experiments are limited to a few specific attacks, we hope these findings will motivate new, more evasive attacks and ultimately, effective defenses. Recent research in adversarial examples in deep learning has examined local neighborhoods in the input space of deep learning models. BID9 and BID15 examine limited regions around benign samples to study why some adversarial examples transfer across different models. BID10 explore regions around benign samples to validate the robustness of an adversarially trained model. BID14 examine regions around adversarial examples to estimate the examples' robustness to random noise. BID0 determine that considering the region around an input instance produces more robust classification than looking at the input instance alone as a single point. In this paper, we argue that information from larger neighborhoods-both in more directions and at greater distances-will better help us understand adversarial examples in high-dimensional datasets.First, we describe a concrete limitation in a system that utilizes information in small neighborhoods. Cao & Gong's region classification defense (2017) takes the majority prediction in a small ball around an input instance. We introduce an attack method, OPTMARGIN, for generating adversarial examples that are robust to small perturbations, which can evade this defense.Second, we provide an example of how to analyze an input instance's surroundings in the model's input space. We introduce a technique that looks at the decision boundaries around an input instance, and we use this technique to characterize our robust OPTMARGIN adversarial examples. Our analysis reveals that, while OPTMARGIN adversarial examples are robust enough to fool region classification, the decision boundaries around them do not resemble the boundaries around benign examples, in terms of distances from the example to the adjacent classes.Third, as an extension to the above observation, we train a classifier to differentiate the decision boundary information that comes from different types of input instances. We show that our classifier can differentiate OPTMARGIN and benign examples with 90.4% accuracy, whereas region classification limits itself to a small region and fails. However, it remains to be seen whether a more sophisticated attack can find adversarial examples surrounded by decision boundaries that more accurately mimic the boundaries around benign examples.To summarize, our contributions are:1. We demonstrate OPTMARGIN, a new attack that evades region classification systems with low-distortion adversarial examples.2. We introduce an analysis of decision boundaries around an input instance that explains the effectiveness of OPTMARGIN adversarial examples and also shows the attack's weaknesses.3. We demonstrate the expressiveness of decision boundary information by using it to classify different kinds of input instances.We have released the code we used at https://github.com/sunblaze-ucb/ decision-boundaries. We considered the benefits of examining large neighborhoods around a given input in input space. We demonstrated an effective OPTMARGIN attack against a region classification defense, which only considered a small ball of the input space around a given instance. We analyzed the neighborhood of examples generated by this new attack by looking at the decision boundaries around them, as well as the boundaries around benign examples and less robust adversarial examples. This analysis incorporated information from many directions in input space and from longer distances than previous work. We found that the comprehensive information about surrounding decision boundaries reveals there are still differences between our robust adversarial examples and benign examples.",886,0.462,525,1.6876190476190476,"Deep neural networks vulnerable adversarial examples carefully crafted instances aiming cause prediction errors for Recent research examined local neighborhoods the input space However previous work limited what regions to consider focusing either low-dimensional subspaces small balls In information larger neighborhoods from more directions will better characterize adversarial examples the DNN models First introduce an attack, OPTMARGIN generates adversarial examples robust These examples successfully evade a defense only considers a small ball around an input instance Second analyze a larger neighborhood around input instances by properties surrounding decision boundaries namely the distances the adjacent classes We find the boundaries around these adversarial examples do resemble benign examples Finally show under scrutiny the surrounding decision boundaries our OPTMARGIN examples convincingly mimic benign examples Although our experiments a few specific attacks motivate ultimately, effective defenses Recent research adversarial examples in examined local neighborhoods the input space BID9 and BID15 examine limited regions around benign samples to study why some adversarial examples transfer different models BID10 explore regions around benign samples validate an adversarially trained model BID14 examine regions around adversarial examples estimate the examples' robustness random noise BID0 determine that considering the region around an input instance produces more robust classification looking as In information larger neighborhoods-both more directions better help adversarial examplesFirst a concrete limitation a system utilizes Cao & Gong's region classification defense2017 takes the majority prediction a small ball around an input instance We introduce an attack method OPTMARGIN generating adversarial examples robust evade this defenseSecond analyze an input instance's surroundings the model's input space We introduce a technique looks the decision boundaries around an input instance we characterize our robust OPTMARGIN adversarial examples Our analysis OPTMARGIN adversarial examples robust fool region classification the decision boundaries around resemble benign examples in terms distances the example the adjacent classesThird as an extension train differentiate the decision boundary information comes input instances We show our classifier differentiate OPTMARGIN benign examples region classification limits itself fails. However remains a more sophisticated attack find adversarial examples surrounded decision boundaries more mimic the boundaries around benign examplesTo summarize, our contributions We demonstrate OPTMARGIN evades region classification systems with low-distortion adversarial examples.2. introduce an analysis decision boundaries around an input instance explains also the expressiveness decision boundary information it classifyWe have released we at We considered examining large neighborhoods around a given input input space We demonstrated an effective OPTMARGIN attack a region classification defense, only considered a small ball the input space around a given instance We analyzed the neighborhood examples generated this new attack the decision boundaries them benign examples less robust adversarial examples This analysis incorporated many directions input space longer distances than We found the comprehensive information surrounding decision boundaries reveals there still differences our robust adversarial examples benign examples",0.01,0.45607208946817934
"Machine learning models are usually tuned by nesting optimization of model weights inside the optimization of hyperparameters.   We give a method to collapse this nested optimization into joint stochastic optimization of both weights and hyperparameters.   Our method trains a neural network to output approximately optimal weights as a function of hyperparameters.   We show that our method converges to locally optimal weights and hyperparameters for sufficiently large hypernets.   We compare this method to standard hyperparameter optimization strategies and demonstrate its effectiveness for tuning thousands of hyperparameters. Hyperparameter λ Training and validation loss of a neural net, estimated by crossvalidation (crosses) or by a hypernet (lines), which outputs 7, 850-dimensional network weights. The training and validation loss can be cheaply evaluated at any hyperparameter value using a hypernet. Standard cross-validation requires training from scratch each time.Model selection and hyperparameter tuning is a major bottleneck in designing predictive models. Hyperparameter optimization can be seen as a nested optimization: The inner optimization finds model parameters w which minimizes the training loss LTrain given hyperparameters λ. The outer optimization chooses λ to minimize a validation loss LValid. : DISPLAYFORM0 Standard practice in machine learning solves (1) by gradient-free optimization of hyperparameters, such as grid search, random search, or Bayesian optimization. Each set of hyperparameters is evaluated by reinitializing weights and training the model to completion. This is wasteful, since it trains the model from scratch each time, even if the hyperparameters change a small amount. Hyperband BID14 and freezethaw Bayesian optimization (Swersky et al., 2014 ) resume model training and do not waste this effort. Furthermore, gradient-free optimization scales poorly beyond 10 or 20 dimensions.How can we avoid re-training from scratch each time?We usually estimate the parameters with stochastic optimization, but the true optimal parameters are a deterministic function of the hyperparameters λ: DISPLAYFORM1 We propose to learn this function. Specifically , we train a neural network with inputs of hyperparameters, and outputs of an approximately optimal set of weights given the hyperparameters.This provides two major benefits: First, we can train the hypernet to convergence using stochastic gradient descent, denoted SGD, without training any particular model to completion. Second, differentiating through the hypernet allows us to optimize hyperparameters with gradient-based stochastic optimization.P a ra m e te r w H y p e r p a r a m e t e r λ Loss L Train (w, In this paper, we:• Presented algorithms that efficiently learn a differentiable approximation to a best-response without nested optimization.• Showed empirically that hypernets can provide a better inductive bias for hyperparameter optimization than Gaussian processes fit directly to the validation loss.• Gave a theoretical justification that sufficiently large networks will learn the best-response for all hyperparameters it is trained against.We hope that this initial exploration of stochastic hyperparameter optimization will inspire further refinements, such as hyper-regularization methods, or uncertainty-aware exploration using Bayesian hypernetworks. A EXTRA EXPERIMENTS A.1 OPTIMIZING 10 HYPERPARAMETERS Here, we optimize a model with 10 hyperparameters, in which a separate L 2 weight decay is applied to the weights for each digit class in a linear regression model to see if we can optimize medium-sized models. The conditional hyperparameter distribution and optimizer for the hypernet and hyperparameters is the same the prior experiments. A linear hypernet is used, resulting in 86, 350 hyper-weights. Algorithm 3 is compared against random search and .Figure 8, right, shows that our method converges more quickly and to a better optimum than either alternative method, demonstrating that medium-sized hyperparameter optimization problems can be solved with Algorithm 3. Figure 8 : Validation and test losses during hyperparameter optimization. A separate L 2 weight decay is applied to the weights of each digit class, resulting in 10 hyperparameters. The weights w φ * are output by the hypernet for current hyperparameterλ, while random losses are for the best result of a random search. Hypernetwork-based optimization converges faster than random search or Bayesian optimization. We also observe significant overfitting of the hyperparameters on the validation set, which may be reduced be introducing hyperhyperparameters (parameters of the hyperparameter prior). The runtime includes the inner optimization for gradient-free approaches so that equal cumulative computational time is compared for each method.Factors affecting this include removing the overhead of constructing tuples of hyperparameters and optimized weights, viewing more hyperparameter samples, or having a better inductive bias from learning weights.",936,0.471,553,1.6925858951175408,"Machine learning models usually tuned nesting optimization of model weights inside of We give a method collapse this nested optimization joint stochastic optimization both weights Our method trains output approximately optimal weights as We show our method converges locally optimal weights sufficiently large hypernets We compare this method standard hyperparameter optimization strategies demonstrate tuning thousands Hyperparameter �� Training validation loss estimated crossvalidation (crosses or a hypernetlines which outputs 7 850-dimensional network weights The training and validation loss can cheaply evaluated any hyperparameter value a hypernet Standard cross requires training scratch eachModel selection designing Hyperparameter optimization seen a nested optimization: The inner optimization finds model parameters w which LTrain given The outer optimization chooses �� minimize a validation loss LValid : DISPLAYFORM0 Standard practice in machine learning solves ( by gradient-free optimization such grid search random search Each set hyperparameters evaluated reinitializing weights training completion This wasteful since trains the model from each even change Hyperband BID14 and freezethaw Bayesian optimizationSwersky ) resume model training do waste this effort Furthermore gradient-free optimization scales poorly beyond 10 or 20 dimensionsHow retraining from scratch each usually estimate the true optimal parameters a deterministic function: DISPLAYFORM1 We propose learn. Specifically , train inputs outputs an approximately optimal set givenThis provides the hypernet convergence using denoted SGD without to completion Second differentiating through the hypernet allows optimize hyperparametersP a ra m te w H y � Loss L Trainw In this paper we:• Presented algorithms efficiently learn a differentiable approximation a best-response without nested optimization.• Showed hypernets provide a better inductive bias processes fit directly the validation sufficiently large networks learn itWe this initial exploration, hyper-regularization methods uncertainty-aware exploration using Bayesian hypernetworks A EXTRA EXPERIMENTS A.1 10 HYPERPARAMETERS Here, optimize a model a separate L 2 weight decay each digit class see medium-sized models The conditional hyperparameter distribution and optimizer the hypernet and the same the prior experiments A linear hypernet used, resulting 86 350 hyperweights Algorithm 3 compared random search .Figure 8, right our method more to optimum either alternative method demonstrating that medium-sized hyperparameter optimization problems Algorithm Figure : Validation and test losses hyperparameter optimization A separate L 2 weight decay applied the weights each digit class 10 hyperparameters The weights w � * are output the hypernet for current hyperparameterλ random losses for the best result Hypernetwork-based optimization converges faster random search or Bayesian optimization We also observe significant overfitting on the validation set reduced be introducing hyperhyperparametersparameters prior The runtime includes the inner optimization gradient-free approaches so equal cumulative computational time compared forFactors affecting include removing constructing tuples optimized weights viewing more hyperparameter samples having a better inductive bias from learning weights",0.01,0.4687271805118902
"Estimating covariances between financial assets plays an important role in risk management. In practice, when the sample size is small compared to the number of variables, the empirical estimate is known to be very unstable. Here, we propose a novel covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM). Our estimator can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Furthermore, our Bayesian treatment naturally shrinks the sample covariance matrix towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. Finally, we discuss some financial applications of the GP-LVM model. Many financial problems require the estimation of covariance matrices between given assets. This may be useful to optimize one's portfolio, i.e.: maximize the portfolio returns w T r and/or minimize the volatility √ w T Kw. Indeed, Markowitz received a Noble Price in economics for his treatment of modern portfolio theory BID9 . In practice, estimating historical returns and high-dimensional covariance matrices is challenging and often times equally weighted portfolio outperforms the portfolio constructed from sample estimates BID6 . The estimation of covariance matrices is especially hard, when the number of assets is large compared to the number of observations. Sample estimations in those cases are very unstable or can even become singular. To cope with this problem, a wide range of estimators, e.g. factor models such as the single-index model BID16 or shrinkage estimators BID8 , have been developed and employed in portfolio optimization.With todays machine learning techniques we can even further improve those estimates. Machine learning has already arrived in finance. BID10 trained an agent via reinforcement learning to optimally execute trades. BID4 forecast asset prices with neural networks and BID1 with Gaussian Processes. Recently, BID5 made an ansatz to optimally allocate portfolios using deep autoencoders. BID21 used Gaussian Processes to build volatility models and BID20 to estimate time varying covariance matrices. Bayesian machine learning methods are used more and more in this domain. The fact, that in Bayesian framework parameters are not treated as true values, but as random variables, accounts for estimation uncertainties and can even alleviate the unwanted impacts of outliers. Furthermore, one can easily incorporate additional information and/or personal views by selecting suitable priors.In this paper, we propose a Bayesian covariance estimator based on the Gaussian Process Latent Variable Model (GP-LVM) BID7 , which can be considered as a non-linear extension of standard factor models with readily interpretable parameters reminiscent of market betas. Our Bayesian treatment naturally shrinks the sample covariance matrix (which maximizes the likelihood function) towards a more structured matrix given by the prior and thereby systematically reduces estimation errors. We evaluated our model on the stocks of S&P500 and found significant improvements in terms of model fit compared to classical linear models. Furthermore we suggest some financial applications, where Gaussian Processes can be used as well. That includes portfolio allocation, price prediction for less frequently traded stocks and non-linear clustering of stocks into their sub-sectors.In section 2 we begin with an introduction to the Bayesian non-parametric Gaussian Processes and discuss the associated requirements for learning. Section 3 introduces the financial background needed for portfolio optimization and how to relate it to Gaussian Processes. In section 4 we conduct experiments on covariance matrix estimations and discuss the results. We conclude in section 5. We applied the Gaussian Process Latent Variable Model (GP-LVM) to estimate the covariance matrix between different assets, given their time series. We then showed how the GP-LVM can be seen as a non-linear extension to the CAPM with latent factors. Based on the R 2 -score and the ELBO, we concluded, that for fixed latent space dimension Q, every non-linear kernel can capture more structure than the linear one.The estimated covariance matrix helps us to build a minimal risk portfolio according to Markowitz Portfolio theory. We evaluated the performance of different models on the S&P500 from year 2008 to 2018. Again, non-linear kernels had lower risk in the suggested portfolio and higher Sharpe ratios than the linear kernel and the baseline measures. Furthermore, we showed how to use the GP-LVM to fill in missing prices of less frequently traded assets and we discussed the role of the latent positions of the assets. In the future, one could also put a Gaussian Process on the latent positions and allow them to vary in time, which would lead to a time-dependent covariance matrix.",898,0.544,499,1.7995991983967936,"Estimating covariances between financial assets plays risk management In practice when compared variables the empirical estimate known unstable Here propose Our estimator can considered standard factor models readily interpretable parameters reminiscent market betas Furthermore our Bayesian treatment naturally shrinks towards given by prior and thereby systematically estimation errors Finally discuss some financial applications the GP-LVM model Many financial problems require the estimation covariance matrices between given assets This may useful optimize maximize returns w T r minimize the volatility �� w T Kw Indeed Markowitz received a Noble Price in economics modern portfolio theory BID9 . In practice estimating historical returns and challenging times equally weighted portfolio outperforms constructed sample BID6 The estimation especially hard when assets compared observations Sample estimations in those cases very unstable or can even become singular To cope estimators factor models such BID16 shrinkage estimators employed portfolio optimizationWith todays machine we even further those estimates Machine learning already arrived finance BID10 trained an agent via reinforcement learning optimally execute trades BID4 forecast asset prices with neural networks with Recently BID5 made an ansatz to optimally allocate portfolios BID21 used Gaussian Processes volatility models estimate time varying covariance matrices Bayesian machine learning methods more this domain The fact, in Bayesian framework parameters treated true values but accounts estimation uncertainties even alleviate the unwanted impacts Furthermore one incorporate additional information personal views by selecting suitable priorsInGP-LVM) BID7 , considered standard factor models readily interpretable parameters reminiscent market betas Our Bayesian treatment naturally shrinks the sample covariance matrixwhich maximizes towards a more structured matrix given by prior and thereby systematically estimation errors We evaluated our model the stocks found significant improvements terms model fit compared classical linear models Furthermore we suggest some financial applications where Gaussian Processes That includes portfolio allocation price prediction for less frequently traded stocks non-linear clustering their subIn section begin the associated requirements learning Section introduces the financial background needed portfolio optimization how relate Gaussian Processes In section we conduct covariance matrix estimations discuss We conclude in section We applied the Gaussian Process Latent Variable Model estimate different assets given We then showed the GPLVM can seen the CAPM with latent factors Based the R 2 -score the ELBO, concluded, for fixed latent space dimension Q capture more structureThe estimated covariance matrix helps build a minimal risk portfolio according Markowitz Portfolio theory We evaluated different models from year 2008 2018 Again non-linear kernels had lower risk the suggested portfolio and higher Sharpe ratios the baseline measures Furthermore showed the GP-LVM fill missing prices less frequently traded assets we discussed the latent positions In one put a Gaussian Process the latent positions allow vary",0.01,0.7413876751814035
"We study how, in generative adversarial networks, variance in the discriminator's output affects the generator's ability to learn the data distribution. In particular, we contrast the results from various well-known techniques for training GANs when the discriminator is near-optimal and updated multiple times per update to the generator. As an alternative, we propose an additional method to train GANs by explicitly modeling the discriminator's output as a bi-modal Gaussian distribution over the real/fake indicator variables. In order to do this, we train the Gaussian classifier to match the target bi-modal distribution implicitly through meta-adversarial training. We observe that our new method, when trained together with a strong discriminator, provides meaningful, non-vanishing gradients. Generative adversarial networks BID7 are a framework for training a generator of some target (i.e., ""real"") distribution without explicitly defining a parametric generating distribution or a tractable likelihood function. Training the generator relies on a learning signal from a discriminator or discriminator, which is optimized on a relatively simple objective to distinguish between (i.e., classify) generated (i.e., ""fake"") and real samples. In order to match the true distribution, the generator parameters are optimized to maximize the loss as defined by the discriminator, which by analogy makes the generator and discriminator adversaries.In recent years, GANs have attained strong recognition as being able to generate high-quality images with sharp edges in comparison to maximum-likelihood estimation-based methods BID4 BID10 BID22 BID2 BID26 . Despite their recent successes, GANs can also be notoriously hard to train, suffering from collapse (i.e., mapping its noise to a very small set of singular outputs), missing modes of the real distribution BID3 , and vanishing and/or unstable gradients . In practice, successful learning is highly reliant on hyperparameter-tuning and model choice, and finding architectures that work with adversarial learning objectives with any / all of the above problems can be challenging BID20 .Many methods have been proposed to address learning difficulties associated with learning instability.• The use of autoencoders or posterior models in the generator or discriminator. These have been shown help to alleviate mode collapse or stabilize learning BID12 BID3 BID5 .• Regularizing the discriminator, such as with input noise , instance noise BID23 , and gradient norm regularization BID21 ).• Alternate difference measures, such as integral probability metrics (IPMs, Sriperumbudur et al., 2009 ) metrics. The most well-known of these use a dual formulation of the Wasserstein distance. These are implemented via either weight clipping or gradient penalty BID8 . These can yeild stable gradients, high-quality samples and work on a variety of architectures.On this last point, it is unclear whether the metric or the associated regularization used to impose Lipschitz is important, as regularization techniques have also been shown to be effective with stabilizing learning in f -divergences BID21 . In this paper, we study the integral role of variance in the discriminator's output in the regime of the generated distribution and how it ultimately affects learning. In the following sections , we describe theoretical motivations, an empirical analysis from multiple variants of GANs, and finally propose a regularization scheme to combat vanishing gradients on part of the discriminator when it is well-trained. In this paper, we have demonstrated the importance of intra-class variance in the discriminator's output. In particular, our results show that methods whose discriminators tend to map inputs of a class to single real values are unable to provide a reliable learning signal for the generator. Furthermore, variance in the discriminator's output is essential to allow the generator to learn in the presence of a well-trained discriminator. We proposed a technique, conceptually in line with LDA, which ensures the discriminator's output distribution follows a specified prior. Taking a broader perspective, we also introduced a new regularization technique called meta-adversarial learning, which can be applied to ensure enforce various desirable properties in GANs.",799,0.381,459,1.7407407407407407,"We study, generative adversarial networks variance learn the data distribution In particular contrast various well-known techniques training GANs when near-optimal and updated multiple times update the generator As an alternative propose train GANs by explicitly modeling the real/fake indicator variables In do train match bi-modal distribution implicitly through We observe our new method when trained together a strong discriminator provides meaningful, non-vanishing gradients Generative adversarial networks BID7 are a framework training a generator some target without explicitly a parametric generating distribution a tractable likelihood function Training the generator relies a learning signal or, optimized on a relatively simple objective to distinguish generated ( ""fake real samples In match the true distribution the generator parameters optimized maximize the loss as defined by analogy makes and discriminator adversariesIn GANs attained strong recognition being sharp edges comparison BID4 BID10 Despite GANs can also notoriously train suffering collapse ( mapping its noise singular outputs missing modes the real distribution BID3 vanishing and/or unstable gradients . In practice successful learning highly hyperparameter-tuning and model choice finding architectures adversarial learning objectives with any / BID20 .Many methods instability.• posterior models the generator or. These have shown help alleviate mode collapse or stabilize learning BID12 BID3 .• Regularizing the discriminator, such with input noise , instance noise BID23 gradient norm regularization ) Alternate difference measures integral probability metrics, Sriperumbudur et 2009 ) metrics. most well use a dual formulation the Wasserstein distance These implemented via either weight clipping or gradient penalty BID8 . These can yeild stable gradients high-quality samples work architecturesOn unclear metric or the associated regularization used impose Lipschitz important regularization techniques also with stabilizing learning f -divergences BID21 In study the integral role variance the discriminator's output the regime the generated distribution ultimately learning In , theoretical motivations from multiple variants GANs finally propose combat vanishing gradients on part when welltrained In have intra-class variance the discriminator's output In particular our results methods whose discriminators tend map inputs single real values unable provide a reliable learning signal the generator Furthermore variance the discriminator's output essential allow the generator learn in We proposed a technique, conceptually in line LDA ensures the discriminator's output distribution follows specified prior Taking a broader perspective also introduced a new regularization technique ensure enforce various desirable properties GANs",0.01,0.5914214963213275
"We introduce NoisyNet, a deep reinforcement learning agent with parametric noise added to its weights, and show that the induced stochasticity of the agent’s policy can be used to aid efficient exploration. The parameters of the noise are learned with gradient descent along with the remaining network weights.   NoisyNet is straightforward to implement and adds little computational overhead. We find that replacing the conventional exploration heuristics for A3C, DQN and Dueling agents (entropy reward and epsilon-greedy respectively) with NoisyNet yields substantially higher scores for a wide range of Atari games, in some cases advancing the agent from sub to super-human performance. Despite the wealth of research into efficient methods for exploration in Reinforcement Learning (RL) (Kearns & Singh, 2002; Jaksch et al., 2010) , most exploration heuristics rely on random perturbations of the agent's policy, such as -greedy BID20 or entropy regularisation BID25 , to induce novel behaviours. However such local 'dithering' perturbations are unlikely to lead to the large-scale behavioural patterns needed for efficient exploration in many environments BID1 .Optimism in the face of uncertainty is a common exploration heuristic in reinforcement learning. Various forms of this heuristic often come with theoretical guarantees on agent performance BID1 Lattimore et al., 2013; Jaksch et al., 2010; BID0 Kearns & Singh, 2002) . However , these methods are often limited to small state-action spaces or to linear function approximations and are not easily applied with more complicated function approximators such as neural networks (except from work by BID12 b) but it doesn't come with convergence guarantees). A more structured approach to exploration is to augment the environment's reward signal with an additional intrinsic motivation term BID19 ) that explicitly rewards novel discoveries. Many such terms have been proposed, including learning progress (Oudeyer & Kaplan, 2007) , compression progress BID17 , variational information maximisation (Houthooft et al., 2016) and prediction gain BID3 . One problem is that these methods separate the mechanism of generalisation from that of exploration; the metric for intrinsic reward, and-importantly-its weighting relative to the environment reward, must be chosen by the experimenter, rather than learned from interaction with the environment. Without due care, the optimal policy can be altered or even completely obscured by the intrinsic rewards; furthermore, dithering perturbations are usually needed as well as intrinsic reward to ensure robust exploration (Ostrovski et al., 2017) . Exploration in the policy space itself, for example, with evolutionary or black box algorithms (Moriarty et al., 1999; BID9 BID16 , usually requires many prolonged interactions with the environment. Although these algorithms are quite generic and can apply to any type of parametric policies (including neural networks), they are usually not data efficient and require a simulator to allow many policy evaluations.We propose a simple alternative approach, called NoisyNet, where learned perturbations of the network weights are used to drive exploration. The key insight is that a single change to the weight vector can induce a consistent, and potentially very complex, state-dependent change in policy over multiple time steps -unlike dithering approaches where decorrelated (and, in the case of -greedy, state-independent) noise is added to the policy at every step. The perturbations are sampled from a noise distribution. The variance of the perturbation is a parameter that can be considered as the energy of the injected noise. These variance parameters are learned using gradients from the reinforcement learning loss function, along side the other parameters of the agent. The approach differs from parameter compression schemes such as variational inference (Hinton & Van Camp, 1993; BID7 BID14 BID8 BID11 and flat minima search (Hochreiter & Schmidhuber, 1997) since we do not maintain an explicit distribution over weights during training but simply inject noise in the parameters and tune its intensity automatically. Consequently, it also differs from Thompson sampling BID22 Lipton et al., 2016) as the distribution on the parameters of our agents does not necessarily converge to an approximation of a posterior distribution.At a high level our algorithm is a randomised value function, where the functional form is a neural network. Randomised value functions provide a provably efficient means of exploration (Osband et al., 2014) . Previous attempts to extend this approach to deep neural networks required many duplicates of sections of the network (Osband et al., 2016) . By contrast in our NoisyNet approach while the number of parameters in the linear layers of the network is doubled, as the weights are a simple affine transform of the noise, the computational complexity is typically still dominated by the weight by activation multiplications, rather than the cost of generating the weights. Additionally, it also applies to policy gradient methods such as A3C out of the box (Mnih et al., 2016) . Most recently (and independently of our work) Plappert et al. (2017) presented a similar technique where constant Gaussian noise is added to the parameters of the network. Our method thus differs by the ability of the network to adapt the noise injection with time and it is not restricted to Gaussian noise distributions. We need to emphasise that the idea of injecting noise to improve the optimisation process has been thoroughly studied in the literature of supervised learning and optimisation under different names (e.g., Neural diffusion process (Mobahi, 2016) and graduated optimisation BID15 ). These methods often rely on a noise of vanishing size that is non-trainable, as opposed to NoisyNet which tunes the amount of noise by gradient descent.NoisyNet can also be adapted to any deep RL algorithm and we demonstrate this versatility by providing NoisyNet versions of DQN (Mnih et al., 2015) , Dueling BID24 and A3C (Mnih et al., 2016) algorithms. Experiments on 57 Atari games show that NoisyNet-DQN and NoisyNetDueling achieve striking gains when compared to the baseline algorithms without significant extra computational cost, and with less hyper parameters to tune. Also the noisy version of A3C provides some improvement over the baseline. We have presented a general method for exploration in deep reinforcement learning that shows significant performance improvements across many Atari games in three different agent architectures. In particular, we observe that in games such as Beam rider, Asteroids and Freeway that the standard DQN, Dueling and A3C perform poorly compared with the human player, NoisyNet-DQN, NoisyNet-Dueling and NoisyNet-A3C achieve super human performance, respectively. Although the improvements in performance might also come from the optimisation aspect since the cost functions are modified, the uncertainty in the parameters of the networks introduced by NoisyNet is the only exploration mechanism of the method. Having weights with greater uncertainty introduces more variability into the decisions made by the policy, which has potential for exploratory actions, but further analysis needs to be done in order to disentangle the exploration and optimisation effects.Another advantage of NoisyNet is that the amount of noise injected in the network is tuned automatically by the RL algorithm. This alleviates the need for any hyper parameter tuning (required with standard entropy bonus and -greedy types of exploration). This is also in contrast to many other methods that add intrinsic motivation signals that may destabilise learning or change the optimal policy. Another interesting feature of the NoisyNet approach is that the degree of exploration is contextual and varies from state to state based upon per-weight variances. While more gradients are needed, the gradients on the mean and variance parameters are related to one another by a computationally efficient affine function, thus the computational overhead is marginal. Automatic differentiation makes implementation of our method a straightforward adaptation of many existing methods. A similar randomisation technique can also be applied to LSTM units BID10 and is easily extended to reinforcement learning, we leave this as future work.Note NoisyNet exploration strategy is not restricted to the baselines considered in this paper. In fact, this idea can be applied to any deep RL algorithms that can be trained with gradient descent, including DDPG (Lillicrap et al., 2015) , TRPO BID18 or distributional RL (C51) BID4 . As such we believe this work is a step towards the goal of developing a universal exploration strategy.",1728,0.776,1052,1.6425855513307985,"We introduce NoisyNet a deep reinforcement learning agent parametric noise added its weights show the agent��s policy aid efficient exploration The parameters the noise are learned with gradient descent along with the remaining network weights NoisyNet straightforward adds little computational overhead We find replacing the conventional exploration heuristics A3C, DQN and Dueling agentsentropy reward-greedy respectively NoisyNet yields substantially higher scores Atari games in advancing the agent from sub to super-human performance Despite the wealth into efficient methods exploration in Reinforcement LearningRLKearns Singh Jaksch , most exploration heuristics the agent's policy -greedy BID20 entropy regularisation BID25 induce novel behaviours However such local 'dithering perturbations lead the large-scale behavioural patterns needed efficient exploration many environments BID1 .Optimism the face uncertainty a common exploration heuristic Various forms this heuristic often come theoretical guarantees on agent performance BID1 Lattimore et Jaksch BID0 Kearns & Singh 2002 . However , these methods limited small state-action spaces linear and easily with neural networksexcept from work BID12 b but it does come convergence guarantees). A more structured approach exploration augment the environment's reward signal an additional intrinsic motivation term BID19 ) explicitly rewards novel discoveries Many such terms proposed learning progressOudeyer Kaplan , compression progress BID17 , variational information maximisationHouthooft 2016 prediction gain One problem these methods separate the mechanism generalisation exploration; the metric for intrinsic reward-importantly-its weighting relative the environment reward must chosen learned interaction Without due care the optimal policy can altered or obscured the intrinsic rewards; furthermore dithering perturbations usually needed as intrinsic reward to robust exploration ( 2017 Exploration in the policy space itself for with evolutionary or black box algorithmsMoriarty BID9 BID16 , usually requires many prolonged interactions. Although these algorithms quite generic apply parametric policies usually data efficient a simulator allow many policy evaluationsWe NoisyNet learned the network weights drive exploration The key insight a single change the weight vector induce policy over multiple time steps -unlike dithering approaches decorrelated (, -greedy, added at The perturbations sampled a noise distribution The variance a parameter considered the energy the injected noise These variance parameters learned gradients the reinforcement learning loss function along side the agent The approach differs parameter compression schemes such variational inferenceHinton Van Camp BID7 BID14 BID8 BID11 and flat minima searchHochreiter since we maintain an explicit distribution weights during but simply inject noise tune its intensity automatically also differs Thompson sampling BID22 Lipton 2016) as the distribution on the parameters our agents does necessarily converge an approximationAt our algorithm a randomised value function the functional form Randomised value functions provide a provably efficient means exploration (Osband . Previous attempts extend this approach required many duplicates sectionsOsband 2016 . By contrast in our NoisyNet approach while the number parameters the linear layers doubled as the weights a simple affine transform the noise typically still dominated by activation multiplications rather generating Additionally also applies policy gradient methods A3C outMnih et . Most recently ( independently our work Plappert (2017 presented a similar technique where constant Gaussian noise the parameters Our method thus differs by the ability the network adapt the noise injection with time it restricted Gaussian noise distributions We need emphasise the idea injecting noise to improve the optimisation process thoroughly of supervised learning under different namesMobahi 2016 graduated BID15 These methods often rely a noise of vanishing size nontrainable NoisyNet which tunes by gradient descent adapted any deep RL algorithm we demonstrate this versatility providing NoisyNet versions DQNMnih et al , Dueling BID24 A3C algorithms Experiments 57 Atari games NoisyNet-DQN NoisyNetDueling achieve striking gains the baseline algorithms without significant extra computational cost with less hyper parameters to tune Also the noisy version A3C provides some improvement the baseline We presented a general method exploration in deep reinforcement learning that across many Atari games three agent architectures In particular observe games Beam rider Asteroids Freeway that the standard DQN, Dueling A3C perform the human player NoisyNet-DQN achieve super human performance respectively Although the improvements might also come the optimisation aspect since the cost functions modified the uncertainty the networks introduced NoisyNet the only exploration mechanism the method Having weights with greater uncertainty introduces the decisions the policy, has potential exploratory actions further analysis the exploration and optimisation effectsAnother advantage NoisyNet the amount noise injected tuned automatically the RL algorithm This alleviates any hyper parameter tuningrequired with standard entropy bonus and -greedy types exploration This also in contrast many other methods add intrinsic motivation signals destabilise learning or change the optimal policy Another interesting feature the NoisyNet approach the degree exploration contextual varies state based perweight variances While more gradients on the mean and variance parameters related one a computationally efficient affine function thus the computational overhead marginal Automatic differentiation makes implementation our method straightforward adaptation A similar randomisation technique LSTM units BID10 is easily extended reinforcement learning we leave future workNote NoisyNet exploration strategy restricted the baselines considered In fact this idea can any deep RL algorithms including DDPGLillicrap et , TRPO BID18 or distributional RL (C51) BID4 As such we believe this work a universal exploration strategy",0.01,0.3413306975254429
"Localization is the problem of estimating the location of an autonomous agent from an observation and a map of the environment. Traditional methods of localization, which filter the belief based on the observations, are sub-optimal in the number of steps required, as they do not decide the actions taken by the agent. We propose ""Active Neural Localizer"", a fully differentiable neural network that learns to localize efficiently. The proposed model incorporates ideas of traditional filtering-based localization methods, by using a structured belief of the state with multiplicative interactions to propagate belief, and combines it with a policy model to minimize the number of steps required for localization. Active Neural Localizer is trained end-to-end with reinforcement learning. We use a variety of simulation environments for our experiments which include random 2D mazes, random mazes in the Doom game engine and a photo-realistic environment in the Unreal game engine. The results on the 2D environments show the effectiveness of the learned policy in an idealistic setting while results on the 3D environments demonstrate the model's capability of learning the policy and perceptual model jointly from raw-pixel based RGB observations. We also show that a model trained on random textures in the Doom environment generalizes well to a photo-realistic office space environment in the Unreal engine. Localization is the problem of estimating the position of an autonomous agent given a map of the environment and agent observations. The ability to localize under uncertainity is required by autonomous agents to perform various downstream tasks such as planning, exploration and targetnavigation. Localization is considered as one of the most fundamental problems in mobile robotics (Cox & Wilfong, 1990; BID1 . Localization is useful in many real-world applications such as autonomous vehicles, factory robots and delivery drones.In this paper we tackle the global localization problem where the initial position of the agent is unknown. Despite the long history of research, global localization is still an open problem, and there are not many methods developed which can be learnt from data in an end-to-end manner, instead typically requiring significant hand-tuning and feature selection by domain experts. Another limitation of majority of localization approaches till date is that they are passive, meaning that they passively estimate the position of the agent from the stream of incoming observations, and do not have the ability to decide the actions taken by the agent. The ability to decide the actions can result in faster as well as more accurate localization as the agent can learn to navigate quickly to unambiguous locations in the environment.We propose ""Active Neural Localizer"", a neural network model capable of active localization using raw pixel-based observations and a map of the environment 12 . Based on the Bayesian filtering algorithm for localization BID13 , the proposed model contains a perceptual model to estimate the likelihood of the agent's observations, a structured component for representing the belief, multiplicative interactions to propagate the belief based on observations and a policy model over the current belief to localize accurately while minimizing the number of steps required for localization. The entire model is fully differentiable and trained using reinforcement learning, allowing the perceptual model and the policy model to be learnt simultaneously in an end-to-end fashion. A variety of 2D and 3D simulation environments are used for testing the proposed model. We show that the Active Neural Localizer is capable of generalizing to not only unseen maps in the same domain but also across domains. In this paper, we proposed a fully-differentiable model for active global localization which uses structured components for Bayes filter-like belief propagation and learns a policy based on the belief to localize accurately and efficiently. This allows the policy and observation models to be trained jointly using reinforcement learning. We showed the effectiveness of the proposed model on a variety of challenging 2D and 3D environments including a realistic map in the Unreal environment. The results show that our model consistently outperforms the baseline models while being order of magnitudes faster. We also show that a model trained on random textures in the Doom simulation environment is able to generalize to photo-realistic Office map in the Unreal simulation environment. While this gives us hope that model can potentially be transferred to real-world environments, we leave that for future work. The limitation of the model to adapt to dynamic lightning can potentially be tackled by training the model with dynamic lightning in random mazes in the Doom environment. There can be several extensions to the proposed model too. The model can be combined with Neural Map BID32 to train an end-to-end model for a SLAM-type system and the architecture can also be utilized for end-to-end planning under uncertainity.",923,0.481,544,1.6966911764705883,"Localization the problem estimating an autonomous agent from an observation Traditional methods localization filter the belief based the observations sub the number steps decide the actions We propose ""Active Neural Localizer a fully differentiable neural network learns localize efficiently The proposed model incorporates ideas traditional filtering-based localization methods by a structured belief of the state with multiplicative interactions propagate belief combines it a policy model minimize steps Active Neural Localizer trained end We use simulation environments which random 2D mazes the Doom game engine The results on the 2D environments show the effectiveness the learned policy an idealistic setting while results demonstrate the model's capability learning the policy and perceptual model jointly from raw-pixel based RGB observations We also show a model trained random textures the Doom environment generalizes a photo-realistic office space environment Localization the problem estimating the position an autonomous agent given agent observations The ability localize under uncertainity required autonomous agents perform various downstream tasks planning exploration targetnavigation Localization considered as mobile robotics (Cox Wilfong 1990 BID1 . Localization useful such autonomous vehicles factory robots delivery dronesIn tackle where the initial position the agent unknown Despite research global localization not developed which learnt data an end instead typically requiring significant hand-tuning and feature selection by domain experts Another limitation majority of localization approaches till passive passively estimate the agent from the stream incoming observations have decide the actions The ability decide the actions can result faster as as the agent learn navigate quickly to unambiguous locationsWe propose ""Active Neural Localizer capable active localization raw pixel-based observations a map 12 Based the Bayesian filtering algorithm for localization BID13 , the proposed model contains a perceptual model to the agent's observations a structured component representing the belief multiplicative interactions to propagate based observations a policy model over the current belief to localize accurately while steps The entire model fully differentiable trained using reinforcement learning allowing the perceptual model and the policy model learnt simultaneously an end A variety used testing the proposed model We show the Active Neural Localizer generalizing not only unseen maps in the same domain across In proposed a fully-differentiable model active global localization which structured components Bayes filter-like belief propagation learns a policy to accurately This allows the policy and observation models trained jointly reinforcement learning We showed the effectiveness the proposed model including a realistic map in the Unreal environment The results show our model consistently the baseline models while being order faster We also show a model trained random textures the Doom simulation environment generalize photo-realistic Office map in While this gives hope that model can potentially transferred leave The limitation adapt dynamic lightning can potentially tackled training random mazes in the Doom environment There can several extensions the proposed model too The model can combined Neural Map BID32 train end model a SLAM-type system and the architecture utilized end planning under uncertainity",0.01,0.47918707671337946
"Machine translation is an important real-world application, and neural network-based AutoRegressive Translation (ART) models have achieved very promising accuracy. Due to the unparallelizable nature of the autoregressive factorization, ART models have to generate tokens one by one during decoding and thus suffer from high inference latency. Recently, Non-AutoRegressive Translation (NART) models were proposed to reduce the inference time. However, they could only achieve inferior accuracy compared with ART models. To improve the accuracy of NART models, in this paper, we propose to leverage the hints from a well-trained ART model to train the NART model. We define two hints for the machine translation task: hints from hidden states and hints from word alignments, and use such hints to regularize the optimization of NART models. Experimental results show that the NART model trained with hints could achieve significantly better translation performance than previous NART models on several tasks. In particular, for the WMT14 En-De and De-En task, we obtain BLEU scores of 25.20 and 29.52 respectively, which largely outperforms the previous non-autoregressive baselines. It is even comparable to a strong LSTM-based ART model (24.60 on WMT14 En-De), but one order of magnitude faster in inference. Neural machine translation has attracted much attention from the research community BID1 BID13 BID5 and has been gradually adopted by industry in the past several years BID22 . Despite the huge variety of model architectures BID1 BID6 BID19 , given a source sentence x = (x 1 , ..., x Tx ) and a target sentence y = (y 1 , ..., y Ty ), most neural machine translation models decompose and estimate the conditional probability P (y|x) in an universal autoregressive manner: P (y|x) = Π Ty t=1 P (y t |y <t , x),where y <t represents the first t − 1 words of y. During inference, given an input sentence, those models generate the translation results sequentially, token by token from left to right. We call all such models AutoRegressive neural machine Translation (ART) models. A state-of-the-art ART model, Transformer BID19 , is shown in the left part of Figure 1 .A well-known limitation of the ART models is that the inference process can hardly be parallelized, and the inference time is linear with respect to the length of the target sequence. As a result, the ART models suffer from long inference time BID22 , which is sometimes unaffordable for industrial applications. Consequently , people start to develop Non-AutoRegressive neural machine Translation (NART) models to speed up the inference process BID7 BID15 . These models use the general encoder-decoder framework: the encoder takes a source sentence x as input and generates a set of contextual embeddings and predicted length T y ; conditioned on the contextual embeddings, the decoder takes a transformed copy of x as input and predicts the target tokens at all the positions independently in parallel according to the following decomposition:P (y|x, T y ) = Π Ty t=1 P (y t |T y , x).While the NART models achieve significant speedup during inference BID7 , their accuracy is considerably lower than their ART counterpart. Most of the previous works attribute the poor performance to this unavoidable conditional independence assumption of the NART model. To tackle this issue , they try to improve the expressiveness and accuracy of the decoder input in different ways: BID7 introduce fertilities from statistical machine translation models into the NART models, BID15 base the decoding process of their proposed model on an iterative refinement process, and take a step further to embed an autoregressive submodule that consists of discrete latent variables into their model. Although such methods provide better expressiveness of decoder inputs and improve the final translation accuracy, the inference speed of these models will be hurt due to the overhead of the introduced modules, which contradicts with the original purpose of introducing the NART models, i.e., to parallelize and speed up neural machine translation models.Different from previous works that develop new submodules for decoder input, we improve the translation model from another perspective. We aim to provide more guided signals during optimization. That is, we do not introduce any new prediction submodule but introduce better regularization. The reason we tackle the problem from this perspective lies in two points: First, the encoder input (source words) contains all semantic information for translation, and the decoder input in the NART model can be considered as a middle layer between input and output. It is not clear how much gain can be achieved by developing a sophisticated submodule for a middle layer in a deep neural network. Second, the encoder-decoder-based NART model is already over-parameterized.We believe that such neural network still has great ability and space to be better optimized if we can provide it with stronger and richer signals, for example, from a much better ART model: Once we have a well-trained ART model, we actually know rich information about the contexts to make the prediction at each time step and the natural word alignments between bilingual sentences. All the information could be invaluable towards the improved training of a NART model.To well leverage an ART model, we use the hint-based training framework BID17 BID3 , in which the information from hidden layers of teacher model (referred as hints) are used to guide the training process of a student model. However, hint-based training was developed for image classification models and it is challenging to define and use hints for translation. First, the translation model is composed of stacked encoder layers, attention layers, and stacked decoder layers. It is not clear how to define hints in such an encoder-decoder framework. Second, the NART and ART models are of different architectures on the decoding stage. It is not obvious how to leverage hints from the teacher to the training of student with a different architecture. We find that directly applying hints used in the classification tasks fails. In this paper, we first investigate the causes of the bad performance of the NART model, and then define hints targeting to solve the problems. According to our empirical study, we find that the hidden states of the NART model differ from the ART model: the positions where the NART model outputs incoherent tokens will have very high hidden states similarity. Also, the attention distributions of the NART model are more ambiguous than those of ART model. Based on these observations, we design two kinds of hints from the hidden states and attention distributions of the ART model, to help the training of the NART model.We have conducted experiments on the widely used WMT14 English-to-German/German-toEnglish (En-De/De-En) task and IWSLT14 German-to-English task. For WMT14 En-De task, our proposed method achieves a BLEU score of 25.20 which significantly outperforms the nonautoregressive baseline models and is even comparable to a strong ART baseline, Google's LSTMbased translation model (24.60 BID22 ). For WMT14 De-En task, we also achieve significant performance gains, reaching 29.52 in terms of BLEU.2 RELATED WORKS 2.1 AUTOREGRESSIVE TRANSLATION Given a sentence x = (x 1 , . . . , x Tx ) from the source language, the straight-forward way for translation is to generate the words in the target language y = (y 1 , . . . , y Ty ) one by one from left to right. This is also known as the autoregressive factorization in which the joint probability is decomposed into a chain of conditional probabilities, as in the Eqn. (1). Deep neural networks are widely used to model such conditional probabilities based on the encoder-decoder framework. The encoder takes the source tokens (x 1 , . . . , x Tx ) as input and encodes x into a set of context states c = (c 1 , . . . , c Tx ). The decoder takes c and subsequence y <t as input and estimates P (y t |y <t , c) according to some parametric function. Non-autoregressive translation (NART) models have suffered from low-quality translation results.In this paper, we proposed to use hints from well-trained autoregressive translation (ART) models to enhance the training of NART models. Our results on WMT14 En-De and De-En significantly outperform previous NART baselines, and achieve comparable accuracy to an LSTM-based ART model, with one order of magnitude faster in inference. In the future, we will focus on designing new architectures and new training methods for NART models to achieve comparable accuracy as the state-of-the-art ART models such as Transformer.",1782,0.972,1063,1.6763875823142051,"Machine translation neural network-based AutoRegressive Translation (ART) models achieved very promising accuracy Due the unparallelizable nature the autoregressive factorization ART models generate tokens one during decoding thus suffer high inference latency Recently Non-AutoRegressive Translation (NART) models proposed the inference time. However they could only achieve inferior accuracy compared ART models To improve NART models in propose leverage the hints a well-trained ART model train We define two hints the machine translation task hints from hidden states word alignments use regularize the optimization NART models Experimental results the NART model trained hints could achieve significantly better translation performance on In particular for the WMT14 En-De and De-En task obtain BLEU scores 25.20 largely outperforms It even comparable a strong LSTM-based ART model24.60 on WMT14 En-De one order inference Neural machine translation attracted BID1 BID13 BID5 has gradually adopted industry BID22 . Despite the huge variety model architectures BID1 BID6 BID19 , given a source sentence x y Ty most neural machine translation models decompose and estimate P (y|x an universal autoregressive manner: �� Ty t=1 , x),where represents − 1 words During inference given an input sentence those models generate the translation results sequentially token from We call all such models AutoRegressive neural machine Translation (ART) models state ART model Transformer BID19 , shown the left part Figure 1 .A well-known limitation the inference process hardly the inference time linear As the ART models suffer long inference time BID22 , sometimes unaffordable industrial applications , people start develop Non-AutoRegressive neural machine Translation (NART) models speed BID7 BID15 These models use the general encoder-decoder framework: takes a source sentence x generates contextual embeddings and predicted length T y ; conditioned a transformed copy predicts the target tokens at all the positions independently in parallel according:P (y|x �� Ty t=1 P x).While the NART models achieve during inference BID7 their accuracy considerably their ART counterpart Most the previous works attribute this unavoidable conditional independence assumption the NART model To tackle , they try improve accuracy the decoder input in BID7 introduce fertilities from statistical machine translation models into the NART models base their proposed model take embed an autoregressive submodule consists discrete latent variables Although such methods provide better expressiveness decoder inputs improve the final translation accuracy the inference speed will hurt due the introduced modules contradicts with introducing the NART models speed neural machine translation modelsDifferent from previous works develop new submodules improve from another perspective We aim more guided signals during optimization That we do introduce any new prediction submodule but introduce better regularization The reason tackle from lies the encoder input (source words contains translation in the NART model a middle layer input It can developing a sophisticated submodule a middle layer Second the encoder-decoder-based NART model already overWe believe such neural network still great ability and space better if provide stronger and richer signals from a much better ART model: Once actually know rich information the contexts to make at the natural word alignments bilingual sentences All the information could invaluable towards the improved training a NART modelTo well leverage an ART model use the hint-based training framework BID17 BID3 in hidden layers teacher modelreferred as hints guide However hint-based training developed image classification models challenging define and hints translation First the translation model composed stacked encoder layers attention layers stacked It to define hints Second the NART and ART models of different architectures on the decoding stage It obvious leverage hints the teacher the training student with a different architecture We find directly applying hints used the classification tasks fails In first the bad performance the NART model define hints targeting to solve According our empirical study we the hidden states the NART model differ the ART model: the positions where outputs incoherent tokens will very high hidden states similarity Also the attention distributions the NART model more ambiguous ART model Based these observations design two kinds hints from the hidden states and attention distributions the ART model the training the NART modelWe have conducted widely WMT14 Englishto/toEnglishEn task IWSLT14 For WMT14 En-De task our proposed method achieves a BLEU score 25.20 which significantly the nonautoregressive baseline models even comparable a strong ART baseline Google's LSTMbased translation model24.60 BID22 For WMT14 De-En task also achieve reaching 29.52 in terms BLEU.2 RELATED AUTOREGRESSIVE Given a sentence x 1 . . . , x Tx ) from the source language for translation generate the words y = 1 . . . , y Ty ) one by from left This also known the autoregressive factorization in the joint probability decomposed a chain (1 Deep neural networks widely such conditional probabilities based The encoder takes tokensx 1 . . . , x Tx ) as input and encodes into context states cc 1 . . . , c Tx ). The decoder takes c and subsequence y <t as estimates P t |y , according some parametric function Non-autoregressive translation (NART) models sufferedIn proposed hints enhance Our results on WMT14 En-De and significantly previous NART baselines achieve comparable accuracy an LSTM-based ART model one order faster in inference In focus designing new architectures new training methods NART models achieve comparable accuracy as state ART such Transformer",0.01,0.42745530265719295
"Artificial neural networks are built on the basic operation of linear combination and non-linear activation function. Theoretically this structure can approximate any continuous function with three layer architecture. But in practice learning  the parameters of such network can be hard. Also the choice of activation function can greatly impact the performance of the network. In this paper we are proposing to replace the basic linear combination operation with non-linear operations that do away with the need of additional non-linear activation function. To this end we are proposing the use of elementary  morphological operations (dilation and erosion) as the basic operation in neurons. We show that these networks (Denoted as Morph-Net) with morphological operations can approximate any smooth function requiring less number of parameters than what is necessary for normal neural networks. The results show that our network perform favorably when compared with similar structured network. We have carried out our experiments on  MNIST, Fashion-MNIST, CIFAR10 and CIFAR100. In artificial neural networks, the basic building block is an artificial neuron or perceptron that simply computes the linear combination of the input BID22 . It is usually followed by a non-linear activation function to model the non-linearity of the output. Although the neurons are simple in nature, when connected together they can approximate any continuous function of the input BID4 . This has been successfully utilized in solving different real world problems like image classification (Krizhevsky et al., 2012) , semantic segmentation BID13 and image generation BID6 . While these models are quite powerful in nature, their efficient training can be hard in general BID12 and they need support of specials techniques, such as batch normalization BID5 and dropout BID24 , in order to achieve better generalization capabilities. Their training time also depends on the choice of activation function BID15 .In this paper we are proposing new building blocks for building networks similar to neural network. Here , instead of the linear combination operation of the artificial neurons, we use a non-linear operation that eliminates the need of additional activation function while requiring a small number of neurons to attain same performance or better. More specifically, We use morphological operations (i.e. dilation and erosion) as the elementary operation of the neurons in the network. Our contribution in this paper is building a network with these operations that has the following properties.1. Networks built with with dilation-erosion neurons followed by linear combination can approximate any continuous function given enough dilation/erosion neurons. 2. As dilation and erosion operation are non-linear by themselves, requirement of separate non-linear activation function is eliminated. 3. The use of dilation-erosion operation greatly increases number of possible decision boundaries. As a result, complex decision boundaries can be learned using small number of parameters.The rest of the paper is organized as follows. Section 2 describes the prior work on morphological neural network. In Section 3, we introduce our proposed network and prove its capabilities theoretically. We further demonstrate its capabilities empirically on a few benchmark datasets in Section 4. Lastly Section 6 concludes the paper. In this paper we have proposed a new class of networks that uses both normal and morphological neurons. These network consists of three layers only: input layer, dilation-erosion layer with dilation and erosion neurons followed by linear combination layer giving the output of the network with normal artificial neurons. We have done our analysis using this three layer network only, but its deeper version can also be explored. We have shown that this three layer architecture can approximate any sufficiently smooth function without requiring any non-linear activation function. These networks are able to learn a large number of hyperplanes with very few neurons in the dilation-erosion layer thereby providing superior results compared to other networks with three layer architecture. The improved results could also be the result of 'feature selection' by the max/min operator in the dilation erosion layer. In this work we have only worked with fully connected layers, i.e. a node in a layer is connected to all the nodes in the previous layer. This type of connectivity is not very efficient for image data where architectures with convolution layers perform better. So, extending this work to the case where a structuring element operates by sliding over the whole image, should be the next logical step.APPENDIX A PROOF OF LEMMA 1 From equation 9 we have DISPLAYFORM0 Now this equation can be rewritten as follows DISPLAYFORM1 where s + ik and s − ik denote the k th component of the i th structuring element of dilation and erosion neurons, respectively. The above equation can be further expressed in the following form, DISPLAYFORM2 Where DISPLAYFORM3 are define in the following way DISPLAYFORM4 Now, without any loss of generality we can write equation 17 as follows DISPLAYFORM5 where DISPLAYFORM6 Finally, we can rewrite equation 18 as DISPLAYFORM7 where l = m + n, α i ∈ {1, −1} and φ i (x)'s are of the following form DISPLAYFORM8 DISPLAYFORM9 In equation 20, v DISPLAYFORM10 represents sum of multi-oder hinge function.However, it may be noted that taking l ≥ d results hinge hyper planes which can span any where in d dimensional input space. We can assume there are l 1 and l 2 number of terms where α = 1 and α = −1 respectively, then DISPLAYFORM11 where l 1 + l 2 = l and φ i (x), φ i (x) is of same form as equation 20. Threfore can write, DISPLAYFORM12 DISPLAYFORM13 where k i ∈ {1, 2, .. , d + 1}∀i. In equation 24 we are taking maximum of (d + 1) l1 terms. Similarly we can derive same expression for Proof From equation 19, without any loss of generality we can assume there are t 1 and t 2 number of terms where α = 1 and α = −1 respectively, then DISPLAYFORM14 where t 1 + t 2 = l and φ i (x), φ i (x) are of same form as equation 20.As sum of PWL functions is also a PWL function, hence each t1 i=1 φ i (x) and t2 i=1 φ i (x) and PWL. Now, if t 1 > 0, from Proposition 3 we can conclude that g(x) is PWL linear function since difference of two continuous PWL function is PWL function . If t 1 = 0 then g(x) becomes PWL concave function.Hence, can say g(x) is PWL function.It may be noted that if l < d then PWL hyperplane will be in parallel to at least one of the axis. Taking l ≥ d results PWL hyperplane which may span anywhere in d dimensional space.Theorem 2 (Universal approximation) Using only a single dilation-erosion layer followed by a linear combination layer any continuous function can be approximated.",1425,0.763,820,1.7378048780487805,"Artificial neural networks built the basic operation linear combination and non-linear activation function Theoretically this structure approximate any continuous function three layer architecture But in practice learning the parameters such network can Also the choice activation function can greatly the network In are replace the basic linear combination operation do away of additional non-linear activation function To this end proposing elementary morphological operationsdilation erosion neurons We show these networks (Denoted Morph-Net with morphological operations approximate any smooth function requiring less number what The results show our network perform favorably similar structured network We carried our experiments MNIST Fashion-MNIST CIFAR10 In artificial neural networks or perceptron simply the linear combination BID22 . It usually followed a non-linear activation function to model Although the neurons simple when connected together approximate any continuous function the input BID4 . This has successfully utilized solving image classification , semantic segmentation BID13 While these models quite powerful nature their efficient training hard in general BID12 they need support of specials techniques batch normalization BID5 dropout , better generalization capabilities Their training time also depends the choice activation function BID15 .In are proposing new building blocks building networks similar neural network. Here , instead the linear combination operation the artificial neurons eliminates additional activation function while requiring attain same performance or More specifically We use morphological operations erosion the elementary operation the neurons Our contribution in building with these operations has Networks built with dilation-erosion neurons followed linear combination can approximate any continuous function given 2 As dilation and erosion operation non by themselves requirement separate non-linear activation function eliminated 3 The use dilation-erosion operation greatly number possible decision boundaries As complex decision boundaries learned using small number parametersThe rest organized Section describes the prior work morphological neural network In Section introduce our proposed network and prove its capabilities theoretically We further demonstrate its capabilities empirically on a few benchmark datasets in Section Lastly Section 6 concludes the paper In have proposed networks uses both normal and morphological neurons These network consists three layers only input layer dilation-erosion layer with dilation and erosion neurons followed linear combination layer giving with normal artificial neurons We done our analysis using this three layer network only its deeper version explored We shown this three layer architecture approximate any sufficiently smooth function without requiring any non-linear activation function These networks able learn hyperplanes with very few neurons the dilation-erosion layer thereby superior results compared three layer architecture The improved results could 'feature selection the max/min operator the dilation erosion layer In this work only worked fully connected layers This type connectivity very efficient image data where architectures with convolution layers perform So extending this work the case where a structuring element operates by sliding the whole image shouldAPPENDIX A PROOF LEMMA 1 From equation 9 DISPLAYFORM0 Now this equation where s + denote k th component i of dilation and erosion neurons The above equation further expressed DISPLAYFORM2 Where are define Now without any loss equation 17 Finally rewrite l m α i �� { (x) of In equation represents sum multi-oder hinge functionHowever taking l ≥ d results hinge hyper planes span any where in d dimensional input space We can assume there l 1 terms where α then DISPLAYFORM11 where l + and � i (x of same form equation 20 Threfore can write DISPLAYFORM12 DISPLAYFORM13 where k i �� { .. , d + 1}��i. In equation 24 taking maximum of (d + 1) l1 terms Similarly we derive same expression Proof From equation 19 without any loss we assume there t 1 and t 2 number terms where α then DISPLAYFORM14 where + l and � i (x of equation 20.As sum PWL functions also a PWL function hence each t1 i=1 �. Now t 1 from Proposition 3 we g(x PWL linear function since difference two continuous PWL function . If t 1 becomes PWL concave functionHence can sayIt noted l < d PWL hyperplane in parallel at the axis Taking l ≥ d results PWL hyperplane which may span anywhere d dimensional spaceTheorem 2 (Universal approximation Using only a single dilation-erosion layer followed a linear combination layer any continuous function",0.01,0.5839411761242886
"With the rapidly scaling up of deep neural networks (DNNs), extensive research studies on network model compression such as weight pruning have been performed for efficient deployment. This work aims to advance the compression beyond the weights to the activations of DNNs. We propose the Integral Pruning (IP) technique which integrates the activation pruning with the weight pruning. Through the learning on the different importance of neuron responses and connections, the generated network, namely IPnet, balances the sparsity between activations and weights and therefore further improves execution efficiency. The feasibility and effectiveness of IPnet are thoroughly evaluated through various network models with different activation functions and on different datasets. With <0.5% disturbance on the testing accuracy, IPnet saves 71.1% ~ 96.35% of computation cost, compared to the original dense models with up to 5.8x and 10x reductions in activation and weight numbers, respectively. Deep neural networks (DNNs) have demonstrated significant advantages in many real-world applications, such as image classification, object detection and speech recognition BID6 BID15 BID16 . On the one hand, DNNs are developed for improving performance in these applications, which leads to intensive demands in data storage, communication and processing. On the other hand, the ubiquitous intelligence promotes the deployment of DNNs in light-weight embedded systems that are equipped with only limited memory and computation resource. To reduce the model size while ensuring the performance quality, DNN pruning is widely explored. Redundant weight parameters are removed by zeroing-out those in small values BID4 BID13 . Utilizing the zero-skipping technique BID5 on sparse weight parameters can further save the computation cost. In addition, many specific DNN accelerator designs BID0 BID14 leveraged the intrinsic zero-activation pattern of the rectified linear unit (ReLU) to realize the activation sparsity. The approach, however, cannot be directly extended to other activation functions, e.g., leaky ReLU.Although these techniques achieved tremendous success, pruning only the weights or activations cannot lead to the best inference speed, which is a crucial metric in DNN deployment, for the following reasons. First, the existing weight pruning methods mainly focus on the model size reduction. However, the most essential challenge of speeding up DNNs is to minimize the computation cost, such as the intensive multiple-and-accumulate operations (MACs). Particularly, the convolution (conv) layers account for most of the computation cost and dominate the inference time in DNNs BID13 . Because weights are shared in convolution, the execution speed of conv layers is usually bounded by computation instead of memory accesses BID7 BID21 . Second, the activation in DNNs is not strictly limited with ReLU. The intrinsic zeroactivation patterns do not exist in non-ReLU activation functions, such as leaky ReLU and sigmoid. Third, the weights and activations of a network together determine the network performance. Our experiment shows that the zero-activation percentage obtained by ReLU decreases after applying the weight pruning BID5 . Such a deterioration in activation sparsity could potentially eliminate the advantage of the aforementioned accelerator designs.In this work, we propose the integral pruning (IP) technique to minimize the computation cost of DNNs by pruning both weights and activations. As the pruning processes for weights and activations are correlated, IP learns dynamic activation masks by attaching activation pruning to weight pruning after static weight masks are well trained. Through the learning on the different importance of neuron responses and connections, the generated network, namely IPnet, balances the sparsity between activations and weights and therefore further improves execution efficiency. Moreover, our method not only stretches the intrinsic activation sparsity of ReLU, but also targets as a general approach for other activation functions, such as leaky ReLU. Our experiments on various network models with different activation functions and on different datasets show substantial reduction in MACs by the proposed IPnet. Compared to the original dense models, IPnet can obtain up to 5.8× activation compression rate, 10× weight compression rate and eliminate 71.1% ∼ 96.35% of MACs. Compared to state-of-the-art weight pruning technique BID4 , IPnet can further reduce the computation cost 1.2× ∼ 2.7×. The static activation pruning approach has been widely adopted in efficient DNN accelerator designs BID0 BID14 . By selecting a proper static threshold θ in Equation (2), more activations can be pruned with little impact on model accuracy. For the activation pruning in IP, the threshold is dynamically set according to the winner rate and activation distribution layer-wise. The comparison between static and dynamic pruning is conducted on ResNet-32 for CIFAR-10 dataset. For the static pruning setup, the θ for leaky ReLU is assigned in the range of [0.07, 0.14], which brings different activation sparsity patterns. To minimize the computation cost in DNNs, IP combining weight pruning and activation pruning is proposed in this paper. The experiment results on various models for MNIST, CIFAR-10 and ImageNet datasets have demonstrated considerable computation cost reduction. In total, a 2.3× -5.8× activation compression rate and a 2.5× -10× weight compression rate are obtained. Only 3.65% -28.9% of MACs are left with marginal effects on model accuracy, which outperforms the weight pruning by 1.2× -2.7×. The IPnets are targeted for the dedicated DNN accelerator designs with efficient sparse matrix storage and computation units on chip. The IPnets featuring compressed model size and reduced computation cost will meet the constraints from memory space and computing resource in embedded systems.",1170,0.628,704,1.6619318181818181,"With rapidly scaling extensive research studies network model compression such weight pruning efficient deployment This work aims advance the compression beyond the weights to the activations DNNs integrates pruning Through the learning on the different importance neuron responses connections the generated network, namely IPnet balances the sparsity activations weights therefore further execution efficiency The feasibility IPnet thoroughly through various network models with different activation functions on different datasets With <0.5% disturbance on the testing accuracy IPnet saves ~ computation cost the original dense models up and reductions activation weight numbers Deep neural networks demonstrated BID6 BID15 BID16 . On DNNs developed improving these applications leads intensive demands communication On ubiquitous intelligence promotes the deployment DNNs equipped only limited memory and computation resource To reduce the model size while ensuring the performance quality DNN pruning widely explored Redundant weight parameters removed zeroing-out those small values BID4 BID13 the zero-skipping technique BID5 on sparse weight parameters further save In many specific DNN accelerator designs BID0 BID14 leveraged the intrinsic zero-activation pattern the rectified linear unitReLU realize the activation sparsity The approach directly extended other activation functions leaky ReLU.Although these techniques achieved tremendous success pruning only the weights or lead the best inference speed DNN deployment First the existing weight pruning methods mainly the model size reduction However the most essential challenge speeding DNNs such the intensive multiple-and-accumulate operations Particularly convolution (conv) layers account dominate DNNs BID13 . Because weights shared convolution the execution speed conv layers usually bounded computation instead BID7 BID21 Second the activation in DNNs strictly with ReLU The intrinsic zeroactivation patterns do non-ReLU activation functions leaky ReLU. Third the weights activations a network together determine Our experiment the zero-activation percentage obtained ReLU decreases applying the weight pruning BID5 . Such a deterioration activation sparsity potentially eliminate the aforementioned accelerator designsIn the integral pruning (IP) technique DNNs both weights As the pruning processes weights activations correlated IP learns dynamic activation masks by attaching activation pruning after static weight masks well Through the learning on the different importance neuron responses connections the generated network, namely IPnet balances the sparsity activations weights therefore further execution efficiency Moreover our method not stretches the intrinsic activation sparsity ReLU targets as other activation functions leaky ReLU Our experiments various network models with different activation functions on substantial reduction MACs by the proposed IPnet. Compared the original dense models IPnet can obtain up to 5.8× activation compression rate eliminate 71.1% ∼ 96.35% MACs Compared state weight pruning technique BID4 , further The static activation pruning approach efficient DNN accelerator BID0 BID14 . By selecting a proper static threshold �� more activations pruned little impact model accuracy For the activation pruning IP, the threshold dynamically according the winner rate activation distribution layer- The comparison conducted ResNet-32 for CIFAR-10 dataset For the static pruning setup the �� for leaky ReLU assigned [ brings different activation sparsity patterns To minimize the computation cost in DNNs IP combining weight pruning activation pruning proposed The experiment results on various models for MNIST ImageNet datasets demonstrated considerable computation cost reduction In total a 2.3× -5.8× activation compression rate obtained -28.9 MACs left marginal effects model accuracy outperforms the weight pruning The IPnets targeted the dedicated DNN accelerator designs efficient sparse matrix storage and computation units on chip The IPnets featuring compressed model size reduced computation cost meet from memory space computing resource in embedded systems",0.01,0.39062328571742044
"The Variational Auto Encoder (VAE) is a popular generative 
latent variable model that is often 
applied for representation learning.
 Standard VAEs assume continuous valued 
latent variables and are trained by maximization
of the evidence lower bound (ELBO). Conventional methods obtain a 
differentiable estimate of the ELBO with reparametrized sampling and
optimize it with Stochastic Gradient Descend (SGD). However, this is not possible if 
we want to train VAEs with discrete valued latent variables, 
since reparametrized sampling is not possible. Till now, there
exist no simple solutions to circumvent this problem.
 In this paper, we propose an easy method to train VAEs 
with binary or categorically valued latent representations. Therefore, we use a differentiable
estimator for the ELBO which is based on importance sampling. In experiments, we verify the approach and
train two different VAEs architectures with Bernoulli and 
Categorically distributed latent representations on two different benchmark
datasets.	 In this paper, we derived an easy estimator for the ELBO, which does not rely on reparametrized sampling and therefore can be used to obtain differentiable estimates, even if reparametrization is not possible, e.g. if the latent variables z are Bernoulli or Categorically distributed. We have shown theoretically and in experiments, close to the optimal parameter configuration, the variance of the estimator approaches zero. This is a very desirable property for training.",305,0.177,185,1.6486486486486487,"The Variational Auto Encoder a popular generative latent variable model often applied for representation learning Standard VAEs assume continuous valued latent variables trained maximization the evidence lowerELBO Conventional methods obtain a differentiable estimate the ELBO with reparametrized sampling optimize Stochastic Gradient Descend ( However possible want train VAEs discrete valued latent variables since reparametrized sampling Till exist no simple solutions circumvent In this paper an easy method train VAEs binary or categorically valued latent representations Therefore use a differentiable estimator the ELBO which importance sampling In experiments we verify the approach and train two different VAEs architectures Bernoulli Categorically distributed latent representations on two different benchmark datasets In derived an easy estimator the ELBO, does reparametrized sampling obtain differentiable estimates, even, the latent variables z Bernoulli or Categorically distributed We shown theoretically and experiments close the optimal parameter configuration the variance approaches zero This a very desirable property training",0.0,0.3567789367934193
"Distributed computing can significantly reduce the training time of neural networks. Despite its potential, however, distributed training has not been widely adopted: scaling the training process is difficult, and existing SGD methods require substantial tuning of hyperparameters and learning schedules to achieve sufficient accuracy when increasing the number of workers. In practice, such tuning can be prohibitively expensive given the huge number of potential hyperparameter configurations and the effort required to test each one.
    
 We propose DANA, a novel approach that scales out-of-the-box to large clusters using the same hyperparameters and learning schedule optimized for training on a single worker, while maintaining similar final accuracy without additional overhead. DANA estimates the future value of model parameters by adapting Nesterov Accelerated Gradient to a distributed setting, and so mitigates the effect of gradient staleness, one of the main difficulties in scaling SGD to more workers.

 Evaluation on three state-of-the-art network architectures and three datasets shows that DANA scales as well as or better than existing work without having to tune any hyperparameters or tweak the learning schedule. For example, DANA achieves 75.73% accuracy on ImageNet when training ResNet-50 with 16 workers, similar to the non-distributed baseline. Modern deep neural networks are comprised of millions of parameters, which require massive amounts of data and time to learn. Steady growth of these networks over the years has made it impractical to train them from scratch on a single GPU. Distributing the computations over several GPUs can drastically reduce this training time. Unfortunately, stochastic gradient descent (SGD), typically used to train these networks, is an inherently sequential algorithm. As a result, training deep neural networks on multiple workers (computational devices) is difficult, especially when trying to maintain high efficiency, scalability and final accuracy.Data Parallelism is a common practice for distributing computation: data is split across multiple workers and each worker computes over its own data. Synchronous SGD (SSGD) is the most straightforward method to distribute the training process of neural networks: each worker computes the gradients over its own separate mini-batches, which are then aggregated to update a single model. The result is identical to multiplying the batch size B by the number of workers N , so the effective batch size is B · N . This severely limits scalability and reduces the model accuracy if not handled carefully BID25 BID6 BID8 . Furthermore, synchronization limits SSGD progress to the slowest worker: all workers must finish their current mini-batch and update the parameter server before any can proceed to the next mini-batch.Asynchronous SGD (ASGD) addresses these drawbacks by removing synchronization between the workers BID5 . Unfortunately, it suffers from gradient staleness: gradients sent by workers are often based on parameters that are older than the master's (parameter server) current parameters. Hence, distributed ASGD suffers from slow convergence and reduced final accuracy, and may not converge at all if the number of workers is high BID34 . Several works attempt to address these issues BID35 BID33 BID34 BID5 , but none has managed to overcome these problems when scaling to a large number of workers.More crucially, many ASGD algorithms require re-tuning of hyperparameters when scaling to different numbers of workers, and several even introduce new hyperparameters that must also be tuned BID35 BID33 BID34 . In practice, the vast number of potential hyperparameter configurations means that tuning is often done in parallel, with each worker independently evaluating a single configuration using standard SGD. Once the optimal hyperparameters are selected, training is completed on larger clusters of workers. Any additional tuning for ASGD can thus be computationally expensive and time-consuming. Though many algorithms have been proposed to reduce the cost of tuning BID2 BID13 BID12 BID9 BID26 , hyperparameter search remains a significant obstacle, and many practitioners cannot afford to re-tune hyperparameters for distributed training.Our contribution: We propose Distributed Accelerated Nesterov ASGD (DANA), a new distributed ASGD algorithm that works out of the box: it achieves state-of-the-art accuracy on existing architectures without any additional hyperparameter tuning or changes to the training schedule, while scaling as well or better than existing ASGD approaches, and without any additional overhead. Our DANA implementation achieves state-of-the-art accuracy on ImageNet when training ResNet-50 with 16 and even 32 workers, as well as on CIFAR-10 and CIFAR-100. DANA is a new asynchronous SGD algorithm for training of neural networks. By mitigating the effect of gradient staleness, DANA scales out-of-the-box to large clusters using the same hyperparameters and learning schedule optimized for training on a single worker, while maintaining similar final accuracy, without adding any overhead at the master. DANA could be used to extend other non-distributed optimization procedures (e.g., Nadam BID7 ) to a distributed setting without adding parameters. Integrating DANA with DC-ASGD could further mitigate gradient staleness, though without eliminating tuning. Finally, we are working to extend DANA with separate, selfadjusting weights per worker to address settings with heterogeneous workers while avoiding tuning.",1035,0.514,597,1.7336683417085428,"Distributed computing can significantly Despite its potential however distributed training: scaling existing SGD methods substantial tuning learning schedules sufficient accuracy when increasing workers In practice such tuning given potential hyperparameter configurations the effort test We propose DANA scales out- large clusters using learning schedule optimized training on a single worker while similar final accuracy without additional overhead DANA estimates the future value model parameters by adapting Nesterov Accelerated Gradient to a distributed setting so gradient staleness, one scaling SGD more workers Evaluation on three state network architectures three datasets shows DANA scales as or existing work without having tune any hyperparameters tweak the learning schedule For example DANA achieves 75.73% accuracy ImageNet when training ResNet-50 16 workers similar the non-distributed baseline Modern deep neural networks comprised millions parameters require Steady growth these networks over impractical train from on a single GPU Distributing the computations over several GPUs drastically this training time Unfortunately stochastic gradient descent typically train these networks an inherently sequential algorithm As training deep neural networks multiple workers (computational devices difficult trying maintain high efficiency final accuracyData Parallelism distributing computation: data over Synchronous SGDSSGD distribute the training process of: each worker over its own separate minibatches update The result identical multiplying the batch size B workers N , · This severely limits scalability reduces the model accuracy if not carefully BID25 BID6 BID8 . Furthermore synchronization limits SSGD progress the slowest worker: all workers finish their current mini and update the parameter server before any can proceedAsynchronous SGD (ASGD addresses these drawbacks removing between BID5 . Unfortunately suffers gradient staleness: gradients sent workers based parameters older the master's (parameter server) current parameters Hence distributed ASGD suffers slow convergence reduced final accuracy may converge workers high BID34 . Several works attempt address BID35 BID33 , managed when scaling workersMore crucially many ASGD algorithms require re hyperparameters when different numbers several even introduce must also In practice the vast number potential hyperparameter configurations means tuning parallel each worker independently evaluating using standard SGD Once the optimal hyperparameters selected training larger clusters workers Any additional tuning ASGD can thus computationally Though many algorithms proposed reduce tuning BID2 BID13 BID12 BID9 BID26 , hyperparameter search remains, many practitioners re distributed trainingOur contribution: Distributed Accelerated Nesterov ASGD works out: achieves state accuracy existing architectures without changes the training schedule scaling as or without Our DANA implementation achieves state accuracy on ImageNet when training ResNet-50 16 and even 32 workers DANA is a new asynchronous SGD algorithm training of By mitigating gradient staleness DANA scales out- large clusters using learning schedule optimized training on a single worker while similar final accuracy without adding at the master DANA could used extend other non-distributed optimization procedures Nadam BID7 ) a distributed setting without adding parameters Integrating DANA DC-ASGD could further mitigate gradient staleness though without eliminating tuning Finally working extend DANA with separate, selfadjusting weights per worker address settings with heterogeneous workers while avoiding tuning",0.01,0.5734016449614721
"This paper proposes a novel approach to train deep neural networks by unlocking the layer-wise dependency of backpropagation training. The approach employs additional modules called local critic networks besides the main network model to be trained, which are used to obtain error gradients without complete feedforward and backward propagation processes. We propose a cascaded learning strategy for these local networks. In addition, the approach is also useful from multi-model perspectives, including structural optimization of neural networks, computationally efficient progressive inference, and ensemble classification for performance improvement. Experimental results show the effectiveness of the proposed approach and suggest guidelines for determining appropriate algorithm parameters. In recent days, deep learning has been remarkably advanced and successfully applied in numerous fields BID14 . A key mechanism behind the success of deep neural networks is that they are capable of extracting useful information progressively through their layered structures. It is an increasing trend that more and more complex deep neural network structures are developed in order to solve challenging real-world problems, e.g., BID7 . Training of deep neural networks is based on backpropagation in most cases, which basically works in a sequential and synchronous manner. During the feedforward pass, the input data is processed through the hidden layers to produce the network output; during the feedback pass, the error gradient is propagated back through the layers to update each layer's weight parameters. Therefore, training of each layer has dependency on all the other layers, which causes the issue of locking BID9 . This is undesirable in some cases, e.g., a system consisting of several interacting models, a model distributed across multiple computing nodes, etc.There have been attempts to remove the locking constraint. In BID0 , the method of auxiliary coordinates (MAC) is proposed. It replaces the original loss minimization problem with an equality-constrained optimization problem by introducing an auxiliary variable for each data and each hidden unit. Then, solving the problem is formulated as iteratively solving several sub-problems independently. A similar approach using the alternating direction method of multipliers (ADMM) is proposed in BID17 . It also employs an equality-constrained optimization but with different auxiliary variables, so that resulting sub-problems have closed form solutions. However, these methods are not scalable to deep learning architectures such as convolutional neural networks (CNNs).The method proposed in BID9 , called decoupled neural interface (DNI), directly synthesizes estimated error gradients, called synthetic gradients, using an additional small neural network for training a layer's weight parameters. As long as the synthetic gradients are close to the actual backpropagated gradients, each layer does not need to wait until the error at the output layer is backpropagated through the preceding layers, which allows independent training of each layer. However , this method suffers from performance degradation when compared to regular backpropagation BID2 . The idea of having additional modules supporting the layers of the main model is also adopted in BID2 , where the additional modules are trained to approximate the main model's outputs instead of error gradients. Due to this , however, the method does not resolve the issue of update locking, and in fact, the work does not intend to design a non-sequential learning algorithm. BID9 and the proposed local critic training. The black, green , and blue arrows indicate feedforward passes, an error gradient flow, and loss comparison, respectively.In this paper, we propose a novel approach for non-sequential learning, called local critic training. The key idea is that additional modules besides the main neural network model are employed, which we call local critics, in order to indirectly deliver error gradients to the main model for training without backpropagation. In other words, a local critic located at a certain layer group is trained in such a way that the derivative of its output serves as the error gradient for training of the corresponding layers' weight parameters. Thus, the error gradient does not need to be backpropagated, and the feedforward operations and gradient-descent learning can be performed independently. Through extensive experiments, we examine the influences of the network structure, update frequency, and total number of local critics, which provide not only insight into operation characteristics but also guidelines for performance optimization of the proposed method.In addition to the capability of implementing training without locking, the proposed approach can be exploited for additional important applications. First, we show that applying the proposed method automatically performs structural optimization of neural networks for a given problem, which has been a challenging issue in the machine learning field. Second, a progressive inference algorithm using the network trained with the proposed method is presented, which can adaptively reduce the computational complexity during the inference process (i.e., test phase) depending on the given data. Third, the network trained by the proposed method naturally enables ensemble inference that can improve the classification performance. In this paper, we proposed the local critic training approach for removing the inter-layer locking constraint in training of deep neural networks. In addition, we proposed three applications of the local critic training method: structural optimization of neural networks, progressive inference, and ensemble classification. It was demonstrated that the proposed method can successfully train CNNs with local critic networks having extremely simple structures. The performance of the method was also evaluated in various aspects, including effects of structures and update intervals of local critic networks and influences of the sizes of layer groups. Finally, it was shown that structural optimization, progressive inference, and ensemble classification can be performed directly using the models trained with the proposed approach without additional procedures. A ADDITIONAL RESULTS",1093,0.616,629,1.7376788553259142,"This paper proposes train by unlocking the layer-wise dependency The approach employs additional modules called local critic networks besides the main network model be trained obtain error gradients without complete feedforward and backward propagation processes We propose a cascaded learning strategy these local networks In addition the approach also useful from multi-model perspectives structural optimization computationally efficient progressive inference ensemble classification for performance improvement Experimental results the effectiveness the proposed approach and guidelines determining appropriate algorithm parameters In deep learning remarkably advanced successfully BID14 . A key mechanism behind extracting progressively their layered structures It more and more complex deep neural network structures developed solve BID7 . Training of deep neural networks based most cases basically works During the feedforward pass the input data processed the hidden layers; during the error gradient update each layer's weight parameters Therefore training each layer has dependency causes the issue locking BID9 . This undesirable a system consisting several interacting models a model distributedThere have remove the locking constraint In BID0 , the method auxiliary coordinatesMAC proposed It replaces the original loss minimization problem by introducing an auxiliary variable each data and each hidden unit Then solving formulated iteratively several sub independently A similar approach using the alternating direction method multipliersADMM BID17 . It also employs an equality-constrained optimization but different auxiliary variables resulting sub closed form solutions However these methods scalable deep learning such proposed BID9 , called decoupled neural interface directly synthesizes estimated error gradients called synthetic gradients using an additional small neural network for training a layer's weight parameters As long the synthetic gradients close each layer does wait the error at through the preceding layers allows independent training However , suffers performance degradation BID2 The idea having additional modules supporting the layers the main model also adopted BID2 , trained approximate instead error gradients Due this , however the method does resolve update locking in the work does intend design a non-sequential learning algorithm BID9 and the proposed local critic training. The black, green , and blue arrows feedforward passes an error gradient flow loss comparisonIn propose non-sequential learning called local critic training The key idea additional modules besides the main neural network model employed we local critics indirectly deliver error gradients for training without In a local critic located a certain layer group trained the derivative its output serves the error gradient training of the corresponding layers' weight parameters Thus the error gradient does need the feedforward operations and gradient-descent learning independently Through extensive experiments examine the influences the network structure update frequency total number local critics provide not only insight operation characteristics guidelines performance optimization the proposed methodIn the capability implementing training without locking exploited additional important applications First show applying the proposed method automatically performs structural optimization for has a challenging issue Second a progressive inference algorithm using the network trained with the proposed method adaptively reduce during depending Third the network trained by the proposed method naturally enables ensemble inference that improve In proposed the local critic training approach removing interlayer locking constraint training In addition proposed three applications the local critic training method structural optimization progressive inference ensemble classification It demonstrated the proposed method can successfully train CNNs local critic networks having extremely simple structures The performance the method also various aspects effects structures update intervals local critic networks influences the sizes layer groups Finally shown structural optimization, progressive inference ensemble classification directly the models trained the proposed approach without additional procedures A ADDITIONAL RESULTS",0.01,0.5836200812986606
"\emph{Truncated Backpropagation Through Time} (truncated BPTT, \cite{jaeger2002tutorial}) is a widespread method for learning recurrent computational graphs. Truncated BPTT keeps the computational benefits of \emph{Backpropagation Through Time} (BPTT \cite{werbos:bptt}) while relieving the need for a complete backtrack through the whole data sequence at every step.   However, truncation favors short-term dependencies: the gradient estimate of truncated BPTT is biased, so that it does not benefit from the convergence guarantees from stochastic gradient theory. We introduce \emph{Anticipated Reweighted Truncated Backpropagation} (ARTBP), an algorithm that keeps the computational benefits of truncated BPTT, while providing unbiasedness. ARTBP works by using variable truncation lengths together with carefully chosen compensation factors in the backpropagation equation. We check the viability of ARTBP on two tasks. First, a simple synthetic task where careful balancing of temporal dependencies at different scales is needed: truncated BPTT displays unreliable performance, and in worst case scenarios, divergence, while ARTBP converges reliably. Second, on Penn Treebank character-level language modelling \cite{ptb_proc}, ARTBP slightly outperforms truncated BPTT.
 We have shown that the bias introduced by truncation in the backpropagation through time algorithm can be compensated by the simple mathematical trick of randomizing the truncation points and introducing compensation factors in the backpropagation equation. The algorithm is experimentally viable, and provides proper balancing of the effects of different time scales when training recurrent models.",332,0.166,202,1.6435643564356435,"\emph{Truncated Backpropagation Through Time \cite{jaeger2002tutorial a widespread method learning recurrent computational graphs Truncated BPTT keeps the computational benefits \emph{Backpropagation Through \cite{werbos: while relieving a complete backtrack the whole data sequence at However truncation favors the gradient estimate truncated BPTT biased benefit the convergence guarantees from We introduce \emph{Anticipated Reweighted Truncated BackpropagationARTBP keeps the computational benefits truncated BPTT, while unbiasedness ARTBP works variable truncation lengths together carefully chosen compensation factors We check the viability ARTBP two tasks First simple synthetic task where careful balancing temporal dependencies at truncated BPTT displays unreliable performance in divergence, while ARTBP reliably Second on Penn Treebank character-level language modelling \cite{ptb_proc ARTBP slightly truncated BPTT We shown the bias introduced truncation through time algorithm compensated the simple mathematical trick introducing compensation factors The algorithm experimentally viable provides proper balancing when training recurrent models",0.0,0.3438246069357116
"Graph convolutional networks (GCNs) have been widely used for classifying graph nodes in the semi-supervised setting.
 Previous works have shown that GCNs are vulnerable to the perturbation on adjacency and feature matrices of existing nodes. However, it is unrealistic to change the connections of  existing nodes in many applications, such as existing users in social networks. In this paper, we investigate methods attacking GCNs by adding fake nodes. A greedy algorithm is proposed to generate adjacency and feature matrices of fake nodes, aiming to minimize the classification accuracy on the existing ones. In additional, we introduce a discriminator to classify fake nodes from real nodes, and propose a Greedy-GAN algorithm to simultaneously update the discriminator and the attacker, to make fake nodes indistinguishable to the real ones.   Our non-targeted attack decreases the accuracy of GCN down to 0.10, and our targeted attack reaches a success rate of 0.99 for attacking the whole datasets, and 0.94 on average for attacking a single node. Graphs play a very important role in many real world applications, such as social networks (Facebook and Twitter), biological networks (protein-protein interaction networks and gene interaction networks), as well as attribute graphs (PubMed and Arxiv) BID12 BID32 BID26 . Node classification is one of the most important tasks on graphs-given a graph with labels associated with a subset of nodes, predict the labels for rest of the nodes. For this node classification task, deep learning models on graphs, such as Graph Convoltional Networks (GCNs), have achieved state of the art performance BID16 . Moreover, GCNs have wide applications in cyber security, where they can learn a close-to-correct node labeling semiautonomously. This reduces the load on security experts and helps to manage networks that add or remove nodes dynamically, such as, WiFi networks in universities and web services in companies.The wide applicability of GCNs motivates recent studies about their robustness. BID34 BID6 developed algorithms to attack GCNs, showing that by altering a small amount of edges and features, the classification accuracy of GCNs can be reduced to chance-level. However, changing edges or features associated with existing nodes is impractical in many cases. For example, in social network applications, an attacker has to login to the users' accounts to change existing connections and features, and gaining login accesses is almost impossible. In comparison, adding fake nodes that correspond to fake accounts or users, can be much easier in practice. But the key question is can we interfere the classification results of existing nodes by adding fake nodes to the network? We answer this question affirmative by introducing novel algorithms to design fake nodes that successfully reduce GCN's performance on existing nodes.To design the adjacency and feature matrices associated with fake nodes, we have to address two challenges. First, the edges and features are usually discrete 0/1 variables. Although there have been many algorithms proposed for attacking image classifiers, such as FGSM, C&W and PGD attacks BID11 BID1 BID21 , they all assume continuous input space and cannot be directly applied to problems with discrete input space. Second, it's not easy to make the fake nodes ""looked"" like the real ones? For example, if we add a fake node that connects to all existing nodes, the system can easily detect and disable such fake node. In this paper, we propose two algorithms, Greedy attack and Greedy-GAN attack, to address these two challenges. Our contributions can be summarized below:• To the best of our knowledge, this is the first paper studying how to add fake nodes to attack GCNs. We do not need to manipulate existing nodes' adjacency and feature matrices.• We propose a Greedy attack algorithm to address the discrete input space problem in designing fake nodes' adjacency and feature matrices.• We introduce a discriminator to classify fake nodes from real nodes, and propose a Greedy-GAN algorithm to simultaneous optimize the discriminator and the attacker. Despite a lower successful rate, this approach can make fake nodes harder to detect.• We conduct experiments on several real datasets. For non-targeted attack, we get accuracy down to 0.10 for the Cora dataset, and 0.14 for the Citeseer dataset. For targeted attack on whole datasets, Greedy attack have up to 99% success rate on Cora and 90% on Citeseer.For targeted attack on a single node, it could reach 94% success rate on Cora and 0.80% success rate on Citeseer. We present two algorithms, Greedy and Greedy-GAN, on adversarial attacks of GCNs by adding fake nodes, without changing any existing edges or features, for both non-targeted and targeted attacks. We successfully attacked existing GCN implementations, and explored parameter sensitives, such as number of fake nodes and different label rates of fake nodes. To make the attack unnoticeable, we added a discriminator using the Greedy-GAN algorithm to generate features of fake nodes. We noticed that data cleaning before training is crucial, and adding a discriminator makes the impact of attacks weaker. There is a trade-off between the efficiency of attack and realness of fake nodes' features.",1066,0.544,593,1.7976391231028668,"Graph convolutional networks graph nodes the semi-supervised setting Previous works GCNs vulnerable on adjacency feature matrices existing nodes However unrealistic change the connections existing nodes many applications existing users in In investigate methods attacking GCNs adding fake nodes A greedy algorithm proposed generate adjacency and feature matrices fake nodes aiming minimize the classification accuracy on the existing ones In additional introduce a discriminator classify fake nodes from propose a Greedy-GAN algorithm simultaneously update the attacker fake nodes indistinguishable to Our non-targeted attack decreases GCN down reaches for attacking the whole datasets on average Graphs play ( biological networks gene interaction networks as attribute graphs (PubMed BID12 BID32 . Node classification one on graphs-given labels associated a subset predict rest For this node classification task deep learning models on graphs such Graph Convoltional Networks achieved state BID16 . Moreover GCNs wide applications cyber security where learn a close-to-correct node labeling semiautonomously This reduces security experts helps manage networks add or nodes dynamically, WiFi networks in universities web services companiesThe wide applicability GCNs motivates recent studies about their robustness BID34 BID6 developed algorithms attack GCNs showing by altering edges features the classification accuracy chance-level However changing edges or features associated existing nodes impractical For example social network applications an attacker has login change existing connections features gaining login accesses almost In comparison adding fake nodes that correspond fake accounts or users, can much in But the key question can interfere the classification results existing nodes by adding fake nodes We answer affirmative introducing novel algorithms design fake nodes successfully reduce GCN's performance existing nodesTo design and feature matrices associated have address First the edges features usually discrete 0/1 variables Although many algorithms proposed attacking image classifiers such FGSM C&W PGD attacks BID11 BID1 BID21 , they assume continuous input space directly problems Second easy the fake nodes ""looked? For example add a fake node that connects all existing nodes the system easily disable such fake node In this paper two algorithms Greedy attack Greedy-GAN attack address Our contributions can summarized below:• To best studying add fake nodes attack GCNs do need manipulate existing nodes' adjacency feature propose a Greedy attack algorithm address the discrete input space problem designing introduce classify from propose simultaneous optimize the attacker Despite a lower successful rate this approach can make fake nodes harder detect.• We conduct several real datasets For non-targeted attack get accuracy down the Cora dataset the Citeseer dataset For targeted attack whole datasets Greedy attack have Cora CiteseerFor a single node it could reach We present two algorithms Greedy Greedy-GAN on adversarial attacks of GCNs by adding fake nodes without changing any existing edges features for We successfully attacked existing GCN implementations explored parameter sensitives number fake nodes different label rates of To make the attack added a discriminator using the Greedy-GAN algorithm generate features fake nodes We noticed data cleaning before training crucial adding a discriminator makes the impact attacks weaker There the efficiency attack realness fake nodes' features",0.01,0.7363935755428103
"Transfer learning aims to solve the data sparsity for a specific domain by applying information of another domain. Given a sequence (e.g. a natural language sentence), the transfer learning, usually enabled by recurrent neural network (RNN), represent the sequential information transfer. RNN uses a chain of repeating cells to model the sequence data. However, previous studies of neural network based transfer learning simply transfer the information across the whole layers, which are unfeasible for seq2seq and sequence labeling. Meanwhile, such layer-wise transfer learning mechanisms also lose the fine-grained cell-level information from the source domain.

 In this paper, we proposed the aligned recurrent transfer, ART, to achieve cell-level information transfer. ART is in a recurrent manner that different cells share the same parameters. Besides transferring the corresponding information at the same position, ART transfers information from all collocated words in the source domain. This strategy enables ART to capture the word collocation across domains in a more flexible way. We conducted extensive experiments on both sequence labeling tasks (POS tagging, NER) and sentence classification (sentiment analysis). ART outperforms the state-of-the-arts over all experiments.
 Most previous NLP studies focus on open domain tasks. But due to the variety and ambiguity of natural language BID7 BID18 , models for one domain usually incur more errors when adapting to another domain. This is even worse for neural networks since embeddingbased neural network models usually suffer from overfitting BID12 . While existing NLP models are usually trained by the open domain, they suffer from severe performance degeneration when adapting to specific domains. This motivates us to train specific models for specific domains.The key issue of training a specific domain is the insufficiency of labeled data. Transfer learning is one promising way to solve the insufficiency BID8 . Existing studies BID3 BID8 have shown that (1) NLP models in different domains still share many common features (e.g. common vocabularies, similar word semantics, similar sentence syntaxes), and (2) the corpus of the open domain is usually much richer than that of a specific domain.Our transfer learning model is under the pre-training framework. We first pre-train the model for the source domain. Then we fine-tune the model for the target domain. Recently, some pre-trained models (e.g. BERT BID4 , ELMo (Peters et al., 2018) , GPT-2 (Radford et al., 2019) ) successfully learns general knowledge for text. The difference is that these models use a large scale and domain-independent corpus for pre-training. In this paper, we use a small scale but domaindependent corpus as the source domain for pre-training. We argue that, for the pre-training corpus, the domain relevance will overcome the disadvantage of limited scale.Most previous transfer learning approaches BID11 BID6 only transfer information across the whole layers. This causes the information loss from cells in the source domain. ''Layer-wise transfer learning"" indicates that the approach represents the whole sentence by a single vector. So the transfer mechanism is only applied to the vector. We highlight the effectiveness of precisely capturing and transferring information of each cell from the source domain in two cases. First, in seq2seq (e.g. machine translation) or sequence labeling (e.g. POS tagging) tasks, all cells directly affect the results. So layer-wise information transfer is unfeasible for these tasks. Second, even for the sentence classification, cells in the source domain provide more fine-grained information to understand the target domain. For example, in figure 1, parameters for ""hate"" are insufficiently trained. The model transfers the state of ""hate"" from the source domain to understand it better.Target: Sometimes I really hate RIBs.Source: Sometimes I really hate RIBs. Figure 1 : Motivation of ART. The orange words ""sometimes"" and ""hate"" are with insufficiently trained parameters. The red line indicates the information transfer from the corresponding position. The blue line indicates the information transfer from a collocated word. Besides transferring the corresponding position's information, the transfer learning algorithm captures the cross-domain long-term dependency. Two words that have a strong dependency on each other can have a long gap between them. Being in the insufficiently trained target domain, a word needs to represent its precise meaning by incorporating the information from its collocated words. Here ""collocate"" indicates that a word's semantics can have long-term dependency on other words. To understand a word in the target domain, we need to precisely represent its collocated words from the source domain. We learn the collocated words via the attention mechanism BID1 . For example, in figure 1, ""hate"" is modified by the adverb ""sometimes"", which implies the act of hating is not serious. But the ""sometimes"" in the target domain is trained insufficiently. We need to transfer the semantics of ""sometimes"" in the source domain to understand the implication. Therefore, we need to carefully align word collocations between the source domain and the target domain to represent the long-term dependency.In this paper, we proposed ART (aligned recurrent transfer), a novel transfer learning mechanism, to transfer cell-level information by learning to collocate cross-domain words. ART allows the celllevel information transfer by directly extending each RNN cell. ART incorporates the hidden state representation corresponding to the same position and a function of the hidden states for all words weighted by their attention scores.Cell-Level Recurrent Transfer ART extends each recurrent cell by taking the states from the source domain as an extra input. While traditional layer-wise transfer learning approaches discard states of the intermediate cells, ART uses cell-level information transfer, which means each cell is affected by the transferred information. For example, in figure 1, the state of ""hate"" in the target domain is affected by ""sometimes"" and ""hate"" in the source domain. Thus ART transfers more fine-grained information.Learn to Collocate and Transfer For each word in the target domain, ART learns to incorporate two types of information from the source domain: (a) the hidden state corresponding to the same word, and (b) the hidden states for all words in the sequence. Information (b) enables ART to capture the cross-domain long-term dependency. ART learns to incorporate information (b) based on the attention scores BID1 of all words from the source domain. Before learning to transfer, we first pre-train the neural network of the source domain. Therefore ART is able to leverage the pre-trained information from the source domain. In this paper, we study the problem of transfer learning for sequences. We proposed the ART model to collocate and transfer cell-level information. ART has three advantages: (1) it transfers more fine-grained cell-level information, and thus can be adapted to seq2seq or sequence labeling tasks; (2) it aligns and transfers a set of collocated words in the source sentence to represent the cross domain long-term dependency; (3) it is general and can be applied to different tasks. Besides, ART verified the effectiveness of pre-training models with the limited but relevant training corpus.",1439,0.917,825,1.7442424242424241,"Transfer learning aims solve the data sparsity for applying information of Given a sequence the transfer learning, usually enabled represent RNN uses a chain repeating cells model the sequence data However previous studies neural based transfer simply transfer across the whole layers seq2seq and sequence labeling Meanwhile such layer-wise transfer learning mechanisms also lose from the source domain In proposed the aligned recurrent transfer, ART achieve ART is in a recurrent manner that different cells share Besides transferring the corresponding information at ART transfers all collocated words This strategy enables ART capture the word collocation across domains We conducted extensive experiments both sequence labeling tasksPOS tagging NER sentence classification ART outperforms the state over all experiments Most previous NLP studies focus open domain tasks But due the variety ambiguity natural language BID7 BID18 , models one domain usually incur adapting This even neural networks since embeddingbased neural network models usually suffer BID12 . While existing NLP models usually trained the open domain suffer severe performance degeneration adapting This motivates train specific models specific domainsThe key issue labeled data Transfer learning one promising way solve BID8 . Existing studies BID3 BID8 have (1) NLP models different domains still share similar word semantics similar sentence syntaxes the open domain usually richerOur transfer learning model under We first pretrain the model the source domain Then we the target domain Recently some pre-trained models (e.g. BERT BID4 , ELMo (Peters et 2018 GPT-2Radford 2019 successfully learns general knowledge for text. The difference these models use a large scale and domain-independent corpus pretraining In but domaindependent corpus as the source domain pretraining We argue the pre-training corpus the domain relevance will overcome limited scaleMost previous transfer learning approaches BID11 BID6 only transfer information across the whole layers This causes the information loss cells the source domain ''Layer-wise transfer learning"" indicates represents the whole sentence by So the transfer mechanism only applied the vector We highlight the effectiveness precisely capturing transferring of each cell from the source domain two cases First in seq2seq machine translation or sequence labeling all cells directly affect So layer-wise information transfer these tasks Second even for the sentence classification cells the source domain provide to understand For example figure parameters ""hate insufficiently trained The model transfers ""hate the source domain understandTarget Sometimes really RIBsSource Sometimes Figure : Motivation ART The orange wordssometimes with insufficiently trained parameters The red line indicates the information transfer from the corresponding position The blue line indicates the information transfer from a collocated word Besides transferring the corresponding position's information learning captures Two words a strong dependency can a long gap Being the insufficiently trained target domain a word needs represent its precise meaning by incorporating its collocated words Here ""collocate indicates a word's semantics have long-term dependency To a word the target domain precisely represent its collocated words from We learn the collocated words via the attention mechanism BID1 For example figure ""hate modified adverbsometimes is serious But ""sometimes the target domain trained insufficiently We need transfer the semanticssometimes the source domain understand the implication Therefore carefully align word collocations the source domain representIn proposed ARTaligned recurrent transfer a novel transfer learning mechanism transfer by learning collocate ART allows the celllevel information transfer by directly extending each RNN cell ART incorporates the hidden state representation corresponding a function all words weighted their attention scoresCell-Level Recurrent Transfer ART extends each recurrent cell taking the source domain While traditional layerwise transfer learning discard states the intermediate cells ART affected For example figure the state ""hate the target domain affectedsometimes Thus ART transfersLearn Collocate Transfer For each word the target domain ART learns incorporate two types from ( hidden state corresponding for the sequence Information (b enables ART capture the cross-domain long-term dependency. ART learns incorporate information (b based the attention scores BID1 of all words from the source domain Before learning transfer pretrain of the source domain Therefore ART able leverage the source domain In study the problem transfer learning sequences We proposed the ART model collocate transfer ART has three advantages transfers thus adapted seq2seq or sequence labeling tasks and transfers collocated words the source sentence represent the cross domain long-term dependency general different tasks Besides ART verified pre-training models the limited but relevant training corpus",0.01,0.6003434782290684
"Addressing uncertainty is critical for autonomous systems to robustly adapt to the real world. We formulate the problem of model uncertainty as a continuous Bayes-Adaptive Markov Decision Process (BAMDP), where an agent maintains a posterior distribution over latent model parameters given a history of observations and maximizes its expected long-term reward with respect to this belief distribution. Our algorithm, Bayesian Policy Optimization, builds on recent policy optimization algorithms to learn a universal policy that navigates the exploration-exploitation trade-off to maximize the Bayesian value function. To address challenges from discretizing the continuous latent parameter space, we propose a new policy network architecture that encodes the belief distribution independently from the observable state. Our method significantly outperforms algorithms that address model uncertainty without explicitly reasoning about belief distributions and is competitive with state-of-the-art Partially Observable Markov Decision Process solvers. At its core, real-world robotics focuses on operating under uncertainty. An autonomous car must drive alongside unpredictable human drivers under road conditions that change from day to day. An assistive home robot must simultaneously infer users' intended goals as it helps them. A robot arm must recognize and manipulate varied objects. These examples share common themes: (1) an underlying dynamical system with unknown latent parameters (road conditions, human goals, object identities), (2) an agent that can probe the system via exploration, while ultimately (3) maximizing an expected long-term reward via exploitation.The Bayes-Adaptive Markov Decision Process (BAMDP) framework BID9 elegantly captures the exploration-exploitation dilemma that the agent faces. Here, the agent maintains a belief, which is a posterior distribution over the latent parameters φ given a history of observations. A BAMDP can be cast as a Partially Observable Markov Decision Process (POMDP) BID7 whose state is (s, φ), where s corresponds to the observable world state. By planning in the belief space of this POMDP, the agent balances explorative and exploitative actions. In this paper, we focus on BAMDP problems in which the latent parameter space is either a discrete finite set or a bounded continuous set that can be approximated via discretization. For this class of BAMDPs, the belief is a categorical distribution, allowing us to represent it using a vector of weights.The core problem for BAMDPs with continuous state-action spaces is how to explore the reachable belief space. In particular, discretizing the latent space can result in an arbitrarily large belief vector, which causes the belief space to grow exponentially. Approximating the value function over the reachable belief space can be challenging: although point-based value approximations BID16 BID26 have been largely successful for approximating value functions of discrete POMDP problems, these approaches do not easily extend to continuous state-action spaces. Monte-Carlo Tree Search approaches (Silver & Veness, 2010; BID10 are also prohibitively expensive in continuous state-action spaces: the width of the search tree after a single iteration is too large, preventing an adequate search depth from being reached.Our key insight is that we can bypass learning the value function and directly learn a policy that maps beliefs to actions by leveraging the latest advancements in batch policy optimization algorithms BID32 . Inspired by previous approaches that train learning algorithms with an ensemble of models BID30 BID43 , we examine model uncertainty through a BAMDP lens. Although our approach provides only locally optimal policies, we believe that it offers a practical and scalable solution for continuous BAMDPs.Our method, Bayesian Policy Optimization (BPO), is a batch policy optimization method which utilizes a black-box Bayesian filter and augmented state-belief representation. During offline training, BPO simulates the policy on multiple latent models sampled from the source distribution FIG0 ). At each simulation timestep, it computes the posterior belief using a Bayes filter and inputs the state-belief pair (s, b) to the policy. Our algorithm only needs to update the posterior along the simulated trajectory in each sampled model, rather than branching at each possible action and observation as in MCTS-based approaches.Our key contribution is the following. We introduce a Bayesian policy optimization algorithm to learn policies that directly reason about model uncertainty while maximizing the expected long-term reward (Section 4). To address the challenge of large belief representations, we introduce two encoder networks that balance the size of belief and state embeddings in the policy network FIG0 . In addition, we show that our method, while designed for BAMDPs, can be applied to continuous POMDPs when a compact belief representation is available (Section 4.2). Through experiments on classical POMDP problems and BAMDP variants of OpenAI Gym benchmarks, we show that BPO significantly outperforms algorithms that address model uncertainty without explicitly reasoning about beliefs and is competitive with state-of-the-art POMDP algorithms (Section 5). Bayesian Policy Optimization is a practical and scalable approach for continuous BAMDP problems. We demonstrate that BPO learns policies that achieve performance comparable to state-of-the-art discrete POMDP solvers. They also outperform state-of-the-art robust policy gradient algorithms that address model uncertainty without formulating it as a BAMDP problem. Our network architecture scales well with respect to the degree of latent parameter space discretization due to its independent encoding of state and belief. We highlight that BPO is agnostic to the choice of batch policy optimization subroutine. Although we used TRPO in this work, we can also use more recent policy optimization algorithms, such as PPO BID33 , and leverage improvements in variance-reduction techniques BID42 ).BPO outperforms algorithms that do not explicitly reason about belief distributions. Our Bayesian approach is necessary for environments where uncertainty must actively be reduced, as shown in FIG1 and FIG2 . If all actions are informative (as with MuJoCo, Chain) and the posterior belief distribution easily collapses into a unimodal distribution, UP-MLE provides a lightweight alternative.BPO scales to fine-grained discretizations of latent space. However , our experiments also suggest that each problem has an optimal discretization level, beyond which further discretization may degrade performance. As a result , it may be preferable to perform variable-resolution discretization rather than an extremely fine, single-resolution discretization. Adapting iterative densification ideas previously explored in motion planning BID8 and optimal control BID20 to the discretization of latent space may yield a more compact belief representation while enabling further improved performance.An alternative to the model-based Bayes filter and belief encoder components of BPO is learning to directly map a history of observations to a lower-dimensional belief embedding, analogous to BID25 . This would enable a policy to learn a meaningful belief embedding without losing information from our a priori choice of discretization. Combining a recurrent policy for unidentified parameters with a Bayes filter for identified parameters offers an intriguing future direction for research efforts.",1372,0.698,787,1.7433290978398983,"Addressing uncertainty is critical autonomous systems robustly adapt We formulate model uncertainty a continuous Bayes-Adaptive Markov Decision Process maintains latent model parameters given a history observations maximizes with this belief distribution Our algorithm Bayesian Policy Optimization builds recent policy optimization algorithms learn a universal policy navigates to the Bayesian value function To address challenges discretizing the continuous latent parameter space propose a new policy network architecture the belief distribution independently Our method significantly algorithms that address model uncertainty without explicitly reasoning belief distributions is competitive state Partially Decision Process solvers At real-world robotics focuses operating under uncertainty An autonomous car must alongside unpredictable human drivers under change An assistive home robot must simultaneously infer users' intended goals as helps. A robot arm must recognize manipulate varied objects These examples share unknown latent parametersroad conditions human goals object identities probe via exploration while ultimately maximizing via exploitation BID9 elegantly Here the agent maintains a belief a posterior distribution � given a history observations BAMDP can cast a Partially Observable Markov Decision Process BID7 whose state (s, � corresponds By planning in the belief space this POMDP the agent balances explorative and exploitative actions In focus BAMDP problems which the latent parameter space either a discrete finite that via For this class BAMDPs the belief a categorical distribution allowing represent it usingThe core problem with continuous state-action spaces explore the reachable belief space In particular discretizing the latent space can result an arbitrarily large belief vector causes Approximating the value function over the reachable belief space can challenging: although BID16 BID26 largely discrete POMDP problems easily extend continuous state-action spaces Monte-Carlo Tree Search approaches (Silver & Veness BID10 are prohibitively continuous state-action spaces: the width after too preventing fromOur key insight bypass learning the value function directly a policy maps beliefs leveraging the latest advancements batch policy optimization algorithms BID32 . Inspired previous approaches train learning algorithms an ensemble models BID30 BID43 examine model uncertainty through a BAMDP lens Although our approach provides only locally optimal policies continuous BAMDPsOur method utilizes augmented state-belief representation During offline training BPO simulates the policy on multiple latent models sampled the source distribution FIG0 At each simulation timestep it the posterior belief using inputs the state-belief pair, the policy Our algorithm only needs update the posterior along the simulated trajectory each sampled model rather branching at each possible action observation as MCTS-based approachesOur key contribution We introduce a Bayesian policy optimization learn policies directly reason model uncertainty while maximizingSection To address large belief representations introduce two encoder networks balance the policy network FIG0 In show our method, designed BAMDPs continuous POMDPs when a compact belief representationSection Through experiments classical POMDP problems BAMDP variants OpenAI Gym benchmarks BPO significantly algorithms that address model uncertainty without explicitly reasoning beliefs is competitive stateSection Bayesian Policy Optimization continuous BAMDP problems We demonstrate BPO learns policies achieve performance comparable state discrete POMDP solvers They also outperform state robust policy gradient algorithms that address model uncertainty without formulating it a BAMDP problem Our network architecture scales respect the degree latent parameter space discretization due its independent encoding state belief We highlight that BPO agnostic to the choice batch policy optimization subroutine Although used TRPO this work more recent policy optimization PPO BID33 , leverage improvements BID42 ).BPO outperforms algorithms explicitly reason belief distributions Our Bayesian approach necessary environments uncertainty must actively FIG1 If all actions informative ( MuJoCo Chain) the posterior belief distribution easily collapses UP-MLE provides a lightweight alternativeBPO scales latent space However , our experiments also each problem beyond degrade As , preferable perform variable-resolution discretization rather Adapting iterative densification ideas previously motion planning BID8 optimal control to latent space may a more compact belief representation while enabling further improved performanceAn alternative the model-based Bayes filter belief encoder components BPO learning directly a history observations analogous This would enable a policy learn a meaningful belief embedding without losing our a priori choice Combining a recurrent policy for unidentified parameters a Bayes filter offers research efforts",0.01,0.5980164027994129
"For many evaluation metrics commonly used as benchmarks for unconditional image generation, trivially memorizing the training set attains a better score than models which are considered state-of-the-art; we consider this problematic.
 We clarify a necessary condition for an evaluation metric not to behave this way: estimating the function must require a large sample from the model. In search of such a metric, we turn to neural network divergences (NNDs), which are defined in terms of a neural network trained to distinguish between distributions. The resulting benchmarks cannot be ``won'' by training set memorization, while still being perceptually correlated and computable only from samples. We survey past work on using NNDs for evaluation, implement an example black-box metric based on these ideas, and validate experimentally that it can measure a notion of generalization.
 In machine learning, it is often difficult to directly measure progress towards our goals (e.g. ""classify images correctly in the real world"", ""generate valid translations of text""). To enable progress despite this difficulty, it is useful to define a standardized benchmark task which is easy to evaluate and serves as a proxy for some final task. This enables much stronger claims of improvement (albeit towards a somewhat artificial task) by reducing the risk of inadequate baselines or evaluation mistakes, with the hope that progress on the benchmark will yield discoveries and methods which are useful towards the final task. This approach requires that a benchmark task satisfy two properties:1. It should define a straightforward and objective evaluation procedure, such that strong claims of improvement can be made. Any off-limits methods of obtaining a high score (e.g. abusing a test set) should be clearly defined. 2. Improved performance on the benchmark should require insights which are likely to be helpful towards the final task. The benchmark should, by construction, reflect at least some of the kinds of difficulty inherent in the final task.Together these imply that a benchmark should at least be nontrivial: we should not know a priori how to obtain an arbitrarily high score, except perhaps by clearly-off-limits methods. Crucial to a useful benchmark is an evaluation metric which measures what we care about for the final task and which satisfies the requirements outlined above.This paper deals with unconditional generation of natural images, which has been the goal of much recent work in generative modeling (e.g. BID35 BID25 . Our ideas are general, but we hope to improve evaluation practice in models like Generative Adversarial Networks (GANs) BID14 . Generative modeling has many possible final tasks BID47 . Of these, unconditional image generation is perhaps not very useful directly, but the insights and methods discovered in its pursuit have proven useful to other tasks like domain adaptation BID42 , disentangled representation learning , and imitation learning BID21 .Some notion of generalization is crucial to why unconditional generation is difficult (and hence interesting). Otherwise , simply memorizing the training data exactly would yield perfect ""generations"" Figure 1 : Common GAN benchmarks prefer training set memorization (p train , red) to a model (q, green) which imperfectly fits the true distribution (p, blue) but covers more of p's support. and the task would be meaningless. One might argue that some work-particularly recent GAN research-merely aims to improve convergence properties of the learning algorithm, and so generalization isn't a big concern. However, generalization is an important part of why GANs themselves are interesting. A GAN with better convergence properties but no ability to generalize is arguably not a very interesting GAN; we believe our definition of the task, and our benchmarks, should reflect this.Because our task is to generate samples, and often our models only permit sampling, recent work (e.g. BID23 BID17 BID48 ) has adopted benchmarks based on evaluation metrics BID20 which measure the perceptual quality and diversity of samples. However these particular metrics are, by construction, trivially ""won"" by a model which memorizes the training set. In other words , they mostly ignore any notion of generalization, which is central to why the task is difficult to begin with. This idea is illustrated in Figure 1 . In this sense they give rise to ""trivial"" benchmark tasks which can lead to less convincing claims of improvement, and ultimately less progress towards useful methods. While ""nontrivial "" benchmark tasks based on downstream applications can be used, the goals of these tasks are at best indirectly related to, and at worst opposite from, sample generation (e.g. for semi-supervised learning BID10 ).This paper considers evaluation metrics for generative models which give rise to nontrivial benchmarks, and which are aligned with the final task of generating novel, perceptually realistic and diverse data. We stress the difference between evaluating models and defining benchmarks. The former assumes that models have been chosen ahead of time, independently of the metric. The latter assumes that models will be developed with the metric in mind, and so seeks to avoid falsely high scores resulting from exploiting undesirable solutions to the benchmark (e.g. memorizing the training set). Our goal is to define benchmarks , and many of our decisions follow from this. Our contributions are as follows:• We establish a framework for sample-based evaluation that permits a meaningful notion of generalization. We clarify a necessary condition for the ability to measure generalization: That the evaluation requires a large sample from the model. • We investigate using neural network divergences as evaluation metrics which have attractive properties for this application. We survey past work exploring the use of neural network divergences for evaluation.• We study an example neural network divergence called ""CNN divergence"" (D CNN ) experimentally.We demonstrate that it can detect and penalize memorization and that it measures diversity relatively more than other evaluation functions. We believe our experiments show that the NNDs are a promising direction for evaluating generative models. They are not trivially solved by memorizing the training set, which satisfies our argument (Section 3) that measuring generalization ability is linked to whether the metric requires a large collection of samples. They also appear to prefer diversity relatively more than the IS and FID metrics. We note that NNDs are almost certainly not the only evaluation metric under which models can meaningfully generalize, and encourage work on alternative metrics.Ultimately, models should be evaluated according to their intended final task BID47 . In our work we assume that our final task is not usefully solved by memorizing the training set, but for many tasks such memorization is a completely valid solution. If so, the evaluation should reflect this: we do not need our model to be closer to the true distribution than the training set, Definition 1 does not apply, and we might be free to consider evaluations which look at only a small sample from the model.",1372,0.718,800,1.715,"For many evaluation metrics commonly unconditional image generation trivially memorizing the training set attains models considered state; we this problematic We clarify a necessary condition an evaluation metric not behave this estimating must require from In search such a metric turn neural network divergences trained distributions The resulting benchmarks ``won training set memorization while still perceptually correlated and computable only from samples We survey past work using NNDs evaluation implement an example black-box metric based these ideas validate experimentally measure a notion In machine learning directly progress towards ""classify images correctly valid translations To enable progress despite this difficulty a standardized benchmark task easy evaluate serves some final task This enables much stronger claims improvement (albeit towards a somewhat artificial task inadequate baselines evaluation mistakes with progress the benchmark yield discoveries methods towards the final task This approach requires a benchmark task satisfy properties:1 It should define a straightforward and objective evaluation procedure such strong claims improvement Any off methods obtaining abusing a test set clearly 2 Improved performance the benchmark should require insights which likely helpful towards the final task The benchmark should, construction reflect difficulty inherent the final taskTogether imply at: we know a obtain except clearly-off Crucial a useful benchmark an evaluation metric we care for the final task satisfies outlinedThis paper deals unconditional generation natural images has generative modeling BID35 BID25 . Our ideas general hope improve evaluation practice models Generative Adversarial Networks (GANs) BID14 . Generative modeling many possible final tasks BID47 . Of these unconditional image generation not very directly the insights methods discovered its pursuit proven other tasks like domain adaptation BID42 , disentangled representation learning imitation BID21 .Some notion crucial why unconditional generation difficult interesting Otherwise , simply memorizing the training data exactly would yield perfect ""generations Figure : Common GAN benchmarks prefer training set memorization (p train red a modelq, imperfectly fits the true distribution blue but covers p's support and the task would meaningless One might some work-particularly recent GAN research- aims convergence properties the learning algorithm generalization is However generalization why GANs themselves interesting A GAN with better convergence properties but no ability generalize arguably; we believe our definition the task, our benchmarksBecause generate samples often our models only permit recent work (e.g. BID23 BID17 BID48 adopted benchmarks evaluation metrics BID20 which the perceptual quality diversity samples However these particular metrics, construction trivially ""won a model memorizes the training set In , mostly ignore any notion generalization central why the task begin This idea illustrated . In this sense they give ""trivial"" benchmark tasks less convincing claims improvement ultimately less progress useful methods While ""nontrivial "" benchmark tasks based downstream applications the goals at indirectly, at worst opposite from, sample generation for BID10 ).This paper considers evaluation metrics which give aligned the final task generating novel perceptually realistic and diverse data We stress the difference evaluating models defining benchmarks former assumes models chosen ahead independently the metric latter assumes models developed metric in so seeks falsely high scores resulting exploiting undesirable solutions the benchmark ( memorizing Our goal define benchmarks , many our decisions follow Our contributions as establish sample-based evaluation permits a meaningful notion We clarify a necessary condition the ability measure generalization That the evaluation requires from the model • We investigate using neural network divergences evaluation metrics which attractive properties this application We survey past work exploring neural network divergences evaluation.• study an example neural network divergence called ""CNN divergence (D CNN experimentallyWe demonstrate detect memorization that measures diversity relatively more other evaluation functions We believe our experiments the NNDs a promising direction evaluating generative models They trivially solved memorizing the training set satisfies our argumentSection measuring generalization ability linked whether requires a large collection samples They also appear prefer diversity relatively the IS and FID metrics We note NNDs almost evaluation metric under models meaningfully encourage workUltimately models their intended final task BID47 . In our work assume our final task not usefully solved memorizing the training set for many tasks a completely valid solution If so the evaluation reflect we our model closer the training set Definition does might free consider evaluations look from",0.01,0.5258363504706739
"Conventional methods model open domain dialogue generation as a black box through end-to-end learning from large scale conversation data. In this work, we make the first step to open the black box by introducing dialogue acts into open domain dialogue generation. The dialogue acts are generally designed and reveal how people engage in social chat. Inspired by analysis on real data, we propose jointly modeling dialogue act selection and response generation, and perform learning with human-human conversations tagged with a dialogue act classifier and a reinforcement approach to further optimizing the model for long-term conversation. With the dialogue acts, we not only achieve significant improvement over state-of-the-art methods on response quality for given contexts and long-term conversation in both machine-machine simulation and human-machine conversation, but also are capable of explaining why such achievements can be made. Conversational agents are becoming ubiquitous recently. Through human-machine conversation, such agents either help users complete specific tasks BID39 or engage them in social chat BID30 . Depending on application scenarios, various conversational agents have been designed including chatbots, personal assistants, and automated customer service, etc.Traditional research on conversational agents focuses on task-oriented dialogue systems BID39 where task specific dialogue acts are handcrafted in a form of slot-value pairs. On the one hand, through slot-filling, the dialogue acts make conversations in such systems interpretable and controllable; on the other hand, they also hinder scaling such systems to new domains. To escape from the limitation, recent interest of research moves to end-to-end dialogue learning without any assumptions on dialogue acts. Most of the effort is paid to non-task-oriented chit-chat BID30 , and there are also a few studies on task-oriented dialogues BID1 BID4 . Without dialogue acts, these work directly constructs a response by learning from large scale data with neural networks, and thus is easy to scale to new domains. On the other hand, due to the absence of dialogue acts, it is hard to interpret the emergence of a response to a dialogue context and predict where the conversation will flow to.In this work, we aim to achieve interpretability and controllability in non-task-oriented dialogues. To this end, we introduce dialogue acts into open domain dialogue generation. Open domain dialogue generation has been widely applied to chatbots which aim at engaging users by keeping conversation going. Existing work concentrates on generating relevant and diverse responses for a static context. However, it is not clear if relevance and diversity are sufficient to engagement in dynamic interactions. Therefore, we investigate the following problems: (1) if we can properly design dialogue acts that can enable us to understand engagement in human-human open domain conversation; (2) how to learn a dialogue generation model with the dialogue acts; and (3) how the model performs in practice and if the performance can be explained by the dialogue acts.To examine how people engage in social chat, we establish a general dialogue act taxonomy for open domain conversation by extending the existing work with high-level dialogue acts regarding to conversational context. The taxonomy, when applied to real data, gives rise to an interesting finding that in addition to replying with relevance and diversity , people are used to driving their social chat by constantly switching to new contexts and properly asking questions. Such behaviors are less explored before, and thus are difficult for the existing end-to-end learning methods to imitate. To mimic human behaviors, we propose jointly modeling dialogue act selection and response generation in open domain dialogue generation. The dialogue model is specified with neural networks. We propose learning from human-human interactions by fitting the model to large scale real world dialogues tagged with a dialogue act classifier and further optimizing the policy of act selection for long-term conversation through a reinforcement learning approach. Our model enjoys several advantages over the existing models: (1) the dialogue acts provide interpretation to response generation from a discourse perspective; (2) the dialogue acts enhance diversity of responses by expanding the search space from language to act × language; (3) the dialogue acts manage the flow of humanmachine conversations and thus enhance human engagement; and (4) the dialogue act selection is compatible with post-engineering work (e.g., combination with rules), and thus allows engineers to flexibly control their systems through picking responses from their desired dialogue acts. Evaluation results on large scale test data indicate that our model can significantly outperform state-of-the-art methods in terms of quality of generated responses regarding to given contexts and lead to longterm conversation in both machine-machine simulation and human-machine conversation in a way similar to how human behave in their interactions.Our contributions in this work include: (1) design of dialogue acts that represent human behavior regarding to conversational context and insights from analysis of human-human interactions with the design; (2) joint modeling of dialogue act selection and response generation in open domain dialogue generation; (3) proposal of a supervised learning approach and a reinforcement learning approach for model optimization; (4) empirical verification of the effectiveness of the model through automatic metrics, human annotations, machine-machine simulation, and human-machine conversation. A response or an answer to the previous utterances in the current context. ""this summer."" after ""when are you going to Tokyo?"". Finally, we study how the generated responses are affected by the dialogue acts. We collect generated responses from a specific dialogue act for the contexts of the test dialogues, and characterize the responses with the following metrics: (1) distinct-1 and distinct-2; (2) words out of context (OOC): ratio of words that are in the generated responses but not contained by the contexts; and (3) average length of the generated responses (Ave Len). TAB9 reports the results 4 . In general, responses generated from CS. * are longer, more informative, and contain more new words than responses generated from CM. *, which has been illustrated by the example in TAB7 . Another interesting finding is that statements and answers are generally more informative than questions in both CS. * and CM.*. In addition to these metrics, we also calculate BLEU scores and embedding based metrics, but do not observe significant difference among responses from different dialogue acts. The reason might be that these metrics are based on comparsion of the generated responses and human responses, but human responses in the test set are inherently mixture of responses from different dialogue acts. We study open domain dialogue generation with generally designed dialogue acts that can describe human behavior in social interactions. To mimic such behavior, we propose jointly modeling dialogue act selection and response generation, and perform both supervised learning with a learned dialogue act classifier and reinforcement learning for long-term conversation. Empirical studies on response generation for given contexts, machine-machine simulation, and human-machine conversation show that the proposed models can significantly outperform state-of-the-art methods.",1334,0.699,751,1.7762982689747004,"Conventional methods model open domain dialogue generation through end learning from large scale conversation data In this work make open by introducing dialogue acts open domain dialogue generation The dialogue acts are generally designed and reveal how people engage social chat Inspired analysis on real data propose jointly modeling dialogue act selection response generation perform learning with human-human conversations tagged a reinforcement approach further optimizing With the dialogue acts not achieve significant improvement over state methods on response quality for given contexts long-term conversation in both machine-machine simulation are capable explaining such achievements Conversational agents becoming ubiquitous recently Through human-machine conversation such agents either help users complete BID39 or engage social chat . Depending application scenarios various conversational agents designed including automated customer service, etcTraditional research focuses task-oriented dialogue systems BID39 where task specific dialogue acts are handcrafted a form slot-value pairs On through slot-filling the dialogue acts make conversations in such systems interpretable; hinder scaling such systems new domains To escape the limitation recent interest of research moves end dialogue learning without any assumptions dialogue acts Most the effort paid nontask chit BID30 , BID1 BID4 Without dialogue acts these work directly constructs a response by learning large scale data with neural networks is easy scale new domains On due dialogue acts interpret the emergence a response a dialogue context predict where flow toIn aim achieve interpretability To this end introduce dialogue acts into open domain dialogue generation Open domain dialogue generation has widely applied chatbots which aim engaging keeping conversation Existing work concentrates generating relevant and diverse responses a static context However relevance and diversity sufficient engagement dynamic interactions Therefore investigate the following problems if can properly design dialogue acts enable engagement human-human open domain conversation; learn a dialogue generation model with the dialogue acts the model performs if explainedTo people social chat establish by extending with regarding to conversational context The taxonomy, when real data gives an interesting finding in addition replying with relevance diversity , people used driving their social chat by constantly switching new contexts properly asking Such behaviors less explored before thus difficult existing end learning imitate To mimic human behaviors propose jointly modeling dialogue act selection response generation open domain dialogue generation The dialogue model specified neural networks We propose learning human-human interactions by fitting large scale real world dialogues tagged a dialogue act classifier further optimizing the policy act selection through Our model enjoys several advantages (1) the dialogue acts provide interpretation to response generation from a discourse perspective enhance diversity expanding from language act × language manage the flow humanmachine conversations thus human engagement the dialogue act selection compatible post-engineering work rules engineers flexibly control their systems through picking responses their desired dialogue acts results on large scale test data indicate our model significantly state terms quality generated responses regarding to given contexts lead longterm conversation both machine-machine simulation in how human behave their interactionsOur contributions dialogue acts represent regarding insights analysis with the design; dialogue act selection response generation open domain dialogue generation and model optimization through automatic metrics human annotations A response or the previous utterances in the current context ""this summer after ""when are Tokyo Finally study the generated responses the dialogue acts We collect generated responses a specific dialogue act for the contexts the test dialogues characterize ( distinct-1 and outOOC): ratio that but contained byAve Len TAB9 reports the results 4 . In general, responses generated CS. * are longer informative contain more new words responses generated CM *, which illustrated TAB7 . Another interesting finding statements and answers generally in both CS. * and CM.*. In addition these metrics calculate BLEU scores embedding based metrics but do observe among responses different dialogue acts The reason might these metrics comparsion the generated responses human responses human responses in the test set inherently mixture responses different dialogue acts We study open domain dialogue generation generally designed dialogue acts describe social interactions To mimic such behavior propose jointly modeling dialogue act selection response generation perform both supervised with a learned dialogue act classifier for response generation for given contexts machine-machine simulation human-machine conversation the proposed models significantly state",0.01,0.6820189542111849
"We discuss the feasibility of the following learning problem: given unmatched samples from two domains and nothing else, learn a mapping between the two, which preserves semantics. Due to the lack of paired samples and without any definition of the semantic information, the problem might seem ill-posed. Specifically, in typical cases, it seems possible to build infinitely many alternative mappings  from every target mapping. This apparent ambiguity stands in sharp contrast to the recent empirical success in solving this problem.

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

 Various predictions are made based on the hypothesis that semantic alignment can be captured by the minimal mapping. These are verified extensively. In addition, a new mapping algorithm is proposed and shown to lead to better mapping results. Multiple recent reports (Xia et al., 2016; BID13 BID12 Yi et al., 2017) convincingly demonstrated that one can learn to map between two domains that are each specified merely by a set of unlabeled examples. For example, given a set of unlabeled images of horses, and a set of unlabeled images of zebras, CycleGAN (Zhu et al., 2017) creates the analog zebra image for a new image of a horse and vice versa.These recent methods employ two types of constraints. First, when mapping from one domain to another, the output has to be indistinguishable from the samples of the new domain. This is enforced using GANs BID9 and is applied at the distribution level: the mapping of horse images to the zebra domain should create images that are indistinguishable from the training images of zebras and vice versa. The second type of constraint enforces that for every single sample, transforming it to the other domain and back (by a composition of the mappings in the two directions) results in the original sample. This is enforced for each training sample from either domain: every training image of a horse (zebra), which is mapped to a zebra (horse) image and then back to the source domain, should be as similar as possible to the original input image.In another example, taken from DiscoGAN BID13 , a function is learned to map a handbag to a shoe of a similar style. One may wonder why striped bags are not mapped, for example, to shoes with a checkerboard pattern. If every striped pattern in either domain is mapped to a checkerboard pattern in the other and vice-versa, then both the distribution constraints and the circularity constraints might hold. The former could hold since both striped and checkerboard patterned objects would be generated. Circularity could hold since, for example, a striped object would be mapped to a checkerboard object in the other domain and then back to the original striped object.One may claim that the distribution of striped bags is similar to those of striped shoes and that the distribution of checkerboard patterns is also the same in both domains. In this case, the alignment follows from fitting the shapes of the distributions. This explanation is unlikely, since no effort is being made to create handbags and shoes that have the same distributions of these properties, as well as many other properties.Our work is dedicated to the alternative hypothesis that the target mapping is implicitly defined by being approximated by the lowest-complexity mapping that has a low discrepancy between the mapped samples and the target distribution, i.e., the property that even a good discriminator cannot distinguish between the generated samples and the target ones. In Sec. 2 we explore the inherent ambiguity of cross domain mapping. In Sec. 3, we present the hypothesis and two verifiable predictions, as well as a new unsupervised mapping algorithm. In Sec. 4, we show that the number of minimal complexity mappings is expected to be small. Sec. 5 verifies the various predictions. Some context to our work, including classical ideas such as Occam's Razor, MDL, and Kolmogorov complexity are discussed in Sec. 6. Our stratified complexity model is related to structural risk minimization (SRM) by Vapnik & Chervonenkis (1971a) , which employs a hierarchy of nested subsets of hypothesis classes in order of increasing complexity. In our stratification, which is based on the number of layers, the complexity classes are not necessarily nested. A major emphasis in SRM is the dependence on the number of samples: the algorithm selects the hypothesis from one of the nested hypothesis classes depending on the amount of training data. In our case, one can expect higher values of k 2 to be beneficial as the number of training samples grows. However, the exact characterization of this relation is left for future work.Alg. 1 can be seen as a form of distillation. The first step of the algorithm finds the minimal complexity for mapping between the two domains and obtains the first generator. Then, a second generator, with a large complexity, is trained while being encouraged to output images which are close to the output of the first generator. This resembles the distillation methods proposed by BID11 and later analyzed by BID10 .Since the method depicted in Alg. 1 optimizes , among other things, the architecture of the network, our method is somewhat related to work that learn the network's structure during training, e.g., (Saxena & Verbeek, 2016; Wen et al., 2016; Liu et al., 2015; BID7 BID15 . This body of work, which deals exclusively with supervised learning, optimizes the networks loss by modifying both the parameters and the hyperparameters. For GAN based loss, this would not work, since with more capacity, one can reduce the discrepancy but quickly lose the alignment.Indeed, we point to a key difference between supervised learning and unsupervised learning. While in the former, deeper networks, which can learn even random labels, work well (Zhang et al., 2017) , unsupervised learning requires a careful control of the network capacity. This realization , which echoes the application of MDL for model selection in unsupervised learning (Zemel, 1994) , was overshadowed by the overgeneralized belief that deeper networks lead to higher accuracy.The limitations of unsupervised based learning that are due to symmetry, are also a part of our model. For example, the mapping of cars in one pose to cars in the mirrored pose that sometimes happens in BID13 , is similar in nature to the mapping of x to 1 − x in the simple example given in Sec. 3.1. Such symmetries occur when we can divide y AB into two functions y AB = y 2 • y 1 such that a function W is a linear mapping and also a DPM of y 1 • D A and, therefore, DISPLAYFORM0 While we focus on unsupervised learning, the emergence of semantics when learning with a restricted capacity is widely applicable, such as with autoencoders, transfer learning, semi-supervised learning and elsewhere. As an extreme example , Sutskever et al. FORMULA0 present empirical evidence that a meaningful mapper can be learned, even from very few examples, if the network trained is kept small. The recent success in mapping between two domains in an unsupervised way and without any existing knowledge, other than network hyperparameters, is nothing less than extraordinary and has far reaching consequences. As far as we know, nothing in the existing machine learning or cognitive science literature suggests that this would be possible.We provide an intuitive definition of function complexity and employ it in order to identify minimal complexity mappings, which we conjecture play a pivotal role in this success. If our hypothesis is correct, simply by training networks that are not too complex, the target mapping stands out from all other alternative mappings.Our analysis leads directly to a new unsupervised cross domain mapping algorithm that is able to avoid the ambiguity of such mapping, yet enjoy the expressiveness of deep neural networks. The experiments demonstrate that the analogies become richer in details and more complex, while maintaining the alignment.We show that the number of low-discrepancy mappings that are of low-complexity is expected to be small. Our main proof is based on the assumption of identifiability, which constitutes an open question. We hope that there would be a renewed interest in this problem, which has been open for decades for networks with more than a single hidden layer and is unexplored for modern activation functions. FIG1 : Results for mapping Males to itself (B=A) using a DiscoGAN architecture and enforcing that the mapping is not the identity mapping. The odd rows present the learned mapping h, and the even rows present the full cycle h • h.",1832,0.973,1053,1.7397910731244064,"We discuss the feasibility the following learning problem given unmatched samples two domains nothing learn a mapping, preserves semantics Due paired samples without any definition the semantic information the problem might illposed Specifically in typical cases seems possible build infinitely many alternative mappings every target mapping This apparent ambiguity stands the recent empirical success solving We identify the abstract notion aligning two domains a semantic way concrete terms minimal relative complexity A theoretical framework measuring the complexity compositions functions show reasonable the minimal complexity mapping unique The measured complexity used directly being learned a semantically aligned mapping could then captured simply learning using architectures much bigger the minimal architecture Various predictions the hypothesis semantic alignment captured the minimal mapping These verified extensively In addition a new mapping algorithm proposed and shown lead Multiple recent reports (Xia et BID13 BID12 Yi convincingly one can learn map between two domains that each specified merely unlabeled examples For example given unlabeled images horses CycleGAN (Zhu et 2017 creates the analog zebra image a new image viceThese recent methods employ two types constraints First when mapping from one domain the output has indistinguishable the samples This enforced using GANs BID9 is applied the distribution level: the mapping horse images the zebra domain should create images indistinguishable the training images vice The second type constraint enforces for every single sample transforming the other domain and back (by a composition This enforced each training sample from either domain every training image of a horse (zebra which mapped back should as similarIn taken DiscoGAN BID13 , a function learned a handbag of a similar style One may striped bags mapped for shoes with If every striped pattern either domain mapped and vice both the distribution constraints might hold former could hold since both striped and checkerboard patterned objects would generated Circularity could hold since, a striped object mapped the other domain and backOne may claim the distribution striped bags similar those striped shoes checkerboard patterns In the alignment follows from fitting the shapes the distributions This explanation unlikely no effort create handbags shoes have the same distributions these properties manyOur work dedicated the alternative hypothesis the target mapping implicitly defined being approximated the lowest-complexity mapping that a low discrepancy the mapped samples the property even a good discriminator In Sec 2 we explore the inherent ambiguity cross domain mapping In Sec 3, we present and two verifiable predictions as a new unsupervised mapping algorithm In Sec 4, we show minimal complexity mappings expected small Sec 5 verifies the various predictions Some context to our work classical ideas such are Sec 6 Our stratified complexity model related structural risk minimization Vapnik & Chervonenkis1971a , employs nested subsets hypothesis classes of In our stratification which layers the complexity classes not nested A major emphasis SRM the dependence the number samples: the algorithm selects the hypothesis one the nested hypothesis classes depending training data In our case one can expect higher values k 2 beneficial training samples grows However the exact characterization this relation left forAlg. 1 can seen distillation The first step the algorithm finds the minimal complexity for mapping between obtains the first generator Then a second generator with a large complexity trained while being encouraged output images which close This resembles the distillation methods proposed BID11 later analyzed .Since depicted Alg. 1 optimizes , among the architecture our method is somewhat related work that learn during (Saxena 2016 Wen Liu BID7 BID15 . This body deals exclusively supervised learning optimizes the networks loss by modifying both the parameters For GAN based loss, this would not work with more capacity one reduce the discrepancy but quickly the alignmentIndeed point supervised learning While in the former, deeper networks, can learn even random labels work (Zhang 2017 , requires a careful control the network capacity This realization , echoes the application MDL for model selection (Zemel 1994 overshadowed the overgeneralized belief deeper networks leadThe limitations that due symmetry are also a part our model For example the mapping cars one pose cars the mirrored pose that sometimes BID13 , similar nature x to 1 − the simple example given Sec Such symmetries occur we can divide y AB two functions y 2 • such a function W a linear mapping and also a DPM 1 • D A and, DISPLAYFORM0 While focus the emergence semantics when learning with a restricted capacity widely applicable such transfer learning elsewhere As an extreme example , Sutskever et al FORMULA0 present empirical evidence a meaningful mapper learned from very few examples if the network trained is kept small The recent success in mapping between two domains and without any existing knowledge, other network hyperparameters nothing less extraordinary has As far nothing the existing machine learning or wouldWe provide an intuitive definition function complexity employ order identify minimal complexity mappings conjecture play this success If our hypothesis simply training networks not too the target mapping stands all other alternative mappingsOur analysis leads directly a new unsupervised cross domain mapping algorithm avoid the ambiguity such mapping yet enjoy The experiments demonstrate the analogies become richer details maintaining the alignment.We show the number low-discrepancy mappings that of expected small Our main proof based identifiability constitutes We hope there would this problem open for networks with more a single hidden layer is unexplored modern activation functions FIG1 : Results for mapping Males itselfB=A using a DiscoGAN architecture enforcing that the identity mapping The odd rows present the learned mapping h, the full cycle •",0.01,0.5890018266717921
"We present a novel approach for the certification of neural networks against adversarial perturbations which combines scalable overapproximation methods with precise (mixed integer) linear programming. This results in significantly better precision than state-of-the-art verifiers on challenging feedforward and convolutional neural networks with piecewise linear activation functions. Neural networks are increasingly applied in critical domains such as autonomous driving BID1 , medical diagnosis BID0 , and speech recognition BID13 . However, it has been shown by BID11 that neural networks can be vulnerable against adversarial attacks, i.e., imperceptible input perturbations cause neural networks to misclassify. To address this challenge and prove that a network is free of adversarial examples (usually, in a region around a given input), recent work has started investigating the use of certification techniques. Current verifiers can be broadly classified as either complete or incomplete.Complete verifiers are exact, i.e., if the verifier fails to certify a network then the network is nonrobust (and vice-versa) . Existing complete verifiers are based on Mixed Integer Linear Programming (MILP) BID19 BID8 BID5 BID3 or SMT solvers BID16 BID7 . Although precise, these can only handle networks with a small number of layers and neurons. To scale, incomplete verifiers usually employ overapproximation methods and hence they are sound but may fail to prove robustness even if it holds. Incomplete verifiers use methods such as duality BID6 , abstract interpretation BID23 , linear approximations BID29 , semidefinite relaxations BID21 , combination of linear and non-linear approximation BID30 , or search space discretization BID14 . Incomplete verifiers are more scalable than complete ones, but can suffer from precision loss for deeper networks. In principle, incomplete verifiers can be made asymptotically complete by iteratively refining the input space BID26 or the neurons BID27 ; however, in the worst case, this may eliminate any scalability gains and thus defeat the purpose of using overapproximation in the first place.This work: boosting complete and incomplete verifiers. A key challenge then is to design a verifier which improves the precision of incomplete methods and the scalability of complete ones. In this work, we make a step towards addressing this challenge based on two key ideas: (i) a combination of state-of-the-art overapproximation techniques used by incomplete methods, including LP relaxations, together with MILP solvers, often employed in complete verifiers; (ii) a novel heuristic, which points to neurons whose approximated bounds should be refined. We implemented these ideas in a system called RefineZono, and showed that is is faster than state-of-the-art complete verifiers on small networks while improving precision of existing incomplete verifiers on larger networks.The recent works of BID27 and BID25 have also explored the combination of linear programming with overapproximation. However, both use simpler and coarser overapproximations than ours. Our evaluation shows that RefineZono is faster than both for complete verification. For example, RefineZono is faster than the work of BID25 for the complete x 7x 8 x 9x 10 x 11x 12x 13 Figure 1 : Robustness analysis of a toy example neural network using our method. Here, approximation results computed with DeepZ (blue box) are refined using MILP whereas those in green are refined using LP. verification of a 3 × 50 network, while for the larger 9 × 200 network their method does not finish within multiple days on images which RefineZono verifies in ≈ 14 minutes. DISPLAYFORM0 We presented a novel refinement-based approach for effectively combining overapproximation techniques used by incomplete verifiers with linear-programming-based methods used in complete verifiers. We implemented our method in a system called RefineZono and showed its effectiveness on verification tasks involving feedforward and convolutional neural networks with ReLU activations.Our evaluation demonstrates that RefineZono can certify robustness properties beyond the reach of existing state-of-the-art complete verifiers (these can fail due to scalability issues) while simultaneously improving on the precision of existing incomplete verifiers (which can fail due to using too coarse of an overapproximation).Overall , we believe combining the strengths of overapproximation methods with those of mixed integer linear programming as done in this work is a promising direction for further advancing the state-of-the-art in neural network verification.",903,0.401,507,1.7810650887573964,"We present the certification neural networks against which combines scalable overapproximation methods precise (mixed integer) linear programming This results significantly better precision state verifiers on challenging with piecewise linear activation functions Neural networks increasingly applied critical domains autonomous driving BID1 , medical diagnosis BID0 However shown by BID11 neural networks vulnerable against cause To address prove a network free adversarial examples (usually a region around a given input recent work started investigating certification techniques Current verifiers can broadly complete exact if certify a network then nonrobustand vice . Existing complete verifiers based Mixed Integer Linear or SMT solvers . Although precise, these can handle networks layers neurons To scale incomplete verifiers usually employ overapproximation methods hence they sound but may prove even holds Incomplete verifiers use methods duality BID6 , abstract interpretation BID23 linear combination or search space discretization BID14 Incomplete verifiers more scalable can suffer precision loss for deeper networks In principle incomplete verifiers made complete iteratively refining the input space BID26 or the neurons ; the worst case eliminate any scalability gains defeat using overapproximationThis work: boosting A key challenge then design a verifier improves incomplete methods complete ones In this work make a step towards addressing based two key ideas a combination state overapproximation used incomplete methods including LP relaxations together MILP solvers often employed complete verifiers novel heuristic points neurons whose approximated bounds refined We implemented these ideas a system RefineZono showed is faster state complete verifiers on small networks while improving precision existing incomplete verifiersThe recent works BID27 explored the combination linear programming overapproximation However both use simpler and coarser overapproximations ours Our evaluation shows RefineZono faster both for complete verification. For example RefineZono faster the work BID25 for the complete x 7x 8 x 13 Figure : Robustness analysis a toy example neural network our method Here approximation results computed DeepZ (blue box refined MILP whereas those green refined LP verification a 3 × 50 network while for the larger 9 × 200 network their method does finish within multiple days on images which RefineZono �� 14 minutes DISPLAYFORM0 We presented a novel refinement-based approach effectively combining overapproximation techniques used incomplete verifiers linear-programming-based methods We implemented our method a system RefineZono showed its effectiveness verification tasks involving with ReLU activationsOur evaluation demonstrates certify robustness properties beyond existing state complete verifiersthese fail while using coarse of an overapproximation).Overall , combining those mixed integer linear programming as done further advancing",0.01,0.6941643922092875
"A distinct commonality between HMMs and RNNs is that they both learn hidden representations for sequential data. In addition, it has been noted that the backward computation of the Baum-Welch algorithm for HMMs is a special case of the back-propagation algorithm used for neural networks (Eisner (2016)). Do these observations suggest that, despite their many apparent differences, HMMs are a special case of RNNs? In this paper, we show that that is indeed the case, and investigate a series of architectural transformations between HMMs and RNNs, both through theoretical derivations and empirical hybridization. In particular, we investigate three key design factors—independence assumptions between the hidden states and the observation, the placement of softmaxes, and the use of non-linearities—in order to pin down their empirical effects. We present a comprehensive empirical study to provide insights into the interplay between expressivity and interpretability in this model family with respect to language modeling and parts-of-speech induction. The sequence is a common structure among many forms of naturally occurring data, including speech, text, video, and DNA. As such, sequence modeling has long been a core research problem across several fields of machine learning and AI. By far the most widely used approach for decades is Hidden Markov Models BID1 BID10 , which assumes a sequence of discrete latent variables to generate a sequence of observed variables. When the latent variables are unobserved, unsupervised training of HMMs can be performed via the Baum-Welch algorithm (which, in turn, is based on the forward-backward algorithm), as a special case of Expectation-Maximization (EM) BID4 . Importantly, the discrete nature of the latent variables has the benefit of interpretability, as they recover contextual clustering of the output variables. In contrast, Recurrent Neural Networks (RNNs) BID11 BID6 introduced later assume continuous latent representations. Their hidden states have no probabilistic interpretation, regardless of many different architectural variants, such as LSTMs BID9 , GRUs BID3 and RANs BID13 .Despite their many apparent differences, both HMMs and RNNs model hidden representations for sequential data. At the heart of both models are: a state at time t, a transition function f : h t−1 → h t in latent space, and an emission function g : h t → x t . In addition , it has been noted that the backward computation in the Baum-Welch algorithm is a special case of back-propagation for neural networks BID5 . Therefore, a natural question arises as to the fundamental relationship between HMMs and RNNs. Might HMMs be a special case of RNNs?In this paper , we investigate a series of architectural transformations between HMMs and RNNsboth through theoretical derivations and empirical hybridization. In particular , we demonstrate that forward marginal inference for an HMM-accumulating forward probabilities to compute the marginal emission and hidden state distributions at each time step-can be reformulated as equations for computing an RNN cell. In addition, we investigate three key design factors-independence Figure 1 : Above each of the models we indicate the type of transition and emission cells used. H for HMM, R for RNN/Elman and F is a novel Fusion defined in §3.3. It is particularly important to track when a vector is a distribution (resides in a simplex) versus in the unit cube (e.g. after a sigmoid non-linearity). These are indicated by c i and c i , respectively. SM stands for softmax rows.assumptions between the hidden states and observations, the placement of softmaxes, and the use of non-linearities-in order to pin down their empirical effects. While we focus on HMMs with discrete outputs, our analysis framework could be extended to HMMs over continuous observations.Our work builds on earlier work that have also noted the connection between RNNs and HMMs BID23 BID25 (see §7). Our contribution is to provide the first thorough theoretical investigation into the model variants, carefully controlling for every design choices, along with comprehensive empirical analysis over the spectrum of possible hybridization between HMMs and RNNs.We find that the key elements to better performance of the HMMs are the use of a sigmoid instead of softmax linearity in the recurrent cell, and the use of an unnormalized output distribution matrix in the emission computation. On the other hand, multiplicative integration of the previous hidden state and input embedding, and intermediate normalizations in the cell computation are less consequential. We also find that HMMs outperform other RNNs variants for unsupervised prediction of the next POS tag, demonstrating the advantages of discrete bottlenecks for increased interpretability.The paper is structured as follows. First, we present the derivation of HMM marginal inference as a special case of RNN computation ( §2). Next we explore a gradual transformation of HMMs into RNNs ( §3), followed by the reverse transformation of Elman RNNs back to HMMs ( §4). Finally we provide empirical analysis in §5 and §6 to pin point the effects of varying design choices over possible hybridizations between HMMs and RNNs.",1087,0.508,661,1.6444780635400909,"A distinct commonality HMMs RNNs learn hidden representations for sequential data In addition the backward computation the Baum-Welch algorithm HMMs neural networksEisner (2016 Do these observations, their many apparent differences HMMs a special case RNNs In this paper that is indeed investigate a series architectural transformations between HMMs both through theoretical derivations empirical hybridization In particular investigate three key design factors—independence assumptions between the hidden states the observation, the placement softmaxes non pin their empirical effects We present provide insights expressivity interpretability this model family with language modeling parts- induction The sequence a common structure among many forms naturally occurring data speech text video DNA As such sequence modeling a core research problem across AI By far decades Hidden Markov Models BID1 BID10 , assumes a sequence discrete latent variables generate observed variables When the latent variables unobserved HMMs via the Baum-Welch algorithmwhich, the forward-backward algorithm Expectation-Maximization (EM) BID4 . Importantly the discrete nature the latent variables has interpretability recover contextual clustering the output variables In contrast Recurrent BID11 BID6 introduced later assume continuous latent representations Their hidden states no probabilistic interpretation regardless many different architectural variants LSTMs BID9 , GRUs RANs .Despite their many apparent differences both HMMs RNNs model hidden representations for sequential data At both models: a state at time t a transition function f : h t−1 → in latent space emission In addition , it the backward computation in the Baum-Welch algorithm for neural networks BID5 Therefore a natural question the fundamental relationship HMMs RNNs Might , investigate a series architectural transformations between RNNsboth through theoretical derivations empirical hybridization In particular , demonstrate forward marginal inference for an HMM forward probabilities to compute the marginal emission and hidden state distributions at-can reformulated equations computing an RNN cell In addition investigate three key design factors-independence Figure : Above each indicate transition and emission cells used H for HMM R RNN/Elman and is a novel Fusion defined § It particularly track when a vector a distributionresides a simplex versus in the unit cube after non These indicated c i and SM stands softmax rows.assumptions between the hidden states observations the placement softmaxes non-in order pin their empirical effects While focus HMMs with discrete outputs our analysis framework could over continuous observationsOur work builds have also noted the connection HMMs BID23 BID25 ( § Our contribution the first thorough theoretical investigation the model variants, carefully controlling every design choices along comprehensive empirical analysis over the spectrum possible hybridization between HMMsWe find the key elements to better performance instead softmax linearity the recurrent cell an unnormalized output distribution matrix the emission computation On multiplicative integration the previous hidden state input embedding, intermediate normalizations in the cell computation are less consequential We also find HMMs outperform other RNNs variants for the next POS tag demonstrating the advantages discrete bottlenecks increased interpretabilityThe paper structured First present HMM marginal inference as RNN computation §2 Next we explore a gradual transformation HMMs RNNs § followed Elman RNNs back Finally provide empirical analysis in § and to pin point varying design choices over possible hybridizations between HMMs",0.01,0.3461526523604151
"Deep neural networks have been tremendously successful in a number of tasks.
 One of the main reasons for this is their capability to automatically
 learn representations of data in levels of abstraction,
 increasingly disentangling the data as the internal transformations are applied.
 In this paper we propose a novel regularization method that penalize covariance between dimensions of the hidden layers in a network, something that benefits the disentanglement.
 This makes the network learn nonlinear representations that are linearly uncorrelated, yet allows the model to obtain good results on a number of tasks, as demonstrated by our experimental evaluation.
 The proposed technique can be used to find the dimensionality of the underlying data, because it effectively disables dimensions that aren't needed.
 Our approach is simple and computationally cheap, as it can be applied as a regularizer to any gradient-based learning model. A good data representation should ultimately uncover underlying factors in the raw data while being useful for a model to solve some task. Deep neural networks learn representations that are increasingly abstract in deeper layers, disentangling the causes of variation in the underlying data BID1 . Formal definitions of disentanglement are lacking, although Ver BID17 ; BID0 both use the total correlation as a measure of disentanglement. Inspired by this, we consider a simpler objective: a representation disentangles the data well when its components do not correlate, and we explore the effects of penalizing this linear dependence between different dimensions in the representation. Ensuring independence in the representation space results in a distribution that is factorizable and thus easy to model BID8 BID14 .We propose a novel regularization scheme that penalizes the cross-correlation between the dimensions of the learned representations, and helps artificial neural networks learn disentangled representations. The approach is very versatile and can be applied to any gradient-based machine learning model that learns its own distributed vector representations. A large body of literature have been published about techniques for learning non-linear independent representations BID12 BID5 BID3 , but in comparison our approach is simpler, and does not impose restrictions on the model used. The proposed technique penalizes representations with correlated activations. It strongly encourages the model to find the dimensionality of the data, and thus to disable superfluous dimensions in the resulting representations. The experimental evaluation on synthetic data verifies this: the model is able to learn all useful dimensions in the data, and after convergence, these are the only ones that are active. This can be of great utility when pruning a network, or to decide when a network needs a larger capacity. The disabling of activations in the internal representation can be viewed as (and used for) dimensionality reduction. The proposed approach allows for interpretability of the activations computed in the model, such as isolating specific underlying factors. The solution is computationally cheap, and can be applied without modification to many gradient-based machine learning models that learns distributed representations.Moreover, we present an extensive experimental evaluation on a range of tasks on different data modalities, which shows that the proposed approach disentangles the data well; we do get uncorrelated components in the resulting internal representations, while retaining the performance of the models on their respective task.Figure 1: When data is distributed along non-linear manifolds, a linear model cannot describe the data well (left). However, with a non-linear model (right), it is possible to capture the variations of the data in a more reasonable way and unfold it into a compact orthogonal representation space.The main contributions of this work include: L Σ regularization, a novel approach penalizing the covariance between dimensions in a representation (see Section 2). The regularizer encourages a model to use the minimal number of dimensions needed in the representation. The approach is computationally cheap and can be applied without any restrictions on the model. The experimental evaluation shows how different models can benefit from using L Σ regularization. From autoencoders on synthetic data to deep convolutional autoencoders trained on CIFAR-10, we show that L Σ helps us learn uncorrelated and disentangled representations (see Section 3). In this paper, we have presented L Σ regularization, a novel regularization scheme based on penalizing the covariance between dimensions of the internal representation learned in a hierarchical model. The proposed regularization scheme helps models learn linearly uncorrelated variables in a non-linear space. While techniques for learning independent components follow criteria that are more strict, our solution is flexible and portable, and can be applied to any feature-learning model that is trained with gradient descent. Our method has no penalty on the performance on tasks evaluated in the experiments, while it does disentangle the data.",930,0.488,547,1.70018281535649,"Deep neural networks tremendously One their capability automatically learn representations data levels increasingly disentangling as the internal transformations In this paper a novel regularization method penalize dimensions the hidden layers something benefits. This makes the network learn nonlinear representations that linearly yet allows obtain good results tasks as demonstrated our experimental evaluation The proposed technique can find the dimensionality the underlying data because effectively dimensions are Our approach computationally cheap as applied as a regularizer A good data representation should ultimately uncover underlying factors the raw data while being useful a model solve some task Deep neural networks learn representations increasingly abstract deeper layers disentangling the causes variation BID1 . Formal definitions lacking Ver BID17 ; BID0 both use the total correlation as Inspired this, consider a simpler objective a representation disentangles well when its components do correlate explore penalizing this linear dependence between different dimensions independence the representation space results a distribution factorizable thus easy model BID8 BID14 .We a novel regularization scheme penalizes the cross the dimensions the learned representations helps artificial neural networks disentangled The approach very versatile any gradient-based machine learning model learns its own distributed vector representations A large body have techniques learning non-linear independent representations BID12 BID5 BID3 in comparison our approach simpler does impose restrictions used The proposed technique penalizes representations with correlated activations It strongly encourages the model find the dimensionality thus disable superfluous dimensions the resulting representations experimental evaluation on synthetic data verifies this: the model able learn all useful dimensions after convergence these active This can of pruning a network to decide a larger capacity The disabling activations the internal representation can viewed (and used dimensionality reduction The proposed approach allows interpretability the activations computed such isolating specific underlying factors The solution computationally cheap can without modification many gradient-based machine learning models that learns distributed representationsMoreover we present an extensive experimental evaluation on tasks on different data modalities well; we do get uncorrelated components the resulting internal representations while retaining on their respective taskFigure When data along describeleft However with a non-linear model (right capture the variations unfold a compact orthogonal representation spaceThe main contributions include L �� regularization a novel approach penalizing dimensions a representation The regularizer encourages a model use the minimal number dimensions the representation The approach computationally cheap without any restrictions the model The experimental evaluation shows how different models benefit using L �� regularization From autoencoders on synthetic data trained CIFAR-10 show L �� helps learn uncorrelated and representations ( Section In this paper have presented L �� regularization penalizing dimensions the internal representation learned The proposed regularization scheme helps models learn linearly uncorrelated variables While techniques learning independent components follow criteria more strict our solution flexible portable any feature-learning model trained gradient descent Our method has no penalty the performance on tasks evaluated the experiments while disentangle",0.01,0.48808346582261863
"This report introduces a training and recognition scheme, in which classification is realized via class-wise discerning. Trained with datasets whose labels are randomly shuffled except for one class of interest, a neural network learns class-wise parameter values, and remolds itself from a feature sorter into feature filters, each of which discerns objects belonging to one of the classes only. Classification of an input can be inferred from the maximum response of the filters. A multiple check with multiple versions of filters can diminish fluctuation and yields better performance. This scheme of discerning, maximum response and multiple check is a method of general viability to improve performance of feedforward networks, and the filter training itself is a promising feature abstraction procedure. In contrast to the direct sorting, the scheme mimics the classification process mediated by a series of one component picking. Suppose given a task of sorting a bunch of colored balls, we can usually do it in two ways. One is to randomly pick up a ball and deposit it to one of the groups according to its color. Or we can collect balls of the same color at a time until the last two colors are separated. Standard neural networks for classification tasks work in the former manner, for which it is an implied principle that every class should be on an equal footing and biases are harmful. This is the reason why the training data contain subsets of identical sample number or close in size for each class. The scheme introduced in this work is an analogue of the latter, in which the networks do not respond equally to features of different classes. Rather, they function more like filters, and ascription of an object is inferred from how strong their responses are.The filter networks are obtained by filter training, from which we have a group of networks or more specifically a batch of parameter values, number of which is equal to the number of classes. Ensemblization appears to be a built-in trait of this recognition scheme. Since a prediction should not refer to a preassigned label, a quantitative evaluation of how each filter responds to an input should be defined on an equal footing. As long as one of the alternative filters scores higher than the correct one, the prediction is wrong. Fluctuation makes the correct filter the weaker in this one to many contest. To do it a favour we introduce another hierarchy of ensemblization that is a batch of versions for the filters, in the hope that the correct filter could be the overall winner in this tournament. These three steps constitute a classification procedure of discerning, maximum response, and multiple check (DMM).The DMM scheme can improve accuracy of mediocre networks, networks already having high accuracy, and those trained with small-scale data. Fundamental reason for the increase is that in the filter training a multiclass problem is reduced to a pseudo binary classification, the class of interest and the others. Intuitively , we have the feeling that telling a component from a mixture is easier than sorting all the ingredients. The pseudo reduction mitigates workload. Depending on capacity of networks and amount of training samples, the increase of accuracy varies. Nevertheless , as performance improvement due to the mitigation is almost sure, the scheme can be a general route to enhance feedforward networks. Moreover, since a filter is specifically trained for one class, the filter training is a feature abstraction procedure in itself.In the following, we first investigate the mechanism of filter training and how it works through a toy model. From this classification of points in a 2D plane, we can clearly view how the decision boundaries are reshaped. Then, we give a probabilistic argument why the maximum response is a proper criterion to infer classification. After remarking on its relation with related works, we experiment MMD on the CIFAR-10 and MNIST datasets. Motivated by the classification process via one component discerning, we propose the filter training and maximum response. The multiple check can build up an increment of performance if the fluctuation in the responses are properly distributed among filter versions. How to deal with the two types of fluctuations is the major concern for it to work well. DMM constitutes a special ensemble learning scheme, which itself can be incorporated into other schemes as an additional hierarchy of ensemblization. It is beneficial if similar mechanism can be integrated into other network architectures, since task simplification is a common strategy in intellegence activities.",863,0.53,493,1.7505070993914806,"This report introduces a training and recognition scheme classification realized via class-wise discerning Trained with datasets whose labels randomly except one class interest class-wise parameter values remolds itself a feature sorter into feature filters each discerns objects belonging only Classification an input can inferred the maximum response the filters A multiple check with multiple versions filters diminish fluctuation yields This scheme of discerning, maximum response multiple check is general viability feedforward networks the filter training itself a promising feature abstraction procedure In contrast the direct sorting the scheme mediated one component picking Suppose given sorting colored balls usually One is randomly deposit according Or we collect balls at until separated Standard neural networks classification tasks work the former manner for an implied principle every class should on biases harmful This the reason the training data contain subsets identical sample number or close in for The scheme introduced this work an analogue latter the networks do respond equally features different classes Rather function filters ascription an object inferred how strong their responsesThe filter networks obtained filter training from a group networks or more specifically a batch parameter values number which equal classes Ensemblization appears this recognition scheme Since a prediction should refer a preassigned label a quantitative evaluation how each filter responds defined on As long one the alternative filters scores the prediction makes correct filter weaker in one to many contest To do a favour we introduce another hierarchy ensemblization a batch versions the filters in the correct filter could the overall winner These three steps constitute a classification procedure discerning, maximum response multiple check (DMM).The DMM scheme can improve mediocre networks networks already having trained Fundamental reason in the filter training a multiclass problem reduced a pseudo binary classification the class interest and the others Intuitively , the feeling telling a component from a mixture sorting The pseudo reduction mitigates workload. Depending capacity networks amount training samples increase accuracy varies Nevertheless , as performance improvement due the mitigation is almost sure the scheme a general route enhance feedforward networks Moreover since a filter specifically trained one class a feature abstraction procedure itselfIn first investigate through From this classification points clearly view the decision boundaries Then give why the maximum response a proper criterion infer classification After remarking its relation related works we experiment MMD on Motivated the classification process via one component discerning, propose the filter training and maximum response. The multiple check can build an increment performance the fluctuation the responses properly distributed filter versions How deal the two types fluctuations is it to work DMM constitutes a special ensemble learning scheme itself incorporated an additional hierarchy ensemblization It beneficial if similar mechanism integrated other network architectures task simplification intellegence activities",0.01,0.616305320100524
"A long-held conventional wisdom states that larger models train more slowly when using gradient descent. This work challenges this widely-held belief, showing that larger models can potentially train faster despite the increasing computational requirements of each training step. In particular, we study the effect of network structure (depth and width) on halting time and show that larger models---wider models in particular---take fewer training steps to converge.

 We design simple experiments to quantitatively characterize the effect of overparametrization on weight space traversal. Results show that halting time improves when growing model's width for three different applications, and the improvement comes from each factor: The distance from initialized weights to converged weights shrinks with a power-law-like relationship, the average step size grows with a power-law-like relationship, and gradient vectors become more aligned with each other during traversal.
 How does overparametrization affect the convergence? BID1 have shown that for a simple LNN increasing depth can accelerate optimization, but increasing width does not affect convergence. However, the conclusion of ""width does not matter"" is a consequence of an implicit assumption that minimum width is larger than input dimensionality. If hidden dimension is wide enough to absorb all the information within the input data, increasing width obviously would not affect convergence. For many real problems, however we are operating in a regime where hidden dimension is generally smaller than input dimension. In particular, RNN operate in this regime.Using the machinery introduced in the work of BID18 , we will show that convergence rate is a function of direct distance from initialization point to final point, average step size and the average angle between gradient vectors and the path that connects current weights to final wights.In this paper, we present a variety of experiments designed to characterize the effect of width on error surface. These experiments are designed to qualitatively answer simple questions. How does width affect the convergence? Why does wider network converge faster? Which factors contribute more to the convergence, increase in the step size, better alignment of gradient vectors towards the final weights or the reduction in direct distance? Is the improvement the result of increasing model capacity or there is a true acceleration phenomenon? Why does the convergence improvement slows down beyond a certain model size?We study the characteristics of convergence curve and show that it can be characterized into a powerlaw region within which the number of gradient updates to convergence has a reciprocal relationship to model size and linear relationship to dataset size, and a flat region within which increasing model size does not affect convergence.We analyze the error surface characteristics of overparametrized models. Our qualitative results suggest that as models get wider (1) direct distance from initial weight to final weights shrinks.(2) Total path length traveled gets shrinks. (3) path length shrinks faster than direct distance. (4) step size gets larger. These results collectively suggests that number of local minimas in higher dimensional space grows asymmetrically wrt. origin and there exists a shorter path within the extra dimension to the newly-found local minimas. We also provide a simple theoretical analysis for a simplified problem of LNN and show that direct distance is expected to shrink as models get wider.",632,0.378,370,1.7081081081081082," states larger models train when using gradient descent This work challenges showing larger models potentially train faster despite the increasing computational requirements each training step In particular study network structuredepth width halting time show larger models---wider modelstake converge We design simple experiments quantitatively characterize overparametrization weight space traversal Results show halting time improves when growing model's width for three different applications comes each factor The distance initialized weights the average step size gradient vectors aligned during How overparametrization the convergence BID1 have shown for a simple LNN increasing depth accelerate optimization increasing width affect convergence However the conclusion ""width does a consequence minimum width larger input dimensionality If hidden dimension wide absorb within increasing width obviously would convergence For many real problems however we operating hidden dimension generally smaller input dimension In particular RNN operate this regimeUsing the machinery introduced the work BID18 , will convergence rate direct distance initialization point average step size the average angle gradient vectors the path that connects current weights final wights designed characterize width error surface These experiments qualitatively answer How width the convergence Why wider network converge Which factors more the convergence, increase the step size better alignment gradient vectors towards the final weights direct distance Is the improvement increasing model capacity there a true acceleration phenomenon Why the convergence improvement slows beyond model size?We study convergence curve show characterized into a powerlaw region within gradient updates to convergence has linear relationship dataset size a flat region analyze the error surface characteristics Our qualitative results as models get wider (1) direct distance initial weight final weights shrinks.(2 Total path traveled gets (3) path length shrinks faster direct distance (4) step size gets These results collectively suggests number local minimas higher dimensional space grows asymmetrically wrt origin and there exists a shorter path within the extra dimension the newly-found local minimas We also provide a simple theoretical analysis a simplified problem LNN show direct distance expected shrink models wider",0.0,0.5082764154451342
"Due to its potential to improve programmer productivity and software quality, automated program repair has been an active topic of research. Newer techniques harness neural networks to learn directly from examples of buggy programs and their fixes. In this work, we consider a recently identified class of bugs called variable-misuse bugs. The state-of-the-art solution for variable misuse enumerates potential fixes for all possible bug locations in a program, before selecting the best prediction. We show that it is beneficial to train a model that jointly and directly localizes and repairs variable-misuse bugs. We present multi-headed pointer networks for this purpose, with one head each for localization and repair. The experimental results show that the joint model significantly outperforms an enumerative solution that uses a pointer based model for repair alone. Advances in machine learning and the availability of large corpora of source code have led to growing interest in the development of neural representations of programs for performing program analyses. In particular, different representations based on token sequences BID10 BID1 , program parse trees BID18 BID16 , program traces (Reed & de Freitas, 2015; BID3 BID26 , and graphs BID0 have been proposed for a variety of tasks including repair BID5 BID0 , optimization BID2 , and synthesis BID17 BID4 .In recent work, BID0 proposed the problem of variable misuse (VARMISUSE): given a program, find program locations where variables are used, and predict the correct variables that should be in those locations. A VARMISUSE bug exists when the correct variable differs from the current one at a location. BID0 show that variable misuses occur in practice, e.g., when a programmer copies some code into a new context, but forgets to rename a variable from the older context, or when two variable names within the same scope are easily confused. FIG0 shows an example derived from a real bug. The programmer copied line 5 to line 6, but forgot to rename object name to subject name. FIG0 shows the correct version. BID0 proposed an enumerative solution to the VARMISUSE problem. They train a model based on graph neural networks that learns to predict a correct variable (among all type-1 def validate_sources(sources): 2 object_name = get_content(sources, 'obj') 3 subject_name = get_content(sources, 'subj') 4 result = Result() 5 result.objects.append(object name) 6 result.subjects.append(object name) 7 return result (a) An example of VARMISUSE shown in red text. At test time, one prediction task is generated for each of the variable-use locations (Blue boxes).1 def validate_sources(sources): 2 object_name = get_content(sources, 'obj') 3 subject_name = get_content(sources, 'subj') 4 result = Result() 5 result.objects.append(object name) 6 result.subjects.append(subject name) 7 return result (b ) The corrected version of FIG0 . If used at train time, one example would be generated for each of the variable-use locations (Blue boxes). correct variables available in the scope) for each slot in a program. A slot is a placeholder in a program where a variable is used. The model is trained on a synthetic dataset containing a training example for each slot in the programs from a corpus of correct source files, and teaching the model to predict the correct, existing variable for each slot. At inference time, a program of unknown correctness is turned into n prediction tasks, one for each of its n slots. Each prediction task is then performed by the trained model and predictions of high probability that differ from the existing variable in the corresponding slot are provided to the programmer as likely VARMISUSE bugs.Unfortunately, this enumerative strategy has some key technical drawbacks. First, it approximates the repair process for a given program by enumerating over a number of independent prediction problems, where important shared context among the dependent predictions is lost. Second, in the training process, the synthetic bug is always only at the position of the slot. If for example, the program in FIG0 were used for training, then five training examples, one corresponding to each identifier in a blue box (a variable read, in this case), would be generated. In each of them, the synthetic bug is exactly at the slot position. However, during inference, the model generates one prediction problem for each variable use in the program. In only one of these prediction problems does the slot coincide with the bug location; in the rest, the model now encounters a situation where there is a bug somewhere else, at a location other than the slot. This differs from the cases it has been trained on. For example, in FIG0 , the prediction problem corresponding to the slot on line 5 contains a bug elsewhere (at line 6) and not in the slot. Only the problem corresponding to the slot on line 6 would match how the model was trained. This mismatch between training and test distributions hampers the prediction accuracy of the model. In our experiments, it leads to an accuracy drop of 4% to 14%, even in the non-enumerative setting, i.e., when the exact location of the bug is provided. Since the enumerative approach uses the prediction of the same variable as the original variable for declaring no bugs at that location, this phenomenon contributes to its worse performance. Another drawback of the enumerative approach is that it produces one prediction per slot in a program, rather than one prediction per program. BID0 deal with this by manually selecting a numerical threshold and reporting a bug (and its repair) only if the predicted probability for a repair is higher than that threshold. Setting a suitable threshold is difficult: too low a threshold can increase false positives and too high a threshold can cause false negatives.In order to deal with these drawbacks, we present a model that jointly learns to perform: 1) classification of the program as either faulty or correct (with respect to VARMISUSE bugs), 2) localization of the bug when the program is classified as faulty, and 3) repair of the localized bug. One of the key insights of our joint model is the observation that, in a program containing a single VARMISUSE bug, a variable token can only be one of the following: 1) a buggy variable (the faulty location), 2) some occurrence of the correct variable that should be copied over the incorrect variable into the faulty location (a repair location), or 3) neither the faulty location nor a repair location. This arises from the fact that the variable in the fault location cannot contribute to the repair of any other variablethere is only one fault location -and a variable in a repair location cannot be buggy at the same time. This observation leads us to a pointer model that can point at locations in the input BID25 by learning distributions over input tokens. The hypothesis that a program that contains a bug at a location likely contains ingredients of the repair elsewhere in the program BID6 has been used quite effectively in practice (Le BID13 . Mechanisms based on pointer networks can play a useful role to exploit this observation for repairing programs.We formulate the problem of classification as pointing to a special no-fault location in the program. To solve the joint prediction problem of classification, localization, and repair, we lift the usual pointer-network architecture to multi-headed pointer networks, where one pointer head points to the faulty location (including the no-fault location when the program is predicted to be non-faulty) and another to the repair location. We compare our joint prediction model to an enumerative approach for repair. Our results show that the joint model not only achieves a higher classification, localization , and repair accuracy, but also results in high true positive score.Furthermore, we study how a pointer network on top of a recurrent neural network compares to the graph neural network used previously by BID0 . The comparison is performed for program repair given an a priori known bug location, the very same task used by that work. Limited to only syntactic inputs, our model outperforms the graph-based one by 7 percentage points . Although encouraging, this comparison is only limited to syntactic inputs; in contrast, the graph model uses both syntax and semantics to achieve state-of-the-art repair accuracy. In future work we plan to study how jointly predicting bug location and repair might improve the graph model when bug location is unknown, as well as how our pointer-network-based model compares to the graphbased one when given semantics, in addition to syntax; the latter is particularly interesting, given the relatively simpler model architecture compared to message-passing networks BID8 . In summary, this paper makes the following key contributions: 1) it presents a solution to the general variable-misuse problem in which enumerative search is replaced by a neural network that jointly localizes and repairs faults; 2) it shows that pointer networks over program tokens provide a suitable framework for solving the VARMISUSE problem; and 3) it presents extensive experimental evaluation over multiple large datasets of programs to empirically validate the claims. BID0 proposed an enumerative approach for solving the VARMISUSE problem by making individual predictions for each variable use in a program and reporting back all variable discrepancies above a threshold, using a graph neural network on syntactic and semantic information. We contrast this paper to that work at length in the previous section. BID5 propose a neural model for semantic code repair where one of the classes of bugs they consider is VARREPLACE, which is similar to the VARMISUSE problem. This model also performs an enumerative search as it predicts repairs for all program locations and then computes a scoring of the repairs to select the best one. As a result, it also suffers from a similar training/test data mismatch issue as BID0 . Similar to us, they use a pooled pointer model to perform the repair task. However, our model uses multi-headed pointers to perform classification, localization, and repair jointly. In this paper, we present an approach that jointly learns to localize and repair bugs. We use a key insight of the VARMISUSE problem that both the bug and repair must exist in the original program to design a multi-headed pointer model over a sequential encoding of program token sequences. The joint model is shown to significantly outperform an enumerative approach using a model that can predict a repair given a potential bug location. In the future, we want to explore joint localization and repair using other models such as graph models and combinations of pointer and graph models, possibly with using more semantic information about programs.",2141,1.092,1250,1.7128,"Due its potential programmer productivity and software quality automated program repair Newer techniques harness neural networks learn directly examples buggy programs their fixes In this work consider a recently identified class bugs called variable-misuse bugs state solution variable misuse enumerates potential fixes all possible bug locations before selecting the best prediction We show it beneficial train a model jointly and directly localizes repairs variable-misuse bugs We present multi-headed pointer networks this purpose one head each localization repair The experimental results the joint model significantly an enumerative solution that a pointer based model repair alone Advances the availability large corpora source code neural representations programs for performing program analyses In particular, different representations based token sequences BID10 BID1 program parse trees , program traces (Reed & de 2015 and graphs have tasks including repair optimization synthesis .In recent proposed the problem variable misuseVARMISUSE): given find program locations variables predict the correct variables in A VARMISUSE bug exists when the correct variable differs at BID0 show that variable misuses occur practice copies a new context rename from within easily FIG0 shows derived a real bug The programmer copied line 5 forgot rename object name subject FIG0 shows the correct version. BID0 proposed an enumerative solution the VARMISUSE problem They train a model based graph neural networks a correct variableamong all type-1 def validate_sources(sources): 2 object_nameobjsubj Result (a An example VARMISUSE shown red text At test time one prediction task generated the variable-use locations (Blue boxes).1 def validate_sources(sources 2 object_nameobjsubj (b ) The corrected version FIG0 . If used at train time one example generated the variable-use locationsBlue boxes correct variables available the scope) for each slot a program A slot a placeholder where The model trained a synthetic dataset containing a training example each slot the programs from a corpus correct source files teaching predict the correct, existing variable At inference time a program of unknown correctness turned n prediction tasks one its n slots Each prediction task then the trained model predictions of high probability that differ the existing variable the corresponding slot provided the programmer as likely VARMISUSE bugsUnfortunately this enumerative strategy some key technical drawbacks First approximates the repair process a given program enumerating over independent prediction problems where important shared context among the dependent predictions lost Second in the training process the synthetic bug always only at the position the slot If for example the program in FIG0 were training then five training examples corresponding each identifier a blue boxa variable read, in In each them the synthetic bug exactly at the slot position However during inference the model generates one prediction problem each variable use in In only these prediction problems the slot coincide the bug location; the model now encounters somewhere at This differs the cases it trained For example FIG0 , the prediction problem corresponding the slot on line contains a bug elsewhereat not Only the problem corresponding the slot on line would match how the model trained This mismatch training and test distributions hampers In our experiments it leads an accuracy drop even the non-enumerative setting the exact location the bug provided Since the enumerative approach uses the prediction the same variable for declaring no bugs at that location this phenomenon contributes its worse performance Another drawback the enumerative approach produces one prediction slot BID0 deal this by manually selecting a numerical threshold reporting a bug (and its repair only the predicted probability a repair that threshold Setting a suitable threshold difficult: too increase false positives tooIn deal these drawbacks present jointly learns perform: 1) classification the program either faultywith respect VARMISUSE bugs when classified One our joint model the observation a program containing a single VARMISUSE bug a variable token onethe faulty location some occurrence that should copied the incorrect variable intoa repair location neither the faulty location This arises the variable in the fault location contribute the repair any other variablethere -and a variable a repair location buggy at This observation leads a pointer model point locations BID25 by learning distributions input tokens The hypothesis a program contains a bug at likely ingredients of the repair elsewhere BID6 used quite effectively practice (Le BID13 . Mechanisms based pointer networks play to exploit this observation for repairing programsWe formulate classification pointing a special no-fault location To solve the joint prediction problem classification localization repair lift the usual pointer-network architecture multi-headed pointer networks one pointer head points the faulty locationincluding when predicted non We compare our joint prediction model an enumerative approach repair Our results the joint model not achieves a higher classification localization , repair accuracy results high true positive scoreFurthermore study a pointer network on top compares the graph neural network used previously by BID0 . The comparison performed program repair given an a priori known bug location the very same task used that work Limited only syntactic inputs our model outperforms graph one . Although encouraging this comparison limited syntactic inputs; contrast the graph model uses both syntax achieve state repair accuracy In future work plan study jointly predicting bug location repair might the graph model when bug location unknown our pointer-network-based model compares the graphbased one when given semantics in syntax; the relatively simpler model architecture compared message-passing networks BID8 . In summary makes it presents a solution the general variable-misuse problem enumerative search replaced jointly localizes repairs faults pointer networks over program tokens solving the VARMISUSE problem extensive experimental evaluation over multiple large datasets programs empirically BID0 proposed an enumerative approach solving the VARMISUSE problem making individual predictions each variable use in reporting back all variable discrepancies above using a graph neural network on syntactic and semantic information We contrast this paper that work at length BID5 propose a neural model semantic code repair where one the classes bugs they consider VARREPLACE similar the VARMISUSE problem This model also performs an enumerative search as predicts repairs all program locations then a scoring select As also suffers a similar training/test data mismatch issue BID0 . Similar us they use a pooled pointer model perform the repair task However our model uses multi-headed pointers perform classification localization repair jointly In jointly learns localize repair bugs We use a key insight the VARMISUSE problem both the bug repair must exist the original program design a multi-headed pointer model over a sequential encoding program token sequences The joint model shown significantly an enumerative approach using a model predict a repair given a potential bug location In want explore joint localization repair using other models graph models combinations pointer and graph models possibly using more semantic information programs",0.01,0.5202309437605604
"Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation) and the fact that humans serve as the gold standard in assessing clustering algorithms, here, we advocate for a unified treatment of the two problems and suggest that hierarchical frameworks that progressively build complex patterns on top of the simpler ones (e.g., convolutional neural networks) offer a promising solution. We do not dwell much on the learning mechanisms in these frameworks as they are still a matter of debate, with respect to biological constraints. Instead, we emphasize on the compositionality of the real world structures and objects. In particular, we show that CNNs, trained end to end using back propagation with noisy labels, are able to cluster data points belonging to several overlapping shapes, and do so much better than the state of the art algorithms. The main takeaway lesson from our study is that mechanisms of human vision, particularly the hierarchal organization of the visual ventral stream should be taken into account in clustering algorithms (e.g., for learning representations in an unsupervised manner or with minimum supervision) to reach human level clustering performance. This, by no means, suggests that other methods do not hold merits. For example, methods relying on pairwise affinities (e.g., spectral clustering) have been very successful in many cases but still fail in some cases (e.g., overlapping clusters). Clustering, a.k.a unsupervised classification or nonparametric density estimation, is central to many data-driven domains and has been studied heavily in the past. The task in clustering is to group a given collection of unlabeled patterns into meaningful clusters such that objects within a cluster are more similar to each other than they are to objects in other clusters. Clustering provides a summary representation of data at a coarse level and is used widely in many disciplines (e.g., computer version, bioinformatics, text processing) for exploratory data analysis (a.k.a pattern mining) as well as representation learning (e.g., bag of words). Despite the introduction of thousands of clustering algorithms in the past BID0 , some challenges still remain. For instance, existing algorithms fall short in dealing with different cluster shapes, high dimensions, automatically determining the number of clusters or other parameters, large amounts of data, choosing the appropriate similarity measure, incorporating domain knowledge, and cluster evaluation. Further, no clustering algorithm can consistently win over other algorithms, handle all test cases, and perform at the level of humans.Deep neural networks have become a dominant approach to solve various tasks across many fields. They have been proven successful in several domains including computer vision BID16 , natural language processing BID6 , and speech recognition BID8 for tasks such as scene and object classification BID16 , pixel-level labeling for image segmentation BID21 ; BID34 , modeling attention ; , image generation BID11 , robot arm control BID19 , speech recognition BID12 , playing Atari games BID23 and beating the Go champion. BID28 adopted in this work.Deep Convolutional Neural Networks (CNNs) BID17 have been particularly successful over vision problems. One reason is that nearby pixels in natural scenes are highly correlated. Further natural objects are compositional. These facts allow applying the same filters across spatial locations (and hence share weights), and build complex filters from simpler ones to detect highlevel patterns (e.g., object parts, objects). We advocate that these properties are highly appealing when dealing with clustering problems. For instance, the classic two half moons example can be solved by applying a filter that is selective to each half moon. Or, when two clusters with different shapes overlap, the problem can be solved by having filters responding to each shape. Solving these cases is very challenging by just looking at local regions around points and being blind to the high-level patterns. Incorporating domain knowledge, while working in some cases, does not give a general solution for solving all clustering problems. The human visual system easily solves these 2D problems because it is a general system with a rich set of learned or evolved filters. We believe that deep CNNs, although imperfect models of the human vision as they lack feedback and lateral connections carry a huge promise for solving clustering tasks. Further, as we will argue, they offer a unified solution to both classification and clustering tasks.The current demarcation between classification and clustering becomes murky when we notice that researchers often refer to human judgments in evaluating the outcomes of clustering algorithms. Indeed, humans learn quite a lot about the visual world during their life time. Moreover, the structure of the visual system has been fine-tuned through the evolution. Thus, certainly, there is a learning component involved which has been often neglected in formulating clustering algorithms. While this is sensible from an application point of view (e.g., pattern mining), not only it limits the pursuit for stronger algorithms but also narrows our understanding of human vision.Learning techniques have been utilized for clustering in the past (e.g., BID1 ; BID25 ), for example for tuning parameters (e.g., BID1 ). Deep networks have also been exploited for clustering (e.g., BID14 ; BID13 BID32 ). However, to our knowledge, while CNNs have been already adopted for image segmentation, so far they have not been exploited for generic clustering. Our goal is to investigate such possibility. To this end, instead of borrowing from clustering to do image segmentation, we follow the opposite direction and propose a deep learning based approach to clustering.Our method builds on the fully convolutional network literature, in particular, recent work on edge detection and semantic segmentation which utilize multi-scale local and non-local cues BID28 . Thanks to a high volume of labeled data, high capacity of deep networks, powerful optimization algorithms, and high computational power, deep models win on these tasks. We are also strongly inspired by the works showing the high resemblance between human vision mechanisms and CNNs from behavioral, electrophysiological, and computational aspects (e.g., BID33 BID9 ; BID17 ; BID16 ; BID3 . Our study enriches our understanding of the concept of clustering and its relation to classification. We argued that deep neural networks, especially CNNs, hold a great promise for data clustering. We are motivated by the fact that human vision (and learning) is a general system capable of solving both classification and clustering tasks thus blurring the current dichotomy in treating these problems. Our results show that CNNs can successfully handle complex and occluded clusters much better than other algorithms. This means that a learning mechanism, unsupervised or with minimal supervision, seems inevitable in capturing complex cluster shapes.While our formulation is supervised, feeding the labels to the network is not always consistent. This is where our work differs from semantic segmentation and instance level segmentation. We exploited the mean squared loss to train the network. It might be possible to define other loss functions to teach the network more efficiency using less number of training data or even with weaker labels. One possibility is the pairwise accuracy that we used here for evaluation. Instead of correctly classifying labels, the emphasis can be placed on correctly predicting whether two points belong to the same cluster, regardless of cluster identities (i.e., class labels may vary).Notice that while here we focused on synthetic stimuli, variations of the proposed CNN architecture, have been successfully applied to natural image segmentation. Thus, CNNs offer a unified solution that can be applied to different data modalities and even to higher dimensional data. Further work is needed to extend this line of work to higher dimensions, and more versatile types of cluster shapes (e.g., free form curves, Gestalt examples, density-based clusters). In this regard, adopting CNNs trained on natural images containing a rich set of intermediate-and high-level patterns can give invaluable insights.",1568,0.838,889,1.763779527559055,"Classification clustering have studied separately machine learning Inspired deep learning models solving various vision problems semantic segmentation humans serve assessing clustering algorithms here, advocate a unified treatment suggest hierarchical frameworks progressively build complex patterns on offer We do dwell much the learning mechanisms these frameworks as still with respect biological constraints Instead emphasize on the compositionality the real world structures objects In particular show CNNs, trained end to using back propagation with noisy labels cluster belonging several overlapping shapes do the state The main takeaway lesson mechanisms human vision particularly the hierarchal organization the visual ventral stream should taken clustering algorithms ( for learning representations or with minimum supervision reach human level clustering performance This, by suggests other methods do hold merits For example methods relying pairwise affinities very but still overlapping clusters Clustering, a.k.a unsupervised classification or nonparametric density estimation central many data-driven domains studied heavily The task in clustering group a given collection meaningful clusters such objects within Clustering provides a summary representation data at widely many disciplines version text processinga.k.a pattern mining as representation learning bag of words Despite the introduction thousands clustering algorithms the past BID0 , some challenges For instance existing algorithms fall dealing different cluster shapes high dimensions automatically determining large amounts choosing the appropriate similarity measure incorporating domain knowledge cluster evaluation Further no clustering algorithm consistently win other algorithms handle all test cases at humansDeep neural networks become solve various tasks across They proven successful several domains computer vision BID16 , for tasks scene and object pixel-level labeling for ; modeling attention ; , image generation robot arm playing Atari games beating the Go champion BID28 adopted this workDeep Convolutional Neural Networks BID17 have particularly over vision problems One reason nearby pixels natural scenes highly correlated Further natural objects compositional These facts allow applying the same filters across spatial locations ( hence share weights build complex filters from simpler ones detect highlevel patterns object parts objects We advocate these properties are highly appealing when dealing clustering problems For instance the classic two half moons example solved applying a filter selective Or when two clusters with shapes overlap the problem having filters responding Solving these cases very by just local regions around points being blind Incorporating domain knowledge, while working some cases does give a general solution solving all clustering problems The human visual system easily solves these 2D problems because a general system learned or evolved filters We believe deep CNNs although imperfect models the human vision as lack feedback lateral connections carry a huge promise solving clustering tasks Further as will argue they offer a unified solution both classification clustering tasksThe current demarcation becomes murky notice researchers human judgments evaluating the outcomes Indeed humans learn during their life time Moreover the structure fine through. Thus certainly a learning component involved which often formulating clustering algorithms While this sensible from (e.g., pattern mining not only it limits the pursuit for stronger algorithms our understanding human visionLearning techniques utilized clustering in BID1 ; BID25 for for tuning parameters Deep networks also exploited clustering ( BID14 ; BID32 However to while CNNs already adopted for image segmentation so exploited generic clustering Our goal investigate such possibility To this end instead borrowing clustering to do image segmentation follow the opposite direction propose based approachOur method builds in particular recent edge detection semantic segmentation which utilize multi-scale local and non-local cues BID28 . Thanks a high volume labeled data high capacity of deep networks powerful optimization computational deep models win on these tasks We also strongly inspired showing the high resemblance human vision mechanisms CNNs from (e.g., BID33 BID9 ; . Our study enriches the concept clustering classification We argued deep neural networks especially CNNs hold data clustering We motivated human vision ( learning a general system capable solving both classification thus blurring treating Our results CNNs can successfully handle complex and occluded clusters much other algorithms This means a learning mechanism unsupervised with seems inevitable capturing complex cluster shapesWhile our formulation supervised feeding the labels always consistent This where our work differs semantic segmentation and instance level segmentation We exploited the mean squared loss train the network It might possible define other loss functions to teach the network more efficiency using less number training data or with weaker labels One possibility the pairwise accuracy that used for evaluation Instead correctly labels the emphasis can correctly predicting whether two points belong regardless cluster identities class labels may vary).Notice while here focused synthetic stimuli variations the proposed CNN architecture, have successfully natural image segmentation Thus CNNs offer a unified solution that different data modalities even higher dimensional data Further work extend this line higher dimensions more versatile types cluster shapes ( Gestalt examples density-based clusters In this regard adopting CNNs trained natural images containing a rich set intermediate-and high-level patterns give invaluable insights",0.01,0.650122300968715
"Instancewise feature scoring is a method for model interpretation, which yields, for each test instance, a vector of importance scores associated with features. Methods based on the Shapley score have been proposed as a fair way of computing feature attributions, but incur an exponential complexity in the number of features.   This combinatorial explosion arises from the definition of Shapley value and prevents these methods from being scalable to large data sets and complex models. We focus on settings in which the data have a graph structure, and the contribution of features to the target variable is well-approximated by a graph-structured factorization.   In such settings, we develop two algorithms with linear complexity for instancewise feature importance scoring on black-box models.   We establish the relationship of our methods to the Shapley value and a closely related concept known as the Myerson value from cooperative game theory. We demonstrate on both language and image data that our algorithms compare favorably with other methods using both quantitative metrics and human evaluation. Although many black box machine learning models, such as random forests, deep neural networks, and kernel methods, can produce highly accurate prediction in many applications, such prediction often comes at the cost of interpretability. Ease of interpretation is a crucial criterion when these tools are applied in areas such as medicine, financial markets, and criminal justice; for more background, see the discussion paper by Lipton (2016) as well as references therein.In this paper, we study instancewise feature importance scoring as a specific approach to the problem of interpreting the predictions of black-box models. Given a predictive model, such a method yields, for each instance to which the model is applied, a vector of importance scores associated with the underlying features. The instancewise property means that this vector, and hence the relative importance of each feature, is allowed to vary across instances. Thus, the importance scores can act as an explanation for the specific instance, indicating which features are the key for the model to make its prediction on that instance.There is now a large body of research focused on the problem of scoring input features based on the prediction of a given instance (see, e.g., Shrikumar et al., 2017; BID0 Ribeiro et al., 2016; Lundberg & Lee, 2017; Štrumbelj & Kononenko, 2010; BID1 BID4 Sundararajan et al., 2017) . Of most relevance to this paper is a line of recent work (Štrumbelj & Kononenko, 2010; Lundberg & Lee, 2017; BID4 ) that has developed methods for model interpretation based on Shapley value (Shapley, 1953) from cooperative game theory. The Shapley value was originally proposed as an axiomatic characterization of a fair distribution of a total surplus from all the players, and can be applied to predictive models, in which case each feature is modeled as a player in the underlying game. While the Shapley value approach is conceptually appealing, it is also computationally challenging: in general, each evaluation of a Shapley value requires an exponential number of model evaluations. Different approaches to circumventing this complexity barrier have been proposed, including those based on Monte Carlo approximation (Štrumbelj & Kononenko, 2010; BID4 and methods based on sampled least-squares with weights (Lundberg & Lee, 2017) .In this paper, we take a complementary point of view, arguing that the problem of explanation is best approached within a model-based paradigm. In this view, explanations are cast in terms of a model, which may or may not be the same model as used to fit the data. Criteria such as Shapley value, which are intractable to compute when no assumptions are made, can be more effectively computed or approximated within the framework of a model. We focus specifically on settings in which a graph structure is appropriate for describing the relations between features in the data (e.g., chains for sequences and grids for images), and distant features according to the graph have weak interaction during the computation of Shapley values. We propose two methods for instancewise feature importance scoring in this framework, which we term L-Shapley and C-Shapley; here the abbreviations ""L"" and ""C"" refer to ""local"" and ""connected,"" respectively. By exploiting the underlying graph structure, the number of model evaluations is reduced to linear-as opposed to exponential-in the number of features. We demonstrate the relationship of these measures with a constrained form of Shapley value, and we additionally relate C-Shapley with another solution concept from cooperative game theory, known as the Myerson value (Myerson, 1977) . The Myerson value is commonly used in graph-restricted games, under a local additivity assumption of the model on disconnected subsets of features. Finally, we apply our feature scoring methods to several state-of-the-art models for both language and image data, and find that our scoring algorithms compare favorably to several existing sampling-based algorithms for instancewise feature importance scoring. We have proposed two new algorithms-L-Shapley and C-Shapley-for instancewise feature importance scoring, making use of a graphical representation of the data. We have demonstrated the superior performance of these algorithms compared to other methods on black-box models for instancewise feature importance scoring in both text and image classification with both quantitative metrics and human evaluation.Geoffrey Hinton, Nitish Srivastava, and Kevin Swersky. Neural networks for machine learninglecture 6a-overview of mini-batch gradient descent. et al., 2011) , which contains 50, 000 binary labeled movie reviews, with a split of 25, 000 for training and 25, 000 for testing.AG news with Char-CNN The AG news corpus is composed of titles and descriptions of 196, 000 news articles from 2, 000 news sources (Zhang et al., 2015) . It is segmented into four classes, each containing 30, 000 training samples and 1, 900 testing samples.Yahoo! Answers with LSTM The corpus of Yahoo! Answers Topic Classification Dataset is divided into ten categories, each class containing 140, 000 training samples and 5, 000 testing samples.Each input text includes the question title, content and best answer.MNIST The MNIST data set contains 28 × 28 images of handwritten digits with ten categories 0 − 9 (LeCun et al., 1998). A subset of MNIST data set composed of digits 3 and 8 is used for better visualization, with 12, 000 images for training and 1, 000 images for testing.",1380,0.559,846,1.6312056737588652,"Instancewise feature scoring model interpretation yields, each test instance a vector importance scores associated features Methods based the Shapley score have proposed a fair way computing feature attributions incur an exponential complexity in the number features This combinatorial explosion arises the definition Shapley value prevents these methods scalable and complex models We focus settings which the data have a graph structure the contribution features the target variable wellapproximated In such settings we develop two algorithms with linear complexity for instancewise feature importance scoring on black-box models We establish our methods the Shapley value a closely related concept known the Myerson value from cooperative game theory We demonstrate on both language image data our algorithms compare favorably using both quantitative metrics human evaluation Although many black box machine learning models, random forests kernel methods produce in many applications such prediction comes interpretability Ease interpretation these tools areas medicine financial markets; for more background the discussion paper Lipton2016 as referencesIn study instancewise feature importance scoring as a specific approach the problem interpreting the predictions black-box models Given a predictive model such method yields, each instance to importance scores associated the underlying features The instancewise property means this vector, and hence the relative importance each feature allowed across instances Thus the importance scores can act an explanation the specific instance, indicating which features the key for the model make on that instanceThere now focused scoring input features based the prediction ( Shrikumar 2017 BID0 Ribeiro et al Lundberg Lee ��trumbelj Kononenko 2010 BID4 Sundararajan) . Of most relevance this paper a line recent work (��trumbelj & Kononenko Lundberg Lee 2017 BID4 ) developed methods model interpretation based Shapley value ( 1953 from cooperative game theory The Shapley value originally proposed an axiomatic characterization a fair distribution a total surplus from all the players can predictive models in each feature modeled a player in the underlying game While the Shapley value approach conceptually appealing computationally: in general each evaluation requires an exponential number model evaluations Different approaches circumventing this complexity barrier those Monte Carlo approximation��trumbelj & Kononenko BID4 and methods based sampled least-squares with weights (Lundberg Lee 2017 .In take a complementary point arguing explanation best approached within In this view explanations cast a model may used fit Criteria such Shapley value which intractable compute when no assumptions more effectively computed or within We focus specifically settings a graph structure appropriate describing the relations features ( for sequences grids images distant features according have weak interaction during Shapley values We propose two methods instancewise feature importance scoring this framework term L-Shapley; here abbreviations "" ""localconnected By exploiting the underlying graph structure the number model evaluations linear-as opposedin the number features We demonstrate the relationship these measures a constrained form Shapley value additionally relate C-Shapley with another solution concept from cooperative game theory known the Myerson value 1977) The Myerson value commonly graph-restricted games under a local additivity assumption the model on disconnected subsets features Finally apply our feature scoring methods several state models both language image data our scoring algorithms compare favorably several existing sampling-based algorithms instancewise feature importance scoring We proposed two new algorithms-L-Shapleyfor instancewise feature importance scoring making a graphical representation We demonstrated the superior performance these algorithms compared on black-box models for instancewise feature importance scoring in both text with both quantitative metrics human evaluationGeoffrey Hinton Nitish Srivastava Kevin Swersky. Neural networks for machine learninglecture 6a-overview mini-batch gradient descent et 2011 which contains 50, 000 binary labeled movie reviews with a split 25 for training testingAG news with Char-CNN The AG news corpus titles descriptions 196, 000 news articles 2015 It segmented containing 30, 000 training samples 1, 900 testing samplesYahoo Answers with LSTM The corpus Yahoo Answers Topic Classification Dataset ten categories classEach input text includes the question title content best answerMNIST 28 × 28 images handwritten digits with ten categories 0 − 9LeCun et 1998 A subset MNIST data set composed digits 3 better visualization, with 12, 000 images training testing",0.01,0.312335769297268
"According to parallel distributed processing (PDP) theory in psychology, neural networks (NN) learn distributed rather than interpretable localist representations. This view has been held so strongly that few researchers have analysed single units to determine if this assumption is correct. However, recent results from psychology, neuroscience and computer science have shown the occasional existence of local codes emerging in artificial and biological neural networks. In this paper, we undertake the first systematic survey of when local codes emerge in a feed-forward neural network, using generated input and output data with known qualities. We find that the number of local codes that emerge from a NN follows a well-defined distribution across the number of hidden layer neurons, with a peak determined by the size of input data, number of examples presented and the sparsity of input data. Using a 1-hot output code drastically decreases the number of local codes on the hidden layer. The number of emergent local codes increases with the percentage of dropout applied to the hidden layer, suggesting that the localist encoding may offer a resilience to noisy networks. This data suggests that localist coding can emerge from feed-forward PDP networks and suggests some of the conditions that may lead to interpretable localist representations in the cortex. The findings highlight how local codes should not be dismissed out of hand. Local neural network models, which are often argued to be biologically implausible, have nevertheless been built or discussed by psychologists such as BID11 ; BID16 ; BID13 , and a few researchers like BID1 have done single neuron probing studies (the equivalent of the neuroscience approach) on their neural networks. However, as parallel distributed processing (PDP) neural networks (NN), as discussed by BID17 b) and BID15 , are generally assumed to learn distributed encodings across all situations, it is often believed that a single neuron in an artificial neural network is not interpretable, and experiments to test if this is true are rarely performed.Recently, however, there has been evidence emerging from neuroscience and modern artificial neural networks that demonstrate the existence of interpretable, local codes. BID10 argued that the neurons in the hippocampus codes for information in a highly selective manner in order to learn quickly without forgetting (catastrophic interference), and BID4 argued that some neurons in cortex are highly selective in order to encode multiple items at the same time in shortterm memory (solving the so-called superposition catastrophe). BID14 reported single cells that fire frequently in response to one stimulus, which suggests that individual neurons can be usefully interpreted.Localist codes have been found in artificial neural networks, see BID2 for full reviews, some examples are Le (2013); BID7 ). BID4 have shown that PDP models learn localist codes when trained to co-activate multiple items at the same time. Deep networks learn selective codes under some conditions. For example, BID8 's found quote mark detectors in RNNs. And there is also some evidence from feed-forward models. For example, BID12 have found that probing individual hidden layer neurons (HLNs) with noise and using activation maximisation they can produce a picture of what that neuron will respond most to, and from this they identified HLNs that act as feature detectors, such as those that only responding to creases (in clothing) or eyes or faces and so on.We would like to elucidate the conditions in which simple networks learn selective units, as this may provide further insight into the conditions in which neurons in cortex respond selectively, and, as we expect such codes are learned for sound information theoretic reasons, we expect that these conditions will also apply to when neural networks might learn them as well. Thus, in this paper, we undertake a study of simple feed-forward neural networks to investigate whether local codes, LCs, do actually emerge in PDP networks, and (as we shall show that they do) we then look at what inhibits or promotes the emergence of LCs by designing input and output data with known properties. And, as this data is structured to have some invariance within a class and some randomness, it is proposed that these experiments could as be modelling the layers within the deep neural network above those which transform the input data from pixel space to feature space.To be clear, we consider a neuron to be interpretable if probing of the activation state of it could give correct and useful information about the classification of the input. We look for information about the presence or absence of a category in the hidden layer (category selective HLNs). We separate the qualitative measure (selective) of whether or not a HLN encodes category presence, from the quantitative measure of how much the HLN responds to a category (selectivity). Thus, a HLN is selective if it encodes the presence/absence of a category. Examples are shown in figure 1, as the neuron encodes the presence or absence of the category shown as red circles, equivalently, it could be claimed that these neurons are selective for that category. As biological neurons use energy to encode information, a selective neuron is usually 'selectively on' (see figure 1(left)), but as there is no energy cost in neural networks 'selectively off' units (figure 1(right)) have also been observed. We use the word 'selectivity' as a quantitative measure of the difference between activations for the two categories, A and not-A, where A is the category a neuron is selective for (and not-A being all other categories). Specifically: DISPLAYFORM0 The important point is the qualitative measure of whether or not a neuron is selective, not how much it is selective by, as we are interested in counting the number of local codes that emerge. Note that the chance that all the members of A would emerge disjoint from the members of not-A is 50 50 / 500 50 is tiny (4.32 × 10 −71 ). Furthermore, we found that the selectivity increased with training as the neural network minimised the loss function, but that the number of selective codes did not change once the neural network achieved 100% accuracy.A criticism often made of a grandmother cell hypothesis is that even if a cell fires consistently to a single class, it is not possible to know that it would not have fired to a stimulus that was not presented. For example, although BID14 found a neuron that responded selectively to images of Jennifer Aniston, the authors only presented approximately 100 images to the human participant, and it is possible that other non-tested images would also drive the neuron. BID20 estimated that between 50-150 other images would drive this neuron. Obviously an experimenter cannot present every possible combination of visual inputs to a patient. However, in neural networks with small datasets, we can present all the possible stimuli to the network. We consider a neuron to be selective if it is selective over all the data it is reasonable to expect the network to differentiate between. For example, it is reasonable to do the test over all training data, and it is reasonable to do it over all test and all verification data or even other data of a similar form (such as different photos of the same class), and choosing what constitutes a reasonable set of data is a decision to be made by the experimenters and reviewers. In this work, we chose to use a simple pattern classification task, rather than an image recognition task, as we could then test the NN with all possible patterns. We have demonstrated that interpretable localised encodings of the presence/absence of some categories can emerge from the hidden layer of a feed-forward neural network. As the number of local codes follows a well-defined pattern with the size of the hidden layer, and it is affected by modifications of the input and output data, it suggests that the number of local codes is related to the computing capacity of the neural network and the difficulty of the problem presented to it, suggesting that the local codes offer some modification to the computing power of the neural network.Furthermore, as the hidden layer size increases, there is so much extra capacity that local codes are not needed. Our results suggest that local codes require more effort to train, but offer more efficient use of the available capacity.As the number of local codes shared invariants within a categories, it does imply that the local codes have some function associated with recognising these invariants. As the average number and range of LCs generally increases with dropout, and the LCs are repressed by a fully locally encoded output layer, it suggests that some local codes are good to have, and that number increases with noisy networks. The fact that the dropout data seems to contain multiple overlapping peaks, and, in our tests, peak numbers of LCs are seen at 500 and 1000 (and 2000 for the S R = 1 9 data) HLNs implies that there are more than one qualitative approaches for the neural network to solve the problem, and tuning the problem and neural network parameters nudges the solution to different distributions of local codes. Do these simple networks tell us anything about deep neural networks? The data presented here was designed to have invariant feature 'short-cuts' that the neural network could make use of in classifying input data into classes and the argument could well be made that the data passed between layers of a deep neural network is not of the same quality. Whilst an obvious next experiment for us is to investigate the qualities of the data passed within a neural network, preliminary feed-forward neural network training on standard simple neural network data (such as the Iris dataset from Fisher (1936)) results also show the emergence of local codes when there is a 'short-cut' in the data (publication in preparation). The observations that local codes are seen under dropout, with distributed input and output codes, when there are invariant features and local codes are inhibited with 1-hot output encodings, suggests that local codes might be found in a the middle and higher layers of a deep network, and not the penultimate layer where the 1-hot output could inhibit them or the early layers where invariant features common to a class have not yet been identified. Another interesting question is whether the local codes might have a diagnostic use, for example, is it the case that they increased in networks that generalise or are they, perhaps, an indicator of over-training? Answering this would also highlight when and where we should expect invariants in the data, as learning an invariant feature, such as, 'presence of eyes implies presence of face', could help with generalisation and classification, however learning an irrelevant invariant feature, such as, presence of 'blue sky implies tanks' would not. Discriminating a blue-sky selective neuron from a tank-selective neuron in such a case would require careful thought about what we should consider reasonable data to test for selectivity.",2177,0.91,1273,1.7101335428122546,"According parallel distributed processing (PDP) theory in psychology learn distributed rather interpretable localist representations This view has held so strongly few researchers analysed single units to this assumption However recent results psychology, neuroscience and computer science the occasional existence local codes emerging artificial and biological neural networks In this paper undertake when local codes emerge a feed-forward neural network generated input with known qualities We find local codes emerge a NN follows across the number hidden layer neurons a peak determined input data number examples presented sparsity Using a 1-hot output code drastically local codes on the hidden layer The number emergent local codes increases dropout applied the hidden layer suggesting the localist encoding offer a resilience noisy networks This data suggests localist coding emerge feed-forward PDP networks suggests some the conditions interpretable localist representations the cortex The findings highlight local codes should not dismissed Local neural network models, argued biologically nevertheless built or discussed psychologists such BID11 ; BID16 a few researchers like done single neuron probing studiesthe equivalent the neuroscience approach However as parallel distributed processing neural as discussed BID17 b) , generally assumed learn distributed encodings across all situations often believed not interpretable, experiments to if rarelyRecently however evidence emerging neuroscience and modern artificial neural networks demonstrate interpretable, local codes BID10 argued the neurons the hippocampus codes information in in order quickly without forgetting (catastrophic interference BID4 some neurons cortex highly encode multiple items shortterm memorysolving the so-called superposition catastrophe BID14 reported single cells that fire frequently response one stimulus suggests individual neurons usefully interpretedLocalist codes have artificial neural networks see BID2 full reviews some examples Le (2013 ). BID4 have shown PDP models learn localist codes when trained to co-activate multiple items Deep networks learn selective codes under For example BID8 's found quote mark detectors in RNNs. And there from feed-forward models For example BID12 have found probing individual hidden layer neuronsHLNs noise and using activation maximisation they a picture what that neuron will respond most from identified HLNs act feature detectors such only responding creases (in clothing eyes or faces andWe would elucidate the conditions simple networks learn selective units as this may the conditions cortex respond selectively, expect such codes learned for sound information theoretic reasons these conditions when might them as Thus undertake simple feed-forward neural networks local codes, LCs do actually emerge PDP networks ( that we then look what inhibits or promotes by designing input with known properties And, this data structured have some invariance within and proposed these experiments as be modelling the layers within above those transform from pixel space featureTo consider a neuron interpretable if probing of the activation state it could give correct and useful information We look for information the presence a category the hidden layercategory selective HLNs We separate the qualitative measure (selective) whether or not a HLN encodes category presence how responds Thus a HLN is selective if encodes a category Examples are figure as the neuron encodes the presence the category shown as red circles equivalently it could claimed selective that category As biological neurons use energy a selective neuron usually 'selectively on ( figure 1(left as there no energy cost in neural networks ' off unitsfigure have also observed We use the wordselectivity a quantitative measure the difference activations for A not-A where the category a neuron selective being all other categories Specifically: DISPLAYFORM0 The important point the qualitative measure whether selective not how by, as are interested counting local codes emerge Note the chance all the members A would emerge disjoint the members not-A 50 50 / 500 50 is tiny4.32 −71 Furthermore we the selectivity increased training as the neural network minimised the loss function that selective codes did once achievedA criticism often a grandmother cell hypothesis even fires consistently to a single class possible that would a stimulus presented For example although BID14 found a neuron responded selectively images Jennifer Aniston the authors only presented approximately 100 images it other non-tested images would drive BID20 estimated between 50-150 other images drive this neuron Obviously an experimenter present every possible combination visual inputs a patient However in neural networks with small datasets present all the possible stimuli We consider a neuron selective if selective over all the data reasonable the network differentiate. For example it reasonable do the test over all training data it and all verification data or even other data of a similar form different photos choosing what constitutes the experimenters reviewers In this work chose a simple pattern classification task rather could then test the NN with all possible patterns We demonstrated that interpretable localised encodings some categories can emerge the hidden layer a feed-forward neural network As the number local codes follows with the size the hidden layer and it affected modifications suggests related the computing capacity presented suggesting offer some modificationFurthermore there so much extra capacity Our results local codes require more effort train, but offer more efficient use the available capacityAs shared invariants within a categories does imply some function associated recognising As the average number and range LCs generally dropout and repressed a fully locally encoded output layer suggests some local codes good to number increases noisy networks The fact the dropout data seems contain multiple overlapping peaks, our tests peak numbers LCs seen 500 ( 2000 for the S R = 1 9 data) HLNs implies more than one qualitative approaches the neural network solve tuning and neural network parameters nudges different distributions local codes Do these simple networks tell deep neural networks The data presented designed have invariant feature 'short-cuts the neural network make classifying input data classes the argument could well made passed between layers of Whilst an obvious next experiment investigate the qualities the data passed within preliminary feed-forward neural network training on standard simple neural network data the Iris dataset from Fisher ( results also the emergence local codes when there a 'short-cutpublication preparation The observations local codes seen under dropout, with distributed input and output codes when there invariant features inhibited with 1-hot output encodings suggests found a the middle and higher layers not the penultimate layer where could inhibit them or the early layers common a class have Another interesting question the local codes might a diagnostic use for is increased in networks generalise or they, perhaps an indicator over-training Answering would also highlight when and invariants learning an invariant feature,, 'presence eyes implies face could with generalisation classification however learning presence 'blue sky implies tanks Discriminating a blue-sky selective neuron a tank-selective neuron such a case careful thought we should reasonable data test selectivity",0.01,0.5134370451185519
"Representing entities and relations in an embedding space is a well-studied approach for machine learning on relational data. Existing approaches however primarily focus on simple link structure between a finite set of entities, ignoring the variety of data types that are often used in relational databases, such as text, images, and numerical values. In our approach, we propose a multimodal embedding using different neural encoders for this variety of data, and combine with existing models to learn embeddings of the entities. We extend existing datasets to create two novel benchmarks, YAGO-10-plus and MovieLens-100k-plus, that contain additional relations such as textual descriptions and images of the original entities. We demonstrate that our model utilizes the additional information effectively to provide further gains in accuracy. Moreover, we test our learned multimodal embeddings by using them to predict missing multimodal attributes. Knowledge bases (KB) are an essential part of many computational systems with applications in variety of domains, such as search, structured data management, recommendations, question answering, and information retrieval. However, KBs often suffer from incompleteness, noise in their entries, and inefficient inference. Due to these deficiencies, learning the relational knowledge representation has been a focus of active research BID1 BID10 BID21 BID29 BID4 . These approaches represent relational triples, consisting of a subject entity, relation, and an object entity, by estimating fixed, low-dimensional representations for each entity and relation from observations, thus encode the uncertainty and infer missing facts accurately and efficiently. The subject and the object entities come from a fixed, enumerable set of entities that appear in the knowledge base.Knowledge bases in the real world, however, are rich with a variety of different data types. Apart from a fixed set of entities, the relations often not only include numerical attributes (such as ages, dates, financial, and geoinformation), but also textual attributes (such as names, descriptions, and titles/designations) and images (profile photos, flags, posters, etc.) . Although these different types of relations cannot directly be represented as links in a graph over a fixed set of nodes, they can be crucial pieces of evidences for knowledge base completion. For example the textual descriptions and images might provide evidence for a person's age, profession, and designation. Further, this additional information still contains similar limitations as the conventional link data; they are often missing, may be noisy when observed, and for some applications, may need to be predicted in order to address a query. There is thus a crucial need for relational modeling that goes beyond just the link-based, graph view of knowledge-base completion, is able to utilize all the observed information, and represent the uncertainty of multimodal relational evidence.In this paper, we introduce a multimodal embedding approach for modeling knowledge bases that contains a variety of data types, such as textual, images, numerical, and categorical values. Although we propose a general framework that can be used to extend many of the existing relational modeling approaches, here we primary apply our method to the DistMult approach . We extend this approach that learns a vector for each entity and relation by augmenting it with additional neural encoders for different evidence data types. For example, when the object of a triple is an image, we encode it into a fixed-length vector using a CNN, while the textual attributes are encoded using sequential embedding approaches like LSTMs. The scoring module remains identical; given the vector representations of the subject, relation, and object of a triple, this module produces a score indicating the probability that the triple is correct. This unified model allows for flow of the information across the different relation types, enabling more accurate modeling of relational data.We provide an evaluation of our proposed approach on two relational databases. Since we are introducing a novel formulation in the relational setting, we introduce two benchmarks, created by extending the existing YAGO-10 and MovieLens-100k datasets to include additional relations such as textual descriptions, numerical attributes, and images of the original entities. In our evaluation, we demonstrate that our model utilizes the additional information effectively to provide gains in link-prediction accuracy, and present a breakdown of how much each relation benefits from each type of the additional information. We also present results that indicate the learned multimodal embeddings are capable of predicting the object entities for different types of data which is based on the similarity between those entities. Motivated by the need to utilize multiple source of information to achieve more accurate link prediction we presented a novel neural approach to multimodal relational learning. In this paper we introduced a universal link prediction model that uses different types of information to model knowledge bases. We proposed a compositional encoding component to learn unified entity embedding that encode the variety of information available for each entity. In our analysis we show that our model in comparison to a common link predictor, DistMult, can achieve higher accuracy, showing the importance of employing the available variety of information for each entity. Since all the existing datasets are designed for previous methods, they lack mentioned kind of extra information. In result, we introduced two new benchmarks YAGO-10-plus and MovieLens-100k-plus, that are extend version of existing datasets. Further, in our evaluation, we showed that our model effectively utilizes the extra information in order to benefit existing relations. We will release the datasets and the open-source implementation of our models publicly.There are number of avenues for future work. We will investigate the performance of our model in completing link prediction task using different scoring function and more elaborate encoding component and objective function. We are also interested in modeling decoding of multimodal values in the model itself, to be able to query these values directly. Further, we plan to explore efficient query algorithms for embedded knowledge bases, to compete with practical database systems.",1152,0.599,684,1.6842105263157894,"Representing entities relations an embedding space machine learning on Existing approaches however primarily simple link structure between a finite set entities ignoring the variety often text numerical values In our approach propose embedding using different neural encoders this variety data combine with learn the entities We extend existing datasets create two novel benchmarks YAGO-10plus MovieLens-100k contain additional relations such textual descriptions images the original entities We demonstrate our model utilizes the additional information effectively further gains Moreover we test our learned multimodal embeddings them predict missing multimodal attributes Knowledge bases (KB many computational systems with applications variety search structured data management recommendations question answering However KBs often suffer noise in their entries inefficient inference Due these deficiencies learning the relational knowledge representation has a focus active research . These approaches represent relational triples consisting a subject entity relation by estimating fixed, low-dimensional representations for relation from observations thus encode the uncertainty and infer missing facts accurately The subject and the object entities come a fixed, enumerable set appear the knowledge baseKnowledge bases in rich Apart a fixed set entities the relations often not include numerical attributes ages dates financial, geoinformation textual attributes descriptions titles/ imagesprofile photos flags posters . Although these different types relations directly represented links over nodes crucial pieces evidences knowledge base completion For example the textual descriptions images might provide evidence profession designation Further this additional information still contains similar limitations the conventional link data; they often missing may noisy when observed for need predicted address a query There thus a crucial need relational modeling goes just the link-based, graph view knowledge-base completion is able utilize all the observed information represent the uncertainty multimodal relational evidenceIn modeling knowledge bases contains textual images numerical categorical values Although we propose extend many here primary apply our method the DistMult approach . We extend this approach that learns a vector for each entity relation augmenting additional neural encoders different evidence data types For example the object a triple is an image encode using a CNN, while the textual attributes sequential embedding approaches like LSTMs The scoring module remains identical; given the vector representations the subject relation produces indicating correct This unified model flow the information the different relation types enabling more accurate modelingWe provide an evaluation our proposed approach on two relational databases Since we introducing a novel formulation in the relational setting introduce two benchmarks created extending the existing YAGO-10 MovieLens-100k datasets additional relations such textual descriptions numerical attributes images the original entities In our evaluation demonstrate our model utilizes the additional information effectively gains link-prediction accuracy present a breakdown how much each relation benefits each type the additional information We also present results that the learned multimodal embeddings capable predicting the object entities for data which based Motivated utilize multiple source achieve more accurate link prediction we presented a novel neural approach multimodal relational learning In introduced a universal link prediction model different types model knowledge bases We proposed a compositional encoding component learn unified entity that encode the variety information available In our analysis show our model in comparison a common link predictor DistMult achieve showing employing the available variety information each entity Since all the existing datasets designed previous methods they lack mentioned kind extra information In result introduced YAGO-10plus MovieLens-100k that extend version existing datasets Further our evaluation showed our model effectively utilizes the extra information benefit existing relations We will release the datasets our models publiclyThere number avenues future work We will investigate the performance our model completing link prediction task different scoring function more elaborate encoding component and objective function We also interested modeling decoding multimodal values itself to query Further plan explore efficient query algorithms embedded knowledge bases to compete practical database systems",0.01,0.4473874766568848
"An ensemble of neural networks is known to be more robust and accurate than an individual network, however usually with linearly-increased cost in both training and testing. 
 In this work, we propose a two-stage method to learn Sparse Structured Ensembles (SSEs) for neural networks.
 In the first stage, we run SG-MCMC with group sparse priors to draw an ensemble of samples from the posterior distribution of network parameters. In the second stage, we apply weight-pruning to each sampled network and then perform retraining over the remained connections.
 In this way of learning SSEs with SG-MCMC and pruning, we not only achieve high prediction accuracy since SG-MCMC enhances exploration of the model-parameter space, but also reduce memory and computation cost significantly in both training and testing of NN ensembles.
 This is thoroughly evaluated in the experiments of learning SSE ensembles of both FNNs and LSTMs.
 For example, in LSTM based language modeling (LM), we obtain 21\% relative reduction in LM perplexity by learning a SSE of 4 large LSTM models, which has only 30\% of model parameters and 70\% of computations in total, as compared to the baseline large LSTM LM.
 To the best of our knowledge, this work represents the first methodology and empirical study of integrating SG-MCMC, group sparse prior and network pruning together for learning NN ensembles. Recently there are increasing interests in using ensembles of Deep Neural Networks (DNNs) BID19 ; BID17 ), which are known to be more robust and accurate than individual networks. An explanation stems from the fact that learning neural networks is an optimization problem with many local minima BID13 ). Multiple models obtained from applying stochastic optimization, e.g. the widely used Stochastic Gradient Descent (SGD) and its variants, converge to different local minima and tend to make different errors. Due to this diversity, the collective prediction produced by an ensemble is less likely to be in error than individual predictions. The collective prediction is usually performed by averaging the predictions of the multiple neural networks.On the other hand, the improved prediction accuracy of such model averaging can be understood from the principled perspective of Bayesian inference with Bayesian neural networks. Specifically, for each test pointx, we consider the predictive distribution P (ỹ|x, D) = ∫ P (ỹ|x, θ)P (θ|D)dθ, by integrating the model distribution P (ỹ|x, θ) with the posterior distribution over the model parameters P (θ|D) given training data D. The predictive distribution is then approximated by Monte Carlo integration P (ỹ|x, D) ≈ DISPLAYFORM0 , where θ (m) ∼ P (θ|D), m = 1, · · · , M , are posterior samples of model parameters. It is well known that such Bayesian model averaging is more accurate in prediction and robust to over-fitting than point estimates of model parameters BID3 ; ; BID9 ).Despite the obvious advantages as seen from both perspectives, a practical problem that hinders the use of DNN ensembles in real-world tasks is that an ensemble requires too much computation in both training and testing. Traditionally , multiple neural networks are trained, e.g. with different random initialization of model parameters. Recent studies in BID21 ; BID17 ) propose to learn an ensemble which consists of multiple snapshot models along the op- timization path within a single training process, by leveraging a special cyclic learning rate schedule. This reduces the training cost, but the testing cost is still high.In this paper we also aim at learning an ensemble within a single training process, but by leveraging the recent progress in Bayesian posterior sampling, namely the Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) algorithms. Moreover, we apply group sparse priors in training to enforce group-level sparsity on the network's connections. Subsequently we can further use model pruning to compress the networks so that the testing cost is reduced with no loss of accuracy.Figure 1 presents a high-level overview of our two-stage method to learn Sparse Structured Ensembles (SSEs) for DNNs. Specifically, in the first stage, we run SG-MCMC with group sparse priors to draw an ensemble of samples from the posterior distribution of network parameters. In the second stage, we apply weight-pruning to each sampled network and then perform retraining over the remained connections as fine-tuning. In this way of learning SSEs with SG-MCMC and pruning, we reduce memory and computation cost significantly in both training and testing of NN ensembles, while maintaining high prediction accuracy. This is empirically verified in our experiments of learning SSE ensembles of both FNNs and LSTMs.We evaluate the performance of the proposed method on two experiments with different types of neural networks. The first is an image classification experiment, which uses Feed-forward Neural Networks (FNNs) on the well-known MNIST dataset (Deng (2012) ). Second, we experiment with the more challenging task of Long Short-term Memory (LSTM, BID15 ) based language modeling, which is conducted on the Penn Treebank dataset BID22 ). It is found that the proposed method works well across both tasks. For example, we obtain 12% relative reduction (from 78.4 to 68.6) in LM perplexity by learning a SSE of 4 large LSTM models, which has only 40% of model parameters and 90% of computations in total, as compared to the large LSTM LM in BID34 . Furthermore, when the embedding weights of input and output are shared as in BID18 , we obtain a perplexity of 62.1 (achieving 21% reduction from 78.4) by 4 large LSTMs with only 30% of model parameters and 70% of computations in total. In this work, we propose a novel method of learning NN ensembles efficiently and cost-friendly by integrating three mutually enhanced techniques: SG-MCMC sampling, group sparse prior and network pruning. The resulting SGLD+GSP+PR method is easy to implement, yet surprisingly effective. This is thoroughly evaluated in the experiments of learning SSE ensembles of both FNNs and LSTMs. The Sparse Structured Ensembles (SSEs) learned by our method gain better prediction performance with reduced training and test cost when compared to traditional methods of learning NN ensembles. Moreover, by proper controlling the number of models used in the ensemble, the method can also be used to produce SSE, which outperforms baseline NN significantly without increasing the model size and computation cost.Some interesting future works: (1) interleaving model sampling and model pruning; (2) application of this new method, as a new powerful tool of learning ensembles, to more tasks.",1378,0.596,786,1.7531806615776082,"An ensemble neural networks known more however usually with linearly-increased cost in both training testing In this work propose learn In run SG-MCMC with group sparse priors draw an ensemble samples the posterior distribution network parameters In the second stage apply weightpruning each sampled network perform retraining over the remained connections In this way of learning SSEs with SG-MCMC pruning not achieve high prediction accuracy since enhances exploration the model-parameter space reduce memory and computation cost significantly both training NN ensembles This thoroughly evaluated the experiments learning SSE ensembles of both FNNs For LSTM based language modelingLM obtain 21\% relative reduction LM perplexity learning 4 large LSTM models model parameters computations total To represents the first methodology and empirical study integrating SG-MCMC, group sparse prior network pruning together learning NN ensembles Recently there are increasing interests using ensembles Deep BID19 ; known accurate individual networks An explanation stems learning neural networks an optimization problem with many local minima BID13 ). Multiple models obtained applying, its variants converge different local minima tend make different errors Due this diversity the collective prediction produced an ensemble is less in individual predictions The collective prediction usually performed averaging the multiple neural networksOn the improved prediction accuracy such model averaging understood the principled perspective with Specifically for each test pointx consider predictive distribution P���|x D �P|D)d� by integrating the model distribution over given training data D. The predictive distribution then Monte Carlo integration P (���|x, D) �� DISPLAYFORM0 ,m ∼ P|D m · · M , are posterior samples model parameters It well such Bayesian model averaging more prediction robust over point estimates model parameters BID3 ; ; BID9 ).Despite as seen both perspectives a practical problem that DNN ensembles an ensemble requires both training , multiple neural networks trained, different random initialization of model parameters Recent in BID21 ; ) propose to learn an ensemble which consists multiple snapshot models along the op- timization path within a single training process by leveraging a special cyclic learning rate schedule This reduces the training cost, the testing costIn also aim learning an ensemble within by leveraging the recent progress Bayesian posterior sampling algorithms Moreover we apply group sparse priors training enforce the network's connections Subsequently we can further use model pruning compress the networks so the testing cost with accuracyFigure presents to learn Specifically in run SG-MCMC group sparse priors draw an ensemble samples network parameters In the second stage apply weightpruning each sampled network perform retraining over the remained connections as In this way of learning SSEs with SG-MCMC pruning reduce memory and computation cost significantly both training NN ensembles while high prediction accuracy This empirically verified of learning SSE ensembles both FNNsWe evaluate the proposed method two experiments different types first is an image classification experiment Feed-forward Neural Networks onDeng ( Second experiment the more challenging task Long Short-term Memory, BID15 ) based language modeling conducted the Penn Treebank BID22 It found the proposed method works across both tasks For example we obtain 12% relative reduction (from LM perplexity by learning a SSE 4 large LSTM models has only 40% model parameters computations total in BID34 . Furthermore when the embedding weights input shared as in BID18 , obtain a perplexity 62.1 (achieving 21% reduction from 78.4 by 4 large LSTMs only 30% model parameters computations total In this work propose learning NN ensembles efficiently costfriendly by integrating three mutually enhanced techniques SG-MCMC sampling group sparse prior network pruning The resulting SGLD+GSP+PR method easy yet surprisingly This thoroughly evaluated the experiments learning SSE ensembles of both FNNs The Sparse learned our method gain better prediction performance reduced training and test cost when traditional methods Moreover by proper controlling models used the ensemble also produce SSE, outperforms baseline NN significantly without increasing and computation costSome interesting future works: (1) interleaving model sampling model pruning; this new method, a new powerful tool of learning more tasks",0.01,0.6231173216541717
"This paper introduces a new framework for data efficient and versatile learning. Specifically:
 1) We develop ML-PIP, a general framework for Meta-Learning approximate Probabilistic Inference for Prediction. ML-PIP extends existing probabilistic interpretations of meta-learning to cover a broad class of methods. 
 2) We introduce \Versa{}, an instance of the framework employing a flexible and versatile amortization network that takes few-shot learning datasets as inputs, with arbitrary numbers of shots, and outputs a distribution over task-specific parameters in a single forward pass. \Versa{} substitutes optimization at test time with forward passes through inference networks, amortizing the cost of inference and relieving the need for second derivatives during training.
 3) We evaluate \Versa{} on benchmark datasets where the method sets new state-of-the-art results, and can handle arbitrary number of shots, and for classification, arbitrary numbers of classes at train and test time. The power of the approach is then demonstrated through a challenging few-shot ShapeNet view reconstruction task. Many applications require predictions to be made on myriad small, but related datasets. In such cases, it is natural to desire learners that can rapidly adapt to new datasets at test time. These applications have given rise to vast interest in few-shot learning BID9 BID32 , which emphasizes data efficiency via information sharing across related tasks. Despite recent advances, notably in meta-learning based approaches BID44 BID54 BID8 BID10 , there remains a lack of general purpose methods for flexible, data-efficient learning.Due to the ubiquity of recent work, a unifying view is needed to understand and improve these methods. Existing frameworks BID16 are limited to specific families of approaches. In this paper we develop a framework for meta-learning approximate probabilistic inference for prediction (ML-PIP), providing this view in terms of amortizing posterior predictive distributions. In Section 4, we show that ML-PIP re-frames and extends existing point-estimate probabilistic interpretations of meta-learning BID16 to cover a broader class of methods, including gradient based meta-learning BID10 BID44 , metric based meta-learning BID48 , amortized MAP inference BID43 and conditional probability modelling BID13 .The framework incorporates three key elements. First , we leverage shared statistical structure between tasks via hierarchical probabilistic models developed for multi-task and transfer learning BID18 BID0 . Second , we share information between tasks about how to learn and perform inference using meta-learning BID37 BID50 BID47 . Since uncertainty is rife in small datasets, we provide a procedure for metalearning probabilistic inference. Third , we enable fast learning that can flexibly handle a wide range of tasks and learning settings via amortization .Building on the framework, we propose a new method -VERSA -which substitutes optimization procedures at test time with forward passes through inference networks. This amortizes the cost of inference, resulting in faster test-time performance, and relieves the need for second derivatives during training. VERSA employs a flexible amortization network that takes few-shot learning datasets, and outputs a distribution over task-specific parameters in a single forward pass. The network can handle arbitrary numbers of shots, and for classification, arbitrary numbers of classes at train and test time (see Section 3). In Section 5, we evaluate VERSA on (i) standard benchmarks where the method sets new state-of-the-art results, (ii) settings where test conditions (shot and way) differ from training, and (iii) a challenging one-shot view reconstruction task. We have introduced ML-PIP, a probabilistic framework for meta-learning. ML-PIP unifies a broad class of recently proposed meta-learning methods, and suggests alternative approaches. Building on ML-PIP, we developed VERSA, a few-shot learning algorithm that avoids the use of gradient based optimization at test time by amortizing posterior inference of task-specific parameters. We evaluated VERSA on several few-shot learning tasks and demonstrated state-of-the-art performance and compelling visual results on a challenging 1-shot view reconstruction task. a We report the performance of Prototypical Networks when training and testing with the same ""shot"" and ""way"", which is consistent with the experimental protocol of the other methods listed. We note that Prototypical Networks perform better when trained on higher ""way"" than that of testing. In particular, when trained on 20-way classification and tested on 5-way, the model achieves 68.20 ± 0.66%.",900,0.492,539,1.6697588126159555,"This paper introduces data efficient versatile learning Specifically 1 We develop ML-PIP Meta-Learning approximate Probabilistic Inference Prediction ML-PIP extends existing probabilistic interpretations meta-learning cover methods 2 We introduce \Versa an instance the framework employing a flexible and versatile amortization network takes few-shot learning datasets with arbitrary numbers shots outputs in a single forward pass \Versa{ substitutes optimization at test time forward passes through inference networks amortizing inference relieving second derivatives during training 3 We evaluate \Versa on benchmark datasets where sets new state results can handle arbitrary number shots for classification, arbitrary numbers classes at train The power the approach then demonstrated a challenging few-shot ShapeNet view reconstruction task Many applications predictions myriad small related datasets In such cases natural desire learners that rapidly new datasets at test time These applications given vast interest few-shot learning BID9 BID32 , emphasizes data efficiency via information sharing related tasks Despite recent advances notably meta-learning based approaches BID44 BID54 BID8 BID10 general purpose methods flexible, data-efficient learningDue recent work a unifying view Existing frameworks BID16 are limited specific families approaches In develop meta-learning approximate probabilistic inference prediction (ML-PIP providing this view amortizing posterior predictive distributions In Section show MLPIP reframes extends existing point-estimate probabilistic interpretations meta-learning BID16 cover methods gradient based metric amortized MAP inference BID43 conditional probability modelling incorporates First , leverage shared statistical structure between tasks via developed multi and transfer BID18 BID0 Second , share information between tasks about learn inference meta-learning BID37 BID50 BID47 Since uncertainty small datasets provide metalearning Third , enable fast learning that flexibly handle learning settings via amortization .Building propose -VERSA substitutes optimization procedures at test time forward passes through inference networks This amortizes inference resulting faster test-time performance second derivatives during training VERSA employs a flexible amortization network takes few-shot learning datasets outputs a distribution a single forward pass The network can handle arbitrary numbers shots for classification classes at train Section In Section evaluate VERSA on ( standard benchmarks where sets new state results test conditionsshot way training (iii) a challenging one-shot view reconstruction task We introduced ML-PIP meta-learning ML-PIP unifies a broad class recently proposed meta-learning methods suggests Building ML-PIP developed VERSA a few-shot learning algorithm avoids gradient based optimization at test time posterior inference We evaluated VERSA on several few-shot learning tasks demonstrated state compelling visual results a challenging 1-shot view reconstruction task a We report Prototypical Networks when training the same ""shot ""way consistent listed We note Prototypical Networks perform trained higher ""way than that testing In particular when trained 20-way classification tested the model achieves 68.20 ±",0.01,0.41056577986339055
"In recent years, softmax together with its fast approximations has become the de-facto loss function for deep neural networks with multiclass predictions. However, softmax is used in many problems that do not fully fit the multiclass framework and where the softmax assumption of mutually exclusive outcomes can lead to biased results. This is often the case for applications such as language modeling, next event prediction and matrix factorization, where many of the potential outcomes are not mutually exclusive, but are more likely to be independent conditionally on the state. To this end, for the set of problems with positive and unlabeled data, we propose a relaxation of the original softmax formulation, where, given the observed state, each of the outcomes are conditionally independent but share a common set of negatives. Since we operate in a regime where explicit negatives are missing, we create an adversarially-trained model of negatives and derive a new negative sampling and weighting scheme which we denote as Cooperative Importance Sampling (CIS). We show empirically the advantages of our newly introduced negative sampling scheme by pluging it in the Word2Vec algorithm and benching it extensively against other negative sampling schemes on both language modeling and matrix factorization tasks and show large lifts in performance. Learning from positive and unlabeled data is a well-defined task in machine learning, known as positive-unlabeled (PU) learning BID6 ; BID14 ; BID13 ; BID22 ; BID19 ). The applications of PU learning are numerous, as in many fields negative data is either too expensive to obtain or too hard to define. This is the case in language modeling, where one only observes examples of valid sentences and documents, and tries to learn a generative process. Similarly, in computer vision, with the recent work on Generative Adversarial Networks (GANs), one tries to learn the underlying generative process that produces meaningful images. In both cases, the space of negatives (e.g., non-sentences or non-images) is not clear. Similarly, in matrix factorization, most of the matrices contain pairs of observed interactions, and there are no available explicit negatives.In all of the applications enumerated above, it is quite common to encounter solutions that are based on a softmax loss function. In language modeling, and more recently in matrix factorization, the Word2Vec algorithm (see BID15 ) models the conditional probability of observing all possible items in the vicinity of a context item as a categorical distribution using the softmax loss.However, modeling the probability of co-occurrence as a categorical distribution is a very biased assumption that is clearly refuted by the data, since for all context words there are multiple words that co-occur at the same time.In our paper we propose Partially Mutual Exclusive Softmax (PMES), a new model that relaxes the mutual exclusivity constraint over the outcomes. PMES relaxes this constraint by splitting the set of all outcomes into a set of possible outcomes that are conditionally independent given the context, and a set of impossible outcomes which become negative examples.The context-dependent negative set is hypothesized but not known, so in our method we introduce a model for negatives that is used to weight the sampled candidate negatives. The training algorithm is based on the simultaneous training of two neural networks. The first network is a generator that fits the positives and the sampled negatives. The second network is the discriminator, which is trained to separate the true positive pairs from generated pairs, and is used as the model of the probability that an example would receive a negative label.The resulting solution has many similarities with other recent negative sampling methods for approximating full softmax. However, unlike most of the previous methods, our method is not trying to faithfully approximate the full softmax formulation, but to fix some of its over-simplifying assumptions. Furthermore, we believe that the observed lift in performance of some of the negative sampling work over the full softmax can be explained through the prism of Partially Mutual Exclusive Softmax.Our hypothesis is further confirmed by experiments on language modeling and matrix factorization, where we show a big lift in performance over previous work on negative sampling and full softmax. We validate some of our intuitions on the advantages of our sampling procedure on an artificial dataset where the support sets are known, and show that our sampling scheme correctly approximates the support, which is not the case for other softmax variants.Overall, the main contributions of this paper are the following:• We propose Partially Mutual Exclusive (PME) Softmax, a modified version of the softmax loss that is a better fit for problems with positive and unlabeled data.• We derive a new negative sampling scheme based on an cooperatively-trained models of negatives which we denote as Cooperative Importance Sampling (CIS)• We show empirically the validity of our proposed approach by plugging our new loss into the Word2Vec model, and evaluating this enhanced Word2Vec model against classical sampling schemes for Word2Vec on language modeling and matrix factorization tasks across six real-world datasets.We discuss related work on Word2Vec, negative sampling schemes for softmax and GANs in Section 2 of this paper. In Section 3 we formally introduce our PME-Softmax loss and the associated CIS negative sampling scheme, and describe the training algorithm. We highlight the performance of our method in Section 4, and conclude with ideas and directions for future work in Section 5. In this paper, we have proposed Partially Mutual Exclusive Softmax, a relaxed version of the full softmax that is more suited in cases with no explicit negatives, e.g., in cases with positive and unlabeled data. In order to model the new softmax we proposed a cooperative negative sampling algorithm. Based on recent progress made on GANs in discrete data settings, our cooperative training approach can be easily applied to models that use standard sampled softmax training, where the generator and discriminator can be of the same family of models. In future work we will investigate the effectiveness of this training procedure on more complex models, and also try to make our mutually exclusive set model more contextual and dependent on both objects i and j within a pair. For example, for a given pair context/target, one might want to use the closest neighbors of the target in the embedding space as negatives. This could enable us to obtain a negative distribution that fits both the context and the target.",1281,0.529,777,1.6486486486486487,"In softmax together its fast approximations the de-facto loss function deep neural networks with multiclass predictions However softmax used many problems do fully fit the multiclass framework where the softmax assumption of mutually exclusive outcomes biased results This often applications such language modeling next event prediction matrix factorization many the potential outcomes mutually more independent conditionally on To this end for the set problems positive and unlabeled data propose a relaxation the original softmax formulation, given the observed state each the outcomes are conditionally independent but share negatives Since we operate a regime explicit negatives missing create an adversarially-trained model negatives derive a new negative sampling and which denote Cooperative Importance Sampling (CIS We show empirically the advantages our newly introduced negative sampling scheme by pluging the Word2Vec algorithm benching extensively against on both language modeling matrix factorization tasks and show large lifts Learning positive and unlabeled data known positive-unlabeled (PU BID6 ; BID14 ; The applications PU learning numerous as in negative data either too expensive define This the case language modeling one only observes examples valid sentences documents tries learn a generative process Similarly computer vision with the recent work one tries learn the underlying generative process produces meaningful images In both cases the space negatives ( nonsentences nonimages clear Similarly matrix factorization most contain pairs observed interactions there no available explicit negativesIn all the applications enumerated it quite encounter solutions based a softmax loss function In language modeling and more matrix factorization the Word2Vec algorithm ( BID15 ) models observing all possible items the vicinity a context item as using the softmax loss.However modeling co as a very biased assumption that clearly refuted since for all context words there multiple wordsIn our paper propose Partially Mutual Exclusive Softmax (PMES relaxes over the outcomes PMES relaxes this constraint splitting the set all outcomes conditionally independent given impossible outcomes which become negative examplesThe context-dependent negative set hypothesized but known in our method introduce negatives used weight the sampled candidate negatives The training algorithm the simultaneous training The first network is a generator fits the positives the sampled negatives The second network the discriminator trained separate the true positive pairs generated pairs is the probability that an example would receive a negative labelThe resulting solution has many similarities other recent negative sampling methods for approximating full softmax However unlike the previous methods our method trying faithfully approximate the full softmax formulation fix Furthermore we the observed lift performance some the negative sampling work over the full softmax can through the prism Partially Mutual Exclusive SoftmaxOur hypothesis further experiments language modeling matrix factorization a big lift previous work We validate some on the advantages our sampling procedure on an artificial dataset where the support sets known show our sampling scheme correctly, other softmax variantsOverall the main contributions propose Partially Mutual Exclusive (PME) Softmax the softmax loss that problems derive a new negative sampling scheme an cooperatively-trained models negatives which denote Cooperative Importance Sampling empirically the validity plugging our new loss the Word2Vec model evaluating this enhanced Word2Vec model classical sampling schemes on language modeling matrix factorization tasks acrossWe discuss related work negative sampling schemes GANs Section In Section we formally our PME-Softmax loss and the associated CIS negative sampling scheme describe the training algorithm We highlight the performance our method Section and conclude ideas directions In this paper have proposed Partially Mutual Exclusive Softmax, a relaxed version more suited in cases with no explicit negatives positive and unlabeled data In order model the new softmax we proposed a cooperative negative sampling algorithm Based recent progress made GANs discrete data settings our cooperative training approach easily models standard sampled softmax training, where the generator and can of the same family models In future work investigate the effectiveness this training procedure more complex models also try make our mutually exclusive set model contextual dependent both objects i within a pair For example for a given pair context/target one the closest neighbors the embedding space as negatives This could enable obtain a negative distribution that fits both the context",0.01,0.3567789367934193
"Over the past few years, various tasks involving videos such as classification, description, summarization and question answering have received a lot of attention. Current models for these tasks compute an encoding of the video by treating it as a sequence of images and going over every image in the sequence, which becomes computationally expensive for longer videos. In this paper, we focus on the task of video classification and aim to reduce the computational cost by using the idea of distillation. Specifically, we propose a Teacher-Student network wherein the teacher looks at all the frames in the video but the student looks at only a small fraction of the frames in the video. The idea is to then train the student to minimize  (i)  the difference between the final representation computed by the student and the teacher and/or (ii) the difference between the distributions predicted by the teacher and the student. This smaller student network which involves fewer computations but still learns to mimic the teacher can then be employed at inference time for video classification. We experiment with the YouTube-8M dataset and show  that the proposed student network can reduce the inference time by upto 30% with a negligent drop in the performance. Today video content has become extremely prevalent on the internet influencing all aspects of our life such as education, entertainment, communication etc. This has led to an increasing interest in automatic video processing with the aim of identifying activities BID16 BID24 , generating textual descriptions BID5 , generating summaries BID25 BID13 , answering questions BID8 and so on. On one hand, with the availability of large scale datasets BID18 BID19 BID9 BID0 BID23 for various video processing tasks, it has now become possible to train increasingly complex models which have high memory and computational needs but on the other hand there is a demand for running these models on low power devices such as mobile phones and tablets with stringent constraints on latency and computational cost. It is important to balance the two and design models which can learn from large amounts of data but still be computationally cheap at inference time.With the above motivation, we focus on the task of video classification BID0 and aim to reduce the computational cost at inference time. Current state of the art models for video classification (Yue-Hei BID24 BID10 BID17 treat the video as a sequence of images (or frames) and compute a representation of the video by using a Recurrent Neural Network (RNN). The input to the RNN at every time step is an encoding of the corresponding image (frame) at that time step as obtained from a Convolutional Neural Network. Computing such a representation for longer videos can be computationally very expensive as it requires running the RNN for many time steps. Further, for every time step the corresponding frame from the video needs to pass through a convolutional neural network to get its representation. Such computations are still feasible on a GPU but become infeasible on low end devices which have power, memory and computational constraints.Typically, one can afford more computational resources at training time but a less expensive model is desired at test time. We propose to achieve this by using the idea of distillation wherein we train a computationally expensive teacher network which computes a representation for the video by processing all frames in the video. We then train a relatively inexpensive student network whose objective is to process only a few frames of the video and produce a representation which is very similar to the representation computed by the teacher. This is achieved by minimizing (i) the squared error loss between the representations of the student network and the teacher network and/or (ii) by minimizing the difference between the output distributions (class probabilities) predicted by the two networks. We refer to this as the matching loss. FIG2 illustrates this idea where the teacher sees every frame of the video but the student sees fewer frames, i.e., every j-th frame of the video. At inference time, we then use the student network for classification thereby reducing the time required for processing the video.We experiment with two different methods of training the Teacher-Student network. In the first method (which we call Serial Training), the teacher is trained independently and then the student is trained to match the teacher with or without an appropriate regularizer to account for the classification loss. In the second method (which we call Parallel Training), the teacher and student are trained jointly using the classification loss as well as the matching loss. We experiment with the YouTube-8M dataset and show that the smaller student network reduces the inference time by upto 30% while still achieving a classification performance which is very close to that of the expensive teacher network. The results of our experiments are summarized mainly in Tables 1 (performance) and 4 (computation time). We also report some additional results in Table 2 equally spaced k frames performs better than all the other baselines. The performance gap between Uniform-k and the other baselines is even more significant when the value of k is small. The main purpose of this experiment was to decide the right way of selecting frames for the student network.Based on these results, we ensured that for all our experiments, we fed equally spaced k frames to the student. Also, these experiments suggest that Uniform-k is a strong baseline to compare against.2. Comparing Teacher-Student Network with Uniform-k Baseline: As mentioned above, the Uniform-k is a simple but effective way of reducing the number of frames to be processed. We observe that all the teacher-student models outperform this strong baseline. Further, in a separate experiment as reported in Table 3 we observe that when we reduce the number of training examples seen by the teacher and the student, then the performance of the Uniform-k baseline drops and is much lower than that of the corresponding teacher student network. This suggests that the teacher student network can be even more useful when the amount of training data is limited.3. Serial Versus Parallel Training of Teacher-Student: While the best results in Table 1 are obtained using Serial training, if we compare the corresponding rows of Serial and Parallel training we observe that there is not much difference between the two. We found this to be surprising and investigated this further. In particular, we compared the performance of the teacher after different epochs in the Parallel training setup with the performance of the a static teacher trained independently (Serial). We plotted this performance in FIG3 and observed that after 3-4 epochs of training, the Parallel teacher is able to perform at par with Serial teacher (the constant blue line). As a result, the Parallel student now learns from this trained teacher for a few more epochs and is almost able to match the performance of the Serial student. This trend is same across the different combinations of loss functions that we used. We proposed a method to reduce the computation time for video classification using the idea of distillation. Specifically, we first train a teacher network which computes a representation of the video using all the frames in the video. We then train a student network which only processes k frames of the video. We use different combinations of loss functions which ensures that (i) the final representation produced by the student is the same as that produced by the teacher and (ii) the output probability distributions produced by the student are similar to those produced by the teacher. We compare the proposed models with a strong baseline and skyline and show that the proposed model outperforms the baseline and gives a significant reduction in terms of computational time and cost when compared to the skyline. In particular, We evaluate our model on the YouTube-8M dataset and show that the computationally less expensive student network can reduce the computation time by upto 30% while giving similar performance as the teacher network.As future work, we would like to evaluate our model on other video processing tasks such as summarization, question answering and captioning. We would also like to experiment with more complex and different teacher networks other than the hierarchical RNN considered in this work. We would also like to independently train an agent which learns to select the most favorable k frames of the video as opposed to simply using equally spaced k frames.",1621,0.799,912,1.7774122807017543,"Over various tasks involving videos such classification description summarization question answering received Current models these tasks compute an encoding the video by treating images going every image becomes longer videos In this paper focus the task video classification aim reduce the idea distillation Specifically propose a Teacher-Student network wherein looks all the frames but looks The idea then train the student minimize (i the difference the final representation computed the distributions predicted This smaller student network which involves fewer computations but still learns mimic the teacher can then employed at inference time video classification We experiment YouTube-8M dataset show the proposed student network can reduce the inference time upto a negligent drop Today video content extremely prevalent influencing such education entertainment communication etc This has led automatic video processing with the aim identifying activities BID16 BID24 , generating textual descriptions BID5 generating summaries answering On with the availability large scale datasets BID18 BID19 BID9 BID0 BID23 for various video processing tasks has now train increasingly complex models which have high memory computational needs but on there running stringent constraints latency computational cost It important balance the two and design models which learn large amounts but still cheap at inference timeWith the above motivation focus the task video classification BID0 aim reduce at Current state video classification (YueHei BID24 BID10 treat the video (or frames compute a representation The input to the RNN at every time an encoding the corresponding imageframe at as obtained Computing such a representation for longer videos very as running the RNN many time steps Further for every time step the corresponding frame from the video needs pass to its representation. Such computations still feasible on a GPU but become low end devices which power, computational constraintsTypically one afford more computational resources at training time a less expensive model desired at We propose achieve the idea distillation wherein train a computationally expensive teacher network which a representation for the video by processing all frames We then train a relatively inexpensive student network whose objective process only a few frames produce a representation which very computed This achieved minimizing ( the squared error loss between the representations the student network by the output distributionsclass probabilities predicted We refer the matching loss FIG2 illustrates this idea where the teacher sees every frame but fewer frames At inference time then the student network classification thereby reducing processing the videoWe experiment training the Teacher-Student network In the first method ( call Serial Training the teacher independently match or an appropriate regularizer to account the classification loss In the second method (which Parallel Training the teacher and jointly using the classification loss as well We experiment YouTube-8M dataset show the smaller student network reduces the inference time upto 30 while still achieving a classification performance which very the expensive teacher network The results our experiments mainly (performance We also report some additional results Table 2 equally spaced k frames performs all the other baselines The performance gap Uniform-k and the other baselines significant the value k small The main purpose decide the right way selecting frames the student networkBased ensured for fed equally spaced k frames. Also these experiments suggest Uniform-k is a strong baseline to compare against.2 Comparing Teacher-Student Network with: As is reducing frames We observe all the teacher-student models outperform this strong baseline Further a separate experiment as Table we observe when reduce training examples seen the teacher then the Uniform-k baseline drops and is much the corresponding teacher student network This suggests the teacher student network can even the amount training data limited.3. Serial Versus Parallel Training of: While the best results Table Serial training if the corresponding rows observe not We found surprising investigated this further In particular compared the teacher after different epochs the Parallel training setup the a static teacher trained independently (Serial We plotted this performance FIG3 observed after the Parallel teacher is at par Serial teacherthe constant blue line As the Parallel student now learns from this trained teacher for a few more epochs is almost able match the Serial student This trend same across the different combinations loss functions that used We proposed reduce the computation time video classification the idea distillation Specifically first train a teacher network which computes a representation the video using all the frames We then train a student network which only processes k frames We use different combinations loss functions which ensures ( the final representation produced the student the output probability distributions produced We compare the proposed models a strong baseline skyline and show gives terms computational time when In particular We evaluate our model on YouTube-8M dataset show the computationally less expensive student network reduce upto while giving asAs future work, evaluate other video processing tasks summarization question captioning We would also experiment more complex and different teacher networks other the hierarchical RNN considered We would also independently train an agent which learns select the most favorable k frames as opposed using equally spaced k frames",0.01,0.6848573582157179
"Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as powerful frameworks for deep generative model learning, have largely been considered as two distinct paradigms and received extensive independent studies respectively. This paper aims to establish formal connections between GANs and VAEs through a new formulation of them. We interpret sample generation in GANs as performing posterior inference, and show that GANs and VAEs involve minimizing KL divergences of respective posterior and inference distributions with opposite directions, extending the two learning phases of classic wake-sleep algorithm, respectively. The unified view provides a powerful tool to analyze a diverse set of existing model variants, and enables to transfer techniques across research lines in a principled way. For example, we apply the importance weighting method in VAE literatures for improved GAN learning, and enhance VAEs with an adversarial mechanism that leverages generated samples. Experiments show generality and effectiveness of the transfered techniques. Deep generative models define distributions over a set of variables organized in multiple layers. Early forms of such models dated back to works on hierarchical Bayesian models BID30 and neural network models such as Helmholtz machines , originally studied in the context of unsupervised learning, latent space modeling, etc. Such models are usually trained via an EM style framework, using either a variational inference (Jordan et al., 1999) or a data augmentation BID35 algorithm. Of particular relevance to this paper is the classic wake-sleep algorithm dates by for training Helmholtz machines, as it explored an idea of minimizing a pair of KL divergences in opposite directions of the posterior and its approximation.In recent years there has been a resurgence of interests in deep generative modeling. The emerging approaches, including Variational Autoencoders (VAEs) BID18 , Generative Adversarial Networks (GANs) BID12 , Generative Moment Matching Networks (GMMNs) BID24 BID10 , auto-regressive neural networks BID21 BID37 , and so forth, have led to impressive results in a myriad of applications, such as image and text generation (Radford et al., 2015; Hu et al., 2017; BID37 , disentangled representation learning BID7 BID20 , and semi-supervised learning (Salimans et al., 2016; BID19 . The deep generative model literature has largely viewed these approaches as distinct model training paradigms. For instance, GANs aim to achieve an equilibrium between a generator and a discriminator; while VAEs are devoted to maximizing a variational lower bound of the data log-likelihood. A rich array of theoretical analyses and model extensions have been developed independently for GANs BID0 BID1 Salimans et al., 2016; BID31 and VAEs BID4 BID8 Hu et al., 2017) , respectively. A few works attempt to combine the two objectives in a single model for improved inference and sample generation BID26 BID22 BID25 BID34 . Despite the significant progress specific to each method, it remains unclear how these apparently divergent approaches connect to each other in a principled way.In this paper, we present a new formulation of GANs and VAEs that connects them under a unified view, and links them back to the classic wake-sleep algorithm. We show that GANs and VAEs involve minimizing opposite KL divergences of respective posterior and inference distributions, and extending the sleep and wake phases, respectively, for generative model learning. More specifically, we develop a reformulation of GANs that interprets generation of samples as performing posterior inference, leading to an objective that resembles variational inference as in VAEs. As a counterpart, VAEs in our interpretation contain a degenerated adversarial mechanism that blocks out generated samples and only allows real examples for model training.The proposed interpretation provides a useful tool to analyze the broad class of recent GAN-and VAEbased algorithms, enabling perhaps a more principled and unified view of the landscape of generative modeling. For instance, one can easily extend our formulation to subsume InfoGAN BID7 that additionally infers hidden representations of examples, VAE/GAN joint models BID22 BID5 ) that offer improved generation and reduced mode missing, and adversarial domain adaptation (ADA) BID11 Purushotham et al., 2017) that is traditionally framed in the discriminative setting.The close parallelisms between GANs and VAEs further ease transferring techniques that were originally developed for improving each individual class of models, to in turn benefit the other class. We provide two examples in such spirit: 1) Drawn inspiration from importance weighted VAE (IWAE) BID4 , we straightforwardly derive importance weighted GAN (IWGAN) that maximizes a tighter lower bound on the marginal likelihood compared to the vanilla GAN. 2) Motivated by the GAN adversarial game we activate the originally degenerated discriminator in VAEs, resulting in a full-fledged model that adaptively leverages both real and fake examples for learning. Empirical results show that the techniques imported from the other class are generally applicable to the base model and its variants, yielding consistently better performance. Our new interpretations of GANs and VAEs have revealed strong connections between them, and linked the emerging new approaches to the classic wake-sleep algorithm. The generality of the proposed formulation offers a unified statistical insight of the broad landscape of deep generative modeling, and encourages mutual exchange of techniques across research lines. One of the key ideas in our formulation is to interpret sample generation in GANs as performing posterior inference. This section provides a more general discussion of this point.Traditional modeling approaches usually distinguish between latent and visible variables clearly and treat them in very different ways. One of the key thoughts in our formulation is that it is not necessary to make clear boundary between the two types of variables (and between generation and inference), but instead, treating them as a symmetric pair helps with modeling and understanding. For instance, we treat the generation space x in GANs as latent, which immediately reveals the connection between GANs and adversarial domain adaptation, and provides a variational inference interpretation of the generation. A second example is the classic wake-sleep algorithm, where the wake phase reconstructs visibles conditioned on latents, while the sleep phase reconstructs latents conditioned on visibles (i.e., generated samples). Hence, visible and latent variables are treated in a completely symmetric manner.• Empirical data distributions are usually implicit, i.e., easy to sample from but intractable for evaluating likelihood. In contrast, priors are usually defined as explicit distributions, amiable for likelihood evaluation.• The complexity of the two distributions are different. Visible space is usually complex while latent space tends (or is designed) to be simpler.However, the adversarial approach in GANs and other techniques such as density ratio estimation (Mohamed & Lakshminarayanan, 2016) and approximate Bayesian computation BID2 have provided useful tools to bridge the gap in the first point. For instance , implicit generative models such as GANs require only simulation of the generative process without explicit likelihood evaluation, hence the prior distributions over latent variables are used in the same way as the empirical data distributions, namely, generating samples from the distributions. For explicit likelihood-based models, adversarial autoencoder (AAE) leverages the adversarial approach to allow implicit prior distributions over latent space. Besides, a few most recent work BID26 BID36 BID34 Rosca et al., 2017) extends VAEs by using implicit variational distributions as the inference model. Indeed, the reparameterization trick in VAEs already resembles construction of implicit variational distributions (as also seen in the derivations of IWGANs in Eq.37). In these algorithms, adversarial approach is used to replace intractable minimization of the KL divergence between implicit variational distributions and priors.The second difference in terms of space complexity guides us to choose appropriate tools (e.g., adversarial approach v.s. reconstruction optimization, etc) to minimize the distance between distributions to learn and their targets. However, the tools chosen do not affect the underlying modeling mechanism.For instance, VAEs and adversarial autoencoder both regularize the model by minimizing the distance between the variational posterior and certain prior, though VAEs choose KL divergence loss while AAE selects adversarial loss.We can further extend the symmetric treatment of visible/latent x/z pair to data/label x/t pair, leading to a unified view of the generative and discriminative paradigms for unsupervised and semi-supervised learning. Specifically, conditional generative models create (data, label) pairs by generating data x given label t. These pairs can be used for classifier training (Hu et al., 2017; BID32 . In parallel, discriminative approaches such as knowledge distillation BID14 BID17 create (data, label) pairs by generating label t conditioned on data x. With the symmetric view of x and t spaces , and neural network based black-box mappings across spaces, we can see the two approaches are essentially the same. A ADVERSARIAL DOMAIN ADAPTATION (ADA)ADA aims to transfer prediction knowledge learned from a source domain with labeled data to a target domain without labels, by learning domain-invariant features. Let D φ (x) = q φ (y|x) be the domain discriminator . The conventional formulation of ADA is as following : DISPLAYFORM0 Further add the supervision objective of predicting label t(z) of data z in the source domain, with a classifier f ω (t|x) parameterized with π: DISPLAYFORM1 We then obtain the conventional formulation of adversarial domain adaptation used or similar in BID11 Purushotham et al., 2017) .B PROOF OF LEMMA 1Proof. DISPLAYFORM2 where DISPLAYFORM3 Note that p θ (x|y = 0) = p g θ (x), and p θ (x|y = 1) = p data (x). DISPLAYFORM4 . Eq.(21) can be simplified as: DISPLAYFORM5 On the other hand , DISPLAYFORM6 Note that DISPLAYFORM7 Taking derivatives of Eq. FORMULA1 w.r.t θ at θ 0 we get DISPLAYFORM8 Taking derivatives of the both sides of Eq. FORMULA1 at w.r.t θ at θ 0 and plugging the last equation of Eq. FORMULA1 , we obtain the desired results. We show that, in Lemma.1 (Eq.6), the JSD term is upper bounded by the KL term, i.e., DISPLAYFORM9 DISPLAYFORM10 Proof. From Eq. FORMULA1 , we have DISPLAYFORM11 From Eq. FORMULA1 and Eq. FORMULA1 , we have DISPLAYFORM12 Eq. FORMULA1 and Eq. FORMULA1",2201,0.948,1310,1.6801526717557251,"Deep generative models achieved Generative Adversarial Networks powerful frameworks deep generative model learning largely considered and received extensive independent studies respectively This paper aims establish formal connections GANs VAEs through a new formulation them We interpret sample generation GANs performing posterior inference show and VAEs involve minimizing KL divergences of respective posterior and inference distributions with opposite directions extending the two learning phases classic wake-sleep algorithm respectively The unified view provides analyze existing model variants enables to transfer techniques research lines For example we apply the importance weighting method VAE literatures improved GAN learning enhance VAEs an adversarial mechanism generated samples Experiments generality effectiveness the transfered techniques Deep generative models define distributions over variables organized multiple layers Early forms such models dated works on hierarchical Bayesian models BID30 neural such Helmholtz machines , originally studied latent space modeling etc Such models usually trained via an EM style framework using either a variational inferenceJordan BID35 algorithm Of particular relevance the classic wake-sleep algorithm dates by for training Helmholtz machines explored an idea minimizing a pair KL divergences opposite directions of the posterior and its approximationIn interests deep generative modeling The emerging approaches, Variational AutoencodersVAEs) BID18 , Generative Moment Matching Networks auto-regressive neural networks so led impressive results a myriad image andRadford Hu BID37 , disentangled representation learningSalimans . The deep generative model literature largely viewed these approaches distinct model training paradigms For instance GANs aim achieve an equilibrium a generator; while VAEs devoted maximizing lower A rich array theoretical analyses model extensions independently GANs BID0 BID1 Salimans et BID31 and VAEs Hu) , A works attempt combine for improved inference sample generation BID26 BID22 BID25 BID34 . Despite the significant progress specific each method these apparently divergent approaches connectIn GANs VAEs connects under links back the classic wake-sleep algorithm We show GANs VAEs involve minimizing opposite KL divergences of respective posterior and inference distributions extending the sleep and phases, generative model learning More specifically develop a reformulation GANs interprets generation samples performing posterior inference leading an objective that resembles as in VAEs As a counterpart in our interpretation contain a degenerated adversarial mechanism blocks out generated samples only real examples for model trainingThe proposed interpretation provides analyze the broad class recent GAN-and VAEbased algorithms enabling perhaps a more principled and unified view the landscape For instance one extend our formulation subsume InfoGAN BID7 that additionally infers hidden representations examples VAE/GAN joint models BID22 BID5 ) offer improved generation reduced mode missing adversarial domain adaptationADA BID11 Purushotham) traditionally framed the discriminative settingThe close parallelisms GANs VAEs further ease transferring techniques were improving each individual class models to in benefit We provide two examples in such spirit Drawn inspiration importance weighted VAEIWAE) BID4 , we straightforwardly derive importance GANIWGAN that a tighter lower the marginal likelihood compared the vanilla 2 Motivated the GAN adversarial game we activate the originally degenerated discriminator VAEs resulting adaptively both real and fake examples for learning the techniques imported the other class generally applicable the base model its variants yielding Our new interpretations GANs VAEs revealed strong connections linked the emerging new approaches the classic wake-sleep algorithm The generality the proposed formulation offers a unified statistical insight of the broad landscape deep generative modeling encourages mutual exchange techniques research lines One our formulation interpret sample generation GANs performing posterior inference This section this pointTraditional modeling approaches usually distinguish latent and visible variables clearly treat One the key thoughts our formulation make clear boundary variables between generation inference treating helps with modeling For instance we treat the generation space x in GANs latent immediately reveals the connection adversarial domain adaptation provides a variational inference interpretation. A second example the classic wake-sleep algorithm the wake phase reconstructs visibles conditioned latents visiblesi.e., generated samples Hence visible and latent variables treated a completely symmetric manner.• Empirical data distributions usually implicit easy sample but evaluating likelihood In contrast priors usually defined explicit distributions amiable for likelihood evaluation.• The complexity different Visible space usually complex while latent space tends ( designed simplerHowever the adversarial approach in GANs other techniques such density ratio estimationMohamed & Lakshminarayanan approximate Bayesian computation BID2 provided bridge the first point For instance , implicit generative models such GANs require only simulation without explicit likelihood evaluation hence the prior distributions over used the empirical data distributions generating samples For explicit likelihood-based modelsAAE leverages allow implicit prior distributions latent space Besides a few most recent work BID26 BID36 BID34 Rosca 2017) extends VAEs implicit variational distributions the inference model Indeed the reparameterization trick in VAEs already resembles construction implicit variational distributionsas also IWGANs Eq.37 In these algorithms adversarial approach replace intractable minimization the KL divergence implicit variational distributions priorsThe second difference terms space complexity guides us choose appropriate tools ( v.s. reconstruction optimization etc distributions to learn their targets However the tools chosen do affect the underlying modeling mechanismFor VAEs both regularize minimizing the variational posterior certain prior, though choose KL divergence loss while AAE selectsWe extend the symmetric treatment visible/latent x/z pair data/label x/t pair leading a unified view Specifically conditional generative models create (data, label pairs by generating x given These pairs can classifier trainingHu 2017 BID32 . In parallel, discriminative approaches such knowledge distillation BID14 BID17 create (data, label pairs by generating label t conditioned x. With the symmetric view x and t spaces , neural network based black-box mappings across spaces the two approaches essentially A ADVERSARIAL DOMAIN ADAPTATIONADA)ADA aims transfer prediction knowledge learned a source domain with labeled data without labels by learning Let D � ( q be the domain discriminator . The conventional formulation ADA as following : DISPLAYFORM0 Further add the supervision objective predicting label t(z data z the source domain with a classifier f ��t|x parameterized: We obtain adversarial domain adaptation used or similar BID11 Purushotham 2017) .B PROOF LEMMA 1Proof. DISPLAYFORM2 where Note p � ( = g p data DISPLAYFORM4 . Eq.(21 can simplified DISPLAYFORM5 On , Note that DISPLAYFORM7 Taking derivatives FORMULA1 w.r.t � at 0 we Taking the both sides at plugging the last equation of , We show, Lemma.1Eq.6 the JSD term upper bounded the KL term DISPLAYFORM9 Proof From Eq FORMULA1 , we DISPLAYFORM11 From",0.01,0.4370484197570445
"Deep neural networks have demonstrated promising prediction and classification performance on many healthcare applications. However, the interpretability of those models are often lacking. On the other hand, classical interpretable models such as rule lists or decision trees do not lead to the same level of accuracy as deep neural networks and can often be too complex to interpret (due to the potentially large depth of rule lists). In this work, we present PEARL,  Prototype lEArning via Rule Lists, which iteratively uses rule lists to guide a neural network to learn representative data prototypes. The resulting prototype neural network provides  accurate prediction, and the prediction can be easily explained by  prototype and its guiding rule lists. Thanks to the prediction power of neural networks, the rule lists from				 prototypes are more concise and hence provide better interpretability. On two real-world electronic healthcare records (EHR) datasets, PEARL consistently outperforms all baselines across both datasets, especially achieving performance improvement over conventional rule learning by up to 28% and over prototype learning by up to 3%. Experimental results also show the resulting interpretation of PEARL is  simpler than the standard rule learning. The rapid growth of sizes and complexities of electronic health records (EHR) data has motivated the use of deep learning models, which demonstrated state-of-the-art performance in many tasks, including diagnostics and disease detection BID7 BID38 , medication prediction BID16 , risk prediction BID9 Xiao et al., 2018b) , and patient subtyping BID1 BID4 . Although deep learning models can produce accurate predictions and classifications, they are often treated as black-box models that lack interpretability and transparency of their inner working BID20 . This is a critical problem as it can limit the adoption of deep learning in medical decision making.Recently, there have been great efforts of trying to explain black-box deep models, including via attention mechanism BID7 BID40 , visualization BID31 , and explanation by examples or prototypes BID17 . To bring deep models into real clinical practice, clinicians often need to understand why a certain output is produced and how the model generates this output for a given input BID24 . Rule learning and prototype learning are two promising directions to achieve clinical model interpretability.Rule learning generates a set of rules from training data, in which its prediction is done at leaf levels via simple models such as majority vote or regression. For example, the results of rule learning are rule lists composed of multiple if-then statements BID0 . Those rules can be interpretable to domain experts as they are expressed in simple logical forms BID30 BID3 . However, because of such a simple prediction model, the accuracy of rule-based models is often lower than deep neural networks. Moreover, the interpretability can be undermined as the depth of rules becomes very large and thus incomprehensible for human with tens or hundreds of levels of the rules.Prototype learning is another interpretable model inspired by case-based reasoning BID14 , where observations are classified based on their proximity to a prototype point in the dataset. Many machine learning models have incorporated prototype concepts BID28 BID2 BID12 , and learn to compute prototypes (as actual data points or synthetic points) that can represent a set of similar points. However prototypes alone may not lead to interpretable models as we still need an intuitive way to represent and explain what a prototype is, especially given recent deep prototype works BID17 .Both approaches were explored in healthcare applications. For example, rule learning was employed to identify how likely patients were to be readmitted to a hospital after they had been released, each probability associated with a set of rules as criteria BID35 . While prototype could be selected from actual patients and genes for clinicians to make sense of large patient cohort or gene data BID2 . However , there are still open challenges: How to construct simple rules with more accurate prediction and classification performance? How to produce accurate and intuitive definitions of prototypes?In this work, we propose Prototype lEArning via Rule List (PEARL), which combines rule learning and prototype learning on deep neural networks to harness the benefits of both approaches and alleviate their shortcomings for an accurate and interpretable prediction model. In particular , we iteratively learn rule lists, via a data reweighing procedure using prototypes, and then update prototypes via neural networks with learned rules. PEARL not only generates simple and interpretable rule lists and prototypes, but also provides neural network models which can infer the similarity of a query datum to all the prototypes. To summarize, we make the following contributions in this paper.1. We propose an integrative method to combine rule list and prototype learning, enabling PEARL to harness the power of these methods.2. PEARL automatically learns prototypes corresponding to rules in a rule list, which are more concise than conventional rule list learning methods and more explainable than prototype learning methods by providing logic reasoning.3. On real-world electronic health record datasets, PEARL demonstrates both accurate prediction performance and simple interpretation. In this paper, we proposed PEARL, an integrative prototype learning neural network that combines rule learning and prototype learning on deep neural networks to harness the benefits of these methods. We empirically demonstrated that PEARL is more accurate , thanks to an iterative data reweighing algorithm, and more interpretable than rule learning, since it explains diagnostic decisions using much fewer clinical variables. PEARL is an initial attempt to combine traditional rule learning with deep neural networks. In future research, we will try to extend PEARL to other interpretable models.",1116,0.532,647,1.7248840803709429,"Deep neural networks demonstrated promising prediction classification performance many healthcare applications However the interpretability those models are often lacking On classical interpretable models such rule lists lead can too interpret (due the potentially large depth rule lists In this work PEARL Prototype lEArning via Rule Lists iteratively uses guide representative data prototypes The resulting prototype neural network provides accurate prediction, easily explained prototype and its guiding rule lists Thanks the prediction power neural networks the rule lists from prototypes more concise hence provide On two real-world electronic healthcare records PEARL consistently all baselines especially achieving performance improvement conventional rule learning by up 28 prototype learning Experimental results also the resulting interpretation PEARL is simpler the standard rule learning The rapid growth sizes complexities motivated deep learning models demonstrated state performance BID7 BID38 , medication prediction BID16 Xiao) and patient subtyping Although deep learning models produce classifications treated lack interpretability transparency of their inner working BID20 . This a critical problem as can limit deep learning medical decision makingRecently great efforts of trying explain black-box deep models including via attention mechanism BID7 BID40 visualization explanation by examples or prototypes To bring deep models real clinical practice often why a certain output generates for BID24 Rule learning prototype learning two promising directions achieve clinical model interpretabilityRule learning generates from in its prediction done leaf levels via simple models majority vote regression For example the results rule learning rule lists composed multiple if BID0 . Those rules can interpretable domain experts they expressed simple logical forms BID30 BID3 However because such a simple prediction model lower deep neural networks Moreover the interpretability can undermined as the depth rules becomes very thus incomprehensible human with tens levels the rulesPrototype learning another interpretable model inspired case-based reasoning BID14 , observations classified a prototype point Many machine learning models incorporated prototype concepts BID28 BID2 BID12 , learn compute prototypes (as actual data points or synthetic points represent similar points However prototypes alone lead interpretable models as we still an intuitive way explain especially recent deep prototype works BID17 .Both approaches were explored healthcare applications For example rule learning was employed how likely patients readmitted released each probability associated a set rules as criteria BID35 . While prototype could selected actual patients genes clinicians make sense large patient cohort or gene data BID2 . However , open challenges: How construct simple rules more accurate prediction and classification performance How produce accurate and intuitive definitions prototypes?In propose Prototype lEArning via Rule List combines rule learning prototype learning on deep neural networks harness alleviate for an accurate and interpretable prediction model In particular , iteratively learn rule lists via a data reweighing procedure using prototypes update prototypes via neural networks with PEARL not generates simple and interpretable rule lists prototypes neural network models infer the similarity a query datum all the prototypes To summarize make combine rule list prototype learning enabling PEARL harness automatically prototypes corresponding rules more concise explainable by logic reasoning.3 On real-world electronic health record datasets demonstrates both accurate prediction performance simple interpretation In proposed PEARL an integrative prototype learning neural network combines rule learning prototype learning on harness We empirically PEARL accurate , thanks reweighing more interpretable rule learning explains diagnostic decisions using much fewer clinical variables PEARL is an initial attempt combine traditional rule learning In future research extend PEARL other interpretable models",0.01,0.5510201188500299
"Generative Adversarial Networks (GANs) are powerful tools for realistic image generation. However, a major drawback of GANs is that they are especially hard to train, often requiring large amounts of data and long training time. In this paper we propose the Deli-Fisher GAN, a GAN that generates photo-realistic images by enforcing structure on the latent generative space using similar approaches in \cite{deligan}. The structure of the latent space we consider in this paper is modeled as a mixture of Gaussians, whose parameters are learned in the training process. Furthermore, to improve stability and efficiency, we use the Fisher Integral Probability Metric as the divergence measure in our GAN model, instead of the Jensen-Shannon divergence. We show by experiments that the Deli-Fisher GAN performs better than DCGAN, WGAN, and the Fisher GAN as measured by inception score. Generative Adversarial Networks (GAN) are powerful unsupervised learning models that have recently achieved great success in learning high-dimensional distributions BID1 ). In the field of image and vision sciences in particular, GAN models are capable of generating ""fake"" images that look authentic to human observers.The basic framework of a GAN model consists of two parts: a generator G = G θ (z) that generates images by translating random input noise z into a particular distribution of interest, and a discriminator D = D p (x) which calculates the probability that an image x is an authentic image as opposed to a generated ""fake"" image from the generator. While the generator G and discriminator D can be modeled as any smooth functions, these two components are usually modeled as two neural networks in practical applications. During the training process, we optimize the generator and the discriminator alternately against each other. Within each step, we first keep D fixed and optimize G so as to improve its capability of generating images that look real to D. Then, we keep G fixed and train D to improve the discriminator's ability to distinguish real and G-generated images. The two parts G and D play a two-player game against each other. At the end of the training, we would be able to have a generator that is capable of generating photo-realistic images.In mathematical form, a GAN model can be described as an optimization problem, as follows: DISPLAYFORM0 where V (D, G) is the objective function measuring the divergence between the two distributions: the distribution of the real existing data D(x), and the that of the generated data D(G(z)), where x follows the distribution of real images and z follows the distribution of input noise. Depending on the choice of function V (D, G), different GAN models have been proposed over time (see BID1 , , BID4 ) to increase stability and achieve faster convergence rates.",558,0.261,324,1.7222222222222223,"Generative Adversarial Networks realistic image generation However a major drawback GANs especially train often data long training time In this paper the Deli-Fisher GAN generates photo-realistic images by enforcing structure the latent generative space using similar approaches in \cite{deligan The structure the latent space we consider modeled a mixture Gaussians whose parameters learned Furthermore to improve stability efficiency use the Fisher Integral Probability Metric as the divergence measure in our GAN model instead the Jensen-Shannon divergence We show by experiments the Deli-Fisher GAN performs DCGAN WGAN Fisher as inception score Generative Adversarial Networks recently achieved learning high-dimensional distributions BID1 ). In the field image and vision sciences in GAN models capable look authentic human observersThe basic framework a generator G = G ��z by translating random input noise z a particular distribution interest which calculates x as opposed from While the generator G and discriminator D can modeled any smooth functions these two components usually modeled two neural networks in practical applications During the training process optimize the generator the discriminator alternately against Within each step first keep D fixed optimize G so as improve its capability generating images look real Then we keep G fixed train D improve the discriminator's ability distinguish real and G-generated images The two parts G and play against At the training, we would have a generator isIn mathematical form a GAN model described an optimization problem as follows DISPLAYFORM0 where V (D, G the objective function measuring the divergence: the distribution the real existing data D(x the that x follows real images and input noise Depending the choice function V (D different GAN models over BID1 , , ) increase stability achieve faster convergence rates",0.0,0.5442379381553898
"Recent work on encoder-decoder models for sequence-to-sequence mapping has shown that integrating both temporal and spatial attentional mechanisms into neural networks increases the performance of the system substantially. We report on a new modular network architecture that applies an attentional mechanism not on temporal and spatial regions of the input, but on sensor selection for multi-sensor setups. This network called the sensor transformation attention network (STAN) is evaluated in scenarios which include the presence of natural noise or synthetic dynamic noise. We demonstrate how the attentional signal responds dynamically to changing noise levels and sensor-specific noise, leading to reduced word error rates (WERs) on both audio and visual tasks using TIDIGITS and GRID; and also on CHiME-3, a multi-microphone real-world noisy dataset. The improvement grows as more channels are corrupted as demonstrated on the CHiME-3 dataset. Moreover, the proposed STAN architecture naturally introduces a number of advantages including ease of removing sensors from existing architectures, attentional interpretability, and increased robustness to a variety of noise environments. Attentional mechanisms have shown improved performance as part of the encoder-decoder based sequence-to-sequence framework for applications such as image captioning BID22 , speech recognition BID1 BID3 , and machine translation BID0 BID21 . Dynamic and shifting attention, for example, on salient attributes within an image helps in image captioning as demonstrated by the state-of-art results on multiple benchmark datasets BID22 . Similarly, an attention-based recurrent sequence generator network can replace the Hidden Markov Model (HMM) typically used in a large vocabulary continuous speech recognition system, allowing an HMM-free RNN-based network to be trained for end-to-end speech recognition BID1 .While attentional mechanisms have mostly been applied to both spatial and temporal features, this work focuses on attention used in sensor selection. We introduce the STAN architecture that embeds an attentional mechanism for sensor selection and supports multi-sensor as well as multi-modal inputs. This attentional mechanism allows STANs to dynamically focus on sensors with higher signal-to-noise ratio (SNR) and its output is highly interpretable. Because of their inherently modular architecture, STANs remain operational even when sensors are removed after training. The same modularity makes STANs attractive for tasks that make use of multi-sensor integration. The STAN architecture can be seen as a generalization of existing less-modular network types that include attention in multi-sensor setups BID11 BID10 .This work consists of three main sections. First, we formally introduce the STAN architecture in section 2. In the first evaluation phase in section 3, we demonstrate the proper function of the attentional mechanism in synthetic noise environments with multiple audio sensors (TIDIGITS dataset) and multiple video sensors (GRID). The second evaluation phase in section 4 covers the multi-microphone real world dataset CHiME-3, where we show the proper functioning of the STAN attentional mechanism on natural noise and the robustness of STANs with respect to altered sensor configurations. The sensor transformation attention network (STAN) architecture has a number of interesting features for sensor selection which we explored in this work. By equipping each sensor with an attentional mechanism for distinguishing meaningful features, networks can learn how to select, transform, and interpret the output of their sensors. Firstly, and by design, we show that STANs exhibit remarkable robustness to both real-world and synthetic dynamic noise sources. By challenging these networks during training with dynamic and persistent noise sources, the networks learn to rapidly isolate sensors corrupted by noise sources. Secondly, we show that this form of training results in even better accuracy performance from STANs than simply concatenating the sensor inputs. This is best demonstrated on the heavily noise corrupted STR environment of the CHiME-3 real-data evaluation set, where STANs achieve 23% lower WER than concatenation models for the 50 most corrupted samples. Thirdly, we find that the output of the attention modules is highly informative, clearly indicating a sub-optimal sensor placement for a sensor pointing away from the speaker on the CHiME-3 dataset. Remarkably, this outcome is even obtained when sharing the weights of the attention modules across sensors, implying that these attention modules learned to successfully differentiate between sensors with higher and lower SNR data in presence of natural noise.Due to their modular architecture, STANs are also remarkably flexible with respect to the sensor configuration, even performing well with the removal of sensors after training. One can train STANs to solve a task with a multi-sensor setup and after training, remove the less informative sensors, with possibly savings of energy consumption and computational load on multi-sensor hardware systems with restricted computational power such as mobile robots. In the case of a defect, a sensor could be removed and STANs would remain operational with the remaining sensors.",988,0.471,594,1.6632996632996633,"Recent work encoder-decoder models sequenceto mapping integrating increases the system substantially We report a new modular network architecture applies an attentional mechanism not on temporal and spatial regions sensor selection for This network called the sensor transformation attention network evaluated scenarios which the presence natural noise synthetic dynamic noise We demonstrate the attentional signal responds dynamically changing noise levels sensor-specific noise leading reduced word error ratesWERs on using TIDIGITS GRID; on CHiME-3 multi realworld noisy dataset The improvement grows more channels corrupted as demonstrated on the CHiME-3 dataset Moreover the proposed STAN architecture naturally introduces advantages including ease removing sensors existing architectures attentional interpretability increased noise environments Attentional mechanisms have shown improved performance as part encoder based sequenceto framework applications image BID22 , speech Dynamic and shifting attention for on salient attributes within helps in image captioning as demonstrated state results on multiple benchmark datasets BID22 . Similarly an attention-based recurrent sequence generator network replace the Hidden Markov Model typically a large vocabulary continuous speech recognition system allowing end BID1 .While attentional mechanisms mostly applied used sensor selection We introduce the STAN architecture that embeds an attentional mechanism sensor selection supports multi as inputs This attentional mechanism allows STANs dynamically focus sensors signal its output highly interpretable Because their inherently modular architecture STANs remain operational sensors after training The same modularity makes STANs attractive tasks make multi-sensor integration The STAN architecture can existing less-modular network types include attention in multi-sensor setups BID11 BID10 .This work consists First formally the STAN architecture section In the first evaluation phase in section demonstrate the proper function the attentional mechanism synthetic noise environments multiple audio sensorsTIDIGITS datasetGRID The second evaluation phase section covers the multi-microphone real world dataset CHiME-3 where show the proper functioning the STAN attentional mechanism on natural noise altered sensor configurations The sensor transformation attention network (STAN) architecture sensor selection which explored By equipping each sensor an attentional mechanism distinguishing meaningful features networks select transform the output Firstly and by design show STANs exhibit remarkable robustness By challenging these networks during training with dynamic and persistent noise sources the networks learn rapidly isolate sensors corrupted Secondly show training results even better accuracy performance from STANs simply the sensor inputs This best demonstrated on the heavily noise corrupted STR environment the CHiME-3 real-data evaluation set STANs achieve 23% lower WER than concatenation models for the 50 most corrupted samples Thirdly find the output the attention modules highly informative clearly pointing away on the CHiME-3 dataset this outcome even obtained sharing the weights the attention modules across sensors implying learned successfully differentiate sensors higher and lower SNR data in presence natural noiseDue their modular architecture STANs remarkably even performing the removal sensors after training One can train STANs solve after remove the less informative sensors with possibly savings energy consumption computational load with restricted computational power such mobile robots In a defect a sensor could STANs remain operational with",0.01,0.39410843490013187
"Massive data exist among user local platforms that usually cannot support deep neural network (DNN) training due to computation and storage resource constraints. Cloud-based training schemes provide beneficial services but suffer from potential privacy risks due to excessive user data collection. To enable cloud-based DNN training while protecting the data privacy simultaneously, we propose to leverage the intermediate representations of the data, which is achieved by splitting the DNNs and deploying them separately onto local platforms and the cloud. The local neural network (NN) is used to generate the feature representations. To avoid local training and protect data privacy, the local NN is derived from pre-trained NNs. The cloud NN is then trained based on the extracted intermediate representations for the target learning task. We validate the idea of DNN splitting by characterizing the dependency of privacy loss and classification accuracy on the local NN topology for a convolutional NN (CNN) based image classification task. Based on the characterization, we further propose PrivyNet to determine the local NN topology, which optimizes the accuracy of the target learning task under the constraints on privacy loss, local computation, and storage. The efficiency and effectiveness of PrivyNet are demonstrated with CIFAR-10 dataset. With the pervasiveness of sensors, cameras, and mobile devices, massive data are generated and stored on local platforms. While useful information can be extracted from the data, the training process can be too computationally intensive that local platforms are not able to support. Cloud-based services provide a viable alternative to enable deep model training but rely on excessive user data collection, which suffers from potential privacy risks and policy violations.To enable the cloud-based training scheme while simultaneously protecting user data privacy, different data pre-processing schemes are proposed. Instead of releasing the original data, transformed representations are usually generated locally and then, uploaded for the target learning tasks. For the intermediate representations to be effective, there are two requirements, i.e. utility and privacy. The utility requirement urges that the target learning task can be accomplished accurately based on the released representations, while the privacy requirement forces the leakage of private information to be constrained within a satisfiable range. Furthermore, the transformation scheme should also be flexible enough for platforms with different computation and storage capabilities and for different types of data, which can be either high dimensional and continuous, like videos or images, or discrete.Related Works Privacy and utility trade-off has been one of the main questions in the privacy research. Different measures of privacy and utility are proposed based on the rate-distortion theory BID18 BID16 du Pin Calmon & Fawaz, 2012) , statistical estimation BID21 , and learnability BID10 . To actively explore the trade-off between privacy and utility, in recent years, many different transformations have been proposed. Syntactic anonymization methods, including k-anonymity BID22 , l-diversity BID14 and t-closeness BID13 , are proposed to anonymize quasiidentifiers and protect sensitive attributes in a static database. However, syntactic anonymization is hard to apply to high-dimensional continuous data because quasi-identifiers and sensitive attributes become hard to define.Differential privacy is proposed to provide a more formal privacy guarantee and can be easily achieved by adding noise BID3 BID4 . However, because differential privacy only prevents an adversary from gaining additional knowledge by inclusion/exclusion of an individual data BID5 , the total information leakage from the released representations is not limited BID8 . Meanwhile, to achieve differential privacy, existing works BID19 BID0 usually require local platforms to get involved in the backward propagation process, which makes it hard to deploy them on lightweight platforms.Non-invertible linear and non-linear transformations are also proposed for data anonymization. Existing linear transformations rely on the covariance between data and labels BID6 or the linear discriminant analysis (LDA) BID24 to filter the training data. However, linear transformations usually suffer from limited privacy protection since the original data can be reconstructed given the released representations. Recently proposed nonlinear transformations based on minimax filter BID8 or Siamese networks BID15 can provide better privacy protection. However, they can only be applied to protect privacy in the inference stage since iteractive training scheme is required between the cloud and local platforms, for which privacy loss becomes very hard to control. Figure 1: The proposed PrivyNet framework: the local NN is derived from pre-trained NNs for feature extraction and the cloud NN is trained for the target learning task. Privacy and utility trade-off is controlled by the topology of the local NN.Contribution To this end, we propose PrivyNet, a flexible DNN training framework to achieve a fine-grained control of the trade-off between privacy and utility. PrivyNet divides a DNN model into two parts and deploys them onto the local platforms and the cloud separately. As shown in Figure 1 , the local NN is used to generate intermediate representations while the cloud NN is trained for the learning task based on the released intermediate representations. The privacy protection is achieved through the transformation realized by the local NN, which is non-linear and consists of different lossy operations, including convolution, pooling, and so on. To avoid local training, we derive the local NN from pre-trained NNs. Our key insight here is that the initial layers of a DNN are usually used to extract general features that are not application specific and can enable different learning tasks. Therefore, by deriving the local NN from pre-trained NNs, a good utility can be achieved since useful features are embedded in the released representations, while privacy can be protected by selecting the topology of the local NN to control the specific features to release. Our main contributions are summarized as follows:• We propose PrivyNet, a novel framework to split DNN model to enable cloud-based training with a fine-grained control of privacy loss.• We characterize the privacy loss and utility of using CNN as the local NN in detail, based on which three key factors that determine the privacy and utility trade-off are identified and compared.• A hierarchical strategy is proposed to determine the topology of the local NN to optimize the utility considering constraints on local computation, storage, and privacy loss.• We verify PrivyNet by using the CNN-based image classification as an example and demonstrate its efficiency and effectiveness. In this section, we provide detailed discussions on the adversarial model adopted in the paper.According to the adversarial model we have defined in Section 3, the transformation induced by the FEN is assumed to be unknown to the attackers. This helps prevent more powerful attacks and enable a better privacy protection. However, because the FEN is derived from the pre-trained NNs, the structure and weights of which are also available to the attackers, we need to provide strategies to protect the anonymity of the FEN. In our framework, we consider the following two methods for the protection of the FEN:• Build a pool of pre-trained NNs to enable FEN derivation from NNs. In our characterization framework, we use VGG16 as an example. The same procedure can be applied to VGG19 BID20 , ResNet BID9 , Inception BID23 . By enlarging the pool, it becomes harder for the attacker to guess how the FEN is derived.• Apply the channel selection procedure to both output channels and intermediate channels.After the channel selection, the number of channels and the subset of selected channels in each layer become unknown to the attackers. Therefore , even if the attackers know the pre-trained NN, from which the FEN is derived, it becomes much harder to guess the channels that form the FEN.One important requirement for the intermediate channel selection is that the utility is not sacrificed and the privacy loss is not increased. We verify the change of privacy and utility empirically. We take the first 6 layers of VGG16, including 4 convolution layers and 2 max-pooling layers, and set the depth of output channel to 8. We use CIFAR-10 dataset and the same ICN and IRN as in Section 2. We first gradually reduce the channel depth of the first convolution layer from 64 to 16. As shown in FIG12 , the privacy and utility are rarely impacted by the change of the channel depth of first convolution layer. Meanwhile, we can observe the dramatic reduction on the runtime. We then gradually reduce the channel depth for each convolution layer. As shown in FIG4 , after we reduce the channel depth for each layer to half of its original depth, we still get similar privacy and utility with a dramatic reduction of the runtime. , 64, 128, 8}, { 32, 32, 128, 8}, {32, 32, 64, 8}, respectively By channel selection for intermediate layers, even if the attackers can know the pre-trained NN that our FEN is derived from, it is still very hard to determine the number of layers for the FEN and the number of channels for each layer. In this way, the anonymity of the FEN can be well protected.",1818,0.874,1068,1.702247191011236,"Massive data exist among user local platforms usually support due computation and storage resource constraints Cloud-based training schemes provide beneficial services but suffer potential privacy risks To enable cloud-based DNN training while protecting simultaneously propose leverage the intermediate representations achieved splitting and deploying separately onto local platforms The local neural network the feature representations To avoid local training protect data privacy the local NN is derived then trained based the extracted intermediate representations for the target learning task We validate the idea DNN splitting characterizing the dependency privacy loss classification accuracy the local NN topology for (CNN based image classification task Based the characterization further propose PrivyNet determine the local NN topology optimizes the target learning task under on privacy loss local computation storage The efficiency PrivyNet demonstrated CIFAR-10 dataset With the pervasiveness sensors massive data are generated local platforms While useful information extracted the training process too computationally that local platforms support Cloud-based services provide enable deep model training but rely excessive user data collection suffers policy violationsTo while simultaneously protecting different data pre-processing schemes Instead releasing the original data transformed representations usually generated locally, uploaded for the target learning tasks For the intermediate representations effective privacy The utility requirement urges that the target learning task can accomplished accurately based the released representations while the privacy requirement forces the leakage constrained within a satisfiable range Furthermore the transformation scheme should flexible platforms different computation and storage capabilities either high dimensional and continuous like videos discreteRelated Works Privacy and utility trade-off has one the privacy research Different measures privacy utility proposed based the rate-distortion theory BID18 BID16 du Pin Calmon & Fawaz 2012) , statistical estimation , learnability To actively explore privacy utility in many different transformations Syntactic anonymization methods k-anonymity BID22 , proposed quasiidentifiers protect sensitive attributes a static database However syntactic anonymization hard apply high-dimensional continuous data quasi sensitive attributes become hardDifferential privacy proposed can easily adding noise BID3 BID4 However because differential privacy only prevents an adversary additional knowledge by inclusion/exclusion an individual data BID5 , the total information leakage the released representations limited BID8 Meanwhile to achieve differential privacy existing works BID19 BID0 usually local platforms get involved the backward propagation process makes deploy lightweight platformsNon-invertible linear and non-linear transformations proposed data anonymization Existing linear transformations rely data labels BID6 or the linear discriminant analysis filter However linear transformations usually suffer limited privacy protection since reconstructed given the released representations Recently proposed nonlinear transformations based minimax filter BID8 or Siamese networks BID15 can provide better privacy protection However they can applied protect privacy the inference stage since iteractive training scheme required between the cloud and local platforms for privacy loss becomes hard control Figure 1: The proposed PrivyNet framework: the local NN is derived for feature extraction trained the target learning task Privacy utility trade-off is controlled the topology the local NN.Contribution To propose PrivyNet a flexible DNN training framework achieve PrivyNet divides a DNN model deploys onto the local platforms and separately As shown the local NN is used generate intermediate representations while trained the learning task based the released intermediate representations The privacy protection is achieved the transformation realized the local NN, nonlinear consists different lossy operations convolution pooling so To avoid local training derive the local NN from Our key insight here the initial layers a DNN usually used extract general features application enable different learning tasks Therefore by deriving the local NN pre-trained NNs a good utility can since useful features embedded the released representations privacy protected selecting the topology control to release Our main contributions summarized as propose PrivyNet split DNN model to enable privacy loss.• characterize utility using CNN the local NN in detail based which three key factors that the privacy and utility trade-off identified A hierarchical strategy determine considering constraints local computation storage privacy verify as its efficiency effectiveness In provide detailed discussions the adversarial model adoptedAccording we defined in the transformation induced the FEN assumed unknown the attackers This helps prevent more powerful attacks enable a better privacy protection However because the FEN derived the pre-trained NNs the structure weights which also available the attackers need provide strategies protect the anonymity In our framework consider the protection FEN:• Build a pool pre-trained NNs enable our characterization framework VGG16 The same procedure VGG19 BID20 , ResNet BID9 Inception BID23 . By enlarging becomes the attacker guess the FEN derived.• Apply the channel selection procedure both output channels intermediate channelsAfter the subset selected channels in each layer become unknown Therefore , even the attackers know the pre-trained NN, from the FEN becomes much guess the channels form the intermediate channel selection the utility sacrificed and the privacy loss increased We verify the change privacy utility empirically We take the first 6 layers VGG16 including 4 convolution layers 2 max-pooling layers set output channel We use CIFAR-10 dataset the same ICN and IRN Section We first gradually reduce the channel depth the first convolution layer from 64 As shown FIG12 the privacy utility are rarely impacted the change the channel depth first convolution layer Meanwhile we can observe the dramatic reduction on the runtime. We then gradually reduce the channel depth for each convolution layer As shown FIG4 after we reduce the channel depth for half still similar privacy utility a dramatic reduction the runtime , 64 128 8 3232 respectively By channel selection for intermediate layers even the attackers know the pre-trained NN that our FEN derived for In this way the anonymity the FEN can well protected",0.01,0.49334331361684963
"Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce realistic real-valued multi-dimensional time series, with an emphasis on their application to medical data. RGANs make use of recurrent neural networks (RNNs) in the generator and the discriminator. In the case of RCGANs, both of these RNNs are conditioned on auxiliary information. We demonstrate our models in a set of toy datasets, where we show visually and quantitatively (using sample likelihood and maximum mean discrepancy) that they can successfully generate realistic time-series. We also describe novel evaluation methods for GANs, where we generate a synthetic labelled training dataset, and evaluate on a real test set the performance of a model trained on the synthetic data, and vice-versa. We illustrate with these metrics that RCGANs can generate time-series data useful for supervised training, with only minor degradation in performance on real test data. This is demonstrated on digit classification from ‘serialised’ MNIST and by training an early warning system on a medical dataset of 17,000 patients from an intensive care unit. We further discuss and analyse the privacy concerns that may arise when using RCGANs to generate realistic synthetic medical time series data, and demonstrate results from differentially private training of the RCGAN. Access to data is one of the bottlenecks in the development of machine learning solutions to domainspecific problems. The availability of standard datasets (with associated tasks) has helped to advance the capabilities of learning systems in multiple tasks. However, progress appears to lag in other fields, such as medicine. It is tempting to suggest that tasks in medicine are simply harder -the data more complex, more noisy, the prediction problems less clearly defined. Regardless of this, the dearth of data accessible to researchers hinders model comparisons, reproducibility and ultimately scientific progress. However, due to the highly sensitive nature of medical data, its access is typically highly controlled, or require involved and likely imperfect de-identification. The motivation for this work is therefore to exploit and develop the framework of generative adversarial networks (GANs) to generate realistic synthetic medical data. This data could be shared and published without privacy concerns, or even used to augment or enrich similar datasets collected in different or smaller cohorts of patients. Moreover, building a system capable of synthesizing realistic medical data implies modelling the processes that generates such information, and therefore it can represent the first step towards developing a new approach for creating predictive systems in medical environments.Beyond the utility to the machine learning research community, such a tool stands to benefit the medical community for use in training simulators. In this work, we focus on synthesising real-valued time-series data as from an Intensive Care Unit (ICU). In ICUs, doctors have to make snap decisions under time pressure, where they cannot afford to hesitate. It is already standard in medical training to use simulations to train doctors, but these simulations often rely on hand-engineered rules and physical props. Thus, a model capable of generating diverse and realistic ICU situations could have an immediate application, especially when given the ability to condition on underlying 'states' of the patient.The success of GANs in generating realistic-looking images BID29 BID20 BID12 BID30 suggests their applicability for this task, however limited work has exploited them for generating time-series data. In addition, evaluation of GANs remains a largely-unsolved problem, with researchers often relying on visual evaluation of generated examples, an approach which is both impractical and inappropriate for multi-dimensional medical time series. For example BID35 ) present a method to use convolutional GANs specifically designed to generate video sequences, and the results were visually evaluated with Amazon Mechanical Turk. In BID25 , authors present a method for voice synthesis based on dilated convolutions, which is also evaluated by humans. This voice synthesis model has been very recently improved by introducing an RNN-based network that generates the spectrogram of the signal BID32 .The primary contributions of this work are:1. Demonstration of a method to generate multivariate real-valued sequences using adversarial training and recurrent neural networks.2. Showing novel approaches for evaluating GANs.3. Generating synthetic medical time series data.4. Empirical privacy analysis of both GANs and differential private GANs. We have described, trained and evaluated a recurrent GAN architecture for generating real-valued sequential data, which we call RGAN. We have additionally developed a conditional variant (RCGAN) to generate synthetic datasets, consisting of real-valued time-series data with associated labels. As this task poses new challenges, we have presented novel solutions to deal with evaluation and questions of privacy. By generating labelled training data -by conditioning on the labels and generating the corresponding samples, we can evaluate the quality of the model using the 'TSTR technique', where we train a model on the synthetic data, and evaluate it on a real, held-out test set. We have demonstrated this approach using 'serialised' multivariate MNIST, and on a dataset of real ICU patients, where models trained on the synthetic dataset achieved performance at times comparable to that of the real data. In domains such as medicine, where privacy concerns hinder the sharing of data, this implies that with refinement of these techniques, models could be developed on synthetic data that are still valuable for real tasks. This could enable the development of synthetic 'benchmarking' datasets for medicine (or other sensitive domains), of the kind which have enabled great progress in other areas. We have additionally illustrated that such a synthetic dataset does not pose a major privacy concern or constitute a data leak for the original sensitive training data, and that for stricter privacy guarantees, differential privacy can be used in training the RCGAN with some loss to performance. : Data from three real eICU patients (purple, blue, gold) of the first five hours after admission. Noise from N (0, σ 2 e ) for σ e = 0.1σ has been added to protect privacy, where σ is the standard deviation of the true data (for that variable). We compare the data at its original sampling resolution with downsampled to one measurement every 15 minutes (the setting used in this paper) and 30 minutes. High-frequency fluctuations are lost through downsampling, but general trends and some variability are preserved in the 15 minute case. These patients were selected randomly from the set of patients with minimal missing data during the time period and so are representative of the cohort used to generate the training data. : Three random samples from the generator trained on eICU data. These samples are from the synthetic datasets used in the TSTR experiments in section 5.1. The generator produces data in [−1, 1], so to obtain medically relevant values, the inverse of the scaling transformation used on the training data has been applied. This transformation was to scale each variable at each time-point independently to the range [−1, 1]. An unusually high value (likely an artefact) in the mean arterial pressure at 135 minutes after admission is responsible for the apparent downward spike in the generated data. A scaling transformation T is applied to the real data (independently for each variable at each timepoint), and the synthetic data is as produced by the generator. , and zooming in. The synthetic data consists of the generated datasets from all five replicates of the TSTR experiment in eICU described in section 5.1 with TSTR results reported in Table 2a . The real data is the training set for those expeirments. between synthetic and real data. The synthetic data is that used in the TSTR experiments (five replicates) in section 5.1.",1596,0.833,919,1.7366702937976062,"Generative Adversarial Networks shown as training models produce In this work propose a Recurrent GAN and to produce an emphasis their application medical data RGANs make the generator In RCGANs both conditioned auxiliary information We demonstrate our models a set toy datasets visually and (using sample likelihood maximum mean discrepancy they successfully generate. We also describe novel evaluation methods GANs where generate a synthetic labelled training dataset on trained vice We illustrate with these metrics RCGANs useful supervised training with only minor degradation on real test data This demonstrated on digit classification from ��serialised�� MNIST and by training an early warning system a medical dataset We further and analyse the privacy concerns RCGANs realistic synthetic medical time series data demonstrate results differentially private training Access data one machine learning solutions domainspecific problems The availability standard datasets (with associated tasks helped advance the capabilities learning systems multiple tasks However progress appears lag other fields It tempting suggest tasks medicine simply harder -the data more complex noisy the prediction problems clearly Regardless this the dearth data accessible hinders model comparisons ultimately scientific progress However due medical data its access typically highly controlled or require involved and likely imperfect de The motivation therefore exploit and develop the framework realistic synthetic medical data This data could shared and published without privacy concerns even used augment enrich similar datasets collected different or smaller cohorts Moreover building capable synthesizing realistic medical data implies modelling the processes generates therefore it represent creating predictive systems medical environmentsBeyond the utility to the machine learning research community stands for use training simulators In this work synthesising as from an Intensive Care Unit In ICUs doctors snap decisions under time pressure where hesitate It already standard medical training simulations train rely hand-engineered rules physical props Thus a model capable generating diverse and realistic ICU situations an immediate application given condition on underlying 'statesThe success GANs generating realistic-looking images BID29 BID20 BID12 BID30 suggests their applicability this task however limited work exploited generating In addition evaluation GANs remains researchers often visual evaluation generated examples both impractical inappropriate multi-dimensional medical time series For example BID35 ) present a method use convolutional GANs specifically designed generate video sequences the results visually evaluated Amazon Mechanical Turk In BID25 , authors present voice synthesis based dilated convolutions also evaluated humans This voice synthesis model very recently improved introducing generates the spectrogram the signal BID32 .The primary contributions Demonstration a method generate multivariate real-valued sequences adversarial training and recurrent neural networks.2 Showing novel approaches evaluating synthetic medical time series Empirical privacy analysis differential private GANs We have, trained evaluated a recurrent GAN architecture RGAN We additionally developed a conditional variant (RCGAN generate synthetic datasets consisting associated labels As this task poses presented novel solutions deal evaluation questions privacy By generating labelled training data -by conditioning on the labels generating the corresponding samples evaluate the model using the 'TSTR technique train the synthetic data evaluate a real, held-out test set We demonstrated this approach 'serialised' multivariate MNIST, on real ICU patients where models trained the synthetic dataset achieved performance at times In domains medicine where privacy hinder the sharing this implies with refinement these techniques models on synthetic data still valuable real tasks This could enable synthetic 'benchmarking' datasets medicine (or other sensitive domains of enabled great progress We additionally illustrated such a synthetic dataset does pose or constitute a data leak for the original sensitive training data for stricter privacy guarantees differential privacy can training the RCGAN with some loss to performance : Data three real eICU patientspurple of the first five hours admission Noise N (0, �� 2 e for has added protect privacy where the true datafor that variable We compare at its original sampling resolution downsampled to one measurement every 15the setting High-frequency fluctuations lost downsampling general trends and some variability the 15 minute case These patients selected randomly the set minimal missing data during and so used generate : Three random samples the generator trained eICU data These samples the synthetic datasets the TSTR experiments in section The generator produces data [−1 so to medically relevant values the inverse the scaling transformation used on has This transformation to scale each variable at independently the range [ An unusually high value (likely an artefact the mean arterial pressure at 135 minutes admission responsible the apparent downward spike the generated data A scaling transformation T is applied the real data (independently for at the synthetic data as produced the generator , zooming The synthetic data consists the generated datasets all five replicates the TSTR experiment in eICU described section with TSTR results 2a . The real data the training set those expeirments between synthetic and real data The synthetic data that used the TSTR experimentsfive replicates in section",0.01,0.5810503551357789
"Emphasis effects – visual changes that make certain elements more
 prominent – are commonly used in information visualization to draw
 the user’s attention or to indicate importance. Although theoretical
 frameworks of emphasis exist (that link visually diverse emphasis
 effects through the idea of visual prominence compared to background
 elements), most metrics for predicting how emphasis effects
 will be perceived by users come from abstract models of human
 vision which may not apply to visualization design. In particular,
 it is difficult for designers to know, when designing a visualization,
 how different emphasis effects will compare and what level of one
 effect is equivalent to what level of another. To address this gap,
 we carried out two studies that provide empirical evidence about
 how users perceive different emphasis effects, using three visual
 variables (colour, size, and blur/focus) and eight strength levels.
 Results from gaze tracking, mouse clicks, and subjective responses
 show that there are significant differences between visual variables
 and between levels, and allow us to develop an initial understanding
 of perceptual equivalence. We developed a model from the data in
 our first study, and used it to predict the results in the second; the
 model was accurate, with high correlations between predictions and
 real values. Our studies and empirical models provide valuable new
 information for designers who want to understand and control how
 emphasis effects will be perceived by users. Emphasis effects are visual changes that make certain elements more prominent, and are commonly used in information visualization to draw the user's attention or to indicate importance. Emphasizing important data points is a common method used by designers to support the user when gradually exploring the data -or in narrative visualization [25] , when known aspects of the data are presented to the users. An effective emphasis effect will alter a data point's visual features [4, 22] , such that a viewer's attention will be guided to the region of interest [61] . The goal of emphasis is to alter important data points to appear more visually prominent and can be achieved through the use of a variety of visual effects [17, 22, 23, 59] . For example, a visualization can use colour changes to emphasize some data points, and differences in the visual prominence of the selected data points will be achieved from variations in color, a visual variable known to guide a user's attention [24] . Although theoretical frameworks of emphasis exist that link visually diverse emphasis effects through the idea of visual prominence compared to background elements [22] , we still know little about how emphasis effects will be perceived by users. In particular, we know little about what visual effects, and what magnitudes of those effects, will be most quickly recognized as emphasis by the viewer of a visualization; in addition, we know little about how different effects compare and what level of an effect is equivalent to what level of another. Many metrics for predicting how emphasis effects will be perceived by users come from abstract models of human vision which may not apply to visualization design. These abstract models from human vision are generally constructed using large and visually isolated stimuli under optimal conditions. Models of human visual attention are effective at predicting perceptibility in isolation but not within a field of distractors, and do not work well with even minor changes to the visual field [3, 58] . Visualizations, in contrast, often consist of large numbers of a variety of marks viewed using a wide range of devices and environments -and designers may use a variety of techniques to emphasize data points. Current guidelines do not address how different emphasis effects are perceived by viewers in visualizations, or provide an equivalence metric for perceived emphasis so designers can choose effects correctly. Without effective models of visual prominence in visualizations, designers lack information on know how different visual effects compare, and don't know what magnitude of effect to use to appropriately guide a viewer's attention to an area of interest. To address this gap, we carried out two studies that provide empirical evidence about how users perceive different emphasis effects, using three visual variables (colour, size, and blur/focus) and eight strength levels. It is important to note that the three emphasis effects are qualitatively different -for example, colour and size manipulate just the emphasized element, whereas blur/focus manipulates everything but the emphasized element -and so our goal is not simply to identify which effect is most perceivable, but rather to establish how the effects compare to one another at different magnitudes. To do this, our first study established a baseline of perceived visual prominence through eye-tracking data, interaction logs, and subjective ratings in simulated static scatterplot visualizations. We then built a model from the first study's data using logarithmic curves, that provides a prediction of equivalence between the three emphasis effects. Our second study then examined perceived emphasis in a more realistic context, by looking at visual prominence in complex visualizations that are taken from real-world applications (the MASSVIS dataset [7] ). We evaluated our model by using it to predict the results of the second study for three different measures; the model was accurate, with R 2 values as high as 0.96. Our two studies provide new findings about how people perceive three emphasis effects and their magnitudes in visualizations: • There were significant differences in both studies for emphasis effect: blur/focus was most prominent, and colour least prominent, with size in between depending on magnitude. • There were also significant differences between the magnitude levels for all effects, providing a graduated way to increase or decrease perceived prominence. • A predictive model based on logarithmic curves fit the Study 1 data well, and was accurate at predicting perceived emphasis in Study 2 (particularly in terms of subjective ratings). Our studies provide an initial empirical foundation for understanding how visual effects operate and are experienced by viewers when used for emphasis in visualizations -and although more work is needed to refine and broaden the models, our work provides useful new information for designers who want to control how emphasis effects will be perceived by users. Emphasis is essential to InfoVis and is used to highlight regions of interest in a visualization. While there is a large body of research in this domain, much of the work seeks to understand how the underlying perceptual system operates -limiting the possibility of extracting design lessons from low-level data and findings. We survey current empirical studies of perception from visualization and vision science to inform our work. Emphasis is an essential component of InfoVis, and is used by designers to draw a user's attention or to indicate importance. However, it is difficult for designers to know how different emphasis effects will compare and what level of one effect is equivalent to what level of another when designing visualizations. We carried out two user studies to evaluate the visual prominence of three emphasis effects (blur/focus, colour, and size) at various strength levels, and developed a predictive model that can indicate equivalence between effects. Results from our two studies provide the beginnings of an empirical foundation for understanding how visual effects operate and are experienced by viewers when used for emphasis in visualizations, and provide new information for designers who want to control how emphasis effects will be perceived by users.",1430,0.676,815,1.7546012269938651,"Emphasis effects – visual changes make certain elements prominent commonly information visualization draw the user��s attention or indicate importance Although theoretical frameworks of emphasis exist (that link visually diverse emphasis effects through the idea visual prominence compared background elements most metrics predicting how emphasis effects come abstract models human vision which may apply visualization design In particular difficult designers know, a visualization how different emphasis effects compare and what level one effect equivalent what level To address this gap carried provide users different emphasis effects, using three visual variablescolour blur/focus eight strength levels Results gaze tracking mouse clicks subjective responses show there visual variables between levels, allow develop an initial understanding perceptual equivalence We developed from in used; accurate, high correlations predictions real values Our studies and empirical models valuable new information designers control how emphasis effects will perceived Emphasis effects visual changes make certain elements prominent commonly information visualization draw or indicate importance Emphasizing important data points is designers support the user when gradually exploring the data -or in narrative visualization [25 when known aspects presented An effective emphasis effect will alter a data point's visual features [4 22 such guided the region61 The goal emphasis alter important data points appear visually prominent can achieved [17 22 59] For example a visualization use colour changes emphasize some data points differences the visual prominence achieved from variations color, a visual variable known to guide [24 Although theoretical frameworks of emphasis exist that link visually diverse emphasis effects through the idea visual prominence compared background elements [22 still know will perceived In particular know little what visual effects, what magnitudes most quickly recognized emphasis by of a visualization; in addition compare and what level an effect equivalent another Many metrics for predicting emphasis effects perceived users come abstract models human vision which may apply visualization design These abstract models from human vision generally constructed large and visually isolated stimuli under Models human visual attention effective predicting perceptibility isolation but within distractors do work even minor changes [3 58 Visualizations, in contrast often consist a variety marks viewed using devices environments -and designers emphasize data points Current guidelines do address how different emphasis effects perceived viewers visualizations provide an equivalence metric perceived emphasis so designers choose effects correctly Without effective models visual prominence visualizations designers lack information know how different visual effects compare do what magnitude appropriately guide To address this gap carried provide users different emphasis effects, using three visual variablescolour blur/focus eight strength levels It important the three emphasis effects qualitatively different -for example, colour and size manipulate just the emphasized element blur/focus everything but our goal identify perceivable establish compare at To do our first study established perceived visual prominence through interaction logs in simulated static scatterplot visualizations We then built from the first study's data using that provides a prediction equivalence the three emphasis effects Our second study then perceived emphasis a more realistic context by visual prominence complex visualizations that takenthe MASSVIS dataset [7 We evaluated our model by it the second study for three different measures; the model accurate, R 2 values as Our two studies provide new findings people three emphasis effects their magnitudes visualizations • There were both studies for: blur/focus was most colour least size in between depending magnitude • There also the magnitude levels all effects providing a graduated way increase perceived prominence • A predictive model based fit the Study 1 data well accurate predicting perceived emphasis Studyparticularly terms subjective ratings Our studies provide an initial empirical foundation visual effects operate are experienced viewers when used emphasis visualizations -and although more work refine broaden the models useful new information designers control emphasis effects will Emphasis essential InfoVis is highlight regions a visualization While there in this domain much seeks the underlying perceptual system -limiting extracting design lessons findings We survey current empirical studies perception from visualization and vision science inform Emphasis an essential component InfoVis designers draw or indicate importance However difficult designers know how different emphasis effects compare and what level one effect equivalent what level when designing visualizations We carried two user studies the visual prominence three emphasis effectsblur/focus colour size at various strength levels developed can indicate equivalence effects Results our two studies provide the beginnings an empirical foundation visual effects operate are experienced viewers when used emphasis visualizations provide designers control emphasis effects will",0.01,0.6267367975252814
"Memory Network based models have shown a remarkable progress on the task of relational reasoning.
 Recently, a simpler yet powerful neural network module called Relation Network (RN) has been introduced. 
 Despite its architectural simplicity, the time complexity of relation network grows quadratically with data, hence limiting its application to tasks with a large-scaled memory.
 We introduce Related Memory Network, an end-to-end neural network architecture exploiting both memory network and relation network structures. 
 We follow memory network's four components while each component operates similar to the relation network without taking a pair of objects. 
 As a result, our model is as simple as RN but the computational complexity is reduced to linear time.
 It achieves the state-of-the-art results in jointly trained bAbI-10k story-based question answering and  bAbI dialog dataset. Neural network has made an enormous progress on the two major challenges in artificial intelligence: seeing and reading. In both areas, embedding methods have served as the main vehicle to process and analyze text and image data for solving classification problems. As for the task of logical reasoning, however, more complex and careful handling of features is called for. A reasoning task requires the machine to answer a simple question upon the delivery of a series of sequential information. For example, imagine that the machine is given the following three sentences: ""Mary got the milk there."", ""John moved to the bedroom."", and ""Mary traveled to the hallway."" Once prompted with the question, ""Where is the milk?"", the machine then needs to sequentially focus on the two supporting sentences, ""Mary got the milk there."" and ""Mary traveled to the hallway."" in order to successfully determine that the milk is located in the hallway.Inspired by this reasoning mechanism, J. has introduced the memory network (MemNN), which consists of an external memory and four components: input feature map (I), generalization (G), output feature map (O), and response (R). The external memory enables the model to deal with a knowledge base without loss of information. Input feature map embeds the incoming sentences. Generalization updates old memories given the new input and output feature map finds relevant information from the memory. Finally, response produces the final output.Based on the memory network architecture, neural network based models like end-to-end memory network (MemN2N) BID11 , gated end-to-end memory network (GMemN2N) BID7 , dynamic memory network (DMN) BID6 , and dynamic memory network + (DMN+) BID13 are proposed. Since strong reasoning ability depends on whether the model is able to sequentially catching the right supporting sentences that lead to the answer, the most important thing that discriminates those models is the way of constructing the output feature map. As the output feature map becomes more complex, it is able to learn patterns for more complicate relations. For example, MemN2N, which has the lowest performance among the four models, measures the relatedness between question and sentence by the inner product, while the best performing DMN+ uses inner product and absolute difference with two embedding matrices.Recently, a new architecture called Relation Network (RN) BID9 has been proposed as a general solution to relational reasoning. The design philosophy behind it is to directly capture the supporting relation between the sentences through the multi-layer perceptron (MLP). Despite its simplicity, RN achieves better performance than previous models without any catastrophic failure.The interesting thing we found is that RN can also be interpreted in terms of MemNN. It is composed of O and R where each corresponds to MLP which focuses on the related pair and another MLP which infers the answer. RN does not need to have G because it directly finds all the supporting sentences at once. In this point of view, the significant component would be MLP-based output feature map. As MLP is enough to recognize highly non-linear pattern, RN could find the proper relation better than previous models to answer the given question.However, as RN considers a pair at a time unlike MemNN, the number of relations that RN learns is n 2 when the number of input sentence is n. When n is small, the cost of learning relation is reduced by n times compared to MemNN based models, which enables more data-efficient learning BID9 . However, when n increases, the performance becomes worse than the previous models. In this case, the pair-wise operation increases the number of non-related sentence pairs more than the related sentence pair, thereby confuses RN's learning. BID9 has suggested attention mechanisms as a solution to filter out unimportant relations; however, since it interrupts the reasoning operation, it may not be the most optimal solution to the problem.Our proposed model, ""Relation Memory Network"" (RMN), is able to find complex relation even when a lot of information is given. It uses MLP to find out relevant information with a new generalization which simply erase the information already used. In other words, RMN inherits RN's MLP-based output feature map on Memory Network architecture. Experiments show its state-ofthe-art result on the text-based question answering tasks.",1034,0.556,626,1.6517571884984026,"Memory Network based models shown a remarkable progress on relational reasoning Recently a simpler yet powerful neural network module Relation Network introduced Despite its architectural simplicity the time complexity relation network grows quadratically data, hence limiting tasks a large-scaled memory We introduce Related Memory Network, end neural architecture exploiting both memory network and relation network structures We follow memory network's four components while each component operates similar the relation network without taking a pair objects As our model as RN but the computational complexity reduced linear time It achieves state results jointly trained bAbI-10k story-based question answering dialog dataset Neural network has made the two major challenges seeing reading In both areas embedding methods served the main vehicle process text solving As for the task logical reasoning however more complex and careful handling features called A reasoning task requires the machine answer upon the delivery sequential information For example imagine the machine given the following three sentencesMary got the milk thereJohn moved the bedroom traveled the hallway Once prompted with then needs sequentially focus the two supporting sentences and in successfully determine locatedInspired this reasoning mechanism J. has introduced the memory network (MemNN consists four components input feature map generalization response The external memory enables the model deal a knowledge base without loss Input feature map embeds the incoming sentences Generalization updates old memories given the new input and output feature map finds relevant information the memory Finally response producesBased the memory network architecture neural based models like end memory networkMemN2N BID11 , gated end + proposed Since strong reasoning ability depends whether the model able sequentially catching the right supporting sentences that lead discriminates those models of constructing the output feature map As the output feature map becomes able learn patterns more complicate relations For example MemN2N the lowest performance among the four models measures the relatedness question sentence by the inner product while the best performing DMN+ uses absolute difference with two embedding matricesRecently a new architecture Relation Network (RN) BID9 relational reasoning The design philosophy it directly capture the supporting relation the sentences through the multi-layer perceptron Despite its simplicity RN achieves better performance previous models without any catastrophic failureThe interesting thing we interpreted MemNN It composed O and where corresponds MLP which focuses the related pair another MLP infers RN does need G because directly finds all the supporting sentences at once In this point the significant component would MLP-based output feature map As MLP enough recognize highly non-linear pattern RN could find the proper relation better previous models to answerHowever considers a pair at unlike MemNN number relations RN learns n 2 when input sentence When n is small the cost learning relation reduced compared MemNN based models enables more data-efficient learning BID9 . However when n increases the performance becomes than the previous models In the pair-wise operation increases non-related sentence more confuses RN's learning BID9 has suggested attention mechanisms as filter unimportant relations; since interrupts the reasoning operationOur proposed model, ""Relation Memory Network able find complex relation even a lot given It uses MLP find relevant information with a new generalization which simply erase already used In RMN inherits RN's MLP-based output feature map on Memory Network architecture Experiments show its state-ofthe-art result on the text-based question answering tasks",0.01,0.3646992232172673
"We investigate in this paper the architecture of deep convolutional networks. Building on existing state of the art models, we propose a reconfiguration of the model parameters into several parallel branches at the global network level, with each branch being a standalone CNN. We show that this arrangement is an efficient way to significantly reduce the number of parameters while at the same time improving the performance. The use of branches brings an additional form of regularization. In addition to splitting the parameters into parallel branches, we propose a tighter coupling of these branches by averaging their log-probabilities. The tighter coupling favours the learning of better representations, even at the level of the individual branches, as compared to when each branch is trained independently. We refer to this branched architecture as ""coupled ensembles"". The approach is very generic and can be applied with almost any neural network architecture. With coupled ensembles of DenseNet-BC and parameter budget of 25M, we obtain error rates of 2.92%, 15.68% and 1.50% respectively on CIFAR-10, CIFAR-100 and SVHN tasks. For the same parameter budget, DenseNet-BC has an error rate of 3.46%, 17.18%, and 1.8% respectively.   With ensembles of coupled ensembles, of DenseNet-BC networks, with 50M total parameters, we obtain error rates of 2.72%, 15.13% and 1.42% respectively on these tasks. The design of early convolutional architectures (CNN) involved choices of hyper-parameters such as: filter size, number of filters at each layer, and padding BID15 BID14 . Since the introduction of the VGGNet BID20 ) the design has moved towards following a template: fixed filter size of 3 × 3 and N features maps, down-sample to half the input resolution only by the use of either maxpool or strided convolutions BID21 , and double the number the computed feature maps following each down-sampling operation. This philosophy is used by state of the art models like ResNet BID8 and DenseNet BID11 . The last two architectures extended the template to include the use of ""skip-connections"" between non-contiguous layers.Our work extends this template by adding another element, which we refer to as ""coupled ensembling"". In this set-up, the network is decomposed into several branches, each branch being functionally similar to a complete CNN. The proposed template achieves performance comparable to state of the art models with a significantly lower parameter count.In this paper, we make the following contributions: (i) we show that given a parameter budget, it is better to have the parameters split among branches rather than having a single branch (which is the case for all current networks), (ii) we compare different ways to combine the activations of the parallel branches and find that it is best to take an arithmetic mean of the individual logprobabilities (iii) combining these elements, we significantly match and improve the performance of convolutional networks on CIFAR and SVHN datasets, with a heavily reduced parameter count. (iv) Further ensembling of coupled ensembles lead to more improvement. This paper is organised as follows: in section 2, we discuss related work; in section 3, we introduce the concept of coupled ensembles and the motivation behind the idea; in section 4, we evaluate the proposed approach and compare it with the state of the art; and we conclude and discuss future work in section 5. The proposed approach consists in replacing a single deep convolutional network by a number of ""element blocks"" which resemble standalone CNN models. The intermediate score vectors produced by each of the elements blocks are coupled via a ""fuse layer"". At training time, this is done by taking an arithmetic average of their log-probabilities for the targets. At test time the score vectors are averaged following the output from each score vector. Both of these aspects leads to a significant performance improvement over a single branch configuration. This improvement comes at the cost of a small increase in the training and prediction times. The proposed approach leads to the best performance for a given parameter budget as can be seen in tables 3 and 4, and in figure 2. Additionally, the individual ""element block"" performance is better as compared to when they are trained independently.The increase in training and prediction times is mostly due to the sequential processing of branches during the forward and backward passes. The smaller size of the branches makes the data parallelism on GPUs less efficient. This effect is not as pronounced for larger models. This could be solved in two ways. First, as there is no data dependency between the branches (before the averaging layer) it is possible to extend the data parallelism to the branches, restoring the initial level of parallelism. This can be done by through a parallel implementation of multiple 2D convolutions at the same time. Second or alternatively, when multiple GPUs are used, it is possible to spread the branches over the GPUs.Preliminary experiments on ImageNet (Russakovsky et al., 2015) show that coupled ensembles have a lower error for the same parameter budget as compared to single branch models. We will expand on these experiments in the future.",1065,0.568,652,1.633435582822086,"We investigate in the architecture Building existing state of propose the model parameters into several parallel branches at the global network level a standalone CNN We show this arrangement significantly parameters while at The use branches brings an additional form regularization In addition splitting the parameters parallel branches propose a tighter coupling these branches by averaging their log-probabilities The tighter coupling favours the learning better representations even at the individual branches compared when trained independently We refer this branched architecture ""coupled ensembles The approach very generic can with almost any neural network architecture With coupled ensembles DenseNet-BC and parameter budget of 25M obtain error rates on CIFAR-10, CIFAR-100 and SVHN tasks For the same parameter budget DenseNet-BC has an error rate 17.18% With ensembles coupled ensembles of DenseNet-BC networks with 50M total parameters obtain error rates on these tasks The design early convolutional architectures involved choices hyper such: filter size number filters at padding BID15 BID14 . Since the VGGNet BID20 ) the design moved towards following a template: fixed filter size 3 × 3 and N features maps down-sample to half the input resolution only by the use either maxpool or strided convolutions BID21 double the number the computed feature maps following each down-sampling operation This philosophy used state of like ResNet BID8 DenseNet BID11 . The last two architectures extended the template the use ""skip-connections between non-contiguous layersOur work extends another element refercoupled ensembling In this set-up the network decomposed several branches functionally a complete CNN The proposed template achieves performance comparable state of a significantly lower parameter countIn make the following contributions we given a parameter budget better the parameters split among branches having (which all current networks compare different ways combine the activations the parallel branches find best take an arithmetic mean the individual logprobabilitiesiii combining these elements significantly match and on CIFAR and SVHN datasets with a heavily reduced parameter count (iv Further ensembling coupled ensembles lead more improvement This paper is organised in section related work; introduce coupled ensembles the motivation evaluate compare the state we and future work section The proposed approach consists in replacing a single deep convolutional network ""element blocks resemble standalone CNN models The intermediate score vectors produced each the elements blocks coupled via a ""fuse layer At training time this done taking an arithmetic average their log-probabilities for the targets At test time the score vectors averaged following the output each score vector Both these aspects leads a significant performance improvement a single branch configuration This improvement comes the training and prediction times The proposed approach leads the best performance a given parameter budget as can tables 3 figure Additionally the individual ""element block"" performance better as when they trained independentlyThe increase training and prediction times mostly the sequential processing branches during the forward and backward passes The smaller size the branches makes the data parallelism on GPUs This effect as for larger models This could solved First as there no data dependency the branches (before the averaging layer extend the data parallelism restoring the initial level This can through a parallel implementation multiple 2D convolutions at Second or alternatively when multiple GPUs spread the branchesPreliminary experiments ImageNet (Russakovsky coupled ensembles have a lower error for the same parameter budget as compared single branch models We will expand these experiments",0.01,0.31801738167268634
"Convolutional Neural Networks (CNN) are very popular in many fields including computer vision, speech recognition, natural language processing, to name a few. Though deep learning leads to groundbreaking performance in these domains, the networks used are very demanding computationally and are far from real-time even on a GPU, which is not power efficient and therefore does not suit low power systems such as mobile devices. To overcome this challenge, some solutions have been proposed for quantizing the weights and activations of these networks, which accelerate the runtime significantly. Yet, this acceleration comes at the cost of a larger error. The NICE method proposed in this work trains quantized neural networks by noise injection and a learned clamping, which improve the accuracy. This leads to state-of-the-art results on various regression and classification tasks, e.g., ImageNet classification with architectures such as ResNet-18/34/50 with low as 3-bit weights and 3 -bit activations. We implement the proposed solution on an FPGA to demonstrate its applicability for low power real-time applications.",212,0.114,120,1.7666666666666666," very including to Though deep learning leads groundbreaking performance these domains the networks used very demanding computationally far real-time even a GPU not power therefore does suit low power systems such To overcome some solutions quantizing the weights activations these networks accelerate the runtime significantly Yet this acceleration comes a larger error The NICE method proposed this work trains quantized by noise injection a learned clamping, improve. This leads state results on various regression and classification tasks, ImageNet classification with architectures ResNet-18/34/50 with low as 3-bit weights 3 -bit activations We implement the proposed solution on to demonstrate",0.0,0.6574784777536408
"In complex transfer learning scenarios new tasks might not be tightly linked to previous tasks. Approaches that transfer information contained only in the final parameters of a source model will therefore struggle. Instead, transfer learning at at higher level of abstraction is needed. We propose Leap, a framework that achieves this by transferring knowledge across learning processes. We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta-learning objective that minimizes the expected length of this path. Our framework leverages only information obtained during training and can be computed on the fly at negligible cost. We demonstrate that our framework outperforms competing methods, both in meta-learning and transfer learning, on a set of computer vision tasks. Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding reinforcement learning environments (Atari) that involve millions of gradient steps. Transfer learning is the process of transferring knowledge encoded in one model trained on one set of tasks to another model that is applied to a new task. Since a trained model encodes information in its learned parameters, transfer learning typically transfers knowledge by encouraging the target model's parameters to resemble those of a previous (set of) model(s) (Pan & Yang, 2009 ). This approach limits transfer learning to settings where good parameters for a new task can be found in the neighborhood of parameters that were learned from a previous task. For this to be a viable assumption, the two tasks must have a high degree of structural affinity, such as when a new task can be learned by extracting features from a pretrained model BID12 BID14 Mahajan et al., 2018) . If not, this approach has been observed to limit knowledge transfer since the training process on one task will discard information that was irrelevant for the task at hand, but that would be relevant for another task BID15 BID1 .We argue that such information can be harnessed, even when the downstream task is unknown, by transferring knowledge of the learning process itself. In particular, we propose a meta-learning framework for aggregating information across task geometries as they are observed during training. These geometries, formalized as the loss surface, encode all information seen during training and thus avoid catastrophic information loss. Moreover , by transferring knowledge across learning processes, information from previous tasks is distilled to explicitly facilitate the learning of new tasks.Meta learning frames the learning of a new task as a learning problem itself, typically in the few-shot learning paradigm BID20 Santoro et al., 2016; Vinyals et al., 2016) . In this environment, learning is a problem of rapid adaptation and can be solved by training a meta-learner by backpropagating through the entire training process (Ravi & Larochelle, 2016; BID6 BID11 . For more demanding tasks, meta-learning in this manner is challenging; backpropagating through thousands of gradient steps is both impractical and susceptible to instability. On the other hand, truncating backpropagation to a few initial steps induces a short-horizon bias (Wu et al., 2018) . We argue that as the training process grows longer in terms of the distance traversed on the loss landscape, the geometry of this landscape grows increasingly important. When adapting to a new task through a single or a handful of gradient steps, the geometry can largely be ignored. In contrast, with more gradient steps, it is the dominant feature of the training process.To scale meta-learning beyond few-shot learning, we propose Leap, a light-weight framework for meta-learning over task manifolds that does not need any forward-or backward-passes beyond those already performed by the underlying training process. We demonstrate empirically that Leap is a superior method to similar meta and transfer learning methods when learning a task requires more than a handful of training steps. Finally, we evaluate Leap in a reinforcement Learning environment (Atari 2600; BID8 , demonstrating that it can transfer knowledge across learning processes that require millions of gradient steps to converge. Transfer learning typically ignores the learning process itself, restricting knowledge transfer to scenarios where target tasks are very similar to source tasks. In this paper, we present Leap, a framework for knowledge transfer at a higher level of abstraction. By formalizing knowledge transfer as minimizing the expected length of gradient paths, we propose a method for meta-learning that scales to highly demanding problems. We find empirically that Leap has superior generalizing properties to finetuning and competing meta-learners.",900,0.473,506,1.7786561264822134,"In complex transfer learning new tasks might tightly Approaches transfer information contained only the final parameters a source model therefore struggle Instead transfer learning at at higher level We propose Leap, achieves transferring knowledge learning We associate each task a manifold on the training process travels initialization final parameters construct a meta-learning objective this path Our framework only information obtained training can computed at negligible cost We demonstrate our framework competing methods both meta-learning and transfer learning on Finally demonstrate Leap can transfer knowledge learning demandingAtari) that involve millions gradient steps Transfer learning encoded one model trained tasks that applied Since a trained model encodes its learned parameters transfer learning typically transfers by encouraging the target model's parameters resemble a previous (setPan Yang This approach limits transfer learning settings good parameters a new task the neighborhood parameters learned For this to a viable assumption the two tasks structural affinity when a new task learned extracting features a pretrained model BID12 BID14 Mahajan et al 2018) . If not this approach observed limit knowledge transfer since the training process on one task will discard irrelevant relevant BID15 BID1 .We argue such information, the downstream task unknown transferring itself In particular propose aggregating across task geometries as they observed during These geometries formalized the loss surface encode all information seen training thus avoid catastrophic information loss Moreover , by transferring knowledge across learning processes information previous tasks distilled explicitly facilitateMeta learning frames itself typically the few-shot learning paradigm BID20 Santoro 2016; Vinyals) In this environment learning a problem rapid adaptation can solved a meta-learner by throughRavi Larochelle 2016 BID6 BID11 . For more demanding tasks meta-learning in this manner challenging; through thousands gradient steps both impractical susceptible instability On truncating a few initial steps induces a short-horizon biasWu 2018 . We argue as the training process grows in the distance traversed on the loss landscape the geometry this landscape grows When adapting through single or a handful gradient steps the geometry largely In contrast with more gradient steps the dominant featureTo scale meta-learning beyond few-shot learning Leap, over task manifolds does any forward-or backward-passes beyond those performed We demonstrate Leap is similar meta and transfer learning methods when learning requires Finally evaluate Leap in a reinforcement Learning environmentAtari; BID8 , demonstrating transfer knowledge that millions gradient steps converge Transfer learning typically ignores restricting knowledge transfer scenarios target tasks very source tasks In Leap, knowledge transfer at By formalizing knowledge transfer as minimizing the expected length gradient paths propose meta-learning scales highly demanding problems We find empirically Leap has superior generalizing properties finetuning competing",0.01,0.6880265679812323
"Given an existing trained neural network, it is often desirable to learn new capabilities without hindering performance of those already learned. Existing approaches either learn sub-optimal solutions, require joint training, or incur a substantial increment in the number of parameters for each added task, typically as many as the original network. We propose a method called Deep Adaptation Networks (DAN) that constrains newly learned filters to be linear combinations of existing ones. DANs preserve performance on the original task, require a fraction (typically 13%) of the number of parameters compared to standard fine-tuning procedures and converge in less cycles of training to a comparable or better level of performance. When coupled with standard network quantization techniques, we further reduce the parameter cost to around 3% of the original with negligible or no loss in accuracy. The learned architecture can be controlled to switch between various learned representations, enabling a single network to solve a task from multiple different domains. We conduct extensive experiments showing the effectiveness of our method on a range of image classification tasks and explore different aspects of its behavior. While deep neural networks continue to show remarkable performance gains in various areas such as image classification BID20 ), semantic segmentation BID24 ), object detection BID9 ), speech recognition BID13 )medical image analysis BID23 ) -and many more -it is still the case that typically, a separate model needs to be trained for each new task. Given two tasks of a totally different modality or nature, such as predicting the next word in a sequence of words versus predicting the class of an object in an image, it stands to reason that each would require a different architecture or computation. However, for a set of related tasks such as classifying images from different domains it is natural to expect that solutions will (1) Utilize the same computational pipeline; (2) Require a modest increment in the number of required parameters for each added task; (3) Be learned without hindering performance of already learned tasks (a.k.a catastrophic forgetting) and (4) Be learned incrementally, dropping the requirement for joint training such as in cases where the training data for previously learned tasks is no longer available.Our goal is to enable a network to learn a set of related tasks one by one while adhering to the above requirements. We do so by augmenting a network learned for one task with controller modules which utilize already learned representations for another. The parameters of the controller modules are optimized to minimize a loss on a new task. The training data for the original task is not required at this stage. The network's output on the original task data stays exactly as it was; any number of controller modules may be added to each layer so that a single network can simultaneously encode multiple distinct tasks, where the transition from one task to another can be done by setting a binary switching variable or controlled automatically. The resultant architecture is coined DAN, standing for Deep Adaptation Networks. We demonstrate the effectiveness of our method on the recently introduced Visual Decathlon Challenge (Rebuffi et al. (2017) ) whose task is to produce a classifier to work well on ten different image classification datasets. Though adding only 13% of the number of original parameters for each newly learned task (the specific number depends on the network architecture), the average performance surpasses that of fine tuning all parameters -without the negative side effects of doubling the number of parameters and catastrophic forgetting. In this work, we focus on the task of image classification on various datasets, hence in our experiments the word ""task"" refers to a specific dataset.Our main contribution is the introduction of an improved alternative to transfer learning, which is as effective as fine-tuning all network parameters towards a new task, precisely preserves old task performance, requires a fraction (network dependent, typically 13%) of the cost in terms of new weights and is able to switch between any number of learned tasks.We introduce two variants of the method, a fully-parametrized version, whose merits are described above and one with far fewer parameters, which significantly outperforms shallow transfer learning (i.e. feature extraction) for a comparable number of parameters. In the next section, we review some related work. Sec. 3 details the proposed method. In Sec. 4 we present various experiments, including comparison to related methods, as well as exploring various strategies on how to make our method more effective, followed by some discussion & concluding remarks. We have observed that the proposed method converges to a a reasonably good solution faster than vanilla fine-tuning and eventually attains slightly better performance. This is despite the network's expressive power, which is limited by our construction. We conjecture that constraining each layer to be expressed as a linear combination of the corresponding layer in the original network serves to regularize the space of solutions and is beneficial when the tasks are sufficiently related to each other. One could come up with simple examples where the proposed method would likely fail: if the required solutions to two tasks are disjoint. For example, one task requires counting of horizontal lines and the other requires counting of vertical ones, and such examples are all that appear in the training sets, then the proposed method will likely work far worse than vanilla fine-tuning or training from scratch. We leave the investigation of this issue, as well as finding ways between striking a balance between reusing features and learning new ones as future work. We have presented a method for transfer learning thats adapts an existing network to new tasks while fully preserving the existing representation. Our method matches or outperforms vanilla finetuning, though requiring a fraction of the parameters, which when combined with net compression Our method achieve better performance over baselines for a large range of parameter budgets. For very few parameters diagonal (ours) outperforms features extraction. To obtain maximal accuracy our full method requires far fewer parameters (see linear vs finetune). (b) Our method (linear) converges to a high accuracy faster than fine-tuning. The weaker variant of our method converges as fast as feature-extraction but reaches an overall higher accuracy (3 (a)). (c) zoom in on top-right of (b).reaches 3% of the original parameters with no loss of accuracy. The method converges quickly to high accuracy while being on par or outperforming other methods with the same goal. Built into our method is the ability to easily switch the representation between the various learned tasks, enabling a single network to perform seamlessly on various domains. The control parameter α can be cast as a real-valued vector, allowing a smooth transition between representations of different tasks. An example of the effect of such a smooth transition can be seen in FIG2 where α is used to linearly interpolate between the representation of differently learned tasks, allowing one to smoothly control transitions between different behaviors. Allowing each added task to use a convex combination of already existing controllers will potentially utilize controllers more efficiently and decouple the number of controllers from the number of tasks.",1397,0.71,813,1.7183271832718328,"Given an existing trained neural network often desirable learn new capabilities without hindering performance those Existing approaches either learn sub-optimal solutions require joint training incur a substantial increment parameters for each added task typically as the original network We propose called Deep Adaptation Networks newly learned filters linear combinations existing ones DANs preserve performance the original task require a fraction (typically 13% parameters compared converge in less cycles training to a comparable or better level When coupled standard network quantization techniques further the parameter cost around 3% original with negligible or no loss accuracy The learned architecture can controlled to switch various learned representations enabling a single network solve from multiple different domains We conduct extensive experiments showing our method image classification tasks explore its behavior While deep neural networks continue show BID20 ), semantic object )medical image analysis -and -it typically a separate model needs Given two tasks of a totally different modality or nature such predicting the next word versus the class stands each would computation However for a set related tasks such classifying images from different domains it natural expect solutions ( Utilize the same computational pipeline; a modest increment required parameters each added task Be learned without hindering performance already learned tasks learned dropping joint training such cases for noOur goal enable a network learn one while We do so by augmenting a network learned for one task controller modules utilize already representations The parameters the controller modules optimized a loss on a new task The training data the original task required at The network's output the original task data stays exactly; any number controller modules may each layer so simultaneously encode multiple distinct tasks where the transition done setting binary switching variable controlled automatically The resultant architecture coined DAN standing Deep Adaptation Networks We demonstrate our method the recently introduced Visual Decathlon ChallengeRebuffi (2017 ) whose task produce work well ten different image classification datasets Though adding only 13% original parameters each newly learned taskthe specific number the network architecture surpasses fine all parameters -without doubling and catastrophic forgetting In this work the task image classification on various datasets hence in our experiments the wordOur main contribution the introduction an improved alternative transfer learning as effective fine all network parameters towards precisely preserves old task performance requires a fraction (network dependent, typically 13% in new weights able switch any number learned tasksWe introduce two variants whose merits above one far fewer parameters significantly shallow transfer learning feature a comparable number In review some related work Sec 3 details the proposed method In Sec 4 we present various experiments comparison related methods as exploring various strategies on make our method followed discussion & concluding We observed the proposed method converges a a reasonably good solution faster vanilla fine eventually attains This despite the network's expressive power limited our construction We conjecture constraining each layer expressed the corresponding layer in serves regularize solutions is beneficial the tasks sufficiently related One could come simple examples where the proposed method likely if the required solutions two tasks. For example one task counting of horizontal lines such examples all that appear the training sets then the proposed method likely far worse vanilla fine or training from We leave the investigation this issue, finding ways between striking reusing features learning as future work We presented transfer learning thats adapts an existing network new tasks while fully preserving the existing representation Our method matches or vanilla finetuning though requiring a fraction the parameters when net compression Our achieve over baselines parameter budgets For very few parameters diagonal (ours outperforms features extraction To obtain maximal accuracy our full method far fewer parameterssee linear vs finetune (b) Our method (linear) converges a high accuracy faster The weaker variant our method converges as fast feature-extraction but reaches an overall higher accuracy3 (a (c) zoom top-right (b).reaches 3% the original parameters with The method converges quickly high accuracy while being on or with Built into our method easily switch the representation the various learned tasks enabling a single network seamlessly various domains The control parameter α can cast allowing a smooth transition representations different tasks An example such a smooth transition can FIG2 where α used linearly the representation differently learned tasks allowing one smoothly control transitions different behaviors Allowing each added task a convex combination already existing controllers potentially utilize controllers more decouple",0.01,0.5343137211241775
"High throughput and low latency inference of deep neural networks are critical for the deployment of deep learning applications. This paper presents a general technique toward 8-bit low precision inference of convolutional neural networks, including 1) channel-wise scale factors of weights, especially for depthwise convolution, 2) Winograd convolution, and 3) topology-wise 8-bit support. We experiment the techniques on top of a widely-used deep learning framework. The 8-bit optimized model is automatically generated with a calibration process from FP32 model without the need of fine-tuning or retraining. We perform a systematical and comprehensive study on 18 widely-used convolutional neural networks and demonstrate the effectiveness of 8-bit low precision inference across a wide range of applications and use cases, including image classification, object detection, image segmentation, and super resolution. We show that the inference throughput
 and latency are improved by 1.6X and 1.5X respectively with minimal within 0.6%1to no loss in accuracy from FP32 baseline. We believe the methodology can provide the guidance and reference design of 8-bit low precision inference for other frameworks. All the code and models will be publicly available soon. While convolutional neural networks (CNN) shows state-of-the-art (SOTA) accuracy for wide range of computation vision tasks, it still faces challenges during industrial deployment due to its high computational complexity of inference. Low precision is one of the key techniques being actively studied recently to conquer the problem BID29 BID8 ; BID20 ; BID18 ; BID17 . With hardware acceleration support, low precision inference can compute more operations per second, reduce the memory access pressure and better utilize the cache, and deliver higher throughput and lower latency.Convolution is the primary operation in CNN models and it is a common practice to enable 8-bit low precision (INT8) inference for convolution in deep learning frameworks (e.g., TensorFlow, MXNet, and TensorRT). To make it work, convolution utilizes INT8 computation, which requires two scale factors for activation and weight, respectively. It is workable for standard convolution with single group and two groups BID13 . However, it does not work well for convolution with large groups, especially for depthwise convolution BID0 . In addition to direct convolution, it is worthwhile to explore INT8 Winograd convolution BID14 for better performance, which is absent in previous research 2 . Although recent work have demonstrated INT8 inference with minimal accuracy loss across various models BID29 BID4 ; ; BID11 , INT8 inference is limited due to more complex topology primarily introduced by sum operation in residual block and concatenation operation in inception block BID0 . Existing solutions need to convert the convolution output from INT8 to FP32, and apply the sum or concatenation operation on FP32. The sacrifice of memory bandwidth and frequent data conversion lead to considerable performance overhead and therefore limit the real deployment. Moreover, there is no systematical study of INT8 inference on various use cases, including image classification BID13 ; BID25 ; BID0 ; ), object detection Ren et al. (2015 ; BID1 ; BID15 , image segmentation BID16 ; BID15 , etc.In this paper, we present a general technique towards efficient INT8 inference of CNN models. We experiment the technique on top of a widely-used deep learning framework. To the best of our knowledge, our work is the first attempt to address the above problems. We summarize our contributions below:1. We provide a systematical approach to channel-wise quantization of convolution, which is essential to keep the accuracy for depthwise convolution. Top1 accuracy of INT8 inference on MobileNet-V1 and MobileNet-V2 is improved by 1.98% and 70.6%, respectively. 2. We explore the approach of INT8 Winograd convolution and present the calibration details that cannot be trivially derived from direct convolution. Our experiment on VGG-16 shows Top1 and Top5 accuracy loss with INT8 Winograd convolution is minimal within 0.30% and 0.25% from FP32 baseline, reducing from 5.31% and 3.38%, respectively. 3. We add the support of sum in residual block, concatenation in inception block, and convolution for classification. We also fuse the memory-bound operation convolution with a rectified linear unit (ReLU) BID19 and fold the parameters of batch normalization BID10 into convolution kernels. With topology-wise INT8 support, inference speed is greatly improved by data conversion reduction and memory saving. 4. To our knowledge, this is the first time such a systematic study is applied to and empirical result is reported on many CNN use cases and models. We develop a calibration tool that automatically generates optimized INT8 model from FP32 model without the need of fine-tuning or retraining for easy and repeatable deployment. We perform a comprehensive study on 18 widely-used CNN models and demonstrate the effectiveness of INT8 inference across a wide range of applications, including image classification, object detection, image segmentation, and super resolution. The inference throughput and latency are improved by 1.6X and 1.5X respectively, while the accuracy loss is minimal within 0.6% to no loss from FP32 baseline.We believe our methodology is general for CNN models and can provide the guide and reference on other frameworks. All the code and models will be publicly available soon.The rest of the paper is organized as follows, Section 2 discusses related work on low-precision inference in deep learning. Section 3 describes INT8 inference quantization approach and recipe for CNN models. Section 4 includes experimental results, comprehensive study, and related discussion. Finally, Section 5 concludes the summary with results and future directions. To align the model with best accuracy, the above performance in TAB2 does not include INT8 Winograd convolution. We expect to deliver similar performance improvement of Winograd on INT8 as FP32 BID14 during our development. Different from previous work BID29 BID26 , we also experiment the first convolution using INT8 than FP32, which shows reasonable accuracy within 1% loss.Our experimental results also demonstrate the impact of calibration process on accuracy with different sampling iteration, different calibration algorithm, or different scale factor mode. We summarize our findings: (1) Channel-wise scaling factors can always deliver better accuracy than single scale factor, especially for depthwise convolution; (2) Direct algorithm is more effective in most cases than KL, while KL algorithm can deliver better accuracy than FP32 baseline in some cases; and (3) More sampling iterations show more stable dynamic data rage and therefore better accuracy. How to select the optimal calibration strategy is an interesting topic as one of our future directions. In this paper, we propose the general recipe of INT8 inference and experiment the techniques on a widely-used deep learning framework. We develop an automatic calibration tool for optimized INT8 model generation and demonstrate the effectiveness on 18 CNN models across a wide range of use cases. The inference throughput and latency are improved by 1.6X and 1.5X respectively, while the accuracy loss is minimal within 0.6% to no loss from FP32 baseline. We believe our methodology is general for CNN models and can provide the guide and reference on other frameworks.",1478,0.821,833,1.7743097238895558,"High throughput low latency inference the deployment This paper a general technique toward 8-bit low precision inference 1) channel-wise scale factors weights especially depthwise convolution Winograd convolution We experiment the techniques on top The 8-bit optimized model automatically a calibration process from FP32 model without We perform a systematical and comprehensive study demonstrate 8-bit low precision inference across applications use super resolution We show the inference throughput and improved minimal within 0.6%1to no loss accuracy from FP32 baseline We believe the methodology can the guidance and reference design of 8-bit low precision inference other frameworks All the code models will publicly soon While shows state (SOTA accuracy wide range computation vision tasks still faces during industrial deployment of inference Low precision is being actively recently conquer BID29 BID8 ; With hardware acceleration support low precision inference compute more operations reduce the memory access pressure better utilize deliverConvolution the primary operation CNN models enableINT8 inference in ( MXNet To convolution utilizes INT8 computation requires two scale factors activation weight It workable standard convolution with single group BID13 . However work convolution with large groups depthwise convolution BID0 In addition direct convolution it worthwhile explore INT8 Winograd convolution BID14 for better performance absent previous research 2 Although recent work have INT8 inference minimal accuracy loss across various models BID29 BID4 ; ; INT8 limited due more complex topology primarily introduced sum operation residual block and concatenation operation inception block BID0 Existing solutions need convert the convolution output INT8 apply The sacrifice memory bandwidth frequent data conversion lead considerable performance overhead therefore limit the real deployment. Moreover no systematical study INT8 inference on various use cases image classification BID13 ; ), object detection Ren et (2015 ; BID1 BID15 , image segmentation BID16 etcIn a general technique towards efficient INT8 inference CNN models We experiment the technique top To our work address We summarize our contributions below:1 We provide a systematical approach channel-wise quantization convolution, essential keep for depthwise convolution Top1 accuracy INT8 inference on MobileNet-V1 and is improved 2 We explore the approach INT8 Winograd convolution and present the calibration details that trivially derived direct convolution Our experiment on VGG-16 shows Top1 Top5 accuracy loss INT8 Winograd convolution is minimal within from FP32 baseline reducing from 3 We add the support sum in residual block inception block convolution classification We also fuse the memory-bound operation convolution a rectified linear unitReLU) BID19 fold the parameters batch normalization BID10 With topology-wise INT8 support inference speed greatly data conversion reduction memory saving 4 To our knowledge is applied and empirical result many CNN use cases models We develop a calibration tool optimized INT8 model from FP32 model without for easy and repeatable deployment We perform 18 widely-used CNN models demonstrate INT8 inference across applications super resolution The inference throughput and improved the accuracy loss minimal within no loss from FP32 baselineWe believe our methodology general for CNN models the guide and reference on other frameworks All the code models will publicly soonThe rest organized Section discusses related work low-precision inference Section describes INT8 inference quantization approach recipe CNN models Section includes experimental results comprehensive study related discussion Finally Section concludes the summary with results and future directions To align the model best accuracy the above performance in TAB2 does INT8 Winograd convolution We expect deliver similar performance improvement of Winograd on INT8 as FP32 BID14 during Different previous work BID29 BID26 , we also experiment the first convolution using INT8 than FP32 shows reasonable accuracy within 1% lossOur experimental results also the impact calibration process accuracy with different sampling iteration different calibration algorithm or different scale factor mode We summarize: (1) Channel-wise scaling factors can always deliver especially depthwise convolution; Direct algorithm is KL, while KL algorithm FP32 baseline in show more stable dynamic data rage How select the optimal calibration strategy is as one our future directions In the general recipe INT8 inference experiment the techniques on We develop an automatic calibration tool optimized INT8 model generation demonstrate on 18 CNN models across The inference throughput and improved the accuracy loss minimal within no loss from FP32 baseline We believe our methodology general for CNN models can the guide reference on other frameworks",0.01,0.6769523160458971
"Recent approaches have successfully demonstrated the benefits of learning the parameters of shallow networks in hyperbolic space. We extend this line of work by imposing hyperbolic geometry on the embeddings used to compute the ubiquitous attention mechanisms for different neural networks architectures. By only changing the geometry of embedding of object representations, we can use the embedding space more efficiently without increasing the number of parameters of the model. Mainly as the number of objects grows exponentially for any semantic distance from the query, hyperbolic geometry  --as opposed to Euclidean geometry-- can encode those objects without having any interference. Our method shows improvements in generalization on neural machine translation on WMT'14 (English to German), learning on graphs (both on synthetic and real-world graph tasks) and visual question answering (CLEVR) tasks while keeping the neural representations compact. The focus of this work is to endow neural network representations with suitable geometry to capture fundamental properties of data, including hierarchy and clustering behaviour. These properties emerge in many real-world scenarios that approximately follow power-law distributions BID28 BID9 ). This includes a wide range of natural phenomena in physics BID23 , biology BID26 , and even human-made structures such as metabolic-mass relationships BID4 , social networks , and frequencies of words BID33 BID32 BID38 ).Complex networks , which connect distinguishable heterogeneous sets of elements represented as nodes, provide us an intuitive way of understanding these structures. They will also serve as our starting point for introducing hyperbolic geometry, which is by itself difficult to visualize. Nodes in complex networks are referred to as heterogeneous, in the sense that they can be divided into sub-nodes which are themselves distinguishable from each other. The scale-free structure of natural data manifests itself as a power law distribution on the node degrees of the complex network that describes it.Complex networks can be approximated with tree-like structures, such as taxonomies and dendrograms, and as lucidly presented by , hyperbolic spaces can be thought of as smooth trees abstracting the hierarchical organization of complex networks. Let us begin by recalling a simple property of n-ary trees that will help us understand hyperbolic space and why hyperbolic geometry is well suited to model relational data.In an n-ary tree, the number of nodes at distance r from the root and the number of nodes at distance no more than r from the root both grow as n r . Similarly, in a two-dimensional hyperbolic space with curvature −ζ 2 ,ζ > 0, the circumference and area of a disc of radius r grows as 2πsinh(ζr) and 2π(cosh(ζr)−1), respectively, both of are exponential in r BID20 . The growth of volume in hyperbolic space should be contrasted with Euclidean space where the corresponding quantities expand polynomially, circumference as 2πr and area as πr 2 .In the two-dimensional example of Figure 1 , the expanding rings show examples at a fixed semantic distance from the central object (""pug""). The number of concepts grows quickly with semantic distance forcing each successive ring to be more crowded in order to maintain a fixed distance to the center. In contrast, the extra volume of hyperbolic spheres (depicted by reducing the size of the examples) allows all of the examples to remain well separated from their semantic neighbours. Figure 1: An intuitive depiction of how images might be embedded in 2D. The location of the embeddings reflects the similarity between each image and that of a pug. Since the number of instances within a given semantic distance from the central object grows exponentially, the Euclidean space is not able to compactly represent such structure (left). In hyperbolic space (right) the volume grows exponentially, allowing for sufficient room to embed the images. For visualization, we have shrunk the images in this Euclidean diagram, a trick also used by Escher.Mechanically, the computed embeddings by a random network for objects at a given semantic distance might still seem epsilon distance away from each other (or crowded) as the ones obtained by using Euclidean geometry. However, enforcing hyperbolic geometry intuitively means that all operations with these embeddings take into account, the density in that particular region of the space. For example, any noise introduced in the system (e.g., in gradients) will also be corrected by the density. In contrast to working in Euclidean space , this means that the embeddings will be equally distinguishable regardless of the density.The intimate connection between hyperbolic space and scale free networks (where node degree follows a power law) is made more precise in . In particular, there it is shown that the heterogeneous topology implies hyperbolic geometry, and conversely hyperbolic geometry yields heterogeneous topology. Moreover, Sarkar (2011) describes a construction that embeds trees in two-dimensional hyperbolic space with arbitrarily low distortion, which is not possible in Euclidean space of any dimension BID24 . Following this exciting line of research, recently the machine learning community has gained interest in learning non-Euclidean embeddings directly from data BID29 BID7 BID34 BID30 BID39 BID5 .Fuelled by the desire of increasing the capacity of neural networks without increasing the number of trainable parameters so as to match the complexity of data, we propose hyperbolic attention networks. As opposed to previous approaches, which impose hyperbolic geometry on the parameters of shallow networks BID29 BID7 , we impose hyperbolic geometry on the activations of deep networks. This allows us to exploit hyperbolic geometry to reason about embeddings produced by deep networks. We introduce efficient hyperbolic operations to express the popular , ubiquitous mechanism of attention BID1 BID12 BID42 BID47 . Our method shows improvements in terms of generalization on neural machine translation BID42 , learning on graphs and visual question answering BID0 BID25 BID16 tasks while keeping the representations compact. Simultaneously to our work, BID8 proposed a method to learn SVMs in the hyperboloid model of hyperbolic space, and Nickel and Kiela (2018) proposed a method to learn shallow embeddings of graphs in hyperbolic space by using the hyperboloid model. We have presented a novel way to impose the inductive biases from hyperbolic geometry on the activations of deep neural networks. Our proposed hyperbolic attention operation makes use of hyperbolic geometry in both the computation of the attention weights, and in the aggregation operation over values. We implemented our proposed hyperbolic attention mechanism in both Relation Networks and the Transformer and showed that we achieve improved performance on a diverse set of tasks. We have shown improved performance on link prediction and shortest path length prediction in scale free graphs, on two visual question answering datasets, real-world graph transduction tasks and finally on English to German machine translation. The gains are particularly prominent in relatively small models, which confirms our hypothesis that hyperbolic geometry induces more compact representations.Yang and Rush (2016) have proposed to imposed the activations of the neural network to lie on a Lie-group manifold in the memory. Similarly as a future work, an interesting potential future direction is to use hyperbolic geometry as an inductive bias for the activation of neural networks in the memory.",1468,0.683,850,1.7270588235294118,"Recent approaches successfully demonstrated learning the parameters shallow networks We extend this line imposing hyperbolic geometry used compute the ubiquitous attention mechanisms architectures By only changing the geometry embedding of object representations use more without parameters of Mainly as the number objects grows exponentially for any semantic distance the query hyperbolic geometry --as can encode without any interference Our method shows improvements generalization on neural machine translation on WMT'14English to learning graphsboth on visual question answeringCLEVR) tasks while keeping compact The focus endow neural network representations suitable geometry capture fundamental properties data hierarchy clustering behaviour These properties emerge that approximately follow power-law distributions BID28 BID9 ). This includes natural phenomena physics BID23 , even human-made structures metabolic-mass relationships social networks , frequencies words ).Complex networks , connect distinguishable heterogeneous sets elements represented nodes provide us They will serve our starting point introducing hyperbolic geometry by itself difficult visualize Nodes complex networks referred, in which themselves distinguishable The scale-free structure natural data manifests a power law distribution on the node degrees the complex network that describesComplex networks as lucidly presented , hyperbolic spaces can thought smooth trees abstracting the hierarchical organization Let recalling a simple property n-ary trees will hyperbolic space why well model relational dataIn at distance r from and no more both grow n r Similarly curvature −�� 2�� > the circumference area a disc radius r grows 2πsinh(r 2π(cosh( both are exponential r BID20 The growth volume hyperbolic space should contrasted the corresponding quantities expand circumference as 2πr area 2 .In two example Figure the expanding rings show examples at a fixed semantic distance the central object (""pug The number concepts grows quickly semantic distance forcing each successive ring crowded In contrast the extra volume hyperbolic spheresdepicted reducing the examples allows all remain well separated their semantic neighbours Figure An intuitive depiction images might embedded 2D. The location the embeddings reflects the similarity each image a pug Since the number instances within a given semantic distance the central object grows not able compactly such structure (left In hyperbolic spaceright the volume grows allowing sufficient room embed the images For visualization shrunk this Euclidean diagram a trick also EscherMechanically the computed embeddings by a random network for objects at a given semantic distance might still seem epsilon distance away crowded the ones obtained using However enforcing hyperbolic geometry intuitively means all operations with these embeddings take into, the density in that particular region For example any noise introduced ( in gradients also corrected the density In contrast working Euclidean space , means will equally distinguishable regardlessThe intimate connection scale free networkswhere node degree follows made precise . In particular it shown implies hyperbolic geometry yields Moreover Sarkar (2011 describes a construction embeds trees arbitrarily low distortion of BID24 . Following this exciting line recently the machine learning community gained interest learning directly data BID29 BID7 BID34 BID30 BID39 BID5 .Fuelled increasing without increasing trainable parameters so match hyperbolic attention networks As opposed previous approaches which impose hyperbolic geometry the parameters shallow networks BID29 BID7 impose the activations This allows exploit hyperbolic geometry reason embeddings produced deep networks We introduce efficient hyperbolic operations express the popular , ubiquitous mechanism attention BID1 BID12 BID42 BID47 Our method shows improvements terms generalization on neural machine translation BID42 , learning on graphs visual question answering BID0 BID25 BID16 tasks while keeping the representations compact Simultaneously to our work BID8 proposed learn SVMs the hyperboloid model Nickel Kiela2018 shallow embeddings graphs by We presented impose the inductive biases from hyperbolic geometry the activations Our proposed hyperbolic attention operation makes both the computation the attention weights the aggregation operation over values We implemented our proposed hyperbolic attention mechanism both Relation Networks the Transformer and showed achieve improved performance We shown improved performance link prediction shortest path length prediction scale free graphs on two visual question answering datasets real-world graph transduction tasks finally English to German machine translation The gains particularly prominent relatively small models confirms hyperbolic geometry induces more compact representationsYang Rush to imposed the activations lie a Lie-group manifold the memory. Similarly as a future work an interesting potential future direction hyperbolic geometry an inductive bias for the activation the memory",0.01,0.5565611733469639
"We present a method for evaluating the sensitivity of deep reinforcement learning (RL) policies. We also formulate a zero-sum dynamic game for designing robust deep reinforcement learning policies. Our approach mitigates the brittleness of policies when agents are trained in a simulated environment and are later exposed to the real world where it is hazardous to employ RL policies. This framework for training deep RL policies involve a zero-sum  dynamic game against an adversarial agent, where the goal is to drive the system dynamics to a saddle region. Using a variant of the guided policy search algorithm, our agent learns to adopt robust policies that require less samples for learning the dynamics and performs better than the GPS algorithm. Without loss of generality, we demonstrate that deep RL policies trained in this fashion will be maximally robust to a ``worst"" possible adversarial disturbances. Deep reinforcement learning (RL) for complex agent behavior in realistic environments usually combines function approximation techniques with learning-based control. A good RL controller should guarantee fulfillment of performance specifications under external disturbances, or modeling errors. Quite often in practice, however, this is not the case -with deep RL policies not often generalizing well to real-world scenarios. This can be attributed to the inherent differences between the training and testing environments. Recently, there have been efforts at integrating function approximation techniques with learning-based control, in an end-to-end fashion, in order to have systems that optimize objectives while guaranteeing generalization to environmental uncertainties. Examples include trajectory-based optimization for known dynamics ( BID16 BID25 ), or trajectory optimization for unknown dynamics such as guided policy search algorithms BID0 BID13 BID15 .While these methods produce performance efficiency for agent tasks in the real world, there are sensitivity questions of such policies that need to be addressed such as, how to guarantee maximally robust deep RL policies in the presence of external disturbances, or modeling errors. A typical approach employed in minimizing sample inefficiency is to engineer an agent's policy in a simulated environment, and later transfer such policies to physical environments. However, questions of robustness persist in such scenarios as the agent often has to cope with modeling errors and new sensory inputs from a different environment. For continuous control tasks, learned policies may become brittle in the presence of external perturbations, or a slight change in the system dynamics may significantly affect the performance of the learned controller BID20 -defeating the purpose of having a robust policy that is learned through environmental interaction .The contribution of this paper is two-fold:• first, we provide a framework that demonstrates the brittleness of a state-of-the-art deep RL policy; specifically, given a trained RL policy, we pose an adversarial agent against the fixed trained policy; the goal is to perturb the parameter space of the learned policy. We demonstrate that the most sophisticated deep policies fail in the presence of adversarial perturbations.• second, we formulate an iterative dynamic zero-sum, two player game, where each agent executes an opposite reaction to its pair: a concave-convex problem follows explicitly, and our goal is to achieve a saddle point equilibrium, where the state is everywhere defined but possibly infinite-valued).Noting that lack of generalization of learned reward functions to the real-world can be thought of as external disturbance that perturb the system dynamics, we formulate the learning of robust control policies as a zero-sum two player Markov game -an iterative dynamic game (iDG) -that pits an adversarial agent against a protagonist agent.The controller aims to minimize a given cost while the second agent, an adversary aims to maximize the given cost in the presence of an additive disturbance. We run the algorithm in finite episodic settings and show a dynamic game approach aimed at generating policies that are maximally robust.The content of this paper is thus organized: we review relevant literature to our contribution in Sec. 2; we then provide an H ∞ background in Sec. BID2 . This H ∞ technical introduction will be used in formulating the design of perturbation signals in Sec. BID3 . Without loss of generality, we provide a formal treatment of the iDG algorithm within the guided policy search framework in Sec. 5. Experimental evaluation on multiple robots is provided in Sec. 6 followed by conclusions in Sec. 7. We have evaluated the sensitivity of select deep reinforcement learning algorithms and shown that despite the most carefully designed policies, such policies implemented on real-world agents exhibit a potential for disastrous performances when unexpected such as when there exist modeling errors and discrepancy between training environment and real-world roll-outs (as evidenced by the results from the two dynamics the agent faces in our sensitivity experiment). We then test the dynamic trajectory optimization two-player algorithm on a robot motor task using Levine et al's BID13 's guided policy search algorithm. In our implementation of the dynamic game algorithm, we focus on the robustness parameters that cause the robot's policy to fail in the presence of the erstwhile sensysensitivity parameter. We demonstrate that our two-player game framework allows agents operating under nonlinear dynamics to learn the underlying dynamics under significantly more finite samples than vanilla GPS algorithm does -thus improving upon the Gaussian model mixture method used in BID0 and BID13 .Having agents that are robust to unmodeled nonlinearities, dynamics, and high frequency modes in a nonlinear dynamical system has long been a fundamental question that control theory strives to achieve. To the best of our knowledge, we are not aware of other works that addresses the robustness of deep policies that are trained end-to-end from a maximal robustness perspective. In future work, we hope to replace the crude Gaussian Mixture Model for the dynamics with a more sophisticated nonlinear model, and evaluate how the agent behaves in the presence of unknown dynamics.",1143,0.557,658,1.737082066869301,"We present evaluating deep reinforcement learning (RL) policies. We also formulate designing robust deep reinforcement learning policies Our approach mitigates policies when agents trained are later where hazardous employ RL policies This framework for training deep RL policies involve against drive the system dynamics a saddle region Using a variant the guided policy search algorithm our agent adopt robust policies require less samples learning the dynamics performs the GPS algorithm Without loss demonstrate deep RL policies trained this fashion maximally robust a ``worst"" possible adversarial disturbances Deep reinforcement learningRL complex agent behavior realistic environments usually combines function approximation techniques A good RL controller guarantee fulfillment performance specifications under external disturbances modeling errors Quite practice however -with deep RL policies not often generalizing well This can attributed the inherent differences the training and testing environments Recently there efforts integrating function approximation techniques learning-based control end have systems optimize objectives while guaranteeing environmental uncertainties Examples include trajectory-based optimization known dynamics ( BID16 BID25 or trajectory optimization such guided policy search algorithms BID0 .While produce performance efficiency for agent tasks sensitivity questions of such policies such guarantee maximally robust deep RL policies external disturbances modeling errors A typical approach employed minimizing sample inefficiency engineer an agent's policy in later transfer physical environments However questions robustness persist such scenarios the agent often cope modeling errors new sensory inputs For continuous control tasks learned policies become brittle a slight change significantly the learned controller BID20 -defeating the purpose having a robust policy learned through environmental interaction .The contribution two first demonstrates state deep RL policy specifically given a trained RL policy pose an adversarial agent against the fixed trained policy the goal perturb the parameter space We demonstrate the most sophisticated deep policies fail adversarial perturbations.• second formulate, two player game executes an opposite reaction its pair: follows explicitly our goal achieve a saddle point equilibrium everywhere defined but possibly infinite-valued).Noting lack learned reward functions to can thought external disturbance that the system dynamics formulate the learning robust control policies (iDG pits a protagonist agentThe controller aims minimize a given cost while, aims in an additive disturbance We run the algorithm finite episodic settings show a dynamic game approach aimed generating policies robustThe content thus organized: review our contribution Sec. 2; we then provide an H �� background Sec BID2 . This H �� technical introduction formulating perturbation signals Sec BID3 . Without loss provide a formal treatment the iDG algorithm within the guided policy search framework in Sec 5 Experimental evaluation on multiple robots provided Sec 6 followed conclusions in Sec 7 We evaluated select deep reinforcement learning algorithms shown despite the most carefully designed policies such policies implemented exhibit a potential disastrous performances unexpected such as when there exist modeling errors discrepancy training environmentas evidenced the two dynamics the agent faces our sensitivity experiment We then test the dynamic trajectory optimization two-player algorithm a robot motor task Levine et al's BID13 's guided policy search algorithm In our implementation the dynamic game algorithm focus the robustness parameters cause the robot's policy fail the erstwhile sensysensitivity parameter We demonstrate our two-player game framework agents operating nonlinear dynamics learn under significantly more finite samples vanilla GPS algorithm does -thus upon the Gaussian model mixture method BID0 BID13 .Having agents robust dynamics high frequency modes in has control theory strives achieve To other works addresses the robustness deep policies trained end from a maximal robustness perspective In future work replace the crude Gaussian Mixture Model for the dynamics with evaluate the agent unknown dynamics",0.01,0.5820995167444708
"Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we provide a quantitative analysis of the robustness of classifiers to universal perturbations, and draw a formal link between the robustness to universal perturbations, and the geometry of the decision boundary. Specifically, we establish theoretical bounds on the robustness of classifiers under two decision boundary models (flat and curved models). We show in particular that the robustness of deep networks to universal perturbations is driven by a key property of their curvature: there exist shared directions along which the decision boundary of deep networks is systematically positively curved. Under such conditions, we prove the existence of small universal perturbations. Our analysis further provides a novel geometric method for computing universal perturbations, in addition to explaining their properties. Despite the success of deep neural networks in solving complex visual tasks BID11 ; BID15 , these classifiers have recently been shown to be highly vulnerable to perturbations in the input space. In BID24 , state-of-the-art classifiers are empirically shown to be vulnerable to universal perturbations: there exist very small imageagnostic perturbations that cause most natural images to be misclassified. The existence of universal perturbation is further shown in Hendrik BID12 to extend to other visual tasks, such as semantic segmentation. Universal perturbations fundamentally differ from the random noise regime, and exploit essential properties of deep networks to misclassify most natural images with perturbations of very small magnitude. Why are state-of-the-art classifiers highly vulnerable to these specific directions in the input space? What do these directions represent? To answer these questions, we follow a theoretical approach and find the causes of this vulnerability in the geometry of the decision boundaries induced by deep neural networks. For deep networks, we show that the key to answering these questions lies in the existence of shared directions (across different datapoints) along which the decision boundary is highly curved. This establishes fundamental connections between geometry and robustness to universal perturbations, and thereby reveals new properties of the decision boundaries induced by deep networks.Our aim here is to derive an analysis of the vulnerability to universal perturbations in terms of the geometric properties of the boundary. To this end, we introduce two decision boundary models: 1) the locally flat model assumes that the first order linear approximation of the decision boundary holds locally in the vicinity of the natural images, and 2) the locally curved model provides a second order local description of the decision boundary, and takes into account the curvature information. We summarize our contributions as follows:• Under the locally flat decision boundary model, we show that classifiers are vulnerable to universal directions as long as the normals to the decision boundaries in the vicinity of natural images are correlated (i.e., they approximately span a low dimensional space). This result formalizes and proves some of the empirical observations made in BID24 .• Under the locally curved decision boundary model, the robustness to universal perturbations is instead driven by the curvature of the decision boundary; we show that the existence of shared directions along which the decision boundary is positively 1 curved implies the existence of very small universal perturbations.• We show that state-of-the-art deep nets remarkably satisfy the assumption of our theorem derived for the locally curved model: there actually exist shared directions along which the decision boundary of deep neural networks are positively curved. Our theoretical result consequently captures the large vulnerability of state-of-the-art deep networks to universal perturbations.• We finally show that the developed theoretical framework provides a novel (geometric) method for computing universal perturbations, and further explains some of the properties observed in BID24 (e.g., diversity, transferability) regarding the robustness to universal perturbations. In this paper, we analyzed the robustness of classifiers to universal perturbations, under two decision boundary models: Locally flat and curved. We showed that the first are not robust to universal directions, provided the normal vectors in the vicinity of natural images are correlated. While this model explains the vulnerability for e.g., linear classifiers, this model discards the curvature information, which is essential to fully analyze the robustness of deep nets to universal perturbations. The second, classifiers with curved decision boundaries, are instead not robust to universal perturbations, provided the existence of a shared subspace along which the decision boundary is positively curved (for most 7 We used m = 1 in this experiment as the matrix H is prohibitively large for ImageNet. Figure 9 : Diversity of universal perturbations randomly sampled from the subspace S c . The normalized inner product between two perturbations is less than 0.1. directions). We empirically verify this assumption for deep nets. Our analysis hence explains the existence of universal perturbations, and further provides a purely geometric approach for computing such perturbations, in addition to explaining properties of perturbations, such as their diversity.Other authors have focused on the analysis of the robustness properties of SVM classifiers (e.g., BID33 ) and new approaches for constructing robust classifiers (based on robust optimization) Caramanis et al. FORMULA2 ; BID16 . More recently, some have assessed the robustness of deep neural networks to different regimes such as adversarial perturbations BID29 ; BID1 , random noise , and occlusions BID28 BID5 . The robustness of classifiers to adversarial perturbations has been specifically studied in BID29 ; BID8 ; ; BID2 ; BID0 , followed by works to improve the robustness BID20 ; BID10 BID26 ; BID3 , and attempts at explaining the phenomenon in BID8 ; BID6 ; BID30 ; BID31 . This paper however differs from these previous works as we study universal (imageagnostic) perturbations that can fool every image in a dataset, as opposed to image-specific adversarial perturbations that are not universal across datapoints (as shown in BID24 ). Moreover, explanations that hinge on the output of a deep network being well approximated by a linear function of the inputs f (x) = W x + b are inconclusive, as the assumption is violated even for relatively small networks. We show here that it is precisely the large curvature of the decision boundary that causes vulnerability to universal perturbations. Our bounds indeed show an increasing vulnerability with respect to the curvature of the decision boundary, and represent up to our knowledge the first quantitative result showing tight links between robustness and curvature. In addition, we show empirically that the first-order approximation of the decision boundary is not sufficient to explain the high vulnerability to universal perturbations ( Fig. 7 (b) ). Recent works have further proposed new methods for computing universal perturbations Mopuri et al. FORMULA2 ; BID14 ; instead, we focus here on an analysis of the phenomenon of vulnerability to universal perturbations, while also providing a constructive approach to compute universal perturbations leveraging our curvature analysis. Finally, it should be noted that recent works have studied properties of deep networks from a geometric perspective (such as their expressivity BID27 ; BID22 ); our focus is different in this paper as we analyze the robustness with the geometry of the decision boundary.Our analysis hence shows that to construct classifiers that are robust to universal perturbations, it is key to suppress this subspace of shared positive directions, which can possibly be done through regularization of the objective function. This will be the subject of future works.",1485,0.712,844,1.759478672985782,"Deep networks recently shown vulnerable universal perturbations: there exist most natural images misclassified such classifiers In this paper provide classifiers universal perturbations draw a formal link to the geometry the decision boundary Specifically establish theoretical bounds classifiers under two decision boundary modelsflat and curved models We show in particular deep networks to universal perturbations driven a key property their curvature there exist shared directions along the decision boundary systematically positively curved Under such conditions we prove small universal perturbations Our analysis further provides a novel geometric method computing universal perturbations addition explaining Despite deep neural networks solving BID11 ; these classifiers recently vulnerable the input space In BID24 , state classifiers empirically shown vulnerable universal perturbations: there exist very small imageagnostic perturbations most natural images misclassified The existence universal perturbation further shown Hendrik BID12 to extend other visual tasks semantic segmentation Universal perturbations fundamentally differ the random noise regime exploit essential properties deep networks misclassify most natural images with Why stateof classifiers highly vulnerable these specific directions in the input space What these directions represent To answer follow and find the causes this vulnerability the geometry the decision boundaries induced For deep networks show the key answering the existence shared directions (across along the decision boundary highly curved This establishes fundamental connections geometry robustness to universal perturbations thereby reveals new properties the decision boundaries induced deep networksOur aim derive an analysis the vulnerability terms To this end introduce two decision boundary models 1) the locally flat model assumes the first order linear approximation holds locally the natural images provides a second order local description takes We summarize our contributions as Under the locally flat decision boundary model show classifiers vulnerable universal directions as the normals to in the vicinity natural images correlated approximately span a low dimensional space This result formalizes and proves some the empirical observations BID24 .• Under the locally curved decision boundary model to instead driven; we the existence shared directions along which positively 1 curved implies very universal state deep nets remarkably satisfy our theorem derived for: there actually of deep neural networks are Our theoretical result consequently captures the large vulnerability state deep networks universal perturbations.• finally the developed theoretical framework computing further explains some observed BID24 ( diversity transferability regarding to In this paper analyzed classifiers universal perturbations under two decision boundary models Locally flat curved We showed first are not robust universal directions provided the normal vectors in the vicinity natural images correlated While this model explains the vulnerability for, linear classifiers discards the curvature information essential fully analyze deep nets to universal perturbations second, classifiers with curved decision boundaries instead not robust universal perturbations provided the existence a shared subspace along positively curvedfor most 7 We used m in as the matrix H prohibitively ImageNet Figure 9 : Diversity universal perturbations randomly the subspace S c The normalized inner product between less directions We empirically verify for deep nets Our analysis hence explains universal perturbations further a purely geometric approach computing explaining properties their diversityOther authors focused the analysis the robustness properties SVM classifiers (e.g., BID33 ) new approaches constructingbased robust optimization Caramanis FORMULA2 ; BID16 . More recently some assessed deep neural networks different regimes such BID29 ; BID1 random noise , occlusions The robustness classifiers to specifically studied BID29 ; BID8 ; ; followed works to BID20 BID26 attempts explaining the phenomenon This paper however differs these previous works as we study universal (imageagnostic) perturbations that fool every image universal acrossas BID24 Moreover explanations hinge the output a deep network being well approximated f = W are inconclusive the assumption violated even for We show here it precisely the large curvature the decision boundary vulnerability universal perturbations Our bounds indeed show an increasing vulnerability with the curvature the decision boundary represent up our knowledge the first quantitative result showing tight links robustness In addition show empirically the decision boundary the high vulnerability universal perturbations Fig 7 (b ). Recent works further proposed new methods computing universal perturbations Mopuri FORMULA2 ; BID14 instead focus here an analysis the phenomenon vulnerability universal perturbations while a constructive approach compute leveraging our curvature analysis Finally should recent works studied properties deep networks fromsuch their expressivity BID27 ; BID22 our focus different analyze with the geometry the decision boundaryOur analysis hence to construct classifiers universal perturbations key suppress this subspace shared positive directions possibly done regularization the objective function This will the subject future works",0.01,0.6391641013849666
"Behavioral skills or policies for autonomous agents are conventionally learned from reward functions, via reinforcement learning, or from demonstrations, via imitation learning. However, both modes of task specification have their disadvantages: reward functions require manual engineering, while demonstrations require a human expert to be able to actually perform the task in order to generate the demonstration. Instruction following from natural language instructions provides an appealing alternative: in the same way that we can specify goals to other humans simply by speaking or writing, we would like to be able to specify tasks for our machines. However, a single instruction may be insufficient to fully communicate our intent or, even if it is, may be insufficient for an autonomous agent to actually understand how to perform the desired task. In this work, we propose an interactive formulation of the task specification problem, where iterative language corrections are provided to an autonomous agent, guiding it in acquiring the desired skill. Our proposed language-guided policy learning algorithm can integrate an instruction and a sequence of corrections to acquire new skills very quickly. In our experiments, we show that this method can enable a policy to follow instructions and corrections for simulated navigation and manipulation tasks, substantially outperforming direct, non-interactive instruction following. Behavioral skills or policies for autonomous agents are typically specified in terms of reward functions (in the case of reinforcement learning) or demonstrations (in the case of imitation learning). However, both reward functions and demonstrations have downsides as mechanisms for communicating goals. Reward functions must be engineered manually, which can be challenging in real-world environments, especially when the learned policies operate directly on raw sensory perception. Sometimes, simply defining the goal of the task requires engineering the very perception system that end-to-end deep learning is supposed to acquire. Demonstrations sidestep this challenge, but require a human demonstrator to actually be able to perform the task, which can be cumbersome or even impossible. When humans must communicate goals to each other, we often use language. Considerable research has also focused on building autonomous agents that can follow instructions provided via language BID7 ; BID8 ). However, a single instruction may be insufficient to fully communicate the full intent of a desired behavior. For example, if we would like a robot to position an object on a table in a particular place, we might find it easier to guide it by telling it which way to move, rather than verbally defining a coordinate in space. Furthermore, an autonomous agent might be unable to deduce how to perform a task from a single instruction, even if it is very precise. In both cases, interactive and iterative corrections can help resolve confusion and ambiguity, and indeed humans often employ corrections when communicating task goals to each other.In this paper, our goal is to enable an autonomous agent to accept instructions and then iteratively adjust its policy by incorporating interactive corrections (illustrated in Figure 1 ). This type of in-theloop supervision can guide the learner out of local optima, provide fine-grained task definition, and is natural for humans to provide to the agent. As we discuss in Section 2, iterative language corrections can be substantially more informative than simpler forms of supervision, such as preferences, while being substantially easier and more natural to provide than reward functions or demonstrations.Figure 1: An example where corrections disambiguate an instruction. The agent is unable to fully deduce the user's intent from the instruction alone and iterative language corrections guide the agent to the correct position. Our method is concerned with meta-learning policies that can ground language corrections in their environment and use them to improve through iterative feedback.In order to effectively use language corrections, the agent must be able to ground these corrections to concrete behavioral patterns. We propose an end-to-end algorithm for grounding iterative language corrections by using a multi-task setup to meta-train a model that can ingest its own past behavior and a correction, and then correct its behavior to produce better actions. During a meta-training phase, this model is iteratively retrained on its own behavior (and the corresponding correction) on a wide distribution of known tasks. The model learns to correct the types of mistakes that it actually tends to make in the world, by interpreting the language input. At meta-test time, this model can then generalize to new tasks, and learn those tasks quickly through iterative language corrections.The main contributions of our work are the formulation of guided policies with language (GPL) via meta-learning, as well as a practical GPL meta-learning algorithm and model. We train on English sentences sampled from a hand-designed grammar as a first step towards real human-in-the-loop supervision. We evaluate our approach on two simulated tasks -multi-room object manipulation and robotic object relocation. The first domain involves navigating a complex world with partial observation, seeking out objects and delivering them to user-specified locations. The second domain involves controlling a robotic gripper in a continuous state and action space to move objects to precise locations in relation to other objects. This requires the policy to ground the corrections in terms of objects and places, and to control and correct complex behavior. We presented meta-learning for guided policies with language (GPL), a framework for interactive learning of tasks with in-the-loop language corrections. In GPL , the policy attempts successive trials in the environment, and receives language corrections that suggest how to improve the next trial over the previous one. The GPL model is trained via meta-learning, using a dataset of other tasks to learn how to ground language corrections in terms of behaviors and objects. While our method currently uses fake language, future work could incorporate real language at training time. To scale corrections to real-world tasks, it is vital to handle new concepts, in terms of actions or objects, not seen at training time. Approachs to handling these new concepts could be innovations at the model level, such as using meta-learning, or at the interface level, allowing humans to describe new objects to help the agent. It is possible to visualize failure cases, which illuminate the behavior of the algorithm on challenging tasks. In the failure case in FIG9 , we note that the agent is able to successfully enter the purple room, pickup the green ball, and exit. However, after it receives the fourth correction telling it to go to the green goal, it forgets to pick up the green ball. This behavior can likely be improved by varying corrections more at training time, and providing different corrections if an agent is unable to comprehend the first one.Additionally, we present a success case in Figure 9 , where the agent successfully learns to solve the task through iterative corrections, making further progress in each frame.",1308,0.691,756,1.7301587301587302,"Behavioral skills or policies for autonomous agents conventionally learned reward functions via demonstrations imitation learning However both modes task specification reward functions require manual engineering demonstrations a human expert be actually generate the demonstration Instruction following from natural language instructions provides an appealing alternative: in specify goals other humans simply speaking or would tasks our machines However a single instruction insufficient fully communicate our intent, an autonomous agent actually how In this work propose an interactive formulation the task specification problem iterative language corrections provided an autonomous agent guiding acquiring the desired skill Our proposed language-guided policy learning algorithm can integrate an instruction and corrections acquire very In our experiments show this method enable a policy follow instructions corrections simulated navigation and manipulation tasks substantially direct, instruction following Behavioral skills or policies for autonomous agents typically specified reward functionsin demonstrations imitation learning However both reward functions demonstrations downsides mechanisms communicating goals Reward functions must engineered manually challenging the learned policies operate directly raw sensory perception Sometimes simply defining the goal the task engineering the very perception system end-to deep acquire Demonstrations sidestep this challenge require a human demonstrator actually perform cumbersome or When humans must communicate goals Considerable research also focused building autonomous agents follow instructions provided via language BID7 ; However a single instruction insufficient fully communicate a desired behavior For example would a robot position an object find guide telling verbally defining a coordinate in space Furthermore an autonomous agent might unable perform a single instruction very precise In both cases interactive and iterative corrections resolve confusion ambiguity indeed humans employ corrections communicating task goalsIn our goal enable an autonomous agent accept instructions then its policy by incorporating ( This type intheloop supervision guide out local optima provide fine-grained task definition is natural humans provide to the agent As discuss Section iterative language corrections substantially informative simpler forms supervision preferences while being substantially natural provide reward functions demonstrationsFigure where corrections an instruction The agent unable fully deduce the instruction alone iterative language corrections guide Our method concerned meta-learning policies ground language corrections their environment use throughIn effectively the agent ground these corrections concrete behavioral patterns We propose end algorithm grounding iterative language corrections by a multi-task setup meta-train a model ingest its own past behavior a correction, correct better actions During a meta-training phase this model iteratively retrained its own behaviorand the corresponding correction on a wide distribution known tasks The model learns correct the types actually tends by interpreting the language input At meta-test time this model can then generalize new tasks learn quickly through iterative language correctionsThe main contributions the formulation guided policies with language (GPL via a practical GPL meta-learning algorithm and model We train on English sentences sampled a hand-designed grammar as real humanin supervision We evaluate our approach on two simulated tasks -multi-room object manipulation robotic object relocation The first domain involves navigating partial observation seeking objects delivering user-specified locations The second domain involves controlling a robotic gripper a continuous state and action space to move to precise locations relation This requires the policy ground the corrections terms objects places control and correct complex behavior We presented meta-learning for guided policies with language (GPL interactive learning tasks in language corrections In GPL , the policy attempts successive trials the environment receives language corrections suggest how the next trial over The GPL model trained via meta-learning using a dataset other tasks ground language corrections terms behaviors objects While our method currently fake language future work incorporate at training time To scale corrections real-world tasks it handle new concepts in actions or objects not seen at training time Approachs handling these new concepts could innovations at meta-learning at allowing humans describe new objects help the agent. It possible visualize failure cases illuminate the algorithm on challenging tasks In the failure case FIG9 note the agent successfully enter the purple room pickup However after it receives the fourth correction telling go the green goal forgets pick This behavior likely improved varying corrections more at training time providing different corrections if an agent unable comprehend first oneAdditionally we present a success case Figure 9 , successfully learns solve through iterative corrections making further progress each frame",0.01,0.5644594630836489
"Deep generative models such as Generative Adversarial Networks (GANs) and
 Variational Auto-Encoders (VAEs) are important tools to capture and investigate
 the properties of complex empirical data. However, the complexity of their inner
 elements makes their functionment challenging to assess and modify. In this
 respect, these architectures behave as black box models. In order to better
 understand the function of such networks, we analyze their modularity based on
 the counterfactual manipulation of their internal variables. Our experiments on the
 generation of human faces with VAEs and GANs support that modularity between
 activation maps distributed over channels of generator architectures is achieved
 to some degree, can be used to better understand how these systems operate and allow meaningful transformations of the generated images without further training.
 erate and edit the content of generated images. Deep generative models have proven powerful in learning to design realistic images in a variety of complex domains (handwritten digits, human faces, interior scenes). Complex neural architectures are now used to learn complex empirical data distributions by designing a non-linear function mapping a latent space to the space observations. In particular, two distinct approaches have recently emerged as state of the art: Generative Adversarial Networks (GANs) BID4 , and Variational Autoencoders (VAEs) BID8 BID17 . Such architectures relate to a question that work in Neuroscience and Computer vision have long since tried to address: the relation between an observed scene and its high level internal representation. This has been framed using two objects: (1) the mapping of a 3D scene to its perceived (2D) image, called forward optics, (2) the converse mapping, called inverse optics, (see e.g. BID7 ). Many computer vision algorithms have relied on inverse graphics approaches that model both forward and inverse optics simultaneously BID9 . In recent years, emphasis has been put on producing compact descriptions of the scene in terms of high level features reflecting a disentangled latent representation that can be mapped back to the image. However, the fundamental asymmetry between the structure of original forward and inverse optics mappings has received less attention. A key difference is that forward optics can be concisely described with a restricted set of equations taking into account physical parameters of the scene, while inverse optics does not have an explicit form and relies heavily on prior assumptions to be solved numerically. The simplicity of the forward optics may allow an agent to efficiently manipulate and update internal representations, for instance to plan interactions with the outside world, following a predictive coding principle BID16 . This supports that modularity of generative models should be assessed and enforced in order to understand and manipulate representations.Achieving this aim for deep architectures is challenging, because they mostly behave as black boxes, making it difficult for users to interact with the generative process. Indeed, we can act on how the network is trained (e.g. the optimized objective), what it learns to generate, but not on how the learned generative process operates. For example, to use a face generator to create a face combining the eyes of one generated face with remaining features of another one may be achieved by either additional training or complex manipulation of the network's input or output. Directly influencing the generative process learned by the network on the other hand is made difficult due to the complexity of the function class entailed by the networks' non-linearities and high dimensional parameter space. To grasp the properties of such a system, a possible approach is to intervene on parts of the architecture that implements the generative function. Ideally, the effect of such interventions on the output would be interpretable. This suggests we should uncover a modular structure in those architectures, such that each part of a network can be assigned a specific function.In this paper, we propose that modularity can be quantified and exploited in a causal framework to infer whether modules within the architecture can be further disentangled. This hypothesis relies on the general principle of Independence of Mechanisms stating that the various mechanisms involved in generating the observed data can be modified individually without affecting each other BID14 . It has been recently demonstrated that this principle can be applied to generative models encountered in machine learning BID0 . One key aspect of causality frameworks is to allow evaluating with counterfactuals how the outcome of a observed system would have changed, provided some variables would have taken different values. We use such counterfactuals to assess the role of specific internal variables in the overall functioning of trained deep generative models and uncover the modular structure of these systems. We start by introducing this perspective formally with the notion of intrinsic disentanglement, and show that it extends the classical notion of disentangled representation investigated in the deep learning literature. Then, we introduce tools to analyze this disentanglement in existing systems. We show empirically how VAEs and GANs trained on a human face dataset express a form of modularity with intermediate activation maps responsible for encoding different parts of the generated images.Related work. The issue of interpretability in convolutional neural networks has been the topic of intensive investigation. Most of that research however has focused on discriminative neural networks, not generative ones. In the discriminative case, efforts have been made to find optimal activation patterns for filters BID20 , BID2 ), to find correlation between intermediate feature space and data features BID3 , BID23 or to disentangle patterns detected by various filters to compute an explanatory graph BID22 . Furthermore, explicitly enforcing modularity in networks has been tried recently with Capsule networks architectures BID18 ), although Capsule network explicitly separate the architecture in different modules before training. A more detailed overview can found in review BID21 . It is important to emphasize discriminative and generative processes differ significantly, and working on generative processes allows to directly observe the effect of changes in intermediate representations on the generated picture rather than having to correlate it back input images. The recent InfoGAN network BID1 ) and other works BID11 ; BID9 ; BID5 ) in disentanglement of latent variables in generative models can be seen as what we define as extrinsic disentanglement. As such, we believe our intrinsic disentanglement perspective should be complementary with such approaches and are not in direct competition. Finally our approach relates to modularity and invariance principles formulated in the field of causality, in particular as formalized by BID0 . The purpose of this paper was to introduce a methodology to assess modularity in deep networks. Modularity may involve different aspects, and strongly depends on the nature of the modeled data. In this paper, we focused on features of the image that preferentially occur in specific parts of the generated images. This is a reasonable assumption for the CelebA dataset, given that the faces are spatially aligned. To some extent this is also true for the CIFAR10 dataset, where objects preferentially appear at the center of the image and the soil and sky in the background will be found at the bottom and top respectively. This approach may however have some limitations when looking at different datasets deprived from such spatial organization. In this case, capturing the structure of output variations induced by hybridization may require a more general approach. In principle, multidimensional technique such as Principal Component Analysis and non-linear generalizations may be able to characterize counterfactuals of each channels in order to further generate relevant modules following the steps described in the present work.Another aspect that is left to further work is how to optimize modularity in deep generative networks. We believe that classical (extrinsic) disentanglement approaches will not help, as they focus on the input of the network without control on its internal structure. While current generative models seem to exhibit some amount of modularity, improving it may require specific learning objectives as well as an appropriate choice of architectures.",1571,0.814,906,1.7339955849889626,"Deep generative models such Variational Auto-Encoders capture investigate complex empirical data However the complexity their inner elements their functionment challenging assess modify In this respect these architectures behave black box models In order better such networks analyze based the counterfactual manipulation their internal variables Our experiments the generation human faces VAEs GANs support that modularity between activation maps distributed channels generator architectures achieved to can better allow meaningful transformations without further training erate and edit generated images Deep generative models proven powerful learning design realistic images complex domains (handwritten digits interior scenes Complex neural architectures now learn complex empirical data distributions by designing mapping a latent space the space observations In particular two distinct approaches recently as state: Generative Adversarial Networks (GANs) BID4 , Such architectures relate a question work Neuroscience and Computer vision since tried the relation an observed scene its high level internal representation This has framed using two objects its perceived (2D) image called forward optics (2see e.g. BID7 Many computer vision algorithms relied inverse graphics approaches model both forward and inverse optics simultaneously BID9 . In emphasis producing compact descriptions the scene high level features reflecting a disentangled latent representation that mapped back However the fundamental asymmetry the structure original forward and inverse optics mappings received A key difference forward optics concisely a restricted set taking while does an explicit form relies prior assumptions solved numerically The simplicity the forward optics may allow an agent efficiently manipulate update internal representations for plan interactions following a predictive coding principle BID16 . This supports that modularity generative models should assessed enforced understand manipulate representationsAchieving for deep architectures challenging they mostly behave black boxes making users interact Indeed we act how the network trained (e.g. the optimized objective what generate but the learned generative process operates For example to use a face generator combining one generated face remaining features may achieved either additional training or complex manipulation Directly influencing the generative process learned the network on made difficult due the function class entailed the networks' non high dimensional parameter space To grasp the properties a possible approach intervene parts implements the generative function Ideally the effect such interventions the output would interpretable. This suggests we uncover a modular structure those architectures each part assignedIn exploited a causal framework infer whether modules within further This hypothesis relies the general principle Independence Mechanisms stating generating the observed data modified individually without each other BID14 . It recently demonstrated this principle generative models encountered machine BID0 . One key aspect causality frameworks allow evaluating with the outcome a observed system would provided some variables would taken different values We use such counterfactuals assess specific internal variables the overall functioning trained deep generative models uncover the modular structure We start introducing this perspective formally with show extends the classical notion investigated the deep learning literature Then we introduce tools analyze this disentanglement existing systems We show empirically VAEs GANs trained a human face dataset express a form modularity with intermediate activation maps responsible encoding different parts the generated imagesRelated work. The issue interpretability intensive investigation Most that research however discriminative neural networks not In the discriminative case efforts find optimal activation patterns filters BID20 , ), to correlation intermediate feature space data features or to patterns detected various filters to compute an explanatory graph Furthermore explicitly enforcing modularity networks tried recently Capsule networks architectures BID18 ), although explicitly separate in different modules before training A more detailed overview found review BID21 . It important emphasize discriminative and generative processes differ significantly, working allows directly observe changes intermediate representations the generated picture rather having correlate back input images The recent InfoGAN network BID1 ) and other works BID11 ; in disentanglement latent variables can what define As such believe our intrinsic disentanglement perspective complementary such approaches are in direct competition Finally our approach relates modularity and invariance principles formulated causality as formalized BID0 . The purpose introduce a methodology modularity deep networks Modularity may involve different aspects strongly the modeled data In focused features the image that occur specific parts the generated images This a reasonable assumption the CelebA dataset the faces spatially aligned To also the CIFAR10 dataset objects appear the soil sky in will found respectively This approach may however when looking different datasets deprived from such spatial organization In capturing the structure output variations induced hybridization may require In principle multidimensional technique such Principal Component Analysis non-linear generalizations may able characterize each channels further generate relevant modules followingAnother aspect left further work how optimize modularity deep generative networks We believe classical (extrinsic) disentanglement approaches will help, focus the input the network without control on While current generative models seem exhibit some amount improving it specific learning objectives as an appropriate choice architectures",0.01,0.5742354320887013
"Relational databases store a significant amount of the worlds data. However, accessing this data currently requires users to understand a query language such as SQL. We propose Seq2SQL, a deep neural network for translating natural language questions to corresponding SQL queries. Our model uses rewards from in the loop query execution over the database to learn a policy to generate the query, which contains unordered parts that are less suitable for optimization via cross entropy loss. Moreover, Seq2SQL leverages the structure of SQL to prune the space of generated queries and significantly simplify the generation problem. In addition to the model, we release WikiSQL, a dataset of 80654 hand-annotated examples of questions and SQL queries distributed across 24241 tables fromWikipedia that is an order of magnitude larger than comparable datasets. By applying policy based reinforcement learning with a query execution environment to WikiSQL, Seq2SQL outperforms a state-of-the-art semantic parser, improving execution accuracy from 35.9% to 59.4% and logical form accuracy from 23.4% to 48.3%. Relational databases store a vast amount of today's information and provide the foundation of applications such as medical records BID12 , financial markets BID3 , and customer relations management BID20 ). However, accessing relational databases requires an understanding of query languages such as SQL, which, while powerful, is difficult to master. Natural language interfaces (NLI), a research area at the intersection of natural language processing and human-computer interactions, seeks to provide means for humans to interact with computers through the use of natural language BID0 . We investigate one particular aspect of NLI applied to relational databases: translating natural language questions to SQL queries.Our main contributions in this work are two-fold. First, we introduce Seq2SQL, a deep neural network for translating natural language questions to corresponding SQL queries. Seq2SQL, shown in FIG0 , consists of three components that leverage the structure of SQL to prune the output space of generated queries. Moreover, it uses policy-based reinforcement learning (RL) to generate the conditions of the query, which are unsuitable for optimization using cross entropy loss due to their unordered nature. We train Seq2SQL using a mixed objective, combining cross entropy losses and RL rewards from in-the-loop query execution on a database. These characteristics allow Seq2SQL to achieve state-of-the-art results on query generation.Next, we release WikiSQL, a corpus of 80654 hand-annotated instances of natural language questions, SQL queries, and SQL tables extracted from 24241 HTML tables from Wikipedia. WikiSQL is an order of magnitude larger than previous semantic parsing datasets that provide logical forms along with natural language utterances. We release the tables used in WikiSQL both in raw JSON format as well as in the form of a SQL database. Along with WikiSQL, we release a query execution engine for the database used for in-the-loop query execution to learn the policy. On WikiSQL, Seq2SQL outperforms a previously state-of-the-art semantic parsing model by BID8 , which obtains 35.9% execution accuracy, as well as an augmented pointer network baseline, which obtains 53.3% execution accuracy. By leveraging the inherent structure of We proposed Seq2SQL, a deep neural network for translating questions to SQL queries. Our model leverages the structure of SQL queries to reduce the output space of the model. To train Seq2SQL, we applied in-the-loop query execution to learn a policy for generating the conditions of the SQL query, which is unordered and unsuitable for optimization via cross entropy loss. We also introduced WikiSQL, a dataset of questions and SQL queries that is an order of magnitude larger than comparable datasets. Finally, we showed that Seq2SQL outperforms a state-of-the-art semantic parser on WikiSQL, improving execution accuracy from 35.9% to 59.4% and logical form accuracy from 23.4% to 48.3%.",797,0.411,458,1.740174672489083,"Relational databases store the worlds data However accessing currently users understand a query language such We propose Seq2SQL translating natural language questions corresponding Our model uses rewards in the loop query execution over learn a policy generate the query contains unordered parts less suitable optimization via cross entropy loss Moreover Seq2SQL leverages the structure SQL prune the space generated queries significantly simplify the generation problem In addition the model release WikiSQL a dataset 80654 hand-annotated examples questions SQL queries distributed 24241 tables fromWikipedia that an order comparable datasets By applying policy based reinforcement learning with a query execution environment to WikiSQL Seq2SQL outperforms a state semantic parser improving execution accuracy from logical form accuracy Relational databases store today's information provide the foundation applications BID12 , financial markets customer relations management However accessing relational databases requires query languages, powerful difficult Natural language interfaces a research area the intersection seeks means humans natural language BID0 . We investigate one particular aspect NLI applied relational translating natural language questionsOur main contributions in two First introduce Seq2SQL translating natural language questions corresponding Seq2SQL, shown FIG0 consists three components that leverage to prune the output space generated queries Moreover uses policy-based reinforcement learningRL generate the conditions the query unsuitable optimization using cross entropy loss due their unordered nature We train Seq2SQL using a mixed objective combining cross entropy losses RL rewards from in query on These characteristics allow Seq2SQL achieve state results query generationNext release WikiSQL a corpus 80654 hand-annotated instances natural language questions SQL queries SQL tables extracted 24241 HTML tables Wikipedia WikiSQL an order previous semantic parsing datasets that provide logical forms along natural language utterances We release the tables used WikiSQL both raw JSON format Along WikiSQL release a query execution engine used in to learn the policy. On WikiSQL Seq2SQL outperforms a previously state semantic parsing model BID8 , obtains 35.9% execution accuracy as an augmented pointer network baseline By leveraging the inherent structure We proposed Seq2SQL translating questions Our model leverages the structure SQL reduce the output space To train Seq2SQL applied in query learn a policy generating the conditions unordered unsuitable optimization via cross entropy loss We also introduced WikiSQL a dataset questions SQL an order comparable datasets Finally showed Seq2SQL outperforms a state semantic parser on WikiSQL improving execution accuracy from logical form",0.01,0.5899792041503163
"We introduce Explainable Adversarial Learning, ExL, an approach for training neural networks that are intrinsically robust to adversarial attacks. We find that the implicit generative modeling of random noise with the same loss function used during posterior maximization, improves a model's understanding of the data manifold furthering adversarial robustness. We prove our approach's efficacy and provide a simplistic visualization tool for understanding adversarial data, using Principal Component Analysis. Our analysis reveals that adversarial robustness, in general, manifests in models with higher variance along the high-ranked principal components. We show that models learnt with our approach perform remarkably well against a wide-range of attacks. Furthermore, combining ExL with state-of-the-art adversarial training extends the robustness of a model, even beyond what it is adversarially trained for, in both white-box and black-box attack scenarios. Despite surpassing human performance on several perception tasks, Machine Learning (ML) models remain vulnerable to adversarial examples: slightly perturbed inputs that are specifically designed to fool a model during test time BID2 BID29 BID6 BID23 . Recent works have demonstrated the security danger adversarial attacks pose across several platforms with ML backend such as computer vision BID29 BID6 BID22 BID15 BID19 , malware detectors BID16 BID33 BID7 BID10 and gaming environments BID11 BID1 . Even worse, adversarial inputs transfer across models: same inputs are misclassified by different models trained for the same task, thus enabling simple Black-Box (BB) 1 attacks against deployed ML systems .Several works BID14 BID24 BID3 demonstrating improved adversarial robustness have been shown to fail against stronger attacks BID0 . The state-of-the-art approach for BB defense is ensemble adversarial training that augments the training dataset of the target model with adversarial examples transferred from other pre-trained models BID30 . BID21 showed that models can even be made robust to White-Box (WB) 1 attacks by closely maximizing the model's loss with Projected Gradient Descent (PGD) based adversarial training. Despite this progress, errors still appear for perturbations beyond what the model is adversarially trained for BID27 .There have been several hypotheses explaining the susceptibility of ML models to such attacks. The most common one suggests that the overly linear behavior of deep neural models in a high dimensional input space causes adversarial examples BID6 BID20 . Another hypothesis suggests that adversarial examples are off the data manifold BID28 BID18 . Combining the two, we infer that excessive linearity causes models to extrapolate their behavior beyond the data manifold yielding pathological results for slightly perturbed inputs. A question worth asking here is: Can we improve the viability of the model to generalize better on such out-of-sample data?In this paper, we propose Explainable Adversarial Learning (ExL), wherein we introduce multiplicative noise into the training inputs and optimize it with Stochastic Gradient Descent (SGD) while minimizing the overall cost function over the training data. Essentially, the input noise (randomly initialized at the beginning) is gradually learnt during the training procedure. As a result, the noise approximately models the input distribution to effectively maximize the likelihood of the class labels given the inputs. FIG0 shows the input noise learnt during different stages of training by a simple convolutional network (ConvN et2 architecture discussed in Section 3 below), learning handwritten digits from MNIST dataset BID17 . We observe that the noise gradually transforms and finally assumes a shape that highlights the most dominant features in the MNIST training data. For instance, the MNIST images are centered digits on a black background. Noise, in fact, learnt this centered characteristic . This suggests that the model not only finds the right prediction but also the right explanation. Noise inculcates this explainable behavior by discovering some knowledge about the input/output distribution during training. FIG0 shows the noise learnt with ExL on colored CIFAR10 images BID13 ) (on ResNet18 architecture BID8 ), which reveals that noise template (also RGB) learns prominent color blobs on a greyish-black background, that de-emphasizes background pixels. A recent theory BID4 suggests that adversarial examples (off manifold misclassified points) occur in close proximity to randomly chosen inputs on the data manifold that are, in fact, correctly classified. With ExL, we hypothesize that the model learns to look in the vicinity of the onmanifold data points and thereby incorporate more out-of-sample data (without using any direct data augmentation) that, in turn, improves its generalization capability in the off-manifold input space. We empirically evaluate this hypothesis by visualizing and studying the relationship between the adversarial and the clean inputs using Principal Component Analysis (PCA). Examining the intermediate layer's output, we discover that models exhibiting adversarial robustness yield significantly lower distance between adversarial and clean inputs in the Principal Component (PC) subspace.We further harness this result to establish that ExL noise modeling, indeed, acquires an improved realization of the input/output distribution characteristics that enables it to generalize better. To further substantiate our hypothesis, we also show that ExL globally reduces the dimensionality of the space of adversarial examples BID31 . We evaluate our approach on classification tasks such as MNIST, CIFAR10 and CIFAR100 and show that models trained with ExL are extensively more adversarially robust. We also show that combining ExL with ensemble/PGD adversarial training significantly extends the robustness of a model, even beyond what it is adversarially trained for, in both BB/WB attack scenarios. We proposed Explainable Adversarial Learning, ExL, as a reliable method for improving adversarial robustness. Specifically, our key findings are: 1) We show that noise modeling at the input during discriminative training improves a model's ability to generalize better for out-of-sample adversarial data (without explicit data augmentation). 2) Our PCA variance and cosine distance analysis provides a significant perspective to visualize and quantify a model's response to adversarial/clean data.A crucial question one can ask is, How to break ExL defense? The recent work BID0 shows that many defense methods cause 'gradient masking' that eventually fail. We reiterate that, ExL alone does not give a strong BB/WB defense. However, the smoothening effect of noise modeling on the loss FIG3 suggests that noise modeling decreases the magnitude of the gradient masking effect. ExL does not change the classification model that makes it easy to be scaled to larger datasets while integrating with other adversarial defense techniques. Coupled with other defense, ExL performs remarkably (even for larger values). We combine ExL with EnsAdv & PGDAdv, which do not cause obfuscated gradients and hence can withstand strong attacks, however, upto a certain point. For WB perturbations much greater than the training value, ExL+PGDAdv also breaks. In fact, for adaptive BB adversaries BID30 or adversaries that query the model to yield full prediction confidence (not just the label), ExL+EnsAdv will be vulnerable. Note, advantage with ExL is, being independent of the attack/defense method, ExL can be potentially combined with stronger attacks developed in future, to create stronger defenses.While variance and principal subspace analysis help us understand a model's behavior, we cannot fully describe the structure of the manifold learnt by the linear subspace view. However, PCA does provide a basic intuition about the generalization capability of complex image models. In fact, our PC results establish the superiority of adversarial training methods (SGD ens ; SGD P GD : BID30 ; BID21 and can be used as a valid metric to gauge adversarial susceptibility in future proposals. Finally, as our likelihood theory (Eqn.1) indicates, better noise modeling techniques with improved gradient penalties can further improve robustness and requires further investigation. Also, performing noise modeling at intermediate layers to improve variance/explainability, and hence robustness, are other future work directions.A APPENDIX A: JUSTIFICATION OF X + N VS X × N AND USE OF ∇L N ≤ 0 FOR NOISE MODELING FIG0 : For MNIST dataset, we show the noise template learnt when we use multiplicative/additive noise (N ) for Explainable Learning. The final noise-integrated image (for a sample digit '9') that is fed to the network before and after training is also shown. Additive noise disrupts the image drastically. Multiplicative noise, on the other hand, enhances the relevant pixels while eliminating the background. Accuracy corrsponding to each scenario is also shown and compared against standard SGD training scenario (without any noise). Here, we train a simple convolutional architecture (ConvNet: 10C-M-20C-M-320FC) of 2 Convolutional (C) layers with 10, 20 filters, each followed by 2×2 Max-pooling (M) and a Fully-Connected (FC) layer of size 320. We use mini-batch SGD with momentum of 0.5, learning rate (η=0.1) decayed by 0.1 every 15 epochs and batchsize 64 to learn the network parameters. We trained 3 ConvNet models independently corresponding to each scenario for 30 epochs. For the ExL scenarios, we conduct noise modelling with only negative loss gradients (∇LN ≤ 0) with noise learning rate, ηnoise = 0.001, throughout the training process. Note, the noise image shown is the average across all 64 noise templates. Figure A2 : Here, we showcase the noise learnt by a simple convolutional network (ConvNet: 10C-M-20C-M-320FC), learning the CIFAR10 data with ExL (multiplicative noise) under different gradient update conditions. As with MNIST ( FIG0 , we observe that the noise learnt enhances the region of interest while deemphasizing the background pixels. Note, the noise in this case has RGB components as a result of which we see some prominent color blobs in the noise template after training. The performance table shows that using only negative gradients (i.e. ∇LN ≤ 0) during backpropagation for noise modelling yields minimal loss in accuracy as compared to a standard SGD trained model. We use mini-batch SGD with momentum of 0.9, weight decay 5e-4, learning rate (η=0.01) decayed by 0.2 every 10 epochs and batch-size 64 to learn the network parameters. We trained 4 ConvNet models independently corresponding to each scenario for 30 epochs. For the ExL scenarios, we conduct noise modelling by backpropagating the corresponding gradient with noise learning rate (ηnoise = 0.001) throughout the training process. Note, the noise image shown is the average across all 64 noise templates. We observe that ExL noise increases the explainability (or variance) along the high rank PCs. Also, as we go deeper into the network, the absolute difference of the variance values between SGD/ExL decreases. This is expected as the contribution of input noise on the overall representations decreases as we go deeper into the network. Moreover, there is a generic-to-specific transition in the hierarchy of learnt features of a deep neural network. Thus, the linear PC subspace analysis to quantify a model's knowledge of the data manifold is more applicable in the earlier layers, since they learn more general input-related characteristics. Nonetheless, we see that ExL model yields widened explainability than SGD for each intermediate layer except the final Block4 that feeds into the output layer. We use mini-batch SGD with momentum of 0.9, weight decay 5e-4, learning rate (η=0.1) decayed by 0.1 every 30 epochs and batch-size 64 to learn the network parameters. We trained 2 ResNet-18 models independently corresponding to each scenario for 60 epochs. For noise modelling, we use ηnoise = 0.001 decayed by 0.1 every 30 epochs. Note, we used a sample set of 700 test images to conduct the PCA. FIG2 : Here, we show the variance captured in the leading Principal Component (PC) dimensions for the Conv1 and Block1 learnt activations in response to both clean and adversarial inputs for ResNet-18 models correponding to the scenarios discussed in FIG1 . The model's variance for both clean and adversarial inputs are exactly same in case of ExL/SGD for Conv1 layers. For Block1, the adversarial input variance is slighlty lower in case of SGD than that of clean input. With ExL, the variance is still the same for Block1. This indicates that PC variance statistics cannot differentiate between a model's knowledge of on-/off-manifold data. It only tells us whether a model's underlying representation has acquired more knowledge about the data manifold. To analyze a model's understanding of adversarial data, we need to look into the relationship between the clean and adversarial projection onto the PC subspace and measure the cosine distance. Note, we used the Fast Gradient Sign Method (FGSM) method BID6 to create BB adversaries with a step size of 8/255, from another independently trained ResNet-18 model (source) with standard SGD. The source attack model has the same hyperparameters as the SGD model in FIG1 and is trained for 40 epochs.",2758,1.403,1576,1.75,"We introduce Explainable Adversarial Learning ExL training are intrinsically robust We find the implicit generative modeling random noise with used during posterior maximization improves the data manifold furthering We prove our approach's efficacy provide a simplistic visualization tool adversarial data Our analysis adversarial robustness manifests models along the high-ranked principal components We show models learnt with our approach perform remarkably attacks Furthermore combining ExL with state adversarial training extends a model even beyond adversarially Despite surpassing human performance several perception tasks vulnerable adversarial examples: slightly inputs specifically fool during BID2 BID29 BID6 BID23 . Recent works the security danger adversarial attacks across with ML backend such computer vision , malware detectors gaming environments Even worse adversarial inputs transfer across models same inputs misclassified trained thus enabling simple Black ( 1 attacks deployed ML systems .Several works BID14 BID24 BID3 demonstrating improved shown fail stronger attacks BID0 state approach BB defense ensemble adversarial training the training dataset transferred BID30 . BID21 showed models can even robust WhiteBox ( 1 attacks closely maximizing with Projected Gradient Descent based Despite this progress errors for perturbations beyond adversarially trained BID27 .There explaining the susceptibility ML models such attacks The most common one suggests the overly linear behavior deep neural models adversarial examples BID6 BID20 . Another hypothesis adversarial examples off the data manifold BID28 BID18 Combining infer excessive linearity causes models their behavior beyond manifold yielding pathological results slightly perturbed inputs A question worth improve the model generalize better such out Explainable Adversarial LearningExL wherein multiplicative noise the training inputs optimize while over Essentially the input noiserandomly initialized gradually learnt during As the noise approximately models the input distribution to effectively maximize the class labels given FIG0 shows the input noise learnt et2 architecture discussed below learning handwritten digits MNIST dataset BID17 . We observe the noise gradually transforms finally assumes highlights For instance the MNIST images centered digits Noise in learnt this centered characteristic . This suggests not finds the right prediction Noise this explainable behavior discovering some knowledge the input/output distribution during training FIG0 shows the noise learnt ExL on colored CIFAR10 images BID13 )on ResNet18 architecture reveals noise templatealso RGB learns prominent color blobs that de background pixels A recent theory BID4 suggests adversarial examplesoff manifold misclassified points occur randomly chosen inputs on manifold, correctly With ExL, hypothesize learns look the onmanifold data points thereby incorporate more outwithout, We empirically evaluate and studying adversarial the clean inputs using the intermediate layer's output discover that models exhibiting adversarial robustness yield significantly lower distanceWe harness establish that ExL noise modeling indeed acquires an improved realization the input/output distribution characteristics enables better To further show ExL globally reduces adversarial examples BID31 . We evaluate our approach on classification tasks such MNIST show models trained ExL are extensively adversarially robust We show combining ExL with ensemble/PGD adversarial training significantly extends beyond adversarially both BB/WB attack scenarios We proposed Explainable Adversarial Learning ExL adversarial robustness Specifically our key findings noise modeling at during better for out adversarialwithout 2) Our PCA variance and cosine distance analysis provides a significant perspective visualize adversarial/clean dataA crucial question one to break ExL defense The recent work BID0 shows many defense methods cause 'gradient masking eventually fail We reiterate ExL alone give a strong BB/WB defense However the smoothening effect noise modeling the loss FIG3 suggests decreases ExL does change the classification model be scaled while integrating other adversarial defense techniques other defense ExL performs remarkably (even larger values We combine ExL with EnsAdv & PGDAdv do cause obfuscated gradients hence withstand strong attacks however upto For WB perturbations much greater the training value ExL+PGDAdv also breaks. fact for adaptive BB adversaries BID30 or adversaries query the model yield full prediction confidencenot just the label ExL+EnsAdv vulnerable Note, advantage with ExL is, being independent the attack/defense method ExL potentially combined stronger attacks developed futureWhile variance principal subspace analysis help describe the manifold learnt the linear subspace view However PCA provide a basic intuition the generalization capability complex image models fact our PC results establish adversarial training methodsSGD ens ; SGD P GD : BID30 ; and can adversarial susceptibility future proposals Finally as our likelihood theory ( better noise modeling techniques with improved gradient penalties further requires Also performing noise modeling intermediate layers to variance/explainability hence other future work directionsA APPENDIX A JUSTIFICATION X + N VS X × AND USE �L N ≤ FOR FIG0 : For MNIST dataset show the noise template learnt when ( ) Explainable Learning The final noise-integrated imagefor a sample digit '9 that fed before training also Additive noise drastically Multiplicative noise on enhances the relevant pixels while eliminating Accuracy corrsponding each scenario shown and standard SGD training scenariowithout any noise Here train: 10C-M-20C-M-320FC 10 20 filters followed 2×2 Max-pooling of size 320 We use minibatch SGD with momentum of learning rate (�= decayed every 15 epochs batchsize 64 to learn the network parameters We trained 3 ConvNet models independently corresponding each scenario For the ExL scenarios conduct noise modelling only negative loss gradients��LN ≤ noise learning,noise throughout Note, the noise image across all 64 noise templates Figure A2 : Here showcase the noise learnt: learning the CIFAR10 data ExL (multiplicative noise under different gradient update conditions As with MNIST FIG0 we observe the noise learnt enhances the region while deemphasizing the background pixels Note, the noise RGB components which see the noise template after training The performance table using only negative gradients during for noise modelling yields minimal loss as a standard SGD trained model We use minibatch SGD with momentum of weight decay 5e-4 learning rate= decayed batch-size 64 to learn the network parameters We trained 4 ConvNet models independently corresponding each scenario For the ExL scenarios conduct noise modelling the corresponding gradient learning rate��noise throughout Note, the noise image across all 64 noise templates We observe ExL noise the explainability variance along the high rank PCs Also go the absolute difference SGD/ExL decreases This expected as the contribution input noise on the overall representations decreases Moreover a generic-to-specific transition learnt features Thus the linear PC subspace analysis to the data manifold more applicable the earlier layers learn more general input-related characteristics Nonetheless see ExL model yields widened explainability than SGD for each intermediate layer except the final Block4 that feeds We use minibatch SGD with momentum of weight decay 5e-4 learning rate= decayed every 30 epochs batch-size 64 to learn the network parameters We trained 2 ResNet-18 models independently corresponding each scenario For noise modelling ��noise decayed every 30 epochs Note, used 700 test images conduct FIG2 : Here the variance captured the leading Principal Component (PC) dimensions the Conv1 Block1 learnt response both clean and adversarial inputs for ResNet-18 models correponding the scenarios discussed The model's variance for both clean and adversarial inputs are exactly same case ExL/SGD for Conv1 layers For Block1 the adversarial input variance slighlty lower case SGD that clean input With ExL, the variance still Block1 This indicates PC variance statistics differentiate a model's knowledge. It only tells whether a model's underlying representation acquired more knowledge the data manifold To analyze a model's understanding adversarial data the clean and adversarial projection onto the PC subspace measure the cosine distance Note, used the Fast Gradient Sign MethodFGSM BID6 BB adversaries a step size 8/255 from another independently trained ResNet-18 model standard SGD The source attack model FIG1 trained 40 epochs",0.02,0.6150132754042966
"We propose a method which can visually explain the classification decision of deep neural networks (DNNs). There are many proposed methods in machine learning and computer vision seeking to clarify the decision of machine learning black boxes, specifically DNNs.   All of these methods try to gain insight into why the network ""chose class A"" as an answer. Humans, when searching for explanations, ask two types of questions. The first question is, ""Why did you choose this answer? "" The second question asks, ""Why did you not choose answer B over A?"" The previously proposed methods are either not able to provide the latter directly or efficiently.

 We introduce a method capable of answering the second question both directly and efficiently. In this work, we limit the inputs to be images. In general, the proposed method generates explanations in the input space of any model capable of efficient evaluation and gradient evaluation. We provide results, showing the superiority of this approach for gaining insight into the inner representation of machine learning models. Deep neural networks (DNN) have shown extraordinary performance on computer vision tasks such as image classification BID25 BID23 BID24 BID7 , image segmentation BID3 , and image denoising BID29 . The first example of such a performance was on image classification, where it outperformed other computer vision methods which were carefully handcrafted for image classification BID12 . Following this success, DNNs continued to grow in popularity. Although the performances of DNNs on different tasks are getting close to human expertise BID17 and in some cases surpass them BID24 , there is hesitation to use them when interpretability of the results is important. Accuracy is a well-defined criterion but does not provide useful understandings of the actual inner workings of the network. If the deployment of a network may result in inputs whose distribution differs from that of the training or testing data, interpretability or explanations of the network's decisions can be important for securing human trust in the network.Explanations are important in settings such as medical treatments, system verification, and human training and teaching. Naturally, one way of getting an explanation is asking the direct question, ""Why did the DNN choose this answer?"" Humans often also seek contrasting explanations. For instance, they maybe more familiar with the contrasting answer, or they want to find the subtle differences in input which change the given answer to the contrasting one. This way of questioning can be phrased as, ""Why did the DNN not choose B (over A)?"" In this work, we present a framework to answer this type of question. We learn a model over the input space which is capable of generating synthetic samples similar to the input. Then, we ask how we can alter this synthetic input to change the classification outcome. Our proposed framework is not based on heuristics, does not need to change the given network, is applicable as long as the given model can handle backpropagation (no further requirements for layers), and can run much faster than methods with input perturbation. The only overhead of this method is the assumed availability of a latent model over the input. If this latent model is not available, we can learn such a model using generative adversarial methods or variational auto encoders. Learning this latent space needs to be done only a single time and is independent of the learned classifier to be explained. Our constrastive explanation method (CDeepEx) provides an effective method for querying a learned network to discover its learned representations and biases. We demonstrated the quality of our method, compared to other current methods and illustrated how these contrastive explanations can shed light on the robustness of a learned network.Asking a network contrastive questions of the form, ""Why is this example not of class B?"" can yield important information about how the network is making its decisions. Most previous explanation methods do not address this problem directly, and modifying their output to attempt to answer constrastive questions fails.Our formulation draws on three ideas: The explanation should be in the space of natural inputs, should be an example that is maximally ambiguous between the true and probe classes, and should not be confused with other classes. The method does not require knowledge of or heuristics related to the architecture or modality of the network. The explanations can point to unintended correlations in the input data that are expressed in the resulting learned network.",869,0.48,512,1.697265625,"We propose which visually explain the classification decision There many proposed methods in machine learning seeking clarify the decision of machine black boxes specifically DNNs All try gain why the network ""chose class A as Humans when searching explanations ask two types The first question this answer "" The second question asks choose answer B over The previously proposed methods either able provide latter directly efficiently We introduce a method capable answering both directly efficiently In this work limit the inputs be images In general the proposed method generates explanations in the input space any model capable efficient evaluation and gradient evaluation We provide results, showing the superiority this approach gaining the inner representation machine learning models Deep neural networks extraordinary performance BID25 BID23 BID24 BID7 , denoising The first example such a performance on image classification it which carefully handcrafted image classification BID12 . Following this success DNNs continued Although the performances DNNs on different tasks getting close human expertise BID17 in surpass , hesitation when interpretability Accuracy but does provide useful understandings the actual inner workings If the deployment a network may result inputs whose distribution differs the training or testing data interpretability or explanations the network's decisions important securing human trustExplanations are settings medical treatments system verification human training teaching Naturally one way an explanation asking the DNN choose this answer Humans often also seek contrasting explanations For instance they maybe more familiar the contrasting answer or they want find the subtle differences input which change the given answer contrasting This way questioning can phrased, the DNN choose B (over this work present this type We learn a model over the input space which capable synthetic samples similar Then we ask how alter this synthetic input change the classification outcome Our proposed framework not heuristics does need change the given network applicable as (no further requirements layers run much methods with input perturbation The only overhead this method the assumed availability a latent model over If this latent model available learn such a model or variational auto encoders Learning this latent space needs only a single is independent the learned classifier to explained Our constrastive explanation method (CDeepEx querying a learned network to discover its learned representations biases We demonstrated the quality our method compared illustrated these contrastive explanations shed a learned networkAsking a network contrastive questions of this example not of class B yield making Most previous explanation methods do address directly modifying their output attempt answer constrastive questions failsOur formulation draws three ideas The explanation in the space natural inputs should an example that maximally ambiguous between the true and probe classes confused other classes The method does knowledge or heuristics related the architecture modality The explanations can point unintended correlations the input data expressed the resulting learned network",0.01,0.48065072109582446
"We flip the usual approach to study invariance and robustness of neural networks by considering the non-uniqueness and instability of the inverse mapping. We provide theoretical and numerical results on the inverse of ReLU-layers. First, we derive a necessary and sufficient condition on the existence of invariance that provides a geometric interpretation. Next, we move to robustness via analyzing local effects on the inverse. To conclude, we show how this reverse point of view not only provides insights into key effects, but also enables to view adversarial examples from different perspectives. Invariance and stability/robustness are two of the most important properties characterizing the behavior of a neural network. Due to growing requirements like robustness to adversarial examples BID16 and the increasing use of deep learning in safety-critical applications, there has been a surge in interest in these properties. Invariance and stability are considered to be the key mechanisms in dealing with uninformative properties of the input BID0 BID6 and are studied from the information theoretical perspective in form of the loss of information about the input BID17 BID11 .Invariance and stability are also tightly linked to robustness against adversarial attacks (Cisse et al., 2017; BID18 BID14 , generalization BID15 Gouk et al., 2018) and even the training of Generative Adversarial Networks BID7 . In general , stability is studied via two basic properties: 1) locally via a norm of the Jacobian BID15 BID14 , 2) globally via the Lipschitz constant (Cisse et al., 2017; BID7 BID18 ). From a high-level perspective, both of these approaches study an upper bound on stability as the Lipschitz constant and a Jacobian norm quantifies the highest possible change under a perturbation with a given magnitude. We, unlike the approaches above, aim to broaden our understanding by analyzing the lowest possible change under a perturbation.More formally, we study which perturbations ∆x do not (or only little) affect the outcome of a network F . Our analysis considers a given input data point x and investigates the ∆x's, such that DISPLAYFORM0 where a small ε > 0 is given. While these properties can be crucial for many discriminative tasks BID6 , the model could be flawed if perturbations that alter the semantics have only a minor impact on the features. This is a reverse perspective on adversarial examples BID16 , which commonly considers small input perturbations that lead to large changes and thus to arbitrary decisions of the network.This flipped view and the study of smallest changes calls for a different approach: we study the instabilities of the inverse instead of the stabilities of the forward mapping. In particular, if F is invariant to perturbations ∆x, then x and x + ∆x lie in the preimage of the output z = F (x), i.e. F is not uniquely invertible. Robustness towards large perturbations induces an instable inverse mapping as small changes in the output can be due to large changes in the input.Based on the piecewise linear nature of ReLU networks BID8 , we characterize the preimage of ReLU-activations as a single point, finite (bounded) or infinite (unbounded) . Further, we study the stability of the linearization of rectifier networks via its singular values. To illustrate these locally changing properties and to demonstrate their tight connection, we visualize the behavior on a synthetic problem in FIG0 . As ReLU-layers are piecewise linear, the local behavior is constant on polytopes. Further, the regions with infinite/finite preimages correspond to regions with condition number of one or zero, while singleton preimages link to condition numbers larger than one. Thus, both properties are tightly connected and investigating one property alone yields an incomplete picture.Our contributions are as follows:• We derive conditions when the preimage of an output of a ReLU-layer has finite or infinite volume or is a single point. Based on these conditions, we derive an algorithm to check these conditions and exemplify its usability by applying it to investigate the preimages of a trained network. (See Section 2.) • We study the stability of the inverse via analyzing the linearization at a point in input space, which is accurate within a polytope. We provide upper bounds on the smallest singular value of a linearization and prove how the removal of uncorrelated features could effect the stability of the inverse mapping. Based on these ideas, we experimentally demonstrate how singular values evolve over the different layers in rectifier networks. (See Section 3.) • We introduce a reverse view on adversarial examples and connect it to invariance and robustness by leveraging our analysis of preimages. (see Section 5) We presented the inverse as an approach to tackle the invariance and robustness properties of ReLU networks. Particularly, we studied two main effects: 1) conditions under which the preimage of a ReLU layer is a point, finite or infinite and 2) how ReLU can effect the inverse stability of the linearization. By deriving approaches to numerically examine these effects, we highlighted the broad range of possible effects. Moreover, controlling such properties may be desirable as our experiment on adversarial examples showed.Besides the open questions on how to control the structure of preimages and inverse stability via architecture design or regularization, we envision several theoretical directions based on our work. Especially, incorporate nonlinear effects like moving between linear regions of rectifier networks could lift the analysis closer to practice. Furthermore, studying similarities of omnidirectionality as a geometrical property and singular values could further strengthen the link between these two crucial properties. Proof (Corollary 2, Equivalences of omnidirectionality) We show the equivalences by proving i) DISPLAYFORM0 Let A ∈ R m×n be omnidirectional, i.e. for every x = 0, it holds that Ax 0. This is equivalent to DISPLAYFORM1 which is ii). The implications from ii) to iii) and from iii) to iv) are obvious. From iv), we have that DISPLAYFORM2 which is equivalent to i), the omnidirectionality of A. Altogether, this shows the equivalence of all four points.Definition 10 (Convex hull) For A ∈ R m×n , the convex hull is defined as DISPLAYFORM3 where a i ∈ R n are the rows of A.Theorem 11 (Stiemke's theorem, see Dantzig (1963) ) Let A ∈ R m×n be a matrix, then the following two expressions are equivalent.• y : Ay 0 DISPLAYFORM4 Here z 0 means that 0 = z 0 . Proof (Theorem 12, Singleton solutions of inequality systems) ""⇐"" Let (A| I , b| I ) be omnirectional for x 0 . Then it holds that A| I x + b| I = A| I (x − x 0 ) 0. Due to the omnidirectionality of A| I , x 0 is the unique solution of the inequality system A| I x + b| I 0. The existence of a solution for the whole system Ax + b 0 is guaranteed by assumption and therefore x 0 is the unique solution of Ax + b 0. ""⇒"" Here we will prove "" I : (A| I , b| I ) omnidirectional for some p ⇒ solution non-unique"".We will start by doing the following logical transformations: This means that A| I is not omnidirectional, because otherwise A| I x 0 + b| I = 0 due to the definition of I, which would lead to the contradiction that (A| I , b| I ) is omnidirectional for x 0 . But this means ∃x = 0 : A| I x 0 as a result of Corollary 2. Since A| I c x 0 + b| I c ≺ 0, we also have ∀x ∃ > 0 : A| I c (x 0 + x) + b| I c ≺ 0. This holds in particular for x , so we define accordingly x * := εx = 0. Therefore, we have A| I c (x 0 + x * ) + b| I c ≺ 0 as well as DISPLAYFORM5 DISPLAYFORM6 Altogether it holds that A(x 0 + x * ) + b 0 with x * = 0, which means that x 0 is a non-unique solution for the inequality system Ax + b 0.Proof (Theorem 4, Preimages of ReLU-layers) We consider the ReLU-layer DISPLAYFORM7 given its output y ∈ R m with A ∈ R m×n , b ∈ R m and x ∈ R n . Clearly, this equation can also be written as the mixed linear system DISPLAYFORM8 This allows us to consider the two cases N (A| y 0 ) = {0} and N (A| y 0 ) = {0}.In the first case , we have a linear system which allows us to calculate x uniquely, i.e. we can do retrieval. This leads us to the second case, the interesting one. In this case we can only recover x uniquely if and only if the system of inequalities ""pins down"" P N (A|y 0) x, where P V is the orthogonal projection into the closed space V . Formally this requires DISPLAYFORM9 to have a unique solution for x ∈ R n and P N (A|y 0) ⊥ x fixed (given via the equality system). By defining b := b| y 0 + A| y 0 (P N (A|y 0 ) ⊥ x) we have DISPLAYFORM10",2041,0.925,1118,1.8255813953488371,"We flip the usual approach study invariance considering nonuniqueness instability the inverse mapping We provide theoretical and numerical results the inverse ReLU-layers First derive invariance that provides a geometric interpretation Next move robustness via analyzing local effects the inverse. To conclude show this reverse point not provides insights key effects enables to view adversarial examples Invariance stability/robustness characterizing Due growing requirements like robustness adversarial examples BID16 these properties Invariance stability considered the key mechanisms dealing uninformative properties the input BID0 BID6 are studied from the information theoretical perspective form the loss information .Invariance tightly robustness againstCisse 2017 generalization even the training In general , stability studied via two basic properties locally via a norm the Jacobian BID15 BID14 globallyCisse 2017 BID7 BID18 From both study an upper stability as the Lipschitz constant a Jacobian norm quantifies the highest possible change under with We, unlike the approaches above aim broaden by analyzing the lowest possible change underMore formally study which �x do ( only little a network F . Our analysis considers a given input data point x investigates the ��x's, such DISPLAYFORM0 where a small �� > While these properties crucial many discriminative tasks BID6 , the model could flawed that alter the semantics have the features This a reverse perspective adversarial examples BID16 , commonly considers small input perturbations lead and arbitrary decisions ofThis flipped view and the study smallest changes calls study the inverse instead the stabilities the forward mapping In particular if F is invariant � xx lie the preimage the output z = F (x uniquely Robustness towards large perturbations induces an instable inverse mapping as small changes the output can dueBased the piecewise linear nature ReLU networks BID8 , characterize the preimage ReLU-activations finite (bounded or . Further study the stability the linearization rectifier networks via its singular values To illustrate these locally changing properties their tight connection visualize on a synthetic problem FIG0 . As ReLU-layers piecewise linear the local behavior constant on polytopes Further the regions infinite/finite preimages correspond condition number one zero singleton link condition larger Thus both properties tightly investigating one property alone yieldsOur contributions as derive conditions when the preimage an output a ReLU-layer has finite or volume or Based these conditions derive check these conditions exemplify its usability applying investigate the preimages a trained network (See Section • We study the stability the inverse via analyzing at input space accurate within a polytope We provide upper bounds the smallest singular value a linearization and prove how the removal could effect the inverse mapping Based these ideas experimentally demonstrate singular values evolve the different layers rectifier networks (See Section • We introduce a reverse view on adversarial examples connect invariance by leveraging our analysis preimages (see Section We presented the inverse as an approach tackle the invariance and robustness properties ReLU networks Particularly studied two main effects 1) conditions under the preimage a ReLU layer a point finite and how can effect the inverse stability By deriving approaches numerically examine these effects highlighted Moreover controlling such properties desirable our experiment on adversarial examplesBesides the open questions on preimages inverse stability via architecture design regularization envision several theoretical directions based Especially, incorporate nonlinear effects moving between linear regions rectifier networks could lift the analysis closer practice Furthermore studying similarities omnidirectionality as a geometrical property and singular values could further strengthen Proof (Corollary, Equivalences omnidirectionality We show by proving i) DISPLAYFORM0 Let A �� R m×n for x = holds Ax 0. This equivalent DISPLAYFORM1 which ii The implications from ii) to obvious From iv), we that DISPLAYFORM2 which equivalent i the omnidirectionality A. Altogether shows the equivalence all four pointsDefinition 10 (Convex hull For A �� R m×n DISPLAYFORM3 where a i are (Stiemke's theorem, Dantzig (1963 ) Let equivalent.• y : Ay 0 Here z 0 means 0 Proof (Theorem 12 Singleton solutions of inequality systems ""���"" LetA| I , omnirectional for x 0 Then holds A| I x +x − x 0 0 Due A| I , x 0 the unique solution the inequality system + The existence a solution the whole system Ax + 0 guaranteed assumption and therefore x the unique solution ""���"" Here prove "" I : (A| I , omnidirectional for some p �� solution nonunique""We start doing This A| otherwise x 0 + due, would lead ( But means ��x : A| I x 0 as Corollary Since A| I c x 0 + �� also > : ( This holds in particular x , define accordingly := �x Therefore A| I c 0 + * ) �� as DISPLAYFORM5 DISPLAYFORM6 Altogether it holds 0 with * a non-unique solution the inequality system Ax + 0.Proof Preimages ReLU-layers We consider given its output y �� R m with Clearly this equation also written the mixed linear system DISPLAYFORM8 This allows consider N (A| y 0 { , allows x uniquely do retrieval This leads interesting In recover x uniquely and of inequalities ""pins P N (A|y 0 x P V into the closed space V . Formally this requires DISPLAYFORM9 a unique solution x � R n P N (A|y 0 � fixed (given via the equality system By defining b := y 0 + A| (P N � DISPLAYFORM10",0.01,0.8075880302443461
"While deep learning has led to remarkable results on a number of challenging problems, researchers have discovered a vulnerability of neural networks in adversarial settings, where small but carefully chosen perturbations to the input can make the models produce extremely inaccurate outputs. This makes these models particularly unsuitable for safety-critical application domains (e.g. self-driving cars) where robustness is extremely important. Recent work has shown that augmenting training with adversarially generated data provides some degree of robustness against test-time attacks. In this paper we investigate how this approach scales as we increase the computational budget given to the defender. We show that increasing the number of parameters in adversarially-trained models increases their robustness, and in particular that ensembling smaller models while adversarially training the entire ensemble as a single model is a more efficient way of spending said budget than simply using a larger single model. Crucially, we show that it is the adversarial training of the ensemble, rather than the ensembling of adversarially trained models, which provides robustness. Deep neural networks have demonstrated state-of-the-art performance in a wide range of application domains BID13 . However, researchers have discovered that deep networks are in some sense 'brittle', in that small changes to their inputs can result in wildly different outputs BID8 BID10 BID27 . For instance, practically imperceptible (to human) modifications to images can result in misclassification of the image with high confidence. Not only are networks susceptible to these 'attacks', but these attacks are also relatively easy to compute using standard optimization techniques BID5 BID6 . These changes are often referred to as adversarial perturbations, in the sense that an adversary could craft a very small change to the input in order to create an undesirable outcome. This phenomenon is not unique to image classification, nor to particular network architectures, nor to particular training algorithms BID23 .Adversarial attacks can be broken into different categories depending on how much knowledge of the underlying model the adversary has access to. In 'white-box ' attacks the adversary has full access to the model, and can perform both forward and backwards passes (though not change the weights or logic of the network) BID4 BID6 . In the 'black-box ' setting the adversary has no access to the model, but perhaps knows the dataset that the model was trained on BID23 . Despite several recent papers demonstrating new defences against adversarial attacks BID1 BID7 BID16 BID26 BID29 BID31 BID32 BID33 , recent papers have demonstrated that most of these new defences are still susceptible to attacks and largely just obfuscate the gradients that the attacker can follow, and that non-gradient based attacks are still effective BID30 ; BID2 . In this section we briefly discuss the possible reasons for the behaviours observed. As we saw, an ensemble of models trained adversarially outperforms the other setups at test time. We suspect, that this might be happening due to a mechanism described below.When the model is being trained, it is exposed to pairs of images, both ""clean"" and adversarially modified. The adversarial training exploits the fact that the original image is close to the decision boundary of the model. The model then, when provided with both clean and adversarial image would attempt to modify the decision boundary in order to engulf them both. It is relatively easy to imagine why SingleAdv would be weaker then the other models-it simply has less parameters than the competition. In order to accommodate the adversarial example it has to compromise the decision boundary somewhere else, pulling it close to other clean images, making it vulnerable to subsequent attack. This is illustrated in Figure 3a .The possible reason why Ensemble2Adv outperforms DoubleAdv is more elusive. Both models have the same number of parameters, so one could expect them to display a similar performance. As Ensemble2Adv is more robust to white box attack during test time we argue, that this might be due to the fact that in abundance of flexibility DoubleAdv tends often to spread out thin ""tentacles"" Figure 3: Different responses of various architectures to adversarial training. Solid lines represent decision boundary of the models that see only ""clean"" images. Dashed lines are the boundaries modified due to the presence of adversarial training. The black dot is a clean image, the red dot is its adversarial modification. In the presence of two models Model 1 is blue and Model 2 is green. In case it needs to be specified with respect to which model the adversarial example is constructed the red dot has a circle in an appropriate color around it.( Figure 3b ) which do not cover up too much of a space. On the other hand, given that Ensemble2Adv is comprised of two separate models they are both subject to lesser ability to overfit following from the smaller number of parameters available in them. Thus we argue, that in most cases the modification of the model with adversarial training covers the adversarial example by modifying one model more than the other. This way the decision boundary of the model modified to a lesser degree still ""provides protection"" for ""clean"" images, while at the same time the ""tentacle"" generated by the model modified more is thicker than the one DoubleAdv creates. We illustrate that with Figure 3c .Finally, it was shown that SeparateEnsemble2Adv is outperformed by a Ensemble2Adv trained ""jointly"". We think that this is due to the fact that the adversarial training has to weaken both of the submodels simultaneously. Figure 3d illustrates that.For a further illustration of the effects of adversarial training we plotted actual images of the decision boundaries for non-adversarially and adversarially trained Baseline and 2-Ensemble models (Figure 4) . DISPLAYFORM0 Figure 4: Decision boundaries for various architectures/training methods. Each column shows the decision regions of two models on the same 2-dimensional plane in the space of all images. On every picture the black dot corresponds to the datapoint-an unaltered (ship ) image from the test dataset. The light rectangle superimposed over the dot represents the bounds of the permitted attack region within the region. The two red arrows are the two vectors-attack directions on the base image, with respect to respectively the first and second tested model. The red dots are the images resulting from the attack. The plane presented is then the ( unique) 2-dimensional plane containing those 3 points. Dark grey is void (outside the slice boundaries), and all other pixels are generated by a forward pass of the model at those coordinates, with the colour used representing the majority class.Decision regions of the models are 3072-dimensional sets, so visualizing them itself poses a challenge. What we present are color-coded values of the models restricted to 2-dimensional planes in the space of all images, chosen so that the original image and the closest adversarial example (or attempt to find one) for both models in a pair being compared are co-planar. We observe, amongst other things, some support for the hypothesis put forward in Figure 3 : adversarial training adds ""thickness"" around the natural image points, pushing the boundary further away from them, and in doing so, making adversarial examples harder to find (even within the test set); ensembling makes some classes more ""consistent"" within the decision plane, but introduce small ""pockets"" or ""tentacles"" of other classes; and the combinator thereof removes said pockets to create large regions of the correct class around images. We believe that such an approach of choosing a good plane and plotting the values of models on it is a more informative way of visualizing phenomena taking place in the universe of robustness and adversarial examples than more traditional approaches like t-SNE plots BID18 . In this paper, we provide an empirical study of the effect of increasing the number of parameters in a model trained with adversarial training methods, with regard to its robustness to test-time adversarial attacks. We showed that while increasing parameters improves robustness, it is better to do so by ensembling smaller models than by producing one larger model. Through our experiments, we show that this result is not only due to ensembling alone, or to the implicit robustness of an ensemble of adversarially trained models, but specifically to due to the adversarial training of an ensemble as if it were a single model. We proposed a high level interpretation of why this phenomenon might occur. Further work should seek to determine whether scaling the number of models in the ensemble while controlling for number of parameters produces significant improvements over the minimal ensembles studied here in an attempt to draw conclusions about why such architectures are generally more robust than larger single models, even under adversarial training.",1768,0.896,1013,1.7453109575518262,"While deep learning led remarkable results challenging problems researchers discovered a vulnerability of adversarial settings small but carefully chosen perturbations the input produce extremely inaccurate outputs This makes these models particularly safety-critical application domains robustness extremely Recent work augmenting training adversarially generated data provides some degree against test-time attacks In investigate this approach scales as we the computational budget given to the defender We show increasing parameters adversarially-trained models increases in ensembling smaller models while as spending said budget simply Crucially show it the adversarial training the ensemble the ensembling adversarially trained models robustness Deep neural networks demonstrated state performance application domains BID13 . However researchers deep networks in 'brittle their inputs BID8 BID10 BID27 . For instance practically imperceptible (to human) modifications images result with high confidence Not networks susceptible these 'attacks relatively compute using standard optimization techniques BID5 BID6 . These changes often adversarial perturbations could craft in create This phenomenon image classification nor particular network BID23 .Adversarial attacks broken how much knowledge access In 'white-box ' attacks the adversary has full access the model perform both forward passes (though change the weights logic BID4 BID6 . In the 'black-box ' setting the adversary the model perhaps knows the dataset trained BID23 . Despite several recent papers demonstrating new defences adversarial attacks BID1 BID7 , recent papers most still susceptible and largely just obfuscate the gradients follow non-gradient based attacks effective BID30 ; . In briefly the behaviours As saw an ensemble models trained adversarially outperforms the other setups at test time We suspect, might happening due a mechanism described belowWhen the model being trained exposed pairs images both ""clean adversarially modified The adversarial training exploits the original image close the decision boundary The model then, when provided both clean and adversarial image would attempt modify the decision boundary engulf both It relatively imagine why SingleAdv would weaker then models-it simply less parameters In order accommodate the adversarial example it compromise the decision boundary somewhere pulling close other clean images making vulnerable subsequent attack This illustrated .The possible reason Ensemble2Adv outperforms DoubleAdv more elusive Both models parameters one display As Ensemble2Adv is more robust to white box attack during test time we argue, might in abundance flexibility DoubleAdv tends often spread thin ""tentacles"" Figure Different responses various architectures adversarial training Solid lines represent decision boundary of the models that see only ""clean"" images Dashed lines the boundaries modified due adversarial training The black dot a clean image its adversarial modification In the presence two models Model is blue In case it needs specified with respect which model the adversarial example constructed the red dot has a circle an appropriate color around.( Figure 3b which do cover up too On given Ensemble2Adv comprised two separate models they both subject lesser ability overfit following from the smaller number parameters them Thus argue modification with adversarial training covers the adversarial example by modifying one model more This way the decision boundary modified a lesser degree still "" protection ""clean"" images generated modified more thicker DoubleAdv creates We illustrate with Figure 3c .Finally SeparateEnsemble2Adv outperformed trained "" We think due the adversarial training weaken both the submodels simultaneously Figure 3d.For a further illustration adversarial training we plotted actual images the decision boundaries non 2-Ensemble models . DISPLAYFORM0 Figure Decision boundaries various architectures/training methods Each column shows the decision regions two models on in all images On every picture the black dot corresponds-an unaltered (ship ) image from the test dataset The light rectangle superimposed the dot the bounds the permitted attack region within The two red arrows the two vectors-attack directions on the base image respect respectively the first and second tested model The red dots the images resulting the attack The plane presented is then the ( unique) 2-dimensional plane containing those 3 points Dark grey void (outside the slice boundaries all other pixels generated a forward pass the model at those coordinates used representing the majority classDecision regions 3072-dimensional sets visualizing itself poses What we present color-coded values the models restricted 2-dimensional planes all images chosen so and the closest adversarial exampleor attempt find for both models in a pair being coplanar We observe amongst some support put Figure : adversarial training adds ""thickness around the natural image points pushing further them in making adversarial exampleseven within ensembling makes some classes "" within the decision plane introduce small ""pockets or other classes the combinator thereof removes said pockets to large regions the correct class around images We believe of choosing a good plane plotting the values models phenomena taking of robustness and adversarial examples t-SNE plots BID18 . In increasing parameters trained regard test-time adversarial attacks We showed while increasing parameters improves better do ensembling smaller models than producing Through our experiments show this result due ensembling alone or the implicit robustness adversarially trained models specifically due as if We proposed a high level interpretation why Further work should seek scaling models while controlling number parameters produces the minimal ensembles studied in draw why such architectures generally larger single models even under adversarial training",0.01,0.6030660072211147
"Multi-task learning (MTL) with neural networks leverages commonalities in tasks to improve performance, but often suffers from task interference which reduces the benefits of transfer. To address this issue we introduce the routing network paradigm, a novel neural network and training algorithm. A routing network is a kind of self-organizing neural network consisting of two components: a router and a set of one or more function blocks. A function block may be any neural network – for example a fully-connected or a convolutional layer. Given an input the router makes a routing decision, choosing a function block to apply and passing the output back to the router recursively, terminating when a fixed recursion depth is reached. In this way the routing network dynamically composes different function blocks for each input. We employ a collaborative multi-agent reinforcement learning (MARL) approach to jointly train the router and function blocks. We evaluate our model against cross-stitch networks and shared-layer baselines on multi-task settings of the MNIST, mini-imagenet, and CIFAR-100 datasets. Our experiments demonstrate a significant improvement in accuracy, with sharper convergence. In addition, routing networks have nearly constant per-task training cost while cross-stitch networks scale linearly with the number of tasks. On CIFAR100 (20 tasks) we obtain cross-stitch performance levels with an 85% average reduction in training time.
 Multi-task learning (MTL) is a paradigm in which multiple tasks must be learned simultaneously. Tasks are typically separate prediction problems, each with their own data distribution. In an early formulation of the problem, BID7 describes the goal of MTL as improving generalization performance by ""leveraging the domain-specific information contained in the training signals of related tasks."" This means a model must leverage commonalities in the tasks (positive transfer) while minimizing interference (negative transfer). In this paper we propose a new architecture for MTL problems called a routing network, which consists of two trainable components: a router and a set of function blocks. Given an input, the router selects a function block from the set, applies it to the input, and passes the result back to the router, recursively up to a fixed recursion depth. If the router needs fewer iterations then it can decide to take a PASS action which leaves the current state unchanged. Intuitively, the architecture allows the network to dynamically self-organize in response to the input, sharing function blocks for different tasks when positive transfer is possible, and using separate blocks to prevent negative transfer.The architecture is very general allowing many possible router implementations. For example, the router can condition its decision on both the current activation and a task label or just one or the other. It can also condition on the depth (number of router invocations), filtering the function module choices to allow layering. In addition, it can condition its decision for one instance on what was historically decided for other instances, to encourage re-use of existing functions for improved compression. The function blocks may be simple fully-connected neural network layers or whole networks as long as the dimensionality of each function block allows composition with the previous function block choice. They needn't even be the same type of layer. Any neural network or part of a network can be ""routed"" by adding its layers to the set of function blocks, making the architecture applicable to a wide range of problems. Because the routers make a sequence of hard decisions, which are not differentiable, we use reinforcement learning (RL) to train them. We discuss the training algorithm in Section 3.1, but one way we have modeled this as an RL problem is to create a separate RL agent for each task (assuming task labels are available in the dataset). Each such task agent learns its own policy for routing instances of that task through the function blocks.To evaluate we have created a ""routed"" version of the convnet used in BID26 and use three image classification datasets adapted for MTL learning: a multi-task MNIST dataset that we created, a Mini-imagenet data split as introduced in BID32 , and CIFAR-100 BID18 , where each of the 20 label superclasses are treated as different tasks. 1 We conduct extensive experiments comparing against cross-stitch networks BID23 and the popular strategy of joint training with layer sharing as described in BID7 . Our results indicate a significant improvement in accuracy over these strong baselines with a speedup in convergence and often orders of magnitude improvement in training time over cross-stitch networks.",901,0.49,523,1.722753346080306,"Multi-task learning ( with leverages commonalities tasks often suffers task interference which reduces transfer To address introduce the routing network paradigm a novel neural network and training algorithm A routing network consisting one or more function blocks A function block may any neural network – for fully or layer Given an input the router makes choosing a function block apply and passing back terminating when a fixed recursion depth In this way the routing network dynamically composes different function blocks We employ a collaborative multi-agent reinforcement learningMARL jointly the router and function blocks We evaluate our model against cross-stitch networks shared-layer baselines on multi-task settings of the MNIST, miniimagenet Our experiments demonstrate accuracy sharper convergence In addition routing networks nearly constant pertask training cost while scale On CIFAR10020 tasks obtain cross-stitch performance levels an 85% average reduction Multi-task learning ( must Tasks typically separate prediction problems each their own data distribution In an early formulation BID7 describes the goal MTL improving generalization performance "" contained the training signals related tasks a model must leverage commonalities (positive transfer while interference In MTL problems called a routing network consists two trainable components function blocks Given an input the router selects a function block applies up a fixed recursion depth If the router needs fewer iterations then decide take a PASS action which leaves Intuitively the architecture allows the network dynamically self sharing function blocks different tasks when positive transfer using separate blocks preventThe architecture general allowing many possible router implementations For example the router condition its decision both the current activation a task label or just It can condition on the depth (number router invocations filtering the function module choices layering In addition can condition its decision for one instance on was historically decided for to encourage reuse existing functions for improved compression The function blocks may simple fully-connected neural network layers whole networks as allows composition with the previous function block choice They need even layer Any neural network or part ""routed adding its layers function blocks making the architecture applicable problems Because the routers make a sequence hard decisions which differentiable use reinforcement learningRL We discuss the training algorithm Section but one way have modeled as an RL problem create a separate RL agentassuming task labels available Each such task agent learns routing instances through the function blocksTo evaluate we created the convnet used BID26 use three image classification datasets adapted MTL learning that a Mini-imagenet data split as introduced , CIFAR-100 BID18 , where the 20 label superclasses treated different tasks 1 We conduct extensive experiments comparing against cross-stitch networks BID23 the popular strategy joint training layer sharing as Our results accuracy these strong baselines with a speedup convergence often orders training time over cross-stitch networks",0.01,0.5455911950817549
"We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of $L_0$ regularization. However, since the $L_0$ norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected $L_0$ regularized objective is differentiable with respect to the distribution parameters. We further propose the \emph{hard concrete} distribution for the gates, which is obtained by ``stretching'' a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer. Deep neural networks are flexible function approximators that have been very successful in a broad range of tasks. They can easily scale to millions of parameters while allowing for tractable optimization with mini-batch stochastic gradient descent (SGD), graphical processing units (GPUs) and parallel computation. Nevertheless they do have drawbacks. Firstly, it has been shown in recent works BID6 that they are greatly overparametrized as they can be pruned significantly without any loss in accuracy; this exhibits unnecessary computation and resources. Secondly, they can easily overfit and even memorize random patterns in the data BID39 , if not properly regularized. This overfitting can lead to poor generalization in practice.A way to address both of these issues is by employing model compression and sparsification techniques. By sparsifying the model, we can avoid unnecessary computation and resources, since irrelevant degrees of freedom are pruned away and do not need to be computed. Furthermore, we reduce its complexity, thus penalizing memorization and alleviating overfitting.A conceptually attractive approach is the L 0 norm regularization of (blocks of) parameters; this explicitly penalizes parameters for being different than zero with no further restrictions. However, the combinatorial nature of this problem makes for an intractable optimization for large models.In this paper we propose a general framework for surrogate L 0 regularized objectives. It is realized by smoothing the expected L 0 regularized objective with continuous distributions in a way that can maintain the exact zeros in the parameters while still allowing for efficient gradient based optimization. This is achieved by transforming continuous random variables (r.v.s) with a hard nonlinearity, the Figure 1 : L p norm penalties for a parameter θ according to different values of p. It is easily observed that both weight decay and Lasso, p = 2 and p = 1 respectively, impose shrinkage for large values of θ. By gradually allowing p < 1 we observe that the shrinkage is reduced and at the limit of p = 0 we observe that the penalty is a constant for θ = 0.hard-sigmoid. We further propose and employ a novel distribution obtained by this procedure; the hard concrete. It is obtained by ""stretching"" a binary concrete random variable BID19 BID12 and then passing its samples through a hard-sigmoid. We demonstrate the effectiveness of this simple procedure in various experiments.2 MINIMIZING THE L 0 NORM OF PARAMETRIC MODELS One way to sparsify parametric models, such as deep neural networks, with the least assumptions about the parameters is the following; let D be a dataset consisting of N i.i.d. input output pairs {(x 1 , y 1 ), . . . , (x N , y N )} and consider a regularized empirical risk minimization procedure with an L 0 regularization on the parameters θ of a hypothesis (e.g. a neural network) h(·; θ) 1 : DISPLAYFORM0 DISPLAYFORM1 where |θ| is the dimensionality of the parameters, λ is a weighting factor for the regularization and L(·) corresponds to a loss function, e.g. cross-entropy loss for classification or mean-squared error for regression. The L 0 norm penalizes the number of non-zero entries of the parameter vector and thus encourages sparsity in the final estimates θ * . The Akaike Information Criterion (AIC) BID0 ) and the Bayesian Information Criterion (BIC) BID28 , well-known model selection criteria, correspond to specific choices of λ. Notice that the L 0 norm induces no shrinkage on the actual values of the parameters θ; this is in contrast to e.g. L 1 regularization and the Lasso BID32 , where the sparsity is due to shrinking the actual values of θ. We provide a visualization of this effect in Figure 1 .Unfortunately , optimization under this penalty is computationally intractable due to the nondifferentiability and combinatorial nature of 2 |θ| possible states of the parameter vector θ. How can we relax the discrete nature of the L 0 penalty such that we allow for efficient continuous optimization of Eq. 1, while allowing for exact zeros in the parameters? This section will present the necessary details of our approach. We have described a general recipe that allows for optimizing the L 0 norm of parametric models in a principled and effective manner. The method is based on smoothing the combinatorial problem with continuous distributions followed by a hard-sigmoid. To this end, we also proposed a novel distribution which we coin as the hard concrete; it is a ""stretched"" binary concrete distribution, the samples of which are transformed by a hard-sigmoid. This in turn better mimics the binary nature of Bernoulli distributions while still allowing for efficient gradient based optimization. In experiments we have shown that the proposed L 0 minimization process leads to neural network sparsification that is competitive with current approaches while theoretically allowing for speedup in training. We have further shown that this process can provide a good inductive bias and regularizer, as on the CIFAR experiments with wide residual networks we improved upon dropout.As for future work; better harnessing the power of conditional computation for efficiently training very large neural networks with learned sparsity patterns is a potential research direction. It would be also interesting to adopt a full Bayesian treatment over the parameters θ, such as the one employed at ; BID18 . This would then allow for further speedup and compression due to the ability of automatically learning the bit precision of each weight. Finally, it would be interesting to explore the behavior of hard concrete r.v.s at binary latent variable models, since they can be used as a drop in replacement that allow us to maintain both the discrete nature as well as the efficient reparametrization gradient optimization.",1471,0.767,848,1.7346698113207548,"We propose $L_0$ norm regularization neural networks pruning during by encouraging weights become exactly Such regularization interesting since ( greatly speed training inference improve AIC and, well-known model selection criteria special cases $L_0$ regularization However since the $L_0$ norm of weights nondifferentiable incorporate directly as the objective function We propose through the inclusion collectively determine weights set to zero We show somewhat for certain distributions over the gates the expected $L_0$ regularized objective differentiable We further propose the \emph{hard concrete} distribution the gates obtained `` a binary concrete distribution and transforming its samples with a hard-sigmoid. The parameters the distribution over the gates can then jointly optimized the original network parameters As our method allows straightforward efficient learning model structures allows conditional computation We perform various experiments demonstrate the resulting approach regularizer Deep neural networks flexible function approximators have very They can easily scale parameters while allowing tractable optimization graphical processing units Nevertheless they drawbacks Firstly shown recent works BID6 that they greatly overparametrized as pruned significantly accuracy; exhibits unnecessary computation resources Secondly they can easily overfit even memorize random patterns BID39 , if not regularized This overfitting can poor generalization practiceA way both employing model compression and sparsification techniques By sparsifying the model unnecessary computation resources since irrelevant degrees pruned do Furthermore reduce its complexity thus penalizing memorization alleviating overfittingA conceptually attractive approach the L 0 norm regularization (blocks of) parameters; explicitly parameters for being different with no further restrictions However for for large modelsIn surrogate L 0 regularized objectives It realized smoothing expected L 0 regularized objective continuous distributions in maintain the exact zeros while efficient gradient based optimization This achieved transforming continuous random variables with a hard nonlinearity the Figure : L p norm penalties according different values It easily observed both weight decay Lasso, p = and impose shrinkage for large values By gradually allowing p < we observe reduced at the limit the penalty a constant for �� = 0.hard-sigmoid We further propose and employ a novel distribution obtained this procedure; the hard concrete. It obtained ""stretching a binary concrete random variable BID19 BID12 passing its samples a hard-sigmoid. We demonstrate this simple procedure various experiments.2 MINIMIZING THE L 0 NORM One sparsify, with the least assumptions the; let D a dataset consisting N i.i.d input output pairs {(x 1 . . . , (x N} and consider a regularized empirical risk minimization procedure an L 0 regularization on of a hypothesis h·; 1 : DISPLAYFORM0 where L( corresponds classification or mean-squared error regression The L 0 norm penalizes the parameter vector thus encourages sparsity the final estimates � * . The Akaike Information Criterion (AIC) BID0 ) correspond specific choices ��. Notice the L 0 norm induces on the actual values; in the Lasso BID32 , due shrinking We provide a visualization this effect Figure .Unfortunately , optimization under this penalty the nondifferentiability and 2 |��| possible states How relax the discrete nature the L 0 penalty such allow efficient continuous optimization while exact zeros This section present our approach We described a general recipe optimizing the L 0 norm of parametric models The method smoothing continuous distributions followed a hard-sigmoid. To this end also proposed a novel distribution which coin the hard concrete; a ""stretched"" binary concrete distribution the samples transformed a hard-sigmoid. This in better the binary nature Bernoulli distributions while efficient gradient based optimization In experiments we the proposed L 0 minimization process leads neural network sparsification that competitive while theoretically speedup training We further shown this process provide a good inductive bias regularizer on wide residual networks we improved upon dropoutAs future work; better harnessing conditional computation efficiently training learned sparsity patterns It would also adopt a full Bayesian treatment over the parameters �� such employed at ; BID18 . This would then further speedup compression due automatically learning the bit precision each weight Finally would explore the behavior hard concrete r.v.s at binary latent variable models since a drop that allow maintain both the discrete nature as the efficient reparametrization gradient optimization",0.01,0.5759533015452302
"Recently popularized graph neural networks achieve the state-of-the-art accuracy on a number of standard benchmark datasets for graph-based semi-supervised learning, improving significantly over existing approaches. These architectures alternate between a propagation layer that aggregates the hidden states of the local neighborhood and a fully-connected layer. Perhaps surprisingly, we show that a linear model, that removes all the intermediate fully-connected layers, is still able to achieve a performance comparable to the state-of-the-art models. This significantly reduces the number of parameters, which is critical for semi-supervised learning where number of labeled examples are small. This in turn allows a room for designing more innovative propagation layers. Based on this insight, we propose a novel graph neural network that removes all the intermediate fully-connected layers, and replaces the propagation layers with attention mechanisms that respect the structure of the graph. The attention mechanism allows us to learn a dynamic and adaptive local summary of the neighborhood to achieve more accurate predictions. In a number of experiments on benchmark citation networks datasets, we demonstrate that our approach outperforms competing methods. By examining the attention weights among neighbors, we show that our model provides some interesting insights on how neighbors influence each other. One of the major bottlenecks in applying machine learning in practice is collecting sizable and reliable labeled data, essential for accurate predictions. One way to overcome the problem of limited labeled data is semi-supervised learning, using additional unlabeled data that might be freely available. In this paper, we are interested in a scenario when this additional unlabeled data is available in a form of a graph. The graph provides underlying pairwise relations among the data points, both labeled and unlabeled.Of particular interest are those applications where the presence or absence of an edge between two data points is determined by nature, for instance as a result of human activities or natural relations. As a concrete example, consider a citation network. Each node in the graph is a published research paper, associated with a bag-of-words feature vector. An (directed) edge indicates a citation link. Presence of an edge indicates that the authors of a paper have consciously determined to refer to the other paper, and hence captures some underlying relation that might not be inferred from the bag-of-words feature vectors alone. Such external graph data are available in several applications of interest, such as classifying users connected via a social network, items and customers connected by purchase history, users and movies connected by viewing history, and entities in a knowledge graph connected by relationships. In this paper, we are interested in the setting where the graph is explicitly given and represents additional information not present in the feature vectors.The goal of such graph-based semi-supervised learning problems is to classify the nodes in a graph using a small subset of labeled nodes and all the node features. There is a long line of literature on this topic since BID6 which seeks graph cuts that preserve the known labels and BID50 which uses graph Laplacian to regularize the nearby nodes to have similar labels. However, BID27 recently demonstrated that the existing approaches can be significantly improved upon on a number of standard benchmark datasets, using an innovative neural network architecture on graph-based data known collectively as graph neural networks.Inspired by this success, we seek to understand the reason behind the power of graph neural networks, to guide our design of a novel architecture for semi-supervised learning on graphs. To this end, we first found that a linear classifier of multinomial logistic regression achieves the accuracy comparable to the best known graph neural network. This linear classifier removes all intermediate non-linear activation layers, and only keeps the linear propagation function from neighbors in graph neural networks. This suggests the importance of aggregation information form the neighbors in the graph. This further motivates us to design a new way of aggregating neighborhood information through attention mechanism since, intuitively, neighbors might not be equally important. This proposed attention-based graph neural network captures this intuition and (a) greatly reduces the model complexity, with only a single scalar parameter at each intermediate layer; (b) discovers dynamically and adaptively which nodes are relevant to the target node for classification; and (c) improves upon state-of-the-art methods in terms of accuracy on standard benchmark datasets. Further, the learned attention strengths provide some form of interpretability. They provide insights on why a particular prediction is made on a target node and which neighbors are more relevant in making that decision. In this paper, we present an attention-based graph neural network model for semi-supervised classification on a graph. We demonstrate that our method consistently outperforms competing methods on the standard benchmark citation network datasets. We also show that the learned attention also provides interesting insights on how neighbors influence each other. In training, we have tried more",941,0.546,537,1.7523277467411547,"Recently popularized graph neural networks achieve state accuracy on standard benchmark datasets for improving significantly existing approaches These architectures alternate a propagation layer aggregates the hidden states the local neighborhood. Perhaps surprisingly we show a linear model, that removes all the intermediate fully-connected layers achieve a performance comparable state This significantly parameters critical where number labeled examples small This in allows a room designing more innovative propagation layers Based this insight propose a novel graph neural network removes all the intermediate fully-connected layers the propagation layers attention mechanisms respect The attention mechanism allows learn a dynamic and adaptive local summary the neighborhood to achieve In a number experiments on benchmark citation networks datasets demonstrate our approach competing methods By examining the attention weights among neighbors show our model provides influence One applying machine learning practice collecting sizable and reliable labeled data essential accurate predictions One way overcome limited labeled data semi-supervised learning using additional unlabeled data might freely In are a scenario when this additional unlabeled data available a graph The graph provides underlying pairwise relations among both labeledOf those applications the presence an edge between determined nature for as human activities natural relations As a concrete example a citation network Each node a published research paper associated bag- feature vector An (directed) edge indicates a citation link Presence an edge indicates the authors consciously determined refer hence captures some underlying relation inferred bag- feature vectors alone Such external graph data several applications of interest classifying users connected items customers purchase history users movies viewing entities in a knowledge graph connected relationships In this paper are the setting where the graph explicitly given represents additional information not the feature vectorsThe goal such graph-based semi-supervised learning problems classify the nodes labeled nodes all the node features There literature since BID6 which seeks graph cuts preserve the known labels BID50 uses to regularize the nearby nodes have However BID27 recently demonstrated the existing approaches significantly upon on standard benchmark datasets using on known collectivelyInspired this success seek understand the reason the power to guide To this end first found that a linear classifier of achieves the accuracy comparable the best known graph neural network This linear classifier removes all intermediate non-linear activation layers only keeps the linear propagation function neighbors graph neural networks This suggests the importance aggregation information form the neighbors This further motivates design aggregating neighborhood information through attention mechanism since, intuitively neighbors might equally This proposed attention-based graph neural network captures this intuition (a greatly with at each intermediate layer; discovers dynamically and relevant the target node for classification improves state methods terms accuracy on standard benchmark datasets Further the learned attention strengths provide some form interpretability They provide insights why a particular prediction made on a target node which neighbors relevant making In an attention-based graph neural network model on We demonstrate our method consistently competing methods on the standard benchmark citation network datasets We also show the learned attention also provides interesting insights neighbors influence In training tried more",0.01,0.6209441695871661
"Modern generative models are usually designed to match target distributions directly in the data space, where the intrinsic dimensionality of data can be much lower than the ambient dimensionality. We argue that this discrepancy may contribute to the difficulties in training generative models. We therefore propose to map both the generated and target distributions to the latent space using the encoder of a standard autoencoder, and train the generator (or decoder) to match the target distribution in the latent space. The resulting method, perceptual generative autoencoder (PGA), is then incorporated with maximum likelihood or variational autoencoder (VAE) objective to train the generative model. With maximum likelihood, PGA generalizes the idea of reversible generative models to unrestricted neural network architectures and arbitrary latent dimensionalities. When combined with VAE, PGA can generate sharper samples than vanilla VAE. Recent years have witnessed great interest in generative models, mainly due to the success of generative adversarial networks (GANs) BID7 BID12 BID1 . Despite the prevalence, the adversarial nature of GANs can lead to a number of challenges, such as unstable training dynamics and mode collapse. Since the advent of GANs, substantial efforts have been devoted to addressing these challenges BID21 BID9 BID19 , while non-adversarial approaches that are free of these issues have also gained attention. Examples include variational autoencoders (VAEs) BID13 , reversible generative models BID5 BID14 , and Wasserstein autoencoders (WAEs) BID22 .However , non-adversarial approaches often have significant limitations. For instance , VAEs tend to generate blurry samples, while reversible generative models require restricted neural network architectures or solving neural differential equations BID8 . Furthermore , to use the change of variable formula, the latent space of a reversible model must have the same dimensionality as the data space, which is unreasonable considering that real-world, high-dimensional data (e.g., images) tends to lie on low-dimensional manifolds, and thus results in redundant latent dimensions and variability. Intriguingly , recent research BID3 suggests that the discrepancy between the intrinsic and ambient dimensionalities of data also contributes to the difficulties in training GANs and VAEs.In this work, we present a novel framework for training autoencoder-based generative models, with non-adversarial losses and unrestricted neural network architectures. Given a standard autoencoder and a target data distribution, instead of matching the target distribution in the data space, we map both the generated and target distributions to the latent space using the encoder, and train the generator (or decoder) to minimize the divergence between the mapped distributions. We prove, under mild assumptions, that by minimizing a form of latent reconstruction error, matching the target distribution in the latent space implies matching it in the data space. We call this framework perceptual generative autoencoder (PGA). We show that PGA enables training generative autoencoders with maximum likelihood, without restrictions on architectures or latent dimensionalities. In addition, when combined with VAE, PGA can generate sharper samples than vanilla VAE. 1 2 METHODS 2.1 PERCEPTUAL GENERATIVE MODEL Let f : R D → R H be the encoder parameterized by φ, and g : R H → R D be the decoder parameterized by θ. Our goal is to obtain a generative model, which maps a simple prior distribution to the data distribution, D. Throughout this paper, we use N (0, I) as the prior distribution.For z ∈ R H , the output of the decoder, g (z), lies in a manifold that is at most H-dimensional. Therefore, if we train the autoencoder to minimize DISPLAYFORM0 DISPLAYFORM1 , thenx can be seen as a projection of the input data, x, onto the manifold of g (z). LetD denote the distribution ofx. Given enough capacity of the encoder,D is the best approximation to D (in terms of L2 distance), that we can obtain from the decoder, and thus can serve as a surrogate target for training the generator.Due to the difficulty of directly training the generator to matchD, we seek to mapD to the latent space, and train the generator to match the mapped distribution,Ĥ, in the latent space. To this end, we reuse the encoder for mappingD toĤ, and train the generator such that h (·) = f (g (·)) maps N (0, I) toĤ. In addition, to ensure that g maps N (0, I) toD, we minimize the following latent reconstruction loss with respect to (w.r.t.) φ: DISPLAYFORM2 Formally, let Z (x) be the set of all z's that are mapped to the same x by the decoder, we have the following theorem: Theorem 1. Assuming the convexity of Z (x) for all x ∈ R D , and sufficient capacity of the encoder; for z ∼ N (0, I), if Eq. (2) is minimized and h (z) ∼Ĥ, then g (z) ∼D.Proof. We first show that any different x's generated by the decoder are mapped to different z's by the encoder. Let x 1 = g (z 1 ), x 2 = g (z 2 ), and x 1 = x 2 . Since the encoder has sufficient capacity and Eq. (2) is minimized, we have f ( DISPLAYFORM3 For z ∼ N (0, I), denote the distributions of g (z) and h (z), respectively, by D and H. We then consider the case where D andD are discrete distributions. If g (z) D , then there exists an x, DISPLAYFORM4 The result still holds when D andD approach continuous distributions.Note that the two distributions compared in Theorem 1, D andD, are mapped respectively from N (0, I) and H. While N (0, I) is supported on the whole R H , there can be z's with low probabilities in N (0, I), but with high probabilities in H, which are not well covered by Eq. (2). Therefore, it is sometimes helpful to minimize another latent reconstruction loss on H: DISPLAYFORM5 By Theorem 1, the problem of training the generative model reduces to training h to map N (0, I) tô H, which we refer to as the perceptual generative model. In the subsequent subsections, we present a maximum likelihood approach, as well as a VAE-based approach, to train the perceptual generative model. We proposed a framework, PGA, for training autoencoder-based generative models, with nonadversarial losses and unrestricted neural network architectures. By matching target distributions in the latent space, PGA trained with maximum likelihood generalizes the idea of reversible generative models to unrestricted neural network architectures and arbitrary latent dimensionalities. In addition, it improves the performance of VAE when combined together.In principle, PGA can be combined with any method that can train the perceptual generative model. While we have only considered two non-adversarial approaches, an interesting future work would be to combine PGA with an adversarial discriminator trained on latent representations. Moreover, the compatibility issue with batch normalization deserves further investigation.",1494,0.716,871,1.7152698048220436,"Modern generative models usually designed match target distributions directly the data space the intrinsic dimensionality data much We argue this discrepancy contribute the difficulties training generative models We therefore propose map both the generated and target distributions the latent space the encoder of train the generator (or match The resulting method, perceptual generative autoencoder then incorporated with maximum likelihood or variational autoencoder (VAE) objective to train With maximum likelihood PGA generalizes the idea reversible generative models unrestricted neural network architectures arbitrary latent dimensionalities When combined VAE PGA can generate sharper samples vanilla VAE Recent years great interest generative models mainly BID7 BID12 BID1 . Despite the prevalence, the adversarial nature GANs can challenges unstable training dynamics mode collapse Since GANs substantial efforts devoted addressing BID21 BID9 BID19 , that free gained attention Examples include variational autoencodersVAEs BID13 , reversible generative models BID5 BID14 BID22 .However , non-adversarial approaches often For instance , VAEs tend generate blurry samples while reversible generative models require restricted neural network architectures or solving neural differential equations BID8 Furthermore , to use the change variable formula the latent space a reversible model unreasonable considering tends lie results redundant latent dimensions and variability , recent research BID3 suggests the discrepancy the intrinsic and ambient dimensionalities data also the difficulties training GANs VAEsIn non-adversarial losses unrestricted neural network architectures Given a standard autoencoder and a target data distribution instead matching the data space map the latent space using, train the generator (or minimize the mapped distributions We prove, under mild assumptions by minimizing a form latent reconstruction error matching the target distribution implies matching it We call this framework perceptual generative autoencoder We show PGA enables training generative autoencoders maximum likelihood without restrictions architectures latent dimensionalities In addition when combined VAE PGA can generate sharper samples vanilla VAE 1 2 METHODS 2.1 PERCEPTUAL GENERATIVE MODEL Let f : R D → R H be the encoder parameterized ��, g Our goal obtain a generative model, maps a simple prior distribution the data distribution D. Throughout this paper use N (0 I the prior distributionFor z �� R H the output, gz lies a manifold at H- Therefore train minimize DISPLAYFORM0 thenx can seen a projection x, onto the manifold g (z LetD denote the distribution ofx Given enough capacity of the encoderD is the best approximation (in L2 distance that obtain can serve a surrogate target training the generatorDue directly matchD seek mapD the latent space train mapped distribution��, To this end reuse the encoder mappingD to�� train the generator such h (· f maps N0 I� In addition to g maps N (0 I) toD minimize the following latent reconstruction loss with ( �� DISPLAYFORM2 Formally let Z's mapped same x by we Theorem Assuming the convexity Z (x for all x �� R D sufficient capacity; for z ∼ N0 I if Eq minimized hz ∼�� g ∼D.Proof We first show any different x's generated the decoder mapped different z Let x 1 gz 1 Since the encoder sufficient capacity Eq minimized f DISPLAYFORM3 For z ∼ N (0 I denote the distributions gz by D We then consider where D andD discrete distributions If g (z D , there exists x, DISPLAYFORM4 The result still andD approach continuous distributionsNote compared mapped respectively from N0 I H. While N (0 I supported the whole R H , can z's with low probabilities in N well covered Eq Therefore sometimes minimize another latent reconstruction loss on H: DISPLAYFORM5 By Theorem the problem training reduces training h map N0 I tô H we refer the perceptual generative model In the subsequent subsections a maximum likelihood approach as a VAE-based approach train the perceptual generative model We proposed, PGA training autoencoder-based generative models with nonadversarial losses unrestricted neural network architectures By matching target distributions the latent space PGA trained with maximum likelihood generalizes the idea reversible generative models unrestricted neural network architectures arbitrary latent dimensionalities In addition improves VAE when combined togetherIn principle PGA can combined any method train the perceptual generative model While only considered two non-adversarial approaches an interesting future work would combine PGA an adversarial discriminator trained latent representations Moreover the compatibility issue batch normalization deserves",0.01,0.5265237894524483
"The quality of the representations achieved by embeddings is determined by how well the geometry of the embedding space matches the structure of the data.
 Euclidean space has been the workhorse for embeddings; recently hyperbolic and spherical spaces have gained popularity due to their ability to better embed new types of structured data---such as hierarchical data---but most data is not structured so uniformly.
 We address this problem by proposing learning embeddings in a product manifold combining multiple copies of these model spaces (spherical, hyperbolic, Euclidean), providing a space of heterogeneous curvature suitable for a wide variety of structures.
 We introduce a heuristic to estimate the sectional curvature of graph data and directly determine an appropriate signature---the number of component spaces and their dimensions---of the product manifold.
 Empirically, we jointly learn the curvature and the embedding in the product space via Riemannian optimization.
 We discuss how to define and compute intrinsic quantities such as means---a challenging notion for product manifolds---and provably learnable optimization functions.
 On a range of datasets and reconstruction tasks, our product space embeddings outperform single Euclidean or hyperbolic spaces used in previous works, reducing distortion by 32.55% on a Facebook social network dataset. We learn word embeddings and find that a product of hyperbolic spaces in 50 dimensions consistently improves on baseline Euclidean and hyperbolic embeddings, by 2.6
 points in Spearman rank correlation on similarity tasks
 and 3.4 points on analogy accuracy.
 With four decades of use, Euclidean space is the venerable elder of embedding spaces. Recently, non-Euclidean spaces-hyperbolic BID27 BID33 and spherical BID42 BID24 )-have gained attention by providing better representations for certain types of structured data. The resulting embeddings offer better reconstruction metrics: higher mean average precision (mAP) and lower distortion compared to their Euclidean counterparts. These three spaces are the model spaces of constant curvature BID21 , and this improvement in representation fidelity arises from the correspondence between the structure of the data (hierarchical, cyclical) and the geometry of non-Euclidean space (hyperbolic: negatively curved, spherical: positively curved). The notion of curvature plays the key role.To improve representations for a variety of types of data-beyond hierarchical or cyclical-we seek spaces with heterogeneous curvature. The motivation for such mixed spaces is intuitive: our data may have complicated, varying structure, in some regions tree-like, in others cyclical, and we seek the best of all worlds. We expect mixed spaces to match the geometry of the data and thus provide higher quality representations. However, to employ these spaces, we face several key obstacles. We must perform a challenging manifold optimization to learn both the curvature and the embedding. Afterwards, we also wish to operate on the embedded points. For example, analogy operations for word embeddings in Euclidean vector space (e.g., a − b + c) must be lifted to manifolds. 2 , Euclidean plane E 2 , and hyperboloid H 2 . Thick lines are geodesics; these get closer in positively curved (K = +1) space S 2 , remain equidistant in flat (K = 0) space E 2 , and get farther apart in negatively curved (K = −1) space H 2 .We propose embedding into product spaces in which each component has constant curvature. As we show, this allows us to capture a wider range of curvatures than traditional embeddings, while retaining the ability to globally optimize and operate on the resulting embeddings. Specifically , we form a Riemannian product manifold combining hyperbolic, spherical, and Euclidean components and equip it with a decomposable Riemannian metric. While each component space in the product has constant curvature (positive for spherical, negative for hyperbolic, and zero for Euclidean), the resulting mixed space has non-constant curvature. However, selecting appropriate curvatures for the embedding space is a potential challenge. We directly learn the curvature for each component space along with the embedding (via Riemannian optimization), recovering the correct curvature, and thus the matching geometry, directly from data. We show empirically that we can indeed recover non-uniform curvatures and improve performance on reconstruction metrics.Another technical challenge is to select the underlying number of components and dimensions of the product space; we call this the signature. This concept is vacuous in Euclidean space: the product of E r1 , . . . , E rn is identical to the single space E r1+...+rn . However, this is not the case with spherical and hyperbolic spaces. For example, the product of the spherical space S 1 (the circle) with itself is the torus S 1 × S 1 , which is topologically distinct from the sphere S 2 . We address this challenge by introducing a theory-guided heuristic estimator for the signature. We do so by matching an empirical notion of discrete curvature in our data with the theoretical distribution of the sectional curvature, a fine-grained measure of curvature on Riemannian manifolds that is amenable to analysis in products. We verify that this approach recovers the correct signature on reconstruction tasks.Standard techniques such as PCA require centering so that the embedded directions capture components of variation. Centering in turn needs an appropriate generalization of the mean. We develop a formulation of mean for embedded points that exploits the decomposability of the distance and has theoretical guarantees. For T = {p 1 , . . . , p n } in a manifold M with dimension r, the mean is µ(T ) := arg min p i d 2 M (p, p i ). We give a global existence result: under symmetry conditions on the distribution of the points in T on the spherical components, gradient descent recovers µ(T ) with error ε in time O(nr log ε −1 ).We demonstrate the advantages of product space embeddings through a variety of experiments; products are at least as good as single spaces, but can offer significant improvements when applied to structures not suitable for single spaces. We measure reconstruction quality (via mAP and distortion ) for synthetic and real datasets over various allocations of embedding spaces. We observe a 32.55% improvement in distortion versus any single space on a Facebook social network graph. Beyond reconstruction, we apply product spaces to skip-gram word embeddings, a popular technique with numerous downstream applications, which crucially require the use of the manifold structure. We find that products of hyperbolic spaces improve performance on benchmark evaluations-suggesting that words form multiple smaller hierarchies rather than one larger one. We see an improvement of 3.4 points over baseline single spaces on the Google word analogy benchmark and of 2.6 points in Spearman rank correlation on a word similarity task using the WS-353 corpus. Our results and initial exploration suggest that mixed product spaces are a promising area for future study. Product spaces enable improved representations by better matching the geometry of the embedding space to the structure of the data. We introduced a tractable Riemannian product manifold class that combines Euclidean, spherical, and hyperbolic spaces. We showed how to learn embeddings and curvatures, estimate the product signature, and defined a tractable formulation of mean. We hope that our techniques encourage further research on non-Euclidean embedding spaces. Table 5 : Accuracy on the Google word analogy dataset. Taking products of smaller hyperbolic spaces significantly improves performance. Unlike conventional embeddings, the operations in hyperbolic and product spaces are defined solely through distances and manifold operations. The Appendix starts with a glossary of symbols and a discussion of related work. Afterwards, we provide the proof of Lemma 2. We continue with a more in-depth treatment of the curvature estimation algorithm. We then introduce two combinatorial constructions-embedding techniques that do not require optimization-that rely on the alternative product distances. We give additional details on our experimental setup. Finally, we additionally evaluate the interpretability of these embeddings (i.e., do the separate components in the embedding manifold capture intrinsic qualities of the data?) through visualizations of the synthetic example from FIG0 . DISPLAYFORM0",1663,1.018,917,1.8135223555070883,"The quality the representations achieved embeddings determined embeddings; recently hyperbolic and spherical spaces gained better embed new types--- hierarchical databut most data structured so uniformly We address proposing learning a product manifold combining multiple copies these model spaces providing suitable structures We introduce a heuristic graph data directly determine an appropriate signature--- component spaces their dimensions manifold jointly learn the curvature embedding the product space via We discuss define compute intrinsic quantities means---a challenging notion product manifolds provably learnable optimization functions On a range datasets reconstruction tasks our product space embeddings single Euclidean or hyperbolic spaces used previous works reducing distortion a Facebook social network dataset We learn word embeddings find a product of hyperbolic spaces 50 dimensions consistently improves by on similarity tasks analogy accuracy With four decades use Euclidean space the venerable elder embedding spaces Recently non-Euclidean spaces-hyperbolic BID27 BID33 spherical BID42 BID24 )-have gained attention better representations certain types structured data The resulting embeddings offer better reconstruction metrics: higher mean average precisionmAP lower distortion compared These three spaces the model spaces constant curvature BID21 , this improvement representation fidelity arises the correspondence cyclical: negatively spherical The notion curvature plays.To improve representations for a variety types-beyond hierarchical or cyclical-we seek spaces The motivation such mixed spaces intuitive our data may complicated, varying structure in tree cyclical we seek We expect mixed spaces match the geometry thus higher quality representations However to employ these spaces face We must perform a challenging manifold optimization learn embedding Afterwards also wish operate the embedded points For example analogy operations a − b + must lifted manifolds 2 , Euclidean plane E 2 hyperboloid H Thick lines geodesics; these get closer positively curved (K = +1) space S 2 remain flat get apart .We propose embedding into product spaces each component As show allows capture curvatures while globally optimize operate Specifically , form manifold combining equip While each component space constant curvaturepositive for spherical the resulting mixed space However selecting appropriate curvatures the embedding space We directly learn the curvature for each component space along embedding (via recovering thus matching geometry directly data We show we indeed recover non-uniform curvatures improve performance reconstruction metricsAnother technical challenge select the underlying number components dimensions the product space; call the signature This concept vacuous Euclidean space the product E r1 . . . , E rn is identical the single space E...+rn However spherical and hyperbolic spaces For example the product the spherical space S 1 with itself topologically distinct We address a theory-guided heuristic estimator the signature. We do so matching an empirical notion discrete curvature on amenable analysis products We verify this approach recovers the correct signature reconstruction tasksStandard techniques PCA require centering so the embedded directions capture components variation Centering in turn needs an appropriate generalization the mean We develop a formulation mean for embedded points exploits the distance has theoretical guarantees For T = {p 1 . . . , p n } in a manifold M with dimension r the mean µ(T arg min i d 2 M We give a global existence result: under symmetry conditions on the distribution the points T on the spherical components gradient descent recovers µ(T ) error �� time O(nr log �� −1.We demonstrate the advantages product space embeddings through experiments; products at single spaces offer structures not suitable We measure reconstruction quality (via mAP and distortion ) synthetic and real datasets over various allocations embedding spaces We observe a 32.55% improvement distortion versus any single space a Facebook social network graph Beyond reconstruction apply product spaces skip-gram word embeddings a popular technique with numerous downstream applications which crucially the manifold structure We find products hyperbolic spaces improve benchmark evaluations-suggesting words form multiple smaller hierarchies rather We see an improvement baseline single spaces the Google word analogy benchmark of using the WS-353 corpus Our results and initial exploration mixed product spaces Product spaces enable improved representations by better We introduced a tractable Riemannian product manifold class We showed learn curvatures estimate the product signature defined a tractable formulation mean. We hope our techniques encourage Table 5 : Accuracy on the Google word analogy dataset Taking products smaller hyperbolic spaces significantly Unlike conventional embeddings the operations hyperbolic and product spaces defined solely distances manifold operations The Appendix starts symbols a discussion related work Afterwards provide the proof Lemma We continue more treatment the curvature estimation algorithm We then introduce two combinatorial constructions-embedding techniques do optimization-that rely the alternative product distances We give additional details our experimental setup Finally additionally evaluate the interpretability do the separate components the embedding manifold capture intrinsic qualities through visualizations the synthetic example from FIG0 DISPLAYFORM0",0.01,0.7768626562232259
"Synthesizing user-intended programs from a small number of input-output exam-
 ples is a challenging problem with several important applications like spreadsheet
 manipulation, data wrangling and code refactoring. Existing synthesis systems
 either completely rely on deductive logic techniques that are extensively hand-
 engineered or on purely statistical models that need massive amounts of data, and in
 general fail to provide real-time synthesis on challenging benchmarks. In this work,
 we propose Neural Guided Deductive Search (NGDS), a hybrid synthesis technique
 that combines the best of both symbolic logic techniques and statistical models.
 Thus, it produces programs that satisfy the provided specifications by construction
 and generalize well on unseen examples, similar to data-driven systems. Our
 technique effectively utilizes the deductive search framework to reduce the learning
 problem of the neural component to a simple supervised learning setup. Further,
 this allows us to both train on sparingly available real-world data and still leverage
 powerful recurrent neural network encoders. We demonstrate the effectiveness
 of our method by evaluating on real-world customer scenarios by synthesizing
 accurate programs with up to 12× speed-up compared to state-of-the-art systems. Automatic synthesis of programs that satisfy a given specification is a classical problem in AI BID29 , with extensive literature in both machine learning and programming languages communities. Recently, this area has gathered widespread interest, mainly spurred by the emergence of a sub-area -Programming by Examples (PBE) BID10 . A PBE system synthesizes programs that map a given set of example inputs to their specified example outputs. Such systems make many tasks accessible to a wider audience as example-based specifications can be easily provided even by end users without programming skills. See Figure 1 for an example. PBE systems are usually evaluated on three key criteria: (a) correctness: whether the synthesized program We studied the problem of real-time program synthesis with a small number of input-output examples. For this problem, we proposed a neural-guided system that builds upon PROSE, a state-of-the-art symbolic logic based system. Our system avoids top-down enumerative grammar exploration required by PROSE thus providing impressive synthesis performance while still retaining key advantages of a deductive system. That is, compared to existing neural synthesis techniques, our system enjoys following advantages: a) correctness: programs generated by our system are guaranteed to satisfy the given input-output specification, b) generalization: our system learns the user-intended program with just one input-output example in around 60% test cases while existing neural systems learn such a program in only 16% test cases, c) synthesis time: our system can solve most of the test cases in less than 0.1 sec and provide impressive performance gains over both neural as well symbolic systems.The key take-home message of this work is that a deep integration of a symbolic deductive inference based system with statistical techniques leads to best of both the worlds where we can avoid extensive engineering effort required by symbolic systems without compromising the quality of generated programs, and at the same time provide significant performance (when measured as synthesis time) gains. For future work, exploring better learning models for production rule selection and applying our technique to diverse and more powerful grammars should be important research directions.A ROBUSTFILL PERFORMANCE WITH DIFFERENT BEAM SIZES",661,0.311,363,1.8209366391184574," user-intended programs from input-output exam- ples with several important applications like spreadsheet manipulation Existing synthesis systems either completely rely deductive logic techniques extensively hand- engineered on purely statistical models need massive amounts fail on challenging benchmarks In this work propose Neural Guided Deductive Search a hybrid synthesis technique best both symbolic logic techniques statistical models Thus produces programs satisfy the provided specifications by construction generalize well unseen examples similar Our technique effectively utilizes the deductive search framework reduce the neural component a simple supervised learning setup Further allows both train on sparingly available real-world data still leverage powerful recurrent neural network encoders We demonstrate our method evaluating on real-world customer scenarios synthesizing accurate programs up to 12× speed-up compared state Automatic synthesis programs satisfy AI BID29 , extensive literature Recently this area gathered widespread interest spurred a sub-area -Programming by Examples BID10 . A PBE system synthesizes programs map example inputs their specified example outputs Such systems make many tasks accessible as example-based specifications provided even programming skills See Figure PBE systems usually evaluated three key criteria: whether the synthesized program We studied the problem input-output examples For this problem proposed a neural-guided system builds PROSE state symbolic logic based system Our system avoids top-down enumerative grammar exploration required PROSE thus impressive synthesis performance while key advantages a deductive system That compared existing neural synthesis techniques our system enjoys following advantages a) correctness: programs generated guaranteed satisfy learns with in around 60% test cases while existing neural systems synthesis time solve most provide impressive performance gains both neural as well symbolic systems a deep integration a symbolic deductive inference based system statistical techniques leads best of both the worlds where avoid extensive engineering effort required without generated programs at (when measured synthesis time gains For future work exploring better learning models production rule selection applying our technique diverse and more powerful should important research directionsA ROBUSTFILL PERFORMANCE WITH",0.0,0.7957535994531589
"Variational auto-encoders
 (VAEs) offer a tractable approach when performing approximate inference in otherwise intractable generative models. However, standard VAEs often produce latent codes that are disperse and lack interpretability, thus making the resulting representations unsuitable for auxiliary tasks (e.g. classification) and human interpretation. We address these issues by merging ideas from variational auto-encoders and sparse coding, and propose to explicitly model sparsity in the latent space of a VAE with a Spike and Slab prior distribution. We derive the evidence lower bound using a discrete mixture recognition function thereby making approximate posterior inference as computational efficient as in the standard VAE case. With the new approach, we are able to infer truly sparse representations with generally intractable non-linear probabilistic models. We show that these sparse representations are advantageous over standard VAE representations on two benchmark classification tasks (MNIST and Fashion-MNIST) by demonstrating improved classification accuracy and significantly increased robustness to the number of latent dimensions. Furthermore, we demonstrate qualitatively that the sparse elements capture subjectively understandable sources of variation. Variational auto-encoders (VAEs) offer an efficient way of performing approximate posterior inference with otherwise intractable generative models and yield probabilistic encoding functions that can map complicated high-dimensional data to lower dimensional representations BID11 BID26 BID31 BID25 . Making such representations meaningful and efficient, however, is a particularly difficult task and currently a major challenge in representation learning BID8 BID2 BID9 BID33 . Large latent spaces often give rise to many latent dimensions that do not carry any information, and obtaining codes that properly capture the complexity of the observed data is generally problematic BID33 BID6 BID2 .In the case of linear mappings, sparse coding offers an elegant solution to the aforementioned problem; the representation space is induced to be sparse. In such a way, the encoding function is encouraged to use the minimum number of non-zero elements necessary to describe each observation and condense information in few active variables, different for each sample BID22 BID7 . In fact, due to their efficiency of representation, sparse codes have been used in many learning and recognition systems, as they provide easier interpretation BID14 BID1 BID18 BID0 and increased efficiency in, for example, classification, clustering, and transmission tasks when used as learning inputs BID38 BID35 BID12 .In this work, we aim to extent the aforementioned capability of linear sparse coding to non-linear probabilistic generative models thus allowing efficient, informative and interpretable representations in the general case. To this end we formulate a new variation of the classical VAE in which we employ a sparsity inducing prior in the latent space based on the Spike and Slab distribution. We match this by a discrete mixture recognition function that can map observations to sparse latent vectors. Efficient inference, comparable in complexity to that of standard VAEs, is achieved by deriving an evidence lower bound (ELBO) for the new model which is optimized using standard gradient methods to recover the encoding and decoding functions. In our experiments , we consider two benchmark dataset (MNIST and Fashion-MNIST) and show how the resulting ELBO is able to recover sparse, informative and interpretable representations regardless of the predefined number of latent dimensions. The ability to adjust to data complexity allows to automatically discover the sources of variation in given observations, without the need to carefully adjust the architecture of a model to the given representation task. We demonstrate these properties by first performing classification experiments using latent vectors as inputs, where we demonstrate that VSC representations marginally outperform VAE ones and display greatly improved robustness over large variations in latent space dimensionality. Secondly we show that many sparse elements in retrieved codes control subjectively recognisable features in the generated observations. 2 BACKGROUND AND RELATED WORK 2.1 SPARSE CODING Sparse coding aims to approximately represent input vectors x i with a weighted linear combination of few unknown basis vectors b j BID14 BID1 BID15 . The problem of determining the optimal basis and weights is generally formulated as the minimisation of an objective function of the following form arg min DISPLAYFORM0 where X ∈ R M ×N is the matrix of data, having as columns the input vectors x i ∈ R M ×1 , B ∈ R M ×J is the matrix having as columns the basis vectors b j ∈ R M ×1 , Z ∈ R J×N is the sparse codes matrix, having as columns the sparse codes z i ∈ R J×1 corresponding to the inputs x i , λ is a real positive parameter and φ(z i ) is a sparsity inducing function.Sparse coding can be probabilistically interpreted as a generative model, where the observed vectors x i are generated from the unobserved latent variables z i through the linear process x i = Bz i + , where is the observation noise and is drawn from an isotropic normal distribution with zero mean BID14 BID1 . The model can then be described with the following prior and likelihood distributions DISPLAYFORM1 where β is a real positive parameter, σ is the standard deviation of the observation noise and I is the identity matrix. Performing maximum a posteriori (MAP) estimation with this model results in the minimisation shown in equation 1 with λ = σ 2 β.In contrast to the MAP formulation, we are interested in maximising the marginal likelihood p(x) = p(x i ) and being able to perform such optimisation for arbitrarily complicated likelihood functions p(x|z).Previous work has demonstrated variational EM inference for such maximisation in the linear generative model case, with a particular choice of sparsity inducing prior BID32 BID4 . However, EM inference becomes intractable for more complicated non-linear posteriors and a large number of input vectors BID11 , making such an approach unsuitable to scale to our desired model. Conversely, some work has been done in generalising sparse coding to non-linear transformations, by defining sparsity on Riemannian manifolds BID7 BID3 . These generalisations, however, perform MAP inference as they define a non-linear equivalent of the objective function in equation 1 and are limited to simple manifolds due to the need to compute the manifold's logarithmic map. In this paper, we lay the general framework to induce sparsity in the latent space of VAEs, allowing approximate variational inference with arbitrarily complicated and probabilistic sparse coding models. We derived a lower bound which is of clear interpretation and efficient to estimate and optimise, as the ELBO of a standard VAE. With the resulting encoders, we recovered efficient sparse codes, which proved to be optimal learning inputs in standard classification benchmarks and exhibit good interpretation in many of their non-zero components. We conclude that inducing sparsity in the latent space of generative models appears to be a promising route to obtaining useful codes, interpretable representations and controlled data synthesis, which are all outstanding challenges in VAEs and representation learning in general. In future work, we aim to further study the properties of a sparse latent space with respect to its interpretation and features disentanglement capability. We expect VSC to be able to model huge ensembles of varied data by sparsely populating large latent spaces, hence isolating the features that govern variability among similar objects in widely diverse aggregates of data.",1486,0.615,855,1.7380116959064327,"Variational auto-encodersVAEs offer a tractable approach when performing approximate inference However standard VAEs often produce latent codes disperse lack interpretability the resulting representations auxiliary taskse.g. classi���cation human interpretation We address merging ideas variational auto-encoders sparse coding propose explicitly model sparsity the latent space a VAE with a Spike and Slab prior distribution We derive the evidence lower using a discrete mixture recognition function thereby making approximate posterior inference as computational ef���cient as the standard VAE case With the new approach infer truly sparse representations with We show these sparse representations advantageous standard VAE representations on two benchmark classi���cation tasksMNIST Fashion-MNIST demonstratingcantly increased the number latent dimensions Furthermore demonstrate qualitatively the sparse elements capture subjectively understandable sources variation Variational auto-encodersVAEs offer performing approximate posterior inference otherwise intractable generative models yield probabilistic encoding functions map lower BID11 BID26 . Making such representations meaningful efficient and currently a major challenge representation learning BID8 . Large latent spaces often give many latent dimensions do carry obtaining codes properly generally problematic BID33 BID6 .In linear mappings sparse coding offers; the representation space induced In the encoding function encouraged necessary describe each observation and condense information few active variables different for BID22 BID7 In fact due their efficiency representation sparse codes many learning and recognition systems easier interpretation BID14 BID1 BID18 BID0 increased efficiency, classification transmission tasks when learning inputs aim extent the aforementioned capability linear sparse thus To this end formulate the classical VAE in employ a sparsity inducing prior in the latent space based the Spike and Slab distribution We match this by a discrete mixture recognition function map observations sparse latent vectors Efficient inference comparable standard VAEs achieved deriving an evidence lowerELBO the new model which optimized using standard gradient methods recover In our experiments , consider two benchmark datasetMNIST Fashion-MNIST the resulting ELBO is able recover sparse, informative and interpretable representations regardless the predefined number latent dimensions The ability adjust data complexity allows to automatically discover the sources variation given observations without carefully the architecture the given representation task We demonstrate these properties first performing classification experiments latent vectors demonstrate VSC representations marginally VAE ones display greatly large variations latent space dimensionality Secondly we show many sparse elements retrieved codes control subjectively recognisable features the generated observations 2 BACKGROUND aims approximately represent input vectors x i with a weighted linear combination few unknown basis vectors b j BID14 BID1 BID15 . The problem determining the optimal basis and weights generally formulated the minimisation an objective function the following form arg min DISPLAYFORM0 where X �� R M ×N data having as columns input vectors is having basis the sparse codes matrix corresponding a real positive parameter( inducingSparse coding can interpreted the observed vectors x generated z through the linear process Bz , the observation noise drawn zero mean BID14 BID1 The model can then described the following prior and likelihood distributions DISPLAYFORM1 where β a real positive parameter the observation noise I Performing maximum a posteriori (MAP) estimation this model results shown equation with 2 β.In contrast are the marginal likelihood p(x = i being perform arbitrarily complicated likelihood functions p(x|z).Previous work variational EM inference such maximisation the linear generative model case a particular choice sparsity inducing prior BID32 BID4 . However EM inference becomes more complicated non-linear posteriors input vectors BID11 , making scale our desired model Conversely some work generalising sparse coding by defining sparsity on BID7 BID3 . These generalisations perform MAP inference define a non-linear equivalent equation and limited simple manifolds due compute In lay the general framework to induce sparsity the latent space VAEs allowing approximate variational inference arbitrarily complicated and probabilistic sparse coding models We derived lower which of clear interpretation efficient and optimise, the ELBO of a standard VAE. With the resulting encoders recovered efficient sparse codes proved optimal learning inputs standard classification benchmarks exhibit good interpretation their non-zero components We conclude inducing sparsity the latent space appears obtaining useful codes interpretable representations controlled data synthesis all outstanding challenges VAEs representation learning In future work aim further study a sparse latent space its interpretation features disentanglement capability We expect VSC model huge ensembles varied data by sparsely populating large latent spaces hence isolating govern variability among similar objects widely diverse aggregates",0.01,0.5844681298547681
"A widely observed phenomenon in deep learning is the degradation problem: increasing
 the depth of a network leads to a decrease in performance on both test and training data. Novel architectures such as ResNets and Highway networks have addressed this issue by introducing various flavors of skip-connections or gating mechanisms. However, the degradation problem persists in the context of plain feed-forward networks. In this work we propose a simple method to address this issue. The proposed method poses the learning of weights in deep networks as a constrained optimization problem where the presence of skip-connections is penalized by Lagrange multipliers. This allows for skip-connections to be introduced during the early stages of training and subsequently phased out in a principled manner. We demonstrate the benefits of such an approach with experiments on MNIST, fashion-MNIST, CIFAR-10 and CIFAR-100 where the proposed method is shown to greatly decrease the degradation effect (compared to plain networks) and is often competitive with ResNets. The representation view of deep learning suggests that neural networks learn an increasingly abstract representation of input data in a hierarchical fashion BID26 BID6 BID7 . Such representations may then be exploited to perform various tasks such as image classification, machine translation and speech recognition.A natural conclusion of the representation view is that deeper networks will learn more detailed and abstract representations as a result of their increased capacity. However, in the case of feed-forward networks it has been observed that performance deteriorates beyond a certain depth, even when the network is applied to training data. Recently, Residual Networks (ResNets; BID9 and Highway Networks BID22 have demonstrated that introducing various flavors of skip-connections or gating mechanisms makes it possible to train increasingly deep networks. However, the aforementioned degradation problem persists in the case of plain deep networks (i.e., networks without skip-connections of some form).A widely held hypothesis explaining the success of ResNets is that the introduction of skipconnections serves to improve the conditioning of the optimization manifold as well as the statistical properties of gradients employed during training. BID19 and BID21 show that the introduction of specially designed skip-connections serves to diagonalize the Fisher information matrix, thereby bringing standard gradient steps closer to the natural gradient. More recently, BID0 demonstrated that the introduction of skip-connections helps retain the correlation structure across gradients. This is contrary to the gradients of deep feed-forward networks, which resemble white noise. More generally, the skip-connections are thought to reduce the effects of vanishing gradients by introducing a linear term BID10 .The goal of this work is to address the degradation issue in plain feed-forward networks by leveraging some of the desirable optimization properties of ResNets. We approach the task of learning parameters for a deep network under the framework of constrained optimization. This strategy allows us to introduce skip-connections penalized by Lagrange multipliers into the architecture of our network. In our setting , skip-connections play an important role during the initial training of the network and are subsequently removed in a principled manner. Throughout a series of experiments we demonstrate that such an approach leads to improvements in generalization error when compared to architectures without skip-connections and is competitive with ResNets in some cases.The contributions of this work are as follows:• We propose alternative training strategy for plain feed-forward networks which reduces the degradation in performance as the depth of the network increases. The proposed method introduces skip-connections which are penalized by Lagrange multipliers. This allows for the presence of skip-connections to be iteratively phased out during training in a principled manner. The proposed method is thereby able to enjoy the optimization benefits associated with skip-connections during the early stages of training.• A number of benchmark datasets are used to demonstrate the empirical capabilities of the proposed method. In particular , the proposed method greatly reduces the degradation effect compared to plain networks and is on several occasions competitive with ResNets. This manuscript presents a simple method for training deep feed-forward networks which greatly reduces the degradation problem. In the past, the degradation issue has been successfully addressed via the introduction of skip-connections. As such, the goal of this work is to propose a new training regime which retains the optimization benefits associated with ResNets while ultimately phasing out skip-connections. This is achieved by posing network training as a constrained optimization problem where skip-connections are introduced during the early stages of training and subsequently phased out in a principled manner using Lagrange multipliers.Throughout a series of experiments we demonstrate that the performance of VAN networks is stable, displaying a far smaller drop in performance as depth increases and thereby largely mitigating the degradation problem.",932,0.496,551,1.691470054446461,"A widely observed phenomenon deep learning the degradation problem increasing leads on both test and training data Novel architectures ResNets and Highway networks addressed various flavors skip-connections or gating mechanisms However the degradation problem persists plain feed-forward networks In this work propose address The proposed method poses the learning weights deep networks where the presence skip-connections penalized Lagrange multipliers This allows skip-connections introduced during training subsequently phased a principled manner We demonstrate experiments MNIST fashion-MNIST where the proposed method shown greatly the degradation effect plain networks often competitive ResNets The representation view deep learning suggests learn an increasingly abstract representation BID26 BID6 BID7 Such representations then exploited perform image classificationA natural conclusion the representation view deeper networks learn their increased capacity However feed-forward networks it observed performance beyond applied training data Recently Residual NetworksResNets; BID9 and Highway Networks BID22 have demonstrated introducing various flavors skip-connections or gating mechanisms makes train increasingly deep networks However the aforementioned degradation problem persists plain deep networks skip-connections of some form).A widely held explaining the success ResNets the introduction serves the conditioning the optimization manifold as gradients employed during training BID19 and show the introduction specially designed skip-connections serves diagonalize the Fisher information matrix bringing standard gradient steps More recently BID0 demonstrated the introduction skip-connections helps retain the correlation structure across gradients This contrary the gradients deep feed-forward networks resemble white noise More generally the skip-connections thought reduce vanishing gradients introducing a linear term BID10 .The goal address the degradation issue plain feed-forward networks leveraging some ResNets We approach learning parameters a deep network under constrained optimization This strategy introduce skip-connections penalized Lagrange multipliers into the architecture In our setting , skip-connections play during the initial training subsequently removed a principled manner Throughout a series experiments we demonstrate leads improvements generalization error when architectures skip-connections is competitive ResNetsThe contributions as alternative training strategy plain feed-forward networks which reduces the degradation as the depth The proposed method introduces skip-connections penalized Lagrange multipliers This allows the presence skip-connections iteratively phased during training in a principled manner The proposed method thereby able enjoy the optimization benefits associated skip-connections during training.• A number benchmark datasets the empirical capabilities In particular , the proposed method greatly the degradation effect compared plain networks on several occasions competitive ResNets This manuscript training deep feed-forward networks which greatly the degradation problem In the degradation issue successfully skip-connections As such the goal propose which retains the optimization benefits associated ResNets while ultimately phasing skip-connections This achieved posing network training a constrained optimization problem where skip-connections introduced during subsequently phased a principled manner using Lagrange multipliersThroughout a series VAN networks stable displaying a far smaller drop depth increases thereby largely mitigating the degradation problem",0.01,0.4658841165186682
"Deep learning is becoming more widespread in its application due to its power in solving complex classification problems. However, deep learning models often require large memory and energy consumption, which may prevent them from being deployed effectively on embedded platforms, limiting their applications. This work addresses the problem by proposing methods {\em Weight Reduction Quantisation} for compressing the memory footprint of the models, including reducing the number of weights and the number of bits to store each weight. Beside, applying with sparsity-inducing regularization, our work focuses on speeding up stochastic variance reduced gradients (SVRG) optimization on non-convex problem. Our method that mini-batch SVRG with $\ell$1 regularization on non-convex problem has faster and smoother convergence rates than SGD by using adaptive learning rates. Experimental evaluation of our approach uses MNIST and CIFAR-10 datasets on LeNet-300-100 and LeNet-5 models, showing our approach can reduce the memory requirements both in the convolutional and fully connected layers by up to 60$\times$ without affecting their test accuracy. Artificial intelligence is finding wider application across a number of domains where computational resources can vary from large data centres to mobile devices. However, state-ofthe-art techniques such as deep learning BID14 require significant resources, including large memory requirements and energy consumption. Reducing the size of the deep learning model to a compact model that has small memory footprint without compromising its performance is a desirable research aim to address the challenges for deploying these leading approaches on mobile devices. 1 regularization can be used as a penalty to train models to prevent the model from over-fitting the training data. As well as providing, 1 regularization is a powerful compression techniques to penalize some weights to be zero. As the results, our research focus on improving the method based on 1 regularization to reduce memory requirements. Moreover, as deep neural network optimization is a non-convex problem, the optimization can be stuck in local-minimal, which can reduce the performance. To address the problem, we improve SGD optimization for non-convex function to enhancing sparse representations obtained with 1 regularization. In this paper, we propose our compression method Weight Reduction Quantisation which reduces both the number of weights and bits-depth of model without sacrificing accuracy. To reduces the number of weights, our method employs sparsity-inducing 1 regularization to encourage many connections in both convolutional and fully connected layers to be zero during the training process. Formally, in this paper we consider the following unconstrained minimization problem, Given training labels y 1 , y 2 , ..., y N as correct outputs for input data x 1 , x 2 , ..., x N , the optimization problem to estimate the weights in all layers, W, is defined by DISPLAYFORM0 L(y i , f(x i ; W)) + λr(W),where λ is a hyper-parameter controlling the degree of regularization and the weights in all layers is given by W. The problem 1 can be strongly convex or possibly non-convex BID2 . Following update rule, the mini-batch SGD method with 1 regularization is a popular approach for performing the optimization, and the weight update rule is given by DISPLAYFORM1 where each weight of network can be represented by w j ,the total number of weights is M. k is the iteration counter and η k is the learning rate and B is mini-batch size (1 < B < N) used to approximate the full gradient. However, SGD optimization with 1 regularization has two challenges: firstly, it inefficiently encourages weight to be zero due to fluctuations generated by SGD BID18 . Secondly, SGD optimization slowing down convergence rate due to the high variance of gradients. The two methods of cumulative 1 regularization and SVRG can solve the two challenges respectively:Cumulative 1 regularization BID18 proposed a method cumulating the 1 penalties to resolve the problem. The method clips regularization at zero, which avoids the derivative DISPLAYFORM2 being non-differentiable when w j = 0 and provides a more stable convergence for the weights. Moreover, the cumulative penalty can reduce the weight to zero more quickly.Mini-batch SVRG As SGD optimization has slow convergence asymptotically due to noise, BID12 proposed SVRG that can efficiently decrease the noise of SGD by reducing the variance of gradients by: DISPLAYFORM3 whereμ j is the average gradient of sub-optimal weightsw j which is the weight after every m SGD iterationsμ DISPLAYFORM4 whereW is the sub-optimal weights after m SGD iterations in all layers. For succinctness we also write ∇ψ i (w DISPLAYFORM5 . They determined that reduction of variance helps initial weights w 0 close to global minima at the beginning in order to boost the convergence rate of SGD in strongly convex problems. BID12 further prove that the performance of SGD degrades with mini-batching by the theoretical result of complexity. Specifically, for batch size of B, SGD has a 1/ √ B dependence on the batch size. In contrast, SVRG in a parallel setting has 1/B dependence on the batch size which is much better than SGD. Hence, SVRG allows more efficient mini-batching. However, for non-strongly convex problems, global minimization of non-convex function is NP-hard BID1 . BID12 have a assumption that SVRG can also be applied in neural networks to accelerate the local convergence rate of SGD. Further, Allen BID1 prove non-asymptotic rates of convergence of SVRG for non-convex optimization and proposed improved SVRG that is provably faster than SGD. Hence, a promising approach is to use mini-batch SVRG instead of SGD with cumulative 1 regularization. In this paper, we proposed Weight Reduction Quantisation that efficiently compressed neural networks without scarifying accuracy. Our method has two stages that reduce the number of weights and reduce the number of bits to store each weight. We show that SVRG and cumulative 1 regularization can improve over SGD and 1-regularization. By combining them, we have presented a new compression method Delicate-SVRG-cumulative-1 that can efficiently reduce the number of parameters by the separate adaptive learning rates. The three adaptive learning rates are applied on SVRG and cumulative 1 penalty, which provides a high accuracy and reduced number of weights. Besides, our method improved SVRG that can be used on non-convex problem with fast convergence rate. In our experiments on LeNet-300-100 and LeNet-5, our method can significantly reduce the memory requirements up to 60× without accuracy loss. After compression by our method, a compact deep neural network can be efficiently deployed on an embedded device with performance of the original model.Algorithm 1 Delicate-SVRG-cumulative-1: Stochastic descent training with cumulative 1 penalty procedure Train( λ) u ← 0 µ ← 0 Initial w j and q j with zero for all number of weights M for k=0 to Maximal Iterations do DISPLAYFORM0 end for u ← u + ηλ/M end for for j ∈ features used in sample i do randomly select m features from train samples DISPLAYFORM1 (∇ψ i (w j ) -∇ψ i (w j )) + β kμ ∇ψ i (w j ) = ∇ψ i (w j ) if w j andw j converge to the same weights theñ µ = 0 end if µ ←μ + The results showed in Figure4.7.3 Using multiple initializations to compare the performance of our method and other three methods.The experiments were run with multiple initializations and there was some small variability in the results. However, the relative performance of the our method is always better than SVRG and SGD combining with cumulative 1 regularization. The results showed in (b) The test loss: MNIST dataset on LeNet-5 (left) and CIFAR-10 dataset on LeNet-300-100 (middle) and Figure 4: Estimate the convergence rate when using four compression methods, including our method Delicate-SVRG-cumulative-1, Delicate-SVRG-cumulative-1 (without BiasPruning) that without bias-based pruning in 1 regularization,SVRG-cumulative-1 and SGD-cumulative-1, on LeNet-300-100 and LeNet-5 models with MNIST and CIFAR-10 datasets. Here we choose the compression rate that equal 90% to observe training and test loss. For MNIST dataset, we did not notice subtle difference train and test loss on LeNet-300-100 model generated by four methods. Figure 5: Using three types of initial weights, we compare our method with other three methods. D-SVRG-C-L1 and D-SVRG-C-L1(wo BiasPruning) are always better than other two methods. This experiment also can verify the our view that the performance of SVRG is better or worse than SGD that depends on the number of training samples. In our experiment, if choosing small dataset (e.g. MNIST), SVRG is better than SGD. Otherwise, if choosing relatively large dataset (e.g. CIFAR-10), SVRG is worse than SGD.",1901,0.919,1053,1.805318138651472,"Deep learning its application due solving However deep learning models often require large memory and energy consumption prevent deployed embedded platforms limiting This work addresses by proposing methods {\em Weight Reduction Quantisation compressing the memory footprint the models reducing weights bits applying with sparsity-inducing regularization our work focuses speeding stochastic variance reduced gradients on. Our method that mini-batch SVRG with $\ell$1 regularization on has faster and smoother convergence rates SGD by adaptive learning rates Experimental evaluation our approach uses on LeNet-300-100 and LeNet-5 models showing our approach reduce both 60$\times$ without their test accuracy finding wider application where computational resources vary large data centres However state-ofthe-art techniques deep BID14 require including large memory requirements Reducing the deep learning model a compact model without a desirable research aim to for deploying these leading approaches 1 regularization can a penalty train models prevent As well, 1 regularization a powerful compression techniques penalize some weights zero As the results, our focus improving the method based 1 regularization to reduce memory requirements Moreover deep neural network optimization stuck local- reduce To address improve SGD optimization to enhancing sparse representations obtained 1 regularization In our compression method Weight Reduction Quantisation which weights bits-depth model without sacrificing To reduces weights our method employs sparsity-inducing 1 regularization encourage many connections zero during Formally in this paper Given training labels y 1 ... as correct outputs input data x optimization to estimate all layers W DISPLAYFORM0 L(y i ; W + controlling is The problem 1 can strongly convex possibly non BID2 . Following update rule the mini-batch SGD method with 1 regularization a popular approach performing the optimization the weight update rule given DISPLAYFORM1 where each weight network can w jthe total number M. k is the iteration counter �� k B mini-batch size1 < B < N used approximate the full gradient However SGD optimization with 1 regularization has two challenges inefficiently encourages weight to zero due fluctuations generated SGD BID18 . Secondly SGD optimization slowing convergence rate due The two methods cumulative 1 regularization SVRG can solve respectivelyCumulative 1 regularization BID18 proposed cumulating the 1 penalties resolve The method clips regularization at zero avoids the derivative DISPLAYFORM2 being non w j provides the weights Moreover the cumulative penalty can reduce to zero moreMini-batch SVRG As SGD optimization slow convergence due noise BID12 proposed that efficiently decrease gradients: DISPLAYFORM3 whereμ j sub-optimal weightsw j which after every m SGD iterationsμ DISPLAYFORM4 whereW m in all layers For succinctness we also write ���� iw DISPLAYFORM5 . They determined reduction variance helps initial weights w 0 close global minima at in boost SGD strongly convex problems BID12 further prove the performance SGD degrades minibatching by the theoretical result complexity Specifically for batch size B, SGD has a 1/ �� B dependence In contrast SVRG in a parallel setting 1/B dependence the batch size which much SGD Hence SVRG allows more efficient minibatching However for non-strongly convex problems global minimization NPhard BID1 . BID12 have a assumption SVRG can also applied neural networks accelerate the local convergence rate SGD Further Allen BID1 prove non-asymptotic rates convergence SVRG for proposed that provably faster SGD Hence a promising approach minibatch SVRG instead SGD with cumulative 1 regularization In proposed Weight Reduction Quantisation that efficiently compressed without scarifying accuracy Our method two stages that reduce weights bits each weight We show SVRG cumulative 1 regularization over SGD 1- By combining them presented Delicate-SVRG-cumulative-1 that efficiently parameters the separate adaptive learning rates The three adaptive learning rates applied on SVRG cumulative 1 penalty provides reduced number weights Besides our method improved SVRG that can fast convergence rate In our experiments LeNet-300100 our method can significantly up 60× without accuracy loss After compression by our method a compact deep neural network efficiently deployed performance the original modelAlgorithm 1 DelicateSVRGcumulative-1 Stochastic descent training cumulative 1 penalty procedure Train( �� u � µ � Initial w j and with zero for all number weights M for Maximal Iterations do DISPLAYFORM0 end for +�λ/ for j �� features used sample i do randomly m features train samples ( if converge theñ µ end if µ ��μ The results showed in Figure4.7.3 Using multiple initializations compare other three methodsThe experiments there some small variability However the relative performance the our method always SVRG combining cumulative 1 regularization The results showed in (b The test loss: MNIST dataset on LeNet-5left-100 Figure: Estimate the convergence rate when four compression methods our method DelicateSVRGcumulative-1without BiasPruning that without in 1 regularization SGD on models Here choose the compression rate equal 90 observe training test loss For MNIST dataset did notice subtle difference train and test loss LeNet-300-100 model generated four methods Figure Using three types initial weights our method other three methods always better other two methods This experiment also can verify the our view the performance SVRG or SGD that depends training samples In our experiment if choosing small dataset SVRG better Otherwise choosing relatively large dataset SVRG worse",0.01,0.7559590324897273
"It has been argued that the brain is a prediction machine that continuously learns how to make better predictions about the stimuli received from the external environment. For this purpose, it builds a model of the world around us and uses this model to infer the external stimulus. Predictive coding has been proposed as a mechanism through which the brain might be able to build such a model of the external environment. However, it is not clear how predictive coding can be used to build deep neural network models of the brain while complying with the architectural constraints imposed by the brain. In this paper, we describe an algorithm to build a deep generative model using predictive coding that can be used to infer latent representations about the stimuli received from external environment. Specifically, we used predictive coding to train a deep neural network on real-world images in a unsupervised learning paradigm. To understand the capacity of the network with regards to modeling the external environment, we studied the latent representations generated by the model on images of objects that are never presented to the model during training. Despite the novel features of these objects the model is able to infer the latent representations for them. Furthermore, the reconstructions of the original images obtained from these latent representations preserve the important details of these objects. The general idea of predictive coding BID8 BID9 BID11 postulates that the brain is continuously trying to predict the information it receives from external environment. An implementation of predictive coding was first proposed as a model of visual information processing in the brain BID12 . Recently, it was described as an implementation of the free-energy principle in the brain BID1 . Predictive coding models the visual information processing pathways as a recurrently connected hierarchical neural network. Feedback connections from higher to lower level areas convey predictions about the activities of the lower level neurons and feedforward connections convey the residual errors in these predictions to higher level areas.Several studies have focused on the biological plausibility of predictive coding and its relation to other learning approaches. In BID14 , the author showed that a model of biased competition BID0 that uses lateral inhibition to suppress the input of other nodes is equivalent to the linear model of predictive coding. An extension to predictive coding has been proposed in BID13 that relaxes the requirement of symmetric weights between two adjacent layers in the network. In a similar study, it was shown that the error-backpropagation and predictive coding use similar forms of weight changes during learning BID16 .From the perspective of training deep neural networks, predictive coding is an approach that is widely supported by neurophysiological data BID3 ) and adheres to the architectural and locality (in terms of learning) constraints imposed by the brain. Existing studies on predictive coding has focused on small neural network models to study the development of orientation selective receptive fields in primary visual cortex BID12 BID13 . It is unclear how predictive coding can be used to build deep neural network models of the brain to study more complicated brain processes like attention, memory, etc. Another important question that arises while building models of the brain is how can we comply with the architectural constraints applicable in the brain like the retinotopic arrangement of receptive fields that is found in the sensory cortical areas. At present, mostly neural networks with fully connected layers are used, which implies that the receptive fields of neurons are as big as the field of view. To overcome this, neural network models are trained on patches from real world images. This approach works well when training small neural network models but it is difficult to extend it for training deep neural networks.In this paper, we present a systematic approach for training deep neural networks using predictive coding in a biologically plausible manner. The network is used to learn hierarchical latent representations for a given input stimulus. The architecture of these neural networks is inspired by convolutional neural networks BID5 . However, to comply with the retinotopic arrangement of receptive fields observed in sensory cortical areas, we employ neural networks in which filters are not applied across the entire layer, similar to locally connected layers used in BID15 . Instead, filters are applied only to a small receptive field which allows us to train the filters associated with different receptive fields independently. This approach can be easily scaled to train deep neural networks for modeling information processing along the sensory processing pathways.In general, the approach proposed in this paper can be used for stimuli in any modality. To illustrate the effectiveness of the approach, we trained a deep neural network using predictive coding on 1000 real-world images of horses and ships from the CIFAR-10 data set. The model is trained in an unsupervised learning paradigm to build a generative model for real-world images and is used to infer latent representations for real-world. To estimate the capacity of the network in modeling real-world images, we used the model to infer latent representations for new images of horses and ships as well as objects that are never presented to the network during training. The model is able to reconstruct the original real-world images from the inferred latent representations while retaining the important features of the objects in these images. This shows that the model can capture the causal regularities in real-world images.The paper is organized as follows: Section 2 describes the architecture and the predictive coding based learning algorithm used for training deep neural network models. Section 3 describes the results of studies conducted using the trained models. Section 4 discusses the computational implications of deep predictive coding and its relationship with other approaches in machine learning. Section 5 summarizes the conclusions from the experiments reported in this paper. In this section, we discuss the computational implications of the algorithm presented in this paper and the similarities it shares with existing approaches in machine learning.Deep neural networks have improved the state-of-the-art performances in many problems related to image processing like classification, semantic segmentation, etc. These improvements have been achieved by exploiting the availability of cheap computational power. However, with increases in the complexity of neural network architectures, the problem of developing efficient learning algorithms has become prominent. A large body of work in machine learning literature has been dedicated to improving the speed of error-backpropagation which is one of the most used learning algorithms for training deep neural networks. However, an inherent property of error-backpropagation is to systematically propagate information through the network in the forward direction and during learning, propagate the error gradients in the backward direction. This imposes restrictions on the extent of parallelization that can be achieved with error back-propagation.In this respect, the proposed learning algorithm can be extensively parallelized. It can be observed from Equations 6 and 7 that the latent representations for the neurons in a given layer depend only on the error in predicting the latent representations at the layer below. This aspect of the learning algorithm can be leveraged to update the latent representations and filters at each layer in the network in parallel. Thus the feedforward and feedback processes can be performed at each layer in parallel. Further, the use of a network architecture with retinotopical arrangement of receptive fields allows us to update the latent representations and filters associated with all positions in a given layer in parallel. Thus, the learning algorithm proposed in this paper is amenable to parallelization and can be useful for speeding up the training of deep neural architectures.Another interesting aspect of the predictive coding is its proximity to the idea of deconvolutional neural networks BID17 . Deconvolutional neural networks have also been used to learn the latent representations for a given input image and have been used for the problem of semantic segmentation BID10 . The problem of learning latent representations is inherently an ill-posed problem as there is no unique solution for a given input stimulus. To overcome this issue deconvolutional neural networks optimize on auxiliary variables and the generated latent representations in alternation. A continuation parameter β is continuously increased during the learning process until the latent representations are strongly clamped to the auxiliary variables. This requires carefully controlling the learning process and increases the computational requirements of the learning algorithm due to an extra optimization step on auxiliary variables. Predictive coding provides an alternate solution to this problem. In Equation 6, the update term associated with td constraint the learning algorithm to generate latent representations that can be easily predicted by the successive layers in the network. The effect of this constraint on the learning algorithm is same as that of the auxiliary variables in deconvolutional neural networks and impart numerical stability to the learning process. This approach provides a more simpler solution to the problem of learning latent representations without imposing the additional computational effort of optimizing auxiliary variables. In this paper, we describe a method to train deep neural networks using predictive coding for modeling information processing along cortical sensory hierarchies. The approach uses a neural network in which neurons project only to neurons in their respective receptive fields. This kind of architecture respects the retinotopic arrangement of receptive fields observed in the visual cortical areas.The method can be used to build a deep generative model for data in any modality. For illustration, we trained the model on a set of real-world images and then used the trained model to infer hierarchical latent representations. Even though the model is trained on a small data set of 1000 images of horses and ships, it can infer effective latent representations for images of other objects like sparrow, cats, trucks, cars, etc. This shows that the trained model is able to capture the statistical regularities present in the real-world images. In this regards, the generalization ability of the model is better than most existing algorithms that usually rely on large amount of data to achieve better generalization.",1895,1.068,1072,1.767723880597015,"It argued the brain a prediction machine continuously the stimuli received For this purpose builds a model around uses infer the external stimulus Predictive coding has proposed through might build such a model However predictive coding build deep neural network models while complying the architectural constraints In this paper build using predictive coding infer latent representations about the stimuli received external environment Specifically used predictive coding train in To understand the capacity the network with regards modeling the external environment studied the latent representations generated images objects never presented during training Despite the novel features these objects the model able infer the latent representations for Furthermore the reconstructions the original images obtained these latent representations preserve these objects The general idea predictive coding BID8 BID9 BID11 postulates continuously trying the information external environment An implementation predictive coding was first as visual information processing BID12 . Recently it described an implementation the free-energy principle the brain BID1 . Predictive coding models the visual information processing pathways as a recurrently connected hierarchical neural network Feedback connections from higher to convey predictions the activities the lower level neurons feedforward connections convey the residual errors these predictionsSeveral studies focused predictive coding its relation other learning approaches In BID14 , the author showed a model biased competition BID0 that uses lateral inhibition suppress the input other nodes equivalent predictive coding An extension to predictive coding has BID13 relaxes symmetric weights between two adjacent layers In a similar study it errorbackpropagation and predictive coding use similar forms weight changes during learning BID16 .From training deep neural networks widely supported BID3 ) adheres architectural and locality (in learning imposed Existing studies predictive coding has small neural network models to study orientation selective receptive fields primary visual cortex BID12 BID13 . It unclear predictive coding build deep neural network models to study more complicated brain processes attention etc Another important question while building models the brain can comply the architectural constraints applicable like receptive fields that found At present mostly neural networks with fully connected layers which implies the receptive fields as big view To overcome neural network models trained patches from real world images This approach training small neural network models but extend for trainingIn predictive coding The network used learn hierarchical latent representations for a given input stimulus The architecture these neural networks inspired BID5 . However to comply the retinotopic arrangement receptive fields observed sensory cortical areas employ neural networks filters not applied across similar locally connected layers used BID15 . Instead filters applied only a small receptive field which allows us train the filters associated different receptive fields independently This approach can easily scaled train modeling information along the sensory processing pathwaysIn general proposed can stimuli any modality To illustrate the approach trained predictive coding on horses ships The model trained to build is infer latent representations. To estimate the capacity modeling real-world images infer latent representations new images horses ships as objects never presented during training The model able reconstruct the inferred latent representations while the objects This shows the model can capture the causal regularities real-world imagesThe paper organized Section describes the architecture the predictive coding based learning training Section describes the results studies using the trained models Section discusses the computational implications deep predictive coding other approaches in Section summarizes the conclusions from the experiments reported In the computational implications the algorithm presented the similarities it shares existing approachesDeep neural networks improved state performances many problems related like classification semantic segmentation etc These improvements achieved exploiting the availability cheap computational power However with increases the complexity developing efficient learning algorithms prominent A large body work machine learning literature dedicated improving error-backpropagation which one training However an inherent property error-backpropagation to systematically propagate information through the forward direction during learning propagate the error gradients This imposes restrictions the extent parallelization errorIn this respect the proposed learning extensively It can observed Equations 6 the latent representations the neurons a given layer depend the error predicting at below This aspect the learning algorithm update the latent representations and filters at each layer in Thus the feedforward and feedback processes can performed at each layer Further the use a network architecture retinotopical arrangement receptive fields allows update the latent representations and filters associated all positions a given layer parallel Thus the learning algorithm proposed amenable parallelization can useful speeding deep architecturesAnother interesting aspect the predictive coding its proximity the idea BID17 . Deconvolutional neural networks also learn the latent representations a given input image have the problem semantic segmentation BID10 . The problem learning latent representations inherently an ill-posed problem as no unique solution a given input stimulus To overcome this issue deconvolutional neural networks optimize on auxiliary variables the generated latent representations alternation A continuation parameter β continuously increased during until the latent representations strongly clamped the auxiliary variables This requires carefully controlling the learning process increases the computational requirements due an extra optimization step on auxiliary variables Predictive coding provides an alternate solution In Equation the update term associated td constraint the learning algorithm to generate latent representations that easily predicted the successive layers The effect this constraint the learning algorithm same the auxiliary variables and impart numerical stability This approach provides a more simpler solution learning latent representations without imposing optimizing auxiliary variables In this paper train predictive coding modeling information processing along cortical sensory hierarchies The approach uses in project only neurons their respective receptive fields This kind architecture respects the retinotopic arrangement receptive fields observed the visual cortical areasThe method can build data in any modality For illustration we trained the model infer hierarchical latent representations Even the model trained small data 1000 images of horses ships infer effective latent representations images like sparrow, cats trucks cars This shows the trained model capture the statistical regularities present In this regards the generalization ability the model better most existing algorithms that usually rely large amount achieve better generalization",0.01,0.6601721659623683
"In this paper, we propose deep convolutional generative adversarial networks (DCGAN) that learn to produce a 'mental image' of the input image as internal representation of a certain category of input data distribution.   This mental image is what the DCGAN 'imagines' that the input image might look like under ideal conditions.   The mental image contains a version of the input that is iconic, without any peculiarities that do not contribute to the ideal representation of the input data distribution within a category. A DCGAN learns this association by training an encoder to capture salient features from the original image and a decoder to convert salient features into its associated mental image representation.   Our new approach, which we refer to as a Mental Image DCGAN (MIDCGAN), learns features that are useful for recognizing entire classes of objects, and that this in turn has the benefit of helping single and zero shot recognition.   We demonstrate our approach on object instance recognition and handwritten digit recognition tasks. Deep convolutional neural networks have had a revolutionary impact on machine learning and computer vision, yet we still fall dramatically short when it comes to learning in a manner that is most similar to people. Consider the way that children interact with objects when they are very young Yu et al., 2009 ): during their interaction, children look at objects from many different perspectives. Eventually they build up a preference for certain viewpoints after examining objects for a long period of time. In this paper, we consider the question of what would happen if we were to train a deep convolutional generative adversarial network in the same manner. For this, we provide the mental image (i.e., an ideal representation), and then provide samples of many different variations of the input image. The Mental Image DCGAN (MIDCGAN) is trained to associate each of these samples in a specific input distribution back to the mental image. This association is learned using a GAN architecture (see FIG1 ) with a generator composed of an encoder and decoder. MID-CGAN trains the encoder to learn salient bottleneck features for each class while the decoder learns to generate a mental image from bottleneck features. We will show that MIDCGAN bottleneck features are better suited for learning than those features that are generated without the benefit of using a mental image.Stated more formally, a typical learning task seeks to learn the data distribution, p(x) mapping to a class or category label y or p(y|x). The diversity of samples in the training data are limiting in the way the learner represents the category class internally. The MIDCGAN approach on the other hand provides a mental imagex as target to be learned and stored as representation of a category target distribution. The learner maps the input data distribution, p(x), to this canonical representation of the category,x, i.e p(x|x). During this mapping process, the MIDCGAN creates an internal bottleneck feature vector that is best representative of the input distribution mapping to the mental image.We demonstrate the effectiveness of mental image DCGANs (MIDCGAN) on two different problems. First, we demonstrate this for handwritten digits as proof of concept. In this case, we assume that a helpful tutor has provided an ideal representation of the digit, so the mental image is a stencil FIG2 . When the MIDCGAN sees a digit, it is trained to think of how it might look if it were looking at the stencil. We mainly demonstrate the performance of MIDCGAN on instance based object recognition. In this case, the helpful tutor provides the system with an iconic view of the object. The MIDCGAN observes the objects from different viewpoints, but at each time it is trained to think of how the object might look like if it were looking at the object from an ideal or iconic perspective. BID22 .We evaluate this in three different ways. First , we evaluate quantitatively the usefulness of the bottleneck features from MIDCGAN on learning tasks (comparing to DCGAN features trained without a mental image). Second , we evaluate qualitatively MIDCGAN's ability to generate mental images. Finally , we evaluate MIDCGAN's ability to perform few shot recognition on objects whose mental image was not learned or transfer learning. More precisely how does MIDCGAN perform when asked to imagine what an object in its frontal view, when it has never seen the object before. In this section, we will present and discuss the four major experiments. In the first two, MNIST and SVHN are evaluated using stencils targets as mental images. In the final two, we evaluate object instance recognition using the Big Berkeley Instance Recognition Database (BigBIRD) and the University of Washington Kinects Objects Dataset. In the first experiment, we learn mental images for each of the objects. In the second experiment, we use the features learned previously to recognize an entirely new database. In all experiments, we show that learning in this manner outperforms features learned from a typical DCGAN architecture. We have demonstrated the use of mental model autoencoder-based DCGAN (MIDCGAN) on digit classification (MNIST), and object recognition on both the Kinects Objects Dataset (RGB-D) and the Bigbird Dataset. Although MIDCGAN was demonstrated on representative viewpoints, the selection of the mental target image could be arbitrary. In cases when MIDCGAN was not sure about the object, the generated image did not resemble the actual representative image, or important details about the representative image were omitted. In essence, it could potentially provide another way to determine the confidence in the prediction of the object class.MIDCGAN can be used on robotics platform with real images in the wild. Given the growing interest in active object manipulation and recognition in the robotics community BID2 . Incorporating real manipulation of objects as separate modality with MIDCGAN could permit robots to learn about objects in their environment with minimal supervision. The mental images described in this paper map very well to the concept of prototype learning in the cognitive science community. Several improvements could be made to MIDCGAN in the future. First, we have generally assumed the availability of a tutor to select a mental image. Autonomous selection of the mental images is an inherent extension to allow semi-supervised and fully unsupervised MIDCGAN training. Alternatively, prototype images can be selected in some systematic manner using some heuristics related to the objects (i.e., a cup holds liquid so prototype is face up, the handle is to be grabbed so that should be visible).",1302,0.784,777,1.6756756756756757,"In learn produce a 'mental image internal representation a certain category input data distribution This mental image what the DCGAN 'imagines that the input image might under The mental image contains a version the input iconic without any peculiarities do contribute the ideal representation the input data distribution within a category A DCGAN learns this association by training an encoder capture salient features salient features its associated mental image representation Our new approach refer a Mental Image DCGANMIDCGAN learns features useful recognizing entire classes this in has single and zero shot recognition We demonstrate our approach on object instance recognition handwritten digit recognition tasks had a revolutionary impact yet fall dramatically in a manner most similar people Consider children interact objects when very Yu et ): during their interaction look Eventually build a preference certain viewpoints after examining objects In consider would train. For this, provide the mental image samples many different variations The Mental Image DCGANMIDCGAN trained associate each these samples a specific input distribution back This association learned using a GAN architecture FIG1 ) a generator composed MID-CGAN trains the encoder learn salient bottleneck each class while generate a mental image bottleneck features We will show MIDCGAN bottleneck features better learning those features generated without using a mental imageStated formally seeks the data distribution, p(x) mapping a class or category label y or The diversity samples the training data limiting the learner represents the category class internally The MIDCGAN approach on provides a mental imagex as target learned stored representation a category target distribution The learner maps the input data distribution p(x this canonical representation the categoryx During this mapping process the MIDCGAN creates an internal bottleneck feature vector best representative the input distribution mapping the mental imageWe demonstrate mental image DCGANs ( First demonstrate this for handwritten digits as proof concept In assume a helpful tutor provided an ideal representation the digit the mental image a stencil FIG2 When the MIDCGAN sees a digit trained think how looking the stencil We mainly demonstrate MIDCGAN instance based object recognition In the helpful tutor provides the system an iconic view the object The MIDCGAN observes the objects from at trained think how looking an ideal or iconic perspective BID22 .We evaluate this in First , evaluate quantitatively the bottleneck features from MIDCGAN on learning taskscomparing to DCGAN features trained without a mental image Second , evaluate qualitatively MIDCGAN's ability generate mental images Finally , evaluate MIDCGAN's ability perform few shot recognition on objects whose mental image learned or transfer learning More precisely how MIDCGAN perform asked imagine an object its frontal view, when never In present and the four major experiments. In, MNIST SVHN evaluated stencils targets as mental images In final two, evaluate object instance recognition the Big Berkeley Instance Recognition DatabaseBigBIRD University Kinects Objects In the first experiment learn mental images for In the second experiment use the features learned previously recognize an entirely new database In all experiments show learning in features learned a typical DCGAN architecture We demonstrated mental model autoencoder-based DCGANMIDCGAN on digit classificationMNIST object recognition on both the Kinects ObjectsRGB-D the Bigbird Dataset. Although MIDCGAN demonstrated on representative viewpoints the selection the mental target image could arbitrary In cases when MIDCGAN sure the object the generated image did resemble the actual representative image important details In essence could potentially provide another way determine the confidence the prediction the object classMIDCGAN can on robotics platform with real images in the wild Given active object manipulation recognition BID2 . Incorporating real manipulation objects as separate modality with MIDCGAN could permit robots learn with minimal supervision The mental images described this paper map very prototype learning Several improvements could MIDCGAN First generally the availability a tutor select a mental image Autonomous selection the mental images an inherent extension allow semi-supervised and fully unsupervised MIDCGAN training Alternatively prototype images selected some systematic manner some heuristics related the objects a cup holds liquid so prototype face the handle to grabbed so should visible",0.01,0.42564142708965313
"An obstacle that prevents the wide adoption of (deep) reinforcement learning (RL) in control systems is its need for a large number of interactions with the environment in order to master a skill. The learned skill usually generalizes poorly across domains and re-training is often necessary when presented with a new task. We present a framework that combines techniques in \textit{formal methods} with \textit{hierarchical reinforcement learning} (HRL). The set of techniques we provide allows for the convenient specification of tasks with logical expressions, learns hierarchical policies (meta-controller and low-level controllers) with well-defined intrinsic rewards using any RL methods and is able to construct new skills from existing ones without additional learning. We evaluate the proposed methods in a simple grid world simulation as well as simulation on a Baxter robot. Reinforcement learning has received much attention in the recent years because of its achievements in games BID17 , , robotics manipulation Jang et al., , BID5 and autonomous driving BID8 , BID16 . However, training a policy that sufficiently masters a skill requires an enormous amount of interactions with the environment and acquiring such experience can be difficult on physical systems. Moreover, most learned policies are tailored to mastering one skill (by maximizing the reward) and are hardly reusable on a new skill.Skill composition is the idea of constructing new skills out of existing skills (and hence their policies) with little to no additional learning. In stochastic optimal control, this idea has been adopted by authors of BID25 and BID4 to construct provably optimal control laws based on linearly solvable Markov decision processes. Authors of BID6 , Tang & Haarnoja have showed in simulated manipulation tasks that approximately optimal policies can result from adding the Q-functions of the existing policies.Hierarchical reinforcement learning is an effective means of achieving transfer among tasks. The goal is to obtain task-invariant low-level policies, and by re-training the meta-policy that schedules over the low-level policies, different skills can be obtain with less samples than training from scratch. Authors of BID7 have adopted this idea in learning locomotor controllers and have shown successful transfer among simulated locomotion tasks. Authors of BID18 have utilized a deep hierarchical architecture for multi-task learning using natural language instructions.Temporal logic is a formal language commonly used in software and digital circuit verification BID1 as well as formal synthesis BID2 . It allows for convenient expression of complex behaviors and causal relationships. TL has been used by BID19 , BID13 to synthesize provably correct control policies. Authors of BID0 have also combined TL with Q-learning to learn satisfiable policies in discrete state and action spaces.In this work, we focus on hierarchical skill acquisition and zero-shot skill composition. Once a set of skills is acquired, we provide a technique that can synthesize new skills without the need to further interact with the environment (given the state and action spaces as well as the transition remain the same). We adopt temporal logic as the task specification language. Compared to most heuristic reward structures used in the RL literature to specify tasks, formal specification language excels at its semantic rigor and interpretability of specified behaviors. Our main contributions are:• We take advantage of the transformation between TL formula and finite state automata (FSA) to construct deterministic meta-controllers directly from the task specification without the necessity for additional learning. We show that by adding one discrete dimension to the original state space, structurally simple parameterized policies such as feed-forward neural networks can be used to learn tasks that require complex temporal reasoning.• Intrinsic motivation has been shown to help RL agents learn complicated behaviors with less interactions with the environment BID22 , BID11 BID9 . However , designing a well-behaved intrinsic reward that aligns with the extrinsic reward takes effort and experience. In our work, we construct intrinsic rewards directly from the input alphabets of the FSA (a component of the automaton), which guarantees that maximizing each intrinsic reward makes positive progress towards satisfying the entire task specification. From a user's perspective, the intrinsic rewards are constructed automatically from the TL formula.• In our framework, each FSA represents a hierarchical policy with low-level controllers that can be re-modulated to achieve different tasks. Skill composition is achieved by manipulating the FSA that results from their TL specifications in a deterministic fashion. Instead of interpolating/extrapolating among existing skills, we present a simple policy switching scheme based on graph manipulation of the FSA. Therefore, the compositional outcome is much more transparent. We introduce a method that allows learning of such hierarchical policies with any non-hierarchical RL algorithm. Compared with previous work on skill composition , we impose no constraints on the policy representation or the problem class. In this paper, we proposed the FSA augmented MDP, a product MDP that enables effective learning of hierarchical policies using any RL algorithm for tasks specified by scTLTL. We also introduced automata guided skill composition, a technique that combines existing skills to create new skills without additional learning. We show in robotic simulations that using the proposed methods we enable simple policies to perform logically complex tasks.Limitations of the current framework include discontinuity at the point of switching (for Equation (15)), which makes this method suitable for high level decision tasks but not for low level control tasks. The technique only compares robustness at the current step and chooses to follow a sub-policy for one time-step, making the switching policy short-sighted and may miss long term opportunities. One way to address this is to impose a termination condition for following each sub-policy and terminate only when the condition is triggered (as in the original options framework). This termination condition can be hand designed or learned",1129,0.622,655,1.7236641221374045,"An obstacle the wide adoption (deep) reinforcement learningRL control systems its need interactions master The learned skill usually generalizes poorly across domains retraining when presented We present combines techniques \textit{formal methods The set techniques provide allows the convenient specification tasks logical expressions learns hierarchical policiesmeta-controller and low-level controllers with well-defined intrinsic rewards using any RL methods construct new skills additional learning We evaluate a simple grid world simulation as simulation on a Baxter robot Reinforcement learning received its achievements games BID17 , , robotics manipulation Jang et al However training a policy sufficiently masters requires interactions acquiring on physical systems Moreover most learned policies tailored mastering one skillby maximizing are hardly reusable onSkill composition the idea constructing out hence their policies In stochastic optimal control this idea adopted authors BID25 construct provably optimal control laws linearly solvable Markov decision processes Authors BID6 , Tang & Haarnoja showed simulated manipulation tasks approximately optimal policies result adding the Q-functionsHierarchical reinforcement learning achieving transfer among tasks The goal obtain task-invariant low-level policies by retraining the meta-policy that schedules over different skills obtain with less samples training from scratch Authors BID7 adopted learning locomotor controllers successful transfer among Authors BID18 utilized a deep hierarchical architecture multi-task learning natural language instructionsTemporal logic commonly software digital circuit verification BID1 as formal synthesis . It allows convenient expression complex behaviors causal relationships TL has used BID19 , to synthesize provably correct control policies Authors BID0 have also combined TL with Q-learning learn satisfiable policies discrete state and action spacesIn hierarchical skill acquisition zero-shot skill composition Once a set skills we provide a technique synthesize without further interact (given the state and action spaces as the transition remain We adopt temporal logic the task specification language Compared most heuristic reward structures used the RL literature to specify tasks formal specification language excels its semantic rigor interpretability of specified behaviors Our main contributions take the transformation between TL formula construct directly the task specification without additional learning We show by adding one discrete dimension structurally simple parameterized policies such feed-forward neural networks learn tasks complex temporal reasoning.• Intrinsic motivation has help RL agents complicated behaviors less interactions BID22 , However , designing a well-behaved intrinsic reward that takes experience In our work construct intrinsic rewards directly the FSAa component guarantees maximizing makes positive progress satisfying the entire task specification From the intrinsic rewards constructed automatically the TL formula.• In our framework each FSA represents a hierarchical policy low-level controllers remodulated Skill composition achieved manipulating the FSA that results their TL specifications Instead interpolating/ among existing skills present a simple policy switching scheme graph manipulation the FSA Therefore the compositional outcome much transparent We introduce learning such hierarchical policies Compared previous work skill composition , impose the policy representation the problem class In proposed the FSA augmented MDP, MDP enables effective learning hierarchical policies any RL algorithm for tasks specified scTLTL We also introduced automata guided skill composition existing skills without additional learning We show in robotic simulations using the proposed methods enable simple policies perform logically complex tasksLimitations discontinuity at switching Equation15 which suitable high level decision tasks but The technique only compares robustness at the current step chooses follow a subpolicy one time-step making the switching policy short may miss long term opportunities One way address impose a termination condition following each subpolicy and terminate only triggered the original options framework This termination condition hand designed learned",0.01,0.5479117724553325
"The tremendous memory and computational complexity of Convolutional Neural Networks (CNNs) prevents the inference deployment on resource-constrained systems. As a result, recent research focused on CNN optimization techniques, in particular quantization, which allows weights and activations of layers to be represented with just a few bits while achieving impressive prediction performance. However, aggressive quantization techniques still fail to achieve full-precision prediction performance on state-of-the-art CNN architectures on large-scale classification tasks. In this work we propose a method for weight and activation quantization that is scalable in terms of quantization levels (n-ary representations) and easy to compute while maintaining the performance close to full-precision CNNs. Our weight quantization scheme is based on trainable scaling factors and a nested-means clustering strategy which is robust to weight updates and therefore exhibits good convergence properties. The flexibility of nested-means clustering enables exploration of various n-ary weight representations with the potential of high parameter compression. For activations, we propose a linear quantization strategy that takes the statistical properties of batch normalization into account. We demonstrate the effectiveness of our approach using state-of-the-art models on ImageNet. The increasing computational complexity and memory requirements of Convolutional Neural Networks (CNNs) have motivated recent research efforts in efficient representation and processing of CNNs. Several optimization and inference approaches have been proposed with the objective of model compression and inference acceleration. The primary aim of model compression is to enable on-device storage (e.g., mobile phones and other resource-constrained devices) and to leverage on-chip memory in order to reduce energy consumption BID13 , latency and bandwidth of parameter accesses. Inference acceleration can be achieved by lowering the precision of computations in terms of resolution, removing connections within networks (pruning), and specialized software/hardware architectures.Quantized Neural Networks are optimization techniques where weights and/or activations of a neural network are transformed from 32-bit floating point into a lower resolution; for aggressive quantization techniques down to binary BID7 BID22 or ternary BID16 BID31 representations. Although prior quantization techniques achieve fullprecision accuracy on highly over-parameterized architectures (e.g., AlexNet, VGG) or toy tasks (e.g., MNIST, SVHN, CIFAR-10), there is still an unacceptable gap between extremely low bitwidth representations and state-of-the-art architectures for real-world tasks. Furthermore, aggressive quantization approaches are usually designed for specific representations (e.g., binary or ternary), and are not scalable in the sense that they do not allow for more quantization levels (i.e., weight values) if required. Thus, accuracy degradation cannot be compensated without changes in the baseline architecture which includes deepening or widening the neural network, and/or using full-precision weights in the input and output layers, respectively.In this work, we address the issue of accuracy degradation by introducing a scalable non-uniform quantization method for weights that is based on trainable scaling factors in combination with a nested-means clustering approach. In particular, nested-means splits the weight distribution iteratively into several quantization intervals until a pre-defined discretization level is reached. Subsequently, all weights within a certain quantization interval are assigned the same weight (i.e., the scaling factor). Nested-means clustering tends to assign small weights to larger quantization intervals while less frequent larger weights are assigned to smaller quantization intervals. This improves classification performance which is in line with recent observations that larger weights carry more information than smaller weights BID9 . We evaluate our approach on state-of-theart CNN architectures in terms of computational requirements and prediction accuracy using the ImageNet classification task.The paper is structured as follows. In Sec. 2 and Sec. 3 related work and background on inference acceleration is discussed. Weight and activation quantization is presented in Sec. 4 and Sec. 5, respectively. Experimental results for ImageNet are shown in Sec. 6. Sec. 7 concludes the paper. We have presented a novel approach for compressing CNNs through quantization and connection pruning, which reduces the resolution of weights and activations and is scalable in terms of the number of quantization levels. As a result, the computational complexity and memory requirements of DNNs are substantially reduced, and an execution on resource-constrained devices is more feasible. We introduced a nested-means clustering algorithm for weight quantization that finds suitable interval thresholds that are subsequently used to assign each weight to a trainable scaling factor. Our approach exhibits both a low computational complexity and robustness to weight updates, which makes it an attractive alternative to other clustering methods. Furthermore, the proposed quantization method is flexible as it allows for various numbers of quantization levels, enabling high compression rates while achieving prediction accuracies close to single-precision floating-point weights.For instance, we utilize this flexibility to add an extra quantization level to ternary weights (quaternary weights), resulting in an improvement in prediction accuracy while keeping the bit width at two. For activation quantization, we developed an approximation based on statistical attributes that have been observed when batch normalization is employed. Experiments using state-of-the-art DNN architectures on real-world tasks, including ResNet-18 and ImageNet, show the effectiveness of our approach.",1055,0.595,632,1.6693037974683544,"The tremendous memory computational complexity prevents the inference deployment on As recent research focused CNN optimization techniques in particular quantization weights activations layers represented while achieving impressive prediction performance However aggressive quantization techniques still fail achieve full-precision prediction performance state CNN architectures on large-scale classification tasks In this work propose weight and activation quantization that scalable terms quantization levels (n-ary representations easy while close full-precision CNNs trainable scaling factors a nested-means clustering strategy which robust weight updates therefore exhibits good convergence properties The flexibility nested-means clustering enables exploration various n-ary weight representations with the potential high parameter compression For activations we propose a linear quantization strategy takes the statistical properties batch normalization We demonstrate our approach state models on ImageNet The increasing computational complexity and memory requirements motivated recent research efforts efficient representation processing CNNs Several optimization and inference approaches with the objective model compression inference acceleration The primary aim model compression enable ondevice storage ( and leverage on in energy consumption BID13 , latency of parameter accesses Inference acceleration can lowering the precision computations terms resolution removing connections within networks (pruning specialized software/hardware architecturesQuantized Neural Networks optimization techniques where weights activations transformed from into a lower resolution; aggressive quantization techniques down binary BID7 BID22 or Although prior quantization techniques achieve fullprecision accuracy on highly over-parameterized architectures or toy tasks MNIST SVHN CIFAR-10 an unacceptable gap extremely low bitwidth representations state architectures for Furthermore aggressive quantization approaches usually designed specific representations binary scalable more quantization levels if required Thus accuracy degradation compensated without changes the baseline architecture which includes deepening or widening the neural network using full-precision weightsIn address introducing a scalable non-uniform quantization method weights trainable scaling factors in combination a nested-means clustering approach In particular nested-means splits the weight distribution iteratively several quantization intervals until a pre-defined discretization level Subsequently all weights within a certain quantization interval assigned Nested-means clustering tends assign small weights larger quantization intervals while less frequent larger weights This improves classification performance which in recent observations larger weights carry BID9 . We evaluate our approach on statetheart CNN architectures computational requirements prediction accuracy using the ImageNet classification taskThe paper structured In Sec 2 and Sec 3 related work and background inference acceleration is discussed Weight and activation quantization is presented Sec 4 and Sec 5, respectively Experimental results for ImageNet Sec 6 Sec 7 concludes the paper We presented compressing CNNs through quantization connection pruning reduces the resolution weights activations is scalable terms quantization levels As the computational complexity and memory requirements DNNs substantially an execution on We introduced a nested-means weight quantization finds suitable interval thresholds that subsequently assign each weight a trainable scaling factor Our approach exhibits both a low computational complexity weight updates alternative other clustering methods Furthermore the proposed quantization method flexible as various numbers quantization levels enabling high compression rates while achieving prediction accuracies close single-precision floating-point weightsFor we utilize this flexibility add ternary weights resulting an improvement while keeping the bit width at two For activation quantization developed an approximation statistical attributes have observed when batch normalization employed Experiments using state DNN architectures on ResNet-18 the effectiveness our approach",0.01,0.4094064412444968
"Reinforcement learning (RL) agents optimize only the features specified in a reward function and are indifferent to anything left out inadvertently. This means that we must not only specify what to do, but also the much larger space of what not to do. It is easy to forget these preferences, since these preferences are already satisfied in our environment. This motivates our key insight: when a robot is deployed in an environment that humans act in, the state of the environment is already optimized for what humans want. We can therefore use this implicit preference information from the state to fill in the blanks. We develop an algorithm based on Maximum Causal Entropy IRL and use it to evaluate the idea in a suite of proof-of-concept environments designed to show its properties. We find that information from the initial state can be used to infer both side effects that should be avoided as well as preferences for how the environment should be organized. Our code can be found at https://github.com/HumanCompatibleAI/rlsp. Deep reinforcement learning (deep RL) has been shown to succeed at a wide variety of complex tasks given a correctly specified reward function. Unfortunately, for many real-world tasks it can be challenging to specify a reward function that captures human preferences, particularly the preference for avoiding unnecessary side effects while still accomplishing the goal BID2 . As a result, there has been much recent work BID8 BID13 Sadigh et al., 2017) that aims to learn specifications for tasks a robot should perform.Typically when learning about what people want and don't want, we look to human action as evidence: what reward they specify BID14 , how they perform a task (Ziebart et al., 2010; BID13 , what choices they make BID8 Sadigh et al., 2017) , or how they rate certain options BID9 . Here, we argue that there is an additional source of information that is potentially rather helpful, but that we have been ignoring thus far:The key insight of this paper is that when a robot is deployed in an environment that humans have been acting in, the state of the environment is already optimized for what humans want.For example, consider an environment in which a household robot must navigate to a goal location without breaking any vases in its path, illustrated in FIG5 . The human operator, Alice, asks the robot to go to the purple door, forgetting to specify that it should also avoid breaking vases along the way. However, since the robot has been deployed in a state that only contains unbroken vases, it can infer that while acting in the environment (prior to robot's deployment), Alice was using one of the relatively few policies that do not break vases, and so must have cared about keeping vases intact. Figure 1: An illustration of learning preferences from an initial state. Alice attempts to accomplish a goal in an environment with an easily breakable vase in the center. The robot observes the state of the environment, s 0 , after Alice has acted for some time from an even earlier state s −T . It considers multiple possible human reward functions, and infers that states where vases are intact usually occur when Alice's reward penalizes breaking vases. In contrast, it doesn't matter much what the reward function says about carpets, as we would observe the same final state either way. Note that while we consider a specific s −T for clarity here, the robot could also reason using a distribution over s −T .The initial state s 0 can contain information about arbitrary preferences, including tasks that the robot should actively perform. For example, if the robot observes a basket full of apples near an apple tree, it can reasonably infer that Alice wants to harvest apples. However , s 0 is particularly useful for inferring which side effects humans care about. Recent approaches avoid unnecessary side effects by penalizing changes from an inaction baseline (Krakovna et al., 2018; Turner, 2018) . However , this penalizes all side effects. The inaction baseline is appealing precisely because the initial state has already been optimized for human preferences, and action is more likely to ruin s 0 than inaction. If our robot infers preferences from s 0 , it can avoid negative side effects while allowing positive ones.This work is about highlighting the potential of this observation, and as such makes unrealistic assumptions, such as known dynamics and hand-coded features. Given just s 0 , these assumptions are necessary: without dynamics, it is hard to tell whether some feature of s 0 was created by humans or not. Nonetheless, we are optimistic that these assumptions can be relaxed, so that this insight can be used to improve deep RL systems. We suggest some approaches in our discussion.Our contributions are threefold. First, we identify the state of the world at initialization as a source of information about human preferences. Second, we leverage this insight to derive an algorithm, Reward Learning by Simulating the Past (RLSP), which infers reward from initial state based on a Maximum Causal Entropy (Ziebart et al., 2010) model of human behavior. Third, we demonstrate the properties and limitations of RLSP on a suite of proof-of-concept environments: we use it to avoid side effects, as well as to learn implicit preferences that require active action. In FIG5 the robot moves to the purple door without breaking the vase, despite the lack of a penalty for breaking vases.",1103,0.574,643,1.7153965785381027,"Reinforcement learning (RL) agents optimize only the features specified a reward function indifferent anything left inadvertently This means must specify to the much space not It easy these preferences since already satisfied our environment This motivates our key insight when a robot deployed humans act the state already optimized what We can therefore this implicit preference information from the state fill We develop Maximum Causal Entropy IRL use evaluate the idea in a suite proof environments designed show its properties We find information the initial state can both side effects that should preferences how organized Our code can https://github.com/HumanCompatibleAI/rlsp Deep reinforcement learningdeep RL succeed given a correctly specified reward function Unfortunately for many real-world tasks challenging specify a reward function captures human preferences particularly the preference avoiding while BID2 . As much recent work BID8 BID13 Sadigh et 2017) aims learn specifications tasks a robot shouldTypically when learning about what people look human action evidence: what reward they specify BID14 , how performZiebart et al what choices , rate certain options Here, argue an additional source information potentially rather helpful been ignoring thusThe key insight when a robot deployed humans acting the state already optimized whatFor consider a household robot must navigate a goal location without breaking any vases illustrated FIG5 The human operator, Alice asks go the purple door forgetting specify also avoid breaking vases along However since the robot deployed a state only contains unbroken vases infer while acting (prior Alice was using one the relatively few policies do break must cared keeping Figure learning preferences from an initial state Alice attempts accomplish an environment an easily breakable vase in The robot observes the state s 0 after Alice acted for from an even earlier state s −T It considers multiple possible human reward functions infers states where vases intact usually occur Alice's reward penalizes breaking In contrast it does much the reward function says carpets we would observe the same final state either Note while consider a specific s −T for clarity here the robot could reason using a distribution over .The initial state s 0 can contain information arbitrary preferences including tasks should actively For example the robot observes a basket full near reasonably Alice wants harvest However , s 0 particularly inferring which side effects humans care Recent approaches avoid unnecessary side effects penalizing changes from an inaction baselineKrakovna 2018 Turner . However , penalizes all side effects The inaction baseline appealing precisely the initial state has optimized human preferences action more ruin s 0 inaction If our robot infers preferences s 0 avoid negative side effects while allowing positive onesThis work about highlighting this observation as such makes unrealistic assumptions known dynamics hand-coded features Given just s 0 these assumptions necessary without dynamics hard some feature was created humans Nonetheless we optimistic these assumptions relaxed so this insight deep RL systems We suggest some approaches our discussionOur contributions threefold First identify the state at initialization as a source human preferences Second leverage this insight derive, Reward Learning by Simulating the Past (RLSP infers reward initial state based a Maximum Causal EntropyZiebart et al Third demonstrate the properties limitations RLSP on a suite proof environments we it avoid side effects as learn implicit preferences require active action In FIG5 the robot moves the purple door without breaking the vase despite a penalty vases",0.01,0.5268467977427499
"Regularization is one of the crucial ingredients of deep learning, yet the term regularization has various definitions, and regularization methods are often studied separately from each other. In our work we present a novel, systematic, unifying taxonomy to categorize existing methods. We distinguish methods that affect data, network architectures, error terms, regularization terms, and optimization procedures. We identify the atomic building blocks of existing methods, and decouple the assumptions they enforce from the mathematical tools they rely on. We do not provide all details about the listed methods; instead, we present an overview of how the methods can be sorted into meaningful categories and sub-categories. This helps revealing links and fundamental similarities between them. Finally, we include practical recommendations both for users and for developers of new regularization methods. Regularization is one of the key elements of machine learning, particularly of deep learning BID37 , allowing to generalize well to unseen data even when training on a finite training set or with an imperfect optimization procedure. In the traditional sense of optimization and also in older neural networks literature, the term ""regularization"" is reserved solely for a penalty term in the loss function BID12 . Recently, the term has adopted a broader meaning: Goodfellow et al. (2016, Chap. 5 ) loosely define it as ""any modification we make to a learning algorithm that is intended to reduce its test error but not its training error"". We find this definition slightly restrictive and present our working definition of regularization, since many techniques considered as regularization do reduce the training error (e.g. weight decay in AlexNet ). Definition 1. Regularization is any supplementary technique that aims at making the model generalize better, i.e. produce better results on the test set.This can include various properties of the loss function, the loss optimization algorithm, or other techniques. Note that this definition is more in line with machine learning literature than with inverse problems literature, the latter using a more restrictive definition.In this work, we create a novel, systematic, unifying taxonomy of regularization methods for deep learning. We analyze existing methods and identify their atomic building blocks. This leads to decoupling of two important concepts: Which assumptions the methods rely on (and try to enforce), and which mathematical and algorithmic tools they use. In turn, this enables better understanding of existing methods and speeds up development of new ones: The researchers can focus either on finding new, better ways of enforcing existing assumptions, or focus on discovery of new assumptions that can be enforced in some existing way.Before we proceed to the presentation of our taxonomy, we revisit some basic machine learning theory in Section 2. This will provide a justification of the top level of the taxonomy. In Sections 3-7, we continue with a finer division of the individual classes of the regularization techniques, aiming at separating as many clearly separable concepts as possible and isolating atomic building blocks of individual methods. Finally, in Section 8 we present our practical recommendations for using existing methods and designing new methods. We are aware that the many research works discussed in this taxonomy cannot be summarized in a single sentence. For the sake of structuring the multitude of papers, we decided to merely describe a certain subset of their properties according to the focus of our taxonomy.",660,0.402,376,1.7553191489361701,"Regularization one the crucial ingredients deep learning yet various definitions regularization methods studied separately each In our work present, systematic unifying taxonomy to existing methods We distinguish methods affect data network architectures error terms regularization terms optimization procedures We identify the atomic building blocks existing methods decouple they enforce the mathematical tools We do provide all details the listed methods; instead present sorted meaningful categories sub This helps revealing links fundamental similarities them Finally include practical recommendations both users new regularization methods Regularization one machine learning particularly of BID37 , allowing to well unseen data even training finite training or an imperfect optimization procedure In optimization and also older neural networks literature reserved solely a penalty term BID12 Recently the term has adopted Goodfellow et (2016 Chap 5 ) loosely define itany modification we a learning intended reduce its test error but We find this definition slightly restrictive present our working definition regularization since many techniques considered reduce the training error in AlexNet Definition 1 Regularization any supplementary technique aims the model generalize better produce onThis can include various properties the loss function the loss optimization algorithm Note this definition more in machine literature inverse problems literature the usingIn create a novel, systematic, unifying taxonomy regularization methods We analyze existing methods identify their atomic building blocks This leads decoupling two important concepts Which assumptions the methods rely try enforce mathematical and tools In turn enables better understanding existing methods speeds: The researchers can focus either finding enforcing existing assumptions focus discovery enforced some existing wayBefore proceed the presentation our taxonomy revisit some basic machine learning theory Section This will provide a justification of the top level the taxonomy In Sections continue a finer division the individual classes the regularization techniques aiming separating as many clearly separable concepts atomic building blocks individual methods Finally in Section we present our practical recommendations existing methods designing We aware the many research works discussed this taxonomy summarized For structuring the multitude papers decided merely describe a certain subset their properties according the focus our taxonomy",0.0,0.6285659995583425
"Deep neural networks are surprisingly efficient at solving practical tasks,
 but the theory behind this phenomenon is only starting to catch up with
 the practice. Numerous works show that depth is the key to this efficiency.
 A certain class of deep convolutional networks – namely those that correspond
 to the Hierarchical Tucker (HT) tensor decomposition – has been
 proven to have exponentially higher expressive power than shallow networks.
 I.e. a shallow network of exponential width is required to realize
 the same score function as computed by the deep architecture. In this paper,
 we prove the expressive power theorem (an exponential lower bound on
 the width of the equivalent shallow network) for a class of recurrent neural
 networks – ones that correspond to the Tensor Train (TT) decomposition.
 This means that even processing an image patch by patch with an RNN
 can be exponentially more efficient than a (shallow) convolutional network
 with one hidden layer. Using theoretical results on the relation between
 the tensor decompositions we compare expressive powers of the HT- and
 TT-Networks. We also implement the recurrent TT-Networks and provide
 numerical evidence of their expressivity. Deep neural networks solve many practical problems both in computer vision via Convolutional Neural Networks (CNNs) BID19 ; BID31 ; BID14 ) and in audio and text processing via Recurrent Neural Networks (RNNs) BID11 ; BID21 BID8 ). However, although many works focus on expanding the theoretical explanation of neural networks success BID20 ; BID6 ; ), the full theory is yet to be developed.One line of work focuses on expressive power, i.e. proving that some architectures are more expressive than others. showed the connection between Hierarchical Tucker (HT) tensor decomposition and CNNs, and used this connection to prove that deep CNNs are exponentially more expressive than their shallow counterparts. However, no such result exists for Recurrent Neural Networks. The contributions of this paper are three-fold.1. We show the connection between recurrent neural networks and Tensor Train decomposition (see Sec. 4); 2. We formulate and prove the expressive power theorem for the Tensor Train decomposition (see Sec. 5), which -on the language of RNNs -can be interpreted as follows: to (exactly) emulate a recurrent neural network, a shallow (non-recurrent) architecture of exponentially larger width is required; DISPLAYFORM0 Figure 1: Recurrent-type neural architecture that corresponds to the Tensor Train decomposition. Gray circles are bilinear maps (for details see Section 4). In this paper, we explored the connection between recurrent neural networks and Tensor Train decomposition and used it to prove the expressive power theorem, which states that a shallow network of exponentially large width is required to mimic a recurrent neural network. The downsides of this approach is that it provides worst-case analysis and do not take optimization issues into account. In the future work, we would like to address the optimization issues by exploiting the Riemannian geometry properties of the set of TT-tensors of fixed rank and extend the analysis to networks with non-linearity functions inside the recurrent connections (as was done for CNNs in ).",636,0.345,373,1.7050938337801609,"Deep neural networks surprisingly efficient practical tasks the theory this phenomenon only starting Numerous works show depth this efficiency A certain class deep convolutional networks – namely those correspond the Hierarchical Tucker (HT) tensor decomposition proven exponentially higher expressive power shallow networks I.e. a shallow network exponential width is required realize the same score function computed the deep architecture In this paper prove the expressive power theoreman exponential lower the width the equivalent shallow network a class – ones correspond the Tensor Train (TT) decomposition This means even processing an image patch by patch with an RNN exponentially one hidden layer Using theoretical results on the relation the tensor decompositions we compare expressive powers the HT- and TT-Networks We also implement the recurrent TT-Networks and provide numerical evidence their expressivity Deep neural networks solve both via BID19 ; BID31 ) audio However although many works focus expanding the theoretical explanation neural networks success BID20 ; ), the full theory yetOne line focuses expressive power proving some architectures showed the connection Hierarchical Tucker (HT tensor decomposition CNNs used this connection prove deep CNNs exponentially expressive their shallow counterparts However no such result Recurrent Neural Networks The contributions this paper three-fold.1 the connection Tensor Train decomposition Sec 4); 2 We formulate prove the expressive power theorem the Tensor Train decomposition Sec 5), which -on the language RNNs follows to (exactly emulate exponentially larger width is DISPLAYFORM0 Figure Recurrent-type neural architecture that corresponds the Tensor Train decomposition Gray circles bilinear maps (for details Section In this paper explored Tensor Train decomposition used it prove the expressive power theorem a shallow network exponentially large width is required mimic The downsides is provides worst-case analysis do optimization issues In the future work, would address the optimization issues by exploiting the Riemannian geometry properties TT-tensors of fixed rank extend networks non-linearity functions inside the recurrent connectionsas was CNNs ).",0.0,0.5005963092887712
"Probabilistic modelling is a principled framework to perform model aggregation, which has been a primary mechanism to combat mode collapse in the context of Generative Adversarial Networks (GAN). In this paper, we propose a novel probabilistic framework for GANs, ProbGAN, which iteratively learns a distribution over generators with a carefully crafted prior. Learning is efficiently triggered by a tailored stochastic gradient Hamiltonian Monte Carlo with a novel gradient approximation to perform Bayesian inference. Our theoretical analysis further reveals that our treatment is the first probabilistic framework that yields an equilibrium where generator distributions are faithful to the data distribution. Empirical evidence on synthetic high-dimensional multi-modal data and image databases (CIFAR-10, STL-10, and ImageNet) demonstrates the superiority of our method over both start-of-the-art multi-generator GANs and other probabilistic treatment for GANs. Generative Adversarial Networks (GAN) BID9 is notoriously hard to train and suffers from mode collapse. There has been a series of works attempting to address these issues. One noticeable thread focuses on objective design, which improves the original JensenShannon divergence with more stable pseudo-metrics such as f -divergence (Nowozin et al., 2016) , χ 2 -divergence (Mao et al., 2017) , and Wasserstein distance BID0 . However, such treatment is inherently limited when a single generator does not include enough model capacity to capture the granularity in data distribution in practice. Clearly, such a generator can hardly produce accurate samples regardless of the choice of objectives.An alternative remedy is to learn multiple generators instead of a single one. This type of methods (Hoang et al., 2018; Tolstikhin et al., 2017; Wang et al., 2016b ) is motivated by a straightforward intuition that multiple generators can better model multi-modal distributions since each generator only needs to capture a subset of the modes. To entail model aggregation, probabilistic modelling is a natural and principled framework to articulate the aggregation process.Recently, Saatci & Wilson (2017) propose Bayesian GAN, a probabilistic framework for GAN under Bayesian inference. It shows that modelling the distribution of generator helps alleviate mode collapse and motivates the interpretability of the learned generators. This probabilistic framework is built upon Bayesian models for generator and discriminator, whose maximum likelihood estimation can be realized as a metaphor of typical GAN objectives.While empirical study on semi-supervised image classification tasks shows the effectiveness of Bayesian GAN, a critical theoretical question on this framework remains unanswered: Does it really converge to the generator distribution that produces the real data distribution? Indeed, our theoretical analysis and experimental results on a simple toy dataset reveal that the current Bayesian GAN falls short of convergence guarantee.With this observation, we follow the prior work to exploit probabilistic modelling as a principled way to realize model aggregation, but approach this problem from a theoretical perspective. We analyze the developed treatment, including the choice of priors, approximate inference, as well as its convergence property, and simultaneously propose a new probabilistic framework with the desirable convergence guarantee and consequently superior empirical performance.Our main contributions are:• We theoretically establish, to our best knowledge, the first probabilistic treatment of GANs such that any generator distribution faithful to the data distribution is an equilibrium.• We prove the previous Bayesian method (Saatci & Wilson, 2017) for any minimax GAN objective induces incompatibility of its defined conditional distributions.• We propose two special Monte Carlo inference algorithms for our probabilistic model which efficiently approximate the gradient of a non-differentiable criterion.• Empirical studies on synthetic high-dimensional multi-modal data and benchmark image datasets, CIFAR-10, STL-10, and ImageNet, demonstrate the superiority of the proposed framework over the state-of-the-art GAN methods. In this paper, we propose ProbGAN, a novel probabilistic modelling framework for GAN. From the perspective of Bayesian Modelling, it contributes a novel likelihood function establishing a connection to existing GAN models and a novel prior stabilizing the inference process. We also design scalable and asymptotically correct inference algorithms for ProbGAN. In the future work, we plan to extend the proposed framework to non-parametric Bayesian modelling and investigate more theoretical properties of GANs in the probabilistic modelling context.Developing Bayesian generalization for deep learning models is not a recent idea and happens in many fields other than generative models such as adversarial training (Ye & Zhu, 2018) and Bayesian neural networks (Wang et al., 2016a) . By this work, we emphasize the importance of going beyond the intuition and understanding the theoretical behavior of the Bayesian model. We hope that our work helps inspire continued exploration into Bayesian deep learning (Wang & Yeung, 2016 ) from a more rigorous perspective. A OMITTED PROOFS Theorem 1. This theorem is general and holds when the GAN objective and the discriminator space have symmetry. The symmetry of GAN objective means its functions φ 1 and φ 2 satisfy that ∃c ∈ R, ∀x ∈ R, φ 1 (x) ≡ φ 2 (c − x). While the symmetry of discriminator space DISPLAYFORM0 Note that the symmetry condition are very weak, first it holds for all the common choices of GAN objectives such as those listed in TAB0 . Second, it holds for neural network which is the most common parameterization for discriminator in practice. DISPLAYFORM1 DISPLAYFORM2 Eqn. 11 and Eqn. 12 prove that q * DISPLAYFORM3 Thus the generator distribution will not change based on the dynamics in Eqn. 2 since q * DISPLAYFORM4 ).",1154,0.539,677,1.7045790251107829,"Probabilistic modelling a principled framework perform model aggregation has a primary mechanism combat mode collapse In GANs ProbGAN, iteratively learns a distribution generators carefully crafted prior Learning is efficiently triggered a tailored stochastic gradient Hamiltonian Monte Carlo with a novel gradient approximation perform Our theoretical analysis further reveals our treatment the first probabilistic framework yields an equilibrium where generator distributions faithful the data distribution on synthetic high-dimensional multi-modal data and image databases STL-10 demonstrates the superiority our method both startof multigenerator GANs other probabilistic treatment for Generative Adversarial Networks (GAN) BID9 notoriously train suffers mode collapse There works attempting One noticeable thread focuses objective design improves the original JensenShannon divergence with more stable pseudometrics f -divergenceNowozin , �Mao Wasserstein distance BID0 However such treatment inherently limited when a single generator does include enough model capacity capture in data distribution in practice Clearly such a generator hardly produce accurate samples regardless the choice objectivesAn alternative remedy learn multiple generators instead This type methods (Hoang 2018 Tolstikhin Wang ) motivated a straightforward intuition multiple generators better model since only capture the modes To entail model aggregation a natural and principled framework articulate the aggregation processRecently Saatci & Wilson2017 propose Bayesian GAN, under It shows modelling the distribution generator helps alleviate mode collapse motivates the interpretability the learned generators This probabilistic framework built generator, whose maximum likelihood estimation realized a metaphor of typical GAN objectivesWhile empirical study semi-supervised image classification tasks shows the effectiveness a critical theoretical question on converge the generator distribution that produces the real data distribution Indeed our theoretical analysis and on a simple toy dataset reveal the current Bayesian GAN falls convergence guaranteeWith this observation follow the prior work to exploit as realize model aggregation approach We analyze the developed treatment, including the choice priors approximate inference as its convergence property simultaneously propose with the desirable convergence guarantee and consequently superior empirical performanceOur main contributions theoretically establish, to GANs such any generator distribution faithful the data distribution an equilibrium.• prove the previous Bayesian methodSaatci Wilson 2017 any minimax GAN objective induces incompatibility its defined conditional distributions.• two special Monte Carlo inference algorithms which efficiently approximate the gradient synthetic high-dimensional multi-modal data benchmark image datasets CIFAR-10 STL-10 state In ProbGAN GAN From Bayesian Modelling contributes a novel likelihood function establishing a connection to existing GAN models prior stabilizing the inference process We also design scalable and asymptotically correct inference algorithms ProbGAN In the future work, plan extend the proposed framework non-parametric Bayesian modelling investigate more theoretical properties GANsDeveloping a recent idea happens otherYe & Zhu 2018 By this work emphasize going the intuition the theoretical behavior We hope our work inspire continued exploration Bayesian deep learning (Wang & Yeung ) from A OMITTED PROOFS Theorem 1 This theorem general holds when the GAN objective and symmetry The symmetry GAN objective means its functions � 1 satisfy that ��c R, �x ( ≡c − x While the symmetry discriminator space DISPLAYFORM0 Note the symmetry condition are very weak first it holds all the common choices GAN objectives such those listed TAB0 . Second holds for neural network which the most common parameterization discriminator in practice DISPLAYFORM1 DISPLAYFORM2 Eqn 11 and Eqn 12 prove q * DISPLAYFORM3 Thus the generator distribution based the dynamics in Eqn 2 since q * DISPLAYFORM4 ).",0.01,0.4992846220297911
"In the adversarial-perturbation problem of neural networks, an adversary starts with a neural network model $F$ and a point $\bfx$ that $F$ classifies correctly, and applies a \emph{small perturbation} to  $\bfx$ to produce another point $\bfx'$ that $F$ classifies \emph{incorrectly}.  In this paper, we propose taking into account \emph{the inherent confidence information} produced by models when studying adversarial perturbations, where a natural measure of ``confidence'' is \|F(\bfx)\|_\infty$ (i.e. how confident $F$ is about its prediction?) . Motivated by a thought experiment based on the manifold assumption, we propose a ``goodness property'' of models which states that \emph{confident regions of a good model should be well separated}. We give formalizations of this property and examine existing robust training objectives in view of them. Interestingly, we find that a recent objective by Madry et al. encourages training a model that satisfies well our formal version of the goodness property, but has a weak control of points that are wrong but with low confidence. However, if Madry et al.'s model is indeed a good solution to their objective, then good and bad points are now distinguishable and we can try to embed uncertain points back to the closest confident region to get (hopefully) correct predictions. We thus propose embedding objectives and algorithms, and perform an empirical study using this method. Our experimental results are encouraging: Madry et al.'s model wrapped with our embedding procedure achieves almost perfect success rate in defending against attacks that the base model fails on, while retaining good generalization behavior.
 In the adversarial perturbation problem of neural networks, an adversary starts with a neural network model F and a point x that F classifies correctly (we assume that F ends with a softmax layer, which is common in the literature), and applies a small perturbation to x to produce another point x that F classifies incorrectly. BID17 first noticed the vulnerability of existing (deep) neural networks to adversarial perturbations, which is a somewhat surprising phenomenon given the great generalization capability of these networks. Since then, a line of research (see, for example, BID5 ; BID14 ; BID9 ; BID8 ) has been devoted to harden neural networks against adversarial perturbation. However, while modest progress has been made, until now there is still a large gap in successfully defending against more advanced attacks, such as attack by BID4 .In this paper, we propose taking into account the inherent confidence information produced by models when studying adversarial perturbations. To this end, a natural measure of confidence is F (x) ∞ (i.e., how confident F is about its prediction?) We motivate this consideration with a thought experiment based on the manifold assumption BID18 ; man) that is commonly made in unsupervised and semi-supervised learning, which states that natural data points lie on (or near to) separate low dimensional manifolds for different classes. Essentially , if one believes that deep neural networks learn to approximate well these low dimensional manifolds, then an ideal model should have the property that it can confidently distinguish points from natural manifolds as they are well separated due to the assumption. Moreover, since the learner never sees points that are far away from the natural manifolds, an ideal model should not claim confidence there.Taking this perspective, we propose a goodness property which states that confident regions of a good model should be well separated. We give formalizations of this property and examine existing robust training objectives in view of them. Interestingly, we find that a recent objective function by BID8 encourages training a model that satisfies well our formal version of the goodness property, in the sense that high-confidence predictions of different classes are well separated. On the other hand, our analysis also indicates that there could be many points with wrong but low-confidence predictions. Therefore, if Madry et al.' s model is indeed a good solution to their objective, then we can distinguish between good and bad points with confidence, and try to embed a low-confidence point back to confident regions to get (hopefully) the correct prediction.We propose two embedding objectives: (1) δ-Most Confident Neighbor (MCN δ ), where MCN δ (F, x) = arg max z∈N (x,δ) F (z) ∞ for a point x, a radius parameter δ > 0, and N (x, δ) the δ-neighborhood around x. (2) p-Nearest Confident Neighbor (NCN p ), where NCN p (F, x) = arg min z z − x subject to F (z) ∞ ≥ p, for a point x and a confidence parameter p ∈ (0, 1). With these, the end to end predictions become F (MCN δ (F, x)) and F (NCN p (F, x)). We note that these objectives are semantic: They fail only when the model has a confident but wrong prediction in the neighborhood.We perform an empirical study over CIFAR10. We first empirically validate that Madry et al.' s model is better, in view of our goodness property, than models trained without a robustness objective. We then give end-to-end defense results based on our method. Specifically, we propose using gradient based optimization, such as Carlini-Wagner attacks BID4 (which, however, are now used for defense) to solve MCN δ or NCN p . Our empirical results are encouraging : (1) It achieves almost perfect success rate in defending against attacks that the base model fails on, and (2) It also retains the good generalization behavior of the base model.The rest of the paper is organized as follows: We first discuss important prior work in Section 2 and some preliminaries in Section 3. Then Section 4 proposes the goodness property, and examines Madry et al.'s robust training objective function in view of the property. We then present embedding objectives and algorithms for handling low-confidence points in Section 5. Section 6 performs an empirical study where we validate that Madry et al.'s robust model satisfies well our goodness property, and then give defense results for our technique. Section 7 concludes with discussions on implications of our method. BID17 first observed the susceptibility of deep neural networks to adversarial perturbations. Since then, a large body of work have been devoted to studying hardening neural networks for this problem (a subset of work in this direction is BID5 BID14 ; BID9 ). Simultaneously, another line of work have been devoted to devise more effective or efficient attacks (a small set of work in this direction is BID10 BID13 BID4 ). Unfortunately, there still seems to be a large gap for the defense methods to defend against more sophisticated attacks, such as CarliniWagner attacks BID4 . For example, while the recent robust residual network constructed by BID8 achieves encouraging robustness results on MNIST, on CIFAR10 the accuracy against a strong adversary, such as attacks by BID4 , can be as low as 45.8%. We now discuss our method and results. (a) Base model on x, unconfident prediction ""automobile"" DISPLAYFORM0 (e) A valid ""ship"" that resembles the ""automobile""(f ) Base model on x, unconfident prediction ""airplane"" ( g) CarliniWagnerShell on x, unconfident prediction ""ship"" (h) Base model on x , unconfident prediction ""ship"" (i) CarliniWagnerShell on x , unconfident prediction ""airplane"" (j) A valid ""ship"" image that resembles the ""airplane"" Figure 2 : The images (a) and (e) are the points where our CarliniWagnerShell makes a wrong prediction. We show the original image on the first column, CarliniWagnerShell perturbations of the original images on the second column, adversarial perturbed images on the third column, and CarliniWagnerShell perturbations of the adversarial examples on the fourth column. Example ship images are presented on the last row for comparison.Our technical contributions. Our first technical contribution is the proposal to take into account the inherent confidence information produced by models when studying adversarial perturbations. Our second technical contribution is a formulation of a goodness property of models, and an analysis of existing models in view of the property. Interestingly, and somewhat surprisingly, we find that a recent robust training objective function by BID8 encourages good separation of highconfidence points, but has essentially no control of low-confidence points. Our third contribution is the proposal of embedding to handle low-confidence points. Our final contribution is a first empirical study that validates Madry et al.'s model in terms of the goodness property, and further demonstrates that a good model, when wrapped with embedding, simultaneously achieves good generalization and almost perfect robustness.Interpretations of our results. One interpretation of our results is that adversarial perturbations can naturally coexist with good generalization. While this is manifested in our analysis of Madry et al.'s objective function, we think that this phenomenon naturally and generally exists if one takes again a manifold point of view: Since natural manifolds reside in low dimensions, it seems much more challenging to control the confidence boundary, where ""adversarial perturbations"" exist in abundance, than controlling separation of the learned structures (i.e. confident regions that approximate the underlying manifolds).On the other hand, if all one cares about is robustness (decision does not change in a small neighborhood), then adversarial perturbation problem can be resolved by combining goodness property with embedding. For example, consider the following ""good model:"" If a data point is from the training set, then it outputs the correct label with confidence 1, otherwise it outputs a uniform distribution over labels. In other words, this model learns nothing but fitting the training set. We note that in this case, the adversarial perturbation problem is only well defined around the training points. Moreover , embedding now becomes 1-nearest neighbor search among the training points. As a result , the model is still perfectly robust with our method if training points are well separated.Highly confident predictions on random noises. We note that several work shows that neural networks can have highly confident predictions on random noises (e.g., BID11 ). In view of our work it is somewhat not surprising that neural networks can have such behaviors: These points are essentially ones that are far away from the ""universe"" the learner is asked to learn, and so if we do not control the training of neural networks to not claim confidence over the structure it has never seen, then it is valid to fit a model that has good behaviors on natural manifolds but also divergent behaviors outside. After all, why is a network supposed to work on points that are far away from the underlying natural manifolds, which is essentially the data generating distribution? Finally, we note that the adversarial perturbation problem is not well defined even near those points.",2271,1.04,1323,1.7165532879818595,"In the adversarial-perturbation problem neural networks an adversary starts $ point $\bfx$ $ classifies correctly applies a \emph{small perturbation $ produce another point In taking \emph{the inherent confidence information produced models when studying where a natural measure ``confidence \|F(\bfx)\|_\infty$ how $F$ about its prediction?) . Motivated a thought experiment based the manifold assumption a ``goodness property models states \emph{confident regions a good model should well separated We give formalizations this property examine existing robust training objectives view them Interestingly we find a recent objective by Madry et encourages training a model satisfies well our formal version the goodness property has a weak control points wrong but with low confidence However Madry et al.'s model indeed a good solution their objective good and bad points now distinguishable try embed uncertain points back the closest confident region get ( We thus propose embedding objectives algorithms, perform Our experimental results encouraging Madry et al.'s model wrapped with our embedding procedure achieves almost perfect success rate defending attacks the base model on retaining good generalization behavior In the adversarial perturbation problem neural networks an adversary starts a neural network model F a point x F classifies correctlywe ends a softmax layer common the literature applies produce another point incorrectly BID17 first noticed the vulnerability of existing (deep) neural networks to a somewhat surprising phenomenon the great generalization capability Since a line research (, BID5 ; devoted harden neural networks against However while modest progress until successfully defending more advanced attacks attack BID4 .In taking the inherent confidence information produced models when studying To this end a natural measure confidence F (x) �� how F about?) We motivate this consideration based the manifold assumption BID18 ; man) that commonly made natural data points lie ( separate low dimensional manifolds different classes Essentially , one believes deep neural networks learn approximate well these low dimensional manifolds an ideal model the property confidently distinguish points as well separated due the assumption. Moreover since the learner never sees points that far the natural manifolds an ideal model claim confidence thereTaking propose a goodness property states confident regions well We give formalizations this property examine existing robust training objectives view them Interestingly we find a recent objective function by BID8 encourages training a model satisfies well our formal version the goodness property high-confidence predictions different classes well separated On our analysis also could many points with wrong but low-confidence predictions Therefore Madry et s model indeed a good solution their objective distinguish with confidence try embed back confident regions get (We propose two embedding objectives (1) ��-Most Confident NeighborMCN � (F, x = arg max z��N F (z) �� for a point x a radius parameter �� > N around (2) p-Nearest Confident NeighborNCN p (F x arg min z z − x subject to F (z) �� ≥ p for a point a confidence parameter p ��0 With these, the end to end predictions become F (MCN �� (, xNCN p We note these objectives semantic They fail only the model a confident but wrong prediction in the neighborhoodWe perform over CIFAR10 We first empirically validate Madry et al s model better, view our goodness property models trained without a robustness objective We then give end defense results our method Specifically propose using gradient based optimization such Carlini-Wagner attacks BID4which, however now defense solve MCN �� or NCN p Our empirical results encouraging : ( It achieves almost perfect success rate defending attacks the base model on also retains the good generalization behaviorThe rest organized We important prior work Section Then Section proposes the goodness property examines Madry et al.'s robust training objective function view the property We then present embedding objectives algorithms handling low-confidence points Section Section performs an empirical study where validate that Madry et al.'s robust model satisfies well our goodness property give defense results our technique Section concludes discussions implications our method BID17 first observed the susceptibility deep neural networks Since a large body have devoted studying hardening for (a subset work BID5 BID14 ; Simultaneously another line have devoted devise more effective or efficient attacks (a small set work BID10 BID13 BID4 Unfortunately still for the defense methods defend more sophisticated attacks CarliniWagner attacks BID4 . For example while the recent robust residual network constructed BID8 achieves encouraging robustness results on MNIST on the accuracy against a strong adversary, attacks , as We now discuss our method results (a) Base model on x, unconfident prediction ""automobile"" DISPLAYFORM0e A valid ""ship that resembles ( g CarliniWagnerShell on x, unconfident prediction ""ship : The images (e the points makes We show the original image the first column CarliniWagnerShell perturbations adversarial perturbed the adversarial examples Example ship images presented the last row forOur technical contributions. Our first technical contribution the proposal take into the inherent confidence information produced models studying Our second technical contribution a formulation a goodness property models existing models view the property Interestingly and somewhat we a recent robust training objective function by BID8 encourages good separation highconfidence points has essentially no control of Our third contribution the proposal embedding to handle low-confidence points Our final contribution a first empirical study Madry the goodness property further, wrapped embedding simultaneously achieves almostInterpretations. One interpretation our results adversarial perturbations naturally good generalization While this manifested our analysis Madry et al.'s objective function think this phenomenon naturally and generally exists if takes again a manifold point Since natural manifolds reside low dimensions much challenging control the confidence boundary, where exist abundance controlling separation the learned structuresi.e. confident regions that approximate all one cares robustnessdecision does a small neighborhood combining goodness property embedding For example consider the following ""good model If a data point from the training set outputs the correct label with confidence 1 a uniform distribution over labels In this model learns nothing fitting the training set We note the adversarial perturbation problem only well around the training points Moreover , embedding now becomes 1-nearest neighbor search among the training points As , the model still perfectly robust our method if training points well separatedHighly confident predictions on random noises We note several work shows neural networks have highly confident predictions on random noises BID11 In view our work it somewhat not neural networks have such behaviors: These points essentially ones far the learner asked learn if do control not claim confidence over the structure it never valid fit good behaviors on natural manifolds but also divergent behaviors outside. After all why a network supposed points far the underlying natural manifolds which essentially the data generating distribution Finally note the adversarial perturbation problem well even near those points",0.01,0.5297939917780616
"Recently Neural Architecture Search (NAS) has aroused great interest in both academia and industry, however it remains challenging because of its huge and non-continuous search space. Instead of applying evolutionary algorithm or reinforcement learning as previous works, this paper proposes a Direct Sparse Optimization NAS (DSO-NAS) method. In DSO-NAS, we provide a novel model pruning view to NAS problem. In specific, we start from a completely connected block, and then introduce scaling factors to scale the information flow between operations. Next, we impose sparse regularizations to prune useless connections in the architecture. Lastly, we derive an efficient and theoretically sound optimization method to solve it. Our method enjoys both advantages of differentiability and efficiency, therefore can be directly applied to large datasets like ImageNet. Particularly, On CIFAR-10 dataset, DSO-NAS achieves an average test error 2.84%, while on the ImageNet dataset DSO-NAS achieves 25.4% test error under 600M FLOPs with 8 GPUs in 18 hours. With no doubt, Deep Neural Networks (DNN) have been the engines for the AI renaissance in recent years. Dating back to 2012, DNN based methods have refreshed the records for many AI applications, such as image classification BID16 ; BID37 ; BID8 ), speech recognition ; BID4 ) and Go Game BID33 ). Considering its amazing representation power, DNNs have shifted the paradigm of these applications from manually designing the features and stagewise pipelines to end-to-end learning. Although DNNs have liberated researchers from such feature engineering, another tedious work has emerged -""network engineering"". In most cases, the neural networks need to be designed based on the specific tasks, which again leads to endless hyperparameters tuning and trails. Therefore, designing a suitable neural network architecture still requires considerable amounts of expertise and experience.To democratize the techniques, Neural Architecture Search (NAS) or more broadly, AutoML has been proposed. There are mainly two streams for NAS: The first one is to follow the pioneering work BID45 , which proposed a reinforcement learning algorithm to train a Recurrent Neural Network (RNN) controller that generates coded architectures ; BID29 ). The second one is the evolutionary algorithm, which iteratively evaluates and proposes new models for evaluation BID30 ; BID36 ). Despite their impressive performance, the search processes are incredibly resource-hungry and unpractical for large datasets like ImageNet, though some acceleration methods have been proposed BID44 ; BID29 ). Very recently, DARTS BID22 ) proposed a gradient-based method in which the connections are selected by a softmax classifier. Although DARTS achieves impressive performance with great acceleration, its search space is still limited to fix-length coding and blocksharing search as in previous works.In this work, we take another view to tackle these problems. We reformulate NAS as pruning the useless connections from a large network which contains the complete network architecture hypothesis space. Thus only one single model is trained and evaluated. Since the network structure is directly optimized during training, we call our method Direct Sparse Optimization NAS (DSO-NAS). We further demonstrate that this sparse regularized problem can be efficiently optimized by a modified accelerated proximal gradient method opposed to the inefficient reinforcement learning or revolutionary search. Notably, DSO-NAS is much simpler than the existing search methods as it unifies the neural network weight learning and architecture search into one single optimization problem. DSO-NAS does not need any controller BID45 ; ; BID29 ) or performance predictor BID21 ) or relaxation of the search space BID45 ; ; BID29 ; BID22 ). As a result of the efficiency and simplicity, DSO-NAS first demonstrate that NAS can be directly applied to large datasets like ImageNet with no block structure sharing. Our experiments show that DSO-NAS can achieve 2.84% average test error on CIFAR-10, as well as top-1 error 25.4% on ImageNet with FLOPs (the number of multiply-adds) under 600M.In summary, our contributions can be summarized as follows:• We propose a novel model pruning formulation for neural architecture search based on sparse optimization. Only one model needs to be trained during the search.• We propose a theoretically sound optimization method to solve this challenging optimization problem both effectively and efficiently.• We demonstrate the results of our proposed method are competitive or better than other NAS methods, while significantly simplifying and accelerating the search process. Neural Architecture Search has been the core technology for realizing AutoML. In this paper, we have proposed a Direct Sparse Optimization method for NAS. Our method is appealing to both academic research and industrial practice in two aspects: First, our unified weight and structure learning method is fully differentiable in contrast to most previous works. It provides a novel model pruning view to the NAS problem. Second, the induced optimization method is both efficient and effective. We have demonstrated state-of-the-art performance on both CIFAR and ILSVRC2012 image classification datasets, with affordable cost (single machine in one day).In the future, we would like to incorporate hardware features for network co-design, since the actual running speed of the same network may highly vary across different hardware because of cache size, memory bandwidth, etc. We believe our proposed DSO-NAS opens a new direction to pursue such objective. It could push a further step to AutoML for everyone's use.",1092,0.615,657,1.6621004566210045,"Recently Neural Architecture Search aroused both academia however challenging because Instead applying evolutionary algorithm or as previous works a Direct Sparse Optimization NAS (DSO-NAS) method In DSO-NAS a novel model pruning view NAS problem. In specific start a completely connected block introduce scaling factors scale the information flow operations Next impose sparse regularizations prune useless connections Lastly derive an efficient and theoretically sound optimization method it Our method enjoys both advantages differentiability efficiency therefore can directly large datasets like ImageNet Particularly On CIFAR-10 dataset DSO-NAS achieves an average test error under 600M FLOPs with 8 GPUs in 18 hours With no doubt Deep Neural Networks the engines the AI renaissance Dating 2012 DNN based methods refreshed the records many AI applications image classification BID16 ; ), ; ) Go Game BID33 Considering its amazing representation power DNNs shifted these applications manually designing the features stagewise pipelines end learning Although DNNs liberated researchers such feature engineering another tedious work -""network engineering In the neural networks need designed based again leads endless hyperparameters tuning trails Therefore designing still considerable amounts expertiseTo democratize Neural Architecture SearchNAS or more AutoML There mainly two streams NAS follow the pioneering work BID45 , proposed reinforcement generates coded architectures ; BID29 The second one the evolutionary algorithm iteratively evaluates proposes evaluation BID30 ; Despite the search processes incredibly resource unpractical large datasets ImageNet though some acceleration methods BID44 ; Very recently DARTS BID22 ) proposed a gradient-based method in the connections selected a softmax classifier Although DARTS achieves great acceleration its search space fix-length coding blocksharing search as in previous worksIn take another view tackle We reformulate NAS as pruning the useless connections which contains the complete network architecture hypothesis space Thus only one single model trained evaluated Since the network structure directly optimized during training call our method Direct Sparse Optimization NAS We further demonstrate this sparse regularized problem efficiently optimized a modified accelerated proximal gradient method opposed the inefficient reinforcement learning or revolutionary search Notably DSO-NAS much simpler the existing search methods as unifies the neural network weight learning and architecture search one single optimization problem DSONAS does need any controller BID45 ; ; BID29 ) or performance predictor relaxation the search space As the efficiency, DSO-NAS first demonstrate NAS directly large datasets like ImageNet no block structure sharing Our experiments DSONAS achieve 2.84% average test error top-1 error 25.4 ImageNet with FLOPsthe number multiplyadds) under 600M.In summary our contributions can propose pruning formulation neural architecture search sparse optimization Only one model needs trained during the search.• We propose a theoretically sound optimization method both effectively are competitive or other NAS methods while significantly accelerating Neural Architecture Search has the core technology realizing AutoML In have a Direct Sparse Optimization method NAS. Our method appealing both academic research industrial practice two aspects our unified weight and structure learning method fully differentiable contrast most previous works It provides pruning view the NAS problem Second the induced optimization method both effective We demonstrated state performance on both CIFAR ILSVRC2012 image classification datasets affordable cost (single machine in one day).In incorporate hardware features network codesign since the actual running speed highly because cache size We believe our proposed DSO-NAS opens pursue such objective It could push a further step to AutoML everyone's use",0.01,0.391052961644056
"Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. The first method we propose is called quantized distillation and leverages distillation during the training process, by incorporating distillation loss, expressed with respect to the teacher, into the training of a student network whose weights are quantized to a limited set of levels. The second method,  differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model.   We validate both methods through experiments on convolutional and recurrent architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision teacher models, while providing order of magnitude compression, and inference speedup that is linear in the depth reduction. In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices.
 Background. Neural networks are extremely effective for solving several real world problems, like image classification BID20 BID10 , translation BID33 , voice synthesis BID27 or reinforcement learning BID26 BID30 . At the same time, modern neural network architectures are often compute, space and power hungry, typically requiring powerful GPUs to train and evaluate. The debate is still ongoing on whether large models are necessary for good accuracy. It is known that individual network weights can be redundant, and may not carry significant information, e.g. BID9 . At the same time, large models often have the ability to completely memorize datasets ), yet they do not, but instead appear to learn generic task solutions. A standing hypothesis for why overcomplete representations are necessary is that they make learning possible by transforming local minima into saddle points BID6 or to discover robust solutions, which do not rely on precise weight values BID13 BID16 .If large models are only needed for robustness during training, then significant compression of these models should be achievable, without impacting accuracy. This intuition is strengthened by two related, but slightly different research directions. The first direction is the work on training quantized neural networks, e.g. BID5 ; BID29 ; BID14 ; BID35 ; BID24 ; BID28 ; BID41 , which showed that neural networks can converge to good task solutions even when weights are constrained to having values from a set of integer levels. The second direction aims to compress already-trained models, while preserving their accuracy. To this end, various elegant compression techniques have been proposed, e.g. BID9 ; BID15 ; BID34 ; BID8 ; BID25 , which combine quantization, weight sharing, and careful coding of network weights, to reduce the size of state-of-the-art deep models by orders of magnitude, while at the same time speeding up inference.Both these research directions are extremely active, and have been shown to yield significant compression and accuracy improvements, which can be crucial when making such models available on embedded devices or phones. However , the literature on compressing deep networks focuses almost exclusively on finding good compression schemes for a given model, without significantly altering the structure of the model. On the other hand, recent parallel work BID3 BID12 introduces the process of distillation, which can be used for transferring the behaviour of a given model to any other structure. This can be used for compression, e.g. to obtain compact representations of ensembles BID12 . However the size of the student model needs to be large enough for allowing learning to succeed. A model that is too shallow, too narrow, or which misses necessary units, can result in considerable loss of accuracy BID31 .In this work, we examine whether distillation and quantization can be jointly leveraged for better compression. We start from the intuition that 1) the existence of highly-accurate, full-precision teacher models should be leveraged to improve the performance of quantized models, while 2) quantizing a model can provide better compression than a distillation process attempting the same space gains by purely decreasing the number of layers or layer width. While our approach is very natural, interesting research questions arise when these two ideas are combined.Contribution. We present two methods which allow the user to compound compression in terms of depth, by distilling a shallower student network with similar accuracy to a deeper teacher network, with compression in terms of width, by quantizing the weights of the student to a limited set of integer levels, and using less weights per layer. The basic idea is that quantized models can leverage distillation loss BID12 , the weighted average between the correct targets (represented by the labels) and soft targets (represented by the teacher's outputs).We implement this intuition via two different methods. The first, called quantized distillation, aims to leverage distillation loss during the training process, by incorporating it into the training of a student network whose weights are constrained to a limited set of levels. The second method, which we call differentiable quantization, takes a different approach, by attempting to converge to the optimal location of quantization points through stochastic gradient descent. We validate both methods empirically through a range of experiments on convolutional and recurrent network architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision and deeper teacher models on datasets such as CIFAR and ImageNet (for image classification) and OpenNMT and WMT (for machine translation), while providing up to order of magnitude compression, and inference speedup that is linear in the depth. While the loss is continuous w.r.t. p, there are indirect effects when changing the way each weight gets quantized. This can have drastic effect on the learning process. As an extreme example, we could have degeneracies, where all weights get represented by the same quantization point, making learning impossible. Or diversity of p i gets reduced, resulting in very few weights being represented at a really high precision while the rest are forced to be represented in a much lower resolution.To avoid such issues, we rely on the following set of heuristics. Future work will look at adding a reinforcement learning loss for how the p i are assigned to weights.Choose good starting points. One way to initialize the starting quantization points is to make them uniformly spaced, which would correspond to use as a starting point the uniform quantization function. The differentiable quantization algorithm needs to be able to use a quantization point in order to update it; therefore, to make sure every quantization point is used we initialize the points to be the quantiles of the weight values. This ensures that every quantization point is associated with the same number of values and we are able to update it.Redistribute bits where it matters. Not all layers in the network need the same accuracy. A measure of how important each weight is to the final prediction is the norm of the gradient of each weight vector. So in an initial phase we run the forward and backward pass a certain number of times to estimate the gradient of the weight vectors in each layer, we compute the average gradient across multiple minibatches and compute the norm; we then allocate the number of points associated with each weight according to a simple linear proportion. In short we estimate DISPLAYFORM0 where l is the loss function,v is the vector of weights in a particular layer and DISPLAYFORM1 = ∂l ∂vi and we use this value to determine which layers are most sensitive to quantization.When using this process, we will use more than the indicated number of bits in some layers, and less in others. We can reduce the impact of this effect with the use of Huffman encoding, see Section 5; in any case, note that while the total number of points stays constant, allocating more points to a layer will increase bit complexity overall if the layer has a larger proportion of the weights.Use the distillation loss. In the algorithm delineated above, the loss refers to the loss we used to train the original model with. Another possible specification is to treat the unquantized model as the teacher model, the quantized model as the student, and to use as loss the distillation loss between the outputs of the unquantized and quantized model. In this case, then, we are optimizing our quantized model not to perform best with respect to the original loss, but to mimic the results of the unquantized model, which should be easier to learn for the model and provide better results.Hyperparameter optimization. The algorithm above is an optimization problem very similar to the original one. As usual, to obtain the best results one should experiment with hyperparameters optimization, and different variants of gradient descent. We have examined the impact of combining distillation and quantization when compressing deep neural networks. Our main finding is that, when quantizing, one can (and should) leverage large, accurate models via distillation loss, if such models are available. We have given two methods to do just that, namely quantized distillation, and differentiable quantization. The former acts directly on the training process of the student model, while the latter provides a way of optimizing the quantization of the student so as to best fit the teacher model.Our experimental results suggest that these methods can compress existing models by up to an order of magnitude in terms of size, on small image classification and NMT tasks, while preserving accuracy. At the same time, we note that distillation also provides an automatic improvement in inference speed, since it generates shallower models. One of our more surprising findings is that naive uniform quantization with bucketing appears to perform well in a wide range of scenarios. Our analysis in Section 2.2 suggests that this may be because bucketing provides a way to parametrize the Gaussian-like noise induced by quantization. Given its simplicity, it could be used consistently as a baseline method.In our experimental results, we performed manual architecture search for the depth and bit width of the student model, which is time-consuming and error-prone. In future work, we plan to examine the potential of reinforcement learning or evolution strategies to discover the structure of the student for best performance given a set of space and latency constraints. The second, and more immediate direction, is to examine the practical speedup potential of these methods, and use them together and in conjunction with existing compression methods such as weight sharing BID9 and with existing low-precision computation frameworks, such as NVIDIA TensorRT, or FPGA platforms.",2149,1.062,1250,1.7192,"Deep neural networks continue make solving tasks from translation or One aspect the field receiving efficiently executing deep models mobile or embedded devices This paper focuses this problem proposes two new compression methods jointly leverage weight quantization distillation larger teacher networks into The first method we propose called quantized distillation leverages during the training process by incorporating distillation loss expressed with respect the teacher of a student network whose weights a limited set levels The second method differentiable quantization optimizes the location through to better fit the behavior the teacher model We validate both methods through experiments convolutional and recurrent architectures We show quantized shallow students reach similar accuracy levels to full-precision teacher models while providing order magnitude compression inference speedup linear the depth reduction In sum our results enable DNNs for leverage architecture accuracy advances developed on more powerful devices Background. Neural networks extremely effective solving like image classification BID20 BID10 , translation BID33 voice synthesis or reinforcement At modern neural network architectures compute, space power typically powerful GPUs train evaluate The debate still large models good accuracy It known individual network weights redundant may carry significant information e.g. BID9 . At large models often completely memorize datasets ), yet, but instead appear learn generic task solutions A standing hypothesis why overcomplete representations necessary make learning possible transforming local minima saddle points BID6 or to discover robust solutions, do precise weight values BID13 BID16 .If large models only robustness during significant compression achievable without impacting accuracy This intuition strengthened two related, but slightly different research directions The first direction the work on training quantized neural networks e.g. BID5 ; BID29 showed converge good task solutions even weights constrained having values from integer levels The second direction aims compress already-trained models preserving To this end various elegant compression techniques BID9 ; combine quantization weight sharing careful coding network weights state deep models by orders speeding inferenceBoth these research directions extremely active significant compression and crucial making such models available embedded devices phones However , the literature compressing deep networks focuses almost finding good compression schemes a given model without significantly On recent parallel work BID3 BID12 introduces the process distillation transferring the behaviour a given model any other structure This can compression obtain compact representations BID12 . However the size the student model needs large allowing learning succeed A model that too shallow which misses necessary units result considerable loss accuracy BID31 .In examine distillation quantization jointly better compression We start from the intuition 1 existence highly-accurate, full-precision teacher models should leveraged quantized models while can provide better compression a distillation process attempting the same space gains by purely decreasing layers or layer width While our approach very natural, interesting research questions these two ideasContribution. We present two methods which compound compression terms depth by distilling a shallower student network with similar accuracy compression width quantizing to a limited set integer levels less weights per The basic idea quantized models leverage distillation loss BID12 , the weighted average between the correct targetsrepresented soft targets teacher outputs).We implement this intuition via first, called quantized distillation aims leverage distillation loss during the training process by incorporating it a student network whose weights constrained levels The second method we differentiable quantization takes by attempting converge the optimal location through We validate both methods empirically through a range experiments on and network We show quantized shallow students reach similar accuracy levels to full-precision and deeper teacher models on datasets such ImageNetfor image classification OpenNMT and WMT machine translation providing up order magnitude compression inference speedup linear the depth While the loss is continuous w.r.t p, indirect effects when changing the way each weight gets quantized This can have drastic effect the learning process As an extreme example could degeneracies where all weights get represented the same quantization point making learning Or diversity p i gets reduced resulting very few weights represented a really high precision while forcedTo avoid rely Future work look adding a reinforcement learning loss for how the p i are assigned weightsChoose good starting points One way initialize the starting quantization points make uniformly would correspond use as the uniform quantization function The differentiable quantization algorithm needs use a quantization point update; therefore used we initialize the quantiles the weight values This ensures every quantization point associated we updateRedistribute bits where it Not all layers in the network need the same accuracy A measure important each weight the final prediction the norm the gradient each weight vector So in an initial phase we run forward pass a certain number estimate the gradient the weight vectors each layer compute across multiple minibatches compute the norm; allocate points associated according a simple linear proportion In short we estimate DISPLAYFORM0 where l the loss functionv weights a particular layervi and we sensitive quantizationWhen using this process more the indicated number bits some layers less We can reduce this effect with Huffman encoding see Section; in note while points stays allocating a layer bit complexity overall if the weightsUse the distillation loss. In the algorithm delineated the loss refers we used train with Another possible specification treat the unquantized model the teacher model, to as loss the distillation loss between the outputs In then optimizing our quantized model not perform best respect the original loss mimic should easier learn for the model and provideHyperparameter optimization. The algorithm above an optimization problem very original As usual to obtain one experiment hyperparameters optimization different variants gradient descent We examined combining distillation quantization when compressing deep neural networks Our main finding quantizing, one ( leverage large, accurate models via distillation loss if We given two methods do just that, namely quantized distillation differentiable quantization former acts directly on the training process the student model while provides optimizing the quantization so bestOur experimental results compress existing models up size on small image classification and NMT tasks preserving accuracy At note distillation also an automatic improvement inference speed generates shallower models One our more surprising findings naive uniform quantization with bucketing appears perform scenarios Our analysis in Section suggests this may bucketing provides the Gaussian-like noise induced quantization Given its simplicity could consistently a baseline methodIn our experimental results performed manual architecture search the depth bit width the student model time error In future work examine reinforcement learning or evolution strategies discover the student for best performance given space and latency constraints second, more immediate direction examine the practical speedup potential these methods use together and existing compression methods such weight sharing BID9 with existing low-precision computation frameworks NVIDIA TensorRT FPGA platforms",0.01,0.5365375814627086
"Previous work has demonstrated the benefits of incorporating additional linguistic annotations such as syntactic trees into neural machine translation. However the cost of obtaining those syntactic annotations is expensive for many languages and the quality of unsupervised learning linguistic structures is too poor to be helpful. In this work, we aim to improve neural machine translation via source side dependency syntax but without explicit annotation. We propose a set of models that learn to induce dependency trees on the source side and learn to use that information on the target side. Importantly, we also show that our dependency trees capture important syntactic features of language and improve translation quality on two language pairs En-De and En-Ru.",132,0.081,77,1.7142857142857142,Previous work incorporating additional linguistic annotations such syntactic trees neural machine translation However the cost obtaining those syntactic annotations expensive the quality unsupervised learning linguistic structures too helpful In this work aim improve neural machine translation via source side dependency syntax but explicit annotation We propose models learn induce dependency trees the source side learn on Importantly show our dependency trees capture improve translation quality on two language pairs En-DeRu,0.0,0.5240164132271301
"Model-free reinforcement learning (RL) requires a large number of trials to learn a good policy, especially in environments with sparse rewards. We explore a method to improve the sample efficiency when we have access to demonstrations. Our approach, Backplay, uses a single demonstration to construct a curriculum for a given task. Rather than starting each training episode in the environment's fixed initial state, we start the agent near the end of the demonstration and move the starting point backwards during the course of training until we reach the initial state. Our contributions are that we analytically characterize the types of environments where Backplay can improve training speed, demonstrate the effectiveness of Backplay both in large grid worlds and a complex four player zero-sum game (Pommerman), and show that Backplay compares favorably to other competitive methods known to improve sample efficiency. This includes reward shaping, behavioral cloning, and reverse curriculum generation. An important goal of AI research is to construct agents that can learn well in new environments BID28 ). An increasingly popular paradigm for this task is deep reinforcement learning (deep RL, BID40 ; BID31 ; ). However, training an RL agent can take a very long time, particularly in environments with sparse rewards. In these settings, the agent typically requires a large number of episodes to stumble upon positive rewards and learn even a moderately effective policy that can then be refined. This is often resolved via hand-engineering a dense reward function. Such reward shaping, while effective, can also change the set of optimal policies and have unintended side effects BID34 BID7 .We consider an alternative technique for accelerating RL in sparse reward settings. The idea is to create a curriculum for the agent via reversing a single trajectory (i.e. state sequence) of reasonably good, but not necessarily optimal, behavior. We start our agent at the end of a demonstration and let it learn a policy in this easier setup. We then move the starting point backward until the agent is training only on the initial state of the task. We call this technique Backplay.Our contributions are threefold:1. We characterize analytically and qualitatively which environments Backplay will aid.2. We demonstrate Backplay's effectiveness on both a grid world task (to gain intuition) as well as the four player stochastic zero-sum game Pommerman BID32 .3. We empirically show that Backplay compares favorably to other methods that improve sample complexity.Besides requiring vastly fewer number of samples to learn a good policy, an agent trained with Backplay can outperform its demonstrator and even learn an optimal policy following a sub-optimal demonstration. Our experiments further show Backplay's strong performance relative to reward shaping (involves hand tuning reward functions), behavioral cloning (not intended for use with sub-optimal experts), and other forms of automatic curriculum generation BID12 , requires a reversable environment).2 RELATED WORK Figure 1 . Backplay : We first collect a demonstration, from which we build a curriculum over the states. We then sample a state according to that curriculum and initialize our agent accordingly.The most related work to ours is a blog post describing a method similar to Backplay used to obtain state-of-theart performance on the challenging Atari game Montezuma's Revenge (Salimans & Chen, 2018) . This work was independent of and concurrent to our own. In addition to reporting results on a different, complex stochastic multi-agent environment, we provide an analytic characterization of the method as well as an in depth discussion of what kinds of environments a practitioner can expect Backplay to out or underperform other existing methods.A popular method for improving RL with access to expert demonstrations is behavioral cloning/imitation learning. These methods explicitly encourage the learned policy to mimic an expert policy BID1 Ross et al., 2011; BID10 BID44 BID24 BID33 BID16 BID17 BID0 BID35 . Imitation learning requires access to both state and expert actions (whereas Backplay only requires states) and is designed to copy an expert, thus it cannot, without further adjustments (e.g. as proposed by BID14 ), surpass a suboptimal expert. We discuss the pros and cons of an imitation learning + adjustment vs. a Backplay-based approach in the main analysis section.Other algorithms BID38 BID29 BID8 , primarily in dialog, use a Backplay-like curriculum, albeit they utilize behavioral cloning for the first part of the trajectory. This is a major difference as we show that for many classes of problems, we only need to change the initial state distribution and do not see any gains from warm-starting with imitation learning. Backplay is more similar to Conservative Policy Iteration BID21 , a theoretical paper which presents an algorithm designed to operate with an explicit restart distribution.Also related to Backplay is the method of automatic reverse curriculum generation BID12 . These approaches assumes that the final goal state is known and that the environment is both resettable and reversible. The curricula are generated by taking random walks in the state space to generate starting states or by taking random actions starting at the goal state BID30 . These methods do not require an explicit 'good enough' demonstration as Backplay does. However, they require the environment to be reversible, an assumption that doesn't hold in many realistic tasks such as a robot manipulating breakable objects or complex video games such as Starcraft. In addition, they may fare poorly when random walks reach parts of the state space that are not actually relevant for learning a good policy. Thus, whether a practitioner wants to generate curricula from a trajectory or a random walk depends on the environment's properties. We discuss this in more detail in our analysis section and show empirical results suggesting that Backplay is superior.Hosu & Rebedea (2016) use uniformly random states of an expert demonstration as starting states for a policy. Like Backplay, they show that using a single loss function to learn a policy from both demonstrations and rewards can outperform the demonstrator and is robust to sub-optimal demonstrations. However, they do not impose a curriculum over the demonstration and are equivalent to the Uniform baseline in our experiments. BID46 We have introduced and analyzed Backplay, a technique which improves the sample efficiency of model-free RL by constructing a curriculum around a demonstration. We showed that Backplay agents can learn in complex environments where standard model-free RL fails, that they can outperform the 'expert' whose trajectories they use while training, and that they compare very favorably to related methods such as reversible curriculum generation. We also presented a theoretical analysis of its sample complexity gains in a simplified setting.An important future direction is combining Backplay with more complex and complementary methods such as Monte Carlo Tree Search (MCTS, BID5 BID42 ). There are many potential ways to do so, for example by using Backplay to warm-start MCTS.Another direction is to use Backplay to accelerate self-play learning in zero-sum games. However, special care needs to be taken to avoid policy correlation during training and thus to make sure that learned strategies are safe and not exploitable BID4 .A third direction is towards non-zero sum games. It is well known that standard independent multiagent learning does not produce agents that are able to cooperate in social dilemmas BID25 BID13 or risky coordination games BID43 . In contrast, humans are much better at finding these coordinating and cooperating equilibria BID3 BID22 . Thus , we conjecture that human demonstrations can be combined with Backplay to construct agents that perform well in such situations.Other future priorities are to gain further understanding into when Backplay works well, when it fails, and how we can make the procedure more efficient. Could we speed up Backplay by ascertaining confidence estimates of state values? Do the gains in sample complexity come from value estimation like our analysis suggests, from policy iteration, or from both? Is there an ideal rate for advancing the curriculum window and is there a better approach than a hand-tuned schedule?Stéphane Ross, Geoffrey Gordon, and Drew Bagnell. A reduction of imitation learning and structured prediction to no-regret online learning. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, pp. 627-635, 2011. A APPENDIX",1650,0.903,976,1.6905737704918034,"Model-free reinforcement learningRL requires trials learn a good policy especially environments sparse rewards We explore a method the sample efficiency when access demonstrations Our approach Backplay a single demonstration construct a curriculum Rather starting each training episode the environment's fixed initial state the agent near the demonstration backwards during until Our contributions that analytically characterize environments Backplay improve training speed demonstrate both large grid worlds a complex four player zero-sum gamePommerman compares other competitive methods known sample efficiency This includes reward shaping behavioral cloning reverse curriculum generation An important goal AI research construct agents well BID28 An increasingly popular paradigm this task deep reinforcement learningdeep RL, BID40 ; However training an RL agent environments sparse rewards In these settings the agent typically requires episodes stumble positive rewards learn even a moderately effective policy then refined This often resolved hand-engineering a dense reward function Such reward shaping while effective change the set optimal policies have BID34 BID7 .We consider an alternative technique accelerating RL sparse reward settings The idea a curriculum the agent via reversing a single trajectory reasonably but We start our agent at a demonstration let learn a policy in this easier setup We then move the starting point backward until the agent training only We call this technique BackplayOur contributions We characterize which environments Backplay aid.2 demonstrate both a grid world taskto gain intuition Pommerman BID32 .3 We empirically Backplay compares improve sample complexityBesides requiring vastly fewer number learn a good policy an agent trained its demonstrator learn following Our experiments further Backplay's strong performance relative reward shapinginvolves hand tuning reward functions behavioral cloningnot intended sub-optimal experts other forms automatic curriculum generation BID12 , requires a reversable environment).2 RELATED WORK Figure . Backplay : We first collect a demonstration, from build a curriculum over the states We then sample a state according that curriculum initialize our agent accordinglyThe most related work ours describing similar Backplay used obtain performance the challenging Atari game Montezuma's Revenge (Salimans & Chen 2018 This work independent and concurrent our In reporting results a different, complex stochastic multi-agent environment an analytic characterization what kinds environments a practitioner Backplay out or other existing methodsA popular method improving RL with access expert demonstrations behavioral cloning/imitation learning These methods explicitly encourage the learned policy mimic an expert policy BID1 Ross . Imitation learning requires access both state and expert actionswhereas Backplay only states designed copy an expert, thus it, further adjustments ( as proposed BID14 surpass We discuss an imitation learning + adjustment a Backplay-based approach in the main analysis sectionOther algorithms BID38 BID29 BID8 , primarily dialog albeit they utilize behavioral cloning the trajectory This a major difference as show for many classes problems only change the initial state distribution do see warm-starting with imitation learning Backplay more similar Conservative Policy Iteration BID21 , a theoretical paper presents designed operate an explicit restart distributionAlso related automatic reverse curriculum generation BID12 These approaches assumes the final goal state known both resettable reversible The curricula generated taking random walks the state space generate starting states or by starting BID30 . These methods do an explicit 'good enough' demonstration as Backplay However require the environment reversible an assumption does many realistic tasks a robot manipulating breakable objects complex video games such Starcraft In they fare random walks reach parts the state space actually relevant learning a good policy Thus whether a practitioner wants generate curricula a trajectory a random walk depends the environment's properties We discuss show empirical results suggesting Backplay superior.Hosu & Rebedea use uniformly random states an expert demonstration as starting states a policy Like Backplay they show using a single loss function learn a policy both demonstrations rewards the demonstrator and is robust However impose a curriculum over the demonstration equivalent the Uniform baseline our experiments BID46 We introduced and analyzed Backplay improves the sample efficiency model-free RL by constructing a curriculum around a demonstration We showed Backplay agents learn in complex environments standard model-free RL fails whose trajectories while training compare very favorably related methods reversible curriculum generation We also presented its sample complexity gains a simplified settingAn important future direction combining Backplay more complex and complementary methods Monte Carlo Tree Search, BID5 BID42 There do for Backplay warm-start MCTS.Another direction accelerate self-play learning However special care to policy correlation during training thus make learned strategies safe not BID4 .A third direction towards non-zero sum games It well standard independent multiagent learning does agents cooperate social dilemmas BID25 BID13 or risky coordination games . In contrast humans finding these coordinating and cooperating equilibria BID3 BID22 . Thus , conjecture human demonstrations combined Backplay construct agentsOther future priorities gain into when the procedure Could speed Backplay ascertaining confidence estimates state values Do the gains sample complexity value estimation like our analysis suggests from policy iteration both Is an ideal rate advancing the curriculum window is Geoffrey Gordon Drew Bagnell A reduction imitation learning structured prediction to no-regret online learning In Proceedings statistics pp 627-635 2011 A APPENDIX",0.01,0.46360046374884795
"Episodic memory is a psychology term which refers to the ability to recall specific events from the past. We suggest one advantage of this particular type of memory is the ability to easily assign credit to a specific state when remembered information is found to be useful. Inspired by this idea, and the increasing popularity of external memory mechanisms to handle long-term dependencies in deep learning systems, we propose a novel algorithm which uses a reservoir sampling procedure to maintain an external memory consisting of a fixed number of past states. The algorithm allows a deep reinforcement learning agent to learn online to preferentially remember those states which are found to be useful to recall later on. Critically this method allows for efficient online computation of gradient estimates with respect to the write process of the external memory. Thus unlike most prior mechanisms for external memory it is feasible to use in an online reinforcement learning setting.
 We present a novel algorithm for integrating a form of external memory with trainable reading and writing into a RL agent. The method depends on the observation that if we restrict the information stored in memory to be a set of past visited states, the information recorded also provides the context in which it was recorded. This means it is possible to assign credit to useful information without needing to backpropagate through time to when it was recorded. To achieve this we devise a reservoir sampling technique which uses a sampling procedure we introduce to generate a distribution over memory configurations for which we can derive gradient estimates. The whole algorithm is O(n) in both the number of trainable parameters and the size of the memory. In particular neither memory required nor computation time increase with history length, making it feasible to run in an online RL setting. We show that the resulting algorithm is able to achieve good performance on a toy problem we introduce designed to have sharp long-term dependencies which can be problematic for recurrent models.",366,0.22,211,1.7345971563981042,Episodic memory a psychology term We suggest one advantage this particular type memory easily assign credit a specific state when remembered information found useful Inspired this idea and increasing external memory mechanisms to handle propose which a reservoir sampling procedure maintain consisting past states The algorithm allows a deep reinforcement learning agent online to preferentially remember those states found useful recall later Critically this method allows efficient online computation gradient estimates respect the write process the external memory Thus unlike most prior mechanisms external memory it feasible in an online reinforcement learning setting We present integrating a form external memory trainable reading into a RL agent The method depends the observation if restrict stored be past visited states recorded also provides This means it assign credit useful information backpropagate through time when recorded To achieve devise a reservoir sampling technique we introduce generate a distribution over memory configurations for which derive gradient estimates The whole algorithm in both the number trainable parameters In particular neither memory required computation time increase history length making feasible run in an online RL setting We show the resulting algorithm able achieve a toy problem we introduce designed have sharp long-term dependencies which problematic recurrent models,0.0,0.5757681831857081
"We achieve bias-variance decomposition for Boltzmann machines using an information geometric formulation. Our decomposition leads to an interesting phenomenon that the variance does not necessarily increase when more parameters are included in Boltzmann machines, while the bias always decreases. Our result gives a theoretical evidence of the generalization ability of deep learning architectures because it provides the possibility of increasing the representation power with avoiding the variance inflation. Understanding why the deep learning architectures can generalize well despite their high representation power with a large number of parameters is one of crucial problems in theoretical deep learning analysis, and there are a number of attempts to solve the problem with focusing on several aspects such as sharpness and robustness BID4 BID25 BID11 BID17 BID10 . However, the complete understanding of this phenomenon is not achieved yet due to the complex structure of deep learning architectures.To theoretically analyze the generalizability of the architectures, in this paper, we focus on Boltzmann machines BID0 and its generalization including higher-order Boltzmann machines BID20 BID14 , the fundamental probabilistic model of deep learning (see the book by Goodfellow et al. (2016, Chapter 20) for an excellent overview), and we firstly present bias-variance decomposition for Boltzmann machines. The key to achieve this analysis is to employ an information geometric formulation of a hierarchical probabilistic model, which was firstly explored by BID1 ; BID15 ; BID16 . In particular, the recent advances of the formulation by BID22 enables us to analytically obtain the Fisher information of parameters in Boltzmann machines, which is essential to give the lower bound of variances in bias-variance decomposition.We show an interesting phenomenon revealed by our bias-variance decomposition: The variance does not necessarily increase while the bias always monotonically decreases when we include more parameters in Boltzmann machines, which is caused by its hierarchical structure. Our result indicates the possibility of designing a deep learning architecture that can reduce both of bias and variance, leading to better generalization ability with keeping the representation power.The remainder of this paper is organized as follows: First we formulate the log-linear model of hierarchical probability distributions using an information geometric formulation in Section 2, which includes the traditional Boltzmann machines (Section 2.2) and arbitrary-order Boltzmann machines (Section 2.3). Then we present the main result of this paper, bias-variance decomposition for Boltzmann machines, in Section 3 and discuss its property. We empirically evaluate the tightness of our theoretical lower bound of the variance in Section 4. Finally, we conclude with summarizing the contribution of this paper in Section 5. In this paper, we have firstly achieved bias-variance decomposition of the KL divergence for Boltzmann machines using the information geometric formulation of hierarchical probability distributions. Our model is a generalization of the traditional Boltzmann machines, which can incorporate arbitrary order interactions of variables. Our bias-variance decomposition reveals the nonmonotonicity of the variance with respect to growth of parameter sets, which has been also reported elsewhere for non-linear models BID5 . This result indicates that it is possible to reduce both bias and variance when we include more higher-order parameters in the hierarchical deep learning architectures. To solve the open problem of the generalizability of the deep learning architectures, our finding can be fundamental for further theoretical development. Hidden layer 1 Hidden layer 2 1 2 3 4 {1} {2} {3} {4} {1,2} {1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,3} {1,4} {2,3} {2,4} {1,2,3,4} {3,4} Ø {1} {2} {3} {4} {1,2} {1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,3} {1,4} {2,3} {2,4} {1,2,3,4} {3,4} Ø Figure 3 : An example of a deep Boltzmann machine (left) with an input (visible) layer V = {1, 2} with two hidden layers H 1 = {3} and H 2 = {4}, and the corresponding domain set S V ∪H (right). In the right-hand side, the colored objects {1}, {2}, {3}, {4}, {1, 3}, {2, 3}, and {3, 4} denote the parameter set B, which correspond to nodes and edges of the DBM in the left-hand side.",976,0.372,551,1.7713248638838475,"We achieve bias-variance decomposition for Boltzmann machines an information geometric formulation Our decomposition leads an interesting phenomenon the variance does necessarily increase when more parameters Boltzmann machines while the bias always Our result gives a theoretical evidence the generalization ability deep learning architectures because provides the possibility increasing the representation power with avoiding the variance inflation Understanding why the deep learning architectures can generalize well despite their high representation power with parameters one crucial problems theoretical deep learning analysis there attempts with focusing several aspects such sharpness robustness BID4 BID25 BID11 BID17 BID10 . However the complete understanding this phenomenon achieved yet due the complex structure deep learning architecturesTo theoretically analyze the architectures in focus Boltzmann machines BID0 its generalization including BID20 BID14 , the fundamental probabilistic modelsee the book by Goodfellow (2016, Chapter 20 for an excellent overview), we firstly present bias-variance decomposition for Boltzmann machines The key achieve this analysis employ an information geometric formulation was firstly explored BID1 ; BID15 In particular the recent advances the formulation by BID22 enables analytically obtain the Fisher information parameters Boltzmann machines essential give the lower bound variances bias-variance decompositionWe show an interesting phenomenon revealed The variance does necessarily increase while always monotonically when we include more parameters caused its hierarchical structure Our result indicates the possibility designing a deep learning architecture reduce both of bias variance, leading better generalization ability with keeping the representation power.The remainder organized First formulate the log-linear model hierarchical probability distributions an information geometric formulation in Section, includes the traditional Boltzmann machinesSection arbitrary-order Boltzmann machines Then we present the main result this paper, bias-variance decomposition for Boltzmann machines in Section and discuss its property We empirically evaluate the tightness our theoretical lower of the variance Section Finally conclude summarizing the contribution this paper in Section In this paper have firstly achieved bias-variance decomposition the KL divergence for Boltzmann machines the information geometric formulation hierarchical probability distributions Our model a generalization the traditional Boltzmann machines can incorporate arbitrary order interactions of variables Our bias-variance decomposition reveals the nonmonotonicity the variance with growth of parameter sets has also reported elsewhere for BID5 . This result indicates it reduce both bias variance when we include more higher-order parameters the hierarchical deep learning architectures To solve the open problem the generalizability the deep learning architectures our finding can fundamental further theoretical development Hidden layer 1 Hidden layer 1 2 {11,2 { : An example a deep Boltzmann machine (left an input (visible) layer V = { with two hidden layers H 1 and the corresponding domain set S V ��H (right In the right-hand side the colored objects {11, and denote the parameter set B correspond nodes and edges the DBM in",0.01,0.669347154998285
"Recurrent Neural Networks (RNNs) are powerful tools for solving sequence-based problems, but their efficacy and execution time are dependent on the size of the network.   Following recent work in simplifying these networks with model pruning and a novel mapping of work onto GPUs, we design an efficient implementation for sparse RNNs.   We investigate several optimizations and tradeoffs: Lamport timestamps, wide memory loads, and a bank-aware weight layout.   With these optimizations, we achieve speedups of over 6x over the next best algorithm for a hidden layer of size 2304, batch size of 4, and a density of 30%.   Further, our technique allows for models of over 5x the size to fit on a GPU for a speedup of 2x, enabling larger networks to help advance the state-of-the-art.   We perform case studies on NMT and speech recognition tasks in the appendix, accelerating their recurrent layers by up to 3x. Many sequence-based problems, including Speech Recognition BID0 and Neural Machine Translation (NMT) BID3 , can be solved effectively with Recurrent Neural Networks (RNNs). BID2 showed that these networks can run efficiently on massively parallel processors such as GPUs, and BID8 found that if the network is small enough to fit in the register file of a GPU, a persistent approach can be used to increase performance.In parallel, many network compression methods BID16 BID12 have been shown to reduce the model size of both Convolutional Neural Networks (CNNs) and RNNs. Recent work in this area has found that model pruning, in particular, can lead to significant reductions in the number of important network parameters for RNNs BID31 We present an approach that combines both of these techniques into an efficient and expandable approach. In particular, our work makes the following contributions:• Larger sparse RNNs can be run more efficiently on GPUs.• Sparse RNNs can be run with smaller batch sizes more efficiently on GPUs.• Various optimizations on top of the naïve implementation, necessary to achieve high performance.• Case studies using our technique showing 1 ) generalization to LSTMs, 2) practical network design considerations, and 3) speedups of up to 3× on two non-synthetic workloads.A naïve implementation of the idea, presented in Section 3, leads to limited benefit; we present a series of optimizations in Section 4 that help to achieve a high level of performance. Section 5 describes the experimental setup and results, and we discuss future work and our conclusions in Sections 6 and 7. The appendix presents a case study on a machine translation task.2 RELATED WORK 2.1 RNNS Recurrent Neural Networks (RNNs) are powerful tools for solving series-based problems, such as NMT BID3 BID18 BID0 BID26 , language modeling BID27 , and various NLP tasks BID7 . More complex recurrent networks have been devised to build on the basic RNN structure, such as Long/Short Term Memory networks (LSTMs) BID20 and Gated Recurrent Units (GRUs) BID6 . Though we focus on RNNs in this work for simplicity, our approach can extend to other recurrent network types, such as the LSTMs used in our case study. In particular, we build on a recent GPU-based method storing recurrent weights on-chip BID8 . Sparse persistent RNNs increase the performance of pruned networks, but without a series of optimizations we described in Section 4, the improvement is much lower. An optimized implementation is critical to achieve peak performance. After these optimizations, we see that our approach works best for sparser workloads, and, for most layer sizes, 10% density is sufficient to beat all other approaches, though for smaller layer sizes (up to 2304), our approach is the winner even up to a density of 30%. Different batch sizes can affect the efficiency of all techniques; in general, dense GEMMs and our approach scale the best, which tempers the benefit offered by other algorithms. Finally, the number of timesteps is largely immaterial to the relative performance of the various techniques.We have described an efficient algorithm for recurrent layers. To exploit this algorithm, one must first prune the recurrent layers of a target network. We perform this pruning during the training process for a nureal machine translation network BID22 , and we look to past work ) that has pruned a commercial speech recognition network, Deep Speech 2 BID0 . The results on these real workloads are promising: for a given accuracy, we show a speedup of between 2.0× to 3.1× in the machine translation network's recurrent layers pruned with load-balancing in mind, and a speedup of 1.2× to 2.9 on Deep Speech 2's recurrent layers pruned without load-balancing. Please refer to Appendix B for more details about the training processes and a full discussion of the results. We introduced sparse persistent RNNs, an efficient new algorithm for accelerating pruned recurrent networks. Further, we explored several optimizations that were needed to achieve these results on V100, a recent GPU. Our optimized technique allows for 7.3×, 3.4×, and 1.8× speedups against dense GEMM, sparse GEMM, and dense persistent implementations for a hidden layer of size 1792, batch size of 4, and a density of 10%. We show that much larger networks can be deployed onto a GPU of a fixed size with performance increases of around 5× over the next best solution for a density of 1-30% on a layer size of 2304; notably, this sparsity range includes denser workloads than typically perform worse with sparse optimizations. We also show promising results on much larger layers -7168 and 11520 achieve speedups of 1.9× for 2.6% and 1% densities, respectively. Our approach speeds up pruned NMT and speech recognition networks' recurrent layers by up to 3×. Finally, load-balanced pruning can significantly improve a network's throughput, and our technique is necessary to achieve both high performance and accuracy in some recurrent layers, as detailed in the case studies in our appendix. Without consideration of the accuracy of pruned networks and their execution speed (on state-of-theart algorithms) together, the conclusion that a large, sparse network is better than a small, dense one is not sufficiently proven. Our technique and these case studies show, among these insights, that this can be the case, however:• Our technique extends to LSTMs with little effort.• Our technique allows for pruned recurrent layers to run more efficiently than with any other existing algorithm.• Naïve pruning is not necessarily better than pruning with load-balancing in mind, especially when considering achievable performance.• Like past work, we see that a larger, sparse network can be more accurate than a smaller, dense one.• Comparisons against persistent kernels, which can beat non-resident sparse approaches,show that for a given accuracy or performance target, pruning a network and using our technique is the best choice.",1468,0.596,877,1.6738882554161916,"Recurrent Neural Networks powerful tools solving their efficacy execution time dependent Following recent work simplifying these networks with model pruning a novel mapping work onto GPUs design sparse RNNs investigate several optimizations tradeoffs: Lamport timestamps wide memory loads a bank-aware weight layout With these optimizations achieve speedups 6x over the next best algorithm a hidden layer size 2304, batch size a density Further, our technique allows models over 5x to fit a GPU for a speedup enabling larger networks help advance the state We perform case studies NMT and speech recognition tasks the appendix accelerating their recurrent layers up 3x Many sequence-based problems Speech Recognition BID0 , effectively BID2 showed these networks can run efficiently massively parallel processors such GPUs BID8 found if small the register file a persistent approach increaseIn parallel many network compression methods BID16 BID12 have shown the model size Recent work found that model pruning in lead important network parameters for BID31 We present combines both into an efficient and expandable approach In particular our work makes the following contributions:• Larger sparse RNNs can run more more on top the naïve implementation, necessary achieve Case studies using our technique showing 1 ) generalization LSTMs 2) practical network design considerations up 3× on two non-synthetic workloadsA naïve implementation the idea presented Section leads limited benefit; we present a series optimizations Section help Section describes the experimental setup results, we future work our conclusions Sections The appendix presents a machine translation task.2 RELATED WORK 2.1 RNNS Recurrent Neural Networks powerful tools solving series-based problems NMT BID3 BID18 BID0 BID26 , language modeling various NLP tasks BID7 More complex recurrent networks devised build the basic RNN structure Long/ Term networks BID20 Gated Units . Though we focus RNNs this work for our approach extend other recurrent network types the LSTMs used our case study In particular build a recent GPU-based method storing recurrent weights- BID8 . Sparse persistent RNNs increase pruned networks without a series optimizations we described the improvement much An optimized implementation is critical achieve peak performance After these optimizations see our approach sparser workloads, most layer sizes 10% density sufficient beat though for (up 2304 the winner even up a density Different batch sizes all techniques; in general, dense GEMMs and our approach scale the best, which tempers the benefit offered other algorithms Finally the number timesteps largely immaterial the relative performance the various techniquesWe described an efficient algorithm recurrent layers To exploit this algorithm one prune the recurrent layers We perform this pruning during the training process a nureal machine translation network BID22 , look past work ) that pruned a commercial speech recognition network Deep Speech 2 BID0 The results on these real workloads promising for a given accuracy show a speedup between 2.0× the machine translation network's recurrent layers pruned load in mind on Deep Speech 2's recurrent layers without Please refer Appendix B the training processes a full discussion We introduced sparse persistent RNNs an efficient new algorithm accelerating pruned recurrent networks Further, explored several optimizations needed achieve on V100 a recent GPU. Our optimized technique 7.3×, against dense GEMM, dense persistent implementations for a hidden layer size 1792, batch size of 4 a density We show much larger networks deployed onto a GPU of performance increases around 5× over the next best solution for a density 1-30% on a layer size 2304; notably this sparsity range includes denser workloads than typically perform worse with sparse optimizations We also show promising results much larger layers -7168 11520 achieve speedups for 1% densities Our approach speeds pruned NMT and speech recognition networks' recurrent layers 3×. Finally load-balanced pruning can significantly a network's throughput our technique necessary both high performance accuracy some recurrent layers detailed the case studies our appendix Without consideration the accuracy pruned networks their execution speed (on statetheart algorithms together conclusion a large, sparse network better sufficiently proven Our technique and these case studies, among these insights this can however:• Our technique extends LSTMs little pruned recurrent layers run more with any existing Naïve pruning necessarily better load in especially considering achievable Like past work see a larger, sparse network accurate against persistent kernels beat nonresident sparse approachesshow for a given accuracy or and using",0.01,0.42108723730951464
"Weight pruning has proven to be an effective method in reducing the model size and computation cost while not sacrificing the model accuracy. Conventional sparse matrix formats, however, involve irregular index structures with large storage requirement and sequential reconstruction process, resulting in inefficient use of highly parallel computing resources. Hence, pruning is usually restricted to inference with a batch size of one, for which an efficient parallel matrix-vector multiplication method exists. In this paper, a new class of sparse matrix representation utilizing Viterbi algorithm that has a high, and more importantly, fixed index compression ratio regardless of the pruning rate, is proposed. In this approach, numerous sparse matrix candidates are first generated by the Viterbi encoder, and then the one that aims to minimize the model accuracy degradation is selected by the Viterbi algorithm. The model pruning process based on the proposed Viterbi encoder and Viterbi algorithm is highly parallelizable, and can be implemented efficiently in hardware to achieve low-energy, high-performance index decoding process. Compared with the existing magnitude-based pruning methods, index data storage requirement can be further compressed by 85.2% in MNIST and 83.9% in AlexNet while achieving similar pruning rate. Even compared with the relative index compression technique, our method can still reduce the index storage requirement by 52.7% in MNIST and 35.5% in AlexNet. Deep neural networks (DNNs) demand an increasing number of parameters as the required complexity of tasks and supporting number of training data continue to grow BID2 . Correspondingly, DNN incurs a considerable number of computations and amount of memory footprint, and thus requires high performance parallel computing systems to meet the target response time. As an effort to realize energy-efficient DNN, researchers have suggested various low-cost hardware implementation techniques. Among them, pruning has been actively studied to reduce the redundant connections while not degrading the model accuracy. It has been shown that pruning can achieve 9× to 13× reduction in connections BID9 .After pruning, the remaining parameters are often stored in sparse matrix formats. Different ways of representing indices of non-zero values constitute the different sparse matrix format, and have a significant impact on the level of achievable computational parallelism when a sparse matrix is used as an input operand BID1 . If the format is not properly designed, then the performance of DNN with a sparse matrix can be even lower than the case with dense matrix BID28 . The two most important characteristics of a hardware-friendly sparse matrix format are 1) reducing index storage footprint and 2) parallelizable index decoding process. As a compromise between index size reduction and index decoding complexity, numerous formats have been proposed BID1 . DNN after pruning heavily involves sparse matrix-vector and matrix-matrix multiplications (SpMV and SpMM, respectively). Despite the sparse content , the computation time for SpMM is longer than that of dense matrix multiplication in the modern graphic processing unit (GPU), due to its serialized index decoding process and irregular memory access patterns. For example, the inference latency of AlexNet and VGG16 with SpMM can be increased by 2× to 5× on GPUs or CPUs BID10 . The traditional pruning technique , therefore, is only attractive in the case where SpMV can be utilized (i.e., batch size of 1) BID11 ) BID28 . Therefore, a sparse matrix representation associated with parallelizable dense-matrix reconstruction in a wide range of computing operations is the key to extending the use of pruning.We propose a new DNN-dedicated sparse matrix format and a new pruning method based on errorcorrection coding (ECC) techniques. A unique characteristic of this sparse matrix format is the fixed, yet high (as shown in Section 3) index compression ratio, regardless of the pruning rate. Moreover, sparse-to-dense matrix conversion employing the proposed format becomes a parallel process and is no longer the performance bottleneck. Notice that conventional sparse matrix formats entail at least one column or row index value for each non-zero parameter such that the amount of index data is larger than that of non-zero values. On the other hand, the proposed approach compresses the locations of non-zero values with a convolutional code which is a type of ECC code. Consequently, the size of the sparse matrix index becomes negligible.Conventional pruning approaches first identify the parameter candidates to be pruned, then construct a matrix (often sparse) using formats such as Compressed Sparse Row (CSR) to represent the survived parameters. On the contrary, in the proposed scheme, pruning is performed in a restricted manner since a specific sparse matrix format is first constructed. A DNN-specific Viterbi encoder takes an input pattern and generates a sequence of random-number, where a ""1"" indicates the parameter had survived, and had been pruned otherwise. Depending on the length of the input pattern, a vast (but limited) number of output patterns (hence candidates of the final sparse matrix representations) are considered. In this case, the input pattern is used as the sparse matrix index . The content of the input pattern, which generates a deterministic output random number sequence, is chosen such that the accuracy degradation is minimized based on a user-defined cost function (more details on Section 2). Both the Viterbi encoder and the algorithm have been shown to be computationally efficient with an inherent parallelizable characteristic, as demonstrated in the digital communication applications BID27 . In this work, we further extend its application and demonstrate how the Viterbi algorithm can be modified to perform energy-efficient DNN pruning.2 PRUNING USING VITERBI-BASED APPROACH Figure 1 illustrates the proposed Viterbi decompressor (VD), which is based on the Viterbi encoder widely used in digital communication. VD has a simple structure consisting only of FlipFlops (FFs) and XOR gates . In this configuration, VD takes one input bit and produces four output bits every clock cycle. Notice that FFs and XOR gates intermingle input bits and generate pseudo random number outputs. Assume that a dense matrix is formed after pruning, as shown in Figure 2 , and an input sequence of {0, 1, 1, 0} is applied to VD through four clock cycles to generate the outputs, where '1' implies that the corresponding parameter has survived. In this case, the overhead in the index for the proposed Viterbi-Compressible Matrix (VCM) format is significantly less than that of CSR. In the VCM format, the input sequence to the VD becomes the index information . This index size is independent of the number of non-zero values and can be determined in advance based on the target index compression ratio 1 . Unlike the CSR format, the available VD-compressible dense matrix representation is limited , meaning that not all possible dense matrix representations after conventional magnitude-based pruning (such as BID9 ) can be reconstructed by VD. Therefore, the pruning method considering VCM may result in a matrix that contains different survived parameters compared to a pruning method using the CSR format. Thus, the key to the success of VCM is to design a VD that allows diversified parameters to survive, and to efficiently search for the optimal VD input sequence that minimizes the accuracy degradation 2 . We proposed a new DNN-dedicated sparse matrix format and pruning method using the Viterbi encoder structure and Viterbi algorithm. Unlike previous methods, we first consider only limited choices of pruning results, all of which have the advantage of a significant index compression ratio by our proposed index decompressing structures. One particular pruning result is selected from the limited pruning solution space based on the Viterbi algorithm with user-defined branch metric equations that aim to minimize the accuracy degradation. As a result, our proposed sparse matrix, VCM, shows noticeable index storage reduction even compared with the relative index scheme. Fixed index compression ratio and inherently parallel reconstruction scheme allows a wide range of applications, such as SpMM, since sparse matrices can be converted into dense matrices efficiently.A APPENDIX",1613,0.84,986,1.6359026369168357,"Weight pruning has proven the model size computation cost while not the model accuracy Conventional sparse matrix formats however involve irregular index structures large storage requirement sequential reconstruction process inefficient use highly parallel computing resources Hence pruning usually restricted inference with a batch size for an efficient parallel matrix-vector multiplication method exists In a new class sparse matrix representation utilizing Viterbi algorithm that a high, and more importantly, fixed index compression ratio regardless the pruning rate In this approach numerous sparse matrix candidates first the Viterbi encoder the one aims minimize the model accuracy degradation The model pruning process based the proposed Viterbi encoder highly parallelizable efficiently hardware to low-energy, high-performance index decoding process Compared the existing magnitude-based pruning methods index data storage requirement further compressed 85.2% MNIST AlexNet while achieving Even compared the relative index compression technique our method still the index storage requirement MNIST AlexNet Deep neural networks demand parameters as the required complexity tasks and supporting number continue BID2 . Correspondingly DNN incurs computations amount memory footprint high performance parallel computing systems the target response time As an effort realize energy-efficient DNN researchers suggested various low-cost hardware implementation techniques Among pruning has actively to the redundant connections while not degrading the model accuracy It shown pruning achieve 9× to connections BID9 .After the remaining parameters often stored sparse matrix formats Different ways representing indices constitute the different sparse matrix format have achievable computational parallelism when BID1 If the format properly designed DNN with even the case BID28 . The two most important characteristics a hardware-friendly sparse matrix format 1 reducing index storage footprint 2) parallelizable index decoding process As a compromise index size reduction and index decoding complexity numerous formats BID1 . DNN after pruning heavily involves sparse matrix-vector andSpMV and, Despite the sparse content , the computation time SpMM longer dense matrix multiplication in the modern graphic processing unit due its serialized index decoding process irregular memory access patterns For example the inference latency AlexNet VGG16 with SpMM can increased 2× on GPUs or CPUs BID10 . The traditional pruning technique , therefore only attractive SpMV can utilized BID11 ) Therefore a sparse matrix representation associated parallelizable dense-matrix reconstruction in computing operations the key extending pruningWe errorcorrection coding (ECC) techniques A unique characteristic this sparse matrix format fixed yet high (as Section 3) index compression ratio regardless the pruning rate Moreover sparse-to-dense matrix conversion employing the proposed format becomes a parallel process no Notice conventional sparse matrix formats entail or row index value such the amount larger On the proposed approach compresses the locations with a convolutional code which a type ECC code the size the sparse matrix index becomes negligibleConventional pruning approaches first identify the parameter candidates construct (often sparse formats Compressed Sparse Row to represent the survived parameters On in the proposed scheme pruning performed since a specific sparse matrix format first constructed A DNN-specific Viterbi encoder takes an input pattern random-number, where ""1 the parameter had survived had pruned otherwise Depending the input pattern a vast (but limited) numberhence candidates of the final sparse matrix representations considered In the input pattern used the sparse matrix index . The content the input pattern, generates a deterministic output random number sequence chosen such the accuracy degradation basedmore details Section Both the Viterbi encoder the algorithm shown with an inherent parallelizable characteristic the digital communication applications BID27 . In this work further extend its application and demonstrate the Viterbi algorithm modified energy-efficient DNN pruning.2 PRUNING USING (VD widely digital communication VD has a simple structure consisting only FlipFlopsFFs XOR gates . In this configuration VD takes one input bit produces every clock cycle Notice FFs XOR gates intermingle input bits generate pseudo random number outputs Assume a dense matrix formed after , an input sequence { applied VD through four clock cycles to the outputs ' implies the corresponding parameter has survived In the overhead in the index for the proposed Viterbi-Compressible Matrix (VCM) format significantly CSR In the VCM format the input sequence to becomes the index information . This index size independent and determined in advance based the target index compression ratio 1 . Unlike the CSR format the available VD-compressible dense matrix representation limited , after conventional magnitude-based pruning BID9 reconstructed Therefore the pruning method considering VCM may result a matrix different survived parameters compared the CSR format Thus the key VCM design a VD that diversified parameters survive efficiently search the optimal VD input sequence the accuracy degradation 2 We proposed a new DNN-dedicated sparse matrix format and pruning method the Viterbi encoder structure Unlike previous methods first consider only limited choices pruning results all a significant index compression ratio by our proposed index decompressing structures One particular pruning result selected the limited pruning solution space based the Viterbi algorithm with user-defined branch metric equations that aim the accuracy degradation As our proposed sparse matrix, VCM shows noticeable index storage reduction even compared the relative index scheme Fixed index compression ratio inherently parallel reconstruction scheme allows applications SpMM since sparse matrices converted efficientlyA APPENDIX",0.01,0.324303218753106
"Learning policies for complex tasks that require multiple different skills is a major challenge in reinforcement learning (RL). It is also a requirement for its deployment in real-world scenarios. This paper proposes a novel framework for efficient multi-task reinforcement learning. Our framework trains agents to employ hierarchical policies that decide when to use a previously learned policy and when to learn a new skill. This enables agents to continually acquire new skills during different stages of training. Each learned task corresponds to a human language description. Because agents can only access previously learned skills through these descriptions, the agent can always provide a human-interpretable description of its choices. In order to help the agent learn the complex temporal dependencies necessary for the hierarchical policy, we provide it with a stochastic temporal grammar that modulates when to rely on previously learned skills and when to execute new skills. We validate our approach on Minecraft games designed to explicitly test the ability to reuse previously learned skills while simultaneously learning new skills. Deep reinforcement learning has demonstrated success in policy search for tasks in domains like game playing BID12 BID7 BID11 and robotic control BID9 b; BID16 . However, it is very difficult to accumulate multiple skills using just one policy network BID24 . Knowledge transfer techniques like distillation BID3 BID18 BID15 BID24 have been applied to train a policy network both to learn new skills while preserving previously learned skill as well as to combine single-task policies into a multi-task policy. Existing approaches usually treat all tasks independently. This often prevents full exploration of the underlying relations between different tasks. They also typically assume that all policies share the same state space and action space. This precludes transfer of previously learned simple skills to a new policy defined over a space with differing states or actions.When humans learn new skills, we often take advantage of our existing skills and build new capacities by composing or combining simpler ones. For instance, learning multi-digit multiplication relies on the knowledge of single-digit multiplication; learning how to properly prepare individual ingredients facilitates cooking dishes based on complex recipes.Inspired by this observation, we propose a hierarchical policy network which can reuse previously learned skills alongside and as subcomponents of new skills. It achieves this by discovering the underlying relations between skills.To represent the skills and their relations in an interpretable way, we also encode all tasks using human instructions such as ""put down."" This allows the agent to communicate its policy and generate plans using human language. Figure 1 illustrates an example: given the instruction ""Stack blue,"" our hierarchical policy learns to compose instructions and take multiple actions through a multi-level hierarchy in order to stack two blue blocks together. Steps from the top-level policy π 3 (i.e., the red Figure 1: Example of our multi-level hierarchical policy for a given task -stacking two blue blocks. Each arrow represents one step generated by a certain policy and the colors of arrows indicate the source policies. Note that at each step, a policy either utters an instruction for the lower-level policy or directly takes an action.branches) outline a learned high-level plan -""Get blue → Find blue → Put blue."" In addition, from lower level policies, we may also clearly see composed plans for other tasks. Based on policy π 2 , for instance, the task ""Get blue"" has two steps -""Find blue → action: turn left,"" whereas ""Put blue"" can be executed by a single action ""put down"" according to π 3 . Through this hierarchical model, we may i) accumulate tasks progressively from a terminal policy to a top-level policy and ii) unfold the global policy from top-level to basic actions.In order to better track temporal relationships between tasks, we train a stochastic temporal grammar (STG) model on the sequence of policy selections (previously learned skill or new skill) for positive episodes. The STG focuses on modeling priorities of tasks: for example, it is necessary to obtain an object before putting it down. Integrating the STG into the hierarchical policy boosts efficiency and accuracy by explicitly modeling such commonsense world knowledge.We validated our approach by testing it on object manipulation tasks implemented in a Minecraft world. Our experimental results demonstrate that this framework can (i) efficiently learn hierarchical policies and representations for multi-task RL; (ii) learn to utter human instructions to deploy pretrained policies, improve their explainability and reuse skills; and (iii) learn a stochastic temporal grammar via self-supervision to predict future actions. In this work, we have proposed a hierarchal policy modulated by a stochastic temporal grammar as a novel framework for efficient multi-task reinforcement learning through multiple training stages. Each task in our settings is described by a human instruction. The resulting global policy is able to reuse previously learned skills for new tasks by generating corresponding human instructions to inform base policies to execute relevant base tasks. We evaluate this framework in Minecraft games and have shown that our full model i) has a significantly higher learning efficiency than a flat policy does, ii) generalizes well in unseen environments, and iii) is capable of composing hierarchical plans in an interpretable manner.Currently, we rely on weak supervision from humans to define what skills to be learned in each training stage. In the future, we plan to automatically discover the optimal training procedures to increase the task set.A PSEUDO CODE OF OUR ALGORITHMS Algorithm 1 RUN(k, g) Input: Policy level k, task g ∈ G k Output: Episode trajectory Γ at the top level policy 1: t ← 0 2: Γ = ∅ 3: Get initial state s0 4: repeat 5:if k == 1 then 6:Sample at ∼ π k (·|st, g) and execute at 7:Get current state st+1 8:rt ← R(st+1, g) 9:Add st, at, rt, π k (·|st, g), g to Γ 10: else 11:Sample et and g t as in Section 3.3 for using STG as guidance 12:Sample at ∼ π aug k (·|st, g) 13:if et = 0 then 14:// Execute base policy π k−1 by giving instruction g t 15:RUN(k − 1, g t ) 16: else 17:Execute at 18: end if 19:Get current state st+1 20:rt ← R(st+1, g) 21:Add st, et, g t , at, rt, π DISPLAYFORM0 end if 23: if in curriculum learning phase 1 then 9: DISPLAYFORM1 Sample a task g from base task set G k−1 10: else 11:Sample a task g from global task set G k 12:end if 13://Run an episode 14: DISPLAYFORM2 if the maximum reward in Γ is +1 then 17: DISPLAYFORM3 Re-estimate the distributions of the STG based on updated D+ by MLE 19:end if 20:Sample n ∼ Possion(λ) 21:for j ∈ {1, · · · , n} do 22:Sample a mini-batch S from D 23:Update Θ based on (9) and the τ -th term in (8) 24:i ← i + 1 25:if i%M = 0 then 26:τ ← τ %3 + 1 27: end if 28: end for 29: until i ≥ N",1521,0.626,868,1.7523041474654377,"Learning policies complex tasks multiple different skills is reinforcement learning It a requirement its deployment This paper efficient multi-task reinforcement learning Our framework trains agents employ hierarchical policies decide a previously learned policy learn a new skill This enables agents continually acquire during different stages Each learned task corresponds a human language description Because agents access previously learned skills these descriptions the agent always provide a human-interpretable description its choices In order help the agent the complex temporal dependencies necessary the hierarchical policy provide it modulates when to rely previously learned skills execute We validate our approach on Minecraft games designed explicitly reuse previously learned skills while learning Deep reinforcement learning demonstrated success policy search tasks domains game playing BID12 BID7 BID11 and robotic control BID9 b; . However very accumulate multiple skills using just one policy network BID24 . Knowledge transfer techniques like distillation BID3 BID18 BID15 BID24 have train a policy network both learn while preserving previously learned skill as combine single-task policies Existing approaches usually treat all tasks independently This often prevents full exploration the underlying relations different tasks They also typically assume all policies share the same state space action space This precludes transfer previously learned simple skills a new policy defined over a space with differing states actionsWhen humans take build composing or simpler ones For instance learning multi-digit multiplication relies how properly prepare individual ingredients facilitates cooking dishes based complex recipesInspired propose a hierarchical policy network which reuse alongside and as subcomponents It achieves discovering the underlying relations skillsTo represent also encode all tasks using human instructions suchput the agent communicate its policy generate plans using Figure illustrates: given the instruction ""Stack blue our hierarchical policy learns compose instructions and take through in stack two blue blocks Steps from the top-level policy � 3 red Figure: Example our multi-level hierarchical policy for a given task -stacking two blue blocks. Each arrow generated a certain policy and the colors the source policies Note at a policy either utters an instruction directly takes an action.branches) outline a learned high-level plan -""Get blue → Find Put In addition from lower level policies clearly composed plans other tasks Based policy �� 2 for the task ""Get blue -""Find blue → action: turn left whereas"" can executed ""put down according Through this hierarchical model may i accumulate tasks progressively from a terminal policy unfold basic actionsIn better track temporal relationships train on policy selectionspreviously learned skill or new skill positive episodes The STG focuses modeling priorities tasks: for it necessary obtain an object before putting down Integrating the STG the hierarchical policy boosts efficiency accuracy explicitly modeling such commonsense world knowledgeWe validated object manipulation tasks implemented a Minecraft world Our experimental results this framework (i efficiently learn hierarchical policies representations multi-task RL; utter human instructions deploy pretrained policies improve their explainability and reuse skills a stochastic temporal grammar via In this work proposed a hierarchal policy modulated a stochastic temporal grammar as efficient multitask reinforcement through multiple training stages Each task our settings described a human instruction The resulting global policy able reuse previously learned skills by generating corresponding human instructions inform base policies to execute relevant base tasks We evaluate this framework Minecraft games have shown our full model i) a flat policy does generalizes unseen environments capable composing hierarchical plans an interpretable mannerCurrently rely weak supervision from humans define what skills be each training stage In plan automatically discover the optimal training procedures increase the task setA PSEUDO CODE OF OUR Algorithm 1 RUN(k g Input Policy level k task � G k Output Episode trajectory �� at the top level policy 1 t � 2 � =� 3 Get initial state s0 4 repeatif k == 1 then 6:Sample at ∼ �� k·|st and execute 7Get current state st+1Add st, at, rt g � elseSample et and g t as in Section for using STG guidanceif et = 14:// Execute base policy � by giving instruction else 18 end ifGet , DISPLAYFORM0 end 23 if in curriculum learning phase 9 Sample a task g from base task 10 global task 12end 13://Run an episode 14 if the maximum reward in then 17 the distributions based updated D+ by MLE 19end n ∼ Possion(λfor { · · , n do a mini-batch S from D 23Update �� based (9 the τ -th termi � i%M =τ τ %3 end end until ≥ N",0.01,0.6208840407060492
"Embeddings are a fundamental component of many modern machine learning and natural language processing models.
 Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior of the models.
 State of the art in analyzing embeddings consists in projecting them in two-dimensional planes without any interpretable semantics associated to the axes of the projection, which makes detailed analyses and comparison among multiple sets of embeddings challenging.
 In this work, we propose to use explicit axes defined as algebraic formulae over embeddings to project them into a lower dimensional, but semantically meaningful subspace, as a simple yet effective analysis and visualization methodology.
 This methodology assigns an interpretable semantics to the measures of variability and the axes of visualizations, allowing for both comparisons among different sets of embeddings and fine-grained inspection of the embedding spaces.
 We demonstrate the power of the proposed methodology through a series of case studies that make use of visualizations constructed around the underlying methodology and through a user study. The results show how the methodology is effective at providing more profound insights than classical projection methods and how it is widely applicable to many other use cases. Learning representations is an important part of modern machine learning and natural language processing research. Those representations are often real-valued vectors also called embeddings and are obtained both as byproducts of supervised learning or as the direct goal of unsupervised methods. Independently of how the embeddings are learned, there is much value in understanding what information they capture, how they relate to each other and how the data they are learned from influences them. A better understanding of the embedded space may lead to a better understanding of the data, of the problem and the behavior of the model, and may lead to critical insights in improving such models. Because of their high-dimensional nature, they are hard to visualize effectively, and the most adopted approach is to project them in a bi-dimensional space. Projections have a few shortcomings: 1) they may not preserve distance in the original space, 2) they are not comparable across models and 3) do not provide interpretable dimensions of variability to project to, preventing for more detailed analysis and understanding. For these reasons, there is value in mapping embeddings into a more specific, controllable and interpretable semantic space.Principal Component Analysis (PCA) BID27 and t-Distributed Stochastic Neighbor Embedding (t-SNE) BID30 are two projection techniques often used for visualizing embeddings in two dimensions, although other techniques can be used. PCA projects embeddings on a lower dimensional space that has the directions of the highest variance in the dataset as axes. Those dimensions do not carry any interpretable meaning, making interpretation difficult. By visualizing the first two dimensions of a PCA projection, the only insight obtainable is semantic relatedness BID5 between points by observing their relative closeness and therefore topical clusters can be identified. The downside is that embeddings that end up being close in the projected space may not be close in the original embedding space and vice versa. Moreover, as the directions of highest variance are different from embedding space to embedding space, the projections are incompatible among different embeddings spaces, and this makes them not comparable, a common issue among dimensionality reduction techniques. t-SNE, differently from PCA, optimizes a loss that encourages embeddings that are close in the original high-dimensional space to be close in the lower dimensional projection space. This helps in visualizing clusters better than with PCA, as t-SNE puts each point in the projected space so that distance in the original space with respect to its nearest neighbors is preserved as much as possible. Visualizations obtained in this way reflect more the original embedding space and topical clusters are more clearly distinguishable, but doesn't solve the issue of comparability of two different sets of embeddings, nor it solves the lack of interpretability of the axes and still doesn't allow for finegrained inspection. Moreover, t-SNE is pretty sensible to hyperparameters, making it unclear how much the projection reflects the data.In this paper, a new and simple method to inspect, explore and debug embedding spaces at a finegrained level is proposed. It consists in defining explicitly the axes of projection through formulae in vector algebra over the embeddings themselves. Explicit axis definition gives an interpretable and fine-grained semantics to the axes of projection. Defining axes explicitly makes it possible to analyze in a detailed way how embeddings relate to each other with respect to interpretable dimensions of variability, as carefully crafted formulas can map (to a certain extent) to semantically meaningful portions of the learned spaces. The explicit axes definition also allows for comparing of embeddings obtained from different datasets, as long as they have common labels.We demonstrate three visualizations for analyzing subspaces of interest of embedding spaces and a set of example case studies including bias detection, polysemy analysis and fine-grained embedding analysis. Additional tasks that may be performed using the proposed methodology and visualization are diachronic analysis and analysis of representations learned from graphs and knowledge bases. The proposed visualizations can moreover be used for debugging purposes and in general for obtaining a better understanding of the embedding spaces learned by different models and representation learning approaches. We are releasing an open-source 1 interactive tool that implements the proposed visualizations, in order to enable researchers in the fields of machine learning, computational linguistics, natural language processing, social sciences and digital humanities to perform exploratory analysis and better understand the semantics of their embeddings.The main contribution of this work lies in the use of explicit user-defined algebraic formulae as axes for projecting embedding spaces into semantically-meaningful subspaces that when visualized provide interpretable axes. We show how this methodology can be widely used through a series of case studies on well known models and data and we furthermore validate the how the visualizations are more interpretable through a user study. We presented a simple methodology for projecting embeddings into lower-dimensional semantically-meaningful subspaces through explicit vector algebra formulae operating on the embedding themselves. Classical projection methods are useful to gather on overall coarse-grained view of the embedding space and how embeddings cluster, but we showed how our approach allows goal-oriented analyses with more fine-grained comparison and enables cross-dataset comparison through a series of case studies and a user study. This is possible thanks to the ability of the proposed methodology to assign an explicit semantics to the measures of variability used as axes of the visualization that in turns makes them interpretable and widely applicable to many use cases in computational linguistics, natural language processing, machine learning, social sciences and digital humanities.A APPENDIX Figure 6 : Professions plotted on ""male"" and ""female"" axes in W ikipedia embeddings.",1330,0.621,760,1.75,"Embeddings a fundamental component many modern machine learning and natural language processing models Understanding them visualizing gathering the information capture the behavior the models State in analyzing embeddings consists projecting them in without any interpretable semantics associated to the axes makes detailed analyses and comparison among multiple sets challenging In this work propose explicit axes defined over project them a lower dimensional, but semantically meaningful subspace a simple yet effective analysis and visualization methodology This methodology assigns an interpretable semantics the measures variability the axes visualizations allowing both comparisons among the embedding spaces We demonstrate the proposed methodology through make visualizations constructed around the underlying methodology through a user study The results show how the methodology effective providing more profound insights classical projection methods how widely Learning representations Those representations often real-valued vectors also obtained both byproducts supervised learning the direct goal Independently how the embeddings learned much value what information capture relate learned influences them A better understanding the embedded space may of the behavior may critical insights improving such models Because their high-dimensional nature hard visualize effectively the most adopted approach project Projections have a few shortcomings they may preserve distance the original space comparable across models 3 do interpretable dimensions variability to project to preventing for more detailed analysis and understanding For these reasons there value mapping embeddingsPrincipal Component AnalysisPCA) BID27 and tDistributed Neighbort two projection techniques often two dimensions although PCA projects embeddings a lower dimensional space has the directions the highest variance the dataset as axes Those dimensions do carry any interpretable meaning making interpretation By visualizing the first two dimensions a PCA projection only insight obtainable semantic relatedness BID5 between points by observing therefore topical clusters can The downside embeddings end close in the projected space may close the original embedding space and vice Moreover as the directions highest variance different embedding space the projections incompatible among this comparable a common among dimensionality reduction techniques t-SNE, differently PCA optimizes a loss that encourages embeddings close in the original high-dimensional space close This helps in clusters better with PCA t-SNE puts each point the projected space so that distance in with respect preserved as much Visualizations obtained in reflect more the original embedding space and topical clusters are clearly does solve comparability two different sets nor it interpretability the axes still does allow finegrained inspection Moreover t-SNE pretty sensible to hyperparameters making unclear the projection reflectsIn a new and simple method inspect, explore debug embedding spaces at a finegrained level It consists in defining explicitly the axes projection through formulae in vector algebra over themselves Explicit axis definition gives to the axes projection Defining axes explicitly makes analyze in embeddings relate with interpretable dimensions variability carefully crafted formulas map (to semantically meaningful portions the learned spaces The explicit axes definition also allows comparing of obtained different datasets common labelsWe demonstrate three visualizations analyzing subspaces interest embedding spaces a set example case studies including bias detection polysemy analysis Additional tasks that using the proposed methodology and visualization diachronic analysis analysis representations learned graphs knowledge bases The proposed visualizations can moreover debugging general obtaining the embedding spaces learned different models representation learning approaches We releasing an open-source 1 interactive tool implements the proposed visualizations in researchers in social sciences perform better the semanticsThe main contribution lies as axes projecting embedding spaces semantically-meaningful subspaces that when provide interpretable axes We show this methodology widely through on well known models data and we furthermore validate how the visualizations more interpretable a user study We presented a simple methodology projecting embeddings lower-dimensional semantically-meaningful subspaces through explicit vector algebra formulae operating the embedding themselves Classical projection methods useful gather on overall coarse-grained view the embedding space how cluster we showed our approach allows goal-oriented analyses with enables through case studies a user study This possible the proposed methodology assign an explicit semantics the measures variability used as axes the visualization that in turns makes widely many use cases digital humanitiesA APPENDIX Figure : Professions plotted ""male W ikipedia embeddings",0.01,0.6150132754042966
"Learning deep networks which can resist large variations between training andtesting data is essential to build accurate and robust image classifiers.   Towardsthis end, a typical strategy is to apply data augmentation to enlarge the trainingset.    However,  standard  data  augmentation  is  essentially  a  brute-force  strategywhich is inefficient,  as it performs all the pre-defined transformations  to everytraining sample. In this paper, we propose a principled approach to train networkswith  significantly  improved  resistance  to  large  variations  between  training  andtesting data.   This is achieved by embedding a learnable transformation moduleinto the introspective networks (Jin et al., 2017; Lazarow et al., 2017; Lee et al.,2018), which is a convolutional neural network (CNN) classifier empowered withgenerative capabilities.   Our approach alternatively synthesizes pseudo-negativesamples with learned transformations and enhances the classifier by retraining itwith synthesized samples.   Experimental results verify that our approach signif-icantly improves the ability of deep networks to resist large variations betweentraining and testing data and achieves classification accuracy improvements onseveral benchmark datasets, including MNIST, affNIST, SVHN and CIFAR-10. Classification problems have rapidly progressed with advancements in convolutional neural networks (CNNs) BID17 BID15 BID25 BID6 BID7 . CNNs are able to produce promising performance, given sufficient training data. However, when the training data is limited and unable to cover all the data variations in the testing data (e.g., the training set is MNIST, while the testing set is affNIST), the trained networks generalize poorly on the testing data. Consequently, how to learn deep networks which can resist large variations between training and testing data is a significant challenge for building accurate and robust image classifiers.To address this issue, a typical strategy is to apply data augmentation to enlarging the training set, i.e., applying various transformations, including random translations, rotations and flips as well as Gaussian noise injection, to the existing training data. This strategy is very effective in improving the performance, but it is essentially a brute-force strategy which is inefficient, as it exhaustively performs all these transformations to every training samples. Neither is it theoretically formulated.Alternatively, we realize that we can synthesize extra training samples with generative models. But, the problem is how to generate synthetic samples which are able to improve the robustness of CNNs to large variations between training and testing data. In this paper, we achieve this by embedding a learnable transformation module into introspective networks , a CNN classifier empowered with generative capabilities. We name our approach introspective transformation network (ITN), which performs training by a reclassification-by-synthesis algorithm. It alternatively synthesizes samples with learned transformations and enhances the classifier by retraining it with synthesized samples. We use a min-max formulation to learn our ITN, where the transformation module transforms the synthesized pseudo-negative samples to maximize their variations to the original training samples and the CNN classifier is updated by minimizing the classification loss of the transformed synthesized pseudo-negative samples. The transformation modules are learned jointly with the CNN classifier, which augments training data in an intelligent manner by narrowing down the search space for the variations.Our approach can work with any models that have generative and discriminative abilities, such as generative adversarial networks (GANs) and introspective networks. In this paper, we choose the introspective networks to generate extra training samples rather than GANs, because introspective networks have several advantages over GANs. Introspective learning framework maintains one single CNN discriminator that itself is also a generator while GANs have separate discriminators and generators. The generative and discriminative models are simultaneously refined over iterations. Additionally, Introspective networks are easier to train than GANs with gradient descent algorithms by avoiding adversarial learning.The main contribution of the paper is that we propose a principled approach that endows classifiers with the ability to resist larger variations between training and testing data in an intelligent and efficient manner. Experimental results show that our approach achieves better performance than standard data augmentation on both classification and cross-dataset generalization. Furthermore, we also show that our approach has great abilities in resisting different types of variations between training and testing data. We only briefly review introspective learning for binary-class problems, since the same idea can be easily extended to multi-class problems. Let us denote x ∈ R d as a data sample and y ∈ +1, −1 as the corresponding label of x. The goal of introspective learning is to model positive samples by learning the generative model p(x|y = +1). Under Bayes rule, we have DISPLAYFORM0 where p(y|x) is a discriminative model. For pedagogical simplicity, we assume p(y = 1) = p(y = −1) and this equation can be further simplified as: DISPLAYFORM1 The above equation suggests that a generative model for the positives p(x|y = +1) can be obtained from the discriminative model p(y|x) and a generative model p(x|y = −1) for the negatives. However, to faithfully learn p(x|y = +1), we need to have a representative p(x|y = −1), which is very difficult to obtain. A solution was provided in BID28 which learns p(x|y = −1) by using an iterative process starting from an initial reference distribution of the negatives p 0 (x|y = −1), e.g., p 0 (x|y = −1) = U (x), a Gaussian distribution on the entire space R d . This is updated by DISPLAYFORM2 where q t (y|x) is a discriminative model learned on a given set of positives and a limited number of pseudo-negatives sampled from p t (x|y = −1) and Z t =qt FORMULA0 qt(y=−1|x) p t (x|y = −1)dx is the normalizing factor. It has been proven that KL(p(x|y = +1)||p t+1 (x|y = −1)) ≤ KL(p(x|y = +1)||p t (x|y = −1))) (as long as each q t (y|x) makes a better-than-random prediction, the inequality holds) in BID28 , where KL(·||·) denotes the Kullback-Leibler divergences, which implies p t (x|y = −1) t=∞ → p(x|y = +1). Therefore, gradually learning p t (x|y = −1) by following this iterative process of Eqn.(3 ), the samples drawn from x ∼ p t (x|y = −1) become indistinguishable from the given training samples. Introspective Convolutional Networks (ICN) and Wasserstein Introspective Neural Networks (WINN) BID19 adopt the introspective learning framework and strengthen the classifiers by a reclassification-by-synthesis algorithm. However, both of them fail to capture large data variations between the training and testing data, since most of the generated pseudo-negatives are very similar to the original samples. But in practice, it is very common that the test data contain unseen variations that are not in training data, such as the same objects viewed from different angles and suffered from shape deformation.To address this issue, we present our approach building upon the introspective learning framework to resist large data variations between training and test data. Arguably, even large training sets cannot fully contains all the possible variations. Our goal is to quickly generate extra training samples with beneficial unseen variations that is not covered by the training data to help classifiers become robust. We assume that we can generates such training samples by applying a transformation function T (· ; σ) parametrized by learnable parameters σ to the original training samples. Let us denote g(· ; ψ) as the function that maps the samples x to the transformation parameters σ, where ψ is the model parameter of the function g. The generated samples still belong to the same category of the original samples, since the transformation function T only changes the high-level geometric properties of the samples. The outline of training procedures of ITN is presented in Algorithm 1. We denote S + = {(x + i , +1), i = 1... |S + |} as the positive sample set, DISPLAYFORM0 ; σ t )} as the transformed positive sample set at t th iteration with transformation parameter σ t and S DISPLAYFORM1 as the set of pseudonegatives drawn from p t (x|y = −1). We then will describe the detail of the training procedure.Discriminative model We first demonstrate the approach of building robust classifiers with given σ t . For a binary classification problem, at t th iteration, the discriminative model is represented as DISPLAYFORM2 Algorithm 1: Outline of ITN Training Algorithm 1: Input: Positive sample set S + , initial reference distribution p0(x|y = −1) and transformation function T 2: Output: Parameters θ, ω and ψ 3: Build S − 0 by sampling |S + | pseudo-negatives samples from p0(x|y = −1) 4: initialize parameters θ, ω and ψ, set t = 1 5: while not converge do 6:for each x DISPLAYFORM3 Compute transformation parameters σi = g(x DISPLAYFORM4 Choose i ∼ U (0, 1) and computexi = iT (x DISPLAYFORM5 9: end for 10:Compute θ, ω by Eqn.(6) 11:Compute ψ by Eqn. FORMULA0 Sample pseudo-negatives samples Zt = {z DISPLAYFORM6 Update all samples in Zt by Eqn. FORMULA0 Augment pseudo-negatives sample set S DISPLAYFORM7 .., |S + |} and t = t + 1 15: end while where θ t represents the model parameters at iteration t, and f t (x; θ t ) represents the model output at t th iteration. Note that, q t (y|x; θ t ) is trained on S + , T (S + ; σ t ) and pseudo-negatives drawn from p t (x|y = −1). In order to achieve stronger ability in resisting unseen variations, we want the distribution of T (S + ; σ t ) to be approximated by the distribution of pseudo negatives p t (x|y = −1), which can be achieved by minimizing the following Wasserstein distance BID5 : DISPLAYFORM8 where ω t is the extra parameter together with f t (·; θ t ) to compute the Wasserstein distance. Eachx in the setX t is computed with the formulax DISPLAYFORM9 2 is the gradient penalty that stabilizes the training procedure of the Wasserstein loss function.The goal of the discriminative model is to correctly classify any given x + , x T and x − . Thus, the objective function of learning the discriminative model at iteration t is DISPLAYFORM10 The classifiers obtain the strong ability in resisting unseen variations by training on the extra samples while preserving the ability to correctly classify the original samples. We discussed the binary classification case above. When dealing with multi-class classification problems, it is needed to adapt the above reclassification-by-synthesis scheme to the multi-class case. We can directly follow the strategies proposed in to extend ITN to deal with multi-class problems by learning a series of one-vs-all classifiers or a single CNN classifier.Exploring variations. The previous section describes how to learn the robust classifiers when the σ t is given. However, σ t is unknown and there are huge number of possibilities to selecting σ t . Now, the problem becomes how do we learn the σ t in a principled manner and apply it towards building robust classifiers? We solve this issue by forming a min-max problem upon the Eqn. FORMULA13 : DISPLAYFORM11 Here, we rewrite J(θ) and D(θ, ω) in Eqn. FORMULA11 and Eqn.(6) as J(θ, σ) and D(θ, ω, σ), since σ is now an unknown variable. We also subsequently drop the subscript t for notational simplicity. This formulation gives us a unified perspective that encompasses some prior work on building robust classifiers. The inner maximization part aims to find the transformation parameter σ that achieves the high loss values. On the other hand, the goal of the outer minimization is expected to find the the model parameters θ that enables discriminators to correctly classify x T and ω allows the negative distribution to well approximate the distribution of T (S + ; σ t ) . However, direclty solving Eqn. 7 is difficult. Thus, we break this learning process and first find a σ * that satisfies DISPLAYFORM12 where θ and ω are fixed. Then, θ and ω are learned with Eqn.(6) by keep σ = σ * . Empirically, the first term in the Eqn. 8 dominates over other terms, therefore we can drop the second and third terms to focus on learning more robust classifiers. The purpose of empirical approximation is to find the σ * that make x T hard to classify correctly. Instead of enumerating all possible examples in the data augmentation, Eqn.(8) efficiently and precisely finds a proper σ that increase the robustness of the current classifiers.We use g(· ; ψ) to learn σ, thus σ = g(x; ψ)+ζ, where ζ is random noise follows the standard normal distribution. The function parameter ψ is learned by Eqn.(8) . Notably, following the standard backpropagation procedure, we need to compute the derivative of the transformation function T in each step. In other words, the transformation function T (·; σ) need to be differentiable with respect to the parameter ψ to allow the gradients to flow through the transformation function T when learning by backpropagation.Generative model In the discriminative models, the updated discriminative model p(y|x) is learned by Eqn.(6). The updated discriminative model is then used to compute the generative model by the Eqn.(3) in section 3.1. The generative is learned by maximizing the likelihood function p(x). However, directly learning the generative model is cumbersome since we only need samples from the latest generative model. DISPLAYFORM13 where Z t indicates the normalizing factor at t th iteration. The random samples x are updated by increasing maximize the log likelihood of p − n (x). Note that maximizing log p Taking natural logarithm on both side of the equation above, we can get ln h t (x) = f t (x; θ t ). Therefore, log p − n (x) can be rewritten as DISPLAYFORM14 where C is the constant computed with normalizing factors Z t . This conversion allows us to maximize log p − n (x) by maximizing n−1 t=1 f t (x; θ t ). By taking the derivative of log p − n (x), the update step ∇x is: DISPLAYFORM15 where η ∼ N (0, 1) is the random Gaussian noise and λ is the step size that is annealed in the sampling process. In practice, we update from the samples generated from previous iterations to reduce time and memory complexity. An update threshold is introduced to guarantee the generated negative images are above certain criteria, which ensures the quality of negative samples. We modify the update threshold proposed in BID19 and keep track of the f t (x; θ t ) in every iteration. In particular, we build a set D by recording E[f t (x; θ t )], where x ∈ S + in every iteration. We form a normal distribution N (a, b) , where a and b represents mean and standard deviation computed from set D. The stop threshold is set to be a random number sampled from this normal distribution. The reason behind this threshold is to make sure the generated negative images are close to the majority of transformed positive images in the feature space. We proposed a principled and smart approach that endows the classifiers with the ability to resist larger variations between training and testing data. Our method, ITN strengthens the classifiers by generating unseen variations with various learned transformations. Experimental results show consistent performance improvements not only on the classification tasks but also on the other challenging classification tasks, such as cross dataset generalization. Moreover, ITN demonstrates its advantages in both effectiveness and efficiency over data augmentation. Our future work includes applying our approach to large scale datasets and extending it to generate samples with more types of variations.",3428,1.689,1924,1.7817047817047817,"Learning deep networks which resist large variations between training andtesting data build accurate and robust image classifiers Towardsthis end a typical strategy apply data augmentation enlarge the trainingset However standard data augmentation essentially a brute-force strategywhich inefficient performs to everytraining sample In train networkswith significantly resistance large variations between training andtesting data This achieved a learnable transformation moduleinto the introspective networks ( 2017 Lee,2018 empowered withgenerative capabilities Our approach alternatively synthesizes pseudonegativesamples learned transformations enhances retraining itwith synthesized samples Experimental results verify our approach signif-icantly deep networks resist large variations betweentraining and testing data and achieves classification accuracy improvements onseveral benchmark datasets MNIST affNIST SVHN Classification problems have rapidly progressed advancements BID17 BID15 BID25 BID6 BID7 . CNNs are able produce promising performance given sufficient training data However the training data limited unable cover all the data variations MNIST while affNIST the trained networks generalize poorly on how learn deep networks which resist large variations between training and testing data building accurate and robust image classifiersTo a typical strategy apply data augmentation enlarging applying various transformations random translations rotations flips as Gaussian noise injection This strategy improving, essentially which inefficient exhaustively performs all these transformations every training samples Neither theoretically formulatedAlternatively realize extra training samples generative models But the problem how generate synthetic samples which able improve CNNs large variations between training and testing data In achieve this a learnable transformation module introspective networks , a CNN classifier empowered generative capabilities We name our approach introspective transformation network performs training by a reclassification-by It alternatively synthesizes samples learned transformations enhances retraining We use a min-max formulation learn our ITN where the transformation module transforms the synthesized pseudo-negative samples maximize their variations to the original training samples the CNN classifier updated by minimizing the classification loss The transformation modules learned jointly the CNN classifier augments training data narrowing the variationsOur approach can work any models introspective networks In choose the introspective networks generate extra training samples rather GANs Introspective learning framework maintains one single CNN discriminator itself also while generators The generative and discriminative models simultaneously refined over iterations Additionally Introspective networks easier train GANs with gradient descent algorithms by avoidingThe main contribution propose endows classifiers resist larger variations between Experimental results our approach achieves standard data augmentation on both classification Furthermore show our approach great abilities resisting different types variations between training and testing data We only briefly review introspective learning for binary-class problems the same idea easily Let denote x �� R d as a data sample� +1, as the corresponding label The goal introspective learning model positive samples by learning the generative model p(x|y = +1 Under Bayes rule we DISPLAYFORM0 where p(y|x For pedagogical simplicity assume p(y = this equation further DISPLAYFORM1 suggests a generative model the positives = However to faithfully learn p(x|y = +1 have representative very A solution was provided BID28 which learns p(x|y = −1 starting an initial reference distribution the negatives p 0 U on the entire space R d This updated by DISPLAYFORM2 where q t (y|x a discriminative model learned positives a limited number pseudo sampled p t = Z t =qt FORMULA0 qt(y=−1|x p is It proven KL(p(x|y = t+1 ≤ (as long each q t makes the inequality holds in BID28 , KL(·||· denotes the Kullback-Leibler divergences implies p t → Therefore gradually learning p tx|y = by following Eqn.(3 ), the samples drawn x ∼ p t become indistinguishable the given training samples Introspective Convolutional Networks Wasserstein Introspective Neural BID19 adopt strengthen a-by However both fail capture large data variations the training and testing data since the generated pseudonegatives very But practice very the test data contain unseen variations in training data the same objects viewed suffered shape deformationTo address present approach building the introspective learning framework to resist large data variations between even large training sets fully contains Our goal quickly generate extra training samples beneficial unseen variations is covered to classifiers become robust We assume generates such training samples applying a transformation function T· ; � learnable parameters �� Let denote g· ; � that maps the samples x the transformation parameters �� where The generated samples still belong since the transformation function T only changes The outline training procedures of ITN Algorithm 1 We denote S + = {( i , +1... |S +} as the positive sample set DISPLAYFORM0 ; �� t )} as at t th iteration with S pseudonegatives drawn p tx|y = We then will describe the detailDiscriminative model We demonstrate building robust classifiers given �� t For a binary classification problem at t th iteration represented DISPLAYFORM2 Algorithm 1 Outline ITN Training Input: Positive sample set S + , initial reference distribution p0(x|y = and transformation function T 2 Parameters �� 3 Build S − 0 by sampling |S pseudonegatives samples initialize parameters set t while not converge do 6for each x DISPLAYFORM3 Compute transformation parameters �i Choose i ∼ U ( computexi iT 9 end for 10Compute � by Eqn.(6 FORMULA0 Sample pseudonegatives samples Zt = {z DISPLAYFORM6 Update all samples by Eqn FORMULA0 Augment pseudo-negatives sample set S DISPLAYFORM7 .., |S +} and t = t 1 15: end while where �� t represents the model parameters at iteration t f t (x; t th Note, q t (y|x; trained S + , TS ; pseudonegatives drawn p t = In order achieve stronger ability resisting unseen variations want the distribution T (S + ; pseudo negatives p tx|y = achieved minimizing the following Wasserstein distance BID5 : DISPLAYFORM8 where the extra parameter together f t·; Eachx in the setX t is computed the formulax DISPLAYFORM9 2 is the gradient penalty stabilizes the training procedure of the Wasserstein loss functionThe goal correctly any x + , x T Thus the objective function learning the discriminative model at iteration t DISPLAYFORM10 The classifiers obtain the strong ability in resisting unseen variations training on the extra samples while preserving correctly We discussed the binary classification case above When dealing multi-class classification problems needed adapt above-by scheme We directly follow the strategies proposed to extend ITN deal multi-class problems learning onevsall classifiers or a single CNN classifierExploring variations. The previous section describes learn the robust classifiers when the �� t given However �� t unknown huge number possibilities selecting Now the problem becomes learn the �� t in a principled manner apply towards building robust classifiers We solve forming a min-max problem upon the Eqn FORMULA13 : DISPLAYFORM11 Here rewrite J(�, � Eqn FORMULA11 and Eqn.(6 as J(��, since now an unknown variable We also subsequently drop the subscript t notational simplicity This formulation gives us a unified perspective encompasses some prior work building robust classifiers The inner maximization part aims find the transformation parameter �� achieves the high loss values On the goal the outer minimization expected find the model parameters � that enables discriminators correctly classify x T and �� allows the negative distribution well approximate (S + ; However, direclty solving Eqn 7 is difficult Thus break this learning process and first find a �� * that DISPLAYFORM12 where fixed Then �� and �� learned with Eqn.(6 by keep * . the Eqn. 8 dominates over other terms therefore drop focus learning more robust classifiers The purpose empirical approximation find * that make x T hard classify correctly Instead enumerating the data augmentation Eqn.(8 efficiently and finds a proper �� that increase the current classifiersWe g· ; learn thus �;�� random noise follows The function parameter �� learned Eqn.(8 Notably following need compute the transformation function T In the transformation function T·; � need differentiable allow flow when learning byGenerative model In p(y|x learned Eqn.(6 The updated discriminative model then by the Eqn.(3 in section is learned maximizing However directly learning the generative model cumbersome since samples DISPLAYFORM13 where Z t indicates the normalizing factor at t th iteration The random samples x are updated increasing maximize the log likelihood p − n Note maximizing log p Taking on both side above ln h t; Therefore log p − n (x can DISPLAYFORM14 where C constant computed normalizing factors Z t This conversion allows maximize log p − nx maximizing n−1 t=1 f t; By taking the derivative log p − nx the update step ��: DISPLAYFORM15 where ∼ N0 annealed In practice update from the samples generated reduce An update threshold introduced guarantee the generated negative images above certain criteria ensures negative samples We modify the update threshold proposed BID19 keep the f t (x; �� t every iteration In particular build a set D by recording E[f t (; � S + in every iteration We form a normal distribution Na, , represents mean computed set D. The stop threshold a random number sampled this normal distribution The reason behind this threshold the generated negative images close the majority transformed positive images the feature space We proposed a principled and smart approach endows the classifiers resist larger variations between training and testing data Our method, ITN strengthens the classifiers generating unseen variations with various learned transformations Experimental results consistent performance improvements not the classification tasks the other challenging classification tasks cross dataset generalization Moreover ITN demonstrates its advantages both effectiveness data augmentation Our future work applying our approach large scale datasets extending generate samples more types variations",0.02,0.6957942736364173
"It is well known that it is possible to construct ""adversarial examples""
 for neural networks: inputs which are misclassified by the network
 yet indistinguishable from true data. We propose a simple
 modification to standard neural network architectures, thermometer
 encoding, which significantly increases the robustness of the network to
 adversarial examples. We demonstrate this robustness with experiments
 on the MNIST, CIFAR-10, CIFAR-100, and SVHN datasets, and show that
 models with thermometer-encoded inputs consistently have higher accuracy
 on adversarial examples, without decreasing generalization.
 State-of-the-art accuracy under the strongest known white-box attack was 
 increased from 93.20% to 94.30% on MNIST and 50.00% to 79.16% on CIFAR-10.
 We explore the properties of these networks, providing evidence
 that thermometer encodings help neural networks to
 find more-non-linear decision boundaries. Adversarial examples are inputs to machine learning models that are intentionally designed to cause the model to produce an incorrect output. The term was introduced by Szegedy et al. (2014) in the context of neural networks for computer vision. In the context of spam and malware detection, such inputs have been studied earlier under the name evasion attacks BID0 . Adversarial examples are interesting from a scientific perspective, because they demonstrate that even machine learning models that have superhuman performance on I.I.D. test sets fail catastrophically on inputs that are modified even slightly by an adversary. Adversarial examples also raise concerns in the emerging field of machine learning security because malicious attackers could use adversarial examples to cause undesired behavior BID15 .Unfortunately , there is not yet any known strong defense against adversarial examples. Adversarial examples that fool one model often fool another model, even if the two models are trained on different training examples (corresponding to the same task) or have different architectures (Szegedy et al., 2014) , so an attacker can fool a model without access to it. Attackers can improve their success rate by sending inputs to a model, observing its output, and fitting their own own copy of the model to the observed input-output pairs BID15 . Attackers can also improve their success rate by searching for adversarial examples that fool multiple different models-such adversarial examples are then much more likely to fool the unknown target model . Szegedy et al. (2014) proposed to defend the model using adversarial training (training on adversarial examples as well as regular examples) but it was not feasible to generate enough adversarial examples in the inner loop of the training process for the method to be effective at the time. Szegedy et al. (2014) used a large number of iterations of L-BFGS to produce their adversarial examples. BID3 developed the fast gradient sign method (FGSM) of generating adversarial examples and demonstrated that adversarial training is effective for reducing the error rate on adversarial examples. A major difficulty of adversarial training is that it tends to overfit to the method of adversarial example generation used at training time. For example, models trained to resist FGSM adversarial examples usually fail to resist L-BFGS adversarial examples. BID9 introduced the basic iterative method (BIM) which lies between FGSM and L-BFGS on a curve trading speed for effectiveness (the BIM consists of running FGSM for a medium number of iterations). Adversarial training using BIM still overfits to the BIM, unfortunately, and different iterative methods can still successfully attack the model. Recently, BID13 showed that adversarial training using adversarial examples created by adding random noise before running BIM results in a model that is highly robust against all known attacks on the MNIST dataset. However, it is less effective on more complex datasets, such as CIFAR. A strategy for training networks which are robust to adversarial attacks across all contexts is still unknown. In this work, we demonstrate that thermometer code discretization and one-hot code discretization of real-valued inputs to a model significantly improves its robustness to adversarial attack, advancing the state of the art in this field. In BID3 , the seeming linearity of deep neural networks was shown by visualizing the networks in several different ways. To test our hypothesis that discretization breaks some of this linearity, we replicate these visualizations and contrast them to visualizations of discretized models. See Appendix G for an illustration of these properties.For non-discretized, clean trained models, test-set examples always yield a linear boundary between correct and incorrect classification; in contrast, non-adversarially-trained models have a more interesting parabolic shape (see Figure 9 ). Loss for iterated white-box attacks on various models on a randomly chosen data point from MNIST. By step 40, which is where we evaluate, the loss of the point found by iterative attacks has converged. DISPLAYFORM0 When discretizing the input, we introduce C w · C h · C o · c · (k − 1) extra parameters, where c is the number of channels in the image, k is the number of levels of discretization, and C w , C h , C o are the width, height, and output channels of the first convolutional layer. Discretizing using 16 levels introduced 0.03% extra parameters for MNIST, 0.08% for CIFAR-10 and CIFAR-100, and 2.3% for SVHN. This increase is negligible, so it is likely that the robustness comes from the input discretization, and is not merely a byproduct of having a slightly higher-capacity model.",1165,0.6,660,1.7651515151515151,"It well it construct ""adversarial examples: inputs which misclassified yet indistinguishable true data We propose a simple modification standard neural network architectures thermometer encoding significantly to adversarial examples We demonstrate this robustness experiments the MNIST, SVHN datasets models thermometer-encoded inputs consistently have on adversarial examples without decreasing generalization State accuracy under the strongest known white-box attack was increased 93.20% MNIST and 79.16 CIFAR-10 We explore the properties these networks providing evidence thermometer encodings help neural networks find more-non-linear decision boundaries Adversarial examples inputs intentionally cause The term was Szegedy (2014 in neural networks for In the context spam malware detection such inputs studied earlier under the name evasion attacks BID0 . Adversarial examples interesting from demonstrate even machine learning models superhuman performance on I.I.D. test sets fail on inputs modified even slightly an adversary Adversarial examples also raise in machine security because malicious attackers cause BID15 .Unfortunately , any known strong defense Adversarial examples that fool one model often fool even trained different training examples have different architecturesSzegedy , so an attacker fool without access it Attackers can improve sending inputs a model observing fitting their own own copy observed- BID15 . Attackers can improve searching adversarial examples fool multiple different models-such adversarial examples then much fool the unknown target model . Szegedy et (2014 proposed defend the model using adversarial trainingtraining adversarial examples as regular examples but feasible generate the inner loop the method Szegedy et (2014 used iterations L-BFGS produce their adversarial examples BID3 developed the fast gradient sign methodFGSM of generating adversarial examples demonstrated adversarial training reducing on A major difficulty adversarial training tends overfit to the method adversarial example generation used at training time For example models trained resist FGSM adversarial examples usually fail BID9 introduced the basic iterative method (BIM which lies FGSM L-BFGS on a curve trading speed for effectivenessthe BIM consists running a medium number Adversarial training using BIM still overfits to, unfortunately different iterative methods still successfully attack the model Recently BID13 showed adversarial training using adversarial examples created adding random noise before running BIM results a model robust against all known attacks However less effective on more complex datasets. A strategy training networks which robust across contexts still unknown In this work demonstrate that thermometer code discretization real-valued inputs to a model significantly to adversarial attack advancing In BID3 , the seeming linearity deep neural networks was visualizing To test discretization breaks some this linearity replicate these visualizations contrast See Appendix G an illustration these propertiesFor non-discretized, clean trained models test-set examples always yield a linear boundary; a more interesting parabolic shape 9 Loss for iterated white-box attacks various models on a randomly chosen data point from MNIST By step 40 which where evaluate, the loss the point found iterative attacks has converged DISPLAYFORM0 When discretizing the input we introduce C w · c (k − extra parameters channels levels C w , output channels Discretizing using 16 levels introduced 0.03% extra parameters MNIST SVHN This increase negligible so the robustness comes the input discretization, is merely having a slightly higher-capacity model",0.01,0.6536180048127914
"Low-precision training is a promising way of decreasing the time and energy cost of training machine learning models.
 Previous work has analyzed low-precision training algorithms, such as low-precision stochastic gradient descent, and derived theoretical bounds on their convergence rates.
 These bounds tend to depend on the dimension of the model $d$ in that the number of bits needed to achieve a particular error bound increases as $d$ increases.
 This is undesirable because a motivating application for low-precision training is large-scale models, such as deep learning, where $d$ can be huge.
 In this paper, we prove dimension-independent bounds for low-precision training algorithms that use fixed-point arithmetic, which lets us better understand what affects the convergence of these algorithms as parameters scale.
 Our methods also generalize naturally to let us prove new convergence bounds on low-precision training with other quantization schemes, such as low-precision floating-point computation and logarithmic quantization. As machine learning models continue to scale to target larger problems on bigger data, the task of training these models quickly and efficiently becomes an ever-more-important problem. One promising technique for doing this is low-precision computation, which replaces the 32-bit or 64-bit floating point numbers that are usually used in ML computations with smaller numbers, often 8-bit or 16-bit fixed point numbers. Low-precision computation is a broadly applicable technique that has received a lot of attention, especially for deep learning, and specialized hardware accelerators have been developed to support it (Jouppi et al., 2017; Burger, 2017; Caulfield et al., 2017) .A major application for low-precision computation is the training of ML models using empirical risk minimization. This training is usually done using stochastic gradient descent (SGD), and most research in low-precision training has focused on low-precision versions of SGD. While most of this work is empirical (Wu et al., 2018; Das et al., 2018; Zhu et al., 2016; Köster et al., 2017; Lee et al., 2017; Hubara et al., 2016; Rastegari et al., 2016; Zhou et al., 2016; Gupta et al., 2015; Courbariaux et al., 2014; 2015; De Sa et al., 2017) , significant research has also been done in the theoretical analysis of low-precision training. This theoretical work has succeeded in proving bounds on the convergence rate of low-precision SGD and related low-precision methods in various settings, including for convex (De Sa et al., 2018; Zhang et al., 2017) and non-convex objectives (De Sa et al., 2015; Li et al., 2017; Alistarh et al., 2017) . One common characteristic of these results is that the bounds tend to depend on the dimension d of the model being learned (equivalently, d is the number of parameters). For example, (Li et al., 2017) gives the convergence bound DISPLAYFORM0 where the objective f is strongly convex with parameter µ, low-precision SGD outputsw T after T iterations, w * is the true global minimizer of the objective, σ 2 max is an upper bound on the second moment of the stochastic gradient samples E[ f (w) 2 2 ] ≤ σ 2 max , and δ is the quantization step, the difference between adjacent numbers in the low-precision format. Notice that, as T → ∞, this bound shows convergence down to a level of error that increases with the dimension d. Equivalently , in order to achieve the same level of error as d increases, we would need to use more bits of quantization to make δ smaller. Similar dimension-dependent results, where either the error or the number of bits needed increases with d, can also be seen in other work on low-precision training algorithms (Alistarh et al., 2017; Zhang et al., 2017; De Sa et al., 2018) . This dependence on d is unsatisfying because the motivation for low-precision training is to tackle large-scale problems on big data, where d can range up to 10 8 or more for commonly used models (Simonyan and Zisserman, Table 1 : Summary of our dimension-free results compared with prior work. The values report the number of bits needed, according to the theoretical bound, for the LP-SGD (Li et al., 2017) algorithm to achieve an expected objective gap (f (w) − f (w * )) of when we let step size α → 0, epoch length T → ∞. Here we let R denote the radius of the range of numbers representable in the low-precision format and assume w * 2 = Θ(R). The rest of the parameters can be found in the assumptions to be introduced later. log 2 O (Rσ/ε) · log 1 + σ1/σ 2014). For example, to compensate for a factor of d = 10 8 in (1), we could add bits to decrease the quantization step δ by a factor of √ d, but this would require adding log 2 (10 4 ) ≈ 13 bits, which is significant compared to the 8 or 16 bits that are commonly used in low-precision training. In this paper, we present dimension-independent bounds on the convergence of SGD when applied to low-precision training. We point out the conditions under which such bounds hold. We further extend our results to non-linear methods of quantization: logarithmic quantization and floating point quantization. We analyze the performance of SGD under logarithmic quantization and demonstrate that NLQ is a promising method for reducing the number of bits required in low-precision training. We also presented ways in which our theory could be used to suggest how to allocate bits between exponent and mantissa when FPQ is used. We hope that our work will encourage further investigation of non-linear quantization techniques. A ALGORITHMIn our work, we presented dimension-free bounds on the performance of low-precision SGD, here we present the algorithm in detail.",1287,0.563,765,1.6823529411764706,"Low-precision training a promising way decreasing and energy cost training machine learning models Previous work analyzed low-precision training algorithms derived theoretical bounds their convergence rates These bounds tend depend the dimension the model $d$ in that the number bits needed achieve a particular error bound increases This undesirable a motivating application low-precision training large-scale models deep learning where $d$ huge In this paper prove dimension-independent bounds low-precision training algorithms lets better what affects the convergence these algorithms as parameters scale Our methods also generalize naturally let prove new convergence bounds on low-precision training with other quantization schemes As machine learning models continue scale target larger problems on bigger data, the task training quickly and One promising technique doing low-precision computation replaces usually ML computations smaller numbers Low-precision computation a broadly applicable technique received deep learning specialized hardware accelerators support (Jouppi 2017 Burger Caulfield) .A major application the training ML models empirical risk minimization This training usually using and most research in low-precision training While most this work empirical (Wu 2018; Das Zhu Köster et al Lee Hubara Rastegari Zhou Gupta Courbariaux 2015 De Sa et 2017 , significant research also the theoretical analysis low-precision training This theoretical work succeeded proving bounds the convergence rate low-precision SGD and related low-precision methods various settings for convex (De Sa et 2018 non-convex objectives Li Alistarh) . One common characteristic these results the bounds tend depend the dimension d being learnedequivalently d parameters For example (Li et 2017 gives the convergence bound DISPLAYFORM0 where the objective f strongly parameter µ low-precision SGD outputsw T after T iterations w * is the true global minimizer the objective, �� 2 max an upper the second moment the stochastic gradient samples E[ f (w) 2 2 ] ≤ �� 2 max the quantization step, the difference adjacent numbers Notice, T → �� this bound shows convergence down a level error that increases the dimension d. Equivalently , in order achieve error d increases would use more bits quantization make �� smaller Similar dimension-dependent results, where either the error bits needed increases d, other work low-precision training algorithmsAlistarh 2017 Zhang De Sa et . This dependence d is unsatisfying because the motivation low-precision training tackle on big data where d can range up 8 or for commonly used models (Simonyan Zisserman Table : Summary our dimension-free results compared prior work. The values report the number bits needed, according theoretical bound LP-SGD (Li et 2017 algorithm to achieve an expected objective gapf (w − fw * )) when we let step size α → 0 epoch length T �. Here we let R denote the radius the range numbers representable the low-precision format and assume w * 2 = ��(R The rest the parameters can the assumptions to introduced later log 2 O (Rσ/ε · log + �1/σ 2014). For example to compensate a factor d = 10 8 in ( could add bits decrease the quantization step �� by �� d, but log10 4 ) �� 13 bits significant compared the 8 or 16 bits commonly low-precision training In this paper dimension-independent bounds the convergence SGD when applied low-precision training We point the conditions such bounds hold We further extend our results non-linear methods quantization: and We analyze SGD under logarithmic quantization demonstrate NLQ a promising method reducing bits low-precision training We also presented ways our theory suggest allocate bits between exponent when FPQ We hope our work further investigation non-linear quantization techniques A ALGORITHMIn our work presented dimension-free bounds the performance low-precision SGD, here the algorithm in detail",0.01,0.4426545129275464
"We consider the problem of exploration in meta reinforcement learning. Two new meta reinforcement learning algorithms are suggested: E-MAML and ERL2. Results are presented on a novel environment we call 'Krazy World'  and a set of maze environments. We show E-MAML and ERL2 deliver better performance on tasks where exploration is important. Supervised learning algorithms typically have their accuracy measured against some held-out test set which did not appear at training time. A supervised learning model generalizes well if it maintains its accuracy under data that has non-trivial dissimilarity from the training data. This approach to evaluating algorithms based on their generalization ability contrasts the approach in reinforcement learning (RL), wherein there is usually no distinction between training and testing environments. Instead, an agent is trained on one environment, and results are reported on this same environment. Most RL algorithms thus favor mastery over generalization.Meta RL is the suggestion that RL should take generalization seriously. In Meta RL, agents are evaluated on their ability to quickly master new environments at test time. Thus, a meta RL agent must not learn how to master the environments it is given, but rather it must learn how to learn so that it can quickly train at test time. Recent advances in meta RL have introduced algorithms that are capable of generating large policy improvements at test time with minimal sample complexity requirements BID5 ; ; BID36 .One key question for meta RL that has been inadequately considered by BID5 ; is that of exploration (see BID10 for an overview of exploration in this context). A crucial step in learning to solve many environments is an initial period of exploration and system identification. Furthermore , we know that real-life agents become better at this exploratory phase with practice. Consider, for example, an individual playing an entirely new video game. They will first need to identify the objective of the game and its mechanics. Further, we would expect that individuals who have played many video games would have a significantly easier time learning new games. Similarly , we would expect a good meta RL agent to become more efficient at this exploratory period. Unfortunately , we have found existing algorithms deficient in this area. We hypothesize that this failure can at least partially be attributed to the tendency of existing algorithms to do greedy, local optimization at each step of meta-training, as discussed further below.To address the problem of exploration in meta RL, we introduce two new algorithms: E-MAML and E-RL 2 . It should come as no surprise that these algorithms are similar to their respective namesakes MAML and RL 2 . The algorithms are derived by reformulating the underlying meta-learning objective to account for the impact of initial sampling on future (post-meta-updated) returns. We show that our algorithms achieve better results than MAML and RL 2 on two environments: a Krazy World environment we developed to benchmark meta RL, and a set of maze environments. In the appendix to this work, we consider a more general form of our E-MAML derivation. This more general derivation suggests several promising directions for future work on exploration in meta-learning and highlights the novelty of our contributions. We considered the problem of exploration in meta reinforcement learning. Two new algorithms were derived and their properties were analyzed. In particular, we showed that these algorithms tend to learn more quickly and explore more efficiently than existing algorithms. It is likely that future work in this area will focus on meta-learning a curiosity signal which is robust and transfers across tasks. Perhaps this will enable meta agents which learn to explore rather than being forced to explore by mathematical trickery in their objectives. See appendix B for more explicit discussion on possible future directions. Figure 7 : Three heuristic metrics for exploration on Krazy World: Fraction of tile types visited during test time, number of times killed at a death square during test time, and number of goal squares visited. We see that E-MAML is consistently the most diligent algorithm at checking every tile type during test time. Beyond that, things are fuzzy with RL 2 and MAML both checking a majority of tile types at test time and E-RL 2 being sporadic in this regard. As for the number of times the death tile type was visited, we see that most algorithms start by dying in all three test episodes, and subsequently decrease to between one and two by the time they have converged. As mentioned above, RL 2 suffers from finding one goal and exploiting it, whereas the other algorithms regularly explore to find more goals. For the most part, the exploratory algorithms consistently deliver the best performance on these metrics. Performance on the death heuristic and the tile types found heuristic seem to indicate the meta learners are learning how to do at least some system identification. Figure 8 : MAML on the right and E-MAML on the left. A look at the number of gradient steps at test time vs reward on the Krazy World environment. Both MAML and E-MAML do not typically benefit from seeing more than one gradient step at test time. Hence, we only perform one gradient step at test time for the experiments in this paper.",1024,0.67,593,1.72681281618887,"We consider the problem exploration meta reinforcement learning Two new meta reinforcement learning algorithms suggested EMAML ERL2 Results are presented a novel environment we 'Krazy World maze environments We show EMAML ERL2 deliver tasks exploration Supervised learning algorithms typically their accuracy against some held test set which did appear at A supervised learning model generalizes well if maintains its accuracy data This approach evaluating algorithms their generalization ability contrasts in reinforcement learningRL wherein there usually Instead an agent trained one environment results reported this same environment Most RL algorithms thus favor masteryMeta RL the suggestion take In Meta RL agents evaluated quickly master new environments at test time Thus a meta RL agent must learn master the environments given it so quickly train at test time Recent advances meta RL introduced algorithms large policy improvements test time minimal sample complexity requirements BID5 ; ; BID36 .One key question that inadequately considered ; exploration ( exploration A crucial step learning solve many environments an initial period exploration and system identification Furthermore , real-life agents become better this exploratory phase with practice Consider, an individual playing They will first identify the objective Further individuals played Similarly , would a good meta RL agent become this exploratory period Unfortunately , found existing algorithms deficient We hypothesize this failure can at existing algorithms do greedy, local optimization at meta-training discussed furtherTo exploration meta RL E-MAMLRL 2 It should these algorithms similar their respective namesakes MAML RL 2 The algorithms derived reformulating the underlying meta-learning objective account initial sampling future (post-meta-updated) returns We show our algorithms achieve MAML RL 2 on two environments a Krazy World environment we developed benchmark meta RL maze environments In the appendix our E-MAML derivation This more general derivation suggests several promising directions exploration in meta-learning highlights the novelty our contributions We considered exploration meta reinforcement learning Two new algorithms derived and their properties In particular showed these algorithms tend learn explore existing algorithms It likely future work metalearning a curiosity signal robust transfers tasks Perhaps enable meta agents which learn explore rather being mathematical trickery in their objectives See appendix B more explicit discussion possible future directions Figure : Three heuristic metrics exploration on Krazy World Fraction tile types visited test time number killed at a death square during goal squares. We see EMAML consistently the most diligent algorithm at checking every tile type during test time Beyond things fuzzy with RL 2 and MAML both checking a majority tile types test time E-RL sporadic As for times the death tile type visited see most algorithms start dying all three test episodes subsequently decrease between by have converged As mentioned RL 2 suffers finding one goal exploiting whereas the other algorithms regularly explore to For the exploratory algorithms consistently deliver these metrics Performance on the death heuristic and the tile types found heuristic seem indicate the meta learners learning how at least some system identification Figure : MAML on E- A look gradient steps at test time vs reward on the Krazy World environment Both MAML E- do typically benefit seeing more than one gradient step test time Hence only perform one gradient step test time the experiments",0.01,0.5559343682572323
"We propose a new class of probabilistic neural-symbolic models for visual question answering (VQA) that provide interpretable explanations of their decision making in the form of programs, given a small annotated set of human programs. The key idea of our approach is to learn a rich latent space which effectively propagates program annotations from known questions to novel questions. We do this by formalizing prior work on VQA, called module networks (Andreas, 2016) as discrete, structured, latent variable models on the joint distribution over questions and answers given images, and devise a procedure to train the model effectively. Our results on a dataset of compositional questions about SHAPES (Andreas, 2016) show that our model generates more interpretable programs and obtains better accuracy on VQA in the low-data regime than prior work. Exciting progress has been made in recent years in deep representation learning BID19 BID32 , which has led to advances in artificial intelligence tasks such as image recognition BID30 BID18 , machine translation BID41 , visual question answering BID0 , visual dialog BID10 , and reinforcement learning BID36 , etc. While deep neural networks achieve such impressive performances, many aspects of human cognition such as compositional generalization and reasoning are harder to model with state-of-the art deep learning approaches BID6 BID5 .Symbolic approaches BID38 on the other hand provide strong compositional and reasoning capabilities which are challenging to model with neural networks BID31 . Consequently , a rich line of work in neuro-symbolic processing sought to build AI systems with both strong learning and reasoning capabilities BID46 BID12 BID4 . As we tackle higher-level tasks which involve reasoning, such as visual question answering BID0 , planning BID3 BID15 etc., it is natural to desire the ability to provide instructions to models to guide them. Symbolic instructions , by their very nature are easier to specify and more interpretable than specifying the parameters of a neural network. For such high-level tasks, a sensible approach is to specify ""what"" to do using symbols and learn how to do the task using modern representation learning techniques.For the example shown in Figure 1 , given a question ""Is a square to the left of a green shape?"", one can ask the model to reason about the answer by first applying a find [green] operator, then find [left] , then And the result together with a find [square] operator in order to predict the answer, in other words specifying ""what"" are the computations we desire to be executed, in the form of a ""program"". BID26 BID21 BID2 . The network can then learn ""how"" to execute such a program from data using deep representation learning BID26 BID21 BID2 . This paper addresses a very natural desiderata for such neuro-symbolic models, in the context of visual question answering -can we retain the intepretability of ""what the network did"" expressed in terms of the syntax and lexicon that we are interested in, while specifying minimal teaching examples of ""what to do"" given an input question? Figure 1 : An illustration of neural module networks for visual question answering. Given a question, the program generator produces a program in prefix notation which is used to construct a neural network from the specified module networks. This network operates on the image and intermediate attention maps to answer the question.We propose to approach this problem with a treatment of programs z as a latent variable, embedded into a generative model of questions x and answers a given images i as visualized in FIG0 . This model class has certain desirable properties: first, a proper treatment of z as a stochastic latent variable is helpful especially in the presence of a limited number of expert human instructions, as we model the uncertainty associated with z explicitly, leading to more interepretable latent spaces (Section 5); second, the model makes intuitive independence assumptions with regards to the question answering task -conditioned on the program z, questions x are independent of the answers a for an image, meaning that the program must be a sufficient statistic for predicting the answer given a question 1 . Third, we parameterize the p(a|i , z) term, which predicts an answer given an image and a program using a popular, related class of question answering models called neural module networks (NMNs) BID21 BID26 BID2 which previous work has shown leads to better fit between the program (or ""what the model is doing"") and the execution (or ""how it is doing what it is doing""). Given the close ties of our model to NMNs, we will refer to our model as variational neural module networks (V-NMN) for the rest of the paper.Apart from our modeling contribution of a probabilistic latent variable, neuro-symbolic model, our key technical contribution is to show how to train this model in the context of visual question answering.Optimizing such generative models with structured discrete latent variables is an intractable problem to solve in genereal -for this particular case, we formulate training into stages of grounding questions into programs (question coding), learning how to execute them and then with those initializations train the full variational objective. We demonstrate that this stage-wise optimization allows us to successfully learn a probabilistic neural-symbolic model that can answer compositional questions about shapes in an image BID2 .While the V-NMN model is instantiated for the specific problem of visual question answering, we believe the tools and techniques we develop are more generally applicable to probabilistic, structured, discrete, interpretable latent spaces for interpretable neuro-symbolic models for planning, instruction following, grounding referring expressions etc. We benchmark our model on the SHAPES BID2 dataset with compositionally novel questions and show that our model is able to provide interpretable explanations of ""what it is doing"" (measured by program correctness) for unseen questions even in the setting where it is given as few as ≈ 20 paired examples of programs and corresponding questions from the dataset, while also getting to high question answering accuracy. We find that the proposed approach outperforms a state of the art neural-symbolic model designed for VQA from BID26 , as well as deterministic ablations of our model. In this paper we presented a novel, probabilistic neural symbolic model for interpretable visual question answering, that provides explanations of ""what"" the model is doing on unseen questions given a minimal number of annotated symbolic traces or programs of ""what it should do"". We demonstrate that our formulation provides more interpretable explanations than previous work on visual question answering called neural module networks, on dataset of compositional questions about shapes BID2 .The key to our approach is a model with programs as a stochastic latent variable, which leads to better sharing of statistics across questions, yielding a latent space where program annotations for known questions propagate effectively to unknown / novel questions without annotations.In general, the model family we study is quite rich, and also supports other inference queries such as counter factual explanations of what programs could have led to particular answers for a given image. We hope our work inspires more work on applying such ideas to other tasks requiring compositional reasoning such as planning, navigation etc.",1441,0.532,825,1.7466666666666666,"We propose visual question answering provide interpretable explanations their decision making programs given a small annotated set human programs The key idea our approach learn a rich latent space which effectively propagates program annotations known questions novel questions We do formalizing prior work VQA called module networksAndreas as discrete, structured, latent variable models on the joint distribution over questions given images devise train effectively Our results on a dataset compositional questions SHAPESAndreas, 2016 our model generates more interpretable programs obtains VQA in the low-data regime prior work Exciting progress deep representation learning BID19 BID32 , led advances artificial intelligence tasks , visual question visual dialog reinforcement etc While deep neural networks achieve such impressive performances many aspects such compositional generalization reasoning harder model approaches BID6 BID5 .Symbolic approaches BID38 on provide which challenging , a rich line work neuro-symbolic processing sought build AI systems both strong learning and reasoning capabilities BID46 BID12 BID4 . As tackle higher-level tasks which reasoning such visual question BID0 , planning BID3 BID15 etc natural desire provide instructions models to guide Symbolic instructions , by easier specify specifying the parameters For such high-level tasks a sensible approach specify ""what using symbols learn modern representation learning techniquesFor shown given a question "" a square to a green shape the model reason first applying a find [green] operator find then And the result together in predict in specifying are we desire be executed BID26 BID21 BID2 . The network can then learn "" execute data using deep representation learning BID26 BID21 BID2 . This paper addresses a very natural desiderata such neuro-symbolic models visual question answering -can retain the intepretability ""what the network did expressed the syntax that specifying minimal teaching examples to given an input question Figure : neural module networks visual question answering Given a question the program generator produces prefix construct the specified module networks This network operates the image intermediate attention maps to answer.We propose approach a treatment programs z as embedded questions x answers a given images i visualized FIG0 This model class certain desirable properties first a proper treatment z as helpful especially expert human instructions model the uncertainty explicitly leading more interepretable latent spacesSection makes intuitive independence assumptions with regards the question answering task -conditioned on the program z questions x are independent a for an image meaning must a sufficient statistic predicting 1 . Third parameterize the p(a|i , z) term predicts an answer an image a program using a popular, related class question answering models neural module networks BID21 BID26 which previous work leads fit between (or ""what the execution what Given our model NMNs will refer variational neural module networksV-NMNApart our modeling contribution of neuro-symbolic model our key technical contribution train visual question answeringOptimizing structured discrete latent variables to genereal -for this particular case formulate training into stages grounding questions into programsquestion coding learning how execute with those initializations train the full variational objective We demonstrate this stage-wise optimization allows successfully learn answer shapes BID2 .While the V-NMN model instantiated for the specific problem visual question answering believe the tools develop generally probabilistic, structured, discrete, interpretable latent spaces for for planning instruction following grounding referring expressions etc We benchmark our model the SHAPES BID2 dataset compositionally novel questions show provide interpretable explanations "" doing program correctness unseen questions even the setting given as few � 20 paired examples programs corresponding questions from getting to high question We find the proposed approach outperforms a state designed VQA from BID26 , as deterministic ablations our model In presented probabilistic neural symbolic model interpretable visual question answering that provides explanations "" the model on unseen questions given annotated symbolic traces or programs "" it should We demonstrate our formulation provides more interpretable explanations visual question answering called neural module networks on dataset compositional questions shapes BID2 .The key a model programs as leads better sharing statistics questions yielding a latent space program annotations for known questions propagate effectively unknown / novel questions without annotationsIn general the model family we study quite rich also supports other inference queries counter factual explanations what programs could led for We hope our work more work applying such ideas other tasks requiring compositional reasoning such planning navigation etc",0.01,0.6065202349344276
"The ability to deploy neural networks in real-world, safety-critical systems is severely limited by the presence of adversarial examples: slightly perturbed inputs that are misclassified by the network. In recent years, several techniques have been proposed for training networks that are robust to such examples; and each time stronger attacks have been devised, demonstrating the shortcomings of existing defenses. This highlights a key difficulty in designing an effective defense: the inability to assess a network's robustness against future attacks. We propose to address this difficulty through formal verification techniques. We construct ground truths: adversarial examples with a provably-minimal distance from a given input point. We demonstrate how ground truths can serve to assess the effectiveness of attack techniques, by comparing the adversarial examples produced by those attacks to the ground truths; and also of defense techniques, by computing the distance to the ground truths before and after the defense is applied, and measuring the improvement. We use this technique to assess recently suggested attack and defense techniques.
 While machine learning, and in particular neural networks, have seen significant success, recent work BID20 has shown that an adversary can cause unintended behavior by performing slight modifications to the input at test-time. In neural networks used as classifiers, these adversarial examples are produced by taking some normal instance that is classified correctly, and applying a slight perturbation to cause it to be misclassified (or even misclassified as a specific target label chosen by the adversary). This phenomenon, which has been shown to affect all state-of-the-art networks, poses a significant hindrance to deploying neural networks in safety-critical settings.Many effective techniques have been proposed for generating adversarial examples BID20 ; ; BID17 ; BID1 ; BID21 ; and, conversely, several techniques have been proposed for training networks that are more robust to these examples BID8 ; BID22 BID6 ; BID7 ; BID16 ; BID21 . Unfortunately, it has proven difficult to accurately assess the robustness of any given defense by evaluating it against existing techniques for generating adversarial examples. In several cases, a defensive technique that was at first thought to produce robust networks was later shown to be susceptible to new kinds of attacks BID2 . This ongoing cycle thus cast a doubt on any newly-proposed defensive technique.In recent years, new techniques have been proposed for the formal verification of neural networks BID18 BID19 ; BID12 ; BID9 ; BID3 . These techniques take a network and a desired property, and formally prove that the network satisfies the property -or provide an input for which the property is violated, if such an input exists. Specifically, for a given input point and some allowed amount of distortion under a given metric, verification can be used for finding an adversarial example or for soundly proving that no such examples exist within the allowed distortion. While verification tends to be significantly slower in finding adversarial examples than the aforementioned heuristic-based techniques BID19 ; BID11 BID0 , it can provide the much-needed rigor for assessing the adversarial robustness of neural networks.In this paper we propose a method for using formal verification to assess the effectiveness of techniques for producing adversarial examples or defending against them. The key idea is to examine networks and apply verification to identify ground-truth adversarial examples. Formally, given a neural network F , a distance metric d, and an input x, we say that another input x is a ground-truth adversarial example for x if it is the nearest point (with respect to the metric d) such that F assigns different labels to x and x . It follows that all points whose distance to x is smaller than the distance between x and x are assigned the same label as x. The distance to the ground truth is thus an indication of how robust the network is to adversarial attacks at point x. Ground truths can serve multiple purposes: (i) if ground-truth adversarial examples are known for a set of points drawn from some meaningful distribution thought to represent real-world inputs, they can serve to estimate the robustness of a network as a whole, against any possible attack; (ii) they can be used for assessing attack techniques, by measuring the proximity of the adversarial examples that these attacks produce to the ground truths; and (iii) they can be used for assessing the effectiveness of defense techniques, by computing new ground truths for the hardened network and comparing them to the ground truths of the original network.Our contributions can thus be summarized as follows:• We suggest to use ground-truth adversarial examples, the provably closest adversarial with respect to some distance metric, as a tool for studying attacks and defenses.• We find that first-order attack algorithms often produce near-optimal results, i.e. results that are close to a ground-truth adversarial example.• We study adversarial training and find that it does increase robustness and does not overfit to a specific attack, as long as the attack is iterative.The rest of this paper is organized as follows. In Section 2 we provide some necessary background. We then describe the experiments that we conducted in Section 3, and analyze their results in Section 4. Finally , we conclude with Section 5. Neural networks hold great potential as controllers in safety-critical systems, but their susceptibility to adversarial examples poses a significant hindrance. The development of defensive techniques is difficult when they are measured only against existing attacks. The burgeoning field of neural network verification can mitigate this problem, by allowing us to obtain an absolute measurement of the usefulness of a defense, regardless of the attack to be used against it.In this paper, we introduce ground-truth adversarial examples and show how to construct them with formal verification approaches. We evaluate one recent attack BID1 and find it often produces adversarial examples whose distance is within 5.9% to 12.9% of optimal, and one defense BID16 , and find that it increases distortion to the nearest adversarial example by an average of 427% on the MNIST dataset for our tested networks. To the best of our knowledge, this is the first proof of robustness increase for a defense.Currently available verification tools afford limited scalability, which means experiments can only be conducted on small networks. However, as better verification techniques are developed, this limitation is expected to be mitigated. Orthogonally, when preparing to use a neural network in a safetycritical setting, users may choose to design their networks as to make them particularly amenable to verification techniques -e.g., by using specific activation functions or network topologies -so that strong guarantees about their correctness and robustness may be obtained.",1316,0.583,767,1.7157757496740547,"The ability deploy neural networks severely adversarial examples: slightly perturbed inputs misclassified In several techniques training networks robust such examples; and each time stronger attacks devised demonstrating the shortcomings existing defenses This highlights a key difficulty designing an effective defense the inability assess a network's robustness against future attacks We propose address this difficulty formal verification techniques We construct ground truths: adversarial examples with a provably-minimal distance a given input point We demonstrate ground truths serve assess attack techniques by comparing the adversarial examples produced those attacks; also of defense techniques computing to before applied measuring the improvement. We use this technique assess recently suggested attack and defense techniques While machine learning, and in seen significant success recent work BID20 has an adversary cause unintended behavior performing slight modifications at test-time In neural networks used as classifiers these adversarial examples produced taking some normal instance that classified correctly cause (or a specific target label chosen This phenomenon shown all state networks poses a significant hindrance deploying neural networks safety-critical settingsMany effective techniques proposed generating adversarial examples BID20 ; ; BID17, several techniques training networks these examples . Unfortunately has proven accurately any given defense by evaluating existing techniques for generating adversarial examples In several cases a defensive technique was at first produce robust networks later susceptible new kinds BID2 . This ongoing cycle thus cast a doubt any newly-proposed defensive techniqueIn new techniques the formal verification neural networks BID18 BID19 ; BID12 . These techniques take a network and a desired property formally prove satisfies the property -or provide an input for which violated if Specifically for a given input point and some allowed amount distortion under a given metric, verification can for finding an adversarial example or soundly no such examples within the allowed distortion While verification tends significantly finding adversarial examples the aforementioned heuristic-based techniques BID19 ; BID11 BID0 it provide the much-needed rigor assessing the adversarial robustness neural networksIn propose using formal verification techniques producing or defending them The key idea examine networks apply verification identify ground-truth adversarial examples Formally given a neural network F , a distance metric d, an input x say another input a ground-truth adversarial example for x if the nearest point (with metric such F assigns different labels . It follows all points whose distance to x smaller x assigned the same label The distance the ground truth thus an indication robust the network to at point x. Ground truths can serve multiple purposes ( if ground-truth adversarial examples known for a set points drawn some meaningful distribution thought represent real-world inputs estimate a network as against any possible attack; assessing attack techniques by measuring the proximity that these attacks produce defense techniques computing the hardened network and comparingOur contributions can thus summarized suggest to the provably closest with some distance metric studying attacks find first-order attack algorithms often results close a ground study adversarial training find it does increase does overfit to a specific attack as long iterativeThe rest organized In Section we provide some necessary background We then describe the experiments Section analyze Finally , conclude Section Neural networks hold great potential controllers in safety-critical systems their susceptibility adversarial examples poses The development defensive techniques difficult when they measured only existing attacks The burgeoning field neural network verification can mitigate us obtain an absolute measurement the usefulness a defense, regardless the attack toIn introduce ground-truth adversarial examples construct them formal verification approaches We evaluate one recent attack BID1 and find often produces adversarial examples whose distance within 5.9% to 12.9% optimal, one defense BID16 , find increases distortion to the nearest adversarial example 427% on the MNIST dataset for our tested networks To the robustness increase a defenseCurrently available verification tools afford limited scalability experiments small networks However as better verification techniques this limitation expected Orthogonally when preparing use a neural network in a safetycritical setting users design to make particularly amenable verification techniques -e.g specific activation functions network topologies -so that strong guarantees about their correctness",0.01,0.5278128924835438
"This paper introduces a new framework for open-domain question answering in which the retriever and the reader \emph{iteratively interact} with each other. The framework is agnostic to the architecture of the machine reading model provided it has \emph{access} to the token-level hidden representations of the reader. The retriever uses fast nearest neighbor search that allows it to scale to corpora containing millions of paragraphs. A gated recurrent unit updates the query at each step conditioned on the \emph{state} of the reader and the \emph{reformulated} query is used to re-rank the paragraphs by the retriever. We conduct analysis and show that iterative interaction helps in retrieving informative paragraphs from the corpus. Finally, we show that our multi-step-reasoning framework brings consistent improvement when applied to two widely used reader architectures (\drqa and \bidaf) on various large open-domain datasets ---\tqau, \quasart, \searchqa, and \squado\footnote{Code and pretrained models are available at \url{https://github.com/rajarshd/Multi-Step-Reasoning}}. Open-domain question answering (QA) BID40 involves a retriever for selecting relevant context from a large corpora of text (e.g. Wikipedia) and a machine reading comprehension (MRC) model for 'reasoning' on the retrieved context. A lot of effort has been put into designing sophisticated neural MRC architectures for reading short context (e.g. a single paragraph), with much success BID41 BID35 BID46 BID44 Yu et al., 2018, inter alia) . However, the performance of such systems degrades significantly when combined with a retriever in open domain settings. For example, the exact match accuracy of DrQA , on the SQUAD dataset BID33 degrades from 69.5% to 28.4% in open-domain settings. The primary reason for this degradation in performance is due to the retriever's failure to find the relevant paragraphs for the machine reading model BID18 .We propose the following two desiderata for a general purpose open-domain QA system -(a) The retriever model should be fast, since it has to find the relevant context from a very large text corpora and give it to the more sophisticated and computationally expensive MRC model (b) Secondly, the retriever and reader models should be interactive, i.e. if the reader model is unable to find the answer from the initial retrieved context, the retriever should be able to learn to provide more relevant context to the reader. Open-domain QA systems such as R 3 BID42 and DS-QA BID25 have sophisticated retriever models where the reader and retriever are jointly trained. However, their retriever computes question-dependent paragraph representation which is then encoded by running an expensive recurrent neural network over the tokens in the paragraph. Since the retriever has to rank a lot of paragraphs, this design does not scale to large corporas. One the other hand, the retriever model of QA systems such as DrQA ) is based on a tf-idf retriever, but they lack trainable parameters and are consequently unable to recover from mistakes. This paper introduces an open domain architecture in which the retriever and reader iteratively interact with each other. Our model first pre-computes and caches representation of context (paragraph). These representations are independent of the query unlike recent architectures BID42 This paper introduces a new framework for open-domain question answering in which the retriever and the reader iteratively interact with each other. The resulting framework improved performance of machine reading over the base reader model uniformly across four open-domain QA datasets. We also show that our fast retrieval method can scale upto millions of paragraphs, much beyond the current capability of existing open-domain systems with a trained retriever module. Finally, we show that our method is agnostic to the architecture of the machine reading system provided we have access to the token level hidden representations of the reader. Our method brings an increase in performance to two popular and widely used neural machine reading architectures, Dr.QA and BiDAF.",837,0.405,507,1.650887573964497,"This paper introduces open-domain question answering which the retriever \emph{iteratively interact with The framework agnostic the machine reading model provided it \emph{access the token-level hidden representations The retriever uses fast nearest neighbor search that scale corpora containing millions paragraphs A gated recurrent unit updates the query at conditioned the \emph{state the reader is rerank by the retriever We conduct analysis show iterative interaction helps in retrieving informative paragraphs Finally show our multi-step-reasoning framework brings consistent improvement two widely used reader architectures\drqa \bidaf various large open-domain datasets ---\tqau \quasart \searchqa \squado\footnote{Code and pretrained models Opendomain question answeringQA) BID40 involves a retriever for selecting relevant context a machine reading comprehension ' A lot effort designing sophisticated neural MRC architectures reading short context with much success BID41 BID35 BID46 BID44 Yu 2018 inter alia) . However the performance such systems degrades significantly combined a retriever in open domain settings For example the exact match accuracy DrQA , on the SQUAD dataset BID33 degrades open-domain settings The primary reason this degradation the retriever's failure find the relevant paragraphs the machine reading model BID18 .We propose a general purpose open-domain QA system -(a fast since from corpora give the more sophisticated and computationally expensive MRC model Secondly interactive if unable the answer from the initial retrieved context learn provide Open-domain QA systems such R 3 BID42 and DS-QA BID25 sophisticated retriever models where the reader jointly However their retriever computes question-dependent paragraph representation which then encoded running an expensive recurrent neural network the tokens Since the retriever to rank paragraphs this design does scale large corporas One the other hand the retriever model QA systems such DrQA ) based a tf-idf retriever they lack trainable parameters consequently unable recover mistakes This paper introduces an open domain architecture the retriever reader iteratively interact Our model first pre caches representation contextparagraph These representations independent the query unlike recent architectures BID42 This paper introduces open-domain question answering the retriever iteratively interact The resulting framework improved machine reading over the base reader model uniformly four open-domain QA datasets We also show our fast retrieval method scale upto millions paragraphs much beyond existing open-domain systems with a trained retriever module Finally show our method agnostic the architecture the machine reading system provided we access the token level hidden representations Our method brings an increase performance two popular and widely used neural machine reading architectures Dr.QA BiDAF",0.0,0.3624835217883735
"Many imaging tasks require global information about all pixels in an image. Conventional bottom-up classification networks globalize information by decreasing resolution; features are pooled and down-sampled into a single output. But for semantic segmentation and object detection tasks, a network must provide higher-resolution pixel-level outputs. To globalize information while preserving resolution, many researchers propose the inclusion of sophisticated auxiliary blocks, but these come at the cost of a considerable increase in network size and computational cost. This paper proposes stacked u-nets (SUNets), which iteratively combine features from different resolution scales while maintaining resolution. SUNets leverage the information globalization power of u-nets in a deeper net- work architectures that is capable of handling the complexity of natural images. SUNets perform extremely well on semantic segmentation tasks using a small number of parameters.",160,0.113,96,1.6666666666666667,Many imaging tasks global information all pixels Conventional bottom-up classification networks globalize decreasing resolution; features pooled down But semantic segmentation object detection tasks a network must higher-resolution pixel-level outputs To globalize information while resolution many researchers propose the inclusion sophisticated auxiliary blocks but come network size This paper stacked unetsSUNets iteratively combine features different resolution scales while resolution SUNets leverage the information globalization power unets a deeper net- work architectures is capable handling natural images SUNets perform extremely semantic segmentation tasks parameters,0.0,0.4026872636575754
"Asking questions is an important ability for a chatbot. This paper focuses on question generation. Although there are existing works on question generation based on a piece of descriptive text, it remains to be a very challenging problem. In the paper, we propose a new question generation problem, which also requires the input of a target topic in addition to a piece of descriptive text. The key reason for proposing the new problem is that in practical applications, we found that useful questions need to be targeted toward some relevant topics. One almost never asks a random question in a conversation. Due to the fact that given a descriptive text, it is often possible to ask many types of questions, generating a question without knowing what it is about is of limited use. To solve the problem, we propose a novel neural network that is able to generate topic-specific questions. One major advantage of this model is that it can be trained directly using a question-answering corpus without requiring any additional annotations like annotating topics in the questions or answers. Experimental results show that our model outperforms the state-of-the-art baseline. The goal of question generation is to generate questions according to some given information (e.g., a sentence or a paragraph). It has been applied in many scenarios, e.g., generating questions for reading comprehension BID8 and generating data for large scale question-answering training (Serban et al., 2016; BID7 . Since questioning is an important communication skill, question generation plays an important role in both general-purpose chatbot systems and goal-oriented dialogue systems. In the context of dialogue, many researchers have studied the problem BID15 BID1 . The generated questions are mainly used to start a conversation or to obtain some specific information.Earlier approaches to question generation mainly used human-crafted rules and patterns to transform a descriptive sentence to a related question BID14 BID2 . However, human-crafted rules are limited. They cannot effectively cover a large number of question generation scenarios. Deep neural networks learned by end-to-end methods can help overcome this problem. This approach has been successfully applied to many NLP tasks, e.g., neural machine translation BID0 BID19 , summarization BID9 , etc. At the same time, some training optimization studies have further guaranteed the performance and stability of end-to-end networks BID13 BID4 . For question generation, Serban et al. (2016) applied a neural network to the knowledge base Freebase to transduce facts to questions. introduced an attention-based sequence learning model, which outperformed state-of-the-art rule-based systems. Two approaches were proposed by BID7 . One is retrieval-based, and the other is generation-based. also studied question-worthy sentences in reading comprehension.Much of the existing question generation studies mainly focused on the task of generating questions from sentences, paragraph, or structured data only. In this paper, we argue that topic-based question generation is also very important. That is, in addition to the given sentence or paragraph, it is also useful to specify a relevant topic contained in the text. The main reason is that a sentence or paragraph often involves multiple topics or concepts that questions can be generated, only arbitrarily choose one or mixing them may be of limited use because we found that in practical applications, questions need to be targeted toward some topics related to the current conversation. One almost never asks a random question in a conversation. Generating a question without knowing what it is about is not very useful. To solve the proposed problem, we propose a novel neural network that can generate topic-based questions. One major advantage of our model is that it can be trained directly using a question-answering corpus without requiring any additional annotations like annotating the topics in the questions or answers. In summary, this paper makes the following contributions:• It proposes the new problem of question generation based on a given sentence and a topic (or concept) in the sentence. To our knowledge, this topic-based question generation has not been studied before. The model can also take a question type because for the same topic, different types of questions can be asked (see section 5.3).• It proposes a novel neural network model to solve the problem. A pre-decode mechanism is also explored to improve the model performance.• The proposed model can be directly trained using a normal question-answering corpus without requiring additional labeling of topics in each input sentence.• The proposed model is evaluated using the Amazon community question-answering corpus. Experimental results show that our model is effective. In this paper, we proposed the new task of topic-based question generation, which has not been investigated before. Based on our experiences, we believe this is a more useful question generation setting than the conventional setting without a given topic because a question without the knowledge of its topic is of limited use in actual conversations. We then proposed a novel network architecture to perform the task, and discussed its generalization ability. Experimental results showed that the proposed model performed slightly better than the state-of-the-art baseline in the conventional setting (although our model not designed for this setting), and performed markedly better in the proposed new setting.",1015,0.665,614,1.6530944625407167,Asking an important ability a chatbot This paper focuses question generation Although existing works question generation based a piece descriptive text remains a very challenging problem In the paper we propose a new question generation problem also requires the input a target topic addition a piece descriptive text The key reason proposing the new problem in practical applications we found useful questions need targeted toward some relevant topics One almost asks a random question Due given a descriptive text often ask many types generating without of To solve propose generate topic-specific questions One major advantage this model trained directly using a question-answering corpus without any additional annotations like annotating topics answers Experimental results our model state baseline. The goal question generation generate according some given information It applied many scenarios generating questions reading comprehension BID8 and generating data large scale question-answering trainingSerban 2016 BID7 . Since questioning is an important communication skill question generation plays both general-purpose chatbot systems goal-oriented dialogue systems In the context dialogue many researchers studied the problem BID15 BID1 . The generated questions mainly used start obtainEarlier approaches mainly human-crafted rules patterns transform a descriptive sentence to a related question BID14 BID2 . However human-crafted rules limited They effectively cover question generation scenarios Deep neural networks learned end methods help overcome This approach successfully many NLP tasks neural machine BID0 BID19 summarization etc At some training optimization studies further guaranteed and end networks BID13 BID4 . For question generation Serban et al (2016 applied a neural network the knowledge base Freebase to transduce facts to questions introduced an attention-based sequence learning model outperformed state rule systems Two approaches BID7 . One is retrieval- generation also studied question-worthy sentences readingMuch the existing question generation studies mainly the task generating questions paragraph structured data only In this paper argue topic-based question generation also very That in addition the given sentence or useful specify a relevant topic contained The main reason a sentence or often involves multiple topics concepts questions can generated only arbitrarily choose mixing may of because we found in practical applications questions need targeted toward some topics related the current conversation One almost asks a random question Generating a question without knowing very To solve the proposed problem propose generate topic-based questions One major advantage our model trained directly using a question-answering corpus without any additional annotations like annotating the topics answers In summary makes the following contributions:• It the new problem question generation based a given sentence a topicor concept To our knowledge this topic-based question generation before The model can take a question type because for the same topic different types ( section 5.3).• It proposes a novel neural network model A pre-decode mechanism also explored improve the model performance.• The proposed model directly trained a normal question-answering corpus without requiring additional labeling topics each input evaluated Experimental results our model effective. In this paper proposed the new task topic-based question generation has not investigated Based our experiences more useful question generation setting the conventional setting without a given topic because a question without the knowledge of actual conversations We then proposed a novel network architecture perform discussed its generalization ability Experimental results showed the proposed model performed slightly state baseline the conventional settingalthough our model not designed performed markedly the proposed new setting,0.01,0.3681064799854709
"Brain-Machine Interfaces (BMIs) have recently emerged as a clinically viable option
 to restore voluntary movements after paralysis. These devices are based on the
 ability to extract information about movement intent from neural signals recorded
 using multi-electrode arrays chronically implanted in the motor cortices of the
 brain. However, the inherent loss and turnover of recorded neurons requires repeated
 recalibrations of the interface, which can potentially alter the day-to-day
 user experience. The resulting need for continued user adaptation interferes with
 the natural, subconscious use of the BMI. Here, we introduce a new computational
 approach that decodes movement intent from a low-dimensional latent representation
 of the neural data. We implement various domain adaptation methods
 to stabilize the interface over significantly long times. This includes Canonical
 Correlation Analysis used to align the latent variables across days; this method
 requires prior point-to-point correspondence of the time series across domains.
 Alternatively, we match the empirical probability distributions of the latent variables
 across days through the minimization of their Kullback-Leibler divergence.
 These two methods provide a significant and comparable improvement in the performance
 of the interface. However, implementation of an Adversarial Domain
 Adaptation Network trained to match the empirical probability distribution of the
 residuals of the reconstructed neural signals outperforms the two methods based
 on latent variables, while requiring remarkably few data points to solve the domain
 adaptation problem. Individuals with tetraplegia due to spinal cord injury identify restoration of hand function as their highest priority BID1 . Over 50% of respondents with a C1-C4 injury would be willing to undergo brain surgery to restore grasp . Brain-Machine Interfaces (BMIs) aim to restore motor function by extracting movement intent from neural signals. Despite its great promise, current BMI technology has significant limitations. A BMI that maps neural activity in primary motor cortex (M1) onto motor intent commands should ideally provide a stable day-to-day user experience. However, the gradual alterations of the activity recorded by chronically implanted multi-electrode arrays, due to neuron turnover or electrode movement and failure BID4 , causes considerable variation in the actions produced by the BMI. This turnover may occur within a single day BID12 , and is estimated to be on the order of 40% over two weeks BID11 ). In the face of changing neural signals, performance can be maintained by daily retraining the interface, but this is not a viable solution as it requires the user to keep on adapting to a new interface BID0 .There is a high degree of correlation across the M1 neural signals. This redundancy implies that the dimensionality of the underlying motor command is much lower than the number of M1 neurons, and even lower than the number of recorded M1 neurons BID15 . The use of dimen-sionality reduction methods is thus a common practice in BMI design, as it provides a more compact and denoised representation of neural activity, and a low-dimensional predictor of movement intent. Most of the earlier work used linear dimensionality reduction methods such as Principal Components Analysis (PCA) and Factor Analysis (FA) BID35 BID30 BID29 BID15 ; more recently, autoencoders (AEs) have been used for the nonlinear dimensionality reduction of neural signals BID27 . Here we develop a deep learning architecture to extract a low-dimensional representation of recorded M1 activity constrained to include features related to movement intent. This is achieved by the simultaneous training of a deep, nonlinear autoencoder network based on neural signals from M1, and a network that predicts movement intent from the inferred low-dimensional signals. We show that this architecture significantly improves predictions over the standard sequential approach of first extracting a low-dimensional, latent representation of neural signals, followed by training a movement predictor based on the latent signals.To stabilize the resulting BMI against continuous changes in the neural recordings, we introduce a novel approach based on the Generative Adversarial Network (GAN) architecture BID17 . This new approach, the Adversarial Domain Adaptation Network (ADAN), focuses on the probability distribution function (PDF) of the residuals of the reconstructed neural signals to align the residual's PDF at a later day to the PDF of the first day the BMI was calculated. The alignment of residual PDFs results in the alignment of the PDFs of the neural data and of their latent representation across multiple days. We show that this method results in a significantly more stable performance of the BMI over time than the stability achieved using several other domain adaptation methods. The use of an ADAN thus results in a BMI that remains stable and consistent to the user over long periods of time. A successful domain adaptation of the neural data eliminates the need for frequent recalibration of the BMI, which remains fixed. This strategy is expected to alleviate the cognitive burden on the user, who would no longer need to learn novel strategies to compensate for a changing interface. We address the problem of stabilizing a fixed Brain-Machine Interface against performance deterioration due to the loss and turnover of recorded neural signals. We introduce a new approach to extracting a low-dimensional latent representation of the neural signals while simultaneously inferring movement intent. We then implement various domain adaption methods to stabilize the latent representation over time, including Canonical Correlation Analysis and the minimization of a Kullback-Leibler divergence. These two methods provide comparable improvement in the performance of the interface. We find that an Adversarial Domain Adaptation Network trained to match the empirical probability distribution of the residuals of the reconstructed neural recordings restores the latent representation of neural trajectories and outperforms the two methods based on latent variables, while requiring remarkably little data to solve the domain adaptation problem. In addition, ADAN solves the domain adaptation problem in a manner that is not task specific, and thus is potentially applicable to unconstrained movements.Here we report on improvements in interface stability obtained offline, without a user in the loop. Online, closed-loop performance is not particularly well correlated with offline accuracy; in an online evaluation of performance, the user's ability to adapt at an unknown rate and to an unknown extent to an imperfect BMI obscures the performance improvements obtained with domain adaptation. Although the open-loop performance improvement demonstrated here is encouraging, additional experiments, both open and closed-loop, with additional animals and involving additional tasks, are required to fully validate our results and to establish that the improvements demonstrated here facilitate the sustained use of a brain-machine interface.",1292,0.674,773,1.6714100905562743,"Brain-Machine Interfaces recently a clinically viable option restore voluntary movements after paralysis These devices based the ability extract movement intent neural signals recorded using chronically However the inherent loss and turnover recorded neurons requires repeated recalibrations the interface potentially alter day user The resulting need continued user adaptation the natural, subconscious use the BMI Here, introduce decodes movement intent a low-dimensional latent representation We implement various domain adaptation methods stabilize the interface over significantly long times This includes Canonical Correlation Analysis used align the latent variables across days; requires prior point correspondence across domains Alternatively match the empirical probability distributions across days through their Kullback-Leibler divergence These two methods provide a significant and comparable improvement the interface However implementation an Adversarial Domain Adaptation Network trained match the empirical probability distribution the reconstructed neural signals outperforms the two methods based latent variables while requiring remarkably few data points solve Individuals due identify restoration hand function BID1 . Over 50% respondents with a C1-C4 injury would grasp . Brain-Machine Interfaces aim restore motor function extracting movement intent Despite its great promise current BMI technology significant limitations A BMI that maps neural activity onto motor intent commands should ideally provide stable day user However the gradual alterations the activity recorded chronically implanted multi-electrode arrays due neuron turnover electrode movement and failure BID4 , causes considerable variation the actions produced the BMI This turnover may occur within BID12 , estimated on over In changing neural signals performance maintained daily retraining the interface, keep on adapting BID0 .There correlation across the M1 neural signals This redundancy implies the dimensionality the underlying motor command much M1 neurons even recorded M1 neurons BID15 . The use dimen-sionality reduction methods thus BMI design compact denoised representation neural activity a low-dimensional predictor movement intent Most the earlier work used linear dimensionality reduction methods Principal Components Analysis Factor Analysis BID35 BID30 BID15 ; moreAEs neural signals BID27 . Here develop extract recorded M1 activity constrained include features related movement intent This achieved the simultaneous training a deep, nonlinear autoencoder network based neural signals M1 predicts movement intent the inferred low-dimensional signals We show this architecture significantly predictions over the standard sequential approach first extracting a low-dimensional, latent representation neural signals followed training a movement predictor basedTo stabilize the resulting BMI against continuous changes the neural recordings introduce Generative architecture BID17 . This new approach the Adversarial Domain Adaptation Network focuses the probability distribution functionPDF the residuals the reconstructed neural signals align the residual's PDF at a later day to the PDF the BMI The alignment residual PDFs results the neural data of their latent representation across multiple days We show this method results the BMI over the stability achieved several other domain adaptation methods The use an ADAN thus results a BMI remains consistent to the user over A successful domain adaptation the neural data eliminates frequent recalibration the BMI remains fixed This strategy expected alleviate the cognitive burden would no learn novel strategies compensate a changing interface We address stabilizing a fixed Brain-Machine Interface against performance deterioration and turnover recorded neural signals We introduce extracting a low-dimensional latent representation the neural signals while movement intent We then implement various domain adaption methods stabilize the latent representation over Canonical Correlation Analysis the minimization a Kullback-Leibler divergence These two methods provide comparable improvement the interface We find an Adversarial Domain Adaptation Network trained match the empirical probability distribution the residuals the reconstructed neural recordings restores the latent representation neural trajectories outperforms the two methods based latent variables while requiring remarkably little data solve In addition ADAN solves the domain adaptation problem task potentially applicable unconstrained movementsHere improvements interface stability obtained offline without a user in Online, closed-loop performance particularly well correlated offline accuracy; an online evaluation adapt at an unknown rate and an unknown extent an imperfect BMI obscures the performance improvements obtained domain adaptation Although the open-loop performance improvement demonstrated encouraging, additional experiments, both open with additional animals involving additional tasks establish that demonstrated facilitate the sustained use",0.01,0.41477309097562937
"Neural network-based systems can now learn to locate the referents of words and phrases in images, answer questions about visual scenes, and even execute symbolic instructions as first-person actors in partially-observable worlds. To achieve this so-called grounded language learning, models must overcome certain well-studied learning challenges that are also fundamental to infants learning their first words. While it is notable that models with no meaningful prior knowledge overcome these learning obstacles, AI researchers and practitioners currently lack a clear understanding of exactly how they do so. Here we address this question as a way of achieving a clearer general understanding of grounded language learning, both to inform future research and to improve confidence in model predictions. For maximum control and generality, we focus on a simple neural network-based language learning agent trained via policy-gradient methods to interpret synthetic linguistic instructions in a simulated 3D world. We apply experimental paradigms from developmental psychology to this agent, exploring the conditions under which established human biases and learning effects emerge. We further propose a novel way to visualise and analyse semantic representation in grounded language learning agents that yields a plausible computational account of the observed effects. The learning challenge faced by children acquiring their first words has long fascinated cognitive scientists and philosophers BID34 BID5 . To start making sense of language, an infant must induce structure in a constant stream of continuous visual input, slowly reconcile this structure with consistencies in the available linguistic observations, store this knowledge in memory, and apply it to inform decisions about how best to respond.Many neural network models also overcome a learning task that is -to varying degrees -analogous to early human word learning. Image classification tasks such as the ImageNet Challenge BID8 ) require models to induce discrete semantic classes, in many cases aligned to words, from unstructured pixel representations of large quantities of photographs BID20 . Visual question answering (VQA) systems BID0 BID41 BID42 ) must reconcile raw images with (arbitrary-length) sequences of symbols, in the form of natural language questions, in order to predict lexical or phrasal answers. Recently, situated language learning agents have been developed that learn to understand sequences of linguistic symbols not only in terms of the contemporaneous raw visual input, but also in terms of past visual input and the actions required to execute an appropriate motor response BID29 BID6 BID15 BID26 . The most advanced such agents learn to execute a range of phrasal and multi-task instructions, such as find the green object in the red room, pick up the pencil in the third room on the right or go to the small green torch, in a continous, simulated 3D world. To solve these tasks, an agent must execute sequences of hundreds of fine-grained actions, conditioned on the available sequence of language symbols and active (first-person) visual perception of the surroundings. Importantly, the knowledge acquired by such agents while mastering these tasks also permits the interpretation of familiar language in entirely novel surroundings, and the execution of novel instructions composed of combinations of familiar words BID6 BID15 .The potential impact of situated linguistic agents, VQA models and other grounded language learning systems is vast, as a basis for human users to interact with situated learning applications such as self-driving cars and domestic robotic tools. However , our understanding of how these agents learn and behave is limited. The challenges of interpreting the factors or reasoning behind the decisions and predictions of neural networks are well known. Indeed, a concerted body of research in both computer vision BID44 BID38 BID43 and natural language processing BID23 BID39 has focused on addressing this uncertainty. As grounded language learning agents become more prevalent, then, understanding their learning dynamics, representation and decision-making will become increasingly important, both to inform future research and to build confidence in users who interact with such models.We therefore aim to establish a better understanding of neural network-based models of grounded language learning, noting the parallels with research in neuroscience and psychology that aims to understand human language acquisition. Extending the approach of BID35 , we adapt various experimental techniques initially developed by experimental psychologists BID21 BID24 BID17 BID7 . In line with typical experiments on humans, our experimental simulations are conducted in a highly controlled environment: a simulated 3D world with a limited set of objects and properties, and corresponding unambiguous, symbolic linguistic stimuli (Figure 1) . However, the simplicity and generality of our architecture and the form of the inputs to the model (continuous visual plus symbolic linguistic) make the proposed methods and approach directly applicable to VQA and other tasks that combine linguistic and visual data. Using these methods, we explore how the training environment of our agent affects its learning outcomes and speed, measure the generality and robustness of its understanding of certain fundamental linguistic concepts, and test for biases in the decisions it takes once trained. Further, by applying layerwise attention , a novel tool for visualising computation in grounded language learning models, we obtain a plausible algorithmic account of some of the effects in terms of representation and processing. Our principal findings about this canonical grounded language learning architecture are the following:Shape / colour biases When the agent is trained on an equal number of shape and colour words, it develops a propensity to extend labels for ambiguous new words according to colour rather than shape (color bias). A human-like bias towards shapes can be induced in the agent, but only if it experiences many more shape terms than colour terms during training.The problem of learning negation The agent learns to execute negated instructions, but if trained on small amounts of data it tends to represent negation in an ad hoc way that does not generalise.Curriculum effects for vocabulary growth The agent learns words more quickly if the range of words to which it is exposed is limited at first and expanded gradually as its vocabulary develops.Semantic processing and representation differences The agent learns words of different semantic classes at different speeds and represents them with features that require different degrees of visual processing depth (or abstraction) to compute.Before describing the experiments that reveal these effects, we briefly outline details of the environment and agent used for the simulations. Models that are capable of grounded language learning promise to significantly advance the ways in which humans and intelligent technology can interact. In this study, we have explored how a situated language learning agent built from canonical neural-network components overcomes the challenge of early language learning. We measured the behaviour exhibited once the first words and simple phrases are acquired, tested factors that speed up this learning, explored aspects of language that pose particular problems and presented a technique, layerwise attention, for better understanding semantic and visual processing in such agents.The application of experimental paradigms from cognitive psychology to better understand deep neural nets was proposed by BID35 , who observed that convolutional architectures exhibit a shape bias when trained on the ImageNet Challenge data. The ability to control precisely both training and test stimuli in our simulated environment allowed us to isolate this effect as deriving from the training data, and indeed to reach the opposite conclusion about the architecture itself. This study also goes beyond that of BID35 in exploring more abstract linguistic operations (negation, abstract category terms) and studying curriculum effects on the dynamics of word learning. Further, we complement these behavioural observations with computatoinal analysis of representation and processing, via layerwise attention.While the control and precision afforded by the simulated environment in the present study has made these analyses and conclusions possible, in future, as our understanding of language learning agents develops, it will be essential to verify conclusions on agents trained on more naturalistic data. At first, this might involve curated sets of images, videos and naturally-occurring text etc, and, ultimately, experiments on robots trained to communicate about perceptible surroundings with human interlocutors. In a world with agents capable of learning such advanced linguistic behaviour, it would certainly be more challenging, but also even more crucial, to understand not just what they can do, but also how they learn to do it. 6 SUPPLEMENTARY MATERIAL",1589,0.691,942,1.686836518046709,"Neural network-based systems now learn locate words images answer visual scenes execute symbolic instructions as partially-observable worlds To achieve this so-called grounded language learning models overcome certain well-studied learning challenges also fundamental infants While notable models no meaningful prior knowledge overcome these learning obstacles AI researchers currently lack exactly Here address this question as achieving a clearer general understanding grounded language learning both to inform improve confidence model predictions For maximum control generality focus a simple neural network-based language agent trained via policy-gradient methods interpret synthetic linguistic instructions a simulated 3D world We apply from developmental psychology this agent exploring the conditions established human biases learning effects We further propose visualise and analyse semantic representation grounded language learning agents that yields a plausible computational account the observed effects The learning challenge faced children acquiring their first words long fascinated cognitive scientists philosophers BID34 BID5 . To start making sense language an infant induce structure a constant stream continuous visual input slowly reconcile consistencies the available linguistic observations store apply inform best respondMany neural network models also overcome a learning task -to varying degrees early word Image classification tasks such the ImageNet Challenge BID8 ) models induce discrete semantic classes in aligned words from unstructured pixel representations large quantities photographs BID20 Visual question answering BID0 ) must reconcile raw images ( symbols in natural language questions predict lexical or phrasal answers Recently situated language learning agents developed learn understand sequences linguistic symbols not the contemporaneous raw visual input past visual input the actions required execute an appropriate motor response BID29 BID6 . The most advanced such agents learn execute a range phrasal and multi-task instructions find the green object pick on or go the small green torch in a continous, simulated 3D world To solve these tasks an agent execute sequences hundreds conditioned the available sequence language symbols active (first-person) visual perception Importantly the knowledge acquired such agents while mastering also permits the interpretation familiar language entirely novel surroundings the execution novel instructions composed combinations BID6 BID15 .The potential impact situated linguistic agents VQA models other grounded language learning systems vast a basis human users interact situated learning applications such domestic robotic tools However , our understanding these agents learn The challenges interpreting the factors or reasoning predictions neural networks Indeed a concerted body both computer vision BID44 BID38 BID43 focused addressing this uncertainty As grounded language learning agents become then understanding their learning dynamics representation both inform build confidence users who interact such modelsWe therefore aim establish noting the parallels research aims Extending the approach BID35 , adapt various experimental techniques initially experimental psychologists BID21 BID24 BID17 BID7 In line typical experiments on humans our experimental simulations are conducted: objects properties corresponding unambiguous, symbolic linguistic stimuli) . However the simplicity generality our architecture the form the inputs (continuous visual plus symbolic linguistic the proposed methods and approach directly VQA other tasks combine Using these methods explore the training environment our agent speed, measure its understanding certain fundamental linguistic concepts test for biases the decisions takes once trained Further by applying layerwise attention , novel tool visualising computation grounded language learning models obtain a plausible algorithmic account some in representation processing Our principal findings about this canonical grounded language learning architecture theShape / colour biases When the agent an equal number shape develops a propensity extend labels for ambiguous new words according colour rather shapecolor bias A human-like bias shapes can induced the agent experiences many more shape terms colour terms during trainingThe problem learning negation The agent execute negated instructions if trained small amounts data tends represent generaliseCurriculum effects for vocabulary growth words more the range to at expanded gradually developsSemantic processing and representation differences of represents features require visual processing depthor abstraction computeBefore describing reveal briefly details the environment agent used the simulations Models that capable grounded language learning promise significantly advance the ways intelligent technology In have explored a situated language learning agent built from canonical neural-network components overcomes early language learning We measured the behaviour exhibited once the first words and simple phrases are acquired tested factors speed this learning explored aspects pose presented a technique, layerwise attention better semantic and visual processing such agentsThe application from better deep neural nets proposed BID35 , who observed architectures exhibit a shape bias trained the ImageNet Challenge data The ability control precisely both training test stimuli our simulated environment allowed isolate this effect as deriving indeed reach the architecture itself This study also goes that BID35 in exploring more abstract linguistic operationsnegation abstract category terms studying curriculum effects the dynamics word learning Further complement these behavioural observations computatoinal analysis representation processing via layerwise attentionWhile the control and precision afforded the simulated environment in has made these analyses and conclusions in future as our understanding language learning agents essential verify conclusions on agents trained more naturalistic data At involve curated sets images videos naturally-occurring text etc, ultimately, experiments robots trained communicate about perceptible surroundings with In with agents capable learning such advanced linguistic behaviour certainly more challenging also even crucial not learn",0.01,0.45407827287015734
"Humans easily recognize object parts and their hierarchical structure by watching how they move; they can then predict how each part moves in the future. In this paper, we propose a novel formulation that simultaneously learns a hierarchical, disentangled object representation and a dynamics model for object parts from unlabeled videos. Our Parts, Structure, and Dynamics (PSD) model learns to, first, recognize the object parts via a layered image representation; second, predict hierarchy via a structural descriptor that composes low-level concepts into a hierarchical structure; and third, model the system dynamics by predicting the future. Experiments on multiple real and synthetic datasets demonstrate that our PSD model works well on all three tasks: segmenting object parts, building their hierarchical structure, and capturing their motion distributions. What makes an object an object? Researchers in cognitive science have made profound investigations into this fundamental problem; results suggest that humans, even young infants, recognize objects as continuous, integrated regions that move together BID6 BID52 . Watching objects move, infants gradually build the internal notion of objects in their mind. The whole process requires little external supervision from experts.Motion gives us not only the concept of objects and parts, but also their hierarchical structure. The classic study from BID27 reveals that humans recognize the structure of a human body from a few moving dots representing the keypoints on a human skeleton. This connects to the classic Gestalt theory in psychology BID31 , which argues that human perception is holistic and generative, explaining scenes as a whole instead of in isolation. In addition to being unsupervised and hierarchical, our perception gives us concepts that are fully interpretable and disentangled. With an object-based representation, we are able to reason about object motion, predict what is going to happen in the near future, and imagine counterfactuals like ""what happens if?"" BID52 How can we build machines of such competency? Would that be possible to have an artificial system that learns an interpretable, hierarchical representation with system dynamics, purely from raw visual data with no human annotations? Recent research in unsupervised and generative deep representation learning has been making progress along this direction: there have been models that efficiently explain multiple objects in a scene BID24 , some simultaneously learning an interpretable representation BID9 . Most existing models however either do not produce a structured, hierarchical object representation, or do not characterize system dynamics.In this paper, we propose a novel formulation that learns an interpretable, hierarchical object representation and scene dynamics by predicting the future. Our model requires no human annotations, learning purely from unlabeled videos of paired frames. During training, the model sees videos of objects moving; during testing, it learns to recognize and segment each object and its parts, build their hierarchical structure, and model their motion distribution for future frame synthesis, all from a single image. Figure 1: Observing human moving, humans are able to perceive disentangled object parts, understand their hierarchical structure, and capture their corresponding motion fields (without any annotations).Our model, named Parts, Structure, and Dynamics (PSD), learns to recognize the object parts via a layered image representation. PSD learns their hierarchy via a structural descriptor that composes low-level concepts into a hierarchical structure. Formulated as a fully differentiable module, the structural descriptor can be end-to-end trained within a neural network. PSD learns to model the system dynamics by predicting the future.We evaluate our model in many possible ways. On real and synthetic datasets, we first examine its ability in learning the concept of objects and segmenting them. We then compute the likelihood that it correctly captures the hierarchical structure in the data. We finally validate how well it characterizes object motion distribution and predicts the future. Our system works well on all these tasks, with minimal input requirement (two frames during training, and one during testing). While previous state-of-the-art methods that jointly discover objects, relations, and predict future frames only work on binary images of shapes and digits, our PSD model works well on complex real-world RGB images and requires fewer input frames. We have presented a novel formulation that simultaneously discovers object parts, their hierarchical structure, and the system dynamics from unlabeled videos. Our model uses a layered image representation to discover basic concepts and a structural descriptor to compose them. Experiments suggest that it works well on both real and synthetic datasets for part segmentation, hierarchical structure recovery, and motion prediction. We hope our work will inspire future research along the direction of learning structural object representations from raw sensory inputs.",898,0.517,516,1.7403100775193798,"Humans easily object parts their hierarchical structure watching; predict In simultaneously learns a dynamics model object parts from unlabeled videos Our Parts, Structure learns, first recognize the object parts via a layered image representation; predict hierarchy via a structural descriptor model the system dynamics predicting Experiments multiple real and synthetic datasets demonstrate our PSD model works all three tasks segmenting object parts building their hierarchical structure capturing their motion distributions What makes an object an Researchers cognitive science made profound investigations; results humans even young infants recognize objects continuous, integrated regions move together BID6 BID52 . Watching objects infants gradually build the internal notion objects The whole process requires little external supervision expertsMotion gives not only the concept objects parts their hierarchical structure The classic study BID27 reveals humans recognize the structure a few moving dots representing the keypoints This connects the classic Gestalt theory psychology BID31 , argues human perception holistic generative explaining scenes instead in In unsupervised hierarchical our perception gives concepts fully With an object-based representation reason object motion predict imagine BID52 How build machines of such competency Would that an artificial system learns an interpretable, hierarchical representation with system dynamics purely raw visual data with no human annotations Recent research and generative deep representation learning making along: there models efficiently explain multiple objects BID24 , some simultaneously learning Most existing models however either produce a structured, hierarchical object representation characterize system dynamicsIn learns scene dynamics predicting. Our model requires no human annotations learning purely unlabeled videos paired frames During training the model sees videos objects; during learns segment build their hierarchical structure model their motion distribution for future frame synthesis all from Figure Observing human moving, humans disentangled object parts understand their hierarchical structure capture their corresponding motion fieldswithout any annotations).Our model, named Parts Structure Dynamics learns via a layered image representation PSD learns their hierarchy via a structural descriptor Formulated as a fully differentiable module the structural descriptor end trained within PSD learns model the system dynamics predictingWe evaluate many possible ways On real and synthetic datasets first examine its ability in learning the concept objects segmenting We then compute it correctly captures the hierarchical structure We finally validate how characterizes object motion distribution predicts Our system all these tasks with minimal input requirementtwo frames during training While previous state methods that jointly discover objects relations predict future frames only binary images shapes digits our PSD model works well requires fewer input frames We presented simultaneously discovers object parts their hierarchical structure the system dynamics from unlabeled videos Our model uses a layered image representation discover basic concepts a structural descriptor compose Experiments suggest it works both real and synthetic datasets for part segmentation hierarchical structure recovery motion prediction We hope our work future research along learning structural object representations from raw sensory inputs",0.01,0.5903242042709569
"A successful application of convolutional architectures is to increase the resolution of single low-resolution images -- a image restoration task called super-resolution (SR). Naturally, SR is of value to resource constrained devices like mobile phones, electronic photograph frames and televisions to enhance image quality. However, SR demands perhaps the most extreme amounts of memory and compute operations of any mainstream vision task known today, preventing SR from being deployed to devices that require them. In this paper, we perform a early systematic study of system resource efficiency for SR, within the context of a variety of architectural and low-precision approaches originally developed for discriminative neural networks. We present a rich set of insights, representative SR architectures, and efficiency trade-offs; for example, the prioritization of ways to compress models to reach a specific memory and computation target and techniques to compact SR models so that they are suitable for DSPs and FPGAs. As a result of doing so, we manage to achieve better and comparable performance with previous models in the existing literature, highlighting the practicality of using existing efficiency techniques in SR tasks. Collectively, we believe these results provides the foundation for further research into the little explored area of resource efficiency for SR. Rapid progress has been made in the development of convolutional networks BID10 that are capable of taking a low-resolution image and producing an image with a significant increase in resolution. This image restoration task is referred to as super-resolution (SR) and has many potential applications in devices with limited memory and compute capacity. The fundamental problem however is that the state-of-the-art networks consist of thousands of layers and are some of the most resource intensive networks currently known. Furthermore, due to the spatial dimensions of feature maps needed to maintain or up-scale the input, the number of operations are counted in the billions as opposed to millions in models for discriminative tasks. As a result, there is a need for a general systematic approach to improve the efficiency of SR models.The challenge of the system resource requirements for deep learning models for tasks other than SR have been carefully studied in previous works BID62 BID40 BID48 , achieving massive gains in size and compute with little to no loss in performance. These reductions are achieved with a wide variety of methods being developed grounded in primarily architecture-level changes and techniques grounded in the use of low precision and quantized model parameters. However, how these efficiency methods behave when applied within SR have not yet been studied in significant depth, with very few results published in the literature. Extrapolating from prior results for other tasks is problematic given that predominantly existing studies are applied to discriminative tasks with substantially different architectures and operations. Due to the up-sampling structure of SR models, these efficiency methods may therefore produce potentially stronger side-effects to image distortion.In this paper, we detail a systematic study that seeks to bridge current understanding in SR and known approaches for scaling down the consumption of system resources by deep models. By examining the impact on image distortion quality when performing various efficiency techniques, we provide the following new insights:• The effectiveness of low rank tensor decomposition and other convolution approximations, which are comparable and successful in discriminative tasks, can vary considerably in SR.(See section 4.1).• Unlike image discriminative networks, SR networks suffer from a worse trade-off between efficiency and performance as more layers are compressed. (See section 4.2)• The practicality of adopting compression techniques for other tasks to SR as our best models are better or comparable to existing literature. For instance , our best model achieves significantly better performance and 6x less compute than MemNet BID51 and VDSR BID27 . Additionally , it also performs better and is 4.1x-5.8x smaller than SRMDNF BID61 . (See section 4.3)• Successful quantization techniques used in image discriminative tasks are equally successful in SR. (See section 5)",779,0.389,447,1.7427293064876956,"A successful application convolutional architectures increase -- a image restoration task called super Naturally SR of value resource constrained devices electronic photograph frames televisions to enhance However SR demands perhaps the most extreme amounts memory and compute operations of any mainstream vision task known today preventing SR deployed devices them In perform a early systematic study system resource efficiency SR, within architectural and low-precision approaches originally discriminative neural networks We present a rich set insights, representative SR architectures efficiency trade; for prioritization ways compress models reach a specific memory and computation target techniques compact SR models so suitable DSPs As doing manage better and comparable performance previous models the existing literature highlighting existing efficiency techniques SR tasks Collectively these results provides the little explored area resource efficiency for SR. Rapid progress BID10 that taking producing This image restoration task referred super devices limited memory compute capacity The fundamental problem however state- networks consist thousands layers some currently known Furthermore due the spatial dimensions feature maps needed maintain or up the input operations are counted the billions as millions models for discriminative tasks As a general systematic approach improve SR modelsThe challenge the system resource requirements for tasks other SR have carefully BID62 BID40 BID48 , achieving massive gains size compute with little These reductions achieved being grounded primarily architecture-level changes techniques grounded low precision quantized model parameters However how these efficiency methods behave within SR have significant depth with published prior results for other tasks is problematic given predominantly existing studies applied with substantially different architectures operations Due the up-sampling structure SR models these efficiency methods therefore produce potentially stronger side-effects to image distortionIn detail seeks bridge current understanding in known approaches scaling the consumption system resources deep models By examining image distortion quality when performing various efficiency techniques provide the following new insights:• The effectiveness low rank tensor decomposition other convolution approximations comparable and successful discriminative tasks vary SR.(See section 4.1).• Unlike image discriminative networks SR networks suffer a worse trade-off efficiency as more layers compressed (See section The practicality adopting compression techniques other tasks to SR as our best models better or comparable existing literature For instance , our best model achieves and 6x compute than MemNet BID51 VDSR BID27 Additionally , also performs and smaller SRMDNF BID61 (See section Successful quantization techniques used image discriminative tasks equally successful SR. (See section",0.0,0.5964881871310925
"Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased towards low frequency functions, meaning that they cannot have local fluctuations without affecting their global behavior. Intuitively, this property is in line with the observation that over-parameterized networks find simple patterns that generalize across data samples. We also investigate how the shape of the data manifold affects expressivity by showing evidence that learning high frequencies gets easier with increasing manifold complexity, and present a theoretical understanding of this behavior. Finally, we study the robustness of the frequency components with respect to parameter perturbation, to develop the intuition that the parameters must be finely tuned to express high frequency functions. While universal approximation properties of neural networks have been known since the early 90s (Hornik et al., 1989; BID6 Leshno et al., 1993; BID2 , recent research has shed light on the mechanisms underlying such expressivity (Montufar et al., 2014; Raghu et al., 2016; Poole et al., 2016) . At the same time, deep neural networks, despite being massively overparameterized, have been remarkably successful at generalizing to natural data. This fact is at odds with the traditional notions of model complexity and their empirically demonstrated ability to fit arbitrary random data to perfect accuracy (Zhang et al., 2017a; BID1 . It has prompted the recent investigations of possible implicit regularization mechanisms inherent in the learning process, inducing biases towards low complexity solutions (Soudry et al., 2017; Poggio et al., 2018; Neyshabur et al., 2017) .In this work, our main goal is to expose one such bias by taking a closer look at neural networks through the lens of Fourier analysis 1 . We focus the discussion on ReLU networks, whose piecewise linear structure enables an analytic treatment. While they can approximate arbitrary functions, we find that these networks favour low frequency ones; in other words, they exhibit a bias towards smooth functions, a phenomenon we call the spectral bias 2 . We find that this bias manifests itself not just in the process of learning, but also in the parameterization of the model itself: in fact we show that the lower frequencies of trained networks are more robust with respect to random parameter perturbations. Finally , we also exhibit and analyze a rather intricate interplay between the spectral bias and the geometry of the data manifold: we show that high frequencies get easier to learn when the data lies on a lower dimensional manifold of complex shape embedded in the input space. CONTRIBUTIONS 1. We exploit the piecewise-linear structure of ReLU networks to evaluate and bound its Fourier spectrum.2. We demonstrate the peculiar behaviour of neural networks with illustrative and minimal experiments and find evidence of a spectral bias: i.e. lower frequencies are learned first. 1 The Fourier transform affords a natural way of measuring how fast a function can change within a small neighborhood in its input of a model. See Appendix B for a brief recap of Fourier analysis.2 A similar result has been independently found and reported in Xu et al. (2018). 3. We illustrate how the manifold hypothesis adds a layer of subtlety by showing how the geometry of the data manifold attenuates the spectral bias in a non-trivial way. We present a theoretical analysis of this phenomenon and derive conditions on the manifolds that facilitate learning higher frequencies.4. Given a trained network, we investigate the relative robustness of the lower frequencies with respect to random perturbations of the network parameters.The paper is organized as follows. In Section 2, we derive the Fourier spectrum of deep ReLU networks. Section 3 presents minimal experiments that demonstrate the spectral bias of ReLU networks. In Section 4, we study and discuss the role of the geometry of the data manifold. In Section 5, we empirically illustrate and theoretically explain our robustness result. We studied deep ReLU networks through the lens of Fourier analysis. Several conclusions can be drawn from our analysis. While neural networks can approximate arbitrary functions, we find that they favour low frequency ones -hence they exhibit a bias towards smooth functions -a phenomenon that we called spectral bias. We also illustrated how the geometry of the data manifold impacts expressivity in a non-trivial way, as high frequency functions defined on complex manifolds can be expressed by lower frequency network functions defined in input space. Finally, we found that the parameters contributing towards expressing lower frequencies are more robust to random perturbations than their higher frequency counterparts.We view future work that explore the properties of neural networks in Fourier domain as promising. For example, the Fourier transform affords a natural way of measuring how fast a function can change within a small neighborhood in its input domain ; as such, it is a strong candidate for quantifying and analyzing the sensitivity of a model -which in turn provides a natural measure of complexity (Novak et al., 2018) . We hope to encourage more research in this direction. We fit a 6 layer ReLU network with 256 units per layer f θ to the target function λ, which is a superposition of sine waves with increasing frequencies: DISPLAYFORM0 where k i = (5, 10, 15, ..., 50), and ϕ i is sampled from the uniform distribution U (0, 2π). In the first setting, we set equal amplitude for all frequencies, i.e. A i = 1 ∀ i, while in the second setting we assign larger amplitudes to the higher frequencies, i.e. A i = (0.1, 0.2, ..., 1). We sample λ on 200 uniformly spaced points in [0, 1] and train the network for 80000 steps of full-batch gradient descent with Adam (Kingma & Ba, 2014) . Note that we do not use stochastic gradient descent to avoid the stochasticity in parameter updates as a confounding factor. We evaluate the network on the same 200 point grid every 100 training steps and compute the magnitude of its (single-sided) discrete fourier transform at frequencies k i which we denote with |f ki |. Finally, we plot in figure 1 the normalized magnitudes |f k i | Ai averaged over 10 runs (with different sets of sampled phases ϕ i ). We also record the spectral norms of the weights at each layer as the training progresses, which we plot in figure 1 for both settings (the spectral norm is evaluated with 10 power iterations). In FIG10 , we show an example target function and the predictions of the network trained on it (over the iterations), and in figure 7 we plot the loss curves. The above theorem provides a recursive relation for computing the Fourier transform of an arbitrary polytope. More precisely, the Fourier transform of a m-dimensional polytope is expressed as a sum of fourier transforms over the m − 1 dimensional boundaries of the said polytope (which are themselves polytopes) times a O(k −1 ) weight term (with k = k ). The recursion terminates if Proj F (k) = 0, which then yields a constant.To structure this computation, BID8 introduce a book-keeping device called the face poset of the polytope. It can be understood as a weighted tree diagram with polytopes of various dimensions as its nodes. We start at the root node which is the full dimensional polytope P (i.e. we initially set m = n). For all of the codimension-one boundary faces F of P , we then draw an edge from the root P to node F and weight it with a term given by: DISPLAYFORM0 and repeat the process iteratively for each F . Note that the weight term is O(k −1 ) where Proj F (k) = 0. This process yields tree paths T : P → F 1 → ... → F q where each F i+1 ∈ ∂F i has one dimension less than F i . For a given path and k, the terminal node for this path, F q , is the first polytope for which Proj Fq (k) = 0. The final Fourier transform is obtained by multiplying the weights along each path and summing over all tree paths: DISPLAYFORM1 where we wrote F 0 = P . Together with Lemma 1, this gives the closed form expression of the Fourier transform of ReLU networks.For a generic vector k, all paths terminate at the zero-dimensional vertices of the original polytope, i.e. dim(F q ) = 0, implying the length of the path q equals the number of dimensions d, yielding a O(k −d ) spectrum. The exceptions occur if a path terminates prematurely, because k happens to lie orthogonal to some d − r-dimensional face F r in the path, in which case we are left with a O(k −r ) term (with r < d) which dominates asymptotically. Note that all vectors orthogonal to the d − r dimensional face F r lie on a r-dimensional subspace of R d . Since a polytope has a finite number of faces (of any dimension), the k's for which the Fourier transform is O(k −r ) (instead of O(k −d )) lies on a finite union of closed subspaces of dimension r (with r < d). The Lebesgue measure of all such lower dimensional subspaces for all such r is 0, leading us to the conclusion that the spectrum decays as O(k −d ) for almost all k's. We formalize this in the following corollary.Corollary 1. Let P be a full dimensional polytope in R n . The Fourier spectrum of its indicator function1 P satisfies the following: DISPLAYFORM2 where 1 ≤ ∆ k ≤ n, and ∆ k = j for k on a finite union of j-dimensional subspaces of R n .",2086,1.057,1223,1.705641864268193,"Neural networks known a class highly expressive functions able fit even random input-output mappings with In this work properties complement this aspect expressivity By using tools from Fourier analysis show deep ReLU networks biased low frequency functions meaning have local fluctuations without their global behavior Intuitively this property in the observation over-parameterized networks find simple patterns data samples We also investigate the shape the data manifold expressivity by showing evidence learning high frequencies gets easier increasing manifold complexity present this behavior Finally study the frequency components with parameter perturbation to develop the intuition must finely express high frequency functions While universal approximation properties (Hornik 1989 BID6 Leshno , recent research shed such expressivity (Montufar Raghu Poole . At deep neural networks despite massively overparameterized remarkably natural data This fact at the traditional notions model complexity their empirically demonstrated ability fit arbitrary random data perfect accuracyZhang 2017a BID1 . It prompted the recent investigations possible implicit regularization mechanisms inherent inducing biases towards low complexity solutionsSoudry 2017 Neyshabur .In expose one such bias taking through 1 We focus the discussion ReLU networks whose piecewise linear structure enables an analytic treatment. While they can approximate arbitrary functions find these networks favour low frequency ones; exhibit a bias smooth functions a the spectral bias 2 We find this bias manifests not the process learning the parameterization we show the lower frequencies trained networks robust with random parameter perturbations Finally , also exhibit and analyze a rather intricate interplay the spectral bias data manifold high frequencies get easier learn lies of complex shape embedded the input space 1 We exploit the piecewise-linear structure ReLU networks evaluate and bound its Fourier spectrum.2. demonstrate the peculiar behaviour neural networks illustrative and minimal experiments find evidence a spectral bias: learned first 1 The Fourier affords measuring how within a small neighborhood in its input of a model See Appendix B Fourier analysis.2 A similar result independently and Xu (2018 3 We illustrate the manifold hypothesis adds subtlety by the geometry the data manifold attenuates the spectral bias We present this phenomenon derive conditions on the manifolds that facilitate learning higher frequencies.4. Given a trained network investigate withThe paper organized In Section derive deep ReLU networks Section presents minimal experiments the spectral bias ReLU networks In Section study and the geometry the data manifold In Section empirically illustrate and theoretically our robustness result We studied deep ReLU networks through Several conclusions While neural networks approximate arbitrary functions find favour low frequency ones -hence exhibit smooth functions -a called spectral bias We also illustrated geometry the data manifold impacts expressivity high frequency functions defined on lower frequency network functions input space Finally found the parameters contributing towards expressing lower frequencies robustWe view future work that explore Fourier domain as promising For example Fourier affords measuring within a small neighborhood in its input domain ; as a strong candidate and analyzing the sensitivity a model -which complexityNovak 2018 We hope encourage more research this direction We fit a 6 layer ReLU network 256 units layer f �� to the target function �� sine waves increasing frequencies: DISPLAYFORM0 where k i5 ... 50 �� sampled the uniform distribution U0 2π In the first setting set equal amplitude� i, while assign ( ... We sample � on 200 uniformly spaced points [0 train the network 80000 steps full-batch gradient descent Adam (Kingma & Ba, . Note avoid in parameter updates as a confounding factor We evaluate the network on the same 200 point grid every 100 training steps compute the magnitude its (single-sided) discrete fourier transform at frequencies k i which we denote |f ki Finally plot in figure the normalized magnitudes |f k i Ai averaged over 10 runs different sets sampled phases � We also record the spectral norms the weights at as the training progresses plot figure for both settings evaluated 10 power iterations In FIG10 an example target function the predictions the network trainedover the iterations figure 7 plot the loss curves The above theorem provides a recursive relation computing an arbitrary polytope More precisely a m-dimensional polytope expressed fourier transforms over − dimensional boundarieswhich themselves polytopes times a O(k −1 weight termwith The recursion terminates if Proj F (k which then yields a constantTo structure BID8 introduce a book-keeping device the face poset of It can understood as a weighted tree diagram polytopes various dimensions as its nodes We start the root node which the full dimensional polytope P ( we initially set m n For the codimension-one boundary faces F of P then draw an edge the root P node F weight a term given DISPLAYFORM0 and repeat iteratively Note the weight term O(k −1 Proj F This process yields tree paths T : P → F 1 ... → F q where each F i+1 � ��F has one dimension less For a given path and k, the terminal node for, F q the first polytope for Proj Fqk The final Fourier transform obtained the weights along each path over all tree paths: DISPLAYFORM1 where we wrote F 0 . Together Lemma 1 gives the closed form expression ReLU networksFor a generic vector k all paths terminate the original polytope i.e. dim(F q implying the length q equals dimensions d yielding O(k −d spectrum The exceptions occur a path terminates prematurely because k happens lie orthogonal some d − r-dimensional face F r in a O(k −r ) termwith r < d which dominates Note all vectors orthogonal the d − r dimensional face F r lie R d Since a polytope facesof any dimension the k's which O(k −r (instead lies a finite union closed subspaces dimension rwith r < d The Lebesgue measure all such lower dimensional subspaces for all such r is leading spectrum decays O(k −d for almost all k's We formalize inCorollary Let P be a full dimensional polytope in R n The Fourier spectrum its indicator function1 P satisfies: DISPLAYFORM2 where 1 ≤ �� k j for on a finite union j-dimensional subspaces R n",0.01,0.5019926428228447
"Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty which can arise when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by “hedging” the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle (Alemi et al., 2016; Achille & Soatto, 2018). Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of “hedging its bets” across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure which is correlated with downstream performance. An instance embedding is a mapping f from an input x, such as an image, to a vector representation, z ∈ R D , such that ""similar"" inputs are mapped to nearby points in space. Embeddings are a versatile representation that support various downstream tasks, including image retrieval (Babenko et al., 2014) and face recognition (Schroff et al., 2015) .Instance embeddings are often treated deterministically, i.e., z = f (x) is a point in R D . We refer to this approach as a point embedding. One drawback of this representation is the difficulty of modeling aleatoric uncertainty (Kendall & Gal, 2017) , i.e. uncertainty induced by the input. In the case of images this can be caused by occlusion, blurriness, low-contrast and other factors.To illustrate this, consider the example in FIG7 . On the left , we show an image composed of two adjacent MNIST digits, the first of which is highly occluded. The right digit is clearly a 7, but the left digit could be a 1, or a 4. One way to express this uncertainty about which choice to make is to map the input to a region of space, representing the inherent uncertainty of ""where it belongs"".We propose a new method, called hedged instance embedding (HIB), which achieves this goal. Each embedding is represented as a random variable, Z ∼ p(z|x) ∈ R D . The embedding effectively spreads probability mass across locations in space, depending on the level of uncertainty. For example in Figure 1b , the corrupted image is mapped to a two-component mixture of Gaussians covering both the ""17"" and ""47"" clusters. We propose a training scheme for the HIB with a learnable-margin contrastive loss and the variational information bottleneck (VIB) principle (Alemi et al., 2016; BID1 . Figure 1: Unlike point embeddings, stochastic embeddings may hedge their bets across the space. When both ""17"" and ""47 "" are plausible, our 2-component Gaussian mixture embedding has the power to spread probability mass on clusters with clean ""17"" and ""47"" images. By contrast, the point embedding will choose to be close to one or the other of these points (or somewhere between).To evaluate our method, we propose a novel dataset, N-digit MNIST, which we will open source.Using this dataset, we show that HIB exhibits several desirable properties compared to point embeddings: (1) downstream task performance (e.g. recognition and verification) improves for uncertain inputs; (2) the embedding space exhibits enhanced structural regularity; and (3) a per-exemplar uncertainty measure that predicts when the output of the system is reliable. Hedged instance embedding is a stochastic embedding that captures the uncertainty of the mapping of an image to a latent embedding space, by spreading density across plausible locations. This results in improved performance on various tasks, such as verification and identification, especially for ambiguous corrupted input. It also allows for a simple way to estimate the uncertainty of the embedding that is correlated with performance on downstream tasks.There are many possible directions for future work, including experimenting with higherdimensional embeddings, and harder datasets. As an early look at these tasks, in the Appendix, Section C.3, we apply HIB towards cat and dog instance embedding directed towards identifying specific animals with 20D embeddings. It would also be interesting to consider the ""open world"" (or ""unknown unknowns"") scenario, in which the test set may contain examples of novel classes, such as digit combinations that were not in the training set (see e.g., Lakkaraju et al. FORMULA1 ; Günther et al. FORMULA1 ). This is likely to result in uncertainty about where to embed the input which is different from the uncertainty induced by occlusion, since uncertainty due to open world is epistemic (due to lack of knowledge of a class), whereas uncertainty due to occlusion is aleatoric (intrinsic, due to lack of information in the input), as explained in Kendall & Gal (2017) . Preliminary experiments suggest that η(x) correlates well with detecting occluded inputs, but does not work as well for novel classes. We leave more detailed modeling of epistemic uncertainty as future work.",1123,0.578,656,1.711890243902439,"Instance embeddings an efficient and versatile image representation that facilitates applications recognition verification retrieval Many metric learning methods represent the input as the embedding space Often the distance points used match confidence However this can fail represent uncertainty which the input ambiguous due blurriness This work addresses explicitly models the uncertainty by ��hedging�� the location each input We introduce the hedged instance embedding (HIB in which modeled random variables the model trained under the variational information bottleneck principleAlemi 2016 Achille & Soatto 2018 Empirical results on our new N-digit MNIST dataset show our method leads the desired behavior ��hedging its bets�� across the embedding space upon encountering ambiguous inputs This results improved performance image matching and classification tasks more structure the learned embedding space an ability compute perexemplar uncertainty measure which correlated downstream performance An instance embedding is a mapping f an input x such z �� R D , such ""similar"" inputs mapped nearby points space Embeddings a versatile representation that support various downstream tasks image retrieval (Babenko faceSchroff .Instance treated deterministically z = f (x is a point R D We refer this approach a point embedding One drawback this representation the difficulty modeling aleatoric uncertaintyKendall Gal, 2017 , induced the input. In images this can caused lowTo illustrate in FIG7 On the left , show composed two adjacent MNIST digits highly The right digit clearly 7 could One way express this uncertainty which choice map the input a region space representing the inherent uncertainty "" itWe propose hedged instanceHIB achieves Each embedding is represented a random variable Z ∼ p(z|x) �� R D embedding effectively spreads probability mass locations space depending uncertainty For example in Figure the corrupted image mapped a two-component mixture Gaussians covering ""17 We propose a training scheme the HIB with a learnable-margin contrastive loss and the variational information bottleneckAlemi 2016 BID1 . Figure Unlike point embeddings may hedge across the space When both ""1747 "" plausible our 2-component Gaussian mixture embedding has spread probability mass on clusters clean "" By contrast the point embedding will choose close one or these points somewhere between).To evaluate our method propose a novel dataset N-digit MNIST open sourceUsing show HIB exhibits several desirable properties compared (1) downstream task performance verification improves for uncertain inputs enhanced structural regularity a perexemplar uncertainty measure that predicts when reliable Hedged instance embedding captures the uncertainty the mapping a latent embedding space by spreading density plausible locations This results improved performance various tasks verification identification especially ambiguous corrupted input It also allows estimate the uncertainty the embedding that correlated performance downstream tasksThere many possible directions experimenting higherdimensional embeddings harder datasets As an early look these tasks in the Appendix Section C.3 apply HIB towards cat and dog instance embedding directed identifying specific animals 20D embeddings It would also consider the ""open world ( test set may examples novel classes digit combinations were insee Lakkaraju FORMULA1 ; Günther et al FORMULA1 ). This likely result uncertainty where embed the input which different the uncertainty induced since uncertainty due open world is epistemicdue lack knowledge a class information in as Kendall & Gal (2017 Preliminary experiments ��x correlates well detecting occluded inputs does work for novel classes We leave more detailed modeling epistemic uncertainty future work",0.01,0.5179129651542717
"Convolution neural networks typically consist of many convolutional layers followed by several fully-connected layers.   While convolutional layers map between high-order activation tensors, the fully-connected layers operate on flattened activation vectors.   Despite its success, this approach has notable drawbacks. Flattening discards the multi-dimensional structure of the activations, and the fully-connected layers require a large number of parameters. 
 We present two new techniques to address these problems.   First, we introduce tensor contraction layers which can replace the ordinary fully-connected layers in a neural network. Second, we introduce tensor regression layers, which express the output of a neural network as a low-rank multi-linear mapping from a high-order activation tensor to the softmax layer.   Both the contraction and regression weights are learned end-to-end by backpropagation. By imposing low rank on both, we use significantly fewer parameters.   Experiments on the ImageNet dataset show that applied to the popular VGG and ResNet architectures, our methods significantly reduce the number of parameters in the fully connected layers (about 65% space savings) while negligibly impacting accuracy. Many natural datasets exhibit pronounced multi-modal structure. We represent audio spectrograms as 2nd-order tensors (matrices) with modes corresponding to frequency and time. We represent images as third-order tensors with modes corresponding to width, height and the color channels. Videos are expressed as 4th-order tensors, and the signal processed by an array of video sensors can be described as a 5th-order tensor. A broad array of multi-modal data can be naturally encoded as tensors. Tensor methods extend linear algebra to higher order tensors and are promising tools for manipulating and analyzing such data.The mathematical properties of tensors have long been the subject of theoretical study. Previously, in machine learning, data points were typically assumed to be vectors and datasets to be matrices. Hence, spectral methods, such as matrix decompositions, have been popular in machine learning. Recently, tensor methods, which generalize these techniques to higher-order tensors, have gained prominence. One class of broadly useful techniques within tensor methods are tensor decompositions, which have been studied for learning latent variables BID0 .Deep Neural Networks (DNNs) frequently manipulate high-order tensors: in a standard deep convolutional Neural Network (CNN) for image recognition, the inputs and the activations of convolutional layers are 3 rd -order tensors. And yet, to wit, most architectures output predictions by first flattening the activations tensors and then connecting to the output neurons via one or more fullyconnected layers. This approach presents several issues: we lose multi-modal information during the flattening process and the fully-connected layers require a large number of parameters.In this paper, we propose Tensor Contraction Layers (TCLs) and Tensor Regression Layers (TRLs) as end-to-end trainable components of neural networks. In doing so, we exploit multilinear structure without giving up the power and flexibility offered by modern deep learning methods. By replacing fully-connected layers with tensor contractions, we can aggregate long-range spatial information while preserving multi-modal structure. Moreover, by enforcing low rank, we can significantly reduce the number of parameters needed with minimal impact on accuracy.Our proposed TRL represent the regression weights through the factors of a low-rank tensor decomposition. The TRL obviates the need for flattening when generating output. By combining tensor regression with tensor contraction, we further increase efficiency. Augmenting the VGG and ResNet architectures, we demonstrate improved performance on the ImageNet dataset despite significantly reducing the number of parameters (almost by 65%). This is the first paper that presents an end-to-end trainable architecture that retains the multi-dimensional tensor structure throughout the network.Related work: Several recent papers apply tensor decomposition to deep learning. BID16 propose using CP decomposition to speed up convolutional layers. BID13 take a pre-trained network and apply tensor (Tucker) decomposition on the convolutional kernel tensors and then fine-tune the resulting network. BID23 propose weight sharing in multi-task learning and BID2 propose sharing residual units. These contributions are orthogonal to ours and can be applied together. BID17 use the Tensor-Train (TT) format to impose low-rank tensor structure on weights. However, they still retain the fully-connected layers for the output, while we present an end-to-end tensorized network architecture.Despite the success of DNNs, many open questions remain as to why they work so well and whether they really need so many parameters. Tensor methods have emerged as promising tools of analysis to address these questions and to better understand the success of deep neural networks. BID3 , for example, use tensor methods as tools of analysis to study the expressive power of CNNs. BID5 derive sufficient conditions for global optimality and optimization of non-convex factorization problems, including tensor factorization and deep neural network training. Other papers investigate tensor methods as tools for devising neural network learning algorithms with theoretical guarantees of convergence BID20 BID11 b) . Several prior papers address the power of tensor regression to preserve natural multi-modal structure and learn compact predictive models BID4 BID18 BID25 BID24 . However, these works typically rely on analytical solutions and require manipulating large tensors containing the data. They are usually used for small dataset or require to downsampled datasets or extract compact features prior to fitting the model, and do not scale to large datasets such as ImageNet.To our knowledge, no prior work combines tensor contraction or tensor regression with deep learning in an end-to-end trainable fashion. Unlike fully-connected layers, TCLs and TRLs obviate the need to flatten input tensors. Our experiments demonstrate that by imposing a low-rank constraint on the weights of the regression, we can learn a low-rank manifold on which both the data and the labels lie. The result is a compact network, that achieves similar accuracies with many fewer parameters. Going forward, we plan to apply the TCL and TRL to more network architectures. We also plan to leverage recent work BID21 on extending BLAS primitives to avoid transpositions needed when computing tensor contractions.",1229,0.753,697,1.7632711621233859,"Convolution neural networks typically followed While convolutional layers map between high-order activation tensors operate flattened activation vectors Despite this approach notable drawbacks Flattening discards the multi-dimensional structure the activations the fully-connected layers require parameters We present two new techniques address First introduce tensor contraction layers which replace the ordinary fully-connected layers Second introduce tensor regression layers express the output a low-rank multi-linear mapping from the softmax layer Both the contraction regression weights learned end by By imposing low rank both, we use significantly fewer parameters Experiments the ImageNet dataset show applied to the popular VGG and ResNet architectures our methods significantly parameters the fully connected layersabout 65% space savings negligibly impacting accuracy Many natural datasets exhibit pronounced multi-modal structure We represent audio spectrograms as 2nd-order tensorsmatrices modes corresponding frequency We represent images as third-order tensors modes corresponding width the color channels Videos are expressed 4th-order tensors the signal processed video sensors described A broad array can naturally encoded tensors Tensor methods extend linear algebra are promising manipulatingThe mathematical properties Previously in machine learning data points typically assumed vectors datasets to Hence spectral methods popular Recently tensor methods generalize these techniques gained One class broadly useful techniques within tensor methods have learning latent variables BID0 .Deep frequently manipulate: for the inputs the activations 3 rd -order tensors And yet to wit most architectures output predictions by first flattening the activations tensors connecting the output neurons one or more fullyconnected layers This approach presents several issues we lose during the flattening process the fully-connected layers require parametersIn Tensor Contraction Layers In doing exploit multilinear structure without giving and offered modern deep learning methods By replacing fully-connected layers tensor contractions aggregate while Moreover by enforcing low rank significantly parameters with minimal impact accuracyOur proposed TRL represent the regression weights through the factors a low-rank tensor decomposition The TRL obviates flattening when generating output By combining tensor regression tensor contraction further increase efficiency Augmenting the VGG and ResNet architectures demonstrate improved performance the ImageNet dataset despite significantly parametersalmost by 65% This presents retains throughoutRelated work Several recent papers apply BID16 propose using CP decomposition speed BID13 take a pre-trained network apply tensor (Tucker) decomposition BID23 propose weight sharing multi-task learning BID2 sharing residual units These contributions orthogonal ours can together BID17 use the Tensor-Train (TT) format impose low-rank tensor structure weights However they still retain the fully-connected layers for the output we present end tensorized network architectureDespite many open questions whether really need so many parameters Tensor methods have emerged promising tools of analysis address these questions the success BID3 , for use tensor methods as tools analysis study the expressive power CNNs derive sufficient conditions global optimality optimization non-convex factorization problems Other papers investigate tensor methods as tools devising neural network learning with theoretical guarantees convergence BID20 BID11 b) . Several prior papers address the power tensor regression preserve natural multi-modal structure learn compact predictive models BID4 BID18 BID25 BID24 . However these works typically rely analytical solutions require manipulating large tensors containing They usually used small dataset require to downsampled datasets extract compact features prior fitting do scale ImageNetTo combines tensor contraction Unlike fully-connected layers TCLs and flatten input tensors Our experiments demonstrate by imposing a low-rank constraint the regression learn on both the data lie The result a compact network achieves similar accuracies many fewer parameters Going apply the TCL and TRL more network architectures We also plan leverage recent work BID21 extending BLAS primitives avoid transpositions needed computing tensor contractions",0.01,0.6488270305031287
"We explore ways of incorporating bilingual dictionaries to enable semi-supervised
 neural machine translation. Conventional back-translation methods have shown
 success in leveraging target side monolingual data. However, since the quality of
 back-translation models is tied to the size of the available parallel corpora, this
 could adversely impact the synthetically generated sentences in a low resource
 setting. We propose a simple data augmentation technique to address both this
 shortcoming. We incorporate widely available bilingual dictionaries that yield
 word-by-word translations to generate synthetic sentences. This automatically
 expands the vocabulary of the model while maintaining high quality content. Our
 method shows an appreciable improvement in performance over strong baselines. Neural Machine Translation (NMT) methods require large amounts of parallel data to perform well. This poses a significant challenge in low-resource and out-of-domain scenarios where the amount of parallel data is usually limited. A proven way to mitigate this issue has been by leveraging the vast amounts of monolingual data in conjunction with parallel data to improve performance. Prior work in the field has explored several methods to achieve this. One of the most successful approaches has been Back-Translation (BT) BID9 , that generates artificial parallel data from target monolingual corpora by training a translation model in the reverse direction. Another approach (COPY) proposed by BID3 directly copies target monolingual data to the source, focused on capturing entities that do not change across languages.The methods mentioned above suffer from a couple of limitations. The quality of the generated source translations in the BT model are dependent on the amount of parallel data. Furthermore, the vocabulary available to the model is also limited to that of the parallel data, which increases the probability of out-of-vocabulary words. The COPY model, on the other hand, adds vocabulary, albeit only on the target side. In this paper, we propose a simple yet effective data augmentation technique that utilizes bilingual dictionaries that expands vocabulary on both source and target sides, thus significantly reducing the probability of out-of-vocabulary words. Our method also ensures that correlations between the source and target languages are modelled in the monolingual data. In particular, our contributions are as follows:• We propose the Word-on-Word (WoW) data augmentation method, that outperforms previous data augmentation methods in a low-resource setting.• We show that our method benefits from both in-domain as well as out-of-domain monolingual data and shows encouraging results for domain-adaptation.• Finally, we also apply our method over other augmentation techniques and show its effectiveness in enhancing performance. We propose a simple yet effective data augmentation technique by utilizing bilingual dictionaries for low resource NMT. In this work, we used ground truth dictionaries. A direct line of future work is to create synthetic samples using induced dictionaries and also incorporating phrase tables.",565,0.352,320,1.765625,"We explore ways incorporating bilingual dictionaries enable semi-supervised neural machine translation Conventional back-translation methods shown success leveraging target side monolingual data However since the quality back-translation models tied the available parallel corpora adversely the synthetically generated sentences a low resource setting We propose a simple data augmentation technique address both this shortcoming. We incorporate widely available bilingual dictionaries yield word to generate synthetic sentences This automatically expands the vocabulary the model while high quality content Our method shows an appreciable improvement strong baselines require parallel data perform This poses lowresource and outdomain scenarios parallel data usually A proven way mitigate by leveraging monolingual data conjunction parallel data to improve Prior work explored several methods achieve One has Back-Translation (BT) BID9 , that generates artificial parallel data target monolingual corpora by training a translation model Another approach (COPY proposed BID3 directly copies target monolingual data focused capturing entities change across languagesThe methods mentioned suffer The quality the generated source translations the BT model dependent parallel data Furthermore the vocabulary available the model also that the parallel data increases outvocabulary words The COPY model on adds vocabulary albeit on the target side In utilizes bilingual dictionaries that expands vocabulary on both source target sides significantly outvocabulary words Our method also ensures correlations the source target languages modelled In particular our contributions as propose WordonWord data augmentation that outperforms show benefits both indomain as monolingual and shows encouraging Finally also apply over other augmentation techniques its effectiveness enhancing performance We propose by utilizing bilingual dictionaries low resource NMT In this work used ground truth dictionaries. A direct line future work synthetic samples induced dictionaries also incorporating phrase tables",0.0,0.6548244026068069
"Rewards are sparse in the real world and most of today's reinforcement learning algorithms struggle with such sparsity. One solution to this problem is to allow the agent to create rewards for itself - thus making rewards dense and more suitable for learning. In particular, inspired by curious behaviour in animals, observing something novel could be rewarded with a bonus. Such bonus is summed up with the real task reward - making it possible for RL algorithms to learn from the combined reward. We propose a new curiosity method which uses episodic memory to form the novelty bonus. To determine the bonus, the current observation is compared with the observations in memory. Crucially, the comparison is done based on how many environment steps it takes to reach the current observation from those in memory - which incorporates rich information about environment dynamics. This allows us to overcome the known ""couch-potato"" issues of prior work - when the agent finds a way to instantly gratify itself by exploiting actions which lead to hardly predictable consequences. We test our approach in visually rich 3D environments in ViZDoom, DMLab and MuJoCo. In navigational tasks from ViZDoom and DMLab, our agent outperforms the state-of-the-art curiosity method ICM. In MuJoCo, an ant equipped with our curiosity module learns locomotion out of the first-person-view curiosity only. The code is available at https://github.com/google-research/episodic-curiosity/. Many real-world tasks have sparse rewards. For example, animals searching for food may need to go many miles without any reward from the environment. Standard reinforcement learning algorithms struggle with such tasks because of reliance on simple action entropy maximization as a source of exploration behaviour.Multiple approaches were proposed to achieve better explorative policies. One way is to give a reward bonus which facilitates exploration by rewarding novel observations. The reward bonus is summed up with the original task reward and optimized by standard RL algorithms. Such an approach is motivated by neuroscience studies of animals: an animal has an ability to reward itself for something novel -the mechanism biologically built into its dopamine release system. How exactly this bonus is formed remains an open question.Many modern curiosity formulations aim at maximizing ""surprise"" -inability to predict the future. This approach makes perfect sense but, in fact, is far from perfect. To show why, let us consider a thought experiment. Imagine an agent is put into a 3D maze. There is a precious goal somewhere in the maze which would give a large reward. Now, the agent is also given a remote control to a TV and can switch the channels. Every switch shows a random image (say, from a fixed set of images). The curiosity formulations which optimize surprise would rejoice because the result of the channel switching action is unpredictable. The agent would be drawn to the TV instead of looking for a goal in the environment (this was indeed observed in BID6 ). So, should we call the channel switching behaviour curious? Maybe, but it is unproductive for the original sparsereward goal-reaching task. What would be a definition of curiosity which does not suffer from such ""couch-potato"" behaviour?We propose a new curiosity definition based on the following intuition. If the agent knew the observation after changing a TV channel is only one step away from the observation before doing that -it probably would not be so interesting to change the channel in the first place (too easy). This Our method is at the intersection of multiple topics: curiosity, episodic memory and temporal distance prediction. In the following, we discuss the relation to the prior work on those topics. In this work we propose a new model of curiosity based on episodic memory and the ideas of reachability. This allows us to overcome the known ""couch-potato"" issues of prior work and outperform the previous curiosity state-of-the-art method ICM in visually rich 3D environments from VizDoom and DMLab. Our method also allows a MuJoCo ant to learn locomotion purely out of first-personview curiosity. In the future, we want to make policy aware of memory not only in terms of receiving reward, but also in terms of acting. Can we use memory content retrieved based on reachability to guide exploration behaviour in the test time? This could open opportunities to learn exploration in new tasks in a few-shot style -which is currently a big scientific challenge.",882,0.602,498,1.7710843373493976,"Rewards sparse most today's reinforcement learning algorithms struggle such sparsity One solution the agent create rewards - thus rewards dense more suitable learning In particular inspired curious behaviour animals observing something novel rewarded Such bonus summed the real task reward - RL algorithms the combined reward We propose a new curiosity method episodic memory form the novelty bonus To determine the bonus the current observation compared memory Crucially the comparison done how many environment steps the current observation from those memory - incorporates rich information environment dynamics This allows overcome prior work - when the agent finds instantly gratify itself exploiting actions lead hardly predictable consequences We test our approach ViZDoom DMLab MuJoCo navigational tasks from our agent outperforms state curiosity method ICM In MuJoCo an ant equipped our curiosity module learns locomotion out the first-person-view curiosity only The code Many real-world tasks sparse rewards For example animals searching go many miles any reward Standard reinforcement learning algorithms struggle such tasks reliance simple action entropy maximization as exploration behaviourMultiple approaches were better explorative policies One way give a reward bonus which facilitates exploration rewarding novel observations The reward bonus summed the original task reward optimized standard RL Such an approach motivated neuroscience studies animals: reward novel -the mechanism biologically built How exactly this bonus formed remainsMany modern curiosity formulations aim maximizing -inability predict This approach makes but To show why Imagine an agent is put There a precious goal somewhere the maze which would a large reward Now the agent also given a TV switch Every switch shows a random imagesay from The curiosity formulations which optimize surprise would rejoice because the channel switching action unpredictable The agent would drawn the TV instead looking a goal the environment (this indeed observed BID6 So should the channel switching behaviour curious Maybe unproductive the original sparsereward goal-reaching task What a definition curiosity which does suffer such ""couch-potato behaviour?We propose If the agent knew the observation after changing a TV channel is only the observation before doing that -it probably interesting change (too easy This Our method at multiple topics curiosity episodic memory temporal distance prediction In the relation to the prior work those topics In propose curiosity the ideas reachability This allows overcome prior work outperform curiosity state method ICM in visually rich 3D environments from VizDoom DMLab Our method also a MuJoCo ant to learn locomotion purely out first-personview curiosity In policy aware memory not receiving reward acting. Can memory content retrieved based reachability guide exploration behaviour the test time This could open opportunities learn exploration new tasks a few-shot style -which currently a big scientific challenge",0.01,0.6687343145209371
"We introduce a new dataset of logical entailments for the purpose of measuring models' ability to capture and exploit the structure of logical expressions against an entailment prediction task. We use this task to compare a series of architectures which are ubiquitous in the sequence-processing literature, in addition to a new model class---PossibleWorldNets---which computes entailment as a ``convolution over possible worlds''. Results show that convolutional networks present the wrong inductive bias for this class of problems relative to LSTM RNNs, tree-structured neural networks outperform LSTM RNNs due to their enhanced ability to exploit the syntax of logic, and PossibleWorldNets outperform all benchmarks. This paper seeks to answer two questions: ""Can neural networks understand logical formulae well enough to detect entailment?"", and, more generally, ""Which architectures are best at inferring, encoding, and relating features in a purely structural sequence-based problem?"". In answering these questions, we aim to better understand the inductive biases of popular architectures with regard to structure and abstraction in sequence data. Such understanding would help pave the road to agents and classifiers that reason structurally, in addition to reasoning on the basis of essentially semantic representations. In this paper, we provide a testbed for evaluating some aspects of neural networks' ability to reason structurally and abstractly. We use it to compare a variety of popular network architectures and a new model we introduce, called PossibleWorldNet.Neural network architectures lie at the heart of a variety of applications. They are practically ubiquitous across vision tasks BID19 BID17 BID29 and natural language understanding, from machine translation BID13 BID33 BID2 to textual entailment BID3 BID27 via sentiment analysis BID31 BID14 and reading comprehension BID9 BID25 . They have been used to synthesise programs BID20 BID23 BID5 or internalise algorithms BID6 BID11 BID12 BID26 . They form the basis of reinforcement learning agents capable of playing video games BID22 , difficult perfect information games BID28 BID35 , and navigating complex environments from raw pixels BID21 ). An important question in this context is to find the inductive and generalisation properties of different neural architectures, particularly towards the ability to capture structure present in the input, an ability that might be important for many language and reasoning tasks. However, there is little work on studying these inductive biases in isolation by running these models on tasks that are primarily or purely about sequence structure, which we intend to address. The paper's contribution is three-fold. First, we introduce a new dataset for training and evaluating models. Second, we provide a thorough evaluation of the existing neural models on this dataset. Third, inspired by the semantic (model-theoretic) definition of entailment, we propose a variant of the TreeNet that evaluates the formulas in multiple different ""possible worlds"", and which significantly outperforms the benchmarks. The structure of this paper is as follows. In Section 2, we introduce the new dataset and describe a generic data generation process for entailment datasets, which offers certain guarantees against the presence of superficial exploitable biases. In Section 3, we describe a series of baseline models used to validate the dataset, benchmarks from which we will derive our analyses of popular model architectures, and also introduce our new neural model, the PossibleWorldNet. In Section 4, we describe the structure of experiments, from which we obtained the results presented and discussed in Section 5. We offer a brief survey of related work in Section 6, before making concluding remarks in Section 7. Experimental results are shown in TAB1 . The test scores of the best performing overall model are indicated in bold. The test scores of the best performing model which does not have privileged access to the syntax or semantics of the logic (i.e. excluding TreeRNN-based models) are italicised. The best benchmark test results are underlined.We observe that the baselines are doing better than random (8.2 points above for the easy test set, for the MLP BoW, and 2.6 above random for the hard test set). This indicates that there are some small number of exploitable regularities at the symbolic level in this dataset, but that they do not provide significant information.The baseline results show that convolution networks and BiDirLSTMs encoders obtain relatively mediocre results compared to other models, as do LSTM and BiDirLSTM Traversal models. LSTM encoders is the best performing model which does not have privileged access to the syntax trees. Their success relative to BiDirLSTMs Encoders could be due to their reduced number of parameters guarding against overfitting, and rendering them easier to optimise, but it is plausible BiDirLSTMs Encoders would perform similarly with a more fine-grained grid search. Both tree-based models take the lead amongst the benchmarks, with the TreeLSTM being the best performing benchmark overall on both test sets. For most models except baselines, the symbol permutation data augmentation yielded 2-3 point increase in accuracy on weaker models (BiDirLSTM encoders and traversals, an convolutional networks) and between 7-15 point increases for the Tree-based models. This indicates that this data augmentation strategy is particularly well fitted for letting structure-aware models capture, at the representational level, the arbitrariness of symbols indicating unbound variables.Overall, these results show clearly that models that exploit structure in problems where it is provided, unambiguous, and a central feature of the task, outperform models which must implicitly model the structure of sequences. LSTM-based encoders provide robust and competitive results, although bidirectionality is not necessarily always the obvious choice due to optimisation and overfitting problems. Perhaps counter-intuitively, given the results of BID27 , traversal models do not outperform encoding models in this pair-of-sequences traversal problem, indicating that they may be better at capturing the sort of long-range dependencies need to recognise textual entailment better than they are at capturing structure in general.We conclude, from these benchmark results, that tree structured networks may be a better choice for domains with unambiguous syntax, such as analysing formal languages or programs. For domains such as natural language understanding, both convolutional and recurrent network architectures have had some success, but our experiments indicate that this may be due to the fact that existing tasks favour models which capture representational or semantic regularities, and do not adequately test for structural or syntactic reasoning. In particular, the poor performance of convolutional nets on this task serves as a useful indicator that while they present the right inductive bias for capturing structure in images, where topological proximity usually indicates a joint semantic contribution (pixels close by are likely to contribute to the same ""part"" of an image, such as an edge or pattern), this inductive bias does not carry over to sequences particularly well (where dependencies may be significantly more sparse, structured, and distant) § . The results for the transformer benchmark indicate that while this architecture can capture sufficient structure for machine translation, allowing for the appropriate word order in the output, and accounting for disambiguation or relational information where it exists within sentences, it does not capture with sufficient precision the more hierarchical structure which exists in logical expressions.The best performing model overall is the PossibleWorldNet, which achieves significantly higher results than the other models, with 99.3% accuracy on test (easy), and 97.3% accuracy on test (hard). This is as to be expected, as it has the strongest inductive bias. This inductive bias has two components. First, the model has knowledge of the syntactic structure of the expression, since it is a variant of a TreeNet. Second, inspired by the definition of semantic (model-theoretic) entailment in § Related to this point, BID15 show that convolutional networks make for good character-level encoders, to produce word representations, which are in turn better exploited by RNNs. This is consistent with our interpretation of our results, since at the character level, topological distance is-like for images-a good indicator of semantic grouping (characters that are close are usually part of the same word or n-gram). general, the model evaluates the pair of formulas in lots of different situations (""possible worlds"") and combines the various results together in a product ¶ .The quality of the PossibleWorldNet depends directly on the number of ""possible worlds"" it considers (see FIG1 . As we increase the number of possible worlds, the validation error rate goes down steadily. Note that the data-efficiency also increases as we increase the number of worlds. This is because adding worlds to the model does not increase the number of model parameters-it just increases the number of different ""possibilities"" that are considered. In propositional logic, of course, if we are allowed to generate every single truth-value assignment, then it is trivial to detect entailment by checking each one. In our big test set, there are on average more than 3,000 possible truth-value assignments. In our massive test set, there are on average over 800,000 possible assignments. (See TAB0 ). The PossibleWorldNet considers at most 256 different worlds, which is only 7% of the expected total number of rows needed in the big test set, and only 0.03% of the expected number of rows needed for the massive test set.To understand this result, we sample 32, 64, 128 and 256 truth table rows (variable truth-value assignments) for each pair of formulas in Test (hard), and reject entailment if a single evaluation for the formulas amongst these finds the left hand side to be true while the right hand side is false. This gives us an estimate of the accuracy of sampling a number of truth table rows equal to the number of possible worlds in our model. We estimate that these statistical methods have 75.9%, 86.5%, 93.4% and 97.2% chance of finding a countermodel, respectively. This seems to indicate that PossibleWorldNet is capable of exploiting repeated computation across projections of random noise in order to learn, solely based on the label likelihood objective, something akin to a modelbased solution to entailment by treating the random-noise as variable valuations.6 RELATED WORK BID39 show how a neural architecture can be used to optimise matrix expressions. They generate all expressions up to a certain depth , group them into equivalence classes, and train a recursive neural network classifier to detect whether two expressions are in the same equivalence class. They use a recursive neural network BID30 to guide the search for an optimised equivalent expression. There are two major differences between this work and ours. First, the classifier is predicting whether two matrix expressions (e.g. A and (A T ) T ) compute the same values; this is an equivalence relation, while entailment is a partial order. Second, their dataset consists of matrix expressions containing at most one variable, while our formulas contain many variables. BID1 use a recursive neural network to learn whether two expressions are equivalent. They tested on two datasets: propositional logic and polynomials. There are two main differences between their approach and ours. First, we consider entailment while they consider equivalence; equivalence is a symmetric relation, while entailment is not symmetric. Second, we consider entailment as a relational classification problem: given a pair of expressions A and B, predict whether A entails B. In their paper, by contrast, they generate a set of k equivalence-classes of ¶ See Formula 2 above. This general notion of entailment as truth-in-all-worlds is not dependent on any particular formal logic, and applies to entailment in both formal logics and natural languages.formulas with the same truth-conditions, and ask the network to predict which of these k classes a single formula falls into. Their task is more specific: their network is only able to classify a formula from a new equivalence class that has not been seen during training if it has additional auxiliary information about that class (e.g. exemplar members of the class).Recognizing textual entailment (RTE) between natural language sentences is a central task in natural language processing. (See Dagan et al. (2006) ; for a recent dataset, see BID3 ). Some approaches (e.g., BID37 and BID27 ) use LSTMs with attention, while others (e.g. , BID38 ) use a convolutional neural network with attention. Of course, recognizing entailment between natural language sentences is a very different task from recognizing entailment between logical formulas. Evaluating an entailment between natural language sentences requires understanding the meaning of the non-logical terms in the sentence. For example, the inference from ""An ice skating rink placed outdoors is full of people"" to ""A lot of people are in an ice skating park"" requires knowing the non-logical semantic information that an outdoors ice skating rink is also an ice skating park.Current neural models do not always understand the structure of the sentences they are evaluating. In BID3 , all the neural models they considered wrongly claimed that ""A man wearing padded arm protection is being bitten by a German shepherd dog"" entails ""A man bit a dog"". We believe that isolating the purely structural sub-problem will be useful because only networks that can reliably predict entailment in a purely formal setting, such as propositional (or first-order) logic, will be capable of getting these sorts of examples consistently correct. In this paper, we have introduced a new process for generating datasets for the purpose of recognising logical entailment. This was used to compare benchmarks and a new model on a task which is primarily about understanding and exploiting structure. We have established two clear results on the basis of this task. First, and perhaps most intuitively, architectures which make explicit use of structure will perform significantly better than those which must implicitly capture it. Second, the best model is the one that has a strong architectural bias towards capturing the possible world semantics of entailment. In addition to these two points, experimental results also shed some light on the relative abilities of implicit structure models-namely LSTM and Convolution networkbased architectures-to capture structure, showing that convolutional networks may not present the right inductive bias to capture and exploit the heterogeneous and deeply structured syntax in certain sequence-based problems, both for formal and natural languages.This conclusion is to be expected: the most successful models are those with the most prior knowledge about the generic structure of the task at hand. But our dataset throws new light on this unsurprising thought, by providing a new data-point on which to evaluate neural models' ability to understand structural sequence problems. Logical entailment, unlike textual entailment, depends only on the meaning of the logical operators, and of the place particular arbitrarily-named variables hold within a structure. Here, we have a task in which a network's understanding of structure can be disentangled from its understanding of the meaning of words.Xiang Zhang, Junbo Zhao, and Yann LeCun. Character-level convolutional networks for text classification. In Advances in neural information processing systems, pp. 649-657, 2015.Xiaodan Zhu, Parinaz Sobihani, and Hongyu Guo. Long short-term memory over recursive structures. In International Conference on Machine Learning, pp. 1604 Learning, pp. -1612 Learning, pp. , 2015 A THE DATASET A.1 DATASET REQUIREMENTS Our dataset D is composed of triples of the form (A, B, A B) , where A B is 1 if A entails B, and 0 otherwise. For example: (p ∧ q, q, 1) (q ∨ r, r, 0)We wanted to ensure that simple baseline models are unable to exploit simple statistical regularities to perform well in this task. We define a series of baseline models which, due to their structure or the information they have access to, should not be able to solve the entailment recognition problem described in this paper. We distinguish baselines for which we believe there is little chance of them detecting entailment, from those for which there categorically cannot be true modelling of entailment. The baselines which categorically cannot detect entailment are encoding models which only observe one side of the sequent: DISPLAYFORM0 where f is a linear bag of words encoder, an MLP bag of words encoder, or a TreeNet.Because the dataset contains a roughly balanced number of positive and negative examples, it follows that we should expect any model which only sees part of the sequent to perform in line with a random classifier. If they outperform a random baseline on test, there is a structural or symbolic regularity on one side (or both) which is sufficient to identify some subset of positive or negative examples. We use these baselines to verify the soundness of the generation process.Let D + and D − be the positive and negative entailments: DISPLAYFORM1 We impose various requirements on the dataset, to rule out superficial syntactic differences between D + and D − that can be easily exploited by the simple baselines described above. We require that our classes are balanced: and , we are guaranteed to produce balanced classes. Unfortunately, this straightforward approach generates datasets that violate most of our requirements above. See TAB3 for the details. DISPLAYFORM2 In particular, the mean number of negations, conjunctions, and disjunctions at the top of the syntax tree (num at(·, 0, op)) is markedly different. A + has significantly more conjunctions at the top of the syntax tree than A − , while B + has significantly fewer than B − . Conversely, A + has significantly fewer disjunctions at the top of the syntax tree than A − , while B + has significantly more than DISPLAYFORM3 The mean number of satisfying truth-value assignments (sat(·)) is also markedly different: A + is true in on average 3.7 truth-value assignments (i.e. it is a very specific formula which is only true under very particular circumstances), while A − is true in 10.3 truth-value assignments (i.e. it is true in a wider range of circumstances). We can use these statistics to develop simple heuristic baselines that will be unreasonably effective on the dataset described above: we can estimate whether A B by comparing the lengths of A and B, or by looking at the number of variables in B that do not appear in A, or by looking at the topmost connective in A and B. In order to satisfy our requirements above, we took a different approach to dataset generation. In order to ensure that there are no crude statistical measurements that can detect differences between D + and D − , we change the generation procedure so that every formula appears in both D + and D − . We sample 4-tuples of formulas FIG1 , B 2 ) such that: DISPLAYFORM4 Here, each of the four formulas appears in one positive entailment and one negative entailment * * .Using this alternative approach, we are able to satisfy the requirements above. By construction , the mean length, number of operators at a certain level in the syntax tree, and the number of satisfying truth-value assignments is exactly the same for D + and D − . See Table 4 . DISPLAYFORM5 (r → c) → ((r → v) ∨ p) * * One consequence of this method is that it rules out A1 from being impossible (if it was impossible, we would not have A1 B2) and B1 from being a tautology (if it was a tautology, we would not have A2 B1).",4001,1.967,2282,1.7532865907099036,"We introduce logical entailments the purpose measuring models' ability capture exploit the structure logical expressions against an entailment prediction task We use this task compare a series architectures which ubiquitous the sequence-processing literature in addition a new model class---PossibleWorldNets entailment as a ``convolution over possible worlds Results show convolutional networks present the wrong inductive bias this class problems relative tree-structured neural networks outperform due their enhanced ability exploit the syntax logic PossibleWorldNets all benchmarks This paper seeks answer ""Can neural networks understand logical formulae well detect entailment moreWhich architectures at, encoding relating features a purely structural sequence-based problem In answering aim better the inductive biases popular architectures with regard structure abstraction sequence data Such understanding would pave agents classifiers that reason structurally in addition reasoning on essentially semantic representations In this paper provide a testbed evaluating some aspects reason structurally abstractly We use it compare a variety popular network architectures a new model we introduce PossibleWorldNetNeural network lie They practically ubiquitous across vision tasks BID19 BID17 BID29 and natural language understanding from machine translation to via sentiment analysis reading . They used synthesise programs BID20 BID23 BID5 or internalise algorithms . They form reinforcement learning agents capable playing BID22 , difficult perfect information games navigating from raw pixels An important question to find the inductive and generalisation properties different neural architectures towards the ability capture structure present, an ability might important many language and reasoning tasks However little work studying these inductive biases isolation by running these models tasks primarily or purely about sequence structure which we intend The paper's contribution three First introduce training and evaluating models Second provide a thorough evaluation the existing neural models on this dataset Third inspired the semantic (model-theoretic) definition entailment the TreeNet that evaluates the formulas multiple different ""possible worlds which significantly the benchmarks The structure this paper In Section introduce the new dataset describe a generic data generation process entailment datasets offers certain guarantees against the presence superficial exploitable biases In Section baseline models used validate the dataset benchmarks from will our analyses popular model architectures also introduce our new neural model the PossibleWorldNet In Section experiments from obtained presented and We offer a brief survey related work Section before making concluding remarks in Experimental results are shown TAB1 . The test scores the best performing overall model indicated bold The test scores the best performing model which does privileged access the syntax the logic ( excluding TreeRNN-based models italicised The best benchmark test results underlinedWe observe the baselines doing random ( points above for easy set for the MLP BoW above random This indicates some small number exploitable regularities at the symbolic level this dataset provideThe baseline results convolution networks and BiDirLSTMs encoders obtain relatively mediocre results compared other models do Traversal models LSTM encoders is the best performing model which does privileged access the syntax trees Their success relative BiDirLSTMs Encoders could their reduced number parameters guarding overfitting rendering easier plausible perform similarly with Both tree-based models take the lead amongst the benchmarks the TreeLSTM overall on both test sets For most models except baselines the symbol permutation data augmentation yielded 2-3 point increase accuracy on weaker modelsBiDirLSTM encoders traversals an convolutional networks between the Tree-based models This indicates this data augmentation strategy particularly well fitted letting structure-aware models capture, at symbols indicating unbound variablesOverall clearly models exploit structure in problems where provided unambiguous a central feature which must implicitly model sequences LSTM-based encoders provide robust and competitive results although bidirectionality necessarily always the obvious choice due optimisation overfitting problems Perhaps counter given the results BID27 , traversal models do encoding pairofsequences traversal problem indicating capturing the sort long-range dependencies need recognise textual entailment better they structure in generalWe conclude, from these benchmark results tree structured networks may domains unambiguous syntax analysing formal languages programs For domains such natural language understanding had our experiments indicate existing tasks favour models capture representational or semantic regularities do adequately test structural or syntactic reasoning In particular the poor performance convolutional nets serves while present the right inductive bias capturing structure images where topological proximity usually indicates a joint semantic contribution (pixels close by likely contribute the same ""part"" such pattern carry sequences particularlywhere dependencies significantly sparse structured distant § . The results for the transformer benchmark indicate while this architecture capture sufficient structure machine translation allowing the appropriate word order and accounting or relational information where exists within sentences with the more hierarchical structure which exists logical expressionsThe best performing model overall the PossibleWorldNet achieves significantly higher results on test (easy This as to the strongest inductive bias This inductive bias has two components First the model knowledge since a variant a TreeNet Second inspired the definition semantic (model-theoretic) entailment § Related this point BID15 show make for good character-level encoders to produce word representations in exploited consistent our interpretation our results at topological distance-like for images-a good indicator semantic groupingcharacters that close are usually part or n general, the model evaluates the pair formulas lots (""possible worlds combines a product ¶ .The quality the PossibleWorldNet depends directly it considers FIG1 . As increase possible worlds the validation error rate goes steadily Note the data-efficiency also increases we worlds This because adding worlds the model does increase model parameters-it different ""possibilities considered In propositional logic of if allowed generate every single truth-value assignment trivial detect entailment checking each In our big test set there on more than 3,000 possible truth-value assignments In our massive test set there on average over 800,000 possible assignments (See TAB0 ). The PossibleWorldNet considers at most 256 different worlds only 7% rows needed the big test setTo this result sample 32 64 128 and 256 truth table rowsvariable truth-value assignments each pair formulas Test (hard reject entailment if a single evaluation for amongst finds to while This gives an estimate the accuracy sampling a number truth table rows equal possible worlds We estimate these statistical methods 75.9% a countermodel This seems indicate PossibleWorldNet capable exploiting repeated computation across projections random noise learn, solely the label likelihood objective something akin a modelbased solution entailment by treating as variable valuations.6 RELATED WORK BID39 show a neural architecture matrix expressions They generate all expressions up , group them equivalence classes train detect They use a recursive neural network BID30 guide an optimised equivalent expression There this work ours First the classifier predicting two matrix expressions (A T ) T compute; while entailment a partial order Second their dataset consists matrix expressions containing at while our formulas contain BID1 use a recursive neural network whether two expressions They tested on two datasets propositional logic There their approach ours First consider entailment while they consider equivalence; while Second consider entailment a relational classification problem given expressions A predict whether entails In their paper by contrast generate k equivalence-classes ¶ See Formula above This general notion entailment as truthinall dependent applies entailment natural languages.formulas with ask the network predict these k classes a single formula falls Their task more specific their network only classify a formula from a new equivalence class that not seen during training if additional auxiliary information the class).Recognizing textual entailmentRTE between natural language sentences (See Dagan et al (2006 ; for a recent dataset BID3 Some approaches ( BID37 ) use LSTMs attention, Of recognizing entailment between natural language sentences logical formulas Evaluating an entailment between natural language sentences requires For example the inference ""An ice skating rink placed outdoors full requires knowing the non-logical semantic information alsoCurrent neural models always understand the sentences they evaluating In BID3 , all the neural models they considered wrongly claimed ""A man wearing padded arm protection being bitten entails bit We believe isolating the purely structural subproblem will useful because only networks reliably predict entailment a purely formal setting capable getting these sorts examples consistently correct In this paper have introduced datasets recognising logical entailment This was used compare benchmarks a new model on a task which primarily understanding exploiting structure We established two clear results this task First and intuitively architectures which make explicit use structure will perform significantly must implicitly capture it Second the best model a strong architectural bias towards capturing the possible world semantics entailment In addition these two points experimental results also shed the relative abilities implicit structure models-namely LSTM Convolution networkbased architectures capture structure, showing may present the right inductive bias and exploit the heterogeneous and deeply structured syntax in certain sequence-based problems both formal and natural languagesThis conclusion to: the most successful models the generic structure the task at But our dataset throws this unsurprising thought by providing which evaluate neural models' ability understand structural sequence problems Logical entailment unlike depends only the logical operators of the place particular arbitrarily-named variables hold within a structure Here, a task which a network's understanding structure the meaning wordsXiang Zhang Junbo Zhao. Character-level convolutional networks for text classification In Advances neural information processing systems pp 649-657, 2015.Xiaodan Zhu Parinaz Sobihani Hongyu Guo Long short-term memory over recursive structures In International Conference Machine Learning pp 1604 Learning, pp -1612 Learning, pp , 2015 A THE DATASET A.1 Our dataset D is composed triples the form A B 1 if entails 0 For example (p � q,, 1� r 0)We wanted ensure simple baseline models unable exploit simple statistical regularities perform well We define a series baseline models which, due or the information have access should able solve the entailment recognition problem described We distinguish baselines which little chance them detecting entailment from categorically true modelling The baselines which categorically detect entailment encoding models only observe one side the sequent: DISPLAYFORM0 where f a linear bag words encoder an MLP bag a TreeNet.Because the dataset a roughly balanced number positive and negative examples follows we any model only part perform in line a random classifier If they outperform a random baseline on test, there a structural or symbolic regularity on ( which sufficient identify some subset positive or negative examples We use these baselines verify the soundness the generation processLet D + and DISPLAYFORM1 We impose various requirements the dataset to rule superficial syntactic differences D that exploited the simple baselines described We require our classes balanced: and , guaranteed produce balanced classes Unfortunately this straightforward approach generates datasets violate most our requirements above See TAB3 for DISPLAYFORM2 In particular the mean number negations, conjunctions atnum at(· 0 op markedly. A + has significantly more conjunctions at A − while than Conversely A + has significantly fewer disjunctions at while than DISPLAYFORM3 The mean number satisfying truth-value assignments (sat(· also markedly different: true on a very specific formula which only under true We can use these statistics develop simple heuristic baselines unreasonably effective on the dataset described: we estimate whether A B by the lengths variables B do topmost connective in In order satisfy above took dataset generation In order there no crude statistical measurements detect differences D + change the generation procedure every formula appears both D We sample 4tuples formulas FIG1 , B 2 ) such DISPLAYFORM4 Here each appears one positive entailment * * .Using alternative are satisfy above By construction , the mean length, number operators at in satisfying truth-value assignments exactly D + and See Table 4 . DISPLAYFORM5 (r → c → ( p * * One consequence rules A1 from being impossibleif we A1 B2",0.03,0.6233872197764284
"Deep convolutional neural network (DCNN) based supervised learning is a widely practiced approach for large-scale image classification.   However, retraining these large networks to accommodate new, previously unseen data demands high computational time and energy requirements. Also, previously seen training samples may not be available at the time of retraining. We propose an efficient training methodology and incrementally growing a DCNN to allow new classes to be learned while sharing part of the base network. Our proposed methodology is inspired by transfer learning techniques, although it does not forget previously learned classes. An updated network for learning new set of classes is formed using previously learned convolutional layers (shared from initial part of base network) with addition of few newly added convolutional kernels included in the later layers of the network. We evaluated the proposed scheme on several recognition applications. The classification accuracy achieved by our approach is comparable to the regular incremental learning approach (where networks are updated with new training samples only, without any network sharing). Deep Convolutional Neural Networks (DCNNs) have achieved remarkable success in various cognitive applications, particularly in computer vision BID14 . They have shown human like performance on a variety of recognition, classification and inference tasks, albeit at a much higher energy consumption. One of the major challenges for convolutional networks is the computational complexity and the time needed to train large networks. Since training of DCNNs requires state-ofthe-art accelerators like GPUs BID0 , large training overhead has restricted the usage of DCNNs to clouds and servers. It is common to pre-train a DCNN on a large dataset (e.g. ImageNet, which contains 1.2 million images with 1000 categories), and then use the trained network either as an initialization or a fixed feature extractor for the specific application BID16 . A major downside of such DCNNs is the inability to learn new information since the learning process is static and only done once before it is exposed to practical applications. In real-world scenarios, classes and their associated labeled data are always collected in an incremental manner. To ensure applicability of DCNNs in such cases, the learning process needs to be continuous. However, retraining these large networks using both previously seen and unseen data to accommodate new data, is not feasible most of the time. Incremental learning plays a critical role in alleviating this issue by ensuring continuity in the learning process through regular model update based only on the new available batch of data. A system that can learn incrementally is beneficial in practical situations, since it can gradually expand its capacity to accommodate increasing number of classes. Nevertheless, incremental learning can be computationally expensive and time consuming, if the network is large enough. This paper focuses on incremental learning of deep convolutional neural network (DCNN) for image classification task. In doing so, we attempt to address the more fundamental issue: an efficient learning system must deal with new knowledge that it is exposed to, as humans do. To achieve this goal, there are two major challenges. First, as new data becomes available, we should not start learning from scratch. Rather, we leverage what we have already learned and combine them with new knowledge in a continuous manner. Second, to accommodate new data, if there is a need to increase the capacity of our network, we will have to do it in an efficient way.There have been several prior works on incremental learning of neural networks. Many of them focus on learning new classes from fewer samples BID2 BID6 ) utilizing transfer learning techniques. To avoid learning new categories from scratch, BID2 proposed a Bayesian transfer learning method using very few training samples. By introducing attribute-based classification the authors BID6 ) achieved zero-shot learning (learning a new class from zero samples). These works rely on shallow models instead of DCNN, and the category size is small in comparison. The challenge of applying incremental learning (transfer learning as well) on DCNN lies in the fact that it consists of both feature extractor and classifier in one architecture. BID13 utilized ensemble of classifiers by generating multiple hypotheses using training data sampled according to carefully tailored distributions. The outputs of the resulting classifiers are combined using a weighted majority voting procedure. Inspired form BID13 , BID8 utilized ensemble of modified convolutional neural networks as classifiers by generating multiple hypotheses. The existing classifiers are improved in BID13 BID8 ) by combining new hypothesis generated from newly available examples without compromising classification performance on old data. The new data in BID13 BID8 ) may or may not contain new classes. BID19 proposed a training algorithm that grows a network not only incrementally but also hierarchically. Classes are grouped according to similarities, and self-organized into different levels of the hierarchy. All new networks are cloned from existing ones and therefore inherit learned features. These new networks are fully retrained and connected to base network. The problem with this method is the increase of hierarchical levels as new set of classes are added over time.Our work differs in goal, as we want to grow a DCNN to accommodate new set of classes by network sharing, without forgetting the old classes. For learning new set of classes, we form a new network by reusing previously learned convolutional layers (shared from initial part of the base network) followed by new (added) trainable convolutional layers towards the later layers of the network. The shared convolutional layers work as fixed feature extractors (learning parameters are frozen) and minimize learning overhead for new set of classes. The error resilience property of neural network ensures that even if we freeze some of the learning parameters, the network will be able to adapt to it and learn. In fact, utilizing this attribute, in recent work BID15 showed the use of fixed Gabor filters as convolutional kernels in conjunction with regular trainable convolutional kernels. Since the frozen parameters are from an already learned network of similar (not same) classes, it further guarantees that the new classes can be learned smoothly without having convergence issues. By sharing initial convolutional layers of the base network, a significant fraction of the powerhungry components of the backpropagation training was eliminated, thereby achieving considerable reduction in training energy while maintaining competitive output accuracy.The novelty of this work lies in the fact that we developed an empirical mechanism to identify how much of the network can be shared as new classes are added. In this work, we also quantified the energy consumption, training time and memory storage savings associated with models trained with different amounts of sharing to emphasize the importance of network sharing from hardware point of view. In summary, the key contributions of our work are as follows:• We propose sharing of convolutional layers to reduce computational complexity while training a network to accommodate new set of classes.• We developed a methodology to identify optimal sharing of convolutional layers in order to get the best trade-off between accuracy and other parameters of interest, especially computation energy consumption, training time and memory access.• We developed an energy model for quantifying energy consumption of the network during training, based on the Multiplication and Accumulation (MAC) operations in the training algorithm.• We substantiate the scalability and robustness of the proposed methodology by applying the proposed method to different network structures trained for different benchmark datasets.We show that our proposed methodology leads to energy efficiency, reduction in storage requirements, memory access and training time, while maintaining classification accuracy. The performance of DCNNs relies greatly on the availability of a representative set of the training examples. Generally, in practical applications, data acquisition and learning process is time consuming. Also, it is very likely that the data are available in small batches over a period of time. A competent classifier should be able to support an incremental method of accommodating new data without losing ground on old data inference capability. In this paper, we introduce an incremental training methodology for DCNNs, which employs partial network sharing. This method allows us to accommodate new, previously unseen data without the need of retraining the whole network with previously seen data. It can preserve existing knowledge, and can accommodate new information. Importantly, all new networks start from an existing base network and share learning parameters. The new updated network inherit features from the base network by sharing convolutional layers, leading to improved computational effort and energy consumption during training and thus, speed up the learning process. We applied the proposed method on different DCNNs trained on real-world recognition applications. Results confirm the scalability of the proposed approach with significant improvements.",1682,0.992,962,1.7484407484407485,"Deep convolutional neural network based supervised learning However retraining these large networks accommodate new, previously unseen data high computational time and energy requirements Also previously seen training samples may retraining We propose an efficient training methodology and incrementally growing a DCNN new classes learned while sharing part the base network Our proposed methodology inspired transfer learning techniques although forget previously classes An updated network for learning new set classes formed using previously learned convolutional layersshared from initial part base network with addition few newly added convolutional kernels included the later layers We evaluated the proposed scheme on several recognition applications The classification accuracy achieved our approach comparable the regular incremental learning approachwhere networks updated new training samples only, without any network sharing achieved various cognitive applications particularly computer vision BID14 . They shown human like performance recognition, albeit One convolutional networks large networks Since training of DCNNs requires state-ofthe-art accelerators GPUs BID0 , large training overhead restricted clouds servers It common pretrain a DCNN on a large dataset which contains with 1000 categories either an initialization a fixed feature extractor the specific application BID16 . A major downside such DCNNs learn since static only done before exposed practical applications In real-world scenarios classes their associated labeled data always collected To ensure applicability DCNNs such cases the learning process needs continuous However retraining these large networks using both previously seen unseen to accommodate most Incremental learning plays alleviating this issue ensuring continuity through regular model update based only the new available batch A system learn incrementally is beneficial practical situations since gradually expand accommodate increasing number classes Nevertheless incremental learning computationally if the network large This paper focuses incremental learning for image classification task In doing attempt address an efficient learning system must deal new knowledge it exposed humans To achieve there First as new data becomes not start learning scratch Rather leverage what combine a continuous manner Second to accommodate new data if increase doThere have several prior works incremental learning Many focus learning new classes from fewer samples BID2 BID6 ) utilizing transfer learning techniques To avoid learning new categories from scratch BID2 proposed a Bayesian transfer learning method using very few training samples By introducing attribute-based classification the authors BID6 ) achieved zero-shot learninglearning from zero samples These works rely shallow models instead DCNN the category size small in The challenge applying incremental learning (transfer learning as on DCNN lies consists both feature extractor in one architecture BID13 utilized ensemble of classifiers by generating multiple hypotheses training data sampled according carefully tailored distributions The outputs the resulting classifiers combined using a weighted majority voting procedure Inspired form BID13 , BID8 utilized ensemble as classifiers by generating multiple hypotheses The existing classifiers improved BID13 BID8 ) combining new hypothesis generated newly available examples without compromising classification performance on old data The new data in BID13 BID8 ) may or contain new classes BID19 proposed a training algorithm grows a network not incrementally hierarchically Classes grouped similarities selforganized into different levels All new networks cloned therefore inherit learned These new networks fully retrained connected base network The problem the increase hierarchical levels as new set classes overOur work differs goal grow a DCNN accommodate by network sharing without forgetting For learning new set classes form by reusing previously learned convolutional layersshared from initial part followed towards the later layers The shared convolutional layers work fixed feature extractorslearning parameters frozen minimize learning overhead new set classes The error resilience property neural network ensures even freeze some the learning parameters In fact utilizing this attribute in recent work BID15 showed fixed Gabor filters convolutional kernels conjunction Since the frozen parameters from an already learned network similar (not same) classes further guarantees learned smoothly convergence issues By sharing initial convolutional layers the base network a significant fraction the powerhungry components was eliminated achieving considerable reduction training energy while competitive output accuracyThe novelty lies developed an empirical mechanism identify how shared new classes are In this work also quantified, training time and memory storage savings models trained different amounts sharing to emphasize network sharing from hardware point In summary the key contributions our work propose sharing convolutional layers while training accommodate new set classes.• developed a methodology optimal sharing get accuracy other parameters interest especially computation energy consumption memory an energy model during based MultiplicationMAC operations substantiate the proposed methodology applying different network structures trained different benchmark datasetsWe show leads energy efficiency reduction storage requirements classification accuracy The performance DCNNs relies greatly a representative set the training examples Generally in practical applications data acquisition learning process time Also the data are available small batches over A competent classifier should support an incremental method accommodating losing ground old data inference capability In an incremental training methodology DCNNs employs partial network sharing This method accommodate new, previously unseen data without retraining the whole network with previously seen data It can preserve existing knowledge can accommodate Importantly all new networks start share learning parameters new updated network inherit features by sharing convolutional layers leading improved computational effort energy consumption during training thus speed We applied the proposed method on different DCNNs trained real-world recognition applications Results confirm the scalability the proposed approach with",0.01,0.6110404394256679
"Recurrent neural networks (RNNs) are widely used to model sequential data but
 their non-linear dependencies between sequence elements prevent parallelizing
 training over sequence length. We show the training of RNNs with only linear
 sequential dependencies can be parallelized over the sequence length using the
 parallel scan algorithm, leading to rapid training on long sequences even with
 small minibatch size. We develop a parallel linear recurrence CUDA kernel and
 show that it can be applied to immediately speed up training and inference of
 several state of the art RNN architectures by up to 9x.  We abstract recent work
 on linear RNNs into a new framework of linear surrogate RNNs and develop a
 linear surrogate model for the long short-term memory unit, the GILR-LSTM, that
 utilizes parallel linear recurrence.  We extend sequence learning to new
 extremely long sequence regimes that were previously out of reach by
 successfully training a GILR-LSTM on a synthetic sequence classification task
 with a one million timestep dependency.
 Recurrent neural networks (RNNs) are widely used for sequence modelling tasks in domains such as natural language processing BID17 , speech recognition BID1 , and reinforcement learning BID9 . Most RNNs, including popular variants such as long short-term memories (LSTMs), introduced by BID10 , and gated recurrent units (GRUs), introduced by BID5 , contain a non-linear dependency between sequential inputs. These non-linear dependencies create a very flexible class of models but limit the feasibility of training RNNs on long sequences as each sequence element must be processed sequentially. Modelling sequences of thousands to millions of elements is important to domains such as robotics, remote sensing, control systems, speech recognition, medicine, and finance.The RNN serial evaluation inefficiency problem is usually mitigated by parallelizing the forward and backward pass over a minibatch of inputs. Without minibatches, RNN evaluation is a sequence of matrix-vector multiplications. Minibatches transform RNN computation into a sequence of more efficient matrix-matrix multiplications, but this speed-up brings several disadvantages. RNN model size is often limited by GPU memory size, and running a forward and backward pass on a minibatch requires memory linear in the minibatch size. Grouping data into minibatches increases the latency of each pass and reduces the rate of optimization steps. Finally, training with larger minibatches damages generalization ability BID12 . Given these effects, it is desirable to obtain high training throughput with small minibatches. Persistent RNNs BID6 ) use a novel implementation that can achieve high GPU utilization with very small minibatch sizes when the recurrent state is larger than 500 elements, but even persistent RNNs become limited by the serial evaluation inefficiency at smaller hidden sizes.Numerous prior works have shown strong performance from neural sequential models with only linear dependence on earlier sequence elements. BID2 investigated RNNs with only elementwise linear recurrence relations h t = α t h t−1 + (1 − α t ) x t and developed linear variants of LSTM and GRU that perform similarly to standard non-linear RNNs on text generation tasks. BID4 , , BID7 , and van den have successfully applied networks of convolutions over sequences for tasks such as machine translation, language modelling, and audio generation. These works have observed up to an order of magnitude increase in training throughput compared to RNN alternatives. Convolutional sequence models typically rely on either an attention mechanism or a (possibly linear) recurrent layer to integrate information at scales larger than the filter width. Introduction of a recurrent layer prevents full parallelization over the sequence length while attention mechanisms are expensive to apply on long sequences in online inference use cases.A linear recurrence is a specific instance of a general form of computation known as a scan. Scans and reductions are computations involving repeated application of a binary operator ⊕ over an array of data. Computing the sum or maximum of an array is an example of a reduction, while a cumulative sum is a common example of a scan operation. Throughout this work, the scan of ⊕ with initial value b is defined as DISPLAYFORM0 The reduction of ⊕ over array A and initial value b is denoted REDUCE(⊕, A, b) and is the final element of SCAN(⊕, A, b). Despite their dependent computation graph, algorithms exist to parallelize scans and reductions when ⊕ is associative BID14 . BID3 shows that first order recurrences of the form h t = (Λ t ⊗ h t−1 ) ⊕ x t can be parallelized with the parallel scan algorithm if three conditions are met: DISPLAYFORM1 Considering the familiar operations in linear algebra, we see that the associative operation of vector addition (x ⊕ y = x + y), the semiassociative operation of matrix-vector multiplication (A ⊗ x = Ax) and the associative operation of matrix-matrix multiplication (A B = AB) satisfy Blelloch's three conditions, allowing h t = Λ t h t−1 + x t to be evaluated in parallel over time steps t for vectors x t and square matrices Λ t .We investigate this idea further and deliver the following contributions:• We classify RNNs which satisfy the conditions above, and show that many RNNs used in practice such as the Quasi-RNNs (QRNNs) introduced by BID4 are contained in this class.• We provide an implementation of the parallel linear recurrence algorithm as a CUDA kernel, and show that it speeds up training of QRNN and BID19 's Simple Recurrent Unit (SRU) architectures by factors of up to 9x.• We describe how several recent linear RNNs can be described as linear surrogates for non-linear architectures. We introduce a linear surrogate for the LSTM and show that we are able to train it with a speedup of 5-10x compared to the CuDNN LSTM when we use the parallel linear recurrence algorithm. A significant portion of the success of deep learning can be attributed to access to massive amounts of computation. Most of this computation is accessed through two highly efficient and parallelizable building blocks: matrix multiplication and convolution. Recent research has demonstrated that linear RNNs can achieve similar prediction accuracy to non-linear RNNs on a wide variety of tasks in a fraction of the training time. We propose the framework of LS-RNNs as a way to tame the growing zoo of sequential neural nets. We identify linear recurrence as another parallelizable building block for current and future sequential models and we use it to obtain significant speedups on already fast models. With the power of parallel linear recurrence we are able to solve a sequential dependency problem multiple orders of magnitude larger than anything done prior. Future applications of parallel linear recurrence within neural nets could include parallel training of memory augmented models or providing a new sort of image filter on very high resolution images. We hope that parallel linear recurrence can be to large scale sequence modelling what fast convolution algorithms are to image recognition.",1431,0.649,854,1.6756440281030445,"Recurrent neural networks widely sequential data but their non-linear dependencies between sequence elements prevent parallelizing training over sequence length We show the training RNNs only linear sequential dependencies can parallelized over the sequence length using the parallel scan algorithm leading rapid training on even small minibatch size We develop a parallel linear recurrence CUDA kernel show immediately speed training inference several state of architectures by up We abstract recent work linear RNNs of linear surrogate RNNs develop the long short-term memory unit the GILR-LSTM utilizes parallel linear recurrence We extend sequence learning new extremely long sequence regimes were out by successfully training a GILR-LSTM on a synthetic sequence classification task with a one million timestep dependency Recurrent neural networks widely sequence modelling tasks domains natural BID17 , speech recognition reinforcement Most RNNs, popular variants long short-term memories introduced BID10 , and gated recurrent units contain sequential inputs These non-linear dependencies create a very flexible class models but limit the feasibility training RNNs long sequences as each sequence element processed Modelling sequences thousands to elements is important domains robotics remote sensing control systems medicine financeThe RNN serial evaluation inefficiency problem usually mitigated parallelizing forward pass over a minibatch inputs Without minibatches RNN evaluation a sequence matrix-vector multiplications Minibatches transform RNN computation more efficient matrix-matrix multiplications but brings several disadvantages RNN model size often limited GPU memory size running a forward and backward pass requires memory linear in Grouping data minibatches increases the latency each pass optimization steps Finally training larger minibatches damages generalization ability BID12 . Given these effects desirable obtain high training throughput small minibatches Persistent RNNs BID6 ) use a novel implementation achieve high GPU utilization very small minibatch sizes when the recurrent state larger 500 elements become limited the serial evaluation inefficiency at smaller hidden sizesNumerous prior works strong performance from neural sequential models only linear dependence earlier sequence elements BID2 investigated RNNs only elementwise linear recurrence relations h t α h + ( ) x t and developed linear variants GRU that perform similarly on text generation tasks BID4 , , van den have successfully applied networks convolutions over sequences for tasks machine translation language modelling audio generation These works observed up an order training throughput compared RNN alternatives Convolutional sequence models typically rely either an attention mechanism a (possibly linear) recurrent layer integrate at scales the filter width Introduction of a recurrent layer prevents full parallelization over the sequence length while attention mechanisms expensive apply on in online inference useA linear recurrence a specific instance a general form computation known a scan Scans reductions computations involving repeated application a binary operator ��� over data Computing the sum or maximum an array an example a reduction while a cumulative sum a scan operation Throughout this work the scan �� with initial value b defined DISPLAYFORM0 The reduction over array A REDUCE( the final element Despite their dependent computation graph algorithms exist scans reductions when ��� associative BID14 BID3 shows first order recurrences the form h t (�� t � �� x can parallelized the parallel scan algorithm if three conditions DISPLAYFORM1 Considering the familiar operations see the associative operation vector addition matrix-vector multiplicationA ��� x = AxA B = AB satisfy Blelloch three allowing + evaluated over time steps t for vectors square matrices � .We investigate and deliver the following contributions:• classify which satisfy show used practice such the Quasi introduced BID4 contained this provide as a CUDA kernel speeds training QRNN and BID19 's Simple Recurrent Unit architectures factors describe how several recent linear RNNs described linear surrogates We introduce a linear surrogate show train a speedup compared the CuDNN when the parallel linear recurrence A significant portion the success deep learning can access computation Most this computation accessed two highly efficient and parallelizable building blocks matrix multiplication Recent research demonstrated linear RNNs achieve similar prediction accuracy on a fraction We propose the framework LS-RNNs tame the growing zoo sequential neural nets We identify linear recurrence another parallelizable building block current and future sequential models we obtain significant speedups already fast models With the power parallel linear recurrence solve a sequential dependency problem multiple orders larger anything done prior Future applications parallel linear recurrence within neural nets parallel training memory augmented models providing a new sort image filter on very high resolution images We hope parallel linear recurrence to large scale sequence modelling what fast convolution algorithms image recognition",0.01,0.4255607918551142
"Neural text generation models are often autoregressive language models or seq2seq models. Neural autoregressive and seq2seq models that generate text by sampling words sequentially, with each word conditioned on the previous model, are state-of-the-art for several machine translation and summarization benchmarks. These benchmarks are often defined by validation perplexity even though this is not a direct measure of sample quality. Language models are typically trained via maximum likelihood and most often with teacher forcing. Teacher forcing is well-suited to optimizing perplexity but can result in poor sample quality because generating text requires conditioning on sequences of words that were never observed at training time. We propose to improve sample quality using Generative Adversarial Network (GANs), which explicitly train the generator to produce high quality samples and have shown a lot of success in image generation. GANs were originally to designed to output differentiable values, so discrete language generation is challenging for them. We introduce an actor-critic conditional GAN that fills in missing text conditioned on the surrounding context. We show qualitatively and quantitatively, evidence that this produces more realistic text samples compared to a maximum likelihood trained model. Recurrent Neural Networks (RNNs) BID8 are the most common generative model for sequences as well as for sequence labeling tasks. They have shown impressive results in language modeling BID19 , machine translation BID32 ) and text classification BID20 . Text is typically generated from these models by sampling from a distribution that is conditioned on the previous word and a hidden state that consists of a representation of the words generated so far. These are typically trained with maximum likelihood in an approach known as teacher forcing, where ground-truth words are fed back into the model to be conditioned on for generating the following parts of the sentence. This causes problems when, during sample generation, the model is often forced to condition on sequences that were never conditioned on at training time. This leads to unpredictable dynamics in the hidden state of the RNN. Methods such as Professor Forcing BID14 and Scheduled Sampling BID1 have been proposed to solve this issue. These approaches work indirectly by either causing the hidden state dynamics to become predictable (Professor Forcing) or by randomly conditioning on sampled words at training time, however, they do not directly specify a cost function on the output of the RNN that encourages high sample quality. Our proposed method does so.Generative Adversarial Networks (GANs) BID7 are a framework for training generative models in an adversarial setup, with a generator generating images that is trying to fool a discriminator that is trained to discriminate between real and synthetic images. GANs have had a lot of success in producing more realistic images than other approaches but they have only seen limited use for text sequences. This is due to the discrete nature of text making it infeasible to propagate the gradient from the discriminator back to the generator as in standard GAN training. We overcome this by using Reinforcement Learning (RL) to train the generator while the discriminator is still trained via maximum likelihood and stochastic gradient descent. GANs also commonly suffer from issues such as training instability and mode dropping, both of which are exacerbated in a textual setting. Mode dropping occurs when certain modalities in the training set are rarely generated by the generator, for example, leading all generated images of a volcano to be multiple variants of the same volcano. This becomes a significant problem in text generation since there are many complex modes in the data, ranging from bigrams to short phrases to longer idioms. Training stability is also an issue since unlike image generation, text is generated autoregressively and thus the loss from the discriminator is only observed after a complete sentence has been generated. This problem compounds when generating longer and longer sentences.We reduce the impact of these problems by training our model on a text fill-in-the-blank or in-filling task. This is similar to the task proposed in BID3 but we use a more robust setup. In this task, portions of a body of text are deleted or redacted. The goal of the model is to then infill the missing portions of text so that it is indistinguishable from the original data. While in-filling text, the model operates autoregressively over the tokens it has thus far filled in, as in standard language modeling, while conditioning on the true known context. If the entire body of text is redacted, then this reduces to language modeling.Designing error attribution per time step has been noted to be important in prior natural language GAN research BID33 . The text infilling task naturally achieves this consideration since our discriminator will evaluate each token and thus provide a fine-grained supervision signal to the generator. Consider, for instance, if the generator produces a sequence perfectly matching the data distribution over the first t − 1 time-steps, but then produces an outlier token y t , (x 1:t−1 y t ). Despite the entire sequence now being clearly synthetic as a result of the errant token, a discriminative model that produces a high loss signal to the outlier token, but not to the others, will likely yield a more informative error signal to the generator. This research also opens further inquiry of conditional GAN models in the context of natural language.In the following sections,• We introduce a text generation model trained on in-filling (MaskGAN).• Consider the actor-critic architecture in extremely large action spaces.• Consider new evaluation metrics and the generation of synthetic training data. Our work further supports the case for matching the training and inference procedures in order to produce higher quality language samples. The MaskGAN algorithm directly achieves this through GAN-training and improved the generated samples as assessed by human evaluators.In our experiments, we generally found training where contiguous blocks of words were masked produced better samples. One conjecture is that this allows the generator an opportunity to explore longer sequences in a free-running mode; in comparison, a random mask generally has shorter sequences of blanks to fill in, so the gain of GAN-training is not as substantial. We found that policy gradient methods were effective in conjunction with a learned critic, but the highly active research on training with discrete nodes may present even more stable training procedures.We also found the use of attention was important for the in-filled words to be sufficiently conditioned on the input context. Without attention, the in-filling would fill in reasonable subsequences that became implausible in the context of the adjacent surrounding words. Given this, we suspect another promising avenue would be to consider GAN-training with attention-only models as in BID31 .In general we think the proposed contiguous in-filling task is a good approach to reduce mode collapse and help with training stability for textual GANs. We show that MaskGAN samples on a larger dataset (IMDB reviews) is significantly better than the corresponding tuned MaskMLE model as shown by human evaluation. We also show we can produce high-quality samples despite the MaskGAN model having much higher perplexity on the ground-truth test set.A TRAINING DETAILSOur model was trained with the Adam method for stochastic optimization BID13 with the default Tensorflow exponential decay rates of β 1 = 0.99 and β 2 = 0.999. Our model uses 2-layers of 650 unit LSTMs for both the generator and discriminator, 650 dimensional word embeddings, variational dropout. We used Bayesian hyperparameter tuning to tune the variational dropout rate and learning rates for the generator, discriminator and critic. We perform 3 gradient descent steps on the discriminator for every step on the generator and critic.We share the embedding and softmax weights of the generator as proposed in BID2 ; BID11 . Furthermore , to improve convergence speed, we share the embeddings of the generator and the discriminator. Additionally , as noted in our architectural section, our critic shares all of the discriminator parameters with the exception of the separate output head to estimate the value. Both our generator and discriminator use variational recurrent dropout BID6 Positive: Follow the Good Earth movie linked Vacation is a comedy that credited against the modern day era yarns which has helpful something to the modern day s best It is an interesting drama based on a story of the famed Negative: I really can t understand what this movie falls like I was seeing it I m sorry to say that the only reason I watched it was because of the casting of the Emperor I was not expecting anything as Negative: That s about so much time in time a film that persevered to become cast in a very good way I didn t realize that the book was made during the 70s The story was Manhattan the Allies were to",1722,0.879,983,1.7517802644964395,"Neural text generation models autoregressive language models or seq2seq models Neural autoregressive and seq2seq models that generate text sampling words conditioned state several machine translation benchmarks These benchmarks often defined validation perplexity even this sample quality Language models typically trained via maximum likelihood most teacher forcing Teacher forcing is well optimizing perplexity but result poor sample quality because generating text requires conditioning sequences were observed at We propose improve sample quality Generative Adversarial Network explicitly train the generator have shown a lot image generation GANs were to designed output differentiable values discrete language generation challenging them We introduce an actor-critic conditional GAN fills missing text conditioned We show qualitatively, evidence this produces more realistic text samples compared a maximum likelihood trained model are sequences as for sequence labeling tasks They shown impressive results language modeling BID19 , machine translation ) text classification Text is typically generated these models sampling conditioned the previous word a hidden state consists generated so These typically trained with maximum likelihood an approach known teacher forcing ground-truth words fed conditioned for generating the following parts This causes problems, sample generation often forced condition on sequences conditioned at training time This leads unpredictable dynamics the hidden state Methods such Professor Forcing BID14 solve These approaches indirectly either causing the hidden state dynamics predictableProfessor Forcing randomly conditioning on sampled words at training time however specify a cost function on that encourages high sample quality Our proposed method does soGenerative Adversarial NetworksGANs) BID7 training a generator generating images is trying fool that discriminate GANs had producing more realistic images other approaches but seen text sequences This due the discrete nature text making propagate the gradient the discriminator back standard GAN training We overcomeRL the generator while trained via maximum likelihood GANs also commonly suffer issues training instability mode dropping both a textual setting Mode dropping occurs certain modalities in the training set rarely generated the generator for leading all generated images a volcano multiple variants This becomes text generation many complex modes, ranging bigrams short phrases longer idioms Training stability since unlike image generation text autoregressively the loss from the discriminator only observed a complete sentence This problem compounds generating longer and longer sentencesWe reduce training our model This similar the task proposed BID3 In this task portions a body deleted redacted The goal the model then infill the missing portions text indistinguishable While in-filling text the model operates autoregressively over the tokens thus filled in standard language modeling conditioning the true known context If the entire body text redacted reduces language modelingDesigning error attribution per time step has noted prior natural language GAN research BID33 . The text infilling task naturally achieves this consideration since our discriminator will evaluate token thus provide Consider, if the generator produces perfectly matching the data distribution over the first t − time-steps token y t ( 1: Despite the entire sequence now clearly synthetic as token a discriminative model produces a high loss signal but likely This research also opens further inquiry of conditional GAN models natural language.In the following sections,• We introduce a text generation model trained infilling (MaskGAN).• Consider the actor-critic architecture extremely large action new evaluation metrics the generation synthetic training data Our work further matching the training and inference procedures order higher quality language samples The MaskGAN algorithm directly achieves through GAN-training improved the generated samples as assessedIn generally training where contiguous blocks words masked produced One conjecture allows the generator an explore longer sequences; comparison a random mask generally of blanks fill the gain GAN-training We found policy gradient methods conjunction a learned critic the highly active research training with discrete nodes may present even more stable training proceduresWe attention was the in-filled words sufficiently conditioned Without attention the in-filling would fill reasonable subsequences that became implausible the adjacent surrounding words Given suspect another promising avenue would consider GAN-training with attention-only models in BID31 .In general the proposed contiguous in-filling task mode collapse help training stability textual GANs show that MaskGAN samples on (IMDB reviews is the corresponding tuned MaskMLE model as human evaluation We also show we produce despite the MaskGAN model having much higher perplexity onA TRAINING DETAILSOur model trained the Adam method BID13 with the default Tensorflow exponential decay rates β Our model uses 650 unit LSTMs both the generator discriminator 650 dimensional word embeddings variational dropout. We used tuning tune learning the generator discriminator critic We perform 3 gradient descent steps the discriminator for every step critic.We share the embedding and softmax weights proposed BID2 ; BID11 Furthermore , to improve convergence speed share the generator Additionally , as our architectural section critic shares all the discriminator parameters the exception the separate output head to estimate Both our generator discriminator use variational recurrent dropout BID6 Positive: Follow the Good Earth movie linked Vacation is a comedy credited against the modern day era yarns which helpful something the modern s best It an interesting drama the famed Negative: I really t understand falls like seeing I m sorry only the casting the Emperor I as Negative That s about so time time a film persevered become cast the book made during Manhattan the Allies to",0.01,0.6195492329288962
"Parametric texture models have been applied successfully to synthesize artificial images. Psychophysical studies show that under defined conditions observers are unable to differentiate between model-generated and original natural textures. In industrial applications the reverse case is of interest: a texture analysis system should decide if human observers are able to discriminate between a reference and a novel texture. For example, in case of inspecting decorative surfaces the de- tection of visible texture anomalies without any prior knowledge is required. Here, we implemented a human-vision-inspired novelty detection approach. Assuming that the features used for texture synthesis are important for human texture percep- tion, we compare psychophysical as well as learnt texture representations based on activations of a pretrained CNN in a novelty detection scenario. Additionally, we introduce a novel objective function to train one-class neural networks for novelty detection and compare the results to standard one-class SVM approaches. Our experiments clearly show the differences between human-vision-inspired texture representations and learnt features in detecting visual anomalies. Based on a dig- ital print inspection scenario we show that psychophysical texture representations are able to outperform CNN-encoded features. The idea of describing the appearance of textures using statistics goes back to the early work by Gibson BID0 BID5 and by Julesz BID10 BID11 BID12 . Since then, a number of Markov random field texture models for modelling and characterizing textures using the statistical description of local neighbourhoods were introduced by BID1 and BID4 . Another category of models tries to find a plausible texture representation for the early visual system of humans BID7 BID14 BID16 . These human-vision-inspired models are based on a decomposition of the texture to frequency and orientation bands. The well-known texture model by BID14 (PS-model) and the recently published image-computable spatial vision model by (SW-model) are two representatives of such psychophysical models. The PSmodel is based on joint statistics of complex wavelet coefficients BID21 and focuses on synthesizing realistic textures. The SW-model is based on a log-Gabor decomposition followed by an accelerating nonlinearity and normalization. In contrast to these psychophysically motivated models (assuming a plausible image representation for the early visual system), BID2 introduced a texture model based on features of a pretrained deep convolutional neural network (CNN). Using these CNN-encoded features, the model shows impressive results in generating artificial textures BID3 BID24 .Specific texture representations are required in industrial applications, e.g. for pattern recognition tasks or modelling human perception. In this work we focus on representing textures in such a way that visual anomalies can be detected when comparing reference and novel examples. This is particularly required whenever a reference texture should be reproduced visually indistinguishable. In general , the task of identifying data that differs from a reference is known as novelty detection. In contrast to classification tasks, only one class of labelled data (reference texture) is available. As an example of application, we use images of artificial wood textures which we digitised using line-scanner cameras, installed in an industrial digital printer for laminate flooring. Here, the reference texture is only available digitally as a scanned image of the initially produced reference decor. From a machine learning point of view, there are no labelled training samples available to train a supervised classifier. Another critical point is the interdependency of the surrounding texture and the visibility of specific anomalies. Hence, isolated anomaly consideration is not feasible (cf. FIG0 . In decorative surfaces , e.g. , a wallpaper of a printed brick wall or a cupboard with an artificial wood texture, each print should be indistinguishable from any other. Since humans perceive small variations in a texture when comparing two examples, the detection of visual anomalies perceived by a human observer is an open challenge in computer vision and a continuous problem in industrial applications.To learn the model of a reference texture and detect visual anomalies in novel examples, we present an unsupervised one-class neural network approach using a parametric texture representation. We summarize our main contributions as follows:• We introduce a novel objective function (MinMax-loss) to train one-class neural networks for novelty detection in textures.• We introduce psychophysically motivated texture models -PS-model and SW-model -for novelty detection using one-class classifiers and provide a comparison with deep CNN texture features.• We show texture dependent differences between the models which are of interest in visual surface inspection applications. In this paper, we evaluated the performance of novelty detection in digital print inspection using psychophysical and learnt texture representations. First we introduced state-of-the art methods for statistical and early vision based modelling of textures. While the model by BID14 focuses on synthesizing realistic textures, the model by focuses on modelling the human early vision system in an image-computable way. Another branch of texture modelling uses learnt representations based on features of a pretrained CNN BID2 . Based on the aforementioned features we learnt the reference model of a texture and detected visual anomalies in novel examples. Therefore, we introduced a novel objective for training neural network based one-class classifiers for novelty detection (OC-NN). Additionally, we compared our OC-NN approach with an OC-SVM based classifier and showed superior results in our application scenario.All texture representations achieve reasonable results, when being evaluated with our OC-NN approach on a quasi-periodic texture (cf. red-bricks). However, when being evaluated by an OC-SVM based classifier, anomalies cannot be detected using SW-as well as VGG-19-features. This might be due to the lack of preprocessing, such as z-normalisation or whitening, but this is referred to future work. Altogether the learnt texture representations provide a set of features for detecting novelties, that performs well, whether or not they are perceived by a human observer. Furthermore, PS-features provide a texture-dependent descriptor, that achieves reasonable results on quasi-periodic textures.Finally the SW-features outperform the PS-and VGG-19-features for small anomalies on aperiodic textures, which is great from the application point of view. However, when anomalies dominate (fixed patch size and increasing anomaly size), the detection rate decreases.As a part of the work for this paper, we evaluated our one-class model for novelty detection on a broad range of industrial printed decors, but more work using psychophysical data from experiments is needed. We plan to validate selected anomalies in psychophysical experiments. Further work will also include evaluating different pooling and averaging methods for SW-features. Finally, we plan to fine-tune an OC-SVM for being able to use SW-features.",1308,0.791,807,1.620817843866171,"Parametric texture models applied successfully synthesize artificial images Psychophysical studies under defined conditions observers model-generated and original natural textures In industrial applications the reverse case of a texture analysis system should decide human observers discriminate a reference For example case inspecting decorative surfaces the de- tection visible texture anomalies without Here implemented a human-vision-inspired novelty detection approach Assuming the features used texture synthesis important human texture percep- tion compare psychophysical as learnt texture representations based activations a pretrained CNN a novelty detection scenario Additionally introduce a novel objective function train one-class neural networks novelty detection compare Our experiments clearly the differences human-vision-inspired texture representations learnt features detecting visual anomalies Based a dig- ital print inspection scenario we show psychophysical texture representations able CNN-encoded features The idea describing the appearance textures using statistics goes Gibson BID0 BID5 by Since Markov random field texture models for modelling characterizing textures using the statistical description local neighbourhoods BID1 . Another category models tries find a plausible texture representation the early visual system humans BID7 BID14 BID16 . These human-vision-inspired models a decomposition the texture to frequency and orientation bands The well-known texture model by BID14PS-model the recently published image-computable spatial vision model ( two representatives such psychophysical models The PSmodel based joint statistics complex wavelet coefficients BID21 focuses synthesizing realistic textures The SW-model based a log-Gabor decomposition followed an accelerating nonlinearity In contrast these psychophysically motivated models (assuming a plausible image representation the early visual system BID2 introduced a texture model featuresCNN Using these CNN-encoded features the model impressive results generating artificial textures BID3 BID24 .Specific texture representations required industrial applications pattern recognition tasks modelling human perception In this work representing textures visual anomalies when comparing reference novel examples This particularly required whenever a reference texture should reproduced visually indistinguishable In general , the task identifying data differs known novelty detection In contrast classification tasks only one class labelled datareference texture As application, images artificial wood textures which digitised line-scanner cameras installed an industrial digital printer for laminate flooring Here the reference texture only digitally the initially produced reference decor From a machine learning point no labelled training samples Another critical point the surrounding texture the visibility specific anomalies Hence isolated anomaly consideration feasible (cf FIG0 . In decorative surfaces , , wallpaper a printed brick wall an artificial wood texture each print should indistinguishable Since humans perceive small variations a texture comparing two examples the detection visual anomalies perceived an open challenge a continuous problem industrial applicationsTo learn the model a reference texture detect novel examples present We summarize our main contributions as a novel objective functionMinMax-loss train novelty detection textures.• psychophysically motivated texture models -PS-model provide deep CNN texture texture dependent differences which of visual surface inspection applications In evaluated novelty detection digital print inspection psychophysical and learnt texture representations First we introduced statistical and early vision based modelling textures While the model by BID14 focuses synthesizing realistic textures focuses modelling the human early vision system an image-computable way Another branch texture modelling uses learnt representations based features a pretrained CNN BID2 . Based the aforementioned features we learnt the reference model a texture detected visual anomalies novel examples Therefore introduced a novel objective training based one-class classifiers novelty detectionOC-NN Additionally compared our OC-NN approach superior results our application scenarioAll texture representations achieve reasonable results when being evaluated on a quasi-periodic texture (cf red-bricks However being evaluated an OC-SVM based classifier anomalies using SW-as well VGG-19-features This might due preprocessing such z-normalisation whitening referred future work Altogether the learnt texture representations provide features detecting novelties that performs whether perceived Furthermore PS-features provide a texture-dependent descriptor that achieves reasonable results quasi-periodic texturesFinally the SW-features outperform the PS-and VGG-19-features small anomalies on great from However anomalies dominate (fixed patch size increasing anomaly sizeAs a part for evaluated our one-class model novelty detection industrial printed decors but more work using psychophysical data experiments is We plan validate selected anomalies psychophysical experiments Further work evaluating different pooling averaging SW-features Finally plan an OC-SVM being SW-features",0.01,0.28586849139543824
"In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regularization approach that encourages the supports of weight vectors in RL models to have small overlap, by simultaneously promoting near-orthogonality among vectors and sparsity of each vector. We apply the proposed regularizer to two models: neural networks (NNs) and sparse coding (SC), and develop an efficient ADMM-based algorithm for regularized SC. Experiments on various datasets demonstrate that weight vectors learned under our regularizer are more interpretable and have better generalization performance. In representation learning (RL), two critical issues need to be considered. First, how to make the learned representations more interpretable? Interpretability is a must in many applications. For instance, in a clinical setting, when applying deep learning (DL) and machine learning (ML) models to learn representations for patients and use the representations to assist clinical decision-making, we need to explain the representations to physicians such that the decision-making process is transparent, rather than being black-box. Second, how to avoid overfitting? It is often the case that the learned representations yield good performance on the training data, but perform less well on the testing data. How to improve the generalization performance on previously unseen data is important.In this paper, we make an attempt towards addressing these two issues, via a unified approach. DL/ML models designed for representation learning are typically parameterized with a collection of weight vectors, each aiming at capturing a certain latent feature. For example, neural networks are equipped with multiple layers of hidden units where each unit is parameterized by a weight vector. In another representation learning model -sparse coding BID74 , a dictionary of basis vectors are utilized to reconstruct the data. In the interpretation of RL models, a major part is to interpret the learned weight vectors. Typically, elements of a weight vector have one-to-one correspondence with observed features and a weight vector is oftentimes interpreted by examining the top observed-features that correspond to the largest weights in this vector. For instance, when applying SC to reconstruct documents that are represented with bag-of-words feature vectors, each dimension of a basis vector corresponds to one word in the vocabulary. To visualize/interpret a basis vector, one can inspect the words corresponding to the large values in this vector. To achieve better interpretability, various constraints have been imposed on the weight vectors. Some notable ones are: (1) Sparsity BID80 -which encourages most weights to be zero. Observed features that have zeros weights are considered to be irrelevant and one can focus on interpreting a few non-zero weights. (2) Diversity BID81 -which encourages different weight vectors to be mutually ""different"" (e.g., having larger angles ). By doing this, the redundancy among weight vectors is reduced and cognitively one can map each weight vector to a physical concept in a more unambiguous way. (3) Non-negativeness BID66 -which encourages the weights to be nonnegative since in certain scenarios (e.g., bag of words representation of documents), it is difficult to make sense of negative weights. In this paper, we propose a new perspective of interpretability: less-overlapness, which encourages the weight vectors to have small overlap in supports 1 . By doing this, each weight vector is anchored on a unique subset of observed features without being redundant with other vectors, which greatly facilitates interpretation. For example, if topic models BID47 are learned in such a way, each topic will be characterized by a few representative words and the representative words of different topics are different. Such topics are more amenable for interpretation. Besides improving interpretability, less-overlapness helps alleviate overfitting. It imposes a structural constraint over the weight vectors, thus can effectively shrink the complexity of the function class induced by the RL models and improve the generalization performance on unseen data.To encourage less-overlapness, we propose a regularizer that simultaneously encourages different weight vectors to be close to being orthogonal and each vector to be sparse, which jointly encourage vectors' supports to have small overlap. The major contributions of this work include:• We propose a new type of regularization approach which encourages less-overlapness, for the sake of improving interpretability and reducing overfitting.• We apply the proposed regularizer to two models: neural networks and sparse coding (SC), and derive an efficient ADMM-based algorithm for the regularized SC problem.• In experiments, we demonstrate the empirical effectiveness of this regularizer. In this paper, we propose a new type of regularization approach that encourages the weight vectors to have less-overlapped supports. The proposed LDD-L1 regularizer simultaneously encourages the weight vectors to be sparse and close to being orthogonal, which jointly produces the effects of less overlap. We apply this regularizer to two models: neural networks and sparse coding (SC), and derive an efficient ADMM-based algorithm for solving the regularized SC problem. Experiments on various datasets demonstrate the effectiveness of this regularizer in alleviating overfitting and improving interpretability.",1046,0.6,604,1.7317880794701987,"In representation learning (RL how the learned representations easy interpret less overfitted training data are two important but challenging issues To address study regularization approach encourages the supports weight vectors RL models have small overlap by simultaneously promoting among vectors sparsity We apply the proposed regularizer two models neural networks sparse coding develop an efficient ADMM-based algorithm regularized SC Experiments various datasets demonstrate weight vectors learned under our regularizer interpretable have In representation learning (RL two critical issues First how the learned representations more interpretable Interpretability a must many applications For instance a clinical setting when applying deep learning ( and models learn representations for patients use assist need explain the representations physicians such transparent rather Second how overfitting? It often the learned representations yield good performance the training data perform less How improve the generalization performance on previously unseen data isIn make towards addressing via DL/ML models designed representation learning typically parameterized a collection weight vectors aiming capturing For example neural networks equipped hidden units where parameterized In another representation learning model -sparse coding BID74 , a dictionary basis vectors are utilized reconstruct In the interpretation RL models a major part interpret the learned weight vectors Typically elements a weight vector observed features oftentimes interpreted examining the top observed-features that For instance applying SC to reconstruct documents represented with bagof feature vectors each dimension a basis vector corresponds To visualize/interpret a basis vector one inspect the words corresponding the large values To achieve better interpretability various constraints the weight vectors Some notable ones (1) Sparsity BID80 -which encourages most weights zero Observed features that zeros weights considered irrelevant one focus interpreting (2) Diversity BID81 -which encourages different weight vectors mutually ""different having larger angles ). By doing the redundancy among weight vectors cognitively one map a physical concept (3) Nonnegativeness BID66 -which encourages the weights nonnegative since in certain scenarios bag of words representation documents make In interpretability less-overlapness encourages the weight vectors have small overlap supports 1 . By doing each weight vector anchored a unique subset observed features without redundant greatly facilitates interpretation For example topic models BID47 are learned each topic will characterized a few representative words the representative words different Such topics more amenable interpretation Besides improving interpretability less-overlapness helps alleviate overfitting It imposes a structural constraint over the weight vectors thus can effectively shrink the function class induced the RL models improve on unseen dataTo encourage less-overlapness propose a regularizer simultaneously encourages close being each sparse jointly encourage vectors' supports have small overlap The major contributions include:• We propose regularization approach encourages less-overlapness for improving interpretability reducing apply two models neural networks sparse coding derive an efficient ADMM-based algorithm regularized SC In experiments the empirical effectiveness In regularization approach encourages the weight vectors less-overlapped supports The proposed LDD-L1 regularizer simultaneously encourages the weight vectors sparse close being jointly the effects less overlap We apply this regularizer two models neural networks sparse coding derive an efficient ADMM-based algorithm solving Experiments various datasets demonstrate this regularizer overfitting improving interpretability",0.01,0.5686109019762053
"Successful recurrent models such as long short-term memories (LSTMs) and gated recurrent units (GRUs) use \emph{ad hoc} gating mechanisms.   Empirically these models have been found to improve the learning of medium to long term temporal dependencies and to help with vanishing gradient issues.
	
 We prove that learnable gates in a recurrent model formally provide \emph{quasi-invariance to general time transformations} in the input data. We recover part of the LSTM architecture from a simple axiomatic approach.
	
 This result leads to a new way of initializing gate biases in LSTMs and GRUs. Experimentally, this new \emph{chrono initialization} is shown to greatly improve learning of long term dependencies, with minimal implementation effort.

 The self loop feedback gating mechanism of recurrent networks has been derived from first principles via a postulate of invariance to time warpings. Gated connections appear to regulate the local time constants in recurrent models. With this in mind, the chrono initialization, a principled way of initializing gate biases in LSTMs, has been introduced. Experimentally, chrono initialization is shown to bring notable benefits when facing long term dependencies.A ADDITIONAL EXPERIMENTS On the generalization capacity of recurrent architectures. We proceeded to test the generalization properties of RNNs, leaky RNNs and chrono RNNs on the pure warping experiments presented in Section 3. For each of the architectures, a recurrent network with 64 recurrent units is trained for 3 epochs on a variable warping task with warps between 1 and 50. Each network is then tested on warped sequences, with warps between 100 and an increasingly big maximum warping. Results are summarized in Figure 5 .All networks display reasonably good, but not perfect, generalization. Even with warps 10 times longer than the training set warps, the networks still have decent accuracy, decreasing from 100% to around 75%.Interestingly , plain RNNs and gated RNNs display a different pattern: overall, gated RNNs perform better but their generalization performance decreases faster with warps eight to ten times longer than those seen during training, while plain RNN never have perfect accuracy, below 80% even within the training set range, but have a flatter performance when going beyond the training set warp range.Pixel level classification: MNIST and pMNIST. This task, introduced in BID15 , consists in classifying images using a recurrent model. The model is fed pixels one by one, from top to bottom, left to right, and has to output a probability distribution for the class of the object in the image.We evaluate standard and chrono initialization on two image datasets: MNIST (LeCun et al., 1999) and permuted MNIST, that is, MNIST where all images have undergone the same pixel permutation.LSTMs with 512 hidden units are used. Once again, standard initialization sets forget biases to 1, and the chrono initialization parameter is set to the length of the input sequences, max = 784. Results on the validation set are provided in Figure 6 . On non-permuted MNIST, there is no clear difference , even though the best validation error is obtained with chrono initialization. On permuted MNIST, chrono initialization performs better, with a best validation result of 96.3%, while standard initialization obtains a best validation result of 95.4%.Next character prediction on text8. Chrono initialization is benchmarked against standard initialization on the character level text8 dataset BID17 . Text8 is a 100M character formatted text sample from Wikipedia. BID21 's train-valid-test split is used: the first 90M characters are used as training set, the next 5M as validation set and the last 5M as test set.The exact same setup as in BID3 ) is used, with the code directly taken from there. Namely: LSTMs with 2000 units, trained with Adam BID13 with learning rate 10 −3 , batches of size 128 made of non-overlapping sequences of length 180, and gradient clipping at 1.0. Weights are orthogonally initialized, and recurrent batch normalization BID3 ) is used.Chrono initialization with max = 8 is compared to standard = 1 initialization. Results are presented in FIG4 . On the validation set, chrono initialization uniformly outperforms standard initialization by a small margin. On the test set, the compression rate is 1.37 with chrono initialization, versus 1.38 for standard initialization.8 This same slight difference is observed on two independent runs.Our guess is that , on next character prediction, with moderately sized networks, short term dependencies dominate, making the difference between standard and chrono initialization relatively small.Next word prediction on Penn Treebank. To attest for the resilience of chrono initialization to more complex models than simple LSTMs, we train on word level Penn Treebank BID21 using the best deep RHN network from BID25 . All hyperparameters are taken from of BID25 . For the chrono bias initialization, a single bias vector is sampled according to ∼ log( (1, max )), the carry gate bias vectors of all layers are initialized to − , and the transform gate biases to . max is chosen to be 11 (because this gives an average bias initialization close to the value 2 from (Zilly et al., 2016)).9 . Without further hyperparameter search and with a single run, we obtain test results similar to BID25 , with a test perplexity of 6.54.",1147,0.558,692,1.657514450867052,"Successful recurrent models such long short-term memories gated recurrent units use \emph{ad hoc gating mechanisms these models found improve learning medium temporal dependencies help vanishing gradient issues We prove learnable gates a recurrent model formally provide \emph{quasi to general time transformations We recover part the LSTM architecture This result leads initializing gate biases GRUs Experimentally this new \emph{chrono initialization shown greatly learning long term dependencies minimal implementation effort The self loop feedback gating mechanism recurrent networks derived first principles via to time warpings Gated connections appear regulate the local time constants recurrent models With the chrono initialization, a principled way gate biases Experimentally chrono initialization shown bring notable benefits facing long term dependenciesA ADDITIONAL EXPERIMENTS On the generalization capacity recurrent architectures. We proceeded test the generalization properties the pure warping experiments presented Section For each the architectures a recurrent network 64 recurrent units trained on a variable warping task warps between 50 Each network then tested warped sequences warps 100 an increasingly big maximum warping Results are summarized 5 .All networks display reasonably, Even warps 10 longer the training set warps the networks decent accuracy decreasing from around 75%.Interestingly , plain RNNs and display: overall perform but their generalization performance faster eight those seen during never have perfect accuracy below even within have goingPixel level classification MNIST pMNIST. This task, introduced BID15 , in classifying images a recurrent model The model fed pixels one from left has to output a probability distribution the classWe evaluate standard and chrono initialization two image datasets MNISTLeCun permuted MNIST, that where undergoneLSTMs with 512 hidden units Once standard initialization sets forget biases the chrono initialization parameter the length the input sequences max 784 Results on the validation set On non-permuted MNIST , the best validation error obtained chrono initialization On permuted MNIST, chrono initialization performs better a best validation result standard initialization obtains 95.4%.Next character prediction on text8 Chrono initialization benchmarked standard initialization on the character level text8 dataset BID17 . Text8 a 100M character formatted text sample Wikipedia BID21 's train-valid-test split used: the first 90M characters training set 5The exact same setup ) directly taken there Namely LSTMs with 2000 units trained with Adam BID13 with learning rate 10 −3 batches size 128 made length 180 gradient clipping at Weights initialized recurrent batch normalization BID3 )Chrono initialization with max = 8 compared standard = 1 initialization Results are presented FIG4 On the validation set chrono initialization uniformly outperforms standard initialization On the test set the compression rate with chrono initialization versus standard initialization.8 This same slight difference two independent runsOur guess , on next character prediction with moderately sized networks short term dependencies dominate making relativelyNext word prediction Penn Treebank To attest for the resilience chrono initialization to more complex models than train on word level Penn Treebank BID21 using the best deep RHN network from BID25 . All hyperparameters taken of BID25 . For the chrono bias initialization a single bias vector sampled according ∼ log (1, max the carry gate bias vectors all layers initialized − , . max is chosen 11because this gives an average bias initialization close 2 from (Zilly et 2016)).9 . Without further hyperparameter search and with a single run obtain test results similar BID25 , a test perplexity",0.01,0.3793682219050452
"Teaching plays a very important role in our society, by spreading human knowledge and educating our next generations. A good teacher will select appropriate teaching materials, impact suitable methodologies, and set up targeted examinations, according to the learning behaviors of the students. In the field of artificial intelligence, however, one has not fully explored the role of teaching, and pays most attention to machine \emph{learning}. In this paper, we argue that equal attention, if not more, should be paid to teaching, and furthermore, an optimization framework (instead of heuristics) should be used to obtain good teaching strategies. We call this approach ``learning to teach''. In the approach, two intelligent agents interact with each other: a student model (which corresponds to the learner in traditional machine learning algorithms), and a teacher model (which determines the appropriate data, loss function, and hypothesis space to facilitate the training of the student model). The teacher model leverages the feedback from the student model to optimize its own teaching strategies by means of reinforcement learning, so as to achieve teacher-student co-evolution. To demonstrate the practical value of our proposed approach, we take the training of deep neural networks (DNN) as an example, and show that by using the learning to teach techniques, we are able to use much less training data and fewer iterations to achieve almost the same accuracy for different kinds of DNN models (e.g., multi-layer perceptron, convolutional neural networks and recurrent neural networks) under various machine learning tasks (e.g., image classification and text understanding). The evolution of modern human society heavily depends on its advanced education system. The goal of education is to equip the students with necessary knowledge and skills, so as to empower them to further deepen the understanding of the world, and push the frontier of our humanity. In general, the growth of a student will be influenced by two factors: his/her own learning ability and the teaching ability of his/her teacher. Among these two, the teacher plays a critical role: an experienced teacher enables faster learning of a student through elaborated strategies such as selecting appropriate teaching materials, imparting suitable methodologies, and setting up targeted examinations.The training of an agent in artificial intelligence (e.g., an image classification model) is very similar to the growth of a student in human society. However, after carefully revisiting the literature of artificial intelligence (AI), we find that the importance role of the teacher has not been fully realized. Researchers put most of their efforts on the student, e.g., designing various optimization algorithms to enhance the learning ability of intelligent agents. In contrast, there are very limited attempts on building good teaching strategies, as briefly summarized below. Machine teaching BID41 BID42 BID21 BID22 studies the problem of how to identify the smallest training set to push the machine learning model towards a pre-defined oracle model. Curriculum learning (CL) BID2 BID31 BID8 and self-paced learning (SPL) BID18 BID19 BID15 heuristically define the scheduling of training data in a from-easy-to-hard order. Graduated optimization BID9 heuristically refines the non-convex loss function in a from-smooth-to-sharp manner, in order to make the machine learning process more robust. These attempts are either based on task-specific heuristic rules, or the strong assumption of a pre-known oracle model. In this regard, these works have not reflected the nature of education and the best practices in human society, where a good teacher is able to adaptively adopt different teaching strategies for different students under different circumstances, and is good at constantly improving his/her own teaching skills based on the feedback from the students.In this paper, we argue that a formal study on the role of 'teaching' in artificial intelligence is sorely needed. Actually, there could be a natural analogy between teaching in artificial intelligence and teaching in human society. For example, selecting training data corresponds to choosing right teaching materials (e.g. textbooks); designing the loss functions corresponds to setting up targeted examinations; defining the hypothesis space corresponds to imparting the proper methodologies. Furthermore, an optimization framework (instead of heuristics) should be used to update the teaching skills based on the feedback from the students, so as to achieve teacher-student co-evolution. Just as French essayist Joseph Joubert said -""To teach is to learn twice"", we call this new approach ""learning to teach"" (L2T).In the L2T framework, there are two intelligent agents: a student model/agent, corresponding to the learner in traditional machine learning algorithms, and a teacher model/agent, determining the appropriate data, loss function, and hypothesis space to facilitate the learning of the student model. The training phase of L2T contains several episodes of sequential interactions between the teacher model and the student model. Based on the state information in each step, the teacher model updates the teaching actions so as to refine the machine learning problem of the student model. The student model then performs its learning process based on the inputs from the teacher model, and provides reward signals (e.g., the accuracy on the held-out development set) back to the teacher afterwards. The teacher model then utilizes such rewards to update its parameters via policy gradient methods (e.g., REINFORCE BID39 ). This interactive process is end-to-end trainable, exempt from the limitations of human-defined heuristics. Once converged, the teacher model could be applied to new learning scenarios and even new students, without extra efforts on re-training.To demonstrate the practical value of our proposed approach, we take a specific problem, training data scheduling, as an example. We show that by using our method to adaptively select the most suitable training data, we can significantly improve the accuracy and convergence speed of various neural networks including multi-layer perceptron (MLP), convolutional neural networks (CNNs) and recurrent neural networks (RNNs), for different applications including image classification and text understanding. Furthermore, the teacher model obtained by our method from one task can be smoothly transferred to other tasks. For example, with the teacher model trained on MNIST with the MLP learner, one can achieve a satisfactory performance on CIFAR-10 only using roughly half of the training data to train a ResNet model as the student. Inspired by the education systems in human society, we have proposed the framework of learning to teach, an end-to-end trainable method to automate the teaching process. Comprehensive experiments on several real-world tasks have demonstrated the effectiveness of the framework.There are many directions to explore for learning to teach in future. First, we have studied the application of L2T to image classification and sentiment analysis. We will study more applications such as machine translation and speech recognition. Second, we have focused on data teaching in this work. As stated in Subsection 3.1, we plan to investigate other teaching problems such as loss function teaching and hypothesis space teaching. Third, we have empirically verified the L2T framework through experiments. It is interesting to build theoretical foundations for learning to teach, such as the consistence and generalization of the teacher model.",1431,0.716,858,1.667832167832168,"Teaching plays by spreading human knowledge educating our next generations A good teacher select appropriate teaching materials impact suitable methodologies set targeted examinations according the learning behaviors In the field however one has not fully explored teaching pays most attention machine \emph{learning In this paper argue equal attention, if more teaching, furthermore an optimization framework (instead heuristics obtain good teaching strategies We call this approach ``learning to teach In the approach two intelligent agents interact: a student model (which corresponds traditional machine learning determines the appropriate data, loss function hypothesis space facilitate The teacher model leverages the feedback optimize its own teaching strategies by means so as achieve teacher-student co To demonstrate the practical value our proposed approach take the training deep neural networks by the learning teach techniques use fewer iterations achieve almost the same accuracy for different kinds DNN models and under various machine learning tasks text understanding The evolution modern human society heavily its advanced education system The goal education equip necessary knowledge as empower further deepen push the frontier our humanity In general the growth a student will influenced his/her own learning ability the teaching ability Among these two the teacher plays: an experienced teacher enables faster learning through elaborated strategies such selecting appropriate teaching materials imparting suitable methodologies setting targeted examinationsThe training an agent artificial intelligence (e.g., an image classification model very the growth a student human society However after carefully revisiting the literature of artificial intelligence the importance role the teacher realized Researchers put most on the student designing various optimization enhance intelligent agents In contrast there very limited attempts on building good teaching strategies as briefly summarized Machine teaching BID41 BID42 BID21 BID22 studies the problem how identify the smallest training set to push the machine learning model towards a pre-defined oracle model Curriculum learning (CL BID2 BID31 BID8 and heuristically define the scheduling training data a from-easy-to-hard order Graduated optimization BID9 heuristically refines the non-convex loss function a from-smooth-to-sharp manner in make the machine learning process These attempts either based task-specific heuristic rules the strong assumption a pre-known oracle model In this regard these works not reflected education the best practices human society where a good teacher able adaptively adopt different teaching strategies under is good constantly basedIn this paper argue a formal study 'teaching artificial intelligence sorely Actually could a natural analogy teaching in artificial intelligence human society For example selecting training data corresponds choosing right teaching materials designing the loss functions corresponds setting targeted examinations defining hypothesis space imparting the proper methodologies Furthermore an optimization framework (instead heuristics should update the teaching skills based the feedback as achieve teacher-student co Just French essayist Joseph Joubert said -""To teach learn twice call this new approachlearningL2T).In the L2T framework there two intelligent agents a student model/agent corresponding traditional machine learning algorithms determining the appropriate data, loss function hypothesis space facilitate The training phase L2T contains several episodes sequential interactions the teacher model Based the state information each step the teacher model updates the teaching actions so as refine the machine learning problem of the student model The student model then performs its learning process based the inputs the teacher model provides reward signals ( the accuracy on the held-out development set back afterwards The teacher model then utilizes such rewards update its parameters via policy gradient methods ( REINFORCE BID39 This interactive process end trainable exempt human-defined heuristics Once converged the teacher model could new learning scenarios even new students without extra efforts retrainingTo demonstrate our proposed approach take a specific problem training data scheduling as We show by our method adaptively select the most suitable training data significantly the accuracy and convergence speed including multi-layer perceptron ( for different applications including text understanding Furthermore the teacher model obtained our method from one task can smoothly transferred For example with the teacher model trained MNIST with the MLP learner one achieve a satisfactory performance CIFAR-10 only using roughly half to train a ResNet model as the student Inspired the education systems human society proposed the framework learning teach automate Comprehensive experiments several real-world tasks the frameworkThere many directions learning teach future First studied the application L2T image classification and sentiment analysis We will study more applications such machine translation Second focused data teaching this work As stated Subsection we plan investigate other teaching problems such loss function teaching hypothesis space teaching Third empirically the L2T framework through experiments It interesting build theoretical foundations learning teach such the consistence the teacher model",0.01,0.40565685822745967
"We present DL2, a system for training and querying neural networks with logical constraints. The key idea is to translate these constraints into a differentiable loss with desirable mathematical properties and to then either train with this loss in an iterative manner or to use the loss for querying the network for inputs subject to the constraints. We empirically demonstrate that DL2 is effective in both training and querying scenarios, across a range of constraints and data sets. With the success of neural networks across a wide range of important application domains, a key challenge that has emerged is that of making neural networks more reliable. Promising directions to address this challenge are incorporating constraints during training BID14 BID16 and inspecting already trained networks by posing specific queries BID7 BID21 BID27 ). While useful, these approaches are described and hardcoded to particular kinds of constraints, making their application to other settings difficult.Inspired by prior work (e.g., BID3 ; BID5 ; BID10 ; BID0 ), we introduce a new method and system, called DL2 (acronym for Deep Learning with Differentiable Logic), which can be used to: (i) query networks for inputs meeting constraints, and (ii) train networks to meet logical specifications, all in a declarative fashion. Our constraint language can express rich combinations of arithmetic comparisons over inputs, neurons and outputs of neural networks using negations, conjunctions, and disjunctions. Thanks to its expressiveness, DL2 enables users to enforce domain knowledge during training or interact with the network in order to learn about its behavior via querying. DL2 works by translating logical constraints into non-negative loss functions with two key properties: (P1) a value where the loss is zero is guaranteed to satisfy the constraints, and (P2) the resulting loss is differentiable almost everywhere. Combined, these properties enable us to solve the problem of querying or training with constraints by minimizing a loss with off-the-shelf optimizers.Training with DL2 To make optimization tractable, we exclude constraints on inputs that capture convex sets and include them as constraints to the optimization goal. We then optimize with projected gradient descent (PGD), shown successful for training with robustness constraints BID14 . The expressiveness of DL2 along with tractable optimization through PGD enables us to train with new, interesting constraints. For example, we can express constraints over probabilities which are not explicitly computed by the network. Consider the following:∀x. p θ people (x) < ∨ p θ people (x) > 1 − This constraint, in the context of CIFAR-100, says that for any network input x (network is parameterized by θ), the probability of people (p people ) is either very small or very large. However, CIFAR-100 does not have the class people, and thus we define it as a function of other probabilities, in particular: p people = p baby + p boy + p girl + p man + p woman . We show that with a similar constraint (but with 20 classes), DL2 increases the prediction accuracy of CIFAR-100 networks in the semi-supervised setting, outperforming prior work whose expressiveness is more restricted. DL2 can capture constraints arising in both, classification and regression tasks. For example, GalaxyGAN BID22 , a generator of galaxy images, requires the network to respect constraints imposed by the underlying physical systems, e.g., flux: the sum of input pixels should equal the sum of output pixels. Instead of hardcoding such a constraint into the network in an ad hoc way, with DL2, this can now be expressed declaratively: sum(x) = sum(GalaxyGAN(x)).Global training A prominent feature of DL2 is its ability to train with constraints that place restrictions on inputs outside the training set. Prior work on training with constraints (e.g., BID27 ) focus on the given training set to locally train the network to meet the constraints. With DL2, we can, for the first time, query for inputs which are outside the training set, and use them to globally train the network. Previous methods that trained on examples outside the training set were either tailored to a specific task BID14 or types of networks BID16 . Our approach splits the task of global training between: (i) the optimizer , which trains the network to meet the constraints for the given inputs, and (ii) the oracle, which provides the optimizer with new inputs that aim to violate the constraints. To illustrate, consider the following Lipshcitz condition: DISPLAYFORM0 Here, for two inputs from the training set (x 1 , x 2 ), any point in their -neighborhood (z 1 , z 2 ) must satisfy the condition. This constraint is inspired by recent works (e.g., BID8 ; BID1 ) which showed that neural networks are more stable if satisfying the Lipschitz condition.Querying with DL2 We also designed an SQL-like language which enables users to interact with the model by posing declarative queries. For example, consider the scenarios studied by a recent work BID23 where authors show how to generate adversarial examples with ACGANs BID17 . The generator is used to create images from a certain class (e.g., 1) which fools a classifier (to classify as, e.g., 7). With DL2, this can be phrased as: DISPLAYFORM1 where n i n [-1, 1], c l a s s (M_NN1(M_ACGAN_G(n, 1))) = 7 r e t u r n M_ACGAN_G (n, 1) This query aims to find an input n ∈ R 100 to the generator satisfying two constraints: its entries are between −1 and 1 (enforcing a domain constraint) and it results in the generator producing an image, which it believes to be classified as 1 (enforced by M_ACGAN_G(n, 1)) but is classified by the network (M_NN1) as 7. DL2 automatically translates this query to a DL2 loss and optimizes it with an off-the-shelf optimizer (L-BFGS-B) to find solutions, in this case, the image to the right. Our language can naturally capture many prior works at the declarative level, including finding neurons responsible for a given prediction BID18 , inputs that differentiate two networks BID21 , and adversarial example generation (e.g., BID24 ). We presented DL2, a system for training and querying neural networks. DL2 supports an expressive logical fragment and provides translation rules into a differentiable (almost everywhere) loss, which is zero only for inputs satisfying the constraints. To make training tractable, we handle input constraints which capture convex sets through PGD. We also introduce a declarative language for querying networks which uses the logic and the translated loss. Experimental results indicate that DL2 is effective in both, training and querying neural networks. DISPLAYFORM0 We start by giving a proof for the if direction of the Theorem 1, i.e. if L(ϕ)(x) = 0, thenx satisfies ϕ. The proof is by induction on the formula structure (we assume ϕ is negation-free as negations can be eliminated as described in the text).As a base case, we consider formulas consisting of a single atomic constraint.• DISPLAYFORM1 , and ϕ is satisfied.• DISPLAYFORM2 and ϕ is satisfied.• DISPLAYFORM3 , and since ξ > 0, we get t 1 (x) < t 2 (x). Thus, ϕ is satisfied .As an induction step, we consider combination of formulas using single logical and or logical or operation.• DISPLAYFORM4 By the induction hypothesis, either ϕ is satisfied or ψ is satisfied, implying that ϕ ∨ ψ is satisfied. DISPLAYFORM5 By the induction hypothesis, ϕ and ψ are satisfied, implying that ϕ ∧ ψ is satisfied.",1627,0.721,891,1.8260381593714927,"We present DL2 training querying logical constraints The key idea translate these constraints a differentiable loss with desirable mathematical properties then either train with for querying inputs subject We empirically demonstrate DL2 effective both training querying scenarios across constraints and data sets With neural networks across important application domains that that of making reliable Promising directions address this challenge incorporating constraints during training BID14 BID16 inspecting already trained networks by posing specific queries ). While useful these approaches described and hardcoded particular kinds constraints making to other settingsInspired prior work ; introduce and system DL2acronym with Differentiable Logic: (i) query networks inputs meeting constraints meet logical specifications all Our constraint language can express rich combinations arithmetic comparisons over inputs neurons using negations Thanks its expressiveness DL2 enables enforce domain knowledge during training or interact learn via querying DL2 works translating logical constraints non-negative loss functions with two key propertiesP1 a value where guaranteed satisfy differentiable almost Combined these properties enable solve querying or training with constraints by minimizing a loss with off optimizersTraining DL2 To make optimization exclude constraints inputs capture convex sets include them the optimization goal We then optimize with projected gradient descent shown successful training robustness constraints BID14 . The expressiveness DL2 along tractable optimization through PGD enables train with new, interesting constraints For example we express constraints over probabilities which explicitly computed the network Consider the following:��x. p �� peoplex > 1 − This constraint, CIFAR-100 says for any network input (network is parameterized peoplep people either very However CIFAR-100 does the class people, we define other probabilities in p people baby + boy man We show with a similar constraintbut 20 classes DL2 increases CIFAR-100 networks outperforming prior work whose expressiveness more DL2 can capture constraints arising both, classification and regression tasks For example GalaxyGAN BID22 , a generator galaxy images requires the network respect constraints the underlying physical systems flux: the sum input pixels should Instead hardcoding such a constraint the network in with DL2 this can now expressed sum(x sum(GalaxyGAN(x)).Global training A prominent feature with constraints place restrictions inputs outside Prior work training with constraints ( BID27 ) focus the given training locally train the network meet With DL2, query inputs which outside globally train Previous methods that trained on examples outside either tailored a specific task BID14 types . Our approach splits global training between: the optimizer , trains meet for the given inputs provides aim violate To illustrate the following Lipshcitz condition DISPLAYFORM0 Here for two inputs from the training setx 1 any point their -neighborhoodz satisfy This constraint inspired recent works ( BID8 ; stable satisfyingQuerying with DL2 We designed enables users interact posing For example consider the scenarios studied a recent work BID23 where authors show generate adversarial examples ACGANs BID17 . The generator used images a certain class ( 1) which fools a classifierto classify as, 7 With DL2 this can phrased DISPLAYFORM1 where n i n [ c lM_NN1(M_ACGAN_G(n 7 r e t u ( This query aims an input n �� R 100 to the generator satisfying two constraints its entries betweenenforcing a domain constraint results producing an image, it believes classified 1enforced but classified the network () 7 DL2 automatically translates this query a DL2 loss and with offL-BFGS-B find solutions, in the image Our language can naturally capture many prior works at including finding neurons responsible a given prediction BID18 inputs differentiate two networks adversarial example generation We presented DL2 training querying DL2 supports an expressive logical fragment and provides translation rules into a differentiable (almost everywhere) loss, zero only inputs satisfying To training tractable handle input constraints which capture convex sets through PGD We also introduce networks which the logic the translated loss. Experimental results DL2 effective both, training querying DISPLAYFORM0 We start giving a proof for the if direction the Theorem 1 L(��)(x thenx satisfies � The proof by induction on the formula structure (we assume �� negation- as negations eliminated described text).As a base case consider formulas consisting atomic constraint.• DISPLAYFORM1 , and �� satisfied.• since �� > get t 1x Thus �� satisfied .As an induction step combination formulas using single logical and or logical or operation.• DISPLAYFORM4 By the induction hypothesis either� implying DISPLAYFORM5 By the induction hypothesis �� and �� satisfied implying",0.01,0.8087518248432243
"Genetic algorithms have been widely used in many practical optimization problems.
 Inspired by natural selection, operators, including mutation, crossover
 and selection, provide effective heuristics for search and black-box optimization.
 However, they have not been shown useful for deep reinforcement learning, possibly
 due to the catastrophic consequence of parameter crossovers of neural networks.
 Here, we present Genetic Policy Optimization (GPO), a new genetic algorithm
 for sample-efficient deep policy optimization. GPO uses imitation learning
 for policy crossover in the state space and applies policy gradient methods for mutation.
 Our experiments on MuJoCo tasks show that GPO as a genetic algorithm
 is able to provide superior performance over the state-of-the-art policy gradient
 methods and achieves comparable or higher sample efficiency. Reinforcement learning (RL) has recently demonstrated significant progress and achieves state-ofthe-art performance in games BID14 , locomotion control BID12 , visual-navigation BID29 , and robotics BID11 . Among these successes, deep neural networks (DNNs) are widely used as powerful functional approximators to enable signal perception, feature extraction and complex decision making. For example, in continuous control tasks, the policy that determines which action to take is often parameterized by a deep neural network that takes the current state observation or sensor measurements as input. In order to optimize such policies, various policy gradient methods BID15 BID19 BID7 have been proposed to estimate gradients approximately from rollout trajectories. The core idea of these policy gradient methods is to take advantage of the temporal structure in the rollout trajectories to construct a Monte Carlo estimator of the gradient of the expected return.In addition to the popular policy gradient methods, other alternative solutions, such as those for black-box optimization or stochastic optimization, have been recently studied for policy optimization. Evolution strategies (ES) is a class of stochastic optimization techniques that can search the policy space without relying on the backpropagation of gradients. At each iteration, ES samples a candidate population of parameter vectors (""genotypes"") from a probability distribution over the parameter space, evaluates the objective function (""fitness"") on these candidates, and constructs a new probability distribution over the parameter space using the candidates with the high fitness. This process is repeated iteratively until the objective is maximized. Covariance matrix adaptation evolution strategy (CMA-ES; BID5 ) and recent work from BID18 are examples of this procedure. These ES algorithms have also shown promising results on continuous control tasks and Atari games, but their sample efficiency is often not comparable to the advanced policy gradient methods, because ES is black-box and thus does not fully exploit the policy network architectures or the temporal structure of the RL problems.Very similar to ES, genetic algorithms (GAs) are a heuristic search technique for search and optimization. Inspired by the process of natural selection, GAs evolve an initial population of genotypes by repeated application of three genetic operators -mutation, crossover and selection. One of the main differences between GA and ES is the use of the crossover operator in GA, which is able to provide higher diversity of good candidates in the population. However, the crossover operator is often performed on the parameter representations of two parents, thus making it unsuitable for nonlinear neural networks. The straightforward crossover of two neural networks by exchanging their parameters can often destroy the hierarchical relationship of the networks and thus cause a catastrophic drop in performance. NeuroEvolution of Augmenting Topologies (NEAT; BID24 a) ), which evolves neural networks through evolutionary algorithms such as GA, provides a solution to exchange and augment neurons but has found limited success when used as a method of policy search in deep RL for high-dimensional tasks. A major challenge to making GAs work for policy optimization is to design a good crossover operator which efficiently combines two parent policies represented by neural networks and generates an offspring that takes advantage of both parents. In addition, a good mutation operator is needed as random perturbations are often inefficient for high-dimensional policies.In this paper, we present Genetic Policy Optimization (GPO), a new genetic algorithm for sampleefficient deep policy optimization. There are two major technical advances in GPO. First, instead of using parameter crossover, GPO applies imitation learning for policy crossovers in the state space. The state-space crossover effectively combines two parent policies into an offspring or child policy that tries to mimic its best parent in generating similar state visitation distributions. Second, GPO applies advanced policy gradient methods for mutation. By randomly rolling out trajectories and performing gradient descent updates, this mutation operator is more efficient than random parameter perturbations and also maintains sufficient genetic diversity. Our experiments on several continuous control tasks show that GPO as a genetic algorithm is able to provide superior performance over the state-of-the-art policy gradient methods and achieves comparable or higher sample efficiency. We presented Genetic Policy Optimization (GPO), a new approach to deep policy optimization which combines ideas from evolutionary algorithms and reinforcement learning. First, GPO does efficient policy crossover in state space using imitation learning. Our experiments show the benefits of crossover in state-space over parameter-space for deep neural network policies. Second, GPO mutates the policy weights by using advanced policy gradient algorithms instead of random perturbations. We conjecture that the noisy gradient estimates used by policy gradient methods offer sufficient genetic diversity, while providing a strong learning signal. Our experiments on several MuJoCo locomotion tasks show that GPO has superior performance over the state-of-the-art policy gradient methods and achieves comparable or higher sample efficiency. Future advances in policy gradient methods and imitation learning will also likely improve the performance of GPO for challenging RL tasks. Table 2 : Mean and standard-error for final performance of GPO and baselines using A2C.",1134,0.625,683,1.6603221083455344,"Genetic algorithms widely many practical optimization problems Inspired natural selection operators, including mutation crossover provide effective heuristics search and black-box optimization However they shown useful deep reinforcement learning possibly the catastrophic consequence parameter crossovers of Here Genetic Policy Optimization sample-efficient deep policy optimization GPO uses imitation learning policy crossover the state space applies policy gradient methods mutation Our experiments MuJoCo tasks GPO as a genetic algorithm provide state policy gradient methods achieves comparable or higher sample efficiency Reinforcement learningRL recently demonstrated significant progress achieves state-ofthe-art performance games BID14 , locomotion control visual- robotics Among these successes deep neural networks widely powerful functional approximators enable signal perception feature For example continuous control tasks the policy that often parameterized takes the current state observation or sensor measurements In order optimize such policies various policy gradient methods BID15 BID19 BID7 have estimate gradients approximately rollout trajectories The core idea these policy gradient methods take the temporal structure in the rollout trajectories constructIn addition other alternative solutions those for recently studied policy optimization Evolution strategies (ES is search the policy space without relying gradients At each iteration ES samples a candidate population parameter vectors ( over evaluates the objective function these candidates constructs the candidates with This process repeated iteratively the objective maximized Covariance matrix adaptation evolution strategy; BID5 ) recent work BID18 examples this procedure These ES algorithms also shown continuous control tasks Atari games their sample efficiency often the advanced policy gradient methods, because ES black-box and thus fully exploit the policy network architectures or temporal structure the RL problemsVery ES genetic algorithms (GAs a heuristic search technique search optimization Inspired the process GAs evolve an initial population by repeated application three genetic operators -mutation crossover selection One GA ES the crossover operator able provide higher diversity good candidates However the crossover operator often performed the parameter representations two parents thus The straightforward crossover two neural networks by exchanging their parameters can often destroy the hierarchical relationship a catastrophic drop NeuroEvolution of Augmenting Topologies (NEAT; BID24 a ), evolves neural networks through evolutionary algorithms such GA provides exchange and augment neurons but found when policy search deep RL for A major challenge making GAs work policy optimization design a good crossover operator which efficiently combines two parent policies represented neural networks generates an offspring takes In addition a good mutation operator needed as random perturbations inefficient high-dimensional policiesIn Genetic Policy Optimization sampleefficient deep policy optimization There two major technical advances GPO First instead parameter crossover GPO applies imitation learning for policy crossovers in the state space The state-space crossover effectively combines two parent policies an offspring or child policy tries mimic its best parent in generating similar state visitation distributions Second GPO applies advanced policy gradient methods mutation By randomly rolling trajectories performing gradient descent updates this mutation operator more random parameter perturbations also maintains sufficient genetic diversity Our experiments several continuous control tasks GPO as a genetic algorithm provide state policy gradient methods achieves comparable or higher sample efficiency We presented Genetic Policy Optimization deep policy optimization which ideas evolutionary algorithms reinforcement learning First GPO does efficient policy crossover state space using imitation learning Our experiments the benefits crossover state-space over parameter-space for deep neural network policies Second GPO mutates the policy weights advanced policy gradient algorithms instead We conjecture the noisy gradient estimates policy gradient methods offer sufficient genetic diversity, while a strong learning signal Our experiments several MuJoCo locomotion tasks GPO state policy gradient methods achieves comparable or higher sample efficiency Future advances policy gradient methods imitation learning likely GPO for challenging RL tasks Table 2 : Mean-error final performance GPO baselines using A2C.",0.01,0.3865218864821293
"To make deep neural networks feasible in resource-constrained environments (such as mobile devices), it is beneficial to quantize models by using low-precision weights. One common technique for quantizing neural networks is the straight-through gradient method, which enables back-propagation through the quantization mapping. Despite its empirical success, little is understood about why the straight-through gradient method works.
 Building upon a novel observation that the straight-through gradient method is in fact identical to the well-known Nesterov’s dual-averaging algorithm on a quantization constrained optimization problem, we propose a more principled alternative approach, called ProxQuant , that formulates quantized network training as a regularized learning problem instead and optimizes it via the prox-gradient method. ProxQuant does back-propagation on the underlying full-precision vector and applies an efficient prox-operator in between stochastic gradient steps to encourage quantizedness. For quantizing ResNets and LSTMs, ProxQuant outperforms state-of-the-art results on binary quantization and is on par with state-of-the-art on multi-bit quantization. We further perform theoretical analyses showing that ProxQuant converges to stationary points under mild smoothness assumptions, whereas variants such as lazy prox-gradient method can fail to converge in the same setting. Deep neural networks (DNNs) have achieved impressive results in various machine learning tasks BID6 . High-performance DNNs typically have over tens of layers and millions of parameters, resulting in a high memory usage and a high computational cost at inference time. However, these networks are often desired in environments with limited memory and computational power (such as mobile devices), in which case we would like to compress the network into a smaller, faster network with comparable performance.A popular way of achieving such compression is through quantization -training networks with lowprecision weights and/or activation functions. In a quantized neural network, each weight and/or activation can be representable in k bits, with a possible codebook of negligible additional size compared to the network itself. For example, in a binary neural network (k = 1), the weights are restricted to be in {±1}. Compared with a 32-bit single precision float, a quantized net reduces the memory usage to k/32 of a full-precision net with the same architecture BID7 BID4 BID19 BID13 BID26 BID27 . In addition, the structuredness of the quantized weight matrix can often enable faster matrixvector product, thereby also accelerating inference BID13 .Typically , training a quantized network involves (1) the design of a quantizer q that maps a full-precision parameter to a k-bit quantized parameter, and (2) the straight-through gradient method BID4 that enables back-propagation from the quantized parameter back onto the original full-precision parameter, which is critical to the success of quantized network training. With quantizer q, an iterate of the straight-through gradient method (see FIG7 proceeds Code available at https://github.com/allenbai01/ProxQuant. as θ t+1 = θ t − η t ∇L(θ)| θ=q(θt) , and q( θ) (for the converged θ) is taken as the output model. For training binary networks, choosing q(·) = sign(·) gives the BinaryConnect method BID4 .Though appealingly simple and empirically effective, it is information-theoretically rather mysterious why the straight-through gradient method works well, at least in the binary case: while the goal is to find a parameter θ ∈ {±1} d with low loss, the algorithm only has access to stochastic gradients at {±1} d . As this is a discrete set , a priori, gradients in this set do not necessarily contain any information about the function values. Indeed, a simple one-dimensional example (Figure 1b) shows that BinaryConnect fails to find the minimizer of fairly simple convex Lipschitz functions in {±1}, due to a lack of gradient information in between.rL(q(✓t)) DISPLAYFORM0 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM1 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM2 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM3 0 B N 6 N u 6 N R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > q(✓t) DISPLAYFORM4 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" DISPLAYFORM5 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" DISPLAYFORM6 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > < l a t e x i t s h a 1 _ b a s e 6 4 = "" DISPLAYFORM7 a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e x i t > rL(✓t) < l a t e x i t s h a 1 _ b a s e 6 4 = "" k M y 6 L o 8 X P y through method computes the gradient at the quantized vector and performs the update at the original real vector; PROXQUANT performs a gradient update at the current real vector followed by a prox step which encourages quantizedness. (b) A two-function toy failure case for BinaryConnect. The two functions are f1(x) = |x + 0.5| − 0.5 (blue) and f−1(x) = |x − 0.5| − 0.5 (orange). The derivatives of f1 and f−1 coincide at {−1, 1}, so any algorithm that only uses this information will have identical behaviors on these two functions. However, the minimizers in {±1} are x 1 = −1 and x −1 = 1, so the algorithm must fail on one of them. DISPLAYFORM8 DISPLAYFORM9 DISPLAYFORM10 DISPLAYFORM11 DISPLAYFORM12 DISPLAYFORM13 In this paper, we formulate the problem of model quantization as a regularized learning problem and propose to solve it with a proximal gradient method. Our contributions are summarized as follows.• We present a unified framework for defining regularization functionals that encourage binary, ternary, and multi-bit quantized parameters, through penalizing the distance to quantized sets (see Section 3.1). For binary quantization, the resulting regularizer is a W -shaped non-smooth regularizer, which shrinks parameters towards either −1 or 1 in the same way that the L 1 norm regularization shrinks parameters towards 0.• We propose training quantized networks using PROXQUANT (Algorithm 1) -a stochastic proximal gradient method with a homotopy scheme. Compared with the straightthrough gradient method, PROXQUANT has access to additional gradient information at non-quantized points, which avoids the problem in FIG7 and its homotopy scheme prevents potential overshoot early in the training (Section 3.2).• We demonstrate the effectiveness and flexibility of PROXQUANT through systematic experiments on (1) image classification with ResNets (Section 4.1); (2) language modeling with LSTMs (Section 4.2). The PROXQUANT method outperforms the state-of-the-art results on binary quantization and is comparable with the state-of-the-art on ternary and multi-bit quantization.• We perform a systematic theoretical study of quantization algorithms , showing that our PROXQUANT (standard prox-gradient method) converges to stataionary points under mild smoothness assumptions (Section 5.1), where as lazy prox-gradient method such as BinaryRelax BID25 fails to converge in general (Section 5.2). Further, we show that BinaryConnect has a very stringent condition to converge to any fixed point (Section 5.3), which we verify through a sign change experiment (Appendix C). In this paper, we propose and experiment with the PROXQUANT method for training quantized networks. Our results demonstrate that PROXQUANT offers a powerful alternative to the straightthrough gradient method and has theoretically better convergence properties. For future work, it would be of interest to propose alternative regularizers for ternary and multi-bit PROXQUANT and experiment with our method on larger tasks.",2704,0.835,1581,1.7103099304237823,"To make deep neural networks feasible in resource-constrained environments (such mobile devices it beneficial quantize models by using low-precision weights One common technique quantizing neural networks the straight-through gradient method enables back-propagation through the quantization mapping Despite its empirical success little understood why the straight-through gradient method works Building upon a novel observation that the straight-through gradient method is in identical the well-known Nesterov��s dual-averaging algorithm on a quantization constrained optimization problem propose a more principled alternative approach, called ProxQuant , that formulates quantized network training as a regularized learning problem instead and optimizes it via the prox-gradient method ProxQuant does back-propagation on the underlying full-precision vector and applies an efficient prox-operator in between stochastic gradient steps encourage quantizedness For quantizing ResNets and LSTMs ProxQuant outperforms state results on binary quantization and is on state on multi-bit quantization We further perform theoretical analyses showing ProxQuant converges stationary points under mild smoothness assumptions, whereas variants such lazy prox-gradient method can fail in the same setting Deep neural networks ( have achieved impressive results various machine BID6 . High-performance DNNs typically have over tens layers and millions parameters resulting a high memory usage a high computational cost at inference time However these networks often desired in environments with limited memory and computational power (such mobile devices in which case we would like compress a smaller, faster network with comparable performanceA popular way achieving such compression through quantization -training networks with lowprecision weights and/or activation functions In a quantized neural network each weight and/or activation can representable k bits with a possible codebook of negligible additional size compared the network itself For example in a binary neural network (k = the weights restricted be in {±1}. Compared a 32-bit single precision float a quantized net reduces the memory usage to k/32 of a full-precision net with the same architecture BID7 BID4 BID19 BID13 BID26 BID27 . In addition the structuredness the quantized weight matrix can often enable faster matrixvector product, thereby also accelerating inference BID13 .Typically , training a quantized network involves ( the design a quantizer q that maps a full-precision parameter a k-bit quantized parameter straightthrough gradient method BID4 that enables back-propagation from back onto, which critical the success quantized network training With quantizer q, an iterate of the straight-through gradient method (see FIG7 proceeds Code available https://github.com/allenbai01/ProxQuant. as �� t+1 = − �� ��L(�)| �=q(�t) , and q �) (for the converged ��) taken the output model For training binary networks choosing q(· = sign(· gives the BinaryConnect method BID4 .Though appealingly and empirically effective information-theoretically rather mysterious why the straight-through gradient method works well, at the binary case: while the goal find a parameter �� �� {±1 d with low loss the algorithm only has access stochastic gradients at {±1} d As this is a discrete set , a priori, gradients in this set do necessarily contain any information the function values Indeed a simple one-dimensional example (Figure 1b BinaryConnect fails find the minimizer of fairly simple convex Lipschitz functions in {±1}, due a lack gradient information in between.rL(q(��t DISPLAYFORM0 0 B N 6 N u 6 R + P F e F 2 O 5 o z V z j H 6 A e P t E 7 v e l p c = < / l a t e x i t > < s h a 1 _ b a s e 6 4 = "" k 8 o W Y E M 4 F 9 J U h g q 5 4 4 1 T N Q W 4 X m E = "" > A A A B / n i c d V D L S g M x F M 3 U V 6 2 v U X H l J l g E V 2 W m t e 1 0 V 3 D j s o J 9 Q K e U T C Z t Q z M P k j t C G Q r + i h s X i r j 1 O 9 z 5 N 2 b a C i p 6 I O R w z r 3 k 5 H i x 4 A o s 6 8 P I r a 1 v b G 7 l t w s 7 u 3 v 7 DISPLAYFORM1 q( a E H 9 I S e j X v j 0 X g x X h e l K 8 a y 5 w j 9 g P H 2 C a M i n A U = < / l a t e = "" DISPLAYFORM5 a M i n A U = < / l a t e x i > < s A U = < / l a t e x i t > rL(��t) < l a t e k M y 6 L o 8 X P y through method computes the gradient at the quantized vector and performs the update at the original real vector; PROXQUANT performs a gradient update followed a prox step which encourages quantizedness (b) A two-function toy failure case for BinaryConnect. The two functions are f1(x = |x + 0.5| − (blue − The derivatives f1 and f−1 coincide at {−1 1 so any algorithm only uses this information will have identical behaviors on these two functions However the minimizers in {±1} x 1 = −1 −1 1 the algorithm must fail on one them DISPLAYFORM8 DISPLAYFORM9 In this paper formulate the problem model quantization as a regularized learning problem and propose to with a proximal gradient method Our contributions are summarized as follows.• We present a unified framework defining regularization functionals that encourage binary, ternary, and multi-bit quantized parameters, through penalizing the distance to quantized sets (see Section For binary quantization the resulting regularizer a W -shaped non-smooth regularizer, shrinks parameters towards either −1 in the same way the L 1 norm regularization shrinks parameters 0.• We propose training quantized networks using PROXQUANT (Algorithm 1 -a stochastic proximal gradient method with a homotopy scheme Compared the straightthrough gradient method PROXQUANT has access additional gradient information at non-quantized points avoids the problem in FIG7 and its homotopy scheme prevents potential overshoot early the training (Section 3.2).• We demonstrate the effectiveness and flexibility through systematic experiments on (1) image classification with ResNetsSection (2) language modeling LSTMs The PROXQUANT method outperforms state results on binary quantization and is comparable with state on ternary and multi-bit quantization.• We perform a systematic theoretical study quantization algorithms , showing our (standard prox-gradient method converges stataionary points under mild smoothness assumptions (Section where as lazy prox-gradient method such BinaryRelax BID25 fails in general ( Further, we show BinaryConnect has a very stringent condition to converge to any fixed point (Section which we verify through a sign change experiment (Appendix C In this paper propose and experiment with the PROXQUANT method training quantized networks. Our results demonstrate PROXQUANT offers a powerful alternative the straightthrough gradient method and has theoretically better convergence properties For future work it would of propose alternative regularizers ternary and multi-bit PROXQUANT and experiment our method on larger tasks",0.02,0.5138864652554784
"Background: Statistical mechanics results (Dauphin et al. (2014); Choromanska et al. (2015)) suggest that local minima with high error are exponentially rare in high dimensions. However, to prove low error guarantees for Multilayer Neural Networks (MNNs), previous works so far required either a heavily modified MNN model or training method, strong assumptions on the labels (e.g., “near” linear separability), or an unrealistically wide hidden layer with \Omega\(N) units. 

 Results: We examine a MNN with one hidden layer of piecewise linear units, a single output, and a quadratic loss. We prove that, with high probability in the limit of N\rightarrow\infty datapoints, the volume of differentiable regions of the empiric loss containing sub-optimal differentiable local minima is exponentially vanishing in comparison with the same volume of global minima, given standard normal input of dimension d_0=\tilde{\Omega}(\sqrt{N}), and a more realistic number of d_1=\tilde{\Omega}(N/d_0) hidden units. We demonstrate our results numerically: for example, 0% binary classification training error on CIFAR with only N/d_0 = 16 hidden neurons. Motivation. Multilayer Neural Networks (MNNs), trained with simple variants of stochastic gradient descent (SGD), have achieved state-of-the-art performances in many areas of machine learning . However, theoretical explanations seem to lag far behind this empirical success (though many hardness results exist, e.g., BID44 BID42 ). For example, as a common rule-of-the-thumb, a MNN should have at least as many parameters as training samples. However, it is unclear why such over-parameterized MNNs often exhibit remarkably small generalization error (i.e., difference between ""training error"" and ""test error""), even without explicit regularization BID54 .Moreover , it has long been a mystery why MNNs often achieve low training error BID10 . SGD is only guaranteed to converge to critical points in which the gradient of the expected loss is zero BID3 , and, specifically, to local minima BID35 ) (this is true also for regular gradient descent BID29 ). Since loss functions parameterized by MNN weights are non-convex, it is unclear why does SGD often work well -rather than converging to sub-optimal local minima with high training error, which are known to exist BID16 BID50 . Understanding this behavior is especially relevant in important cases where SGD does get stuck BID20 ) -where training error may be a bottleneck in further improving performance.Ideally, we would like to quantify the probability to converge to a local minimum as a function of the error at this minimum, where the probability is taken with the respect to the randomness of the initialization of the weights, the data and SGD. Specifically, we would like to know, under which conditions this probability is very small if the error is high, as was observed empirically (e.g., BID10 BID17 ). However, this seems to be a daunting task for realistic MNNs, since it requires a characterization of the sizes and distributions of the basins of attraction for all local minima.Previous works BID10 BID7 , based on statistical physics analogies, suggested a simpler property of MNNs: that with high probability, local minima with high error diminish exponentially with the number of parameters. Though proving such a geometric property with realistic assumptions would not guarantee convergence to global minima, it appears to be a necessary first step in this direction (see discussion on section 6). It was therefore pointed out as an open problem at the Conference of Learning Theory (COLT) 2015. However, one has to be careful and use realistic MMN architectures, or this problem becomes ""too easy"".For example, one can easily achieve zero training error (Nilsson, 1965; BID2 -if the MNN's last hidden layer has more neurons than training samples. Such extremely wide MNNs are easy to optimize (Yu, 1992; BID23 BID31 BID19 BID43 Nguyen & Hein, 2017) . In this case, the hidden layer becomes linearly separable in classification tasks, with high probability over the random initialization of the weights. Thus, by training the last layer we get to a global minimum (zero training error). However, such extremely wide layers are not very useful, since they result in a huge number of weights, and serious overfitting issues. Also, training only the last layer seems to take little advantage of the inherently non-linear nature of MNNs.Therefore, in this paper we are interested to understand the properties of local and global minima, but at a more practical number of parameters -and when at least two weight layers are trained. For example, Alexnet BID27 is trained using about 1.2 million ImageNet examples, and has about 60 million parameters -16 million of these in the two last weight layers. Suppose we now train the last two weight layers in such an over-parameterized MNN. When do the sub-optimal local minima become exponentially rare in comparison to the global minima?Main contributions. We focus on MNNs with a single hidden layer and piecewise linear units, optimized using the Mean Square Error (MSE) in a supervised binary classification task (Section 2). We define N as the number of training samples, d l as the width of the l-th activation layer, and g (x)<h (x) as an asymptotic inequality in the leading order (formally: lim x→∞ log g(x)log h(x) < 1). We examine Differentiable Local Minima (DLMs) of the MSE: sub-optimal DLMs where at least a fraction of > 0 of the training samples are classified incorrectly, and global minima where all samples are classified correctly.Our main result, Theorem 10, states that, with high probability, the total volume of the differentiable regions of the MSE containing sub-optimal DLMs is exponentially vanishing in comparison to the same volume of global minima, given that: Assumption 1. The datapoints (MNN inputs) are sampled from a standard normal distribution. 4 N neurons. This improves over previously known results (Yu, 1992; BID23 BID31 BID43 Nguyen & Hein, 2017 ) -which require an extremely wide hidden layer with d 1 ≥ N neurons (and thus N d 0 parameters) to remove sub-optimal local minima with high probability.In section 5 we validate our results numerically. We show that indeed the training error becomes low when the number of parameters is close to N . For example, with binary classification on CIFAR and ImageNet, with only 16 and 105 hidden neurons (about N/d 0 ), respectively, we obtain less then 0.1% training error. Additionally, we find that convergence to non-differentiable critical points does not appear to be very common.Lastly, in section 6 we discuss our results might be extended, such as how to apply them to ""mildly"" non-differentiable critical points.Plausibility of assumptions. Assumption 1 is common in this type of analysis (Andoni et al. , 2014; BID7 BID53 BID51 BID4 . At first it may appear rather unrealistic, especially since the inputs are correlated in typical datasets. However, this no-correlation part of the assumption may seem more justified if we recall that datasets are many times whitened before being used as inputs. Alternatively, if, as in our motivating question, we consider the input to the our simple MNN to be the output of the previous layers of a deep MNN with fixed random weights, this also tends to de-correlate inputs (Poole et al., 2016, Figure 3) . The remaining part of assumption 1, that the distribution is normal , is indeed strong, but might be relaxed in the future, e.g. using central limit theorem type arguments.In assumption 2 we use this asymptotic limit to simplify our proofs and final results. Multiplicative constants and finite (yet large) N results can be found by inspection of the proofs. We assume a constant error since typically the limit → 0 is avoided to prevent overfitting.In assumption 3, for simplicity we have d 0≤ N , since in the case d 0 ≥ N the input is generically linearly separable, and sub-optimal local minima are not a problem BID18 BID39 . Additionally, we have √ N<d 0 , which seems very reasonable, since for example, d 0 /N ≈ 0.016, 0.061 and 0.055 MNIST, CIFAR and ImageNet, respectively.In assumption 4, for simplicity we have d 1< N , since, as mentioned earlier, if d 1 ≥ N the hidden layer is linearly separable with high probability, which removes sub-optimal local minima. The other bound N log 4 N<d 0 d 1 is our main innovation -a large over-parameterization which is nevertheless asymptotically mild and improves previous results.Previous work. So far, general low (training or test) error guarantees for MNNs could not be found -unless the underlying model (MNN) or learning method (SGD or its variants) have been significantly modified. For example, BID10 made an analogy with high-dimensional random Gaussian functions, local minima with high error are exponentially rare in high dimensions; BID7 BID25 replaced the units (activation functions) with independent random variables; BID36 replaces the weights and error residuals with independent random variables; (Baldi, 1989; BID40 BID20 BID32 BID57 used linear units; BID55 used unconventional units (e.g., polynomials) and very large hidden layers (d 1 = poly (d 0 ), typically N ); BID4 BID11 BID41 used a modified convnet model with less then d 0 parameters (therefore, not a universal approximator BID9 BID22 ); BID51 BID47 BID30 assume the weights are initialized very close to those of the teacher generating the labels; and BID24 BID56 ) use a non-standard tensor method during training. Such approaches fall short of explaining the widespread success of standard MNN models and training practices.Other works placed strong assumptions on the target functions. For example, to prove convergence of the training error near the global minimum, BID18 assumed linearly separable datasets, while BID39 assumed strong clustering of the targets (""near"" linear-separability). Also, (Andoni et al., 2014) showed a p-degree polynomial is learnable by a MNN, if the hidden layer is very large ( DISPLAYFORM0 , typically N ) so learning the last weight layer is sufficient. However, these are not the typical regimes in which MNNs are required or used. In contrast, we make no assumption on the target function. Other closely related results BID48 BID53 ) also used unrealistic assumptions, are discussed in section 6, in regards to the details of our main results. Therefore, in contrast to previous works, the assumptions in this paper are applicable in some situations (e.g., Gaussian input) where a MNN trained using SGD might be used and be useful (e.g., have a lower test error then a linear classier). In this paper we examine Differentiable Local Minima (DLMs) of the empiric loss of Multilayer Neural Networks (MNNs) with one hidden layer, scalar output, and LReLU nonlinearities (section 2). We prove (Theorem 10) that with high probability the angular volume (definition 3) of sub-optimal DLMs is exponentially vanishing in comparison to the angular volume of global minima (definition 4), under assumptions 1-4. This results from an upper bound on sub-optimal DLMs (Theorem 6) and a lower bound on global minima (Theorem 9). 2 /5 for 1000 epochs, then decreased the learning rate exponentially for another 1000 epochs. This was repeated 30 times. For all d and repeats, we see that (left) the final absolute value of the minimal neural input (i.e., min i,n w i x (n) ) in the range of 10 −3 − 10 0 , which is much larger then (right) the final MSE error for all d and all repeats -in the range 10 −31 − 10 −7 .Convergence of SGD to DLMs. These results suggest a mechanism through which low training error is obtained in such MNNs. However, they do not guarantee it. One issue is that sub-optimal DLMs may have exponentially large basins of attraction. We see two possible paths that might address this issue in future work, using additional assumptions on y. One approach is to show that, with high probability, no sub optimal DLM falls within the vanishingly small differentiable regions we bounded in Theorem 6. Another approach would be to bound the size of these basins of attraction, by showing that sufficiently large of number of differentiable regions near the DLM are also vanishingly small (other methods might also help here BID15 ). Another issue is that SGD might get stuck near differentiable saddle points, if their Hessian does not have strictly negative eigenvalues (i.e., the strict saddle property ). It should be straightforward to show that such points also have exponentially vanishing angular volume, similar to sub-optimal DLMs. Lastly, SGD might also converge to non-differentiable critical points, which we discuss next.Non-differentiable critical points. The proof of Theorem 6 stems from a first order necessary condition (Lemma 2): (A • X) e = 0, which is true for any DLM. However, non-differentiable critical points, in which some neural inputs are exactly zero, may also exist (though, numerically, they don't seem very common -see FIG1 .2). In this case, to derive a similar bound , we can replace the condition with P (A • X) e = 0, where P is a projection matrix to the subspace orthogonal to the non-differentiable directions. As long as there are not too many zero neural inputs, we should be able to obtain similar results. For example, if only a constant ratio r of the neural inputs are zero, we can simply choose P to remove all rows of (A • X) corresponding to those neurons, and proceed with exactly the same proof as before, with d 1 replaced with (1 − r) d 1 . It remains a theoretical challenge to find reasonable assumptions under which the number of non-differentiable directions (i.e., zero neural inputs) does not become too large.Related results. Two works have also derived related results using the (A • X) e = 0 condition from Lemma 2. In BID48 , it was noticed that an infinitesimal perturbation of A makes the matrix A • X full rank with probability 1 (Allman et al., 2009, Lemma 13 ) -which entails that e = 0 at all DLMs. Though a simple and intuitive approach, such an infinitesimal perturbation is problematic: from continuity, it cannot change the original MSE at sub-optimal DLMs -unless the weights go to infinity, or the DLM becomes non-differentiable -which are both undesirable results. An extension of this analysis was also done to constrain e using the singular values of A•X BID53 , deriving bounds that are easier to combine with generalization bounds. Though a promising approach, the size of the sub-optimal regions (where the error is high) does not vanish exponentially in the derived bounds. More importantly, these bounds require assumptions on the activation kernel spectrum γ m , which do not appear to hold in practice (e.g., BID53 , Theorems 1,3) require mγ m 1 to hold with high probability, while mγ m < 10 −2 in BID53 , FIG9 ).Modifications and extensions. There are many relatively simple extensions of these results: the Gaussian assumption could be relaxed to other near-isotropic distributions (e.g., sparse-land model, (Elad, 2010, Section 9 .2)) and other convex loss functions are possible instead of the quadratic loss. More challenging directions are extending our results to MNNs with multi-output and multiple hidden layers, or combining our training error results with novel generalization bounds which might be better suited for MNNs (e.g., BID14 BID46 BID12 ) than previous approaches BID54 .",3484,1.496,2054,1.6962025316455696,"Background Statistical mechanics results ( (2014 Choromanska et (2015)) suggest local minima with high error are exponentially rare high dimensions However to prove low error guarantees Multilayer Neural Networks previous works so required either a heavily modified MNN model training method strong assumptions the labelsnear�� linear separability an unrealistically wide hidden layer \Omega\(N Results We examine a MNN with one hidden layer piecewise linear units a single output We prove, high probability in the limit the volume differentiable regions the empiric loss containing sub-optimal differentiable local minima exponentially vanishing comparison given standard normal input dimension a more realistic number We demonstrate our results numerically: for 0 binary classification training error on with only N/d_0 16 hidden neurons Motivation. Multilayer Neural Networks trained simple variants achieved state performances . However theoretical explanations seem lag this empirical success (though many hardness results exist BID44 BID42 For example as a common rule- a MNN should training samples However such over-parameterized MNNs often exhibit remarkably small generalization error ""training error without explicit regularization BID54 .Moreover , long a mystery achieve low training error BID10 SGD only guaranteed converge critical points which the gradient the expected loss zero BID3 ,, specifically local minima BID35 )this true also regular gradient descent BID29 Since loss functions parameterized MNN weights non unclear does SGD often work -rather converging sub-optimal local minima with high training error are exist BID16 BID50 . Understanding this behavior especially important cases SGD get stuck BID20 ) -where training error a bottleneck further improving performanceIdeally quantify to converge a local minimum as at this minimum taken with the respect the initialization the data Specifically would under this probability very if the error high as was empirically BID10 BID17 However seems realistic MNNs a characterization the sizes distributions the basins attraction all local minimaPrevious works BID10 BID7 , based statistical physics analogies suggested a simpler property with high probability with high error diminish parameters Though proving such a geometric property with realistic assumptions guarantee convergence global minima appears ( discussion section It therefore pointed as an open problem at Learning TheoryCOLT 2015 However one has and use realistic MMN architectures this problem ""For achieve zero training errorNilsson 1965 BID2 -if the MNN's last hidden layer more neurons training samples. Such extremely wide MNNs easy optimize (Yu 1992 BID23 BID31 BID19 BID43 Nguyen & Hein 2017 . In the hidden layer becomes linearly classification tasks high probability over the random initialization Thus by training the last layer we get a global minimum (zero training error However such extremely wide layers very result weights serious overfitting issues Also training only the last layer seems take little advantage MNNsTherefore local and global minima but at a more practical number parameters -and when at least two weight layers trained For example Alexnet BID27 trained using about 1.2 million ImageNet examples about 60 million parameters -16 these in the two last weight layers Suppose now train the last two weight layers such an over-parameterized MNN When do the sub-optimal local minima exponentially rare comparison the global minima?Main contributions. We focus MNNs a single hidden layer piecewise linear units optimized using the Mean Square Error in a supervised binary classification taskSection We define N as training samples d l the l-th activation layer (x)<h the leading orderformally lim x→�� log g(x)log h(x < We examine Differentiable Local Minima the MSE sub-optimal DLMs where at least a fraction > 0 of classified incorrectly global minima whereOur main result, Theorem 10 high probability the total volume containing exponentially vanishing comparison given: Assumption (MNN inputs sampled 4 N neurons This improves over previously known resultsYu 1992 BID23 BID31 BID43 Nguyen & Hein 2017 ) -which require an extremely wide hidden layer with d 1 ≥ N neuronsand thus N d 0 parameters remove with high probabilityIn section validate numerically We show indeed the training error becomes low parameters close N . For example with binary classification on CIFAR ImageNet with only 16 and 105 hidden neuronsabout Nd 0 respectively obtain Additionally find convergence non-differentiable critical points does veryLastly section might extended, such how apply themPlausibility assumptions Assumption is common this typeAndoni , 2014 BID7 BID53 BID51 BID4 . At rather unrealistic especially the inputs correlated typical datasets However this no-correlation part the assumption seem more justified recall datasets many whitened inputs Alternatively, our motivating question consider the input the our simple MNN to the previous layers fixed random weights this also tends (Poole . The remaining part assumption that the distribution normal , indeed strong might relaxed using central limit theorem type argumentsIn assumption simplify our proofs final results Multiplicative constants finite (yet large N results inspection the proofs We assume a constant error since typically the limit → avoided to overfittingIn assumption 3 for simplicity d 0� N since in the input generically sub-optimal local minima BID18 BID39 Additionally � N<d 0 seems very for d /N � 0.055 MNIST, CIFAR ImageNetIn assumption for simplicity d< N, if ≥ the hidden layer high probability removes sub-optimal local minima The other bound N log 4 N<d 0 d is our main innovation -a large over-parameterization which nevertheless mild improves previous resultsPrevious work. So general low (training or test) error guarantees for MNNs could -unless or learning methodSGD or its variants have significantly For example BID10 made an analogy high-dimensional random Gaussian functions local minima with high error are exponentially rare high dimensions; BID7 BID25 replaced the units (activation functions independent random variables replaces error residuals (Baldi 1989 used linear units unconventional units ( very large hidden layersd 1 poly ( 0 typically N a modified convnet model less then d 0 parameterstherefore not assume initialized very those the teacher generating the labels ) during Such approaches fall explaining the widespread success standard MNN models training practicesOther works placed strong assumptions the target functions For example to prove convergence the training error near the global minimum BID18 assumed linearly separable datasets while strong clustering the targets (""near"" linear-separability Also (Andoni et a p-degree polynomial is learnable a MNN if the hidden layer very large ( DISPLAYFORM0 typically N ) so learning the last weight layer sufficient However these the typical regimes MNNs required or used In contrast we make no assumption on the target function Other closely related results BID48 BID53 ) also used unrealistic assumptions are discussed in regards the details our main results Therefore contrast previous works the assumptions applicable a MNN trained using SGD might and be useful have a lower test error then a linear classier In Differentiable Local Minima the empiric loss Multilayer Neural Networks one hidden layer scalar output LReLU nonlinearitiessection We prove (Theorem 10 with high probability the angular volumedefinition 3 sub-optimal DLMs exponentially vanishing in comparison global minima under assumptions 1 This results an upper bound sub-optimal DLMsTheorem 6 global minima 2 /5 for 1000 epochs then decreased the learning rate exponentially for This was repeated 30 For all d and repeats we see (left the final absolute value the minimal neural inputn w i x ( in 10 −3 − 10 which much then the final MSE error -in .Convergence SGD to DLMs a mechanism low training error obtained such MNNs guarantee it One issue sub-optimal DLMs exponentially large basins attraction We see two possible paths address future work using additional assumptions on y. One approach show, high probability no sub optimal DLM falls the vanishingly small differentiable regions we bounded 6 Another approach bound the size these basins of attraction showing sufficiently of number differentiable regions near the DLM also vanishinglyother methods help BID15 Another issue SGD might get near differentiable saddle points if their Hessian does strictly negative eigenvalues It should straightforward such points also exponentially vanishing angular volume similar sub-optimal DLMs Lastly SGD might converge non-differentiable critical points discuss next. The proof Theorem 6 stems a first order necessary condition (A • X e 0 any DLM However non-differentiable critical points in some neural inputs exactly zero exist (though numerically very common -see FIG1 .2 In to derive a similar bound , replace PA • X e a projection matrix to the non-differentiable directions As long not too many zero neural inputs obtain For example only a constant ratio r the neural inputs zero simply choose P remove all rows (A • X corresponding those neurons proceed exactly the same proof d 1 replaced d It remains a theoretical challenge reasonable assumptions under non-differentiable directions does become tooRelated results. Two works have also derived related results using the (A • X) e = 0 condition from Lemma In BID48 , it noticed A makes the matrix • X full rank with probabilityAllman, Lemma 13 ) -which entails e at all DLMs Though a simple and intuitive approach problematic: from continuity change the original MSE at the weights go are both undesirable results An extension this analysis also done constrain e using the singular values A•X BID53 , deriving bounds that easier combine generalization bounds Though a promising approach the size (where the error vanish exponentially the derived bounds More importantly these bounds require assumptions on the activation kernel spectrum �� m do appear hold practice BID53 , Theorems 1,3) require mγ m 1 hold with high probability < 10 −2 in BID53 , FIG9 ).Modifications and extensions. There many relatively simple extensions these results the Gaussian assumption could relaxed other near-isotropic distributions (Elad, 2010 Section .2 other convex loss functions instead More challenging directions extending our results MNNs multi-output and multiple hidden layers combining our training error results novel generalization bounds which might ( BID14 BID46 BID12 ) than BID54",0.02,0.47794205263109657
"Deep neural networks are vulnerable to adversarial examples, which can mislead classifiers by adding imperceptible perturbations. An intriguing property of adversarial examples is their good transferability, making black-box attacks feasible in real-world applications. Due to the threat of adversarial attacks, many methods have been proposed to improve the robustness, and several state-of-the-art defenses are shown to be robust against transferable adversarial examples. In this paper, we identify the attention shift phenomenon, which may hinder the transferability of adversarial examples to the defense models. It indicates that the defenses rely on different discriminative regions to make predictions compared with normally trained models. Therefore, we propose an attention-invariant attack method to generate more transferable adversarial examples. Extensive experiments on the ImageNet dataset validate the effectiveness of the proposed method. Our best attack fools eight state-of-the-art defenses at an 82% success rate on average based only on the transferability, demonstrating the insecurity of the defense techniques. Recent progress in machine learning and deep neural networks has led to substantial improvements in various pattern recognition tasks such as image understanding BID21 BID9 , speech recognition BID7 , and machine translation . However, deep neural networks are highly vulnerable to adversarial examples BID2 BID24 BID6 . They are maliciously generated by adding small perturbations to legitimate examples, but make deep neural networks produce unreasonable predictions. The existence of adversarial examples, even in the physical world BID11 BID5 BID1 , has raised concerns in security-sensitive applications, e.g., self-driving cars, healthcare and finance.Attacking deep neural networks has drawn an increasing attention since the generated adversarial examples can serve as a surrogate to evaluate the robustness of different models BID3 and help to improve the robustness BID6 BID16 . Several methods have been proposed to generate adversarial examples with the knowledge of the gradient information of a given model, such as fast gradient sign method BID6 , basic iterative method BID11 , and BID3 's method, which are known as white-box attacks. Moreover, it is shown that adversarial examples have cross-model transferability BID15 , i.e., the adversarial examples crafted for one model can fool a different model with a high probability. The transferability of adversarial examples enables practical black-box attacks to real-world applications and induces serious security issues.The threat of adversarial examples has motivated extensive research on building robust models or techniques to defend against adversarial attacks. These include training with adversarial examples BID6 BID12 BID27 BID16 , image denoising/transformation BID29 BID8 , leveraging generative models to move adversarial examples towards data manifold BID20 , and theoretically-certified defenses BID19 BID28 . Although the non-certified defenses have demonstrated robustness against common attacks, they do so by causing obfuscated gradients, which can be easily circumvented by new attacks BID0 . However, some of the defenses BID27 BID29 ; BID8 Figure 1: Demonstration of the attention shift phenomenon of the defense models compared with normally trained models. We adopt class activation mapping (Zhou et al., 2016) to visualize the attentive regions of three normally trained models-Inception v3 BID25 , Inception ResNet v2 BID26 , ResNet 152 BID9 and four defense models BID27 BID29 BID8 . These defense models focus their attention on slightly different regions compared with normally trained models, which may affect the transferability of adversarial examples. BID8 claim to be resistant to transferable adversarial examples, making black-box attacks difficult to evade these defenses.In this paper, we identify attention shift, that the defenses make predictions based on slightly different discriminative regions compared with normally trained models, as a phenomenon which may hinder the transferability of adversarial examples to the defense models. For example, we show the attention maps of several normally trained models and defense models in Fig. 1 , to represent the discriminative regions for their predictions. It is apparent that the normally trained models have similar attention maps while the defenses induce shifting attention maps. The attention shift of the defenses is caused by either training under different data distributions BID27 or transforming the inputs before classification BID29 BID8 . Therefore, the transferability of adversarial examples is largely reduced to the defenses since the structure information hidden in adversarial perturbations may be easily overlooked if a model focuses its attention on different regions.To mitigate the effect of attention shift and evade the defenses by transferable adversarial examples, we propose an attention-invariant attack method. In particular, we generate an adversarial example for an ensemble of examples composed of an legitimate one and its shifted versions. Therefore the resultant adversarial example is less sensitive to the attentive region of the white-box model being attacked and may have a bigger chance to fool another black-box model with a defense mechanism based on attention shift. We further show that this method can be simply implemented by convolving the gradient with a pre-defined kernel under a mild assumption. The proposed method can be integrated into any gradient-based attack methods such as fast gradient sign method and basic iterative method. Extensive experiments demonstrate that the proposed attention-invariant attack method helps to improve the success rates of black-box attacks against the defense models by a large margin. Our best attack reaches an average success rate of 82% to evade eight state-of-the-art defenses based only on the transferability, thus demonstrating the insecurity of the current defenses. In this paper, we propose an attention-invariant attack method to mitigate the attention shift phenomenon and generate more transferable adversarial examples against the defense models. Our method optimizes an adversarial image by using a set of shifted images. Based on an assumption, our method is simply implemented by convolving the gradient with a pre-defined kernel, and can be integrated into any gradient-based attack methods. We conduct experiments to validate the effectiveness of the proposed method. Our best attack A-DIM, the combination of the proposed attentioninvariant method and diverse input iterative method BID30 , can fool eight state-of-the-art defenses at an 82% success rate on average, where the adversarial examples are generated against four normally trained models. The results identify the vulnerability of the current defenses, which raises security issues for the development of more robust deep learning models.",1248,0.655,729,1.7119341563786008,"Deep neural networks vulnerable adversarial examples mislead classifiers adding An intriguing property adversarial examples their good transferability making black-box attacks feasible Due the threat adversarial attacks many methods improve, and several state defenses shown robust transferable adversarial examples In identify the attention shift phenomenon hinder the transferability adversarial examples the defense models It indicates the defenses rely different discriminative regions make predictions compared normally trained models Therefore an attention-invariant attack method generate more transferable adversarial examples Extensive experiments the ImageNet dataset validate Our best attack fools eight state defenses at on based only the transferability, demonstrating the insecurity the defense techniques Recent progress machine learning substantial improvements various pattern recognition tasks understanding BID21 BID9 , machine translation . However deep neural networks highly vulnerable adversarial examples BID2 BID24 BID6 . They maliciously generated adding small perturbations legitimate examples make deep neural networks produce unreasonable predictions The existence adversarial examples even BID11 BID5 , raised security-sensitive applications healthcare financeAttacking drawn serve a surrogate evaluate different models help improve Several methods generate adversarial examples with the knowledge the gradient information fast gradient sign method BID6 , basic white-box attacks Moreover shown adversarial examples cross-model transferability BID15 , crafted one model fool with The transferability adversarial examples enables practical black-box attacks inducesThe threat motivated building robust models or techniques defend These include training with adversarial examples BID6 BID12 BID27 BID16 , image denoising/transformation leveraging move towards data manifold theoretically-certified defenses Although the non-certified defenses demonstrated common attacks causing obfuscated gradients new attacks BID0 . However some the defenses BID27 BID29 ; BID8 Figure: Demonstration the attention shift phenomenon the defense models compared normally trained models We adopt class activation mappingZhou visualize the attentive regions three normally trained models-Inception v3 BID25 , ResNet 152 BID9 four defense models These defense models focus their attention slightly different regions compared normally trained models affect the transferability adversarial examples BID8 claim resistant transferable adversarial examples making black-box attacks evade these defensesIn identify attention shift that the defenses make predictions slightly different discriminative regions compared normally trained models a phenomenon hinder the defense models For example show the attention maps several normally trained models defense models Fig 1 , to represent the discriminative regions for their predictions It apparent the normally trained models similar attention maps while the defenses induce shifting attention maps The attention shift the defenses caused either training under different data distributions BID27 transforming the inputs before classification BID29 BID8 . Therefore the transferability adversarial examples largely reduced the defenses since the structure information hidden overlooked if a model focuses different regionsTo mitigate attention shift evade the defenses In particular generate an adversarial example an ensemble examples composed an legitimate one its shifted versions Therefore the resultant adversarial example less sensitive the attentive region being attacked may a bigger chance fool a defense mechanism based attention shift We further show this method simply convolving with under a mild assumption The proposed method can integrated any gradient-based attack methods fast gradient sign method basic iterative method Extensive experiments demonstrate the proposed attention-invariant attack method helps black-box attacks the defense models Our best attack reaches to evade eight state defenses based only the transferability, thus demonstrating the insecurity In mitigate the attention shift phenomenon generate more transferable adversarial examples against the defense models Our method optimizes an adversarial image shifted images Based an assumption our method simply implemented convolving with can integrated any gradient-based attack methods We conduct experiments validate the proposed method Our best attack A-DIM, the combination the proposed attentioninvariant method diverse input iterative method BID30 , fool eight state defenses at on where the adversarial examples generated against four normally trained models The results identify the vulnerability the current defenses raises the development more robust deep learning models",0.01,0.5180248502854239
"We present Merged-Averaged Classifiers via Hashing (MACH) for $K$-classification with large $K$. Compared to traditional one-vs-all classifiers that require $O(Kd)$ memory and inference cost, MACH only need $O(d\log{K})$ memory while only requiring $O(K\log{K} + d\log{K})$ operation for inference. MACH is the first generic $K$-classification algorithm, with provably theoretical guarantees, which requires $O(\log{K})$ memory without any assumption on the relationship between classes. MACH uses universal hashing to reduce classification with a large number of classes to few independent classification task with very small (constant) number of classes. We provide theoretical quantification of accuracy-memory tradeoff by showing the first connection between extreme classification and heavy hitters. With MACH we can train ODP dataset with 100,000 classes and 400,000 features on a single Titan X GPU (12GB), with the classification accuracy of 19.28\%, which is the best-reported accuracy on this dataset. Before this work, the best performing baseline is a one-vs-all classifier that requires 40 billion parameters (320 GB model size) and achieves 9\% accuracy.   In contrast, MACH can achieve 9\% accuracy with 480x reduction in the model size (of mere 0.6GB). With MACH, we also demonstrate complete training of fine-grained imagenet dataset (compressed size 104GB), with 21,000 classes, on a single GPU. We run MACH on these two datasets varying B and R. B and R are two knobs in MACH to balance resource and accuracy. We used plain logistic regression classifier, i.e., cross entropy loss without any regularization, in the Tensorflow environment BID0 . We plot the accuracy as a function of different values of B and R in FIG1 .The plots show that for ODP dataset MACH can even surpass OAA achieving 18% accuracy while the best-known accuracy on this partition is only 9%. LOMtree and Recall Tree can only achieve 6-6.5% accuracy. It should be noted that with 100,000 classes, a random accuracy is 10 −5 . Thus, the improvements are staggering with MACH. Even with B = 32 and R = 25, we can obtain more than 15% accuracy with 105,000 32×25 = 120 times reduction in the model size. Thus, OAA needs 160GB model size, while we only need around 1.2GB. To get the same accuracy as OAA, we only need R = 50 and B = 4, which is a 480x reduction in model size requiring mere 0.3GB model file.We believe that randomization and averaging in MACH cancel the noise and lead to better generalization. Another reason for the poor accuracy of other baselines could be due to the use of VW BID10 platforms. VW platform inherently uses feature hashing that may lose some information in features, which is critical for high dimensional datasets such as ODP.On Imagenet dataset, MACH can achieve around 11% which is roughly the same accuracy of LOMTree and Recall Tree while using R = 20 and B = 512. With R = 20 and B = 512 , the memory requirement is 21841 512×20 = 2 times less than that of OAA. On the contrary, Recall Tree and LOMTree use 2x more memory than OAA. OAA achieves the best result of 17%. With MACH, we can run at any memory budget.",752,0.413,432,1.7407407407407407,"We present Merged-Averaged Classifiers via HashingMACH $K$-classification large $K$. Compared traditional onevsall classifiers $O(Kd)$ memory and inference cost MACH only need while only requiring + for MACH is the first generic $K$-classification provably theoretical guarantees requires without classes MACH uses universal hashing classification with classes few independent classification task with We provide theoretical quantification accuracy-memory tradeoff showing the first connection extreme classification heavy hitters With MACH we train ODP dataset on a single Titan X GPU the classification accuracy 19.28\% Before this work the best performing baseline onevsall classifier requires 40 billion parameters320 GB model size achieves 9\% accuracy contrast MACH can achieve 9\% accuracy 480x reduction the model sizeof mere 0.6GB With MACH also demonstrate complete training fine-grained imagenet datasetcompressed size 104GB 21,000 classes on We run MACH on these two datasets varying B B and two knobs MACH to balance resource accuracy We used plain logistic regression classifier cross entropy loss without the Tensorflow environment BID0 . We plot the accuracy as different values B FIG1 .The plots ODP dataset MACH can even surpass OAA achieving while on this partition LOMtree and Recall Tree can only achieve should with 100,000 classes a random accuracy 10 −5 Thus the improvements staggering with MACH Even B = 32 25 obtain 105,000 32×25 120 times reduction the model size Thus OAA needs 160GB model size we To the same accuracy OAA only R = 50 a 480x reduction model size requiring mere 0.3GB model fileWe believe averaging MACH cancel the noise lead Another reason other baselines could VW BID10 platforms VW platform inherently feature hashing that may lose features critical high dimensional datasets ODP.On Imagenet dataset MACH which LOMTree and Recall Tree while R = B 512 With R = 512 the memory requirement 21841 512×20 times less that OAA On Recall Tree LOMTree use 2x OAA OAA achieves 17% With MACH run at any memory budget",0.0,0.5914214963213275
"Gradient-based optimization is the foundation of deep learning and reinforcement learning.
 Even when the mechanism being optimized is unknown or not differentiable, optimization using high-variance or biased gradient estimates is still often the best strategy. We introduce a general framework for learning low-variance, unbiased gradient estimators for black-box functions of random variables, based on gradients of a learned function.
 These estimators can be jointly trained with model parameters or policies, and are applicable in both discrete and continuous settings. We give unbiased, adaptive analogs of state-of-the-art reinforcement learning methods such as advantage actor-critic. We also demonstrate this framework for training discrete latent-variable models. Gradient-based optimization has been key to most recent advances in machine learning and reinforcement learning. The back-propagation algorithm BID21 , also known as reverse-mode automatic differentiation BID25 BID16 computes exact gradients of deterministic, differentiable objective functions. The reparameterization trick BID33 BID7 BID17 allows backpropagation to give unbiased, lowvariance estimates of gradients of expectations of continuous random variables. This has allowed effective stochastic optimization of large probabilistic latent-variable models.Unfortunately, there are many objective functions relevant to the machine learning community for which backpropagation cannot be applied. In reinforcement learning, for example, the function being optimized is unknown to the agent and is treated as a black box BID23 . Similarly, when fitting probabilistic models with discrete latent variables, discrete sampling operations create discontinuities giving the objective function zero gradient with respect to its parameters. Much recent work has been devoted to constructing gradient estimators for these situations. In reinforcement learning, advantage actor-critic methods BID27 give unbiased gradient estimates with reduced variance obtained by jointly optimizing the policy parameters with an estimate of the value function. In discrete latent-variable models, low-variance but biased gradient estimates can be given by continuous relaxations of discrete variables BID10 BID4 .A recent advance by BID30 used a continuous relaxation of discrete random variables to build an unbiased and lower-variance gradient estimator, and showed how to tune the free parameters of these relaxations to minimize the estimator's variance during training. We generalize the method of BID30 to learn a free-form control variate parameterized by a neural network. This gives a lower-variance, unbiased gradient estimator which can be applied to a wider variety of problems. Most notably, our method is applicable even when no continuous relaxation is available, as in reinforcement learning or black-box function optimization. In this work we synthesized and generalized several standard approaches for constructing gradient estimators. We proposed a generic gradient estimator that can be applied to expectations of known or black-box functions of discrete or continuous random variables, and adds little computational overhead. We also derived a simple extension to reinforcement learning in both discrete and continuous-action domains.Future applications of this method could include training models with hard attention or memory indexing BID36 . One could also apply our estimators to continuous latentvariable models whose likelihood is non-differentiable, such as a 3D rendering engine. Extensions to the reparameterization gradient estimator BID20 BID14 could also be applied to increase the scope of distributions that can be modeled.In the reinforcement learning setting, our method could be combined with other variance-reduction techniques such as generalized advantage estimation BID5 BID24 , or other optimization methods, such as KFAC BID35 . One could also train our control variate off-policy, as in Q-prop .",685,0.398,423,1.6193853427895981,"Gradient-based optimization Even the mechanism being optimized unknown differentiable optimization using high-variance or biased gradient estimates often We introduce a general framework learning low-variance, unbiased gradient estimators of gradients a learned function These estimators can jointly trained model parameters or policies applicable We give unbiased, adaptive analogs state reinforcement such advantage actor-critic. We also demonstrate this framework training discrete latent-variable models Gradient-based optimization has key most recent advances The back-propagation algorithm BID21 , also reverse-mode automatic differentiation BID25 BID16 computes exact gradients deterministic, differentiable objective functions reparameterization trick BID33 BID7 BID17 allows give unbiased, lowvariance estimates gradients expectations continuous random variables This has allowed effective stochastic optimizationUnfortunately many objective functions relevant for In reinforcement learning for the function being optimized unknown treated BID23 Similarly fitting probabilistic discrete latent variables discrete sampling operations create giving the objective function zero gradient with its parameters Much recent work constructing gradient estimators these situations In reinforcement learning advantage actor-critic methods BID27 give unbiased gradient estimates with reduced variance obtained jointly optimizing the policy parameters an estimate the value function In discrete latent-variable models but biased gradient estimates given continuous relaxations discrete variables BID10 BID4 .A recent advance by BID30 used build showed how tune the free parameters during We generalize the method BID30 learn a free-form control variate parameterized This gives a lower-variance, unbiased gradient estimator which problems Most notably our method applicable even no continuous relaxation reinforcement learning or black-box function optimization In this work synthesized generalized several standard approaches constructing gradient estimators We proposed a generic gradient estimator expectations known or black-box functions discrete or continuous random variables adds little computational overhead We also derived a simple extension reinforcement learning both discrete and continuous-action domainsFuture applications training models hard attention memory indexing BID36 . One could apply our estimators continuous latentvariable models whose likelihood nondifferentiable a 3D rendering engine Extensions the reparameterization gradient estimator BID20 BID14 could increase the scope distributions that modeledIn the reinforcement learning setting our method combined generalized advantage estimation BID5 BID24 KFAC BID35 One could train our control variate off-policy Q-prop .",0.0,0.28221860451049924
"Do GANS (Generative Adversarial Nets) actually learn the target distribution? The foundational paper of Goodfellow et al. (2014) suggested they do, if they were given sufficiently large deep nets, sample size, and computation time. A recent theoretical analysis in Arora et al. (2017) raised doubts whether the same holds when discriminator has bounded size. It showed that the training objective can approach its optimum value even if the generated distribution has very low support. In other words, the training objective is unable to prevent mode collapse. The current paper makes two contributions. (1) It proposes a novel test for estimating support size using the birthday paradox of discrete probability. Using this  evidence is presented that well-known GANs approaches do learn distributions of fairly low support.   (2) It theoretically studies encoder-decoder GANs architectures (e.g., BiGAN/ALI), which were proposed to learn more meaningful features via GANs, and consequently to also solve the mode-collapse issue. Our result shows that such encoder-decoder training objectives also cannot guarantee learning of the full distribution because they cannot prevent serious mode collapse. More seriously, they cannot prevent learning meaningless codes for data, contrary to usual intuition. From the earliest papers on Generative Adversarial Networks the question has been raised whether or not they actually come close to learning the distribution they are trained with (henceforth refered to as the target distribution)? These methods train a generator deep net that converts a random seed into a realistic-looking image. Concurrently they train a discriminator deep net to discriminate between its output and real images, which in turn is used to produce gradient feedback to improve the generator net. In practice the generator deep net starts producing realistic outputs by the end, and the objective approaches its optimal value. But does this mean the deep net has learnt the target distribution of real images? Standard analysis introduced in BID3 shows that given ""sufficiently large"" generator and discriminator, sample size, and computation time the training does succeed in learning the underlying distribution arbitrarily closely (measured in JensenShannon divergence). But this does not settle the question of what happens with realistic sample and net sizes.Note that GANs differ from many previous methods for learning distributions in that they do not provide an estimate of a measure of distributional fit -e.g., perplexity score. Therefore researchers have probed their performance using surrogate qualitative tests, which were usually designed to rule out the most obvious failure mode of the training, namely, that the GAN has simply memorized the training data. One test checks the similarity of each generated image to the nearest images in the training set. Another takes two random seeds s 1 , s 2 that produced realistic images and checks the images produced using seeds lying on the line joining s 1 , s 2 . If such ""interpolating"" images are reasonable and original as well, then this may be taken as evidence that the generated distribution has many novel images. Yet other tests check for existence of semantically meaningful directions in the latent space, meaning that varying the seed along these directions leads to predictable changes e.g., (in case of images of human faces) changes in facial hair, or pose. A recent test proposed by BID12 checks the log-likelihoods of GANs using Annealed Importance Sampling, whose results indicate the mismatch between generator's distribution and the target distribution. BID8 proposed a method to trade-off between sample quality and sample diversity but they don't provide a clear definition or a quantitative metric of sample diversity.Recently a new theoretical analysis of GANs with finite sample sizes and finite discriminator size revealed the possibility that training objective can sometimes approach optimality even if the generator is far from having actually learnt the distribution. Specifically, if the discriminator has size p, then the training objective could be close to optimal even though the output distribution is supported on only O(p log p/ 2 ) images. By contrast one imagines that the target distribution usually must have very large support. For example, the set of all possible images of human faces (a frequent setting in GANs work) must involve all combinations of hair color/style, facial features, complexion, expression, pose, lighting, race, etc., and thus the possible set of images of faces approaches infinity. The above paper raises the possibility that the discriminator may be unable to meaningfully distinguish such a diverse target distribution from a trained distribution with fairly small support. Furthermore, the paper notes that this failure mode is different from the one usually feared, namely the generator memorizing training samples. The analysis of raises the possibility that the trained distribution has small support, and yet all its samples could be completely disjoint from the training samples.However, the above analysis was only a theoretical one, exhibiting a particular near-equilibrium solution that can happen from certain hyper-parameter combinations. It left open the possibility that real-life GANs training avoids such solutions thanks to some not-as-yet-understood property of SGD, or hyper-parameter choices. Thus further experimental investigation seems necessary. And yet it seems difficult at first sight to do such an empirical evaluation of the support size of a distribution: it is not humanly possible to go through hundreds of thousands of images, whereas automated tests of image similarity can be thrown off by small changes in lighting, pose etc.The current paper makes two important contributions. On the empirical side it introduces a new test for the support size of the trained distribution, and uses it to find that unfortunately these mode collapse problems do arise in many well-regarded GAN training methods. On the theoretical side we prove the limitations of encoder-decoder frameworks like BiGAN BID1 and Adversarially Learned Inference or ALI BID2 , which, inspired by autoencoder models, require the setup to learn an inference mechanism as well as a generative mechanism. The result of applies only to standard GAN training objectives (including JS and Wasserstein), but not to encoder-decoder setups. The clear hope in defining encoder-decoder setups is that the encoding mechanism ""inverts"" the generator and thus forces the generator to learn meaningful featurizations of data that are useful in downstream applications. In fact it has often been proposed that this need to learn meaningful featurizations will also solve the mode collapse problem: BID2 provide experiments on 2-dimensional mixtures of Gaussians suggesting this phenomenon. Our analysis shows not only that encoder-decoder training objectives cannot avoid mode collapse, but that they also cannot enforce learning of meaningful codes/features. The paper reveals gaps in current thinking about GANs, and hopes to stimulate further theoretical and empirical study. GANs research has always struggled with the issue of mode collapse, and recent theoretical analysis of shows that the GANs training objective is not capable of preventing mode collapse. This exhibits the existence of bad solutions in the optimization landscape. This in itself is not definitive, since existence of bad solutions is also known for the more traditional classification tasks , where heldout sets can nevertheless prove that a good solution has been reached. The difference in case of GANs is lack of an obvious way to establish that training succeeded.Our new Birthday Paradox test gives a new benchmark for testing the support size (i.e., diversity of images) in a distribution. Though it may appear weak, experiments using this test suggest that current GANs approaches, specifically, the ones that produce images of higher visual quality, do suffer mode collapse. Our rough experiments also suggest -again in line with the previous theoretical analysis-that the size of the distribution's support scales near-linearly with discriminator capacity.Researchers have raised the possibility that the best use of GANs is not distribution learning but feature learning. Encoder-decoder GAN architectures seem promising since they try to force the generator to use ""meaningful"" encodings of the image. While such architectures do exhibit slightly better diversity in our experiments, our theoretical result suggest that the the encoder-decoder objective is also unable to avoid mode collapse, furthermore, also fails to guarantee meaningful codes.",1608,0.881,938,1.7142857142857142,"Do GANS (Generative Adversarial Nets actually learn the target distribution The foundational paper Goodfellow (2014 suggested they, if given sufficiently large deep nets sample size computation time A recent theoretical analysis in Arora et (2017 raised doubts whether same holds when discriminator has bounded size It showed the training objective can approach even the generated distribution very low support In the training objective unable prevent mode collapse The current paper makes two contributions (1 It proposes a novel test estimating support size the birthday paradox discrete probability Using this evidence presented well-known GANs approaches learn distributions fairly low support (2 It theoretically studies encoder GANs architectures were learn more meaningful features via consequently also solve the mode-collapse issue Our result such encoder-decoder training objectives also guarantee learning the full distribution because prevent serious mode collapse More seriously prevent learning meaningless codes data contrary usual intuition From the earliest papers the question actually come learning the distribution they trained with refered These methods train a generator deep net converts Concurrently they train a discriminator deep net discriminate its output and real images produce gradient feedback the generator net In practice the generator deep net starts producing realistic outputs by, the objective approaches its optimal value But does the deep net learnt the target distribution real images Standard analysis introduced BID3 shows given ""sufficiently large"" generator and discriminator sample size computation the training does succeed learning the underlying distribution arbitrarily closely JensenShannon divergence But does settle realistic sample and net sizesNote GANs differ many previous methods learning distributions provide a measure distributional fit perplexity score Therefore researchers their performance surrogate qualitative tests usually rule the most obvious failure mode the GAN has simply memorized One test checks the similarity each generated image the nearest images Another takes two random seeds s 1 , that produced realistic images checks produced seeds lying joining If such ""interpolating"" images reasonable original as may taken the generated distribution many novel images Yet other tests check existence semantically meaningful directions the latent space meaning varying the seed along leads predictable changes (in case images changes facial hair pose A recent test proposed BID12 checks GANs Annealed Importance Sampling whose results the mismatch generator's distribution BID8 proposed trade-off sample quality sample diversity but they doRecently GANs with finite discriminator size revealed training objective can sometimes approach optimality even the generator far having actually learnt Specifically the discriminator size p the training objective could close optimal even the output distribution supported on only O(p log 2 images By contrast one imagines the target distribution usually must very large support For example the set all possible imagesa frequent setting GANs work must involve all combinations hair color/style complexion expression pose lighting race approaches infinity The above paper raises the discriminator unable meaningfully such a diverse target distribution a trained distribution fairly small support Furthermore this failure mode different usually feared namely the generator memorizing training samples The analysis raises the trained distribution has small support yet all its samples could completelyHowever exhibiting happen from certain hyper-parameter combinations It left open real-life GANs training avoids such solutions thanks SGD hyper-parameter choices Thus further experimental investigation seems And difficult at do such an empirical evaluation the support size a distribution: humanly go images whereas automated tests image similarity thrown lighting pose etcThe current paper makes On the empirical side it introduces the support size the trained distribution uses unfortunately these mode collapse problems arise many well-regarded GAN training methods On the theoretical side we prove the limitations BiGAN BID1 Adversarially Learned or ,, inspired require the setup to learn an inference mechanism as The result applies only standard GAN training objectives JS Wasserstein encoder-decoder setups The clear hope defining encoder-decoder setups the encoding mechanism ""inverts the generator forces learn meaningful featurizations useful downstream applications In fact it often proposed need learn meaningful featurizations also solve the mode collapse problem BID2 provide experiments Gaussians suggesting this phenomenon Our analysis not only that encoder-decoder training objectives avoid mode collapse enforce learning meaningful codes/ The paper reveals gaps current thinking GANs hopes stimulate GANs research always struggled mode collapse recent theoretical analysis shows the GANs training objective capable preventing This exhibits the existence bad solutions the optimization landscape This in definitive existence bad solutions also the more traditional classification tasks , heldout sets nevertheless prove that The difference case GANs lack an obvious way establish training succeededOur new Birthday Paradox test gives testing the support size images a distribution Though weak experiments this test current GANs approaches, specifically the ones produce images higher visual quality suffer mode collapse Our rough experiments also -again in line- the distribution's support scales nearlinearly discriminator capacityResearchers raised the best use GANs distribution learning feature Encoder-decoder GAN architectures seem promising since try force the generator While such architectures do exhibit slightly better diversity our experiments our theoretical result suggest the the encoder-decoder objective unable avoid mode collapse furthermore also fails guarantee meaningful codes",0.01,0.5240164132271301
"Due to their complex nature, it is hard to characterize the ways in which machine learning models can misbehave or be exploited when deployed. Recent work on adversarial examples, i.e. inputs with minor perturbations that result in substantially different model predictions, is helpful in evaluating the robustness of these models by exposing the adversarial scenarios where they fail. However, these malicious perturbations are often unnatural, not semantically meaningful, and not applicable to complicated domains such as language. In this paper, we propose a framework to generate natural and legible adversarial examples that lie on the data manifold, by searching in semantic space of dense and continuous data representation, utilizing the recent advances in generative adversarial networks. We present generated adversaries to demonstrate the potential of the proposed approach for black-box classifiers for a wide range of applications such as image classification, textual entailment, and machine translation. We include experiments to show that the generated adversaries are natural, legible to humans, and useful in evaluating and analyzing black-box classifiers. With the impressive success and extensive use of machine learning models in various securitysensitive applications, it has become crucial to study vulnerabilities in these systems. BID7 show that adversarial manipulations of input data often result in incorrect predictions from classifiers. This raises serious concerns regarding the security and integrity of existing machine learning algorithms, especially when even state-of-the-art models including deep neural networks have been shown to be highly vulnerable to adversarial attacks with intentionally worst-case perturbations to the input BID28 BID10 BID16 BID22 BID17 . These adversaries are generated effectively with access to the gradients of target models, resulting in much higher successful attack rates than data perturbed by random noise of even larger magnitude. Further, training models by including such adversaries can provide machine learning models with additional regularization benefits BID10 .Although these adversarial examples expose ""blind spots"" in machine learning models, they are unnatural, i.e. these worst-case perturbed instances are not ones the classifier is likely to face when deployed. Due to this , it is difficult to gain helpful insights into the fundamental decision behavior inside the black-box classifier: why is the decision different for the adversary, what can we change in order to prevent this behavior, and is the classifier robust to natural variations in the data when not in an adversarial scenario? Moreover, there is often a mismatch between the input space and the semantic space that we can understand. Changes to the input we may not think meaningful, like slight rotation or translation in images, often lead to substantial differences in the input instance. For example , BID24 show that minimal changes in the lighting conditions can fool automated-driving systems, a behavior adversarial examples are unable to discover. Due to the unnatural perturbations, these approaches cannot be applied to complex domains such as language, in which enforcing grammar and semantic similarity is difficult when perturbing instances. Therefore, existing approaches that find adversarial examples for text often result in ungrammatical sentences, as in the examples generated by BID19 , or require manual intervention, as in BID14 .In this paper , we introduce a framework to generate natural adversarial examples, i.e. instances that are meaningfully similar, valid/legible, and helpful for interpretation. The primary intuition Given an instance (a), existing FGSM approach BID10 adds small perturbations in (b) , that change the prediction of the model (to be ""2"", in this case).Instead of such random-looking noise, our framework generates natural adversarial examples, such as in (e), where the differences, shown in (d) (with blue/+, red/-), are meaningful changes to the strokes.behind our proposed approach is to perform the search for adversaries in a dense and continuous representation of the data instead of searching in the input data space directly. We use generative adversarial networks (GANs) to learn a projection to map normally distributed fixed-length vectors to data instances. Given an input instance, we search for adversaries in the neighborhood of its corresponding representation in latent space by sampling within a range that is recursively tightened. FIG0 provides an example of adversaries for digit recognition. Given a multi-layer perceptron (MLP) for MNIST and an image from test data FIG0 ), our approach generates a natural adversarial example ( FIG0 ) which is classified incorrectly as ""2"" by the classifier. Compared to the adversary generated by the existing Fast Gradient Sign Method (FGSM) BID10 that adds gradient-based noise FIG0 , our adversary ( FIG0 ) looks like a hand-written digit similar to the original input. Further, the difference ( FIG0 ) provides some insight into the classifier's behavior, such as the fact that slightly thickening (blue) the bottom stroke and thinning (red) the one above it, fools the classifier.We apply our approach to both image and text domains, and generate adversaries that are more natural and grammatical, semantically close to the input, and helpful to interpret the local behavior of black-box models. We present examples of natural adversaries for image classification, textual entailment, and machine translation. Experiments and human evaluation also demonstrate that our approach can help evaluate the robustness of black-box classifiers, even without labeled training data. Our framework builds upon GANs as the generative models, and thus the capabilities of GANs directly effects the quality of generated examples. In visual domains, although there have been lots of appealing results produced by GANs, the training is well known to be brittle. Many recent approaches address how to improve the training stability and the objective function of GANs BID27 . BID11 further improve the training of WGAN with regularization of gradient penalty instead of weight clipping. In our practice, we observe that we need to carefully balance the capacities of the generator, the critic, and the inverter that we introduced, to avoid situations such as model collapse. For natural languages, because of the discrete nature and non-differentiability, applications related to text generation have been relatively less studied. BID31 propose to incorporate a discrete structure autoencoder with continuous code space regularized by WGAN for text generation. Given that there are some concerns about whether GANs actually learn the distribution BID3 , it is worth noting that we can also incorporate other generative models such as Variational Auto-Encoders (VAEs) (Kingma & Welling, 2014) into our framework, as used in BID13 to generate text with controllable attributes, which we will explore in the future. We focus on GANs because adversarial training often results in higher quality images, while VAEs tend to produce blurrier ones BID8 . We also plan to apply the fusion and variant of VAEs and GANs such as α-GAN in BID26 and Wasserstein Auto-Encoders in BID29 . Note that as more advanced GANs are introduced to address these issues, they can be directly incorporated into our framework.Our iterative stochastic search algorithm for identifying adversaries is computationally expensive since it is based on naive sampling and local-search. Search based on gradients such as FGSM are not applicable to our setup because of black-box classifiers and discrete domain applications. We improve the efficiency with hybrid shrinking search by using a coarse-to-fine strategy that finds the upper-bounds by using fewer samples, and then performs finer search in the restricted range. We observe around 4× speedup with this search while achieving similar results as the iterative search. The accuracy of our inverter mapping the input to its corresponding dense vector in latent space is also important for searching adversaries in the right neighborhood. In our experiments, we find that fine-tuning the latent vector produced by the inverter with a fixed GAN can further refine the generated adversarial examples, and we will investigate other such extensions of the search in future.There is an implicit assumption in this work that the generated samples are within the same class if the added perturbations are small enough, and the generated samples look as if they belong to different classes when the perturbations are large. However, note that it is also the case for FGSM and other such approaches: when their is small, the noise is imperceptible; but with a large , one often finds noisy instances that might be in a different class (see TAB0 , digit 8 for an example). While we do observe this behavior in some cases, the corresponding classifiers require much more substantial changes to the input, which is why we can utilize our approach to evaluate black-box classifiers. In this paper, we propose a framework for generating natural adversaries against black-box classifiers, and apply the same approach to both visual and textual domains. We obtain adversaries that are legible, grammatical, and meaningfully similar to the input. We show that these natural adversaries can help in interpreting the decision behavior and evaluating the accuracy of black-box classifiers even in absence of labeled training data. We use our approach, built upon recent work in GANs, to generate adversaries for a wide range of applications including image classification, textual entailment, and machine translation (via the Google Translate API). Code used to generate such natural adversaries is available at https://github.com/zhengliz/natural-adversary.",1862,0.868,1096,1.698905109489051,"Due their complex nature it characterize the ways machine learning models misbehave exploited when deployed Recent work adversarial examples inputs with minor perturbations result substantially different model predictions helpful evaluating by exposing where fail However these malicious perturbations often unnatural not semantically meaningful not applicable complicated domains language In generate natural and legible adversarial examples lie data manifold by searching in semantic space of dense and continuous data representation utilizing We present generated adversaries demonstrate the proposed approach black-box classifiers applications such textual entailment We include experiments the generated adversaries natural legible to useful evaluating analyzing black-box classifiers With the impressive success and extensive use machine learning models various securitysensitive applications crucial study vulnerabilities BID7 show adversarial manipulations input data often incorrect predictions from classifiers This raises regarding existing machine learning even state including shown with intentionally worst-case perturbations the input BID28 BID10 BID16 BID22 BID17 . These adversaries generated effectively with access the gradients target models resulting much higher successful attack rates data perturbed of even larger magnitude Further training models by including such adversaries can machine learning models additional regularization benefits BID10 .Although these adversarial examples expose ""blind spots unnatural these worst-case perturbed instances ones face when deployed Due this , difficult gain helpful insights the fundamental decision behavior inside: why the decision different the adversary what can change is robust natural variations when not Moreover often the input space understand Changes the input we may not think meaningful like slight rotation translation in images often substantial differences the input instance For example , BID24 show minimal changes the lighting conditions fool automated-driving systems a behavior adversarial examples unable discover Due the unnatural perturbations, these approaches complex domains language in enforcing grammar semantic similarity when instances Therefore existing approaches that find adversarial examples text often result ungrammatical sentences as generated BID19 , require manual intervention , instances meaningfully valid/legible helpful interpretation The primary intuition Given an instance ( existing FGSM approach BID10 adds ( , that change the predictionto ""2 this case).Instead such random-looking noise our framework generates natural adversarial examples the differences, shownwith blue/+, red/- meaningful changes the strokes.behind our proposed approach perform the search adversaries a dense and continuous representation instead searching in directly We use generative adversarial networks learn a projection to map normally distributed fixed-length vectors data instances Given an input instance search adversaries the neighborhood its corresponding representation latent space by sampling within that tightened FIG0 provides adversaries for digit recognition Given a multi-layer perceptronMLP MNIST an image from test data FIG0 our approach generates a natural adversarial example FIG0 classified incorrectly2 Compared the adversary generated the existing Fast Gradient Sign MethodFGSM BID10 that adds FIG0 , our adversary ( FIG0 looks a hand-written digit similar the original input Further the difference ( FIG0 provides slightly thickeningblue the bottom stroke and the one foolsWe apply our approach both image text domains generate adversaries natural grammatical semantically close helpful interpret the local behavior black-box models We present examples natural adversaries for image classification textual entailment machine translation Experiments human evaluation also demonstrate our approach evaluate black-box classifiers even without labeled training data Our framework builds GANs as the generative models, thus the capabilities directly effects generated examples In visual domains although lots appealing results produced GANs the training is well brittle Many recent approaches address how improve the training stability the objective function GANs BID27 . BID11 further improve the training WGAN with regularization gradient penalty instead weight clipping In our practice observe we need carefully balance the capacities the generator the critic that introduced situations such model collapse For natural languages because the discrete nature and nondifferentiability, applications related text generation have relatively less studied BID31 propose incorporate a discrete structure autoencoder continuous code space regularized WGAN for text generation Given some concerns whether GANs actually learn the distribution BID3 , incorporate other generative models Variational Auto-Encoders (Kingma Welling used BID13 to text controllable attributes We focus GANs because adversarial training often higher quality images while VAEs blurrier ones BID8 . We also plan apply the fusion and variant of VAEs GANs such α-GAN in BID26 Wasserstein Auto-Encoders . Note as more advanced GANs address directly incorporated our frameworkOur iterative stochastic search algorithm for identifying adversaries computationally since naive sampling local-search Search based gradients such FGSM are applicable our setup because black-box classifiers discrete domain applications We improve with hybrid shrinking search a coarse-to-fine strategy finds the upper-bounds by fewer samples performs finer search the restricted range We observe around 4× speedup with this search while achieving The accuracy inverter mapping the input its corresponding dense vector latent space also searching adversaries the right neighborhood In our experiments find fine the latent vector produced the inverter with a fixed GAN can further refine the generated adversarial examples will investigate other such extensions the searchThere the generated samples within if look belong when However note for FGSM other such approaches: when their is small the noise but with a large , one often noisy instances that might in a different class TAB0 , digit 8 While do observe the corresponding classifiers require much more substantial changes, can utilize our approach evaluate In generating natural adversaries against apply both visual and textual domains We obtain adversaries legible grammatical meaningfully similar the input We show these natural adversaries help in interpreting the decision behavior evaluating black-box classifiers even absence labeled training data We use our approach, built recent work GANs generate adversaries image classification textual entailmentvia Code used such natural adversaries",0.01,0.4848279835303943
"Kronecker-factor Approximate Curvature (Martens & Grosse, 2015) (K-FAC) is a 2nd-order optimization method which has been shown to give state-of-the-art performance on large-scale neural network optimization tasks (Ba et al., 2017).   It is based on an approximation to the Fisher information matrix (FIM) that makes assumptions about the particular structure of the network and the way it is parameterized. The original K-FAC method was applicable only to fully-connected networks, although it has been recently extended by Grosse & Martens (2016) to handle convolutional networks as well. In this work we extend the method to handle RNNs by introducing a novel approximation to the FIM for RNNs. This approximation works by modelling the covariance structure between the gradient contributions at different time-steps using a chain-structured linear Gaussian graphical model, summing the various cross-covariances, and computing the inverse in closed form. We demonstrate in experiments that our method significantly outperforms general purpose state-of-the-art optimizers like SGD with momentum and Adam on several challenging RNN training tasks. As neural networks have become ubiquitous in both research and applications the need to efficiently train has never been greater. The main workhorses for neural net optimization are stochastic gradient descent (SGD) with momentum and various 2nd-order optimizers that use diagonal curvature-matrix approximations, such as RMSprop BID32 and Adam BID1 . While the latter are typically easier to tune and work better out of the box, they unfortunately only offer marginal performance improvements over well-tuned SGD on most problems.Because modern neural networks have many millions of parameters it is computationally too expensive to compute and invert an entire curvature matrix and so approximations are required. While early work on non-diagonal curvature matrix approximations such as TONGA BID17 and the Hessian-free (HF) approach BID20 BID21 BID4 BID30 demonstrated the potential of such methods, they never achieved wide adoption due to issues of scalability (to large models in the case of the former, and large datasets in the case of the latter).Motivated in part by these older results and by the more recent success of centering and normalization methods (e.g. BID31 BID34 BID15 a new family of methods has emerged that are based on non-diagonal curvature matrix approximations the rely on the special structure of neural networks. Such methods , which include Kronecker-factored approximated curvature (K-FAC) BID24 , Natural Neural Nets BID5 , Practical Riemannian Neural Networks BID18 , and others BID29 , have achieved state-of-the-art optimization performance on various challenging neural network training tasks and benchmarks.While the original K-FAC method is applicable only to standard feed-forward networks with fully connected layers, it has recently been extended to handle convolutional networks BID8 through the introduction of the ""Kronecker Factors for Convolution"" (KFC) approximation. BID2 later developed a distributed asynchronous version which proposed additional approximations to handle very large hidden layers.In this work we develop a new family of curvature matrix approximations for recurrent neural networks (RNNs) within the same design space. As in the original K-FAC approximation and the KFC approximation, we focus on the Fisher information matrix (a popular choice of curvature matrix), and show how it can be approximated in different ways through the adoption of various approximating assumptions on the statistics of the network's gradients. Our main novel technical contribution is an approximation which uses a chain-structured linear Gaussian graphical model to describe the statistical relationship between gradient contributions coming from different time-steps. Somewhat remarkably, it is possible to sum the required cross-moments to obtain a Fisher approximations which has enough special algebraic structure that it can still be efficiently inverted. In experiments we demonstrate the usefulness of our approximations on several challenging RNN training tasks. We have presented a new family of approximations to the Fisher information matrix of recurrent neural networks (RNNs), extending previous work on Kronecker-factored approximations. With this contribution, recurrent networks can now finally be trained with the K-FAC optimization method. We have demonstrated that our new approximations substantially reduce the required number of iterations for convergence vs standard baseline optimizers on several realistic tasks. And we have also shown that in a modern distributed training setup this results in a substantial savings in wallclock time as well.Jason Weston, Sumit Chopra, and Antoine Bordes. A SUPPLEMENTARY COMPUTATIONS A.1 PROOFS FOR SECTION 3.5.1Proposition 1 GivenF DISPLAYFORM0 , which can be seen as follows: DISPLAYFORM1 And using DISPLAYFORM2 Setting d = 1 and multiplying both sides by V 0 (which is assumed to be invertible) one can also derive the following simple formula for Ψ: DISPLAYFORM3 To proceed from here we define a ""transformed"" version of the original chain-structured linearGaussian graphical model whose variables areŵ t = V −1/2 0 w t . (Here we assume that V 0 is invertible -it is symmetric by definition.) All quantities related to the original model have their analogues in the transformed model, which we indicate with the hat symbol·.In the transformed model the 2nd-order moments of theŵ t 's are given bŷ DISPLAYFORM4 We observe thatV 0 = I.Analogously to the original model, the transformed version obeyŝ DISPLAYFORM5 =V 1 (usingV 0 = I). This can be seen by noting that DISPLAYFORM6 It also remains true that the spectral radius ofΨ is less than 1, which can be seen in at least one of two ways: by noticing that the transformed model is well-defined in the infinite limit if and only if the original one is, or thatΨ DISPLAYFORM7 is a similar matrix to Ψ (in the technical sense) and hence has the same eigenvalues.As the transformed model is isomorphic to the original one, all of the previously derived relationships which held for it also hold here, simply by replacing each quantity with its transformed version (denoted by the hat symbol·).Given these relations (included the transformed analogue of equation 5) we can expressF T aŝ DISPLAYFORM8 It is a well-known fact that one can evaluate rational functions, and functions that are the limiting values of sequences of rational functions, with matrix arguments. This is done by replacing scalar multiplication with matrix multiplication, division with matrix inversion, and scalar constants with scalar multiples of the identity matrix, etc. Note that because sums of powers and inverses of matrices are co-diagonalizable/commutative when the matrices themselves are, there is no issue of ambiguity caused by mixing commutative and non-commutative algebra in this way.Moreover, the value of some such function f (x), given a matrix argument B, is DISPLAYFORM9 DISPLAYFORM10 undefined from some i, either because of a division by zero, or because the limit which defines f (x) doesn't converge for x = [b] i , then f (B) doesn't exist for that particular B (and otherwise it does).We observe that our above expression for F T can be rewritten aŝ DISPLAYFORM11 By Proposition 3 in Appendix B.1, we have for x = 1 that DISPLAYFORM12 Let U diag(ψ)U −1 =Ψ be the eigendecomposition ofΨ. BecauseΨ has a spectral radius less than 1, we have |[ψ] i | < 1 for each i (so that in particular [ψ] i = 1), and thus we can evaluate ζ T (Ψ) and ζ T (Ψ ) according to the above formula for ζ T (x).",1600,0.541,952,1.680672268907563,"Kronecker-factor Approximate CurvatureMartens & Grosse 2015 (K-FAC is has give stateBa et 2017 It based an approximation to the Fisher information matrix makes assumptions the particular structure parameterized The original K-FAC method applicable fully-connected networks although recently by Grosse & Martens handle In this work extend the method handle RNNs by introducing a novel approximation the FIM for works modelling the gradient contributions at using a chain-structured linear Gaussian graphical model summing the various crosscovariances computing in closed form We demonstrate in experiments our method significantly general purpose state optimizers like SGD with momentum Adam on several challenging RNN training tasks As neural networks have ubiquitous both research applications the need efficiently has never The main workhorses neural net optimization with momentum various 2nd-order optimizers that diagonal curvature-matrix approximations RMSprop BID32 Adam BID1 . While latter are typically easier tune work better out unfortunately only marginal performance improvements well-tuned SGD on most problemsBecause modern neural networks many millions parameters it computationally too compute invert an entire curvature matrix and approximations While early work non-diagonal curvature matrix approximations such TONGA BID17 the Hessianfree (HF approach BID20 BID21 BID4 demonstrated such methods never wide adoption due issues (to large models in the former, and large datasets latter).Motivated in these older results centering and normalization methods a new family has the rely the special structure neural networks Such methods , include Kronecker-factored approximated curvatureK-FAC) BID24 Natural Neural Nets BID5 others BID29 achieved state optimization performance various challenging neural network training tasks benchmarksWhile applicable standard feed-forward networks fully connected layers handle BID8 through the introduction the ""Kronecker Factors for"" BID2 later developed a distributed asynchronous version which proposed additional approximations handle very large hidden layersIn develop a new family curvature matrix approximations within As in the original K-FAC approximation and the KFC approximation focus the Fisher information matrixa popular choice curvature matrix show through the adoption various approximating assumptions on the statistics the network's gradients Our main novel technical contribution an approximation which uses a chain-structured linear Gaussian graphical model the statistical relationship gradient contributions coming different time-steps remarkably possible sum the required crossmoments obtain a Fisher approximations which has enough special algebraic structure that still efficiently inverted In experiments we demonstrate the usefulness our approximations on several challenging RNN training tasks We presented a new family the Fisher information matrix of recurrent neural networks extending Kronecker-factored approximations With this contribution recurrent networks now finally trained the K-FAC optimization method We demonstrated our new approximations substantially iterations convergence vs standard baseline optimizers on several realistic tasks And we also shown in a modern distributed training setup this results a substantial savings wallclock timeJason Weston Sumit Chopra Antoine Bordes. A SUPPLEMENTARY COMPUTATIONS A.1 PROOFS FOR SECTION 3.5.1Proposition GivenF DISPLAYFORM0 , which can seen And using DISPLAYFORM2 Setting d multiplying both sides V 0which assumed one also derive �� To proceed here define the original chain-structured linearGaussian graphical model whose variables�� t −1/2 0 w t (Here we assume V 0 -it symmetric by All quantities related the original model their analogues the transformed model indicate the hat symbol·.In the 2nd-order moments the�� t 's given b�� DISPLAYFORM4 We observe thatV I.Analogously to the transformed version obey�� DISPLAYFORM5 =VusingV This can noting DISPLAYFORM6 It also remains the spectral radius�� can at noticing the transformed model well the infinite limit if the original one,�� DISPLAYFORM7 a similar matrixin hence hasAs isomorphic all the previously derived relationships which held also here simply replacing each quantity its transformed versiondenoted the hat symbol·).Given these relations (included the transformed analogue equation 5 expressF T a�� It one evaluate rational functions, functions the limiting values sequences matrix arguments This done replacing scalar multiplication division matrix inversion scalar constants of the identity matrix etc Note because sums powers inverses matrices co-diagonalizable/commutative when, there no issue ambiguity caused mixing inMoreover the value some such function f (x given a matrix argument B DISPLAYFORM9 undefined from some i, either a division the limit which defines does converge for x = [b] i , thenB does that particular Band otherwise does).We observe our above expression F T can a�� DISPLAYFORM11 By Proposition 3 in for x that Let U diag(��)U −1�� be the eigendecomposition�� Because�� has a spectral radius less |[� i < (so in particular evaluate �� T and ) according forx",0.01,0.4383723076486209
"Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior distributions for convolutional neural networks, deep weight prior (DWP), that exploit generative models to encourage a specific structure of trained convolutional filters e.g., spatial correlations of weights. We define DWP in the form of an implicit distribution and propose a method for variational inference with such type of implicit priors. In experiments, we show that DWP improves the performance of Bayesian neural networks when training data are limited, and initialization of weights with samples from DWP accelerates training of conventional convolutional neural networks.
 Bayesian inference is a tool that, after observing training data, allows to transforms a prior distribution over parameters of a machine learning model to a posterior distribution. Recently, stochastic variational inference (Hoffman et al., 2013 ) -a method for approximate Bayesian inference -has been successfully adopted to obtain a variational approximation of a posterior distribution over weights of a deep neural network . Currently, there are two major directions for the development of Bayesian deep learning. The first direction can be summarized as the improvement of approximate inference with richer variational approximations and tighter variational bounds BID4 . The second direction is the design of probabilistic models, in particular, prior distributions, that widen the scope of applicability of the Bayesian approach.Prior distributions play an important role for sparsification BID25 , quantization and compression BID6 of deep learning models. Although these prior distributions proved to be helpful, they are limited to fully-factorized structure. Thus, the often observed spatial structure of convolutional filters cannot be enforced with such priors. Convolutional neural networks are an example of the model family, where a correlation of the weights plays an important role, thus it may benefit from more flexible prior distributions.Convolutional neural networks are known to learn similar convolutional kernels on different datasets from similar domains BID31 BID39 . Based on this fact, within a specific data domain, we consider a distribution of convolution kernels of trained convolutional networks. In the rest of the paper, we refer to this distribution as the source kernel distribution. Our main assumption is that within a specific domain the source kernel distribution can be efficiently approximated with convolutional kernels of models that were trained on a small subset of problems from this domain. For example, given a specific architecture, we expect that kernels of a model trained on notMNIST dataset -a dataset of grayscale images -come from the same distribution as kernels of the model trained on MNIST dataset. In this work, we propose a method that estimates the source kernel distribution in an implicit form and allows us to perform variational inference with the specific type of implicit priors.Our contributions can be summarized as follows:1. We propose deep weight prior, a framework that approximates the source kernel distribution and incorporates prior knowledge about the structure of convolutional filters into the prior distribution. We also propose to use an implicit form of this prior (Section 3.1).2. We develop a method for variational inference with the proposed type of implicit priors (Section 3.2).3. In experiments (Section 4), we show that variational inference with deep weight prior significantly improves classification performance upon a number of popular prior distributions in the case of limited training data. We also find that initialization of conventional convolution networks with samples from a deep weight prior leads to faster convergence and better feature extraction without training i.e., using random weights. In this work we propose deep weight prior -a framework for designing a prior distribution for convolutional neural networks, that exploits prior knowledge about the structure of learned convolutional filters. This framework opens a new direction for applications of Bayesian deep learning, in particular to transfer learning.Factorization. The factorization of deep weight prior does not take into account inter-layer dependencies of the weights. Although a more complex factorization might be a better fit for CNNs. Accounting inter-layer dependencies may give us an opportunity to recover a distribution in the space of trained networks rather than in the space of trained kernels. However, estimating prior distributions of more complex factorization may require significantly more data and computational budget, thus the topic needs an additional investigation.Inference. An alternative to variational inference with auxiliary variables is semi-implicit variational inference BID38 . The method was developed only for semiimplicit variational approximations, and only the recent work on doubly semi-implicit variational inference generalized it for implicit prior distributions . These algorithms might provide a better way for variational inference with a deep weight prior, however, the topic needs further investigation. DISPLAYFORM0 is a transition operator, and z = (z 0 , . . . , z T ) . Unfortunately, gradients of L cannot be efficiently estimated, but we construct a tractable lower bound L aux for L: DISPLAYFORM1 Inequality 13 has a very natural interpretation. The lower bound L aux is tight if and only if the KLdivergence between the auxiliary reverse model and the posterior intractable distribution p(z | w) is zero.The deep weight prior (Section 3) is a special of Markov chain prior for T = 0 and p(w) = p(w | z)p(z)dz. The auxiliary variational bound has the following form: DISPLAYFORM2 where the gradients in equation 14 can be efficiently estimated in case q(w), for explicit distributions q(w), p φ (w | z), r(z | w) that can be reparametrized. During variational inference with deep weight prior (Algorithm 1) we optimize a new auxiliary lower bound L aux (θ, ψ) on the evidence lower bound L(θ). However, the quality of such inference depends on the gap G(θ, ψ) between the original variational lower bound L(θ) and the variational lower bound in auxiliary space L aux (θ, ψ):",1210,0.643,696,1.7385057471264367,"Bayesian inference known provide incorporating prior knowledge or specific properties via carefully choosing a prior distribution In this work propose prior distributions deep weight prior (DWP exploit generative models encourage a specific structure trained convolutional filters spatial correlations We define DWP an implicit distribution propose variational inference such type of implicit priors In experiments we show DWP improves training data are limited, initialization weights with samples accelerates Bayesian inference, after observing training data transforms a prior distribution parameters Recently stochastic variationalHoffman ) -a successfully adopted obtain weights . Currently two major directions Bayesian deep learning The first direction can summarized the improvement approximate inference richer variational approximations tighter bounds BID4 The second direction the design particular, prior distributions widenPrior distributions play for sparsification BID25 , quantization compression of Although these prior distributions proved helpful limited fully-factorized structure Thus the often observed spatial structure convolutional filters enforced such priors an example the model family a correlation plays thus it benefit more flexible prior distributions known learn similar convolutional kernels on from similar domains BID31 BID39 . Based this fact within a specific data domain consider a distribution convolution kernels In the rest refer this distribution the source kernel distribution Our main assumption within a specific domain the source kernel distribution can efficiently approximated models were trained problems from For example given a specific architecture expect kernels a model trained notMNIST dataset -a dataset -come In this work propose estimates the source kernel distribution an implicit form allows perform variational inference the specific type implicit priorsOur contributions can We propose deep weight prior, a framework the source kernel distribution incorporates prior knowledge convolutional filters into We also propose an implicit form this prior (Section 3.1).2 We develop variational inference the proposed type implicit priorsSection. In experiments (Section show variational inference with deep weight prior significantly classification performance upon a number popular prior distributions the case limited training data We also find that initialization conventional convolution networks samples a deep weight prior leads faster convergence feature without training using random weights In this work propose deep weight prior -a framework designing a prior distribution that exploits prior knowledge learned convolutional filters This framework opens applications in transfer learning.Factorization. The factorization deep weight prior does take account inter-layer dependencies Although a more complex factorization might CNNs. Accounting inter-layer dependencies give recover a distribution in the space trained networks rather trained kernels However estimating prior distributions more complex factorization may computational budget thus the topic needs an additional investigationInference. An alternative variational inference auxiliary variables semi BID38 . The method was only semiimplicit variational approximations only the recent work generalized it implicit prior distributions . These algorithms might provide variational inference with a deep weight prior however the topic needs DISPLAYFORM0 is a transition operator z = 0 . . . , z T ) . Unfortunately gradients L cannot efficiently estimated construct tractable lower L aux for: DISPLAYFORM1 Inequality 13 has a very natural interpretation The lower bound L aux is tight if and the KLdivergence between the auxiliary reverse model the posterior intractable distribution p(z | w zeroThe deep weight priorSection a special of Markov chain prior for T = The auxiliary variational bound DISPLAYFORM2 where the gradients equation 14 can efficiently estimated case q(w for explicit distributions q(w p �� | z that reparametrized During variational inference with deep weight priorAlgorithm optimize new auxiliary lower L aux (�� the evidence lower( However the quality such inference the gap G the original variational lower bound L in auxiliary space L aux):",0.01,0.5857269289564727
"The high dimensionality of hyperspectral imaging forces unique challenges in scope, size and processing requirements.   Motivated by the potential for an in-the-field cell sorting detector, we examine a Synechocystis sp. PCC 6803 dataset wherein cells are grown alternatively in nitrogen rich or deplete cultures.   We use deep learning techniques to both successfully classify cells and generate a mask segmenting the cells/condition from the background. Further, we use the classification accuracy to guide a data-driven, iterative feature selection method, allowing the design neural networks requiring 90% fewer input features with little accuracy degradation. Hyperspectral confocal fluorescence microscopy and hyperspectral imaging are powerful tools for the biological sciences, allowing high-content views of multiple pigments and proteins in individual cells within larger populations. As the technology has advanced in speed and ease of use, it is has become practical to think of applications such as high-throughput screening, or understanding heterogeneous cell response to changing environmental conditions, where one might want to identify cells of certain characteristics including phenotype, pigment content, protein expression, as determined by their spatially resolved fluorescence emission for subsequent analysis. Although a few researchers have used classification techniques such as support vector machines BID13 to identify cells of that exhibit similar spectral emission characteristics, the majority of the analysis of hyperspectral images has been exploratory-developing spectral models for identifying the underlying spectral components BID15 BID11 .In this work, we employ deep artificial neural network algorithms to classify individual cyanobacterial cells based on their hyperspectral fluorescence emission signatures. Such deep learning methods have increasingly seen extensive use in conventional image processing tasks with relatively low numbers of channels (such as processing RGB images) BID8 , however their utility in tasks with larger numbers of sensors, such as hyperspectral systems, remains an area of active research. In particular , in biological systems, non-trivial processes may yield complex interactions that can be detected through hyperspectral imaging that are in addition to the long-acknowledged challenges of automated data processing of spatial structure.In addition to classifying the experimental effects on individual cells, we show how this method can help identify which spectral wavelengths are most useful for the classification. Importantly, the feature selection information could allow customized sensors to be designed for specific applications. This work demonstrates that this technique is suitable for real-time image analysis and high-throughput screening of heterogeneous populations of cyanobacterial cells for differentiating environmental response. The method can be further extended to other cell populations or complex tissue containing multiple cell types. In this study, we demonstrate that modern deep artificial neural network approaches can be used to perform rapid classification of biological data sampled by hyperspectral imaging. Both the pixelbased and whole image-based classification results demonstrate that these approaches are highly effective with the class of data represented by this experimental data and suggest that deep neural network approaches are well suited for hyperspectral imaging analysis even in non-trivial application domains such as biological tissue.We believe that the sampling reduction technique we describe here is a unique use of a neural network's classification ability to guide the identification of which particular sensors-in this case wavelengths-are necessary to measure. Most dimensionality reduction methods, such as PCA and non-linear variants such as local linear embedding (LLE), are focused primarily on reducing the size. While they can identify channels that are not used at all, they are more directed towards storing and communicating data in fewer dimensions which still leverage information sampled across the original cadre of sensors. Thus these dimensionality reduction do not necessarily reduce the demands on the sensor side, even though they do often compress and describe data quite effectively.The methods described here share some similarities to existing techniques for hyperspectral imaging using techniques such as deep stacked autoencoders or principal components analysis coupled with a deep convolutional network that extract high-level features which can then be fed into a simple classifier BID2 BID17 . In contrast, our approach is focused on directly going from the data to the classification of either pixels or whole regions (in our case, cells). This allows us to better leverage the structure of the dimensionality of the data, which for hyperspectral scenarios is often sparser in absolute numbers of images but is proportionally richer in terms of dimensionality.Given deep neural networks' history of broad applicability in other domains, we fully expect that these methods will be generalizable to other, similar datasets and anticipate subsequent analysis of a variety of cell types under experimental conditions. Further refinement of our convolutional neural network should provide effective and efficient sub-cellular segmentation via embedded computing platforms, and ultimately we aim to extend the use of these neural network algorithms to inform experimental results.",922,0.402,552,1.6702898550724639,"The high dimensionality hyperspectral imaging forces unique challenges scope size processing requirements Motivated an in cell sorting detector examine a Synechocystis sp PCC 6803 dataset wherein cells grown alternatively nitrogen rich or deplete cultures We use deep learning techniques both successfully cells a mask segmenting the cells/condition from Further use the classification accuracy guide a data-driven, iterative feature selection method allowing the design neural networks requiring 90% fewer input features with little accuracy degradation Hyperspectral confocal fluorescence and powerful tools the biological sciences allowing high-content views multiple pigments proteins within larger populations As the technology speed ease has practical think applications such high-throughput screening or understanding heterogeneous cell response changing where one identify cells of certain characteristics including phenotype pigment content as determined their spatially resolved fluorescence emission for subsequent analysis Although a few researchers used classification techniques support vector machines BID13 cells that exhibit similar spectral emission characteristics the analysis hyperspectral images exploratory-developing spectral models for identifying BID15 BID11 .In employ deep artificial neural network algorithms Such deep learning methods increasingly seen conventional image processing tasks with relatively low numbers channels processing BID8 , however their utility tasks sensors hyperspectral systems remains In particular , in biological systems yield complex interactions detected that in addition the long-acknowledged challenges automated data processing of spatial structureIn classifying the experimental effects on individual cells show this method which spectral wavelengths useful the classification Importantly the feature selection information could allow customized sensors designed This work demonstrates this technique suitable heterogeneous populations for differentiating environmental response The method can further other cell populations or complex tissue containing In demonstrate modern deep artificial neural network approaches rapid classification biological data sampled Both the pixelbased and whole image-based classification results demonstrate these approaches with the class represented this experimental data and suggest deep neural network approaches well hyperspectral imaging analysis even biological tissueWe believe the sampling reduction technique a unique use a neural network's classification ability guide which particular sensors- wavelengths necessary measure. Most dimensionality reduction methods PCA non-linear variants such local linear embedding focused primarily reducing. While they can identify channels not used at directed storing communicating fewer dimensions which still leverage information sampled across the original cadre sensors Thus these dimensionality reduction do necessarily reduce the demands the sensor side even often compress describe data quite effectivelyThe methods share existing techniques using techniques deep stacked autoencoders principal components analysis coupled that extract which fed a simple classifier BID2 BID17 . In contrast our approach focused directly going the classification either pixels whole regionsin cells This allows better leverage the structure the dimensionality for hyperspectral scenarios often sparser in absolute numbers of images but proportionally richer termsGiven deep neural networks' history broad applicability fully these methods generalizable other, similar datasets anticipate subsequent analysis a variety cell types under Further refinement should effective and efficient sub-cellular segmentation via embedded computing platforms ultimately we extend inform experimental results",0.01,0.41191882938569374
"Data Interpretation is an important part of Quantitative Aptitude exams and requires an individual to answer questions grounded in plots such as bar charts, line graphs, scatter plots, \textit{etc}. Recently, there has been an increasing interest in building models which can perform this task by learning from datasets containing triplets of the form \{plot, question, answer\}. Two such datasets have been proposed in the recent past which contain plots generated from synthetic data with limited (i) $x-y$ axes variables (ii) question templates and (iii) answer vocabulary and hence do not adequately capture the challenges posed by this task. To overcome these limitations of existing datasets, we introduce a new dataset containing $9.7$ million question-answer pairs grounded over $270,000$ plots with three main differentiators. First, the plots in our dataset contain a wide variety of realistic $x$-$y$ variables such as CO2 emission, fertility rate, \textit{etc. } extracted from  real word data sources such as World Bank, government sites, \textit{etc}. Second, the questions in our dataset are more complex as they are based on templates extracted from interesting questions asked by a crowd of workers using a fraction of these plots. Lastly, the answers in our dataset are not restricted to a small vocabulary and a large fraction of the answers seen at test time are not present in the training vocabulary. As a result, existing models for Visual Question Answering which largely use end-to-end models in a multi-class classification framework cannot be used for this task. We establish initial results on this dataset and emphasize the complexity of the task using a multi-staged modular pipeline with various sub-components to (i) extract relevant data from the plot and convert it to a semi-structured table (ii) combine the question with this table and use compositional semantic parsing to arrive at a logical form from which the answer can be derived. We believe that such a modular framework is the best way to go forward as it would enable the research community to independently make progress on all the sub-tasks involved in plot question answering. Data plots such as bar charts, line graphs, scatter plots, etc. provide an efficient way of summarizing numeric information and are frequently encountered in textbooks, research papers, professional reports, newspaper articles, etc. Machine comprehension of these plots with the aim of answering questions grounded in them is an interesting research problem which lies at the intersection of Language and Vision and has widespread applications. For example, such a system could enable financial analysts to use natural language questions to access the information locked in a collection of data plots within financial reports, journals, etc. Such a system could also serve as an important educational assistant for the visually impaired by helping them understand the information summarized in a plot by asking a series of questions.Recently, two datasets , viz., FigureQA BID6 and DVQA BID5 have been released for this task which contain triplets of the form {plots, questions, answers}. These datasets clearly show that despite its apparent similarity to Visual Question Answering (VQA), this task has several additional challenges due to which existing state of the art VQA methods do not perform well on this task. However, both FigureQA and DVQA themselves have some limitations which warrants the creation of more challenging datasets which adequately capture a wider range of Figure 1 shows a sample triplet from FigureQA, DVQA and DIP (our dataset). First, we note that FigureQA and DVQA contain plots created from synthetic data. In particular, note that the label names (either x-axis or y-axis or legend names) in FigureQA and DVQA come from a limited vocabulary (color names and top-1000 nouns from Brown corpus respectively). This clearly reduces the vocabulary that a model needs to deal with. Further, the label names are not really meaningful in the context of the plot leading to unnatural questions. In contrast, the plots in our dataset are based on World Bank Open Data which contains realistic variable names such as mortality rate, crop yield, country names, etc. The values associated with each plot are also realistic with different scales including floating point numbers as opposed to DVQA which contains only integers in a fixed range. Secondly, the questions in FigureQA and DVQA are based on a smaller number of templates (15 and 25). Instead of hand designing a small number of templates, we first show a fraction of the plots to crowdsourced workers and ask them to create natural language questions which can be answered from these plots. We then analyze these questions and extract templates from them which results in a richer question repository with more templates (74) and more complex questions. Lastly, unlike FigureQA and DVQA the answers in our dataset do not come from a small fixed set of vocabulary. For example, the answer to the question shown in FIG0 is 60.49, which is not present in the training data. More specifically, the answer vocabulary for the test data is 248, 878 words of which 187, 688 are not seen in the training data. This is quite natural and expected when the plots and questions are extracted from real world data. In addition to the above differentiators, we also include an extra novel test set which contains plots based on data extracted from Open Government Data as opposed to World Bank Data. This test set contains additional variable and legend names which are not seen in the World Bank Data.Given the large answer vocabulary, it is infeasible to use any of the existing VQA models on our dataset as they largely treat VQA as a multi-class classification problem where the task is to select the right answer from a fixed vocabulary. Even the recent models proposed on DVQA take a similar multi-class classification approach. Further, we believe that given the various sub-tasks involved in this problem it is not prudent to use a single end-to-end system which simply takes the plot and question as input and generates as answer. Instead, as a baseline we propose a modular multi-staged pipeline wherein the first stage in the pipeline extracts (i) data objects in the plot such as bars, lines, etc.(ii ) text objects in the plot such as titles, legend names, x-y axes names, etc. (iii ) the numeric objects in the plot such as tick values, scales, etc. At the end of this stage, the plot is converted to a semi-structured table. We then use a method BID13 which combines the question with this table and uses compositional semantic parsing to arrive at a logical form from which the answer can be derived. The key point here is that the output is neither selected from a fixed vocabulary nor generated using a decoder but it is derived from a logical form. Our experiments using this model suggest that this dataset is indeed very challenging and requires the community to look beyond existing end-to-end models. We introduced the DIP dataset for Data Interpretation over Plots which contains scientific plots created from real world data sources such as World Bank, stock market, etc. Further, the questions in our dataset are based on templates which were manually extracted from realistic questions created by crowd-workers. One of the primary challenges of this dataset is that it has a large vocabulary because of which existing VQA models which treat this as a multi-class classification model cannot be applied. Instead we propose a modular pipeline which first converts the plot to a semi-structured table and then learns to answer questions from this table using compositional semantic parsing. Our experiments suggest that this is a very challenging dataset and requires significant progress on multiple sub-tasks. In particular, we need improved models for reasoning over structured data.Ray Smith. TAB7 presents the detailed statistics of the number of plots present in each of our data splits according to plot type. Note that the plot type k-multi means that the number of lines/bars on each tick is k. In the above mentioned samples, the horizontal bar graph is 3-multi and so on. (e) In how many <plural form of X label>, is the <Y label> of/in <legend label> greater than <N> <units>? (f) What is the ratio of the <Y label> of/in <legend label1> in < i th x tick> to that in < j th x tick>? (g) Is the <Y label> of/in <legend label> in < i th x tick> less than that in < j th x tick> ? 5. Compound : (a) Is the difference between the <Y label> in < i th x tick> and < j th x tick> greater than the difference between any two <plural form of X label> ? (b) What is the difference between the highest and the second highest <Y label> ? (c) Is the sum of the <Y label> in < i th x tick> and < (i + 1) th x tick> greater than the maximum <Y label> across all <plural form of X label> ? (d) What is the difference between the highest and the lowest <Y label> ? (e) In how many <plural form of X label>, is the <Y label> greater than the average <Y label> taken over all <plural form of X label> ? (f) Is the difference between the <Y label> of/in <legend label1> in < i th x tick> and < j th x tick> greater than the difference between the <Y label> of/in <legend label2> in < i th x tick> and < j th x tick> ? (g) What is the difference between the highest and the second highest <Y label> of/in <legend label> ? (h) What is the difference between the highest and the lowest <Y label> of/in <legend label> ? (i) In how many <plural form of X label>, is the <Y label> of/in <legend label> greater than the average <Y label> of/in <legend label> taken over all <plural form of X label> ? (j) Is it the case that in every <singular form of X label>, the sum of the <Y label> of/in <legend label1> and <legend label2> is greater than the <Y label> of/in <legend label3> ? (k) Is the sum of the <Y label> of/in <legend label1> in < i th x tick> and < j th x tick> greater than the maximum <Y label> of/in <legend label2> across all <plural form of X label>? (l) Is it the case that in every <singular form of X label>, the sum of the <Y label> of/in <legend label1> and <legend label2> is greater than the sum of <Y label> of <legend label3> and <Y label> of <legend label4> ? D. QUESTION TYPES TAB8 presents the distribution of the number of questions, categorized by their template type, that are present in each of the data splits.",2251,1.165,1316,1.7104863221884499,"Data Interpretation is Quantitative Aptitude exams requires an individual answer grounded plots such bar charts \textit{etc Recently there building models which perform by learning datasets containing triplets the form \{plot question answer\ Two such datasets proposed which contain plots generated synthetic data with limited (i $-y$ axes variablesii) question templates and hence do adequately the challenges this task To overcome of existing datasets introduce containing $9.7$ million question-answer pairs grounded over $270,000$ plots with three main differentiators First the plots our dataset contain realistic $x$-$y$ variables such CO2 emission fertility rate \textit{etc. } extracted real word data sources such World Bank government sites \textit{etc Second the questions in our dataset more as templates extracted interesting questions asked a crowd workers using a fraction these plots Lastly the answers in our dataset restricted a small vocabulary and a large fraction seen at test time present the training vocabulary As existing models Visual Question Answering which largely end models in a multi-class classification framework We establish initial results on this dataset emphasize the complexity using a multi-staged modular pipeline various sub ( extract the plot convert combine the question with this table use compositional semantic parsing arrive a logical form from We believe such a modular framework go as would the research community independently make all the sub plot question answering Data plots such bar charts etc provide an efficient way summarizing numeric information are frequently encountered textbooks professional reports Machine comprehension these plots with the aim answering grounded them an interesting research problem which lies Language Vision widespread applications For example such a system enable financial analysts use natural language questions access locked a collection data plots within financial reports journals etc Such a system serve an important educational assistant visually by summarized a plot by asking a seriesRecently two datasets , viz FigureQA BID6 have this task which contain triplets the form {plots questions These datasets clearly despite its apparent similarity Visual Question Answering this task several additional challenges due which existing state on However both FigureQA DVQA themselves which warrants the creation more challenging datasets which adequately Figure 1 shows a sample triplet from DIP (our dataset First note FigureQA and DVQA contain plots created synthetic data In particular note the label names (either x FigureQA and DVQA come a limited vocabularycolor names top-1000 nouns from Brown corpus respectively This clearly reduces the vocabulary that a model deal Further the label names really meaningful the plot leading unnatural questions In contrast the plots our dataset World Bank Open Data which contains realistic variable names mortality rate crop yield country names The values associated each plot also realistic with different scales including floating point numbers as opposed DVQA which contains only integers in Secondly the questions in FigureQA and DVQA based a smaller number templates15 25 Instead hand designing a small number templates first show a fraction the plots crowdsourced workers ask natural language questions which from these plots We then analyze these questions extract templates which results richer question repository (74 Lastly unlike FigureQA DVQA the answers in our dataset do come a small fixed set vocabulary For example the answer shown FIG0 60.49 not present the training data More specifically the answer vocabulary the test data 248 878 words of 187 688 not seen This quite natural expected when the plots and questions extracted In addition the above differentiators include an extra novel test set plots data extracted Open Government Data as opposed World Bank Data This test set additional variable and legend names which seen the World Bank DataGiven the large answer vocabulary infeasible use any the existing VQA models on our dataset as largely treat where the task select the right answer a fixed vocabulary Even the recent models proposed on DVQA take a similar multi-class classification approach Further given the various sub this problem it prudent use end system which simply takes the plot question as generates as answer Instead as a baseline we propose a modular multi-staged pipeline wherein in extracts (i) data objects in the plot such bars etc.(ii ) text objects titles legend names x-y axes names (iii ) the numeric objects the plot such tick values scales At this stage the plot converted a semi-structured table We then use a method BID13 which combines the question with this table uses compositional semantic parsing arrive a logical form from The key point the output neither selected from a fixed vocabulary generated but it derived a logical form Our experiments using this model this dataset indeed very challenging the community look existing end We introduced the DIP dataset Data Interpretation over Plots which contains scientific plots created real world data sources World Bank stock market etc Further the questions in our dataset templates which manually extracted realistic questions created crowd-workers One this dataset a large vocabulary because which existing VQA models which treat this Instead we propose a modular pipeline which first converts the plot learns answer from using compositional semantic parsing Our experiments suggest this a very challenging dataset requires significant progress multiple sub In particular improved models reasoning over structured dataRay Smith. TAB7 presents the detailed statistics plots present our data splits according plot type Note the plot type k-multi means lines/bars on each tick In the above mentioned samples the horizontal bar graph 3-multi and so (e In how many <plural form of X label is of/inlegend label greaterN <units (f What the ratio the <Y label/in <legend label1 i th x tick that (g Is the <Y label/in <legend label i th x tick less that j 5 Compound : (a Is the difference the <Y label in < i th x tick j greater any two <plural form X label (b What highest the second highest <Y label ? (c Is the sum the <Y label in i th x tick ( + th greater across all <plural form of X label ? (d What highest the lowest <Y label ? (e In how many <plural form of X label is greater taken over (f Is the difference the <Y label/in <legend label1 in i th x tick j greater ? (g What highest the second highest <Y label/in <legend label ? (h What highest the lowest <Y label/in <legend label ? (i how many <plural form of X label is the <Y label of/inlegend label greater taken over (j Is in every <singular form X label the sum the <Y label of/inlegend label1 (k Is the sum the <Y label/inlegend label1 in i th x tick j greater across all <plural form X label? (l Is in every <singular form X label the sum the <Y label of/inlegend label1 D. QUESTION TYPES TAB8 presents the distribution the number questions, categorized their template type present the data splits",0.01,0.5143358959742403
"Learning to predict complex time-series data is a fundamental challenge in a range of disciplines including Machine Learning, Robotics, and Natural Language Processing. Predictive State Recurrent Neural Networks (PSRNNs) (Downey et al.) are a state-of-the-art approach for modeling time-series data which combine the benefits of probabilistic filters and Recurrent Neural Networks into a single model. PSRNNs leverage the concept of Hilbert Space Embeddings of distributions (Smola et al.) to embed predictive states into a Reproducing Kernel Hilbert Space, then estimate, predict, and update these embedded states using Kernel Bayes Rule. Practical implementations of PSRNNs are made possible by the machinery of Random Features, where input features are mapped into a new space where dot products approximate the kernel well. Unfortunately PSRNNs often require a large number of RFs to obtain good results, resulting in large models which are slow to execute and slow to train. Orthogonal Random Features (ORFs) (Choromanski et al.) is an improvement on RFs which has been shown to decrease the number of RFs required for pointwise kernel approximation. Unfortunately, it is not clear that ORFs can be applied to PSRNNs, as PSRNNs rely on Kernel Ridge Regression as a core component of their learning algorithm, and the theoretical guarantees of ORF do not apply in this setting. In this paper, we extend the theory of ORFs to Kernel Ridge Regression and show that ORFs can be used to obtain Orthogonal PSRNNs (OPSRNNs), which are smaller and faster than PSRNNs. In particular, we show that OPSRNN models clearly outperform LSTMs and furthermore, can achieve accuracy similar to PSRNNs with an order of magnitude smaller number of features needed. Learning to predict temporal sequences of observations is a fundamental challenge in a range of disciplines including machine learning, robotics, and natural language processing. There exist a wide variety of approaches to modeling time series data, however recurrent neural networks (RNNs) have emerged as the clear frontrunner, achieving state-of-the-art performance in applications such as speech recognition (Heigold et al., 2016) , language modeling BID5 , translation (Cho et al., 2014b) , and image captioning BID13 .Predictive State Recurrent Neural Networks (PSRNNs) are a state-of-the-art RNN architecture recently introduced by Downey et al. (2017) that combine the strengths of probabilistic models and RNNs in a single model. Specifically PSRNNs offer strong statistical theory, globally consistent model initializations, and a rich functional form which is none-the-less amenable to refinement via backpropogation through time (BPTT). Despite consisting of a simple bi-linear operations, PSRNNs have been shown to significantly outperform more complex RNN architectures (Downey et al., 2017) , such as the widely used LSTMs BID3 and GRUs (Cho et al., 2014a) .PSRNNs leverage the concept of Hilbert Space embeddings of distributions BID10 to embed predictive states into a Reproducing Kernel Hilbert Space (RKHS), then estimate, predict, and update these embedded states using Kernel Bayes Rule (KBR) BID10 . Because PSRNNs directly manipulate (kernel embeddings of) distributions over observations, they can be initialized via a globally consistent method-of-moments algorithm which reduces to a series of linear ridge regressions.Practical implementations of PSRNNs are made possible by the machinery of Random Features (RFs): input features are mapped into a new space where dot products approximate the kernel well BID7 . RFs are crucial to the success of PSRNNs, however PSRNNs often require a significant number of RFs in order to obtain good results. And, unfortunately, the number of required RFs grows with the dimensionality of the input, resulting in models which can be large, slow to execute, and slow to train.One technique that has proven to be effective for reducing the required number of RFs for kernel machines is Orthogonal Random Features (ORFs) BID14 . When using ORFs, the matrix of RFs is replaced by a properly scaled random orthogonal matrix, resulting in significantly decreased kernel approximation error. A particularly nice feature of ORFs is that BID14 Choromanski et al., 2017) prove that using ORFs results in a guaranteed improvement in pointwise kernel approximation error when compared with RFs.Unfortunately the guarantees in BID14 are not directly applicable to the PSRNN setting. PSRNNs first obtain a set of model parameters via ridge regression, then use these model parameters to calculate inner products in RF space. This ""downstream"" application of RFs goes beyond the results proven in BID14 and Choromanski et al. (2017) . Hence it is not clear whether or not ORF can be applied to obtain an improvement in the PSRNN setting.In this work, we show that ORFs can be used to obtain OPSRNNs: PSRNNs initialized using ORFs which are smaller, faster to execute and train than PSRNNs initialized using conventional unstructured RFs. We theoretically analyze the orthogonal version of the KRR algorithm that is used to initialize OPSRNNs. We show that orthogonal RNNs lead to kernel algorithms with strictly better spectral properties and explain how this translates to strictly smaller upper bounds on failure probabilities regarding KRR empirical risk. We compare the performance of OPSRNNs with that of LSTMs as well as conventional PSRNNs on a number of robotics tasks, and show that OPSRRNs are consistently superior on all tasks. In particular, we show that OPSRNN models can achieve accuracy similar to PSRNNs with an order of magnitude smaller number of features needed. We showed how structured orthogonal constructions can be effectively integrated with recurrent neural network based architectures to provide models that consistently achieve performance superior to the baselines. They also provide significant compression, achieving similar accuracy as PSRNNs with an order of magnitude smaller number of features needed. Furthermore, we gave the first theoretical guarantees showing that orthogonal random features lead to exponentially small bounds on the failure probability regarding empirical risk of the kernel ridge regression model. The latter one is an important component of the RNN based architectures for state prediction that we consider in this paper. Finally, we proved that these bounds are strictly better than for the standard nonorthogonal random feature map mechanism. Exhaustive experiments conducted on several robotics task confirm our theoretical findings.",1356,0.559,821,1.6516443361753959,"Learning predict complex time-series data a range disciplines Machine Learning Robotics Predictive State Recurrent Neural Networks (Downey are state which combine the benefits probabilistic filters into PSRNNs leverage the concept Hilbert Space Embeddings of distributionsSmola.) embed predictive states a Reproducing Kernel Hilbert Space, then estimate, predict update these embedded states using Kernel Bayes Rule Practical implementations PSRNNs made the machinery Random Features where input features mapped a new space where dot products approximate the kernel well Unfortunately PSRNNs often require RFs obtain good results resulting large models which slow execute slow train Orthogonal Random Features (Choromanski is an improvement RFs which has decrease required pointwise kernel approximation Unfortunately ORFs applied PSRNNs rely Kernel Ridge Regression as a core component their learning algorithm the theoretical guarantees do in this setting In this paper extend the theory ORFs Kernel Ridge Regression obtain Orthogonal PSRNNs (OPSRNNs smaller faster OPSRNN models clearly furthermore can achieve accuracy similar with an order magnitude smaller number features needed Learning predict temporal sequences observations a range disciplines robotics There exist approaches modeling time series data however recurrent neural networks emerged the clear frontrunner, achieving state applications (Heigold 2016 , language modeling BID5 translation (Cho image captioning BID13 .Predictive State Recurrent Neural Networks state architecture recently (2017 that combine the strengths in Specifically PSRNNs offer strong statistical theory globally consistent model initializations a rich functional form which none- amenable refinement via backpropogation through time (BPTT Despite consisting a simple bi-linear operations PSRNNs significantly more complex RNN architecturesDowney 2017 , such the widely used LSTMs BID3 GRUs (Cho) leverage Hilbert Space embeddings of distributions BID10 embed predictive states a Reproducing Kernel Hilbert Space then estimate, update these embedded states Kernel Bayes Rule BID10 Because PSRNNs directly manipulate (kernel embeddings of distributions over observations initialized via globally consistent method-ofmoments algorithm which reduces to a series linear ridge regressionsPractical implementations made the machinery Random Features (RFs): input features mapped a new space where dot products approximate the kernel well BID7 . RFs crucial PSRNNs however often require obtain And, unfortunately the number required RFs grows with the dimensionality the input resulting models can large slow to execute slow trainOne technique proven reducing kernel machines Orthogonal Random FeaturesORFs) BID14 . When using ORFs the matrix RFs replaced a properly scaled random orthogonal matrix resulting significantly decreased kernel approximation error A particularly nice feature ORFs BID14 Choromanski 2017) prove using a guaranteed improvement pointwise kernel approximation error when RFsUnfortunately the guarantees directly the PSRNN setting PSRNNs first obtain a set model parameters via ridge regression inner products in RF space This ""downstream"" application of RFs goes the results proven BID14 Choromanski et (2017 . Hence it clear ORF can applied obtain an improvement the PSRNN settingIn this work show OPSRNNs: initialized which smaller, faster to execute train conventional unstructured RFs theoretically analyze the orthogonal version the KRR algorithm that initialize lead kernel algorithms strictly better spectral properties explain translates strictly smaller upper bounds failure probabilities regarding KRR empirical risk We compare OPSRNNs that LSTMs as conventional PSRNNs on robotics tasks OPSRRNs consistently on In particular we show OPSRNN models achieve accuracy similar PSRNNs with an order magnitude smaller number features needed We showed how structured orthogonal constructions effectively integrated recurrent neural network based architectures provide models consistently achieve performance superior the baselines They also provide significant compression achieving similar accuracy PSRNNs with an order features needed Furthermore we gave the first theoretical guarantees showing orthogonal random features lead exponentially small bounds the failure probability regarding empirical risk the kernel ridge regression model The latter one an important component the RNN based architectures for state prediction that consider Finally proved these bounds strictly better for the standard nonorthogonal random feature map mechanism Exhaustive experiments conducted several robotics task confirm our theoretical findings",0.01,0.36441168541334285
"Training deep neural networks requires many training samples, but in practice training labels are expensive to obtain and may be of varying quality, as some may be from trusted expert labelers while others might be from heuristics or other sources of weak supervision such as crowd-sourcing. This creates a fundamental quality- versus-quantity trade-off in the learning process. Do we learn from the small amount of high-quality data or the potentially large amount of weakly-labeled data? We argue that if the learner could somehow know and take the label-quality into account when learning the data representation, we could get the best of both worlds. To this end, we propose “fidelity-weighted learning” (FWL), a semi-supervised student- teacher approach for training deep neural networks using weakly-labeled data. FWL modulates the parameter updates to a student network (trained on the task we care about) on a per-sample basis according to the posterior confidence of its label-quality estimated by a teacher (who has access to the high-quality labels). Both student and teacher are learned from the data. We evaluate FWL on two tasks in information retrieval and natural language processing where we outperform state-of-the-art alternative semi-supervised methods, indicating that our approach makes better use of strong and weak labels, and leads to better task-dependent data representations. The success of deep neural networks to date depends strongly on the availability of labeled data which is costly and not always easy to obtain. Usually it is much easier to obtain small quantities of high-quality labeled data and large quantities of unlabeled data. The problem of how to best integrate these two different sources of information during training is an active pursuit in the field of semi-supervised learning BID6 . However, for a large class of tasks it is also easy to define one or more so-called ""weak annotators"", additional (albeit noisy) sources of weak supervision based on heuristics or ""weaker"", biased classifiers trained on e.g. non-expert crowd-sourced data or data from different domains that are related. While easy and cheap to generate, it is not immediately clear if and how these additional weakly-labeled data can be used to train a stronger classifier for the task we care about. More generally, in almost all practical applications machine learning systems have to deal with data samples of variable quality. For example, in a large dataset of images only a small fraction of samples may be labeled by experts and the rest may be crowd-sourced using e.g. Amazon Mechanical Turk BID68 . In addition, in some applications, labels are intentionally perturbed due to privacy issues BID69 Papernot et al., 2017 ).Assuming we can obtain a large set of weakly-labeled data in addition to a much smaller training set of ""strong"" labels, the simplest approach is to expand the training set by including the weakly-supervised samples (all samples are equal). Alternatively , one may pretrain on the weak data and then fine-tune on observations from the true function or distribution (which we call strong data). Indeed, it has recently been shown that a small amount of expert-labeled data can be augmented in such a way by a large set of raw data, with labels coming from a heuristic function, to train a more accurate neural ranking model BID12 . The downside is that such approaches are oblivious to the amount or source of noise in the labels. Step 1: Pre-train student on weak data, Step 2: Fit teacher to observations from the true function, and Step 3: Fine-tune student on labels generated by teacher, taking the confidence into account. Red dotted borders and blue solid borders depict components with trainable and non-trainable parameters, respectively.In this paper, we argue that treating weakly-labeled samples uniformly (i.e. each weak sample contributes equally to the final classifier) ignores potentially valuable information of the label quality. Instead, we propose Fidelity-Weighted Learning (FWL), a Bayesian semi-supervised approach that leverages a small amount of data with true labels to generate a larger training set with confidence-weighted weakly-labeled samples, which can then be used to modulate the fine-tuning process based on the fidelity (or quality) of each weak sample. By directly modeling the inaccuracies introduced by the weak annotator in this way, we can control the extent to which we make use of this additional source of weak supervision: more for confidently-labeled weak samples close to the true observed data, and less for uncertain samples further away from the observed data.We propose a setting consisting of two main modules. One is called the student and is in charge of learning a suitable data representation and performing the main prediction task, the other is the teacher which modulates the learning process by modeling the inaccuracies in the labels. We explain our approach in much more detail in Section 2, but at a high level it works as follows (see FIG0 ): We pretrain the student network on weak data to learn an initial task-dependent data representation which we pass to the teacher along with the strong data. The teacher then learns to predict the strong data, but crucially, based on the student's learned representation. This then allows the teacher to generate new labeled training data from unlabeled data, and in the process correct the student's mistakes, leading to a better final data representation and better final predictor.We introduce the proposed FWL approach in more detail in Section 2. We then present our experimental setup in Section 3 where we evaluate FWL on a toy task and two real-world tasks, namely document ranking and sentence sentiment classification. In all cases, FWL outperforms competitive baselines and yields state-of-the-art results, indicating that FWL makes better use of the limited true labeled data and is thereby able to learn a better and more meaningful task-specific representation of the data. Section 4 provides analysis of the bias-variance trade-off and the learning rate, suggesting also to view FWL from the perspective of Vapnik's learning with privileged information (LUPI) framework BID64 . Section 5 situates FWL relative to related work, and we end the paper by drawing the main conclusions in Section 6. We conducted k-fold cross validation on D s (the strong data) and report two standard evaluation metrics for ranking: mean average precision (MAP) of the top-ranked 1,000 documents and normalized discounted cumulative gain calculated for the top 20 retrieved documents (nDCG@20). TAB0 shows the performance on both datasets. As can be seen, FWL provides a significant boost on the performance over all datasets. In the ranking task, the student is designed in particular to be trained on weak annotations BID12 , hence training the network only on weak supervision, i.e. NN W performs better than NN S . This can be due to the fact that ranking is a complex task requiring many training samples, while relatively few data with true labels are available.Alternating between strong and weak data during training, i.e. NN S + /W seems to bring little (but statistically significant) improvement. However, we can gain better results by the typical fine-tuning strategy, NN W→S . Comparing the performance of FWL unsuprep to FWL indicates that, first of all learning the representation of the input data downstream of the main task leads to better results compared to a task-independent unsupervised or self-supervised way. Also the dramatic drop in the performance compared to the FWL, emphasizes the importance of the preretraining the student on weakly labeled data. We can gain improvement by fine-tuning the NN W using labels generated by the teacher without considering their confidence score, i.e. FWL \Σ. This means we just augmented the fine-tuning process by generating a fine-tuning set using teacher which is better than D s in terms of quantity and D w in terms of quality. This baseline is equivalent to setting β = 0 in Equation 1. However, we see a big jump in performance when we use FWL to include the estimated label quality from the teacher, leading to the best overall results. We report Macro-F1, the official SemEval metric, in TAB1 . We see that the proposed FWL is the best performing approach.For this task, since the amount of data with true labels are larger compared to the ranking task, the performance of NN S is acceptable. Alternately sampling from weak and strong data gives better results. Pretraining on weak labels then fine-tuning the network on true labels, further improves the performance. Weighting the gradient updates from weak labels during pretraining and fine-tuning the network with true labels, i.e. NN W ω →S seems to work quite well in this task. For this task, like ranking task, learning the representation in an unsupervised task independent fashion, i.e. FWL unsuprep , does not lead to good results compared to the FWL. Similar to the ranking task, fine-tuning NN S based on labels generated by GP instead of data with true labels, regardless of the confidence score, works better than standard fine-tuning.Besides the baselines, we also report the best performing systems which are also convolution-based models (Rouvier & Favre 2016 on SemEval-14; Deriu et al. 2016 on SemEval-15) . Using FWL and taking the confidence into consideration outperforms the best systems and leads to the highest reported results on both datasets. Training neural networks using large amounts of weakly annotated data is an attractive approach in scenarios where an adequate amount of data with true labels is not available, a situation which often arises in practice. In this paper, we introduced fidelity-weighted learning (FWL), a new student-teacher framework for semi-supervised learning in the presence of weakly labeled data. We applied FWL to document ranking and sentiment classification, and empirically verified that FWL speeds up the training process and improves over state-of-the-art semi-supervised alternatives.",2033,0.976,1160,1.7525862068965516,"Training deep neural networks requires many training samples practice training labels expensive obtain may of some may from trusted expert labelers while heuristics weak supervision such crowd This creates a fundamental quality- versus-quantity trade-off the learning process Do learn the small amount or We argue if the learner could somehow know and take the label-quality into learning the data representation get To this end propose ��fidelity-weighted learning�� a semi-supervised student- teacher approach training FWL modulates the parameter updates a student networktrained the task we care onsample according the posterior confidence its label-quality estimated a teacherwho access Both student learned the data We evaluate FWL on two tasks information retrieval where outperform state alternative semi methods indicating makes strong and weak labels leads better task-dependent data representations The success deep neural networks to date depends strongly labeled data which costly not Usually it much obtain small quantities high-quality labeled data The problem how best integrate these two different sources during training an active pursuit semisupervised BID6 . However for a large class tasks also easy define additional (albeit noisy sources weak supervision based ""weaker"", biased classifiers trained different domains that related While easy and generate immediately and these additional weakly-labeled data train a stronger classifier we care More generally in almost all practical applications machine learning systems data samples variable quality For example a large dataset images samples may labeled experts crowd using Amazon Mechanical Turk BID68 . In addition some applications labels intentionally perturbed due privacy issues BID69 Papernot ).Assuming we obtain addition a much smaller training set the simplest approach expand includingall samples equal Alternatively , one pretrain on the weak data on observations the true function or distributionwhich we strong data Indeed recently expert-labeled data augmented by with labels coming a heuristic function to train a more accurate neural ranking model BID12 . The downside such approaches oblivious the amount or source noise the labels Step Pre-train student on weak data Step Fit teacher observations from the true function labels generated teacher taking the confidence into Red dotted borders depict components with trainable and non-trainable parametersIn argue treating weakly-labeled samples uniformly each weak sample contributes equally ignores potentially valuable information of the label quality Instead propose Fidelity-Weighted Learning with true labels a larger training confidence-weighted weakly-labeled samples modulate based the fidelity ( quality each weak sample By directly modeling the inaccuracies introduced the weak annotator this way control make use this additional source weak supervision: more for confidently-labeled weak samples close the true observed data uncertain samples furtherWe propose a setting consisting two main modules One is called the student is in learning a suitable data representation performing the main prediction task which modulates modeling the inaccuracies the labels We explain Section at works ( FIG0 ): We pretrain the student network weak data learn an initial task-dependent data representation which pass along The teacher then learns predict the strong data crucially based the student's learned representation This then allows the teacher generate new labeled training data in correct leading a better final data representation better final predictorWe introduce the proposed FWL approach Section We then present our experimental setup Section where evaluate FWL on a toy task namely document ranking and sentence sentiment classification In all cases FWL outperforms competitive baselines yields state results indicating makes the limited true labeled data thereby learn a better and more meaningful task-specific representation Section provides analysis the learning rate suggesting also to view FWL from Vapnik's learning with privileged information (LUPI) framework BID64 . Section situates FWL relative related work we end drawing in We conducted k-fold cross validation D sthe strong data report two standard evaluation metrics ranking: mean average precisionMAP normalized discounted cumulative gain calculatednDCG@20 TAB0 shows the performance on both datasets As can FWL provides on over all datasets In the ranking task the student designed in particular trained weak annotations BID12 , hence training the network only weak supervision performs This can due ranking requiring many training samples while relatively few data with true labelsAlternating during i.e. NN S + /W seems bring However we gain better results the typical fine-tuning strategy NN W→S . Comparing FWL unsuprep to indicates, first learning the representation downstream the main task leads compared Also the dramatic drop the performance compared the FWL emphasizes the preretraining the student on weakly labeled data We gain improvement fine the NN W using labels generated the teacher without considering their confidence score i.e. FWL \�� This means just augmented generating using teacher which better D s in quantity D w This baseline equivalent setting β in Equation However we see a big jump performance FWL include the estimated label quality from the teacher leading We report Macro-F1 the official SemEval metric TAB1 . We see the proposed FWL the best performing approachFor this task since the amount with true labels are larger compared the ranking task NN S acceptable Alternately sampling weak and strong data gives Pretraining on weak labels then fine the network on true labels further improves Weighting gradient updates weak labels during pretraining fine the network true labels i.e. NN W �� →S seems For this task like ranking task learning the representation an unsupervised task independent fashion i.e. FWL unsuprep , does lead compared. Similar the ranking task, fine-tuning NN S based labels generated GP instead data with true labels regardless the confidence score worksBesides the baselines report the best performing systems which convolution-based modelsRouvier Favre 2016 on SemEval-14; Deriu 2016 on SemEval-15) . Using FWL taking the confidence into outperforms the best systems leads the highest reported results on both datasets Training neural networks large amounts weakly annotated data scenarios an adequate amount with true labels a situation often practice In introduced fidelity-weighted learningFWL the presence weakly labeled data We applied FWL document ranking and sentiment classification empirically speeds over state semi alternatives",0.01,0.6216027033550567
"Online learning has attracted great attention due to the increasing demand for systems that have the ability of learning and evolving. When the data to be processed is also high dimensional and dimension reduction is necessary for visualization or prediction enhancement, online dimension reduction will play an essential role. The purpose of this paper is to propose new online learning approaches for supervised dimension reduction. Our first algorithm is motivated by adapting the sliced inverse regression (SIR), a pioneer and effective algorithm for supervised dimension reduction, and making it implementable in an incremental manner. The new algorithm, called incremental sliced inverse regression (ISIR), is able to update the subspace of significant factors with intrinsic lower dimensionality fast and efficiently when new observations come in. We also refine the algorithm by using an overlapping technique  and develop an incremental overlapping sliced inverse regression (IOSIR) algorithm. We verify the effectiveness and efficiency of both algorithms by simulations and real data applications. Dimension reduction aims to explore low dimensional representation for high dimensional data. It helps to promote our understanding of the data structure through visualization and enhance the predictive performance of machine learning algorithms by preventing the ""curse of dimensionality"". Therefore, as high dimensional data become ubiquitous in modern sciences, dimension reduction methods are playing more and more important roles in data analysis. Dimension reduction algorithms can be either unsupervised or supervised. Principle component analysis (PCA) might be the most popular unsupervised dimension reduction method. Other unsupervised dimension reduction methods include the kernel PCA, multidimensional scaling, and manifold learning based methods such as isometric mapping and local linear embedding. Unlike unsupervised dimension reduction, supervised dimension reduction involves a response variable. It finds the intrinsic lower-dimensional representations that are relevant to the prediction of the response values. Supervised dimension reduction methods can date back to the well known linear discriminant analysis (LDA) while its blossom occurred in the last twenty years. Many approaches have been proposed and successfully applied in various scientific domains; see BID21 ; BID9 ; BID22 ; BID35 ; BID31 ; BID14 ; BID24 ; BID33 ; BID34 ; BID10 and the references therein.We are in a big data era and facing the challenges of big data processing, thanks to the fast development of modern information technology. Among others, two primary challenges are the big volume and fast velocity of the data. When a data set is too big to be stored in a single machine or when the data arrives in real time and information update is needed frequently, analysis of the data in an online manner is necessary and efficient. If the data is simultaneously big and high dimensional, it becomes necessary to develop online learning approaches for dimension reduction. As PCA and LDA are the most wildly used dimension reduction techniques, a bunch of PCA-based and LDA-based online dimension reduction algorithms has been proposed. Incremental PCA have been described in BID17 BID18 ; BID32 ; BID43 ; BID29 . Incremental LDA have been developed in BID27 ; BID42 ; BID20 ; BID7 . Other strategies like QR decomposition or SVD have also been used in BID6 ; BID36 ; BID28 .In this paper, our purpose is to propose a new online learning approach for supervised dimension reduction. Our motivation is to implement the sliced inverse regression (SIR) in an incremental manner. SIR was proposed in BID21 and has become one of the most efficient supervised dimension reduction method. SIR and its refined versions have been found successful in many scientific areas such as bioinformatics, hyperspectral image analysis, and physics; see BID8 BID4 ; BID3 ; BID12 ; BID15 ; BID19 ; BID0 ; BID23 BID11 ; BID41 . SIR can be implemented by solving an generalized eigen-decomposition problem, Γβ = λΣβ, where Γ is a matrix depending on the response variable (whose definition is described in the next section) and Σ is the covariance matrix. To make it implementable in an online manner we rewrite it as standard eigendecomposition problem Σ − 1 2 ΓΣ − 1 2 η = λη where η = Σ 1 2 β and adopt the ideas from incremental PCA. We need to overcome two main challenges in this process. First , how do we transform the data so that they are appropriate for the transformed PCA problem? Note that simply normalizing the data does not work. Second , online update of Σ − 1 2 , if not impossible, seems very difficult. The first contribution of this paper is to overcome these difficulties and design a workable incremental SIR method. Our second contribution will be to refine the method by an overlapping technique and design an incremental overlapping SIR algorithm.The rest of this paper is arranged as follows. We review SIR algorithm in Section 2 and the incremental PCA algorithm in Section 3. We propose the incremental SIR algorithm in Section 4 and refine it in Section 5. Simulations are done in Section 6. We close with discussions in Section 7. We proposed two online learning approaches for supervised dimension reduction, namely, ISIR and IOSIR. They are motivated by standardizing the data and reformulate the SIR algorithm to a PCA problem. However, data standardization is only used to motivate the algorithm while not explicitly calculated in the algorithms. We proposed to use Sherman Morrison formula to online update Σ −1 and some approximated calculations to circumvent explicit data standardization. This novel idea played a key role in our algorithm design. Both algorithms are shown effective and efficient. While IOSIR does not apply to classification problems, it is usually superior over ISIR in regression problems.We remark that the purpose of ISIR and IOSIR is to keep the dimension reduction accuracy in the situation that a batch learning is not suitable. This is especially the case for streaming data where information update and system involving is necessary whenever new data becomes available. When the whole data set is given and one only needs the EDR space from batch learning, ISIR or IOSIR is not necessarily more efficient than SIR because their complexity to run over the whole sample path is O(p 2 N ), comparable to the complexity O(p 3 + p 2 N ) of SIR.There are two open problems worth further investigation. First, the need to store and use Σ −1 during the updating process is the main bottleneck for ISIR and IOSIR when the dimensionality of the data is ultrahigh. Second, for SIR and other batch dimension reduction methods, many methods have been proposed to determine the intrinsic dimension K; see e.g. BID21 ; Schott (1994); BID5 ; BID1 ; BID2 ; Nkiet (2008) . They depend on all p eigenvalues of the generalized eigen-decomposition problem and are impractical for incremental learning. We do not have obvious solutions to these problems at this moment and would like to leave them for future research.",1390,0.837,824,1.6868932038834952,"Online learning attracted due systems have of evolving When the data to processed also high dimensional and dimension reduction necessary visualization or prediction enhancement, online dimension reduction will play The purpose propose new online learning approaches supervised dimension reduction Our first algorithm motivated adapting the sliced inverse regression a pioneer and effective algorithm supervised dimension reduction and making implementable an incremental manner The new algorithm incremental sliced inverse regressionISIR able update the subspace significant factors with intrinsic lower dimensionality fast when new observations come We also refine the algorithm an overlapping technique and develop an incremental overlapping sliced inverse regressionIOSIR We verify the effectiveness efficiency both algorithms simulations real data applications Dimension reduction aims explore low dimensional representation for It helps promote our understanding the data structure through visualization enhance the predictive performance preventing the ""curse dimensionality Therefore as high dimensional data become ubiquitous modern sciences dimension reduction methods playing Dimension reduction algorithms either Principle component analysis might the most popular unsupervised dimension reduction method Other unsupervised dimension reduction methods the kernel PCA manifold learning based methods isometric mapping local linear embedding Unlike unsupervised dimension reduction response variable It finds the intrinsic lower-dimensional representations that relevant the prediction the response values Supervised dimension reduction methods date the well known linear discriminant analysis while its blossom occurred Many approaches successfully various scientific domains; see BID21 ; and the referencesWe in a big data era facing big data processing thanks the fast development Among others two primary challenges the big volume fast velocity When a data set too stored when arrives real time and information update frequently analysis in an online manner and efficient If the data simultaneously big high dimensional becomes necessary develop online learning approaches dimension reduction As PCA and LDA the most wildly used dimension reduction techniques a bunch has proposed Incremental PCA have described BID17 BID18 ; BID32 Incremental LDA have developed BID27 ; BID42 Other strategies like QR decomposition SVD have BID6 ; BID36 ; BID28 .In our purpose propose a new online learning approach supervised dimension reduction Our motivation implement the sliced inverse regression an incremental manner SIR was proposed BID21 become the most efficient supervised dimension reduction method. SIR and its refined versions found successful many scientific areas physics; see BID8 BID4 ; . SIR can implemented solving an generalized eigen-decomposition problem ��β�β depending the response variablewhose definition To make implementable an online manner rewrite standard eigendecomposition problem � − 1 2 ��� where � 1 β and adopt the ideas incremental PCA We need overcome two main challenges First , how transform so they appropriate the transformed PCA problem Note simply normalizing does Second , online update �� − 2 if not impossible seems very difficult The first contribution overcome these difficulties design a workable incremental SIR method Our second contribution will refine by an overlapping technique and design an incremental overlapping SIR algorithmThe rest arranged We review SIR algorithm Section and the incremental PCA algorithm We propose the incremental SIR algorithm Section and refine Simulations done Section We close discussions in Section 7 We proposed two online learning approaches supervised dimension reduction namely ISIR They motivated standardizing the data reformulate the SIR algorithm a PCA problem However data standardization only used motivate the algorithm while not explicitly calculated We proposed Sherman Morrison formula online update �� −1 some approximated calculations circumvent explicit data standardization This novel idea played our algorithm design Both algorithms shown effective and efficient While IOSIR does apply classification problems usually superior over ISIR regression problemsWe remark the purpose and keep the dimension reduction accuracy the situation that a batch learning suitable This especially streaming data where information update and system involving is necessary whenever becomes When the whole data given and one only the EDR space from batch learning ISIR or IOSIR necessarily more SIR because their complexity to run over the whole sample path O(p 2 N comparable + two open problems worth further First the need store �� −1 during the updating process the main bottleneck ISIR and IOSIR when the dimensionality ultrahigh Second for SIR and other batch dimension reduction methods many methods determine the intrinsic dimension K; BID21 ; Schott1994 BID5 Nkiet2008 . They depend all p eigenvalues of the generalized eigen-decomposition problem impractical incremental learning We do obvious solutions at and would leave",0.01,0.45422270340192517
"This paper presents a storage-efficient learning model titled Recursive Binary Neural Networks for embedded and mobile devices having a limited amount of on-chip data storage such as hundreds of kilo-Bytes. The main idea of the proposed model is to recursively recycle data storage of weights (parameters) during training. This enables a device with a given storage constraint to train and instantiate a neural network classifier with a larger number of weights on a chip, achieving better classification accuracy. Such efficient use of on-chip storage reduces off-chip storage accesses, improving energy-efficiency and speed of training. We verified the proposed training model with deep and convolutional neural network classifiers on the MNIST and voice activity detection benchmarks. For the deep neural network, our model achieves data storage requirement of as low as 2 bits/weight, whereas the conventional binary neural network learning models require data storage of 8 to 32 bits/weight. With the same amount of data storage, our model can train a bigger network having more weights, achieving 1% less test error than the conventional binary neural network learning model. To achieve the similar classification error, the conventional binary neural network model requires 4× more data storage for weights than our proposed model. For the convolution neural network classifier, the proposed model achieves 2.4% less test error for the same on-chip storage or 6× storage savings to achieve the similar accuracy.
 Deep Neural Networks (DNN) have demonstrated the state-of-the-art results in a wide range of cognitive workloads such as computer vision BID10 and speech recognition ), achieving better-than-human performance for the tasks often considered too complex for machines. The success of DNNs has indeed motivated scientists and engineers to implement a DNN in mobile and embedded devices, dubbed as Internet of Smart Things BID9 ). The recent works in this area, however, mostly implement the inference function of DNN, rather than training, while training is performed in cloud computers and posttraining weights are downloaded to mobile and embedded devices BID11 ).On-device learning, however, becomes increasingly important for the mobile and embedded devices for the following three reasons. First, an intelligent device benefits to have the model that is custombuilt for the device itself, its end user, and environment. This is because the model tends to be more accurate and effective if constructed with the consideration of those factors. Second, the training data from mobile and embedded devices can contain security-sensitive information, e.g., personal health data from wearable medical devices. At the risk of being leaked, users typically do not want to upload such data onto cloud computers. Finally, in the era of Internet of Things (IoT), we anticipate a drastic increase in the number of deployed devices, which can proportionally increase the number of learning tasks to be done in the cloud. Coupled with the complexity of training, even for powerful cloud computers, this can be a computationally challenging task.On-device learning, however, entails various challenges in algorithms, data, and systems BID15 ; BID18 ). The most eminent challenge regarding computing systems is high energy consumption caused by dense computation and data access, which is considered prohibitive for the limited resources of embedded devices. The high overhead of data access is caused by fetching DNN weights from DRAM (or FLASH) external to a computing chip on an embedded device. Since the data storage size is limited for such computing chip, the parameters of a DNN have to be stored in external DRAM and FLASH during training. For example, ARM Cortex M3 processor, a processor widely used in commercial wearable devices such as FitBit, has only 64 kilo-Byte (kB) on-chip data storage. This can only store very small size of DNN especially if each weight is 32-bit float point number. Compared to accessing on-chip SRAM, accessing off-chip DRAM incurs 3 to 4 orders of magnitudes more energy and delay overhead. Therefore, fetching weights every time for each data makes training prohibitive to be implemented on a mobile and embedded device BID5 ).Recently several techniques such as pruning, distilling, and binarizing weights have been proposed to compress the parameters of a DNN. This makes it more feasible to fit weights in on-chip SRAM BID5 ; BID2 ; BID14 ; BID8 ). These techniques can also reduce computation overhead. However, these works focused on weight size compression after training is finished. The data storage requirement during training remains the same.Similarly, several learning models, which belong to so-called Binary Neural Networks (BNN), have been proposed BID2 ; BID14 ). These model uses sign bits (or binary information ) of weights in several parts of the learning model notably the part of multiplying and accumulating weights with inputs/activations. Although this greatly reduces computational complexity , each weight still needs to be represented in high precision number with multiple bits (e.g. 32 bits in BID2 ; BID14 ) during the end-to-end training process. This is because weights have to be fine-tuned in the weight update part. Therefore, this so-called BNN models have not demonstrated to scale storage requirement for training below 32 bits/weight.Our goal is, therefore, to efficiently use the limited amount of on-chip data storage during training. We also aim to scale computational complexity. Toward this goal, we propose a new learning model, Recursive Binary Neural Network (RBNN). This model is based on the process of weight training, weight binarization, recycling storage of the non-sign-bit portion of weights to add more weights to enlarge the neural network for accuracy improvement. We recursively perform this process until either accuracy stops improving or we use up all the storage on a chip.We verified the proposed RBNN model on a Multi-Layer Perceptron (MLP)-like and a convolutional neural network classifier on the MNIST and Voice Activity Detection (VAD) benchmark. We considered typical storage constraints of embedded sensing devices in the order of hundreds of kB. The experiment in the MLP-like classifier on MNIST confirms that the proposed model (i) demonstrates 1% less test error over the conventional BNN learning model specifically following BID2 for the same storage constraints or (ii) scales on-chip data storage requirement by 4× for the same classification test error rate(∼2%), marking the storage requirement of 2 bits/weight. The conventional BNN models in BID2 ; BID14 exhibit a significantly larger storage requirements of 8 to 32 bits/weight. The experiment of the CNN classifier for MNIST confirms up to 6× reduction of data storage requirement and 2.4% less test error. For the VAD benchmark, the proposed RBNN achieves 9× savings in data storage requirement .The remainder of the paper is as follow. In Sec. 2 we will introduce the works related to this paper, including comparison to existing works on distillation, compression, BNNs, and low-precision weights. In Sec. 3 we will describe our proposed model. Sec. 4 will present the experimental results and comparisons to the conventional BNN model. Finally , in Sec. 5, we will conclude the paper. The paper includes Appendix A to D to describe additional experiments and analysis.2 RELATED WORK 2.1 DISTILLATION AND COMPRESSION OF DNN PARAMETERS Knowledge distillation BID8 ) is a technique to compress knowledge of an ensemble of DNNs into one small DNN while maintaining the accuracy. Although this technique can scale the number of weights for deployment systems post-training, it cannot scale data storage requirement Under review as a conference paper at ICLR 2018 for training. Specifically, during training, each of weights is represented in high-precision number, which needs to be stored in multi-bit data storage.Another technique is to compress the data size of weights by exploiting redundancies in them. In BID5 , the authors combine four sub-techniques, namely weight pruning, quantization, sharing, and compression coding to reduce the data size of weights. Similar to the knowledge distillation, this technique can be applied to the weights that are already trained, and cannot scale data storage requirement of weights during training. This paper presents a new learning model for on-device training with limited data storage. The proposed RBNN model efficiently uses limited on-chip data storage resources by recycling the part of data storage that would have been wasted in conventional BNN model, to add and train more weights to a neural network classifier. We verified the proposed model with MLP-like DNN and CNN classifiers on the MNIST and VAD benchmark under the typical embedded device storage constraints. The results of MLP-like DNNs on MNIST show that the proposed model achieves 2 bits/weight storage requirement while achieving 1% less test error as compared to the conventional BNN model for the same storage constraint. Our proposed model also achieves 4× less data storage than the conventional model for the same classification error. The similar to greater savings are verified with the CNN classifiers and the VAD benchmarks. We expect the future work of further reduce computation complexity, such as binarization of activation function of BNN BID3 ). We also expect to apply the RBNN model to the ensembles of neural networks BID20 , and the mixture of experts BID16 ).",1876,1.051,1112,1.6870503597122302,"This paper a storage-efficient learning model titled Recursive Binary Neural Networks embedded and mobile devices having on such hundreds kilo-Bytes The main idea the proposed model recursively recycle data storage of weightsparameters during This enables a device a given storage constraint train and weights on a chip achieving Such efficient use onchip storage reduces off accesses improving speed training We verified the proposed training model deep and convolutional neural network classifiers the MNIST and voice activity detection benchmarks For the deep neural network our model achieves data storage requirement as low as 2 bits/weight whereas the conventional binary neural network learning models With data storage our model train a bigger network having more weights achieving 1% less test error the conventional binary neural network learning model To achieve the similar classification error the conventional binary neural network model requires 4× more data storage weights our proposed model For the convolution neural network classifier achieves 2.4% less test error same on storage or 6× storage savings to Deep Neural Networks demonstrated state results computer vision BID10 ), achieving often too machines The success DNNs indeed motivated scientists implement dubbed as Internet Smart Things BID9 ). The recent works in mostly implement the inference function DNN training while training cloud computers posttraining weights downloaded mobile and embedded devices BID11 ).On-device learning becomes for First, an intelligent device benefits to have the model custombuilt itself its end user environment This because the model tends accurate effective constructed the consideration those factors Second the training data mobile and embedded devices contain from At leaked users typically upload such data onto cloud computers Finally the era Internet of anticipate deployed devices proportionally learning to the complexity training even powerful cloud computersOn-device entails various challenges algorithms systems BID15 ; The most eminent challenge regarding computing systems high energy consumption caused dense computation and data access considered the limited resources embedded devices The high overhead data access caused fetching DNN weights DRAM FLASH external a computing chip on Since the data storage size such computing chip the parameters a DNN external DRAM FLASH during training For example ARM Cortex M3 processor a processor widely only kiloByte on data This can store very small size DNN especially each weight 32-bit float point number Compared accessing onchip SRAM accessing off incurs 3 to 4 orders magnitudes delay overhead Therefore fetching weights every for makes training prohibitive to be implemented a mobile and embedded device BID5 ).Recently several techniques such distilling binarizing weights compress the parameters This makes feasible fit weights onchip SRAM BID5 ; ; These techniques reduce computation However these works focused weight size compression after training is finished The data storage requirement during training remainsSimilarly several learning models belong so-called Binary Neural Networks BID2 ; BID14 These model uses sign bits binary information ) weights several parts notably the part multiplying accumulating inputs/activations Although greatly computational complexity , each weight still high precision number with multiple bits BID2 ; during end training This because weights fine the weight update part Therefore this so-called BNN models demonstrated to scale storage requirement training below 32 bits/weightOur goal, efficiently on storage during We also aim scale computational complexity Toward Recursive Binary Neural This model the process weight training weight binarization recycling storage of the non-sign-bit portion weights add more weights enlarge for accuracy improvement We recursively perform until either accuracy stops improving use a chipWe verified the proposed RBNN model and the MNIST and Voice Activity Detection We considered typical storage constraints embedded sensing devices the order hundreds The experiment the MLP-like classifier on confirms (i demonstrates 1% less test error over the conventional BNN learning model specifically following BID2 for the same storage constraints or scales on- data storage requirement 4× rate(� marking the storage requirement 2 bits/weight The conventional BNN models in BID2 ; BID14 exhibit a significantly larger storage requirements 8 to 32 bits/weight The experiment of the CNN classifier MNIST confirms up 6× reduction data storage requirement For the VAD benchmark the proposed RBNN achieves 9× savings data storage requirement .The remainder as follow In Sec 2 we introduce the works related this paper comparison distillation compression BNNs low-precision weights In Sec 3 we describe Sec 4 will present the experimental results comparisons the conventional BNN model Finally , in Sec 5, we conclude The paper includes Appendix A D to additional experiments analysis.2 RELATED DNN PARAMETERS Knowledge distillation BID8 ) is compress knowledge an ensemble while Although this technique scale weights deployment systems posttraining data storage requirement Under review as a conference paper at ICLR for training. Specifically during training each weights represented high-precision number needs stored multi-bit data storageAnother technique compress exploiting redundancies them In BID5 , combine four subtechniques namely weight pruning quantization sharing compression coding reduce weights Similar the knowledge distillation the weights that already trained scale data storage requirement weights during This paper ondevice training limited data storage The proposed RBNN model efficiently limited on resources by recycling the part wasted conventional BNN model to add and train more weights We verified the proposed model MLP-like DNN CNN classifiers on the MNIST and VAD benchmark under the typical embedded device storage constraints The results MLP-like DNNs on MNIST show the proposed model achieves 2 bits/weight storage requirement while achieving 1% less test error as for the same storage constraint Our proposed model also achieves 4× less data storage the same classification error similar to greater savings are verified the CNN classifiers the VAD benchmarks We expect the future work further reduce computation complexity binarization activation function of BNN BID3 ). We also expect apply the RBNN model BID20 , the mixture experts BID16",0.01,0.45462312264598176
"Within-class variation in a high-dimensional dataset can be modeled as being on a low-dimensional manifold due to the constraints of the physical processes producing that variation (e.g., translation, illumination, etc.). We desire a method for learning a representation of the manifolds induced by identity-preserving transformations that can be used to increase robustness, reduce the training burden, and encourage interpretability in machine learning tasks. In particular, what is needed is a representation of the transformation manifold that can robustly capture the shape of the manifold from the input data, generate new points on the manifold, and extend transformations outside of the training domain without significantly increasing the error. Previous work has proposed algorithms to efficiently learn analytic operators (called transport operators) that define the process of transporting one data point on a manifold to another.   The main contribution of this paper is to define two transfer learning methods that use this generative manifold representation to learn natural transformations and incorporate them into new data. The first method uses this representation in a novel randomized approach to transfer learning that employs the learned generative model to map out unseen regions of the data space. These results are shown through demonstrations of transfer learning in a data augmentation task for few-shot image classification. The second method use of transport operators for injecting specific transformations into new data examples which allows for realistic image animation and informed data augmentation.   These results are shown on stylized constructions using the classic swiss roll data structure and in demonstrations of transfer learning in a data augmentation task for few-shot image classification. We also propose the use of transport operators for injecting transformations into new data examples which allows for realistic image animation. While significant progress has been made in training classifiers that can effectively discriminate between thousands of classes, the increasing classifier complexity obfuscates the reasoning behind class selection and requires large training datasets to capture variations within each class. In many settings, the within-class variation in a high-dimensional dataset can be modeled as being lowdimensional due to the constraints of the physical processes producing that variation (e.g., translation, illumination, etc.). When these variations are within a linear subspace, classic techniques such as principal component analysis (PCA) can be used to efficiently capture the transformations within the data. However, the manifold hypothesis states that in many cases of interest (e.g., images, sounds, text), the within-class variations lie on or near a low-dimensional nonlinear manifold BID5 . In the neuroscience literature there is a hypothesis that the manifold nature of these variations is explicitly exploited by hierarchical processing stages to untangle the representations of different objects undergoing the same physical transformations (e.g., pose) BID7 .By learning manifold representations of identity-preserving transformations on a subset of classes or data points, we gain the ability to transfer these natural variations to previously unseen data. A generative model of the transformation manifold trained on a dataset rich in variation can be used to transfer knowledge of those variations to previously unseen domains. This can increase robustness and reduce the training burden for machine learning tasks as well as enable the generation of novel examples. Additionally , an explicit understanding of the transformations occuring within a dataset provides interpretibility of machine learning tasks that is typically unavailable. One can view this approach as a variant of pattern theory that seeks transformations that operate on representational primitives BID15 , but with an explicit unsupervised learning of the low-dimensional manifold structure of many real-world datasets.There are a large number of ""manifold learning"" algorithms that have been introduced in the literature to discover manifold structure from data. The most common approach to this task is to perform an embedding of the original data points after performing a transformation to preserve either local or global properties of the manifold (e.g., local neighborhood relationships, global geodesic distances, etc.) BID32 BID29 BID37 BID1 . Unfortunately, such approaches capture manifold structure through a transformation of the data points themselves into a lower dimensional space and therefore are not suitable for the desired tasks. Specifically, there is no generative model of the data in the original high-dimensional space, meaning that the inferred manifold structure is not transferable to other data classes, is not amenable to strong interpolation/extrapolation, and does not provide a probabilistic model that can be used in machine learning tasks. More recently , there there are a number of methods that have been introduced that capture manifold structure through a variety of approaches that involve estimating local tangent planes BID9 a; BID3 BID26 . While these methods can admit representations that have some of the above advantages of generative models, the linear approximations can cause challenges when trying to perform transfer learning by extrapolating to out-of-sample points in manifold locations not well-represented in the training data.As an alternative to the above, previous work has proposed unsupervised learning algorithms to efficiently learn Lie group operators that capture the structure of low-dimensional manifolds BID6 BID33 BID24 BID28 . The manifold representation that is described by analytic operators (called transport operators) defines the process of transporting one data point to another, thereby providing a probabilistic generative model for the manifold structure BID6 ). The main contribution of this paper is to define two transfer learning methods that use this generative manifold representation to learn natural transformations and incorporate them into new data. The first method uses this representation in a novel randomized approach to transfer learning that employs the learned generative model to map out unseen regions of the data space. These results are shown through demonstrations of transfer learning in a data augmentation task for few-shot image classification. The second method use of transport operators for injecting specific transformations into new data examples which allows for realistic image animation and informed data augmentation. We have shown that we can transfer meaninful transformation information between classes and examples using manifold transport operators which provide accurate and robust characterization of manifold data in the context of a probabilistic generative model. We have demonstrated that the learned transformations can be transferred accurately to other portions of the manifold (including out-of-sample extensions) through applying the generative model with both randomized and structured coefficients. The transfer learning potential was shown in the context of data generation and augmentation applications by animating individuals with new facial expression and providing examples of few-shot learning on digit and facial expression classification. These results constitute some Classification Accuracy Figure 9 : The boxes represent the classification accuracy distribution when the classifier is trained using the transport operator-augmented dataset (transport operator), using only one example per expression without data augmentation (single example), and using landmarks from the expression frames in all of the training sequences from the CK+ database (CK+).of the first demonstrations that transport operators can form the basis of a learned representation for manifold data that has utility in applications and transfer learning tasks. The presented simulations are proof-of-concept simulations that allow us to fully explore and visualize the results in a way that is impossible with larger or more complex datasets.While successful in these demonstrations, as with any algorithm the results depend on the data characteristics being sufficiently captured by the model family. Though there is evidence in the literature that Lie group operators can capture complex transformations in images BID6 , it is unknown if the transport operator approach will be sufficient to represent the rich variations in more complex datasets. Future work will be required to determine the complexity of manifold models that can be captured successfully by the proposed manifold transport operator approach, including demonstrations of similar tasks on more complex image classification tasks. Additionally , the current model only captures local transformations between points, but it will likely be beneficial to develop the model further to capture more regularity in the coefficient behavior across multiple pairs of points.",1508,0.693,884,1.7058823529411764,"Within- variation a high-dimensional dataset modeled being on due the physical processes producing translation illumination We desire a method learning a representation the manifolds induced identity-preserving transformations that increase reduce the training burden encourage interpretability In particular what needed a representation the transformation manifold robustly capture from generate new points extend transformations outside the training domain without significantly Previous work proposed algorithms efficiently learn analytic operatorscalled transport operators define the process transporting on The main contribution define two transfer learning methods use this generative manifold representation natural transformations incorporate new data The first method uses this representation a novel randomized approach transfer learning that employs the learned generative model map out unseen regions the data space These results shown through demonstrations transfer learning a data augmentation task for few-shot image classification The second method use transport operators injecting specific transformations new data examples which allows realistic image animation informed data augmentation These results shown stylized constructions the classic swiss roll data structure in demonstrations transfer learning a data augmentation task for few-shot image classification We also propose transport operators injecting transformations new data examples which allows realistic image animation While significant progress training classifiers that effectively discriminate thousands classes the increasing classifier complexity obfuscates the reasoning requires large training datasets capture variations In many settings withinclass variation a high-dimensional dataset modeled being lowdimensional due the physical processes producing translation illumination When these variations within a linear subspace classic techniques efficiently capture the transformations However the manifold hypothesis states in of interest images text within variations lie on or a low-dimensional nonlinear manifold BID5 . In the neuroscience literature a hypothesis the manifold nature these variations explicitly exploited hierarchical processing stages untangle the representations different objects undergoing pose) BID7 .By learning manifold representations identity-preserving transformations on classes or data points gain transfer these natural variations previously unseen data A generative model the transformation manifold trained dataset rich variation can transfer knowledge those variations previously unseen domains This can increase robustness the training burden machine learning tasks as enable the generation novel examples Additionally , an explicit understanding the transformations occuring a dataset provides interpretibility machine learning tasks is typically unavailable. One can view this approach a variant pattern theory seeks transformations operate representational primitives BID15 , but the low-dimensional manifold structureThere ""manifold learning"" algorithms introduced discover manifold structure from The most common approach this task an embedding after performing preserve either local or global properties global geodesic distances BID32 BID29 . Unfortunately such approaches capture manifold structure through a transformation points themselves the desired tasks Specifically there no generative model the data meaning the inferred manifold structure transferable other data classes is amenable strong interpolation/extrapolation More recently , there there are methods introduced capture manifold structure through involve estimating local tangent planes BID9 a; . While these methods admit representations of of the linear approximations cause challenges perform transfer learning by out points manifold locations not wellAs above previous work proposed efficiently Lie group operators that capture BID6 BID33 The manifold representation that described analytic operatorscalled transport operators defines transporting thereby BID6 The main contribution define two transfer learning methods use this generative manifold representation natural transformations incorporate new data The first method uses this representation a novel randomized approach transfer learning that employs the learned generative model map out unseen regions the data space These results shown through demonstrations transfer learning a data augmentation task for few-shot image classification The second method use transport operators injecting specific transformations new data examples which allows realistic image animation informed data augmentation We shown we transfer meaninful transformation information classes examples manifold transport operators which provide accurate and robust characterization manifold data We demonstrated the learned transformations transferred accurately other portions the manifoldincluding outsample extensions applying with both randomized and structured coefficients The transfer learning potential was shown the context data generation and augmentation applications by animating individuals new facial expression providing examples few-shot learning on digit and facial expression classification These results constitute some Classification Accuracy Figure 9 : The boxes when trained the transport operator-augmented dataset using only one example per expression without data augmentationsingle example landmarks the expression frames all from the CK+ databaseCK+).of the first demonstrations that form a learned representation manifold data that utility applications and transfer learning tasks The presented simulations proof fully visualize impossibleWhile successful these demonstrations as any algorithm the results depend the data characteristics being sufficiently captured the model family Though evidence in Lie group operators capture complex transformations images BID6 unknown the transport operator approach represent the rich variations more complex datasets Future work required the complexity manifold models captured successfully the proposed manifold transport operator approach demonstrations similar tasks on more complex image classification tasks Additionally , the current model only captures local transformations between points likely beneficial develop more regularity the coefficient behavior across multiple pairs",0.01,0.5026053868325028
"The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such representations are compositional and hierarchical, they can be recombined into an exponentially large set of new concepts. This paper describes SCAN (Symbol-Concept Association Network), a new framework for learning such abstractions in the visual domain. SCAN learns concepts through fast symbol association, grounding them in disentangled visual primitives that are discovered in an unsupervised manner. Unlike state of the art multimodal generative model baselines, our approach requires very few pairings between symbols and images and makes no assumptions about the form of symbol representations. Once trained, SCAN is capable of multimodal bi-directional inference, generating a diverse set of image samples from symbolic descriptions and vice versa. It also allows for traversal and manipulation of the implicit hierarchy of visual concepts through symbolic instructions and learnt logical recombination operations. Such manipulations enable SCAN to break away from its training data distribution and imagine novel visual concepts through symbolically instructed recombination of previously learnt concepts. State of the art deep learning approaches to machine learning have achieved impressive results in many problem domains, including classification BID7 BID33 , density modelling BID6 Oord et al., 2016a; , and reinforcement learning BID17 BID10 BID28 . They are still, however, far from possessing many traits characteristic of human intelligence. Such deep learning techniques tend to be overly data hungry, often rely on significant human supervision and tend to overfit to the training data distribution BID14 BID5 ). An important step towards bridging the gap between human and artificial intelligence is endowing algorithms with compositional concepts BID14 BID5 . Compositionality allows for reuse of a finite set of primitives (addressing the data efficiency and human supervision issues) across many scenarios by recombining them to produce an exponentially large number of novel yet coherent and potentially useful concepts (addressing the overfitting problem). Compositionality is at the core of such human abilities as creativity, imagination and language-based communication.We propose that concepts are abstractions over a set of primitives. For example, consider a toy hierarchy of visual concepts shown in Fig. 1 . Each node in this hierarchy is defined as a subset of visual primitives that make up the scene in the input image. These visual primitives might include factors like object identity, object colour, floor colour and wall colour. As one traverses the hierarchy from the subordinate over basic to superordinate levels of abstraction BID27 (i.e. from the more specific to the more general concepts corresponding to the same visual scene), the number of concept-defining visual primitives decreases. Hence, each parent concept in such a hierarchy is an Figure 1 : Schematic of an implicit concept hierarchy built upon a subset of four visual primitives: object identity (I), object colour (O), floor colour (F ) and wall colour (W ) (other visual primitives necessary to generate the scene are ignored in this example). Concepts form an implicit hierarchy, where each parent is an abstraction over its children and over the original set of visual primitives (the values of the concept-defining sets of visual primitives are indicated by the bold capital letters). In order to generate an image that corresponds to a concept, one has to fill in values for the factors that got abstracted away (represented as ""_""), e.g. by sampling from their respective priors. Given certain nodes in the concept hierarchy, one can traverse the other nodes using logical operations. See Sec.3 for our formal definition of concepts. abstraction (i.e. a subset) over its children and over the original set of visual primitives. A more formal definition of concepts is provided in Sec. 3.Intelligent agents are able to discover and learn abstract compositional concepts using little supervision BID1 BID31 BID2 BID29 . Think of human word learning -we acquire the meaning of words through a combination of a continual stream of unsupervised visual data occasionally paired with a corresponding word label. This paper describes SCAN (Symbol-Concept Association Network, see Fig. 2A ), a neural network model capable of learning grounded visual concepts in a largely unsupervised manner through fast symbol association. First, we use the β-VAE BID8 to learn a set of independent representational primitives through unsupervised exposure to the visual data. This is equivalent to learning a disentangled (factorised and interpretable) representation of the independent ground truth ""generative factors"" of the data BID3 . Next, we allow SCAN to discover meaningful abstractions over these disentangled primitives by exposing it to a small number of symbol-image pairs that apply to a particular concept (e.g. a few example images of an apple paired with the symbol ""apple""). SCAN learns the meaning of the concept by identifying the set of visual primitives that all the visual examples have in common (e.g. all observed apples are small, round and red). The corresponding symbol (""apple"") then becomes a ""pointer"" to the newly acquired concept {small, round, red} -a way to access and manipulate the concept without having to know its exact representational form. Our approach does not make any assumptions about how these symbols are encoded, which also allows SCAN to learn multiple referents to the same concept, i.e. synonyms.Once a concept is acquired, it should be possible to use it for bi-directional inference: the model should be able to generate diverse visual samples that correspond to a particular concept (sym2img) and vice versa (img2sym). Since the projection from the space of visual primitives to the space of concepts (img2sym, red dash arrow in Fig. 1 ) involves abstraction and hence a loss of information, one then needs to add compatible information back in when moving from the space of concepts to that of visual primitives (sym2img, blue dot arrow in Fig. 1 ). In our setup, concepts are defined in terms of a set of relevant visual primitives (e.g. colour, shape and size for ""apple""). This leaves a set of irrelevant visual attributes (e.g. lighting, position, background) to be ""filled in"". We do so by defaulting them to their respective priors, which ensures high diversity of samples (in both image or symbol space) for each concept during img2sym and sym2img inferences.The structured nature of learnt concepts acquired by SCAN allows for sample efficient learning of logical recombination operators: AND (corresponding to a set union of relevant primitives), IN COMMON (corresponding to set intersection) and IGNORE (corresponding to set difference), by pairing a small number of valid visual examples of recombined concepts with the respective operator names. Once the meaning of the operators has been successfully learned, SCAN can exploit the compositionality of the acquired concepts, and traverse previously unexplored parts of the implicit underlying concept hierarchy by manipulating and recombining existing concepts in novel ways. For example, a new node corresponding to the concept {blue, small} can be reached through the following instructions: ""blue"" AND ""small"" (going down the hierarchy from more general to more specific), ""blueberry"" IN COMMON ""bluebell"" (going up the hierarchy from more specific to more general) or ""blueberry"" IGNORE ""round"" (also going up the hierarchy). DISPLAYFORM0 To summarise, our paper 1) presents SCAN, a neural network model capable of learning compositional and hierarchical representations of visual concepts; 2) demonstrates that SCAN can be successfully trained with very little supervised data; 3) shows that after training, SCAN can perform multimodal (visual and symbolic) bi-directional inference and generation with high accuracy and diversity, outperforming all baselines; 4) shows that the addition of logical recombination operations allows SCAN to break out of its limited training data distribution and reach new nodes within the implicit hierarchy of concepts. This paper introduced a new approach to learning grounded visual concepts. We defined concepts as abstractions over independent (and often interpretable) visual primitives, where each concept is given by learned distributions over a set of relevant visual factors. We proposed that all other (irrelevant) visual factors should default to their prior in order to produce a diverse set of samples corresponding to a concept. We then proposed SCAN, a neural network implementation of such an approach, which was able to discover and learn an implicit hierarchy of abstract concepts from as few as five symbolimage pairs per concept and no assumptions on the nature of symbolic representations. SCAN was then capable of bi-directional inference, generating diverse and accurate image samples from symbolic instructions, and vice versa, qualitatively and quantitatively outperforming all baselines, including on a realistic CelebA dataset with noisy attribute labels. The structure of the learnt concepts allowed us to train an extension to SCAN that could perform logical recombination operators. We demonstrated how such operators could be used to traverse the implicit concept hierarchy, including imagining completely new concepts. Due to the sample efficiency and the limited number of assumptions in our approach, the representations learnt by SCAN should be immediately applicable within a large set of broader problem domains, including reinforcement learning, classification, control and planning.",1901,0.952,1145,1.6602620087336244,"The seemingly infinite diversity arises coherent rules such We conjecture these rules give regularities discovered primarily unsupervised experiences represented abstract concepts If such representations compositional hierarchical recombined an exponentially large set new concepts This paper SCAN (Symbol-Concept Association Network learning such abstractions SCAN learns concepts through fast symbol association grounding them disentangled visual primitives that discovered Unlike state of the art multimodal generative model baselines requires very few pairings between symbols images makes the form symbol representations Once trained SCAN multimodal bi-directional inference generating image samples symbolic descriptions vice It also allows traversal manipulation the implicit hierarchy visual concepts through symbolic instructions learnt logical recombination operations Such manipulations enable SCAN break away its training data distribution imagine novel visual concepts through symbolically instructed recombination previously learnt concepts State deep approaches achieved many problem domains classification BID7 BID33 , density modelling BID6 Oord et 2016a; , reinforcement They still, far possessing many traits characteristic human intelligence Such deep learning techniques tend overly data hungry often rely significant human supervision tend overfit to the training data distribution BID14 BID5 ). An important step endowing algorithms compositional concepts BID14 BID5 . Compositionality allows reuse a finite setaddressing the data efficiency human supervision issues across many scenarios by recombining an exponentially large number novel yet coherent and potentially useful concepts Compositionality at such human abilities imaginationWe propose concepts abstractions over primitives For example consider a toy hierarchy visual concepts shown 1 . Each node this hierarchy defined visual primitives make the scene These visual primitives might include factors object identity object colour floor colour wall As one traverses the hierarchy from the subordinate over basic superordinate levels abstraction BID27 ( from more specific corresponding the same visual scene concept-defining visual primitives decreases Hence each parent concept in such a hierarchy an Figure : Schematic an implicit concept hierarchy built a subset four visual primitives object identityI object colourO floor colour ) ) necessary generate the scene are ignored Concepts form an implicit hierarchy each parent over the original set visual primitivesthe values the concept-defining sets indicated the bold capital letters In order generate corresponds a concept fill values the factors got abstracted away (represented ""_ by sampling from their respective priors Given certain nodes the concept hierarchy one traverse logical operations See Sec.3 for our formal definition concepts abstraction ( over its children over the original set visual primitives A more formal definition concepts Sec 3.Intelligent agents able discover learn abstract compositional concepts using little supervision BID1 . Think human word learning -we acquire a continual stream unsupervised visual data occasionally paired a corresponding word label This paper SCAN (Symbol-Concept Association Network see Fig 2A ), a neural network model capable grounded visual concepts through fast symbol association First use the β-VAE BID8 learn a set independent representational primitives through unsupervised exposure the visual data This equivalent learning a disentangled (factorised and interpretable) representation the independent ground truth ""generative factors BID3 . Next allow SCAN discover meaningful abstractions over these disentangled primitives by exposing it symbol-image pairs apply a particular concept an apple paired SCAN learns the meaning the concept by identifying the set visual primitives all the visual examples (e.g. all observed apples small round red The corresponding symbolapple then the newly acquired concept {small round red -a way access and without know its exact representational form Our approach does make these symbols encoded which also allows SCAN learn multiple referentsOnce acquired should bi-directional inference: the model generate diverse visual samplessym2img (img2sym Since the projection from the space visual primitives concepts (img2sym, red dash arrow in Fig 1 ) involves abstraction hence a loss information one then add compatible information back when moving the space concepts that visual primitivessym2img blue dot arrow Fig 1 ). In our setup concepts relevant visual primitives for ""apple This leaves a set irrelevant visual attributes position background ""filled We do so by defaulting them their respective priors ensures high diversity samplesin both image or symbol space each concept during img2sym and sym2img inferencesThe structured nature learnt concepts acquired SCAN allows sample efficient learning logical recombination operators: AND a set union relevant primitives IN COMMON set intersection IGNORE difference by pairing a small number valid visual examples recombined concepts the respective operator names Once the meaning the operators successfully learned SCAN exploit the compositionality the acquired concepts traverse previously unexplored parts the implicit underlying concept hierarchy by manipulating and recombining For example a new node corresponding the concept {blue small reached ""blue ANDgoing down more general ""blueberry IN COMMON ""bluebell or ""roundalso DISPLAYFORM0 To summarise our paper 1) presents SCAN, capable learning compositional and hierarchical representations visual concepts demonstrates successfully very little supervised data after perform generation with diversity all baselines the addition logical recombination operations allows break its limited training data distribution reach new nodes the implicit hierarchy This paper introduced learning grounded visual concepts We defined concepts over independent (and often interpretable) visual primitives where given by learned distributions relevant visual factors We proposed all other (irrelevant) visual factors default prior in produce a diverse set samples corresponding a concept We then proposed SCAN such an approach able discover learn an implicit hierarchy abstract concepts as few as five symbolimage pairs per concept and no assumptions SCAN was then capable bi-directional inference generating diverse and accurate image samples symbolic instructions vice qualitatively outperforming all baselines on a realistic CelebA dataset noisy attribute labels The structure the learnt concepts allowed train an extension SCAN that perform logical recombination operators We demonstrated how such operators traverse the implicit concept hierarchy including imagining completely new concepts Due the sample efficiency assumptions the representations learnt SCAN should immediately applicable within broader problem domains reinforcement learning classification control planning",0.01,0.38636875795127684
"Despite much success in many large-scale language tasks, sequence-to-sequence (seq2seq) models have not been an ideal choice for conversational modeling as they tend to generate generic and repetitive responses. In this paper, we propose a Latent Topic Conversational Model (LTCM) that augments the seq2seq model with a neural topic component to better model human-human conversations. The neural topic component encodes information from the source sentence to build a global “topic” distribution over words, which is then consulted by the seq2seq model to improve generation at each time step. The experimental results show that the proposed LTCM can generate more diverse and interesting responses by sampling from its learnt latent representations. In a subjective human evaluation, the judges also confirm that LTCM is the preferred option comparing to competitive baseline models.
 Sequence-to-Sequence model (seq2seq) BID35 , as a data-driven approach to mapping between two arbitrary length sequences, has attracted much attention and been widely applied to many natural language processing tasks such as machine translation BID20 , syntactic parsing , and summarisation BID28 . Neural conversational models BID32 BID30 are the latest development in open-domain conversational modelling, where seq2seq-based models are employed for learning dialogue decisions in an end-to-end fashion. Despite promising results, the lack of explicit knowledge representations (or the inability to learn them from data) impedes the model from generating causal or even rational responses. This leads to many problems discussed in previous literature such as generic responses BID17 , inconsistency BID18 , and redundancy and contradiction BID33 .On the other hand, goal-oriented dialogues BID45 use the notion of dialogue ontology to constrain the scope of conversation and facilitate rational system behaviour within the domain. Neural network-based task-oriented dialogue systems usually retrieve knowledge from a pre-defined database either by discrete accessing BID41 BID3 or through an attention mechanism BID8 . The provision of this database offers a proxy for language grounding, which is crucial to guide the generation or selection of the system responses. As shown in BID40 , a stochastic neural dialogue model can generate diverse yet rational responses mainly because they are heavily driven by the knowledge the model is conditioned on.Despite the need for explicit knowledge representations, building a general-purpose knowledge base and actually making use of it have been proven difficult BID22 BID25 . Therefore, progress has been made in conditioning the seq2seq model on coarse-grained knowledge representations, such as a fuzzily-matched retrieval result via attention BID10 or a set of pre-organised topic or scenario labels . In this work, we propose a hybrid of a seq2seq conversational model and a neural topic model -Latent Topic Conversational Model (LTCM) -to jointly learn the useful latent representations and the way to make use of them in a conversation. LTCM uses its underlying seq2seq model to capture the local dynamics of a sentence while extracts and represents its global semantics by a mixture of topic components like topic models BID2 . This separation of global semantics and local dynamics turns out to be crucial to the success of LTCM.Recent advances in neural variational inference BID27 BID23 have sparked a series of latent variable models applied to conversational modeling BID31 BID5 . The majority of the work passes a Gaussian random variable to the hidden state of the LSTM decoder and employs the reparameterisation trick BID15 to build an unbiased and low-variance gradient estimator for updating the model parameters. However, studies have shown that training this type of models for language generation tasks is tough because the effect of the latent variable tends to vanish and the language model would take over the entire generation process over time BID4 . This results in several workarounds such as KL annealing BID4 BID5 , word dropout and historyless decoding BID4 , as well as auxiliary bag-of-word signals . Unlike previous approaches, LTCM is similar to TopicRNN (Dieng et al., 2017) where it passes the latent variable to the output layer of the decoder and only back-propagates the gradient of the topic words to the latent variable.In summary, the contribution of this paper is two-fold: first and most importantly, we show that LTCM can learn to generate more diverse and interesting responses by sampling from the learnt topic representations. The results were confirmed by a corpus-based evaluation and a human assessment; secondly, we conducted a series of experiments to understand the properties of seq2seq-based latent variables models better, which may serve as rules of thumb for future model development. In this paper, we have proposed the Latent Topic Conversational Model (LTCM) for general-purpose conversational modeling. We have shown that LTCM can generate more interesting and diverse responses by combining the seq2seq model and neural topic model so that global semantic representations and local word transitions can be modeled separately but learned jointly. Both a corpus-based evaluation and a human assessment confirm this finding. Future work would be to study the learned representations and use them to control the meaning of the generated responses.",1008,0.457,622,1.6205787781350482,"Despite much success many large-scale language tasks sequencetoseq2seq models an ideal choice conversational modeling as generate generic and repetitive responses In a Latent Topic Conversational Model augments the seq2seq model a neural topic component better model human-human conversations The neural topic component encodes the source sentence build a global ��topic�� distribution words consulted the seq2seq model improve generation at The experimental results the proposed LTCM can generate more diverse and interesting responses by sampling its learnt latent representations In a subjective human evaluation the judges also confirm that LTCM comparing competitive baseline models Sequence-to modelseq2seq BID35 , as mapping between two arbitrary length sequences attracted been BID20 syntactic parsing , summarisation Neural conversational models BID32 are open-domain conversational modelling seq2seq-based models employed learning dialogue decisions an end Despite promising results the lack explicit knowledge representations ( data impedes the model from generating causal or even rational responses This leads many problems discussed previous literature such generic responses BID17 , inconsistency redundancy and contradiction BID33 .On, goal-oriented dialogues use dialogue ontology conversation and facilitate rational system behaviour within Neural network-based task-oriented dialogue systems usually retrieve knowledge either discrete accessing BID41 BID3 through an attention mechanism The provision this database offers a proxy language grounding crucial guide the generation or selection the system responses As shown BID40 , a stochastic neural dialogue model generate diverse yet rational responses mainly because they heavily driven the knowledge the model conditionedDespite explicit knowledge representations building actually have proven difficult BID22 BID25 Therefore progress conditioning the seq2seq model on coarse-grained knowledge representations a fuzzily-matched retrieval result via attention BID10 pre-organised topic or scenario labels . In this work propose a hybrid a seq2seq conversational model a neural topic model -Latent Topic Conversational Model jointly learn the useful latent representations the way make LTCM uses its underlying seq2seq model capture the local dynamics a sentence while extracts represents its global semantics a mixture topic components like topic models BID2 . This separation global semantics local dynamics turns crucial LTCM.Recent advances neural variational inference BID27 BID23 have sparked latent variable models applied conversational modeling . The majority the work passes a Gaussian random variable to the hidden state employs the reparameterisation trick BID15 build updating However studies training this type models language generation tasks tough the effect the latent variable tends vanish and would take over BID4 This results such KL annealing BID4 BID5 , word dropout historyless decoding as auxiliary bagofword signals . Unlike previous approaches LTCM similar TopicRNN (Dieng 2017 passes the latent variable only back the gradient the topic wordsIn summary the contribution this paper two and learn more diverse and interesting responses sampling the learnt topic representations The results confirmed a corpus-based evaluation and a human assessment; secondly experiments understand the properties seq2seq-based latent variables models better serve rules In have the Latent Topic Conversational Model We shown that LTCM generate more interesting and diverse responses combining the seq2seq model neural topic model so global semantic representations local word transitions separately but learned jointly Both a corpus-based evaluation confirm Future work would study the learned representations use control the meaning the generated responses",0.01,0.28525937291662323
"Most of the existing Graph Neural Networks (GNNs) are the mere extension of the Convolutional Neural Networks (CNNs) to graphs. Generally, they consist of several steps of message passing between the nodes followed by a global indiscriminate feature pooling function. In many data-sets, however, the nodes are unlabeled or their labels provide no information about the similarity between the nodes and the locations of the nodes in the graph. Accordingly, message passing may not propagate helpful information throughout the graph. We show that this conventional approach can fail to learn to perform even simple graph classification tasks. We alleviate this serious shortcoming of the GNNs by making them a two step method. In the first of the proposed approach, a graph embedding algorithm is utilized to obtain a continuous feature vector for each node of the graph. The embedding algorithm represents the graph as a point-cloud in the embedding space. In the second step, the GNN is applied to the point-cloud representation of the graph provided by the embedding method. The GNN learns to perform the given task by inferring the topological structure of the graph encoded in the spatial distribution of the embedded vectors. In addition, we extend the proposed approach to the graph clustering problem and a new architecture for graph clustering is proposed. Moreover, the spatial representation of the graph is utilized to design a graph pooling algorithm. We turn the problem of graph down-sampling into a column sampling problem, i.e., the sampling algorithm selects a subset of the nodes whose feature vectors preserve the spatial distribution of all the feature vectors. We apply the proposed approach to several popular benchmark data-sets and it is shown that the proposed geometrical approach strongly improves the state-of-the-art result for several data-sets. For instance, for the PTC data-set, we improve the state-of-the-art result for more than 22 %. Many of the modern data/signals are naturally represented by graphs BID2 BID5 BID4 BID31 and it is of great interest to design data analysis algorithms which can work directly with graphs. Due to the remarkable success of deep learning based methods in many machine learning applications, it is an attractive research problem to design new neural network architectures which can make the deep networks able to work with graphs. The adjacency matrix of a graph exhibits the local connectivity of the nodes. Thus, it is straightforward to extend the local feature aggregation in the Convolutional Neural Networks (CNNs) to the Graph Neural Networks (GNNs) BID34 BID38 BID0 BID28 BID3 BID11 . The local feature aggregation in the graphs is equivalent to message passing between the nodes BID38 BID12 . However, if the graph is not labeled (the nodes/edges do not have feature vectors) or the feature vectors of the nodes do not carry information about the similarities between the nodes or any information about their structural role, the message passing may not propagate informative features throughout the graph. Thus, the GNN can fail to infer the topological structure of the graph. Another limitation of the current GNN architectures is that they are mostly unable to do the hierarchical feature learning employed in the CNNs BID26 BID19 . The main reason is that graphs lack the tensor representation and it is hard to measure how accurate a subset of nodes represent the topological structure of the given graph. In this paper, we address these two shortcomings of the GNNs.In the proposed approach, we provide a spatial representation of the graph to the GNN. The spatial representation makes the network aware of the similarity/difference between the nodes and also the location of the nodes in the graph. Accordingly, the local feature aggregation can propagate informative messages throughout the graph. In addition, we propose a down-sampling method to perform graph pooling. The proposed node sampling approach measures the similarities between the nodes in the spatial domain and merges the closest pairs of nodes. The main contributions of the proposed approach can be summarized as follows:• It is shown that the existing GNNs lack the important embedding step. The proposed approach enhances the capability of the GNNs in inferring the topological structure of the graphs.• A new graph pooling method is proposed which can be implemented in any GNN. The proposed pooling method preserves the spatial representation of the graph by merging the closest pairs of nodes in the spatial domain.• To the best of our knowledge, the proposed approach advances the state-of-the-art results for 5 established benchmark data-sets. For instance, the improvement in accuracy with the PTC data-set is more than 22 %.• An architecture for graph clustering is presented. In contrary to the conventional GNNs which can not be trained to cluster unlabeled graphs, the proposed approach utilizes the geometrical representation of the graph to infer the structure of the graph. We pointed this important fact out that the GNNs which are the mere extension of the CNNs to graphs may not be able to infer the structure of the graphs. In the proposed approach, the GNN analyzes a spatial representation of the graph provided by the embedding step. In other word, the graph data analysis problem is translated into a point-cloud data analysis problem. We also extended the proposed approach to a graph clustering method. In addition, we addressed one of the challenges of extending the architecture of the CNNs to graphs by proposing a graph pooling method. The proposed pooling method merges the closest pairs of nodes in the spatial domain. We showed that the proposed approach outperforms most of the existing graph classification methods. For instance, for the PTC data-set the proposed approach advances the state-of-the-art result for more than 22 %.",1127,0.68,664,1.697289156626506,Most the existing Graph Neural Networks the mere extension to graphs Generally they consist several steps message followed a global indiscriminate feature pooling function In many data-sets however the nodes or their labels provide the similarity the locations Accordingly message passing may propagate helpful information throughout the graph We show this conventional approach fail learn to perform even simple graph classification tasks We alleviate this serious shortcoming of the GNNs a two step method In first the proposed approach a graph embedding algorithm utilized obtain a continuous feature vector The embedding algorithm represents the graph as a point-cloud In the second step the GNN applied the point-cloud representation provided The GNN learns to perform the given task inferring encoded the spatial distribution the embedded vectors In addition extend the proposed approach the graph clustering problem a new architecture is Moreover the spatial representation the graph utilized design pooling We turn the problem graph down-sampling a column sampling problem the sampling algorithm selects whose feature vectors preserve We apply the proposed approach several popular benchmark data-sets it shown strongly state result For instance for the PTC data-set improve state result for more than 22 % Many the modern data/signals are naturally represented graphs BID2 BID5 BID4 BID31 and it of design data analysis algorithms work directly Due the remarkable success deep learning based methods an attractive research problem design which make the deep networks able work graphs The adjacency matrix a graph exhibits the local connectivity Thus straightforward extend the local feature aggregation in the Graph Neural Networks BID34 BID38 BID0 . The local feature aggregation in the graphs equivalent message passing between BID38 BID12 . However if the graph labeled (the nodes/edges do feature vectors of carry the similarities any information their structural role the message passing may propagate informative features throughout Thus the GNN can fail infer Another limitation GNN architectures mostly unable do hierarchical feature learning employed the CNNs BID26 BID19 . The main reason graphs lack the tensor representation it measure accurate a subset nodes represent In this paper address these two shortcomings the GNNsIn the proposed approach provide a spatial representation to The spatial representation makes the network aware the similarity/difference Accordingly the local feature aggregation can propagate informative messages throughout the graph In addition propose perform graph pooling The proposed node sampling approach measures the similarities the spatial domain merges the closest pairs The main contributions the proposed approach can It shown the existing GNNs lack the important embedding step The proposed approach enhances the GNNs inferring the graphs.• A new graph pooling method The proposed pooling method preserves the spatial representation the graph merging the closest pairs the spatial domain.• To the advances state results 5 established benchmark data-sets For instance the improvement accuracy the PTC data-set more than 22 %.• An architecture for graph clustering presented In contrary the conventional GNNs which can not trained cluster unlabeled graphs the proposed approach utilizes infer We pointed this important fact that the GNNs which the mere extension the CNNs to graphs may infer In the proposed approach the GNN analyzes a spatial representation the graph provided the embedding step In other word the graph data analysis problem translated We also extended the proposed approach a graph clustering method In addition addressed one extending the architecture the CNNs graphs by proposing The proposed pooling method merges the closest pairs nodes the spatial domain We showed the proposed approach outperforms most the existing graph classification methods For instance for PTC data-set the proposed approach advances state result more than 22 %,0.01,0.48071067761269576
"Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results.
 Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. 
 In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. 
 For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses.  
 We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly.
 Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack  has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge. Deep Neural Networks (DNNs) have achieved great successes in a variety of applications ranging from image recognition BID19 BID12 to speech processing and from robotics training BID23 to medical diagnostics BID7 . However, recent work has demonstrated that DNNs are vulnerable to adversarial perturbations BID32 BID10 . An adversary can add small-magnitude perturbations to inputs and generate adversarial examples to mislead DNNs. Such maliciously perturbed instances can cause the learning system to misclassify them into either a maliciously-chosen target class (in a targeted attack) or classes that are different from the ground truth (in an untargeted attack). Different algorithms have been proposed for generating such adversarial examples, such as the fast gradient sign method (FGSM) BID10 and optimization-based methods (Opt.) BID4 BID24 .Most of the the current attack algorithms BID4 BID24 rely on optimization schemes with simple pixel space metrics, such as L ∞ distance from a benign image, to encourage visual realism. To generate more perceptually realistic adversarial examples, in this paper, we propose to train a feed-forward network to generate perturbations such that the resulting example must be realistic according to a discriminator network. We apply generative adversarial networks (GANs) to produce adversarial examples in both the semi-whitebox and black-box settings. As conditional GANs are capable of producing high-quality images BID16 , we apply a similar paradigm to produce perceptually realistic adversarial instances. We name our method AdvGAN.Note that in the previous white-box attacks, such as FGSM and optimization methods, the adversary needs to have white-box access to the architecture and parameters of the model all the time. However, by deploying AdvGAN, once the feed-forward network is trained, it can instantly pro-duce adversarial perturbations for any input instances without requiring access to the model itself anymore. We name this attack setting semi-whitebox.To evaluate the effectiveness of our attack strategy AdvGAN, we first generate adversarial instances based on AdvGAN and other attack strategies on different target models. We then apply the stateof-the-art defenses to defend against these generated adversarial examples BID10 BID33 BID27 . We evaluate these attack strategies in both semi-whitebox and black-box settings. We show that adversarial examples generated by AdvGAN can achieve a high attack success rate, potentially due to the fact that these adversarial instances appear closer to real instances compared to other recent attack strategies.Our contributions are listed as follows.• Different from the previous optimization-based methods, we train a conditional adversarial network to directly produce adversarial examples, which are both perceptually realistic and achieve state-of-the-art attack success rate against different target models.• We show that AdvGAN can attack black-box models by training a distilled model. We propose to dynamically train the distilled model with query information and achieve high black-box attack success rate and targeted black-box attack, which is difficult to achieve for transferability-based black-box attacks.• We use the state-of-the-art defense methods to defend against adversarial examples and show that AdvGAN achieves much higher attack success rate under current defenses.• We apply AdvGAN on Mądry et al.'s MNIST challenge (2017a ) and achieve 88.93% accuracy on the published robust model in the semi-whitebox setting and 92.76% in the blackbox setting, which wins the top position in the challenge BID28 . In this paper, we propose AdvGAN to generate adversarial examples using generative adversarial networks (GANs). In our AdvGAN framework, once trained, the feed-forward generator can produce adversarial perturbations efficiently. It can also perform both semi-whitebox and black-box attacks with high attack success rate. In addition, when we apply AdvGAN to generate adversarial instances on different models without knowledge of the defenses in place, the generated adversarial examples can attack the state-of-the-art defenses with higher attack success rate than examples generated by the competing methods. This property makes AdvGAN a promising candidate for improving adversarial training defense methods. The generated adversarial examples produced by AdvGAN preserve high perceptual quality due to GANs' distribution approximation property.A ARCHITECTURE OF MODELS BID16 . Let c3s1-k denotes 3 × 3 Convolution-InstanceNorm-ReLU layer with k filter and stride 1. Rk means residual block that contains two 3 × 3 convolution layers with the same numbers of filters. dk denotes the 3 × 3 Convolution-InstanceNorm-ReLU layer with k filters and stride 2. uk denotes a 3 × 3 fractional-strided-ConvolutionInstanceNorm-ReLU layer with k filters, and stride c3s1-8, d16, d32, r32, r32, r32, r32, u16, u8, c3s1-3 Discriminator architecture We use CNNs as our discriminator network BID31 . Let Ck denote a 4 × 4 Convolution-InstanceNorm-LeakyReLU layer with k filters and stride 2. After the last conv layer, we apply a FC layer to produce a 1 dimensional output. We do not use InstanceNorm for the first C8 layer. We use leaky ReLUs with slope 0.2. c7s1-8, d16, d32, d64, d64, d64, d64, r64, r64, r64, r64, u64, u64, u64, u64, u32, u16, u8, c7s1-3 The architecture of discriminator for ImageNet is: C8, C16, C32, FC",1428,0.665,860,1.6604651162790698,"Deep neural networks found vulnerable adversarial examples resulting adding inputs Such adversarial examples mislead DNNs produce adversary-selected results Different attack strategies generate adversarial examples how produce with high perceptual quality more efficiently requires In AdvGAN generate adversarial examples learn approximate original instances For AdvGAN once the generator trained adversarial perturbations efficiently for any instance so as potentially accelerate as defenses We apply AdvGAN in both semi-whitebox and black-box attack settings In semi-whitebox attacks there access the original target model after the generator trained in contrast In black-box attacks we dynamically train a distilled model optimize the generator Adversarial examples generated AdvGAN on different target models high attack success rate under state defenses compared other attacks Our attack has placed first with 92.76% accuracy a public MNIST black-box attack challenge Deep Neural Networks achieved ranging BID19 BID12 speech processing from robotics training . However recent work DNNs vulnerable BID32 BID10 . An adversary add inputs generate adversarial examples mislead DNNs Such maliciously perturbed instances the learning system themin a targeted attack classes different the ground truth Different algorithms generating such adversarial examples the fast gradient sign methodFGSM BID10 and optimization-based methodsOpt.) BID4 BID24 .Most the the current attack rely optimization schemes with simple pixel space metrics L �� distance from a benign image encourage visual realism To generate more perceptually realistic adversarial examples in propose train such the resulting example must realistic according a discriminator network We apply generative adversarial networks produce adversarial examples both the semi-whitebox and black-box settings As conditional GANs capable producing BID16 , apply a similar paradigm produce perceptually realistic adversarial instances We name our method AdvGAN.Note in the previous white-box attacks such FGSM and optimization methods the adversary needs the architecture parameters the model all However by deploying AdvGAN once trained instantly pro adversarial for any input instances without access the model anymore We name this attack setting semiwhiteboxTo evaluate our attack strategy AdvGAN generate adversarial instances based AdvGAN other attack strategies on different target models We then apply stateof- defenses defend these generated adversarial examples BID10 BID33 BID27 . We evaluate these attack strategies both semi-whitebox and black-box settings We show adversarial examples generated AdvGAN achieve a high attack success rate potentially due appear closer real instances compared other recent attack strategiesOur contributions listed follows.• Different from train directly produce both perceptually realistic achieve state against different target AdvGAN attack black-box models training a distilled model We propose dynamically train the distilled model query information achieve high black-box attack success rate and, difficult transferability- black attacks.• state defense methods defend adversarial examples show AdvGAN achieves under current defenses.• apply on M��dry2017a ) achieve 88.93% accuracy the published robust model the semi-whitebox setting wins BID28 . In AdvGAN generate adversarial examples In our AdvGAN framework once trained the feed-forward generator produce adversarial perturbations efficiently It can perform both semi-whitebox and black-box attacks high attack success rate In addition when apply AdvGAN generate adversarial instances on different models without knowledge the defenses attack state defenses with higher attack success rate examples the competing methods This property makes AdvGAN a promising candidate improving adversarial training defense methods The generated adversarial examples produced AdvGAN preserve high perceptual quality due GANs' distribution approximation propertyA ARCHITECTURE BID16 . Let c3s1-k denotes 3 × 3 Convolution-InstanceNorm-ReLU layer k filter stride 1 Rk means residual block that two 3 × 3 convolution layers with filters dk denotes the 3 × 3 Convolution-InstanceNorm-ReLU layer with k filters stride 2 uk denotes a 3 × 3 fractional-strided-ConvolutionInstanceNorm-ReLU layer k filters stride c3s18 d16 r32 c3s1-3 Discriminator architecture We CNNs BID31 . Let Ck denote a 4 × 4 Convolution-InstanceNorm-LeakyReLU layer k filters stride 2 After the last conv layer apply a FC layer produce a 1 dimensional output We do use InstanceNorm for the first C8 layer We use leaky ReLUs slope c7s1-8 d16 r643 The architecture discriminator for ImageNet C8 FC",0.01,0.38688625813223787
"This paper proposes a new model for the rating prediction task in recommender systems which significantly outperforms previous state-of-the art models on a time-split Netflix data set. Our model is based on deep autoencoder with 6 layers and is trained end-to-end without any layer-wise pre-training. We empirically demonstrate that: a) deep autoencoder models generalize much better than the shallow ones, b) non-linear activation functions with negative parts are crucial for training deep models, and c) heavy use of regularization techniques such as dropout is necessary to prevent over-fitting. We also propose a new training algorithm based on iterative output re-feeding to overcome natural sparseness of collaborate filtering. The new algorithm significantly speeds up training and improves model performance. Our code is publicly available. Sites like Amazon, Netflix and Spotify use recommender systems to suggest items to users. Recommender systems can be divided into two categories: context-based and personalized recommendations.Context based recommendations take into account contextual factors such as location, date and time BID0 . Personalized recommendations typically suggest items to users using the collaborative filtering (CF) approach. In this approach the user's interests are predicted based on the analysis of tastes and preference of other users in the system and implicitly inferring ""similarity"" between them. The underlying assumption is that two people who have similar tastes, have a higher likelihood of having the same opinion on an item than two randomly chosen people.In designing recommender systems, the goal is to improve the accuracy of predictions. The Netflix Prize contest provides the most famous example of this problem BID1 : Netflix held the Netflix Prize to substantially improve the accuracy of the algorithm to predict user ratings for films. This is a classic CF problem: Infer the missing entries in an mxn matrix, R, whose (i, j) entry describes the ratings given by the ith user to the jth item. The performance is then measured using Root Mean Squared Error (RMSE).Training very deep autoencoders is non trivial both from optimization and regularization points of view. Early works on training auto-enocoders adapted layer-wise pre-training to solve optimization issues BID5 . In this work , we empirically show that optimization difficulties of training deep autoencoders can be solved by using scaled exponential linear units (SELUs) BID9 . This enables training without any layer-wise pre-training or residual connections. Since publicly available data sets for CF are relatively small, sufficiently large models can easily overfit. To prevent overfitting we employ heavy dropout with drop probability as high as 0.8. We also introduce a new output re-feeding training algorithm which helps to bypass the natural sparseness of updates in collaborative filtering and helps to further improve the model performance. Deep learning has revolutionized many areas of machine learning, and it is poised do so with recommender systems as well. In this paper we demonstrated how very deep autoencoders can be successfully trained even on relatively small amounts of data by using both well established (dropout) and relatively recent (""scaled exponential linear units"") deep learning techniques. Further, we introduced iterative output re-feeding -a technique which allowed us to perform dense updates in collaborative filtering, increase learning rate and further improve generalization performance of our model. On the task of future rating prediction, our model outperforms other approaches even without using additional temporal signals.While our code supports item-based model (such as I-AutoRec) we argue that this approach is less practical than user-based model (U-AutoRec). This is because in real-world recommender systems, there are usually much more users then items. Finally, when building personalized recommender system and faced with scaling problems, it can be acceptable to sample items but not users.",754,0.427,458,1.6462882096069869,"This paper proposes the rating prediction task which significantly on timesplit Netflix data Our model deep autoencoder with 6 layers is trained end without layer pre We empirically demonstrate: a deep autoencoder models generalize much the shallow ones non-linear activation functions with negative parts crucial training deep models regularization techniques such dropout is prevent We also propose a new training algorithm iterative output refeeding overcome natural sparseness collaborate filtering The new algorithm significantly speeds training model performance Our code publicly Sites Amazon Netflix Spotify use recommender systems suggest items Recommender systems divided context-based and personalized recommendationsContext based recommendations take location date BID0 . Personalized recommendations typically suggest items users using the collaborative filtering (CF) approach In this approach the user's interests predicted the analysis tastes preference implicitly inferring ""similarity The underlying assumption two people similar tastes have an itemIn designing recommender systems improve predictions The Netflix Prize contest provides this problem BID1 : Netflix held to substantially user ratings films This a classic CF problem Infer the missing entries an mxn matrix R whose (i, j) entry describes the ratings given the ith user the jth item The performance then Root Mean Squared ErrorRMSE).Training very deep autoencoders non trivial both from optimization regularization points Early works training auto-enocoders adapted layer pre solve optimization issues BID5 . In this work , empirically optimization difficulties training deep autoencoders scaled exponential linear unitsSELUs) BID9 This enables training without any layer-wise pre-training or residual connections Since publicly available data sets CF are relatively sufficiently large models overfit To prevent overfitting we employ heavy dropout with drop probability as introduce a new output re-feeding training algorithm helps bypass the natural sparseness updates collaborative filtering helps further Deep learning poised do recommender systems as In demonstrated how very deep autoencoders successfully trained even by both well established (dropout relatively recent (""scaled exponential linear units Further introduced iterative output re-feeding -a technique allowed perform dense updates collaborative filtering increase learning rate further generalization performance On the task future rating prediction our model outperforms even without additional temporal signalsWhile our code supports item-based model (such I-AutoRec) argue practical This because in real-world recommender systems usually much more users then items Finally when building personalized recommender system and faced scaling acceptable sample items but not users",0.0,0.3507647455011716
"Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them slow to train. Feed-forward and convolutional architectures have recently been shown to achieve superior results on some sequence modeling tasks such as machine translation, with the added advantage that they concurrently process all inputs in the sequence, leading to easy parallelization and faster training times. Despite these successes, however, popular feed-forward sequence models like the Transformer fail to generalize in many simple tasks that recurrent models handle with ease, e.g. copying strings or even simple logical inference when the string or formula lengths exceed those observed at training time. We propose the Universal Transformer (UT), a parallel-in-time self-attentive recurrent sequence model which can be cast as a generalization of the Transformer model and which addresses these issues. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs. We also add a dynamic per-position halting mechanism and find that it improves accuracy on several tasks. In contrast to the standard Transformer, under certain assumptions UTs can be shown to be Turing-complete. Our experiments show that UTs outperform standard Transformers on a wide range of algorithmic and language understanding tasks, including the challenging LAMBADA language modeling task where UTs achieve a new state of the art, and machine translation where UTs achieve a 0.9 BLEU improvement over Transformers on the WMT14 En-De dataset. Convolutional and fully-attentional feed-forward architectures like the Transformer have recently emerged as viable alternatives to recurrent neural networks (RNNs) for a range of sequence modeling tasks, notably machine translation BID8 Vaswani et al., 2017) . These parallel-in-time architectures address a significant shortcoming of RNNs, namely their inherently sequential computation which prevents parallelization across elements of the input sequence, whilst still addressing the vanishing gradients problem as the sequence length gets longer BID15 . The Transformer model in particular relies entirely on a self-attention mechanism BID23 BID20 to compute a series of context-informed vector-space representations of the symbols in its input and output, which are then used to predict distributions over subsequent symbols as the model predicts the output sequence symbol-by-symbol. Not only is this mechanism straightforward to parallelize, but as each symbol's representation is also directly informed by all other symbols' representations, this results in an effectively global receptive field across the whole sequence. This stands in contrast to e.g. convolutional architectures which typically only have a limited receptive field.Notably, however, the Transformer with its fixed stack of distinct layers foregoes RNNs' inductive bias towards learning iterative or recursive transformations. Our experiments indicate that this inductive The Universal Transformer repeatedly refines a series of vector representations for each position of the sequence in parallel, by combining information from different positions using self-attention (see Eqn 2) and applying a recurrent transition function (see Eqn 4) across all time steps 1 ≤ t ≤ T . We show this process over two recurrent time-steps. Arrows denote dependencies between operations. Initially, h 0 is initialized with the embedding for each symbol in the sequence. h t i represents the representation for input symbol 1 ≤ i ≤ m at recurrent time-step t. With dynamic halting, T is dynamically determined for each position (Section 2.2).bias may be crucial for several algorithmic and language understanding tasks of varying complexity: in contrast to models such as the Neural Turing Machine BID12 , the Neural GPU BID17 or Stack RNNs , the Transformer does not generalize well to input lengths not encountered during training.In this paper, we introduce the Universal Transformer (UT), a parallel-in-time recurrent self-attentive sequence model which can be cast as a generalization of the Transformer model, yielding increased theoretical capabilities and improved results on a wide range of challenging sequence-to-sequence tasks. UTs combine the parallelizability and global receptive field of feed-forward sequence models like the Transformer with the recurrent inductive bias of RNNs, which seems to be better suited to a range of algorithmic and natural language understanding sequence-to-sequence problems. As the name implies, and in contrast to the standard Transformer, under certain assumptions UTs can be shown to be Turing-complete (or ""computationally universal"", as shown in Section 4).In each recurrent step, the Universal Transformer iteratively refines its representations for all symbols in the sequence in parallel using a self-attention mechanism BID23 BID20 , followed by a transformation (shared across all positions and time-steps) consisting of a depth-wise separable convolution BID4 BID18 or a position-wise fully-connected layer (see FIG0 . We also add a dynamic per-position halting mechanism BID11 , allowing the model to choose the required number of refinement steps for each symbol dynamically, and show for the first time that such a conditional computation mechanism can in fact improve accuracy on several smaller, structured algorithmic and linguistic inference tasks (although it marginally degraded results on MT).Our strong experimental results show that UTs outperform Transformers and LSTMs across a wide range of tasks. The added recurrence yields improved results in machine translation where UTs outperform the standard Transformer. In experiments on several algorithmic tasks and the bAbI language understanding task, UTs also consistently and significantly improve over LSTMs and the standard Transformer. Furthermore , on the challenging LAMBADA text understanding data set UTs with dynamic halting achieve a new state of the art. When running for a fixed number of steps, the Universal Transformer is equivalent to a multi-layer Transformer with tied parameters across all its layers. This is partly similar to the Recursive Transformer, which ties the weights of its self-attention layers across depth BID13 5 . However, as the per-symbol recurrent transition functions can be applied any number of times, another and possibly more informative way of characterizing the UT is as a block of parallel RNNs (one for each symbol, with shared parameters) evolving per-symbol hidden states concurrently, generated at each step by attending to the sequence of hidden states at the previous step. In this way, it is related to architectures such as the Neural GPU BID17 and the Neural Turing Machine BID12 . UTs thereby retain the attractive computational efficiency of the original feedforward Transformer model, but with the added recurrent inductive bias of RNNs. Furthermore, using a dynamic halting mechanism, UTs can choose the number of processing steps based on the input data.The connection between the Universal Transformer and other sequence models is apparent from the architecture: if we limited the recurrent steps to one, it would be a Transformer. But it is more interesting to consider the relationship between the Universal Transformer and RNNs and other networks where recurrence happens over the time dimension. Superficially these models may seem closely related since they are recurrent as well. But there is a crucial difference: time-recurrent models like RNNs cannot access memory in the recurrent steps. This makes them computationally more similar to automata, since the only memory available in the recurrent part is a fixed-size state vector. UTs on the other hand can attend to the whole previous layer, allowing it to access memory in the recurrent step.Given sufficient memory the Universal Transformer is computationally universal -i.e. it belongs to the class of models that can be used to simulate any Turing machine, thereby addressing a shortcoming of the standard Transformer model 6 . In addition to being theoretically appealing, our results show that this added expressivity also leads to improved accuracy on several challenging sequence modeling tasks. This closes the gap between practical sequence models competitive on large-scale tasks such as machine translation, and computationally universal models such as the Neural Turing Machine or the Neural GPU BID12 BID17 , which can be trained using gradient descent to perform algorithmic tasks.To show this, we can reduce a Neural GPU to a Universal Transformer. Ignoring the decoder and parameterizing the self-attention module, i.e. self-attention with the residual connection, to be the identity function, we assume the transition function to be a convolution. If we now set the total number of recurrent steps T to be equal to the input length, we obtain exactly a Neural GPU. Note that the last step is where the Universal Transformer crucially differs from the vanilla Transformer whose depth cannot scale dynamically with the size of the input. A similar relationship exists between the Universal Transformer and the Neural Turing Machine, whose single read/write operations per step can be expressed by the global, parallel representation revisions of the Universal Transformer. In contrast to these models, however, which only perform well on algorithmic tasks, the Universal Transformer also achieves competitive results on realistic natural language tasks such as LAMBADA and machine translation.Another related model architecture is that of end-to-end Memory Networks BID27 . In contrast to end-to-end memory networks, however, the Universal Transformer uses memory corresponding to states aligned to individual positions of its inputs or outputs. Furthermore, the Universal Transformer follows the encoder-decoder configuration and achieves competitive performance in large-scale sequence-to-sequence tasks. This paper introduces the Universal Transformer, a generalization of the Transformer model that extends its theoretical capabilities and produces state-of-the-art results on a wide range of challenging sequence modeling tasks, such as language understanding but also a variety of algorithmic tasks, thereby addressing a key shortcoming of the standard Transformer. The Universal Transformer combines the following key properties into one model:Weight sharing: Following intuitions behind weight sharing found in CNNs and RNNs, we extend the Transformer with a simple form of weight sharing that strikes an effective balance between inductive bias and model expressivity, which we show extensively on both small and large-scale experiments.Conditional computation: In our goal to build a computationally universal machine, we equipped the Universal Transformer with the ability to halt or continue computation through a recently introduced mechanism, which shows stronger results compared to the fixed-depth Universal Transformer.We are enthusiastic about the recent developments on parallel-in-time sequence models. By adding computational capacity and recurrence in processing depth, we hope that further improvements beyond the basic Universal Transformer presented here will help us build learning algorithms that are both more powerful, data efficient, and generalize beyond the current state-of-the-art.The code used to train and evaluate Universal Transformers is available at https: //github.com/tensorflow/tensor2tensor BID31 .",2137,0.895,1264,1.6906645569620253,"Recurrent neural networks sequentially process data updating with have long the de facto choice sequence modeling tasks However their inherently sequential computation makes slow train Feed-forward and convolutional architectures recently shown achieve superior results some sequence modeling tasks such machine translation with concurrently process all inputs leading easy parallelization faster training times Despite these successes however popular feed sequence models like Transformer fail generalize many simple tasks recurrent models handle with copying strings even simple logical inference when the string or formula lengths exceed those observed We propose the Universal Transformer parallelin selfattentive recurrent sequence model which cast addresses these issues UTs combine the parallelizability global receptive field feed-forward sequence models like the Transformer the recurrent inductive bias also add dynamic perposition halting mechanism find accuracy several tasks In contrast the standard Transformer under certain assumptions UTs shown Turing Our experiments UTs standard Transformers on algorithmic and language understanding tasks the challenging LAMBADA language modeling task where achieve a new state machine where a 0.9 BLEU improvement Transformers on the WMT14 En-De dataset Convolutional and fully-attentional feed-forward architectures like the Transformer recently sequence modeling tasks notably machine translation BID8 Vaswani) . These parallelin architectures address namely their inherently sequential computation which prevents across elements whilst addressing the vanishing gradients problem as gets BID15 . The Transformer model in particular relies entirely a self-attention mechanism BID23 BID20 to compute context-informed vector-space representations the symbols its input and predict distributions subsequent symbols as predicts the output sequence symbol Not mechanism straightforward parallelize as each symbol's representation also directly informed results an effectively global receptive field across This stands typically a limited receptive fieldNotably however the Transformer with its fixed stack distinct layers foregoes RNNs' inductive bias towards learning iterative or recursive transformations Our experiments indicate this inductive The Universal repeatedly refines vector representations each position the sequence parallel by combining information using self-attention Eqn applying a recurrent transition function across all time 1 ≤ t ≤ T . We show this process over two recurrent time-steps Arrows denote dependencies operations Initially h 0 initialized the embedding for each symbol h t represents the representation for input symbol 1 ≤ m at recurrent time-step With dynamic halting T is dynamically determined forSection 2.2).bias may crucial several algorithmic and language understanding tasks of: in contrast models the Neural Turing Machine BID12 , the Neural GPU BID17 or Stack RNNs the Transformer does generalize well input lengths not encounteredIn parallelin recurrent selfattentive sequence model cast yielding increased theoretical capabilities improved results on challenging sequenceto UTs combine the parallelizability global receptive field feed-forward sequence models like the Transformer the recurrent inductive bias seems better a range natural understanding sequence-to As the name and contrast the standard Transformer under certain assumptions UTs shown Turing universal shown Section 4).In each recurrent step iteratively its representations for all symbols in parallel using a self-attention mechanism BID23 BID20 , followedshared across all positions consisting a depth-wise separable convolution or FIG0 . We also add dynamic perposition halting mechanism BID11 , allowing the model choose the required number refinement steps each symbol dynamically show for such a conditional computation mechanism in improve accuracy on several smaller, structured algorithmic and linguistic inference tasksalthough marginally degraded results MT).Our strong experimental results UTs Transformers across The added recurrence yields improved results machine translation where UTs the standard Transformer In experiments several algorithmic tasks and the bAbI language understanding task UTs also consistently and significantly over standard Transformer Furthermore , on the challenging LAMBADA text understanding data UTs with dynamic halting achieve a new state When running a fixed number steps the Universal Transformer equivalent tied parameters across This partly similar the Recursive Transformer ties the weights its self-attention layers across depth BID13 5 . However persymbol recurrent transition functions can applied any number another and the UT a block parallel RNNsone shared parameters evolving per hidden states concurrently generated at attending In this way related architectures the Neural GPU BID17 . UTs thereby retain the attractive computational efficiency the original feedforward Transformer model the added recurrent inductive bias Furthermore using a dynamic halting mechanism choose processing steps basedThe connection other sequence models apparent the architecture: if limited the recurrent steps a Transformer But more interesting the Universal Transformer RNNs other networks where recurrence happens over the time dimension these models may closely since recurrent as But time-recurrent models like access memory the recurrent steps This makes them computationally similar automata the only memory available the recurrent part UTs on can attend the whole previous layer allowing it access memory the recurrent stepGiven sufficient memory the Universal Transformer computationally universal belongs models thereby addressing a shortcoming 6 . In addition theoretically appealing our results this added expressivity also improved accuracy on several challenging sequence modeling tasks This closes practical sequence models competitive on large-scale tasks machine translation computationally universal models the Neural Turing Machine the Neural GPU BID12 BID17 , trainedTo show this can reduce a Neural GPU a Universal Transformer Ignoring the decoder parameterizing the self-attention module with the residual connection to be the identity function assume the transition function. If now set recurrent steps T to equal the input length obtain exactly a Neural GPU Note the last step where the Universal Transformer crucially differs the vanilla whose depth scale dynamically A similar relationship the Universal Transformer the Neural Turing Machine whose single read/ per step the global, parallel representation revisions In contrast these models however which only perform algorithmic tasks the Universal Transformer also achieves competitive results realistic natural language tasks LAMBADA machine translationAnother related model architecture end Memory Networks BID27 . In contrast end memory networks however the Universal Transformer uses memory corresponding states aligned individual positions its inputs or Furthermore the Universal Transformer follows the encoder-decoder configuration and achieves competitive performance large sequenceto tasks This paper introduces the Universal Transformer extends its theoretical capabilities produces state results on challenging sequence modeling tasks language understanding but a variety thereby addressing The Universal Transformer combines the following key propertiesWeight sharing Following intuitions behind found CNNs extend strikes inductive bias model expressivity show extensivelyConditional computation our goal build a computationally universal machine equipped halt continue through a recently introduced mechanism shows stronger results compared are enthusiastic on parallel-in sequence models By adding computational capacity recurrence in processing depth beyond the basic Universal Transformer presented build learning algorithms both data efficient generalize beyondThe code train Universal Transformers:/tensorflow/tensor2tensor BID31 .",0.01,0.4638317796985615
"We present a framework for interpretable continual learning (ICL). We show that explanations of previously performed tasks can be used to improve performance on future tasks. ICL generates a good explanation of a finished task, then uses this to focus attention on what is important when facing a new task. The ICL idea is general and may be applied to many continual learning approaches. Here we focus on the variational continual learning framework to take advantage of its flexibility and efficacy in overcoming catastrophic forgetting. We use saliency maps to provide explanations of performed tasks and propose a new metric to assess their quality. Experiments show that ICL achieves state-of-the-art results in terms of overall continual learning performance as measured by average classification accuracy, and also in terms of its explanations, which are assessed qualitatively and quantitatively using the proposed metric. Continual learning, also called lifelong learning, refers to frameworks where knowledge acquired from past tasks is accumulated for use on future tasks, i.e. where learning continually proceeds in an online fashion. Data belonging to different tasks might be non i.i.d. BID17 BID20 BID25 BID24 BID29 . Crucially, a continual learner must be able to learn a new task without forgetting how to perform previous tasks BID19 BID27 . Continual learning frameworks need to continually adapt to the domain shift occurring across tasks, without revisiting data from previous tasks. An appropriate balance is required between stability and adapting to new tasks and data, since excessive adaptation might lead to dramatic degradation in performance of earlier tasks, known as catastrophic forgetting BID6 BID7 BID16 BID18 .Several approaches have been introduced to address catastrophic forgetting. One approach is based on regularisation where stability is maintained by restricting the change of parameters with high influence while allowing the other parameters to vary freely BID14 BID17 BID11 BID30 BID35 . Another approach divides the network architecture into reusable parts that are less prone to changes, and parts devoted to individual tasks BID4 BID23 a; BID34 . The framework in BID33 constructs the neural network architecture via designed reinforcement learning (RL) strategies. The framework in BID13 bases its solution on moment matching. Another RL based framework is presented in BID9 where catastrophic forgetting is mitigated at multiple time scales by using RL agents with a synaptic model. BID15 propose a framework where multiple agents jointly learn to achieve multiple goals at once in a parallel offpolicy setup. The work in BID3 proposes experimental evaluations of continual learning as well as a variational Bayesian loss, via which they categorise a few previous works into either prior-focused or likelihood-focused. Attention mechanisms have been developed in rather similar problems before, e.g. in BID10 BID28 BID31 BID8 . Other saliency metrics have been introduced in BID2 BID0 . To the best of our knowledge , our framework is the first piece of work to pursue a comprehensive interpretability approach in the continual learning setting.Our work is based on the idea of imitating some aspects of how humans learn continually. We suggest that humans are quite successful in achieving goals and performing tasks sequentially, partly because we manage to understand and explain to ourselves certain aspects of the tasks we have already accomplished. This provides a contribution to our performance on similar tasks in the future.When given a task, we typically not only accomplish it, but also often (perhaps unconsciously) gain a useful interpretable concept. For instance, when a child tries to grasp an object, the progress in the child's skill is accompanied by improvements in similar tasks, e.g. grasping other objects which the child has never seen before. The development of the child's cognitive abilities shows an understanding of the concepts of gravity, geometric characteristics of the object, etc BID26 . We suggest that this development may be established by the consolidation of interpretable information from past experience. With this motivation, here we consider and analyse the impact of interpretable methods on continual learning. While there can be a tradeoff between performance and interpretability when considering just one task, here we show that interpretability can help performance when a learner faces consecutive tasks over time, as in continual learning.We propose a continual learning framework where the training phase of each task is followed by an explanation stage, which provides insights to be utilised along with the established training platform in learning the subsequent tasks. We focus on image classification tasks where training of the first task proceeds normally, before providing a saliency map for each test data point (image). By highlighting the most relevant areas of the test image w.r.t. the classification prediction, an understanding of the individual decisions taken by the classifier is attained. Afterwards, we compute a saliency map representing a summary (or average) of the saliency maps of test images per class, i.e. a summary of the classifier's decisions on the test data. This represents a summarised belief of the relevant areas of the input for each class. After completing the current task, we can use the explanation , depicted by the average saliency map, to achieve two goals:i Assessing how good the developed continual learning framework is at eradicating catastrophic forgetting. This evaluation is typically performed by measuring the difference in the classification performance on a certain task when it is the most recently encountered vs. when other tasks subsequently followed. Here we propose a new measure by adding a test which compares the saliency map resulting from testing a task right after finishing the corresponding training phase, with the saliency map of the same test on the same task after having other tasks subsequently trained by our continual learner. Degradation of the provided explanations provides a measure of the level of catastrophic forgetting induced in the continual learning framework. ii Providing interpretable attention information for subsequent tasks by involving the obtained saliency maps of the current task in the optimisation for the future tasks.To achieve the first goal, we need a metric to assess the quality of the extracted saliency maps. We propose a new metric for evaluating saliency maps resulting from the classification decisions on test data. Measuring the quality of a saliency map is not a straightforward task. Saliency maps typically aim at explaining the classification decision taken by a classifier. In other words, a saliency map seeks the subset of features that are the most influential in the resulting prediction of the classifier. As such, the explanation provided by a saliency map comes out in the form of a summary of the significant parts (features) of the input data, from the classifier's point of view. We propose a metric to assess the quality of an explanation resulting from a saliency map.To achieve the second goal, we need to involve the saliency maps in the learning procedure, not just during the test phase. We propose an attention mechanism that exploits the feature relevance values learnt in the latest task to focus the attention of the new learner on what is believed to be the most important parts of the input as per the latest task, which (w.r.t. continual learning) is assumed to be similar. Thus, an explanation of a task evolving over time is utilised to help the emerging tasks.Note that there is a difference in the nature of the two proposed goals described above. The optimisation needed to achieve the second goal does not guarantee that the first goal is automatically achieved, since the first goal addresses explanations (saliency maps) related to the same task at different time steps, whereas the second goal is concerned with exchanging interpretable information among different tasks. Hence, the assessment involved in the first goal is still needed regardless of the level of perfection of the second goal.In this work we perform experiments for the classification case illustrated above, but the same paradigm could be applied in future work to tasks other than classification, where the personalisation or notion of the explanation will need to be adapted to the nature of the task, i.e. saliency maps should be replaced with something more suitable to the task.We highlight the following contributions of our framework: 1) the interpretable continual learning (ICL) framework where, in addition to the ordinary understanding benefits of interpretable frame-works, explanations of the finished tasks are used to enhance the attention of the learner during the future tasks. Although we focus on performing within the variational continual learning framework BID17 , our proposed methodology is flexible and can be deployed with other continual learning frameworks, and also with other saliency detection methods. To the best of our knowledge, ICL represents a novel direction in the continual learning literature that focuses on interpretability; 2) introducing a new metric for saliency maps that aims at robustly assessing their quality without significant engineering required, i.e. no need to construct bounding rectangles of the relevant zones or similar; 3) learning from past experiences using an attention mechanism based on explanations (saliency maps) from the latest task; 4) Our quantitative and qualitative state-of-the-art results in four experiments on three datasets demonstrate the efficacy of the proposed framework. We introduced a continual learning framework incorporating interpretability, where saliency based explanations of previously learnt tasks are used to enhance the attention of the learner during future tasks. This framework demonstrates that interpretability is not only useful for increasing the understanding of the obtained results, but can also improve the performance of a sequential learning procedure. The proposed framework is flexible and can enhance both the interpretability and performance of continual learning methods, especially in terms of mitigating catastrophic forgetting. We proposed a new metric for saliency maps. We believe that adopting a Bayesian attention mechanism could be a fruitful direction for future work, especially when integrated with fully Bayesian variational continual learning.",1903,0.964,1103,1.7252946509519493,"We present interpretable continual learningICL We show explanations previously performed tasks future tasks ICL generates a good explanation a finished task then focus when facing The ICL idea general may many continual learning approaches Here focus the variational continual learning framework to take efficacy overcoming catastrophic forgetting We use saliency maps provide explanations performed tasks propose assess their quality Experiments show ICL achieves state results terms overall continual learning performance as average classification accuracy its explanations, assessed qualitatively the proposed metric Continual learning also refers frameworks where knowledge acquired past tasks accumulated for on where continually proceeds an online fashion Data belonging different tasks might non i.i.d . Crucially a continual learner must forgetting how perform previous tasks BID19 BID27 . Continual learning frameworks need continually adapt the domain shift occurring tasks without revisiting data An appropriate balance stability adapting new tasks data since excessive adaptation might dramatic degradation of earlier tasks known catastrophic forgetting BID6 BID7 BID16 BID18 .Several approaches introduced catastrophic forgetting One approach based regularisation where stability restricting parameters with high influence while allowing vary freely BID14 . Another approach divides the network architecture reusable parts less prone changes devoted individual tasks BID4 BID23 a; . The framework in BID33 constructs via designed reinforcement learning (RL) strategies The framework in BID13 bases its solution moment matching Another RL based framework presented BID9 where catastrophic forgetting at multiple time scales RL agents a synaptic model BID15 propose where multiple agents jointly learn achieve a parallel offpolicy setup The work in BID3 proposes experimental evaluations continual learning as a variational Bayesian loss, via they categorise a few previous works either priorfocused likelihood Attention mechanisms have rather similar problems before BID10 BID28 BID31 BID8 . Other saliency metrics have introduced BID2 BID0 . To , our framework the first piece work pursue a comprehensive interpretability approach the continual learning settingOur work imitating some aspects how continually We suggest humans quite successful achieving goals performing sequentially partly manage understand explain to certain aspects have already This provides a contribution our performance on similar tasksWhen given typically not accomplish often (perhaps gain a useful interpretable concept For instance tries grasp the progress in accompanied improvements similar tasks grasping other objects which The development the child's cognitive abilities shows an understanding the concepts gravity geometric characteristics etc BID26 . We suggest this development established the consolidation interpretable information past experience With this motivation here consider and analyse interpretable methods continual learning While can interpretability when considering just one task here interpretability help performance a learner faces consecutive tasks over in continual learningWe propose a continual learning framework the training phase an explanation stage provides insights utilised along the established training platform learning the subsequent tasks We focus image classification tasks training the first task proceeds normally before providing a saliency map each test data pointimage By highlighting the test image w.r.t the classification prediction an understanding the individual decisions taken attained Afterwards compute a saliency map representing a summary ( average test images per class the classifier's decisions This represents a summarised belief the relevant areas the input for each class After completing the current task the explanation , depicted the average saliency map achieve two goalsi Assessing good the developed continual learning framework eradicating catastrophic forgetting This evaluation typically measuring the classification performance on a certain task when the recently encountered vs. when other tasks subsequently followed Here propose by adding which compares the saliency map resulting testing a task right finishing the corresponding training phase on after having other tasks subsequently by our continual learner the provided explanations provides a measure catastrophic forgetting induced the continual learning framework ii Providing interpretable attention information subsequent tasks by involving the obtained saliency maps the optimisation forTo achieve need a metric We propose evaluating saliency maps resulting the classification decisions on test data Measuring a saliency map Saliency maps typically aim explaining the classification decision taken In a saliency map seeks the subset features the influential the resulting prediction As such the explanation provided a saliency map comes out the significant parts (features from We propose a metric assess an explanation resulting a saliency mapTo achieve need involve the learning procedure not during We propose an attention mechanism exploits the feature relevance values learnt the latest task focus what believed as per ( continual learning assumed similar. Thus an explanation a task evolving utilised help the emerging tasksNote the two proposed goals described The optimisation needed the second goal does guarantee automatically since the first goal addresses explanations (saliency maps related the same task at concerned exchanging interpretable information among Hence the assessment involved the first goal still needed regardless perfectionIn this work perform experiments for the classification case illustrated the same paradigm could tasks other classification the personalisation or notion the explanation will adapted should replaced somethingWe highlight the following contributions our framework 1) the interpretable continual learning where, the ordinary understanding benefits interpretable frame-works explanations the finished tasks used enhance the attention during the future tasks Although we focus performing within the variational continual learning framework BID17 our proposed methodology flexible deployed other continual learning frameworks and other saliency detection methods To ICL represents a novel direction the continual learning literature that interpretability; 2 introducing saliency maps aims robustly their quality without significant engineering required no need construct bounding rectangles the relevant zones similar; learning using an attention mechanism based explanations from the latest task Our quantitative state results four experiments on three datasets demonstrate the proposed framework We introduced a continual learning framework incorporating interpretability where saliency based explanations previously learnt tasks enhance the attention during future tasks This framework demonstrates interpretability useful increasing the obtained results a sequential learning procedure The proposed framework flexible enhance both the interpretability performance continual learning methods terms mitigating catastrophic forgetting We proposed saliency maps We believe adopting a Bayesian attention mechanism could integrated fully Bayesian variational continual learning",0.01,0.5520662166180975
"The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of research has also happened in the domain of low and mixed-precision Integer training, these works either present results for non-SOTA networks (for instance only AlexNet for ImageNet-1K), or relatively small datasets (like CIFAR-10). In this work, we train state-of-the-art visual understanding neural networks on the ImageNet-1K dataset, with Integer operations on General Purpose (GP) hardware. In particular, we focus on Integer Fused-Multiply-and-Accumulate (FMA) operations which take two pairs of INT16 operands and accumulate results into an INT32 output.We propose a shared exponent representation of tensors and develop a Dynamic Fixed Point (DFP) scheme suitable for common neural network operations. The nuances of developing an efficient integer convolution kernel is examined, including methods to handle overflow of the INT32 accumulator. We implement CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; and these networks achieve or exceed SOTA accuracy within the same number of iterations as their FP32 counterparts without any change in hyper-parameters and with a 1.8X improvement in end-to-end training throughput. To the best of our knowledge these results represent the first INT16 training results on GP hardware for ImageNet-1K dataset using SOTA CNNs and achieve highest reported accuracy using half precision While single precision floating point (FP32) representation has been the mainstay for deep learning training, half-precision and sub-half-precision arithmetic has recently captured interest of the academic and industrial research community. Primarily this interest stems from the ability to attain potentially upto 2X or more speedup of training as compared to FP32, when using half-precision fused-multiply and accumulate operations. For instance NVIDIA Volta NVIDIA (2017) provides 8X more half-precision Flops as compared to FP32.Unlike single precision floating point, which is a unanimous choice for 32b training, half-precision training can either use half-precision floating point (FP16), or integers (INT16). These two options offer varying degrees of precision and range; with INT16 having higher precision but lower dynamic range as compared to FP16. This also leads to residues between half-precision representation and single precision to be fundamentally different -with integer representations contributing lower residual errors for larger (and possibly more important) elements of a tensor. Beyond this first order distinction in data types, there are multiple algorithmic and semantic differences (for example FP16 multiply-and-accumulate operation accumulating into FP32 results) for each of these data types. Hence, when discussing half-precision training, the whole gamut of tensor representation, semantics of multiply-and-accumulate operation, down-conversion scheme (if the accumulation is to a higher precision), scaling and normalization techniques, and overflow management methods must be considered in totality to achieve SOTA accuracy. Indeed, unless the right combination of the aforesaid vectors are selected, half precision training is likely to fail. Conversely, drawing conclusions on the efficacy of a method by not selecting all vectors properly can lead to inaccurate conclusions.In this work we describe a mixed-precision training setup which uses:• INT16 tensors with shared tensor-wide exponent, with a potential to extend to sub-tensor wide exponents.• An instruction which multiplies two INT16 numbers and stores the output into a INT32 accumulator.• A down-convert scheme based on the maximum value of the output tensor in the current iteration using multiple rounding methods like nearest, stochastic, and biased rounding.• An overflow management scheme which accumulates partial INT32 results into FP32, along with trading off input precision with length of accumulate chain to gain performance.The compute for neural network training is dominated by GEMM-like, convolution, or dot-product operations. These are amenable to speedup via specialized low-precision instructions for fusedmultiply-and-accumulate (FMA), like AVX512_4VNNI 1 . However , this does not necessarily mean using half-precision representation for all tensors, or using only half-precision operations. In fact , performance speedups by migrating the compute intensive operations in both forward and back prorogation (FPROP, BPROP and WTGRAD) is often close to the maximum achievable speedup obtained by replacing all operations (for instance SGD) in half-precision. In cases where it is not, performance degradation typically happens due to limitations of memory bandwidth, and other architectural reasons.Hence on a balanced general purpose machine, a mixed-precision strategy of keeping precision critical operations (like SGD and some normalizations) in single precision and compute intensive operations in half precision can be employed. The proposed integer-16 based mixed-precision training follows this template.Using the aforesaid method, we train multiple visual understanding CNNs and achieve Top-1 accuracies BID16 on the ImageNet-1K dataset BID2 which match or exceed single precision results. These results are obtained without changing any hyper-parameters, and in as many iterations as the baseline FP32 training. We achieve 75.77 % Top-1 accuracy for ResNet-50 which, to the best of our knowledge, significantly exceeds any result published for halfprecision training, for example ; . Further, we also demonstrate our methodology achieves state-of-the-art accuracy (comparable to FP32 baseline) with int16 training on GoogLeNet-v1, VGG-16 and AlexNet networks. To the best of our knowledge, these are first such results using int16 training.The rest of the paper is organized as follows: Section 2 discusses the literature pertaining to various aspects of half-precision training. The dynamic fixed point format for representing half-precision tensors is described in Section 3. Dynamic fixed point kernels and neural network training operations are described in Section 4, and experimental results are presented in Section 5. Finally, we conclude this work in Section 6. We demonstrate industry-first reduced precision INT-based training result on large networks/data-sets. Showing on-par or better than FP32 baseline accuracies and potentially 2× savings in computation, communication and storage. Further, we propose a general dynamic fixed point representation scheme, with associated compute primitives and algorithm for the shared exponent management. This DFP solution can be used with general purpose hardware, leveraging the integer compute pipeline. We demonstrate this with implementation of CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; training these networks with mixed precision DFP16 for the ImageNet-1K classification task. While this work focuses on visual understanding CNNs, in future we plan to demonstrate the efficacy of this method for other types of networks like RNNs, LSTMs, GANs and extend this to wider set of applications.",1429,0.632,888,1.6092342342342343,"The state (SOTA for mixed precision training dominated variants low precision floating point operations in accumulating into FP32 Micikevicius et (2017 On while research also happened the domain low and mixed-precision Integer training these works either present results for non-SOTA networks only AlexNet for ImageNet-1K relatively small datasetslike In this work train state visual understanding the ImageNet-1K dataset Integer operations General Purpose (GP) hardware In particular focus Integer Fused-Multiply-and-Accumulate (FMA) operations two pairs INT16 operands accumulate resultsWe propose a shared exponent representation tensors develop suitable common neural network operations The nuances developing an efficient integer convolution kernel examined methods handle overflow the INT32 accumulator We implement CNN training ResNet-50 GoogLeNet-v1 VGG-16 AlexNet; these networks achieve or SOTA accuracy within iterations as their FP32 counterparts without hyper end training throughput To these results represent the first INT16 training results on GP hardware ImageNet-1K dataset using SOTA CNNs achieve highest reported accuracy half precision While single precision floating point (FP32) representation recently captured interest of Primarily this interest stems attain potentially upto 2X or more speedup training as FP32 when half-precision fused-multiply accumulate operations For instance NVIDIA Volta NVIDIA (2017 provides 8X more half-precision Flops as FP32.Unlike a unanimous choice 32b training either integers These two options offer precision range; with INT16 having but as FP16 This also leads residues between half-precision representation to fundamentally -with integer representations contributing lower residual errors for Beyond this first order distinction in data types ( FP16 multiply operation accumulating into FP32 results for Hence discussing half-precision training tensor representation semantics of multiply-and-accumulate operation down schemeif the accumulation to a higher precision scaling techniques overflow management methods must totality to achieve SOTA accuracy Indeed unless the right combination the aforesaid vectors half precision training Conversely drawing conclusions a method by not selecting all vectors properlyIn describe a mixed-precision training setup which uses:• INT16 tensors shared tensor-wide exponent a potential extend sub wide An instruction which two INT16 numbers stores INT32 A down-convert scheme based the maximum value using multiple rounding methods like nearest biased An overflow management scheme partial INT32 results FP32 along trading input precision length accumulate chain to performanceThe compute for neural network training dominated GEMM,, dot-product operations These amenable speedup via specialized low-precision instructions fusedmultiply-and-accumulate (FMA like AVX512_4VNNI 1 . However , using half-precision representation all tensors In fact , performance speedups by migrating the compute intensive operations both forward and back prorogationFPROP, WTGRAD is often close obtained replacingfor SGD half-precision In cases, performance degradation typically happens limitations memory bandwidth other architectural reasonsHence on a balanced general purpose machine a mixed-precision strategy keeping precision critical operations SGD some normalizations single precision compute half precision employed The proposed integer-16 based mixed-precision training follows this templateUsing the aforesaid method train multiple visual understanding CNNs achieve Top-1 accuracies BID16 on the ImageNet-1K dataset BID2 which match or single precision results These results obtained without changing any hyper- in as many iterations the baseline FP32 training We achieve 75.77 % Top-1 accuracy ResNet-50 which, to the significantly any result published halfprecision training for ; . Further demonstrate our methodology achieves state accuracy (comparable FP32 baseline int16 training on GoogLeNet-v1, VGG-16 and AlexNet networks To these first such results using int16 trainingThe rest organized Section discusses pertaining various aspects The dynamic fixed point format representing half-precision tensors Dynamic fixed point kernels neural network training operations described and experimental results Finally conclude this work Section We demonstrate industry-first reduced precision INT-based training result on large networks/data-sets Showing on-par or better FP32 baseline accuracies and potentially 2× savings computation communication storage Further propose a general dynamic fixed point representation scheme associated compute primitives algorithm the shared exponent management This DFP solution general purpose hardware leveraging the integer compute pipeline We demonstrate this implementation CNN training ResNet-50 GoogLeNet-v1 VGG-16 AlexNet; training these networks mixed precision DFP16 for the ImageNet-1K classification task While this work focuses visual understanding CNNs in future demonstrate networks like extend wider set",0.01,0.25635447177807813
"In this paper we introduce a new speech recognition system, leveraging a simple letter-based ConvNet acoustic model. The acoustic model requires only audio transcription for training -- no alignment annotations, nor any forced alignment step is needed. At inference, our decoder takes only a word list and a language model, and is fed with letter scores from the acoustic model -- no phonetic word lexicon is needed. Key ingredients for the acoustic model are Gated Linear Units and high dropout. We show near state-of-the-art results in word error rate on the LibriSpeech corpus with MFSC features, both on the clean and other configurations.
 Top speech recognition systems are either complicated pipelines or using more data that is publicly available. We set out to show that it is possible to train a nearly state of the art speech recognition system for read speech, with a public dataset (LibriSpeech), on a GPU-equipped workstation. Thus, we present an end-to-end system for speech recognition, going from Mel-Frequency Spectral Coefficients (MFSCs) to the transcription in words. The acoustic model is trained using letters (graphemes) directly, which take out the need for an intermediate (human or automatic) phonetic transcription.The classical pipeline to build state of the art systems for speech recognition consists in first training an HMM/GMM model to force align the units on which the final acoustic model operates (most often context-dependent phone states). This approach takes its roots in HMM/GMM training BID31 . The improvements brought by deep neural networks (DNNs) and convolutional neural networks (CNNs) BID26 BID27 for acoustic modeling only extend this training pipeline. The current state of the art on LibriSpeech belongs to this approach too BID16 BID19 , with an additional step of speaker adaptation BID22 BID18 . Recently, BID25 proposed GMM-free training, but the approach still requires to generate a forced alignment.An approach that cut ties with the HMM/GMM pipeline (and with forced alignment) was to train with a recurrent neural network (RNN) BID7 ) for phoneme transcription. There are now competitive end-to-end approaches of acoustic models toppled with RNNs layers as in BID9 BID14 BID23 BID0 , trained with a sequence criterion BID8 . However these models are computationally expensive, and thus often take a long time to train. On conversational speech (that is not the topic of this paper), the state of the art is still held by complex ConvNets+RNNs acoustic models, coupled to domain-adapted language models BID32 BID24 .Compared to classical approaches that need phonetic annotation (often derived from a phonetic dictionary, rules, and generative training), we propose to train the model end-to-end, using graphemes directly. Compared to sequence criterion based approaches that train directly from speech signal to graphemes BID14 , we propose an RNN-free architecture based on convolutional networks for the acoustic model, toppled with a simple sequence-level variant of CTC.We reach the clean speech performance of BID19 , but without performing speaker adaptation. Our word-error-rate on clean speech is better than BID0 , while being worse on noisy speech, but they train on 11,900 hours while we only train on the 960h available in LibriSpeech's train set. The rest of the paper is structured as follows: the next section presents the convolutional networks used for acoustic modeling, along with the automatic segmentation criterion and decoding approaches. The last section shows experimental results on LibriSpeech. Figure 1: Overview of our acoustic model, which computes MFSC features which are fed to a Gated ConvNet. The ConvNet output one score for each letter in the dictionary, and for each MFSC frame. At inference time, theses scores are fed to a decoder (see Section 2.4) to form the most likely sequence of words. At training time, the scores are fed to the ASG criterion (see FIG1 ) which promotes sequences of letters leading to the transcrition sequence (here ""c a t""). We have introduced a simple end-to-end automatic speech recognition system, which combines a large (208M parameters) but efficient ConvNet acoustic model, an easy sequence criterion which can infer the segmentation, and a simple beam-search decoder. The decoding results are competitive on the LibriSpeech corpus (4.8% WER dev-clean). Our approach breaks free from HMM/GMM pre-training and forced alignment, as well as not being as computationally intensive as RNN-based approaches BID0 . We based all our work on a publicly available (free) dataset, all of which should make it easier to reproduce. Further work should include leveraging speaker identity, training from the raw waveform, data augmentation, training with more data, better language models.",980,0.505,610,1.6065573770491803,"In leveraging a simple letter-based ConvNet acoustic model The acoustic model requires only audio transcription training -- no alignment annotations nor any forced alignment step is At inference our decoder takes only a word list a language model is fed letter scores the acoustic model -- no phonetic word lexicon is Key ingredients the acoustic model Gated Linear Units high dropout We show near state results word error rate on the LibriSpeech corpus MFSC features both the clean and other configurations Top speech recognition systems either complicated pipelines using more data that publicly We set show train a nearly state read speech a public dataset (LibriSpeech a GPU-equipped workstation Thus end system speech recognition going Mel-Frequency Spectral Coefficients the transcription in words The acoustic model trained lettersgraphemes directly take out an intermediate (human or automatic) phonetic transcriptionThe classical pipeline to build state consists first training an HMM/GMM model force align the units which operatesmost often context-dependent phone states This approach takes its roots HMM/GMM training BID31 . The improvements brought deep neural networks BID26 BID27 for acoustic modeling only extend this training pipeline on LibriSpeech belongs this approach too BID16 BID19 , speaker adaptation Recently BID25 proposed GMM-free training the approach to generate a forced alignmentAn approach cut ties the HMM/GMM pipeline forced alignment train ) phoneme transcription There now competitive end approaches of acoustic models toppled RNNs layers as in BID9 BID14 BID23 BID0 , trained a sequence criterion However these models computationally thus often take train On conversational speech (that not the topic the state still held complex ConvNets+RNNs acoustic models coupled domain-adapted language models BID32 BID24 .Compared need phonetic annotationoften derived rules generative training we train end graphemes directly Compared sequence criterion based train directly from speech signal BID14 , an RNN-free architecture the acoustic model toppled with a simple sequence-level variant CTC.We reach the clean speech performance without performing speaker adaptation Our word-error-rate on clean speech better BID0 , while being worse noisy speech they train 11,900 hours while only the 960h available LibriSpeech's train set The rest structured the next section acoustic modeling along the automatic segmentation criterion decoding approaches The last section shows experimental results LibriSpeech Figure Overview our acoustic model MFSC features which fed a Gated ConvNet The ConvNet output one score each letter for each MFSC frame At inference time theses scores fed form the most likely sequence words At training time the scores fed the ASG criterion FIG1 ) promotes sequences letters leading the transcrition sequencehere ""c a We introduced combines a large (208M parameters but efficient ConvNet acoustic model an easy sequence criterion which infer, a simple beam-search decoder The decoding results competitive on the LibriSpeech corpus WER devclean Our approach breaks free HMM/GMM pre-training and forced alignment not as computationally RNN-based approaches BID0 . We based all should reproduce Further work should leveraging speaker identity training from the raw waveform data augmentation training more data better language models",0.01,0.24953407485666143
"Generative adversarial networks (GANs) are a powerful framework for generative tasks. However, they are difficult to train and tend to miss modes of the true data generation process. Although GANs can learn a rich representation of the covered modes of the data in their latent space, the framework misses an inverse mapping from data to this latent space. We propose Invariant Encoding Generative Adversarial Networks (IVE-GANs), a novel GAN framework that introduces such a mapping for individual samples from the data by utilizing features in the data which are invariant to certain transformations. Since the model maps individual samples to the latent space, it naturally encourages the generator to cover all modes. We demonstrate the effectiveness of our approach in terms of generative performance and learning rich representations on several datasets including common benchmark image generation tasks. Generative Adversarial Networks (GANs) BID4 emerged as a powerful framework for training generative models in the recent years. GANs consist of two competing (adversarial) networks: a generative model that tries to capture the distribution of a given dataset to map from an arbitrary latent space (usually drawn from a multi-variate Gaussian) to new synthetic data points, and a discriminative model that tries to distinguish between samples from the generator and the true data. Iterative training of both models ideally results in a discriminator capturing features from the true data that the generator does not synthesize, while the generator learns to include these features in the generative process, until real and synthesized data are no longer distinguishable. Experiments by BID10 showed that a GAN can learn rich representation of the data in the latent space in which interpolations produce semantic variations and shifts in certain directions correspond to variations of specific features of the generated data. However, due to the lack of an inverse mapping from data to the latent space, GANs cannot be used to encode individual data points in the latent space BID2 . Moreover, although GANs show promising results in various tasks, such as the generation of realistic looking images BID9 BID0 BID11 or 3D objects BID13 , training a GAN in the aforementioned ideal way is difficult to set up and sensitive to hyper-parameter selection BID10 . Additionally, GANs tend to restrict themselves on generating only a few major modes of the true data distribution, since such a so-called mode collapse is not penalized in the GAN objective, while resulting in more realistic samples from these modes BID1 . Hence, the majority of the latent space only maps to a few regions in the target space resulting in poor representation of the true data. We propose a novel GAN framework, Invariant-Encoding Generative Adversarial Networks (IVE-GAN), which extends the classical GAN architecture by an additional encoding unit E to map samples from the true data x to the latent space z (compare FIG0 ). To encourage the encoder to learn a rich representation of the data in the latent space, the discriminator D is asked to distinguish between different predefined transformations T(x) of the input sample and generated samples G(E(x)) by taking the the original input as condition into account. While the discriminator has to learn what the different variations have in common with the original input, the encoder is forced to encode the necessary information in the latent space so that the generator can fool the discriminator by generating samples which are similar to the original samples. Since the discriminator is invariant to the predefined transformations, the encoder can ignore these variations in the input space and learn a rich and to such transformations invariant representation of the data. The variations of the generated samples are modeled by an additional latent vector z (drawn from a multi-variate Gaussian). Thus, the encoded samples condition the generator G(z , E(x)). Moreover, since the discriminator learns to distinguish between generated samples and variations of the original for each individual sample x in the data, the latent space can not collapse to a few modes of the true data distribution since it will be easy for the discriminator to distinguish generated samples from original ones if the mode is not covered by the generator. Thus, the proposed IVE-GAN learns a rich and to certain transformations invariant representation of a dataset and naturally encourages the generator to cover all modes of the data distribution.To generate novel samples, the generator G(z) can be fed with an arbitrary latent representation z ∼ P noise .In summary, we make the following contributions:• We derive a novel GAN framework for learning rich and transformation invariant representation of the data in the latent space.• We show that our GANs reproduce samples from a data distribution without mode collapsing issues.• We demonstrate robust GAN training across various data sets and showcase that our GAN produces very realistic samples. With this work we proposed a novel GAN framework that includes a encoding unit that maps data to a latent representation by utilizing features in the data which are invariant to certain transformations.We evaluate the proposed model on three different dataset and show the IVE-GAN can generate visually appealing images of high variance while learning a rich representation of the dataset also covering subtle features. B NETWORK ARCHITECTURE AND HYPERPARAMETERS",1016,0.443,584,1.7397260273972603,"Generative adversarial networks generative tasks However they difficult train tend miss modes the true data generation process Although GANs learn a rich representation the covered modes the data their latent space the framework misses an inverse mapping from data We propose Invariant Encoding Generative Adversarial NetworksIVE-GANs introduces such a mapping individual samples from by utilizing features which certain transformations Since the model maps individual samples the latent space naturally encourages the generator cover all modes We demonstrate our approach terms generative performance learning rich representations on several datasets including common benchmark image generation tasks Generative BID4 emerged training GANs consist tries to map from an arbitrary latent spaceusually drawn new synthetic data points distinguish samples the generator the true data Iterative training both models ideally results a discriminator capturing features the true data that the generator synthesize learns include until real and synthesized data no distinguishable Experiments by BID10 showed a GAN can learn rich representation interpolations produce semantic variations shifts certain directions correspond variations specific features However due an inverse mapping from data the latent space GANs encode individual data points BID2 . Moreover although GANs show various tasks the generation realistic looking images BID9 BID0 BID11 or , training the aforementioned ideal way to set sensitive hyper-parameter selection BID10 Additionally GANs tend restrict themselves on generating only a few major modes the true data distribution since such a so-called mode collapse penalized the GAN objective while resulting more realistic samples from BID1 . Hence the majority the latent space only maps resulting poor representation the true data We propose a novel GAN frameworkIVE-GAN extends an additional encoding unit E to map samples the true data x the latent space zcompare FIG0 To encourage the encoder learn a rich representation the latent space the discriminator D asked distinguish different predefined transformations T(x of the input sample generated samples G(E(x by the the original input condition into While the discriminator learn what the different variations have with the original input the encoder forced encode the latent space the generator fool generating samples which similar Since the discriminator invariant the predefined transformations ignore these variations the input space learn rich to such transformations invariant representation The variations the generated samples modeled an additional latent vector zdrawn Thus the encoded samples condition the generator G(z , Moreover since the discriminator learns generated samples variations for x in the latent space not collapse a few modes the true data distribution since easy generated samples original ones if the mode covered the generator Thus the proposed IVE-GAN learns rich to certain transformations invariant representation a dataset naturally encourages the generator cover all modesTo generate novel samples G(z fed an arbitrary latent representation z ∼ P noise .In summary make derive a novel GAN framework show reproduce samples without mode collapsing robust GAN training across showcase produces very realistic samples With this work proposed a novel GAN framework includes a encoding unit maps data a latent representation by utilizing features which certain transformationsWe evaluate three different dataset the IVE-GAN can generate visually appealing images high variance while learning a rich representation also covering subtle features B NETWORK ARCHITECTURE",0.01,0.5888360958738791
"We propose a method for learning the dependency structure between latent variables in deep latent variable models.   Our general modeling and inference framework combines the complementary strengths of deep generative models and probabilistic graphical models. In particular, we express the latent variable space of a variational autoencoder (VAE) in terms of a Bayesian network with a learned, flexible dependency structure.   The network parameters, variational parameters as well as the latent topology are optimized simultaneously with a single objective.   Inference is formulated via a sampling procedure that produces expectations over latent variable structures and incorporates top-down and bottom-up reasoning over latent variable values.   We validate our framework in extensive experiments on MNIST, Omniglot, and CIFAR-10. Comparisons to state-of-the-art structured variational autoencoder baselines show improvements in terms of the expressiveness of the learned model.",174,0.108,98,1.7755102040816326,"We propose learning the dependency structure between latent variables deep latent variable models Our general modeling and inference framework combines the complementary strengths In particular express the latent variable spaceVAE a learned, flexible dependency structure The network parameters, variational parameters as the latent topology optimized simultaneously a single objective Inference formulated via a sampling procedure produces expectations over latent variable structures incorporates over We validate our framework extensive experiments MNIST Omniglot Comparisons state structured variational baselines show improvements terms the expressiveness the learned model",0.0,0.6800110341022725
"Many real-world time series, such as in activity recognition, finance, or climate science, have changepoints where the system's structure or parameters change. Detecting changes is important as they may indicate critical events. However, existing methods for changepoint detection face challenges when (1) the patterns of change cannot be modeled using simple and predefined metrics, and (2) changes can occur gradually, at multiple time-scales. To address this, we show how changepoint detection can be treated as a supervised learning problem, and propose a new deep neural network architecture that can efficiently identify both abrupt and gradual changes at multiple scales. Our proposed method, pyramid recurrent neural network (PRNN), is designed to be scale-invariant, by incorporating wavelets and pyramid analysis techniques from multi-scale signal processing. Through experiments on synthetic and real-world datasets, we show that PRNN can detect abrupt and gradual changes with higher accuracy than the state of the art and can extrapolate to detect changepoints at novel timescales that have not been seen in training. Changepoints, when the structure or parameters of a system change, are critical to detect in many domains. In medicine, finance, climate science and other fields, these changes can indicate that important events have occurred (e.g. onset of illness or a financial crisis), or changed in important ways (e.g. increasing illness severity). In both cases, these affect decision-making. Changepoint detection (CPD) aims to find these critical times. However, changes may result in complex patterns across multiple observed variables, and can be hard to recognize, especially in multivariate timeseries where interdependencies exist among variables. Further, not all changepoints lead to a sudden transition, many occur over a duration of time (e.g. weightloss, transition between activities) and are harder to identify.Various methods have been proposed for CPD including parametric methods BID0 BID49 BID34 , which make strong assumptions about data distributions, and nonparametric methods BID12 BID39 , which are based on engineered divergence metrics or kernel functions. Most parametric methods are highly context specific, and face difficulty when changes result in complex temporal patterns that are hard to model manually. For nonparametic methods, the main drawback is that these methods rely heavily on the choice of parameters or kernels. To handle data from different domains, BID8 proposed a nonparametric CPD method. However, like many other CPD methods, it can only detect abrupt changes. Yet in real-world applications, the effect of a change may be gradual and may happen over different durations. Some methods have been explicitly designed for detecting gradual changepoints BID2 BID20 , but cannot handle changes occurring at arbitrary timescales. In some applications, like detecting changes in activity, how quickly someone transitions from sitting to standing should not affect accuracy at detecting the transition.In contrast, Deep Neural Networks (DNN) have been used for time series forecasting BID43 and classification as they can learn functions automatically. These can be more easily adapted to new tasks if there is sufficient training data. However, DNNs typically need enough examples of all possible ways a pattern can appear, and thus all possible transition speeds, to reliably detect it in test data. Since this data is costly and may be infeasible to collect in some cases, it is ideal to have a scale-invariant approach that can generalize beyond observed timescales.We propose a novel DNN architecture for CPD using supervised learning. Our approach makes two key contributions to neural network architecture: a trainable wavelet layer that transforms input into a pyramid of multiscale feature maps; and Pyramid recurrent neural networks (PRNN), which build a multi-scale Recurrent Neural Network (RNN) on top of a multi-channel Convolutional Neural Network (CNN) processing the wavelet layer. Finally, we use a binary classifier on the PRNN output to detect changepoints. On both simulated and real-world data, we show that the proposed model can encode short-term and long-term temporal patterns and detect from abrupt to extremely gradual changepoints. The model is scale invariant, and can detect changes at any timescale, regardless of those seen in training. We focus on the task of CPD, but this architecture may have more general applications in time series analysis. We propose a new class of DNNs that are scale-invariant, and show they can detect from abrupt to gradual changepoints in multimodality time series. The core is 1) augmenting CNNs with trainable Wavelet layers to recognize short-term multi-scale patterns; and 2) building a pyramid-shaped RNN on top of the multi-scale feature maps to simultaneously model long-term patterns and fuse multiscale information. The final model can detect events involving short-and long-term patterns at various scales, which is a difficult task for conventional DNNs. Although this reduces the amount of training data required to learn from changes, the proposed method still requires clean labels. Experiments show our approach detects changes quickly, with lower sensitivity to the tolerance parameter than other approaches. For real-world applications, this leads to much higher reliability. In future work we will real-world challenges (e.g. noisy data, missing/noisy labels) by incorporating robustness, semi-supervised learning methods, and multi-view learning techniques. TAB0 -3 show the AUC (Area Under the ROC Curve) results for synthetic data. To detect changepoints, we apply non-maximum suppression with a sliding window of length ω and filter the maximum values with a threshold. We evaluate AUC by iterating over this threshold. Since changepoints may not exactly match the true changepoints, we use a tolerance parameter η that sets how close a detected change must be to a true change to be considered a correct detection. We match detected changepoints to the closest true changepoint within η time step. TAB0 shows the results for the experiment of ""train abrupt and test gradual"" for synthetic data. TAB1 shows the results for the experiment of ""train gradual and test abrupt"" for synthetic data. TAB2 shows the results for the experiment of ""train all and test all"" for synthetic data. TAB3 shows the results for Opportunity data. TAB4 shows the results for Bee Waggle Dance data.",1277,0.715,743,1.7187079407806192,"Many real-world time series, in activity recognition finance climate science changepoints where the system's structure parameters Detecting changes is as critical events However existing methods changepoint detection face challenges when ( the patterns modeled simple and predefined metrics gradually To address show changepoint detection treated propose efficiently identify both abrupt and gradual changes at Our proposed method, pyramid recurrent neural network scale by incorporating wavelets pyramid analysis techniques from multi-scale signal processing Through experiments synthetic and real-world datasets show PRNN detect abrupt and gradual changes with the state and detect changepoints that training Changepoints, when the structure or parameters critical detect in many domains In medicine finance climate science these changes indicate important events illness changed in increasing illness In both cases these affect Changepoint detection ( aims find these critical times However changes may result complex patterns across multiple observed variables can hard recognize multivariate timeseries interdependencies exist among Further not all changepoints lead a sudden transition many occur a duration between activities harderVarious methods CPD including parametric methods BID0 BID49 BID34 make strong assumptions data distributions engineered divergence metrics or kernel functions Most parametric methods highly context face difficulty changes result complex temporal patterns model manually For nonparametic methods the main drawback rely the choice or kernels To handle data different domains BID8 proposed a nonparametric CPD method However like many other CPD methods only detect abrupt changes Yet in the effect a change may gradual may happen different durations Some methods explicitly detecting gradual changepoints BID2 BID20 , handle occurring arbitrary timescales In some applications like detecting changes activity how quickly someone transitions sitting should accuracy at detectingIn contrast Deep Neural Networks time series forecasting BID43 classification as they learn functions automatically These can more adapted new tasks if there sufficient training data However DNNs typically need enough examples all possible ways a pattern appear thus all possible transition speeds reliably test data Since this data costly may ideal generalize beyond observed timescalesWe propose a novel DNN architecture CPD supervised learning Our approach makes two key contributions neural network architecture a trainable wavelet layer transforms input a pyramid multiscale feature maps; Pyramid recurrent neural networks build processing Finally use a binary classifier on the PRNN output detect changepoints On both simulated and real-world data show the proposed model encode detect from abrupt to extremely gradual changepoints The model scale detect changes at any timescale those seen training We focus the task CPD this architecture time series analysis We propose DNNs scale show they detect from abrupt to gradual changepoints multimodality time series The core is 1) augmenting CNNs trainable Wavelet layers recognize short-term multi-scale patterns a pyramid-shaped RNN on simultaneously model fuse multiscale information The final model can detect events involving at various scales conventional DNNs Although reduces learn from changes the proposed method clean labels Experiments show our approach detects changes quickly lower sensitivity the tolerance parameter For leads much higher reliability In future work real-world challenges ( missing/noisy labels by incorporating robustness multiview learning TAB0 -3 show the AUC (Area the ROC Curve results synthetic data To detect changepoints apply non-maximum suppression with a sliding window length �� filter the maximum values We evaluate AUC by iterating this threshold Since changepoints may exactly the true changepoints use a tolerance parameter �� that sets how close a detected change must to a correct detection We match detected changepoints the closest true changepoint within �� time step TAB0 shows for the experiment ""train abrupt and test gradual for synthetic data TAB1 shows for the experiment ""train gradual and test abrupt for synthetic data TAB2 shows for the experiment ""train all and test for synthetic data TAB3 shows for Opportunity data TAB4 shows for Bee Waggle Dance data",0.01,0.5352838578035763
"We demonstrate how to learn efficient heuristics for automated reasoning algorithms through deep reinforcement learning. We focus on backtracking search algorithms for quantified Boolean logics, which already can solve formulas of impressive size - up to 100s of thousands of variables. The main challenge is to find a representation of these formulas that lends itself to making predictions in a scalable way. For challenging problems, the heuristic learned through our approach reduces execution time by a factor of 10 compared to the existing handwritten heuristics. Automated reasoning and machine learning have both made tremendous progress over the last decades. Automated reasoning algorithms are now able to solve challenging logical problems that once seemed intractable, and today are used in industry for the verification of hardware and software systems. At the core of this progress are logic solvers for Boolean Satisfiability (SAT), Satisfiability Modulo Theories (SMT), and recently also Quantified Boolean Formulas (QBF). These solvers rely on advanced backtracking search algorithms, such as conflict-driven clause learning (CDCL) BID30 , to solve formulas with thousands or even millions of variables. Many automated reasoning algorithms are not only able to answer challenging queries, but also to explain their answer by providing detailed mathematical proofs. However, when problems lack a formal semantics automated reasoning algorithms are hard to apply, and they tend to scale poorly for problems involving uncertainty (e.g. in form of probabilities).Machine learning, on the other hand, recently experienced several breakthroughs in object recognition, machine translation, board games, and language understanding. At the heart of the recent progress in machine learning lie optimization algorithms that train deep and overparameterized models on large amounts of data. The resulting models generalize to unseen inputs and can generally deal well with uncertainty. However, the predictions made by learned models are often hard to explain and hard to restrict to safe behaviors.The complementary strengths of machine learning and automated reasoning raise the question how the methods of the two fields can be combined. In this paper we study how neural networks can be employed within automated reasoning algorithms. We discuss the unique challenges that arise in applying neural networks to vast logical formulas and how reinforcement learning can be used to learn better heuristics for backtracking search algorithms.Backtracking search algorithms in automated reasoning are highly nondeterministic: at many points in their execution there are multiple options for how to proceed. These choices have a big impact on performance; in fact we often see that some problems cannot be solved within hours of computation that under different heuristics are solved within milliseconds. The most prominent heuristic choice in CDCL-style search algorithms is the variable selection heuristic, which is to select a variable (and which value to assign to that variable). Until today, Variable State Independent Decaying Sum (VSIDS) BID33 and its variants are used as the variable selection heuristic in some of the most competitive SAT solvers BID4 Soos, 2014; BID2 and QBF solvers BID28 BID36 . Even small improvements over VSIDS, such as the recent introduction of learning rate branching BID27 , are highly interesting for the automated reasoning community.Designing heuristics for backtracking search algorithms is often counter-intuitive: For example, it is well-known that heuristics that aim to find a correct solution perform worse than heuristics that aim to quickly cause a conflict (i.e. reach a dead-end in the search tree). This is because running into a conflict allows us to apply clause learning, a process that (deductively) derives a new constraint that prevents running into the similar conflicts again. This can cut off an exponential number of branches and can therefore save a lot of computation time in the future. Heuristics for search algorithms are an interesting target for machine learning with immediate impact in verification.The Problem We want to learn a heuristic for a backtracking search algorithm such that it solves more formulas in less time. We view this as a reinforcement learning problem where we are given a formula from some distribution of formulas, and we run the backtracking search algorithm until it reaches a decision point and then query the neural network to predict an action. We iterate this process until termination (at which point the formula is proven or refuted) or a time limit is reached. The input to the neural network is thus the current state of the algorithm, including the formula, and we reward it for reaching termination quickly.In this work, we focus on learning heuristics for the solver CADET BID36 BID38 . CADET is a competitive solver for QBF formulas with the quantifier prefix ∀X ∃Y , which covers most of the known applications of QBF. For all purposes of this work, we can assume the algorithm works exactly like a SAT solver. The heuristic we address in this work is the variable selection heuristic.Challenges The setting comes with several unique challenges:Size: While typical reinforcement learning settings have a small, fixed-size input (a Go board or an Atari screen), the formulas that we consider have hundreds of variables and thousands of clauses, each with several data points. All variables appear both as part of the state and as actions in the reinforcement learning environment. At the same time, the size of the formulas varies dramatically (from tens of variables up to 700k variables) and is hardly correlated with their 'difficulty' -while some of the largest formulas can be solved with little effort, some of the formulas with only 100 variables cannot be solved by any modern QBF solver. We presented an approach to improve the heuristics of a backtracking search algorithm for Boolean logic through deep reinforcement learning. The setting is new and challenging to reinforcement learning, featuring an unbounded input-size and action space, a connection between the length of episodes and rewards. We demonstrate that these problems can be overcome, and learn a heuristic that reduces the overall execution time of a competitive QBF solver by a factor of 10 after training on similar formulas.We believe that this work motivates more aggressive research efforts in the area and will lead to a significant improvement in the performance of logic solvers. Our experiments uncover particu-lar challenges to be addressed in the future. The transfer of the learned insights between different sets of formulas is still limited, learning from long episodes seems to be challenging, andcounterintuitively-it does not seem to help to consider multiple iterations of the GNN.14. Number of successful propagation steps indicates whether the variable is universally quantified, DISPLAYFORM0 indicates whether the variable is existentially quantified, y 2 ∈ {0, 1}indicates whether the variable has a Skolem function already, y 3 ∈ {0, 1} indicates whether the variable was assigned constant True, y 4 ∈ {0, 1} indicates whether the variable was assigned constant False, DISPLAYFORM1 indicates whether the variable was decided positive, y 6 ∈ {0, 1} indicates whether the variable was decided negative, and DISPLAYFORM2 indicates the activity level of the variable. There is no way to assign variables strings as names. The reasoning behind this decision is that this format is only meant to be used for the computational backend.",1434,0.691,838,1.7112171837708832,"We demonstrate learn efficient heuristics automated reasoning algorithms through deep reinforcement learning We focus backtracking search algorithms quantified Boolean logics already can solve formulas of impressive size - up 100s variables The main challenge a representation these formulas lends making predictions in For challenging problems the heuristic learned through our approach reduces execution time compared the existing handwritten heuristics Automated reasoning have both tremendous progress Automated reasoning algorithms now challenging logical problems once today are industry for the verification At this progress are logic solvers for Boolean SatisfiabilitySAT Satisfiability Modulo Theories recently also Quantified Boolean Formulas These solvers rely advanced backtracking search algorithms conflict-driven clause learningCDCL BID30 , solve formulas thousands variables Many automated reasoning algorithms not only able answer challenging queries explain their answer by providing detailed mathematical proofs However when problems lack a formal semantics automated reasoning algorithms hard apply they scale for problems uncertainty in form probabilities).Machine learning, recently experienced object recognition machine translation board games language understanding At the recent progress machine lie optimization train deep and overparameterized large amounts The resulting models generalize unseen inputs can generally deal well uncertainty However the predictions learned models hard explain hard restrict safe behaviorsThe complementary strengths machine learning automated reasoning raise how the methods the two fields In this paper study neural networks employed within automated reasoning algorithms We discuss the unique challenges applying neural networks vast logical formulas reinforcement learning learn better heuristics backtracking searchBacktracking search algorithms in automated reasoning highly nondeterministic: at there multiple options These choices performance; in we often that some problems within hours computation that under different heuristics solved milliseconds The most prominent heuristic choice CDCL-style search algorithms the variable selection heuristic to (and which value assign Until today Variable State Independent Decaying SumVSIDS BID33 and its variants the variable selection heuristic some of the most competitive SAT solvers BID4 Soos 2014; QBF solvers . Even small improvements over VSIDS the recent introduction learning rate branching BID27 , highly interesting the automated reasoning communityDesigning heuristics backtracking search algorithms often counter: For well aim find a correct solution perform quickly cause a conflict ( reach in This because running into a conflict allows apply clause learning (deductively derives a new constraint prevents running the similar conflicts again This can cut off an exponential number branches can therefore save computation time in Heuristics search algorithms an interesting target machine with immediate impact verificationThe Problem We want learn a heuristic a backtracking search algorithm such solves more formulas We view a reinforcement learning problem where given a formula from some distribution formulas run the backtracking search algorithm until reaches and query predict an action We iterate this process until termination (at the formula proven or refuted a time limit The input to thus including the formula we reward reaching termination quicklyIn focus learning heuristics the solver CADET BID36 BID38 . CADET is a competitive solver QBF formulas with the quantifier prefix ��X � covers most the known applications For all purposes this work we can the algorithm works exactly a SAT solver The heuristic we address the variable selection heuristicChallenges The setting comesSize While typical reinforcement learning settings (a Go board an Atari screen the formulas consider have hundreds thousands clauses several data points All variables appear both as part the state actions the reinforcement learning environment At the size the formulas varies dramatically (from tens variables up 700k variables hardly correlated their 'difficulty -while some solved the formulas only 100 variables any modern QBF We presented an approach improve the heuristics a backtracking search algorithm Boolean logic through deep reinforcement learning The setting new challenging reinforcement learning featuring an unbounded input-size and action space connection the length episodes rewards We demonstrate these problems, learn a heuristic reduces the overall execution time a competitive QBF solver after training on similar formulasWe believe this work motivates more aggressive research efforts and logic solvers Our experiments uncover particu-lar challenges be The transfer the learned insights between different sets formulas still limited learning long episodes seems challenging andcounterintuitively-it does help consider multiple iterations the GNN.14. Number successful propagation steps indicates the variable universally quantified DISPLAYFORM0 indicates existentially y 2 � {0 has a Skolem function already y indicates was assigned decided and the activity level There assign variables strings as names The reasoning this format only meant the computational backend",0.01,0.5161980670734838
"We consider the question of how to assess generative adversarial networks, in particular with respect to whether or not they generalise beyond memorising the training data. We propose a simple procedure for assessing generative adversarial network performance based on a principled consideration of what the actual goal of generalisation is. Our approach involves using a test set to estimate the Wasserstein distance between the generative distribution produced by our procedure, and the underlying data distribution. We use this procedure to assess the performance of several modern generative adversarial network architectures. We find that this procedure is sensitive to the choice of ground metric on the underlying data space, and suggest a choice of ground metric that substantially improves performance.   We finally suggest that attending to the ground metric used in Wasserstein generative adversarial network training may be fruitful, and outline a concrete pathway towards doing so. Generative adversarial networks (GANs) BID6 have attracted significant interest as a means for generative modelling. However, recently concerns have been raised about their ability to generalise from training data and their capacity to overfit . Moreover, techniques for evaluating the quality of GAN output are either ad hoc, lack theoretical rigor, or are not suitably objective -often times ""visual inspection"" of samples is the main tool of choice for the practitioner. More fundamentally, it is sometimes unclear exactly what we want a GAN to do: what is the learning task that we are trying to achieve?In this paper, we provide a simple formulation of the GAN training framework, which consists of using a finite dataset to estimate an underlying data distribution. The quality of GAN output is measured precisely in terms of a statistical distance D between the estimated and true distribution. Within this context, we propose an intuitive notion of what it means for a GAN to generalise.We also show how our notion of performance can be measured empirically for any GAN architecture when D is chosen to be a Wasserstein distance, which -unlike other methods such as the inception score BID14 ) -requires no density assumptions about the data-generating distribution. We investigate this choice of D empirically, finding that its performance is heavily dependent on the choice of ground metric underlying the Wasserstein distance. We suggest a novel choice of ground metric that we show performs well, and also discuss how we might otherwise use this observation to improve the design of Wasserstein GANs (WGANs) . We believe our work reveals two promising avenues of future inquiry. First, we suggest that W L p •η is an appealing choice of D, both due to its nice theoretical properties -it metricises weak convergence, and does not require us to make any density assumptions about π -and due to its sound empirical performance demonstrated above. It would be very interesting to use this D to produce a systematic and objective comparison of the performance of all current major GAN implementations, and indeed to use this as a metric for guiding future GAN design. We also view the test (5) as potentially useful for determining whether our algorithms are overfitting. This would be particularly so if applied via a cross-validation procedure: if we consistently observe that (5) holds when training a GAN according to many different X and Y partitions of our total π samples, then it seems reasonable to infer that α(X) has indeed learnt something useful about π.We also believe that the empirical inadequacy of W L 2 that we observed suggests a path towards a better WGAN architecture. At present, WGAN implementations implicitly use W L 2 for their choice of D Γ . We suspect that altering this to our suggested W L 2 •η may yield better quality samples. We briefly give here one possible way to do so that is largely compatible with existing WGAN setups. In particular, following , we take DISPLAYFORM0 for a class F of functions f : X → R that are all (L 2 • η, d R )-Lipschitz for some fixed Lipschitz constant K. Here d R denotes the usual distance on R. To optimise over such an F in practice, we can require our discriminator f : X → R to have the form f (x) := h(η(x)), where h : Y → R is (d Y , d R )-Lipschitz, which entails that f is Lipschitz provided η is (which is almost always the case in practice). In other words, we compute DISPLAYFORM1 where F is a class of (d Y , d R )-Lipschitz functions. Optimising over this objective may now proceed as usual via weight-clipping like , or via a gradient penalty like BID8 . Note that this suggestion may be understood as training a standard WGAN with the initial layers of the discriminator fixed to the embedding η; our analysis here shows that this is equivalent to optimising with respect to W L 2 •η instead of W L 2 . We have begun some experimentation in this area but leave a more detailed empirical inquiry to future work.It is also clearly important to establish better theoretical guarantees for our method. At present, we have no guarantee that the number of samples in A and Y are enough to ensure that DISPLAYFORM2 (perhaps with some fixed bias that is fairly independent of α, so that it is valid to use the value of D(Â,Ŷ ) to compare different choices of α), or that (5) entails (2) with high probability. We do however note that some recent theoretical work on the convergence rate of empirical Wasserstein estimations BID18 does suggest that it is plausible to hope for fast convergence of D(Â,Ŷ ) to D(α(X),Ŷ ). We also believe that the convincing empirical behaviour of W L 2 •η does suggest that it is possible to say something more substantial about our approach, which we leave to future work.",1180,0.576,713,1.6549789621318374,"We consider assess generative adversarial networks with whether generalise beyond memorising We propose assessing generative adversarial network performance a principled consideration what the actual goal generalisation Our approach involves a test estimate the Wasserstein distance the generative distribution produced our procedure the underlying data distribution We use this procedure assess several modern generative network We find this procedure sensitive the choice ground metric on the underlying data space suggest a choice substantially We finally suggest attending to the ground metric used Wasserstein generative adversarial network training may fruitful outline a concrete pathway Generative adversarial networks (GANs) BID6 have attracted generative modelling However recently concerns their ability generalise from training data their capacity overfit . Moreover techniques evaluating GAN output either ad lack suitably objective -often times ""visual inspection samples the practitioner More fundamentally sometimes unclear we a GAN the learning task consists using a finite dataset estimate an underlying data distribution The quality GAN output measured precisely a statistical distance D between the estimated and true distribution Within propose an intuitive notion a GAN generaliseWe also show our notion performance measured for when D chosen a Wasserstein distance -unlike such the inception score BID14 ) density assumptions the data-generating distribution We investigate this choice D empirically finding its performance heavily ground metric underlying the Wasserstein distance We suggest a novel choice ground metric show performs also discuss otherwise this observation Wasserstein GANs . We believe reveals two promising avenues future inquiry First suggest W L p •�� an appealing choice D both due its nice theoretical properties -it metricises weak convergence does us make any density assumptions due its sound empirical performance demonstrated It would very use this D to produce a systematic and objective comparison all current major GAN implementations indeed guiding We also view the test (5 potentially determining our algorithms overfitting This would particularly so applied via: consistently observe (5 holds training a GAN according many different X Y partitions our total �� samples α(X has indeed learnt something.We believe the empirical inadequacy W L 2 that suggests a path towards a better WGAN architecture At present WGAN implementations implicitly W L 2 their choice D �� We suspect altering to our suggested W L 2 •�� may yield better quality samples We briefly give here one possible way do that largely existing WGAN setups In particular following , take DISPLAYFORM0 a class F of functions : X → R that all (L 2 • ��, d R )-Lipschitz for Here d R denotes the usual distance on To optimise over such an F in practice require our discriminator f : X → R h(� Y (d Y , d R )-Lipschitz entails providedwhich almost In compute DISPLAYFORM1 where F a class (d Y , d R )-Lipschitz functions Optimising over this objective may now proceed usual via weight-clipping like , via a gradient penalty BID8 Note this suggestion understood training a standard WGAN with the initial layers the discriminator fixed the embedding ��; our analysis here equivalent optimising with respect W L 2 •�� instead We begun some experimentation but leave a more detailed empirical inquiryIt also clearly establish better theoretical guarantees our method At present no guarantee the number samples A and Y enough ensure that DISPLAYFORM2 (perhaps some fixed bias that fairly independent α so valid D(Â�� ) compare different choices α (5 entails ( with high probability We do however note some recent theoretical work the convergence rate empirical Wasserstein estimations BID18 does plausible hope fast convergence D(Â,�� ) We also believe the convincing empirical behaviour W L 2 •�� does suggest say something substantial our approach leave",0.01,0.37290801937332274
"The choice of activation functions in deep networks has a significant effect on the training dynamics and task performance. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU). Although various hand-designed alternatives to ReLU have been proposed, none have managed to replace it due to inconsistent gains. In this work, we propose to leverage automatic search techniques to discover new activation functions. Using a combination of exhaustive and reinforcement learning-based search, we discover multiple novel activation functions. We verify the effectiveness of the searches by conducting an empirical evaluation with the best discovered activation function. Our experiments show that the best discovered activation function, f(x) = x * sigmoid(beta * x), which we name Swish, tends to work better than ReLU on deeper models across a number of challenging datasets. For example, simply replacing ReLUs with Swish units improves top-1 classification accuracy on ImageNet by 0.9% for Mobile NASNet-A and 0.6% for Inception-ResNet-v2. The simplicity of Swish and its similarity to ReLU make it easy for practitioners to replace ReLUs with Swish units in any neural network. At the heart of every deep network lies a linear transformation followed by an activation function f (·). The activation function plays a major role in the success of training deep neural networks. Currently, the most successful and widely-used activation function is the Rectified Linear Unit (ReLU) BID12 BID21 BID29 , defined as f (x) = max(x, 0). The use of ReLUs was a breakthrough that enabled the fully supervised training of state-of-the-art deep networks BID25 . Deep networks with ReLUs are more easily optimized than networks with sigmoid or tanh units, because gradients are able to flow when the input to the ReLU function is positive. Thanks to its simplicity and effectiveness, ReLU has become the default activation function used across the deep learning community.While numerous activation functions have been proposed to replace ReLU (Maas et al., 2013; BID13 BID5 BID23 , none have managed to gain the widespread adoption that ReLU enjoys. Many practitioners have favored the simplicity and reliability of ReLU because the performance improvements of the other activation functions tend to be inconsistent across different models and datasets.The activation functions proposed to replace ReLU were hand-designed to fit properties deemed to be important. However, the use of search techniques to automate the discovery of traditionally human-designed components has recently shown to be extremely effective BID51 BID3 . For example, used reinforcement learningbased search to find a replicable convolutional cell that outperforms human-designed architectures on ImageNet.In this work, we use automated search techniques to discover novel activation functions. We focus on finding new scalar activation functions, which take in as input a scalar and output a scalar, because scalar activation functions can be used to replace the ReLU function without changing the network architecture. Using a combination of exhaustive and reinforcement learning-based search, we find a number of novel activation functions that show promising performance. To further validate the effectiveness of using searches to discover scalar activation functions, we empirically evaluate the best discovered activation function. The best discovered activation function, which we call Swish, is f (x) = x · sigmoid(βx), where β is a constant or trainable parameter. Our extensive experiments show that Swish consistently matches or outperforms ReLU on deep networks applied to a variety of challenging domains such as image classification and machine translation. On ImageNet, replacing ReLUs with Swish units improves top-1 classification accuracy by 0.9% on Mobile NASNet-A and 0.6% on Inception-ResNet-v2 BID40 . These accuracy gains are significant given that one year of architectural tuning and enlarging yielded 1.3% accuracy improvement going from Inception V3 BID39 to Inception-ResNet-v2 BID40 . In this work, we utilized automatic search techniques to discover novel activation functions that have strong empirical performance. We then empirically validated the best discovered activation function, which we call Swish and is defined as f (x) = x · sigmoid(βx). Our experiments used models and hyperparameters that were designed for ReLU and just replaced the ReLU activation function with Swish; even this simple, suboptimal procedure resulted in Swish consistently outperforming ReLU and other activation functions. We expect additional gains to be made when these models and hyperparameters are specifically designed with Swish in mind. The simplicity of Swish and its similarity to ReLU means that replacing ReLUs in any network is just a simple one line code change.",948,0.503,570,1.6631578947368422,"The choice activation functions deep networks the training dynamics Currently the most successful and widely-used activation function the Rectified Linear Unit Although various hand-designed alternatives ReLU managed replace it due inconsistent gains In this work propose leverage automatic search techniques discover new activation functions Using exhaustive and reinforcement learning-based search discover multiple novel activation functions We verify the effectiveness the searches conducting an empirical evaluation with the best discovered activation function Our experiments that the best discovered activation function * * which name Swish tends work ReLU on deeper models across challenging datasets For example simply replacing ReLUs Swish units improves top-1 classification accuracy on ImageNet Mobile NASNet-A Inception-ResNet-v2 The simplicity Swish and its similarity ReLU make practitioners replace ReLUs any neural network At every deep network lies a linear transformation followed an activation function f· The activation function plays the success training deep neural networks Currently the most successful and widely-used activation function Rectified Linear Unit BID12 BID21 , defined f The use ReLUs was a breakthrough enabled the fully supervised training state deep networks BID25 . Deep networks with ReLUs more easily optimized networks sigmoid or tanh units gradients able flow when to positive Thanks its simplicity effectiveness ReLU the default activation function used acrossWhile numerous activation functions proposed replaceMaas BID13 BID5 , none managed enjoys Many practitioners favored the simplicity reliability ReLU because the performance improvements the other activation functions tend inconsistent datasetsThe activation functions proposed replace handdesigned fit properties deemed. However the use search techniques automate traditionally human-designed components recently shown extremely effective BID51 BID3 . For example used reinforcement learningbased search to a replicable convolutional cell that outperforms human-designed architectures on ImageNetIn automated search techniques discover novel activation functions We focus finding new scalar activation functions take as output because replace without the network architecture Using exhaustive and reinforcement learning-based search find novel activation functions show promising performance To further validate using searches discover scalar activation functions empirically evaluate the best discovered activation function The best discovered activation function, Swish f (x · sigmoid(βx a constant or trainable parameter Our extensive experiments Swish consistently matches or ReLU deep networks applied challenging domains On ImageNet replacing ReLUs Swish units improves top-1 classification accuracy Mobile NASNet-A InceptionResNetv2 BID40 . These accuracy gains significant one year architectural tuning enlarging yielded going Inception V3 BID39-ResNetv2 . In this work utilized automatic search techniques discover novel activation functions strong empirical performance We then empirically validated the best discovered activation function Swish and is f · sigmoid(βx Our experiments used models designed ReLU just replaced Swish; even this simple, suboptimal procedure resulted We expect additional gains when these models and hyperparameters specifically with Swish The simplicity Swish and its similarity ReLU means replacing ReLUs any network just a simple one line code change",0.01,0.3937472210577134
"Successful training of convolutional neural networks is often associated with suffi-
 ciently deep architectures composed of high amounts of features. These networks
 typically rely on a variety of regularization and pruning techniques to converge
 to less redundant states. We introduce a novel bottom-up approach to expand
 representations in fixed-depth architectures. These architectures start from just a
 single feature per layer and greedily increase width of individual layers to attain
 effective representational capacities needed for a specific task. While network
 growth can rely on a family of metrics, we propose a computationally efficient
 version based on feature time evolution and demonstrate its potency in determin-
 ing feature importance and a networks’ effective capacity. We demonstrate how
 automatically expanded architectures converge to similar topologies that benefit
 from lesser amount of parameters or improved accuracy and exhibit systematic
 correspondence in representational complexity with the specified task. In contrast
 to conventional design patterns with a typical monotonic increase in the amount of
 features with increased depth, we observe that CNNs perform better when there is
 more learnable parameters in intermediate, with falloffs to earlier and later layers. Estimating and consequently adequately setting representational capacity in deep neural networks for any given task has been a long standing challenge. Fundamental understanding still seems to be insufficient to rapidly decide on suitable network sizes and architecture topologies. While widely adopted convolutional neural networks (CNNs) such as proposed by BID17 ; BID27 ; BID12 ; Zagoruyko & Komodakis (2016) demonstrate high accuracies on a variety of problems, the memory footprint and computational complexity vary. An increasing amount of recent work is already providing valuable insights and proposing new methodology to address these points. For instance, the authors of BID2 propose a reinforcement learning based meta-learning approach to have an agent select potential CNN layers in a greedy, yet iterative fashion. Other suggested architecture selection algorithms draw their inspiration from evolutionary synthesis concepts BID25 BID22 . Although the former methods are capable of evolving architectures that rival those crafted by human design, it is currently only achievable at the cost of navigating large search spaces and hence excessive computation and time. As a trade-off in present deep neural network design processes it thus seems plausible to consider layer types or depth of a network to be selected by an experienced engineer based on prior knowledge and former research. A variety of techniques therefore focus on improving already well established architectures. Procedures ranging from distillation of one network's knowledge into another , compressing and encoding learned representations BID8 , pruning alongside potential re-training of networks BID7 BID26 BID10 , small capacity increases on trained networks in transfer-learning scenarios (WardeFarley et al., 2014) and the employment of different regularization terms during training BID11 BID15 BID23 BID0 , are just a fraction of recent efforts in pursuit of reducing representational complexity while attempting to retain accuracy. Underlying mechanisms rely on a multitude of criteria such as activation magnitudes BID26 and small weight values BID7 that are used as pruning metrics for either single neurons or complete feature maps, in addition to further combination with regularization and penalty terms.Common to these approaches is the necessity of training networks with large parameter quantities for maximum representational capacity to full convergence and the lack of early identification of insufficient capacity. In contrast, this work proposes a bottom-up approach with the following contributions:• We introduce a computationally efficient, intuitive metric to evaluate feature importance at any point of training a neural network. The measure is based on feature time evolution, specifically the normalized cross-correlation of each feature with its initialization state.• We propose a bottom-up greedy algorithm to automatically expand fixed-depth networks that start with one feature per layer until adequate representational capacity is reached. We base addition of features on our newly introduced metric due to its computationally efficient nature, while in principle a family of similarly constructed metrics is imaginable.• We revisit popular CNN architectures and compare them to automatically expanded networks. We show how our architectures systematically scale in terms of complexity of different datasets and either maintain their reference accuracy at reduced amount of parameters or achieve better results through increased network capacity.• We provide insights on how evolved network topologies differ from their reference counterparts where conventional design commonly increases the amount of features monotonically with increasing network depth. We observe that expanded architectures exhibit increased feature counts at early to intermediate layers and then proceed to decrease in complexity. In this work we have introduced a novel bottom-up algorithm to start neural network architectures with one feature per layer and widen them until a task depending suitable representational capacity is achieved. For the use in this framework we have presented one potential computationally efficient and intuitive metric to gauge feature importance. The proposed algorithm is capable of expanding architectures that provide either reduced amount of parameters or improved accuracies through higher amount of representations. This advantage seems to be gained through alternative network topologies with respect to commonly applied designs in current literature. Instead of increasing the amount of features monotonically with increasing depth of the network, we empirically observe that expanded neural network topologies have high amount of representations in early to intermediate layers.Future work could include a re-evaluation of plainly stacked deep architectures with new insights on network topologies and extended evaluation on different domain data. We have furthermore started to replace the currently present re-initialization step in the proposed expansion algorithm by keeping learned filters. In principle this approach looks promising but does need further systematic analysis of new feature initialization with respect to the already learned feature subset and accompanied investigation of orthogonality to avoid falling into local minima.",1104,0.54,620,1.7806451612903227,"Successful training suffi- ciently deep architectures composed high amounts features These networks typically rely regularization converge less redundant states We introduce expand representations fixed-depth architectures These architectures start per greedily increase width attain effective representational capacities needed While network growth can rely a family metrics propose based feature time evolution demonstrate its potency determin- ing feature importance a networks�� effective capacity We demonstrate how automatically expanded architectures converge similar topologies benefit lesser amount parameters or improved accuracy exhibit systematic correspondence representational complexity with the specified task In contrast conventional design patterns with features with increased depth observe CNNs perform more learnable parameters intermediate, with falloffs to earlier and later layers Estimating and consequently adequately setting representational capacity Fundamental understanding still seems insufficient rapidly decide suitable network sizes architecture topologies While widely adopted such proposed BID17 ; Zagoruyko Komodakis demonstrate the memory footprint vary An increasing amount recent work already providing proposing new methodology these points For instance BID2 propose a reinforcement learning based have an agent select potential CNN layers Other suggested architecture selection algorithms draw evolutionary synthesis concepts BID25 BID22 . Although the former methods capable evolving architectures rival crafted human design currently only achievable at navigating large search spaces hence excessive computation As present deep neural network design processes it thus layer types or depth selected an experienced engineer based former research A variety techniques therefore focus improving already well established architectures ranging distillation one network's knowledge , compressing encoding learned representations BID8 pruning alongside potential re small capacity increases on trained networks transfer-learning scenariosWardeFarley the employment different regularization terms during are just a fraction recent efforts pursuit reducing while attempting retain accuracy Underlying mechanisms rely criteria activation magnitudes BID26 small weight values that pruning metrics either single neurons complete feature maps further combination with regularization and penalty termsCommon to training networks large parameter quantities maximum representational capacity full convergence early identification insufficient capacity In contrast this work proposes with feature importance training The measure based feature time evolution specifically the normalized cross each feature its initialization state.• We propose automatically expand fixed-depth networks start per until adequate representational capacity We base addition features newly metric due in principle a family similarly constructed metrics imaginable.• revisit popular CNN architectures automatically expanded networks We show our architectures systematically scale different datasets either maintain their reference accuracy reduced amount parameters achieve increased network capacity.• insights evolved network topologies differ where conventional design commonly increases features monotonically with We observe expanded architectures exhibit increased feature counts early to intermediate layers then proceed decrease In start neural network one feature widen until a task depending suitable representational capacity For the use in this framework presented one potential computationally efficient and intuitive metric gauge feature importance The proposed algorithm capable expanding architectures provide either reduced amount parameters improved accuracies through higher amount representations This advantage seems gained alternative network topologies with respect commonly applied designs in current literature Instead increasing features monotonically with increasing depth the network empirically observe expanded neural network topologies high amount representations early toFuture work a re plainly stacked deep architectures new insights extended evaluation on different domain data We furthermore started replace the currently present re-initialization step the proposed expansion algorithm keeping learned filters In principle looks does further systematic analysis of new feature initialization with the already learned feature subset accompanied investigation falling local minima",0.01,0.6930944539176074
"Deep neural networks are almost universally trained with reverse-mode automatic differentiation (a.k.a. backpropagation). Biological networks, on the other hand, appear to lack any mechanism for sending gradients back to their input neurons, and thus cannot be learning in this way. In response to this, Scellier & Bengio (2017) proposed Equilibrium Propagation - a method for gradient-based train- ing of neural networks which uses only local learning rules and, crucially, does not rely on neurons having a mechanism for back-propagating an error gradient. Equilibrium propagation, however, has a major practical limitation: inference involves doing an iterative optimization of neural activations to find a fixed-point, and the number of steps required to closely approximate this fixed point scales poorly with the depth of the network. In response to this problem, we propose Initialized Equilibrium Propagation, which trains a feedforward network to initialize the iterative inference procedure for Equilibrium propagation. This feed-forward network learns to approximate the state of the fixed-point using a local learning rule. After training, we can simply use this initializing network for inference, resulting in a learned feedforward network. Our experiments show that this network appears to work as well or better than the original version of Equilibrium propagation. This shows how we might go about training deep networks without using backpropagation. Deep neural networks are almost always trained with gradient descent, and gradients are almost always computed with backpropagation. For those interested in understanding the working of the brain in the context of machine learning, it is therefore distressing that biological neurons appear not to send signals backwards.Biological neurons communicate by sending a sequence of pulses to downstream neurons along a one-way signaling pathway called an ""axon"". If neurons were doing backpropagation, one would expect a secondary signalling pathway wherein gradient signals travel backwards along axons. This appears not to exist, so it seems that biological neurons cannot be doing backpropagation.Moreover, backpropagation may not be the ideal learning algorithm for efficient implementation in hardware, because it involves buffering activations for each layer until an error gradient returns. This requirement becomes especially onerous when we wish to backpropagate through many steps of time, or through many layers of depth. For these reasons, researchers are looking into other means of neural credit assignment -mechanisms for generating useful learning signals without doing backpropagation.Recently, BID19 proposed a novel algorithm called Equilibrium Propagation, which enables the computation of parameter gradients in a deep neural network without backpropagation. Equilibrium Propagation defines a neural network as a dynamical system, whose dynamics follow the negative-gradient of an energy function. The ""prediction"" of this network is the fixedpoint of the dynamics -the point at which the system settles to a local minimum energy given the input, and ceases to change. Because of this inference scheme, Equilibrium Propagation is impractically slow for large networks -the network has to iteratively converge to a fixed point at every training iteration.In this work, we take inspiration from BID6 and distill knowledge from a slow, energy based equilibrating network into a fast feedforward network by training the feedforward network to predict the fixed-points of the equilibrating network with a local loss. At the end of training, we can then discard the equilibrating network and simply use our feedforward network for testtime inference. We thus have a way to train a feedforward network without backpropagation. The resulting architecture loosely resembles a Conditional Generative Adversarial Network BID17 , where the feedforward network produces a network state which is evaluated by the energy-based equilibrating network.To aid the reader, this paper contains a glossary of symbols in Appendix A. In this paper we describe how to use a recurrent, energy-based model to provide layerwise targets with which to train a feedforward network without backpropagation. This work helps us understand how the brain might be training fast inference networks. In this view, neurons in the inference network learn to predict local targets, which correspond to the minimal energy states, which are found by the iterative settling of a separate, recurrently connected equilibrating network.More immediately perhaps, this could lead towards efficient analog neural network designs in hardware. As pointed out by BID19 , it is much easier to design an analog circuit to minimize some (possibly unknown) energy function than it is to design a feedforward circuit and a parallel backwards circuit which exactly computes its gradients. However it is very undesirable for the function of a network to depend on peculiarities of a particular piece of analog hardware, because then the network cannot be easily replicated. We could imagine using a hybrid circuit to train a digital, copy-able feedforward network, which is updated by gradients computed in the analog hardware. Without the constraint of having to backpropagate through the feedforward network, designs could be simplified, for example to do away with the need for differentiable activation functions or to use feedforward architectures which would otherwise suffer from vanishing/exploding gradient effects.",1012,0.498,612,1.65359477124183,"Deep neural networks almost universally trained reverse-mode automatic differentiation Biological networks on appear lack any mechanism sending gradients back their input neurons learning in In response Scellier & Bengio2017 Equilibrium - gradient-based train- ing which only local learning rules, neurons having a mechanism back an error gradient Equilibrium propagation however a major practical limitation inference involves doing an iterative optimization neural activations, the number steps closely this fixed point scales poorly the depth In response this problem propose Initialized Equilibrium Propagation trains a feedforward network initialize the iterative inference procedure Equilibrium propagation This feed-forward network learns approximate the fixed-point using a local learning rule After training can simply use this initializing network inference resulting a learned feedforward network Our experiments this network appears work or Equilibrium propagation This shows we might go training deep networks without Deep neural networks almost gradient descent gradients almost computed For understanding the working the brain machine learning therefore distressing biological neurons appear not send backwardsBiological neurons communicate a sequence pulses downstream along If neurons doing one a secondary signalling pathway wherein gradient signals travel backwards This appears not exist biological neurons doingMoreover the ideal learning algorithm efficient implementation hardware buffering activations for each layer until an error gradient returns This requirement becomes especially onerous we wish backpropagate through many steps time through many layers depth For these reasons researchers other means neural credit assignment -mechanisms generating useful learning signals without doingRecently BID19 proposed called Equilibrium Propagation enables the computation parameter gradients Equilibrium Propagation defines a neural network whose dynamics follow the negative-gradient of an energy function The ""prediction this network the fixedpoint the dynamics -the point settles to a local minimum energy given ceases change Because this inference scheme Equilibrium Propagation impractically slow for large networks -the network has iteratively converge every training iterationIn take inspiration BID6 distill knowledge a slow, energy based equilibrating network by training predict the fixed-points with a local loss At training we can then discard the equilibrating network simply our feedforward network testtime inference We thus train a feedforward network without The resulting architecture loosely a Conditional Generative Adversarial Network BID17 , where the feedforward network produces a network state evaluated the energy-based equilibrating networkTo aid the reader contains symbols Appendix A. In this paper a recurrent, energy-based model provide layerwise targets with which train without This work helps might training fast inference networks In this view neurons the inference network learn local targets correspond the minimal energy states found by the iterative settling a separate, recurrently connected equilibrating networkMore immediately perhaps could towards efficient analog neural network designs hardware As pointed BID19 , much design an analog circuit minimize some (possibly unknown) energy function a feedforward circuit and a parallel backwards circuit which exactly its gradients However it very undesirable the function a network peculiarities a particular piece analog hardware because then easily replicated We could imagine using a hybrid circuit train a digital, copy-able feedforward network updated gradients computed the analog hardware Without the constraint backpropagate through the feedforward network designs could simplified for do differentiable activation functions or feedforward architectures which otherwise suffer vanishing/exploding gradient effects",0.01,0.3693812225992657
"We propose a novel generative model architecture designed to learn representations for images that factor out a single attribute from the rest of the representation. A single object may have many attributes which when altered do not change the identity of the object itself. Consider the human face; the identity of a particular person is independent of whether or not they happen to be wearing glasses. The attribute of wearing glasses can be changed without changing the identity of the person. However, the ability to manipulate and alter image attributes without altering the object identity is not a trivial task. Here, we are interested in learning a representation of the image that separates the identity of an object (such as a human face) from an attribute (such as 'wearing glasses'). We demonstrate the success of our factorization approach by using the learned representation to synthesize the same face with and without a chosen attribute. We refer to this specific synthesis process as image attribute manipulation. We further demonstrate that our model achieves competitive scores, with state of the art, on a facial attribute classification task. Latent space generative models, such as generative adversarial networks (GANs) BID11 BID27 and variational autoencoders (VAEs) BID28 BID14 , learn a mapping from a latent encoding space to a data space, for example, the space of natural images. It has been shown that the latent space learned by these models is often organized in a near-linear fashion BID27 BID14 , whereby neighbouring points in latent space map to similar images in data space. Certain ""directions"" in latent space correspond to changes in the intensity of certain attributes. In the context of faces, for example, directions in latent space would correspond to the extent to which someone is smiling. This may be useful for image synthesis where one can use the latent space to develop new design concepts BID9 Zhu et al., 2016) , edit an existing image (Zhu et al., 2016) or synthesize avatars BID35 BID32 . This is because semantically meaningful changes may be made to images by manipulating the latent space BID27 Zhu et al., 2016; BID17 .One avenue of research for latent space generative models has been class conditional image synthesis BID25 BID24 , where an image of a particular object category is synthesized. Often , object categories may be sub-divided into fine-grain subcategories. For example, the category ""dog"" may be split into further sub-categories of different dog breeds. Work by BID3 propose latent space generative models for synthesizing images from fine-grained categories, in particular for synthesizing different celebrities' faces conditional on the identity of the celebrity.Rather than considering fine-grain categories, we propose to take steps towards solving the different, but related problem of image attribute manipulation. To solve this problem we want to be able to synthesize images and only change one element or attribute of its content. For example , if we are synthesizing faces we would like to edit whether or not a person is smiling. This is a different problem to fine-grain synthesis; we want to be able to synthesize two faces that are similar, with only a single chosen attribute changed, rather than synthesizing two different faces. The need to synthesis two faces that are similar makes the problem of image attribute manipulation more difficult than the fine-grain image synthesis problem; we need to learn a latent space representation that separates an object category from its attributes.In this paper, we propose a new model that learns a factored representation for faces, separating attribute information from the rest of the facial representation. We apply our model to the CelebA BID21 dataset of faces and control several facial attributes.Our contributions are as follows:1. Our core contribution is the novel cost function for training a VAE encoder to learn a latent representation which factorizes binary facial attribute information from a continuous identity representation (Section 3.2). 2. We provide an extensive quantitative analysis of the contributions of each of the many loss components in our model (Section 4.2). 3. We obtain classification scores that are competitive with state of the art (Zhuang et al., 2018) using the classifier that is already incorporated into the encoder of the VAE (Section 4.3). 4. We provide qualitative results demonstrating that our latent variable, generative model may be used to successfully edit the 'Smiling' attribute in more than 90% of the test cases (Section 4.4). 5. We discuss and clarify the distinction between conditional image synthesis and image attribute editing (Section 5). 6. We present code to reproduce experiments shown in this paper: (provided after review). We have proposed a novel perspective and approach to learning representations of images which subsequently allows elements, or attributes, of the image to be modified. We have demonstrated our approach on images of the human face, however, the method is generalisable to other objects. We modelled a human face in two parts, with a continuous latent vector that captures the identity of a person and a binary unit vector that captures a facial attribute, such as whether or not a person is smiling. By modelling an image with two separate representations, one for the object and the other for the object's attribute, we are able to change attributes without affecting the identity of the object. To learn this factored representation we have proposed a novel model aptly named Information Factorization conditional VAE-GAN. The model encourages the attribute information to be factored out of the identity representation via an adversarial learning process. Crucially, the representation learned by our model both captures identity faithfully and facilitates accurate and easy attribute editing without affecting identity. We have demonstrated that our model performs better than pre-existing models intended for category conditional image synthesis (Section 4.4), and have performed a detailed ablation study TAB0 which confirms the importance and relevance of our proposed method. Indeed, our model is highly effective as a classifier, achieving state of the art accuracy on facial attribute classification for several attributes (Figure 2 ). Our approach to learning factored representations for images is both a novel and important contribution to the general field of representation learning.",1244,0.72,717,1.7350069735006974,"We propose a novel generative model architecture designed learn representations for images factor a single attribute A single object may many attributes which when altered do the identity itself Consider the human face; the identity independent whether happen wearing glasses The attribute wearing glasses changed without the identity However the ability manipulate alter image attributes without altering the object identity Here, interested learning a representation the image separates the identitysuch an attribute 'wearing glasses We demonstrate the success our factorization approach the learned representation to the same face with and a chosen attribute We refer this specific synthesis process image attribute manipulation We further demonstrate our model achieves competitive scores state of, on a facial attribute classification task Latent space generative models BID11 BID27VAEs , learn a mapping encoding for space natural images It shown the latent space learned these models often organized BID27 BID14 , whereby neighbouring points latent space map similar images data space Certain ""directions latent space correspond changes certain attributes In the context faces for directions in latent space would correspond the extent someone smiling This may useful image synthesis where one the latent space develop new design concepts BID9 Zhu) , edit avatars BID35 BID32 . This because semantically meaningful changes may images manipulating the latent space BID27 Zhu BID17 .One avenue research latent space generative models class conditional image synthesis BID25 BID24 where a particular object category Often , object categories may sub For example the category ""dog may split further sub Work by BID3 propose latent space generative models synthesizing images in for synthesizing different celebrities conditionalRather considering fine-grain categories take steps solving different, image attribute manipulation To solve want be synthesize images only change or attribute its content For example , synthesizing faces edit whether smiling This a different problem fine-grain synthesis; we two faces that only a single chosen attribute changed rather synthesizing The need synthesis two faces that makes the problem image attribute manipulation the fine-grain image synthesis problem; we learn a latent space representation separates an object categoryIn learns a factored representation faces separating attribute information We apply our model the CelebA BID21 dataset faces control several facial attributesOur contributions as Our core contribution the novel cost function training a VAE encoder learn a latent representation which factorizes binary facial attribute information a continuous identity representationSection 2 We provide an extensive quantitative analysis each the many loss components (Section 3 We obtain classification scores that competitive state of (Zhuang et al 2018 using that already incorporated the encoder of the VAESection 4 We provide qualitative results demonstrating our latent variable, generative model may successfully edit the 'Smiling' attributeSection 5 We discuss and clarify the distinction conditional image synthesis image attribute editingSection 6 We present code reproduce experiments shownprovided after review We proposed a novel perspective and learning representations images which subsequently allows elements, or attributes modified We demonstrated our approach on images however the method generalisable We modelled a human face a continuous latent vector that captures a binary unit vector a facial attribute whether By modelling an image with two separate representations one are change attributes without To learn this factored representation we proposed aptly Information Factorization conditional VAE-GAN The model encourages the attribute information factored out the identity representation via an adversarial learning process Crucially the representation learned our model both captures identity faithfully facilitates accurate and easy attribute editing without affecting identity We demonstrated our model performs intended category conditional image synthesisSection have performed a detailed ablation study TAB0 which confirms and relevance our proposed method Indeed our model highly effective as achieving state of on facial attribute classification for several attributes (Figure Our approach learning factored representations for images both a novel and important contribution the general field representation learning",0.01,0.5768123611569788
"Stochastic video prediction models take in a sequence of image frames, and generate a sequence of consecutive future image frames. These models typically generate future frames in an autoregressive fashion, which is slow and requires the input and output frames to be consecutive. We introduce a model that overcomes these drawbacks by generating a latent representation from an arbitrary set of frames that can then be used to simultaneously and efficiently sample temporally consistent frames at arbitrary time-points. For example, our model can ""jump"" and directly sample frames at the end of the video, without sampling intermediate frames. Synthetic video evaluations confirm substantial gains in speed and functionality without loss in fidelity. We also apply our framework to a 3D scene reconstruction dataset. Here, our model is conditioned on camera location and can sample consistent sets of images for what an occluded region of a 3D scene might look like, even if there are multiple possibilities for what that region might contain. Reconstructions and videos are available at https://bit.ly/2O4Pc4R.
 The ability to fill in the gaps in high-dimensional data is a fundamental cognitive skill. Suppose you glance out of the window and see a person in uniform approaching your gate carrying a letter. You can easily imagine what will (probably) happen a few seconds later. The person will walk up the path and push the letter through your door. Now suppose you glance out of the window the following day and see a person in the same uniform walking down the path, away from the house. You can easily imagine what (probably) happened a few seconds earlier. The person came through your gate, walked up the path, and delivered a letter. Moreover, in both instances, you can visualize the scene from different viewpoints. From your vantage point at the window, you can imagine how things might look from the gate, or from the front door, or even from your neighbour's roof. Essentially, you have learned from your past experience of unfolding visual scenes how to flexibly extrapolate and interpolate in both time and space. Replicating this ability is a significant challenge for AI.To make this more precise, let's first consider the traditional video prediction setup. Video prediction is typically framed as a sequential forward prediction task. Given a sequence of frames f 1 , ..., f t , a model is tasked to generate future frames that follow, f t+1 , ..., f T . Existing models BID0 BID7 carry out the prediction in an autoregressive manner, by sequentially sampling frame f t+n from p(f t+n |f 1 , ..., f t+n−1 ).This traditional setup is often limiting -in many cases, we are interested in what happens a few seconds after the input sequence. For example, in model based planning tasks, we might want to predict what frame f T is, but might not care what intermediate frames f t+1 , ..., f T −1 are. Existing models must still produce the intermediate frames, which is inefficient. Instead, our model is ""jumpy"" -it can directly sample frames in the future, bypassing intermediate frames. For example , in a 40-frame video, our model can sample the final frame 12 times faster than an autoregressive model like SV2P BID0 .More generally , existing forward video prediction models are not flexible at filling in gaps in data. Instead, our model can sample frames at arbitrary time points of a video, given a set of frames at arbitrary time points as context. So it can, for example, be used to infer backwards or interpolate between frames, as easily as forwards. Our model is also not autoregressive on input or output frames -it takes in each input frame in parallel, and samples each output frame in parallel.In our setup of ""jumpy"" video prediction, a model is given frames f 1 , ..., f n from a single video along with the arbitrary time-points t 1 , ..., t n at which those frames occurred. To be clear, t 1 , ..., t n need not be consecutive or even in increasing order. The model is then asked to sample plausible frames at arbitrary time points t 1 , ..., t k . In many cases there are multiple possible predicted frames given the context, making the problem stochastic. For example, a car moving towards an intersection could turn left or turn right. Although our model is not autoregressive, each set of k sampled frames is consistent with a single coherent possibility, while maintaining diversity across sets of samples. That is, in each sampled set all k sampled frames correspond to the car moving left, or all correspond to the car moving right.At a high level, our model, JUMP, takes in the input frames and samples a stochastic latent that models the stochasticity in the video. Given an arbitrary query time-point, the model uses the sampled latent to render the frame at that time-point. The model is not autoregressive on input or output frames, but still captures correlations over multiple target frames. Our method is not restricted to video prediction. When conditioned on camera position , our model can sample consistent sets of images for an occluded region of a scene, even if there are multiple possibilities for what that region might contain.We test JUMP on multiple synthetic datasets. To summarize our results: on a synthetic video prediction task involving five shapes, we show that JUMP produces frames of a similar image quality to modern video prediction methods. Moreover, JUMP converges more reliably, and can do jumpy predictions. To showcase the flexibility of our model we also apply it to stochastic 3D reconstruction, where our model is conditioned on camera location instead of time. For this, we introduce a dataset that consists of images of 3D scenes containing a cube with random MNIST digits engraved on each of its faces. JUMP outperforms GQN (Eslami et al., 2018) on this dataset, as GQN is unable to capture several correlated frames of occluded regions of the scene. We focus on synthetic datasets so that we can quantify how each model deals with stochasticity. For example, in our 3D reconstruction dataset we can control when models are asked to sample image frames for occluded regions of the scene, to quantify the consistency of these samples. We strongly encourage the reader to check the project website https://bit.ly/2O4Pc4R to view videos of our experiments.To summarize, our key contributions are as follows.1. We motivate and formulate the problem of jumpy stochastic video prediction, where a model has to predict consistent target frames at arbitrary time points, given context frames at arbitrary time points. We observe close connections with consistent stochastic 3D reconstruction tasks, and abstract both problems in a common framework.2. We present a model for consistent jumpy predictions in videos and scenes. Unlike existing video prediction models, our model consumes input frames and samples output frames entirely in parallel. It enforces consistency of the sampled frames by training on multiple correlated targets, sampling a global latent, and using a deterministic rendering network.3. We show strong experimental results for our model. Unlike existing sequential video prediction models, our model can also do jumpy video predictions. We show that our model also produces images of similar quality while converging more reliably. Our model is not limited to video prediction -we develop a dataset for stochastic 3D reconstruction. Here, we show that our model significantly outperforms GQN. We have presented an architecture for learning generative models in the visual domain that can be conditioned on arbitrary points in time or space. Our models can extrapolate forwards or backwards in time, without needing to generate intermediate frames. Moreover, given a small set of contextual frames they can be used to render 3D scenes from arbitrary camera positions. In both cases, they generate consistent sets of frames for a given context, even in the presence of stochasticity. One limitation of our method is that the stochastic latent representation is of a fixed size, which may limit its expressivity in more complicated applications -fixing this limitation and testing on more complex datasets are good avenues for future work. Among other applications, video prediction can be used to improve the performance of reinforcement learning agents on tasks that require lookahead BID21 . In this context, the ability to perform jumpy predictions that look many frames ahead in one go is an important step towards agents that can explore a search space of possible futures, as it effectively divides time into discrete periods. This is an avenue we will be exploring in future work.",1716,1.013,973,1.763617677286742,"Stochastic video prediction models take in a sequence image frames generate consecutive future image frames These models typically generate future frames slow requires consecutive We introduce a model overcomes these drawbacks generating a latent representation from frames simultaneously and efficiently sample temporally consistent frames at For example our model can ""jump directly sample frames at sampling intermediate frames Synthetic video evaluations confirm substantial gains speed functionality without loss fidelity We also apply our framework a 3D scene reconstruction dataset Here our model conditioned camera location can sample consistent sets what an occluded region even multiple possibilities contain videos The ability fill high-dimensional data Suppose glance out uniform approaching your gate carrying You easily imagine will ( a seconds The person will walk the path push the letter through your door Now suppose glance out the walking away You easily imagine (probably a seconds earlier The person came through your gate walked delivered Moreover both instances you visualize the scene different viewpoints From your vantage point at imagine things the gate your neighbour's roof Essentially learned from unfolding visual scenes how flexibly extrapolate in both time Replicating this ability AI.To more precise let the traditional video prediction setup Video prediction typically framed a sequential forward prediction task Given a sequence frames f 1 ... a model tasked generate future frames follow, f T Existing models BID0 BID7 carry the prediction in by sequentially sampling frame f t+n from p(f |f 1 , ....This traditional setup often limiting -in we interested what a For example model based planning tasks predict what frame f T might care what intermediate frames f t+1 ... Existing models must still produce the intermediate frames inefficient Instead our model ""jumpy -it directly sample frames bypassing intermediate frames For example , a 40-frame video our model sample the final frame 12 faster like SV2P BID0 .More generally existing forward video prediction models flexible at filling Instead our model can sample frames at arbitrary time points of given at as context So can, infer backwards or interpolate frames as easily forwards Our model also not autoregressive on input or output frames -it takes parallel samplesIn our setup of ""jumpy"" video prediction a model given frames f ... from along the arbitrary time-points t at occurred To t 1 ... n need consecutive even increasing order The model then asked sample plausible frames at arbitrary time points t 1 ... In many cases there multiple possible predicted frames given making problem stochastic For example a car moving towards turn turn Although our model autoregressive each set k sampled frames consistent a single coherent possibility while maintaining diversity sets That in each sampled set all k sampled frames correspond car moving left or all correspondAt our model, JUMP takes in samples a stochastic latent that models in the video Given an arbitrary query time-point the model uses the sampled latent to render the frame The model not autoregressive on input or output frames still captures correlations over multiple target frames Our method restricted video prediction When conditioned camera position , our model sample consistent sets an occluded region even multiple possibilities whatWe test JUMP on multiple synthetic datasets To summarize on a synthetic video prediction task involving five shapes show JUMP produces frames a similar image quality modern video prediction methods Moreover JUMP converges more reliably, can do jumpy predictions To showcase the flexibility our model also apply stochastic 3D reconstruction conditioned camera location instead For this, introduce a dataset consists images containing a cube random MNIST digits engraved JUMP outperforms GQN (Eslami 2018 this dataset unable several correlated frames occluded regions We focus synthetic datasets so quantify each model deals For example our 3D reconstruction dataset control when models asked sample image frames to quantify the consistency We strongly the reader the project website videosTo summarize our key contributions motivate formulate the problem jumpy stochastic video prediction where a model has consistent target frames at given context frames at We observe close connections consistent stochastic 3D reconstruction tasks abstract both problems a common framework.2. present consistent jumpy predictions videos scenes Unlike existing video prediction models our model consumes input frames samples output frames entirely parallel It enforces consistency the sampled frames training on multiple correlated targets sampling a global latent, a deterministic rendering network.3. We strong experimental results our model Unlike existing sequential video prediction models our model also do jumpy video predictions We show our model also produces images similar quality while converging more reliably Our model not limited video prediction -we develop a dataset stochastic 3D reconstruction Here our model significantly GQN. We presented an architecture learning generative models conditioned arbitrary points or Our models extrapolate forwards without generate intermediate frames Moreover given a small set contextual frames they render arbitrary camera positions In both cases generate consistent sets frames even One limitation our method the stochastic latent representation of limit its expressivity more complicated applications -fixing and testing on are good avenues Among other applications video prediction reinforcement learning agents on lookahead BID21 . In this context the ability perform jumpy predictions that look many frames one go agents explore a search space effectively divides time This an avenue we future work",0.01,0.6497099206948708
"The ADAM optimizer is exceedingly popular in the deep learning community. Often it works very well, sometimes it doesn’t. Why? We interpret ADAM as a combination of two aspects: for each weight, the update direction is determined by the sign of the stochastic gradient, whereas the update magnitude is solely determined by an estimate of its relative variance. We  disentangle these two aspects and analyze them in isolation, shedding light on ADAM ’s inner workings. Transferring the ""variance adaptation” to momentum- SGD gives rise to a novel method, completing the practitioner’s toolbox for problems where ADAM fails. Many prominent machine learning models pose empirical risk minimization problems of the form DISPLAYFORM0 where θ ∈ R d is a vector of parameters, {x 1 , . . . , x M } a training set, and (θ; x) is a loss quantifying the performance of parameter vector θ on example x. Computing the exact gradient in each step of an iterative optimization algorithm becomes inefficient for large M . Instead, we construct a minibatch B ⊂ {1, . . . , M } of |B| M data points sampled uniformly and independently from the training set and compute an approximate stochastic gradient DISPLAYFORM1 which is an unbiased estimate, E[g(θ)] = ∇L(θ). We will denote by σ(θ) The basic stochastic optimizer is stochastic gradient descent (SGD, Robbins & Monro, 1951) and its momentum variants (Polyak, 1964; Nesterov, 1983) . A number of methods, widely-used in the deep learning community, choose per-element update magnitudes based on the history of stochastic gradient observations. Among these are ADAGRAD (Duchi et al., 2011) , RMSPROP (Tieleman & Hinton, 2012) , ADADELTA (Zeiler, 2012) and ADAM (Kingma & Ba, 2015) . We have argued that ADAM combines two aspects: taking signs and variance adaptation. Our separate analysis of both aspects provides some insight into the inner workings of this method. Taking the sign can be beneficial, but does not need to be. Our theoretical analysis suggests that it depends on the interplay of stochasticity, the conditioning of the problem, and its ""axis-alignment"". Our experiments confirm that sign-based methods work well on some, but not all problems.Variance adaptation can be applied to any stochastic update direction. In our experiments it was beneficial in all cases, but its effect can sometimes be minuscule. M-SVAG, a variance-adapted variant of momentum-SGD, is a useful addition to the practitioner's toolbox for problems where sign-based methods like ADAM fail. Its memory and computation cost are identical to ADAM and it has two hyper-parameters, the momentum constant µ and the global step size α. Our TensorFlow (Abadi et al., 2015) implementation of this method will be made available upon publication. MNIST We train a simple fully-connected neural network with three hidden layers of 1000, 500 and 100 units with ReLU activation. The output layer has 10 units with softmax activation. We use the cross-entropy loss function and apply L 2 -regularization on all weights, but not the biases. We use a batch size of 128. The global learning rate α stays constant.",699,0.496,428,1.6331775700934579,"The ADAM optimizer exceedingly Often works very sometimes�� Why We interpret ADAM two aspects for each weight the update direction the sign whereas solely an estimate its relative variance We disentangle analyze isolation shedding ADAM ��s inner workings Transferring the ""variance adaptation�� momentum- SGD gives a novel method, completing the practitioner��s toolbox problems where ADAM fails Many prominent machine learning models pose empirical risk minimization problems of DISPLAYFORM0 where �� �� R d parameters { 1 . . . , x M } a training set (�; a loss quantifying parameter vector �� on example Computing the exact gradient each step becomes inefficient large M . Instead construct a minibatch B ��� {1 . . . , M } of |B| M data points sampled uniformly independently the training set compute DISPLAYFORM1 which an unbiased estimate, E[g� = ��L We will denote �� The basic stochastic optimizer, Robbins Monro 1951 its momentum variantsPolyak 1964 Nesterov A number methods widely- choose perelement update magnitudes the history stochastic gradient observations Among these ADAGRADDuchi et , RMSPROPTieleman Hinton ADADELTA (Zeiler (Kingma Ba, We argued ADAM combines taking signs variance adaptation Our separate analysis both aspects provides this method Taking the sign can beneficial does need Our theoretical analysis it depends conditioning the problem its ""axis Our experiments confirm sign-based methods some, problemsVariance adaptation any stochastic update direction In our experiments it beneficial in its effect can sometimes M-SVAG a variance-adapted variant momentum-SGD a useful addition problems where sign-based methods like ADAM fail Its memory and computation cost identical ADAM two hyper the momentum constant µ the global step size α Our TensorFlow (Abadi et implementation this method will made upon publication MNIST We train a simple fully-connected neural network three hidden layers 1000 500 and 100 units with ReLU activation The output layer 10 units with softmax activation We use the cross-entropy loss function and apply L 2 -regularization all weights not the biases We use a batch size 128 The global learning rate α stays",0.0,0.3173599879088926
"We propose a novel framework to adaptively adjust the dropout rates for the deep neural network based on a Rademacher complexity bound. The state-of-the-art deep learning algorithms impose dropout strategy to prevent feature co-adaptation. However, choosing the dropout rates remains an art of heuristics or relies on empirical grid-search over some hyperparameter space. In this work, we show the network Rademacher complexity is bounded by a function related to the dropout rate vectors and the weight coefficient matrices. Subsequently, we impose this bound as a regularizer and provide a theoretical justified way to trade-off between model complexity and representation power. Therefore, the dropout rates and the empirical loss are unified into the same objective function, which is then optimized using the block coordinate descent algorithm. We discover that the adaptively adjusted dropout rates converge to some interesting distributions that reveal meaningful patterns.Experiments on the task of image and document classification also show our method achieves better performance compared to the state-of the-art dropout algorithms. Dropout training BID19 has been proposed to regularize deep neural networks for classification tasks. It has been shown to work well in reducing co-adaptation of neurons-and hence, preventing model overfitting. The idea of dropout is to stochastically set a neuron's output to zero according to Bernoulli random variables. It has been a crucial component in the winning solution to visual object recognition on ImageNet BID7 . Ever since, there have been many follow-ups on novel learning algorithms (Goodfellow et al., 2013; BID1 , regularization techniques BID23 , and fast approximations BID25 .However , the classical dropout model has a few limitations. First, the model requires to specify the retain rates, i.e., the probabilities of keeping a neuron's output, a priori to model training. Subsequently , these retain rates are kept fixed throughout the training process thereafter. It is often not clear how to choose the retain rates in an optimal way. They are usually set via grid-search over hyper-parameter space or simply according to some rule-of-thumb. Another limitation is that all neurons in the same layer share the same retain rate. This exponentially reduces the search space of hyper-parameter optimization. For example, BID19 use a fixed retain probability throughout training for all dropout variables in each layer.In this paper, we propose a novel regularizer based on the Rademacher complexity of a neural network BID16 . Without loss of generality , we use multilayer perceptron with dropout as our example and prove its Rademacher complexity is bounded by a term related to the dropout probabilities. This enables us to explicitly incorporate the model complexity term as a regularizer into the objective function.This Rademacher complexity bound regularizer provides us a lot of flexibility and advantage in modeling and optimization. First, it combines the model complexity and the loss function in an unified objective. This offers a viable way to trade-off the model complexity and representation power through the regularizer weighting coefficient. Second, since this bound is a function of dropout probabilities, we are able to incorporate them explictly into the computation graph of the optimization procedure. We can then adaptively optimize the objective and adjust the dropout probabilities throughout training in a way similar to ridge regression and the lasso BID4 . Third, our proposed regularizer assumes a neuron-wise dropout manner and models different neurons to have different retain rates during the optimization. Our empirical results demonstrate interesting trend on the changes in histograms of dropout probabilities for both hidden and input layers. We also discover that the distribution over retain rates upon model convergence reveals meaningful pattern on the input features.To the best of our knowledge, this is the first ever effort of using the Rademacher complexity bound to adaptively adjust the dropout probabilities for the neural networks. We organize the rest of the paper as following . Section 2 reviews some past approaches well aligned with our motivation, and highlight some major difference to our proposed approach. We subsequently detail our proposed approach in Section 3. In Section 4, we present our thorough empirical evaluations on the task of image and document classification on several benchmark datasets. Finally, Section 5 concludes this paper and summarizes some possible future research ideas. Imposing regularizaiton for a better model generalization is not a new topic. However we tackle the problem for the dropout neural network regularization in a different way. The theoretical upper bound we proved on the Rademacher complexity facilitates us to directly incorporate the dropout rates into the objective function. In this way the dropout rate can be optimized by block coordinate descent procedure with one consistent objective. Our empirical evaluation demonstrates promising results and interesting patterns on adapted retain rates.In the future, we would like to investigate the sparsity property of the learnt retain rates to encourage a sparse representation of the data and the neural network structure BID26 , similar to the sparse Bayesian models and relevance vector machine BID21 . We would also like to explore the applications of deep network compression (Han et al., 2015a; BID5 BID13 BID9 . In addition, one other possible research direction is to dynamically adjust the architecture of the deep neural networks BID17 BID3 Guo et al., 2016) , and hence reduce the model complexity via dropout rates. Features include words associated with the 20 largest and smallest retain rates, as well as a collection of movie related entities, e.g., actor, director, etc. From our model, words like ""love"", ""great"", ""terribl(e)"", ""perfect"", ""uniqu(e)"", ""fine(st)"", ""supris(e)"", and ""silli(y)"" yield large retain rates and hence are indicative feature for predication (in the top half). On the other hand, words like ""say"", ""pretti(y)"", ""young"", ""review"", ""role"", ""anim(ation)"" and ""actual"" have near zero retain rates upon model convergence, which are less informative. For named entities that are relevant to movie industry, we also observe some interesting pattern. Some actors (e.g., ""baldwin"" and ""kidman"", etc.) and directors (e.g., ""kurosawa"" and ""eastwood"" etc.), yield high retain rates shortly after initialization. The retain rates of actors like ""downey"" or ""spacey"", and directors like ""spielberg"" or ""cameron"" slightly increase or remain similar throughout optimization. Note that higher retain rate means the corresponding features are more indicative in classifying IMDB reviews into positive or negative labels, i.e., no explicit association with the label itself. Proof. In the analysis of Rademacher complexity, we treat the functions fed into the neurons of the l th layer as one function class F l = f l (x; w :l ). Here again we are using the notation w :l = {w 1 , . . . , w l }, and w = w :L . As a consequence ∀j, f DISPLAYFORM0 Note here f L (x; W ) used in section 3 is a vector, but f L (x; w) used in this subsection is a scalar. The connection between f L (x; W ) and f L (x; w) is that each dimension of f L (x; W ) is viewed as one instance coming from the same function classs f L (x; w). Similar ways of proof have been adopted in BID24 .To simplify our analysis, we follow BID24 and reformulate the cross-entropy loss on top of the softmax into a single logistic function DISPLAYFORM1 .The function class fed into the neurons of the l th layer f l (x; w :l ) admits a recursive expression DISPLAYFORM2 Given the neural network function (1) and the logistic loss function l is 1 Lipschitz, by Contraction lemma (a variant of the lemma 26.9 on page 381, Chapter 26 of BID16 ), the empirical Rademacher complexity of the loss function is bounded by DISPLAYFORM3 Note the empirical Rademacher complexity of the function class of the L th layer, i.e., the last output layer, is DISPLAYFORM4 To prove the bound in a recursive way, let's also define a variant of the Rademacher complexity with absolute value inside the supremum: DISPLAYFORM5 Note hereR S (f ) is not exactly the same as the Rademacher complexity defined before in this paper. And we have DISPLAYFORM6 Now we start the recursive proof. The empirical Rademacher complexity (with absolute value inside supremum) of the function class of the l th layer is DISPLAYFORM7 DISPLAYFORM8 By the calculous of Rademacher complexity, DISPLAYFORM9 Now we havê DISPLAYFORM10 Let g DISPLAYFORM11 Combining the inequalities (6), FORMULA22 , FORMULA5 , FORMULA5 , and (19), we have DISPLAYFORM12",1797,0.982,1079,1.6654309545875812,"We propose adaptively adjust the deep neural network based a Rademacher complexity bound state deep impose dropout strategy feature co However choosing the dropout rates remains heuristics or relies empirical grid-search over some hyperparameter space In this work the network Rademacher complexity is bounded related the dropout rate vectors the weight coefficient matrices Subsequently impose this bound as a regularizer provide a theoretical justified way trade-off model complexity and representation power Therefore the dropout rates and the empirical loss unified the same objective function then optimized the block coordinate descent algorithm We discover the adaptively adjusted dropout rates converge some interesting distributions reveal meaningful patternsExperiments the task image and document classification also our method achieves compared the state Dropout training BID19 has proposed regularize deep neural networks classification tasks It shown reducing coadaptation-and hence preventing model overfitting The idea dropout stochastically set a neuron's output according Bernoulli random variables It a crucial component the winning solution visual object recognition on ImageNet BID7 . Ever, novel learning algorithmsGoodfellow BID1 , regularization techniques BID23 .However , the classical dropout model First the model requires to specify the retain rates the probabilities keeping a neuron's output a to model training Subsequently , these retain rates kept fixed throughout thereafter It often not choose the retain rates an optimal way They usually set via grid-search over hyper-parameter space simply according some rule Another limitation all neurons share the same retain rate This exponentially reduces the search space hyper-parameter optimization For example BID19 use a fixed retain probability throughout training all dropout variables each layerIn a novel regularizer the Rademacher complexity Without loss , use multilayer perceptron with dropout as our example prove its Rademacher complexity is bounded a term related This enables explicitly incorporate the model complexity term a regularizer the objective functionThis Rademacher complexity bound regularizer provides a lot advantage modeling optimization First combines the model complexity the loss function an unified objective This offers trade-off the model complexity and representation power through regularizer weighting coefficient Second since bound dropout probabilities incorporate explictly the computation graph the optimization procedure We then adaptively optimize the objective adjust the dropout probabilities throughout training in similar ridge regression the lasso BID4 . Third our proposed regularizer assumes a neuron-wise dropout manner models different neurons have different retain rates during the optimization Our empirical results interesting trend on histograms dropout probabilities both hidden and input layers We also discover the distribution over retain rates upon model convergence reveals meaningful pattern on input featuresTo the using the Rademacher complexity bound adaptively the dropout probabilities We organize the rest the paper following . Section reviews some past approaches well aligned our motivation highlight some major difference to We subsequently detail our proposed approach Section In Section present our thorough empirical evaluations the task image and document on several benchmark datasets Finally Section concludes this paper summarizes some possible future research ideas Imposing regularizaiton for a better model generalization However we tackle for the dropout neural network regularization The theoretical upper bound we proved the Rademacher complexity facilitates us directly incorporate the dropout rates the objective function In the dropout rate can optimized block coordinate descent procedure with one consistent objective Our empirical evaluation demonstrates promising interesting patterns on adapted retain ratesIn the sparsity property the learnt retain rates encourage a sparse representation BID26 , similar and relevance vector machine BID21 We would explore the applications deep network compressionHan BID5 BID13 . In addition one other possible research direction dynamically adjust the architecture BID17 BID3 Guo) , hence reduce via dropout rates Features include words associated the 20 largest and smallest retain rates movie related entities actor From our model wordsgreat"", ""terribl(eperfectuniqu(efine(st ""silli(y yield large retain rates hence indicative feature for predicationin the top half On wordssay ""pretti(yyoungreview ""roleanim(ationactual near zero retain rates upon model convergence less informative For named entities relevant movie industry also observe some interesting pattern Some actors ( ""kidman andkurosawa ""eastwood yield high retain rates shortly initialization The retain rates actors like ""downey or directors slightly or remain similar throughout optimization Note higher retain rate the corresponding features indicative in classifying IMDB reviews into the label Proof. In the analysis Rademacher complexity treat fed the neurons the l th layer one function class F l = f l; w :l Here again using the notation w :l { 1 . . . , w l }, and w = w :L As a consequence ��j f DISPLAYFORM0 Note here f L (; W ) used section is this subsection The connection f L (x; W each dimension viewed one instance coming the same function classs f L Similar ways proof have BID24 .To simplify follow reformulate on top the softmax into DISPLAYFORM1 .The function class fed the neurons l th layer f l (x; w :l admits a recursive expression Given1 is 1 Lipschitz by Contraction lemmaa variant 26.9 on page 381 Chapter 26 the empirical Rademacher complexity bounded th layer the last output layer To prove the bound in a recursive way also with absolute value inside the supremum hereR S ) not exactly defined before And DISPLAYFORM6 Now we start the recursive proof The empirical Rademacher complexitywith absolute value inside supremum the function class the l th layer DISPLAYFORM7 DISPLAYFORM8 By calculous of Now havê Let g Combining the inequalities6 FORMULA22 , (19",0.01,0.3995387778485415
"Sensor fusion is a key technology that integrates various sensory inputs to allow for robust decision making in many applications such as autonomous driving and robot control. Deep neural networks have been adopted for sensor fusion in a body of recent studies. Among these, the so-called netgated architecture was proposed, which has demonstrated improved performances over the conventional convolu- tional neural networks (CNN). In this paper, we address several limitations of the baseline negated architecture by proposing two further optimized architectures: a coarser-grained gated architecture employing (feature) group-level fusion weights and a two-stage gated architectures leveraging both the group-level and feature- level fusion weights. Using driving mode prediction and human activity recogni- tion datasets, we demonstrate the significant performance improvements brought by the proposed gated architectures and also their robustness in the presence of sensor noise and failures.
 Sensor fusion is an essential technology to autonomous systems such as self-driving cars and mobile robots. In advanced driver-assistance systems (ADAS), many sensors such as cameras, ultrasonic sensors, and LiDARs are utilized for enhanced safety and driving experience. Sensor fusion based vehicle and robot control technologies have been explored BID9 BID7 BID4 BID2 BID8 . In addition, devices like smartphones and smartwatches typically integrate a number of sensors, making these devices a suitable platform for running sensor fusion applications such as activity recognition. Several sensor fusion techniques for activity recognition have been proposed BID10 BID3 BID11 BID5 .More specifically, in BID2 , a deep reinforcement learning based sensor fusion algorithm is discussed for robot control. A Kuka YouBot is used with multiple LiDAR sensors for simulations. In terms of sensor fusion, early fusion which concatenates all inputs as feature planes is compared with three other fusion techniques: concatenating convolution layer outputs, reducing the concatenated features with a 1x1 convolution, and accumulating convolution outputs. However, sensor noise and failures are not considered in this work. In addition , due to the fact that only the same type of sensory inputs is used in the experiments, the performance of sensor fusion based on different kinds of sensory inputs is unclear.Among sensor fusion techniques employed in automobiles, BID9 exploit neural networks with a Kalman filter for vehicle roll angle estimation, and show the advantage of using an inertial measurement unit (IMU) without additional suspension deflection sensors. BID7 consider a sensor-rich platform with a learning algorithm for maneuver prediction. Long short-term memory (LSTM) networks, which are a type of recurrent neural networks (RNN) are used with sensory inputs from cameras, GPS, and speedometers. BID4 propose joint probabilistic data fusion for road environments. However, neither a multiplicity of sensory inputs nor sensory noise and failures are considered. The adopted architecture is simplistic where input data are only fused in one layer.In the field of wearable devices, BID10 utilize early fusion, which concatenates sensory inputs. With this simple fusion approach, classical supervised learning methods such as Bayesian classifiers, k-nearest-neighbors, support vector machines, and artificial neural networks are compared. BID3 use deep convolutional neural networks with IMU data. BID11 use a CNN with angle embedded gate dynamic images, which are pre-processed inputs for gait recognition. BID5 summarize three fusion methods, namely, data, feature, and decision level fusion. However, effective sensor fusion network architectures for coping with sensor failures are not deeply investigated.In terms of sensor fusion architectures, BID8 propose a so-called netgated architecture in which the information flow in a given convolutional neural network (CNN) is gated by fusion weights extracted from camera and LiDAR inputs. These fusion weights are used for computing a weighted sum of the sensory inputs. The weighted sum passes through fully connected layers to create a steering command. The gated networks (netgated) is shown to be robust to sensor failures, comparing to basic CNNs. However, a deep understanding of the relationships between sensory inputs, fusion weights, network architecture, and the resulting performances are not examined.The main objective of this paper is to propose optimized gated architectures that can address three limitations of the baseline netgated architecture of BID8 and investigate how different fusion architectures operate under clean sensory data and in the presence of snesor noise and failures. Our main contributions are:• Propose a new coarser-grained gated architecture which learns robustly a set of fusion weights at the (feature) group level;• Further propose a two-stage gating architecture which exploits both the feature-level and group-level fusion weights, leading to further performance improvements.• Analyze the characteristics of the proposed architectures and show how they may address the limitations of the negated architecture in terms of inconsistency of fusion weights, overfitting, and lack of diverse fusion mechanisms.By utilizing driving mode prediction and human activity recognition datasets, we demonstrate the significant performance improvements brought by the proposed architectures over the conventional CNN and netgated architectures under various settings including cases where random sensor noise and failures are presented. Empirical evidence is also analyzed to help shed light on the underlying causes that may be responsible for the observed improvements of the two proposed architectures.",1027,0.512,628,1.6353503184713376,"Sensor fusion integrates various sensory inputs allow robust decision making many applications robot control Deep neural networks adopted sensor fusion a body recent studies Among these the so-called netgated architecture proposed, has demonstrated improved performances the conventional convolu- tional neural networksCNN In this paper address several limitations the baseline negated architecture by proposing two further optimized architectures coarser gated employing (feature group-level fusion weights two architectures leveraging Using driving mode prediction human activity recogni- tion datasets demonstrate the significant performance improvements brought the proposed gated architectures also their robustness sensor noise failures Sensor fusion an essential technology autonomous systems such mobile robots In advanced driver-assistance systems many sensors such LiDARs utilized enhanced safety and driving experience Sensor fusion based vehicle and robot control technologies explored BID9 BID7 BID4 BID2 BID8 . In addition devices smartphones typically integrate making a suitable running sensor fusion applications activity recognition Several sensor fusion techniques for activity recognition BID10 BID3 .More in deep reinforcement discussed for robot control A Kuka YouBot used with multiple LiDAR sensors simulations In terms sensor fusion early fusion which concatenates all inputs as feature planes compared three other fusion techniques concatenating convolution layer outputs reducing with accumulating However sensor noise failures considered in this work In addition , due only the same type sensory inputs is the experiments the performance sensor fusion based different kinds unclearAmong sensor fusion techniques employed automobiles BID9 exploit neural a Kalman filter vehicle roll angle estimation show the advantage an inertial measurement unit without additional suspension deflection sensors BID7 consider a sensor-rich platform a learning algorithm maneuver prediction Long short-term memory (LSTM) networks with sensory inputs cameras GPS speedometers BID4 propose joint probabilistic data fusion road environments However neither a multiplicity sensory inputs sensory noise and failures considered The adopted architecture simplistic where input data only fused inIn the field wearable devices BID10 utilize early fusion, concatenates sensory inputs With this simple fusion approach classical supervised learning methods such support vector machines compared BID3 use IMU data BID11 use a CNN with angle embedded gate dynamic images pre-processed inputs gait recognition BID5 summarize three fusion methods namely data, feature decision level fusion However effective sensor fusion network architectures for coping sensor failures deeply investigatedIn terms BID8 propose a so-called netgated architecture in information in gated fusion weights extracted camera and LiDAR inputs These fusion weights computing a weighted sum the sensory inputs The weighted sum passes fully connected layers a steering command The gated networks (netgated) is shown robust sensor failures comparing basic CNNs a deep understanding the relationships sensory inputs fusion weights network architecture the resulting performances are examinedThe main objective propose optimized gated architectures address three limitations the baseline netgated architecture of BID8 investigate how different fusion architectures operate clean sensory data in snesor noise failures Our main contributions are:• Propose a new coarser-grained gated architecture which learns robustly a set fusion weights at the (feature) group Further propose exploits leading the characteristics the proposed architectures show address the negated architecture inconsistency overfitting lack diverse fusion mechanismsBy utilizing driving mode prediction human activity recognition datasets brought the conventional CNN netgated under various settings including cases random sensor noise failures presented also analyzed help shed that of the two proposed architectures",0.01,0.3228959598801449
"We develop a mean field theory for batch normalization in fully-connected feedforward neural networks. In so doing, we provide a precise characterization of signal propagation and gradient backpropagation in wide batch-normalized networks at initialization. Our theory shows that gradient signals grow exponentially in depth and that these exploding gradients cannot be eliminated by tuning the initial weight variances or by adjusting the nonlinear activation function. Indeed, batch normalization itself is the cause of gradient explosion. As a result, vanilla batch-normalized networks without skip connections are not trainable at large depths for common initialization schemes, a prediction that we verify with a variety of empirical simulations. While gradient explosion cannot be eliminated, it can be reduced by tuning the network close to the linear regime, which improves the trainability of deep batch-normalized networks without residual connections. Finally, we investigate the learning dynamics of batch-normalized networks and observe that after a single step of optimization the networks achieve a relatively stable equilibrium in which gradients have dramatically smaller dynamic range. Our theory leverages Laplace, Fourier, and Gegenbauer transforms and we derive new identities that may be of independent interest. Deep neural networks have been enormously successful across a broad range of disciplines. These successes are often driven by architectural innovations. For example, the combination of convolutions BID15 , residual connections BID12 , and batch normalization BID13 has allowed for the training of very deep networks and these components have become essential parts of models in vision (Zoph et al.) , language BID4 , and reinforcement learning (Silver et al., 2017) . However, a fundamental problem that has accompanied this rapid progress is a lack of theoretical clarity. An important consequence of this gap between theory and experiment is that two important issues become conflated. In particular, it is generally unclear whether novel neural network components improve generalization or whether they merely increase the fraction of hyperparameter configurations where good generalization can be achieved. Resolving this confusion has the promise of allowing researchers to more effectively and deliberately design neural networks.Recently, progress has been made (Poole et al., 2016; Schoenholz et al., 2016; BID6 BID16 BID11 in this direction by considering neural networks at initialization, before any training has occurred. In this case, the parameters of the network are random variables which induces a distribution of the activations of the network as well as the gradients. Studying these distributions is equivalent to understanding the prior over functions that these random neural networks compute. Picking hyperparameters that correspond to well-conditioned priors ensures that the neural network will be trainable and this fact has been extensively verified experimentally. However, to fulfill its promise of making neural network design less of a black box, these techniques must be applied to neural network architectures that are used in practice. Over the past year, this gap has closed significantly and theory for networks with skip connections (Yang & Schoenholz, 2017; , convolutional networks (Xiao et al., 2018) , and gated recurrent networks BID3 BID9 have been developed. More recently, Yang (2019) devised a formalism that extends this approach to include an even wider range of architectures.Before state-of-the-art models can be analyzed in this framework, a slowly-decreasing number of architectural innovations must be studied. One particularly important component that has thus-far remained elusive is batch normalization.Our Contributions. In this paper, we develop a theory of fully-connected networks with batch normalization whose weights and biases are randomly distributed. A significant complication in the case of batch normalization (compared to e.g. layer normalization or weight normalization) is that the statistics of the network depend non-locally on the entire batch. Thus, our first main result is to recast the theory for random fully-connected networks so that it can be applied to batches of data. We then extend the theory to include batch normalization explicitly and validate this theory against Monte-Carlo simulations. We show that as in previous cases we can leverage our theory to predict valid hyperparameter configurations.In the process of our investigation, we identify a number of previously unknown properties of batch normalization that make training unstable. In particular, for most nonlinearities used in practice, batchnorm in a deep, randomly initialized network induces high degree of symmetry in the embeddings of the samples in the batch (Thm 3.4) . Whenever this symmetry takes hold, we show that for any choice of nonlinearity, gradients of fully-connected networks with batch normalization explode exponentially in the depth of the network (Thm 3.9) . This imposes strong limits on the maximum trainable depth of batch normalized networks. This limit can be lifted partially but not completely by pushing activation functions to be more linear at initialization. It might seem that such gradient explosion ought to lead to learning dynamics that are unfavorable. However, we show that networks with batch normalization causes the scale of the gradients to naturally equilibrate after a single step of gradient descent (provided the initial gradients are not so large as to cause numerical instabilities). For shallower networks, this equilibrating effect is sufficient to allow adequate training.Finally, we note that there is a related vein of research that has emerged that leverages the prior over functions induced by random networks to perform exact Bayesian inference BID16 BID7 BID18 BID8 . One of the natural consequences of this work is that the prior for networks with batch normalization can be computed exactly in the wide network limit. As such, it is now possible to perform exact Bayesian inference in the case of wide neural networks with batch normalization. In this work we have presented a theory for neural networks with batch normalization at initialization. In the process of doing so, we have uncovered a number of counterintuitive aspects of batch normalization and -in particular -the fact that at initialization it unavoidably causes gradients to explode with depth. We have introduced several methods to reduce the degree of gradient explosion, enabling the training of significantly deeper networks in the presence of batch normalization. Finally, this work paves the way for future work on more advanced, state-of-the-art, network architectures and topologies. : Batch norm leads to a chaotic input-output map with increasing depth. A linear network with batch norm is shown acting on two minibatches of size 64 after random orthogonal initialization. The datapoints in the minibatch are chosen to form a 2d circle in input space, except for one datapoint that is perturbed separately in each minibatch (leftmost datapoint at input layer 0). Because the network is linear, for a given minibatch it performs an affine transformation on its inputs -a circle in input space remains an ellipse throughout the network. However, due to batch norm the coefficients of that affine transformation change nonlinearly as the datapoints in the minibatch are changed. (a) Each pane shows a scatterplot of activations at a given layer for all datapoints in the minibatch, projected onto the top two PCA directions. PCA directions are computed using the concatenation of the two minibatches. Due to the batch norm nonlinearity, minibatches that are nearly identical in input space grow increasingly dissimilar with depth. Intuitively, this chaotic input-output map can be understood as the source of exploding gradients when batch norm is applied to very deep networks, since very small changes in an input correspond to very large movements in network outputs. (b) The correlation between the two minibatches, as a function of layer, for the same network. Despite having a correlation near one at the input layer, the two minibatches rapidly decorrelate with depth. See Appendix H for a theoretical treatment.A VGG19 WITH BATCHNORM ON CIFAR100Even though at initialization time batchnorm causes gradient explosion, after the first few epochs, the relative gradient norms ∇ θ L / θ for weight parameters θ = W or BN scale parameter θ = γ, equilibrate to about the same magnitude. See Fig. 7 . with batchnorm on CIFAR100 with data augmentation. We use 8 random seeds for each combination, and assign to each combination the median training/validation accuracy over all runs. We then aggregate these scores here. In the first row we look at training accuracy with different learning rate vs β initialization at different epochs of training, presenting the max over . In the second row we do the same for validation accuracy. In the third row, we look at the matrix of training accuracy for learning rate vs , taking max over β. In the fourth row, we do the same for validation accuracy.",1720,1.006,982,1.7515274949083504,"We develop a mean field theory batch normalization fully-connected feedforward neural networks In so provide a precise characterization signal propagation gradient backpropagation wide batch-normalized networks at initialization Our theory shows gradient signals grow depth these exploding gradients eliminated tuning the initial weight variances or Indeed batch normalization itself the cause gradient explosion As vanilla batch-normalized networks without skip connections trainable at large depths for common initialization schemes a prediction we verify a variety empirical simulations While gradient explosion eliminated tuning the network close the linear regime improves the trainability deep batch-normalized networks without residual connections Finally investigate the learning dynamics batch-normalized networks observe after optimization achieve gradients have dramatically smaller dynamic range Our theory leverages Laplace, transforms we derive new identities may independent interest Deep neural networks enormously across These successes often driven architectural innovations For example the combination convolutions BID15 , residual connections has allowed the training very deep networks these components become essential parts models vision (Zoph et al.) , language BID4Silver 2017 However a fundamental problem accompanied this rapid progress theoretical clarity An important consequence this gap theory experiment two important issues become In particular generally unclear novel neural network components improve generalization merely the fraction hyperparameter configurations where good generalization Resolving this confusion the promise allowing researchers more and deliberately designRecently progress (Poole BID6 BID16 BID11 in this direction by considering at initialization before any training has In the parameters the network random variables induces a distribution Studying these distributions equivalent understanding prior over functions these random neural compute Picking hyperparameters that correspond well-conditioned priors ensures trainable this fact extensively verified However to fulfill making neural design less of these techniques used practice Over this gap closed significantly theory for networks with skip connections (Yang , convolutional networksXiao and gated recurrent networks BID3 BID9 have More recently Yang (2019 devised a formalism extends include architecturesBefore state models analyzed architectural innovations studied One particularly important component thus- batch normalizationOur Contributions. In develop fully-connected networks batch normalization whose weights biases randomly A significant complication batch normalizationcompared the statistics the network depend non Thus our first main result recast for random fully-connected networks so batches We then extend batch normalization explicitly validate this theory against We show as in leverage our theory valid hyperparameter configurationsIn our investigation identify previously unknown properties batch normalization make training unstable In particular for most nonlinearities used practice batchnorm in a deep, randomly initialized network induces high degree symmetry the batch (Thm Whenever this symmetry takes show for any choice gradients fully-connected networks with batch normalization explode exponentially the depthThm This imposes strong limits the maximum trainable depth batch normalized networks This limit lifted partially but pushing activation functions be linear at initialization It might such gradient explosion ought lead learning dynamics that unfavorable. However we show networks batch normalization causes the scale naturally afterprovided so numerical instabilities For shallower networks this equilibrating effect sufficient allow adequate trainingFinally a related vein emerged leverages prior over functions induced random networks perform exact Bayesian inference BID16 BID7 BID18 BID8 . One the natural consequences this work prior for networks with batch normalization computed exactly the wide network limit As such now perform exact Bayesian inference wide neural networks batch normalization In this work presented neural networks batch normalization at initialization In uncovered counterintuitive aspects batch normalization -in particular at initialization unavoidably causes gradients explode with depth We introduced several methods reduce the degree gradient explosion enabling the training significantly deeper networks batch normalization Finally this work paves more, state network architectures topologies : Batch norm leads a chaotic input-output map with increasing depth A linear network batch norm is shown acting size 64 after random orthogonal initialization chosen form input space except perturbed separately at input layer Because the network linear for performs an affine transformation -a circle input space remains throughout However due batch norm the coefficients that affine transformation change nonlinearly in (a Each pane shows a scatterplot activations at a given layer for projected the top two PCA directions PCA directions computed Due the batch norm nonlinearity minibatches that nearly input space grow increasingly with depth Intuitively this chaotic input-output map understood exploding gradients when batch norm is very deep networks since very small changes an input correspond network outputs (b) The correlation the two minibatches layer for the same network Despite a correlation near one at the input layer rapidly decorrelate depth See Appendix H a theoretical treatmentA VGG19 WITH BATCHNORM ON CIFAR100Even at initialization time batchnorm causes gradient explosion after the relative gradient norms �� �� L / �� for weight parameters � = W or BN scale parameter, See Fig 7 . with batchnorm on CIFAR100 with data augmentation We use 8 random seeds each combination assign to the median training/validation accuracy over We then aggregate these scores here In the first row we look training accuracy with different learning rate vs β initialization at presenting the max over . In the second row we do validation accuracy In the third row look the matrix training accuracy learning rate vs , taking max over β In the fourth row do validation accuracy",0.01,0.6189051982265381
"We present NeuroSAT, a message passing neural network that learns to solve SAT problems after only being trained as a classifier to predict satisfiability.   Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve problems that are substantially larger and more difficult than it ever saw during training by simply running for more iterations. Moreover, NeuroSAT generalizes to novel distributions; after training only on random SAT problems, at test time it can solve SAT problems encoding graph coloring, clique detection, dominating set, and vertex cover problems, all on a range of distributions over small random graphs. The propositional satisfiability problem (SAT) is one of the most fundamental problems of computer science. BID4 showed that the problem is NP-complete, which means that searching for any kind of efficiently-checkable certificate in any context can be reduced to finding a satisfying assignment of a propositional formula. In practice, search problems arising from a wide range of domains such as hardware and software verification, test pattern generation, planning, scheduling, and combinatorics are all routinely solved by constructing an appropriate SAT problem and then calling a SAT solver BID9 . Modern SAT solvers based on backtracking search are extremely well-engineered and have been able to solve problems of practical interest with millions of variables BID2 ).We consider the question: can a neural network learn to solve SAT problems? To answer, we develop a novel message passing neural network (MPNN) BID21 BID16 BID8 , NeuroSAT, and train it as a classifier to predict satisfiability on a dataset of random SAT problems. We provide NeuroSAT with only a single bit of supervision for each SAT problem that indicates whether or not the problem is satisfiable. When making a prediction about a new SAT problem, we find that NeuroSAT guesses unsatisfiable with low confidence until it finds a solution, at which point it converges and guesses satisfiable with very high confidence. The solution itself can almost always be automatically decoded from the network's activations, making NeuroSAT an end-to-end SAT solver. See Figure 1 for an illustration of the train and test regimes.Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve SAT problems that are substantially larger and more difficult than it ever saw during training by simply performing more iterations of message passing. Despite only running for a few dozen iterations during training, at test time NeuroSAT continues to find solutions to harder problems after hundreds and even thousands of iterations. The learning process has yielded not a traditional classifier but rather a procedure that can be run indefinitely to search for solutions to problems of varying difficulty. Our main motivation has been scientific: to better understand the extent to which neural networks are capable of precise, logical reasoning. Our work has definitively established that neural networks can learn to perform discrete search on their own without the help of hard-coded search procedures, even after only end-to-end training with minimal supervision. We found this result surprising and think it constitutes an important contribution to the community's evolving understanding of the capabilities and limitations of neural networks.Although not our primary concern, we also hope that our findings eventually lead to improvements in practical SAT solving. As we stressed early on, as an end-to-end SAT solver the trained NeuroSAT system discussed in this paper is still vastly less reliable than the state-of-the-art. We concede that we see no obvious path to beating existing SAT solvers. One approach might be to continue to train NeuroSAT as an end-to-end solver on increasingly difficult problems. A second approach might be to use a system like NeuroSAT to help guide decisions within a more traditional SAT solver, though it is not clear that NeuroSAT provides any useful information before it finds a satisfying assignment. However, as we discussed in §8, when we trained our architecture on different data it learned an entirely different procedure. In a separate experiment omitted for space reasons, we also trained our architecture to predict whether there is a satisfying assignment involving each individual literal in the problem and found that it was able to predict these bits with high accuracy as well. Unlike NeuroSAT, it made both type I and type II errors, had no discernable phase transition, and could make reasonable predictions within only a few rounds. We believe that architectures descended from NeuroSAT will be able to learn very different mechanisms and heuristics depending on the data they are trained on and the details of their objective functions. We are cautiously optimistic that a descendant of NeuroSAT will one day lead to improvements to the state-of-the-art.",913,0.459,534,1.7097378277153559,"We present NeuroSAT a message passing neural network solve SAT problems after only being as to predict satisfiability Although competitive state SAT solvers NeuroSAT solve substantially larger it ever saw during training by simply running for more iterations Moreover NeuroSAT generalizes novel distributions; after training only on random SAT problems at test time it solve encoding graph coloring clique detection dominating set vertex cover problems all on a range distributions over small random graphs The propositional satisfiability problemSAT BID4 showed the problem NP searching any kind efficiently-checkable certificate any context reduced finding a satisfying assignment a propositional formula In practice search problems arising domains such hardware and software verification test pattern generation planning scheduling combinatorics all routinely constructing an appropriate SAT problem calling a SAT solver BID9 . Modern SAT solvers based backtracking search are extremely well able practical interest with millions variables BID2 ).We consider To answer, develop a novel message passingMPNN BID21 BID16 BID8 , NeuroSAT and train as satisfiability on random SAT problems We provide NeuroSAT with only a single bit supervision each SAT problem that indicates satisfiable When making a prediction a new SAT problem find NeuroSAT guesses unsatisfiable with low confidence until at converges guesses satisfiable The solution itself can almost automatically decoded the network's activations making NeuroSAT end SAT See Figure the train and test regimesAlthough competitive state SAT NeuroSAT solve SAT problems substantially it ever saw during training by simply performing more iterations message Despite only running a few dozen iterations during training, at test time NeuroSAT continues find solutions harder problems after hundreds and The learning process has yielded not a traditional classifier run indefinitely search solutions varying difficulty Our main motivation has scientific: better the extent precise, logical reasoning Our work definitively neural networks discrete search on their hard-coded search procedures even after only end with minimal supervision We found this result surprising think constitutes the capabilitiesAlthough not our primary concern hope eventually practical SAT solving As stressed early as an end SAT the trained NeuroSAT system discussed still vastly less reliable the state. We concede see no obvious path beating existing SAT solvers One approach might continue train NeuroSAT as end solver on increasingly difficult problems A second approach might NeuroSAT help guide decisions within a more traditional SAT solver though provides before finds a satisfying assignment However as §8 when trained our architecture on different data it learned an entirely different procedure In a separate experiment omitted for space reasons also trained our architecture predict there a satisfying assignment involving each individual literal the problem found able these bits with as Unlike NeuroSAT it made both type had no discernable phase transition make reasonable predictions within We believe architectures descended NeuroSAT will learn very different mechanisms depending trained the details their objective functions We cautiously a descendant NeuroSAT lead to improvements.",0.01,0.5124287978188022
"Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on road networks, (2) non-linear temporal dynamics with changing road conditions and (3) inherent difficulty of long-term forecasting. To address these challenges, we propose to model the traffic flow as a diffusion process on a directed graph and introduce Diffusion Convolutional Recurrent Neural Network (DCRNN), a deep learning framework for traffic forecasting that incorporates both spatial and temporal dependency in the traffic flow. Specifically, DCRNN captures the spatial dependency using bidirectional random walks on the graph, and the temporal dependency using the encoder-decoder architecture with scheduled sampling. We evaluate the framework on two real-world large-scale road network traffic datasets and observe consistent improvement of 12% - 15% over state-of-the-art baselines Spatiotemporal forecasting is a crucial task for a learning system that operates in a dynamic environment. It has a wide range of applications from autonomous vehicles operations, to energy and smart grid optimization, to logistics and supply chain management. In this paper, we study one important task: traffic forecasting on road networks, the core component of the intelligent transportation systems. The goal of traffic forecasting is to predict the future traffic speeds of a sensor network given historic traffic speeds and the underlying road networks. This task is challenging mainly due to the complex spatiotemporal dependencies and inherent difficulty in the long term forecasting. On the one hand, traffic time series demonstrate strong temporal dynamics. Recurring incidents such as rush hours or accidents can cause nonstationarity, making it difficult to forecast longterm. On the other hand, sensors on the road network contain complex yet unique spatial correlations. FIG0 illustrates an example. Road 1 and road 2 are correlated, while road 1 and road 3 are not. Although road 1 and road 3 are close in the Euclidean space, they demonstrate very different behaviors. Moreover, the future traffic speed is influenced more by the downstream traffic than the upstream one. This means that the spatial structure in traffic is nonEuclidean and directional.Traffic forecasting has been studied for decades, falling into two main categories: knowledgedriven approach and data-driven approach. In transportation and operational research, knowledgedriven methods usually apply queuing theory and simulate user behaviors in traffic BID6 . In time series community, data-driven methods such as Auto-Regressive Integrated Moving Average (ARIMA) model and Kalman filtering remain popular BID22 BID21 . However, simple time series models usually rely on the stationarity assumption, which is often violated by the traffic data. Most recently, deep learning models for traffic forecasting have been developed in BID23 ; BID35 , but without considering the spatial structure. BID31 and BID24 model the spatial correlation with Convolutional Neural Networks (CNN), but the spatial structure is in the Euclidean space (e.g., 2D images). BID4 , studied graph convolution, but only for undirected graphs.In this work, we represent the pair-wise spatial correlations between traffic sensors using a directed graph whose nodes are sensors and edge weights denote proximity between the sensor pairs measured by the road network distance. We model the dynamics of the traffic flow as a diffusion process and propose the diffusion convolution operation to capture the spatial dependency. We further propose Diffusion Convolutional Recurrent Neural Network (DCRNN) that integrates diffusion convolution, the sequence to sequence architecture and the scheduled sampling technique. When evaluated on realworld traffic datasets, DCRNN consistently outperforms state-of-the-art traffic forecasting baselines by a large margin. In summary:• We study the traffic forecasting problem and model the spatial dependency of traffic as a diffusion process on a directed graph. We propose diffusion convolution, which has an intuitive interpretation and can be computed efficiently.• We propose Diffusion Convolutional Recurrent Neural Network (DCRNN), a holistic approach that captures both spatial and temporal dependencies among time series using diffusion convolution and the sequence to sequence learning framework together with scheduled sampling. DCRNN is not limited to transportation and is readily applicable to other spatiotemporal forecasting tasks.• We conducted extensive experiments on two large-scale real-world datasets, and the proposed approach obtains significant improvement over state-of-the-art baseline methods. In this paper, we formulated the traffic prediction on road network as a spatiotemporal forecasting problem, and proposed the diffusion convolutional recurrent neural network that captures the spatiotemporal dependencies. Specifically, we use bidirectional graph random walk to model spatial dependency and recurrent neural network to capture the temporal dynamics. We further integrated the encoder-decoder architecture and the scheduled sampling technique to improve the performance for long-term forecasting. When evaluated on two large-scale real-world traffic datasets, our approach obtained significantly better prediction than baselines. For future work, we will investigate the following two aspects (1) applying the proposed model to other spatial-temporal forecasting tasks; (2) modeling the spatiotemporal dependency when the underlying graph structure is evolving, e.g., the K nearest neighbor graph for moving objects.",1039,0.588,582,1.7852233676975946,"Spatiotemporal forecasting various applications neuroscience, climate and transportation domain Traffic forecasting one canonical example such learning task The task challenging due (1) complex spatial dependency road networks with changing road conditions To address propose model as on introduce traffic forecasting incorporates in Specifically DCRNN captures the spatial dependency using bidirectional random walks on with scheduled sampling We evaluate the framework on two real-world large-scale road network traffic datasets observe consistent improvement 12% state baselines Spatiotemporal forecasting is a crucial task a learning system operates It autonomous vehicles operations energy smart grid optimization In study one important task traffic forecasting on road networks the core component the intelligent transportation systems The goal traffic forecasting a sensor network given historic traffic speeds the underlying road networks This task challenging mainly inherent difficulty the long term forecasting On traffic time series demonstrate strong temporal dynamics Recurring incidents such rush hours accidents nonstationarity making forecast longterm. On sensors the road network contain complex yet unique spatial correlations FIG0 illustrates. Road 1 and correlated while 3 Although road 1 3 close in the Euclidean space demonstrate Moreover the future traffic speed is influenced more the downstream traffic This means the spatial structure in traffic directionalTraffic forecasting studied falling knowledgedriven approach and data-driven approach In transportation and operational research knowledgedriven methods usually apply queuing theory simulate user behaviors traffic BID6 . In time series community, data-driven methods Auto-Regressive Integrated Moving Average (ARIMA) model Kalman filtering remain popular BID22 BID21 . However simple time series models usually rely the stationarity assumption violated the traffic data Most recently deep learning models traffic forecasting BID23 ; BID35 but without considering the spatial structure. BID31 and BID24 model the spatial correlation with but the spatial structure in BID4 , studied graph convolution butIn represent the pair-wise spatial correlations traffic sensors using a directed graph whose nodes sensors edge weights denote proximity measured the road network distance We model the dynamics the traffic flow a diffusion process propose the diffusion convolution operation capture the spatial dependency We further propose Diffusion Convolutional Recurrent Neural Network that integrates, the sequence to sequence architecture the scheduled sampling technique When evaluated realworld traffic datasets DCRNN consistently state forecasting baselines In summary:• We study the traffic forecasting problem model the spatial dependency as a diffusion process on a directed graph We propose diffusion convolution has an intuitive interpretation computed efficiently.• a holistic approach captures among time series using the sequence to sequence learning framework together scheduled sampling DCRNN not limited transportation is readily applicable spatiotemporal forecasting tasks.• We conducted extensive experiments the proposed approach obtains state baseline In formulated the traffic prediction on road network as proposed captures. Specifically use bidirectional graph random walk model spatial dependency recurrent neural network to capture We further integrated the scheduled sampling technique for long-term forecasting When evaluated our approach obtained baselines For future work investigate the following two aspects ( applying other spatial-temporal forecasting tasks modeling when the underlying graph structure evolving the K nearest neighbor graph moving objects",0.01,0.7047593216065193
"Obtaining reliable uncertainty estimates of neural network predictions is a long standing challenge. Bayesian neural networks have been proposed as a solution, but it remains open how to specify their prior. In particular, the common practice of a standard normal prior in weight space imposes only weak regularities, causing the function posterior to possibly generalize in unforeseen ways on inputs outside of the training distribution. We propose noise contrastive priors (NCPs) to obtain reliable uncertainty estimates. The key idea is to train the model to output high uncertainty for data points outside of the training distribution. NCPs do so using an input prior, which adds noise to the inputs of the current mini batch, and an output prior, which is a wide distribution given these inputs. NCPs are compatible with any model that can output uncertainty estimates, are easy to scale, and yield reliable uncertainty estimates throughout training. Empirically, we show that NCPs prevent overfitting outside of the training distribution and result in uncertainty estimates that are useful for active learning. We demonstrate the scalability of our method on the flight delays data set, where we significantly improve upon previously published results. Many successful applications of neural networks BID25 BID53 BID57 are in restricted settings where predictions are only made for inputs similar to the training distribution. In real-world scenarios, neural networks can face truly novel data points during inference, and in these settings it can be valuable to have good estimates of the model's uncertainty. For example, in healthcare, reliable uncertainty estimates can prevent overconfident decisions for rare or novel patient conditions BID49 . Similarly, autonomous agents that actively explore their environment can use uncertainty estimates to decide what data points will be most informative.Epistemic uncertainty describes the amount of missing knowledge about the data generating function. Uncertainty can in principle be completely reduced by observing more data points at the right locations and training on them. In contrast, the data generating function may also have inherent randomness, which we call aleatoric noise. This noise can be captured by models outputting a distribution rather than a point prediction. Obtaining more data points allows the noise estimate to move closer to the true value, which is usually different from zero. For active learning, it is crucial to separate the two types of randomness: we want to acquire labels in regions of high uncertainty but low noise BID36 .Bayesian analysis provides a principled approach to modeling uncertainty in neural networks BID8 BID37 . Namely, one places a prior over the network's weights and biases. This effectively places a distribution over the functions that the network represents, capturing uncertainty about which function best fits the data. Specifying this prior remains an open challenge. Common practice is to use a standard normal prior in weight space, which imposes weak shrinkage regularities analogous to weight decay. It is neither informative about the induced function class nor the data (e.g., it is sensitive to parameterization). This can cause the induced function posterior to generalize in unforeseen ways on out-of-distribution (OOD) inputs, which are inputs outside of the distribution that generated the training data.Motivated by these challenges, we introduce noise contrastive priors (NCPs), which encourage uncertainty outside of the training distribution through a loss in data space. NCPs are compatible with any model that represents functional uncertainty as a random variable, are easy to scale, and yield reliable uncertainty estimates that show significantly improved active learning performance.",691,0.412,400,1.7275,"Obtaining reliable uncertainty estimates neural network predictions Bayesian neural networks, open how specify prior In particular the common practice a standard normal prior in weight space imposes only weak regularities causing the function posterior possibly generalize unforeseen ways on inputs outside the training distribution We propose noise contrastive priorsNCPs obtain reliable uncertainty estimates The key idea train the model output high uncertainty data points outside the training distribution NCPs do so using an input prior adds noise the current mini batch a wide distribution given these inputs NCPs compatible output uncertainty estimates are scale yield throughout training show NCPs prevent overfitting outside the training distribution result uncertainty estimates useful active learning We demonstrate our method on flight delays data significantly upon Many successful applications BID25 BID53 BID57 in restricted settings predictions only inputs similar the training distribution In neural networks face truly novel data points during inference these settings valuable good estimates For example healthcare reliable uncertainty estimates prevent for rare or novel patient conditions BID49 . Similarly autonomous agents actively explore uncertainty estimates decide data pointsEpistemic uncertainty describes missing knowledge the data generating function can in principle completely reduced observing more data points training In contrast the data generating function may inherent randomness we aleatoric noise This noise captured models outputting a distribution rather a point prediction Obtaining more data points allows the noise estimate move different zero For active learning separate randomness we acquire labels regions high uncertainty but low noise BID36 .Bayesian analysis modeling uncertainty BID8 BID37 Namely one places prior over the network's weights biases This effectively places a distribution over the functions the network represents capturing uncertainty best Specifying this prior remains Common practice standard normal prior in weight space imposes weak shrinkage regularities analogous weight decay It neither informative about the induced function class the data ( it sensitive parameterization This can cause the induced function posterior generalize unforeseen ways on outOOD inputs inputs outside generatedMotivated these challenges introduce noise contrastive priors encourage uncertainty outside through data space NCPs compatible represents functional uncertainty are easy scale yield reliable uncertainty show significantly active learning performance",0.0,0.557685252232682
"Convolutional neural networks (CNNs) were inspired by human vision and, in some settings, achieve a performance comparable to human object recognition. This has lead to the speculation that both systems use similar mechanisms to perform recognition. In this study, we conducted a series of simulations that indicate that there is a fundamental difference between human vision and CNNs: while object recognition in humans relies on analysing shape, CNNs do not have such a shape-bias. We teased apart the type of features selected by the model by modifying the CIFAR-10 dataset so that, in addition to containing objects with shape, the images concurrently contained non-shape features, such as a noise-like mask. When trained on these modified set of images, the model did not show any bias towards selecting shapes as features. Instead it relied on whichever feature allowed it to perform the best prediction -- even when this feature was a noise-like mask or a single predictive pixel amongst 50176 pixels. We also found that regularisation methods, such as batch normalisation or Dropout, did not change this behaviour and neither did past or concurrent experience with images from other datasets. Object recognition in humans is largely a function of analyzing shape BID1 BID6 . A wealth of data from psychological experiments show that shape plays a privileged role in object recognition compared to other diagnostic features such as size, colour, luminance or texture. For example, BID2 showed that error rates and reaction times are virtually identical in a recognition task when full coloured photographs of objects are replaced by their line drawings even when colour was a diagnostic feature. This indicates that shape-based representations mediate recognition. Similarly, BID11 found that, for patients with an object recognition deficit (visual agnosia), surface colour played minimal role in aiding object recognition unless the shape of the object was ambiguous, indicating that shape is instrumental to recognition, whereas surface characteristics such as colour and texture play only a secondary role. More recently, BID0 have shown that participants extract shape information automatically from arrays of dot patterns within the first 100ms of stimulus onset, even for tasks where extracting this information may be detrimental to performance on a task. Experiments from developmental psychology show that this privileged status of shape starts early in life and becomes stronger with age. For example, BID10 found that 2-3-year-old children as well as adults weight shape more heavily than size or texture when generalising the name of a learnt object to novel instances. They also found that the weight placed on shape increases in strength and generality from early childhood to adulthood. Following BID10 , we will call this privileged status of shape in performing recognition a ""shape bias"".By contrast, it is unclear whether shape plays a privileged role in how convolutional neural networks (CNNs) categorise objects. It is often claimed that CNNs learn representations of objects that are similar to the representations that monkeys and humans use when identifying objects BID14 , and that CNNs largely rely on learning shape representations in order to categorise objects BID9 BID15 BID7 . On the other hand, there are a growing number of studies that show that CNNs often categorise images on the basis on nonshape attributes of images. This is demonstrated by the existence of adversarial images that are confidently classified as a familiar category despite the lack of any shape information in the input BID13 , adversarial images that contain the correct shape but altered colours that are confidently misclassified (e.g., categorizing an image of an airplane as a dog when only the colour of the plane has been manipulated), and large reductions in performance when trained coloured images are converted to greyscale BID3 or the colours are inverted BID5 . In addition , there are demonstrations that CNNs can easily learn to categorise random patterns of pixels that have no shape BID4 . All of these findings suggest that shape may not play a privileged role in CNN's object categorisation, or that the relevant role of shape and non-shape features depends on the specific model or training conditions.Here we systematically explore the impact of non-shape features in the categorisation performance of convolutional neural networks on CIFAR-10 images. We introduced non-shape features to images by adding informative noise-like masks to the training set. We tried several types of masks and an extreme version where the non-shape feature consisted of just a single pixel with a location correlated to the image category (see FIG0 and Appendix B). We show that CNNs often learn and depend on non-shape features that are highly diagnostic of object categories and often fails to learn anything about shape under these conditions. This highlights that CNNs simply picks up whatever statistical structure is most relevant to learning the training set, with shape playing no special role. Note that this does not imply that CNNs do not encode shape information under any circumstance, but that shape does not seem to be weighted more than other diagnostic features, even when these features are noise-like masks or the luminance of a single pixel. Importantly, this behaviour contrasts with humans, for whom shape plays a privileged role in performing recognition, even in the presence of much more salient diagnostic features such as size, colour or texture. If the models are to more closely capture human performance, these results suggest that additional machinery needs to be added to networks in order to prioritize the role of learning shape-based representations while performing the object categorisations. This might also reduce the model's susceptibility to being fooled by non-shape features of images, and being more robust to various forms of non-shape noise that currently reduce performance. The non-shape features used in the experiments above have all been completely invariant from one image to another within a category. It can be argued that these features are selected by the model over other shape-based features because they provide a very strong predictive signal and consequently suppress the selection of any shape-based features. It is possible that if these features contained larger variance, the model would be more likely to rely on shape-based features while performing categorisation. In a series of experiments where we increased the variability of the non-shape (noiselike) features, we noticed that this was generally not the case -the model still relied a lot more on these features than on any shape-based features to perform categorisation.The first type of variability we introduced was to sample the noise mask independently from a distribution for each training and test image within a category. In order to make these noise masks diagnostic of an image's category, a parameter of this distribution correlated with an image's category. For the salt-and-pepper noise, this meant that the probability, p, of changing a pixel to black or white was different for each category. Thus, the parameter, p, became diagnostic of the category. However, the masks now varied from image to image and were independently sampled with the (category-dependent) probability, p. Similarly, for the additive uniform noise, masks could vary from one image to other within a category but the mean of the distribution depended on each category (see Appendix A for details). For the single diagnostic pixel, the inserted pixel could vary in location from one image to the other, but was generated from a Gaussian distribution with a mean determined by the category of the image and a fixed standard deviation. Similarly the colour of the pixel was sampled from a Gaussian distribution with a mean determined by the category of the image and a fixed standard deviation. FIG1 ). Performance in the NoPix condition was somewhat better for ResNet, however the pattern of result remained the same -performance dropped substantially from the Same to NoPix condition. Similarly, introducing variability in the salt-and-pepper masks lead to only a minor change in behaviour of the model, with accuracy in 'Diff' condition dropping to chance, rather than 0%. The most intriguing change in behaviour occurred when variability was introduced to the additive uniform noise mask FIG4 ). While the VGG and ResNet networks differed quantitatively in these results, the pattern of results remained the same: when the noise mask was completely removed (NoPix condition) the model performed worse than when the images contained a noise mask from a different category (Diff condition). In other words, removing the mask makes the image less informative for the model, not only compared to images with the correct category-correlated (Same) mask, but also compared to images with the incorrect (Diff) maskthe model seems to rely on the presence of noise to make an inference.Next, we examined how the model changes it's behaviour when only a subset of images contain a diagnostic non-shape feature. We restricted this experiment to the case of a single diagnostic pixel. The location and colour of this pixel were fixed across all images of a category, but we introduced stochasticity in the presence of this pixel within a training image. FIG5 shows the change in accuracy for the 'NoPix' condition with an decrease in the probability with which a pixel is present in a training image. We specifically focus on the 'NoPix' condition as the accuracy on this condition is inversely correlated with how much the network relies on this pixel to predict the output category. It can be seen from this figure that accuracy increases smoothly, rising sharply at first and then slowing down as the probability of the pixel being present in a training image decreases. This smooth increase is consistent with the hypothesis that the learning algorithm selects the feature based on the predictive power of the feature; as the single pixel becomes less predictive, the network starts relying on other features to choose the output category. This smooth increase also indicates that the model is able to combine information from this diagnostic pixel with other features that it uses to predict the output category. For example, when the pixel is present in only 90% of the images, the model is able to correctly categorise an image containing no diagnostic pixel 70% of the time, indicating that it simultaneously represents both the diagnostic pixel as well as other features that it uses to perform categorisation.The figure also shows that a single pixel present in training images adversely affects the performance of the network even when it is present on only a fraction of the images. When the network is trained on images from the original CIFAR-10 dataset, it's accuracy is close to 90% (dotted black line); inserting a single pixel on 70% of the images meant that the performance decreased by more than 10%. This reduction in performance could be due to one of two reasons: (a) the network mistakes a pixel value in one of the original images as a predictive pixel and performs an incorrect classification based on this pixel, or (b) adding a mask to a subset of training images means that the network has to learn the correct classification function on a fraction of the original dataset. This decrease in the size of the dataset may be affecting its performance. Further testing will be needed to correctly establish which of these reasons is responsible for a reduction in performance. Lastly, we also observed that L2 regularisation made the performance of the network worse on the original images when a diagnostic pixel was inserted on a fraction of the images. While L2 regularisation should help the network learn a more general solution, in this case it lead to the opposite effect. In a series of simulations we found that the VGG network trained to categorise CIFAR-10 images that included noise-like masks diagnostic of the output categories often learned to categorise on the basis of these masks rather than the CIFAR images themselves. Indeed, the models often entirely relied on the masks, and performed at floor when the noise was removed from the images. Even though we specifically engineered our dataset to contain non-shape features, it is well-known that popular datasets such as CIFAR and ImageNet contain various biases due to conditions under which the images were captured as well as the different motivations for construction of the datasets (Torralba & Efros, 2011) . Our results suggest that CNNs may be relying too heavily on non-shape features when categorising images and therefore may be extremely susceptible to non-shape biases present within datasets. This, in turn, could be the source of various idiosyncratic behaviours such as being confounded by fooling images BID13 or being overly sensitive to colour BID5 , noise BID3 or even single pixels in images BID18 . This contrasts with human visual object recognition that is largely based on shape BID1 . It will be important to introduce shape biases to CNNs if they are to mirror human object recognition performance more closely. The introduction of shape biases may also prove useful in making CNNs more robust to various non-shape manipulations of images (e.g., changes in colour or the introduction of noise) that often impair performance. We used a method similar to BID3 to transform images from the CIFAR-10 dataset (https://www.cs.toronto.edu/˜kriz/cifar.html). All transformations were performed using the Pillow fork of the Python Imaging Library (https://pillow. readthedocs.io). Each 32x32 pixel image was rescaled to 224x224 pixels using the PIL.Image.LANCZOS method. For the salt-and-pepper and additive noise masks, each image was transformed from RGB to greyscale using PIL.Image.convert() method. For the extreme case of single pixel, the images were not colour transformed (we obtained qualitatively similar results if images were transformed to greyscale). When images were transformed to greyscale, their contrast was adjusted to 80% by scaling the value of each pixel using the formula: DISPLAYFORM0 × 128, where v was the original value of the pixel in the range [0, 255] .The salt-and-pepper mask was created by taking the transformed greyscale image and setting each pixel to either black or white with a probability p. When the mask was fixed for a category, all images had the exact same set of pixels that were turned either black or white and the p was set to 0.05. When the mask varied from image to image within a category, the pixels were sampled independently for each image and the probability p was fixed for each category but varied between categories in the range [0.03, 0.06].The additive uniform noise mask was created by taking the transformed greyscale image and adding a value sampled from the uniform distribution [−w, w] to this image, where 2w was the width of the uniform distribution and was set to 8. When the noise mask was fixed, this sampling was done only once per category and the same mask was added to each image. When the mask was variable, it was sampled independently for each image from a distribution [µ − w, µ + w], where µ was the mean that depended on the category and varied in the range [−50, 50] .The single pixel mask was created by choosing a random location, (x, y), (sampled from a uniform distribution on the interval [0, 224]) on the image and changing the colour of the pixel to a value c (sampled from a uniform distribution on the interval [0, 255] ). When the mask was fixed for each category, (x, y, c) remained constant for all images in a category, but varied between categories. In other words, the pixel was inserted at different locations and was of different colours for different categories, but all images within a category had the pixel at the same location and of same colour. When the mask was variable , each of x, y and c were sampled independently for each image from a Gaussian distribution with a constant variance and a mean that depended on the category of the image. If any value in a sampled set of (x, y, c) values fell out of their respective range, that value was re-sampled.All simulations reported in this study (except for the Conv Drop simulation in FIG2 were carried out using a pre-trained 16-layer VGG network BID17 provided by the torchvision package of Pytorch. This network had been pre-trained on the ImageNet dataset. We replaced the fully-connected layers of this pre-trained model with three fully-connected layers with Dropout after the first two layers. This model was then trained on the modified training set using the RMSProp gradient descent optimization algorithm (see BID16 with learning rate of 1e−5, a momentum of 0.9 and a cross-entropy loss function. We also experimented with Adam (Kingma & Ba , 2014) and results remained qualitatively same. For testing the effect of Dropout in the early layers, we constructed a six-layer convolutional neural network with three convolutional layers and three fully connected layers and dropout after every convolutional layer. The same learning rule and parameters were used as for the VGG network and we experimented with several model architectures with most architectures giving similar results. This network was able to achieve an accuracy of 70% on categorising the CIFAR-10 dataset. The input to both types of networks was a 3-channel RGB image. For greyscale images, all three channels were set to the same value. Figure 8 : Examples of images used for training and testing. The columns show the condition under which the image was used and the rows show the type of noise-like mask inserted. These noise masks are, respectively, (row 1) salt-and-pepper noise with a fixed mask, (row 2) salt-and-pepper noise with a variable mask, (row 3) additive uniform noise with fixed mask, (row 4) additive uniform noise with a variable mask, (row 5) single diagnostic pixel, fixed location and colour and (row 6) single diagnostic pixel with variable location and colour.",3572,1.711,1978,1.8058645096056622," were inspired human vision, some settings achieve a performance human object recognition This has lead the speculation both systems use similar mechanisms perform recognition In conducted simulations indicate there human vision CNNs while object recognition relies analysing shape such a shape-bias We teased apart the type features selected the model by modifying the CIFAR-10 dataset so, containing objects shape the images concurrently a noise-like mask When trained on these modified set images the model did selecting shapes as features Instead it relied whichever feature allowed the best prediction -- even this feature a noise-like mask a single predictive pixel amongst 50176 pixels We also found regularisation methods, batch normalisation Dropout this behaviour and neither past or concurrent experience images from Object recognition humans largely analyzing shape BID1 BID6 . A wealth psychological experiments show that shape plays object recognition compared other diagnostic features size colour luminance texture For example BID2 showed error rates and reaction times virtually a recognition task full coloured photographs objects replaced their line drawings even colour a diagnostic feature This indicates that shape-based representations mediate recognition Similarly BID11 found, patients an object recognition deficitvisual agnosia surface colour played minimal role aiding unless the shape ambiguous indicating that shape instrumental recognition surface characteristics More recently BID0 have shown participants extract shape information automatically arrays dot patterns within the first 100ms stimulus onset even for tasks extracting may detrimental on Experiments from developmental psychology this privileged status shape starts becomes stronger For example BID10 found as well adults weight shape more heavily size or texture when generalising the name a learnt object novel instances They also the weight placed shape increases strength generality from early childhood Following BID10 , call this privileged status shape in performing recognition a ""shape bias""By contrast it unclear plays how convolutional categorise It often CNNs learn representations objects similar monkeys identifying BID14 , largely learning shape representations categorise On studies CNNs often categorise images on on nonshape attributes images This demonstrated the existence adversarial images confidently classified a familiar category despite any shape information BID13 , adversarial images contain but altered colours that confidently misclassified ( categorizing an airplane a dog when manipulated large reductions performance trained coloured images converted or the colours inverted In addition , demonstrations that CNNs can easily learn categorise random patterns pixels that no shape BID4 All these findings shape may a privileged role CNN's object categorisation or the relevant role depends or training conditionsHere systematically explore on CIFAR-10 images We introduced non-shape features images by informative noise-like masks the training set We tried several types masks an extreme version where the non-shape feature consisted with a location correlated the image category FIG0 and Appendix B We show CNNs often learn and depend non-shape features highly diagnostic object categories often fails learn shape under This highlights CNNs simply picks whatever statistical structure learning the training set with shape playing Note does CNNs do encode shape information under that shape does seem weighted more other diagnostic features even noise-like masks the luminance Importantly this behaviour contrasts humans for shape plays performing recognition even much more salient diagnostic features size texture If the models to more capture human performance these results additional machinery needs networks prioritize the role learning shape-based representations while performing the object categorisations This might also reduce the model's susceptibility being fooled non-shape features images being more robust various forms that currently reduce performance The non-shape features used the experiments above all completely invariant from one image within a category It can these features selected the model over other shape-based features because a very strong predictive signal and consequently suppress It possible if these features contained larger variance rely shape-based features while performing categorisation In experiments where increased the variability non-shape (noiselike) features noticed this generally -the model still relied a these features to perform categorisationThe first type variability introduced to sample the noise mask independently a distribution for each training and test image within a category In order these noise masks diagnostic of an image's category a parameter this distribution correlated For meant the probability, p changing a pixel to black different each category Thus the parameter, p became diagnostic the category However the masks now varied image independently sampled the (category-dependent) probability, p. Similarly for the additive uniform noise masks could vary one image other within a category but the mean depended each category ( For the single diagnostic pixel the inserted pixel could vary location was generated determined the category Similarly the colour the pixel was sampled determined the category FIG1 ). Performance in the NoPix condition somewhat for ResNet however the pattern result remained the same -performance dropped substantially Same to Similarly introducing variability the salt-and-pepper masks lead only a minor change behaviour accuracy 'Diff' condition dropping chance, The most intriguing change behaviour occurred variability the additive uniform noise mask FIG4 While the VGG and ResNet networks differed quantitatively these results the pattern remained when the noise mask completelyNoPix condition the model performed the images contained from a different category (Diff condition In removing the mask makes less informative for the model not only compared images the correct category-correlated (Same) mask compared the incorrect (Diff) maskthe model seems rely the presence noise an inferenceNext examined changes it behaviour only a subset contain a diagnostic non-shape feature We restricted this experiment the case a single diagnostic pixel The location colour this pixel were fixed across of a category introduced the presence within a training image FIG5 shows the change accuracy the 'NoPix' condition an decrease with present a training image We specifically focus the 'NoPix' condition as the accuracy on this condition inversely how the network relies this pixel predict the output category It can seen this figure accuracy increases smoothly rising sharply first slowing the probability the pixel present in a training image This smooth increase consistent the hypothesis the learning algorithm selects the feature based; as the single pixel becomes predictive starts relying choose the output category This smooth increase also indicates the model able combine information this diagnostic pixel other features it the output category For example the pixel present only 90% the model able correctly categorise containing no diagnostic pixel 70% indicating simultaneously as other features it uses performThe figure present training images adversely even When the network trained images the original CIFAR-10 dataset's accuracy inserting on 70% meant the performance decreased This reduction performance could one the network mistakes a pixel value one as a predictive pixel and performs an incorrect classification based adding a subset training images means learn on a fraction This decrease the dataset may affecting its performance Further testing correctly establish these reasons a reduction performance Lastly also observed L2 regularisation made the performance the network on the original images when a diagnostic pixel inserted on a fraction While L2 regularisation should the network learn a more general solution in lead In simulations we the VGG network trained categorise CIFAR-10 images that included noise-like masks diagnostic the output categories often learned on rather images Indeed the models often entirely relied the masks performed at floor when removed Even specifically engineered our dataset contain non-shape features contain various biases due conditions under captured as the different motivations constructionTorralba Efros) Our results CNNs may relying non-shape features when categorising images therefore extremely susceptible present datasets This, various idiosyncratic behaviours being confounded fooling images BID13 or overly colour BID5 , noise even single pixels images This contrasts human visual object recognition largely shape BID1 . It will important introduce shape biases CNNs if mirror human object recognition performance more The introduction shape biases may prove making CNNs robust various non-shape manipulations of images changes colour the introduction noise often impair performance We used a method BID3 transform images All transformations were the Pillow fork the Python Imaging Library readthedocs.io). Each 32x32 pixel image was rescaled the PIL.Image.LANCZOS method For the salt-and-pepper and additive noise masks each image transformed RGB PIL.Image.convert() method For the extreme case single pixel, the images not colour transformedwe obtained if images transformed When images transformed their contrast adjusted 80% by scaling using DISPLAYFORM0 × 128 v was the range [ .The salt-and-pepper mask created taking setting either black with a probability p. When the mask fixed for a category all images had pixels that turned either black and the p was When the mask varied image within a category the pixels sampled independently the probability p fixed but varied [ 0.06].The additive uniform noise mask taking sampled−w w 2w was set 8 When the noise mask fixed this sampling only category the same mask added each image When the mask variable sampled independently for from a distribution [� − w µ + that depended the category varied−50 .The single pixel mask created choosing (x (sampled on the interval 224 on changing c 255] When the mask fixed for each category (x c remained all images varied In the pixel was inserted different locations of for different categories all images within a category of When the mask variable , each x c sampled independently from and that depended the category If any value a sampled set ( fell reAll simulations reported (except the Conv Drop simulation FIG2 were carried a pre-trained 16-layer VGG network BID17 provided the torchvision package Pytorch. This network had pretrained the ImageNet dataset We replaced the fully-connected layers this pre-trained model with Dropout after This model then trained modified training the RMSProp gradient descent optimization BID16 with learning rate 1e−5 a momentum of and. We also experimented Adam (Kingma & Ba , 2014 results remained qualitatively same For testing the effect Dropout in the early layers constructed dropout after The same learning rule and parameters were as the VGG network we experimented model architectures with most architectures giving This network able achieve an accuracy categorising the CIFAR-10 dataset The input to both types networks a 3-channel RGB image For greyscale images all three channels set Figure : Examples images training The columns show the condition under the image used the rows noise-like mask inserted These noise masks, respectively (row 1) salt-and-pepper noise with a fixed mask single diagnostic pixel, fixed location colour and variable location",0.02,0.7573511376773767
"The development of high-dimensional generative models has recently gained a great surge of interest with the introduction of variational auto-encoders and generative adversarial neural networks. Different variants have been proposed where the underlying latent space is structured, for example, based on attributes describing the data to generate. We focus on a particular problem where one aims at generating samples corresponding to a number of objects under various views. We assume that the distribution of the data is driven by two independent latent factors: the content, which represents the intrinsic features of an object, and the view, which stands for the settings of a particular observation of that object. Therefore, we propose a generative model and a conditional variant built on such a disentangled latent space. This approach allows us to generate realistic samples corresponding to various objects in a high variety of views. Unlike many multi-view approaches, our model doesn't need any supervision on the views but only on the content. Compared to other conditional generation approaches that are mostly based on binary or categorical attributes, we make no such assumption about the factors of variations. Our model can be used on problems with a huge, potentially infinite, number of categories. We experiment it on four images datasets on which we demonstrate the effectiveness of the model and its ability to generalize. Multi-view learning aims at developing models that are trained over datasets composed of multiple views over different objects. The problem of handling multi-view inputs has mainly been studied from the predictive point of view where one wants, for example, to learn a model able to predict/classify over multiple views of the same object BID25 ; BID23 ). For example, using deep learning approaches, different strategies have been explored to aggregate multiple views but a common general idea is based on the (early or late) fusion of the different views at a particular level of a deep architecture. Few other studies have proposed to predict missing views from one or multiple remaining views as in Arsalan BID0 .Recent research has focused on identifying factors of variations from multiview datasets. The underlying idea is to consider that a particular data sample may be thought as the mix of a content information (e.g. related to its class label like a given person in a face dataset) and of a side information, the view, which accounts for factors of variability (e.g. exposure, viewpoint, with/wo glasses...). All samples of a given class share the same content information while they differ on the view information. A number of approaches have been proposed to disentangle the content from the view, also referred as the style in some papers BID19 ; BID4 ). For instance, different models have been built to extract from a single photo of any object both the characteristics of the object but also the camera position. Once such a disentanglement is learned, one may build various applications like predicting how an object looks like under different viewpoints BID19 ; BID28 ). In the generative domain, models with a disentangled latent space BID18 ; BID5 ) have been recently proposed with applications to image editing, where one wants to modify an input sample by preserving its content while changing its view BID13 ; BID10 ) (see Section 6).Yet most existing controlled generative approaches have two strong limitations: (i) they usually consider discrete views that are characterized by a domain or a set of discrete (binary/categorical) attributes (e.g. face with/wo glasses, the color of the hair, etc.) and could not easily scale to a large number of attributes or to continuous views. (ii) most models are trained using view supervision (e.g. the view attributes), which of course greatly helps learning such model, yet prevents their use on many datasets where this information is not available. Recently, some attempts have been made to learn such models without any supervision ; BID7 ), but they cannot disentangle high level concepts as only simple features can be reliably captured without any guidance.In this paper, we are interested in learning generative models that build and make use of a disentangled latent space where the content and the view are encoded separately. We propose to take an original approach by learning such models from multi-view datasets, where (i) samples are labeled based on their content, and without any view information, and (ii) where the generated views are not restricted to be one view in a subset of possible views. Following with our same example above, it means first, learning from a face dataset including multiple photos of multiple persons taken in various conditions related to exposure, viewpoint etc. and second, being able to generate an infinity of views of an imaginary person (or the same views of an infinity of imaginary persons) -see FIG0 . This contrast with most current approaches that use information about the style, and cannot generate multiple possible outputs.More precisely, we propose two models to tackle this particularly difficult setting: a generative model (GMV -Generative Multi-view Model) that generates objects under various views (multiview generation), and a conditional extension (C-GMV) of this model that generates a large number of views of any input object (conditional multi-view generation). These two models are based on the adversarial training schema of Generative Adversarial Networks (GAN) proposed in BID6 ). The simple but strong idea is to focus on distributions over pairs of examples (e.g. images representing a same object in different views) rather than distribution on single examples as we will explain later.Our contributions are the following: (i) We propose a new generative model able to generate data with various content and high view diversity using a supervision on the content information only.(ii) We extend the model to a conditional model that allows generating new views over any input sample. (iii) We report experimental results on four different images datasets that show the ability of our models to generate realistic samples and to capture (and generate with) the diversity of views.The paper is organized as follows. We first remind useful background on GANs and their conditional variant (Section 2). Then we successively detail our proposal for a generative multiview model (Section 3.2) and for its conditional extension (Section 4). Finally, we report experimental results on the various generative tasks allowed by our models in Section 5.2. We have proposed a generative model operating on a disentangled latent space which may be learned from multiview data without any view supervision, allowing its application to many multiview dataset. Our model allows generating realistic data with a rich view diversity. We also proposed a conditional version of this model which allows generating new views of an input image which may again be learned without view supervision. Our experimental results show the quality of the produced outputs, and the ability of the model to capture content and view factors. They also illustrate the ability of GMV and CGMV to capture the diversity over the CelebA dataset, and to generate more realistic samples than baseline models. In a near future, we plan to investigate the use of such an approach for data augmentation. Indeed, when only a few training data are available, one elegant solution for learning a model could be to generate new views of the existing data in order to increase the size of the training set. This solution will be explored in both semi-supervised and one-shot/few-shot learning settings. APPENDIX Figure 9 : Additional results on GMV: All images in a row have been generated with the same content vector, and all images in a column have been generated with the same view vector TAB7 : Distribution of the different attributes over generated samples. For example, 3.8 % of the samples generated by the GMV model exhibit the ""Eyeglasses"" attribute. 23",1551,0.752,913,1.6987951807228916,"The development high-dimensional generative models recently a great surge variational auto-encoders Different variants where the underlying latent space structured for based attributes describing to generate. We focus where one aims generating samples corresponding objects under various views We assume the distribution driven two independent latent factors the content, represents the intrinsic features the view stands the settings a particular observation of Therefore and a conditional variant built such a disentangled latent space This approach generate realistic samples corresponding various objects a high variety views Unlike many multi-view approaches our model does need any supervision on but Compared other conditional generation approaches mostly binary or categorical attributes make the factors variations Our model can problems a huge, potentially infinite, number categories We experiment it four images datasets on demonstrate the effectiveness Multi-view learning aims developing models trained over datasets composed over different objects The problem handling multi-view inputs mainly studied from the predictive point where wants, learn able/ over BID25 ; BID23 For example using deep learning approaches different strategies have explored aggregate multiple views but a common general idea based the (early or late) fusion at a deep architecture Few other studies proposed to predict missing views one or multiple remaining views as in Arsalan BID0 .Recent identifying factors variations from multiview datasets The underlying idea consider that a particular data sample thought as the mix a content information related its class label like a given person in a face dataset of a side information the view accounts factors variability viewpoint with/wo glasses... All samples a given class share while they differ on the view information A number approaches the content the view also as the style in some papers BID19 ; For instance different models built extract from any object both the characteristics but Once such a disentanglement learned one build various applications like predicting an object looks under different viewpoints BID19 ; BID28 In the generative domain models a disentangled latent space BID18 ; ) recently with applications image editing where one wants modify an input sample preserving while changing its view BID13 ( Section 6).Yet most existing controlled generative approaches two strong limitations usually consider discrete views characterized a domain or (binary/categorical attributes face with/wo glasses the color could easily scale attributes continuous views (ii most models trained using view supervision the view attributes of greatly helps learning such model yet prevents their use many datasets where this information Recently some attempts learn such models without any supervision ; BID7 ), high level concepts as only simple features reliably captured withoutIn build and make a disentangled latent space where the content the view encoded separately We propose take by learning such models multi-view datasets (i) samples labeled based without any view information where the generated views restricted be one view in Following with our same example it means first learning a face dataset including multiple photos multiple persons taken various conditions related exposure viewpoint etc and second being generate an infinity views an imaginary person the same views -see FIG0 This contrast most current approaches that information the style and cannot generate multiple possible outputsMore precisely two models tackle this particularly difficult setting generativeGMV -Generative Multi-view Model objects under various viewsmultiview generation conditional extension of any input object These two models based the adversarial training schema proposed BID6 ). The simple but strong idea focus distributions over pairs examples representing a same object distribution on as explainOur contributions the ( propose able generate data various content high view diversity using a supervision on the content information only.(ii extend a conditional model generating new views any input sample (iii We report experimental results four different images datasets our models realistic samples capture ( generate with the diversity viewsThe paper organized We first remind useful background GANs their conditional variantSection Then successively detail our proposal a generative multiview modelSection for its conditional extension Finally report experimental results the various generative tasks allowed our models Section proposed operating a disentangled latent space which may learned multiview data without any view supervision allowing its application Our model allows generating realistic data a rich view diversity We also proposed a conditional version this model allows generating new views an input image which again learned without view supervision Our experimental results the quality the produced outputs content view factors They also illustrate the ability GMV capture the diversity over the CelebA dataset generate more realistic samples baseline models In a near future plan investigate such an approach data augmentation Indeed when only a few training data are elegant learning a model could generate new views increase This solution explored both semisupervised and one-shot/few-shot learning settings APPENDIX Figure : Additional results GMV: All images a row have generated the same content vector TAB7 : Distribution the different attributes over generated samples For example 3.8 % the samples generated the GMV model exhibit 23",0.01,0.48454789469245585
"The huge size of deep networks hinders their use in small computing devices. In this paper, we consider compressing the network by weight quantization. We extend a recently proposed loss-aware weight binarization scheme to ternarization, with possibly different scaling parameters for the positive and negative weights, and m-bit (where m > 2) quantization. Experiments on feedforward and recurrent neural networks show that the proposed scheme outperforms state-of-the-art weight quantization algorithms, and is as accurate (or even more accurate) than the full-precision network. The last decade has witnessed huge success of deep neural networks in various domains. Examples include computer vision, speech recognition, and natural language processing BID16 . However, their huge size often hinders deployment to small computing devices such as cell phones and the internet of things. Many attempts have been recently made to reduce the model size. One common approach is to prune a trained dense network BID5 BID29 . However, most of the pruned weights may come from the fully-connected layers where computations are cheap, and the resultant time reduction is insignificant. BID21 and Molchanov et al. (2017) proposed to prune filters in the convolutional neural networks based on their magnitudes or significance to the loss. However, the pruned network has to be retrained, which is again expensive.Another direction is to use more compact models. GoogleNet (Szegedy et al., 2015) and ResNet BID7 replace the fully-connected layers with simpler global average pooling. However, they are also deeper. SqueezeNet BID11 reduces the model size by replacing most of the 3 × 3 filters with 1 × 1 filters. This is less efficient on smaller networks because the dense 1 × 1 convolutions are costly. MobileNet BID10 compresses the model using separable depth-wise convolution. ShuffleNet (Zhang et al., 2017) utilizes pointwise group convolution and channel shuffle to reduce the computation cost while maintaining accuracy. However, highly optimized group convolution and depth-wise convolution implementations are required. Alternatively, Novikov et al. (2015) compressed the model by using a compact multilinear format to represent the dense weight matrix. The CP and Tucker decompositions have also been used on the kernel tensor in CNNs BID15 BID13 . However, they often need expensive fine-tuning.Another effective approach to compress the network and accelerate training is by quantizing each full-precision weight to a small number of bits. This can be further divided to two sub-categories, depending on whether pre-trained models are used BID22 BID24 or the quantized model is trained from scratch BID1 BID20 . Some of these also directly learn with low-precision weights, but they usually suffer from severe accuracy deterioration BID20 BID26 . By keeping the full-precision weights during learning, BID1 pioneered the BinaryConnect algorithm, which uses only one bit for each weight while still achieving state-of-the-art classification results. Rastegari et al. (2016) further incorporated weight scaling, and obtained better results. Instead of simply finding the closest binary approximation of the full-precision weights, a loss-aware scheme is proposed in . Beyond binarization, TernaryConnect BID23 quantizes each weight to {−1, 0, 1}. BID19 and added scaling to the ternarized weights, and DoReFa-Net (Zhou et al., 2016) further extended quantization to more than three levels. However, these methods do not consider the effect of quantization on the loss, and rely on heuristics in their procedures (Zhou et al., 2016; . Recently, a loss-aware low-bit quantized neural network is proposed in BID18 . However, it uses full-precision weights in the forward pass and the extra-gradient method (Vasilyev et al., 2010) for update, both of which are expensive.In this paper, we propose an efficient and disciplined ternarization scheme for network compression. Inspired by , we explicitly consider the effect of ternarization on the loss. This is formulated as an optimization problem which is then solved efficiently by the proximal Newton algorithm. When the loss surface's curvature is ignored, the proposed method reduces to that of BID19 , and is also related to the projection step of BID18 . Next, we extend it to (i) allow the use of different scaling parameters for the positive and negative weights; and (ii) the use of m bits (where m > 2) for weight quantization. Experiments on both feedforward and recurrent neural networks show that the proposed quantization scheme outperforms state-of-the-art algorithms.Notations: For a vector x, √ x denotes the element-wise square root (i.e., [ DISPLAYFORM0 p is its p-norm, and Diag(x) returns a diagonal matrix with x on the diagonal. For two vectors x and y, x y denotes the element-wise multiplication and x y the element-wise division. Given a threshold ∆, I ∆ (x) returns a vector such DISPLAYFORM1 In this paper, we proposed a loss-aware weight quantization algorithm that directly considers the effect of quantization on the loss. The problem is solved using the proximal Newton algorithm. Each iteration consists of a preconditioned gradient descent step and a quantization step that projects fullprecision weights onto a set of quantized values. For ternarization, an exact solution and an efficient approximate solution are provided. The procedure is also extended to the use of different scaling parameters for the positive and negative weights, and to m-bit (where m > 2) quantization. Experiments on both feedforward and recurrent networks show that the proposed quantization scheme outperforms the current state-of-the-art.",1182,0.746,739,1.5994587280108254,"The huge size deep networks hinders small computing devices In consider compressing the network by weight quantization We extend a recently proposed loss-aware weight binarization scheme ternarization possibly different scaling parameters m-bit (where m > 2) quantization Experiments feedforward and recurrent neural networks the proposed scheme state weight quantization as (or The last decade huge success of deep neural networks Examples include computer vision natural language processing BID16 . However their huge size often deployment to small computing devices Many attempts recently reduce the model size One common approach prune a trained dense network BID5 BID29 . However most the pruned weights may come the fully-connected layers where computations cheap the resultant time reduction insignificant BID21 and Molchanov et (2017 proposed prune filters based their magnitudes or significance to the loss. However the pruned network to retrained again expensiveAnother direction more compact models GoogleNet (Szegedy et ResNet BID7 replace the fully-connected layers simpler global average pooling However they deeper SqueezeNet BID11 reduces the model size replacing most the 3 × 3 filters This less efficient on smaller networks the dense 1 × 1 convolutions costly MobileNet BID10 compresses the model using separable depth-wise convolution ShuffleNet (Zhang et utilizes pointwise group convolution channel shuffle reduce while accuracy However highly optimized group convolution and depth-wise convolution implementations required Alternatively, Novikov (2015 compressed the model by represent the dense weight matrix The CP and Tucker decompositions also on the kernel tensor in CNNs BID15 BID13 . However they often need expensive fine-tuningAnother effective approach compress the network and accelerate training quantizing each full-precision weight This can further divided to depending pre-trained models BID22 BID24 the quantized model trained from . Some also directly learn with low-precision weights usually suffer severe accuracy deterioration BID20 BID26 . By keeping the full-precision weights during learning BID1 pioneered the BinaryConnect algorithm while achieving state classification results Rastegari et al (2016 further incorporated weight scaling obtained better results Instead simply finding the closest binary approximation the full-precision weights a loss-aware scheme in . Beyond binarization TernaryConnect BID23 quantizes each weight to { BID19 and added scaling the ternarized weights DoReFa-Net (Zhou further extended quantization more than three levels However these methods consider quantization the loss, rely in their procedures (Zhou 2016 . Recently a loss-aware low-bit quantized neural network is BID18 . However uses full-precision weights the forward pass the extra-gradient methodVasilyev update both expensiveIn an efficient and disciplined ternarization scheme network compression Inspired , explicitly consider the effect ternarization the loss. This formulated an optimization problem which then efficiently the proximal Newton algorithm When the loss surface's curvature ignored the proposed method reduces to that BID19 , also related the projection step Next extend it (i allow different scaling parameters m bitswhere > weight quantization Experiments both feedforward and recurrent neural networks the proposed quantization scheme state algorithmsNotations: For vector x � denotes the element-wise square root ( [ DISPLAYFORM0 p is its p-norm Diag(x returns on. For two vectors x x y denotes x Given a threshold ��, I � returns such DISPLAYFORM1 In this paper proposed a loss-aware weight quantization algorithm directly considers quantization The problem solved using the proximal Newton algorithm Each iteration consists a preconditioned gradient descent step projects fullprecision weights For ternarization an exact solution and an efficient approximate solution provided The procedure also extended different scaling parameters m-bit (where m > 2) quantization Experiments both feedforward and recurrent networks the proposed quantization scheme",0.01,0.2314473407874183
"In the pursuit of increasingly intelligent learning systems, abstraction plays a vital role in enabling sophisticated decisions to be made in complex environments. The options framework provides formalism for such abstraction over sequences of decisions.   However most models require that options be given a priori, presumably specified by hand, which is neither efficient, nor scalable. Indeed, it is preferable to learn options directly from interaction with the environment. Despite several efforts, this remains a difficult problem: many approaches require access to a model of the environmental dynamics, and inferred options are often not interpretable, which limits our ability to explain the system behavior for verification or debugging purposes.   In this work we develop a novel policy gradient method for the automatic learning of policies with options.   This algorithm uses inference methods to simultaneously improve all of the options available to an agent, and thus can be employed in an off-policy manner, without observing option labels. Experimental results show that the options learned can be interpreted. Further, we find that the method presented here is more sample efficient than existing methods, leading to faster and more stable learning of policies with options. Recent developments in reinforcement learning (RL) methods have enabled agents to solve problems in increasingly complicated domains BID14 . However, in order for agents to solve more difficult and realistic environments-potentially involving long sequences of decisions-more sample efficient techniques are needed. One way to improve on existing agents is to leverage abstraction. By reasoning at various levels of abstraction, it is possible to infer, learn and plan much more efficiently. Recent developments have lead to breakthroughs in terms of learning rich representations for perceptual information BID2 . In RL domains, however, while efficient methods exist to plan and learn when abstraction over sequences of actions is provided a priori, it has proven more difficult to learn this type of temporal abstraction from interaction data.Many frameworks for formalizing temporal abstraction have been proposed; most recent developments build on the Options framework BID21 BID16 , which offers a flexible parameterization, potentially amenable to learning. The majority of prior work on learning options has centered around the idea of discovering subgoals in state space, and constructing a set of options such that each option represents a policy leading to that subgoal BID11 BID12 BID20 ). These methods can lead to useful abstraction, however, they often require access to a model of the environment dynamics, which is not always available, and can be infeasible to learn. Our contributions instead build on the work of BID1 , and exploits a careful parameterization of the policy of the agent, in order to simultaneously learn a set of options, while directly optimizing returns. We relax a few key assumptions of this previous work, including the expectation that only options that were actually executed during training can be learned, and the focus on executing options in an on-policy manner, with option labels available. By relaxing these, we can improve sample efficiency and practical applicability, including the possibility to seed control policies from expert demonstrations. In this paper, we have introduced a new algorithm for learning hierarchical policies within the options framework, called inferred option policy gradients. This algorithm treats options as latent variables. Gradients are propagated through a differentiable inference step that allows end-to-end learning of option policies, as well as option selection and termination probabilities.In our algorithms policies take responsibility for state-actions pairs they could have generated. In contrast, in learning algorithms for hierarchical policies that use an augmented state space, option policies are updated using only those state-action pairs the actually generated. As a result, in our algorithm options do not tend to become 'responsible' for unlikely states or actions they generated. Thus, options are stimulated more strongly to specialize in a part of the state space. We conjecture that this specialization caused the discussed increase in the interpretability of options.(a ) Performance in the Walker2d environment as a function of available options. We see that in this environment, having several options available to the agent leads to an improved policy.(b) In the Walker2d environment, initially option selection is uniform. After training only 3 options tend to be selected, even when more are available. Selection frequencies are averaged over 100 sampled states.(c) As the options improve during training, the probability of remaining in the active option increases, plateauing at around 0.85. This suggests that the options learned here exhibit temporal extension. Furthermore, in our experiments learning with inferred options was significantly faster than learning with an option-augmented state space. In fact, learning with inferred options proved equally fast, or sometimes even faster, than using a comparable non-hierarchical policy gradient method despite IOPG having many more parameters. We conjecture that option inference encourages intra-option learning, thus allowing multiple options to improve as the result of a single learning experience, causing this speed-up.In future work, we want to quantify the suitability of the learned options for transfer between tasks. Our experiments so far were in the episodic setting. We want to investigate an on-line, actor-critic version of learning with inferred options to learn continuously in infinite-horizon problems.",1015,0.602,590,1.7203389830508475,"In the pursuit increasingly intelligent learning systems abstraction plays enabling sophisticated decisions The options framework formalism such abstraction over sequences decisions However most models require options given presumably specified hand neither efficient scalable Indeed preferable learn options directly interaction Despite several efforts this remains: many approaches require access a model the environmental dynamics inferred options interpretable explain the system behavior for verification debugging In this work develop a novel policy gradient method the automatic learning policies options This algorithm inference methods simultaneously improve all thus can employed an off-policy manner observing option labels Experimental results the options learned can interpreted. Further the method presented sample efficient leading policies with options Recent developments reinforcement learning enabled agents solve increasingly complicated domains BID14 . However agents solve more difficult and realistic environments-potentially long sequences decisionsmore sample efficient techniques One way improve existing agents to leverage abstraction By reasoning at infer, learn plan much Recent developments lead breakthroughs terms learning rich representations perceptual information BID2 . In RL domains however while efficient methods plan learn when abstraction over sequences actions provided a more learn this type temporal abstraction interaction dataMany frameworks for; most recent developments build the Options framework BID21 BID16, potentially amenable learning. The majority prior work learning options discovering subgoals state space constructing options such a policy leading BID11 BID12 ). These methods lead useful abstraction however access the environment dynamics learn Our contributions instead build BID1 , exploits a careful parameterization the policy the agent simultaneously learn options while directly optimizing returns We relax a few key assumptions of this previous work only options actually executed training learned executing onpolicy option labels available By relaxing these, sample efficiency practical applicability including seed control policies from expert demonstrations In have learning hierarchical policies within the options framework inferred option policy gradients This algorithm treats options latent variables Gradients propagated a differentiable inference step end learning option policies option termination probabilitiesIn our algorithms policies take responsibility stateactions pairs they could generated In contrast learning algorithms hierarchical policies that an augmented state space option policies updated using only those state-action pairs the actually generated As in our algorithm options do tend become 'responsible unlikely states actions they generated Thus options stimulated more to specialize a part the state space We conjecture this specialization caused the discussed increase the interpretability options.(a ) Performance the Walker2d environment as available options We see this environment having several options the agent leads policy.(b the Walker2d environment initially option selection uniform After training only 3 options tend selected even more Selection frequencies averaged over 100 sampled states.(c As the options improve during training remaining the active option increases plateauing This suggests the options learned here exhibit temporal extension Furthermore our experiments learning with inferred options an option-augmented state space In fact learning with inferred options proved equally fast or sometimes a comparable non-hierarchical policy gradient method despite IOPG having We conjecture option inference encourages intra-option learning thus multiple options improve as causing this speed-upIn quantify the learned options transfer tasks Our experiments so in the episodic setting We want investigate an on, actorcritic version learning with inferred options continuously infinite-horizon problems",0.01,0.5394396102063113
"The paper, interested in unsupervised feature selection, aims to retain the features best accounting for the local patterns in the data. The proposed approach, called Locally Linear Unsupervised Feature Selection, relies on a dimensionality reduction method to characterize such patterns; each feature is thereafter assessed according to its compliance w.r.t. the local patterns, taking inspiration from Locally Linear Embedding (Roweis and Saul, 2000). The experimental validation of the approach on the scikit-feature benchmark suite demonstrates its effectiveness compared to the state of the art. Machine Learning faces statistical and computational challenges due to the increasing dimension of modern datasets. Dimensionality reduction aims at addressing such challenges through embedding the data in a lower dimensionality space, in an unsupervised BID17 BID28 BID34 BID41 or supervised BID9 BID8 BID25 way.The requirement for understandable Machine Learning BID36 BID5 however makes it desirable to achieve interpretable dimensionality reduction. In order to do so, the simplest way is to select a subset of the initial features, i.e. to achieve feature selection (FS), as opposed to generating compound new features from the initial ones, a.k.a. feature construction. For instance, determining the genes most important w.r.t. a given disease or the underlying generative model of the data can be viewed as the mother goal in bioinformatics BID13 BID23 .In the supervised ML setting, features are assessed and selected based on their relevance to the prediction goal BID11 BID31 BID3 . Unsupervised learning, aimed at making sense of the data, however constitutes a primary and most important task of ML, as emphasized by BID20 , while supervised ML intervenes at a later stage of the data exploitation process.Unsupervised FS approaches BID14 BID47 BID2 BID22 BID48 ) (more in section 2) essentially rely on the assumption that the data samples are structured in clusters, and use the cluster partition in lieu of labels, making it possible to fall down on supervised FS, and select the features most amenable to characterize and separate the clusters. A main limitation of this methodology is that clusters are bound to rely on some metric defined from the initial features (with the notable exception of BID22 ), although this metric can be arbitrarily corrupted based on irrelevant or random features. On the other hand , as far as one considers the unsupervised setting, a feature can hardly be considered irrelevant per se.The main contribution of the paper is to address both limitations: the proposed approach, called Locally Linear Unsupervised Feature Selection (LLUFS) jointly determines patterns in the data, and features relevant to characterize these patterns. LLUFS is a 2-step process (Sec. 3): In a first step, a compressed representation of the data is built using Auto-Encoders BID37 BID7 . In a second step, viewing the initial dataset as a high-dimensional embedding of the compressed dataset, each feature is scored according to its contribution to the reconstruction error of the embedding, taking inspiration from Locally Linear Embedding BID28 BID29 BID40 .After describing the goals of experiments and the experimental setting used to validate the approach, extensively relying on the scikit-feature project BID21 SKf, 2018) (Sec. 4) , the empirical validation is presented and discussed (Sec. 5), establishing the merits and discussing the weaknesses of the approach. The paper concludes with a discussion and some perspectives for further research. One weakness of the method is that the distorsion scores depend on the latent representation produced by the auto-encoder, which might be biased due to the redundancy of the initial features; typically, duplicating an initial feature will entail that the latent representation is more able to express this feature, mechanically reducing its distorsion score. For this reason, a preliminary step is to detect and reduce the redundancy of the initial features.In order to do so, LLUFS i) normalizes the initial features (with zero mean and unit variance); ii) uses Agglomerative Hierarchical feature clustering BID18 BID35 , using a high number of clusters n c (n c = 3 4 D in the experiments); iii) selects one feature per cluster (the nearest one to the cluster mean); iv) apply the auto-encoder on the pruned data.Further work is concerned with taking into account the feature redundancy within the AE loss.A second limitation is due to the sensitivity of the distorsion score to the feature distribution. Typically, while a constant feature carries no information, its distorsion is null. Likewise, the distorsion of discrete features depends on their being balanced. In order to alleviate this issue, the reliability of the distorsion associated to each feature is measured through an empirical p-value BID33 . Given a p-value threshold τ , 1/τ copies of each feature are generated and independently shuffled. The feature distorsion is deemed relevant iff it is lower than the distorsion of all shuffled copies. A novel approach to unsupervised feature selection has been proposed in this paper, with a proof of concept of its empirical merits. The core idea is to find an ""oracle"" representation of the data, and to consider the actual data as an inflated and corrupted image of the oracle data. The quality of each feature is thereafter assessed depending on how it contributes to the loss of information between the ""oracle"" and the actual data.A first perspective for further research, taking inspiration from NDFS, is to allow a feature to be partially relevant, e.g. through considering the quantiles of its distorsion. A second perspective is to integrate the feature redundancy in the auto-encoder loss, to decrease the bias in favor of redundant features. The approach will also be extended to supervised feature selection.",1168,0.514,709,1.6473906911142455,"The paper interested unsupervised feature selection aims retain best accounting the local patterns The proposed approach Locally Linear Unsupervised Feature Selection relies a dimensionality reduction method characterize such patterns; each feature thereafter assessed according its compliance w.r.t the local patterns taking inspirationRoweis Saul The experimental validation the approach on the scikit-feature benchmark suite demonstrates its effectiveness compared the state Machine Learning faces statistical and computational challenges due the increasing dimension modern datasets Dimensionality reduction aims addressing such challenges embedding a lower dimensionality space an unsupervised BID17 BID28 BID34 BID41 or supervisedThe requirement understandable Machine Learning BID36 BID5 however makes desirable achieve In order do the simplest way select the initial features achieve feature selectionFS generating compound new features For instance determining the genes most important w.r.t a given disease the underlying generative model the data can viewed the mother goal BID13 BID23 .In the supervised ML setting features assessed selected the prediction goal Unsupervised learning aimed sense however constitutes a primary and most important task ML emphasized BID20 , while supervised ML intervenes at the data exploitation processUnsupervised FS approaches ) (more in section 2 essentially rely structured clusters use the cluster partition in lieu labels making fall down supervised FS, select the features most amenable characterize separate A main limitation clusters bound rely some metric defined from the initial featureswith BID22 although arbitrarily corrupted based irrelevant or random features On , as one considers the unsupervised setting a feature can hardly irrelevant perThe main contribution address both limitations: called Locally Linear Unsupervised Feature Selection jointly determines patterns features relevant characterize LLUFS is (Sec 3): In a first step a compressed representation built Auto-Encoders BID37 BID7 . In a second step viewing the initial dataset the compressed dataset each feature scored the reconstruction error taking inspiration Locally Linear BID28 BID29 BID40 .After describing the goals experiments used validate extensively relying the scikit-feature project BID21 SKf, 2018) (Sec 4 , the empirical validation is presented and (Sec 5), establishing the merits discussing The paper concludes and some perspectives for One weakness the method the distorsion scores depend the latent representation produced the auto-encoder might biased the redundancy the initial features; typically duplicating entail able express mechanically reducing For a preliminary step detect reduce the redundancy the initial featuresIn LLUFS i) normalizeswith zero mean and unit variance uses Agglomerative Hierarchical feature BID18 BID35 , a high number clusters n c (n c = 3 4 D in the experiments selects one featurethe nearest the cluster mean apply the auto-encoder on the pruned dataFurther work concerned taking the feature redundancy within the AE lossA second limitation due the distorsion score Typically while a constant feature carries no information its distorsion null Likewise the distorsion discrete features depends being balanced In order alleviate the reliability the distorsion associated to each feature an empirical p-value BID33 Given a p-value threshold τ 1/τ copies each feature independently The feature distorsion deemed relevant iff lower all shuffled copies A novel approach unsupervised feature selection a proof its empirical merits The core idea find an ""oracle"" representation consider an inflated and corrupted image The quality each feature thereafter depending contributes the loss information between the ""oracleA first perspective for further research, taking inspiration NDFS allow a feature partially relevant through considering the quantiles its distorsion A second perspective integrate the feature redundancy the auto-encoder loss, to decrease the bias favor redundant features The approach will extended supervised feature selection",0.01,0.35357377151870056
"Humans can understand and produce new utterances effortlessly, thanks to their systematic compositional skills. Once a person learns the meaning of a new verb ""dax,"" he or she can immediately understand the meaning of ""dax twice"" or ""sing and dax."" In this paper, we introduce the SCAN domain, consisting of a set of simple compositional navigation commands paired with the corresponding action sequences. We then test the zero-shot generalization capabilities of a variety of recurrent neural networks (RNNs) trained on SCAN with sequence-to-sequence methods. We find that RNNs can generalize well when the differences between training and test commands are small, so that they can apply ""mix-and-match"" strategies to solve the task. However, when generalization requires systematic compositional skills (as in the ""dax"" example above), RNNs fail spectacularly. We conclude with a proof-of-concept experiment in neural machine translation, supporting the conjecture that lack of systematicity is an important factor explaining why neural networks need very large training sets. Human language and thought are characterized by systematic compositionality, the algebraic capacity to understand and produce a potentially infinite number of novel combinations from known components. For example, if a person knows the meaning and usage of words such as ""twice,"" ""and,"" and ""again,"" once she learns a new verb such as ""to dax"" she can immediately understand or produce instructions such as ""dax twice and then dax again."" This type of compositionality is central to the human ability to make strong generalizations from very limited data. In a set of influential and controversial papers, Jerry Fodor and other researchers have argued that neural networks are not plausible models of the mind because they are associative devices that cannot capture systematic compositionality BID11 BID22 BID10 BID23 Calvo & Symons, 2014, a.o.) .In the last few years, neural network research has made astounding progress in practical domains where success crucially depends on the generalization capabilities of a system. Perhaps most strikingly, end-to-end recurrent neural networks currently dominate the state-of-the-art in machine translation BID2 BID30 . 1 Since the overwhelming majority of sentences or even word sequences in a language only occur once, even in a large corpus BID1 , this points to strong generalization abilities. Still, it is commonly observed that neural networks are extremely sample inefficient, requiring very large training sets, which suggests they may lack the same algebraic compositionality that humans exploit, and they might only be sensitive to broad patterns over lots of accumulated statistics BID21 .In this paper, we introduce a grounded navigation environment where the learner must translate commands given in a limited form of natural language into a sequence of actions. This problem is naturally framed as a sequence-to-sequence task, and, due to its simplicity, it is ideal to study the systematic generalization capabilities of computational systems to novel examples in a controlled setup. We thus use it to test a wide range of modern recurrent network architectures in terms of their compositional skills. Our results suggest that, although standard architectures such as LSTMs with attention BID0 do generalize when novel examples feature a mixture of constructions that have been observed in training, the models are catastrophically affected by systematic differences between training and test sentences, of the sort that would be trivial for an agent equipped with an ""algebraic mind"" BID23 . In the thirty years since the inception of the systematicity debate, many authors on both sides have tested the ability of neural networks to solve tasks requiring compositional generalization, with mixed results (e.g., BID6 BID22 BID25 BID5 BID27 BID29 BID3 BID12 . However, to the best of our knowledge, ours is the first study testing systematicity in modern seq2seq models, and our results confirm the mixed picture. On the one hand, standard recurrent models can reach very high zero-shot accuracy from relatively few training examples, as long as the latter are generally representative of the test data (Experiment 1). However, the same networks fail spectacularly when there are systematic differences between training and testing. Crucially, the training data of the relevant experiments provide enough evidence to learn composition rules affording the correct generalizations. In Experiment 2, the training data contain examples of all modifiers and connectives that are needed at test time for producing longer action sequences. In Experiment 3, the usage of modifiers and connectives is illustrated at training time by their application to some primitive commands, and, at test time, the model should apply them to a new command it encountered in isolation during training. Nonetheless, this evidence was not sufficient for each of the networks we tested. Generalization only occurs when the networks are also exposed to the target command (or the corresponding action) in a fair number of composed contexts during training.Given the astounding successes of seq2seq models in challenging tasks such as machine translation, one might argue that failure to generalize by systematic composition indicates that neural networks are poor models of some aspects of human cognition, but it is of little practical import. However, systematicity is an extremely efficient way to generalize. Once a person learns the new English adjective ""daxy"", he or she can immediately produce and understand an infinity of sentences containing it. The SCAN experiments and a proof-of-concept machine translation experiment (Experiment 4) suggest that this ability is still beyond the grasp of state-of-the-art networks, likely contributing to their striking sample-inefficiency. These results give us hope that a model capable of systematic compositionality could greatly benefit machine translation and other applications.A natural way of achieving stronger compositionality is through learning more structured representations. Recently, neural networks with external memories have shown promise for extracting algorithm-like representations from input/output examples BID19 BID15 ; for instance, these networks can outperform standard RNNs on generalizing to longer sequences. Future work will explore these approaches on SCAN and other tests of zero-shot compositional generalization. Ultimately, we see systematic compositionality as key both to developing more powerful algorithms and to enriching our computational understanding of the human mind.",1246,0.565,746,1.6702412868632708,"Humans can understand produce new utterances effortlessly thanks their systematic compositional skills Once learns a new verb ""dax immediately understand twicesing and this paper the SCAN domain consisting simple compositional navigation commands paired the corresponding action sequences We then test the zero-shot generalization capabilities a variety trained SCAN with sequenceto methods We find RNNs generalize well the differences training and test commands apply "" solve However when generalization requires systematic compositional skillsas the ""dax"" example RNNs fail We conclude proof experiment neural machine translation supporting the conjecture lack systematicity explaining why need very large training sets Human language thought characterized systematic compositionality the algebraic capacity understand produce a potentially infinite number novel combinations from known components For example knows the meaning and usage wordstwiceandagain once she learns a new verb such dax immediately understand or produce instructions twice This type compositionality central make strong generalizations from In a set influential and controversial papers Jerry Fodor other researchers neural networks plausible models associative devices capture systematic compositionality BID11 BID22 BID10 BID23 Calvo & Symons 2014 a.o.) .In last made astounding progress practical domains where success crucially the generalization capabilities Perhaps strikingly end recurrent currently dominate the state machine translation BID2 BID30 . 1 Since the overwhelming majority sentences or even word sequences a language only occur even BID1 , points strong generalization abilities Still, commonly observed neural networks extremely sample inefficient requiring suggests lack the same algebraic compositionality humans exploit they only sensitive broad patterns over lots accumulated statistics BID21 .In introduce a grounded navigation environment must translate commands given a limited form of actions This problem naturally framed sequence-to task, due ideal study the systematic generalization capabilities computational systems novel examples in a controlled setup We thus use it test modern recurrent network in terms their compositional skills Our results, standard architectures such LSTMs with attention BID0 do generalize when novel examples feature a mixture constructions have observed training the models catastrophically affected systematic differences training and test sentences of trivial an agent equipped an ""algebraic mind BID23 . In the thirty years the systematicity debate many authors on tested the ability neural networks solve tasks requiring compositional generalization with . However to ours the first study testing systematicity modern seq2seq models confirm the mixed picture On standard recurrent models reach very high zero-shot accuracy from relatively few training examples latter generally representativeExperiment However the same networks fail there systematic differences training testing Crucially the training data of the relevant experiments provide enough evidence learn composition rules affording the correct generalizations In Experiment the training data contain examples all modifiers connectives needed at test time producing longer action sequences In Experiment the usage modifiers connectives illustrated at training time their application some primitive commands, the model should apply it encountered isolation during Nonetheless this evidence was each the networks we Generalization only occurs the networks also exposed the target command the corresponding action a fair number composed contexts during trainingGiven the astounding successes seq2seq models challenging tasks machine translation one argue failure by systematic composition indicates poor models some aspects of However systematicity an extremely efficient way generalize Once learns the new English adjective ""daxy immediately produce and understand an infinity sentences containing it The SCAN experiments and a proof machine translation experimentExperiment suggest this ability still beyond state networks likely contributing their striking sample-inefficiency These results give hope a model capable systematic compositionality greatly machine translationA natural way achieving stronger compositionality learning more structured representations Recently neural networks with external memories extracting algorithm-like representations input/output examples BID19 BID15 ; for these networks on generalizing longer sequences Future work explore these approaches on SCAN other tests zero-shot compositional generalization Ultimately see systematic compositionality key both developing more powerful algorithms enriching our computational understanding",0.01,0.41179508185582603
"This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how  Graph Neural Networks (GNN), which have emerged as an effective model for various supervised prediction problems defined on structured data, can be trained to produce embedding of graphs in vector spaces that enables efficient similarity reasoning. Second, we propose a novel Graph Matching Network model that, given a pair of graphs as input, computes a similarity score between them by jointly reasoning on the pair through a new cross-graph attention-based matching mechanism. We demonstrate the effectiveness of our models on different domains including the challenging problem of control-flow-graph based function similarity search that plays an important role in the detection of vulnerabilities in software systems. The experimental analysis demonstrates that our models are not only able to exploit structure in the context of similarity learning but they can also outperform domain-specific baseline systems that have been carefully hand-engineered for these problems. Graphs are natural representations for encoding relational structures that are encountered in many domains. Expectedly, computations defined over graph structured data are employed in a wide variety of fields, from the analysis of molecules for computational biology and chemistry BID22 BID38 , to the analysis of knowledge graphs or graph structured parses for natural language understanding.In the past few years graph neural networks (GNNs) have emerged as an effective class of models for learning representations of structured data and for solving various supervised prediction problems on graphs. Such models are invariant to permutations of graph elements by design and compute graph node representations through a propagation process which iteratively aggregates local structural information (Scarselli et al., 2009; BID31 BID22 ). These node representations are then used directly for node classification, or pooled into a graph vector for graph classification. Problems beyond supervised classification or regression are relatively less well-studied for GNNs.In this paper we study the problem of similarity learning for graph structured objects, which appears in many important real world applications, in particular similarity based retrieval in graph databases. One motivating application is the computer security problem of binary function similarity search, where given a binary which may or may not contain code with known vulnerabilities, we wish to check whether any control-flow-graph in this binary is sufficiently similar to a database of known-vulnerable functions. This helps identify vulnerable statically linked libraries in closed-source software, a recurring problem (CVE, 2010; BID16 for which no good solutions are currently available. Figure 1 shows one example from this application, where the binary functions are represented as control flow graphs annotated with assembly instructions. This similarity learning problem is very challenging as subtle differences can make two graphs be semantically very different, while graphs with different structures can still be similar. A successful model for this problem should therefore (1) exploit the graph structures, and (2) be able to reason about the similarity of graphs both from the graph structures as well as from learned semantics. Figure 1 : The binary function similarity learning problem. Checking whether two graphs are similar requires reasoning about both the structure as well as the semantics of the graphs. Here the left two control flow graphs correspond to the same function compiled with different compilers (and therefore similar), while the graph on the right corresponds to a different function.In order to solve the graph similarity learning problem, we investigate the use of GNNs in this context, explore how they can be used to embed graphs into a vector space, and learn this embedding model to make similar graphs close in the vector space, and dissimilar graphs far apart. One important property of this model is that, it maps each graph independently to an embedding vector, and then all the similarity computation happens in the vector space. Therefore, the embeddings of graphs in a large database can be precomputed and indexed, which enables efficient retrieval with fast nearest neighbor search data structures like k-d trees BID4 or locality sensitive hashing BID23 .We further propose an extension to GNNs which we call Graph Matching Networks (GMNs) for similarity learning. Instead of computing graph representations independently for each graph, the GMNs compute a similarity score through a cross-graph attention mechanism to associate nodes across graphs and identify differences. By making the graph representation computation dependent on the pair, this matching model is more powerful than the embedding model, providing a nice accuracy-computation trade-off.We evaluate the proposed models and baselines on three tasks: a synthetic graph edit-distance learning task which captures structural similarity only, and two real world tasks -binary function similarity search and mesh retrieval, which require reasoning about both the structural and semantic similarity. On all tasks , the proposed approaches outperform established baselines and structure agnostic models; in more detailed ablation studies, we found that the Graph Matching Networks consistently outperform the graph embedding model and Siamese networks.To summarize, the contributions of this paper are:(1) we demonstrate how GNNs can be used to produce graph embeddings for similarity learning; (2) we propose the new Graph Matching Networks that computes similarity through cross-graph attention-based matching; (3) empirically we show that the proposed graph similarity learning models achieve good performance across a range of applications, outperforming structure agnostic models and established hand-engineered baselines. In this paper we studied the problem of graph similarity learning using graph neural networks. Compared to standard prediction problems for graphs, similarity learning poses a unique set of challenges and potential benefits. For example, the graph embedding models can be learned through a classification setting when we do have a set of classes in the dataset, but formulating it as a similarity learning problem can handle cases where we have a very large number of classes and only very few examples for each class. The representations learned from the similarity learning setting can also easily generalize to data from classes unseen during training (zero-shot generalization).We proposed the new graph matching networks as a stronger alternative to the graph embedding models. The added power for the graph matching models comes from the fact that they are not independently mapping each graph to an embedding, but rather doing comparisons at all levels across the pair of graphs, in addition to the embedding computation. The model can then learn to properly allocate capacity toward the embedding part or the matching part. The price to pay for this expressivity is the added computation cost in two aspects: (1) since each cross-graph matching step requires the computation of the full attention matrices, which requires at least O(|V 1 ||V 2 |) time, this may be expensive for large graphs; (2) the matching models operate on pairs, and cannot directly be used for indexing and searching through large graph databases. Therefore it is best to use the graph matching networks when we (1) only care about the similarity between individual pairs, or (2) use them in a retrieval setting together with a faster filtering model like the graph embedding model or standard graph similarity search methods, to narrow down the search to a smaller candidate set, and then use the more expensive matching model to rerank the candidates to improve precision.Developing neural models for graph similarity learning is an important research direction with many applications. There are still many interesting challenges to resolve, for example to improve the efficiency of the matching models, study different matching architectures, adapt the GNN capacity to graphs of different sizes, and applying these models to new application domains. We hope our work can spur further research in this direction.",1483,0.638,886,1.6738148984198646,"This paper addresses the challenging problem retrieval matching graph structured objects makes First demonstrate Graph Neural Networks emerged an effective model various supervised prediction problems defined on structured data produce embedding of graphs vector spaces that enables efficient similarity reasoning Second propose a novel Graph Matching Network model, given graphs as a similarity score jointly reasoning on through a new cross-graph attention-based matching mechanism We demonstrate our models different domains including the challenging problem control-flow-graph based function similarity search that plays vulnerabilities software systems The experimental analysis demonstrates our models exploit structure similarity learning they domain-specific baseline systems carefully hand these problems Graphs natural representations for encoding relational structures that encountered many domains Expectedly computations defined over graph structured data employed fields the analysis molecules for computational biology chemistry BID22 BID38 , knowledge graphs or graph structured parsesIn graph neural networks an effective class models learning representations solving various supervised prediction problems on graphs Such models invariant permutations graph elements by design and compute graph node representations through a propagation process which iteratively local structural informationScarselli BID31 BID22 These node representations then directly node classification or pooled a graph vector Problems beyond supervised classification or regression relatively less well for GNNsIn study similarity learning graph structured objects appears many important real world applications in particular similarity based retrieval in graph databases One motivating application the computer security problem binary function similarity search given which may code with known vulnerabilities we wish check any control-flow-graph in sufficiently a database This helps identify vulnerable statically linked libraries closed-source software a recurring problem (CVE, 2010; BID16 for which no good solutions. Figure shows one example from this application the binary functions represented control flow graphs annotated assembly instructions This similarity learning problem very challenging as subtle differences two graphs be semantically very while graphs different structures still similar A successful model this problem should therefore ( exploit the graph structures reason the similarity graphs both as learned semantics Figure : The binary function similarity learning problem Checking whether two graphs similar requires reasoning both the structure as Here the left two control flow graphs correspond compiledand therefore similar), while the graphIn solve the graph similarity learning problem investigate GNNs explore embed graphs learn this embedding model make similar graphs close in dissimilar graphs far One important property, it maps each graph independently an embedding vector all the similarity computation Therefore the embeddings graphs a large database indexed enables efficient retrieval with fast nearest neighbor search data structures like k-d trees BID4 or locality sensitive hashing BID23 .We further GNNs we Graph Matching Networks similarity learning Instead computing graph representations independently for GMNs compute a similarity score through a cross-graph attention mechanism associate nodes across identify differences By making the graph representation computation dependent the pair this matching model powerful providing a nice accuracy-computation trade-offWe evaluate the proposed models baselines three tasks a synthetic graph edit-distance learning task which captures structural similarity only two real world tasks -binary function similarity search mesh retrieval require reasoning On all tasks , the proposed approaches outperform established baselines structure agnostic models; more detailed ablation studies the Graph Matching Networks consistently Siamese networksTo the contributions are:(1 we produce similarity learning propose computes similarity through cross-graph attention-based matching empirically we the proposed graph similarity learning models achieve across applications outperforming structure established hand-engineered baselines In this paper studied the problem graph similarity learning graph neural networks Compared standard prediction problems for graphs similarity learning poses potential benefits For example the graph embedding models learned through a classification setting when we do have classes formulating it a similarity learning problem handle cases for The representations learned the similarity learning setting can easily generalize data classes unseen duringzeroshot generalization).We proposed the new graph matching networks a stronger alternative The added power for the graph matching models comes independently mapping each graph embedding, doing comparisons at all levels across the pair in The model can then learn properly allocate capacity toward the embedding part or The price to this expressivity the added computation cost in two aspects since each cross-graph matching step the full attention matrices which at least O(|V 1 ||V this may expensive large graphs operate pairs, directly indexing searching through large graph databases Therefore best the graph matching networks when we ( only the similarity individual pairs a retrieval setting together a faster filtering model like standard graph similarity search methods to narrow a smaller candidate set the more expensive matching model rerank improve precisionDeveloping neural models graph similarity learning an important research direction with There still many interesting challenges resolve for to improve the matching models study different matching architectures adapt the GNN capacity graphs applying these models new application domains We hope our work spur this direction",0.01,0.4209003301279488
"Context information plays an important role in human language understanding, and it is also useful for machines to learn vector representations of language. In this paper, we explore an asymmetric encoder-decoder structure for unsupervised context-based sentence representation learning. As a result, we build an encoder-decoder architecture with an RNN encoder and a CNN decoder, and we show that neither an autoregressive decoder nor an RNN decoder is required.   We further combine a suite of effective designs to significantly improve model efficiency while also achieving better performance. Our model is trained on two different large unlabeled corpora, and in both cases transferability is evaluated on a set of downstream language understanding tasks. We empirically show that our model is simple and fast while producing rich sentence representations that excel in downstream tasks. Learning distributed representations of sentences is an important and hard topic in both the deep learning and natural language processing communities, since it requires machines to encode a sentence with rich language content into a fixed-dimension vector filled with continuous values. We are interested in learning to build a distributed sentence encoder in an unsupervised fashion by exploiting the structure and relationship in a large unlabeled corpus. Since humans interpret sentences by composing from the meanings of the words, we decompose the task of learning a sentence encoder into two essential components: learning distributed word representations, and learning how to compose a sentence representation from the representations of words in the given sentence.Numerous studies in human language processing have claimed that the context in which words and sentences are understood plays an important role in human language understanding BID1 BID4 . The idea of learning from the context information BID35 was recently successfully applied to vector representation learning for words in ; BID30 . BID8 proposed a unified framework for learning language representation from the unlabeled data, and it is able to generalize to various NLP tasks. Inspired by the prior work on incorporating context information into representation learning, proposed the Skipthought model, which is an encoder-decoder model for unsupervised sentence representation learning. The paper exploits the semantic similarity within a tuple of adjacent sentences as supervision, and successfully built a generic, distributed sentence encoder. Rather than applying the conventional autoencoder model, the skip-thought model tries to reconstruct the surrounding 2 sentences instead of the input sentence. The learned sentence representation encoder outperforms previous unsupervised pretrained models on the evaluation tasks with no finetuning, and the results are comparable to the models which were trained directly on the datasets in a supervised fashion.The usage of 2 independent decoders in Skip-thought model matches our intuition that, given the current sentence, inferring the previous sentence and inferring the next one should be different.Figure 1: Our proposed model is composed of an RNN encoder, and a CNN decoder. During training, a batch of sentences are sent to the model, and the RNN encoder computes a vector representation for each of sentences; then the CNN decoder needs to reconstruct the paired target sequence, which contains 30 contiguous words right after the input sentence, given the vector representation. 300 is the dimension of word vectors. D is the dimension of sentence representation, and it varies along with the change of the RNN encoder size. (Better view in color.) DISPLAYFORM0 Representation: We aim to provide a model with faster training speed with better transferability than existing algorithms, thus we choose to apply a parameter-free composition function, which is a concatenation of the outputs from a global mean pooling over time and a global max pooling over time, on the computed sequence of hidden states. The composition function can be represented as DISPLAYFORM1 where max H d· is the max operation on the d-th row of the matrix H, which outputs a scalar. Thus the representation z has a dimension of 2d.Decoder: The decoder is a 3-layer CNN to reconstruct the paired target sequence t, which needs to expand z from length 1 to the length of t. Intuitively, the decoder could be a stack of deconvolution layers. For fast training speed, we optimized the architecture to make it plausible to use fullyconnected layers and convolution layers in the decoder, since generally, convolution layers run faster than deconvolution layers in modern deep learning frameworks.Suppose that the target sequence t has N words, the first layer of deconvolution will expand z, which could be considered as a sequence with length 1, into a feature map with length N . It can be easily implemented as a concatenation of outputs from N linear transformations in parallel. Then the second and third layer are 1D-convolution layers with kernel size 3 and 1, respectively. The output feature DISPLAYFORM2 , where v ∈ R e , and e is dimension of the word vectors.Note that our decoder is not an autoregressive model, and it brings us high training efficiency. We will discuss the reason of choosing this decoder which we call a predict-all-words CNN decoder.Objective: A softmax layer is applied after the decoder to produce a probability distribution over words at each position, softmax(Ev n ), and the training objective is to minimize the sum of the negative log-likelihood over all positions in the target sequence t: DISPLAYFORM3 The loss function L is summed over all sentences in the training corpus. Inspired by learning to exploit the contextual information present in adjacent sentences, we proposed an asymmetric encoder-decoder model with a suite of techniques for improving context-based unsupervised sentence representation learning. Since we believe that a simple model will be faster in training and easier to analyze, we opt to use simple techniques in our proposed model, including 1) an RNN as the encoder, and a predict-all-words CNN as the decoder, 2) learning by inferring next contiguous words, 3) mean+max pooling, and 4) tying word vectors with word prediction. With thorough discussion and extensive evaluation, we justify our decision making for each component in our RNN-CNN model. In terms of the performance and the efficiency of training, we justify that our model is a fast and simple algorithm for learning generic sentence representations from unlabeled corpora. Further research will focus on how to maximize the utility of the context information, and how to design simple architectures to best make use of it. 9 , and 12) works better than other asymmetric models (CNN-LSTM, row 11), and models with symmetric structure (RNN-RNN, row 5 and 10). In addition, with larger encoder size, our model demonstrates stronger transferability. The default setting for our CNN decoder is that it learns to reconstruct 30 words right next to every input sentence. ""CNN(10)"" represents a CNN decoder with the length of outputs as 10, and ""CNN(50)"" represents it with the length of outputs as 50. "" †"" indicates that the CNN decoder learns to reconstruct next sentence. "" ‡"" indicates the results reported in Gan et al. as future predictor. The CNN encoder in our experiment, noted as "" §"", was based on AdaSent in Zhao et al. and Conneau et al.. Bold numbers are best results among models at same dimension, and underlined numbers are best results among all models. For STS14, the performance measures are Pearson's and Spearman's score. For MSRP, the performance measures are accuracy and F1 score.",1491,0.757,879,1.6962457337883958,"Context information plays human language understanding also useful machines vector representations In explore unsupervised context-based sentence representation learning As build an encoder-decoder architecture show neither an autoregressive decoder required We further combine a suite effective designs significantly model efficiency while achieving Our model trained two different large unlabeled corpora in transferability evaluated downstream language understanding tasks We empirically our model simple fast while producing rich sentence representations excel downstream tasks Learning distributed representations sentences an important and hard topic since machines encode rich language content into a fixed-dimension vector filled continuous values We interested to a distributed sentence encoder by exploiting relationship in Since humans interpret sentences composing from the meanings decompose the task learning a sentence encoder two essential components distributed word representations how compose the representationsNumerous studies in claimed the context and understood plays BID1 BID4 The idea learning the context information BID35 was recently successfully vector representation learning for words ; BID8 proposed a unified framework learning language representation from the unlabeled data able generalize various NLP tasks Inspired the prior work incorporating context information representation learning proposed the Skipthought model unsupervised sentence representation learning The paper exploits the semantic similarity within a tuple adjacent sentences supervision successfully built a generic, distributed sentence encoder Rather applying the conventional autoencoder model the skip-thought model tries reconstruct the surrounding 2 sentences instead The learned sentence representation encoder outperforms previous unsupervised pretrained models on the evaluation tasks with no finetuning comparable which directly the datasetsThe usage 2 independent decoders Skip-thought model matches our intuition, the current sentence inferring and differentFigure Our proposed model composed an RNN encoder CNN During training a batch sentences the model the RNN encoder sentences; needs reconstruct the paired target sequence contains 30 contiguous words right given 300 is the dimension word vectors D is the dimension sentence representation varies along the change the RNN encoder size (Better view in color DISPLAYFORM0 Representation: We aim a model faster training speed with better transferability existing algorithms thus we choose apply a parameter-free composition function the outputs a global mean pooling over global max on the computed sequence hidden states The composition function can represented DISPLAYFORM1 where max H d· is the max operation which outputs Thus the representation z has a dimension 2dDecoder: a 3-layer CNN to reconstruct the paired target sequence t needs expand z length Intuitively the decoder could a stack deconvolution layers For fast training speed optimized the architecture plausible fullyconnected layers convolution layers since generally run modern deepSuppose the target sequence t N words the first layer will expand z which could considered length into a feature map . It can easily implemented outputs N linear transformations in parallel Then the second and third layer 1D-convolution layers kernel size 1, The output feature DISPLAYFORM2 , where v � R e and e dimension the word vectorsNote our decoder an autoregressive model brings high training efficiency We will discuss the reason of choosing this decoder which a predict-all-words CNN decoderObjective A softmax layer applied after to produce words at softmax(Ev n the training objective minimize the sum over all positions the target sequence t: DISPLAYFORM3 The loss function L summed Inspired learning exploit the contextual information present adjacent sentences proposed a suite techniques improving context-based unsupervised sentence representation learning Since we believe a simple model will faster in training easier analyze opt simple techniques our proposed model 1 an RNN as the encoder a predict-all-words CNN learning by inferring next contiguous words 3) mean+max pooling tying word vectors word prediction With thorough discussion extensive evaluation justify for each component our RNN-CNN model In terms the performance and the efficiency training justify our model a fast and simple algorithm learning generic sentence representations Further research focus maximize the context information design simple architectures best make 9 , and 12) works better other asymmetric modelsCNN-LSTM row 11 models 5 In addition with larger encoder size our model demonstrates stronger transferability default our CNN decoder that learns reconstruct 30 words right next every input sentence ""CNN(10 represents a CNN decoder the length outputs as it "" �� indicates the CNN decoder learns reconstruct next sentence "" ��"" indicates the results reported Gan et al as future predictor The CNN encoder in our experiment noted as §"", based AdaSent in Zhao et and Conneau et.. Bold numbers best results among models at same dimension underlined numbers For STS14 the performance measures Pearson's and Spearman's score For MSRP the performance measures accuracy and F1 score",0.01,0.47805212789531915
"Building on the success of deep learning, two modern approaches to learn a probability model of the observed data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-bound on the log-likelihood function. GANs, however, compute a generative model by minimizing a distance between observed and generated probability distributions without considering an explicit model for the observed data. The lack of having explicit probability models in GANs prohibits computation of sample likelihoods in their frameworks and limits their use in statistical inference problems. In this work, we show that an optimal transport GAN with the entropy regularization can be viewed as a generative model that maximizes a lower-bound on average sample likelihoods, an approach that VAEs are based on. In particular, our proof constructs an explicit probability model for GANs that can be used to compute likelihood statistics within GAN's framework. Our numerical results on several datasets demonstrate consistent trends with the proposed theory. Learning generative models is becoming an increasingly important problem in machine learning and statistics with a wide range of applications in self-driving cars BID26 , robotics BID10 , natural language processing BID14 , domain-transfer BID25 , computational biology BID6 , etc. Two modern approaches to deal with this problem are Generative Adversarial Networks (GANs) BID7 and Variational AutoEncoders (VAEs) BID13 BID15 BID23 BID28 BID17 .VAEs BID13 ) compute a generative model by maximizing a variational lowerbound on average sample likelihoods using an explicit probability distribution for the data. GANs , however, learn a generative model by minimizing a distance between observed and generated distributions without considering an explicit probability model for the data. Empirically , GANs have been shown to produce higher-quality generative samples than that of VAEs BID12 . However, since GANs do not consider an explicit probability model for the data, we are unable to compute sample likelihoods using their generative models. Computations of sample likelihoods and posterior distributions of latent variables are critical in several statistical inference. Inability to obtain such statistics within GAN's framework severely limits their applications in such statistical inference problems.In this paper, we resolve these issues for a general formulation of GANs by providing a theoreticallyjustified approach to compute sample likelihoods using GAN's generative model. Our results can open new directions to use GANs in massive-data applications such as model selection, sample selection, hypothesis-testing, etc (see more details in Section 5). Now, we state our main results informally without going into technical conditions while precise statements of our results are presented in Section 2. Let Y andŶ ∶= G(X) represent observed (i.e. real) and generative (i.e. fake or synthetic) variables, respectively. X (i.e. the latent variable) is the randomness used as the input to the generator G(.). Consider the following explicit probability By training a GAN model, we first compute optimal generator G * and optimal coupling between the observed variable Y and the latent variable X. The likelihood of a test sample y test can then be lower-bounded using a combination of three terms: (1) the expected distance of y test to the distribution learnt by the generative model, (2) the entropy of the coupled latent variable given y test and (3) the likelihood of the coupled latent variable with y test .model of the data given a latent sample X = x: f Y X=x (y) ∝ exp(− (y, G(x))), (1.1)where (., .) is a loss function. f Y X=x (y) is the model that we are considering for the underlying data distribution. This is a reasonable model for the data as the function G can be a complex function. Similar data models have been used in VAEs . Under this explicit probability model, we show that minimizing the objective of an optimal transport GAN (e.g. Wasserstein BID0 ) with the cost function (., .) and an entropy regularization BID2 BID27 ) maximizes a variational lower-bound on average sample likelihoods. I.e.average sample likelihoods ≥ − (entropic GAN objective) + constants.(1.2)If (y,ŷ) = y −ŷ 2 , the optimal transport (OT) GAN simplifies to WGAN while if (y,ŷ) = y −ŷ 2 2 , the OT GAN simplifies to the quadratic GAN (or, W2GAN) BID3 ). The precise statement of this result can be found in Theorem 1. This result provides a statistical justification for GAN's optimization and puts it in par with VAEs whose goal is to maximize a lower bound on sample likelihoods. We note that the entropy regularization has been proposed primarily to improve computational aspects of GANs BID5 . Our results provide an additional statistical justification for this regularization term. Moreover, using GAN's training, we obtain a coupling between the observed variable Y and the latent variable X. This coupling provides the conditional distribution of the latent variable X given an observed sample Y = y. The explicit model of equation 1.1 acts similar to the decoder in the VAE framework, while the coupling computed using GANs acts as an encoder.Connections between GANs and VAEs have been investigated in some of the recent works as well BID11 BID16 . In BID11 , GANs are interpreted as methods performing variational inference on a generative model in the label space. In their framework, observed data samples are treated as latent variables while the generative variable is the indicator of whether data is real or fake. The method in BID16 , on the other hand, uses an auxiliary discriminator network to rephrase the maximum-likelihood objective of a VAE as a twoplayer game similar to the objective of a GAN. Our method is different from both these approaches as we consider an explicit probability model for the data, and show that the entropic GAN objective maximizes a variational lower bound under this probability model, thus allowing sample likelihood computation in GANs similar to VAEs.Of relevance to our work is BID30 , in which annealed importance sampling (AIS) is used to evaluate the approximate likelihood of decoder-based generative models. More specifically, a Gaussian observation model with a fixed variance is used as the generative distribution for GANbased models on which the AIS is computed. Gaussian observation models may not be proper specially in high-dimensional spaces . Our approach, on the other hand, makes a connection between GANs and VAEs by constructing a theoretically-motivated model for the data distribution in GANs. We then leverage this approach in computing sample likelihood estimates in GANs.Another key question that we address here is how to estimate the likelihood of a new sample y test given the generative model trained using GANs. For instance, if we train a GAN on stop-sign images, upon receiving a new image, one may wish to compute the likelihood of the new sample y test according to the trained generative model. In standard GAN formulations, the support of the generative distribution lies on the range of the optimal generator function. Thus, if the observed sample y test does not lie on that range (which is very likely in practice ), there is no way to assign a sensible likelihood score to that sample. Below, we show that using the explicit probability model of equation 1.1, we can lower-bound the likelihood of this sample y test . This is similar to the variational lower-bound on sample likelihoods used in VAEs. Our numerical results show that this lower-bound well-reflect the expected trends of the true sample likelihoods.Let G * and P * Y,X be the optimal generator and the optimal coupling between real and latent variables, respectively. The optimal coupling P * Y,X can be computed efficiently for entropic GANs as we explain in Section 3. For other GAN architectures, one may approximate such couplings as we explain in Section 4. The log likelihood of a new test sample y test can be lower-bounded as DISPLAYFORM0 distance to the generative model DISPLAYFORM1 We present the precise statement of this result in Corollary 2. This result combines three components in order to approximate the likelihood of a sample given a trained generative model:• The distance between y test to the generative model. If this distance is large, the likelihood of observing y test from the generative model is small.• The entropy of the coupled latent variable. If the entropy term is large, the coupled latent variable has a large randomness. This contributes positively to the sample likelihood.• The likelihood of the coupled latent variable. If latent samples have large likelihoods, the likelihood of the observed test sample will be large as well. FIG2 provides a pictorial illustration of these components. In what follows, we explain the technical ingredients of our main results. In Section 3, we present computational methods for GANs and entropic GANs, while in Section 4, we provide numerical experiments on benchmark datasets. In this paper, we have provided a statistical framework for a family of GANs. Our main result shows that the entropic GAN optimization can be viewed as maximization of a variational lower-bound on average log-likelihoods, an approach that VAEs are based upon. This result makes a connection between two most-popular generative models, namely GANs and VAEs. More importantly, our result constructs an explicit probability model for GANs that can be used to compute a lower-bound on sample likelihoods. Our experimental results on various datasets demonstrate that this likelihood surrogate can be a good approximation of the true likelihood function. Although in this paper we mainly focus on understanding the behavior of the sample likelihood surrogate in different datasets, the proposed statistical framework of GANs can be used in various statistical inference applications. For example, our proposed likelihood surrogate can be used as a quantitative measure to evaluate the performance of different GAN architectures, it can be used to quantify the domain shifts, it can be used to select a proper generator class by balancing the bias term vs. variance, it can be used to detect outlier samples, it can be used in statistical tests such as hypothesis testing, etc. We leave exploring these directions for future work. APPENDIX A PROOF OF THEOREM 1Using the Baye's rule, one can compute the log-likelihood of an observed sample y as follows: DISPLAYFORM0 where the second step follows from equation 2.4.Consider a joint density function P X,Y such that its marginal distributions match P X and P Y . Note that the equation A.1 is true for every x. Thus, we can take the expectation of both sides with respect to a distribution P X Y =y . This leads to the following equation: DISPLAYFORM1 where H(.) is the Shannon-entropy function.Next we take the expectation of both sides with respect to P Y : DISPLAYFORM2 Here, we replaced the expectation over P X with the expectation over f X since one can generate an arbitrarily large number of samples from the generator. Since the KL divergence is always nonnegative, we have DISPLAYFORM3 Moreover, using the data processing inequality, we have BID1 . Thus, DISPLAYFORM4 DISPLAYFORM5 GAN objective with entropy regularizer DISPLAYFORM6 This inequality is true for every P X,Y satisfying the marginal conditions. Thus, similar to VAEs, we can pick P X,Y to maximize the lower bound on average sample log-likelihoods. This leads to the entropic GAN optimization 2.3.",2368,1.185,1381,1.714699493120927,"Building deep learning two modern approaches learn a probability model of the observed data Variational AutoEncoders VAEs consider an explicit probability model the data compute a generative distribution by maximizing lower GANs however compute minimizing a distance observed and generated probability distributions without considering an explicit model The lack having explicit probability models GANs prohibits computation sample likelihoods their frameworks limits statistical inference problems In this work an optimal transport GAN with the entropy regularization can viewed a lowerbound average sample likelihoods VAEs based In particular our proof constructs an explicit probability model GANs likelihood statistics within Our numerical results on several datasets demonstrate consistent trends the proposed theory Learning generative models becoming statistics with BID26 , robotics natural domaintransfer computational etc Two modern approaches deal Generative Adversarial Networks (GANs) BID7 Variational AutoEncoders ) compute by maximizing a variational lowerbound average sample likelihoods GANs , however learn a generative model minimizing a distance observed and generated distributions without considering an explicit probability model , GANs higher-quality generative samples that VAEs BID12 However since GANs consider an explicit probability model for compute sample likelihoods their generative models Computations sample likelihoods posterior distributions critical several statistical inference. Inability obtain such statistics within GAN's framework severely their applications such statistical inference problemsIn resolve for a general formulation a theoreticallyjustified approach compute sample likelihoods Our results can open new directions use GANs massive-data applications model selection sample selection etc ( more details Section Now state our main results informally without going technical conditions while precise statements presented Section Let Y and�� ��= G(X) represent observed ( real generative fake or synthetic variables X ( latent variable the randomness used as G.). Consider the following explicit probability By training a GAN model first compute optimal generator G * and optimal coupling the observed variable Y The likelihood a test sample y test can then lower- using three terms the distribution learnt the entropy the coupled latent variable given y with y test .model of given a latent sample X =: f Y X=x (y) �� exp(− (, G(x., .) f Y X=x is the model that considering the underlying data distribution This a reasonable model the data as the function G can Similar data models VAEs . Under this explicit probability model show minimizing the objective of an optimal transport GAN (e.g. Wasserstein BID0 ) with the cost function., .) an entropy regularization BID2 BID27 ) a variational lower average sample likelihoods I.e.average sample likelihoods ≥ − (entropic GAN objective + constants.(1.2)If (y�� −� 2 optimal transport (OT simplifies WGAN while if 2 OT, W2GAN) BID3 ). The precise statement this result Theorem This result provides a statistical justification GAN's optimization puts par VAEs whose goal a lower bound sample likelihoods We note the entropy regularization has proposed primarily computational aspects GANs BID5 . Our results provide an additional statistical justification this regularization term Moreover using GAN's training obtain a coupling the observed variable Y This coupling provides the conditional distribution the latent variable X given an observed sample Y = y. The explicit model equation acts similar the decoder the VAE framework while the coupling computed GANs actsConnections investigated some as BID11 BID16 . In BID11 , GANs interpreted methods performing variational inference in the label space In their framework observed data samples treated latent variables while the generative variable the indicator whether real fake The method in BID16 , on an auxiliary discriminator network rephrase the maximum-likelihood objective a VAE as a twoplayer game similar the objective a GAN Our method different both these approaches consider an explicit probability model show the entropic GAN objective a variational lower under thus sample likelihood computation similar VAEsOf relevance BID30 , annealed importance samplingAIS evaluate decoder-based generative models More specifically a Gaussian observation model the generative distribution GANbased models on which the AIS computed Gaussian observation models may proper specially . Our approach, on makes a connection GANs VAEs by constructing a theoretically-motivated model the data distribution leverage computing sample likelihood estimatesAnother key question estimate a new sample y test given trained using stop images upon receiving one wish compute according In standard GAN formulations the support the generative distribution lies the range the optimal generator function Thus the observed sample y test does lie that range very in practice there assign a sensible likelihood score Below show using the explicit probability model equation lower-bound this sample y test . This similar variational lower sample likelihoods used VAEs Our numerical results wellreflect the expected trendsLet G * and Y,X the optimal generator the optimal coupling real and latent variables The optimal coupling P * Y,X can efficiently entropic GANs we explain For other GAN architectures one approximate such couplings we explain The log likelihood a new test sample y test can lower- as DISPLAYFORM0 distance to the generative model We present the precise statement this result Corollary This result combines three components in approximate a sample given a trained generative model:• The distance y test to If this distance large the likelihood observing y test from the generative model small.• The entropy the coupled latent variable. If the entropy term large the coupled latent variable has This contributes positively the sample likelihood.• the coupled latent variable. If latent samples large likelihoods the observed test sample will large as FIG2 provides these components In what follows explain the technical ingredients our main results In Section present computational methods GANs while numerical experiments benchmark datasets In have provided a family GANs Our main result viewed maximization variational lowerbound on an VAEs based This result makes a connection two most-popular generative models namely GANs VAEs More our result constructs an explicit probability model lowerbound sample likelihoods Our experimental results on various datasets demonstrate this likelihood surrogate can Although in this paper mainly understanding the sample likelihood surrogate different datasets the proposed statistical framework GANs various statistical inference applications For example our proposed likelihood surrogate can different GAN architectures it quantify the domain shifts select a proper generator class by balancing the bias term variance it detect outlier samples statistical tests such hypothesis testing We leave exploring these directions future work APPENDIX THEOREM 1Using the Baye's rule one compute an observed sample y as DISPLAYFORM0 where the second step follows equation 2.4.Consider a joint density function P X,Y such its marginal distributions match Note the equation A.1 true Thus take the expectation both sides with respect a distribution P X Yy This leads DISPLAYFORM1 where H.)Next the expectation both sides with P Y Here replaced over f X since one generate samples the generator Since the KL divergence always nonnegative DISPLAYFORM3 Moreover using the data processing inequality BID1 . Thus DISPLAYFORM4 DISPLAYFORM5 GAN objective with entropy regularizer DISPLAYFORM6 This inequality true every P X,Y satisfying the marginal conditions Thus similar VAEs pick P X,Y maximize lower average sample log-likelihoods This leads the entropic GAN optimization 2.3",0.01,0.5250706853450412
"We introduce geomstats, a Python package for Riemannian modelization and optimization over manifolds such as hyperspheres, hyperbolic spaces, SPD matrices or Lie groups of transformations. Our contribution is threefold. First, geomstats allows the flexible modeling of many a machine learning problem through an efficient and extensively unit-tested implementations of these manifolds, as well as the set of useful Riemannian metrics, exponential and logarithm maps that we provide. Moreover, the wide choice of loss functions and our implementation of the corresponding gradients allow fast and easy optimization over manifolds. Finally, geomstats is the only package to provide a unified framework for Riemannian geometry, as the operations implemented in geomstats are available with different computing backends (numpy,tensorflow and keras), as well as with a GPU-enabled mode–-thus considerably facilitating the application of Riemannian geometry in machine learning. In this paper, we present geomstats through a review of the utility and advantages of manifolds in machine learning, using the concrete examples that they span to show the efficiency and practicality of their implementation using our package From soft-classification to image recognition, Riemannian manifolds provide a natural framework to many a machine learning problem. Consider the following standard supervised learning problem: given an input X, the goal is to predict an output Y . The relation between X and Y is typically modeled by a function f θ : X → Y , characterized by a set of parameters θ. Riemannian geometry often naturally arises at each of the three different stages of the modelization: through the input X, the output Y , or the parameters θ. For instance, the input X might belong to a Riemannian manifold. This is typically the case in image processing, where images X are frequently modeled as elements of a low-dimensional manifold (17; 57; 61; 67; 18; 6) . Such is the case in BID61 , in which the authors consider spherical images as elements of the orthogonal rotation group SO BID2 . In some cases, X can even be a manifold itself-in BID7 for instance, the authors propose to model images as a function of a 2D smooth surface representing a shape such as a human pose. Similarly, the output Y often belongs to a Riemannian manifold (42; 47) . Such is the case in problems where the output is a member of the set of doubly stochastic matrices -as for instance in some neurosciences applications (48; 11)-. or when the optimization is carried on a given manifold (2; 44; 27) . In BID27 for example, the authors use a neural network to predict the pose of a camera Y , which is defined as an element of the Lie group SE(3). Finally, the parameter θ of a model can be constrained on a Riemannian manifold, such as in the work of BID28 which constrains the weights of a neural network on multiple dependent Stiefel manifolds.Manifolds offer intuitive and practical advantages for modeling inputs, outputs and parameters. When applied to the input, they constitute lower dimensional spaces with fewer degrees of freedom, thus potentially allowing faster computations and less substantial memory allocation costs. Moreover, the non-linear degrees of freedom in these manifolds are often more intuitive and benefit from more expressive power. For instance, the geolocation of points of interest on Earth is more efficiently achieved through their longitude and latitude-i.e., their 2D manifold coordinates-rather than through their position (x, y, z) in the 3D Cartesian space. Most current machine learning problems make little use of this underlying manifold structure -rather viewing their optimization task as a constrained optimization over Euclidean space. Riemannian geometry, on the other hand, attempts to leverage the manifold structure to solve the corresponding optimization problem, replacing lines by geodesics, partial differential by covariate differentiation (59)-thus potentially reducing the dimension of the prblem space and the memory allocation costs.Yet, the adoption of Riemannian geometry by the machine learning community has been largely hindered by the lack of a modular framework for implementing such methods. Code sequences are often custom tailored for specific problems and/or computing backends, and are thus not easily re-usable: . To address this issue, some packages have been written to perform computations on manifolds. The theanogeometry package BID38 provides an implementation of differential geometric tensors on manifolds where closed forms do not necessarily exist, using the automatic differentiation tool theano to integrate differential equations that define the geometric tensors. The pygeometry package (10) offers an implementation primarily focused on the Lie groups SO(3) and SE(3) for robotics applications. However, no implementation of non-canonical metrics on these Lie groups is provided. The pymanopt package BID62 , originally implemented in Matlab as manopt, provides a very comprehensive toolbox for optimization on a extensive list of manifolds. However, not only is the choice of metrics on these manifolds rather restricted, the manifolds themselves are often implemented using canonical embeddings in higher-dimensional euclidean spaces, with high computational costs. This paper presents geomstats, a package specifically targeted at the machine learning community to perform computations on Riemannian manifolds with a flexible choice of Riemannian metrics. The geomstats package makes three contributions. First, geomstats is the first Riemannian geometry package to be extensively unit-tested with more than 90 % code coverage. Second, geomstats implements numpy (51) and tensorflow (1) backends, providing vectorized, intuitive computations, and available for GPU implementation. We also provide an updated version of the deep learning framework,keras, equipped with Riemannian gradient descent on manifolds. Finally, geomstats strives to be a user-friendly and educational a tool, presenting Riemannian geometry to computer scientists and facilitating its use as a complement to theoretical papers or books. We refer to BID54 for the theory and expect the reader to have a high-level understanding of Riemannian geometry.Our paper is organized as follows. We begin by providing an overview of geomstats in Section 2. We then present concrete use cases of geomstats for machine learning on manifolds of increasing geometric complexity, starting with manifolds embedded in flat spaces in Section 3, to a manifold embedded in a Lie group with a Lie group action in Section 4, to the Lie groups SO(n) and SE(n) in Section 5. Along the way, we present a review of the occurrences of each manifold in the machine learning literature, some educational visualizations of the Riemannian geometry as well as implementations of machine learning models where the inputs, the outputs and the parameters successively belong to manifolds. We introduce the open-source package geomstats to democratize the use of Riemannian geometry in machine learning for a wide range of applications. Regarding the geometry, we have presented manifolds of increasing complexity: manifolds embedded in flat Riemannian spaces, then the case of the SPD matrices space and lastly Lie groups with invariant Riemannian metrics. This provides an educational tool for users who want to delve into Riemannian geometry through a hands-on approach, with intuitive visualizations for example in subsections 3.4 and 5.2.In regard to machine learning, we have presented concrete use cases where inputs, outputs and parameters belong to manifolds, in the respective examples of subsection 4.2, subsection 5.3 and subsection 3.2. They demonstrate the usability of geomstats package for efficient and userfriendly Riemannian geometry. Regarding the machine learning applications, we have reviewed the occurrences of each manifold in the literature across many different fields. We kept the range of applications very wide to show the many new research avenues that open at the cross-roads of Riemannian geometry and machine learning.geomstats implements manifolds where closed-forms for the Exponential and the Logarithm maps of the Riemannian metrics exist. Future work will involve implementing manifolds where these closed forms do not necessarily exist. We will also provide the pytorch backend.",1667,0.826,949,1.7565858798735512,"We introduce geomstats Riemannian modelization optimization over manifolds such hyperspheres SPD matrices or Lie groups of transformations Our contribution threefold First geomstats allows the flexible modeling many a machine learning problem through an efficient and extensively unit-tested implementations these manifolds the set useful Riemannian metrics exponential and logarithm maps that Moreover the wide choice loss functions our implementation the corresponding gradients allow fast and easy optimization over manifolds Finally geomstats the only package a unified framework Riemannian geometry as the operations implemented available with different computing backendsnumpy a GPU-enabled mode–-thus considerably facilitating In geomstats through a review the utility advantages manifolds the concrete examples that they span the efficiency using our package From soft-classification image recognition many a machine learning problem Consider the following standard supervised learning problem given the goal predict . The relation X typically modeled a function f �� : characterized. Riemannian geometry often naturally at each the modelization: through the input X , the parameters � For instance the input X might belong a Riemannian manifold This typically image processing images X frequently modeled elements17; 57 18 6 . Such BID61 , in the authors consider spherical images elements the orthogonal rotation group SO BID2 In X can a manifold itself- BID7 for the authors propose model images a 2D smooth surface representing such a human pose Similarly the output Y often belongs a Riemannian manifold42; 47 . Such problems the output a member doubly stochastic matrices -as for some neurosciences applications48; 11)-. or when the optimization carried on a given manifold2; 44 27 . In BID27 for the authors use the pose a camera Y , defined an element the Lie group SE(3 Finally the parameter �� of constrained on such the work BID28 which the weights multiple dependent Stiefel manifoldsManifolds offer intuitive and practical advantages modeling inputs parameters When applied the input they constitute lower dimensional spaces fewer degrees thus potentially less substantial memory allocation costs Moreover the non-linear degrees these manifolds often more intuitive benefit more expressive power For instance points Earth more efficiently achieved their- 2D manifold coordinates-rather through (x Most current machine learning problems make little use this underlying manifold structure -rather viewing their optimization task a constrained optimization over Riemannian geometry on attempts leverage the manifold structure solve replacing lines geodesics partial differential by covariate differentiation59)-thus potentially the prblem space the memory allocation costsYet the adoption hindered a modular framework implementing Code sequences custom tailored specific problems computing backends thus easily reusable: . To address some packages written perform computations manifolds The theanogeometry package BID38 provides differential geometric tensors on where closed forms do necessarily using the automatic differentiation tool theano to integrate differential equations that define The pygeometry package (10 offers primarily focused the Lie groups SO(3 robotics applications However no implementation non-canonical metrics on these Lie groups provided The pymanopt package BID62 , originally implemented Matlab as manopt optimization on a extensive list manifolds However not the choice metrics on these manifolds rather restricted implemented canonical embeddings with high computational costs This paper presents geomstats specifically targeted perform a flexible choice The geomstats package makes three contributions First geomstats the first Riemannian geometry package extensively unit more than 90 % code coverage Second geomstats implements numpy (51 providing vectorized, intuitive computations available GPU implementation We also provide the deep learning frameworkkeras equipped Riemannian gradient descent on manifolds Finally geomstats strives presenting Riemannian geometry computer facilitating a complement theoretical papers or books We refer BID54 for the theory expect the readerOur paper organized We begin providing geomstats Section We then present concrete use cases geomstats machine on manifolds of increasing geometric complexity starting embedded flat spaces in Section to a manifold embedded a Lie group a Lie group action in the Lie groups SO(n Along present the occurrences each manifold some educational visualizations as implementations where the inputs, successively belong We introduce the open-source package geomstats democratize Riemannian geometry machine for Regarding the geometry presented manifolds increasing complexity: embedded then the case the SPD matrices space lastly Lie groups with This provides users delve Riemannian geometry through intuitive visualizations for example in subsections 3.4 and 5.2.In regard machine learning presented concrete use cases inputs, parameters belong manifolds in the respective examples subsection subsection They demonstrate the usability geomstats package Regarding the machine learning applications reviewed the occurrences each manifold across We kept the range applications very wide to show the many new research avenues open at the cross Riemannian geometry machine learning.geomstats implements manifolds where closed-forms for the Exponential exist Future work implementing manifolds where these closed forms do necessarily We will pytorch backend",0.01,0.6317935186930261
"We propose to execute deep neural networks (DNNs) with dynamic and sparse graph (DSG) structure for compressive memory and accelerative execution during both training and inference. The great success of DNNs motivates the pursuing of lightweight models for the deployment onto embedded devices. However, most of the previous studies optimize for inference while neglect training or even complicate it. Training is far more intractable, since (i) the neurons dominate the memory cost rather than the weights in inference; (ii) the dynamic activation makes previous sparse acceleration via one-off optimization on fixed weight invalid; (iii) batch normalization (BN) is critical for maintaining accuracy while its activation reorganization damages the sparsity. To address these issues, DSG activates only a small amount of neurons with high selectivity at each iteration via a dimensionreduction search and obtains the BN compatibility via a double-mask selection. Experiments show significant memory saving (1.7-4.5x) and operation reduction (2.3-4.4x) with little accuracy loss on various benchmarks. Deep Neural Networks (DNNs) BID23 have been achieving impressive progress in a wide spectrum of domains (Simonyan & Zisserman, 2014; BID0 Redmon & Farhadi, 2016; , while the models are extremely memory-and compute-intensive. The high representational and computational costs motivate many researchers to investigate approaches on improving the execution performance, including matrix or tensor decomposition BID44 Novikov et al., 2015; Garipov et al., 2016; BID47 BID3 , data quantization (Courbariaux et al., 2016; BID51 BID27 BID24 BID39 BID33 , and network pruning BID4 BID8 a; BID30 BID13 Molchanov et al., 2016; BID13 Spring & Shrivastava, 2017; BID28 BID49 BID12 Chin et al., 2018; BID31 BID14 . However, most of the previous work aim at inference while the challenges for reducing the representational and computational costs of training are not well-studied. Although some works demonstrate acceleration in the distributed training BID29 BID6 BID47 , we target at the single-node optimization, and our method can also boost training in a distributed fashion. DNN training, which demands much more hardware resources in terms of both memory capacity and computation volume, is far more challenging than inference. Firstly, activation data in training will be stored for backpropagation, significantly increasing the memory consumption. Secondly, training iteratively updates model parameters using mini-batched stochastic gradient descent. We almost always expect larger mini-batches for higher throughput FIG0 ), faster convergence, and better accuracy (Smith et al., 2017) . However, memory capacity is often the limitation factor FIG0 Upper and lower one are the feature maps before and after BN, respectively. However, using BN damages the sparsity through information fusion; (f) There exists such great representational redundancy that more than 80% of activations are close to zero.that may cause performance degradation or even make large models with deep structures or targeting high-resolution vision tasks hard to train BID42 .It is difficult to apply existing sparsity techniques towards inference phase to training phase because of the following reasons: 1) Prior arts mainly compress the pre-trained and fixed weight parameters to reduce the off-chip memory access in inference BID9 , while instead, the dynamic neuronal activations turn out to be the crucial bottleneck in training BID17 , making the prior inference-oriented methods inefficient. Besides , during training we need to stash a vast batched activation space for the backward gradient calculation. Therefore , neuron activations creates a new memory bottleneck (Figure 1(c) ). In this paper, we will sparsify the neuron activations for training compression.2) The existing inference accelerations usually add extra optimization problems onto the critical path Molchanov et al., 2016; BID30 BID27 BID49 BID31 , i.e., 'complicated training ⇒ simplified inference', which embarrassingly complicates the training phase. 3) Moreover , previous studies reveal that batch normalization (BN) is crucial for improving accuracy and robustness FIG0 ) through activation fusion across different samples within one mini-batch for better representation (Morcos et al., 2018; BID16 . BN almost becomes a standard training configuration; however, inference-oriented methods seldom discuss BN and treat BN parameters as scaling and shift factors in the forward pass. We further find that BN will damage the sparsity due to the activation reorganization FIG0 ). Since this work targets both training and inference, the BN compatibility problem should be addressed.From the view of information representation, the activation of each neuron reflects its selectivity to the current stimulus sample (Morcos et al., 2018) , and this selectivity dataflow propagates layer by layer forming different representation levels. Fortunately , there is much representational redundancy, for example, lots of neuron activations for each stimulus sample are so small and can be removed FIG0 ). Motivated by above comprehensive analysis regarding memory and compute, we propose to search critical neurons for constructing a sparse graph at every iteration. By activating only a small amount of neurons with a high selectivity, we can significantly save memory and simplify computation with tolerable accuracy degradation. Because the neuron response dynamically changes under different stimulus samples, the sparse graph is variable. The neuronaware dynamic and sparse graph (DSG) is fundamentally distinct from the static one in previous work on permanent weight pruning since we never prune the graph but activate part of them each time. Therefore, we maintain the model expressive power as much as possible. A graph selection method , dimension-reduction search, is designed for both compressible activations with elementwise unstructured sparsity and accelerative vector-matrix multiplication (VMM) with vector-wise structured sparsity. Through double-mask selection design, it is also compatible with BN. We can use the same selection pattern and extend our method to inference. In a nutshell, we propose a compressible and accelerative DSG approach supported by dimension-reduction search and doublemask selection. It can achieve 1.7-4.5x memory compression and 2.3-4.4x computation reduction with minimal accuracy loss. This work simultaneously pioneers the approach towards efficient online training and offline inference, which can benefit the deep learning in both the cloud and the edge. In this work, we propose DSG (dynamic and sparse graph) structure for efficient DNN training and inference through a dimension-reduction search based sparsity forecast for compressive memory and accelerative execution and a double-mask selection for BN compatibility without sacrificing model's expressive power. It can be easily extended to the inference by using the same selection pattern after training. Our experiments over various benchmarks demonstrate significant memory saving (up to 4.5x for training and 1.7x for inference) and computation reduction (up to 2.3x for training and 4.4x for inference). Through significantly boosting both forward and backward passes in training, as well as in inference, DSG promises efficient deep learning in both the cloud and edge. DISPLAYFORM0 Further recalling the norm preservation in equation (3) of the main text: there exist a linear map f : R d ⇒ R k and a 0 ∈ (0, 1), for 0 < ≤ 0 we have DISPLAYFORM1 Substituting the equation FORMULA0 into equation FORMULA0 yields DISPLAYFORM2 Combining equation FORMULA0 and FORMULA0 , finally we have DISPLAYFORM3 It can be seen that, for any given X i and W j pair, the inner product can be preserved if the is sufficiently small. Actually, previous work BID1 BID5 BID36 discussed a lot on the random projection for various big data applications, here we re-organize these supporting materials to form a systematic proof. We hope this could help readers to follow this paper. In practical experiments, there exists a trade-off between the dimension reduction degree and the recognition accuracy. Smaller usually brings more accurate inner product estimation and better recognition accuracy while at the cost of higher computational complexity with larger k, and vice versa. Because the X i 2 and W j 2 are not strictly bounded, the approximation may suffer from some noises. Anyway, from the abundant experiments in this work, the effectiveness of our approach for training dynamic and sparse neural networks has been validated.",1718,0.809,975,1.7620512820512821,"We propose execute compressive memory accelerative execution during both training inference The great success DNNs motivates the pursuing lightweight models the deployment onto However most optimize inference while neglect training or even complicate Training far since ( the neurons dominate the memory cost rather the weights inference the dynamic activation makes previous sparse acceleration via one-off optimization on fixed weight invalid;BN critical maintaining accuracy while its activation reorganization damages To address DSG activates neurons with each iteration via a dimensionreduction search obtains the BN compatibility via Experiments significant memory saving ( operation reduction little accuracy loss various benchmarks Deep Neural BID23 have achieving (Simonyan & Zisserman BID0 Redmon Farhadi , while the models extremely memoryand compute The high representational and computational costs motivate approaches on improving, matrix or BID44 Novikov Garipov BID47 BID3 , data quantizationCourbariaux network pruning a; Molchanov Spring & Chin . However most the previous work aim inference while the challenges reducing training well Although some works demonstrate acceleration the distributed training BID29 BID6 target at the single-node optimization our method boost DNN training demands much more hardware resources in both memory capacity computation volume far inference Firstly activation data training will significantly Secondly training iteratively updates model parameters We almost expect larger minibatches higher throughput FIG0 ), faster convergence accuracy (Smith 2017 However memory capacity the limitation factor FIG0 Upper one are the feature maps before BN However using BN damages the sparsity through information fusion; (f There exists such great representational redundancy activations close zero.that may make large models with deep structures or targeting high-resolution vision tasks hard train BID42 .It apply towards inference phase to training phase 1 Prior arts mainly compress the pre-trained and fixed weight parameters the off-chip memory access in inference BID9 while instead the dynamic neuronal activations turn the crucial bottleneck making the prior inference-oriented methods inefficient Besides , during training need stash a vast batched activation space the backward gradient calculation Therefore , neuron activations creates a new memory bottleneckFigure In sparsify the neuron activations for training compression.2) The existing inference accelerations usually add extra optimization problems onto the critical path Molchanov 2016 BID30 BID27 , i.e., 'complicated training �� simplified inference embarrassingly 3 Moreover , previous studies reveal that batch normalizationBN crucial improving accuracy FIG0 ) through activation fusion across different samples within one mini for better representationMorcos 2018 BID16 . BN almost becomes a standard training configuration; inference-oriented methods seldom discuss treat scaling and shift factors the forward pass We further BN will damage the sparsity due the activation reorganization FIG0 Since this work targets both training inference the BN compatibility problemFrom information representation the activation each neuron reflects the current stimulus sampleMorcos 2018 , this selectivity dataflow propagates layer forming different representation levels Fortunately , much representational redundancy for lots neuron activations each stimulus sample so can removed FIG0 Motivated above comprehensive analysis regarding memory compute search critical neurons constructing a sparse graph at every iteration By activating neurons with significantly save memory simplify computation with tolerable accuracy degradation Because the neuron response dynamically under different stimulus samples the sparse graph variable The neuronaware dynamic and sparse graph ( fundamentally distinct static previous work permanent weight pruning since never prune but activate part them each Therefore maintain the model expressive power much A graph selection method , dimension-reduction search is designed both compressible activations with elementwise unstructured sparsity accelerative vector-matrix multiplication Through double-mask selection design also compatible BN. We the same selection pattern extend our method inference In propose a compressible and accelerative DSG approach supported dimension-reduction search doublemask selection It can achieve minimal accuracy loss This work simultaneously pioneers towards efficient online training offline inference benefit in the edge In DSG (dynamic and sparse graph) structure efficient DNN training through a dimension-reduction search based sparsity forecast compressive memory accelerative execution and a double-mask selection BN compatibility without sacrificing model's expressive power It can easily extended the inference by the same selection pattern after training Our experiments over various benchmarks demonstrate significant memory saving training inference computation reduction Through significantly boosting both forward passes training as inference DSG promises efficient deep learning edge. DISPLAYFORM0 Further recalling the norm preservation equation the main text: there exist a linear map f : R d �� R k and 0 < ≤ we FORMULA0 yields , finally It X i W j pair the inner product can preserved is sufficiently Actually previous work BID1 discussed on the random projection for various big data applications here re these supporting materials form a systematic proof We hope could readers follow this paper In practical experiments there exists the dimension reduction degree the recognition accuracy Smaller usually brings more accurate inner product estimation better recognition accuracy while higher computational complexity with larger k, vice Because the X i 2 W j strictly bounded the approximation may suffer some noises Anyway from the abundant experiments the effectiveness our approach training dynamic and sparse neural networks validated",0.01,0.6457188832568996
"Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper confidence bound algorithms and Thompson sampling fail to appropriately account for heteroscedasticity, even in the bandit setting. Motivated by recent findings that address this issue in bandits, we propose to use Information-Directed Sampling (IDS) for exploration in reinforcement learning. As our main contribution, we build on recent advances in distributional reinforcement learning and propose a novel, tractable approximation of IDS for deep Q-learning. The resulting exploration strategy explicitly accounts for both parametric uncertainty and heteroscedastic observation noise. We evaluate our method on Atari games and demonstrate a significant improvement over alternative approaches. In Reinforcement Learning (RL), an agent seeks to maximize the cumulative rewards obtained from interactions with an unknown environment. Given only knowledge based on previously observed trajectories, the agent faces the exploration-exploitation dilemma: Should the agent take actions that maximize rewards based on its current knowledge or instead investigate poorly understood states and actions to potentially improve future performance. Thus, in order to find the optimal policy the agent needs to use an appropriate exploration strategy.Popular exploration strategies, such as -greedy BID37 , rely on random perturbations of the agent's policy, which leads to undirected exploration. The theoretical RL literature offers a variety of statistically-efficient methods that are based on a measure of uncertainty in the agent's model. Examples include upper confidence bound (UCB) BID0 and Thompson sampling (TS) BID40 . In recent years, these have been extended to practical exploration algorithms for large state-spaces and shown to improve performance BID27 O'Donoghue et al., 2018; BID15 . However, these methods assume that the observation noise distribution is independent of the evaluation point, while in practice heteroscedastic observation noise is omnipresent in RL. This means that the noise depends on the evaluation point, rather than being identically distributed (homoscedastic). For instance, the return distribution typically depends on a sequence of interactions and, potentially, on hidden states or inherently heteroscedastic reward observations. BID20 recently demonstrated that, even in the simpler bandit setting, classical approaches such as UCB and TS fail to efficiently account for heteroscedastic noise.In this work, we propose to use Information-Directed Sampling (IDS) BID31 BID20 for efficient exploration in RL. The IDS framework can be used to design exploration-exploitation strategies that balance the estimated instantaneous regret and the expected information gain. Importantly, through the choice of an appropriate information-gain function, IDS is able to account for parametric uncertainty and heteroscedastic observation noise during exploration.As our main contribution, we propose a novel, tractable RL algorithm based on the IDS principle. We combine recent advances in distributional RL BID4 BID12 and approximate parameter uncertainty methods in order to develop both homoscedastic and heteroscedastic variants of an agent that is similar to DQN BID25 , but uses informationdirected exploration. Our evaluation on Atari 2600 games shows the importance of accounting for heteroscedastic noise and indicates that at our approach can substantially outperform alternative state-of-the-art algorithms that focus on modeling either only epistemic or only aleatoric uncertainty. To the best of our knowledge, we are the first to develop a tractable IDS algorithm for RL in large state spaces. We extended the idea of frequentist Information-Directed Sampling to a practical RL exploration algorithm that can account for heteroscedastic noise. To the best of our knowledge, we are the first to propose a tractable IDS algorithm for RL in large state spaces. Our method suggests a new way to use the return distribution in combination with parametric uncertainty for efficient deep exploration and demonstrates substantial gains on Atari games. We also identified several sources of heteroscedasticity in RL and demonstrated the importance of accounting for heteroscedastic noise for efficient exploration. Additionally, our evaluation results demonstrated that similarly to the bandit setting, IDS has the potential to outperform alternative strategies such as TS in RL.There remain promising directions for future work. Our preliminary results show that similar improvements can be observed when IDS is combined with continuous control RL methods such as the Deep Deterministic Policy Gradient (DDPG) BID23 . Developing a computationally efficient approximation of the randomized IDS version, which minimizes the regret-information ratio over the set of stochastic policies, is another idea to investigate. Additionally, as indicated by BID31 , IDS should be seen as a design principle rather than a specific algorithm, and thus alternative information gain functions are an important direction for future research.",953,0.507,594,1.6043771043771045,"Efficient exploration remains reinforcement learning One reason the variability the returns often and action, heteroscedastic Classical exploration strategies such upper confidence bound algorithms Thompson sampling fail appropriately even the bandit setting Motivated recent findings address this issue bandits Information-Directed Sampling (IDS exploration in reinforcement learning As our main contribution build recent advances distributional reinforcement learning propose tractable approximation IDS deep Q-learning The resulting exploration strategy explicitly accounts both parametric uncertainty heteroscedastic observation noise We evaluate our method on Atari games demonstrate alternative approaches In Reinforcement LearningRL an agent seeks maximize the cumulative rewards obtained interactions an unknown environment Given only knowledge based previously observed trajectories the agent faces the exploration-exploitation dilemma Should take actions maximize rewards based instead investigate poorly understood states actions potentially. Thus find the optimal policy the agent use an appropriate exploration strategyPopular exploration strategies -greedy BID37 , rely random perturbations leads undirected exploration The theoretical RL literature offers statistically-efficient methods a measure uncertainty Examples include upper confidence bound (UCB) BID0 Thompson sampling In these have extended practical exploration algorithms large state-spaces shown BID27 O'Donoghue 2018 . However these methods assume the observation noise distribution the evaluation point while practice heteroscedastic observation noise omnipresent RL This means the noise depends the evaluation point rather being identically (homoscedastic For instance the return distribution typically a sequence interactions and, potentially hidden states inherently heteroscedastic reward observations BID20 recently demonstrated, the simpler bandit setting classical approaches such UCB TS fail efficiently accountIn Information-Directed Sampling (IDS BID31 BID20 efficient exploration in RL. The IDS framework can design exploration-exploitation strategies balance the estimated instantaneous regret the expected information gain Importantly through the choice an appropriate information-gain function IDS account parametric uncertainty heteroscedastic observation noise during explorationAs our main contribution propose, tractable RL We combine recent advances distributional RL BID4 BID12 approximate parameter uncertainty methods an agent similar DQN BID25 , uses informationdirected exploration Our evaluation on Atari 2600 games the importance accounting heteroscedastic noise indicates at our approach can substantially alternative state algorithms focus modeling either only epistemic only aleatoric uncertainty To we develop a tractable IDS algorithm RL in large state spaces We extended the idea frequentist Information-Directed Sampling a practical RL exploration algorithm account heteroscedastic noise To we propose a tractable IDS algorithm RL in large state spaces Our method suggests use the return distribution combination parametric uncertainty for efficient deep exploration demonstrates substantial gains on Atari games We also identified several sources RL and demonstrated accounting for efficient exploration Additionally our evaluation results demonstrated similarly to the bandit setting IDS alternative strategies TS in RL.There remain promising directions Our preliminary results similar improvements IDS continuous control RL methods the Deep Deterministic Policy Gradient BID23 . Developing a computationally efficient approximation the randomized IDS version the regret-information ratio over stochastic policies another idea investigate Additionally as indicated BID31 , IDS should seen a design principle alternative information gain functions an important direction",0.01,0.24397893164487455
"We address the problem of learning structured policies for continuous control. In traditional reinforcement learning, policies of agents are learned by MLPs which take the concatenation of all observations from the environment as input for predicting actions. In this work, we propose NerveNet to explicitly model the structure of an agent, which naturally takes the form of a graph. Specifically, serving as the agent's policy network, NerveNet first propagates information over the structure of the agent and then predict actions for different parts of the agent. In the experiments, we first show that our NerveNet is comparable to state-of-the-art methods on standard MuJoCo environments. We further propose our customized reinforcement learning environments for benchmarking two types of structure transfer learning tasks, i.e., size and disability transfer. We demonstrate that policies learned by NerveNet are significantly better than policies learned by other models and are able to transfer even in a zero-shot setting.
 Deep reinforcement learning (RL) has received increasing attention over the past few years, with the recent success of applications such as playing Atari Games, Mnih et al. (2015) , and Go, BID26 . Significant advances have also been made in robotics using the latest RL techniques, e.g., BID1 ; BID19 .Many RL problems feature agents with multiple dependent controllers. For example, humanoid robots consist of multiple physically linked joints. Action to be taken by each joint or the body should thus not only depend on its own observations but also on actions of other joints.Previous approaches in RL typically use MLP to learn the agent's policy. In particular , MLP takes the concatenation of observations from the environment as input, which may be measurements like positions, velocities of body and joints in the current time instance. The MLP policy then predicts actions to be taken by every joint and body. Thus the task of the MLP policy is to discover the latent relationships between observations. This typically leads to longer training times, requiring more exposure of the agent to the environment. In our work, we aim to exploit the body structure of an agent, and physical dependencies that naturally exist in such agents.We rely on the fact that bodies of most robots and animals have a discrete graph structure. Nodes of the graph may represent the joints, and edges represent the (physical) dependencies between them. In particular, we define the agent's policy using a Graph Neural Network, Scarselli et al. (2009) , which is a neural network that operates over graph structures. We refer to our model as NerveNet due to the resemblance of the neural nervous system to a graph. NerveNet propagates information between different parts of the body based on the underlying graph structure before outputting the action for each part. By doing so, NerveNet can leverage the structure information encoded by the agent's body which is advantageous in learning the correct inductive bias, and thus is less prone to Figure 1: Visualization of the graph structure of CentipedeEight in our environment. We use this agent for testing the ability of transfer learning of our model. Since for this agent, each body node is paired with at least one joint node, we omit the body nodes and fill up the position with the corresponding joint nodes. By omitting the body nodes, a more compact graph is constructed, the details of which are illustrated in the experimental section.overfitting. Moreover, NerveNet is naturally suitable for structure transferring tasks as most of the model weights are shared across the nodes and edges, respectively.We first evaluate our NerveNet on standard RL benchmarks such as the OpenAI Gym, BID5 which stem from MuJoCo. We show that our model achieves comparable results to state-of-the-art MLP based methods. To verify our claim regarding the structure transfer , we further introduce our customized RL environments which are based on the ones of Gym. Two types of structure transfer tasks are designed, size transfer and disability transfer. In particular, size transfer focuses on the scenario in which policies are learned for small-sized agents (simpler body structure) and applied directly to large-sized agents which are composed by some repetitive components shared with the small-sized agent. Secondly, disability transfer investigates scenarios in which policies are learned for one agent and applied to the same agent with some components disabled. Our experiments demonstrate that for structure transfer tasks our NerveNet is significantly better than all other competitors, and can even achieve zero-shot learning for some agents. For the multi-task learning tasks, NerveNet is also able to learn policies that are more robust with better efficiency.The main contribution of this paper is the following: We explore the problem of learning transferable and generalized features by incorporating a prior on the structure via graph neural networks. NerveNet permits powerful transfer learning from one structure to another, which goes well beyond the ability of previous models. NerveNet is also more robust and has more potential in performing multi-task learning. The demo and code for this project are released, under the project page of http://www.cs.toronto.edu/˜tingwuwang/nervenet.html. In this paper, we aimed to exploit the body structure of Reinforcement Learning agents in the form of graphs. We introduced a novel model called NerveNet which uses a Graph Neural Network to represent the agent's policy. At each time instance of the environment, NerveNet takes observations for each of the body joints, and propagates information between them using non-linear messages computed with a neural network. Propagation is done through the edges which represent natural dependencies between joints, such as physical connectivity. We experimentally showed that our NerveNet achieves comparable performance to state-of-the-art methods on standard MuJoCo environments. We further propose our customized reinforcement learning environments for benchmarking two types of structure transfer learning tasks, i.e., size and disability transfer. We demonstrate that policies learned by NerveNet are significantly better than policies learned by other models and are able to transfer even in a zero-shot setting.",1203,0.698,710,1.6943661971830986,"We address learning structured policies continuous control In traditional reinforcement learning policies agents learned MLPs which take all observations for predicting actions In NerveNet explicitly model an agent naturally takes Specifically serving the agent's policy network NerveNet first propagates over the structure predict actions different parts In the experiments first show our NerveNet comparable state methods on standard MuJoCo environments We further propose our customized reinforcement learning environments benchmarking two types structure transfer learning tasks size disability transfer We demonstrate policies learned NerveNet significantly able transfer even in a zero-shot setting Deep reinforcement learningRL received applications playing Atari Games Mnih et al (2015 , and Go BID26 . Significant advances also robotics using the latest RL techniques BID1 ; BID19 .Many RL problems feature agents multiple dependent controllers For example humanoid robots consist multiple physically linked joints Action to each joint or the body should thus depend its own observations actionsPrevious approaches RL typically use MLP learn the agent's policy In particular , MLP takes observations the environment measurements like positions of body joints the current time instance The MLP policy then predicts actions every joint and body. Thus the task the MLP policy discover the latent relationships observations. This typically leads longer training times requiring of In our work aim exploit the body structure an agent physical dependencies naturallyWe rely bodies most robots a discrete graph structure Nodes the graph may represent the joints edges the (physical) dependencies In particular define the agent's policy using a Graph Neural Network Scarselli et al (2009 , which operates graph structures We refer our model NerveNet due a graph NerveNet propagates between based the underlying graph structure before the action for By doing NerveNet leverage the structure information encoded which advantageous learning the correct inductive bias is Figure: Visualization the graph structure CentipedeEight our environment We use this agent testing transfer learning of our model Since for this agent each body node paired omit fill up By omitting the body nodes a more compact graph the details the experimental section.overfitting Moreover NerveNet naturally suitable structure transferring tasks most the model weights shared edges respectivelyWe first evaluate on standard RL benchmarks such the OpenAI Gym BID5 which stem MuJoCo state MLP based methods To verify our claim regarding the structure transfer , further introduce our customized RL environments the ones Gym. Two types structure transfer tasks designed size transfer disability transfer In particular size transfer focuses the scenario policies learned for small-sized agentssimpler body structure directly which composed by some repetitive components shared Secondly disability transfer investigates scenarios policies learned for one agent with some components disabled Our experiments demonstrate for structure transfer tasks our NerveNet all other competitors can zero-shot learning some agents For the multi-task learning tasks NerveNet also learn policies robust with better efficiencyThe main contribution We explore transferable and generalized features incorporating prior on via graph neural networks NerveNet permits powerful transfer learning one structure goes previous models NerveNet also more robust potential performing The demo and code released, under the project page http://www.cs.toronto.edu/˜tingwuwang/nervenet.html In aimed exploit the body structure Reinforcement Learning agents graphs We introduced called NerveNet a Graph Neural Network the agent's policy At each time instance the environment NerveNet takes observations for the body joints information between computed Propagation done the edges which represent natural dependencies joints physical connectivity We experimentally showed our NerveNet achieves comparable performance state methods on standard MuJoCo environments We further propose our customized reinforcement learning environments benchmarking two types structure transfer learning tasks size disability transfer We demonstrate policies learned NerveNet significantly able transfer even in a zero-shot setting",0.01,0.47326323375930224
"Real-world tasks are often highly structured. Hierarchical reinforcement learning (HRL) has attracted research interest as an approach for leveraging the hierarchical structure of a given task in reinforcement learning (RL). However, identifying the hierarchical policy structure that enhances the performance of RL is not a trivial task. In this paper, we propose an HRL method that learns a latent variable of a hierarchical policy using mutual information maximization. Our approach can be interpreted as a way to learn a discrete and latent representation of the state-action space. To learn option policies that correspond to modes of the advantage function, we introduce advantage-weighted importance sampling.  
 In our HRL method, the gating policy learns to select option policies based on an option-value function, and these option policies are optimized based on the deterministic policy gradient method. This framework is derived by leveraging the analogy between a monolithic policy in standard RL and a hierarchical policy in HRL by using a deterministic option policy.   Experimental results indicate that our HRL approach can learn a diversity of options and that it can enhance the performance of RL in continuous control tasks. Reinforcement learning (RL) has been successfully applied to a variety of tasks, including board games BID13 , robotic manipulation tasks (Levine et al., 2016) , and video games (Mnih et al., 2015) . Hierarchical reinforcement learning (HRL) is a type of RL that leverages the hierarchical structure of a given task by learning a hierarchical policy BID15 Dietterich, 2000) . Past studies in this field have shown that HRL can solve challenging tasks in the video game domain BID18 BID0 and robotic manipulation BID3 BID9 . In HRL, lower-level policies, which are often referred to as option policies, learn different behavior/control patterns, and the upper-level policy, which is often referred to as the gating policy, learns to select option policies. Recent studies have developed HRL methods using deep learning (Goodfellow et al., 2016) and have shown that HRL can yield impressive performance for complex tasks BID0 Frans et al., 2018; BID18 Haarnoja et al., 2018a) . However, identifying the hierarchical policy structure that yields efficient learning is not a trivial task, since the problem involves learning a sufficient variety of types of behavior to solve a given task.In this study, we present an HRL method via the mutual information (MI) maximization with advantage-weighted importance, which we refer to as adInfoHRL. We formulate the problem of learning a latent variable in a hierarchical policy as one of learning discrete and interpretable repre-sentations of states and actions. Ideally, each option policy should be located at separate modes of the advantage function. To estimate the latent variable that corresponds to modes of the advantage function, we introduce advantage-weighted importance weights. Our approach can be considered to divide the state-action space based on an information maximization criterion, and it learns option policies corresponding to each region of the state-action space. We derive adInfoHRL as an HRL method based on deterministic option policies that are trained based on an extension of the deterministic policy gradient BID12 Fujimoto et al., 2018) . The contributions of this paper are twofold:1. We propose the learning of a latent variable of a hierarchical policy as a discrete and hidden representation of the state-action space. To learn option policies that correspond to the modes of the advantage function, we introduce advantage-weighted importance. 2. We propose an HRL method, where the option policies are optimized based on the deterministic policy gradient and the gating policy selects the option that maximizes the expected return. The experimental results show that our proposed method adInfoHRL can learn a diversity of options on continuous control tasks. Moreover, our approach can improve the performance of TD3 on such tasks as the Walker2d and Ant tasks in OpenAI Gym with MuJoco simulator. We proposed a novel HRL method, hierarchical reinforcement learning via advantage-weighted information maximization. In our framework, the latent variable of a hierarchical policy is learned as a discrete latent representation of the state-action space. Our HRL framework is derived by considering deterministic option policies and by leveraging the analogy between the gating policy for HRL and a monolithic policy for the standard RL. The results of the experiments indicate that adInfoHRL can learn diverse options on continuous control tasks. Our results also suggested that our approach can improve the performance of TD3 in certain problem domains.",915,0.53,573,1.5968586387434556,"Real-world tasks highly structured Hierarchical reinforcement learning attracted research interest leveraging the hierarchical structureRL However identifying the hierarchical policy structure enhances RL In an HRL method learns a latent variable a hierarchical policy using mutual information maximization Our approach can interpreted learn a discrete and latent representation the state-action space To learn option policies that correspond modes the advantage function introduce advantage-weighted importance sampling In our HRL method the gating policy learns select option policies an option-value function optimized the deterministic policy gradient method This framework derived by leveraging the analogy a monolithic policy in standard RL HRL by a deterministic option policy Experimental results our HRL approach learn a diversity options that enhance RL in continuous control tasks Reinforcement learningRL successfully board games BID13 , robotic manipulation tasksLevine 2016Mnih et al Hierarchical reinforcement learning RL by a hierarchical policy BID15 Dietterich 2000) Past studies HRL can solve challenging tasks the video game domain BID18 BID0 and robotic manipulation In HRL lower-level policies referred option policies learn different behavior/control patterns the gating policy select option policies Recent studies developed HRL methods using deep learningGoodfellow have yield impressive performance BID0 Frans 2018 BID18 Haarnoja) . However identifying the hierarchical policy structure yields efficient learning involves learning a sufficient variety types behavior solveIn an HRL method via mutual information (MI maximization with advantage-weighted importance, refer adInfoHRL We formulate the problem learning a latent variable a hierarchical policy as one learning discrete and interpretable repre states actions Ideally each option policy located separate modes the advantage function To estimate the latent variable that corresponds modes the advantage function introduce advantage-weighted importance weights Our approach can considered divide the state-action space based an information maximization criterion learns option policies corresponding each region We derive adInfoHRL as based deterministic option policies trained based an extension the deterministic policy gradient BID12 Fujimoto et al 2018) . The contributions this paper We propose the learning a latent variable a hierarchical policy as a discrete and hidden representation the state-action space To learn option policies that correspond the modes the advantage function introduce advantage-weighted importance 2 We propose an HRL method, the option policies optimized based the deterministic policy gradient the gating policy selects The experimental results our proposed method adInfoHRL can learn a diversity options on continuous control tasks Moreover our approach can improve TD3 on such tasks the Walker2d Ant tasks OpenAI Gym with MuJoco simulator We proposed a novel HRL method hierarchical reinforcement learning via advantage-weighted information maximization In our framework the latent variable a hierarchical policy learned a discrete latent representation the state-action space Our HRL framework derived by considering deterministic option policies by leveraging the analogy the gating policy for a monolithic policy the standard RL The results the experiments indicate adInfoHRL can learn diverse options on continuous control tasks Our results also suggested our approach can TD3 certain problem domains",0.01,0.2248225417755051
"Deep neural networks (DNNs) have achieved impressive predictive performance due to their ability to learn complex, non-linear relationships between variables. However, the inability to effectively visualize these relationships has led to DNNs being characterized as black boxes and consequently limited their applications. To ameliorate this problem, we introduce the use of hierarchical interpretations to explain DNN predictions through our proposed method: agglomerative contextual decomposition (ACD). Given a prediction from a trained DNN, ACD produces a hierarchical clustering of the input features, along with the contribution of each cluster to the final prediction. This hierarchy is optimized to identify clusters of features that the DNN learned are predictive. We introduce ACD using examples from Stanford Sentiment Treebank and ImageNet, in order to diagnose incorrect predictions, identify dataset bias, and extract polarizing phrases of varying lengths. Through human experiments, we demonstrate that ACD enables users both to identify the more accurate of two DNNs and to better trust a DNN's outputs. We also find that ACD's hierarchy is largely robust to adversarial perturbations, implying that it captures fundamental aspects of the input and ignores spurious noise. Deep neural networks (DNNs) have recently demonstrated impressive predictive performance due to their ability to learn complex, non-linear, relationships between variables. However, the inability to effectively visualize these relationships has led DNNs to be characterized as black boxes. Consequently, their use has been limited in fields such as medicine (e.g. medical image classification BID19 ), policy-making (e.g. classification aiding public policy makers BID6 ), and science (e.g. interpreting the contribution of a stimulus to a biological measurement BID2 ). Moreover, the use of black-box models like DNNs in industrial settings has come under increasing scrutiny as they struggle with issues such as fairness BID8 and regulatory pressure BID13 .To ameliorate these problems, we introduce the use of hierarchical interpretations to explain DNN predictions. Our proposed method, agglomerative contextual decomposition (ACD) 1 , is a general technique that can be applied to a wide range of DNN architectures and data types. Given a prediction from a trained DNN, ACD produces a hierarchical clustering of the input features, along with the contribution of each cluster to the final prediction. This hierarchy is optimized to identify clusters of features that the DNN learned are predictive (see FIG0 .The development of ACD consists of two novel contributions. First, importance scores for groups of features are obtained by generalizing contextual decomposition (CD), a previous method for obtaining importance scores for LSTMs BID23 . This work extends CD to arbitrary DNN architectures, including convolutional neural networks (CNNs). Second, most importantly , we introduce the idea of hierarchical saliency, where a group-level importance measure, in this case CD, is used as a joining metric in an agglomerative clustering procedure. While we focus on DNNs and use CD as our importance measure, this concept is general, and could be readily applied to any model with a suitable measure for computing importances of groups of variables.We demonstrate the utility of ACD on both long short term memory networks (LSTMs) BID15 trained on the Stanford Sentiment Treebank (SST) (Socher et al., 2013) and CNNs trained on MNIST BID17 and ImageNet (Russakovsky et al., 2015) . Through human experiments , we show that ACD produces intuitive visualizations that enable users to better reason about and trust DNNs. In particular, given two DNN models, we show that users can use the output of ACD to select the model with higher predictive accuracy, and that overall they rank ACD as more trustworthy than prior interpretation methods. In addition, we demonstrate that ACD's hierarchy is robust to adversarial perturbations (Szegedy et al., 2013) in CNNs. : ACD illustrated through the toy example of predicting the phrase ""not very good"" as negative. Given the network and prediction , ACD constructs a hierarchy of meaningful phrases and provides importance scores for each identified phrase. In this example, ACD identifies that ""very"" modifies ""good"" to become the very positive phrase ""very good"", which is subsequently negated by ""not"" to produce the negative phrase ""not very good"". Best viewed in color. In this work, we introduce agglomerative contextual decomposition (ACD), a novel hierarchical interpretation algorithm. ACD is the first method to use a hierarchy to interpret individual neural network predictions. Doing so enables ACD to automatically detect and display non-linear contributions to individual DNN predictions, something prior interpretation methods are unable to do. The benefits of capturing the non-linearities inherent in DNNs are demonstrated through human experiments and examples of diagnosing incorrect predictions and dataset bias. We also demonstrate that ACD's hierarchy is robust to adversarial perturbations in CNNs, implying that it captures fundamental aspects of the input and ignores spurious noise.ACD SUPPLEMENT S1 CD SCORE COMPARISONS FIG0 : Intuition for CD run on a corner-shaped blob compared to build-up and occlusion. CD decomposes a DNN's feedforward pass into a part from the blob of interest (top row) and everything else (second row). Left column shows original image with overlaid blob. Other columns show DNN activations summed over the filter dimension. Top and third rows are on same color scale. Second and bottom rows are on same color scale. FIG1 : Comparing unit-level CD scores for the correct class to scores from baseline methods. In each case, the model correctly predicts the label, shown on the y axis. Blue is positive, white is neutral, and red is negative. Best viewed in color. FIG0 gives intuition for CD on the VGG-16 ImageNet model described in Sec 4. CD keeps track of the contributions of the blob and non-blob throughout the network. This is intuitively similar to the occlusion and build-up methods, shown in the bottom two rows. The build-up method sets everything but the patch of interest to a references value (often zero). These rows compare the CD decomposition to perturbing the input as in the occlusion and build-up methods. They are similar in early layers, but differences become apparent in later layers.",1287,0.728,763,1.6867627785058978,"Deep neural networks achieved impressive predictive performance due learn variables However the inability effectively visualize these relationships DNNs characterized black boxes consequently limited their applications To introduce hierarchical interpretations DNN predictions through our proposed method: agglomerative contextual decomposition Given a prediction a trained DNN ACD produces the input features along the contribution each cluster This hierarchy optimized identify clusters features the DNN learned are predictive We introduce ACD using examples Stanford Sentiment Treebank ImageNet in diagnose incorrect predictions, identify dataset bias extract polarizing phrases of varying lengths Through human experiments demonstrate ACD enables users both identify more accurate of two DNNs better trust We also find ACD's hierarchy largely robust implying captures fundamental aspects the input ignores spurious noise Deep neural networks impressive predictive performance due learn variables However the inability effectively visualize these relationships DNNs characterized black boxes their use has fields ( BID19 policy- classification aiding public policy makers science interpreting the contribution a stimulus a biological measurement Moreover the use black-box models like DNNs industrial settings come struggle issues fairness BID8 regulatory pressure BID13 .To introduce hierarchical interpretations explain DNN predictions Our proposed method, agglomerative contextual decomposition 1 a general technique DNN architectures data types Given a prediction a trained DNN ACD produces the input features along the contribution each cluster This hierarchy optimized identify clusters features the DNN learned are predictive ( FIG0 .The development ACD consists two novel contributions. First importance scores groups features obtained generalizing contextual decompositionCD a previous method obtaining LSTMs BID23 . This work extends CD to arbitrary DNN architectures Second most importantly , introduce hierarchical saliency a group-level importance measure in CD a joining metric While focus DNNs use CD as our importance measure this concept general could readily any model a suitable measure computing importances groups variablesWe demonstrate ACD on both long short term memory networks BID15 trained the Stanford Sentiment Treebank (Socher CNNs and ImageNetRussakovsky . Through human experiments , show ACD produces intuitive visualizations enable better reason and trust DNNs given users the output select overall they rank prior interpretation methods In addition demonstrate ACD's hierarchy robustSzegedy CNNs : illustrated through the toy example predicting the phrasenot very as negative Given the network and prediction , ACD constructs a hierarchy meaningful phrases provides importance scores In ACD identifies that ""very"" modifies ""good become the very positive phrase subsequently negatednot produce Best viewed color In this work introduce agglomerative contextual decomposition a novel hierarchical interpretation algorithm ACD the first method use a hierarchy interpret individual neural network predictions Doing enables ACD automatically display non-linear contributions individual DNN predictions something prior interpretation methods are The benefits capturing nonlinearities inherent DNNs demonstrated through human experiments examples diagnosing incorrect predictions dataset bias We also demonstrate ACD's hierarchy robust CNNs implying captures fundamental aspects the input ignores spurious noiseACD SUPPLEMENT S1 CD SCORE COMPARISONS FIG0 : for CD run on a corner-shaped blob compared build-up and CD decomposes a DNN's feedforward pass into a part from the blob interesttop row everything Left column shows original image with overlaid blob Other columns show DNN activations summed the filter dimension Top and third rows on same color scale Second and bottom rows on same color scale FIG1 : Comparing unit-level CD scores the correct class to scores baseline methods In each case the model correctly the label shown Blue is positive Best viewed color FIG0 gives intuition CD on the VGG-16 ImageNet model described Sec 4 CD keeps the contributions the blob non throughout This intuitively similar the occlusion and build-up methods shown the bottom two rows The build-up method sets everything but the patch of interest a references valueoften zero These rows compare the CD decomposition to perturbing the input as in the occlusion and build-up methods They similar early layers differences become",0.01,0.45389039099885553
"Principal Filter Analysis (PFA) is an easy to implement, yet effective method for neural network compression. PFA exploits the intrinsic correlation between filter responses within network layers to recommend a smaller network footprint. We propose two compression algorithms: the first allows a user to specify the proportion of the original spectral energy that should be preserved in each layer after compression, while the second is a heuristic that leads to a parameter-free approach that automatically selects the compression used at each layer. Both algorithms are evaluated against several architectures and datasets, and we show considerable compression rates without compromising accuracy, e.g., for VGG-16 on CIFAR-10, CIFAR-100 and ImageNet, PFA achieves a compression rate of 8x, 3x, and 1.4x with an accuracy gain of 0.4%, 1.4% points, and 2.4% respectively. In our tests we also demonstrate that networks compressed with PFA achieve an accuracy that is very close to the empirical upper bound for a given compression ratio. Finally, we show how PFA is an effective tool for simultaneous compression and domain adaptation. Despite decades of research, the design of neural networks is still an empirical process. Practitioners make design choices, such as the number of layers, type of layers, number of filters per layer, etc., based on intuition or brute-force search. Nevertheless, the performance of these algorithms, together with the advances of GPU devices, have led to a growing popularity of these techniques in both academia and industry. Recent advances are unveiling some properties of neural networks. For example, there is a consensus that depth can accelerate learning, and that wider layers help optimization BID2 BID29 . However, in practical applications, the size of these networks is often a limiting factor when deploying on devices with constrained storage, memory, and computation resources.Another known neural network property is that the responses of a layer exhibit considerable correlation BID12 , inspiring the idea of learning decorrelated filters BID8 BID38 . These algorithms propose a modified loss function to encourage decorrelation during training and show that accuracy improves with decorrelated filters. However, such algorithms focus on training and do not address network compression. Our hypothesis is that layers that exhibit high correlation in filter responses could learn equally well using a smaller number of filters.Principal Filter Analysis (PFA) draws from the recent findings that it is easier to start with an overparametrized network and it then exploits intra-layer correlation for guiding network compression. PFA analyzes a trained network and is agnostic to the training methodology and the loss function. Inference is performed on a dataset, and the correlation within the responses of each layer is used to provide a compression recipe. A new smaller architecture based on this recipe can then be retrained.We propose two closed-form algorithms based on spectral energy analysis for suggesting the number of filters to remove in a layer:PFA-En uses Principal Component Analysis (PCA) BID21 to allow a user to specify the proportion of the energy in the original response that should be preserved in each layer; PFA-KL is a heuristic that leads to a parameter-free approach that uses Kullback-Leibler (KL) divergence BID24 to identify the number of redundant filters.Based on the new suggested number of filters per layer identified by PFA, we remove those that are maximally correlated with other filters and fine-tune the network by retraining. Both PFA algorithms are straightforward to implement and, as shown in Sec. 4, they achieve better compression and, in most cases, better accuracy than the state of the art on several datasets and architectures. In Sec. 4 we also show how PFA can be used to perform simulations compression and domain adaptation. Two effective, and yet easy to implement techniques for the compression of neural networks using Principal Filter Analysis were presented: PFA-En and PFA-KL. These techniques exploit the inherent correlation of filter responses within layers to compress networks without compromising accuracy. These techniques can be applied to the output response of any layer with no knowledge of the training procedure or the loss function. While easy to implement, both algorithms surpass state of the art results in terms or compression ratio with the advantage that PFA-KL is parameter free and PFA-En has only a single intuitive parameter: the energy to be preserved in each layer or a desired network characteristic (such as a target footprint or FLOPs).By performing spectral analysis on the responses rather than the weights, PFA allows users to take advantage of transfer learning in order to perform domain adaptation and derive smaller specialized networks that are optimally designed for a specific task, while starting from the same base model.It is interesting to observe that all compression algorithms in the state of art, including PFA-KL, do not converge if applied repeatedly. This is due to the retraining step which alters the weights in order to optimize an objective function that does not take into account compression criteria. In practical applications this is not a limitation since most of the models tend to be over specified and users can apply compression algorithms until the accuracy falls below an acceptable level. However, it is an interesting theoretical limitation that could inspire future work. Specifically for PFA, this could be a strategy that can also suggest expanding layers so that an optimal size could be reached at convergence.",1069,0.523,618,1.7297734627831716,"Principal Filter Analysis easy implement neural network compression PFA exploits the intrinsic correlation filter responses within network layers recommend a smaller network footprint We propose two compression allows the proportion the original spectral energy preserved after a heuristic leads automatically used at Both algorithms evaluated several architectures datasets we show considerable compression rates without compromising accuracy VGG-16 on ImageNet PFA achieves 8x with an accuracy gain 1.4% points respectively In our tests also demonstrate networks compressed PFA achieve an accuracy very empirical upper a given compression ratio Finally show PFA simultaneous compression and domain adaptation Despite decades the design an empirical process Practitioners make design choices such layers type layers number filters per intuition brute-force search Nevertheless the performance these algorithms, together the advances GPU devices these techniques both academia Recent advances are unveiling some properties neural networks For example there a consensus depth can accelerate learning wider layers help optimization BID2 BID29 . However practical applications the size these networks deploying on devices constrained storage memory computation resourcesAnother known neural network property the responses a layer exhibit considerable correlation BID12 , inspiring learning decorrelated filters BID8 BID38 These algorithms propose a modified loss function encourage decorrelation during training show accuracy improves decorrelated filters However such algorithms focus training do address network compression Our hypothesis layers that exhibit high correlation filter responses could learn equally usingPrincipal Filter Analysis draws the recent findings it easier start an overparametrized network it then exploits intra-layer correlation guiding network compression PFA analyzes a trained network is agnostic the loss function Inference is performed the correlation within the responses each layer provide a compression recipe A new smaller architecture based this recipe then retrainedWe propose two closed-form algorithms spectral energy analysis for suggesting the number filters removePFA-En uses Principal Component Analysis (PCA) BID21 allow a user specify the proportion the original response preserved; a heuristic leads Kullback-Leibler divergence BID24 identify redundant filtersBased the new suggested number per identified, remove those maximally correlated the network retraining. Both PFA algorithms straightforward, shown Sec 4, they achieve better compression, the state on several datasets and architectures In Sec 4 we also show PFA perform simulations compression and domain adaptation Two effective, and yet easy techniques the compression Principal Filter Analysis were presented: PFA-En and These techniques exploit the inherent correlation filter responses within layers compress networks without compromising accuracy These techniques the output response any layer with no knowledge the training procedure the loss function While easy implement both algorithms surpass state terms or compression ratio with the advantage PFA-KL parameter free and PFA-En has only a single intuitive parameter: the energy to preserved each layer or a desired network characteristic a target footprint FLOPs).By performing spectral analysis the responses rather allows users take transfer learning perform domain adaptation derive smaller specialized networks designed startingIt observe all compression algorithms the state art, converge if applied repeatedly This due the retraining step which alters the weights optimize an objective function that does take account compression criteria In practical applications this a limitation since tend over specified users apply compression algorithms until the accuracy falls However an interesting theoretical limitation could inspire Specifically PFA could a strategy also suggest expanding layers so an optimal size could convergence",0.01,0.5634778356599469
"We propose a method to efficiently learn diverse strategies in reinforcement learning for query reformulation in the tasks of document retrieval and question answering. In the proposed framework an agent consists of multiple specialized sub-agents and a meta-agent that learns to aggregate the answers from sub-agents to produce a final answer. Sub-agents are trained on disjoint partitions of the training data, while the meta-agent is trained on the full training set. Our method makes learning faster, because it is highly parallelizable, and has better generalization performance than strong baselines, such as an ensemble of agents trained on the full data. We show that the improved performance is due to the increased diversity of reformulation strategies. Reinforcement learning has proven effective in several language processing tasks, such as machine translation BID12 Ranzato et al., 2015; BID1 , question-answering BID9 Hu et al., 2017) , and text summarization (Paulus et al., 2017) . In reinforcement learning efficient exploration is key to achieve good performance. The ability to explore in parallel a diverse set of strategies often speeds up training and leads to a better policy (Mnih et al., 2016; Osband et al., 2016) .In this work, we propose a simple method to achieve efficient parallelized exploration of diverse policies, inspired by hierarchical reinforcement learning (Singh, 1992; Lin, 1993; Dietterich, 2000; Dayan & Hinton, 1993) . We structure the agent into multiple sub-agents, which are trained on disjoint subsets of the training data. Sub-agents are co-ordinated by a meta-agent, called aggregator, that groups and scores answers from the sub-agents for each given input. Unlike sub-agents , the aggregator is a generalist since it learns a policy for the entire training set.We argue that it is easier to train multiple sub-agents than a single generalist one since each sub-agent only needs to learn a policy that performs well for a subset of examples. Moreover, specializing agents on different partitions of the data encourages them to learn distinct policies, thus giving the aggregator the possibility to see answers from a population of diverse agents. Learning a single policy that results in an equally diverse strategy is more challenging.Since each sub-agent is trained on a fraction of the data, and there is no communication between them, training can be done faster than training a single agent on the full data. Additionally, it is easier to parallelize than applying existing distributed algorithms such as asynchronous SGD or A3C (Mnih et al., 2016) , as the sub-agents do not need to exchange weights or gradients. After training the sub-agents , only their actions need to be sent to the aggregator.We build upon the works of Nogueira & Cho (2017) and Buck et al. (2018b) . Therefore, we evaluate the proposed method on the same tasks they used: query reformulation for document retrieval and question-answering. We show that it outperforms a strong baseline of an ensemble of agents trained on the full dataset. We also found that performance and reformulation diversity are correlated (Sec. 5.5).Our main contributions are the following:1 Under review as a conference paper at ICLR 2019• A simple method to achieve more diverse strategies and better generalization performance than a model average ensemble.• Training can be easily parallelized in the proposed method.• An interesting finding that contradicts our, perhaps naive, intuition: specializing agents on semantically similar data does not work as well as random partitioning. An explanation is given in Appendix F. We proposed a method to build a better query reformulation system by training multiple sub-agents on partitions of the data using reinforcement learning and an aggregator that learns to combine the answers of the multiple agents given a new query. We showed the effectiveness and efficiency of the proposed approach on the tasks of document retrieval and question answering. One interesting orthogonal extension would be to introduce diversity on the beam search decoder BID8 Li et al., 2016) , thus shedding light on the question of whether the gains come from the increased capacity of the system due to the use of the multiple agents, the diversity of reformulations, or both.",872,0.416,517,1.6866537717601546,"We propose efficiently learn diverse strategies for query reformulation the tasks document retrieval question In the proposed framework an agent consists multiple specialized sub learns aggregate the answers sub Sub-agents trained disjoint partitions the training data while the meta-agent Our method makes learning faster because highly parallelizable has better generalization performance strong baselines an ensemble agents trained the full data. We show the improved performance is the increased diversity reformulation strategies Reinforcement learning has proven effective several language processing tasks machine translation BID12 Ranzato BID1 ,) , text summarizationPaulus In reinforcement learning efficient exploration is key achieve The ability explore in parallel a diverse set strategies often speeds training leads a better policy (Mnih et al 2016 Osband .In propose achieve efficient parallelized exploration diverse policies inspired hierarchical reinforcement learningSingh 1992 Lin 1993 Dietterich Dayan & Hinton 1993 We structure the agent multiple sub trained disjoint subsets Sub-agents co a meta-agent called aggregator groups and scores answers for each given input Unlike subagents , the aggregator a generalist since learns a policy the entire training setWe argue easier train one since only that performs examples Moreover specializing agents on different partitions encourages them learn distinct policies thus giving the aggregator the possibility see answers a population diverse agents Learning a single policy that results an equally diverse strategy moreSince each subagent trained a fraction there no communication training faster training Additionally easier parallelize than applying existing distributed algorithms such asynchronous SGD A3C (Mnih et , the subagents exchange weights After training the subagents , only their actions need sent the aggregatorWe build upon the works Nogueira & Cho (2017 Buck (2018b . Therefore evaluate on the same tasks they: query reformulation document retrieval We show it outperforms a strong baseline an ensemble agents trained the full dataset We also found performance reformulation diversitySec 5.5).Our main contributions Under review as a conference paper at ICLR 2019• A simple method achieve more diverse strategies better generalization performance than a model average ensemble.• Training can easily the proposed method.• An interesting finding contradicts our, perhaps naive, intuition specializing agents on semantically similar data does work random partitioning An explanation We proposed build a better query reformulation system training multiple subagents partitions using reinforcement learning an aggregator combine the answers given a new query We showed the effectiveness and efficiency the proposed approach on the tasks document retrieval question One interesting orthogonal extension would introduce diversity on the beam search decoder BID8 Li et) , thus shedding the gains come the increased capacity due the multiple agents the diversity reformulations",0.01,0.4536126513879298
"Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that 'similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if 'similar' means being 'more likely to be connected') or classification (if 'similar' means 'being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes.

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

 We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization. Network Embeddings (NEs) map nodes into d-dimensional Euclidean space R d such that an ordinary distance measure allows for meaningful comparisons between nodes. Embeddings directly enable the use of a variety of machine learning methods (classification, clustering, etc.) on networks, explaining their exploding popularity. NE approaches typically have three components (Hamilton et al., 2017) : (1) A measure of similarity between nodes. E.g. nodes can be deemed more similar if they are adjacent, have strongly overlapping neighborhoods, or are otherwise close to each other (link and path-based measures) BID18 BID20 , or if they have similar functional properties (structural measures) BID19 . FORMULA3 A metric in the embedding space. (3) A loss function comparing similarity between node pairs in the network with the proximity of their embeddings. A good NE is then one for which the average loss is small. The literature on NE has so far considered embeddings as tools that are used on their own. Yet, Euclidean embeddings are unable to accurately reflect certain kinds of network topologies, such that this approach is inevitably limited. We proposed the notion of Conditional Network Embeddings (CNEs), which seeks an embedding of a network that maximally adds information with respect to certain given prior knowledge about the network. This prior knowledge can encode information about the network that cannot be represented well by means of an embedding.We implemented this conceptually novel idea in a new algorithm based on a simple probabilistic model for the joint of the data and the network, which scales similarly to state-of-the-art NE approaches. The empirical evaluation of this algorithm confirms our intuition that the combination of structural prior knowledge and a Euclidean embedding is extremely powerful. This is confirmed empirically for both the tasks of link prediction and multi-label classification, where CNE outperforms a range of state-of-the-art baselines on a wide range of networks.In our future work we intend to investigate other models implementing the idea of conditional NEs, alternative and more scalable optimization strategies, as well as the use of other types of structural information as prior knowledge on the network.",745,0.371,451,1.6518847006651884,"Network Embeddings (NEs map the nodes into $d$-dimensional Euclidean space $ Ideally this mapping such 'similar' nodes mapped onto nearby points such the NE can purposes link predictionif ' means being 'more classificationbeing the same label In various methods NE have all following defining a notion similarity nodestypically some distance measure within a distance measure penalizes large distances similar nodes and A difficulty faced existing methods certain networks fundamentally hard embed due their structural properties: ( multipartiteness, certain degree distributions assortativity To overcome introduce a conceptual innovation the NE literature propose create \emph{Conditional Network Embeddings embeddings maximally add information with given structural properties block densities We use a simple Bayesian approach achieve propose a block stochastic gradient descent fitting it efficiently We demonstrate CNEs superior for link prediction multi-label classification when state methods this without adding significant mathematical or computational complexity Finally illustrate CNE network visualization Network Embeddings (NEs) map nodes into d-dimensional Euclidean space R d such an ordinary distance measure allows meaningful comparisons Embeddings directly enable machine learning methods (classification on networks explaining their exploding popularity NE approaches typically three components (Hamilton et 2017 : A measure similarity nodes. E.g. nodes deemed more similar if adjacent, have strongly overlapping neighborhoods otherwise close each other (link and path-based measures) BID18 BID20 , or similar functional propertiesstructural measures FORMULA3 A metric in the embedding space (3) A loss function comparing similarity node pairs with the proximity their embeddings A good NE is then one for the average loss small The literature NE has so considered embeddings tools on their Yet Euclidean embeddings unable accurately certain kinds network topologies that this approach inevitably limited We proposed the notion Conditional Network Embeddings seeks an embedding that maximally adds information with certain given prior knowledge This prior knowledge can encode the network cannot represented well means.We implemented this conceptually novel idea for the joint of scales similarly state NE approaches The empirical evaluation this algorithm confirms our intuition the combination structural prior knowledge a Euclidean embedding extremely This confirmed empirically for both the tasks link prediction multi-label classification CNE outperforms a range state baselines on networksIn our future work other models implementing the idea conditional NEs alternative and more scalable optimization strategies other types structural information as prior knowledge on",0.0,0.3650241130151412
"This paper studies a class of adaptive gradient based momentum algorithms that update the  search directions and learning rates simultaneously using past gradients. This class, which we refer to as the ''``Adam-type'', includes the popular algorithms such as Adam, AMSGrad, AdaGrad. Despite their popularity in training deep neural networks (DNNs), the convergence of these algorithms for solving  non-convex problems remains an open question. In this paper, we develop an analysis framework and a set of mild sufficient conditions that guarantee the convergence of the Adam-type methods, with a convergence rate of order   $O(\log{T}/\sqrt{T})$ for non-convex stochastic optimization. Our convergence analysis applies to a new algorithm called AdaFom (AdaGrad with First Order Momentum). We show that the conditions are essential, by identifying concrete examples in which violating the conditions makes an algorithm diverge. Besides providing one of the first comprehensive analysis for Adam-type methods in the non-convex setting, our results can also help the practitioners to easily  monitor the progress of algorithms and determine their convergence behavior. First-order optimization has witnessed tremendous progress in the last decade, especially to solve machine learning problems BID3 . Almost every first-order method obeys the following generic form BID4 ), x t+1 = x t − α t ∆ t , where x t denotes the solution updated at the tth iteration for t = 1, 2, . . . , T , T is the number of iterations, ∆ t is a certain (approximate) descent direction, and α t > 0 is some learning rate. The most well-known first-order algorithms are gradient descent (GD) for deterministic optimization (Nesterov, 2013; BID5 and stochastic gradient descent (SGD) for stochastic optimization (Zinkevich, 2003; Ghadimi & Lan, 2013) , where the former determines ∆ t using the full (batch) gradient of an objective function, and the latter uses a simpler but more computationally-efficient stochastic (unbiased) gradient estimate.Recent works have proposed a variety of accelerated versions of GD and SGD (Nesterov, 2013) . These achievements fall into three categories: a) momentum methods (Nesterov, 1983; Polyak, 1964; BID10 which carefully design the descent direction ∆ t ; b) adaptive learning rate methods BID1 BID9 Zeiler, 2012; BID7 which determine good learning rates α t , and c) adaptive gradient methods that enjoy dual advantages of a) and b). In particular, Adam (Kingma & Ba, 2014) , belonging to the third type of methods, has become extremely popular to solve deep learning problems, e.g., to train deep neural networks. Despite its superior performance in practice, theoretical investigation of Adam-like methods for non-convex optimization is still missing.Very recently, the work (Reddi et al., 2018) pointed out the convergence issues of Adam even in the convex setting, and proposed AMSGrad, a corrected version of Adam. Although AMSGrad has made a positive step towards understanding the theoretical behavior of adaptive gradient methods, the convergence analysis of (Reddi et al., 2018) was still very restrictive because it only works for convex problems, despite the fact that the most successful applications are for non-convex problems. Apparently, there still exists a large gap between theory and practice. To the best of our knowledge,• (Practicality) The sufficient conditions we derive are simple and easy to check in practice. They can be used to either certify the convergence of a given algorithm for a class of problem instances, or to track the progress and behavior of a particular realization of an algorithm.• (Tightness and Insight) We show the conditions are essential and ""tight"", in the sense that violating them can make an algorithm diverge. Importantly , our conditions provide insights on how oscillation of a so-called ""effective stepsize"" (that we define later) can affect the convergence rate of the class of algorithms. We also provide interpretations of the convergence conditions to illustrate why under some circumstances, certain Adam-type algorithms can outperform SGD. Notations We use z = x/y to denote element-wise division if x and y are both vectors of size d; x y is element-wise product, x 2 is element-wise square if x is a vector, √ x is element-wise square root if x is a vector, (x) j denotes jth coordinate of x, x is x 2 if not otherwise specified. We use [N ] to denote the set {1, · · · , N }, and use O(·), o(·), Ω(·), ω(·) as standard asymptotic notations. We provided some mild conditions to ensure convergence of a class of Adam-type algorithms, which includes Adam, AMSGrad, AdaGrad, AdaFom, SGD, SGD with momentum as special cases. Apart from providing general convergence guarantees for algorithms, our conditions can also be checked in practice to monitor empirical convergence. To the best of our knowledge, the convergence of Adam-type algorithm for non-convex problems was unknown before. We also provide insights on how oscillation of effective stepsizes can affect convergence rate for the class of algorithms which could be beneficial for the design of future algorithms. This paper focuses on unconstrained non-convex optimization problems, and one future direction is to study a more general setting of constrained non-convex optimization.",1131,0.519,652,1.7346625766871167,"This paper studies a class adaptive gradient based momentum algorithms update the search directions learning simultaneously past gradients This class, we refer the ''``Adam-type includes the popular algorithms such Adam AMSGrad AdaGrad. Despite their popularity training deep neural networks the convergence for solving In develop an analysis framework and mild sufficient conditions guarantee the convergence the Adam-type methods a convergence rate order $ Our convergence analysis applies a new algorithm AdaFom (AdaGrad with First Order Momentum We show the conditions essential, by identifying concrete examples violating makes algorithm diverge Besides providing one the first comprehensive analysis for Adam-type methods the non-convex setting can the practitioners easily monitor algorithms determine their convergence behavior First-order optimization has witnessed tremendous progress especially to solve BID3 . Almost every first-order method obeys the following generic form BID4 ), x t+1 = x t − α t �� t denotes the solution updated the tth iteration for . . . , T , T is iterations �� t a certain (approximate) descent direction α > some learning rate The most well-known first-order algorithms gradient descentGD for deterministic optimizationNesterov BID5 andZinkevich 2003 Ghadimi Lan , where the former determines �� t using the full (batch) gradient an objective functionRecent works proposed accelerated versions GD These achievements fall a) momentum methodsNesterov 1983 Polyak 1964 BID10 which carefully design the descent direction �� t ; b adaptive learning rate methods BID1 BID9 Zeiler 2012 determine good learning rates α t that enjoy dual advantages a and In particular Adam (Kingma & Ba, 2014 , belonging the third type methods become extremely to solve to train Despite its superior performance practice theoretical investigation Adam-like methods missingVery (Reddi 2018 pointed the convergence issues Adam even the convex setting proposed AMSGrad, a corrected version Although AMSGrad made a positive step understanding the theoretical behavior adaptive gradient methods the convergence analysis (Reddi 2018 was very restrictive because works convex problems despite the most successful applications Apparently still exists theory To our knowledge,• (Practicality The sufficient conditions we derive simple easy check in They can either certify the convergence a given algorithm for a class problem instances track and behavior a particular realization an algorithm.• (Tightness Insight We show the conditions are essential and ""tight violating make diverge Importantly , our conditions provide insights on how oscillation a so-called ""effective stepsizethat we define later the class algorithms We also provide interpretations the convergence conditions to illustrate why under certain Adam-type algorithms SGD Notations We z = x/y element-wise division if vectors size d; x y x 2 if � if (x) j denotes jth coordinate x x 2 not otherwise We use [N ] { · · N use O· o �� � standard asymptotic notations We provided some mild conditions convergence a class Adam-type algorithms includes Adam AMSGrad AdaGrad AdaFom SGD with momentum as special cases Apart providing general convergence guarantees algorithms our conditions checked practice monitor empirical convergence To the convergence Adam-type algorithm for unknown We also provide insights oscillation of effective stepsizes can convergence rate for the class algorithms which could beneficial This paper focuses unconstrained non-convex optimization problems one future direction study a more general setting",0.01,0.5759348683343481
"This research paper describes a simplistic architecture named as AANN: Absolute Artificial Neural Network, which can be used to create highly interpretable representations of the input data. These representations are generated by penalizing the learning of the network in such a way that those learned representations correspond to the respective labels present in the labelled dataset used for supervised training; thereby, simultaneously giving the network the ability to classify the input data. The network can be used in the reverse direction to generate data that closely resembles the input by feeding in representation vectors as required. This research paper also explores the use of mathematical abs (absolute valued) functions as activation functions which constitutes the core part of this neural network architecture. Finally the results obtained on the MNIST dataset by using this technique are presented and discussed in brief. In the field of philosophy, there has been a principle known as 'Ockham's Razor' which, in a simplified relevant language states that ""Among the available multiple solutions to the same problem, the simplest one is the best one"". For instance, if there are multiple polynomial functions that fit a given data distribution, the lowest degree one would be preferred BID12 . The technique AANN is driven by this principle. In spite of being elementary in its construction, an AANN is able to classify inputs in the forward direction while being able to generate them back in the reverse direction. It can be visualized to be doing classification in the forward direction whereas performing a regression task in the backward direction.A standalone GAN (Generative Adversarial Network) described in BID2 is able to create representations of the input data by using a novel technique of generating a distribution that contains the original data points as well as data points generated by the Generator part of the network; the distribution is then used by the Discriminator part of the network to classify the data points as genuine or generated. The representations generated by a GAN, although being very effective in creating undistinguishable data points, are however not interpretable and also highly entangled BID1 BID8 . Using an InfoGAN, the problem of entanglement is solved by training in such a way that the network maximises mutual information within small clusters of related latent representations BID1 . Auto-encoder is another technique that uses the concept of encoder-decoder architecture for creating low dimensional representations of the originally very high dimensional input data points. A VAE: Variational Auto-Encoder tries to make the learned representations sparse by using the KL-divergence cost as a regularizer on the final cost of an autoencoder BID5 . Various attempts at combining the two techniques of GAN and VAE have also been made in the unsupervised as well as semi-supervised learning directions BID8 BID7 . However, these techniques kept getting more and more complicated and somewhere in synthesizing these techniques, it is felt that the 'striving for simplicity' principle has been neglected.The Absolute Artificial Neural Network exploits all possible information available in the labelled training datasets to structure the learned representations of the input data. Structurally, an AANN is very similar to a feed forward Neural Network with the distinction that AANN uses the abs function as the activation function of the neurons. Due to this, all the activations produced, including the hidden layer activations, contain positive real number values. Thus, the network runs on the assumption that the input data as well as the label information comes from a positive data distribution. This doesn't create an issue for the computer vision based tasks. However, for those situations, where this is not possible, the feature values in the input dataset can be easily moved 1 into the positive region of the multi-dimensional input data space. The AANN transforms the n-dimensional input data into a space whose number of dimensions are equal to the number of labels used in the training dataset. For instance, presume that, the task is to classify images of cats and dogs and there is a labelled dataset present for achieving this classification. So, the learned representations will contain two dimensions corresponing to each label: cat and dog. The input images are transformed into 2-dimensional vectors by the AANN in such a way that the vectors are as close as possible to their ideal axes. This is achieved by constructing the cost function in a manner that it maximises the cosine value of the angle formed by the vector with its ideal axis. As a result, the representation space generated by this AANN can be visualized as shown in the FIG0 The AANN is constructed by using a 'Bidirectional Neuron' FIG1 ) as the building block for the hidden layers of a preliminary feed forward neural network. This bidirectional neuron uses the abs (mathematical absolute valued) function as the activation function. The computation performed by the neuron is similar in the forward and the backward directions. In the forward direction, the computation is given by: DISPLAYFORM0 Whereas, in the backward direction, the neuron computes: DISPLAYFORM1 The weights of the hidden layers of the AANN in forward direction learn to compute a function for transforming the input data into the representation vectors. While in the reverse direction, the weights constitute a function for constructing data points that closely resemble the data points belonging to the input dataset from the representation vectors. It is highly intriguing, and at the same time enigmatic, that the same set of weights constitute two entirely distinct functions. This research paper put forth an elementary but potent neural network architecture, named as AANN, that has the ability to learn in the forward as well as the backward direction. It also proposed the Abs function as a viable activation function for a neural network architecture. Due to lack of hardware resources, the experimentation had to be limited to the preliminary MNIST dataset, but it is firmly believed that the technique will perform equally well upon tackling other robust datasets, because of the theoretical evidence shown in the performed experiments.The AANN presently encodes the information in real number valued ranges across the the dedicated label axes in the the representation space. Certain regularization functions can be synthesized in order to stretch these ranges so that more information can be incorporated in them. The number of dimensions of the learned representations can be manually controlled by setting certain number of dedicated axes to a single label and by modifiying the forward cost function in such a way that the representation vectors lie inside the space generated by the coordinate axes dedicated to the ideal label. An in depth mathematical study of the Abs activation function could reveal the underlying behaviour of AANN. This forms the future scope for research.This technique also opens up new research opportunities for considering the AANN architectural modifications to certain network architectures like BID10 for semi-supervised learning. Moreover, it would be interesting to note the implications of applying the corresponding modifications to more advanced architectures such as Conv-nets BID6 and Recurrent Nets with LSTM cells BID3 .",1366,0.696,795,1.7182389937106919,"This research paper a simplistic architecture named as AANN: Absolute Artificial Neural Network highly interpretable representations These representations generated penalizing the learning the network those learned representations correspond the respective labels present the labelled dataset used supervised training; thereby simultaneously giving classify The network can the reverse direction generate data closely by feeding in representation vectors as required This research paper also explores mathematical abs (absolute valued) functions activation functions which constitutes this neural network architecture Finally the results obtained the MNIST dataset by this technique and brief In the field philosophy a principle, simplified relevant language states ""Among the available multiple solutions For instance there multiple polynomial functions fit the lowest degree one preferred BID12 . The technique AANN driven this principle In spite elementary in its construction an AANN is able classify inputs the forward direction while being generate them back It can visualized to doing classification the forward direction whereas performing a regression taskA standalone GAN described BID2 able create representations a novel technique generating a distribution contains generated the Generator part; by classify genuine generated The representations generated a GAN, although being very effective creating undistinguishable data points however interpretable also highly entangled BID1 BID8 . Using an InfoGAN, the problem training in maximises mutual information within small clusters related latent representations BID1 . Auto-encoder another technique uses the concept low dimensional representations the originally very high dimensional input data points A VAE: Variational Auto-Encoder tries the learned representations sparse the KL-divergence cost as on the final cost BID5 . Various attempts combining GAN VAE also BID8 BID7 . However these techniques kept complicated somewhere synthesizing felt 'strivingThe Absolute Artificial Neural Network exploits all possible information the labelled training datasets structure the learned representations Structurally an AANN very a feed forward Neural Network with uses the abs function Due this all the activations produced, the hidden layer activations contain positive real number values Thus the network runs as the label information comes a positive data distribution This does create the computer vision based tasks However for those situations where this the feature values the input dataset easily moved 1 into the positive region The AANN transforms the n-dimensional input data whose number labels used For instance presume, the task classify images cats there a labelled dataset present achieving So the learned representations will contain two dimensions corresponing each label cat The input images transformed the AANN in as their ideal axes This achieved constructing the cost function it maximises the cosine value formed with its ideal axis As the representation space generated this AANN can visualized shown the FIG0 The AANN constructed a 'Bidirectional Neuron' FIG1 ) the hidden layers a preliminary feed forward This bidirectional neuron uses the abs (mathematical absolute valued) function The computation performed the neuron similar the forward In the forward direction the computation given DISPLAYFORM0 Whereas neuron: The weights the hidden layers the AANN in forward direction learn compute transforming the representation vectors While in the reverse direction the weights constitute for constructing data points closely belonging dataset from the representation vectors It highly intriguing at enigmatic the same set weights constitute two entirely distinct functions This research paper put an elementary but potent neural network architecture named as AANN learn in forward as It also proposed the Abs function a viable activation function a neural network architecture Due lack hardware resources the experimentation had the preliminary MNIST dataset firmly the technique perform equally upon tackling other robust datasets because the theoretical evidence shown the performed experimentsThe AANN presently encodes real number valued ranges across the the dedicated label axes the the representation space Certain regularization functions synthesized stretch these ranges so more information incorporated The number dimensions the learned representations can manually setting certain number dedicated axes a single label by modifiying the forward cost function the representation vectors lie inside generated dedicated the ideal label An in mathematical the Abs activation function could the underlying behaviour AANN This forms the future scope researchThis technique also opens considering the AANN architectural modifications certain network like BID10 for Moreover interesting note the implications applying the corresponding modifications more advanced architectures Conv-nets BID6 Recurrent Nets with LSTM cells BID3 .",0.01,0.5340890218706407
"Current state-of-the-art relation extraction methods typically rely on a set of lexical, syntactic, and semantic features, explicitly computed in a pre-processing step. Training feature extraction models requires additional annotated language resources, which severely restricts the applicability and portability of relation extraction to novel languages. Similarly, pre-processing introduces an additional source of error. To address these limitations, we introduce TRE, a Transformer for Relation Extraction, extending the OpenAI Generative Pre-trained Transformer [Radford et al., 2018]. Unlike previous relation extraction models, TRE uses pre-trained deep language representations instead of explicit linguistic features to inform the relation classification and combines it with the self-attentive Transformer architecture to effectively model long-range dependencies between entity mentions. TRE allows us to learn implicit linguistic features solely from plain text corpora by unsupervised pre-training, before fine-tuning the learned language representations on the relation extraction task. TRE obtains a new state-of-the-art result on the TACRED and SemEval 2010 Task 8 datasets, achieving a test F1 of 67.4 and 87.1, respectively. Furthermore, we observe a significant increase in sample efficiency. With only 20% of the training examples, TRE matches the performance of our baselines and our model trained from scratch on 100% of the TACRED dataset. We open-source our trained models, experiments, and source code. Relation extraction aims to identify the relationship between two nominals, typically in the context of a sentence, making it essential to natural language understanding. Consequently, it is a key component of many natural language processing applications, such as information extraction BID2 , knowledge base population BID6 , and question answering BID26 . Table 1 lists exemplary relation mentions.State-of-the-art relation extraction models, traditional feature-based and current neural methods, typically rely on explicit linguistic features: prefix and morphological features BID11 , syntactic features such as part-of-speech tags BID28 , and semantic features like named entity tags and WordNet hypernyms BID25 . Most recently, BID32 combined dependency parse features with graph convolutional neural networks to considerably increase the performance of relation extraction systems. Table 1 : Relation extraction examples, taken from TACRED (1-3) and SemEval 2010 Task 8 (4-6) . TACRED relation types mostly focus on named entities, whereas SemEval contains semantic relations between concepts.However, relying on explicit linguistic features severely restricts the applicability and portability of relation extraction to novel languages. Explicitly computing such features requires large amounts of annotated, language-specific resources for training; many unavailable in non-English languages. Moreover, each feature extraction step introduces an additional source of error, possibly cascading over multiple steps. Deep language representations, on the other hand, have shown to be a very effective form of unsupervised pre-training, yielding contextualized features that capture linguistic properties and benefit downstream natural language understanding tasks, such as semantic role labeling, coreference resolution, and sentiment analysis BID13 . Similarly, fine-tuning pre-trained language representations on a target task has shown to yield state-of-the-art performance on a variety of tasks, such as semantic textual similarity, textual entailment, and question answering BID14 .In addition, classifying complex relations requires a considerable amount of annotated training examples, which are time-consuming and costly to acquire. BID5 showed language model fine-tuning to be a sample efficient method that requires fewer labeled examples.Besides recurrent (RNN) and convolutional neural networks (CNN), the Transformer BID21 is becoming a popular approach to learn deep language representations. Its self-attentive structure allows it to capture long-range dependencies efficiently; demonstrated by the recent success in machine translation BID21 , text generation , and question answering BID14 .In this paper, we propose TRE: a Transformer based Relation Extraction model. Unlike previous methods, TRE uses deep language representations instead of explicit linguistic features to inform the relation classifier. Since language representations are learned by unsupervised language modeling, pre-training TRE only requires a plain text corpus instead of annotated language-specific resources. Fine-tuning TRE, and its representations, directly to the task minimizes explicit feature extraction, reducing the risk of error accumulation. Furthermore , an increased sample efficiency reduces the need for distant supervision methods BID11 BID15 , allowing for simpler model architectures without task-specific modifications.The contributions of our paper are as follows:• We describe TRE, a Transformer based relation extraction model that, unlike previous methods, relies on deep language representations instead of explicit linguistic features.• We are the first to demonstrate the importance of pre-trained language representations in relation extraction, by outperforming state-of-the-art methods on two supervised datasets, TACRED and SemEval 2010 Task 8.• We report detailed ablations, demonstrating that pre-trained language representations prevent overfitting and achieve better generalization in the presence of complex entity mentions. Similarly, we demonstrate a considerable increase in sample efficiency over baseline methods.• We make our trained models, experiments, and source code available to facilitate wider adoption and further research. We proposed TRE, a Transformer based relation extraction method that replaces explicit linguistic features, required by previous methods, with implicit features captured in pretrained language representations. We showed that our model outperformes the state-ofthe-art on two popular relation extraction datasets, TACRED and SemEval 2010 Task 8. We also found that pre-trained language representations drastically improve the sample efficiency of our approach. In our experiments we observed language representations to capture features very informative to the relation extraction task.While our results are strong, important future work is to further investigate the linguistic features that are captured by TRE. One question of interest is the extent of syntactic structure that is captured in language representations, compared to information provided by dependency parsing. Furthermore, our generic architecture enables us to integrate additional contextual information and background knowledge about entities, which could be used to further improve performance.",1186,0.591,722,1.6426592797783934,"Current state- relation extraction typically rely explicitly computed Training feature extraction models requires additional annotated language resources severely portability relation extraction novel languages Similarly preprocessing introduces To address these limitations introduce TRE, a Transformer for Relation Extraction extending the OpenAI Generative Pre-trained Transformer [Radford 2018 Unlike previous relation extraction models TRE uses pre-trained deep language representations instead explicit linguistic features inform the relation classification combines the self-attentive Transformer architecture effectively long-range dependencies entity mentions TRE allows us learn implicit linguistic features solely plain text corpora by pretraining before fine the learned language representations on the relation extraction task TRE obtains new state result on the TACRED and SemEval 2010 Task 8 datasets achieving a test F1 and Furthermore observe sample efficiency With only 20% the training examples, TRE matches our baselines our model trained from on the TACRED dataset We open-source our trained models experiments Relation extraction aims identify two nominals typically a sentence making essential natural language understanding a key component many natural language processing applications information extraction BID2 , knowledge base population BID6 question Table 1 lists exemplary relation mentionsState relation extraction models traditional feature-based and current neural methods typically rely explicit linguistic features: prefix and morphological BID11 , such part tags like named entity tags WordNet hypernyms BID25 Most recently BID32 combined dependency parse features considerably relation extraction systems Table 1 : Relation extraction examples, taken TACRED1 SemEval 2010 Task 8 TACRED relation types mostly focus named entities whereas SemEval contains semantic relations conceptsHowever relying explicit linguistic features severely and portability relation extraction novel languages Explicitly computing such features annotated, language-specific resources for training; many unavailable in Moreover each feature extraction step introduces possibly cascading over Deep language representations on shown pretraining yielding contextualized features capture linguistic properties benefit downstream natural language understanding tasks semantic role labeling coreference resolution sentiment BID13 . Similarly fine-tuning pre-trained language representations on a target task state semantic textual similarity textual entailment question BID14 .In addition classifying complex relations requires annotated training examples time acquire BID5 showed language model fine-tuning be a sample efficient method requires fewer labeled examplesBesides recurrent ( the Transformer BID21 becoming learn deep language representations Its self-attentive structure capture long-range dependencies efficiently; demonstrated the recent success in machine translation BID21 , text generation , question BID14 .In TRE: a Transformer based Relation Extraction model Unlike previous methods TRE uses deep language representations explicit linguistic features inform the relation classifier Since language representations learned unsupervised language modeling pre TRE only plain corpus instead annotated language-specific resources Fine-tuning TRE, its representations directly the task minimizes explicit feature extraction reducing error accumulation Furthermore , an increased sample efficiency reduces distant supervision methods BID11 BID15 allowing simpler model architectures without task-specific modificationsThe contributions our paper as describe TRE, a Transformer based relation extraction model, deep language representations instead explicit linguistic are the by outperforming state on two supervised datasets TACRED SemEval 2010 Task detailed ablations demonstrating prevent achieve complex entity mentions Similarly demonstrate a considerable increase sample efficiency baseline methods.• make our trained models, experiments source code facilitate wider adoption We proposed TRE, a Transformer based relation extraction method replaces explicit linguistic features, required previous methods captured pretrained language representations We showed our model outperformes the state-ofthe-art on two popular relation extraction datasets TACRED SemEval 2010 Task 8 We also pre-trained language representations drastically the sample efficiency our approach In our experiments observed language representations to capture features very informative the relation extraction taskWhile strong, important future work to further TRE One question of syntactic structure captured language representations compared information provided dependency parsing Furthermore our generic architecture integrate additional contextual information background knowledge entities further performance",0.01,0.34151855113220414
"Neural networks have recently had a lot of success for many tasks. However, neural
 network architectures that perform well are still typically designed manually
 by experts in a cumbersome trial-and-error process. We propose a new method
 to automatically search for well-performing CNN architectures based on a simple
 hill climbing procedure whose operators apply network morphisms, followed
 by short optimization runs by cosine annealing. Surprisingly, this simple method
 yields competitive results, despite only requiring resources in the same order of
 magnitude as training a single network. E.g., on CIFAR-10, our method designs
 and trains networks with an error rate below 6% in only 12 hours on a single GPU;
 training for one day reduces this error further, to almost 5%. Neural networks have rapidly gained popularity over the last few years due to their success in a variety of tasks, such as image recognition BID16 , speech recognition and machine translation BID1 . In most cases, these neural networks are still designed by hand, which is an exhausting, time-consuming process. Additionally, the vast amount of possible configurations requires expert knowledge to restrict the search. Therefore, a natural goal is to design optimization algorithms that automate this neural architecture search.However, most classic optimization algorithms do not apply to this problem, since the architecture search space is discrete (e.g., number of layers, layer types) and conditional (e.g., the number of parameters defining a layer depends on the layer type). Thus, methods that rely on, e.g., differentiability or independent parameters are not applicable. This led to a growing interest in using evolutionary algorithms BID22 BID26 and reinforcement learning BID2 BID6 for automatically designing CNN architectures. Unfortunately, most proposed methods are either very costly (requiring hundreds or thousands of GPU days) or yield non-competitive performance.In this work, we aim to dramatically reduce these computational costs while still achieving competitive performance. Specifically, our contributions are as follows:• We propose a baseline method that randomly constructs networks and trains them with SGDR BID20 . We demonstrate that this simple baseline achieves 6%-7% test error on CIFAR-10, which already rivals several existing methods for neural archictecture search. Due to its simplicity, we hope that this baseline provides a valuable starting point for the development of more sophisticated methods in the future.• We formalize and extend the work on network morphisms BID27 BID6 in order to provide popular network building blocks, such as skip connections and batch normalization.• We propose Neural Architecture Search by Hillclimbing (NASH), a simple iterative approach that, at each step, applies a set of alternative network morphisms to the current network, trains the resulting child networks with short optimization runs of cosine annealing BID20 , and moves to the most promising child network. NASH finds and trains competitive architectures at a computational cost of the same order of magnitude as training a single network; e.g., on CIFAR-10, NASH finds and trains CNNs with an error rate below 6 % in roughly 12 hours on a single GPU. After one day the error is reduced to almost 5%. Models from different stages of our algorithm can be combined to achieve an error of 4.7 % within two days on a single GPU. On CIFAR-100 , we achieve an error below 24% in one day and get close to 20% after two days.• Our method is easy to use and easy to extend, so it hopefully can serve as a basis for future work.We first discuss related work in Section 2. Then, we formalize the concept of network morphisms in Section 3 and propose our architecture search methods based on them in Section 4. We evaluate our methods in Section 5 and conclude in Section 6. We proposed NASH, a simple and fast method for automated architecture search based on a hill climbing strategy, network morphisms, and training via SGDR. Experiments on CIFAR-10 and CIFAR-100 showed that our method yields competitive results while requiring considerably less computational resources than most alternative approaches. Our algorithm is easily extendable, e.g., by other network morphisms, evolutionary approaches for generating new models, other methods for cheap performance evaluation (such as, e.g., learning curve prediction BID15 or hypernetworks BID10 BID5 ), or better resource handling strategies (such as Hyperband BID18 ). In this sense, we hope that our approach can serve as a basis for the development of more sophisticated methods that yield further improvements of performance. B SOME MODELS",921,0.451,512,1.798828125,"Neural networks recently had for many tasks However neural network perform typically designed manually experts We propose automatically search well-performing CNN architectures a simple hill climbing procedure whose operators apply network morphisms, followed short optimization runs by cosine annealing Surprisingly this simple method yields competitive results only requiring resources training a single network on CIFAR-10 our method designs and trains networks an error rate below only 12 hours on a single GPU; training for one day reduces further to Neural networks rapidly gained their success image recognition BID16 , In these neural networks still designed hand Additionally the vast amount possible configurations requires expert knowledge restrict the search Therefore a natural goal design optimization algorithms automate this neural architecture searchHowever most classic optimization algorithms apply the architecture search space discrete layers layer types conditional parameters defining depends Thus methods rely, differentiability independent parameters applicable This led using evolutionary algorithms BID22 BID26 reinforcement automatically designing CNN architectures Unfortunately most proposed methods either very costlyrequiring hundreds GPU days yieldIn this work aim dramatically Specifically our contributions as propose a baseline method randomly constructs networks trains SGDR BID20 . We demonstrate this simple baseline achieves 6%-7% test error already rivals several existing methods neural archictecture search Due its simplicity we hope this baseline provides more sophisticated methods in the future.• We formalize on network morphisms BID27 BID6 in popular network building blocks skip connections batch propose Neural Architecture Search by Hillclimbing (, applies trains the resulting child networks short optimization runs of cosine BID20 , moves the most promising child network NASH finds and trains competitive architectures at a computational cost the same order training a single network; on CIFAR-10 NASH finds CNNs below 6 % roughly 12 hours on After one day the error reduced almost 5% Models from different stages our algorithm achieve an error 4.7 % within two days on On CIFAR-100 , achieve an error below 24% one day get close 20 after two days.• Our method easy extend hopefully can serveWe first discuss related work Section Then we formalize network morphisms Section and propose our architecture search methods based them in We evaluate our methods Section and conclude in We proposed NASH, automated architecture search based a hill climbing strategy network morphisms training via SGDR Experiments CIFAR-10 showed our method yields competitive results while requiring most alternative approaches Our algorithm easily other network morphisms evolutionary approaches for generating new models other cheap performance evaluation, learning curve prediction BID15 or hypernetworks BID5 better resource handling strategies Hyperband BID18 In this sense hope more sophisticated methods that yield further improvements of performance B SOME MODELS",0.01,0.7394230479121412
"We propose GraphGAN - the first implicit generative model for graphs that enables to mimic real-world networks.
 We pose the problem of graph generation as learning the distribution of biased random walks over a single input graph.
 Our model is based on a stochastic neural network that generates discrete output samples, and is trained using the Wasserstein GAN objective. GraphGAN enables us to generate sibling graphs, which have similar properties yet are not exact replicas of the original graph. Moreover, GraphGAN learns a semantic mapping from the latent input space to the generated graph's properties. We discover that sampling from certain regions of the latent space leads to varying properties of the output graphs, with smooth transitions between them. Strong generalization properties of GraphGAN are highlighted by its competitive performance in link prediction as well as promising results on node classification, even though not specifically trained for these tasks. Generative models for graphs have a longstanding history, with applications including data augmentation, anomaly detection and recommendation BID6 . Explicit probabilistic models such as Barabási-Albert or stochastic blockmodels are the de-facto standard in this field BID11 . However, it has also been shown on multiple occasions that our intuitions about structure and behavior of graphs may be misleading. For instance, heavy-tailed degree distributions in real graphs were in stark disagreement with the models existing at the time of their discovery BID2 . More recent works, like BID9 , keep bringing up other surprising characteristics of real-world networks, not accounted for by the models at hand. This leads us to the question: ""How do we define a model that captures all the essential (potentially still unknown) properties of real graphs?"" An increasingly popular way to address this issue in other fields is by switching from explicit (prescribed) models to implicit ones. This transition is especially notable in Computer Vision, where Variational Autoencoder BID23 and Generative Adversarial Networks (GANs) BID13 significantly advanced the state of the art over the classic prescribed approaches like Mixtures of Gaussians BID5 . GANs achieve unparalleled results in scenarios such as image and 3D objects generation (e.g., BID32 BID4 . However, despite their massive success when dealing with real-valued data, adapting GANs to handle discrete objects like graphs or text remains an open research problem BID12 . Indeed, the combinatorial structure of the graph is only one of the obstacles when applying GANs to graphs. Second, large repositories of graphs, which all come from the same distribution, do not exist. This means that in a typical setting one has to learn from a single graph. And last, any model operating on a graph necessarily has to be permutation invariant, as the graphs remain isomorphic under node reordering.In this work we introduce GraphGAN -the first implicit generative model for graphs, that tackles all of the above challenges. We formulate the problem of learning the graph topology as learning the distribution of biased random walks over the graph. Like in the typical GAN setting, the generator G -in our case defined as a stochastic neural network with discrete output samples -learns to generate random walks that are plausible in the real graph, while the discriminator D then has to distinguish them from the true ones that are sampled from the original graph. The objective function of our model is based on the Wasserstein GAN , which allows to learn multimodal distributions and leads to more stable convergence. Our GraphGAN exhibits strong generalization properties, which we study in detail in the experimental section. The example in FIG0 shows that the graphs generated by GraphGAN possess similar properties as the input graph, as shown by the degree distributions in FIG0 . The generated graphs, however, are not simply exact replicas: as the visualized subset of nodes in Figs. 1a and 1b shows, the graphs exhibit similar structure while being not identical; in fact, the two graphs have less than 50% of edges in common. This initial insight is underlined by an extensive comparison of graphs generated by GraphGAN and the respective input networks in the experimental section of this work. And even more, when generating graphs based on specific regions of the latent space learned by GraphGAN, we can smoothly interpolate between graphs with varying properties. Our main contributions are:• We introduce GraphGAN -the first of its kind GAN that generates graphs via random walks. Our model tackles the associated challenges of staying permutation invariant, learning from a single graph and generating discrete output.• We show that our model generalizes, and is able to produce sibling graphs to the given input graph. These graphs posses similar topological characteristics, but are not exact replicas (see FIG0 ). We further demonstrate how latent space interpolation leads to generation of graphs with smoothly changing properties.• We highlight the generalization properties of GraphGAN by its link prediction performance, which is competitive with the state of the art on real-word datasets, although not trained explicitly for this task. Additionally, to give the reader a better insight about the behavior of our model, we analyze the learned weights of our model -that can be viewed as node ""embeddings"" -and by using them in a node classification task we show that they capture meaningful structural information. When evaluating different graph generative models in Sec. 4.1, we observed a major limitation of explicit models. While the prescribed approaches excel at recovering the properties that are directly included in their definition, they perform significantly worse with respect to the rest of the metrics. This phenomenon clearly indicates the need for implicit graph generators, such as GraphGAN. Indeed, we notice that our model is able to consistently capture all the important graph characteristics (see TAB1 ). Moreover, GraphGAN generalizes beyond the input graph, as can be seen by its strong link prediction performance in Sec. 4.2.Still, being the first model of its kind, GraphGAN possesses certain limitations, and a number of related questions could be addressed in follow-up works:Scalability. We have observed in Sec. 4.2 that it takes a large number of generated random walks to get representative transition counts for large graphs. While sampling random walks from GraphGAN is trivially parallelizable, a possible extension of our model is to use a conditional generator, i.e. the generator can be provided a desired starting node, thus ensuring a more even coverage. On the other hand, the sampling procedure itself can be sped up by incorporating a hierarchical softmax output layer -a method commonly used in natural language processing.Evaluation. It is nearly impossible to judge whether a graph is realistic by visually inspecting it (unlike images, for example). In this work we already quantitatively evaluate the performance of GraphGAN on a large number of standard graph statistics. However, developing new measures applicable to (implicit) graph generative models will deepen our understanding of their behavior.Experimental scope. In the current work we focused on the setting of a single connected graph.Other scenarios, such as dealing with a collection of smaller i.i.d. graphs, that frequently occur in other fields (e.g., chemistry, biology), would be an important application area for the proposed model. Studying the influence of the graph topology (e.g., sparsity, diameter) on performance of GraphGAN will shed more light on its properties.Other types of graphs. While plain graphs are ubiquitous, many of real-world applications deal with attributed, k-partite or heterogeneous networks. Adapting the GraphGAN model to handle these other modalities of the data is a promising direction for future research. Especially important would be an adaptation to the dynamic / inductive setting, when new nodes are added over time. GraphGAN is the first work to successfully bridge the worlds of implicit modeling and graphs. Our work enables future researchers to gain better insight into the properties of real networks and opens new and exciting lines of research. We are able to generate realistic graphs by learning to generate (biased) random walks from the same distribution as the random walks from an input graph. We employ the GAN framework to learn our implicit generative model, overcoming key challenges such as permutation invariance, working in the discrete domain and having a single graph as input. Our generator is able to generate sibling graphs that maintain structural similarity with the original graph without being exact replicas. Better yet, using our defined stopping criteria, we can control how close are the generated graphs to the original. We further show that GraphGAN learns a semantic mapping from the latent space to the properties of the generated graph, which is evidenced by the smooth transitions of the output. GraphGAN shows strong generalization properties, as demonstrated by the competitive performance on the link prediction and the promising results on the node classification task, without being explicitly trained with these tasks in mind.",1750,1.014,1035,1.6908212560386473,"We propose GraphGAN - the first implicit generative model graphs enables to mimic We pose graph generation as learning the distribution biased random walks a single input graph Our model generates discrete output samples the Wasserstein GAN objective GraphGAN enables us sibling graphs have yet Moreover GraphGAN learns a semantic mapping the latent input space the generated graph's properties We discover sampling certain regions the latent space leads varying properties the output graphs smooth transitions them Strong generalization properties GraphGAN highlighted its competitive performance link prediction as promising results node classification even not specifically trained Generative models graphs a longstanding history applications data augmentation anomaly detection recommendation BID6 . Explicit probabilistic models such Barabási-Albert or stochastic blockmodels BID11 . However on our intuitions structure behavior of graphs misleading For instance heavy-tailed degree distributions real graphs in stark disagreement existing BID2 . More recent works BID9 , keep bringing other surprising characteristics not accounted at This leads define a model captures essential (potentially still unknown) properties real graphs An increasingly popular way address in other fields switching explicit (prescribed) models This transition especially notable Computer Vision where Variational Autoencoder BID23 and BID13 significantly advanced over the classic prescribed approaches like Mixtures . GANs achieve unparalleled results scenarios image 3D objects generation ( BID32 BID4 . However despite their massive success when dealing real-valued data adapting GANs handle discrete objects graphs text remains an open research problem BID12 . Indeed the combinatorial structure only the obstacles when applying GANs Second, large repositories graphs all come do exist This means in a typical setting one has learn from a single graph And last any model operating a graph necessarily permutation the graphs remain isomorphic under node reorderingIn introduce GraphGAN -the first implicit generative model graphs tackles all We formulate the problem learning the graph topology as learning biased random walks Like in the typical GAN setting the generator G -in our case defined discrete output samples -learns random walks that plausible the real graph then has distinguish them that sampled The objective function our model based the Wasserstein GAN , allows to learn multimodal distributions leads more stable convergence Our GraphGAN exhibits strong generalization properties study The example in FIG0 shows the graphs generated GraphGAN possess the degree distributions The generated graphs, however simply exact replicas: as the visualized subset nodes Figs 1a and shows, the graphs exhibit similar structure while being not; in edges This initial insight underlined an extensive comparison graphs generated GraphGAN the respective input networks And even when generating graphs based specific regions the latent space learned GraphGAN smoothly graphs varying properties Our main contributions are:• introduce GraphGAN -the that generates via random walks Our model tackles the associated challenges staying permutation learning a single graph generating discrete output.• generalizes, produce sibling the given input graph These graphs posses similar topological characteristics ( FIG0 We further demonstrate latent space interpolation leads generation graphs smoothly changing properties.• highlight GraphGAN by its link prediction performance competitive the state on real-word datasets although trained explicitly Additionally to give the behavior our model analyze the learned weights -that can viewed node ""embeddings by a node classification task show they capture meaningful structural information When evaluating different graph generative models Sec, we observed a major limitation explicit models While the prescribed approaches excel recovering the properties that directly included their definition perform significantly the metrics This phenomenon clearly indicates implicit graph generators GraphGAN Indeed we notice our model able consistently capture all the important graph characteristicssee TAB1 Moreover GraphGAN generalizes beyond the input graph can its strong link prediction performance Sec 4.2.Still being the first model GraphGAN possesses certain limitations related questions couldScalability We observed Sec that it takes generated random walks representative transition counts large graphs While sampling random walks GraphGAN trivially parallelizable a possible extension our model a conditional generator provided a desired starting node thus ensuring a more even coverage On the sampling procedure itself sped incorporating a hierarchical softmax output layer -a method commonlyEvaluation. It nearly judge a graph realistic visually ( images for In this work already quantitatively GraphGAN standard graph statistics However developing new measures applicable (implicit) graph generative models deepen their behaviorExperimental scope In the current work focused the setting a single connected graphOther scenarios dealing smaller i.i.d. graphs that frequently other fields an important application area the proposed model Studying the influence the graph topology diameter performance GraphGAN will shed its propertiesOther types. While plain graphs ubiquitous many deal attributed, k-partite or heterogeneous networks Adapting the GraphGAN model handle these other modalities a promising direction Especially important would an adaptation the dynamic / inductive setting when new nodes over GraphGAN the first work successfully bridge the worlds implicit modeling graphs Our work enables future researchers gain real networks opens We able generate realistic graphs learning (biased) random walks the same distribution We employ the GAN framework learn our implicit generative model overcoming key challenges permutation invariance working the discrete domain having a single graph Our generator able sibling graphs maintain structural similarity without being exact replicas Better using our defined stopping criteria control close are the generated graphs We further show GraphGAN learns a semantic mapping the latent space to the properties evidenced the smooth transitions GraphGAN shows strong generalization properties demonstrated the competitive performance on the link prediction the promising results the node classification task without being explicitly trained these tasks",0.01,0.46423103517836395
"The ability of a classifier to recognize unknown inputs is important for many classification-based systems. We discuss the problem of simultaneous classification and novelty detection, i.e. determining whether an input is from the known set of classes and from which specific class, or from an unknown domain and does not belong to any of the known classes. We propose a method based on the Generative Adversarial Networks (GAN) framework. We show that a multi-class discriminator trained with a generator that generates samples from a mixture of nominal and novel data distributions is the optimal novelty detector. We approximate that generator with a mixture generator trained with the Feature Matching loss and empirically show that the proposed method outperforms conventional methods for novelty detection. Our findings demonstrate a simple, yet powerful new application of the GAN framework for the task of novelty detection. In recent years we have witnessed incredible progress in AI, largely due to the success of Deep Learning, and more specifically Supervised Deep Learning. One of the basic requirements from a good supervised learning algorithm is generalization -the ability to classify input that is reasonably similar to the training data. However, usually there are no requirements whatsoever on how the classifier should behave for new types of input that differ substantially from the data that are available during training. In fact for such novel input the algorithm will produce erroneous output and classify it as one of the classes that were available to it during training. Ideally, we would like that the classifier, in addition to its generalization ability, be able to detect novel inputs, or in other words, we would like the classifier to say, ""I don't know."" Novelty detection can be defined as the task of recognizing that test data differs in some manner from the data that was available during training. The problem of novelty detection arises in many fields and is closely related, but not identical, to the problems of anomaly detection (also outlier detection), where the goal is to recognize anomalous examples in a dataset BID2 . Novelty detection is a hard problem that has received relatively little attention in the ML literature. Nevertheless, in our opinion novelty detection should be a central part of every recognition system. For a comprehensive in-depth review of the topic of novelty detection, we refer the reader to BID18 . Popular conventional novelty detection methods such as Probabilistic methods BID18 , which perform density estimation of the examples from a nominal class, or Domainbased methods BID23 ; BID27 , which re-formulate novelty detection as a ""one-class classification"" problem and define a boundary around the nominal class, do not scale well to large high-dimensional datasets. Another class of novelty detection methods is distance-based methods, which assume that the nominal data are tightly clustered, while novel data occur far from their nearest neighbors. These methods require computationally expensive clustering or nearest neighbors search. One of the major drawbacks of conventional novelty detection methods is that at test time, they are separated from the classification algorithm and therefore increase the overall computational and design complexity of the system. Furthermore, combining novelty detection with a multi-class classifier into a single algorithm may leverage important intra and inter-class information in the training data which can benefit both tasks.In this paper we are interested in methods for simultaneous classification and novelty detection. A popular heuristic approach to simultaneous classification and novelty detection is thresholding the maximum of estimated class probability BID9 , or alternatively, to threshold the entropy of the estimated probability distribution. Another practical approach is to collect ""backgroundclass"" samples, that is, samples that are not from the nominal set and hopefully represent novel data. In this case, novelty detection can be reduced to a supervised learning problem. Unfortunately, this solution requires collecting a large set of background inputs -a time-consuming task and moreover, it is very difficult to sample a large enough background class that will represent all possible novel examples.We embrace the ""background-class"" sampling idea and ask is it possible to generate novel data? To the best of our knowledge, no method for novelty detection is based on generating novel examples. In this paper we examine whether Generative Adversarial Networks (GAN), a popular generative framework that can be used to generate novel examples. The GAN framework was proposed by BID8 , as a generative modeling method, mostly used for generating realistic samples of natural images. More specifically, GAN is an approach to generative modeling where two models are trained simultaneously: a generator and a discriminator. The task of the discriminator is to classify an input as either the output of the generator (""fake"" data), or actual samples from the underlying data distribution (""real"" data). The goal of the generator is to produce outputs that are classified by the discriminator as ""real"", or as coming from the underlying data distribution.In some formulations of GANs Odena (2016); BID25 , the discriminator is trained to classify data not only into two classes ""real"" and ""fake"", but rather into multiple classes. If the ""real"" data consists of K classes, then the output of the discriminator is K + 1 class probabilities where K probabilities corresponds to K known classes, and the K + 1 probability correspond to the ""fake"" class.In this paper, we propose to use a multi-class GAN framework for simultaneous classification and novelty detection. If during training the generator generates a mixture of nominal data and novel data, the multi-class discriminator learns to discriminate novel data from nominal data and essentially became a novelty detector. At test time, when the discriminator classifies a real example to the K + 1 th class, i.e., class which represented ""fake examples"" during training, this the example is most likely a novel example and not from one of the K nominal classes. In fact, we prove that in this case the discriminator become an optimal novelty detector (for a given false positive rate). We approximate such a mixture generator with a generator trained with specifically designed loss functions. In Section 2 we provide background and a theoretical justification to our proposed method and its connection to existing novelty detection methods. We validate the proposed method by a set of experiments in Section 3. The ability to identify novelties or say ""I don't know"" is an important tool for many classificationbased systems. In this work, we propose to solve a problem of simultaneous classification and novelty detection within the GAN framework. We propose to use a GAN with a mixture generator to turn this problem into a supervised learning problem without collecting ""background-class"" data.In the case where a mixture generator generates samples from a mixture of nominal data distribution and novel data distribution, we showed that the GAN's discriminator is an optimal novelty detector. We approximate that generator with a mixture generator trained with the Feature Matching loss. This mixture generator generates samples scattered around and in the low-density areas of the data manifold, and this makes a multi-class discriminator a powerful novelty detector. We empirically validate that the performance of the proposed solution is comparable to several popular novelty detection methods, and sometimes outperforms them.Clearly, evaluation of the proposed framework on more challenging datasets is required. As a future research direction we would like to search for new loss functions for mixture generators that will enrich the generator distribution and will improve novelty detection. Classification with asymmetric label noise problem BID24 is closely related to semi-supervised novelty detection, and it will be interesting to see whether the GAN framework can be used to solve this problem. Finally, it is interesting to see if the suggested framework can be applied to detecting the adversarial examples.",1492,0.794,881,1.6935300794551646,"The ability a classifier recognize unknown inputs many classification-based systems We discuss the problem simultaneous classification and novelty detection determining an input from the known set classes from which specific class, an unknown domain and does We propose based We show a multi-class discriminator trained a generator that samples a mixture nominal and novel data distributions the optimal novelty detector We approximate that generator with a mixture generator trained the Feature Matching loss and empirically show the proposed method novelty detection Our findings demonstrate simple powerful new application the GAN framework the task novelty detection In we incredible progress AI largely more specifically Supervised Deep Learning One the basic requirements from a good supervised learning generalization -the ability classify input that reasonably However usually there no requirements whatsoever the classifier behave for new types input that differ substantially available during training In fact for such novel input the algorithm will produce erroneous output classify one the classes were available during training Ideally that the classifier, in its generalization ability novel inputs or in we say Novelty detection defined the task recognizing test data differs available during training The problem novelty detection arises and closely, anomaly detection (also outlier detection recognize anomalous examples a dataset BID2 . Novelty detection received the ML literature Nevertheless in our opinion novelty detection should every recognition system For novelty detection we refer BID18 . Popular conventional novelty detection methods Probabilistic methods BID18 , which perform density estimation the examples from a nominal class Domainbased methods ; reformulate novelty detection and define a boundary around do scale Another class novelty detection methods distance-based methods assume the nominal data tightly clustered while novel data occur far These methods require computationally expensive clustering or nearest neighbors search One conventional novelty detection methods at test time separated the classification algorithm therefore increase the overall computational and design complexity Furthermore combining novelty detection a multi-class classifier into leverage important intra and which benefit both tasksIn are methods simultaneous classification novelty detection A popular heuristic approach simultaneous classification novelty detection thresholding the maximum of estimated class probability BID9 , or alternatively to threshold the entropy the estimated probability distribution Another practical approach collect ""backgroundclass"" samples from the nominal set and hopefully represent novel data In novelty detection can reduced a supervised learning problem Unfortunately this solution requires collecting background inputs -a moreover sample a large enough background class that represent all possible novel examplesWe embrace the ""background-class"" sampling idea ask is novel data? To no method novelty detection based generating novel examples In this paper whether Generative Adversarial Networks novel examples. The GAN framework proposed BID8 , as a generative modeling method mostly generating realistic samples natural images More specifically GAN an approach generative modeling where two models trained simultaneously: a generator The task the discriminator classify either the output the generator (""fake"" data actual samples the underlying data distribution The goal the generator outputs classified the discriminatorreal coming the underlying data distributionIn some formulations GANs Odena2016 BID25 , trained not into two classes "" rather If the ""real"" data consists K classes the output K + 1 class probabilities where K probabilities corresponds K known classes.In propose a multi-class GAN framework simultaneous classification novelty detection If during training the generator generates a mixture nominal data novel data the multi-class discriminator learns discriminate novel data essentially became a novelty detector At test time when the discriminator classifies a real example to the K + 1 th class which represented ""fake examples during training this the example most a novel example from one the K nominal classes In fact we prove in the discriminator become an optimal novelty detectorfor a given false positive rate We approximate such a mixture generator a generator trained with specifically designed loss functions In Section we provide background a theoretical justification to our proposed method and its connection existing novelty detection methods We validate the proposed method a set experiments Section The ability identify novelties or say many classificationbased systems In this work propose solve simultaneous classification novelty detection within the GAN framework We propose a GAN with a mixture generator turn this problem without collecting ""background-class"" dataIn where generates samples nominal data distribution showed an optimal novelty detector We approximate that generator with a mixture generator trained the Feature Matching loss. This mixture generator generates samples scattered and the data manifold this makes a multi-class discriminator a powerful novelty detector We empirically validate the performance the proposed solution several popular novelty detection methods sometimesClearly evaluation on more challenging datasets required As a future research direction we search new loss functions mixture generators enrich the generator distribution will improve novelty detection Classification with asymmetric label noise problem BID24 is closely semi-supervised novelty detection will the GAN framework Finally it interesting if the suggested framework detecting the adversarial examples",0.01,0.471132879249027
"Verifying a person's identity based on their voice is a challenging, real-world problem in biometric security. A crucial requirement of such speaker verification systems is to be domain robust. Performance should not degrade even if speakers are talking in languages not seen during training. To this end, we present a flexible and interpretable framework for learning domain invariant speaker embeddings using Generative Adversarial Networks. We combine adversarial training with an angular margin loss function, which encourages the speaker embedding model to be discriminative by directly optimizing for cosine similarity between classes. We are able to beat a strong baseline system using a cosine distance classifier and a simple score-averaging strategy. Our results also show that models with adversarial adaptation perform significantly better than unadapted models. In an attempt to better understand this behavior, we quantitatively measure the degree of invariance induced by our proposed methods using Maximum Mean Discrepancy and Frechet distances. Our analysis shows that our proposed adversarial speaker embedding models significantly reduce the distance between source and target data distributions, while performing similarly on the former and better on the latter.",218,0.144,125,1.744,Verifying based their voice biometric security A crucial requirement such speaker verification systems domain robust Performance should degrade even speakers talking languages seen during training To this end present learning domain invariant speaker embeddings We combine adversarial training an angular margin loss function encourages the speaker embedding model by directly optimizing for cosine similarity classes We able beat a strong baseline system using a cosine distance classifier a simple score-averaging strategy Our results also models adversarial adaptation perform significantly In better this behavior quantitatively measure invariance induced our proposed methods Maximum Mean Discrepancy and Frechet distances Our analysis our proposed adversarial speaker embedding models significantly source data distributions performing similarly former better,0.0,0.5997258025585327
"Learning disentangling representations of the independent factors of variations that explain the data in an unsupervised setting is still a major challenge. In the following paper we address the task of disentanglement and introduce a new state-of-the-art approach called Non-synergistic variational Autoencoder (Non-Syn VAE). Our model draws inspiration from population coding, where the notion of synergy arises when we describe the encoded information by neurons in the form of responses from the stimuli. If those responses convey more information together than separate as independent sources of encoding information, they are acting synergetically. By penalizing the synergistic mutual information within the latents we encourage information independence and by doing that disentangle the latent factors. Notably, our approach could be added to the VAE framework easily, where the new ELBO function is still a lower bound on the log likelihood. In addition, we qualitatively compare our model with Factor VAE and show that this one implicitly minimises the synergy of the latents. Our world is hierarchical and compositional, humans can generalise better since we use primitive concepts that allow us to create complex representations BID11 ). Towards the creation of truly intelligent systems, they should learn in a similar way resulting in an increase of their performance since they would capture the underlying factors of variation of the data BID2 ; ; ). In addition, good representations improve the performance for tasks involving transfer learning and multi-task learning; since it will capture the explanatory factors.According to BID18 , a compositional representation should create new elements from the combination of primitive concepts resulting in a infinite number of new representations. For example if our model is trained with images of white wall and then is presented a boy with a white shirt, it should identify the color white as a primitive element. Intuitively, our model will be able to construct different and multiple representations from the primitives.Furthermore, a disentangled representation has been interpreted in different ways, for instance BID2 define it as one where single latent variables are sensitive to changes in generative factors, while being invariant to changes in other factors. In addition, we agree with BID12 , which mentions that a disentangle representation should be factorised and interpretable. Intuitevely, the model could learn generative factors such as position, scale or colour; if it is disentangle it should be able to traverse along the position variable without changing the scale or the colour. It's worth noting that disentangled representations have been useful for a variety of downstream tasks such as domain adaptation by training a Reinforcement Learning agent that uses a disentangled representation of its environment BID13 ; or for learning disentangled primitives grounded in the visual domain discovered in an unsupervised manner BID14 .",550,0.265,306,1.7973856209150327,"Learning disentangling representations the independent factors variations that explain still In the following paper address the task introduce state calledNon-Syn VAE Our model draws population coding the notion synergy describe the encoded information by neurons responses from the stimuli If those responses convey together separate as independent sources encoding acting synergetically By penalizing the synergistic mutual information within the latents we encourage information independence by doing that the latent factors Notably our approach could added the VAE framework easily where the new ELBO function still lower bound the log likelihood In qualitatively compare Factor VAE show this one implicitly minimises the synergy the latents Our world hierarchical compositional humans generalise better since use primitive concepts allow complex representations BID11 ). the creation truly intelligent systems they learn in resulting their performance since would capture variation of BID2 ; ; In good representations improve for tasks transfer learning; since will capture the explanatory factors.According BID18 , should create new elements the combination primitive concepts resulting a infinite number For example if our model trained images white wall is presented a boy identify a primitive element Intuitively our model will construct different and multiple representations fromFurthermore a disentangled representation has interpreted BID2 define one where single latent variables sensitive changes generative factors being In agree BID12 , mentions a disentangle representation factorised interpretable Intuitevely the model could learn generative factors position scale colour; if disentangle it should traverse along the position variable It worth disentangled representations useful downstream tasks domain adaptation by training a Reinforcement Learning agent BID13 ; or grounded discovered",0.0,0.7357476742406678
"Metric embeddings are   immensely useful representations of associations between entities   (images, users, search queries, words, and more).   Embeddings are learned by  optimizing a loss objective of the general form of a sum over example associations. Typically, the optimization uses stochastic gradient updates over minibatches of examples that are arranged  independently at random. In this work, we propose the use of {\em structured arrangements} through randomized {\em microbatches} of examples that are more likely to include similar ones. We make a principled argument for the properties of our arrangements  that accelerate the training and present efficient algorithms to generate microbatches that respect the marginal  distribution of training examples.   Finally, we observe experimentally that our structured arrangements accelerate training by 3-20\%. Structured arrangements emerge as a powerful and novel performance knob for SGD that is independent and complementary to other SGD  hyperparameters and thus is a candidate for wide deployment. Metric embeddings of entities that are trained to capture example associations are common representations that also allow for inference of associations not present in the data. Embeddings are used in complex learning tasks or directly applied for similarity and recommendations tasks. Example usage domains includes embeddings of text document from occurrences of words BID2 ; BID9 ; BID7 , users and videos from watch or ratings BID15 , words from co-occurrence frequencies in a corpus BID16 , and nodes in a graph from co-occurrence in short random walks BID19 . The example associations may involve entities of the same type (word co-occurrences, video co-watch, social) or different types (such as users and products) and often are distilled by reweighing frequencies of raw interactions Salton & Buckley (1988) ; BID7 ; BID16 ; BID18 .Embeddings are computed by minimizing a loss objective of the form of a sum over example associations. The optimization starts with random initialization followed by gradient updates. In modern applications , the objective can have billions of terms or more, and the de facto method at such scale is stochastic gradient descent (SGD) Robbins & Siegmund (1971) ; BID14 ; Salakhutdinov et al. (2007) ; BID11 ; BID16 . The terms (examples) are randomly grouped into minibatches. Gradient updates, that are equal in expectation to the full gradient, are then computed sequentially for each minibatch. SGD is much more efficient than working with full gradients and the minibatch size determines the amount of concurrency. There are numerous tunable parameters and methods aimed to improve quality and speed of convergence. Some notable recent work includes per-parameter tuning of the learning rate BID8 and altering the distribution of training examples by gradient magnitude BID1 , negatives selection with triplet loss Schroff et al. (2015) , clustering BID10 and diversity criteria BID10 .In this work we introduce principled schemes that control the arrangement of examples into minibatches. Note that arrangement tuning is separate and orthogonal to optimizations knobs that alter the distribution of training examples, learning rate, or minibatch size. The baseline practice of independent arrangements places examples into minibatches independently at random. This practice is supported by classic SGD convergence analysis and has the upside of controlling the variance of the stochastic gradients. We make a novel case here for an antithesis of independent arrangements which we term coordinated arrangements. Coordinated arrangements are much more likely to place corresponding associations in the same minibatch. We show that coordination offers different upsides: At the micro level , updates are more effective in pulling vectors of similar entities closer. At a macro level, the examples in small fractions of epochs encode (in expectation) the similarity structure in the full set of example associations whereas independent arrangement disperse that information. This ""self similarity"" of the training sequence effectively allows a single epoch to act as multiple passes.We specify coordinated arrangements through a distribution on randomized subsets of associations which we refer to as microbatches. Basic coordinated microbatches co-place corresponding associations to the maximum extent possible while adhering to the marginal distribution of training examples. Locality Sensitive Hashing (LSH) maps allow for refining our microbatches so that corresponding associations are more likely to be co-placed when the overall similarity of the entities is higher. The LSH maps we apply leverage some available coarse proxy of entity similarity. A readily available first-order proxy is the similarity of the sparse association vectors. Another proxy is an embedding obtained by a weaker model. We present efficient generators of basic and refined microbatches for both LSH functions. Finally, microbatches are independently grouped into minibatches of desired size, which allows us to retain the traditional advantages of independent arrangements at the microbatch level. This design enables us to tune the microbatches to the problem and even the stage of training. We compare the effectiveness of different arrangements through experiments on synthetic stochastic block matrices and on recommendation data sets. The stochastic block data, with its simplicity and symmetry, allows us to factor out the potential effect of other optimizations. We learn that basic coordination is always beneficial earlier in training whereas LSH refinements are more effective later on. We obtain consistent 3%-30% reduction in training with respect to the independent arrangements baseline that holds across other training hyperparameters.The paper is organized as follows. Section 2 presents necessary background on the loss objective we use in our experiments and working with minibatches with one-sided gradient updates. In Section 3 we define LSH microbatches and coordinated minibatch arrangements. In We report our experiment results comparing different arrangement methods on stochastic blocks and on recommendation data sets in Section 4. In Section 5 we examine properties of coordinated arrangements that are helpful for faster convergence. We conclude in Section 6. We consider embedding computations with stochastic gradients and establish that the arrangement of training examples into minibatches can be a powerful performance knob. In particular, we introduced coordinated arrangements as a principled method to accelerate SGD training of embedding vectors. Our experiments focused on the popular SGNS loss and our methods were designed for pairwise associations. In future we hope to explore the use of coordinated arrangement with other loss objectives, deeper networks, and more complex association structures. . We observe that the training gain of coordinated arrangements over the baseline IND increases with minibatch size. The methods that cap the microbatch size by the minibatch size (Jaccard* and Angular*) perform much better with larger minibatches, as larger minibatches allow for a higher recall of helpful co-placements. In particular we can see that in early training on small minibatches (b = 4) these methods are outperformed by COO (which produces our largest (and unrefined) microbatches).0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00Training ( We quantify the gains of different methods over the baseline IND arrangements in the following tables. Results for precision at k = 10 are reported in TAB2 for Jaccard LSH MIX, in Table 3 for (pure) Jaccard*, and in TAB6 for angular* LSH MIX(where angular LSH is applied with respect to a d = 3 embedding). Results for cosine gap are reported in Table 5 for Jaccard LSH MIX and in Table 6 for angular* LSH MIX.The tables report results for different minibatch sizes b and block sizes B. In each table we list the peak quality (cosine gap or precision) of the respective coordinated method and the amount of training used by IND to reach 0.75, 0.95, or 0.99 of that peak. We also show the reduction in training 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Training ( that is gained by using the respective coordinated method instead of IND. Overall, we can see that the coordinated methods consistently had training gains of 5-30%. The gain is larger with smaller blocks and also with larger minibatches. The emphasized numbers in the Jaccard MIX and Jaccard* correspond to the method that provided the higher gain. We can see that Jaccard* performed better than Jaccard MIX for larger minibatch sizes.",1687,0.997,972,1.73559670781893,"Metric embeddings immensely useful representations associations entitiesimages users search queries words Embeddings learned optimizing a loss objective the general form a sum over example associations Typically the optimization uses updates over minibatches examples arranged independently at In {\em structured arrangements through randomized {\em microbatches examples more include similar ones We make a principled argument the properties our arrangements accelerate the training present efficient algorithms generate microbatches respect the marginal distribution training examples Finally observe experimentally our structured arrangements accelerate training 320\% Structured arrangements emerge a powerful and novel performance knob SGD that independent complementary thus wide deployment Metric embeddings entities trained capture example associations common representations also inference not present Embeddings used complex learning tasks or directly applied for similarity and recommendations tasks Example usage domains includes text document from occurrences BID2 ; users videos watch or ratings words co-occurrence frequencies nodes co in short random walks The example associations may involve entitiesword co video cowatch social)such users products often distilled reweighing frequencies raw interactions Salton & Buckley ; BID7 ; computed minimizing a loss objective example associations The optimization starts random initialization followed gradient updates In modern applications , the objective can have billions terms the de facto method at such scaleSGD) Robbins Siegmund1971 ; BID14 Salakhutdinov (2007 ; BID11 ; The terms (examples randomly grouped minibatches Gradient updates that equal expectation then SGD much efficient working full gradients the minibatch size determines concurrency There numerous tunable parameters methods aimed quality convergence Some notable recent work per tuning BID8 altering training examples gradient magnitude , negatives selection with triplet loss Schroff (2015 , clustering BID10 and diversity criteria this work principled schemes control the arrangement examples into minibatches Note arrangement tuning separate optimizations knobs that alter training examples learning rate The baseline practice independent arrangements places examples into minibatches independently at This practice supported classic SGD convergence analysis the upside controlling We make a novel case here an antithesis independent arrangements term coordinated arrangements Coordinated arrangements much place corresponding associations the same minibatch We show coordination offers different upsides At , updates pulling vectors similar entities closer. At a macro level examples small fractions epochs encode ( expectation the similarity structure example associations whereas independent arrangement disperse This ""self similarity of the training sequence effectively a single epoch act multiple passesWe specify coordinated arrangements through a distribution on randomized subsets associations which microbatches Basic coordinated microbatches co-place corresponding associations the maximum extent while the marginal distribution training examples Locality Sensitive Hashing (LSH) maps allow refining our microbatches so corresponding associations coplaced the overall similarity the entities The LSH maps we apply leverage some available coarse proxy of entity similarity A readily available first-order proxy the similarity the sparse association vectors Another proxy obtained a weaker model We present efficient generators basic and refined microbatches both LSH functions Finally microbatches independently grouped minibatches of desired size retain independent arrangements at This design enables tune the microbatches the problem even the stage training We compare different arrangements through experiments synthetic stochastic block matrices recommendation data sets The stochastic block data, with symmetry factor other optimizations We learn basic coordination always beneficial earlier training whereas LSH refinements We obtain consistent 3%-30% reduction training with the independent arrangements baseline that holds across other training hyperparametersThe paper organized Section presents necessary background the loss objective we working minibatches one-sided gradient updates In Section we define LSH microbatches coordinated minibatch arrangements In We report our experiment results comparing different arrangement methods stochastic blocks recommendation data sets Section In Section we examine properties coordinated arrangements helpful faster convergence We conclude in Section We consider embedding computations establish the arrangement training examples into a powerful performance knob In particular introduced coordinated arrangements as a principled method accelerate SGD training embedding vectors Our experiments focused the popular SGNS loss and our methods pairwise associations In future we hope explore coordinated arrangement other loss objectives deeper networks more complex association structures . We observe the training gain coordinated arrangements over baseline IND increases minibatch size The methods cap the microbatch size byJaccard* Angular perform much a higher recall helpful coplacements In particular we early training on small minibatchesb = these methods COO (which produces our largest ( unrefined microbatches).0.00 ( We quantify over the baseline IND arrangements Results precision at k TAB2 for Jaccard LSH MIX in Table*, angular* LSH MIX(where angular LSH applied a d embedding Results cosine gap for Jaccard LSH MIX angular* LSH MIX.The tables report results different minibatch sizes b and block sizes In each table the peak qualitycosine gap precision the respective coordinated method training IND to reach We also show the reduction training 0.00 ( that gained the respective coordinated method instead IND. Overall the coordinated methods consistently had training gains The gain larger with smaller blocks also The emphasized numbers the Jaccard MIX and* correspond the method provided the higher gain We Jaccard* performed for larger minibatch sizes",0.01,0.5783149523863448
"Ubuntu dialogue corpus is the largest public available dialogue corpus to make it feasible to build end-to-end
deep neural network models directly from the conversation data. One challenge of Ubuntu dialogue corpus is 
the large number of out-of-vocabulary words. In this paper we proposed an algorithm which combines the general pre-trained word embedding vectors with those  generated on the task-specific training set to address this issue.   We integrated character embedding into Chen et al's Enhanced LSTM method (ESIM) and used it to evaluate the effectiveness of our proposed method. For the task of next utterance selection, the proposed method has demonstrated a significant performance improvement against original ESIM and the new model has achieved state-of-the-art results on both Ubuntu dialogue corpus and Douban conversation corpus. In addition, we investigated the performance impact of end-of-utterance and end-of-turn token tags. The ability for a machine to converse with human in a natural and coherent manner is one of challenging goals in AI and natural language understanding. One problem in chat-oriented humanmachine dialog system is to reply a message within conversation contexts. Existing methods can be divided into two categories: retrieval-based methods BID31 BID8 BID36 and generation based methods BID28 . The former is to rank a list of candidates and select a good response. For the latter, encoder-decoder framework BID28 or statistical translation method BID19 are usually used to generate a response. It is not easy to main the fluency of the generated texts.Ubuntu dialogue corpus BID13 is the public largest unstructured multi-turns dialogue corpus which consists of about one-million two-person conversations. The size of the corpus makes it attractive for the exploration of deep neural network modeling in the context of dialogue systems. Most deep neural networks use word embedding as the first layer. They either use fixed pre-trained word embedding vectors generated on a large text corpus or learn word embedding for the specific task. The former is lack of flexibility of domain adaptation. The latter requires a very large training corpus and significantly increases model training time. Word out-of-vocabulary issue occurs for both cases. Ubuntu dialogue corpus also contains many technical words (e.g. ""ctrl+alt+f1"", ""/dev/sdb1""). The ubuntu corpus (V2) contains 823057 unique tokens whereas only 22% tokens occur in the pre-built GloVe word vectors 1 . Although character-level representation which models sub-word morphologies can alleviate this problem to some extent BID7 BID3 BID11 , character-level representation still have limitations: learn only morphological and orthographic similarity, other than semantic similarity (e.g. 'car' and 'bmw') and it cannot be applied to Asian languages (e.g. Chinese characters).In this paper, we generate word embedding vectors on the training corpus based on word2vec BID16 . Then we propose an algorithm to combine the generated one with the pre-trained word embedding vectors on a large general text corpus based on vector concatenation. The new word representation maintains information learned from both general text corpus and taskdomain. The nice property of the algorithm is simplicity and little extra computational cost will be added. It can address word out-of-vocabulary issue effectively. This method can be applied to most NLP deep neural network models and is language-independent. We integrated our methods with ESIM(baseline model) . The experimental results have shown that the proposed method has significantly improved the performance of original ESIM model and obtained state-ofthe-art results on both Ubuntu Dialogue Corpus and Douban Conversation Corpus BID34 . On Ubuntu Dialogue Corpus (V2), the improvement to the previous best baseline model (single) on R 10 @1 is 3.8% and our ensemble model on R 10 @1 is 75.9%. On Douban Conversation Corpus, the improvement to the previous best model (single) on P @1 is 3.6%.Our contributions in this paper are summarized below:1. We propose an algorithm to combine pre-trained word embedding vectors with those generated on the training corpus to address out-of-vocabulary word issues and experimental results have shown that it is very effective.2. ESIM with our method has achieved the state-of-the-art results on both Ubuntu Dialogue corpus and Douban conversation corpus.3. We investigate performance impact of two special tags on Ubuntu Dialogue Corpus: endof-utterance and end-of-turn.The rest paper is organized as follows. In Section 2, we review the related work. In Section 3 we provide an overview of ESIM (baseline) model and describe our methods to address out-ofvocabulary issues. In Section 4, we conduct extensive experiments to show the effectiveness of the proposed method. Finally we conclude with remarks and summarize our findings and outline future research directions. We propose an algorithm to combine pre-trained word embedding vectors with those generated on training set as new word representation to address out-of-vocabulary word issues. The experimental results have shown that the proposed method is effective to solve out-of-vocabulary issue and improves the performance of ESIM, achieving the state-of-the-art results on Ubuntu Dialogue Corpus and Douban conversation corpus. In addition, we investigate the performance impact of two special tags: end-of-utterance and end-of-turn. In the future, we may design a better neural architecture to leverage utterance structure in multi-turn conversations.",1078,0.637,667,1.616191904047976,"Ubuntu dialogue corpus the largest public available dialogue corpus to make feasible build end deep neural directly One challenge Ubuntu dialogue corpus outvocabulary In proposed combines the general pre-trained word vectors those on task address We integrated character embedding Chen et al's Enhanced LSTM methodESIM used evaluate our proposed method For the task next utterance selection the proposed method demonstrated against original ESIM the new model has achieved state on both Ubuntu dialogue corpus Douban conversation corpus In addition investigated the performance impact endutteranceturn token tags The ability a machine converse in challenging goals One problem in chat-oriented humanmachine dialog system to reply a message within conversation contexts Existing methods can divided retrieval-based methods BID31 BID8 BID36 generation based methods . former is to rank a list candidates and select a good response For the latter, encoder-decoder framework BID28 or statistical translation method usually a response It easy main the fluency the generated textsUbuntu dialogue corpus BID13 the public largest unstructured multi-turns dialogue corpus which consists about one-million two-person conversations The size the corpus makes attractive the exploration dialogue systems Most deep neural networks word They either use fixed pre-trained word embedding vectors generated on learn word for former is lack flexibility of domain adaptation The latter requires a very large training corpus significantly model training time Word out-vocabulary issue occurs for both cases Ubuntu dialogue corpus also many technical words "" ubuntu corpus (V2 823057 unique tokens whereas only 22% tokens occur the pre-built GloVe word vectors 1 . Although character-level representation which models sub-word morphologies alleviate to BID7 BID3 BID11 , character-level representation still have: learn only morphological and orthographic similarity other semantic similarity 'carbmw it Asian languages characters).In generate word vectors on the training corpus based word2vec BID16 Then propose combine generated one vectors on a large general text corpus based vector concatenation The new word representation maintains information learned both general text corpus taskdomain The nice property the algorithm simplicity little extra computational cost will It can address word outvocabulary issue effectively This method most NLP deep neural network models language We integrated our methods ESIM(baseline model . The experimental results the proposed method significantly original ESIM model obtained state-ofthe-art results on both Ubuntu Dialogue Corpus Douban Conversation Corpus BID34 . On Ubuntu Dialogue CorpusV2 the improvement the previous best baseline modelsingle) on R 10 @1 is our ensemble model On Douban Conversation Corpus, the improvement to the previous best modelsingle on P @1 is 3.6%.Our contributions summarized We propose combine pre-trained word vectors those on the training corpus address out-of-vocabulary word issues experimental results have ESIM with our method achieved state on both Ubuntu Dialogue corpus Douban conversation investigate performance impact two special tags Ubuntu Dialogue Corpus endof-utteranceturnThe rest paper organized In Section review the related work In Section we provide ESIM (baseline) model describe our methods address out-ofvocabulary issues In Section conduct extensive experiments show the proposed method Finally conclude remarks and summarize outline We propose combine pre-trained word vectors those on training set as new word representation to address The experimental results the proposed method to solve outvocabulary issue improves ESIM achieving state on Ubuntu Dialogue Corpus Douban conversation corpus In addition investigate the performance impact two special tags endutteranceturn In design a better neural architecture leverage utterance structure multi-turn conversations",0.01,0.27408200316930603
"Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned update functions may similarly outperform current hand-designed optimizers, especially for specific tasks. However, learned optimizers are notoriously difficult to train and have yet to demonstrate wall-clock speedups over hand-designed optimizers, and thus are rarely used in practice. Typically, learned optimizers are trained by truncated backpropagation through an unrolled optimization process. The resulting gradients are either strongly biased (for short truncations) or have exploding norm (for long truncations). In this work we propose a training scheme which overcomes both of these difficulties, by dynamically weighting two unbiased gradient estimators for a variational loss on optimizer performance. This allows us to train neural networks to perform optimization faster than well tuned first-order methods. Moreover, by training the optimizer against validation loss, as opposed to training loss, we are able to use it to train models which generalize better than those trained by first order methods. We demonstrate these results on problems where our learned optimizer trains convolutional networks in a fifth of the wall-clock time compared to tuned first-order methods, and with an improvement Gradient based optimization is a cornerstone of modern machine learning. Improvements in optimization have been critical to recent successes on a wide variety of problems. In practice, this typically involves analysis and development of hand-designed optimization algorithms BID22 BID7 BID34 BID15 . These algorithms generally work well on a wide variety of tasks, and are tuned to specific problems via hyperparameter search. On the other hand, a complementary approach is to learn the optimization algorithm BID5 BID30 BID13 BID0 BID36 BID19 BID2 . That is, to learn a function to perform optimization, targeted to particular problems of interest. In this way, the algorithm may learn task specific structure, enabling dramatic performance improvements over more general optimizers.However, training learned optimizers is notoriously difficult. Existing work in this vein can be classified into two broad categories. On one hand are black-box methods such as evolution BID11 BID3 , random search BID6 , reinforcement learning BID2 BID18 BID40 , or Bayesian optimization BID31 . However, these methods scale poorly with the number of optimizer parameters. The other approach is to use first-order methods, by computing the gradient of some measure of optimizer effectiveness with respect to the optimizer parameters. Computing these gradients is costly as we need to iteratively apply the learned update rule, and then backpropagate through these applications, a technique commonly referred to as ""unrolled optimization"" BID4 BID21 . To address the problem of backpropagation through many optimization steps (analogous to many timesteps in recurrent neural networks), many works make use of truncated backpropagation though time (TBPTT) to partition the long unrolled computational graph into separate pieces BID35 BID33 . This yields computational savings, but at the cost of increased bias BID33 and/or exploding gradients due to many iterated update steps BID26 BID25 . Existing methods address the bias at the cost of increased variance or computa-tional complexity BID38 BID24 BID33 . Previous techniques for training RNNs via TBPTT have thus far not been effective for training optimizers.In this paper, we analytically and experimentally explore the debilitating role of bias and exploding gradients on training optimizers ( §2.3). We then show how these pathologies can be remedied by optimizing the parameters of a distribution over the optimizer parameters, known as variational optimization BID32 ) ( §3). We define two unbiased gradient estimators for this objective: a reparameterization based gradient, and evolutionary strategies BID27 BID23 . By dynamically reweighting the contribution of these two gradient estimators, we are able to avoid strongly biased or exploding gradients, and thus stably and efficiently train learned optimizers.We demonstrate the utility of this approach by training a learned optimizer to target optimization of convolutional networks on image classification ( §4). On the targeted task distribution, this learned optimizer achieves better validation loss, and is five times faster in wall-clock time, compared to well tuned hand-designed optimizers such as SGD+Momentum, RMSProp, and ADAM ( FIG0 ). While not the explicit focus of this work, we also find that the learned optimizer demonstrates promising generalization ability on out of distribution tasks ( Figure 6 ). Training and validation curves for a three layer CNN, trained on a subset of 32x32 imagenet classes not seen during outer-training of the optimizer. Dashed lines indicate the best achieved performance over an additional 130 seconds. We show two learned optimizers -one trained to minimize training loss, and the other trained to minimize validation loss on the inner-problem. We compare against Adam, RMSProp, and SGD+Momentum, individually tuned for the train and validation loss (Panel (a) and (b), respectively). On training loss (a), our learned optimizer approaches zero training loss, and achieves it's smallest loss values in less than one quarter the wall-clock time.On validation loss (b), our learned optimizer achieves a lower minimum, in roughly one third the wall-clock time. Shaded regions correspond to 25 and 75 percentile over five random initializations of the CNN. For plots showing performance in terms of step count rather than wall clock (where we achieve even more dramatic speedups), and for more task instances, see Appendix D. (c) Distribution of the performance difference between the learned optimizers and a tuned baseline of either Adam, RMSProp, or Momentum (loss improvement). Positive values indicate performance better than baseline. We show training and validation losses for the outer-testing task distribution. On the majority of tasks, the learned optimizers outperform the baseline. In this work we demonstrate two difficulties when training learned optimizers: ""exploding"" gradients, and a bias introduced by truncated backpropagation through time. To combat this, we construct a variational bound of the outer-objective and minimize this via a combination of reparameterization and ES style gradient estimators. By using our combined estimator and a curriculum over truncation step we are able to train learned optimizers that achieve more than five times speedup on wallclock time as compared to existing optimizers.In this work, we focused on applying optimizers to a restricted family of tasks. While useful on its own right (e.g. rapid retraining of models on new data), future work will explore the limits of ""no free lunch"" BID39 to understand how and when learned optimizers generalize across tasks. We are also interested in using these methods to better understand what problem structure our learned optimizers exploit. By analyzing the trained optimizer, we hope to develop insights that may transfer back to hand-designed optimizers. Outside of meta-learning, we believe the gradient estimator presented here can be used to train other long time dependence recurrent problems such as neural turning machines BID12 , or neural GPUs BID14 .Much in the same way deep learning has replaced feature design for perceptual tasks, we see metalearning as a tool capable of learning new and interesting algorithms, especially for domains with unexploited problem-specific structure. With better outer-training stability, we hope to improve our ability to learn interesting algorithms, both for optimizers and beyond.",1465,0.814,868,1.6877880184331797,"Deep learning shown learned functions dramatically on Analogously suggests learned update functions similarly current hand-designed optimizers specific tasks However learned optimizers notoriously train have yet demonstrate wall-clock speedups over hand-designed optimizers rarely Typically learned optimizers trained through an unrolled optimization process The resulting gradients either strongly biasedfor short truncations have exploding norm ( In this work propose a training scheme overcomes both dynamically weighting two unbiased gradient estimators a variational loss on optimizer performance This allows train optimization faster well tuned Moreover by training the optimizer against validation loss as training loss use it train models trained first order methods We demonstrate these results problems where our learned optimizer trains a fifth of compared tuned an improvement Gradient based optimization is a cornerstone Improvements optimization have critical recent successes on problems In practice typically analysis development hand-designed optimization BID22 BID7 BID34 BID15 . These algorithms generally tuned specific problems via hyperparameter search On a complementary approach learn the optimization BID5 BID30 . That to learn a function to optimization targeted particular problems of In the algorithm may learn task specific structure enabling dramatic performance improvements more general optimizersHowever training learned notoriously Existing work this vein classified On are black-box methods evolution BID11 BID3 , reinforcement However these methods scale poorly optimizer parameters The other approach first-order methods by computing some measure optimizer effectiveness with Computing these gradients costly as iteratively apply the learned update rule through these applications a technique ""unrolled optimization BID4 BID21 To address through many optimization steps many timesteps many works make though timeTBPTT partition the long unrolled computational graph separate pieces BID35 BID33 . This yields computational savings at increased bias BID33 exploding gradients due many iterated update steps . Existing methods address the bias at increased variance or computa-tional complexity BID38 BID24 BID33 . Previous techniques training RNNs via TBPTT thus optimizersIn explore the debilitating role bias exploding gradients § We then show these pathologies optimizing the parameters a distribution the optimizer parameters known BID32 ) § We define two unbiased gradient estimators this objective a reparameterization based gradient evolutionary strategies BID27 BID23 By dynamically reweighting the contribution these two gradient estimators avoid strongly or exploding stably and train learned optimizersWe demonstrate training target optimization image classification § On the targeted task distribution this learned optimizer achieves better validation loss five wall-clock time well tuned hand-designed optimizers SGD+Momentum RMSProp ADAM ( FIG0 While not explicit focus also find the learned optimizer demonstrates promising generalization ability on out distribution tasks Figure Training and validation curves a three layer CNN, trained 32x32 imagenet classes not seen during outer-training of Dashed lines indicate the best achieved performance over an additional 130 seconds We show two learned optimizers -one trained minimize training loss validation loss on the inner-problem We compare against Adam RMSProp SGD+Momentum individually tuned the train and validation lossPanel ( On training loss (a our learned optimizer approaches achieves's smallest loss values less than one quarter the wall-clock timeOn validation loss achieves, in Shaded regions correspond 25 and 75 percentile over five random initializations the CNN. For plots showing performance terms step count rather wallwhere we achieve even more dramatic speedups and more task instances (c) Distribution the performance difference the learned optimizers a tuned baseline either Adam, RMSProp Momentumloss improvement Positive values indicate performance better baseline We show training and validation losses the outer-testing task distribution On the majority tasks the learned optimizers the baseline In this work demonstrate two difficulties when training learned optimizers ""exploding gradients a bias introduced through time To combat construct variational bound the outer-objective minimize this via ES style gradient estimators By using our combined estimator a curriculum over truncation step train learned optimizers that achieve more five speedup wallclock time asIn focused applying a restricted family tasks While useful on ( rapid retraining models on new data future work explore ""no free lunch"" BID39 to and learned optimizers generalize across tasks We also using these methods better problem structure our learned optimizers exploit By analyzing the trained optimizer hope insights transfer back Outside meta-learning believe the gradient estimator presented train other long time dependence recurrent problems neural turning machines BID12 , or neural GPUs BID14 .Much in deep learning replaced feature design perceptual tasks see metalearning capable domains unexploited problem-specific structure With better outer-training stability we hope learn interesting algorithms both optimizers beyond",0.01,0.45650261225697464
"Asynchronous distributed gradient descent algorithms for training of deep neural
 networks are usually considered as inefficient, mainly because of the Gradient delay
 problem. In this paper, we propose a novel asynchronous distributed algorithm
 that tackles this limitation by well-thought-out averaging of model updates, computed
 by workers. The algorithm allows computing gradients along the process
 of gradient merge, thus, reducing or even completely eliminating worker idle time
 due to communication overhead, which is a pitfall of existing asynchronous methods.
 We provide theoretical analysis of the proposed asynchronous algorithm,
 and show its regret bounds. According to our analysis, the crucial parameter for
 keeping high convergence rate is the maximal discrepancy between local parameter
 vectors of any pair of workers. As long as it is kept relatively small, the
 convergence rate of the algorithm is shown to be the same as the one of a sequential
 online learning. Furthermore, in our algorithm, this discrepancy is bounded
 by an expression that involves the staleness parameter of the algorithm, and is
 independent on the number of workers. This is the main differentiator between
 our approach and other solutions, such as Elastic Asynchronous SGD or Downpour
 SGD, in which that maximal discrepancy is bounded by an expression that
 depends on the number of workers, due to gradient delay problem. To demonstrate
 effectiveness of our approach, we conduct a series of experiments on image
 classification task on a cluster with 4 machines, equipped with a commodity communication
 switch and with a single GPU card per machine. Our experiments
 show a linear scaling on 4-machine cluster without sacrificing the test accuracy,
 while eliminating almost completely worker idle time. Since our method allows
 using commodity communication switch, it paves a way for large scale distributed
 training performed on commodity clusters. Distributed training of deep learning models is devised to reduce training time of the models. Synchronous distributed SGD methods, such as BID0 and BID7 , perform training using mini-batch size of several dozens of thousands of images. However, they either require expensive communication switch for fast gradient sharing between workers or, otherwise, introduce a high communication overhead during gradient merge, where workers are idle waiting for communicating gradients over communication switch.Distributed asynchronous SGD methods reduce the communication overhead on one hand, but usually introduce gradient delay problem on the other hand, as described in BID0 . Indeed, usually in an asynchronous distributed approach, a worker w obtains a copy of the central model, computes a gradient on this model and merges this gradient back into the central model. Note, however, that since the worker obtained the copy of the central model till it merges its gradient back into the central model, other workers could have merged their gradients into the central model. Thus, when the worker w merges its gradient into a central model, that model may have been updated and, thus, the gradient of the worker w is delayed, leading to gradient delay problem. We will refer to algorithms that suffer from gradient delay problem as gradient delay algorithms, e.g. Downpour SGD BID1 .As our analysis reveals in Section 3, the quantity that controls the convergence rate of an asynchronous distributed algorithm, is maximal pairwise distance -the maximal distance between local models of any pair of workers at any iteration. Usually gradient delay algorithms do not limit this distance and it may depend on the number of asynchronous workers, which may be large in large clusters. This may explain their poor scalability, convergence rate and struggle to reach as high test accuracy as in synchronous SGD algorithms, as experimentally shown in BID0 .While Elastic Averaging SGD Zhang et al. (2015) is also a gradient delay algorithm, it introduces a penalty for workers, whose models diverge too far from the central model. This, in turn , helps to reduce the maximal pairwise distance between local models of workers and, thus, leads to better scalability and convergence rate. In contrast, our analysis introduces staleness parameter that directly controls the maximal pair distance of the asynchronous workers.Our analysis builds on the work of BID10 , who studied convergence rate of gradient delay algorithms, when the maximum delay is bounded. They provided analysis for Lipschitz continuous losses, strongly convex and smooth losses. While they show that bounding staleness can improve convergence rate of a gradient delay algorithm, in their algorithm each worker computes exactly one gradient and is idle, waiting to merge the gradient with PS model and download the updated PS model back to the worker.The main contributions of this paper are the following. We present and analyze a new asynchronous distributed SGD method that both reduces idle time and eliminates gradient delay problem. Our main theoretic result shows that an asynchronous distributed SGD algorithm can achieve convergence rate as good as in sequential online learning. We support this theoretic result by conducting experiments that show that on a cluster with up to 4 machines, with a single GPU per machine and a commodity communication switch, our asynchronous method achieves linear scalability without degradation of the test accuracy. We presented a new asynchronous distributed SGD method. We show empirically that it reduces both idle time and gradient delay. We analyze the synchronous part of the algorithm, and show theoretical regret bounds.The proposed method shows promising results on distributed training of deep neural networks. We show that our method eliminates waiting times, which allows significant improvements in run time, compared to fully synchronous setup. The very fact of efficient hiding of communication overhead opens opportunity for distributed training over commodity clusters. Furthermore, the experiments show linear scaling of training time from 1 to 4 GPU's without compromising the final test accuracy.Proof. We start with RHS of (8) DISPLAYFORM0 By the definition of average parameter vector (1), the first summand in RHS of (29) equals x iβ+t , while the last two summands cancel each other.Proof of Lemma 3.3.Proof. At iteration (i − 1)β after reset operation FORMULA7 , workers w and w start updating their local parameter vectors for β iterations, so that at the end of the cycle before the reset operation (7), DISPLAYFORM1 The reset operation FORMULA7 at iteration iβ adds the updates of workers w and w , computed at iterations (i − 1)β + 1, . . . , iβ, to the common copy of PS model, so that x (i−1)β,w − x (i−1)β,w = 0. Thus, after the reset operation DISPLAYFORM2 Finally, from (31), our assumption on the size of the gradient ∇f t (x) and from decreasing learning rate, during this cycle that started at iteration (i − 1)β, the distance between workers w and w grows at most by DISPLAYFORM3 Proof of Lemma 3.4.Proof. We decompose our progress as follows DISPLAYFORM4 To prove (33) from (32), we used (12) Dividing both sides by η iτ +t and moving < x iτ +t − x * ,g iτ +t > to the LHS completes the proof.Proof of Theorem 3.5.Proof. First we state a useful inequality: For n vectors a i , i = 1, . . . , n (by induction on n): DISPLAYFORM5 Also we will use the following sum bounds: DISPLAYFORM6 and DISPLAYFORM7 We start with summing (13) along iterations: DISPLAYFORM8 Next, we borrow the derivation of expressions (38) and (39) from the proof of Theorem 2, BID9 . Note, however, that we added a new term to (37) -the last term that is specific to Algorithm 2. This term does not appear in the proof of Theorem 2, BID9 . By the Lipschitz property of gradients and the definition of η t , we can bound the first summand of the above regret expression via DISPLAYFORM9 Also DISPLAYFORM10 We omit the negative factor − DISPLAYFORM11 . Now we start the analysis of the last term in (37), which is new and specific to Algorithm 2. Using (34), we bound the last summand of (37) DISPLAYFORM12 Substituting FORMULA3 , FORMULA3 and FORMULA4 into FORMULA3 , we get DISPLAYFORM13 We use (14) in the above expression DISPLAYFORM14 Now, note that the last summand in (50) corresponds to the summand in (18) for k = j − 1. This completes the proof.Proof of Lemma 3.7.Proof. First note that from (19) it follows that η t βH ≤ 0.1 .Since η i shrinks down, as i grows up, and η t H + 1 > 1, (18) yields ||x iβ+j,w − x iβ+j,w || ≤ (η iβ H + 1) β · ||x iβ,w − x iβ,w || + η iβ β−1 k=0 ||e iβ+k,w − e iβ+k,w || .After the expansion of (η iβ H + 1) β in (52) into Taylor sequence and applying a simple algebra DISPLAYFORM15 From FORMULA1 we can bound DISPLAYFORM16 Assigning FORMULA4 into FORMULA2 , ||x iβ+j,w − x iβ+j,w || ≤ 1.2 · ||x iβ,w − x iβ,w || + 1.2 · η iβ β−1 k=0 ||e iβ+k,w − e iβ+k,w || .Since e iτ +k,w and e iτ +k,w are i.i.d. with mean 0, E||e iβ+k,w − e iβ+k,w || = var(e iβ+k,w − e iβ+k,w ) = 2var(e iβ+k,w ) .Taking expectation of the both sides of (55), substituting (56) into the resulting inequality and using the assumption on variance of random variables e t,w , we complete the proof.Proof of Lemma 3.8.Proof. From Lemma 3.3, ||x i0β,w − x i0β,w || ≤ 2Lτ η (i0−1)β .From FORMULA2 , each cycle j after iteration i 0 β, reduces the distance between w and w by factor of 0.2, while adding to the distance the value of 1.2 · η iβ+j τ s. This means that after the number of cycles j 0 j 0 = log 1.2 · η i0β τ s 2Lτ η (i0−1)β = log s L , for any i ≥ i 0 + j 0 , the first summand in (22) gets bounded by 0.8 · η iβ τ s.Proof of Theorem 3.9.Proof. To prove this theorem , we follow the proof of Theorem 3.5 and develop an alternative bound on ||x t,w − x t || in (42).We will split the sum in (40) into two ranges of t: t < t 0 + j 0 β and t ≥ t 0 + j 0 β for t 0 , j 0 , defined in FORMULA1 and FORMULA2 respectively. To simplify notation, from (23), we can assume that j 0 is a constant and we can assume that t 0 + j 0 ≤ 2t 0 . For t < 2t 0 , we use (48) to show 2t0−1 t=1 ||x t − x * || · ||g t −g t || ≤ 2τ F LH(2τ + 2σ DISPLAYFORM17 For t ≥ 2t 0 , we first observe DISPLAYFORM18 Next we use (24) to bound the above expression.E||x t,w − x t || ≤ 2η t−τ τ s .Substituting this bound into (42), we get E||g t −g t || ≤ 2Hη t−τ τ s .Using FORMULA1 Combining FORMULA5 and FORMULA2 in FORMULA4 and using the definition (19) of t 0 DISPLAYFORM19 Using the assumption (25), and substituting into (41) we prove (26). Finally we use value σ = F L to prove (27).",2551,1.151,1384,1.8432080924855492,"Asynchronous distributed gradient descent algorithms training of usually inefficient mainly the Gradient delay problem In a novel asynchronous distributed algorithm tackles this limitation well-thought-out averaging model updates computed workers The algorithm allows computing gradients along the process gradient merge thus, reducing or completely worker idle time due communication existing asynchronous methods We provide theoretical analysis the proposed asynchronous algorithm show its regret bounds According our analysis the crucial parameter keeping high convergence rate the maximal discrepancy local parameter vectors any pair workers As long kept relatively the convergence rate the algorithm shown a sequential online learning. Furthermore our algorithm this discrepancy bounded an expression involves the staleness parameter independent on workers This the main differentiator our approach other solutions Elastic Asynchronous SGD or Downpour SGD that maximal discrepancy bounded an expression depends workers due gradient delay problem To demonstrate effectiveness our approach conduct image classification task on a cluster with 4 machines equipped a commodity communication switch a single GPU card per Our experiments a linear scaling on 4-machine cluster without sacrificing the test accuracy eliminating almost completely worker idle Since our method allows using commodity communication switch paves large scale distributed training performed commodity clusters Distributed training devised of Synchronous distributed SGD methods BID0 perform training using mini-batch size several dozens thousands images However they either require expensive communication switch for fast gradient sharing workers, otherwise introduce high communication during gradient merge idle waiting communicating gradients over communication switchDistributed asynchronous SGD methods reduce on one hand usually introduce gradient delay problem described BID0 . Indeed usually an asynchronous distributed approach a worker w obtains the central model a gradient on back Note, since the worker obtained the central model till merges its gradient back other workers merged Thus the worker w merges its gradient a central model may updated, w delayed leading gradient delay problem We refer algorithms suffer gradient delay problem algorithms Downpour SGD BID1 .As our analysis reveals in the quantity that controls an asynchronous distributed algorithm maximal pairwise distance -the maximal distance local models any pair workers any iteration Usually gradient delay algorithms do limit this distance depend asynchronous workers large large clusters This may explain their poor scalability convergence rate struggle reach as high test accuracy in synchronous SGD algorithms experimentally shown BID0 .While Elastic Averaging SGD Zhang (2015 is also a gradient delay algorithm introduces a penalty workers, whose models diverge too the central model This, , helps the maximal pairwise distance local models workers, leads better scalability and convergence rate In contrast our analysis introduces staleness parameter directly the maximal pair distance the asynchronous workersOur analysis builds BID10 , studied convergence rate gradient delay algorithms when bounded They provided analysis Lipschitz continuous losses strongly convex and smooth losses While they show bounding staleness improve convergence rate a gradient delay algorithm in their algorithm each worker exactly is idle waiting merge PS model download backThe main contributions We present and a new asynchronous distributed SGD method both reduces idle time eliminates gradient delay problem Our main theoretic result shows an asynchronous distributed SGD algorithm convergence rate as good in sequential online learning We support this theoretic result conducting on a cluster with up to 4 machines with per a commodity communication switch our asynchronous method linear scalability degradation the test accuracy We presented a new asynchronous distributed SGD method We show empirically it reduces both idle time gradient delay We analyze the synchronous part theoretical regret boundsThe proposed method shows on distributed training We show our method eliminates waiting times allows significant improvements run time compared fully synchronous setup The very fact efficient hiding communication overhead opens opportunity distributed training over commodity clusters Furthermore the experiments linear scaling training time from to 4 GPU's without compromising the final test accuracyProof. We start RHS of (8) DISPLAYFORM0 By the definition average parameter vector the first summand in29 equals x iβ+t , while cancelProof. At iteration (i − 1)β after reset operation FORMULA7 , workers w and start updating their local parameter vectors β iterations so at before7 DISPLAYFORM1 The reset at iβ adds workers , computed + . . . , iβ to the common copy PS model so xw Thus after the reset operation DISPLAYFORM2 Finally from (31 our assumption on the gradient ��f t from decreasing learning rate during this cycle that started iteration − 1)β the distance workers w grows most by DISPLAYFORM3 Proof We decompose our progress as follows DISPLAYFORM4 To prove (33 from ( used (12 both sides �� iτ +t moving < x − * ,g > to the LHS completes the proofProof. First we state a useful inequality For n vectors a i . . . , n (by induction on n): DISPLAYFORM5 Also we the following sum bounds and We start summing13 along iterations Next borrow expressions38 BID9 . Note, we added (37 -the last specific Algorithm 2 This term does the proof Theorem 2 BID9 . By the Lipschitz property gradients the definition �� t bound the first summand the above regret expression via DISPLAYFORM9 Also We omit − Now start the analysis the last term (37 new specific Algorithm Using (34 bound the last summand37 DISPLAYFORM12 Substituting FORMULA3 , and we We14 Now note in50 corresponds18 k = j − This completes the proof.Proof Lemma 3.7.Proof. First note from (19 it �� t βH ≤ .Since i shrinks down as i grows H + > ( yields ||x iβ+jw || ≤� H β ·, .After the expansion� in52 into Taylor sequence applying a simple algebra DISPLAYFORM15 From FORMULA1 bound Assigning FORMULA4 into , 1.2 · e iτk and with mean 0 ) .Taking expectation the both sides55 the resulting inequality on variance random variables e tw we completeProof. From Lemma 3.3, ||x i0βw − x i0βw || ≤ 2Lτ �� .From FORMULA2 each cycle j after iteration 0 reduces w by factor adding the value 1.2 · �� iβ+j τ s. This means after the number cycles j 0 j log 1.2 · �� i0β τ s 2Lτ �� ( s L , for i ≥ the first summand in22 gets bounded. To prove this theorem , follow develop bound ||x t,w − x t || in (42).We split the sum in ( two ranges t < 0 + j for defined FORMULA1 To simplify notation from (23 assume j 0 constant we t + ≤ 2t For t < 2t 0 we (48 show 2t0−1 ||x t − * || · ||g t −g t || ≤ 2τ F LH(2τ + DISPLAYFORM17 For ≥ first observe Next24 bound the above expressionE||x,w − t ≤� t−τ τ s bound into42 FORMULA1 Combining the definition19 t 0 DISPLAYFORM19 Using the assumption and into we prove Finally use value �� = F L to prove (27",0.02,0.8524993058840111
"Neural network quantization is becoming an industry standard to efficiently deploy deep learning models on hardware platforms, such as CPU, GPU, TPU, and FPGAs. However, we observe that the conventional quantization approaches are vulnerable to adversarial attacks. This paper aims to raise people's awareness about the security of the quantized models, and we designed a novel quantization methodology to jointly optimize the efficiency and robustness of deep learning models. We first conduct an empirical study to show that vanilla quantization suffers more from adversarial attacks. We observe that the inferior robustness comes from the error amplification effect, where the quantization operation further enlarges the distance caused by amplified noise. Then we propose a novel Defensive Quantization (DQ) method by controlling the Lipschitz constant of the network during quantization, such that the magnitude of the adversarial noise remains non-expansive during inference. Extensive experiments on CIFAR-10 and SVHN datasets demonstrate that our new quantization method can defend neural networks against adversarial examples, and even achieves superior robustness than their full-precision counterparts, while maintaining the same hardware efficiency as vanilla quantization approaches. As a by-product, DQ can also improve the accuracy of quantized models without adversarial attack. Neural network quantization BID10 BID34 BID12 ) is a widely used technique to reduce the computation and memory costs of neural networks, facilitating efficient deployment. It has become an industry standard for deep learning hardware. However, we find that the widely used vanilla quantization approaches suffer from unexpected issues -the quantized model is more vulnerable to adversarial attacks ( FIG1 ). Adversarial attack is consist of subtle perturbations on the input images that causes the deep learning models to give incorrect labels BID28 . Such perturbations are hardly detectable by human eyes but can easily fool neural networks. Since quantized neural networks are widely deployed in many safety-critical scenarios, e.g., autonomous driving BID1 , the potential security risks cannot be neglected. The efficiency and latency in such applications are also important, so we need to jointly optimize them.The fact that quantization leads to inferior adversarial robustness is counter intuitive, as small perturbations should be denoised with low-bit representations. Recent work BID31 ) also demonstrates that quantization on input image space , i.e. color bit depth reduction, is quite effective to defend adversarial examples. A natural question then rises, why the quantization operator is yet effective when applied to intermediate DNN layers ? We analyze that such issue is caused by the error amplification effect of adversarial perturbation BID15 -although the magnitude of perturbation on the image is small, it is amplified significantly when passing through deep neural network (see FIG4 . The deeper the layers are, the more significant such side effect is. Such amplification pushes values into a different quantization bucket, which is undesirable. We conducted empirical experiments to analyze how quantization influences the activation error between clean and adversarial samples FIG4 ): when the magnitude of the noise is small, activation quantization is capable of reducing the errors by eliminating small perturbations; However, when the magnitude of perturbation is larger than certain threshold, quantization instead amplify the errors, which causes the quantized model to make mistakes. We argue that this is the main reason causing the inferior robustness of the quantized models.In this paper, we propose Defensive Quantization (DQ) that not only fixes the robustness issue of quantized models, but also turns activation quantization into a defense method that further boosts adversarial robustness. We are inspired by the success of image quantization in improving robustness. Intuitively, it will be possible to defend the attacks with quantization operations if we can keep the magnitude of the perturbation small. However, due to the error amplification effect of gradient based adversarial samples, it is non-trivial to keep the noise at a small scale during inference. Recent works BID5 BID21 have attempted to make the network non-expansive by controlling the Lipschitz constant of the network to be smaller than 1, which has smaller variation change in its output than its input. In such case, the input noise will not propagate through the intermediate layers and impact the output, but attenuated. Our method is built on the theory. Defensive quantization not only quantizes feature maps into low-bit representations, but also controls the Lipschitz constant of the network, such that the noise is kept within a small magnitude for all hidden layers. In such case, we keep the noise small, as in the left zone of FIG4 , quantization can reduce the perturbation error. The produced model with our method enjoys better security and efficiency at the same time.Experiments show that Defensive Quantization (DQ) offers three unique advantages. First, DQ provides an effective way to boost the robustness of deep learning models while maintains the efficiency. Second, DQ is a generic building block of adversarial defense, which can be combined with other adversarial defense techniques to advance state-of-the-art robustness. Third, our method makes quantization itself easier thanks to the constrained dynamic range. In this work, we aim to raise people's awareness about the security of the quantized neural networks, which is widely deployed in GPU/TPU/FPGAs, and pave a possible direction to bridge two important areas in deep learning: efficiency and robustness. We connect these two domains by designing a novel Defensive Quantization (DQ) module to defend adversarial attacks while maintain the efficiency. Experimental results on two datasets validate that the new quantization method can make the deep learning models be safely deployed on mobile devices. BID16 . To make a comparison, we also trained a full precision model and a ReLU6 quantized model following same setting. All the quantized models use bit=2. We tested the trained model using PGD attack by BID16 under both white-box and black-box setting. We use a VGG-16 model separately trained with PGD adversarial training as the black-box attacker. The results are provided in TAB8 . Our white-box result is consistent with BID22 , where Tanh based quantizaion with PGD training gives much higher white-box accuracy compared to the full precision model. However, we can see that the black-box robustness decreases. Worse still, the black-box attack successful rate is even lower than white-box, which is abnormal since black-box attack is generally weaker than white-box. This phenomenon indicates severe gradient masking problem BID19 BID2 , which gives a false sense of security. As a comparison, we also trained a ReLU6 quantized model. With ReLU6 quantization, there is no sign of gradient masking, nor improvement in robustness, indicating that gradient masking problem majorly comes from Tanh activation function. Actually, ReLU6 quantized model has slightly worse robustness.",1373,0.793,818,1.678484107579462,"Neural network quantization becoming to efficiently deploy hardware platforms CPU TPU we observe the conventional quantization approaches vulnerable This paper aims raise the security the quantized models we designed jointly optimize We first conduct show vanilla quantization suffers more adversarial attacks We observe the inferior robustness comes the error amplification effect the quantization operation further caused amplified noise Then propose a novel Defensive Quantization (DQ) method by controlling the Lipschitz constant the network during quantization such remains nonexpansive inference Extensive experiments CIFAR-10 and SVHN datasets demonstrate our new quantization method defend neural networks adversarial examples even achieves superior robustness than their full-precision counterparts while the same hardware efficiency vanilla quantization approaches As DQ can improve quantized models without adversarial attack Neural network quantization BID10 BID34 BID12 ) reduce facilitating efficient deployment It deep learning hardware However we find the widely used vanilla quantization approaches suffer unexpected issues -the quantized model vulnerable FIG1 Adversarial attack consist subtle perturbations on the input images causes give incorrect labels BID28 . Such perturbations hardly detectable but easily fool neural networks Since quantized neural networks widely deployed many safety-critical scenarios autonomous BID1 , neglected The efficiency latency in such applications also jointlyThe fact quantization leads inferior adversarial robustness counter should denoised low-bit representations Recent work BID31 ) also demonstrates quantization on input image space , quite to defend adversarial examples A natural question then rises the quantization operator yet effective intermediate DNN layers ? We analyze that such issue caused the error amplification effect BID15 -although on the image amplified significantly passing deep neural networksee FIG4 . deeper the more significant such side effect Such amplification pushes values a different quantization bucket undesirable We conducted empirical experiments analyze quantization the activation error between clean and adversarial samples FIG4 ): when the magnitude activation quantization capable eliminating; However certain threshold instead amplify causes the quantized model make mistakes We argue this causing the inferior robustness the quantized modelsIn Defensive Quantization that not fixes turns activation quantization a defense method further boosts We inspired image quantization improving robustness Intuitively will possible defend the attacks quantization operations if keep small However due the error amplification effect gradient based adversarial samples non keep during inference Recent works BID5 BID21 have attempted make the network nonexpansive controlling the Lipschitz constant of to smaller smaller variation change its output its input In such case the input noise propagate impact, attenuated Our method built. Defensive quantization not feature maps into low-bit representations controls the Lipschitz constant the network such kept a small magnitude for all hidden layers In such case keep the noise small the left zone FIG4 quantization can reduce The produced model with our method enjoys better security efficiency atExperiments Defensive Quantization offers three unique advantages First DQ provides boost deep learning models while maintains Second DQ a generic building block adversarial defense combined advance state robustness Third our method makes quantization itself thanks the constrained dynamic range In this work aim raise the security the quantized neural networks widely deployed GPU/TPU/FPGAs pave a possible direction bridge two important areas efficiency We connect these two domains designing a novel Defensive Quantization (DQ) module defend adversarial attacks while maintain. Experimental results two datasets validate the new quantization method make be safely deployed BID16 . To also trained a full precision model a ReLU6 quantized model following same setting All the quantized models use bit=2 We tested the trained model PGD attack by BID16 under We use a VGG-16 model separately trained PGD adversarial training as the black-box attacker The results provided TAB8 . Our white-box result consistent BID22 , where Tanh based quantizaion with PGD training gives the full precision model However we the black-box robustness decreases. Worse the black-box attack successful rate even, abnormal since generally weaker This phenomenon indicates severe gradient masking problem BID19 BID2 , gives As a comparison also trained a ReLU6 quantized model With ReLU6 quantization gradient masking improvement robustness indicating majorly comes Tanh activation function Actually ReLU6 quantized model has slightly worse robustness",0.01,0.43279706483437186
"Recurrent Neural Networks (RNNs) continue to show  outstanding performance in sequence modeling tasks. However, training RNNs on long sequences often face challenges like slow inference, vanishing gradients and difficulty in capturing long term dependencies. In backpropagation through time settings, these issues are tightly coupled with the large, sequential computational graph resulting from unfolding the RNN in time. We introduce the Skip RNN model which extends existing RNN models by learning to skip state updates and shortens the effective size of the computational graph. This model can also be encouraged to perform fewer state updates through a budget constraint. We evaluate the proposed model on various tasks and show how it can reduce the number of required RNN updates while preserving, and sometimes even improving, the performance of the baseline RNN models. Source code is publicly available at https://imatge-upc.github.io/skiprnn-2017-telecombcn/. Recurrent Neural Networks (RNNs) have become the standard approach for practitioners when addressing machine learning tasks involving sequential data. Such success has been enabled by the appearance of larger datasets, more powerful computing resources and improved architectures and training algorithms. Gated units, such as the Long Short-Term Memory (Hochreiter & Schmidhuber, 1997 ) (LSTM) and the Gated Recurrent Unit (Cho et al., 2014 ) (GRU), were designed to deal with the vanishing gradients problem commonly found in RNNs (Bengio et al., 1994) . These architectures have been popularized, in part, due to their impressive results on a variety of tasks in machine translation (Bahdanau et al., 2015) , language modeling BID17 and speech recognition (Graves et al., 2013) .Some of the main challenges of RNNs are in their training and deployment when dealing with long sequences, due to their inherently sequential behaviour. These challenges include throughput degradation, slower convergence during training and memory leakage, even for gated architectures (Neil et al., 2016) . Sequence shortening techniques, which can be seen as a sort of conditional computation (Bengio et al., 2013; Bengio, 2013; Davis & Arel, 2013) in time, can alleviate these issues. The most common approaches, such as cropping discrete signals or reducing the sampling rate in continuous signals, are based on heuristics and can be suboptimal. In contrast , we propose a model that is able to learn which samples (i.e., elements in the input sequence) need to be used in order to solve the target task. Consider a video understanding task as an example: scenes with large motion may benefit from high frame rates, whereas only a few frames are needed to capture the semantics of a mostly static scene.The main contribution of this work is a novel modification for existing RNN architectures that allows them to skip state updates, decreasing the number of sequential operations performed, without requiring any additional supervision signal. This model , called Skip RNN, adaptively determines whether the state needs to be updated or copied to the next time step. We show how the network can be encouraged to perform fewer state updates by adding a penalization term during training, allowing us to train models under different computation budgets. The proposed modification can generally be integrated with any RNN and we show, in this paper, implementations with well-known RNNs, namely LSTM and GRU. The resulting models show promising results on a series of sequence modeling tasks. In particular , we evaluate the proposed Skip RNN architecture on six sequence learning problems: an adding task, sine wave frequency discrimination, digit classification, sentiment analysis in movie reviews, action classification in video, and temporal action localization in video 1 . We presented Skip RNNs as an extension to existing recurrent architectures enabling them to skip state updates thereby reducing the number of sequential operations in the computation graph. Unlike other approaches, all parameters in Skip RNN are trained with backpropagation. Experiments conducted with LSTMs and GRUs showed that Skip RNNs can match or in some cases even outperform the baseline models while relaxing their computational requirements. Skip RNNs provide faster and more stable training for long sequences and complex models, owing to gradients being backpropagated through fewer time steps resulting in a simpler optimization task. Moreover, the introduced computational savings are better suited for modern hardware than those methods that reduce the amount of computation required at each time step (Koutnik et al., 2014; Neil et al., 2016; Chung et al., 2017) .A ADDITIONAL EXPERIMENTS",943,0.451,566,1.6660777385159011,"Recurrent Neural Networks continue show outstanding performance sequence modeling tasks However training RNNs long sequences often face like slow inference vanishing gradients difficulty capturing long term dependencies In backpropagation through time settings these issues tightly the large, sequential computational graph resulting unfolding the RNN We introduce the Skip RNN model extends learning skip state updates shortens the effective size the computational graph This model can encouraged perform fewer state updates through a budget constraint We evaluate the proposed model on various tasks show reduce required RNN updates while preserving, sometimes Source code publicly https://imatge-upc.github.io/skiprnn-2017-telecombcn/. Recurrent Neural Networks practitioners when addressing machine learning tasks involving sequential data Such success enabled the appearance larger datasets more powerful computing resources improved architectures and training algorithms Gated units such the Long Short-Term MemoryHochreiter & 1997 ) (LSTM the Gated Recurrent UnitCho 2014 deal the vanishing gradients problem commonly foundBengio 1994) . These architectures popularized, in due their impressive results in machine translationBahdanau 2015) , language modeling BID17Graves .Some in their training deployment when dealing long sequences due their inherently sequential behaviour These challenges include throughput degradation slower convergence during training and memory leakage even gated architecturesNeil et) . Sequence shortening techniques seen conditional computation (Bengio Bengio Davis & Arel in time alleviate The most common approaches, cropping discrete signals reducing in continuous signals based heuristics can suboptimal In contrast , we propose able learn which samples ( need used solve Consider a video understanding task as scenes large motion may benefit whereas capture the semantics a mostly static sceneThe main contribution a novel modification for existing RNN architectures them skip state updates decreasing sequential operations performed without any additional supervision signal This model , called Skip RNN adaptively determines the state needs copied the next time step We show the network encouraged perform fewer state updates by adding a penalization term during training allowing us train models under different computation budgets The proposed modification can generally integrated any RNN and we show, implementations with GRU The resulting models show promising results on a series sequence modeling tasks In particular , evaluate the proposed Skip RNN architecture on six sequence learning problems an adding task sine wave frequency discrimination digit classification sentiment in movie reviews action classification temporal action localization 1 We presented Skip RNNs existing recurrent architectures enabling them skip state updates thereby sequential operations in the computation graph Unlike other approaches all parameters Skip RNN trained Experiments conducted LSTMs GRUs Skip RNNs match or in even the baseline models while relaxing Skip RNNs provide faster and more stable training long sequences complex models owing gradients being through fewer time steps resulting a simpler optimization task Moreover the introduced computational savings better modern hardware those methods reduce atKoutnik Neil Chung) .A ADDITIONAL EXPERIMENTS",0.01,0.4011867264720862
"We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard forward passes and is easy to implement. Our method addresses long-standing issues with current second-order solvers, which invert an approximate Hessian matrix every iteration exactly or by conjugate-gradient methods, procedures that are much slower than a SGD step. Instead, we propose to keep a single estimate of the gradient projected by the inverse Hessian matrix, and update it once per iteration with just two passes over the network. This estimate has the same size and is similar to the momentum variable that is commonly used in SGD. No estimate of the Hessian is maintained.
 We first validate our method, called CurveBall, on small problems with known solutions (noisy Rosenbrock function and degenerate 2-layer linear networks), where current deep learning solvers struggle. We then train several large models on CIFAR and ImageNet, including ResNet and VGG-f networks, where we demonstrate faster convergence with no hyperparameter tuning. We also show our optimiser's generality by testing on a large set of randomly-generated architectures. Stochastic Gradient Descent (SGD) and back-propagation BID16 are the algorithmic backbone of current deep network training. The success of deep learning demonstrates the power of this combination, which has been successfully applied on various tasks with large datasets and very deep networks BID11 ).Yet , while SGD has many advantages, speed of convergence (in terms of number of iterations) is not necessarily one of them. While individual SGD iterations are very quick to compute and lead to rapid progress at the beginning of the optimisation, it soon reaches a slower phase where further improvements are achieved slowly. This can be attributed to entering regions of the parameter space where the objective function is poorly scaled. In such cases, rapid progress would require vastly different step sizes for different directions in parameter space, which SGD cannot deliver.Second-order methods, such as Newton's method and its variants, eliminate this issue by rescaling the gradient according to the local curvature of the objective function. For a scalar loss in R, this rescaling takes the form H −1 J where H is the Hessian matrix (second-order derivatives) or an approximation of the local curvature in the objective space, and J is the gradient of the objective. They can in fact achieve local scale-invariance (Wright & Nocedal, 1999, p. 27) , and make provably better progress in the regions where gradient descent stalls. While they are unmatched in other domains, there are several obstacles to their application to deep models. First, it is impractical to invert or even store the Hessian, since it grows quadratically with the number of parameters, and there are typically millions of them. Second, any Hessian estimate is necessarily noisy and ill-conditioned due to stochastic sampling, to which classic inversion methods such as conjugate-gradient are not robust.In this paper, we propose a new algorithm that can overcome these difficulties and make second order optimisation practical for deep learning. We show in particular how to avoid the storage of any estimate of the Hessian matrix or its inverse. Instead, we treat the computation of the Newton update, H −1 J, as solving a linear system that itself can be solved via gradient descent. The cost of solving this system is amortized over time by interleaving its steps with the parameter update steps. Our proposed method adds little overhead, since a Hessian-vector product can be implemented for modern networks with just two steps of automatic differentiation. Interestingly , we show that our method is equivalent to momentum SGD (also known as the heavy-ball method) with a single additional term, accounting for curvature. For this reason we named our method CURVEBALL. Unlike other proposals , the total memory footprint is as small as that of momentum SGD. This paper is structured as follows. We introduce relevant technical background in sec. 2, and present our method in sec. 3. We evaluate our method and show experimental results in sec. 4. Related work is discussed in sec. 5. Finally we summarise our findings in sec. 6. In this work, we have proposed a practical second-order solver that has been specifically tailored for deep-learning-scale stochastic optimisation problems. We showed that our optimiser can be applied to a large range of datasets and reach better training error than first order method with the same number of iterations, with essentially no hyper-parameters tuning. In future work, we intend to bring more improvements to the wall-clock time of our method by engineering the FMAD operation to the same standard as back-propagation, and study optimal trust-region strategies to obtain λ in closed-form.We now perform a change of variables to diagonalize the Hessian, H = Qdiag(h)Q T , with Q orthogonal and h the vector of eigenvalues. Let w * = arg min w f (w) = H −1 b be the optimal solution of the minimization. Then, replacing w t = Qx t + w * in eq. 30: DISPLAYFORM0 Then, expanding H with its eigendecomposition, DISPLAYFORM1 Left-multiplying by Q T ,and canceling out Q due to orthogonality, DISPLAYFORM2 Similarly for eq. 29, replacing z t = Qy t yields DISPLAYFORM3 Note that each pair formed by the corresponding element of y t and x t is an independent system with only 2 variables, since the pairs do not interact (eq. 33 and 34 only contain element-wise operations).From now on, we will be working on the ith element of each vector.We can thus write eq. 33 and 34 (for a single element i of each) as a vector equation: DISPLAYFORM4 The matrix on the left is necessary to express the fact that the y t+1 factor in eq. 34 must be moved to the left-hand side, which corresponds to iteration t + 1 (x t+1 − y t+1 = x t ). Left-multiplying eq. 35 by the inverse, DISPLAYFORM5 This is the transition matrix R i that characterizes the iteration, and taking its power models multiple iterations in closed-form: DISPLAYFORM6 The two eigenvalues of R i are given in closed-form by: DISPLAYFORM7 The series in eq. 37 converges when |eig (R i )| < 1 simultaneously for both eigenvalues, which is equivalent to: DISPLAYFORM8 with ρ > 0 and βh i > 0. Note that when using the Gauss-Newton approximation of the Hessian, h i > 0 and thus the last condition simplifies to β > 0.Since eq. 39 has to be satisfied for every eigenvalue, we have 3 2 βh max − 1 < ρ < 1 + βh min ,with h min and h max the smallest and largest eigenvalues of the Hessian H, respectively, proving the result.The rate of convergence is the largest of the two values |eig (R i )|. When the argument of the square root in eq. 38 is non-negative, it does not admit an easy interpretation; however, when it is negative, eq. 38 simplifies to: The convergence rate for a single eigenvalue is illustrated in FIG3 . Graphically, the regions of convergence for different eigenvalues will differ only by a scale factor along the βh i axis (horizontal stretching of FIG3 ). Moreover, the largest possible range of βh i values is obtained when ρ = 1, and that range is 0 < βh i < 4 3 . We can infer that the intersection of the regions of convergence for several eigenvalues will be maximized with ρ = 1, for any fixed β. DISPLAYFORM9",1626,0.956,941,1.7279489904357066,"We propose a fast second-order method current deep learning solvers Compared only two additional forward-mode automatic differentiation operations per iteration has comparable two standard forward passes and easy Our method addresses current second-order solvers invert an approximate Hessian matrix every iteration exactly or by conjugate-gradient methods procedures much a SGD step Instead propose keep a single estimate the gradient projected the inverse Hessian matrix update once iteration just two passes over This estimate has is similar the momentum variable commonly SGD No estimate the Hessian is maintained We first validate our method called CurveBall small problems known solutionsnoisy Rosenbrock function degenerate 2-layer linear networks current deep learning solvers struggle We then train several large models CIFAR ImageNet ResNet VGG-f networks where demonstrate faster convergence no hyperparameter tuning We also show our optimiser's generality testing on randomly-generated architectures back-propagation BID16 the algorithmic backbone current deep network training The success deep learning demonstrates this combination successfully various tasks very deep networks BID11 ).Yet , SGD speed convergence (in number necessarily one While individual SGD iterations very quick compute lead rapid progress at soon reaches a slower phase further improvements achieved slowly This can attributed entering regions the parameter space the objective function poorly scaled In such cases rapid progress would vastly different step sizes different directions parameter space SGD deliverSecond-order methods Newton's method its variants eliminate rescaling according the objective function For a scalar loss R this rescaling takes H −1 J where the Hessian matrix (second-order derivatives or an approximation the objective space They can in achieve local scale-invariance (Wright Nocedal 27) , and make provably better progress the regions gradient stalls While they unmatched other domains there several obstacles deep models First impractical invert or even store the Hessian, grows parameters there typically millions Second any Hessian estimate necessarily noisy illconditioned due to which classic inversion methods robustIn overcome make second order optimisation practical We show in particular avoid the storage any estimate the Hessian matrix or Instead treat the computation the Newton update, H −1 J solving itself via gradient descent The cost solving this system amortized interleaving its steps the parameter update steps Our proposed method adds little overhead since a Hessian-vector product implemented modern networks of automatic differentiation Interestingly , show our method equivalent momentum SGDalso the heavy-ball method a single additional term accounting For named our method CURVEBALL Unlike other proposals , the total memory footprint as momentum SGD This paper structured We introduce relevant technical background sec 2 and present our method sec 3 We evaluate our method show experimental results sec. 4 Related work is discussed sec 5 Finally summarise sec 6 In this work proposed has specifically We showed our optimiser datasets reach better training error than first order method with essentially hyper tuning In future work intend bring more improvements the wall-clock time our method engineering the FMAD operation study optimal trust-region strategies obtain �� in closed-formWe now perform a change variables diagonalize the Hessian, H = Qdiag(h)Q T h the vector Let w * = arg min w f H −1 b be the optimal solution. Then replacing w t = Qx t * in eq 30 DISPLAYFORM0 Then expanding H with its eigendecomposition by Q Tand canceling due Similarly for eq 29, replacing z t = Qy t yields DISPLAYFORM3 Note each pair formed the corresponding element y t an independent system only 2 variables since doeq 33 and only contain element- operations).From now working the ith element each vectorWe thus eq 33 and (for a single element i of each as a vector equation DISPLAYFORM4 The matrix on necessary express y t+1 factor eq 34 must moved corresponds iteration t +x − y Left-multiplying eq 35 by the inverse DISPLAYFORM5 This the transition matrix R i that characterizes the iteration, taking its power models multiple iterations closed-form: given in eq 37 converges when |eig (R i < simultaneously for DISPLAYFORM8 with �� > βh i Note when the Gauss-Newton approximation h i > thus the last condition simplifies β > 0.Since eq 39 has to satisfied every eigenvalue we 3 2 βh max − < � +with h min the Hessian H, proving the resultThe rate largest |eig (R i When the argument of the square root in eq 38 is nonnegative it admit an easy interpretation; however when eq 38 simplifies to: The convergence rate illustrated FIG3 Graphically the regions convergence for will only a scale factor along βh i (horizontal stretching FIG3 Moreover largest possible range βh i values obtained 0 < 3 We infer the intersection the regions convergence for will for any fixed β DISPLAYFORM9",0.01,0.5588292404149939
"The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms. Imagine yourself travelling to a scientific conference. The field is popular, and surely you do not want to miss out on anything. You have selected several posters you want to visit, and naturally you must return to the place where you are now: the coffee corner. In which order should you visit the posters, to minimize your time walking around? This is the Travelling Scientist Problem (TSP).You realize that your problem is equivalent to the Travelling Salesman Problem (conveniently also TSP). This seems discouraging as you know the problem is (NP-)hard (Garey & Johnson, 1979) . Fortunately , complexity theory analyzes the worst case, and your Bayesian view considers this unlikely. In particular , you have a strong prior: the posters will probably be laid out regularly. You want a special algorithm that solves not any, but this type of problem instance. You have some months left to prepare. As a machine learner , you wonder whether your algorithm can be learned?Motivation Machine learning algorithms have replaced humans as the engineers of algorithms to solve various tasks. A decade ago, computer vision algorithms used hand-crafted features but today they are learned end-to-end by Deep Neural Networks (DNNs). DNNs have outperformed classic approaches in speech recognition, machine translation, image captioning and other problems, by learning from data (LeCun et al., 2015) . While DNNs are mainly used to make predictions, Reinforcement Learning (RL) has enabled algorithms to learn to make decisions, either by interacting with an environment, e.g. to learn to play Atari games (Mnih et al., 2015) , or by inducing knowledge through look-ahead search: this was used to master the game of Go (Silver et al., 2017) .The world is not a game, and we desire to train models that make decisions to solve real problems. These models must learn to select good solutions for a problem from a combinatorially large set of potential solutions. Classically, approaches to this problem of combinatorial optimization can be divided into exact methods, that guarantee finding optimal solutions, and heuristics, that trade off optimality for computational cost, although exact methods can use heuristics internally and vice versa. Heuristics are typically expressed in the form of rules, which can be interpreted as policies to make decisions. We believe that these policies can be parameterized using DNNs, and be trained to obtain new and stronger algorithms for many different combinatorial optimization problems, similar to the way DNNs have boosted performance in the applications mentioned before. In this paper, we focus on routing problems: an important class of practical combinatorial optimization problems.The promising idea to learn heuristics has been tested on TSP BID4 . In order to push this idea, we need better models and better ways of training. Therefore, we propose to use a powerful model based on attention and we propose to train this model using REINFORCE with a simple but effective greedy rollout baseline. The goal of our method is not to outperform a nonlearned, specialized TSP algorithm such as Concorde BID0 . Rather, we show the flexibility of our approach on multiple (routing) problems of reasonable size, with a single set of hyperparameters. This is important progress towards the situation where we can learn strong heuristics to solve a wide range of different practical problems for which no good heuristics exist. In this work we have introduced a model and training method which both contribute to significantly improved results on learned heuristics for TSP and additionally learned strong (single construction) heuristics for multiple routing problems, which are traditionally solved by problem-specific approaches. We believe that our method is a powerful starting point for learning heuristics for other combinatorial optimization problems defined on graphs, if their solutions can be described as sequential decisions. In practice, operational constraints often lead to many variants of problems for which no good (human-designed) heuristics are available such that the ability to learn heuristics could be of great practical value.Compared to previous works, by using attention instead of recurrence (LSTMs) we introduce invariance to the input order of the nodes, increasing learning efficiency. Also this enables parallelization, for increased computational efficiency. The multi-head attention mechanism can be seen as a message passing algorithm that allows nodes to communicate relevant information over different channels, such that the node embeddings from the encoder can learn to include valuable information about the node in the context of the graph. This information is important in our setting where decisions relate directly to the nodes in a graph. Being a graph based method, our model has increased scaling potential (compared to LSTMs) as it can be applied on a sparse graph and operate locally.Scaling to larger problem instances is an important direction for future research, where we think we have made an important first step by using a graph based method, which can be sparsified for improved computational efficiency. Another challenge is that many problems of practical importance have feasibility constraints that cannot be satisfied by a simple masking procedure, and we think it is promising to investigate if these problems can be addressed by a combination of heuristic learning and backtracking. This would unleash the potential of our method, already highly competitive to the popular Google OR Tools project, to an even larger class of difficult practical problems. A ATTENTION MODEL DETAILS FIG4 : Illustration of weighted message passing using a dot-attention mechanism. Only computation of messages received by node 1 are shown for clarity. Best viewed in color.Attention mechanism We interpret the attention mechanism by Vaswani et al. FORMULA9 as a weighted message passing algorithm between nodes in a graph. The weight of the message value that a node receives from a neighbor depends on the compatibility of its query with the key of the neighbor, as illustrated in FIG4 . Formally, we define dimensions d k and d v and compute the key k i ∈ R dk , value v i ∈ R dv and query q i ∈ R dk for each node by projecting the embedding h i : DISPLAYFORM0 From the queries and keys, we compute the compatibility u ij ∈ R of the query q i of node i with the key k j of node j as the (scaled, see Vaswani et al. FORMULA9 ) dot-product: DISPLAYFORM1 In a general graph, defining the compatibility of non-adjacent nodes as −∞ prevents message passing between these nodes. From the compatibilities u ij , we compute the attention weights a ij ∈ [0, 1] using a softmax: DISPLAYFORM2 Finally, the vector h i that is received by node i is the convex combination of messages v j : DISPLAYFORM3 Multi-head attention As was noted by Vaswani et al. (2017) and Velickovic et al. (2018) , it is beneficial to have multiple attention heads. This allows nodes to receive different types of messages from different neighbors. Especially, we compute the value in equation 13 M = 8 times with different parameters, using DISPLAYFORM4 We denote the result vectors by h im for m ∈ 1, . . . , M . These are projected back to a single d h -dimensional vector using DISPLAYFORM5 The final multi-head attention value for node i is a function of h 1 , . . . , h n through h im : DISPLAYFORM6 Feed-forward sublayer The feed-forward sublayer computes node-wise projections using a hidden (sub)sublayer with dimension d ff = 512 and a ReLu activation: DISPLAYFORM7 Batch normalization We use batch normalization with learnable d h -dimensional affine parameters w bn and b bn : DISPLAYFORM8 Here denotes the element-wise product and BN refers to batch normalization without affine transformation.",1773,0.953,1009,1.7571853320118929,"The recently presented idea learn heuristics promising save costly development. However to push towards practical implementation better models training We contribute in both directions propose attention layers with benefits the Pointer Network train REINFORCE with a simple baseline based a deterministic greedy rollout, find a value function We significantly over recent learned heuristics the Travelling Salesman Problem getting close optimal results problems up to 100 nodes With the same hyperparameters learn strong heuristics two variants the Vehicle Routing Problem Orienteering (a variant Prize Collecting TSP outperforming baselines getting results close highly optimized and specialized algorithms Imagine yourself travelling The field popular surely do anything You selected several posters you visit naturally must return the place now: coffee corner In which order should visit the posters to minimize walking This the Travelling Scientist Problem ( realize your problem equivalentconveniently also TSP This seems discouraging as the problem (NP-)hard (Garey & Johnson 1979 . Fortunately , complexity theory analyzes the worst case your Bayesian view considers unlikely In particular , you strong prior: the posters will probably laid regularly You want a special algorithm solves not any, this type problem instance You some months As a machine learner , wonder your algorithm learned?Motivation Machine learning algorithms replaced humans the engineers algorithms to various tasks decade computer vision algorithms used hand-crafted features but today learned end Deep Neural Networks DNNs outperformed classic approaches speech recognition machine translation image captioning other problems by learning data (LeCun . While DNNs mainly make predictions Reinforcement LearningRL enabled algorithms decisions either interacting to learn playMnih et al , inducing knowledge look-ahead search: this masterSilver 2017 .The world desire train models make to solve These models must learn select good solutions from a combinatorially large set Classically approaches of exact methods that guarantee finding trade optimality computational cost although exact methods use internally vice Heuristics typically expressed rules policies We believe these policies parameterized DNNs be trained obtain new and stronger algorithms similar boosted the applications mentioned In focus routing problems: an important classThe promising idea to learn has tested TSP BID4 . In order push better models training Therefore a powerful model based attention we train REINFORCE with a simple but effective greedy rollout baseline The goal our method a nonlearned, specialized TSP algorithm such Concorde BID0 . Rather show the flexibility on multiple (routing) problems of reasonable size This important progress towards the situation learn strong heuristics solve different practical problems for which In this work a model and training method both contribute significantly improved results learned heuristics TSP additionally learned strong (single construction) heuristics multiple routing problems traditionally We believe our method defined on graphs if their solutions sequential decisions In practice operational constraints often many variants problems for such learn could ofCompared previous works by using attention instead recurrenceLSTMs introduce invariance the input order the nodes increasing learning efficiency Also this enables parallelization for increased computational efficiency The multi-head attention mechanism can a message passing algorithm nodes relevant information over that the node embeddings from learn include valuable information the graph This information important in our setting decisions relate directly the nodes Being a graph based method our model increased scaling potential ( operate locallyScaling larger problem instances an important direction where think made sparsified improved computational efficiency Another challenge many problems practical importance feasibility constraints satisfied a simple masking procedure we think promising if heuristic learning backtracking This would unleash our method already highly competitive to the popular Google OR Tools project an even larger class difficult practical problems ATTENTION MODEL DETAILS FIG4 : weighted message passing using a dot-attention mechanism Only computation messages received node 1 are shown clarity Best viewed colorAttention mechanism We interpret Vaswani FORMULA9 as a weighted message passing algorithm between nodes The weight the message value a node a neighbor depends the compatibility its query the key FIG4 Formally define dimensions d k and compute key k i �� R dk value query q by projecting the embedding h : DISPLAYFORM0 From the queries and keys compatibility u ij of of node i of (scaled, see Vaswani FORMULA9 ) dot-product: DISPLAYFORM1 In a general graph defining the compatibility as −�� prevents message From the compatibilities u ij , compute the attention weights [0 using a softmax: DISPLAYFORM2 Finally the vector h that received node the convex combination messages v j : DISPLAYFORM3 Multi-head attention As was Vaswani (2017 and Velickovic et al (2018 , it beneficial multiple attention heads This allows nodes receive different types different neighbors Especially, we compute equation 13 M 8 times with different parameters using DISPLAYFORM4 We denote the result vectors h im for m �� . . . , M . These projected back a single d h -dimensional vector using DISPLAYFORM5 The final multi-head attention value node i h 1 . . . , h n through h im : DISPLAYFORM6 Feed-forward sublayer node-wise projections using a hidden (sub)sublayer with dimension ff = 512 and a ReLu activation: We learnable d h -dimensional affine parameters w bn and : Here denotes and BN refers batch without",0.01,0.6333208700742318
"We propose an efficient online hyperparameter optimization method which uses a joint dynamical system to evaluate the gradient with respect to the hyperparameters. While similar methods are usually limited to hyperparameters with a smooth impact on the model, we show how to apply it to the probability of dropout in neural networks. Finally, we show its effectiveness on two distinct tasks. With the growing size and complexity of both datasets and models, training times keep increasing and it is not uncommon to train a model for several days or weeks. This effect is compounded by the number of hyperparameters a practitioner has to search through. Even though search through hyperparameter space has improved beyond grid search, this task is still often computationally intensive, mainly because these techniques are offline, in that they need to perform a full learning before trying a new value. Recently, several authors proposed online hyperparameter optimization techniques, where the hyperparameters are tuned alongside the parameters of the model themselves by running short runs of training and updating the hyperparameter after each such run. By casting the joint learning of parameters and hyperparameters as a dynamical system, we show that these approaches are unstable and need to be stopped using an external process, like early stopping, to achieve a good performance. We then modify these techniques such that the joint optimization procedure is stable as well as efficient by changing the hyperparameter at every time step. Further, while existing techniques are limited in the type of hyperparameters they can optimize, we extend the process to dropout probability optimization, a popular regularization technique in deep learning.",307,0.165,175,1.7542857142857142,"We propose an efficient online hyperparameter optimization method which a joint dynamical system evaluate the gradient with While similar methods usually limited hyperparameters with a smooth impact show it the probability dropout neural networks Finally show its effectiveness two distinct tasks With the growing size both datasets models training times keep it train This effect compounded the number hyperparameters a practitioner search Even search through hyperparameter space improved beyond grid search this task often mainly these techniques offline in that need a full learning before trying a new value Recently several authors proposed online hyperparameter optimization techniques where tuned alongside themselves by running short runs training updating after By casting the joint learning of parameters a dynamical system these approaches unstable need stopped using an external process like early stopping We then modify these techniques such the joint optimization procedure stable as by changing at Further, while existing techniques limited the type hyperparameters optimize we extend the process dropout probability optimization a popular regularization technique",0.0,0.6259328988655565
"Ongoing innovations in recurrent neural network architectures have provided a steady influx of apparently state-of-the-art results on language modelling benchmarks. However, these have been evaluated using differing codebases and limited computational resources, which represent uncontrolled sources of experimental variation. We reevaluate several popular architectures and regularisation methods with large-scale automatic black-box hyperparameter tuning and arrive at the somewhat surprising conclusion that standard LSTM architectures, when properly regularised, outperform more recent models. We establish a new state of the art on the Penn Treebank and Wikitext-2 corpora, as well as strong baselines on the Hutter Prize dataset.
 The scientific process by which the deep learning research community operates is guided by empirical studies that evaluate the relative quality of models. Complicating matters, the measured performance of a model depends not only on its architecture (and data), but it can strongly depend on hyperparameter values that affect learning, regularisation, and capacity. This hyperparameter dependence is an often inadequately controlled source of variation in experiments, which creates a risk that empirically unsound claims will be reported.In this paper, we use a black-box hyperparameter optimisation technique to control for hyperparameter effects while comparing the relative performance of language modelling architectures based on LSTMs, Recurrent Highway Networks BID26 and NAS BID27 . We specify flexible, parameterised model families with the ability to adjust embedding and recurrent cell sizes for a given parameter budget and with fine grain control over regularisation and learning hyperparameters.Once hyperparameters have been properly controlled for, we find that LSTMs outperform the more recent models, contra the published claims. Our result is therefore a demonstration that replication failures can happen due to poorly controlled hyperparameter variation, and this paper joins other recent papers in warning of the under-acknowledged existence of replication failure in deep learning BID7 BID21 . However, we do show that careful controls are possible, albeit at considerable computational cost.Several remarks can be made in light of these results. First, as (conditional) language models serve as the central building block of many tasks, including machine translation, there is little reason to expect that the problem of unreliable evaluation is unique to the tasks discussed here. However, in machine translation, carefully controlling for hyperparameter effects would be substantially more expensive because standard datasets are much larger. Second, the research community should strive for more consensus about appropriate experimental methodology that balances costs of careful experimentation with the risks associated with false claims. Finally, more attention should be paid to hyperparameter sensitivity. Models that introduce many new hyperparameters or which perform well only in narrow ranges of hyperparameter settings should be identified as such as part of standard publication practice. During the transitional period when deep neural language models began to supplant their shallower predecessors, effect sizes tended to be large, and robust conclusions about the value of the modelling innovations could be made, even in the presence of poorly controlled ""hyperparameter noise."" However, now that the neural revolution is in full swing, researchers must often compare competing deep architectures. In this regime, effect sizes tend to be much smaller, and more methodological care is required to produce reliable results. Furthermore, with so much work carried out in parallel by a growing research community, the costs of faulty conclusions are increased.Although we can draw attention to this problem, this paper does not offer a practical methodological solution beyond establishing reliable baselines that can be the benchmarks for subsequent work. Still, we demonstrate how, with a huge amount of computation, noise levels of various origins can be carefully estimated and models meaningfully compared. This apparent tradeoff between the amount of computation and the reliability of results seems to lie at the heart of the matter. Solutions to the methodological challenges must therefore make model evaluation cheaper by, for instance, reducing the number of hyperparameters and the sensitivity of models to them, employing better hyperparameter optimisation strategies, or by defining ""leagues"" with predefined computational budgets for a single model representing different points on the tradeoff curve.",800,0.38,494,1.6194331983805668,"Ongoing innovations recurrent neural network architectures provided a steady influx apparently state results on language modelling benchmarks However these have evaluated differing codebases limited computational resources represent uncontrolled sources experimental variation We reevaluate several popular architectures regularisation methods with large-scale automatic black-box hyperparameter tuning arrive the somewhat surprising conclusion standard LSTM architectures, when properly regularised more recent models We establish on the Penn Treebank Wikitext-2 corpora as strong baselines the Hutter Prize dataset The scientific process by the deep learning research community operates guided empirical studies evaluate the relative quality models Complicating matters the measured performance a model depends its architectureand data it can strongly hyperparameter values affect learning regularisation capacity This hyperparameter dependence an often inadequately controlled source variation experiments creates empirically unsound claims reportedIn control while comparing language modelling architectures based Recurrent Highway Networks BID26 NAS BID27 . We specify flexible, parameterised model families the ability adjust embedding and recurrent cell sizes a given parameter budget with fine grain control regularisation and learning hyperparametersOnce properly controlled find LSTMs the more recent models contra the published claims Our result therefore a demonstration replication failures happen due poorly controlled hyperparameter variation this paper joins warning the under-acknowledged existence BID7 BID21 . However we show careful controls possible albeit considerable computational costSeveral remarks can light First as (conditional) language models serve many tasks including machine translation there the problem unreliable evaluation unique the tasks discussed However in machine translation carefully controlling for hyperparameter effects would substantially expensive because standard datasets Second the research community strive more consensus appropriate experimental methodology that balances costs careful experimentation false claims Finally more attention should hyperparameter sensitivity Models that introduce many new hyperparameters which perform well only narrow ranges should identified as part standard publication practice During the transitional period when deep neural language models began their shallower predecessors effect sizes tended large robust conclusions the value the modelling innovations could poorly controlled ""hyperparameter noise now the neural revolution researchers must often compare competing deep architectures In this regime effect sizes tend more methodological care produce Furthermore with carried parallel a growing research community the costs faulty conclusions increasedAlthough we draw attention offer a practical methodological solution beyond establishing reliable baselines that the benchmarks subsequent work Still, we demonstrate, a huge amount computation noise levels of various origins carefully estimated models meaningfully compared This apparent tradeoff the amount computation the reliability results seems lie Solutions the methodological challenges must therefore make model evaluation cheaper by, the sensitivity them employing defining ""leagues with predefined computational budgets a single model representing different points on the tradeoff curve",0.0,0.2823405363517411
"Residual and skip connections play an important role in many current
  generative models. Although their theoretical and numerical advantages
  are understood, their role in speech enhancement systems has not been
  investigated so far. When performing spectral speech enhancement,
  residual connections are very similar in nature to spectral subtraction,
  which is the one of the most commonly employed speech enhancement approaches.
   Highway networks, on the other hand, can be seen as a combination of spectral
  masking and spectral subtraction. However, when using deep neural networks, such operations would
  normally happen in a transformed spectral domain, as opposed to traditional speech
  enhancement where all operations are often done directly on the spectrum.
   In this paper, we aim to investigate the role of residual and highway
  connections in deep neural networks for speech enhancement, and verify whether
  or not they operate similarly to their traditional, digital signal processing
  counterparts. We visualize the outputs of such connections, projected back to
  the spectral domain, in models trained for speech denoising, and show that while
  skip connections do not necessarily improve performance with regards to the
  number of parameters, they make speech enhancement models more interpretable. Highway BID7 and residual networks BID1 have been proposed with the objective of improving activation and gradient flow in the training of deep neural networks. On the other hand, in tasks like image reconstruction or speech enhancement, the use of such skip connections serves a different purpose: if we model a corrupted signal x = y + n as the addition of noise n to a clean signal y and x is the input to a neural network, we know that the task at hand is to predict n. In other words, to predict y, we have to alter the input x by subtracting n.In speech enhancement, the two more commonly used approaches are spectral subtraction and spectral masking. In the first, a statistical model of n is used to predict its magnitude spectrum N , which is then subtracted from the input spectrum X to yield a clean magnitude spectrum estimateŶ . In spectral masking, instead of performing subtraction, we find a multiplicative mask M which aims at either blocking time-frequency cells dominated by noise (in the case of binary masks) or scaling down energies in such time-frequency cells to make them match that of the original clean signal. Recent work in speech enhancement has explored skip connections as a way of performing masking BID4 and spectral estimation BID6 . Time domain approaches, such as SEGAN BID5 , use a UNet-style network which employs multiple skip connections as well. Other works, such as BID12 , perform spectral masking but Figure 1: Diagrams for highway, residual, and masking blocks used in this paper learn how to estimate an ideal mask instead of having the masking mechanism embedded in the neural network as a skip connection.For better understanding of such models, we would like to understand whether there are any parallels between such connections and two traditional DSP approaches to speech enhancement, namely spectral subtraction and spectral masking. We also want to understand whether models using skip connections perform better for enhancement when such connections appear only once (resembling their DSP counterparts) or repeated as multiple blocks (like in highway and residual networks). This paper shows early results of our investigation on the role of skip connections in speech enhancement models. Our preliminary experiments show that, although they have no significant impact in the performance of the models, such connections might help making the models more interpretable, as we can identify the contribution of each individual layer to the task. In the future, we intend to investigate more complex models, such as models based on the UNet architecture, as well as models that employ a temporal context window at the input instead of a single frame (such as the work in BID6 ), since those are more in line with state-of-the-art models in the literature.",774,0.35,433,1.7875288683602772,"Residual and skip connections play many current generative models Although their theoretical and numerical advantages understood their role speech enhancement systems investigated so When performing spectral speech enhancement residual connections very similar nature spectral subtraction one of Highway networks on seen spectral masking spectral subtraction However when using deep neural networks such operations would normally happen a transformed spectral domain traditional speech enhancement where all operations often directly the spectrum In aim residual and highway connections deep neural networks for speech enhancement verify or operate similarly their traditional, digital signal processing counterparts We visualize the outputs such connections projected back the spectral domain models trained speech denoising while skip connections necessarily improve with regards the number parameters make speech enhancement models interpretable Highway BID7 and residual networks BID1 have proposed with improving activation gradient flow the training On tasks image reconstruction speech enhancement such skip connections serves if model a corrupted signal x = y n as the addition noise n a clean signal and x the input at predict n. In to predict y, alter x byIn speech enhancement the two more commonly used approaches spectral subtraction In, a statistical model n is its magnitude spectrum N , then the input spectrum X yield a clean magnitude spectrum estimate�� In spectral masking instead performing subtraction find M which aims either blocking time-frequency cells dominated noisein binary masks scaling down energies make match that the original clean signal Recent work speech enhancement explored skip connections as performing masking BID4 spectral estimation BID6 Time domain approaches, such SEGAN BID5 , use a UNet-style network which employs multiple skip connections as Other works, BID12 , perform spectral masking but Figure: Diagrams for highway, residual masking blocks used learn estimate an ideal mask instead having the masking mechanism embedded as a skip connectionFor better understanding such models would understand whether any parallels such connections two traditional DSP approaches speech enhancement namely spectral subtraction We also understand whether models using skip connections perform for enhancement when such connections appear onlyresembling their DSP counterparts repeated as multiple blockslike highway and residual networks This paper early results our investigation skip connections speech enhancement models Our preliminary experiments, they in the models such connections making identify the contribution each individual layer In intend investigate more complex models models the UNet architecture as employ a temporal context window at instead the work BID6 since those in state",0.01,0.7106335347359612
"Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We provide two innovations that aim to turn VB into a robust inference tool for Bayesian neural networks: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel Empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate good predictive performance over alternative approaches. Bayesian approaches to neural network training marry the representational flexibility of deep neural networks with principled parameter estimation in probabilistic models. Compared to ""standard"" parameter estimation by maximum likelihood, the Bayesian framework promises to bring key advantages such as better uncertainty estimates on predictions and automatic model regularization (MacKay, 1992; Graves, 2011) . These features are often crucial for informing downstream decision tasks and reducing overfitting, particularly on small datasets. However, despite potential advantages, such Bayesian neural networks (BNNs) are often overlooked due to two limitations: First, posterior inference in deep neural networks is analytically intractable and approximate inference with Monte Carlo (MC) techniques can suffer from crippling variance given only a reasonable computation budget (Kingma et al., 2015; Molchanov et al., 2017; Miller et al., 2017; BID8 . Second, performance of the Bayesian approach is sensitive to the choice of prior BID1 , and although we may have a priori knowledge concerning the function represented by a neural network, it is generally difficult to translate this into a meaningful prior on neural network weights. Sensitivity to priors and initialization makes BNNs non-robust and thus often irrelevant in practice.In this paper, we describe a novel approach for inference in feed-forward BNNs that is simple to implement and aims to solve these two limitations. We adopt the paradigm of variational Bayes (VB) for BNNs (Hinton & van Camp, 1993; MacKay, 1995c) which is normally deployed using Monte Carlo variational inference (MCVI) (Graves, 2011; Blundell et al., 2015) . Within this paradigm we address the two shortcomings of current practice outlined above: First, we address the issue of high variance in MCVI, by reducing this variance to zero through novel deterministic approximations to variational inference in neural networks. Second, we derive a general and robust Empirical Bayes (EB) approach to prior choice using hierarchical priors. By exploiting conjugacy we derive data-adaptive closed-form variance priors for neural network weights, which we experimentally demonstrate to be remarkably effective.Combining these two novel ingredients gives us a performant and robust BNN inference scheme that we refer to as ""deterministic variational inference"" (DVI). We demonstrate robustness and improved predictive performance in the context of non-linear regression models, deriving novel closed-form results for expected log-likelihoods in homoscedastic and heteroscedastic regression (similar derivations for classification can be found in the appendix).Experiments on standard regression datasets from the UCI repository, (Dheeru & Karra Taniskidou, 2017) , show that for identical models DVI converges to local optima with better predictive loglikelihoods than existing methods based on MCVI. In direct comparisons , we show that our Empirical Bayes formulation automatically provides better or comparable test performance than manual tuning of the prior and that heteroscedastic models consistently outperform the homoscedastic models.Concretely, our contributions are:• Development of a deterministic procedure for propagating uncertain activations through neural networks with uncertain weights and ReLU or Heaviside activation functions.• Development of an EB method for principled tuning of weight priors during BNN training.• Experimental results showing the accuracy and efficiency of our method and applicability to heteroscedastic and homoscedastic regression on real datasets. We introduced two innovations to make variational inference for neural networks more robust: 1. an effective deterministic approximation to the moments of activations of a neural networks; and 2. a simple empirical Bayes hyperparameter update. We demonstrate that together these innovations make variational Bayes a competitive method for Bayesian inference in neural heteroscedastic regression models.Bayesian neural networks have been shown to substantially improve upon standard networks in these settings where calibrated predictive uncertainty estimates, sequential decision making, or continual learning without catastrophic forgetting are required (see e.g. BID3 Gal et al. (2017) ; Nguyen et al. FORMULA0 ). In future work, the new innovations proposed in this paper can be applied to these areas. In the sequential decision making and continual learning applications, approximate Bayesian inference must be run as an inner loop of a larger algorithm. This requires a robust and automated version of BNN training: this is precisely where we believe the innovations in this paper will have large impact since they pave the way to automated and robust deployment of BBNs that do not involve an expert in-the-loop.",1153,0.51,686,1.6807580174927115,"Bayesian neural networks hold a flexible and principled solution deal uncertainty when learning finite data Among approaches realize variational BayesVB theoretically grounded generally applicable With wide recognition potential advantages why variational Bayes seen very limited practical use for BNNs real applications We argue variational inference fragile: successful implementations careful initialization tuning prior variances controlling Monte Carlo gradient estimates We provide two innovations aim turn VB a robust inference tool first approximate moments eliminating gradient variance; hierarchical prior parameters a novel Empirical Bayes procedure automatically selecting prior variances Combining these two innovations the resulting method highly robust On the application heteroscedastic regression we demonstrate good predictive performance over alternative approaches Bayesian approaches marry the representational flexibility principled parameter estimation Compared ""standard"" parameter estimation by maximum likelihood promises bring key advantages such better uncertainty estimates on predictions automatic model regularizationMacKay 1992 Graves 2011) . These features often crucial informing downstream decision tasks reducing overfitting particularly on small datasets However despite potential advantages such Bayesian neural networks overlooked two limitations posterior inference in analytically intractable and approximate inference with Monte suffer crippling variance given only a reasonable computation budgetKingma Molchanov Miller BID8 . Second performance the Bayesian approach sensitive prior BID1 , although a priori knowledge concerning represented generally translate meaningful prior on neural network weights Sensitivity priors initialization makes BNNs non thus often irrelevant practiceIn inference simple aims solve these two limitations We adopt the paradigm variational Bayes (VB BNNsHinton van Camp 1993 MacKay 1995c normally deployed usingMCVIGraves 2011 . Within this paradigm address the two shortcomings current practice outlined First address high variance MCVI by reducing through novel deterministic approximations to variational inference in Second derive general and robust (EB approach prior choice using hierarchical priors By exploiting conjugacy we derive data-adaptive closed-form variance priors neural network weights experimentally demonstrate remarkablyCombining these two novel ingredients gives a performant and robust BNN inference scheme we refer We demonstrate robustness improved predictive performance deriving novel closed-form results (similar derivations classification can the appendix).Experiments on standard regression datasets from the UCI repository (Dheeru & Karra Taniskidou 2017 , for identical models DVI converges local optima better predictive loglikelihoods existing methods based MCVI In direct comparisons , our Empirical Bayes formulation automatically provides better or comparable test performance manual tuning prior and that heteroscedastic models consistentlyConcretely, our contributions Development propagating uncertain activations through uncertain weights ReLU or Heaviside activation an EB method principled tuning weight priors during BNN Experimental results the accuracy applicability on real datasets We introduced two innovations variational inference for more 1 an effective deterministic approximation the moments activations a neural networks; 2 a simple empirical Bayes hyperparameter update We demonstrate together these innovations make variational Bayes competitive method neural heteroscedastic regression modelsBayesian neural networks substantially upon standard networks these settings where calibrated predictive uncertainty, sequential decision making continual learning without catastrophic forgettingsee BID3 Gal et (2017 ; Nguyen FORMULA0 ). In future work the new innovations proposed these areas In the sequential decision making and continual learning applications approximate Bayesian inference must run an inner loop a larger algorithm This requires a robust and automated version BNN training: this precisely where believe the innovations this paper have large impact since pave automated and robust deployment BBNs that do involve an expert-",0.01,0.43859078750979075
"Skills learned through (deep) reinforcement learning often generalizes poorly
 across tasks and re-training is necessary when presented with a new task. We
 present a framework that combines techniques in formal methods with reinforcement
 learning (RL) that allows for the convenient specification of complex temporal
 dependent tasks with logical expressions and construction of new skills from existing
 ones with no additional exploration. We provide theoretical results for our
 composition technique and evaluate on a simple grid world simulation as well as
 a robotic manipulation task. Policies learned using reinforcement learning aim to maximize the given reward function and are often difficult to transfer to other problem domains. Skill composition is the process of constructing new skills out of existing ones (policies) with little to no additional learning. In stochastic optimal control, this idea has been adopted by BID20 and BID9 to construct provably optimal control laws based on linearly solvable Markov decision processes.Temporal logic (TL) is a formal language commonly used in software and digital circuit verification BID7 as well as formal synthesis BID8 . It allows for convenient expression of complex behaviors and causal relationships. TL has been used by BID19 , BID11 , BID10 to synthesize provably correct control policies. BID6 have also combined TL with Q-learning to learn satisfiable policies in discrete state and action spaces.We make the distinction between skill composition and multi-task learning/meta-learning where the latter often requires a predefined set of tasks/task distributions to learn and generalize from, whereas the focus of the former is to construct new policies from a library of already learned policies that achieve new tasks (often some combination of the constituent tasks) with little to no additional constraints on task distribution at learning time. In this work, we focus on skill composition with policies learned using automata guided reinforcement learning BID15 . We adopt the syntactically co-safe truncated linear temporal logic (scTLTL) as the task specification language. Compared to most heuristic reward structures used in the RL literature, formal specification language has the advantage of semantic rigor and interpretability.In our framework, skill composition is accomplished by taking the product of finite state automata (FSA). Instead of interpolating/extrapolating among learned skills/latent features, our method is based on graph manipulation of the FSA. Therefore, the outcome is much more transparent. Compared with previous work on skill composition, we impose no constraints on the policy representation or the problem class. We validate our framework in simulation (discrete state and action spaces) and experimentally on a Baxter robot (continuous state and action spaces). In FIG6 (left), we report the discounted return as a function of policy update steps for task φ ∧ . 5 evaluation episodes are collected after each set policy updates to calculate the performance statistics. As comparison, we learn the same task using SQL with FSA augmented MDP. We can see that our composition method takes less update steps to reach a policy that achieves higher returns with lower variance than the policy obtained from learning. FIG6 (right) shows the episode length as a function of policy update (upper bound clipped at 100 steps). As mentioned in the previous section, a shorter episode length indicates faster accomplishment of the task. It can be observed that both the composition and learning method result in high variances likely due to the randomized task configuration (some plate/joint/hand configurations make the task easier to accomplish than others). However, the policy obtained from composition achieves a noticeable decrease in the average episode length.It is important to note that the wall time for learning a policy is significantly longer than that from composition. For robotic tasks with relatively simple policy representations (feed-forward neural networks), learning time is dominated by the time used to collect experiences and the average episode length (recall that we update the policy 100 times with each 5 episodes of exploration). Since skill composition uses already collected experience, obtaining a policy can be much faster. TAB1 shows the mean training time and standard deviation (over 5 random seeds) for each task (tasks φ traverse , φ interrupt and φ ∧ (learned) are trained for 80K policy updates. φ ∧ (composed) is trained for 40K policy updates). In general, training time is shorter for tasks with higher episodic success rate and shorter episode length. We also show the task success rate evaluated on the real robot over 20 evaluation trials. Task success is evaluated by calculating the robustness of the trajectories resulting from executing each policy. A robustness of greater than 0 evaluates to success and vice versa. π φ∧ (learned) fails to complete the task even though a convergence is reached during training. This is likely due to the large FSA of φ ∧ with complex per-step reward (D q φ in Equation FORMULA15 ) which makes learning difficult. FIG5 shows an evaluation run of the composed policy for task φ ∧ . We provide a technique that takes advantage of the product of finite state automata to perform deterministic skill composition. Our method is able to synthesize optimal composite policies for −AN D− and −OR− tasks. We provide theoretical results on our method and show its effectiveness on a grid world simulation and a real world robotic task. For future work, we will adapt our method to the more general case of task-space transfer -given a library of optimal policies (Qfunctions) that each satisfies its own specification, construct a policy that satisfies a specification that's an arbitrary (temporal) logical combination of the constituent specifications.",1104,0.642,662,1.6676737160120847,"Skills learned (deep) reinforcement learning often generalizes poorly re when presented We present combines techniques formal methods reinforcement learning that the convenient specification complex temporal dependent tasks logical expressions construction new skills from with no additional exploration We provide theoretical results our composition technique evaluate on a simple grid world simulation as a robotic manipulation task learned using reinforcement learning aim maximize the given reward function are difficult transfer Skill composition constructing out In stochastic optimal control this idea adopted BID20 construct provably optimal control laws linearly solvable Markov decision processesTemporal logicTL commonly software digital circuit verification BID7 as formal synthesis . It allows convenient expression complex behaviors causal relationships TL has used BID19 , to provably correct control policies BID6 have also combined TL with Q-learning learn satisfiable policies discrete state and action spacesWe make skill composition where often tasks/task distributions the focus former construct new policies a library achieveoften some combination the constituent tasks at learning time In this work skill composition with policies learned using automata guided reinforcement BID15 . We adopt the syntactically co-safe truncated linear temporal logicscTLTL the task specification language Compared most heuristic reward structures used formal specification language semantic rigor interpretabilityIn our framework skill composition accomplished taking the product finite state automata Instead interpolating/ among learned skills/latent features our method graph manipulation the FSA Therefore the outcome much transparent Compared previous work skill composition impose the policy representation the problem class We validate our framework simulation (discrete state and action spaces on a Baxter robot In FIG6left report the discounted return as policy update steps task �� �� . 5 evaluation episodes are collected after each set policy updates calculate the performance statistics As comparison learn the same task using SQL with FSA augmented MDP We our composition method takes less update steps reach a policy achieves higher returns with obtained learning FIG6 (right the episode length policy updateupper bound clipped 100 steps As mentioned a shorter episode length indicates faster accomplishment It can observed both composition learning method result high variances likely the randomized task configurationsome plate/joint/hand configurations make However the policy obtained composition achieves a noticeable decrease the average episode lengthIt the wall time learning a policy significantly from For robotic tasks with relatively simple policy representationsfeed- learning time dominated used collect experiences the average episode lengthrecall update the policy 100 with each 5 episodes exploration Since skill composition uses already collected obtaining a policy TAB1 shows the mean training timeover 5 random seeds �� traverse (learned are trained 80K policy updates �� ��composed is trained 40K policy updates). In general training time shorter tasks higher episodic success rate shorter episode length We also show the task success rate evaluated the real robot over 20 evaluation trials Task success evaluated calculating resulting executing each policy A robustness greater evaluates success vice π ����learned fails complete even a convergence during This likely the large FSA of �� �� with complex perstep rewardD q �� in Equation FORMULA15 ) learning FIG5 an evaluation run the composed policy task �� �� We provide a technique takes the product deterministic skill composition Our method able optimal composite policies −AN D− −OR− tasks We provide theoretical results our method show its effectiveness a grid world simulation and a real world robotic task For future work adapt task-space transfer -given a library optimal policiesQfunctions each satisfies construct's an arbitrary (temporal) logical combination the constituent specifications",0.01,0.4052531369113123
"The application of multi-modal generative models by means of a Variational Auto Encoder (VAE) is an upcoming research topic for sensor fusion and bi-directional modality exchange.
 This contribution gives insights into the learned joint latent representation and shows that expressiveness and coherence are decisive properties for multi-modal datasets.
 Furthermore, we propose a multi-modal VAE derived from the full joint marginal log-likelihood that is able to learn the most meaningful representation for ambiguous observations.
 Since the properties of multi-modal sensor setups are essential for our approach but hardly available, we also propose a technique to generate correlated datasets from uni-modal ones.
 Auto Encoder (AE), Variational Auto Encoder (VAE), and more recently Disentangled Variational Auto Encoder (β-VAE) have a considerable impact on the field of data-driven leaning of generative models. Furthermore, recent investigations have shown the fruitful applicability to deep reinforcement learning (DRL) as well as bi-directionally exchange of multi-modal data. VAEs tend to encode the data into latent space features that are (ideally) linearly separable as shown by BID4 . They also allow the discovery of generative joint models (e.g. BID17 ), as well as zero-shot domain transfer in DRL as shown by BID5 .However , a good generative model should not just generate good data and achieve a good quantitative score, but also gives a coherent and expressive latent space representation. This property is decisive for multi-modal approaches if the data shows correlation, as it is the case for every sensor setup designed for sensor fusion. With this contribution , we investigate the characteristic of the latent space as well as the quantitative features for existing multi-modal VAEs. Furthermore, we propose a novel approach to build and train a novel multi-modal VAE (M 2 VAE) which comprises the complete marginal joint log-likelihood without simplifying assumptions. As our objective is the consideration of raw multi-modal sensor data, we also propose an approach to generate correlated multi-modal datasets from available uni-modal ones. Lastly, we draw connections to in-place sensor fusion and epistemic (ambiguity-resolving) active-sensing.Section 2 comprises the related work on multi-modal VAEs. Our comprehensive approach (i.e. M 2 VAE) is given in Sec. 3. Furthermore, we describe multi-modal datasets as well as the generation of correlated sets in Sec. 4 which are evaluated in Sec. 5. Finally, we conclude our work in Sec. 6. This work presents a novel multi-modal Variational Auto Encoder which is derived from the complete marginal joint log-likelihood. We showed that this expression can jointly be trained on an Mixture-of-Gaussian dataset with ambiguous observations, as well as on a complex dataset derived from MNIST and fashion-MNIST. Furthermore, we formulated requirements and characteristics for multi-modal data for sensor fusion and derived a technique to learn new datasets, namely the proposed entangled-MNIST, which suffice these requirements. Lastly, we developed the idea of in-place sensor fusion in distributed, active sensing scenarios and formulated the requirements, by means of auto re-encoding, to VAEs. This revealed the properties of VAEs, that they tend to denoise the observable data which leads to an attractor behavior in latent space. However, we performed all qualitative evaluations of the latent space with the premise in mind, that a good generative model should not just generate good data but also gives a good latent representation. This does also correlate with the quantitative behaviors, as our proposed model achieved the highest ELBO values. Future work will concentrate on the integration of the ambiguous resolving characteristics to an epistemic-exploration scenario.",743,0.408,451,1.647450110864745,"The application by means a Variational Auto Encoder an upcoming research topic sensor fusion This contribution gives insights the learned joint latent representation shows expressiveness decisive properties Furthermore propose a multi-modal VAE derived the full joint marginal log-likelihood that able learn the most meaningful representation ambiguous observations Since the properties multi-modal sensor setups essential our approach but hardly available also propose generate correlated datasets Auto EncoderAE Variational Auto Encoder (β-VAE data-driven leaning of Furthermore recent investigations the fruitful applicability to deep reinforcement learning bi-directionally exchange VAEs tend encode latent space features ( linearly as shown BID4 . They also allow the discovery generative joint models as zero-shot domain transfer DRL as shown BID5 .However , a good generative model just generate good data achieve a good quantitative score gives a coherent and expressive latent space representation This property decisive multi-modal approaches if shows correlation every sensor setup designed sensor fusion With this contribution , investigate the characteristic the latent space as for existing multi-modal VAEs Furthermore build train (M 2 VAE which comprises the complete marginal joint log-likelihood without simplifying assumptions As our objective the consideration raw multi-modal sensor data also propose generate available uni-modal ones Lastly draw connections inplace sensor fusion epistemic (resolving activeSection comprises the related work multi-modal VAEs Our comprehensive approach (i.e. M 2 VAE given Sec 3 Furthermore describe multi-modal datasets the generation correlated sets Sec 4 which evaluated Sec 5 Finally conclude Sec 6 This work presents a novel multi-modal Variational Auto Encoder which derived the complete marginal joint log-likelihood. We showed this expression jointly trained an Mixture-of-Gaussian dataset ambiguous observations derived MNIST and fashion-MNIST Furthermore formulated requirements characteristics for sensor fusion derived a technique learn new datasets namely the proposed entangled-MNIST, suffice these requirements Lastly developed inplace sensor fusion distributed, active sensing scenarios and formulated, by means auto re VAEs revealed the properties tend denoise which leads an attractor behavior latent space However we performed all qualitative evaluations the latent space with the premise in a good generative model just generate gives a good latent representation This does also correlate the quantitative behaviors our proposed model achieved the highest ELBO values Future work concentrate the integration the ambiguous resolving characteristics to an epistemic-exploration scenario",0.0,0.3537251678224111
"We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models. We build upon AESMC , a method for model learning that itself builds on variational auto-encoders (VAEs) BID4 BID10 and importance weighted auto-encoders (IWAEs) BID0 . AESMC is similarly based on maximizing a lower bound to the log marginal likelihood, but uses SMC BID3 as the underlying marginal likelihood estimator instead of importance sampling (IS). For a very wide array of models, particularly those with sequential structure, SMC forms a substantially more powerful inference method than IS, typically returning lower variance estimates for the marginal likelihood. Consequently, by using SMC for its marginal likelihood estimation, AESMC often leads to improvements in model learning compared with VAEs and IWAEs. We provide experiments on structured time-series data that show that AESMC based learning was able to learn useful representations of the latent space for both reconstruction and prediction more effectively than the IWAE counterpart.AESMC was introduced in an earlier preprint concurrently with the closely related methods of ; BID7 . In this work we take these ideas further by providing new theoretical insights for the resulting evidence lower bounds (ELBOs), extending these to explore the relative efficiency of different approaches to proposal learning, and using our results to develop a new and improved training procedure. In particular, we introduce a method for expressing the gap between an ELBO and the log marginal likelihood as a Kullback-Leibler (KL) divergence between two distributions on an extended sampling space. Doing so allows us to investigate the behavior of this family of algorithms when the objective is maximized perfectly, which occurs only if the KL divergence becomes zero. In the IWAE case, this implies that the proposal distributions are equal to the posterior distributions under the learned model. In the AESMC case, it has implications for both the proposal distributions and the intermediate set of targets that are learned. We demonstrate that, somewhat counter-intuitively, using lower variance estimates for the marginal likelihood can actually be harmful to proposal learning. Using these insights, we experiment with an adaptation to the AESMC algorithm, which we call alternating ELBOs, that uses different lower bounds for updating the model parameters and proposal parameters. We observe that this adaptation can, in some cases, improve model learning and proposal adaptation. We have developed AESMC-a method for performing model learning using a new ELBO objective which is based on the SMC marginal likelihood estimator. This ELBO objective is optimized using SGA and the reparameterization trick. Our approach utilizes the efficiency of SMC in models with intermediate observations and hence is suitable for highly structured models. We experimentally demonstrated that this objective leads to better generative model training than the IWAE objective for structured problems, due to the superior inference and tighter bound provided by using SMC instead of importance sampling.Additionally, in Claim 1, we provide a simple way to express the bias of objectives induced by log of marginal likelihood estimators as a KL divergence on an extended space. In Propositions 1 and 2, we investigate the implications of these KLs being zero in the case of IWAE and AESMC. In the latter case, we find that we can achieve zero KL only if we are able to learn SMC intermediate target distributions corresponding to marginals of the target distribution. Using our assertion that tighter variational bounds are not necessarily better, we then introduce and test a new method, alternating ELBOs, that addresses some of these issues and observe that, in some cases, this improves both model and proposal learning.",832,0.406,477,1.7442348008385744,"We build auto-encoding sequential Monte CarloAESMC): model proposal learning maximizing lower to the log marginal likelihood in a broad family Our approach relies the efficiency sequential Monte Carlo ( for performing inference the flexibility model We develop additional theoretical insights introduce which improves both model proposal learning We demonstrate our approach provides simultaneous model learning proposal adaptation deep generative models We build upon AESMC , a method model learning itself builds variational autoVAEs BID4 BID10 importance weighted AESMC similarly based maximizing a lower the log marginal likelihood uses SMC BID3 importance samplingIS For a very wide array models particularly those sequential structure SMC forms a substantially more powerful inference method IS, typically returning lower variance estimates the marginal likelihood by SMC for its marginal likelihood estimation AESMC often leads improvements model learning compared VAEs IWAEs provide experiments structured time-series data was useful representations both reconstruction more introduced an earlier preprint concurrently the closely related methods ; BID7 . In this work take these ideas further new theoretical insights the resulting evidence lower bounds (ELBOs extending explore the relative efficiency proposal learning In particular introduce expressing the gap an ELBO the log marginal likelihood as on an extended sampling space Doing allows investigate this family algorithms when the objective maximized perfectly occurs only the KL divergence becomes In the IWAE case this implies the proposal distributions equal under the learned model In the AESMC case implications both the proposal distributions the intermediate set targets learned We demonstrate somewhat counter using lower variance estimates the marginal likelihood can actually harmful proposal learning Using these insights experiment an adaptation the AESMC algorithm alternating ELBOs that different lower bounds updating the model parameters proposal parameters We observe this adaptation can, improve model learning proposal adaptation We developed AESMCa method performing model learning a new ELBO objective the SMC marginal likelihood estimator This ELBO objective optimized using SGA the reparameterization trick Our approach utilizes the efficiency SMC in models intermediate observations hence suitable highly structured models We experimentally demonstrated this objective leads better generative model training than the IWAE objective structured problems due the superior inference tighter bound provided using SMC instead importance samplingAdditionally Claim provide express objectives induced log of marginal likelihood estimators a KL divergence on an extended space In Propositions investigate these KLs being zero IWAE AESMC In find we achieve zero KL only learn SMC intermediate target distributions corresponding marginals Using our assertion tighter variational bounds introduce and alternating ELBOs addresses observe this improves both model proposal learning",0.01,0.6003240544658441
"A key component for many reinforcement learning agents is to learn a value function, either for policy evaluation or control. Many of the algorithms for learning values, however, are designed for linear function approximation---with a fixed basis or fixed representation. Though there have been a few sound extensions to nonlinear function approximation, such as nonlinear gradient temporal difference learning, these methods have largely not been adopted, eschewed in favour of simpler but not sound methods like temporal difference learning and Q-learning. In this work, we provide a two-timescale network (TTN) architecture that enables linear methods to be used to learn values, with a nonlinear representation learned at a slower timescale. The approach facilitates the use of algorithms developed for the linear setting, such as data-efficient least-squares methods, eligibility traces and the myriad of recently developed linear policy evaluation algorithms, to provide nonlinear value estimates. We prove convergence for TTNs, with particular care given to ensure convergence of the fast linear component under potentially dependent features provided by the learned representation. We empirically demonstrate the benefits of TTNs, compared to other nonlinear value function approximation algorithms, both for policy evaluation and control.     Value function approximation-estimating the expected returns from states for a policy-is heavily reliant on the quality of the representation of state. One strategy has been to design a basis-such as radial basis functions (Sutton and Barto, 1998) or a Fourier basis BID17 )-for use with a linear function approximator and temporal difference (TD) learning (Sutton, 1988) . For low-dimensional observation vectors, this approach has been effective, but can be onerous to extend to high-dimensional observations, potentially requiring significant domain expertise. Another strategy has been to learn the representation, such as with basis adaptation or neural networks. Though there is still the need to specify the parametric form, learning these representations alleviates the burden of expert specification. Further, it is more feasible to scale to high-dimensional observations, such as images, with neural networks (Mnih et al., 2015; BID16 . Learning representations necessitates algorithms for nonlinear function approximation.Despite the deficiencies in specification for fixed bases, linear function approximation for estimating value functions has several benefits over nonlinear estimators. They enable least-squares methods, which can be much more data-efficient for policy evaluation BID5 Szepesvari, 2010; van Seijen and Sutton, 2015) , as well as robust to meta-parameters (Pan et al., 2017) . Linear algorithms can also make use of eligibility traces, which can significantly speed learning (Sutton, 1988; BID9 White and White, 2016 ), but have not been able to be extended to nonlinear value function approximation. Additionally, there have been a variety of algorithms derived for the linear setting, both for on-policy and off-policy learning (Sutton et al., 2009; BID23 van Seijen and Sutton, 2014; van Hasselt et al., 2014; Mahadevan et al., 2014; Sutton et al., 2016; Mahmood et al., 2017) . These linear methods have also been well-explored theoretically (Tsitsiklis and Van Roy, 1997; BID23 Mahmood and Sutton, 2015; Yu, 2015) and empirically BID9 White and White, 2016) , with some insights into improvements from gradient methods (Sutton et al., 2009 ), true-online traces (van Seijen and Sutton, 2014) and emphatic weightings (Sutton et al., 2016) . These algorithms are easy to implement, with relatively simple objectives. Objectives for nonlinear value function approximation, on the other hand, can be quite complex (Maei et al., 2009) , resulting in more complex algorithms (Menache et al., 2005; BID10 BID2 or requiring a primal-dual formulation as has been done for control BID8 .In this work, we pursue a simple strategy to take advantage of the benefits of linear methods, while still learning the representation. The main idea is to run two learning processes in parallel: the first learns nonlinear features using a surrogate loss and the second estimates the value function as a linear function of those features. We show that these Two-timescale Networks (TTNs) converge, because the features change on a sufficiently slow scale, so that they are effectively fixed for the fast linear value function estimator. Similar ideas have previously been explored for basis adaptation, but without this key aspect of TTNs-namely the separation of the loss for the representation and value function. This separation is critical because it enables simpler objectives-for which the gradient can be easily sampled-to drive the representation, but still enables use of the mean squared projected Bellman error (MSPBE)-on which all the above linear algorithms are based. This separation avoids the complexity of the nonlinear MSPBE, but maintains the useful properties of the (linear) MSPBE. A variety of basis adaptation approaches have used a two-timescale approach, but with the same objective for the representation and the values (Menache et al., 2005; BID10 BID2 . Yu and Bertsekas ( 2009) provided algorithms for basis adaptation using other losses, such as Bellman error using Monte carlo samples, taking derivatives through fixed point solutions for the value function. BID21 periodically compute a closed form least-squares solution for the last layer of neural network, with a Bayesian update to prevent too much change. Because these methods did not separate the value learn and basis adaptation, the resulting algorithms are more complex. The strategy of using two different heads-one to drive the representation and one to learn the values-has yet to be systematically explored.We show that TTNs are a promising direction for nonlinear function approximation, allowing us to leverage linear algorithms while retaining the flexibility of nonlinear function approximators. We first discuss a variety of possible surrogate losses, and their potential for learning a useful representation. We then show that TTNs converge , despite the fact that a linear algorithm is used with a changing representation. This proof is similar to previous convergence proofs for policy evaluation, but with a relaxation on the requirement that features be independent, which is unlikely for learned features. We then show empirically that TTNs are effective compared to other nonlinear value function approximations and that they can exploit several benefits of linear value approximations algorithms. In particular, for both low-dimensional and high-dimensional (image-based) observations, we show (a) the utility of least-squares (or batch ) methods, (b) advantages from eligibility traces and (c) gains from being able to select amongst different linear policy evaluation algorithms. We demonstrate that TTNs can be effective for control with neural networks, enabling use of fitted Q-iteration within TTNs as an alternative to target networks. In this work, we proposed Two-timescale Networks as a new strategy for policy evaluation with nonlinear function approximation. As opposed to many other algorithms derived for nonlinear value function approximation, TTNs are intentionally designed to be simple to promote ease-of-use. The algorithm combines a slow learning process for adapting features and a fast process for learning a linear value function, both of which are straightforward to train. By leveraging these two timescales, we are able to prove convergence guarantees for a broad class of choices for both the fast and slow learning components. We highlighted several cases where the decoupled architecture in TTNs can improve learning, particularly enabling the use of linear methods-which facilitates use of least-squares methods and eligibility traces.This work has only begun the investigation into which combinations for surrogate losses and linear value function approximation algorithms are most effective. We provided some evidence that, when using stochastic approximation algorithms rather than least-squares algorithms, the addition of traces can have a significant effect within TTNs. This contrasts nonlinear TD, where traces were not effective. The ability to use traces is potentially one of the most exciting outcomes for TTNs, since traces have been so effective for linear methods. More generally, TTNs provide the opportunity to investigate the utility of the many linear value function algorithms, in more complex domains with learned representations. For example, emphatic algorithms have improved asymptotic properties (Sutton et al., 2016) , but to the best of our knowledge, have not been used with neural networks.Another promising direction for TTNs is for off-policy learning, where many value functions are learned in parallel. Off-policy learning can suffer from variance due to large magnitude corrections (importance sampling ratios). With a large collection of value functions, it is more likely that some of them will cause large updates, potentially destabilizing learning in the network if trained in an end-to-end fashion. TTNs would not suffer from this problem, because a different objective can be used to drive learning in the network. We provide some preliminary experiments in the appendix supporting this hypothesis (Appendix C.7). θ,w ← GradientDescent on L slow using sample (s, r, s ) DISPLAYFORM0 w ← Update on L value using sample (s, r, s )8: DISPLAYFORM1 end while 10:return learned parameters w, θ,w 11: end procedure B CONVERGENCE PROOF OF TWO-TIMESCALE NETWORKS B.1 DEFINITIONS & NOTATIONS -Let R + denote the set of non-negative real numbers, N = {0, 1, 2, . . . } and · denote the Euclidean norm or any equivalent norm. DISPLAYFORM2 3. h is upper-semicontinuous, i.e., if {x n } n∈N → x and {y n } n∈N → y, where x n ∈ R d , y n ∈ h(x n ), ∀n ∈ N, then y ∈ h(x).-For x 1 , x 2 ∈ R d and D ∈ R k×k a diagonal matrix, we define the inner-product < x 1 , x 2 > D x 1 Dx 2 . We also define the semi-norm DISPLAYFORM3 D . If all the diagonal elements of D are strictly positive, then · D is a norm.-For any set X, letX denote the interior of X and ∂X denote the boundary of X. -For brevity, letθ = (θ,w) and Φθ be the feature matrix corresponding to the feature parameterθ, i.e. DISPLAYFORM4 where x θ (s) is the row-vector corresponding to state s. Further, define the |S| × |S|-matrix P π as follows: P π s,s a∈A π(s, a)P (s, a, s ), s, s ∈ S.-Also, recall that DISPLAYFORM5 is Frechet differentiable at x ∈ U if there exists a bounded linear operator Γ x : R d1 → R d2 such that the limit DISPLAYFORM6 exists and is equal to Γ x (y). We say Γ is Frechet differentiable if Frechet derivative of Γ exists at every point in its domain.",2272,1.065,1342,1.6929955290611027,"A key component for many reinforcement learning agents a value function either for policy evaluation control Many the algorithms for learning values however designed linear function approximation---with a fixed basis or fixed representation Though a few sound extensions nonlinear function approximation nonlinear gradient temporal difference learning largely not, eschewed of simpler but not sound methods Q-learning In this work provide a two-timescale network (TTN architecture linear methods learn values with learned a slower timescale The approach facilitates algorithms developed the linear setting data-efficient least-squares methods eligibility traces the myriad recently developed linear policy evaluation nonlinear value estimates We prove convergence for TTNs with particular care ensure convergence the fast linear component under potentially dependent features provided the learned representation We empirically demonstrate TTNs compared nonlinear value function approximation both policy evaluation control Value function approximation-estimating the expected returns states for a policyis heavily reliant. One strategy has design a basis-such radial basis functionsSutton Barto a Fourier basis BID17 )-for use a linear function approximator temporal difference (TD) learning 1988 . For low-dimensional observation vectors effective can onerous extend potentially significant domain expertise Another strategy has learn the representation, such with basis adaptation neural networks Though the need specify the parametric form learning these representations alleviates expert specification Further more feasible scale high-dimensional observations images neural networksMnih et al BID16 . Learning representations necessitates algorithms nonlinear function approximationDespite the deficiencies specification fixed bases for estimating value functions several benefits They enable least-squares methods much data policy evaluation BID5 Szepesvari 2010 van Seijen and Sutton 2015) , as robust toPan 2017 Linear algorithms make eligibility traces significantly speed learning (Sutton 1988 BID9 White White 2016 ), have able extended nonlinear value function approximation Additionally algorithms derived for the linear setting both onpolicy learningSutton BID23 van Seijen Sutton Mahadevan Sutton Mahmood) . These linear methods also well-explored theoretically (Tsitsiklis Van Roy BID23 Mahmood Sutton 2015 Yu empirically BID9 White and White) , some insights improvements from gradient methods trueonline tracesvan Seijen Sutton emphatic weightings These algorithms easy with relatively simple objectives Objectives for nonlinear value function approximation, on quite (Maei , resultingMenache et BID10 BID2 or requiring a primal-dual formulation as has control BID8 .In pursue a simple strategy take the benefits linear methods while learning the representation. The main idea run two learning processes learns nonlinear features using a surrogate loss and estimates the value function as We show these Two-timescale Networks (TTNs converge, because the features change on a sufficiently slow scale effectively fixed for the fast linear value function estimator Similar ideas previously basis adaptation without this key aspect TTNs-namely the separation the loss for the representation and value function This separation critical enables simpler objectives- the gradient can sampled drive the representation, still enables use the mean squared projected Bellman errorMSPBE)-on all the above linear algorithms This separation avoids the complexity the nonlinear MSPBE maintains the useful properties A variety basis adaptation approaches used a two-timescale approach with for the representation the values (Menache et al BID10 BID2 . Yu and Bertsekas ( 2009) provided algorithms basis adaptation using other losses Bellman error using Monte carlo samples taking derivatives through fixed point solutions for the value function BID21 periodically compute a closed form least-squares solution the last layer neural network a Bayesian update prevent too much change Because these methods did separate the value learn basis adaptation the resulting algorithms The strategy using two different headsone drive the representation learn the values- yet systematicallyWe show TTNs a promising direction nonlinear function approximation allowing leverage linear algorithms while We first discuss a variety possible surrogate losses their potential learning a useful representation We then show TTNs converge , despite a linear algorithm with a changing representation This proof similar previous convergence proofs policy evaluation a relaxation on features independent unlikely for learned features We then show empirically TTNs effective compared other nonlinear value function approximations exploit several benefits value algorithms In particular for show ( the utility least-squares (or batch ) methods from eligibility traces being select amongst linear policy evaluation We demonstrate TTNs effective control with neural networks enabling use fitted Q-iteration within target networks In this work proposed Two-timescale Networks policy evaluation with nonlinear function approximation As opposed many other algorithms derived for nonlinear value function approximation TTNs intentionally simple promote ease The algorithm combines a slow learning process adapting features a linear value function both straightforward train By leveraging these two timescales prove convergence guarantees a broad class choices both the fast and slow learning components We highlighted several cases the decoupled architecture in TTNs can improve learning enabling linear methods-which facilitates use eligibility tracesThis work only begun the investigation which combinations for surrogate losses linear value function approximation algorithms We provided some evidence, using stochastic approximation algorithms rather the addition traces within TTNs contrasts nonlinear TD, traces effective The ability use traces potentially TTNs traces so effective linear methods More generally TTNs provide investigate the utility many linear value function algorithms more complex domains with learned representations For example emphatic algorithms improved asymptotic propertiesSutton 2016 , to have withAnother promising direction TTNs off-policy learning many value functions learned Off-policy learning can suffer variance due large magnitude correctionsimportance sampling ratios With a large collection value functions more some cause large updates potentially destabilizing learning the network if trained end TTNs would suffer a different objective can drive learning the network We provide some preliminary experiments the appendix supporting ( ��,w �� GradientDescent on L slow using sample (s, r ) DISPLAYFORM0 w �� Update on L value using8 end while 10:return learned parameters w, � 11 end procedure B CONVERGENCE PROOF OF & NOTATIONS -Let R + denote N { . . . } and · denote or any equivalent norm DISPLAYFORM2 3 h is uppersemicontinuous if {x n } n��N → and where R d h(x ��n then h(x).-For k×k a diagonal matrix innerproduct < > D 1 Dx We also define semi-norm DISPLAYFORM3 D . If all the diagonal elements D are strictly positive · D a norm.-For any set X letX denote the interior -For brevity�w and� be the feature matrix corresponding the feature parameter�� i.e. DISPLAYFORM4 where x (s the row-vector corresponding state s. Further define the |S| × |S|-matrix P �� as,s( ),, �� S.-Also recall DISPLAYFORM5 Frechet differentiable at x �� U if there a bounded linear operator �� x : R d1 such the limit exists andy We say �� Frechet differentiable if Frechet derivative exists its domain",0.01,0.46977089181004134
"Large-scale Long Short-Term Memory (LSTM) cells are often the building blocks of many state-of-the-art algorithms for tasks in Natural Language Processing (NLP). However, LSTMs are known to be computationally inefficient because the memory capacity of the models depends on the number of parameters, and the inherent recurrence that models the temporal dependency is not parallelizable. In this paper, we propose simple, but effective, low-rank matrix factorization (MF) algorithms to compress network parameters and significantly speed up LSTMs with almost no loss of performance (and sometimes even gain). To show the effectiveness of our method across different tasks, we examine two settings: 1) compressing core LSTM layers in Language Models, 2) compressing biLSTM layers of ELMo~\citep{ELMo} and evaluate in three downstream NLP tasks (Sentiment Analysis, Textual Entailment, and Question Answering). The latter is particularly interesting as embeddings from large pre-trained biLSTM Language Models are often used as contextual word representations. Finally, we discover that matrix factorization performs better in general, additive recurrence is often more important than multiplicative recurrence, and we identify an interesting correlation between matrix norms and compression performance.

 Long Short-Term Memory (LSTM) networks (Hochreiter & Schmidhuber, 1997; BID11 have become the core of many models for tasks that require temporal dependency. They have particularly shown great improvements in many different NLP tasks, such as Language Modeling (Sundermeyer et al., 2012; Mikolov, 2012) , Semantic Role Labeling (He et al., 2017) , Named Entity Recognition (Lee et al., 2017) , Machine Translation BID0 , and Question Answering (Seo et al., 2016) . Recently, a bidirectional LSTM has been used to train deep contextualized Embeddings from Language Models (ELMo) (Peters et al., 2018a) , and has become a main component of state-of-the-art models in many downstream NLP tasks.However, there is an obvious drawback of scalability that accompanies these excellent performances, not only in training time but also during inference time. This shortcoming can be attributed to two factors: the temporal dependency in the computational graph, and the large number of parameters for each weight matrix. The former problem is an intrinsic nature of RNNs that arises while modeling temporal dependency, and the latter is often deemed necessary to achieve better generalizability of the model (Hochreiter & Schmidhuber, 1997; BID11 . On the other hand, despite such belief that the LSTM memory capacity is proportional to model size, several recent results have empirically proven the contrary, claiming that LSTMs are indeed over-parameterized BID4 James Bradbury & Socher, 2017; Merity et al., 2018; Melis et al., 2018; Levy et al., 2018) . Naturally, such results motivate us to search for the most effective compression method for LSTMs in terms of performance, time, and practicality, to cope with the aforementioned issue of scalability. There have been many solutions proposed to compress such large, over-parameterized neural networks including parameter pruning and sharing BID12 Huang et al., 2018) , low-rank Matrix Factorization (MF) (Jaderberg et al., 2014) , and knowledge distillation (Hinton et al., 2015) . However, most of these approaches have been applied to Feed-forward Neural Networks and Convolutional Neural Networks (CNNs), while only a small attention has been given to compressing LSTM architectures (Lu et al., 2016; BID1 , and even less in NLP tasks. Notably, See et al. (2016) applied parameter pruning to standard Seq2Seq (Sutskever et al., 2014) architecture in Neural Machine Translation, which uses LSTMs for both encoder and decoder. Furthermore, in language modeling, BID13 uses Tensor-Train Decomposition (Oseledets, 2011 BID18 uses binarization techniques, and Kuchaiev & Ginsburg (2017) uses an architectural change to approximate low-rank factorization.All of the above mentioned works require some form of training or retraining step. For instance, Kuchaiev & Ginsburg (2017) requires to be trained completely from scratch, as well as distillation based compression techniques (Hinton et al., 2015) . In addition, pruning techniques (See et al., 2016) often accompany selective retraining steps to achieve optimal performance. However, in scenarios involving large pre-trained models, e.g. ELMo (Peters et al., 2018a) , retraining can be very expensive in terms of time and resources. Moreover, compression methods are normally applied to large and over-parameterized networks, but this is not necessarily the case in our paper. We consider strongly tuned and regularized state-of-the-art models in their respective tasks, which often already have very compact representations. These circumstances make the compression much more challenging, but more realistic and practically useful.In this work, we advocate low-rank matrix factorization as an effective post-processing compression method for LSTMs which achieve good performance with guaranteed minimum algorithmic speed compared to other existing techniques. We summarize our contributions as the following:• We thoroughly explore the limits of several different compression methods (matrix factorization and pruning), including fine-tuning after compression, in Language Modeling, Sentiment Analysis, Textual Entailment, and Question Answering.• We consistently achieve an average of 1.5x (50% faster) speedup inference time while losing ∼1 point in evaluation metric across all datasets by compressing additive and/or multiplicative recurrences in the LSTM gates.• In PTB, by further fine-tuning very compressed models (∼98%) obtained with both matrix factorization and pruning, we can achieve ∼2x (200% faster) speedup inference time while even slightly improving the performance of the uncompressed baseline.• We discover that matrix factorization performs better in general, additive recurrence is often more important than multiplicative recurrence, and we identify clear and interesting correlations between matrix norms and compression performance. In conclusion, we exhaustively explored the limits of compressing LSTM gates using low-rank matrix factorization and pruning in four different NLP tasks. Our experiment results and norm analysis show that show that Low-Rank Matrix Factorization works better in general than pruning, but if the matrix is particularly sparse, Pruning works better. We also discover that inherent low-rankness and low nuclear norm correlate well, explaining why compressing multiplicative recurrence works better than compressing additive recurrence. In future works, we plan to factorize all LSTMs in the model, e.g. BiDAF model, and try to combine both Pruning and Matrix Factorization. In this section, we provide the semi-NMF algorithm and we elaborate the optimization and the aim of each step. This algorithm is an extension of NMF, where the data matrix is remained unconstrained BID7 . The original NMF optimization function shows in 8. Semi-NMF ignores the constraint in U as showed in 9. DISPLAYFORM0 Exploring the relationships between matrix factorization and K-means clustering has implications for the interpretability of matrix factors Ding et al. FORMULA0 1. Initialize U and run k-means clustering Hartigan & Wong (1979) . DISPLAYFORM1 The objective function of k-means clustering DISPLAYFORM2 We can relax the range of v ki over the values in (0, 1) or (0, ∞). This restricts V to accept only nonnegative values and allow U to have mixed signs values.2. Update U by fixing V using this constraint. By fixing V, the solution of U can be obtained by calculating the derivative of dJ/dU = −2WV T + 2U VV T = 0. Then we can get the DISPLAYFORM3 The positive and negative parts are computed A DISPLAYFORM4 According to BID7 , this method will reach convergence. By fixing U, the residual ||W − UV T || 2 will decrease monotonically, and after fixing V, we get the optimal solution for the objective function.The algorithm is computed by using an iterative updating algorithm that alternates between the update of U and V BID7 . The steps are very similar to coordinate descent Luo & Tseng (1992) with some modifications. The optimization is convex in U or V, not both.In the latent space derived by the NMF factorization family, each axis captures the centroid of a particular cluster, and each sample is represented as an additive combination of the centroids. The cluster membership of each document can be easily determined by finding the corresponding cluster centroid (the axis) with which the document has the largest projection value. Note in particular that the result of a K-means clustering run can be written as a matrix factorization W = UV , where W ∈ R nm is the data matrix, U ∈ R nr contains the cluster centroids, and V ∈ R rm contains the cluster membership indicators.• Perform the NMF or semi-NMF on W to obtain the two non-negative matrices U and V.• Matrix U contains r n−dimensional cluster centers and matrix V contains membership weight for each of the m samples in each of the r clusters. One can assign data i to the cluster c if c = argmax j V ij . DISPLAYFORM5 The algorithm complexity in terms of time and memory is shown in TAB4 .",1984,0.843,1218,1.6288998357963875," often state algorithms tasks in Natural Language Processing However LSTMs known computationally the memory capacity the models parameters the inherent recurrence that models the temporal dependency is parallelizable In this paper simple, but effective, low-rank matrix factorizationMF compress network parameters significantly speed almost no lossand sometimes gain To show the effectiveness our method across different tasks examine two settings 1 compressing core LSTM layers Language Models of ELMo~\citep{ELMo evaluate in three downstream NLP tasks (Sentiment Analysis Textual Entailment Question Answering The latter particularly embeddings from large pre-trained biLSTM Language Models contextual word representations Finally discover matrix factorization performs general additive recurrence is often important identify an interesting correlation matrix norms compression performance Long Short Memory networks (Hochreiter & 1997 BID11 have become the core many models tasks temporal dependency They particularly shown great improvements many different NLP tasks Language ModelingSundermeyer Mikolov , Semantic Role LabelingHe et 2017 Named Entity Recognition Machine Translation BID0 , Question AnsweringSeo Recently a bidirectional LSTM has used train deep contextualized Embeddings from Language ModelsELMoPeters 2018a , has become a main component state models many downstream NLP tasksHowever scalability that accompanies these excellent performances not training time during This shortcoming can the temporal dependency in the computational graph parameters for each weight matrix The former problem an intrinsic nature RNNs arises while modeling temporal dependency often deemed necessary achieveHochreiter BID11 . On despite such belief the LSTM memory capacity proportional model size several recent results empirically proven claiming indeed over-parameterized BID4 James Bradbury & Socher 2017 Merity Melis Levy) . Naturally such results motivate search the most effective compression method LSTMs terms time practicality to cope the aforementioned issue There many solutions proposed compress such large, over-parameterized neural networks including parameter pruning sharing BID12 Huang et al 2018) , low-rank Matrix FactorizationMFJaderberg knowledge distillationHinton However most these approaches applied Feed-forward Neural Networks while only a small attention compressing LSTM architecturesLu 2016 BID1 , and even in NLP tasks. Notably See et (2016 applied parameter pruning standard Seq2Seq (Sutskever et al., 2014) architecture in Neural Machine Translation, which both encoder Furthermore in language modeling BID13 uses Tensor-Train DecompositionOseledets 2011 BID18 uses binarization techniques Kuchaiev & Ginsburg2017 an architectural change approximate low-rank factorizationAll require some form retraining step For instance Kuchaiev & Ginsburg2017 requires to trained completely from as distillation based compressionHinton . In addition pruning techniques (See et 2016 often accompany selective retraining steps achieve However in scenarios large pre-trained models e.g. ELMo (Peters 2018a , retraining can very Moreover compression methods normally large and over-parameterized networks our paper We consider strongly tuned regularized state models in their respective tasks often already very compact representations These circumstances make the compression much challenging more realistic and practically usefulIn this work advocate low-rank matrix factorization which achieve guaranteed minimum algorithmic speed compared other existing techniques We summarize our contributions as the following:• thoroughly explore the limits several different compression methodsmatrix factorization pruning after in Language Modeling Sentiment Textual Entailment Question consistently achieve (50 faster speedup inference time while losing ∼1 point evaluation metric across all datasets by compressing additive and/or multiplicative recurrences In PTB by further fine very compressed models98% obtained200 even slightly the uncompressed baseline.• discover performs general additive recurrence is often identify clear and interesting correlations matrix norms compression performance In conclusion exhaustively explored the limits compressing LSTM gates low-rank matrix factorization pruning four different NLP tasks Our experiment results and norm analysis show Low-Rank Matrix Factorization works general pruning if particularly sparse works We also discover inherent lowrankness nuclear norm correlate, explaining compressing multiplicative recurrence works In future works plan factorize all LSTMs e.g. BiDAF model try combine both Pruning Matrix Factorization In provide the semi-NMF algorithm we elaborate the optimization the aim each step This algorithm NMF where the data matrix remained unconstrained BID7 . The original NMF optimization function shows in 8 SemiNMF ignores the constraint in U as showed 9 DISPLAYFORM0 Exploring the relationships matrix factorization has implications the interpretability matrix factors Ding FORMULA0 1 Initialize U and run k-means clustering Hartigan & Wong1979 . DISPLAYFORM1 The objective function k-means We can relax the range v ki over the values ( or This restricts V to accept only nonnegative values allow U have mixed signs values.2 Update U by fixing using this constraint By fixing V, the solution of U can obtained calculating the derivative dJ/dU = −2WV T VV = Then get the DISPLAYFORM3 The positive and negative parts computed A According BID7 , this method reach convergence By fixing U, the residual ||W − UV T || 2 will decrease monotonically after fixing V we the optimal solution the objective functionThe algorithm computed an iterative updating algorithm the update V BID7 . The steps very coordinate descent Luo & Tseng1992 with some modifications The optimization convex U or V not bothIn the latent space derived the NMF factorization family each axis captures a particular cluster each sample represented an additive combination The cluster membership each document can easily finding the corresponding cluster centroidthe axis with which the largest projection value Note in particular the result a K-means clustering run can written a matrix factorization W = UV , W �� R nm is the data matrix U �� R nr contains the cluster centroids the cluster membership indicators.• Perform the NMF or semi on W U Matrix U contains r n−dimensional cluster centers membership weight for the m samples One can assign data i to the cluster c if c = argmax j V ij DISPLAYFORM5 The algorithm complexity terms time TAB4 .",0.01,0.30646069675758325
"Manipulation and re-use of images in scientific publications is a recurring problem, at present lacking a scalable solution.   Existing tools for detecting image duplication are mostly manual or semi-automated, despite the fact that generating data for a learning-based approach is straightforward, as we here illustrate. This paper addresses the problem of determining if, given two images, one is a manipulated version of the other by means of certain geometric and statistical manipulations, e.g. copy, rotation, translation, scale, perspective transform, histogram adjustment, partial erasing, and compression artifacts. We propose a solution based on a 3-branch Siamese Convolutional Neural Network. The ConvNet model is trained to map images into a 128-dimensional space, where the Euclidean distance between duplicate (respectively, unique) images is no greater (respectively, greater) than 1. Our results suggest that such an approach can serve as tool to improve surveillance of the published and in-peer-review literature for image manipulation. We also show that as a byproduct the network learns useful representations for semantic segmentation, with performance comparable to that of domain-specific models. Duplicative data reporting in the biomedical literature is more prevalent than most people realize BID1 ). One common form of data duplication, regardless of intent, is the re-use of scientific images, across multiple publications or even within the same publication. In some cases, images are altered before being re-used BID1 ). Changing orientation, perspective or image statistics, introducing skew or crop, and deleting or inserting data into the original image plane are all ways in which image data may be altered prior to inappropriate introduction, or re-introduction, into the reporting of experimental outcomes BID13 ; BID4 ; BID2 ). While the scientific community has affirmatively recognized the need for preventing the incorporation of duplicative or flawed image data into the scientific record, a consistent approach to screening and identifying problematic image data has yet to be established BID11 BID12 ).Cases of image data duplication and/or manipulation have often been detected by fellow scientists 1 or by editorial staff during the manuscript review process. Efforts to move towards automation include tools developed to isolate regions of manipulation within images already flagged as suspicious BID9 ). However , current methods for identifying duplicative and/or manipulated images largely rely on individual visual identification with accompanying application of qualitative similarity measures 2 . Given the rate at which the scientific literature is expanding, it is not feasible for all cases of potential image manipulation to be detected by human eyes. Thus, there is a continued need for automated tools to detect potential duplications, even in the presence of manipulation, to allow for more focused, thorough evaluation of this smaller errant image candidate pool. Such a tool would be invaluable to scientists and research staff on many levels, from figure screening as a step in improving raw data maintenance and manuscript preparation at the laboratory level BID13 ), to the routine screening by journal editorial staff of submitted manuscripts prior to the peer-review process BID11 BID5 ).The general problem of detecting similar images has been well studied in the field of computer vision (e.g. BID17 ; BID16 ; BID15 ). The one application that stands out is determining if two given faces are of the same person, where recent breakthroughs in deep Convolutional Neural Networks have allowed rapid progress BID14 ).In this paper, we apply modern methods in metric learning to address the problem of detecting image manipulation and re-use in scientific work. Specifically, we train a ConvNet to learn an image embedding such that images with the same original content, albeit altered through a common set of image manipulations, appear close to each other in the embedding space. We train this model on a large corpus of simulated image manipulations, and test on a small set of manipulated images from known instances of image duplication/manipulation 3 . To our knowledge, this is the first application of deep learning to the detection of image re-use in the scientific literature, although there have been works on the area of detecting image manipulation (e.g. BID0 ).We focus on the domain of biological images, since we have easy access to one such dataset, but naturally the model to be described is agnostic to the image domain. We test the learned forensic representation not only on new/unseen synthetic and real data for the problem of duplicate-detection, but also on a somewhat unrelated area: semantic segmentation. We show that the features learned in the convolution layers of the siamese network can be readily plugged into a pixel classifier, yielding results comparable with those of state-of-the art, domain-specific architectures. We have demonstrated that siamese networks have the potential to improve surveillance of the published and in-peer-review literature for duplicated images. This approach may not prove accurate enough to definitively determine image duplication, but rather could serve to narrow down the pool of images which are subjected to further review.We found that most errors in the real-world test set involved histogram/contrast alterations that are difficult to simulate, or scale changes beyond those the network was trained to detect. We will continue to explore synthetic manipulations as a way to improve accuracy of the algorithm.As indicated by the self-similarity matrices in Figure 3 , improvements are needed when different images are from the same category. We will improve the training procedure to sample more of these hard cases.One of the main roadblocks to this research is the lack of a public, large-scale database of image manipulation cases on which to further test the model. The challenge here is not only of generating one such dataset, but also of securing the proper permissions to release the data, given the legal issues involved. We are continually expanding our dataset and will make it available as soon as possible.The application to semantic segmentation was discovered somewhat by chance in an attempt to circumvent issues with the U-Net, mainly the need for a large corpus of annotations and difficulty setting hyperparameters. In contrast, the representation provided by the forensic siamese net is quite easy to deploy in conjunction with a random forest classifier.",1201,0.548,673,1.7845468053491829,"Manipulation reuse images scientific publications at present lacking a scalable solution Existing tools detecting image duplication mostly manual semi despite generating data a learning-based approach straightforward as we here illustrate This paper addresses determining, given two images a manipulated version by means certain geometric and statistical manipulations copy, rotation translation scale perspective transform histogram adjustment partial erasing compression artifacts We propose a 3-branch Siamese Convolutional Neural Network The ConvNet model trained map images into duplicate (respectively unique no ( greater) Our results such an approach can serve tool surveillance published and inpeer-review for image manipulation We also show as a byproduct the network learns useful representations semantic segmentation with performance comparable Duplicative data reporting more prevalent most people BID1 ). One common form data duplication regardless intent the re scientific images across even In images altered before reused BID1 ). Changing orientation perspective or image statistics introducing skew crop deleting inserting the original image plane ways in prior inappropriate introduction re the reporting experimental outcomes BID13 ; BID4 While the scientific community affirmatively preventing the incorporation duplicative or flawed image data a consistent approach screening identifying yet BID11 BID12 ).Cases often detected fellow scientists 1 or by editorial staff during move towards automation include tools developed isolate regions manipulation within images already flagged suspicious BID9 ). However , current methods identifying duplicative and/or manipulated images largely individual visual identification with accompanying application qualitative similarity measures 2 Given the rate the scientific literature expanding feasible all cases potential image manipulation detected Thus there a continued need automated tools detect potential duplications even manipulation allow more focused, thorough evaluation this smaller errant image candidate pool Such a tool invaluable scientists research staff on figure screening as a step improving raw data maintenance and manuscript preparation at BID13 ), the routine screening by journal editorial staff submitted manuscripts prior ).The general problem detecting similar images has BID17 ; The one application stands determining two given faces of where recent breakthroughs rapid progress BID14 ).In apply modern methods in metric learning address detecting image manipulation reuse scientific work Specifically train a ConvNet learn an image embedding such that images, albeit altered through a common set appear close We train this model a large corpus simulated image manipulations test on manipulated images from known instances image duplication/manipulation 3 . To our knowledge deep learning the detection image reuse although works the area detecting image manipulation (e.g. BID0 ).We focus the domain biological images since easy access one such dataset naturally the model to described agnostic We test the learned forensic representation not new/unseen synthetic and real data for the problem duplicate-detection a somewhat unrelated area semantic segmentation We show the features learned the convolution layers the siamese network readily plugged a pixel classifier yielding results comparable with state, domain architectures We demonstrated siamese networks surveillance published and inpeer-review for duplicated images This approach may prove accurate enough definitively image duplication rather could serve narrow which subjected further reviewWe found most errors set involved histogram/contrast alterations difficult simulate scale changes beyond the network was trained We will explore synthetic manipulations as accuracy the algorithmAs indicated improvements needed when different images from We will improve the training procedure sample more of these hard casesOne this research image manipulation cases on further test The challenge here of generating one such dataset securing release given We continually expanding our dataset makeThe application to semantic segmentation discovered somewhat chance circumvent issues the U-Net, mainly need annotations difficulty setting hyperparameters In contrast the representation provided the forensic siamese net quite easy deploy conjunction a random forest classifier",0.01,0.7030355001848843
"Training generative adversarial networks is unstable in high-dimensions as the true data distribution tends to be concentrated in a small fraction of the ambient space. The discriminator is then quickly able to classify nearly all generated samples as fake, leaving the generator without meaningful gradients and causing it to deteriorate after a point in training. In this work, we propose training a single generator simultaneously against an array of discriminators, each of which looks at a different random low-dimensional projection of the data. Individual discriminators, now provided with restricted views of the input, are unable to reject generated samples perfectly and continue to provide meaningful gradients to the generator throughout training.   Meanwhile, the generator learns to produce samples consistent with the full data distribution to satisfy all discriminators simultaneously. We  demonstrate the practical utility of this approach experimentally, and show that it is able to produce image samples with higher quality than traditional training with a single discriminator. Generative adversarial networks (GANs), introduced by BID12 , endow neural networks with the ability to express distributional outputs. The framework includes a generator network that is tasked with producing samples from some target distribution, given as input a (typically low dimensional) noise vector drawn from a simple known distribution, and possibly conditional side information. The generator learns to generate such samples, not by directly looking at the data, but through adversarial training with a discriminator network that seeks to differentiate real data from those generated by the generator. To satisfy the objective of ""fooling"" the discriminator, the generator eventually learns to produce samples with statistics that match those of real data.In regression tasks where the true output is ambiguous, GANs provide a means to simply produce an output that is plausible (with a single sample), or to explicitly model that ambiguity (through multiple samples). In the latter case, they provide an attractive alternative to fitting distributions to parametric forms during training, and employing expensive sampling techniques at the test time. In particular, conditional variants of GANs have shown to be useful for tasks such as in-painting BID7 , and super-resolution BID16 . Recently, BID13 demonstrated that GANs can be used to produce plausible mappings between a variety of domains-including sketches and photographs, maps and aerial views, segmentation masks and images, etc. GANs have also found uses as a means of un-supervised learning, with latent noise vectors and hidden-layer activations of the discriminators proving to be useful features for various tasks BID7 .Despite their success, training GANs to generate high-dimensional data (such as large images) is challenging. Adversarial training between the generator and discriminator involves optimizing a min-max objective. This is typically carried out by gradient-based updates to both networks, and the generator is prone to divergence and mode-collapse as the discriminator begins to successfully distinguish real data from generated samples with high confidence. Researchers have tried to address this instability and train better generators Figure 1 : Overview of our approach. We train a single generator against an array of discriminators, each of which receives lower-dimensional projections-chosen randomly prior to training-as input. Individually, these discriminators are unable to perfectly separate real and generated samples, and thus provide stable gradients to the generator throughout training. In turn, by trying to fool all the discriminators simultaneously, the generator learns to match the true full data distribution. through several techniques . BID8 proposed generating an image by explicitly factorizing the task into a sequence of conditional generations of levels of a Laplacian pyramid, while demonstrated that specific architecture choices and parameter settings led to higher-quality samples. Other techniques include providing additional supervision BID20 , adding noise to the discriminator input BID0 , as well as modifying or adding regularization to the training objective functions BID18 BID1 BID23 .We propose a different approach to address this instability, where the generator is trained against an array of discriminators, each of which looks at a different, randomly-chosen, low-dimensional projection of the data. Each discriminator is unable to perfectly separate real and generated samples since it only gets a partial view of these samples. At the same time, to satisfy its objective of fooling all discriminators, the generator learns to match the true full data distribution. We describe a realization of this approach for training image generators, and discuss the intuition behind why we expect this training to be stable-i.e., the gradients to the generator to be meaningful throughout training-and consistent-i.e., for the generator to learn to match the full real data distribution. Despite its simplicity, we find this approach to be surprisingly effective in practice. We demonstrate this efficacy by using it to train generators on standard image datasets, and find that these produce higher-quality samples than generators trained against a single discriminator. In this paper, we proposed a new framework to training GANs for high-dimensional outputs. Our approach employs multiple discriminators on random low-dimensional projections of the data to stabilize training, with enough projections to ensure that the generator learns the true data distribution. Experimental results demonstrate that this approaches leads to more stable training, with generators continuing to improve for longer to ultimately produce higher-quality samples. Source code and trained models for our implementation is available at the project page [anonymized for review].In our current framework, the number of discriminators is limited by computational cost. In future work, we plan to investigate training with a much larger set of discriminators, employing only a small subset of them at each iteration, or every set of iterations. We are also interested in using multiple discriminators with modified and regularized objectives (e.g., BID18 BID1 BID23 ). Such modifications are complementary to our approach, and deploying them together will likely be beneficial.",1135,0.588,652,1.74079754601227,"Training generative adversarial networks unstable as the true data distribution tends concentrated the ambient space The discriminator then quickly able classify nearly all generated samples fake leaving the generator without meaningful gradients causing deteriorate after a point training In this work propose training a single generator simultaneously against discriminators looks Individual discriminators now provided restricted views the input unable reject generated samples perfectly continue provide meaningful gradients throughout training Meanwhile the generator learns produce samples consistent the full data distribution to satisfy all discriminators simultaneously We demonstrate experimentally able image samples traditional training with a single discriminator Generative adversarial networks introduced BID12 , endow neural networks express distributional outputs The framework includes a generator network tasked producing samples some target distribution given as a (typically low dimensional) noise vector drawn a simple known distribution possibly conditional side information The generator learns such samples not directly looking adversarial training a discriminator network seeks differentiate To satisfy the objective "" the discriminator the generator eventually learns samples statisticsIn regression tasks the true output ambiguous GANs provide simply produce plausiblewith explicitly model that ambiguitythrough multiple samples In they provide fitting distributions parametric forms during training employing expensive sampling techniques at the test time In particular conditional variants GANs tasks in-painting BID7 , super-resolution BID16 Recently BID13 demonstrated GANs produce plausible mappings a variety domains- sketches photographs maps aerial views segmentation masks images etc GANs also found uses as latent noise vectors hidden-layer activations the discriminators proving various tasks BID7 .Despite training ( large images Adversarial training between the generator discriminator involves optimizing a min-max objective This typically carried gradient-based updates both networks the generator prone divergence mode-collapse the discriminator begins successfully distinguish real data generated samples with high confidence Researchers tried address this instability train better generators Figure : Overview our approach We train a single generator against discriminators receives lower-dimensional projections-chosen randomly prioras input Individually these discriminators unable perfectly separate real and generated samples provide stable gradients the generator throughout training In turn by trying fool all the discriminators simultaneously the generator learns match the true full data distribution through several techniques . BID8 proposed generating an image by explicitly factorizing the task into conditional generations levels a Laplacian pyramid while demonstrated specific architecture choices parameter settings led higher-quality samples Other techniques providing additional supervision BID20 , adding noise the discriminator as modifying or regularization the training objective functions .We propose address this instability the generator against looks Each discriminator unable perfectly separate real and generated samples since gets At to satisfy its objective fooling all discriminators the generator learns match the true full data distribution We describe a realization this approach training image generators the intuition why expect this training stable- to meaningful throughout-and consistent for learn match the full real data distribution Despite its simplicity we find this approach practice We demonstrate this efficacy it train generators standard image datasets find produce generators trained against In proposed training GANs high-dimensional outputs Our approach employs multiple discriminators on random low-dimensional projections stabilize training enough projections the generator learns the true data distribution Experimental results demonstrate this approaches leads more stable training generators continuing for to ultimately Source code trained models our implementation is [anonymized for review].In our current framework discriminators computational cost In future work investigate training with discriminators employing at each iteration or every set iterations We also using multiple discriminators modified and regularized objectives BID18 BID1 BID23 Such modifications complementary our approach deploying together likely",0.01,0.5915662311623275
"We present a novel method to precisely impose tree-structured category information onto word-embeddings, resulting in ball embeddings in higher dimensional spaces (N-balls for short). Inclusion relations among N-balls implicitly encode subordinate relations among categories. The similarity measurement in terms of the cosine function is enriched by category information. Using a geometric construction method instead of back-propagation, we create large N-ball embeddings that satisfy two conditions: (1) category trees are precisely imposed onto word embeddings at zero energy cost; (2) pre-trained word embeddings are well preserved. A new benchmark data set is created for validating the category of unknown words. Experiments show that N-ball embeddings, carrying category information, significantly outperform word embeddings in the test of nearest neighborhoods, and demonstrate surprisingly good performance in validating categories of unknown words. Source codes and data-sets are free for public access \url{https://github.com/gnodisnait/nball4tree.git} and \url{https://github.com/gnodisnait/bp94nball.git}. Words in similar contexts have similar semantic and syntactic information. Word embeddings are vector representations of words that reflect this characteristic BID16 BID19 and have been widely used in AI applications such as question-answering BID24 , text classification BID22 , information retrieval BID14 , or even as a building-block for a unified NLP system to process common NLP tasks BID2 . To enhance semantic reasoning, researchers proposed to represent words in terms of regions instead of vectors. For example, BID5 extended a word vector into a region by estimating the log-linear probability of weighted feature distances and found that hyponym regions often do not fall inside of their hypernym regions. By using external hyponym relations, she obtained 95.2% precision and 43.4% recall in hypernym prediction for a small scale data set. Her experiments suggest that regions structured by hyponym relations may not be located within the same dimension as the space of word embeddings. Yet, how to construct strict inclusion relations among regions is still an open problem when representing hypernym relations.In this paper, we restrict regions to be n dimensional balls (N -ball for short) and propose a novel geometrical construction approach to impose tree-structured category information onto word embeddings. This is guided by two criteria: (1) Subordinate relations among categories shall be implicitly and precisely represented by inclusion relations among corresponding N -balls. This way, the energy costs of imposing structure will be zero; (2) Pre-trained word embeddings shall be well-preserved. Our particular contributions are as follows: (1) The proposed novel geometric approach achieves zero energy costs of imposing tree structures onto word-embeddings. (2) By considering category information in terms of the boundary of an N -ball, we propose a new similarity measurement that is We create a large data set of N -ball embeddings using the pre-trained GloVe embeddings and a large category tree of word senses extracted from Word-Net 3.0.The remainder of our presentation is structured as follows: Section 2 presents the structure of N -ball embeddings; Section 3 describes the geometric approach to construct N -ball embeddings; Section 4 presents experiment results; Section 5 briefly reviews related work; Section 6 concludes the presented work, and lists on-going research. FIG0 (a), so they are not RCC regions that can be either open or closed, or even a mixture, thus avoiding a number of problems BID4 BID3 . We proposed a novel geometric method to precisely impose external tree-structured category information onto word embeddings, resulting in region-based (N -ball embeddings) word sense embeddings. They can be viewed as Venn diagrams (Venn, 1880) of the tree structure, if zero energy cost is achieved. Our N -ball method has demonstrated great performance in validating the category of unknown words, the reason for this being under further investigation. Our on-going work also includes multi-lingual region-based knowledge graph embedding where multiple relations on directed acyclic graphs need to be considered. N -balls carry both vector information from deep learning and region information from symbolic structures. Therefore, N -balls establish a harmony between Connectionism and Symbolicism, as discussed by BID15 , and thus may serve as a novel building block for the commonsense representation and reasoning in Artificial Intelligence. N -balls, in particular, contribute a new topic to Qualitative Spatial Reasoning (QSR) that dates back to BID26 .",906,0.447,526,1.7224334600760456,"We present precisely impose tree-structured category information word-embeddings resulting ball embeddings higher dimensional spacesN-balls for Inclusion relations among N-balls implicitly encode subordinate relations categories The similarity measurement terms the cosine function enriched category information Using a geometric construction method instead create large N-ball embeddings satisfy category trees precisely imposed onto at zero energy cost well preserved A new benchmark data created validating the category unknown words Experiments N-ball embeddings carrying category information significantly nearest neighborhoods demonstrate surprisingly good performance validating categories unknown words Source codes data-sets free \url{https://github.comgnodisnait/nball4tree.git and Words in similar contexts similar semantic and syntactic information Word embeddings vector representations reflect this characteristic BID16 BID19 have widely , or even as a unified NLP system to common NLP tasks To enhance semantic reasoning researchers proposed represent words regions instead vectors For example BID5 extended a word vector estimating the log-linear probability weighted feature distances found hyponym regions often do fall inside their hypernym regions By using external hyponym relations she obtained 95.2% precision hypernym prediction for Her experiments suggest regions structured hyponym relations not located Yet how construct strict inclusion relations regions when representing hypernym relationsIn restrict regions be n dimensional ballsN -ball for propose impose tree-structured category information onto This guided two criteria categories shall implicitly precisely represented inclusion relations corresponding N -balls This way the energy costs imposing structure zero; (2) Pre-trained word embeddings shall well Our particular contributions as The proposed novel geometric approach achieves zero energy costs imposing tree structures onto word-embeddings (2 By considering category information terms the boundary an N -ball we propose a new similarity measurement We create using a large category tree word senses extracted Word-Net 3.0.The remainder our presentation structured Section; the geometric approach construct experiment results briefly reviews related work concludes lists FIG0 ( so they RCC regions that either open even mixture, thus avoiding a number BID4 BID3 . We proposed a novel geometric method precisely impose external tree-structured category information resulting region-based (N -ball embeddings) word sense embeddings They can viewed Venn diagrams (, 1880 the tree structure if zero energy cost achieved Our N -ball method demonstrated validating the category unknown words the reason under further investigation Our on-going work also multi-lingual region-based knowledge graph embedding where multiple relations on directed acyclic graphs need considered N -balls carry both vector information from deep learning region information symbolic structures Therefore N -balls establish a harmony Connectionism discussed BID15 , may a novel building block the commonsense representation reasoning Artificial Intelligence N -balls in particular contribute a new topic Qualitative Spatial Reasoning dates BID26 .",0.01,0.5447761536477765
"For the challenging semantic image segmentation task the best performing models
 have traditionally combined the structured modelling capabilities of Conditional
 Random Fields (CRFs) with the feature extraction power of CNNs. In more recent
 works however, CRF post-processing has fallen out of favour. We argue that this
 is mainly due to the slow training and inference speeds of CRFs, as well as the
 difficulty of learning the internal CRF parameters. To overcome both issues we
 propose to add the assumption of conditional independence to the framework of
 fully-connected CRFs. This allows us to reformulate the inference in terms of
 convolutions, which can be implemented highly efficiently on GPUs.Doing so
 speeds up inference and training by two orders of magnitude. All parameters of
 the convolutional CRFs can easily be optimized using backpropagation. Towards
 the goal of facilitating further CRF research we have made our implementations
 publicly available. Semantic image segmentation, which aims to produce a categorical label for each pixel in an image, is a very import task for visual perception. Convolutional Neural Networks have been proven to be very strong in tackling semantic segmentation tasks BID23 BID5 BID40 . While simple feed-forward CNNs are extremely powerful in extracting local features and performing good predictions utilizing a small field of view, they lack the capability to utilize context information and cannot model interactions between predictions directly. Thus it has been suggested that such deep neural networks may not be the perfect model for structured predictions tasks such as semantic segmentation BID40 BID20 BID41 . Several authors have successfully combined the effectiveness of CNNs to extract powerful features, with the modelling power of CRFs in order to address the discussed issues BID20 Chandra & Kokkinos, 2016; BID41 . Despite their indisputable success, structured models have fallen out of favour in more recent approaches BID38 BID4 BID40 .We believe that the main reasons for this development are that CRFs are notoriously slow and hard to optimize. Learning the features for the structured component of the CRF is an open research problem BID37 BID20 and many approaches rely on entirely hand-crafted Gaussian features BID41 BID31 BID5 . In addition , CRF inference is typically two orders of magnitude slower than CNN inference. This makes CRF based approaches too slow for many practical applications. The long training times of the current generation of CRFs also make more in-depth research and experiments with such structured models impractical.To solve both of these issues we propose to add the strong and valid assumption of conditional independence to the existing framework of fully-connected CRFs (FullCRFs) introduced by . This allows us to reformulate a large proportion of the inference as convolutions, which can be implemented highly efficiently on GPUs. We call our method convolutional CRFs (ConvCRFs). Backpropagation BID30 can be used to train all parameters of the ConvCRF. Inference in ConvCRFs can be performed in less then 10ms. This is a speed increase of two-orders of magnitude compared to FullCRFs. We believe that those fast train and inference speeds will greatly benefit future research and hope that our results help to revive CRFs as a popular method to solve structured tasks. In this work we proposed Convolutional CRFs, a novel CRF design. Adding the strong and valid assumption of conditional independence enables us to remove the permutohedral lattice approximation. This allows us to implement the message passing highly efficiently on GPUs as convolution operations. This increases training and inference speed by two orders of magnitude. In addition we observe a modest accuracy improvement when computing the message passing exactly. Our method also enables us to easily train the Gaussian features of the CRF using backpropagation.In future work we will investigate the potential of learning Gaussian features further. We are also going to examine more sophisticated CRF architectures, towards the goal of capturing context information even better. Lastly we are particularly interested in exploring the potential of ConvCRFs in other structured applications such as instance segmentation, landmark recognition and weakly supervised learning.",811,0.448,481,1.686070686070686,"For the challenging semantic image segmentation task the best performing models traditionally combined the structured modelling capabilities Conditional Random Fields CNNs more recent works however fallen We argue this mainly the slow training and inference speeds CRFs learning the internal CRF parameters To overcome both issues propose add the assumption conditional independence fully-connected CRFs reformulate in convolutions highly on GPUsDoing speeds inference training All parameters the convolutional CRFs easily optimized the goal facilitating further CRF research we made our implementations publicly Semantic image segmentation aims produce a categorical label a very import task visual perception have proven strong tackling semantic segmentation tasks BID23 BID5 BID40 . While simple feed-forward CNNs extremely extracting local features performing good predictions utilizing a small field lack utilize context information model interactions predictions directly Thus such deep neural networks structured predictions tasks such semantic segmentation BID40 BID20 BID41 . Several authors successfully combined the effectiveness CNNs extract powerful features with the modelling power CRFs in order address the discussed issues BID20 Chandra & Kokkinos 2016; . Despite their indisputable success structured models fallen more recent approaches BID38 BID4 .We believe CRFs notoriously hard optimize Learning the features for the structured component the CRF an open research problem BID37 BID20 and many approaches rely entirely hand-crafted Gaussian features . In addition , CRF inference typically two orders CNN inference This makes CRF based approaches too The long training times CRFs also more in experiments with such structured models impracticalTo solve both add the strong and valid assumption conditional independenceFullCRFs introduced . This allows reformulate a large proportion the inference as convolutions implemented highly on GPUs call our method convolutional CRFs Backpropagation BID30 can train all parameters the ConvCRF Inference in ConvCRFs can less then 10ms This a speed increase two-orders compared FullCRFs believe those fast train and inference speeds greatly future research hope help revive CRFs solve structured tasks In this work proposed Convolutional CRFs Adding the strong and valid assumption conditional independence enables remove the permutohedral lattice approximation This allows implement the message passing highly efficiently GPUs as convolution operations This increases training inference speed In addition we observe a modest accuracy improvement computing the message passing exactly. Our method also enables easily train the Gaussian features the CRF usingIn future work investigate learning further We also examine more sophisticated CRF architectures towards capturing context information even Lastly particularly exploring ConvCRFs other structured applications instance segmentation landmark recognition weakly supervised learning",0.0,0.4521270002805122
"Deep Learning NLP domain lacks procedures for the analysis of model robustness. In this paper we propose a framework which validates robustness of any Question Answering model through model explainers. We propose that output of a robust model should be invariant to alterations that do not change its semantics. We test this property by manipulating question in two ways: swapping important question word for 1) its semantically correct synonym and 2) for word vector that is close in embedding space. We estimate importance of words in asked questions with Locally Interpretable Model Agnostic Explanations method (LIME). With these two steps we compare state-of-the-art Q&A models. We show that although accuracy of state-of-the-art models is high, they are very fragile to changes in the input. We can choose architecture that is more immune to attacks and thus more robust and stable in production environment. Morevoer, we propose 2 adversarial training scenarios which raise model sensitivity to true synonyms by up to 7% accuracy measure. Our findings help to understand which models are more stable and how they can be improved. In addition, we have created and published a new dataset that may be used for validation of robustness of a Q&A model. Up-to-date advancements in natural language processing show that it is possible to achieve high accuracy on tasks that from human point of view require language understanding. However, recent research on adversarial examples revealed shortcomings of neural network models, despite their great performance on selected datasets BID10 . Most adversarial examples studies in Question Answering (Q&A) task focus on designing sophisticated attacks that prove overstability understood as an inability of the model to distinguish sentences that answer the question from sentences that have words in common with the question BID3 . BID5 and BID2 also show that the whole question itself is not crucial to get the right answer. Despite growing research in the area of adversarial attacks, little is still known about the source of lacking robustness of Q&A models and effective ways of overcoming this problem. In order to come up with a solution it is crucial to understand the inner workings of task specific architectures and benchmark their performance on adversarial attacks.In this work we propose a model agnostic framework that checks stability of three state-of-the-art Q&A architectures in terms of their ability to respond to semantically similar questions. We formulate two aspects which are subject to tests: semantic input stability (relying on true semantics) and numerical input stability (purely induced by similarity between word embeddings). These terms are explained later on in the article. We state that a robust and reliable Q&A model should be invariant to changes in the input until they induce semantic changes. Having said that, we state that a stable model must display higher semantic input stability measure than numerical input stability measure. We claim that a robust Q&A model should possess high sensitivity to true semantics, as opposed to closeness between word embeddings. Otherwise, attacks based on commonly accessible sets of embeddings become possible, including antonymous questions, as antonyms are often close in embedding space.We make the following contributions:• We investigate robustness of the model in the face of semantic and numerical changes to the input.• We use output of Locally Interpretable Model Agnostic Explanations BID9 to create attacks.• We offer 2 approaches to adversarial training which increase model sensitivity to true semantic differences by a maximum of 7% in accuracy.• We release a collection of 1500 semantically coherent questions from SQuAD dataset BID8 preprocessed by LIME and human annotators, that we used in this study, as a reference dataset for further works on this problem.In section 2 we explain measures and tools that we used in the study. In section 3 we conduct experiments on three popular Q&A architectures, then we introduce two modifications to one of the models in order to increase ability to answer semantically similar questions and finally we refer to related work and conclude. In our study we focused on one particular aspect of model robustness -ability to answer semantically coherent questions. We show that performance of all tested models decreases once we change important question words indicated by LIME. However, we observe that models have higher performance once we swap tokens in questions for words close in their embedding space defined by word vectors they were trained on, in comparison to accuracy obtained by asking semantically correct questions. We manage to increase ability of the model to answer this kind of questions but it does not mean that they understand semantics -it is reflected in increased accuracy of questions with GloVe embeddings once we test our newly trained models on num-Dataset.We show that the reason behind the success of some adversarial examples lies in the way input words are represented. Popular embeddings do not include knowledge about real meaning of the words, but rather incorporate knowledge about their context. Our work serves as a starting point for future research on more semantically-conscious representation of words.",984,0.522,581,1.693631669535284,Deep Learning NLP domain lacks procedures the analysis model robustness In which validates robustness any Question Answering model through model explainers We propose output a robust model invariant alterations that do its semantics We test this property manipulating question in swapping important question word 1) its semantically correct synonym for word vector close in embedding space We estimate importance words asked questions with Locally Interpretable Model Agnostic Explanations method With these two steps compare state Q&A models We show although accuracy state models high very fragile changes the input. We can choose architecture immune attacks thus robust stable production environment Morevoer we propose 2 adversarial training scenarios which raise model sensitivity true synonyms by up to 7% accuracy measure Our findings help which models stable how In addition created and may validation robustness a Q&A model Up- advancements natural language processing show achieve tasks from human point language understanding However recent research adversarial examples revealed shortcomings neural network models despite their great performance on selected datasets BID10 . Most adversarial examples studies in Question task focus designing sophisticated attacks prove overstability understood an inability the model distinguish sentences answer have words BID3 BID5 and also show the whole question itself crucial get Despite growing research adversarial attacks little still lacking robustness Q&A models effective ways overcoming In order come it crucial task specific architectures benchmark adversarial attacksIn propose a model agnostic framework checks stability three state Q&A terms respond semantically similar questions We formulate two aspects which subject tests semantic input stabilityrelying true semanticspurely induced similarity These terms explained later We state a robust and reliable Q&A model invariant changes the input until they induce semantic changes Having state a stable model must display higher semantic input stability measure We claim a robust Q&A model should possess high sensitivity true semantics closeness between Otherwise attacks based commonly accessible sets become possible antonymous questions as are close in embedding spaceWe make investigate robustness the model semantic and numerical changes output Locally Interpretable Model Agnostic Explanations BID9 create attacks.• offer 2 approaches adversarial training which increase model sensitivity true semantic differences by a maximum release a collection 1500 semantically coherent questions SQuAD dataset BID8 preprocessed LIME and human annotators that used further worksIn section explain measures tools In section we conduct three popular Q&A architectures then two modifications one increase ability finally refer related work and conclude. In our study focused one particular aspect model robustness -ability answer semantically coherent questions We show performance all tested models decreases once important question words indicated LIME However we observe models have higher performance once swap tokens questions for words close in their embedding space defined word vectors they were trained in comparison accuracy obtained asking We manage increase ability the model answer this kind but they understand semantics -it reflected increased accuracy questions with GloVe embeddings once test our newly trained models num-DatasetWe show the reason behind some adversarial examples lies input words Popular embeddings do knowledge real meaning incorporate Our work serves more semantically-conscious representation words,0.01,0.4713917218475642
"In this paper, we propose a mix-generator generative adversarial networks (PGAN) model that works in parallel by mixing multiple disjoint generators to approximate a complex real distribution. In our model, we propose an adjustment component that collects all the generated data points from the generators, learns the boundary between each pair of generators, and provides error to separate the support of each of the generated distributions. To overcome the instability in a multiplayer game, a shrinkage adjustment component method is introduced to gradually reduce the boundary between generators during the training procedure. To address the linearly growing training time problem in a multiple generators model, we propose a method to train the generators in parallel. This means that our work can be scaled up to large parallel computation frameworks. We present an efficient loss function for the discriminator, an effective adjustment component, and a suitable generator. We also show how to introduce the decay factor to stabilize the training procedure. We have performed extensive experiments on synthetic datasets, MNIST, and CIFAR-10. These experiments reveal that the error provided by the adjustment component could successfully separate the generated distributions and each of the generators can stably learn a part of the real distribution even if only a few modes are contained in the real distribution. Generative Adversarial Networks were proposed by BID7 , where two neural networks, generator and discriminator, are trained to play a minimax game. The generator is trained to fool the discriminator while the discriminator is trained to distinguish fake data (generated data) from real data. When Nash Equilibrium is reached, generated distribution P G will be equal to the real distribution P real . Unlike Restricted Boltzmann Machine (RBM, BID20 or Variational Auto-encoder (VAE, BID11 ), that explicitly approximate data distribution, the approximation of GAN is implicit. Due to this property, training GAN is challenging. It has been reported that GAN suffers from the mode collapse problem BID6 , BID14 ). Many methods have been proposed to solve this problem BID21 , BID22 , BID8 , ). In this paper, we propose a new model to solve this problem.Similar to the work of BID18 ), we use a set of generators to replace the single, complex generator. Each generator only captures a part of the real distribution, while the distance between the mix-generated distribution and the real distribution should be minimized. An adjustment component is added to achieve separation between each pair of generators, and a penalty will be passed to the generator if an overlap is detected. Moreover, we propose a shrinkage adjustment component method to gradually reduce the effect of the penalty, since the strict boundary will lead to a nonconvergence problem. Practically, forcing each generated distribution to be totally disjoint will cause potential problems. More specifically, we observe two problems in practice: (1) competition: multiple generators try to capture one mode, but are hampered by a strict boundary. This happens when the total number of generators K is greater than the actual number of modes of P real . (2) One beats all: One or a few of the generators are strong enough to capture all the modes, while the other generators are blocked outside and capture nothing. To solve these problems, we propose the following approach: (1) use reverse KL divergence instead of JS Divergence as the generator loss, to reduce the generator's ability to capture all the modes, and (2) introduce a shrinkage adjustment method to gradually reduce the weight of the adjustment component C based on the training time and the difference between each generator loss. We will discuss the details in part 3. Benefiting from such design, there is no need to pre-define the number of generators, and stable convergence can be obtained when the new component shrinks to zero. Finally, our model can allow parallelized training among generators, with synchronized or asynchronized updated for the discriminator, which reduces the training time.To highlight, our main contributions are:1. In Sections 3.1 and 2, we propose a multi-generator model where each generator captures different parts of the real data distribution while the mixing distribution captures all the data.2. We introduce an adjustment component to separate between generated distributions. The adjustment can work with any discriminator.3. In Section 3.3, we propose a shrinkage component method which reduces the penalty to guarantee convergence. If the penalty shrinks to zero, we will minimize DISPLAYFORM0 We organize the shared memory to allow for parallel training to reduce the training time.Our algorithm scales well even on large parallel platforms.5. In Section 4, we use synthetic and real data to illustrate the effectiveness of our design. In this paper, we propose a mixed generator method to solve the mode collapse problem of GAN, and our algorithm is parallelizable, and can be scaled to large platforms. To conquer the competition and one-beat all problems in the mix generator model, we have designed the reverse KL divergence loss function, and an adjustment component decay to produce a stable, converging, and fast training method. The results show we can handle the situation when the generators compete for the same mode even when the number of generators is greater than the number of modes. The shrinkage method which gradually reduced extra component to zero will eliminate the adjustment player and reduce to multi-generator vs discriminator game.More works need to be done in this multi-player game. First, the shrinkage method can also be improved if we can have a better heuristic for β. Or we can train to learn β, to achieve balance between competition and convergence. Second, the weight for each generator can also be dynamic. The generator learns more should have higher weight. Finally, new parallelization algorithm with less communication cost could be investigate to accelerate the multi-generator model since currently the run time is far from optimal.",1162,0.692,674,1.7240356083086052,"In a mix-generator generative adversarial networksPGAN) model works by mixing multiple disjoint generators approximate a complex real distribution In our model propose an adjustment component collects the generators learns the boundary provides error to separate the support the generated distributions To overcome the instability a multiplayer game a shrinkage adjustment component method gradually the boundary generators during the training procedure To address the linearly growing training time problem a multiple generators model propose train the generators This means our work scaled large parallel computation frameworks We present an efficient loss function the discriminator an effective adjustment component a suitable generator We also show introduce the decay factor stabilize the training procedure We performed synthetic datasets MNIST These experiments reveal the error provided the adjustment component could successfully separate the generated distributions each the generators can stably learn a part even only a few modes contained Generative Adversarial Networks were proposed BID7 , where generator play a minimax game The generator trained fool while distinguish fake datagenerated data When Nash Equilibrium reached generated distribution P G real Unlike Restricted Boltzmann Machine, BID20 or Variational Auto-encoder (VAE, that explicitly approximate data distribution the approximation GAN implicit Due this property training GAN challenging It GAN suffers the mode collapse problem BID6 , BID14 Many methods BID21 , ). In solveSimilar BID18 ), generators replace the single, complex generator Each generator only captures the real distribution while the distance the mix-generated distribution should An adjustment component achieve separation each pair generators a penalty will passed an overlap Moreover propose a shrinkage adjustment component method gradually the penalty since the strict boundary will lead a nonconvergence problem Practically forcing each generated distribution totally potential problems More specifically observe two problems practice: multiple generators try capture one mode hampered a strict boundary This happens generators K modes P real . (2 One beats all: One or a the generators strong capture all the modes while blocked outside and capture nothing To solve propose ( use reverse KL divergence instead JS Divergence the generator loss, to the generator's ability capture all the modes introduce a shrinkage adjustment method gradually the adjustment component C based difference each generator loss We will discuss part Benefiting such design there predefine generators stable convergence obtained new component shrinks Finally our model can allow parallelized training among generators synchronized or updated for the discriminator reducesTo highlight our main contributions In Sections propose where captures different parts the real data distribution while the mixing distribution. an adjustment component separate between generated distributions The adjustment can work any discriminator.3. Section propose a shrinkage component method guarantee convergence If the penalty shrinks we minimize DISPLAYFORM0 We organize the shared memory allow parallel trainingOur algorithm scales well even large parallel platforms.5 In Section use synthetic and real data illustrate In a mixed generator method solve the mode collapse problem GAN our algorithm parallelizable scaled large platforms To conquer the competition onebeat all problems the mix generator model designed the reverse KL divergence loss function an adjustment component decay to produce a stable, converging, and fast training method The results we handle when the generators compete the same mode even greater modes The shrinkage method which gradually reduced extra component to zero eliminate the adjustment player to multigenerator vs discriminator gameMore works need First the shrinkage method can also improved have a better heuristic β Or we train learn β, to achieve balance competition convergence Second the weight for each generator also dynamic The generator learns more should have higher weight Finally new parallelization algorithm with less communication cost could investigate accelerate since currently far",0.01,0.5488582865811339
"We capitalize on the natural compositional structure of images in order to learn object segmentation with weakly labeled images. The intuition behind our approach is that removing objects from images will yield natural images, however removing random patches will yield unnatural images. We leverage this signal to develop a generative model that decomposes an image into layers, and when all layers are combined, it reconstructs the input image. However, when a layer is removed, the model learns to produce a different image that still looks natural to an adversary, which is possible by removing objects. Experiments and visualizations suggest that this model automatically learns object segmentation on images labeled only by scene better than baselines. Visual recognition models demand large amounts of annotated data that is expensive to collect, and this cost is amplified for tasks that require densely labeled data, such as semantic segmentation. In this paper, we develop an approach where object segmentation emerges automatically for images only labeled by scene category.We capitalize on the natural compositional structure of images to learn object segmentation through counterfactual images. An image is counterfactual if it shows a real scene, except part of it has been removed or changed. To learn to segment, we train a model to generate counterfactual images such that they are perceptually realistic, a task the model can solve by removing objects and filling in the holes. For example, if you fully remove the bed from the scene in Figure 1 , the image is still realistic. However, if you only partially remove the bed, the image is not realistic anymore. We use this intuition to automatically learn object segmentation.We develop a stochastic layered model that decomposes an input image into several layers. We train this model so that when all layers are combined together in some order, it reconstructs the input image. However, we also train the model so that if we randomly permute the layers and remove a layer, the combination still appears perceptually real to an adversary. Consequently, the model learns a layered image decomposition that allows parts of the image to be removed. We show that the model automatically learns to isolate objects in different layers in order to make the output image still appear realistic, a signal we capitalize on for learning to segment.We present three main experiments to analyze this approach. Firstly, experiments show that our model learns to automatically segment images into objects for some scene categories, with only weakly labeled training data, and our approach outperforms several baselines. Secondly, we show that we use a small amount of densely labeled data with our approach to further improve performance. Finally, visualizations suggest that the model can generate the scene behind objects that it learns to segment, enabling us to remove pictures from a wall or take off the bed sheets.Our main contribution is to introduce a novel method for object segmentation on data only labeled by scene by capitalizing on natural compositional structures in images. While the focus of this paper is on images, the method is general and could be applied to other signals, such as audio. The remainder of this paper describes this contribution. Section 2 reviews related work. Section 3 present our method to auto-encode images with a layered decomposition, and shows how removing image regions is a useful signal for segmentation. Section 4 shows several experiments for semantic segmentation, and section 5 offers concluding remarks. We plan to release all code, data, and models.",675,0.419,373,1.8096514745308312,We capitalize the natural compositional structure images learn object segmentation with weakly labeled images The intuition our approach removing objects images yield natural images however removing random patches We leverage this signal develop decomposes an image layers when However when a layer learns produce still natural an adversary possible objects Experiments visualizations suggest this model automatically learns object segmentation on images labeled only scene better baselines Visual recognition models demand annotated data expensive collect this cost amplified tasks densely labeled data semantic segmentation In develop where object segmentation emerges automatically images only labeled scene categoryWe capitalize learn through counterfactual images An image is counterfactual a real scene except part removed To to segment train a model generate counterfactual images such realistic a task solve removing objects filling For example fully remove the bed the scene in Figure realistic However only partially remove the bed the image realistic anymore We use this intuition automatically learn object segmentationWe develop We train this model so all layers some order reconstructs However we train the model so if randomly the layers remove the combination still appears perceptually real an adversary the model learns a layered image decomposition parts removed We show the model automatically learns isolate objects different layers the output image still realistic a signal we capitalize learning segmentWe present three main experiments analyze Firstly experiments our model learns automatically segment images objects for some scene categories with only weakly labeled training data our approach several baselines Secondly show use densely labeled data with our approach further improve performance Finally visualizations suggest the model generate the scene behind objects it learns segment enabling remove pictures a wall take off the bed sheetsOur main contribution introduce on data only labeled scene by capitalizing natural compositional structures images While the focus images the method general could other signals audio The remainder this contribution Section reviews related work Section present our method auto-encode images a layered decomposition shows removing image regions a useful signal segmentation Section shows several experiments for semantic segmentation offers concluding remarks We plan all code data models.,0.0,0.7669999915876069
"Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. We propose a geometric framework, drawing on tools from the manifold reconstruction literature, to analyze the high-dimensional geometry of adversarial examples. In particular, we highlight the importance of codimension: for low-dimensional data manifolds embedded in high-dimensional space there are many directions off the manifold in which to construct adversarial examples. Adversarial examples are a natural consequence of learning a decision boundary that classifies the low-dimensional data manifold well, but classifies points near the manifold incorrectly. Using our geometric framework we prove (1) a tradeoff between robustness under different norms, (2) that adversarial training in balls around the data is sample inefficient, and (3) sufficient sampling conditions under which nearest neighbor classifiers and ball-based adversarial training are robust. Deep learning at scale has led to breakthroughs on important problems in computer vision (Krizhevsky et al. (2012) ), natural language processing (Wu et al. (2016) ), and robotics (Levine et al. (2015) ). Shortly thereafter, the interesting phenomena of adversarial examples was observed. A seemingly ubiquitous property of machine learning models where perturbations of the input that are imperceptible to humans reliably lead to confident incorrect classifications (Szegedy et al. (2013) ; BID21 ). What has ensued is a standard story from the security literature: a game of cat and mouse where defenses are proposed only to be quickly defeated by stronger attacks BID3 ). This has led researchers to develop methods which are provably robust under specific attack models (Madry et al. (2018) ; Wong & Kolter (2018) ; Sinha et al. (2018) ; Raghunathan et al. (2018) ). As machine learning proliferates into society, including security-critical settings like health care BID18 ) or autonomous vehicles BID10 ), it is crucial to develop methods that allow us to understand the vulnerability of our models and design appropriate counter-measures.In this paper, we propose a geometric framework for analyzing the phenomenon of adversarial examples. We leverage the observation that datasets encountered in practice exhibit low-dimensional structure despite being embedded in very high-dimensional input spaces. This property is colloquially referred to as the ""Manifold Hypothesis"": the idea that low-dimensional structure of 'real' data leads to tractable learning. We model data as being sampled from class-specific low-dimensional manifolds embedded in a high-dimensional space. We consider a threat model where an adversary may choose any point on the data manifold to perturb by in order to fool a classifier. In order to be robust to such an adversary, a classifier must be correct everywhere in an -tube around the data manifold. Observe that, even though the data manifold is a low-dimensional object, this tube has the same dimension as the entire space the manifold is embedded in. Our analysis argues that adversarial examples are a natural consequence of learning a decision boundary that classifies all points on a low-dimensional data manifold correctly, but classifies many points near the manifold incorrectly. The high codimension, the difference between the dimension of the data manifold and the dimension of the embedding space, is a key source of the pervasiveness of adversarial examples.Our paper makes the following contributions. First, we develop a geometric framework, inspired by the manifold reconstruction literature, that formalizes the manifold hypothesis described above and our attack model. Second, we highlight the role codimension plays in vulnerability to adversarial DISPLAYFORM0 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 rch 2 ⇤ 2 Figure 1 : Examples of the decision axis Λ 2 , shown here in green, for different data manifolds. Intuitively, the decision axis captures an optimal decision boundary between the data manifolds. It's optimal in the sense that each point on the decision axis is as far away from each data manifold as possible. Notice that in the first example, the decision axis coincides with the maximum margin line.examples. As the codimension increases, there are an increasing number of directions off the data manifold in which to construct adversarial perturbations. Prior work has attributed vulnerability to adversarial examples to input dimension BID20 ). This is the first work that investigates the role of codimension in adversarial examples. Interestingly, we find that different classification algorithms are less sensitive to changes in codimension. Third, we apply this framework to prove the following results: (1) we show that the choice of norm to restrict an adversary is important in that there exists a tradeoff between being robust to different norms: we present a classification problem where improving robustness under the · ∞ norm requires a loss of Ω(1−1/ √ d) in robustness to the · 2 norm; (2) we show that a common approach, training against adversarial examples drawn from balls around the training set, is insufficient to learn robust decision boundaries with realistic amounts of data; and (3) we show that nearest neighbor classifiers do not suffer from this insufficiency, due to geometric properties of their decision boundary away from data, and thus represent a potentially robust classification algorithm. Finally we provide experimental evidence on synthetic datasets and MNIST that support our theoretical results. We have presented a geometric framework for proving robustness guarantees for learning algorithms. Our framework is general and can be used to describe the robustness of any classifier. We have shown that no single model can be simultaneously robust to attacks under all norms and that nearest neighbor classifiers are theoretically more sample efficient than adversarial training. Most importantly, we have highlighted the role of codimension in contributing to adversarial examples and verified our theoretical contributions with experimental results.We believe that a geometric understanding of the decision boundaries learned by deep networks will lead to both new geometrically inspired attacks and defenses. In Appendix C we provide a novel gradient-free geometric attack in support of this claim. Finally we believe future work into the geometric properties of decision boundaries learned by various optimization procedures will provide new techniques for black-box attacks.",1266,0.724,691,1.8321273516642547,"Adversarial examples a pervasive phenomenon machine learning models where lead for otherwise statistically accurate models We propose a geometric framework, drawing tools the manifold reconstruction literature analyze adversarial examples In particular highlight codimension for low-dimensional data manifolds embedded there many directions off the manifold in construct adversarial examples Adversarial examples a natural consequence learning a decision boundary classifies the low-dimensional data manifold well classifies points near manifold incorrectly Using our geometric framework prove robustness under different norms adversarial training balls around the data sample inefficient sufficient sampling conditions under nearest neighbor classifiers and robust Deep learning at led on important problems ( (2012 ), natural language processing (2016 ), roboticsLevine (2015 ). Shortly thereafter the interesting phenomena adversarial examples observed A seemingly ubiquitous property machine learning models where that humans reliably confident incorrect classificationsSzegedy (2013 ; BID21 ). What has ensued a standard story the security literature a game defenses proposed only quickly stronger attacks BID3 ). This has led researchers develop methods which provably robust under specific attack modelsMadry et al (2018 ; Wong Kolter Sinha (2018 ; Raghunathan et (2018 ). As machine society including security-critical settings health care BID18 ) or BID10 crucial develop methods the vulnerability our models design appropriate counter-In a geometric framework analyzing the phenomenon adversarial examples We leverage the observation datasets encountered practice exhibit low-dimensional structure despite embedded This property colloquially low-dimensional structure of 'real' data leads tractable learning We model data as being sampled class-specific low-dimensional manifolds embedded We consider a threat model where may choose any point manifold perturb by in fool In order robust such an adversary a classifier correct everywhere an -tube around the data manifold Observe, manifold this tube the manifold embedded Our analysis argues adversarial examples learning a decision boundary classifies all points manifold correctly classifies near manifold incorrectly The high codimension the difference the dimension data manifold a key source adversarial examplesOur paper makes First develop a geometric framework inspired the manifold reconstruction literature described our attack model Second highlight the role codimension vulnerability : Examples the decision axis �� 2 shown here green different data manifolds Intuitively the decision axis captures an optimal decision boundary manifolds It optimal in each point the decision axis as far each data manifold Notice the decision axis coincides the maximum margin line.examples As the codimension increases directions off data manifold construct Prior work attributed vulnerability adversarial examples to input dimension BID20 ). This the first work investigates codimension adversarial examples Interestingly we find different classification algorithms less changes codimension Third apply this framework prove the following results the choice norm to restrict an adversary important that there being robust different norms: present a classification problem improving under the · �� norm requires ���(� d a common approach, training against adversarial examples drawn balls around the training set insufficient learn robust decision boundaries with realistic amounts nearest suffer this insufficiency due geometric properties their decision boundary away data represent Finally provide experimental evidence synthetic datasets MNIST that support our theoretical results We presented a geometric framework proving robustness guarantees learning Our framework general can describe the robustness any classifier We shown no single model simultaneously robust attacks under all norms nearest neighbor classifiers theoretically sample adversarial training Most importantly highlighted codimension contributing adversarial examples verified our theoretical contributions withWe believe a geometric understanding the decision boundaries learned deep networks both new geometrically inspired attacks defenses In Appendix C a novel gradient-free geometric attack support Finally believe future work into the geometric properties decision boundaries learned various optimization procedures new techniques black-box attacks",0.01,0.8242665518145965
"Character-based neural machine translation (NMT) models alleviate out-of-vocabulary issues, learn morphology, and move us closer to completely end-to-end translation systems.   Unfortunately, they are also very brittle and easily falter when presented with noisy data. In this paper, we confront NMT models with synthetic and natural sources of noise. We find that state-of-the-art models fail to translate even moderately noisy texts that humans have no trouble comprehending. We explore two approaches to increase model robustness: structure-invariant word representations and robust training on noisy texts. We find that a model based on a character convolutional neural network is able to simultaneously learn representations robust to multiple kinds of noise. Humans have surprisingly robust language processing systems that can easily overcome typos, misspellings, and the complete omission of letters when reading BID34 . A particularly extreme and comical exploitation of our robustness came years ago in the form of a popular meme: ""Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae."" A person's ability to read this text comes as no surprise to the psychology literature. BID38 found that this robustness extends to audio as well. They experimented with playing parts of audio transcripts backwards and found that it did not affect comprehension. BID35 found that in noisier settings reading comprehension only slowed by 11%. BID27 found that the common case of swapping letters could often go unnoticed by the reader. The exact mechanisms and limitations of our understanding system are unknown. There is some evidence that we rely on word shape BID26 , that we can switch between whole word recognition and piecing together words from letters BID36 BID33 , and there appears to be no evidence that the first and last letter positions are required to stay constant for comprehension. 1 In stark contrast, neural machine translation (NMT) systems, despite their pervasive use, are immensely brittle. For instance, Google Translate produces the following unintelligible translation for a German version of the above meme: 2 ""After being stubbornly defiant, it is clear to kenie Rlloe in which Reiehnfogle is advancing the boulders in a Wrot that is integral to Sahce, as the utterance and the lukewarm boorstbaen stmimt.""While typos and noise are not new to NLP, our systems are rarely trained to explicitly address them, as we instead hope that the relevant noise will occur in the training data.Despite these weaknesses, the move to character-based NMT is important. It helps us tackle the long tailed distribution of out-of-vocabulary words in natural language, as well as reduce computation load of dealing with large word embedding matrices. NMT models based on characters and other sub-word units are able to extract stem and morphological information to generalize to unseen words and conjugations. They perform very well in practice on a range of languages BID44 BID53 . In many cases, these models actually discover an impressive amount of morphological information about a language BID2 . Unfortunately, training (and testing) on clean data makes models brittle and, arguably, unfit for broad deployment. Figure 1 shows how the performance of two state-of-the-art NMT systems degrades when translating German to English as a function of the percent of German words modified. Here we show three types of noise: 1) Random permutation of the word, 2) Swapping a pair of adjacent letters, and 3) Natural human errors. We discuss these types of noise and others in depth in section 4.2. The important thing to note is that even small amounts of noise lead to substantial drops in performance. Figure 1: Degradation of Nematus and char2char BID21 performance as noise increases.To address these trends and investigate the effects of noise on NMT, we explore two simple strategies for increasing model robustness: using structure-invariant representations and robust training on noisy data, a form of adversarial training BID49 BID14 . We find that a character CNN representation trained on an ensemble of noise types is robust to all kinds of noise. We shed some light on the model ability to learn robust representations to multiple types of noise, and point to remaining difficulties in handling natural noise. Our goal is two fold: 1) initiate a conversation on robust training and modeling techniques in NMT, and 2) promote the creation of better and more linguistically accurate artificial noise to be applied to new languages and tasks.",952,0.492,559,1.70304114490161,"Character-based neural machine translation (NMT) models alleviate outvocabulary issues learn morphology move us completely end systems Unfortunately they also brittle easily falter presented noisy data In confront NMT models synthetic and natural sources noise We find state models fail translate even moderately noisy texts that humans no trouble We explore two approaches increase model robustness structure word representations robust training on noisy texts We find a model based simultaneously representations robust multiple kinds noise Humans surprisingly robust language processing systems easily overcome the complete omission letters when BID34 . A particularly extreme and comical exploitation our robustness came yearsAoccdrnig to a rscheearch at Cmabrigde Uinervtisy it deosn't mttaer in waht oredr the ltteers a wrod are, the olny iprmoetnt tihng is the frist and lsat ltteer be at the rghit pclae A person's ability comes as the psychology literature BID38 found this robustness extends audio as They experimented playing parts audio transcripts backwards found comprehension BID35 found noisier settings reading comprehension only slowed BID27 found the common case swapping letters could often go The exact mechanisms limitations our understanding system There we rely word shape BID26 , that switch whole word recognition piecing letters BID36 BID33 there appears required stay constant comprehension 1 In stark contrast neural machine translation despite immensely brittle For instance produces the above meme 2 ""After being stubbornly defiant it kenie Rlloe in which Reiehnfogle advancing the boulders a Wrot that integral Sahce the utterance and the lukewarm boorstbaen stmimt.""While typos noise new NLP our systems rarely trained explicitly address instead hope the relevant noise occur the training dataDespite the move character-based NMT important It helps tackle the long tailed distribution outvocabulary reduce computation load of dealing large word NMT models based characters other sub-word units able extract stem to generalize unseen words They perform very practice on languages BID44 BID53 . In these models actually discover an impressive amount a language BID2 . Unfortunately training ( testing clean data makes models brittle, arguably unfit broad deployment Figure the performance two state NMT systems degrades translating German as the percent modified Here show three types noise Swapping adjacent letters Natural human errors We discuss these types noise others depth section lead substantial drops Figure Degradation Nematus and char2char BID21 performance as noise increasesTo address these trends investigate NMT explore two simple strategies model robustness using robust training a form adversarial training BID49 BID14 We find a character CNN representation trained an ensemble noise types robust We shed the model ability learn robust representations to multiple types noise point remaining difficulties handling natural noise Our goal two fold initiate robust training modeling techniques NMT promote better and more linguistically accurate artificial noise to new languages tasks",0.01,0.4953662383734967
"As neural networks grow deeper and wider, learning networks with hard-threshold activations is becoming increasingly important, both for network quantization, which can drastically reduce time and energy requirements, and for creating large integrated systems of deep networks, which may have non-differentiable components and must avoid vanishing and exploding gradients for effective learning. However, since gradient descent is not applicable to hard-threshold functions, it is not clear how to learn them in a principled way. We address this problem by observing that setting targets for hard-threshold hidden units in order to minimize loss is a discrete optimization problem, and can be solved as such. The discrete optimization goal is to find a set of targets such that each unit, including the output, has a linearly separable problem to solve. Given these targets, the network decomposes into individual perceptrons, which can then be learned with standard convex approaches. Based on this, we develop a recursive mini-batch algorithm for learning deep hard-threshold networks that includes the popular but poorly justified straight-through estimator as a special case. Empirically, we show that our algorithm improves classification accuracy in a number of settings, including for AlexNet and ResNet-18 on ImageNet, when compared to the straight-through estimator.",255,0.127,156,1.6346153846153846,"As neural networks deeper wider learning networks with hard-threshold activations is both network quantization drastically creating large integrated systems deep networks may non-differentiable components must avoid vanishing and exploding gradients for effective learning However since gradient descent applicable hard-threshold functions learn them We address observing setting targets hard-threshold hidden units order loss is a discrete optimization problem can as such The discrete optimization goal find targets such each unit, including a linearly separable problem to Given these targets the network decomposes individual perceptrons learned with standard convex approaches Based this develop a recursive mini-batch algorithm learning deep hard-threshold networks that includes the popular but poorly justified straight-through estimator as we show our algorithm improves classification accuracy settings for AlexNet ResNet-18 on ImageNet when the straight-through estimator",0.0,0.3210234129857592
"The robust and efficient recognition of visual relations in images is a hallmark of biological vision. Here, we argue that, despite recent progress in visual recognition, modern machine vision algorithms are severely limited in their ability to learn visual relations. Through controlled experiments, we demonstrate that visual-relation problems strain convolutional neural networks (CNNs). The networks eventually break altogether when rote memorization becomes impossible such as when the intra-class variability exceeds their capacity. We further show that another type of feedforward network, called a relational network (RN), which was shown to successfully solve seemingly difficult visual question answering (VQA) problems on the CLEVR datasets, suffers similar limitations. Motivated by the comparable success of biological vision, we argue that feedback mechanisms including working memory and attention are the key computational components underlying abstract visual reasoning. Consider the two images in Fig. 1 . The image on the left was correctly classified as a flute by a deep convolutional neural network (CNN) BID13 . This is quite a remarkable feat for such a complicated image, which includes distractors that partially occlude the object of interest. After the network was trained on millions of photographs, this and many other images were accurately categorized into one thousand natural object categories, surpassing, for the first time, the accuracy of a human observer on the ImageNet classification challenge. Now, consider the image on the right. On its face, it is quite simple compared to the image on the left. It is just a binary image containing two curves. Further, it has a rather distinguishing property, at least to the human eye: both curves are the same. The relation between the two items in this simple scene is rather intuitive and immediately obvious to a human observer. Yet, the CNN failed to learn this relation even after seeing millions of training examples.Why is it that a CNN can accurately detect the flute in Fig. 1a while struggling to recognize the simple relation depicted in Fig. 1b? (a) (b) Figure 1: Two images: The image in panel (a) can be classified with high confidence as containing a flute by contemporary computer vision algorithms. However, these same algorithms struggle to learn the concept of ""sameness"" as exemplified by the image with the two curves shown in panel (b) . The image in panel (b) is sampled from the SVRT challenge BID6 .That such task is difficult, and even sometimes impossible for contemporary computer vision algorithms including CNNs, is known BID6 BID12 BID4 BID26 but has, so far, been overlooked. To make matters worse, the issue has been overshadowed by the recent success of a novel class of neural networks called relational networks (RNs) on seemingly challenging visual question answering (VQA) benchmarks. However , RNs have so far only been tested using toy datasets like the sort-of-CLEVR dataset which depicts combinations of items of only a handful of colors and shapes BID22 . As we will show, RNs suffer the same limitations as CNNs for a same-different task such as the one shown in Fig. 1b .This failure of modern computer vision algorithms is all the more striking given the widespread ability to recognize visual relations across the animal kingdom, from human and non-human primates BID3 BID15 to rodents BID28 , birds BID2 BID18 and even insects BID10 . Examining the failures of existing models is a critical step on the path to understanding the computational principles underlying visual reasoning. Yet, to our knowledge , there has not been any systematic exploration of the limits of contemporary machine learning algorithms on relational reasoning problems.Previous work by BID6 showed that black-box classifiers fail on most tasks from the synthetic visual reasoning test (SVRT), a battery of twenty-three visual-relation problems, despite massive amounts of training data. More recent work by BID4 and BID26 each showed how two different CNN architectures could only solve a handful of the twentythree SVRT problems. Similarly, BID12 , after showing how CNNs fail to learn a same-different task with simple binary ""sprite"" items, only managed to train a multi-layer perceptron on this task by providing carefully engineered training schedules. However, these results of BID4 , BID12 and BID26 were inconclusive: does the inability of feedforward neural networks to solve various visual-relation problems reflect a poor choice of hyperparameters for their particular implementation or rather a systematic failure of the entire class of feedforward models?Here, we propose to systematically probe the limits of CNNs and other state-of-the-art visual reasoning networks (RNs) on visual-relation tasks. Through a series of controlled experiments , we demonstrate that visual-relation tasks strain CNNs and that these limitations are not alleviated in RNs, which were specifically designed to tackle visual-relation problems. A brief review of the biological vision literature suggests that two key brain mechanisms, working memory and attention, underlie primates' ability to reason about visual relations. We argue that these mechanisms and possibly other feedback mechanisms are needed to extend current computer vision models to efficiently learn to solve complex visual reasoning tasks.Our contributions are threefold: (i) We perform the first systematic performance analysis of CNN architectures on each of the twenty-three SVRT problems. This yields a dichotomy of visual-relation problems, hard same-different problems vs. easy spatial-relation problems.(ii) We describe a novel, controlled, visual-relation challenge which convincingly shows that CNNs solve same-different tasks via rote memorization. (iii) We show that a simple modification of the sort-of-CLEVR challenge similarly breaks state-of-the-art relational network architectures.Overall, we wish to motivate the computer vision community to reconsider existing visual question answering challenges and turn to neuroscience and cognitive science for inspiration to help with the design of visual reasoning architectures. Our results indicate that visual-relation problems can quickly exceed the representational capacity of CNNs. While learning templates for individual objects appears to be quite tractable for today's deep networks, learning templates for arrangements of objects become rapidly intractable because of the combinatorial explosion in the number of templates needed. That stimuli with a combinatorial structure are difficult to represent with feedforward networks has been long acknowledged by cognitive scientists at least as early as BID7 . However, this limitation seems to have been somehow overlooked by current computer vision scientists.Compared to the feedforward networks in this study, biological visual systems excel at detecting relations. BID6 found that humans are capable of learning rather complicated visual rules and generalizing them to new instances from just a few SVRT training examples. For instance, their participants could learn the rule underlying the hardest SVRT problem for CNNs in our Experiment 1, problem 20, from an average of about 6 examples. Moreover, problem 20 is rather complicated, involving two shapes such that ""one shape can be obtained from the other by reflection around the perpendicular bisector of the line joining their centers."" In contrast, the best performing network for this problem in our high-throughput search could not get significantly above chance after a million training examples.Visual reasoning ability is not just found in humans. For example, birds and primates can be trained to recognize same-different relations and then transfer this knowledge to novel objects BID29 . A recent, striking example of same-different learning in animals comes from BID18 who essentially showed that ducklings can perform a one-shot version of our Experiment 3 from birth. During a training phase, newly hatched ducklings were exposed to a single pair of simple 3D objects that were either the same or different. Later, they demonstrated a preference for novel objects obeying the relationship observed in the training phase. This result suggests that these animals can either rapidly learn the abstract concepts of same and different from a single example or they simply possess these concepts innately. Contrast the behavior of these ducklings with the CNN+RN of Experiment 3, which demonstrated no ability to transfer the concept of same-different to novel objects FIG2 even after hundreds of thousands of training examples. For a recent review of similar literature (including additional evidence for abstract relational reasoning in pigeons and nutcrackers), see BID30 .There is substantial evidence that the neural substrate of visual-relation detection may depend on reentrant/feedback signals beyond feedforward, pre-attentive processes. It is relatively well accepted that, despite the widespread presence of feedback connections in our visual cortex, certain visual recognition tasks, including the detection of natural object categories, are possible in the near absence of cortical feedback -based primarily on a single feedforward sweep of activity through our visual cortex BID23 . However , psychophysical evidence suggests that this feedforward sweep is too spatially coarse to localize objects even when they can be recognized BID5 . The implication is that object localization in clutter requires attention BID31 .It is difficult to imagine how one could recognize the spatial relation between two objects without spatial information. Indeed, converging neuroscience evidence BID17 BID19 BID21 BID14 BID8 BID27 suggests that the processing of spatial relations between pairs of objects in a cluttered scene requires attention, even when participants are able to detect the presence of the individual objects pre-attentively, presumably in a single feedforward sweep.Another brain mechanism that has been implicated in our ability to process visual relations is working memory BID16 BID11 BID1 BID0 . In particular, imaging studies BID16 BID11 have highlighted the role of working memory in prefrontal and premotor cortices when participants solve Raven's progressive matrices which require both spatial and same-different reasoning.What is the computational role of attention and working memory in the detection of visual relations? One assumption BID8 is that these two mechanisms allow flexible representations of relations to be constructed dynamically at run-time via a sequence of attention shifts rather than statically by storing visual-relation templates in synaptic weights (as done in feedforward neural networks). Such representations built ""on-the-fly"" circumvent the combinatorial explosion associated with the storage of templates for all possible relations, helping to prevent the capacity overload associated with feedforward neural networks.Humans can easily detect when two objects are the same up to some transformation BID24 or when objects exist in a given spatial relation BID6 BID8 . More generally, humans can effortlessly construct an unbounded set of structured descriptions about the visual world around them BID9 . Given the vast superiority of humans over modern computers in their ability to detect visual relations, we see the exploration of attentional and mnemonic mechanisms as an important step in our computational understanding of visual reasoning.",2135,1.053,1230,1.7357723577235773,"The robust and efficient recognition visual relations images biological vision Here argue recent progress visual recognition modern machine vision algorithms severely learn visual relations Through controlled experiments visual-relation problems strain The networks eventually break altogether when rote memorization impossible such the intra-class variability exceeds We further show another type feedforward network a relational networkRN which shown successfully solve seemingly difficult visual question answering ( on the CLEVR datasets suffers similar limitations Motivated the comparable success biological vision argue feedback mechanisms including working memory the key computational components abstract visual reasoning Consider the two images Fig 1 . The image correctly classified a flute BID13 . This quite a remarkable feat such a complicated image includes distractors partially of After the network trained millions photographs this and accurately categorized one thousand natural object categories surpassing, on the ImageNet classification challenge Now consider the image On quite compared the image It just a binary image containing two curves Further a rather distinguishing property at both curves the The relation the two items this simple scene rather intuitive immediately a human observer Yet the CNN failed learn this relation even seeing millions training examplesWhy can accurately detect the flute Fig 1a while struggling recognize the simple relation depicted Fig 1b? (a) (b) Figure Two images: panel can classified with high confidence containing a flute by contemporary computer vision However these same algorithms struggle learnsameness the image with the two curves shown panel (b The image in panel (b sampled the SVRT challenge BID6 .That such task difficult even sometimes including CNNs known but, overlooked To the issue overshadowed a novel class neural networks relational networks on seemingly challenging visual question answering benchmarks However , RNs so using toy datasets like sortCLEVR dataset depicts combinations items only a handful colors shapes BID22 As will show RNs suffer CNNs for a same-different task such shown Fig 1b .This failure modern computer vision algorithms all the widespread ability recognize visual relations across BID3 BID15 rodents , birds insects the failures existing models on the computational principles visual reasoning Yet to , the limits contemporary machine learning algorithms relational reasoning problemsPrevious work BID6 showed fail most tasks from the synthetic visual reasoning test a battery twenty-three visual-relation problems despite massive amounts More recent work BID4 and BID26 each how two different CNN architectures only solve a handful the twentythree SVRT problems Similarly BID12 , after showing how CNNs fail learn a same-different task with simple binary ""sprite"" items only managed train providing carefully engineered training schedules However these results of BID4 ,: does the inability feedforward neural networks solve various visual-relation problems reflect a poor choice their particular implementation rather a systematic failure the entire class feedforward models?Here systematically probe the limits CNNs state visual reasoningRNs Through controlled experiments , that visual-relation tasks strain CNNs these limitations RNs were specifically tackle A brief review the biological vision literature two brain working memory reason visual relations We argue these mechanisms and possibly other feedback mechanisms needed extend current computer vision models efficiently learn solveOur contributions perform CNN architectures each the twenty-three SVRT problems This yields a dichotomy visual-relation problems hard same-different problems easy spatial-relation problems.(ii We describe controlled, visual-relation challenge which convincingly CNNs solve same-different tasks via (iii We show a simple modification sort-CLEVR challenge similarly breaks state relational networkOverall wish motivate reconsider existing visual question answering challenges turn inspiration with visual reasoning architectures Our results visual-relation problems quickly exceed CNNs While learning templates individual objects appears quite today's deep networks arrangements become rapidly because the combinatorial explosion templates That stimuli with difficult represent feedforward networks has long at least BID7 . However this limitation seems somehow current computer vision scientistsCompared the feedforward networks this study, biological visual systems excel relations. BID6 found humans learning rather complicated visual rules generalizing new instances from just a few SVRT training examples For instance their participants could learn the rule underlying the hardest SVRT problem for CNNs our Experiment problem 20 from about 6 examples Moreover problem 20 rather complicated involving two shapes such "" obtained by reflection around the perpendicular bisector joining their centers contrast the best performing network in could get significantly above chance after a million training examplesVisual reasoning ability just found humans For example birds primates recognize same-different relations then transfer BID29 . A recent, striking example same-different learning animals comes BID18 who essentially showed ducklings perform our Experiment from birth During a training phase newly hatched ducklings exposed a single pair simple 3D objects either the Later they demonstrated a preference novel objects obeying the relationship observed the training phase This result suggests these animals either rapidly learn the abstract concepts same and from a single example simply possess innately Contrast the behavior these ducklings the CNN+RN of Experiment demonstrated no ability transfer the concept samedifferent to novel objects FIG2 even hundreds of thousands training examples For a recent review similar literature additional evidence abstract relational reasoning pigeons nutcrackers BID30 .There visual-relation detection may reentrant/feedback signals beyond It relatively well accepted, feedback connections certain visual recognition tasks natural object categories possible -based primarily a single feedforward sweep activity through BID23 However , psychophysical evidence this feedforward sweep too spatially coarse localize objects even can recognized BID5 The implication object localization clutter requires attention BID31 .It difficult one recognize the spatial relation spatial information Indeed converging neuroscience evidence suggests the processing spatial relations pairs requires attention participants able detect preattentively presumably a single feedforward sweepAnother brain mechanism visual relations working . In particular imaging studies BID16 BID11 have highlighted working memory when participants solve Raven's progressive matrices which require both spatial and same-different reasoningWhat the computational role attention the detection visual relations One assumption BID8 these two mechanisms allow flexible representations relations dynamically at via a sequence attention shifts rather statically storing visual-relation templates synaptic weightsas done Such representations built ""- circumvent the combinatorial explosion associated the storage templates all possible relations helping prevent the capacity overload associated feedforward neural networksHumans easily detect two objects the up some transformation BID24 or objects exist More generally humans effortlessly construct structured descriptions about around BID9 . Given the vast superiority humans modern computers detect visual relations see the exploration attentional and mnemonic mechanisms our computational understanding visual reasoning",0.01,0.5787624929109542
"Visual Active Tracking (VAT) aims at following a target object by autonomously controlling the motion system of a tracker given visual observations. Previous work has shown that the tracker can be trained in a simulator via reinforcement learning and deployed in real-world scenarios. However, during training, such a method requires manually specifying the moving path of the target object to be tracked, which cannot ensure the tracker’s generalization on the unseen object moving patterns. To learn a robust tracker for VAT, in this paper, we propose a novel adversarial RL method which adopts an Asymmetric Dueling mechanism, referred to as AD-VAT. In AD-VAT, both the tracker and the target are approximated by end-to-end neural networks, and are trained via RL in a dueling/competitive manner: i.e., the tracker intends to lockup the target, while the target tries to escape from the tracker. They are asymmetric in that the target is aware of the tracker, but not vice versa. Specifically, besides its own observation, the target is fed with the tracker’s observation and action, and learns to predict the tracker’s reward as an auxiliary task. We show that such an asymmetric dueling mechanism produces a stronger target, which in turn induces a more robust tracker. To stabilize the training, we also propose a novel partial zero-sum reward for the tracker/target. The experimental results, in both 2D and 3D environments, demonstrate that the proposed method leads to a faster convergence in training and yields more robust tracking behaviors in different testing scenarios. For supplementary videos, see: https://www.youtube.com/playlist?list=PL9rZj4Mea7wOZkdajK1TsprRg8iUf51BS 
 The code is available at https://github.com/zfw1226/active_tracking_rl Visual Active Tracking (VAT) aims at following a target object by autonomously controlling the motion system of a tracker given visual observations. VAT is demanded in many real-world applications such as autonomous vehicle fleet (e.g., a slave-vehicle should follow a master-vehicle ahead), service robots and drones (e.g., a drone is required to follow a person when recording a video). To accomplish the VAT task, one typically needs to perform a sequence of tasks such as recognition, localization, motion prediction, and camera control. However, conventional visual tracking BID0 BID29 BID24 BID11 BID3 BID13 aims to solely propose a 2D bounding box of the target frame by frame, and does not actively take into consideration the control of camera. Thus, compared to the problem of ""passive"" tracking, VAT is more practical and challenging.With the advancement of deep reinforcement learning BID35 BID25 BID26 , training an end-to-end deep neural network via reinforcement learning for VAT is shown to be feasible BID21 BID20 . The authors learn a policy that maps raw-pixel observation to control signal straightly with a Conv-LSTM network. Such an end-to-end approach could save the effort of tuning an extra camera controller. Meanwhile, it also outperforms the conventional methods where the passive tracker is equipped with a hand-engineered camera controller. However, the performance of the deep reinforcement learning based tracker is still limited by the training methods. Due to the ""trial-and-error"" nature of reinforcement learning, it is infeasible to directly train the tracker in the real world. Alternatively, virtual environments are always utilized to generate sufficient data for training without tedious human labeling. Nevertheless, to deploy the trained tracker in the real world, one has to overcome the virtual-to-real gap. One solution can be building numbers of high-fidelity environments . However, it is expensive and tedious to build such environments for VAT. Both the visual rendering (illumination, texture, etc.) and the physical properties should be carefully designed to emulate the real world. Suppose we carry out VAT where the target is a pedestrian. To build the environment, one has to not only model the human's appearance, but also design physical rules and the pedestrian's trajectory so that it moves naturally like a human beings. Recently, BID21 tried to overcome the virtual-to-real gap by applying the so-called environment augmentation technique. They diversify the visual appearance by changing the placement of the background objects and by flipping left-right the screen frame. However, they neglect another important factor, that is, the motion of the target for VAT task. Intuitively, the complexity and diversity of the target motion in training will impact the generalization of the data-driven tracker. For example, if the target only moves forward during training, the tracker may over fit to move straightly and fail to track other motion patterns, like a sharp turn. In this paper, we have proposed an asymmetric dueling mechanism for visual active tracking (AD-VAT). Within AD-VAT, agents of tracker and target are learned in an adversarial manner. With the design of the partial zero-sum reward structure and tracker-aware model, the reinforced active tracker outperforms baseline methods. Experiments including ablation study in both 2D and 3D environments verify the effectiveness of the proposed mechanism.As future work, we would like to: 1) investigate the theoretical justification of applying modern Multi-Agent RL methods BID18 BID32 to solving Partially Observable Markov Game and finding Nash Equilibrium. 2) further develop the mechanism/model for active tracking in more complex environment (e.g., environments with a number of obstacles and moving distractors); 3) adapt the mechanism to other tasks (e.g., learning to grab a moving object).",1124,0.608,659,1.7056145675265555,"Visual Active Tracking aims following a target object autonomously controlling the motion system a tracker given visual observations Previous work the tracker trained a simulator via deployed However during training such a method requires manually specifying the moving path tracked ensure the tracker��s generalization on the unseen object moving patterns To learn a robust tracker VAT in propose a novel adversarial RL method adopts an Asymmetric Dueling mechanism referred AD-VAT In AD-VAT both the tracker approximated end neural trained via RL in a dueling/competitive manner: intends lockup tries They asymmetric the target aware the tracker vice Specifically besides its own observation the target fed with the tracker��s observation action learns predict as an auxiliary task We show such an asymmetric dueling mechanism produces a stronger target a more robust tracker To stabilize the training also propose a novel partial zero-sum reward the tracker/target The experimental results, in both 2D demonstrate the proposed method leads a faster convergence training yields more robust tracking behaviors different testing scenarios For supplementary videos The code https://github.com/zfw1226/active_tracking_rl Visual Active Tracking aims following a target object by autonomously controlling the motion system given visual observations VAT is demanded autonomous vehicle fleet ( a slave-vehicle should follow ahead service robots drones when recording To accomplish the VAT task one typically perform a sequence recognition localization motion prediction camera control However conventional visual tracking BID0 BID29 BID24 BID11 BID3 BID13 aims solely propose the target frame by frame does actively take the control camera. Thus compared the problem ""passive"" tracking VAT practical challengingWith the advancement deep reinforcement BID35 BID25 BID26 , training an end deep via for VAT shown The authors learn a policy maps raw-pixel observation control signal straightly with a Conv-LSTM network Such end save the effort tuning an extra camera controller Meanwhile it also outperforms the conventional methods where the passive tracker equipped a hand-engineered camera controller However the performance deep reinforcement based tracker Due reinforcement learning directly the tracker Alternatively virtual environments always utilized generate sufficient data training without tedious human labeling Nevertheless to deploy the trained tracker overcome the virtual-to-real gap One solution can building numbers high-fidelity environments . However expensive tedious such environments VAT Both the visual rendering ( texture the physical properties should carefully designed emulate Suppose carry VAT where a pedestrian To build the environment one not model the human's appearance design physical rules the pedestrian's trajectory so moves naturally like Recently BID21 tried overcome the virtual-to-real gap applying the so-called environment augmentation technique They diversify the visual appearance by changing the background objects flipping left-right the screen frame However they neglect another important factor for VAT task Intuitively the complexity diversity the target motion training will impact the data-driven tracker For example only moves forward during training the tracker over fit to move straightly fail other motion patterns a sharp turn In have proposed an asymmetric dueling mechanism visual active tracking Within AD-VAT agents tracker target learned With the design the partial zero-sum reward structure and tracker-aware model the reinforced active tracker outperforms baseline methods Experiments including ablation study both 2D verify the proposed mechanismAs future work,: the theoretical justification applying modern Multi-Agent RL methods BID18 BID32 solving Partially Observable Markov Game and finding Nash Equilibrium 2 further develop the mechanism/model active tracking more complex environment a number obstacles moving distractors adapt other tasks learning grab",0.01,0.501923093123418
"Identifying the hypernym relations that hold between words is a fundamental task in NLP. Word embedding methods have recently shown some capability to encode hypernymy. However, such methods tend not to explicitly encode the hypernym hierarchy that exists between words. In this paper, we propose a method to learn a hierarchical word embedding in a specific order to capture the hypernymy. To learn the word embeddings, the proposed method considers not only the hypernym relations that exists between words on a taxonomy, but also their contextual information in a large text corpus. The experimental results on a supervised hypernymy detection and a newly-proposed hierarchical path completion tasks show the ability of the proposed method to encode the hierarchy. Moreover, the proposed method outperforms previously proposed methods for learning word and hypernym-specific word embeddings on multiple benchmarks. Hypernymy relation is an essential component for many Natural Language Processing (NLP) tasks. It represents an asymmetric relation between name of a class (hypernym) and a particular instance of it (hyponym). For example, given the hypernymy pair (bird, vertebrate), the hyponym word bird is a particular instance of the hypernym word vertebrate, and one can simply say ""a bird is a vertebrate"". Hypernymy identification plays a major role in various NLP tasks such as question answering BID14 , taxonomy construction BID25 , textual entailment BID8 and text generation BID5 , to name a few.The task of identifying hypernymy has been long addressed by relying on either the lexicalsyntactic patterns where a particular textual pattern suggests the existence of a hypernymy relation, or the distributional representation of a given pair of words. In a pattern-based approach, from a sentence like ""a bird such as a falcon"" we can identify a hypernymy relation between bird and fal-con. Despite its simplicity and efficiency, pattern-based approaches suffer from a low precision and coverage issue BID44 . For example, let us consider the sentence ""some birds recorded in Africa such as Gadwall"", a typical lexical-pattern based approach may incorrectly detect (Gadwall, Africa) as hypernymy.In contrast to the requirement of the pattern-based approaches to have the hypernym and hyponym words occurring in the same sentence, the distributional family of approaches rely on the words co-occurrence statistics in a large text corpus to represent the words and then deduce the hold of hypernymy. It works on the assumption that taxonomically related words tend to occur in a similar context. In particular, a hypernym word has a broader context than its hypernym, and therefore the contextual features of the hyponym word are usually a subset of that of its hypernym. However, such approaches commonly struggle from discriminating the hypernym relations from other lexico-semantic relations BID34 .Lately , distributed word representations (a.k.a word embeddings) BID22 BID29 have shown some capability to encode hypernymy. Such methods typically embed the words into dense, low-dimensional, real-valued vectors, using the co-occurrence statistics obtained from a text corpora, and then used in a supervised settings to detect hypernymy. However , typical word embeddings models rely only on co-occurrence based similarity, and therefore are insufficient to encode taxonomic relations in the learnt word embeddings BID2 .Several recent studies have proposed methods for learning hypernymy-specific word embeddings BID44 BID2 BID26 . BID44 design a neural network to learn word embeddings that perceive hypernymy, purely relying on extracted pairwise training data from a web corpus. Moreover, Anh et al. [2016] proposed a similar approach, but further utilise the contextual information of the pre-extracted pairwise hypernymy. Similarly, Nguyen et al. [2017] introduce the HyperVec model that use the Skip-gram with Negative Sampling (SGNS) BID22 objective to learn the word embeddings from a corpus subject to pairwise hypernymy constraints extracted from a taxonomy. Moreover, BID27 proposed a new model that embed symbolic data into hyperbolic space, particularly into Poincaré ball, to learn hierarchical embeddings. Another model that is recently proposed is the LEAR model of BID39 . LEAR is a post-processing model that takes any word vectors and then adjust the input vectors to emphasis the hypernym relations. The aforementioned methods merely consider pairwise hypernymy relations rather than the hierarchical hypernymy path connecting a word to the root in a taxonomy.In this paper, we propose a method that jointly learns hierarchical word embeddings (HWE) from a corpus and a taxonomy. The proposed method begins by embedding the words into random low-dimensional real-valued vectors, and subsequently updates the embeddings to encode the hierarchical structure available in the taxonomy. To train the proposed method, we use a taxonomy to extract the hierarchical hypernymy paths for the hyponym words, and use the global vector BID29 as a context-aware objective between the hypernym and hyponym words. As such, the proposed model benefits from both the contextual information as well as the taxonomic relations to learn the embeddings.In our experiments, we evaluate our hierarchical word embeddings on the standard supervised hypernymy task on various benchmarks, graded lexical entailment prediction and a newly-proposed hierarchical path completion task. On the supervised hypernymy identification , the proposed method reports an improvement over several previously proposed methods, showing the benefit of considering the full hierarchical hypernymy paths instead of only pairwise relations. Moreover, a quantitative and qualitative analysis on the newly-proposed hierarchical path completion task further illustrate the ability of the proposed method to encode hypernymy in the learn embeddings. We presented a method to learn a Hierarchical Word Embedding (HWE) for identifying the hypernymy relations between words. For this purpose, we introduced a joint objective that make use of both a taxonomy and a large text corpus to learn hierarchical word embeddings. We evaluated HWE on the standard supervised hypernymy identification and a newly-proposed hierarchical hypernymy path completion tasks. The experiments conducted in this paper on the above mentioned two tasks demonstrate that HWE was able to encode the hypernymy relations between words into the learnt embeddings, and reports an improvement over several previously proposed methods that learn either general word embeddings or hypernymy-specific word embeddings.",1282,0.638,786,1.6310432569974556,"Identifying the hypernym relations hold words NLP Word embedding methods recently shown some capability encode hypernymy However such methods tend explicitly encode the hypernym hierarchy that words In learn a hierarchical word a speci���c order capture the hypernymy. To the word embeddings the proposed method considers not only the hypernym relations exists words on their contextual information a large text corpus The experimental results on a supervised hypernymy detection a newly-proposed hierarchical path completion tasks the proposed method encode the hierarchy. Moreover the proposed method outperforms previously learning word and hypernym-speci��� on multiple benchmarks Hypernymy relation many Natural It represents an asymmetric relation name of a class (hypernym a particular instance For example given the hypernymy pairbird, vertebrate the hyponym word bird a particular instance one simply Hypernymy identification plays various NLP tasks question BID14 , taxonomy construction textual entailment BID8 text generation toThe task long addressed relying either the lexicalsyntactic patterns where a particular textual pattern suggests a given pair In a pattern-based approach from a sentence likea bird such we a hypernymy relation bird fal-con Despite its simplicity efficiency pattern-based approaches suffer a low precision and coverage issue BID44 . For example let the sentencesome birds recorded Africa such Gadwall a typical lexical-pattern based approach may incorrectly detect ( Africa hypernymyIn the requirement the pattern-based approaches have the hypernym and hyponym words occurring the distributional family approaches rely co-occurrence statistics represent then the hold It works the assumption taxonomically related words tend occur In particular a hypernym word a broader context, therefore the contextual features usually a subset However such approaches commonly struggle from discriminating the hypernym relations from BID34 .Lately , distributed word representations BID22 BID29 shown some capability. Such methods typically embed the words dense, low-dimensional, real-valued vectors using obtained a text corpora used a supervised settings detect hypernymy However , typical word embeddings models rely only co insufficient encode taxonomic relations BID2 .Several proposed methods learning hypernymy-specific word embeddings BID44 BID2 BID26 BID44 design a neural network perceive hypernymy purely relying extracted pairwise training data a web corpus Moreover, Anh et al [2016 proposed a similar approach further utilise the contextual information the pre-extracted pairwise hypernymy Similarly, Nguyen et al [2017 introduce the HyperVec model that use the Skip-gram with Negative Sampling (SGNS BID22 objective learn a corpus subject pairwise hypernymy constraints extracted Moreover BID27 proposed embed symbolic data particularly into Poincaré ball, learn hierarchical embeddings Another model recently proposed the LEAR model BID39 . LEAR is any word vectors then adjust emphasis the hypernym relations The aforementioned methods merely consider pairwise hypernymy relations rather connecting a word a taxonomyIn jointly learns The proposed method begins the words random low-dimensional real-valued vectors subsequently updates encode available To train the proposed method use extract the hierarchical hypernymy paths the hyponym words the global vector BID29 a context-aware objective between As such, the proposed model benefits both the contextual information as the taxonomic relations learn the embeddingsIn our experiments evaluate our hierarchical word embeddings the standard supervised hypernymy task on various benchmarks graded lexical entailment prediction a newly-proposed hierarchical path completion task On the supervised hypernymy identification , the proposed method reports showing considering the full hierarchical hypernymy paths only pairwise relations Moreover quantitative and on the newly-proposed hierarchical path completion task further illustrate encode hypernymy the learn embeddings We presented learn identifying the hypernymy relations For this purpose introduced a joint objective make both a taxonomy a large text corpus learn hierarchical word embeddings We evaluated HWE on the standard supervised hypernymy identification a newly-proposed hierarchical hypernymy path completion tasks The experiments conducted on above two tasks demonstrate HWE was encode the hypernymy relations words into the learnt embeddings reports over several previously proposed methods that learn",0.01,0.31192194565897696
"While self-organizing principles have motivated much of early learning models, such principles have rarely been included in deep learning architectures. Indeed, from a supervised learning perspective it seems that topographic constraints are rather decremental to optimal performance. Here we study a network model that incorporates self-organizing maps into a supervised network and show how gradient learning results in a form of a self-organizing learning rule. Moreover, we show that such a model is robust in the sense of its application to a variety of  areas, which is believed to be a hallmark of biological learning systems. Machine learning has made significant improvements, specifically with deep neural network models BID13 , BID0 , BID4 . Deep learning was made possible by much faster computer technology such as GPUs, and with algorithmic advancement such as BID17 BID3 BID10 , BID2 . Learning tasks that, due to their complexity or data volume, were impossible to execute a decade ago, now can be run in reasonable time scale. The improvements allow the applications of Deep Learning to many real world problems.Learning good internal representations is a key aspect of deep learning. Indeed, it is interesting to recall that the first breakthrough in deep learning came from an application of unsupervised pretraining with gradient-based fine tuning BID7 . Restricted Boltzmann Machines (RBMs) BID6 and Autoencoders BID1 BID8 are utilized for constructing the hidden layers of early models such as Deep Belief Networks (DBN) and Deep Boltzmann Machine (DBM), , BID16 . While much research of deep learning research focuses on learning efficiency and running performances, there is much less research into the understanding of the formation of internal representation in hierarchical neural networks. Moreover, while self-organizing maps have been and integral part of biologically motivated learning theories since the 1970s BID19 , BID12 the role of such self-organizing mechansims are less understood in modern deep learning theories. Topographical self-organization is often observed in biological neural networks BID11 , BID15 and thus may give new insights in understanding learning and self-organization in artificial neural networks.Here, we propose a network that combines aspects of self-organization into a supervised network model for classification. More specifically, in this study we modify the previously proposed Restricted Radial Basis Function Networks (rRBF) BID5 with a softmax output layer that is trained on a crossentropic cost function. This is more consistent with a probabilistic interpretation of the class membership output function than the previous implementation which allows a more clear derivation of the emergence of the self-organizing learning aspects of this network. We call this modified network the Softmax Restricted Radial Basis Function Networks (S-rRBF). Through this network we argue that it is possible to build a learning model in which unsupervised self-organization and supervised learning are just different aspect of a single learning mechanism. We show that the network achieves compatible performance with other deep network architectures while having the added feature of robustness in the sense that it compares favorable with the best performers in the studied examples, while the best performer changes for different applications. While the results are consistent with BID20 'No free lunch theorem', they also highlight that robustness against variation of applications and not the best performance is an important part in flexible learner, which is thought to be of importance when understanding biological learning systems.We highlight our ideas here with well understood applications examples of moderate complexity. However, the proposed architecture can also be scaled to deeper layers and hence applied to deeper learning problems. The main contribution here is showing algebraically the emergence of the selforganizing structures from supervised gradient learning. We believe that this research opens new insights into the relation between unsupervised and supervised learning. Also, we illustrate on some examples the internal representation in the competitive layer and compare it to a standard selforganizing map (SOM) BID12 and to t-Stochastic Neighborhood Embedding (t-SNE) BID18 ) that represents a deeper transformation of the feature space. In this research we showed that it is possible to build a hierarchical neural network that self-organizes with context-relevant topographical internal representation. More specifically, we showed that topographical self-organization can emerge as an implication of the supervised learning. Thus, the two learning processes of self-organization and supervised learning, which are often considered to be unrelated, are can be viewed as two different aspects of a single learning mechanism. The two learning processes are only distinguished by the layers where they occurs. The internal self-organization in this network is not fully unsupervised. However, the direction of the self-organization process in a hidden neuron is only decided by the relative value of the connection weight leading from the neuron to the output neuron relevant to the true label of the input and thus not dependent on the supervised error.The experiments show that the classification performance of the proposed model is comparable to that of standard supervised networks. While the proposed model does not always outperform existing conventional models, we found that the performance was comparable to the best performer for most of the diverse benchmark applications. Specific machine learning methods often perform well on datasets for which they have been designed, but it is well acknowledged that sufficient performance in a variety of tasks is useful in many applications such as robotics and probably to understand better human abilities. Another advantage of our system is its 2-dimensional internal layer offers auxiliary visual information on its learning representations. The S-rRBFcan can readily expanded into deep networks. As layered networks transfer transform inputs (physical stimuli) into labels (concepts) in a layer by layer manner, the visualization of internal layers in multi-layered S-rRBF can be considered as concept-forming visualization. The visualization can potentially offer new insights for machine learning.",1152,0.604,689,1.671988388969521,"While self-organizing principles motivated much early learning models rarely included deep architectures Indeed from a supervised learning perspective topographic constraints rather decremental to optimal performance Here study a network model incorporates self-organizing maps into show how gradient learning results a form Moreover we show such a model robust its application areas which believed biological learning systems Machine learning significant improvements, specifically BID13 , BID0 Deep learning was made much faster computer technology such with algorithmic advancement such BID17 BID3 BID10 , . Learning tasks, due their complexity or data volume were impossible execute a decade can run reasonable time scale The improvements allow the applications of Deep Learning many real world problemsLearning good internal representations Indeed interesting recall the first breakthrough deep learning an application pretraining with gradient- fine BID7 . Restricted Boltzmann MachinesRBMs) BID6 and utilized constructing the hidden layers early models such Deep Belief Networks , . While much research of deep learning research focuses learning efficiency running performances the understanding the formation internal representation Moreover while self-organizing maps and integral biologically motivated learning theories the 1970s BID19 , the role such self-organizing mechansims are modern deep learning theories Topographical self-organization observed biological neural networks BID11 , thus give in understanding learningHere propose combines aspects classification More specifically in modify the previously proposed Restricted Radial Basis Function NetworksrRBF) BID5 with a softmax output layer trained a crossentropic cost function This more consistent the class membership output function which allows a more clear derivation the emergence the self-organizing learning aspects this network We call this modified network the Softmax Restricted Radial Basis Function NetworksS-rRBF Through this network argue it a learning model supervised just different aspect We show the network achieves compatible performance other deep network while having the added feature robustness the sense compares favorable with the best performers the studied examples the best changes for While the results consistent BID20 'No free lunch theorem they highlight robustness against variation applications not the best performance in flexible learner, thought of understanding biological learning systemsWe highlight our ideas well understood applications examples moderate complexity However the proposed architecture can scaled deeper layers hence applied deeper learning problems The main contribution here showing algebraically the emergence the selforganizing structures from supervised gradient learning We believe this research opens new insights Also we illustrate on some examples the internal representation in the competitive layer compare a standard selforganizing mapSOM) BID12 and to t-Stochastic Neighborhoodt ) represents a deeper transformation In this research showed it build self with context-relevant topographical internal representation More specifically showed topographical self-organization emerge an implication the supervised learning. Thus the two learning processes supervised learning often considered unrelated can viewed The two learning processes only distinguished the layers where occurs The internal self-organization in this network fully unsupervised However the direction a hidden neuron only decided the relative value the connection weight leading from relevant the true label and thus dependent the supervised errorThe experiments show the classification performance the proposed model comparable standard supervised networks While the proposed model does always outperform we the best performer most the diverse benchmark applications Specific machine learning methods often perform datasets for well acknowledged sufficient performance a variety useful such robotics probably to understand better human abilities Another advantage our system its 2-dimensional internal layer offers auxiliary visual information on its learning representations The S-rRBFcan can readily expanded deep networks As layered networks transfer transform inputs (physical stimuli labels by the visualization internal layers multi-layered S-rRBF can considered concept-forming visualization The visualization can potentially offer machine learning",0.01,0.416246544523839
"Quantization of a neural network has an inherent problem called accumulated quantization error, which is the key obstacle towards ultra-low precision, e.g., 2- or 3-bit precision. To resolve this problem, we propose precision highway, which forms an end-to-end high-precision information flow while performing the ultra-low-precision computation. First, we describe how the precision highway reduce the accumulated quantization error in both convolutional and recurrent neural networks. We also provide the quantitative analysis of the benefit of precision highway and evaluate the overhead on the state-of-the-art hardware accelerator. In the experiments, our proposed method outperforms the best existing quantization methods while offering 3-bit weight/activation quantization with no accuracy loss and 2-bit quantization with a 2.45 % top-1 accuracy loss in ResNet-50. We also report that the proposed method significantly outperforms the existing method in the 2-bit quantization of an LSTM for language modeling. Energy-efficient inference of neural networks is becoming increasingly important in both servers and mobile devices (e.g., smartphones, AR/VR devices, and drones). Recently, there have been active studies on ultra-low-precision inference using 1 to 4 bits BID21 BID9 BID27 BID25 BID28 BID2 BID15 BID1 and their implementations on CPU and GPU BID23 , and dedicated hardware BID19 BID22 . However, as will be explained in section 5.2, the existing quantization methods suffer from a problem called accumulated quantization error where large quantization errors get accumulated across layers, making it difficult to enable ultra-low precision in deep neural networks.In order to address this problem, we propose a novel concept called precision highway where an end-to-end path of high-precision information reduces the accumulated quantization error thereby enabling ultra-low-precision computation. Our proposed work is similar to recent studies BID15 BID2 which propose utilizing pre-activation residual networks, where skip connections are kept in full precision while the residual path performs low-precision computation. Compared with these works, our proposed method offers a generalized concept of high-precision information flow, namely, precision highway, which can be applied to not only the pre-activation convolutional networks but also both the post-activation convolutional and recurrent neural networks. Our contributions are as follows.• We propose a novel idea of network-level approach to quantization, called precision highway and quantitatively analyze its benefits in terms of the propagation of quantization errors and the difficulty of convergence in training based on the shape of loss surface.• We provide the detailed analysis of the energy and memory overhead of precision highway based on the state-of-the-art hardware accelerator model. According to our experiments, the overhead is negligible while offering significant improvements in accuracy.• We apply precision highway to both convolution and recurrent networks. We report a 3-bit quantization of ResNet-50 without accuracy loss and a 2-bit quantization with a very small accuracy loss. We also provide the sub 4-bit quantization results of long short-term memory (LSTM) for language modeling.2 RELATED WORK BID16 presented an int8 quantization method that selects an activation truncation threshold to minimize the Kullback-Leibler divergence between the distributions of the original and quantized data. BID12 proposed a quantization scheme that enables integer-arithmetic only matrix multiplications (practically, 8-bit quantization for neural networks). These methods are implemented on existing CPUs or GPUs BID11 ACL) . BID9 presented a binarization method and demonstrated the performance benefit on a GPU. BID21 proposed a binary network called XNOR-Net in which a weight-binarized AlexNet gives the same accuracy as a full-precision one. BID25 presented DoReFa-Net, which applies tanh-based weight quantization and bounded activation. BID26 proposed a balanced quantization that attempts to balance the population of values on quantization levels. BID7 proposed utilizing full precision for internal cell states in the LSTM because of their wide value distributions. This work is similar to ours in that high-precision data are selectively utilized to improve the quantized network. Our difference is proposing a network-level end-to-end flow of high-precision activation. Recently, BID28 presented 4-bit quantization with ResNet-50 . They adopt Dorefa-net style weight quantization with static bounded activation, and improve accuracy by adopting multi-step quantization and knowledge distillation during fine-tuning. proposed a trade-off between the number of channels and precision . Clustering-based methods have the potential to further reduce the precision BID5 . However, they require a lookup table and full-precision computation , which makes them less hardware-friendly.Recently, BID2 a) and BID15 proposed utilizing full-precision on the skip connections in pre-activation residual networks 1 . Compared with those works, our proposed idea has a salient difference in that it offers a network-level solution and demonstrates that the end-to-end flow of high-precision information is crucial. In addition, our method is not limited to pre-activation residual networks , but general enough to be applied to both post-activation convolutional and recurrent neural networks. In this paper, we proposed the concept of end-to-end precision highway which can be applied to both feedforward and feedback networks and enable ultra-low precision in deep neural networks. The proposed precision highway reduces quantization errors by keeping high-precision activation from the input to output of the network with small computation costs. We described how it reduces the accumulated quantization error and presented quantitative analyses in terms of accuracy and hardware cost as well as training characteristics. Our experiments showed that the proposed method outperforms the state-of-the-art methods in the 3-and 2-bit quantizations of ResNet-18/50 and 2-bit quantization of an LSTM model. We believe that our work will serve as a step toward mixed precision networks for computational efficiency.",1197,0.612,695,1.7223021582733813,"Quantization a neural network has an inherent problem called accumulated quantization error the key obstacle towards ultra-low precision, To resolve propose precision highway, forms end high information flow while performing First describe the precision highway reduce the accumulated quantization error We also provide the quantitative analysis the benefit precision highway and evaluate the overhead on state hardware accelerator In the experiments our proposed method outperforms the best existing quantization methods while offering 3-bit weight/activation quantization no accuracy loss a 2.45 % top-1 accuracy loss ResNet-50 We also report the proposed method significantly the 2-bit quantization for language modeling Energy-efficient inference becoming both servers ( smartphones AR drones Recently there active studies ultra-low-precision inference 1 to 4 bits BID21 BID9 their implementations on CPU , dedicated hardware However will section the existing quantization methods suffer called accumulated quantization error where get accumulated across layers making enable ultra-low precisionIn precision highway where an end path reduces thereby Our proposed work similar recent studies BID15 BID2 which propose utilizing pre-activation residual networks where skip connections kept full precision while the residual path performs Compared these works our proposed method offers a generalized concept namely, precision highway, not only the pre-activation convolutional networks both recurrent Our contributions as follows.• propose network-level approach quantization called precision highway and quantitatively analyze its benefits the propagation quantization errors the difficulty convergence training based the shape loss provide the detailed analysis the energy memory overhead based state hardware accelerator model According our experiments the overhead is negligible while offering accuracy.• apply precision highway to both convolution We report a 3-bit quantization ResNet-50 without accuracy loss with We also provide the sub 4-bit quantization results long short language modeling.2 RELATED WORK BID16 presented an int8 quantization method selects an activation truncation threshold the Kullback-Leibler divergence the distributions BID12 proposed a quantization scheme enables integer-arithmetic only matrix multiplications neural networks These methods implemented existing CPUs or BID11 ACL) . BID9 presented a binarization method and demonstrated on a GPU BID21 proposed a binary network called XNOR-Net in a weight-binarized AlexNet gives full one BID25 presented DoReFa-Net applies tanh-based weight quantization bounded activation BID26 proposed a balanced quantization that attempts balance the population values on quantization levels BID7 proposed utilizing full precision for internal cell states because their wide value distributions This work similar ours selectively utilized the quantized network Our difference proposing network- end flow high-precision activation Recently BID28 presented 4-bit quantization ResNet-50 . They adopt Dorefa-net style weight quantization static bounded activation improve adopting knowledge distillation during proposed channels precision . Clustering-based methods further the precision BID5 . However they require a lookup table full-precision computation , makes hardwareRecently BID2 a) and proposed utilizing on the skip connections pre-activation residual networks 1 Compared those works our proposed idea a salient difference offers and demonstrates end flow crucial In addition our method pre-activation residual networks , general enough In proposed end precision highway which feedforward feedback networks enable ultra-low precision in The proposed precision highway reduces quantization errors keeping high-precision activation from the input output with small computation costs We described it reduces the accumulated quantization error presented quantitative analyses terms accuracy and hardware cost as training characteristics Our experiments the proposed method outperforms state the 3-and 2-bit quantizations ResNet-18/50 We believe serve mixed precision networks computational efficiency",0.01,0.5444416081906381
"The vast majority of natural sensory data is temporally redundant. For instance, video frames or audio samples which are sampled at nearby points in time tend to have similar values.   Typically, deep learning algorithms take no advantage of this redundancy to reduce computations.   This can be an obscene waste of energy.   We present a variant on backpropagation for neural networks in which computation scales with the rate of change of the data - not the rate at which we process the data.   We do this by implementing a form of Predictive Coding wherein neurons communicate a combination of their state, and their temporal change in state, and quantize this signal using Sigma-Delta modulation.   Intriguingly, this simple communication rule give rise to units that resemble biologically-inspired leaky integrate-and-fire neurons, and to a spike-timing-dependent weight-update similar to Spike-Timing Dependent Plasticity (STDP), a synaptic learning rule observed in the brain.   We demonstrate that on MNIST, on a temporal variant of MNIST, and on Youtube-BB, a dataset with videos in the wild, our algorithm performs about as well as a standard deep network trained with backpropagation, despite only communicating discrete values between layers.   Currently, most algorithms used in Machine Learning work under the assumption that data points are independent and identically distributed, as this assumption provides good statistical guarantees for convergence. This is very different from the way data enters our brains. Our eyes receive a single, never-ending stream of temporally correlated data. We get to use this data once, and then it's gone. Moreover, most sensors produce sequential, temporally redundant streams of data. This can be both a blessing and a curse. From a statistical learning point of view this redundancy may lead to biased estimators when used to train models which assume independent and identically distributed input data. However, the temporal redundancy also implies that intuitively not all computations are necessary.Online Learning is the study of how to learn in this domain -where data becomes available in sequential order and is given to the model only once. Given the enormous amount of sequential data, mainly videos, that are being produced nowadays, it seems desirable to develop learning systems that simply consume data on-the-fly as it is being generated, rather than collect it into datasets for offline-training. There is, however a problem of efficiency, which we hope to illustrate with two examples:1. CCTV feeds. CCTV Cameras collect an enormous amount of data from mostly-static scenes.The amount of new information in a frame, given the previous frame, tends to be low, i.e. the data tends to be temporally redundant. If we want to train a model from of this data (for example a pedestrian detector), we need to process a large amount of mostly-static frames. If the frame rate doubles, so does the amount of computation. Intuitively, it feels that this should not be necessary. It would be nice to still be able to use all this data, but have the amount of computation scale with the amount of new information in each frame, not just the number of frames and dimensions of the data.2. Robot perception. Robots have no choice but to learn online -their future input data (e.g. camera frames) are dependent on their previous predictions (i.e. motor actions). Not only does their data come in nonstationary temporal streams, but it typically comes from several sensors running at different rates. The camera may produce 1MB images at 30 frames/s, while the gyroscope might produce 1-byte readings at 1000 frames/s. It is not obvious, using current methods in deep learning, how we can integrate asynchronous sensory signals into a unified, trainable, latent representation, without undergoing the inefficient process of recomputing the function of the network every time a new signal arrives.These examples point to the need for a training method where the amount of computation required to update the model scales with the amount of new information in the data, and not just the dimensionality of the data.There has been a lot of work on increasing the computational efficiency of neural networks by quantizing neural weights or activations (see Section 4), but comparatively little work on exploiting redundancies in the data to reduce the amount of computation. BID12 , set out to exploit the temporal redundancy in video by having neurons only send their quantized changes in activation to downstream neurons, and having the downstream neurons integrate these changes over time. This approach (take the temporal difference, multiply by weights, temporally integrate) works for efficiently approximating the function of the network, but fails for training. The reason for this failure is that when the weights are functions of time, we no longer reconstruct the correct activation for the next layer. In other words, given a sequence of inputs x 0 ...x t with x 0 = 0 and weights w 1 ...w t :t τ =1 (x τ − x τ −1 ) · w τ = x t · w t unless w t = w 0 ∀t. FIG0 describes the problem visually.In this paper, we correct for this problem by encoding a mixture of two components of the layers activation x t : the proportional component k p x t , and the derivative component k d (x t − x t−1 ). When we invert this encoding scheme, we get a decoding scheme which corresponds to taking an exponentially decaying temporal average of past inputs. Interestingly, the resulting neurons begin to resemble models of biological spiking neurons, whose membrane potentials can approximately be modeled as an exponentially decaying temporal average of past inputs.In this work, we present a scheme wherein the temporal redundancy of input data is used to reduce the computation required to train a neural network. We demonstrate this on the MNIST and Youtube-BB datasets. To our knowledge we are the first to create a neural network training algorithm which uses less computation as data becomes more temporally redundant. We set out with the objective of reducing the computation in deep networks by taking advantage of temporal redundancy in data. We described a simple rule (Equation 4) for sparsifying the communication between layers of a neural network by having our neurons communicate a combination of their temporal change in activation, and the current value of their activation. We show that it follows from this scheme that neurons should behave as leaky integrators (Equation 5 ). When we quantize our neural activations with Sigma-Delta modulation, a common quantization scheme in signal processing, we get something resembling a leaky integrate-and-fire neuron. We derive efficient update rules for the weights of our network, and show these to be related to STDP -a learning rule first observed in neuroscience. Finally, we train our network, verify that it does indeed compute more efficiently on temporal data, and show that it performs about as well as a traditional deep network of the same architecture, but with significantly reduced computation. Finally, we show that our network can train on real video data.The efficiency of our approach hinges on the temporal redundancy of our input data and neural activations. There is an interesting synergy here with the concept of slow-features BID17 . Slow-Feature learning aims to discover latent objects that persist over time. If the hidden units were to specifically learn to respond to slowly-varying features of the input, the layers in a spiking implementation of such a network would have to communicate less often. In such a network, the tasks of feature-learning and reducing inter-layer communication may be one and the same.Code is available at github.com/petered/pdnn.",1528,0.818,881,1.7343927355278093,"The vast majority natural sensory data temporally redundant For instance video frames or audio samples which sampled nearby points tend similar values Typically deep learning algorithms take no advantage this redundancy to reduce This can an obscene waste energy We present a variant for neural networks computation scales the rate - not process We do implementing a form Predictive Coding wherein neurons communicate a combination their state their temporal change state quantize this signal Sigma-Delta modulation this simple communication rule give rise units resemble biologically-inspired leaky integrate-and-fire neurons to a spike-timing-dependent weight-update similar Spike-Timing Dependent Plasticity a synaptic learning rule observed We demonstrate on MNIST on a temporal variant and Youtube-BB a dataset videos in the wild our algorithm performs about standard deep network trained despite only communicating discrete values layers Currently most algorithms used Machine Learning work under data points independent identically as provides good statistical guarantees convergence This very different data enters Our eyes receive temporally correlated data We get use this data once, Moreover most sensors produce sequential, temporally redundant streams This can both a blessing From a statistical learning point this redundancy lead biased estimators when used train models which assume independent and identically input data However the temporal redundancy also implies intuitively not all computations necessaryOnline Learning the study this domain -where data becomes sequential order given the model only Given sequential data mainly videos nowadays desirable develop learning systems simply consume on- as being collect into datasets offline-training There, a problem of efficiency we hope illustrate two examples:1 CCTV feeds. CCTV Cameras collect mostly-static scenesThe amount new information in given the previous frame tends low tends temporally redundant If we train a model from of this data (for a pedestrian detector process mostly-static frames If the frame rate doubles so computation Intuitively feels that should necessary It would still all this data have the amount computation scale new information each frame and dimensions Robot perception Robots no choice online -their future input data ( dependent their previous predictions ( Not their data come nonstationary temporal streams typically several sensors running The camera may produce 1MB images while might 1-byte readings It obvious using current methods in deep learning we integrate asynchronous sensory signals a unified, trainable, latent representation, without undergoing the inefficient process the function everyThese examples point where amount update scales dimensionalityThere has increasing quantizing neural weights or activations Section comparatively little work exploiting redundancies reduce BID12 , set out exploit the temporal redundancy video by having neurons only send their quantized changes activation downstream having integrate over This approach (take the temporal difference multiply weights temporally integrate works efficiently the function the network fails training The reason when the weights functions time no reconstruct the correct activation for the next layer In given a sequence inputs x 0 ...x t with weights w :t τ1 ( τ − −1 · unlesst. FIG0 describes the problem visuallyIn this paper correct encoding a mixture two components the layers activation x t : the proportional component k p x t When we invert this encoding scheme a decoding scheme corresponds taking an exponentially decaying temporal average past inputs Interestingly the resulting neurons begin resemble models biological spiking neurons whose membrane potentials can approximately modeled an exponentially decaying temporal average past inputsIn present a scheme wherein the temporal redundancy input data used reduce the computation train We demonstrate this on the MNIST and Youtube-BB datasets To our knowledge we create a neural network training algorithm which less computation as data becomes temporally redundant We set reducing the computation in deep networks taking temporal redundancy data We described a simple rule (Equation sparsifying the communication layers by having our neurons a combination their temporal change activation the current value We show it follows from this scheme neurons should behave leaky integratorsEquation When we quantize our neural activations Sigma-Delta modulation a common quantization scheme in get something resembling a leaky integrate-and-fire neuron We derive efficient update rules the weights our network show these related STDP -a learning rule first observed neuroscience Finally train our network verify does compute more on temporal data show about traditional deep network of significantly reduced computation Finally show our network train on real video dataThe efficiency our approach hinges the temporal redundancy neural activations There an interesting synergy here slow-features BID17 . Slow-Feature learning aims discover latent objects persist If the hidden units specifically learn respond slowly-varying features the input the layers a spiking implementation such a network communicate less In such a network the tasks featurelearning reducing inter-layer communication may oneCode available github.com/petered/pdnn",0.01,0.5752473367684179
"Information bottleneck (IB) is a method for extracting information from one random variable X that is relevant for predicting another random variable Y. To do so, IB identifies an intermediate ""bottleneck"" variable T that has low mutual information I(X;T) and high mutual information I(Y;T). The ""IB curve"" characterizes the set of bottleneck variables that achieve maximal I(Y;T) for a given I(X;T), and is typically explored by maximizing the ""IB Lagrangian"", I(Y;T) - βI(X;T). In some cases, Y is a deterministic function of X, including many classification problems in supervised learning where the output class Y is a deterministic function of the input X. We demonstrate three caveats when using IB in any situation where Y is a deterministic function of X: (1) the IB curve cannot be recovered by maximizing the IB Lagrangian for different values of β; (2) there are ""uninteresting"" trivial solutions at all points of the IB curve; and (3) for multi-layer classifiers that achieve low prediction error, different layers cannot exhibit a strict trade-off between compression and prediction, contrary to a recent proposal. We also show that when Y is a small perturbation away from being a deterministic function of X, these three caveats arise in an approximate way. To address problem (1), we propose a functional that, unlike the IB Lagrangian, can recover the IB curve in all cases. We demonstrate the three caveats on the MNIST dataset. The information bottleneck (IB) method BID29 provides a principled way to extract information that is present in one variable that is relevant for predicting another variable. Given two random variables X and Y , IB posits a ""bottleneck"" variable T that obeys the Markov condition Y − X − T . By the data processing inequality (DPI) BID9 , this Markov condition implies that I(X; T ) ≥ I(Y ; T ), meaning that the bottleneck variable cannot contain more information about Y than it does about X. In fact, any particular choice of the bottleneck variable T can be quantified by two terms: the mutual information I(X; T ), which reflects how much T compresses X, and the mutual information I(Y ; T ), which reflects how well T predicts Y . In IB, bottleneck variables are chosen to maximize prediction given a constraint on compression BID32 BID1 BID13 , where ∆ is the set of random variables T obeying the Markov condition Y − X − T . The values of F (r) for different r specify the IB curve. In order to explore the IB curve, one must find optimal T for different values of r. It is known that the IB curve is concave in r but may not be strictly concave. This seemingly minor issue of non-strict concavity will play a central role in our analysis.In practice, the IB curve is almost always explored not via the constrained optimization problem of Eq.(1), but rather by maximizing the so-called IB Lagrangian, Several recent papers have drawn connections between IB and supervised learning, in particular classification using neural networks. In this context, X represents input vectors, Y represents the output classes, and T represents intermediate representations used by the network architecture, such as the activity of hidden layer(s ) BID30 . Some of these papers modify neural network training algorithms so as to optimize the IB Lagrangian BID2 BID7 , thereby permitting the use of IB with high-dimensional, continuousvalued random variables. Some papers have also suggested that by controlling the amount of compression, one can tune desired characteristics of trained models such as generalization error BID23 BID30 BID31 , robustness to adversarial inputs BID2 , and detection of out-of-distribution data BID3 . Other research (ShwartzZiv & Tishby, 2017) has suggested -somewhat controversially BID22 -that stochastic gradient descent (SGD) training dynamics may implicitly favor hidden layer mappings that balances compression and prediction, with earlier hidden layers favoring prediction over compression and latter hidden layers favoring compression over prediction. Finally , there is the general notion that intermediate representations that are optimal in the IB sense correspond to ""interesting"" or ""useful"" compressions of input vectors BID4 .There are also numerous application domains of IB beyond supervised learning, including clustering BID25 , coding theory and quantization BID6 BID34 BID8 , and cognitive science BID33 . In most of these applications, it is of central interest to explore solutions at different points on the IB curve, for example to control the number of detected clusters, or to adapt codes to available channel capacity.In some scenarios, Y may be a deterministic function of X, i.e., Y = f (X) for some single-valued function f . For example , in many classification problems, it is assumed that any given input belongs to a single class, which implies a deterministic relationship between X and Y . In this paper , we demonstrate three caveats for IB that appear whenever Y is a deterministic function of X: 1. There is no one-to-one mapping between different points on the IB curve and maximizers of the IB Lagrangian L β IB for different β, thus the IB curve cannot be explored by maximizing L β IB while varying β. This occurs because when Y = f (X), the IB curve has a piecewise linear shape and is therefore not strictly concave. The dependence of the IB Lagrangian on the strict concavity of F (r) has been previously noted BID13 BID24 , but the implications and pervasiveness of this problem (e.g., in many classification scenarios) has not been fully recognized. We analyze this issue and propose a solution in the form of an alternative objective function, which can be used to explore the IB curve even when Y = f (X). 2. All points on the IB curve contain uninteresting trivial solutions (in particular, stochastic mixtures of two very simple solutions). This suggests that IB-optimality is not sufficient for an intermediate representation to be an interesting or useful compression of input data. 3. For a neural network with several hidden layers that achieves a low probability of error, the hidden layers cannot display a strict trade-off between compression and prediction (in particular, different layers can only differ in the amount of compression, not prediction). In Appendix B, we show that the above three caveats also apply to the recently proposed deterministic IB variant of IB BID26 , in which the compression term is quantified using the entropy H(T ) rather than the mutual information I(X; T ). In that Appendix, we propose an alternative objective function that can be used to resolve the first problem for dIB.We also show, in Appendix C, that our results apply when Y is not exactly a deterministic function of X, but -close to one. In this case: (1) it is hard to explore the IB curve by optimizing the IB Lagrangian, because all optimizers will fall within O(− log ) of a single ""corner"" point on the information plane; (2) along all points on the IB curve, there are ""uninteresting"" trivial solutions that are no more than O(− log ) away from being optimal; (3) different layers of a neural networks can trade-off at most O(− log ) amount of prediction.A recent paper BID4 ) also discusses several difficulties in using IB to analyze intermediate representations in supervised learning. That paper does not consider the particular 1 Note that optimizing L β IB is still a constrained problem in that p(t|x) must be a valid conditional probability. However, this constraint is usually easier to handle, e.g., by using an appropriate parameterization.issues that arise when Y is a deterministic function of X, and its arguments are complementary to ours. BID24 [Sec. 2.4 ] discuss another caveat for IB in deterministic settings, concerning the relationship between sufficient statistics and the complexity of the inputoutput mapping, which is orthogonal to the three caveats analyzed here. Finally, BID22 and BID4 observed that when T is continuous-valued and a deterministic function of a continuous-valued X, I(X; T ) can be unbounded, making the application of the IB framework problematic. We emphasize that the caveats discussed in this paper are unrelated to that problem.Note that our results are based on analytically-provable properties of the IB curve, i.e., global optima of Eq. (1), and do not concern practical issues of optimization (which may be important in realworld scenarios). Our theoretical results are also independent of the practical issue of estimating MI between neural network layers, an active area of recent research BID5 BID14 BID10 BID12 , though our empirical experiments in Section 7 rely on the estimator proposed in . Finally, our results are also independent of issues related to the relationship between IB, finite data sampling, and generalization error BID23 BID30 BID31 .In the next section, we review some of the connections between supervised learning and IB. In Section 3, we show that when Y = f (X), the IB curve has a piecewise linear (not strictly concave) shape. In Sections 4, 5 and 6, we discuss the three caveats mentioned above. In Section 7, we demonstrate the caveats using a neural-network implementation of IB on the MNIST dataset. The information bottleneck principle has attracted a great deal of attention in various fields, including information theory, cognitive science, and machine learning, particularly in the context of classification using neural networks. In this work, we showed that in any scenario where Y is a deterministic function of X -which includes many classification problems -IB demonstrates behavior that is qualitatively different from when the mapping from X to Y is stochastic. In particular, in such cases: (1) the IB curve cannot be recovered by maximizing the IB Lagrangian I(Y ; T ) − βI(X; T ) while varying β; (2) all points on the IB curve contain ""uninteresting"" representations of inputs; (3) multi-layer classifiers that achieve zero probability of error cannot have a strict trade-off between prediction and compression among successive layers, contrary to a recent proposal.Our results should not be taken to mean that the application of IB to supervised learning is without merit. First, they do not apply to various non-deterministic classification problems where the output is stochastic. Second, even for deterministic scenarios, one may still wish to control the amount of compression during training, e.g., to improve generalization or robustness to adversarial inputs. In this case, however, our work shows that to achieve varying rates of compression, one should use a different objective function than the IB Lagrangian.",2193,0.98,1304,1.6817484662576687,"Information bottleneck (IB extracting one random variable X relevant predicting To do IB identifies an intermediate ""bottleneck"" variable T low mutual information I(X;T The ""IB curve characterizes the set bottleneck variables achieve maximal I(Y;T typically explored maximizing "" Lagrangian - In Y is X including many classification problems supervised learning where the output class Y We demonstrate three caveats when IB in any situation Y X ( the IB curve recovered maximizing the IB Lagrangian for different values β ""uninteresting"" trivial solutions at for multi-layer classifiers that achieve low prediction error different layers exhibit a strict trade-off compression, contrary We also show when Y is a small perturbation away a deterministic function X these three caveats arise an approximate way To address problem ( a functional that, unlike the IB Lagrangian recover the IB curve We demonstrate the three caveats on the MNIST dataset The information bottleneck (IB method BID29 provides a principled way extract that present one variable that relevant predicting another variable Given two random variables X IB posits a ""bottleneck"" variable T obeys the Markov condition Y − X − T By the data processing inequality (DPI) BID9 , this Markov condition implies that I(X; T ) ≥ ; meaning the bottleneck variable contain more information Y In fact any particular choice the bottleneck variable T can quantified two terms the mutual information I(X; reflects how compresses X ; well predicts In IB, bottleneck variables chosen maximize prediction given a constraint compression BID32 , �� the set random variables T obeying the Markov condition Y − X − T The values F (r for different r specify the IB curve In order explore the IB curve one find optimal T for different values r. It known the IB curve concave r but may strictly This seemingly minor issue non-strict concavity will play our analysisIn practice the IB curve almost explored not via the constrained optimization problem Eq.(1 maximizing the so-called IB Lagrangian Several recent papers drawn connections IB supervised in particular classification using neural networks In this context X represents input vectors Y the output classes T intermediate representations used the network architecture the activity of hidden layer(s ) BID30 Some these papers modify neural network training algorithms so the IB Lagrangian BID2 BID7 , thereby permitting IB with high-dimensional, continuousvalued random variables Some papers also by controlling compression one tune desired characteristics trained models such generalization error BID23 BID30 BID31 , robustness detection outdistribution data Other research (ShwartzZiv & Tishby -somewhat BID22 (SGD) training dynamics implicitly favor hidden layer mappings that balances compression prediction earlier hidden layers favoring prediction latter hidden layers Finally , there the general notion intermediate representations that optimal the IB sense correspond ""interesting compressions input vectors BID4 .There numerous application domains of beyond supervised learning BID25 coding theory quantization BID6 BID34 BID8 cognitive science In most these applications of central interest explore solutions at different points on the IB curve for control detected clusters adapt codes available channel capacityIn Y may X for For example , many classification problems assumed any given input belongs implies a deterministic relationship X In , three caveats IB that appear whenever Y X 1 There different points the IB curve maximizers the IB Lagrangian L β IB for different β, thus explored maximizing L while varying β This occurs when Y = fX the IB curve has a piecewise linear shape therefore strictly concave The dependence the IB Lagrangian the strict concavity F (r has previously BID13 BID24 , the implications and ( many classification scenarios has recognized We analyze this issue in an alternative objective function explore the IB curve even Y = fX 2 All points the IB curve contain uninteresting trivial solutions This suggests IB-optimality sufficient an intermediate representation an interesting or useful compression of 3 For a neural network several hidden layers achieves a low probability display a strict trade-off compression prediction (in different layers only differ compression not prediction In Appendix B the above three caveats also the recently proposed deterministic IB variant IB BID26 , the compression term quantified the entropy H(T ) rather the mutual information I(X; T In that Appendix propose an alternative objective function resolve for dIB.We also show, Appendix C our results apply when Y not X -close one In: ( it hard explore the IB curve by optimizing the IB Lagrangian because all optimizers fall within O(− log ) a single ""corner"" point the information plane along all points ""uninteresting"" trivial solutions no away a neural networks trade- at predictionA recent paper BID4 ) also discusses several difficulties IB analyze intermediate representations supervised learning That paper does consider the particular 1 Note that optimizing L β IB still a constrained problem that p(t|x must a valid conditional probability However this constraint usually easier an appropriate parameterization.issues that arise Y X its arguments complementary ours BID24 [Sec ] discuss another caveat IB in deterministic settings concerning the relationship sufficient statistics the complexity the inputoutput mapping the three caveats analyzed Finally BID22 and observed when T is continuous-valued a; T ) can unbounded making the application the IB framework problematic We emphasize the caveats discussed unrelated that problemNote analytically-provable properties the IB curve Eq do concern practical issues optimizationwhich important realworld scenarios Our theoretical results also independent the practical issue estimating MI between neural network layers an active area recent research BID5 BID14 BID10 BID12 , though our empirical experiments in Section rely the estimator proposed . Finally our results also independent issues the relationship IB, finite data sampling generalization error BID23 BID30 .In review the connections supervised learning IB In Section show when Y = fX the IB curve has (not strictly concave) shape In Sections the three caveats mentioned In Section demonstrate the caveats using a neural-network implementation IB on The information bottleneck principle attracted particularly classification using In this work showed in any scenario Y X -which includes many classification problems -IB demonstrates behavior when the mapping from In particular in such cases: the IB curve recovered maximizing the IB Lagrangian I(Y ; T − βI(X while varying β; contain ""uninteresting"" representations inputs achieve zero probability error have a strict trade-off prediction compression among successive layers contraryOur results should the application IB supervised without merit First they do apply various non-deterministic classification problems where Second even for deterministic scenarios one wish control compression during training improve generalization or to adversarial inputs In however our work shows to achieve varying rates compression a different objective function the IB Lagrangian",0.01,0.44111436394302483
"We prove, under two sufficient conditions, that idealised models can have no adversarial examples. We discuss which idealised models satisfy our conditions, and show that idealised Bayesian neural networks (BNNs) satisfy these. We continue by studying near-idealised BNNs using HMC inference, demonstrating the theoretical ideas in practice. We experiment with HMC on synthetic data derived from MNIST for which we know the ground-truth image density, showing that near-perfect epistemic uncertainty correlates to density under image manifold, and that adversarial images lie off the manifold in our setting. This suggests why MC dropout, which can be seen as performing approximate inference, has been observed to be an effective defence against adversarial examples in practice; We highlight failure-cases of non-idealised BNNs relying on dropout, suggesting a new attack for dropout models and a new defence as well. Lastly, we demonstrate the defence on a cats-vs-dogs image classification task with a VGG13 variant. Adversarial examples, inputs to machine learning models that an adversary designs to manipulate model output, pose a major concern in machine learning applications. Many hypotheses have been suggested in the literature trying to explain the existence of adversarial examples. For example, BID31 hypothesise that these examples lie near the decision boundary, while BID22 hypothesise that these examples lie in low density regions of the input space. However, adversarial examples can lie far from the decision boundary (e.g. ""garbage"" images BID22 ), and using a simple spheres dataset it was shown that adversarial examples can exist in high density regions as well BID9 . In parallel work following BID22 's low-density hypothesis, BID17 empirically modelled input image density on MNIST and successfully detected adversarial examples by thresholding low input density. This puzzling observation, seemingly inconsistent with the spheres experiment in BID9 , suggests that perhaps additional conditions beyond the ability to detect low input density have led to the observed robustness by BID17 .Suggesting two sufficient conditions, here we prove that an idealised model (in a sense defined below) cannot have adversarial examples, neither in low density nor in high density regions of the input space. We concentrate on adversarial examples in discriminative classification models, models which are used in practical applications. To formalise our treatment, and to gain intuition into the results, we use tools such as discriminative Bayesian neural network (BNN) classifiers BID19 BID21 together with their connections to modern techniques in deep learning such as stochastic regularisation techniques BID6 . This pragmatic Bayesian perspective allows us to shed some new light on the phenomenon of adversarial examples. We further discuss which models other than BNNs abide by our conditions. Our hypothesis suggests why MC dropout-based techniques are sensible for adversarial examples identification, and why these have been observed to be consistently effective against a variety of attacks BID18 BID5 BID27 BID0 .We support our hypothesis mathematically and experimentally using HMC and dropout inference. We construct a synthetic dataset derived from MNIST for which we can calculate ground truth input densities, and use this dataset to demonstrate that model uncertainty correlates to input density, and that under our conditions this density is low for adversarial examples. Using our new-found insights we develop a new attack for MC dropout-based models which does not require gradient information, by looking for ""holes"" in the epistemic uncertainty estimation, i.e. imperfections in the uncertainty approximation, and suggest a mitigation technique as well. We give illustrative examples using MNIST BID15 , and experiment with real-world cats-vs-dogs image classification tasks BID3 ) using a VGG13 variant BID28 . Our result gives intuition into why dropout, a technique shown to relate to Bayesian modelling, seems to be effective in identifying adversarial examples. We presented several idealised models which satisfy the conditions we defined for robustness, opening the door for research into how various practical tools can approximate our idealised conditions. We highlighted that the main difficulty with modern BNNs is not coverage, but rather that approximate inference doesn't increase the un-certainty fast enough with practical BNN tools (we show this in figures 7a, demonstrating that we have holes in the dropout uncertainty). In contrast, HMC (which is not scalable for practical applications) does not have such uncertainty holes, suggesting that we must improve practical inference techniques in BNNs to improve robustness.",894,0.439,525,1.7028571428571428,"We prove under two sufficient conditions idealised models no adversarial examples We discuss which idealised models satisfy our conditions show Bayesian neural networks satisfy. We continue by studying near-idealised BNNs HMC inference demonstrating the theoretical ideas We experiment HMC on synthetic data derived MNIST for which know the ground-truth image density showing near-perfect epistemic uncertainty correlates density under image manifold adversarial images lie off the manifold our setting This suggests why MC dropout which can performing approximate inference observed an effective defence adversarial examples practice; We highlight failure-cases relying suggesting a new attack for dropout models as Lastly demonstrate the defence on catsvs image classification task a VGG13 variant Adversarial examples inputs an adversary designs manipulate model output pose Many hypotheses trying adversarial examples For example BID31 hypothesise these examples lie near the decision boundary low density regions However adversarial examples lie far the decision boundary BID22 using a simple spheres dataset it exist high density regions BID9 In parallel work following BID22 's low-density hypothesis empirically input image density MNIST successfully detected adversarial examples by low input density This puzzling observation seemingly inconsistent the spheres experiment BID9 perhaps additional conditions beyond low input density by BID17 .Suggesting two sufficient conditions here prove an idealised model (in a sense defined below have adversarial examples neither low density We concentrate adversarial examples discriminative classification models models practical applications To formalise our treatment and gain intuition into use tools classifiers BID19 BID21 together their connections modern techniques such . This pragmatic Bayesian perspective shed adversarial examples We further which models other BNNs abide our conditions Our hypothesis suggests why MC dropout-based techniques sensible adversarial examples identification have observed consistently attacks BID18 BID5 BID27 BID0 .We support mathematically HMC and dropout inference We construct a synthetic dataset derived MNIST for which calculate ground truth input densities demonstrate that model uncertainty correlates input under our conditions this density low adversarial examples Using our new-found insights develop for MC dropout-based models does gradient information by looking ""holes the epistemic uncertainty estimation imperfections suggest a mitigation technique as We give illustrative examples using MNIST BID15 , experiment real cats-vs image tasks BID3 ) a VGG13 variant Our result gives intuition into why dropout, a technique shown relate Bayesian modelling seems effective adversarial examples We presented several idealised models which satisfy robustness opening research how various practical tools approximate We highlighted the main difficulty modern BNNs coverage that approximate inference does increase uncertainty fast with practical BNN toolswe show figures demonstrating holes the dropout uncertainty In contrast HMC ( scalable practical applications such uncertainty holes suggesting must improve practical inference techniques BNNs",0.01,0.4948974173304371
"Deep neural networks are susceptible to adversarial attacks. In computer vision, well-crafted perturbations to images can cause neural networks to make mistakes such as confusing a cat with a computer. Previous adversarial attacks have been designed to degrade performance of models or cause machine learning models to produce specific outputs chosen ahead of time by the attacker. We introduce attacks that instead reprogram the target model to perform a task chosen by the attacker without the attacker needing to specify or compute the desired output for each test-time input. This attack finds a single adversarial perturbation, that can be added to all test-time inputs to a machine learning model in order to cause the model to perform a task chosen by the adversary—even if the model was not trained to do this task. These perturbations can thus be considered a program for the new task. We demonstrate adversarial reprogramming on six ImageNet classification models, repurposing these models to perform a counting task, as well as classification tasks: classification of MNIST and CIFAR-10 examples presented as inputs to the ImageNet model. The study of adversarial examples is often motivated in terms of the danger posed by an attacker whose goal is to cause model prediction errors with a small change to the model's input. Such an attacker could make a self-driving car react to a phantom stop sign BID6 by means of a sticker (a small L 0 perturbation), or cause an insurance company's damage model to overestimate the claim value from the resulting accident by subtly doctoring photos of the damage (a small L ∞ perturbation). With this context, various methods have been proposed both to construct BID40 BID32 BID3 BID24 and defend against BID9 BID17 BID25 BID42 BID14 BID13 this style of adversarial attack. Thus far, the majority of adversarial attacks have consisted of untargeted attacks that aim to degrade the performance of a model without necessarily requiring it to produce a specific output, or targeted attacks in which the attacker designs an adversarial perturbation to produce a specific output for that input. For example, an attack against a classifier might target a specific desired output class for each input image, or an attack against a reinforcement learning agent might induce that agent to enter a specific state BID22 .In practice, there is no requirement that adversarial attacks will adhere to this framework. Thus , it is crucial to proactively anticipate other unexplored adversarial goals in order to make machine learning systems more secure. In this work, we consider a novel and more challenging adversarial goal: reprogramming the model to perform a task chosen by the attacker, without the attacker needing to compute the specific desired output. Consider a model trained to perform some original task: for inputs x it produces outputs f (x). Consider an adversary who wishes to perform an adversarial task:for inputsx (not necessarily in the same domain as x) the adversary wishes to compute a function g(x). We show that an adversary can accomplish this by learning adversarial reprogramming functions h f (·; θ) and h g (·; θ) that map between the two tasks. Here, h f converts inputs from the domain of x into the domain of x (i.e., h f (x; θ) is a valid input to the function f ), while h g maps output of f (h(x; θ)) back to outputs of g (x) . The parameters θ of the adversarial program are then adjusted to achieve h g (f (h f (x))) = g (x).In our work, for simplicity, we definex to be a small image, g a function that processes small images, x a large image, and f a function that processes large images. Our function h f then just consists of drawing x in the center of the large image and θ in the borders (though see Section 4.5 for other schemes), and h g is simply a hard coded mapping between output class labels. However, the idea is more general; h f (h g ) could be any consistent transformation that converts between the input (output) formats for the two tasks and causes the model to perform the adversarial task.We refer to the class of attacks where a model is repurposed to perform a new task as adversarial reprogramming. We refer to θ as an adversarial program. In contrast to most previous adversarial work, the attack does not need to be imperceptible to humans, or even subtle, in order to be considered a success. However, we note that it is still possible to construct reprogramming attacks that are imperceptible. Potential consequences of adversarial reprogramming include theft of computational resources from public facing services, repurposing of AI-driven assistants into spies or spam bots, and abusing machine learning services for tasks violating the ethical principles of system providers. Risks stemming from this type of attack are discussed in more detail in Section 5.2.It may seem unlikely that an additive offset to a neural network's input would be sufficient on its own to repurpose the network to a new task. However, this flexibility stemming only from changes to a network's inputs is consistent with results on the expressive power of deep neural networks. For instance, in BID36 it is shown that, depending on network hyperparameters, the number of unique output patterns achievable by moving along a one-dimensional trajectory in input space increases exponentially with network depth. Further, BID21 shows that networks can often be trained to high accuracy even if parameter updates are restricted to occur only in a low dimensional subspace. An additive offset to a neural network's input is equivalent to a modification of its first layer biases (for a convolutional network with biases shared across space, this operation effectively introduces new parameters because the additive input is not shared across space), and therefore an adversarial program corresponds to an update in a low dimensional parameter subspace.In this paper, we present the first instances of adversarial reprogramming. In Section 2, we discuss related work. In Section 3, we present a training procedure for crafting adversarial programs, which cause a neural network to perform a new task. In Section 4, we experimentally demonstrate adversarial programs that target several convolutional neural networks designed to classify ImageNet data. These adversarial programs alter the network function from ImageNet classification to: counting squares in an image, classifying MNIST digits, and classifying CIFAR-10 images. Next, we examine the susceptibility of trained and untrained networks to adversarial reprogramming. We then demonstrate the possibility of reprograming adversarial tasks with adversarial data that has no resemblance to original data, demonstrating that results from transfer learning do not fully explain adversarial reprogramming. Further, we demonstrate the possibility of concealing adversarial programs and data. Finally, we end in Sections 5 and 6 by discussing and summarizing our results. In this work, we proposed a new class of adversarial attacks that aim to reprogram neural networks to perform novel adversarial tasks. Our results demonstrate for the first time the possibility of such attacks. They are also illustrative of both surprising flexibility and surprising vulnerability in deep neural networks. Future investigation should address the properties and limitations of adversarial reprogramming, and possible ways to mitigate or defend against it.",1478,0.741,837,1.7658303464755079,"Deep neural networks susceptible In computer vision well-crafted perturbations to images make mistakes such confusing a cat a computer Previous adversarial attacks designed degrade performance models or cause machine learning models produce specific outputs chosen ahead We introduce attacks instead reprogram the target model perform chosen without needing specify or compute for each test-time input This attack finds a single adversarial perturbation that can added all test-time inputs in cause chosen—even trained These perturbations thus a program the new task We demonstrate adversarial reprogramming on six ImageNet classification models repurposing a counting task classification: classification MNIST and CIFAR-10 examples presented inputs The study adversarial examples motivated in terms the danger an attacker whose goal cause model prediction errors with a small change Such an attacker make react a phantom stop BID6 by means a sticker (a small L 0 perturbation cause an insurance company's damage model overestimate the claim value from the resulting accident by subtly doctoring photos the damage With this context various methods both construct BID40 BID32 BID3 BID24 defend this style adversarial attack Thus adversarial attacks consisted aim degrade a model without necessarily requiring produce targeted attacks in designs produce for that input For example an attack a classifier a specific desired output class for each input image a reinforcement learning agent induce that agent enter BID22 .In practice there adversarial attacks will adhere this framework Thus , it crucial proactively anticipate other unexplored adversarial goals make machine systems secure In this work consider a novel and more challenging adversarial goal reprogramming the model perform chosen without needing compute the specific desired output Consider a model trained some original task for inputs x it produces outputs f (x Consider an adversary wishes performfor inputsx (not necessarily in wishes compute We show an adversary accomplish learning adversarial reprogramming functions h f·; � that map between Here, h f converts inputs the domain x x while g maps output of back outputs The parameters � of the adversarial program then adjusted achieve h gf (h fx).In our work for simplicity definex to a small image g a function processes small images x Our function h f then just consists drawing x in the large image and �� the borders (though see Section other schemes h g simply a hard coded mapping output class labels However the idea more general; h f (h g could any consistent transformation converts between the input (output) formats for the two tasks causes the model perform the adversarial taskWe refer the class attacks where repurposed as adversarial reprogramming We refer �� an adversarial program In contrast most previous adversarial work the attack does need imperceptible humans subtle considered However we note it still construct reprogramming attacks imperceptible. Potential consequences adversarial reprogramming theft computational resources public facing services repurposing AI-driven assistants spies spam bots abusing machine learning services tasks violating system providers Risks stemming this type attack discussed may seem unlikely an additive offset to on repurpose a new task However this flexibility stemming only changes a network's inputs consistent results on the expressive power For instance BID36 it shown, depending network hyperparameters number unique output patterns achievable moving along in input space increases network depth Further BID21 shows networks often trained high accuracy even parameter updates restricted occur a low dimensional subspace An additive offset a neural network's input equivalent a modification its first layer biasesfor biases shared space this operation effectively introduces new parameters because the additive input shared therefore an adversarial program corresponds an update in a low dimensional parameter subspaceIn the first instances In Section related work In Section present a training procedure crafting adversarial programs cause In Section experimentally demonstrate adversarial programs target designed classify ImageNet data These adversarial programs alter the network function from ImageNet classification: counting squares classifying MNIST digits CIFAR-10 images Next examine the susceptibility trained and untrained networks We then demonstrate the possibility reprograming adversarial tasks that has no resemblance original data demonstrating results transfer learning do fully explain Further demonstrate the possibility concealing adversarial programs data Finally end in Sections by and In this work proposed adversarial attacks aim reprogram Our results demonstrate for the possibility such attacks They also illustrative both surprising flexibility surprising vulnerability deep neural networks Future investigation should address the properties limitations adversarial reprogramming possible ways or defend",0.01,0.6553476073848569
"As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of generalization. This leads to the crucial question of how generalization gap should be predicted from the training data and network parameters. In this paper, we propose such a measure, and conduct extensive empirical studies on how well it can predict the generalization gap. Our measure is based on the concept of margin distribution, which are the distances of training points to the decision boundary. We find that it is necessary to use margin distributions at multiple layers of a deep network. On the CIFAR-10 and the CIFAR-100 datasets, our proposed measure correlates very strongly with the generalization gap. In addition, we find the following other factors to be of importance: normalizing margin values for scale independence, using characterizations of margin distribution rather than just the margin (closest distance to decision boundary), and working in log space instead of linear space (effectively using a product of margins rather than a sum).
 Our measure can be easily applied to feedforward deep networks with any architecture and may point towards new training loss functions that could enable better generalization. Generalization, the ability of a classifier to perform well on unseen examples, is a desideratum for progress towards real-world deployment of deep neural networks in domains such as autonomous cars and healthcare. Until recently, it was commonly believed that deep networks generalize well to unseen examples. This was based on empirical evidence about performance on held-out dataset. However, new research has started to question this assumption. Adversarial examples cause networks to misclassify even slightly perturbed images at very high rates BID9 BID22 . In addition, deep networks can overfit to arbitrarily corrupted data BID10 , and they are sensitive to small geometric transformations BID2 BID6 . These results have led to the important question about how the generalization gap (difference between train and test accuracy) of a deep network can be predicted using the training data and network parameters. Since in all of the above cases, the training loss is usually very small, it is clear that existing losses such as cross-entropy cannot serve that purpose. It has also been shown (e.g. in BID10 ) that regularizers such as weight decay cannot solve this problem either.Consequently, a number of recent works BID21 BID4 BID23 BID1 have started to address this question, proposing generalization bounds based on analyses of network complexity or noise stability properties. However, a thorough empirical assessment of these bounds in terms of how accurately they can predict the generalization gap across various practical settings is not yet available.In this work, we propose a new quantity for predicting generalization gap of a feedforward neural network. Using the notion of margin in support vector machines (Vapnik, 1995) and extension to deep networks BID5 , we develop a measure that shows a strong correlation with generalization gap and significantly outperforms recently developed theoretical bounds on Test Acc. : 55.2% Test Acc. : 70.6% Test Acc. : 85.1% Figure 1 : (Best seen as PDF) Density plots (top) and box plots (bottom) of normalized margin of three convolutional networks trained with cross-entropy loss on CIFAR-10 with varying test accuracy: left: 55.2%, middle: 70.6%, right: 85.1%. The left network was trained with 20% corrupted labels. Train accuracy of all above networks are close to 100%, and training losses close to zero. The densities and box plots are computed on the training set. Normalized margin distributions are strongly correlated with test accuracy (moving to the right as accuracy increases). This motivates our use of normalized margins at all layers. The (Tukey) box plots show the median and other order statistics (see section 3.2 for details), and motivates their use as features to summarize the distributions. generalization 2 . This is empirically shown by studying a wide range of deep networks trained on the CIFAR-10 and CIFAR-100 datasets. The measure presented in this paper may be useful for a constructing new loss functions with better generalization. Besides improvement in the prediction of the generalization gap, our work is distinct from recently developed bounds and margin definitions in a number of ways:1. These recently developed bounds are typically functions of weight norms (such as the spectral, Frobenius or various mixed norms). Consequently, they cannot capture variations in network topology that are not reflected in the weight norms, e.g. adding residual connections BID10 without careful additional engineering based on the topology changes. Furthermore, some of the bounds require specific treatment for nonlinear activations. Our proposed measure can handle any feedforward deep network. 2. Although some of these bounds involve margin, the margin is only defined and measured at the output layer BID4 BID21 . For a deep network, however, margin can be defined at any layer BID5 . We show that measuring margin at a single layer does not suffice to capture generalization gap. We argue that it is crucial to use margin information across layers and show that this significantly improves generalization gap prediction. 3. The common definition of margin, as used in the recent bounds e.g. BID21 , or as extended to deep networks, is based on the closest distance of the training points to the decision boundary. However, this notion is brittle and sensitive to outliers. In contrast, we adopt margin distribution BID7 BID13 Zhang & Zhou, 2017; by looking at the entire distribution of distances. This is shown to have far better prediction power. 4. We argue that the direct extension of margin definition to deep networks BID5 , although allowing margin to be defined on all layers of the model, is unable to capture generalization gap without proper normalization. We propose a simple normalization scheme that significantly boosts prediction accuracy. We have presented a predictor for generalization gap based on margin distribution in deep networks and conducted extensive experiments to assess it. Our results show that our scheme achieves a high adjusted coefficient of determination (a linear regression predicts generalization gap accurately). Specifically, the predictor uses normalized margin distribution across multiple layers of the network. The best predictor uses quartiles of the distribution combined in multiplicative way (additive in log transform). Compared to the strong baseline of spectral complexity normalized output margin BID4 , our scheme exhibits much higher predictive power and can be applied to any feedforward network (including ResNets, unlike generalization bounds such as BID4 BID21 BID1 ). We also find that using hidden layers is crucial for the predictive power. Our findings could be a stepping stone for studying new generalization theories and We use an architecture very similar to Network in Network BID16 ), but we remove all dropout and max pool from the network.Layer Index Layer Type Output Shape 0 Input 32 × 32 × 3 1 3 × 3 convolution + stride 2 16 × 16 × 192 Residual plots for all explanatory variables, row: h0, h1, h2, h3, column: lower fence, Q 1 , Q 2 , Q 3 , upper fence. lower fence is clipped because distance cannot be smaller than 0. The residual is less evenly distributed as are in other two settings; this fact is well reflected in the cluster along the x axis and in theR 2 ; we speculate that this is due to not having diverse enough generalization gap in the models trained to cover the entire space of the ""model"" unlike in the other two settings. 3.45e-13 3.04e-16 9.21e-9 4.07e-4 6.59e-3 h3 4.14e-13 0.60 0.27 7.14e-3 2.4e-10 Table 6 : F score (top) and p-values (bottom) for all 20 variables. Using p = 0.05, we see that the null hypotheses are not rejected for 4 of the variables. We believe having a more diverse generalization behavior in the study will solve this problem. Residual plots for all explanatory variables, row: h0, h1, h2, h3, column: lower fence, Q 1 , Q 2 , Q 3 , upper fence. lower fence is clipped because distance cannot be smaller than 0. The residual is fairly evenly distributed around 0. There is one outlier in this experimental setting as shown in the plots. 9 APPENDIX: SOME OBSERVATIONS AND CONJECTURES Everythig here uses the full quartile description. DISPLAYFORM0",1797,1.084,998,1.8006012024048097,"As shown recent research perfectly fit randomly labeled data with on held out data This phenomenon indicates loss functions such cross This leads generalization gap should predicted network parameters In such a measure conduct well predict the generalization gap Our measure the concept margin distribution are training points the decision boundary We find it necessary margin distributions at multiple layers a deep network On the CIFAR-10 and our proposed measure correlates very the generalization gap In addition find the following other factors normalizing margin values scale independence using characterizations margin distribution rather just (closest distance decision boundary working log spaceeffectively a product margins rather Our measure can feedforward deep networks any architecture may point new training loss functions enable Generalization, the ability a classifier perform well unseen examples progress towards domains autonomous cars healthcare Until commonly deep networks generalize unseen examples This was based empirical evidence about performance held-out dataset However new research started question Adversarial examples cause networks even slightly perturbed images at BID9 BID22 . In addition deep networks overfit to arbitrarily corrupted data BID10 , they sensitive small geometric transformations These results led the generalization gap ( train test accuracy a deep network predicted network parameters Since in all the training loss usually very it clear existing losses such crossentropy serve It shown ( BID10 ) regularizers such weight decay solve eitherConsequently recent works started proposing generalization bounds based analyses network complexity or noise stability properties However, a thorough empirical assessment these bounds in how accurately predict the generalization gap across various practical settingsIn propose a new quantity a feedforward neural network Using the notion margin in support vector machinesVapnik 1995 extension deep networks BID5 , develop generalization gap significantly outperforms recently theoretical bounds Test Acc. : 55.2% Test Acc. : 70.6% Test Acc. : 85.1 Figure (Best seen as PDF Density plotstop normalized margin three convolutional networks trained on with varying test accuracy: left The left network trained with 20% corrupted labels Train accuracy of all above networks are training losses close zero The densities box plots computed the training set Normalized margin distributions strongly test accuracymoving to as accuracy increases This motivates our use normalized margins at all layers The (Tukey) box plots show the median and other order statistics section motivates features summarize generalization 2 . This empirically shown studying deep networks trained The measure presented may a constructing new loss functions with Besides improvement the prediction the generalization gap our work distinct recently developed bounds margin definitions ways:1 These recently developed bounds typically functions weight norms spectral, Frobenius or various mixed norms they capture variations network topology reflected the weight norms adding residual connections BID10 without careful additional engineering based Furthermore some the bounds require specific treatment nonlinear activations Our proposed measure can handle any feedforward deep network 2 Although some these bounds involve margin only and measured the output layer BID4 BID21 For a deep network however margin can defined at any layer BID5 . We show measuring margin at a single layer does suffice capture generalization gap We argue crucial use margin information across layers show significantly generalization gap prediction 3 The common definition margin the recent bounds BID21 , or extended deep networks based the closest distance the training points the decision boundary However this notion brittle sensitive outliers In contrast we adopt margin distribution BID7 BID13 Zhang & Zhou by looking distances This shown far better prediction power 4 We argue the direct extension margin definition deep networks BID5 , although allowing margin unable capture generalization gap without proper normalization We propose significantly boosts prediction accuracy We presented a predictor generalization gap based margin distribution deep networks conducted extensive experiments it Our results our scheme achieves a high adjusted coefficient determinationa linear regression predicts generalization gap accurately Specifically the predictor uses normalized margin distribution across multiple layers The best predictor uses quartiles combined multiplicative wayadditive in log transform Compared the strong baseline spectral complexity normalized output margin BID4 our scheme exhibits can any feedforward network ResNets unlike generalization bounds such We also find using hidden layers crucial the predictive power Our findings could studying new generalization theories We use an architecture very Network in Network BID16 ), remove all dropout and max pool fromLayer Index Layer Type Output Shape 0 Input 32 × 32 × 3 1 3 × 3 convolution + stride 16 × 192 Residual plots all explanatory variables row: h0 column lower fence clipped because distance smaller The residual is less evenly as are in other two settings; this fact well reflected the cluster along theR 2 ; we speculate not diverse enough generalization gap trained cover the ""model unlike : F scoretop all 20 variables Using p = see the null hypotheses rejected 4 the variables We believe having a more diverse generalization behavior will solve Residual plots all explanatory variables row: h0 column lower fence Q 1 upper lower fence clipped because distance smaller residual is fairly evenly 0 There one outlier this experimental setting as shown the plots 9 APPENDIX: CONJECTURES Everythig here uses the full quartile description DISPLAYFORM0",0.01,0.7439406933587188
"We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other complex models. While our focus is theoretical, we also present experiments that illustrate our theoretical findings. Giving provably efficient algorithms for learning neural networks is a core challenge in machine learning theory. The case of convolutional architectures has recently attracted much interest due to their many practical applications. Recently BID2 showed that distributionfree learning of one simple non-overlapping convolutional filter is NP-hard. A natural open question is whether we can design provably efficient algorithms to learn convolutional neural networks under mild assumptions.We consider a convolutional neural network of the form f px, w, aq "" k ÿ j""1 a j σ`w J P j x˘(1)where w P R r is a shared convolutional filter, a P R k is the second linear layer and P j "" r 0 lo omo on pj´1qs I lo omo on r 0 lo omo on d´pj´1qs`r s P R rˆd selects the ppj´1qs`1q-th to ppj´1qs`rq-th coordinates of x with stride s and σ p¨q is the activation function. Note here that both w and a are unknown vectors to be learned and there may be overlapping patches because the stride size s may be smaller than the filter size r.Our Contributions We give the first efficient algorithm that can provably learn a convolutional neural network with two unknown layers with commonly used overlapping patches. Our main result is the following theorem. Theorem 1.1 (Main Theorem (Informal)). Suppose s ě t r 2 u`1 and the marginal distribution is symmetric and isotropic. Then the convolutional neural network defined in equation 1 with piecewise linear activation functions is learnable in polynomial time.We refer readers to Theorem 3.1 for the precise statement.Technical Insights Our algorithm is a novel combination of the algorithm for isotonic regression and the landscape analysis of non-convex problems. First, inspired by recent work on isotonic regression, we extend the idea in BID13 to reduce learning a CNN with piecewise linear activation to learning a convolutional neural network with linear activation (c.f. Section 4). Second, we show learning a linear convolutional filter can be reduced to a non-convex matrix factorization problem which admits a provably efficient algorithm based on non-convex geometry BID8 . Third, in analyzing our algorithm, we present a robust analysis of Convotron algorithm proposed by BID13 , in which we draw connections to the spectral properties of Toeplitz matrices. We believe these ideas may inspire further development in designing provable learning algorithms for neural networks and other complex models.Related Work From the point of view of learning theory, it is well known that training is computational infeasible in the worst case BID12 BID2 . Thus distributional assumptions are needed for efficient learning. A line of research has focused on analyzing the dynamics of gradient descent conditioned on the input distribution being standard Gaussian BID29 BID28 BID21 BID32 BID2 BID31 BID5 . Specifically for convolutional nets, existing analyses heavily relied on the analytical formulas which can only be derived if the input is Gaussian and patches are non-overlapping.Recent work has tried to relax the Gaussian input assumption and the non-overlapping structure for learning convolutional filters. BID5 showed if the patches are sufficiently close to each other then stochastic gradient descent can recover the true filter. BID13 proposed a modified iterative algorithm inspired from isotonic regression that gives the first recovery guarantees for learning a filter for commonly used overlapping patches under much weaker assumptions on the distribution. However, these two analyses only work for learning one unknown convoutional filter.Moving away from gradient descent, various works have shown positive results for learning general simple fully connected neural networks in polynomial time and sample complexity under certain assumptions using techniques such as kernel methods BID12 BID30 BID10 BID0 and tensor decomposition BID27 BID18 . The main drawbacks include the shift to improper learning for kernel methods and the knowledge of the probability density function for tensor methods. In contrast to this, our algorithm is proper and does not assume that the input distribution is known.Learning a neural network is often formulated as a non-convex problem. If the objective function satisfies (1) all saddle points and local maxima are strict (i.e., there exists a direction with negative curvature), and (2) all local minima are global (no spurious local minmum), then noise-injected (stochastic) gradient descent BID7 BID19 ) finds a global minimum in polynomial time. Recent work has studied these properties for the landscape of neural networks BID20 BID3 BID15 BID14 BID22 BID6 BID25 Zhou & Feng, 2017; BID23 BID0 BID9 Zhou & Feng, 2017; BID26 BID4 . A crucial step in our algorithm is reducing the convolutional neural network learning problem to matrix factorization and using the geometric properties of matrix factorization. In this paper, we propose the first efficient algorithm for learning a one-hidden-layer convolutional neural network with possibly overlapping patches. Our algorithm draws ideas from isotonic regression, landscape analysis of non-convex problem and spectral analysis of Toeplitz matrices. These findings can inspire further development in this field. Our next step is extend our ideas to design provable algorithms that can learn complicated models consisting of multiple filters. To solve this problem, we believe the recent progress on landscape design BID9 may be useful.",1211,0.595,637,1.901098901098901,"We propose learn where the outputs weights parameters learned Our algorithm a general class ( overlapping patches including commonly used structures for computer vision tasks Our algorithm draws ideas (1) isotonic regression for learning non-convex matrix factorization problems We believe these findings may inspire designing provable algorithms learning While our focus theoretical also present experiments illustrate our theoretical findings Giving provably efficient algorithms for learning The case convolutional architectures recently Recently BID2 showed distributionfree learning of NP A natural open question design provably efficient algorithms learn under mild assumptionsWe consider of f px, w aq "" k �� j""1 a j ��`w J P j x�� P R the second linear layer "" r 0 lo omo on pj´1qs I lod selects-th to x with stride s and �� p¨q Note here both w and a unknown vectors to learned there overlapping patches because the stride size sOur Contributions give the first efficient algorithm provably two unknown layers with commonly used overlapping patches Our main result the following theorem Theorem (Main Theorem (Informal Suppose s �� t r 2 u`1 and the marginal distribution Then defined equation with piecewise linear activation functions learnableWe refer readers Theorem the precise statementTechnical Insights Our algorithm a novel combination isotonic regression the landscape analysis First inspired recent work isotonic regression extend in BID13 reduce learning a CNN with piecewise linear activation to learning Second show learning a linear convolutional filter can reduced which admits a provably efficient algorithm based BID8 . Third analyzing our algorithm present Convotron algorithm proposed BID13 , draw connections the spectral properties Toeplitz matrices We believe these ideas may inspire designing provable learning algorithmsRelated Work From the point learning theory well training is computational BID12 BID2 . Thus distributional assumptions needed efficient learning A line research focused analyzing gradient descent conditioned the input distribution being standard Gaussian BID29 BID28 BID21 BID32 BID2 BID31 BID5 . Specifically convolutional nets existing analyses heavily the analytical formulas which can if patches nonRecent work tried relax for learning BID5 showed if the patches sufficiently close recover the true filter BID13 proposed a modified iterative inspired from isotonic regression that gives the first recovery guarantees learning a filter commonly overlapping patches under much weaker assumptions on However these two analyses only work learning one unknown convoutional filterMoving away gradient descent various works positive results general simple fully connected neural networks sample complexity under certain assumptions using techniques kernel methods BID12 BID30 BID10 BID0 . The main drawbacks include the shift improper learning for kernel methods the knowledge the probability density function tensor methods In contrast our algorithm proper does assume the input distribution knownLearning often formulated If the objective function satisfies ( all saddle points local maxima strict a direction and global (no spurious local minmum noise-injected (stochastic) gradient descent BID7 BID19 ) finds Recent work studied these properties the landscape & Feng; . A crucial step our algorithm reducing matrix using the geometric properties In learning possibly overlapping patches Our algorithm draws ideas isotonic regression landscape analysis of non-convex problem and spectral analysis Toeplitz matrices These findings can inspire Our next step extend our ideas design provable algorithms learn complicated models consisting multiple filters To solve believe the recent progress landscape design BID9 may",0.01,1.0
"Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. Augmenting the loss by a regularization term that penalizes the deviation of the gradient norm of the critic (as a function of the network's input) from one, was proposed as an alternative that improves training. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on several data sets. General adversarial networks (GANs) BID8 are a class of generative models that have recently gained a lot of attention. They are based on the idea of defining a game between two competing neural networks (NNs): a generator and a classifier (or discriminator). While the classifier aims at distinguishing generated from real data, the generator tries to generate samples which the classifier can not distinguish from the ones from the empirical distribution. Realizing the potential behind this new approach to generative models, more recent contributions focused on the stabilization of training, including ensemble methods BID18 , improved network structure BID14 BID15 and theoretical improvements BID13 BID15 that helped to successfully model complex distributions using GANs.It was proposed by to train generator and discriminator networks by minimizing the Wasserstein-1 distance, a distance with properties superior to the Jensen-Shannon distance (used in the original GAN) in terms of convergence. Accordingly, this version of GAN was called Wasserstein GAN (WGAN) . The change of metric introduces a new minimization problem, which requires the discriminator function to lie in the space of 1-Lipschitz functions. In the same paper, the Lipschitz constraint was guaranteed by performing weight clipping, i.e., by constraining the parameters of the discriminator NN to be smaller than a given value in magnitude. An improved training strategy was proposed by BID9 based on results from optimal transport theory (see BID19 . Here, instead of clipping weights, the loss gets augmented by a regularization term that penalizes any deviation of the norm of the gradient of the critic function (with respect to its input) from one.We review these results and present both theoretical considerations and empirical results, leading to the proposal of a less restrictive regularization term for WGANs.1 More precisely, our contributions are as follows:• We review the arguments that the regularization technique proposed by BID9 is based on and make the following two observations: (i) The regularization strategy requires training samples and generated samples to be drawn from a certain joint distribution. In practice, however, samples are drawn independently from their marginals.(ii ) The arguments further assume the discriminator to be differentiable. We explain why both can be harmful for training.• We propose a less restrictive regularization term and present empirical results strongly supporting our theoretical considerations. For stable training of Wasserstein GANs, we propose to use the following penalty term to enforce the Lipschitz constraint that appears in the objective function: DISPLAYFORM0 We presented theoretical and empirical evidence that this gradient penalty performs better than the previously considered approaches of clipping weights and of applying the stronger gradient penalty given by Ex ∼τ [(||∇f (x)|| 2 − 1) 2 ]. In addition to more stable learning behavior, the proposed regularization term leads to lower sensitivity to the value of the penalty weight λ (demonstrating smooth convergence and well-behaved critic scores throughout the whole training process for different values of λ).",780,0.35,455,1.7142857142857142,"Since their invention generative adversarial networks learning a distribution Convergence problems during training overcome Wasserstein GANs which minimize the model the empirical distribution in a different metric thereby introduce a Lipschitz constraint into A simple way enforce the Lipschitz constraint functions modeled weight clipping Augmenting the loss by a regularization term penalizes the deviation the gradient norm the critic (as the network's input from one, was proposed that improves training We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint These arguments supported experimental results on General adversarial networks (GANs) BID8 generative models They based defining a game between): a generatoror While the classifier aims distinguishing generated from the generator generate samples which not the ones from the empirical distribution Realizing behind generative models more recent contributions focused the stabilization training, ensemble methods BID18 , improved network structure BID14 BID15 and theoretical improvements that helped successfully complex distributions using GANsIt proposed to train generator and minimizing the Wasserstein-1 distance a distance with properties superior the Jensen-Shannon distanceused convergence Accordingly this version GAN was called Wasserstein GANWGAN . The change metric introduces the discriminator function lie 1-Lipschitz functions In the same paper the Lipschitz constraint guaranteed performing weight clipping constraining the discriminator NN smaller magnitude An improved training strategy was BID9 based results optimal transport theorysee . Here instead clipping weights the loss gets augmented a regularization term penalizes any deviation the critic functionwith its input one.We review present both theoretical considerations leading WGANs.1 More our contributions as review proposed BID9 based make requires training samples generated samples drawn a certain joint distribution In practice samples drawn independently their marginals.(ii ) The arguments further assume the discriminator differentiable We explain both can harmful training.• propose a less restrictive regularization term present empirical results strongly our theoretical considerations For stable training Wasserstein GANs propose the following penalty term enforce the Lipschitz constraint that appears the objective function DISPLAYFORM0 We presented this gradient penalty performs the previously considered approaches clipping weights of applying given Ex ∼τ [(||��f 2 − 2 In addition more stable learning behavior the proposed regularization term leads lower sensitivity the value the penalty weight �� smooth convergence well-behaved critic scores throughout for different values",0.0,0.5240164132271301
"We introduce a new method for training GANs by applying the Wasserstein-2 metric proximal on the generators. 
 The approach is based on the gradient operator induced by optimal transport, which connects the geometry of sample space and parameter space in implicit deep generative models. From this theory, we obtain an easy-to-implement regularizer for the parameter updates. Our experiments demonstrate that this method improves the speed and stability in training GANs in terms of wall-clock time and Fr\'echet Inception Distance (FID) learning curves. Generative Adversarial Networks (GANs) BID11 are a powerful approach to learning generative models. Here, a discriminator tries to tell apart the data generated from a real source and the data generated by a generator, whereas the generator tries to fool the discriminator. This adversarial game is formulated as an optimization problem over an implicit generative model for the generator. An implicit generative model is a parametrized family of functions mapping a noise source to sample space. In trying to fool the discriminator, the generator should try to recreate the density distribution from the real source.The problem of matching a target density can be formulated as the minimization of a discrepancy measure. The Kullback-Leibler (KL) divergence is known to be difficult when the distributions have a low dimensional support set, as is commonly the case in applications with structured data and high dimensional sample spaces. An alternative approach to define a discrepancy measure between densities is optimal transport, a.k.a. Wasserstein distance, or Earth Mover's distance. This has been used recently to define the loss function for learning generative models BID30 BID10 . In particular, the Wasserstein GAN BID4 has attracted much interest in recent years.Besides defining the loss function, optimal transport can also be used to introduce structures serving the optimization itself, in terms of the gradient operator. In full probability space, this is known as the Wasserstein steepest descent flow BID15 BID32 . In this paper we derive the Wasserstein steepest descent flow for deep generative models in GANs. We use the Wasserstein-2 metric function, which allows us to obtain a Riemannian structure and a corresponding natural (i.e., Riemannian) gradient. A well known example of a natural gradient is the Fisher-Rao natural gradient, which is induced by the KL divergence. In learning problems, one often finds that the natural gradients can offer advantages compared to the Euclidean gradient BID1 BID2 . In GANs, because of the low dimensional support sets and the associated difficulties with the KL divergence, the Fisher-Rao natural gradient is problematic. Therefore, we propose to use the gradient operator induced by the Wasserstein-2 metric BID21 b) .We compute the proximal operator for the generators of GANs, where the regularization is the squared constrained Wasserstein-2 distance. In practice, the constrained distance can be approximated by a simple neural network. In implicit generative models, the constrained Wasserstein-2 metric exhibits a simple structure. We generalize the metric and introduce the relaxed proximal operator for generators, which allows us to further simplify the computation. The resulting relaxed proximal operator involves only the difference of outputs, so that the proximal computation has very simple parameter updates. The method can be easily implemented and used as a drop-in regularizer for the generator updates. This paper is organized as follows. In Section 2, we briefly introduce the Wasserstein natural gradient. A Wasserstein proximal method is introduced in Algorithm 1. In Section 3, we demonstrate the effectiveness of the proposed methods in experiments with various types of GANs. Section 4 reviews related work. In this work, we apply the constrained Wasserstein gradient and its relaxations on implicit generative models. Whereas much work has focused on regularizing the discriminator, in this work we focus on regularizing the generator. For Wasserstein GAN (with gradient penalty), we compute the Wasserstein-2 gradient flow of Wasserstein-1 distance on parameter space. Experimentally, the proposed method allows us to obtain a better minimizer in the sense of FID, with faster convergence speeds in wall-clock time.",841,0.519,492,1.7093495934959348,"We introduce training GANs by applying the Wasserstein-2 metric proximal on the generators The approach the gradient operator induced optimal transport connects the geometry sample space parameter space implicit deep generative models From this theory obtain the parameter updates Our experiments demonstrate this method improves in training GANs terms wall-clock time Fr\'echet Inception Distance learning curves Generative BID11 are learning Here a discriminator tries tell apart generated a real source whereas fool This adversarial game formulated an optimization problem over an implicit generative model the generator An implicit generative model functions mapping a noise source sample In trying fool the discriminator the generator should recreate the density distributionThe problem matching can formulated the minimization a discrepancy measure Kullback-Leibler ( divergence known difficult when the distributions have a low dimensional support set commonly applications structured data high dimensional sample spaces An alternative approach define a discrepancy measure between densities optimal transport Wasserstein distance Earth Mover's distance This has used recently define the loss function learning generative models BID30 BID10 In particular the Wasserstein GAN BID4 has attractedBesides defining the loss function optimal transport can introduce structures serving the optimization itself the gradient operator In full probability space known Wasserstein steepest descent flow BID15 BID32 . In derive the Wasserstein steepest descent flow for deep generative models GANs and A well known example a natural gradient the Fisher-Rao natural gradient induced the KL divergence In learning problems one the natural gradients can offer advantages compared the Euclidean gradient BID1 BID2 In GANs because the low dimensional support sets the associated difficulties the KL divergence the Fisher-Rao natural gradient problematic Therefore the gradient operator induced the Wasserstein-2 metric BID21 b) .We compute the proximal operator the generators GANs In practice the constrained distance can approximated In implicit generative models constrained Wasserstein-2 metric exhibits We generalize the metric and introduce the relaxed proximal operator for generators further The resulting relaxed proximal operator involves only the difference outputs has very simple parameter updates The method can easily and the generator updates This paper organized In Section briefly introduce the Wasserstein natural gradient A Wasserstein proximal method introduced Algorithm In Section demonstrate the proposed methods experiments various types GANs Section reviews related work In this work apply the constrained Wasserstein gradient its relaxations implicit generative models Whereas much work focused regularizing the discriminator in the generator For Wasserstein GAN (with gradient penalty compute of on parameter space Experimentally the proposed method allows obtain a better minimizer FID, faster convergence speeds in wall-clock time",0.01,0.511439611137603
"Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables.
 MDPs and POMDPS, widely used for planning under uncertainty can also be represented by influence diagrams.
 The time and space complexity of computing the maximum expected utility (MEU) and its maximizing policy is exponential in the induced width of the underlying graphical model, which is often prohibitively large due to the growth of the information set under the sequence of decisions.
 In this paper, we develop a weighted mini-bucket approach for bounding the MEU.  These bounds can be used as a stand-alone approximation that can be improved as a function of a controlling i-bound parameter .
They can also be used as heuristic  functions to guide search, especially for planning 
 such as MDPs and POMDPs.
 We evaluate the scheme empirically against state-of-the-art, thus illustrating its potential.
 An influence diagram (ID) BID4 ) is a graphical model for sequential decision-making under uncertainty that compactly captures the local structure of the conditional independence of probability functions and the additivity of utility functions. Its structure is captured by a directed acyclic graph (DAG) over nodes representing the variables (decision and chance variables). The standard query on an ID is finding the maximum expected utility (MEU) and the corresponding optimal policy for each decision, subject to the history of observations and decisions.Computing the MEU is recognized as one of the hardest tasks over graphical models, and hence recent work aims at developing anytime bounding schemes that tighten the bounds if more time and memory is available. Often, the target is to incorporate such bounds as heuristic functions to guide search algorithms. In this paper, we focus on computing the upper bound of MEU for a single agent sequential decision making problem with no-forgetting assumptions. We build on the methodology of weighted mini-bucket with costshifting that was used in the past for bounding probabilistic queries such as the partition function, Maximum A Posteriori (MAP) and Marginal MAP (MMAP) BID0 BID12 BID5 BID14 BID13 ). We presented a new bounding scheme for influence diagrams, called WMBE-ID, which computes upper bounds of the MEU by interleaving variable elimination with optimizing partial decomposition within each variable's bucket. Compared with the previous approaches, our proposed upper bounding scheme produces high quality upper bounds in shorter time bounds. This is instrumental for our plan to Table 2 : The performance of the bounding schemes on individual instances. n is the number of variables, f is the number of functions, k is the maximum domain size, s is the maximum scope size, w is the constrained induced width. We show the (time, upper bound) for various i-bounds and number of iterations for algorithms updating the costs or weights. WMBE-U is the mini-bucket elimination with uniform weights, WMBE-UC preforms cost shifting without optimizing the weight, WMBE-WC optimizes both weights and costs, JGDID is the fully decomposed bound over a join graph that optimizes both weights and costs, MBE is the simple mini-bucket elimination, and MBE-Re is mini-bucket elimination with relaxed variable ordering. MBE, MBE-RE, and WMBE-U do not optimize the bound. The best upper bounds are highlighted. Table 3 : Comparing the ratio of time and quality of upper bounds against JGDID(i=1). WMBE-UC and WMBE-WC were provided with i-bound 10 and 15 with the number of iteration fixed to 5, and JGDID were provided i-bound 1 and 10 with the maximum number iteration limited by 100. All the quantities are normalized by the statistics of JGDID(i=1). DISPLAYFORM0 use such bounds as a heuristic evaluation function for search algorithms for solving influence diagrams.",808,0.424,476,1.6974789915966386,"Influence diagrams provide sequential decision problems representing by the preferences utility functions over decision variables MDPs POMDPS widely planning under uncertainty can represented influence diagrams The time and space complexity computing the maximum expected utility its maximizing policy is exponential the induced width the underlying graphical model often due the growth set under the sequence decisions In develop a weighted mini-bucket approach bounding the MEU. These bounds that improved as a controlling i-bound parameter . They can heuristic functions guide search especially planning such MDPs POMDPs We evaluate the scheme against state thus illustrating. An influence diagram (ID) BID4 ) sequential decision-making under uncertainty that compactly the local structure the conditional independence probability functions the additivity Its structure captured a directed acyclic graph over nodes representing the variablesdecision chance variables The standard query on an ID finding the maximum expected utility the corresponding optimal policy each decision subject the history observations decisionsComputing recognized over graphical models hence recent work aims anytime bounding schemes tighten if more time memory Often the target to incorporate such bounds heuristic functions guide search algorithms In focus computing MEU for a single agent sequential decision making problem no-forgetting assumptions We build the methodology weighted mini with costshifting that bounding probabilistic queries such the partition function Maximum A Posteriori (MAP Marginal MAP BID0 ). We presented a new bounding scheme influence diagrams called WMBE-ID upper bounds the MEU by interleaving variable elimination optimizing partial decomposition within each variable's bucket Compared the previous approaches our proposed upper bounding scheme produces high quality upper bounds shorter time bounds This instrumental our plan Table : The performance the bounding schemes individual instances n is variables f k the constrained induced width We show the (time, upper bound for various i-bounds number algorithms updating the costs or weights WMBE-U is the mini-bucket elimination with uniform weights WMBE-UC preforms cost shifting without optimizing both weights costs JGDID fully decomposed bound over a join graph that MBE relaxed variable ordering MBE do optimize the bound. The best upper bounds highlighted Table 3 : the ratio time quality upper bounds against JGDID(i=1 WMBE-UC and WMBE-WC provided ibound 10 and with the number iteration fixed JGDID were i limited 100 All the quantities normalized the statistics JGDID(i=1 DISPLAYFORM0 use such bounds a heuristic evaluation function search algorithms solving influence diagrams",0.0,0.4811943604378755
"Probabilistic Neural Networks deal with various sources of stochasticity: input noise, dropout, stochastic neurons, parameter uncertainties modeled as random variables, etc.
 In this paper we revisit a feed-forward propagation approach that allows one to estimate for each neuron its mean and variance w.r.t. all mentioned sources of stochasticity. In contrast, standard NNs propagate only point estimates, discarding the uncertainty.
 Methods propagating also the variance have been proposed by several authors in different context. The view presented here attempts to clarify the assumptions and derivation behind such methods, relate them to classical NNs and broaden their scope of applicability.
 The main technical contributions are new approximations for the distributions of argmax and max-related transforms, which allow for fully analytic uncertainty propagation in networks with softmax and max-pooling layers as well as leaky ReLU activations.
 We evaluate the accuracy of the approximation and suggest a simple calibration. Applying the method to networks with dropout allows for faster training and gives improved test likelihoods without the need of sampling. Despite the massive success of Neural Networks (NNs) considered as deterministic predictors, there are many scenarios where a probabilistic treatment is highly desirable. One of the best known techniques to improve the network generalization is dropout BID29 , which introduces multiplicative Bernoulli noise in the network. At test time, however, it is commonly approximated by substituting the mean value of the noise variables. Computing the expectation more accurately by Monte Carlo (MC) sampling has been shown to improve test likelihood and accuracy BID29 BID5 but is computationally expensive.Another challenging problem in NNs is the sensitivity of the output to perturbations of the input, in particular random and adversarial perturbations BID19 BID3 BID23 . In FIG6 we illustrate the point that the average of the network output under noisy input differs from propagating the clean input. It is therefore desirable to estimate the output uncertainty resulting from the uncertainty of the input. In classification networks, propagating the uncertainty of the input can impact the confidence of the classifier and its robustness BID1 . We would like that a classifier is not overconfident when making errors. However such high confidences of wrong predictions are typically observed in NNs. Similarly, when predicting real values (e.g. in optical flow estimation), it is desirable to estimate also their confidences. Taking into account uncertainties from input or dropout allows to predict output uncertainties better correlated with the test error BID14 BID6 BID26 . Another important problem is overfitting, which may be addressed in a sound way with Bayesian learning. The parameters are considered as random variables and are determined up to an uncertainty implied by the training data. This uncertainty needs then to be propagated to predictions at the test-time.The above scenarios motivate considering NNs with different sources of stochasticity not as deterministic feed-forward networks but as directed probabilistic graphical models. We focus on the We have described uncertainty propagation method for approximate inference in probabilistic neural networks that takes into account all noises analytically. Latent variable models allow a transparent interpretation of standard propagation in NNs as the simplest approximation and facilitate the devel- Table 3 : Results for All-CNN on CIFAR-10 test set: negative log likelihood (NLL) and accuracy. Left: state of the art results for this network BID6 , table 3). Middle: All-CNN trained with standard dropout (our learning schedule and analytic normalization) evaluated using different test-time methods. Observe that ""AP2 calibrated"" well approximates dropout: the test likelihood is better than MC-100. Right: All-CNN trained with analytic dropout (same schedule and normalization). Observe that ""AP2 calibrated"" achieves the best likelihood and accuracy.opment of variance propagating approximations. We proposed new such approximations allowing to handle max, argmax, softmax and log-softmax layers using latent variable models ( § 4 and § A.2).We measured the quality of the approximation of posterior in isolated layers and complete networks. The accuracy is improved compared to standard propagation and is sufficient for several use cases such as estimating statistics over the dataset (normalization) and dropout training, where we report improved test likelihoods. We identified the factorization assumption as the weakest point of the approximation. While modeling of correlations is possible (e.g. BID22 , it is also more expensive. We showed that a calibration of a cheap method can give a significant improvement and thus is a promising direction for further research. Argmax and softmax may occur not only as the final layer but also inside the network, in models such as capsules BID25 or multiple hypothesis BID11 , etc. Further applications of the developed technique may include generative and semi-supervised learning and Bayesian model estimation.",956,0.567,527,1.8140417457305502," deal various sources input dropout neurons parameter uncertainties modeled In revisit a feed-forward propagation approach one estimate for all mentioned sources In contrast standard NNs propagate only point estimates discarding Methods propagating also the variance have proposed different context The view presented attempts derivation behind such methods relate classical NNs broaden The main technical contributions the distributions argmax max-related transforms fully analytic uncertainty propagation networks softmax and max-pooling layers as leaky ReLU activations We evaluate the approximation suggest a simple calibration Applying networks dropout allows faster training gives improved test likelihoods without sampling Despite considered deterministic predictors many scenarios highly One the network generalization dropout BID29 , introduces At test time however commonly approximated the noise variables Computing the expectation more Monte Carlo has test likelihood accuracy BID29 BID5 butAnother challenging problem NNs In FIG6 we the point the average the network output under noisy input differs propagating the clean input It therefore desirable estimate the output uncertainty resulting In classification networks propagating the uncertainty can impact its robustness BID1 We would that a classifier errors However such high confidences wrong predictions typically observed NNs Similarly predicting real values optical flow estimation desirable estimate also Taking account uncertainties from input or dropout allows output uncertainties better correlated the test error BID14 BID6 BID26 . Another important problem overfitting addressed a sound way Bayesian learning The parameters considered random variables up an uncertainty implied This uncertainty needs then propagated predictions at the test-timeThe above scenarios motivate considering NNs different sources not We focus We described uncertainty propagation method approximate inference that takes all noises analytically Latent variable models allow a transparent interpretation standard propagation NNs the simplest approximation and facilitate the devel- Table : Results All-CNN on test negative log likelihood accuracy. Left state this network BID6 , table Middle: All-CNN trained with standard dropout (our learning schedule analytic normalization evaluated using different test-time methods Observe ""AP2 calibrated well approximates dropout: the test likelihood better MC-100 Right: All-CNN trained with analytic dropout (same schedule normalization Observe ""AP2 calibrated achieves the best likelihood and accuracy.opment variance propagating approximations We proposed new such approximations allowing handle max, argmax softmax log-softmax layers using latent variable models § 4 and § A.2).We measured posterior in isolated layers complete networks The accuracy is improved compared standard propagation sufficient estimating statistics over the dataset (normalization dropout training report improved test likelihoods We identified the factorization assumption While modeling of correlations possible BID22 , it more expensive. We showed a calibration a cheap method give and thus is Argmax softmax may occur not the final layer inside models capsules BID25 multiple hypothesis , etc Further applications the developed technique",0.01,0.7781860168794809
"Generative Adversarial Networks are one of the leading tools in generative modeling, image editing and content creation. 
 However, they are hard to train as they require a delicate balancing act between two deep networks fighting a never ending duel. Some of the most promising adversarial models today minimize a Wasserstein objective. It is smoother and more stable to optimize. In this paper, we show that the Wasserstein distance is just one out of a large family of objective functions that yield these properties. By making the discriminator of a GAN robust to adversarial attacks we can turn any GAN objective into a smooth and stable loss. We experimentally show that any GAN objective, including Wasserstein GANs, benefit from adversarial robustness both quantitatively and qualitatively. The training additionally becomes more robust to suboptimal choices of hyperparameters, model architectures, or objective functions. Generative adversarial networks (GANs) BID4 are at the forefront of generative modeling. They cast generative modeling as a never ending duel between two networks: a generator network produces synthetic samples from random noise and a discriminator network distinguishes synthetic from real data samples. GANs produce visually appealing samples, but are often hard to train. Much recent work, tries to stabilize GAN training through novel architecture BID25 BID3 or training objectives BID17 BID6 .In this paper, we show that GAN objectives significantly stabilize, if the discriminator is robust to adversarial attacks. Specifically , we show that a robust discriminator leads to a robust minimax objective for the generator irrespective of the training objective used. In addition , any training objective is smooth and Lipschitz as long as the discriminator is Lipschitz. Finally, we show that this robustness does not need to be enforced for every single input of the discriminator, but rather just in expectation over the generated samples. We present two new regularization terms, borrowed from the adversarial training literature. Both terms ensure the robustness of the discriminator. They are easy to optimize and can be added to any existing GAN objective.Our experiments show that adversarial robustness both improves the visual quality of the results, as well as stabilizes the training procedure across a wide range of architectures, hyper-parameters and training objectives. We will publish the code and data used to perform our experiments upon acceptance. In this paper, we established a clear connection between robust discriminators in generative adversarial networks and the overall smoothness of the optimization and the quality of the results. To our knowledge, we are the first to show that a robustness regularization guarantees a smooth and robust loss function for any GAN objective. Finally, our results suggest that robust regularization leads to better training and visual results than standard gradient penalties.",537,0.353,313,1.7156549520766773,"Generative Adversarial Networks one generative modeling image editing However they hard train as require two deep networks fighting never duel Some the most promising adversarial models today minimize a Wasserstein objective It smoother optimize. In the Wasserstein distance just out a large family objective functions yield these properties By making the discriminator a GAN robust adversarial attacks we turn any GAN objective a smooth and stable loss We experimentally show any GAN objective Wasserstein GANs benefit adversarial robustness both The training additionally becomes robust to suboptimal choices hyperparameters model architectures objective functions Generative adversarial networks (GANs) BID4 at generative modeling They cast generative modeling never duel two networks a generator network produces synthetic samples random noise synthetic from GANs produce visually appealing samples hard train Much recent work, tries stabilize GAN training through novel architecture BID25 BID3 or training objectives .In significantly stabilize, if the discriminator robust adversarial attacks Specifically , show a robust discriminator leads a robust minimax objective the generator irrespective the training objective used In addition , any training objective smooth Lipschitz as long Finally show this robustness does need enforced every single input of just expectation over the generated samples We present two new regularization terms borrowed the adversarial training literature Both terms ensure the robustness the discriminator They easy optimize added any existing GAN objectiveOur experiments adversarial robustness both across We will publish data used perform upon acceptance In established a clear connection robust discriminators the overall smoothness the optimization and the quality To our knowledge we show a robustness regularization guarantees any GAN objective Finally our results robust regularization leads better training visual results standard gradient penalties",0.0,0.5275051108185871
"We propose a method to learn stochastic activation functions for use in probabilistic neural networks.
 First, we develop a framework to embed stochastic activation functions based on Gaussian processes in probabilistic neural networks.
 Second, we analytically derive expressions for the propagation of means and covariances in such a network, thus allowing for an efficient implementation and training without the need for sampling.
 Third, we show how to apply variational Bayesian inference to regularize and efficiently train this model.
 The resulting model can deal with uncertain inputs and implicitly provides an estimate of the confidence of its predictions.
 Like a conventional neural network it can scale to datasets of arbitrary size and be extended with convolutional and recurrent connections, if desired. The popularity of deep learning and the implied race for better accuracy and performance has lead to new research of the fundamentals of neural networks. Finding an optimal architecture often focusses on a hyperparameter search over the network architecture, regularization parameters, and one of a few standard activation functions: tanh, ReLU BID5 ), maxout ) . . . Focussing on the latter, looking into activation functions has only taken off since BID12 introduced the rectified linear unit (ReLU), which were shown to produce significantly better results on image recognition tasks BID10 . BID11 then introduced the leaky ReLU, which has a very small, but non-zero, slope for negative values. BID8 proposed the parameterized ReLU, by making the slope of the negative part of the leaky ReLU adaptable. It was trained as an additional parameter for each neuron alongside the weights of the neural network using stochastic gradient descent. Thus, the activation function was not treated as a fixed hyper-parameter anymore but as adaptable to training data. While the parameterized ReLU only has one parameter, this was generalized in BID0 to piecewise linear activation functions that can have an arbitrary (but fixed) number of points where the function changes it slope. This can be interpreted as a different parameterization of a Maxout network ), in which each neuron takes the maximum over a set of different linear combinations of its inputs.Instead of having a fixed parameter for the negative slope of the ReLU, BID18 introduced stochasticity into the activation function by sampling the value for the slope with each training iteration from a fixed uniform distribution. BID3 and BID9 replaced the negative part of ReLUs with a scaled exponential function and showed that, under certain conditions, this leads to automatic renormalization of the inputs to the following layer and thereby simplifies the training of the neural networks, leading to an improvement in accuracy in various tasks.Nearly fully adaptable activation functions have been proposed by BID4 . The authors use a Fourier basis expansion to represent the activation function; thus with enough coefficients any (periodic) activation function can be represented. The coefficients of this expansion are trained as network parameters using stochastic gradient descent or extensions thereof.Promoting a more general approach, BID1 proposed to learn the activation functions alongside the layer weights. Their adaptive piecewise linear units consist of a sum of hinge-shaped functions with parameters to control the hinges and the slopes of the linear segments. However, by construction the derivative of these activation functions is not continuous at the joints between two linear segments, which often leads to non-optimal optimizer performance.To our knowledge, previous research on learning activation functions took place in a fully deterministic setting, i.e. deterministic activation functions were parameterized and included in the optimization of a conventional neural network. Here instead, we explore the setting of probabilistic activation functions embedded in a graphical model of random variables resembling the structure of a neural network. We develop the theory of Gaussian-process neurons and subsequently derive a lower-bound approximation using variational inference, in order to develop a computationally efficient version of the Gaussian Process neuron. We have presented a non-parametric model based on GPs for learning of activation functions in a multi-layer neural network. We then successively applied variational to make fully Bayesian inference feasible and efficient while keeping its probabilistic nature and providing not only best guess predictions but also confidence estimations in our predictions. Although we employ GPs, our parametric approximation allows our model to scale to datasets of unlimited size like conventional neural networks do.We have validated networks of Gaussian Process Neurons in a set of experiments, the details of which we submit in a subsequent publication. In those experiments, our model shows to be significantly less prone to overfitting than a traditional feed-forward network of same size, despite having more parameters.",902,0.482,491,1.8370672097759675,"We propose learn stochastic activation functions use First develop embed stochastic activation functions based Gaussian processes Second analytically derive expressions the propagation means covariances such a network thus and training without sampling Third show apply regularize efficiently train The resulting model can deal uncertain inputs implicitly provides the confidence Like a conventional neural network it scale datasets be extended if The popularity deep learning the implied race better accuracy lead of the fundamentals Finding an optimal architecture often focusses a hyperparameter search over the network architecture regularization parameters one a few standard activation functions tanh ReLU BID5 ), maxout ) . . latter looking into activation functions has only taken BID12 introduced the rectified linear unitReLU were shown produce BID10 . BID11 then introduced the leaky ReLU, very, nonzero slope for negative values BID8 proposed the parameterized ReLU by making the slope the negative part leaky ReLU adaptable It trained an additional parameter each neuron alongside the weights using Thus the activation function treated a fixed hyper anymore but adaptable training data While the parameterized ReLU only was generalized BID0 piecewise linear activation functions have points where changes it slope This can interpreted a different parameterization a Maxout network ), in each neuron takes over different linear combinationsInstead the negative slope BID18 introduced sampling for with each training iteration from BID3 and replaced the negative part ReLUs a scaled exponential function showed, under leads automatic renormalization the following layer and thereby, leadingNearly fully adaptable activation functions . The authors use a Fourier basis expansion represent the activation function; thus with enough coefficients any (periodic) activation function The coefficients this expansion trained network parameters using or extensions thereofPromoting BID1 proposed learn alongside the layer weights Their adaptive piecewise linear units consist hinge-shaped functions parameters to control the hinges the slopes However by construction the derivative these activation functions continuous the joints between two linear segments often non-optimal optimizer performanceTo previous research learning activation functions took a fully deterministic setting parameterized included Here instead explore the setting probabilistic activation functions embedded random variables resembling We develop the theory Gaussian-process neurons subsequently derive a lower-bound approximation using develop We presented based GPs for learning activation functions We then successively applied variational to make fully Bayesian inference feasible efficient while providing not only best guess predictions our predictions Although employ GPs our parametric approximation allows our model scale datasets unlimited size like conventional neural networks doWe validated networks the details submit In those experiments our model to significantly prone a traditional feed-forward network of same size despite more parameters",0.01,0.8368528762720526
"Recent results from linear algebra stating that any matrix can be decomposed into products of diagonal and circulant matrices has lead to the design of compact deep neural network architectures that perform well in practice. In this paper, we bridge the gap between these good empirical results 
 and the theoretical approximation capabilities of Deep diagonal-circulant ReLU networks. More precisely, we first demonstrate  that a Deep diagonal-circulant ReLU networks of
 bounded width and small depth can approximate a deep ReLU network in which the dense matrices are
 of low rank. Based on this result, we provide new bounds on the expressive power and universal approximativeness of this type of networks. We support our experimental results with thorough experiments on a large, real world video classification problem. Recent progress in deep neural networks came at the cost of an important increase of model sizes. Nowadays, state-of-the-art architectures for common tasks such as object recognition typically have tens of millions of parameters BID13 ) and up to a billion parameters in some cases BID10 . Best performing (ensemble) models typically combine dozens of such models, and their size can quickly add up to ten or twenty gigabytes. Large models are often more accurate, but training them requires time and large amounts of computational resources. Even when they are trained, they remain difficult to deploy, especially on mobile devices where memory or computational power is limited.In linear algebra, it is common to exploit structural properties of matrices to speedup computations, or reduce memory usage. BID7 have applied this principle in the context of deep neural networks, and proposed a network architecture in which large unstructured weight matrices have been replaced with more compact matrices with a circulant structure. Since any n-by-n circulant matrix can be represented in memory using only a vector of dimension n, the change resulted in a drastic reduction of the model size (from 230MB to 21MB). Furthermore, Cheng et al. have shown empirically that their network architecture can be almost as accurate as the original network. BID23 have proposed a more principled approach leveraging a result by BID16 stating that any matrix A ∈ C n×n can be decomposed into 2n − 1 diagonal and circulant matrices. They use this result to design Deep diagonal-circulant ReLU networks. However their experiments show good results even with a small number of factors (down to 2 factors), suggesting that Deep diagonal-circulant ReLU networks can achieve good approximation error, even with few factors.In this paper, we bridge the gap between the good empirical results observed by BID23 , and the theoretical approximation capabilities of Deep diagonal-circulant ReLU networks. We prove that Deep diagonal-circulant ReLU networks with bounded width and small depth can approximate any dense neural network. We obtain this result by showing that any matrix A can be decomposed into 4k + 1 diagonal and circulant matrices where k is the rank of the matrix A. In practice, this result is more useful than the one by Huhtanen & Perämäki since one can rely on a low rank SVD decomposition of A while controlling the approximation error.In addition to this theoretical contribution, we also conduct thorough experiments on synthetic and real datasets. In accordance with the theory, our experiments demonstrate that we can easily tradeoff accuracy for model size by adjusting the number of factors in the matrix decomposition. Finally we evaluate the applicability of this approach on state-of-the-art neural network architectures trained for video classification on the Youtube-8m Video dataset (over 1TB of training data). This experiment demonstrates that Deep diagonal-circulant ReLU networks can be used to train more compact neural networks on large scale, real world scenarios. In this paper we provided a theoretical study of the properties of Deep diagonal-circulant ReLU networks and demonstrated that they are bounded width universal approximators. The bound on this decomposition allowed us to calculate the error bound on any Deep diagonal-circulant ReLU networks given the depth on the network and the singular values associated with the weight matrices. Our empirical study demonstrate that we can trade-off model size for accuracy in accordance with the theory, and that we can use Deep diagonal-circulant ReLU networks in large scale machine learning applications.",862,0.451,539,1.5992578849721706,"Recent results from linear algebra stating any matrix products diagonal and circulant matrices has lead the design compact deep neural network architectures perform practice In this paper bridge these good empirical results the theoretical approximation capabilities Deep diagonal-circulant ReLU networks More precisely first demonstrate a Deep diagonal-circulant ReLU networks bounded width small depth approximate which the dense matrices of low rank Based this result provide new bounds the expressive power and universal approximativeness this type networks We support our experimental results thorough experiments a large, real world video classification problem Recent progress deep neural networks came an important increase of model sizes Nowadays state architectures common tasks object recognition typically parameters BID13 ) Best performing (ensemble) models typically combine dozens such models their size quickly add Large models more accurate training requires large amounts computational resources Even trained remain difficult deploy memory or computational powerIn linear algebra exploit structural properties speedup reduce BID7 have applied this principle deep neural networks proposed large unstructured weight matrices have replaced a circulant structure Since any n-by circulant matrix represented memory only a vector dimension the change resulted the model size 230MB 21MB Furthermore, Cheng et al have shown empirically their network architecture almost accurate BID23 have proposed a more principled approach leveraging a result by BID16 stating any matrix A �� C n×n can decomposed 2n − 1 diagonal and circulant matrices They use this result design Deep diagonal-circulant ReLU networks However their experiments show good results even factorsdown 2 factors suggesting Deep diagonal-circulant ReLU networks achieve good approximation error, few factorsIn bridge the good empirical results observed BID23 , the theoretical approximation capabilities We prove Deep diagonal-circulant ReLU networks with bounded width small depth approximate any dense neural network We obtain this result showing any matrix A can 4k + 1 diagonal and circulant matrices where k the rank In practice this result more useful by Huhtanen & Perämäki since one rely a low rank SVD decomposition A while controlling the approximation errorIn addition this theoretical contribution conduct thorough experiments synthetic and real datasets In accordance the theory our experiments demonstrate we easily tradeoff accuracy model size adjusting factors the matrix decomposition Finally evaluate on state neural trained for video classification on the Youtube-8m Video datasetoverTB This experiment demonstrates Deep diagonal-circulant ReLU networks train more compact neural networks real world scenarios In this paper provided Deep diagonal-circulant ReLU networks demonstrated bounded width universal approximators bound on this decomposition allowed calculate the error bound any Deep diagonal-circulant ReLU networks given the depth on the singular values associated the weight matrices Our empirical study demonstrate we trade- model size accuracy accordance Deep diagonal-circulant ReLU networks",0.0,0.23093561037080215
"Camera drones, a rapidly emerging technology, offer people the ability to remotely inspect an environment with a high degree of mobility and agility. However, manual remote piloting of a drone is prone to errors. In contrast, autopilot systems can require a significant degree of environmental knowledge and are not necessarily designed to support flexible visual inspections. Inspired by camera manipulation techniques in interactive graphics, we designed StarHopper, a novel touch screen interface for efficient object-centric camera drone navigation, in which a user directly specifies the navigation of a drone camera relative to a specified object of interest. The system relies on minimal environmental information and combines both manual and automated control mechanisms to give users the freedom to remotely explore an environment with efficiency and accuracy. A lab study shows that StarHopper offers an efficiency gain of 35.4% over manual piloting, complimented by an overall user preference towards our object-centric navigation system. Researchers in telepresence have long envisioned 'beyond being there' [21] . Replicating all relevant local experiences, while remote, should not be the only goal of telepresence; rather, we should also strive to create telepresence systems which can enable benefits that are not possible when the person is physically present. As such, telepresence goes from replication to augmentation. One particular instance of this vision is enabled by camera drones: our local bodies can only walk on the ground, but our remote bodies can fly. Current commercial remote robotic presence platforms have mostly been designed to replicate face-to-face conversation experiences [38, 55, 56] . Researchers have also explored their usage in a wider range of scenarios, such as shopping in a mall [55] or attending conferences [41] , and noted a number of social and functional issues due to their insufficient mobility [2, 19, 55] . With unmanned micro aerial vehicles (called 'drones' hereafter) becoming more affordable and reliable, they hold the potential for enabling more flexible remote presence and visual inspection experiences [16, 20, 25, 39, 48, 56] for the general population. While drones offer promise for such telepresence applications, they are challenging to manually control remotely, due to numerous factors including high degrees of freedom, narrow camera field-of-views, and network delays [40] . Their control interfaces -virtual or physical joysticks for consumer drones -are also unfamiliar for many users and take extended training time to master [48] . To relieve the burden of manual piloting, autopilot techniques have been applied to drone control. Most existing drone autopilot interfaces are based on specifying a series of planned waypoints in a 2D or 3D global map [10, 13, 48, 58] . However, in a situation where a user wishes to perform a real-time inspection, setting waypoints a priori may not be efficient for producing the viewer's desired viewpoints. For example, the viewer may wish to see something from a closer distance, from a different viewpoint, or view an area they didn't know about when the waypoints were set. Some autonomous systems avoid the use of waypoints and execute higher-level plans [11, 26, 33] , such as following a subject to form canonical shots [26] , but they typically do not offer the flexibility for exploring remote environments. The difficulty of drone piloting poses a significant barrier for the widespread adoption of free-flying robots. The goal of this research is to design a camera drone control interface to support efficient and flexible remote visual inspection for now universally adopted touchscreens. Inspired by recent work in semi-autonomous hybrid systems [33, 40] , we wish to combine the strengths of both manual and automatic piloting into a single hybrid navigation interface. Our work is also inspired by decades of research in interactive graphics, for which many camera navigation techniques have been established [5, 18, 29, 34] . Most relevant, we build upon object-centric techniques, where zooming, panning, and orbiting occurs relative to the location of a 3D object of interest. Existing object-aware drone navigation interfaces, such as DJI ActiveTrack [61] and XPose [33] , have been designed for aerial photography within visual line-of-sight. As such, they lack support for two important requirements of remote navigation and inspection: first, free exploration of a remote environment, which may include objects out of the initial camera field-of-view; and second, flexible inspection from various viewing angles or distances in relation to the objectof-interest. We propose StarHopper, a remote object-centric camera drone navigation interface that is operated through familiar touch interactions and relies on minimal geometric information of the environment (Figure 1 ). The system is designed based on a set of design goals for remote objectcentric drone navigation. It consists of an overhead camera view for context and a 3D-tracked drone's first-person view for focus. New objects of interest can be specified through simple touch gestures on both camera views. We combine automatic and manual control via four navigation mechanisms that can complement each other with unique strengths, to support efficient and flexible visual inspection. The system focuses on indoor environments, representative of tasks such as remote warehouse inspection [48] and museum visits [50, 51] , and where positional tracking technology is more reliable. A remote object inspection study showed that StarHopper was 35.4% faster than a manual baseline interface, for both simple and complex navigation routes. Users expressed general preferences towards object-centric navigation for remote inspection. We conclude by discussing potential design opportunities and future research to further increase the efficiency of remote visual inspection tasks. In this section, we discuss the implications of the results from our study, clarify important considerations and limitations related to our work, and propose future lines of research. To remove the barriers of using drones as free-flying remote inspection platforms, we explored touch-based object-centric navigation for camera drones through our prototype system, StarHopper. An in-lab study showed that users were able to achieve notable efficiency improvement using StarHopper for remote visual inspection, in comparison to a baseline condition using a touchscreen joystick for manual control. A strength of StarHopper comes from its combined use of a suite of automated, semiautomated, and manual control mechanisms to achieve efficiency and flexibility. In future work, we plan to empirically study users' mental models when working with automated camera drones, to understand how to build better human-automation collaboration for remote inspection. We are also interested in extending the usage of StarHopper to larger spaces and outdoor environments with a second drone as the overview camera. Our object-centric navigation techniques took inspiration from classical techniques in interactive graphics. As 3D sensing, reconstruction, object recognition, and other related fields advance, more powerful techniques initially developed for the virtual world may be applicable to telepresence navigation, taking us even closer to the vision of unconstrained 'beyond being there' telepresence.",1404,0.776,836,1.6794258373205742,"Camera drones a rapidly emerging technology offer people remotely inspect an environment mobility agility However manual remote piloting prone errors In contrast autopilot systems require environmental knowledge are support flexible visual inspections Inspired camera manipulation techniques in interactive graphics we designed StarHopper a novel touch screen interface efficient object-centric camera drone navigation in directly specifies the navigation of a drone camera relative of The system relies minimal environmental information combines both manual give remotely explore efficiency accuracy A lab study StarHopper offers an efficiency gain manual piloting complimented an overall user preference towards our object-centric navigation system Researchers in telepresence long envisioned 'beyond being there [21 Replicating all relevant local experiences while remote should; rather enable benefits when As such telepresence goes from replication augmentation One particular instance this vision enabled camera drones: our local bodies only walk fly Current commercial remote robotic presence platforms mostly designed replicate face conversation experiences [38 55 Researchers also explored their usage scenarios shopping [55 attending conferences41 noted social and functional issues due their insufficient mobility2 19 With unmanned micro aerial vehiclescalled 'drones' hereafter affordable hold enabling more flexible remote presence visual inspection experiences [16 20 39 48] While drones offer promise such telepresence applications challenging manually remotely due numerous factors high degrees narrow camera field-views network delays [40 Their control interfaces -virtual physical joysticks for consumer drones also unfamiliar for and take extended training time [48 To relieve manual piloting autopilot techniques applied drone control Most existing drone autopilot interfaces specifying planned waypoints or [10 13 48 However a situation a user wishes perform setting waypoints a priori efficient producing the viewer's desired viewpoints For example the viewer wish something from a closer distance from view an area they did when the waypoints set Some autonomous systems avoid waypoints execute higher-level plans [11 26 , such following a subject form canonical shots typically offer for exploring remote environments The difficulty drone piloting poses the widespread adoption The goal design a camera drone control interface support efficient and flexible remote visual inspection for now universally adopted touchscreens Inspired recent work semi-autonomous hybrid systems [33 40 wish combine both manual into a single hybrid navigation interface Our work also inspired decades interactive graphics for many camera navigation techniques established [5 18] Most relevant we build upon object-centric techniques where zooming, orbiting occurs relative of Existing object-aware drone navigation interfaces DJI ActiveTrack [61 XPose33 aerial photography within visual line As such they lack support two important requirements remote navigation inspection first free exploration may objects out the initial camera field- from various viewing angles or distances in the objectof-interest We propose StarHopper a remote object-centric camera drone navigation interface operated familiar touch interactions relies minimal geometric information of (Figure The system based design goals remote objectcentric drone navigation It consists an overhead camera view for context a 3D-tracked drone's first-person view focus New objects of can specified through simple touch gestures on both camera views We combine automatic and manual control via four navigation mechanisms complement unique strengths to support efficient and flexible visual inspection The system focuses indoor environments representative tasks remote warehouse inspection [48] and museum visits50 , where positional tracking technology more reliable A remote object inspection study showed StarHopper 35.4 faster a manual baseline interface for both simple and complex navigation routes Users expressed general preferences towards object-centric navigation for remote inspection We conclude potential design opportunities future research increase remote visual inspection tasks In clarify important considerations limitations related propose future lines To remove the barriers using drones free-flying remote inspection platforms we explored touch-based object-centric navigation for camera drones through our prototype system StarHopper An inlab showed users achieve notable efficiency improvement using StarHopper for remote visual inspection in a baseline condition using a touchscreen joystick for A strength StarHopper comes its combined use a suite achieve efficiency flexibility In future work empirically study users' mental models when working automated camera drones to to build better human-automation collaboration for remote inspection We also interested extending the usage StarHopper larger spaces outdoor environments with a second drone as the overview camera Our object-centric navigation techniques took inspiration classical techniques interactive graphics As 3D sensing, reconstruction object recognition advance more powerful techniques initially developed the virtual world applicable navigation taking even unconstrained 'beyond being there",0.01,0.435196509475255
"Recurrent neural networks (RNN), convolutional neural networks (CNN) and self-attention networks (SAN) are commonly used to produce context-aware representations. RNN can capture long-range dependency but is hard to parallelize and not time-efficient. CNN focuses on local dependency but does not perform well on some tasks. SAN can model both such dependencies via highly parallelizable computation, but memory requirement grows rapidly in line with sequence length. In this paper, we propose a model, called ""bi-directional block self-attention network (Bi-BloSAN)"", for RNN/CNN-free sequence encoding. It requires as little memory as RNN but with all the merits of SAN. Bi-BloSAN splits the entire sequence into blocks, and applies an intra-block SAN to each block for modeling local context, then applies an inter-block SAN to the outputs for all blocks to capture long-range dependency. Thus, each SAN only needs to process a short sequence, and only a small amount of memory is required. Additionally, we use feature-level attention to handle the variation of contexts around the same word, and use forward/backward masks to encode temporal order information. On nine benchmark datasets for different NLP tasks, Bi-BloSAN achieves or improves upon state-of-the-art accuracy, and shows better efficiency-memory trade-off than existing RNN/CNN/SAN. Context dependency provides critical information for most natural language processing (NLP) tasks. In deep neural networks (DNN), context dependency is usually modeled by a context fusion module, whose goal is to learn a context-aware representation for each token from the input sequence. Recurrent neural networks (RNN), convolutional neural networks (CNN) and self-attention networks (SAN) are commonly used as context fusion modules. However, each has its own merits and defects, so which network to use is an open problem and mainly depends on the specific task.RNN is broadly used given its capability in capturing long-range dependency through recurrent computation. It has been applied to various NLP tasks, e.g., question answering BID51 , neural machine translation BID0 , sentiment analysis , natural language inference BID29 , etc. However, training the basic RNN encounters the gradient dispersion problem, and is difficult to parallelize. Long short-term memory (LSTM) BID14 effectively avoids the vanishing gradient. Gated recurrent unit (GRU) BID5 and simple recurrent unit (SRU) BID24 improve the efficiency by reducing parameters and removing partial temporal-dependency, respectively. However, they still suffer from expensive time cost, especially when applied to long sequences.CNN becomes popular recently on some NLP tasks because of its the highly parallelizable convolution computation BID7 . Unlike RNN, CNN can simultaneously apply convolutions defined by different kernels to multiple chunks of a sequence BID19 . It is mainly used for sentence-encoding tasks BID25 BID17 . Recently, hierarchical CNNs, e.g. ByteNet BID18 , and ConvS2S BID8 , are proposed to capture relatively long-range dependencies by using stacking CNNs to increase the number of input BID2 . The details of all the models are provided in Section 4.We propose an attention mechanism, called ""bidirectional block self-attention (Bi-BloSA)"", for fast and memory-efficient context fusion. The basic idea is to split a sequence into several length-equal blocks (with padding if necessary), and apply an intra-block SAN to each block independently. The outputs for all the blocks are then processed by an inter-block SAN. The intra-block SAN captures the local dependency within each block, while the inter-block SAN captures the long-range/global dependency. Hence, every SAN only needs to process a short sequence. Compared to a single SAN applied to the whole sequence, such two-layer stacked SAN saves a significant amount of memory. A feature fusion gate combines the outputs of intra-block and inter-block SAN with the original input, to produce the final contextaware representations of all the tokens. Similar to directional self-attention (DiSA) BID42 , BiBloSA uses forward/backward masks to encode the temporal order information, and feature-level attention to handle the variation of contexts around the same word. Further, a RNN/CNN-free sequence encoding model we build based on Bi-BloSA, called ""bi-directional block self-attention network (Bi-BloSAN)"", uses an attention mechanism to compress the output of Bi-BloSA into a vector representation.In experiments 1 , we implement Bi-BloSAN and popular sequence encoding models on several NLP tasks, e.g., language inference, sentiment analysis, semantic relatedness, reading comprehension, question-type classification, etc. The baseline models include Bi-LSTM, Bi-GRU, Bi-SRU, CNNs, multi-head attention and DiSAN. A thorough comparison on nine benchmark datasets demonstrates the advantages of Bi-BloSAN in terms of training speed, inference accuracy and memory consumption. FIG0 shows that Bi-BloSAN obtains the best accuracy by costing similar training time to DiSAN, and as little memory as Bi-LSTM, Bi-GRU and multi-head attention. This shows that Bi-BloSAN achieves a better efficiency-memory trade-off than existing RNN/CNN/SAN models.Our notations follow these conventions: 1) lowercase denotes a vector; 2) bold lowercase denotes a sequence of vectors (stored as a matrix); and 3) uppercase denotes a matrix or a tensor. This paper presents an attention network, called bi-directional block self-attention network (BiBloSAN) , for fast, memory-efficient and RNN/CNN-free sequence modeling. To overcome large memory consumption of existing self-attention networks, Bi-BloSAN splits the sequence into several blocks and employs intra-block and inter-block self-attentions to capture both local and long-range context dependencies, respectively. To encode temporal order information, Bi-BloSAN applies forward and backward masks to the alignment scores between tokens for asymmetric selfattentions.Our experiments on nine benchmark datasets for various different NLP tasks show that Bi-BloSAN can achieve the best or state-of-the-art performance with better efficiency-memory trade-off than existing RNN/CNN/SAN models. Bi-BloSAN is much more time-efficient than the RNN models (e.g., Bi-LSTM, Bi-GRU, etc.), requires much less memory than DiSAN, and significantly outperforms the CNN models and multi-head attention on prediction quality.",1294,0.679,814,1.5896805896805897,"Recurrent neural networks self-attention networksSAN commonly produce context-aware representations RNN can capture long-range dependency but hard parallelize not time CNN focuses local dependency but perform some tasks SAN can model both such dependencies via highly parallelizable computation memory requirement grows rapidly line sequence length In, called ""bi-directional block self-attention networkBi-BloSAN RNN/CNN-free sequence encoding It requires as RNN but with all the merits SAN Bi-BloSAN splits the entire sequence blocks applies an intra-block SAN for modeling local context then the outputs capture long-range dependency Thus each SAN only process a short sequence, memory Additionally use feature-level attention handle the variation contexts around forward/backward masks to encode temporal order information On nine benchmark datasets for different NLP tasks Bi-BloSAN achieves or improves state accuracy shows better efficiency-memory trade-off existing RNN/CNN/SAN Context dependency provides critical information In deep neural networks context dependency usually modeled a context fusion module whose goal learn token from Recurrent neural networks self-attention networksSAN commonly context fusion modules However each has defects which network an open problem mainlyRNN broadly given capturing long-range dependency through recurrent computation It applied various NLP tasks question answering BID51 , neural machine translation BID0 sentiment , etc However training the basic RNN encounters the gradient dispersion problem difficult Long short-term memory (LSTM) BID14 effectively avoids the vanishing gradient Gated recurrent unit (GRU) BID5 and improve by parameters removing partial temporal-dependency However they still suffer expensive time cost especially applied long sequencesCNN becomes popular recently on some NLP tasks its the highly parallelizable convolution computation BID7 . Unlike RNN CNN can simultaneously apply convolutions defined different kernels multiple chunks a sequence BID19 . It mainly sentence-encoding tasks BID25 BID17 . Recently hierarchical CNNs e.g. ByteNet BID18 , ConvS2S BID8 proposed capture relatively long-range dependencies by stacking CNNs increase input BID2 . The details all the models provided Section 4.We propose an attention mechanism called ""bidirectional block self-attention (Bi-BloSA fast and memory-efficient context fusion The basic idea split a sequence several length-equal blocks padding if apply an intra-block SAN independently The outputs all the blocks then processed an inter-block SAN intrablock SAN captures the local dependency within while Hence every SAN only process a short sequence. Compared a single SAN applied the whole sequence such two-layer stacked SAN saves A feature fusion gate combines the outputs intra-block and inter-block SAN with, the final contextaware representations all the tokens Similar directional self-attention (DiSA) BID42 , BiBloSA forward/backward masks encode the temporal order information feature attention handle the variation contexts around Further a RNN/CNN-free sequence encoding model we build based Bi-BloSA calledbi-directional block self-attention network (Bi-BloSAN an attention mechanism compressIn experiments 1 , implement and popular sequence on several NLP tasks language inference sentiment semantic relatedness reading question-type classification etc The baseline models include Bi-LSTM CNNs multi-head attention DiSAN A thorough comparison on nine benchmark datasets demonstrates Bi-BloSAN training speed inference accuracy memory consumption FIG0 shows that Bi-BloSAN obtains costing similar training time DiSAN as little memory Bi-LSTM multi-head attention This shows Bi-BloSAN achieves a better efficiency-memory trade-off existing RNN/CNN/SAN modelsOur notations follow these conventions lowercase denotes a vector; bold lowercasestored This paper an attention network, called bi-directional block self-attention networkBiBloSAN , fast, memory-efficient and RNN/CNN-free sequence modeling To overcome large memory consumption of existing self-attention networks Bi-BloSAN splits the sequence several blocks employs capture To encode temporal order information Bi-BloSAN applies forward masks the alignment scores tokens for asymmetric selfattentionsOur experiments on nine benchmark datasets for various different NLP tasks Bi achieve or state better efficiency-memory trade-off than existing RNN/CNN/SAN models Bi-BloSAN much time the RNN models Bi requires DiSAN significantly the CNN models and multi-head attention on prediction quality",0.01,0.2065335034198178
"End-to-end neural models have made significant progress in question answering, however recent studies show that these models implicitly assume that the answer and evidence appear close together in a single document. In this work, we propose the Coarse-grain Fine-grain Coattention Network (CFC), a new question answering model that combines information from evidence across multiple documents. The CFC consists of a coarse-grain module that interprets documents with respect to the query then finds a relevant answer, and a fine-grain module which scores each candidate answer by comparing its occurrences across all of the documents with the query. We design these modules using hierarchies of coattention and self-attention, which learn to emphasize different parts of the input. On the Qangaroo WikiHop multi-evidence question answering task, the CFC obtains a new state-of-the-art result of 70.6% on the blind test set, outperforming the previous best by 3% accuracy despite not using pretrained contextual encoders. A requirement of scalable and practical question answering (QA) systems is the ability to reason over multiple documents and combine their information to answer questions. Although existing datasets enabled the development of effective end-to-end neural question answering systems, they tend to focus on reasoning over localized sections of a single document (Hermann et al., 2015; Rajpurkar et al., 2016; 2018; Trischler et al., 2017) . For example, Min et al. (2018) find that 90% of the questions in the Stanford Question Answering Dataset are answerable given 1 sentence in a document. In this work, we instead focus on multi-evidence QA, in which answering the question requires aggregating evidence from multiple documents (Welbl et al., 2018; Joshi et al., 2017) .Our multi-evidence QA model, the Coarse-grain Fine-grain Coattention Network (CFC), selects among a set of candidate answers given a set of support documents and a query. The CFC is inspired by coarse-grain reasoning and fine-grain reasoning. In coarse-grain reasoning, the model builds a coarse summary of support documents conditioned on the query without knowing what candidates are available, then scores each candidate. In fine-grain reasoning, the model matches specific finegrain contexts in which the candidate is mentioned with the query in order to gauge the relevance of the candidate. These two strategies of reasoning are respectively modeled by the coarse-grain and fine-grain modules of the CFC. Each module employs a novel hierarchical attention -a hierarchy of coattention and self-attention -to combine information from the support documents conditioned on the query and candidates. FIG0 illustrates the architecture of the CFC.The CFC achieves a new state-of-the-art result on the blind Qangaroo WikiHop test set of 70.6% accuracy, beating previous best by 3% accuracy despite not using pretrained contextual encoders. In addition , on the TriviaQA multi-paragraph question answering task (Joshi et al., 2017) , reranking Most of this work was done while Victor Zhong was at Salesforce Research. outputs from a traditional span extraction model (Clark & Gardner, 2018) using the CFC improves exact match accuracy by 3.1% and F1 by 3.0%.Our analysis shows that components in the attention hierarchies of the coarse and fine-grain modules learn to focus on distinct parts of the input. This enables the CFC to more effectively represent a large collection of long documents. Finally, we outline common types of errors produced by CFC, caused by difficulty in aggregating large quantity of references, noise in distant supervision, and difficult relation types. We presented CFC, a new state-of-the-art model for multi-evidence question answering inspired by coarse-grain reasoning and fine-grain reasoning. On the WikiHop question answering task, the CFC achieves 70.6% test accuracy, outperforming previous methods by 3% accuracy. We showed in our analysis that the complementary coarse-grain and fine-grain modules of the CFC focus on different aspects of the input, and are an effective means to represent large collections of long documents.",860,0.416,522,1.6475095785440612,"End- neural models made question answering however recent studies show implicitly the answer and evidence appear close In this work propose the Coarse-grain Fine-grain Coattention Network a new question answering model combines information evidence across multiple documents The CFC consists a coarse-grain module interprets documents with respect the query then finds a relevant answer a fine scores each candidate answer comparing its occurrences across We design these modules hierarchies coattention learn emphasize the input On the Qangaroo WikiHop multi-evidence question answering task the CFC obtains new state result 70.6% the blind test set outperforming best by 3% accuracy despite pretrained contextual encoders A requirement scalable practical question answering reason over multiple documents combine Although existing datasets enabled effective end neural question answering tend reasoning localized sectionsHermann 2015 Rajpurkar 2018 Trischler . For example Min et (2018 find that the questions the Stanford Question Answering Dataset given 1 sentence a document In this work instead multi-evidence QA answering requires aggregatingWelbl et 2018 Joshi .Our, the Coarse-grain Fine-grain Coattention Network selects among candidate answers given support documents a query The CFC inspired coarse-grain reasoning In coarse-grain reasoning the model builds a coarse summary support documents conditioned the query without knowing candidates available then scores. In fine-grain reasoning the model matches specific finegrain contexts the candidate mentioned with the query in order gauge These two strategies of reasoning respectively modeled Each module employs a novel hierarchical attention -a hierarchy coattention combine information the support documents conditioned the query candidates FIG0 illustrates achieves new state result on blind Qangaroo WikiHop test set 70.6% accuracy beating previous best 3% accuracy despite not pretrained contextual encoders In addition , on the TriviaQA multi-paragraph question answering taskJoshi et al 2017 reranking Most of this work while Victor Zhong Salesforce Research outputs from a traditional span extraction modelClark Gardner 2018 using the CFC improves exact match accuracy F1 components the attention hierarchies the coarse and fine-grain modules learn focus distinct parts This enables the CFC more represent a large collection long documents Finally outline common types errors produced CFC caused difficulty aggregating large quantity references noise distant supervision difficult relation types We presented CFC, state model multievidence question answering inspired coarse-grain reasoning On the WikiHop question answering task the CFC achieves 70.6% test accuracy outperforming previous methods 3% accuracy We showed the complementary coarse-grain and fine-grain modules the CFC focus the input an effective means represent large collections long documents",0.01,0.3538766862445356
"Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. We provide theoretical justification for this formulation, showing that it is closely related to an existing static formulation by Liero et al. (2018). We then propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practice to GANs, and perform numerical experiments demonstrating how this methodology can be applied to population modeling. We consider the problem of unbalanced optimal transport: given two measures, find a cost-optimal way to transform one measure to the other using a combination of mass variation and transport. Such problems arise, for example, when modeling the transformation of a source population into a target population ( Figure 1a ). In this setting, one needs to model mass transport to account for the features that are evolving, as well as local mass variations to allow sub-populations to become more or less prominent in the target population BID34 .Classical optimal transport (OT) considers the problem of pushing a source to a target distribution in a way that is optimal with respect to some transport cost without allowing for mass variations. Modern approaches are based on the Kantorovich formulation BID24 , which seeks the optimal probabilistic coupling between measures and can be solved using linear programming methods for discrete measures. Recently, BID13 showed that regularizing the objective using an entropy term allows the dual problem to be solved more efficiently using the Sinkhorn algorithm. Stochastic methods based on the dual objective have been proposed for the continuous setting BID19 . Optimal transport has been applied to many areas, such as computer graphics BID17 BID36 and domain adaptation (Courty et al., 2014; .In many applications where a transport cost is not available, transport maps can also be learned using generative models such as generative adversarial networks (GANs) BID20 , which push a source distribution to a target distribution by training against an adversary. Numerous transport problems in image translation BID30 BID38 BID37 , natural language translation BID22 , domain adaptation BID5 and biological data integration (Amodio & (a) (b)Figure 1: (a) Illustration of the problem of modeling the transformation of a source population µ to a target population ν. In this example, one sub-population is growing more rapidly than the others. (b) Schematic of Monge-like formulations of unbalanced optimal transport. The objective is to learn a transport map T (for transporting mass) and scaling factor ξ (for mass variation) to push the source µ to the target ν, using a deterministic transport map (top) BID7 or a stochastic transport map (bottom).Krishnaswamy, 2018) have been tackled using variants of GANs, with strategies such as conditioning or cycle-consistency employed to enforce correspondence between original and transported samples. However, all these methods conserve mass between the source and target and therefore cannot handle mass variation.Several formulations have been proposed for extending the theory of OT to the setting where the measures can have unbalanced masses BID7 BID26 BID27 BID18 . In terms of numerical methods, a class of scaling algorithms BID8 ) that generalize the Sinkhorn algorithm for balanced OT have been developed for approximating the solution to optimal entropy-transport problems; this formulation of unbalanced OT by BID27 corresponds to the Kantorovich OT problem in which the hard marginal constraints are relaxed using divergences to allow for mass variation. In practice, these algorithms have been used to approximate unbalanced transport plans between discrete measures for applications such as computer graphics BID8 , tumor growth modeling BID6 and computational biology BID34 . However, while optimal entropy-transport allows mass variation , it cannot explicitly model it, and there are currently no methods that can perform unbalanced OT between continuous measures.Contributions. Inspired by the recent successes of GANs for high-dimensional transport problems, we present a novel framework for unbalanced optimal transport that directly models mass variation in addition to transport. Concretely, our contributions are the following:• We propose to solve a Monge-like formulation of unbalanced OT, in which the goal is to learn a stochastic transport map and scaling factor to push a source to a target measure in a cost-optimal manner. This generalizes the unbalanced Monge OT problem by BID7 .• By relaxing this problem, we obtain an alternative form of the optimal entropy-transport problem by BID27 , which confers desirable theoretical properties.• We develop scalable methodology for solving the relaxed problem . Our derivation uses a convex conjugate representation of divergences , resulting in an alternating gradient descent method similar to GANs BID20 ).• We demonstrate in practice how our methodology can be applied towards population modeling using the MNIST and USPS handwritten digits datasets, the CelebA dataset, and a recent single-cell RNA-seq dataset from zebrafish embrogenesis.In addition to these main contributions, for completeness we also propose a new scalable method (Algorithm 2) in the Appendix for solving the optimal-entropy transport problem by BID27 in the continuous setting. The algorithm extends the work of to unbalanced OT and is a scalable alternative to the algorithm of BID8 for very large or continuous datasets.",1122,0.491,676,1.6597633136094674,"Generative adversarial networks an expressive class tremendous success modeling high-dimensional continuous measures In unbalanced optimal transport (OT based We formulate unbalanced OT as simultaneously learning a transport map a scaling factor push a source measure We provide theoretical justification this formulation showing closely an existing static formulation by (2018 We then propose solving based stochastic alternating gradient updates similar practice GANs perform numerical experiments demonstrating this methodology population modeling We consider the problem unbalanced optimal transport: given two measures find transform using mass variation Such problems modeling the transformation a source population In this setting one needs model mass transport account the features evolving local mass variations to allow sub become or prominent the target population BID34 .Classical optimal transport (OT considers the problem pushing a source a target distribution with some transport cost without allowing Modern approaches the Kantorovich formulation BID24 , seeks the optimal probabilistic coupling measures can solved linear programming methods for discrete measures Recently BID13 showed regularizing the objective using an entropy term allows the dual problem the Sinkhorn algorithm Stochastic methods based the dual objective have the continuous setting BID19 . Optimal transport has applied computer graphics BID17 BID36 and domain adaptationCourty et .In many applications where a transport cost transport maps learned BID20 push a source distribution by training against an adversary Numerous transport problems image translation BID30 , natural language translation domain adaptation BID5 and biological data integration (Amodio & (a (b)Figure: the problem modeling the transformation a source population µ to In one subpopulation growing (b) Schematic Monge-like formulations unbalanced optimal transport The objective learn a transport map T (for transporting mass scaling factor �� mass variation push the source µtop) BID7 orbottom).Krishnaswamy 2018) have tackled variants GANs strategies conditioning or cycle-consistency employed enforce correspondence original and transported samples However all these methods conserve mass between the source therefore handle mass variationSeveral formulations extending the theory OT the setting the measures have unbalanced masses BID7 BID26 . In terms numerical methods a class scaling BID8 ) generalize the Sinkhorn algorithm balanced OT have approximating the solution optimal entropy-transport problems; this formulation unbalanced OT by BID27 corresponds the Kantorovich OT problem the hard marginal constraints relaxed using divergences allow mass variation In practice these algorithms approximate unbalanced transport plans between discrete measures for applications computer graphics BID8 , tumor growth However while optimal entropy-transport allows mass variation , explicitly model it currently perform unbalanced OT between continuous measuresContributions. Inspired the recent successes GANs for high-dimensional transport problems present unbalanced optimal transport that directly models mass variation addition Concretely our contributions propose solve a Monge-like formulation unbalanced OT learn a stochastic transport map scaling push a source a target measure This generalizes the unbalanced Monge OT problem by BID7 .• By relaxing obtain an alternative form the optimal entropy-transport problem confers desirable theoretical develop scalable methodology the relaxed problem . Our derivation uses divergences , resulting an alternating gradient descent method similar GANs BID20 ).• demonstrate in practice our methodology towards population modeling the MNIST and USPS handwritten digits datasets the CelebA dataset recent singlecell RNA zebrafish embrogenesisIn these main contributions for propose (Algorithm in the Appendix solving the optimal-entropy transport problem BID27 in the continuous setting The algorithm extends to unbalanced OT and is a scalable alternative BID8 for very large or continuous datasets",0.01,0.3850981265897993
"Extracting saliency maps, which indicate parts of the image important to classification, requires many tricks to achieve satisfactory performance when using classifier-dependent methods. Instead, we propose classifier-agnostic saliency map extraction, which finds all parts of the image that any classifier could use, not just one given in advance. We observe that the proposed approach extracts higher quality saliency maps and outperforms existing weakly-supervised localization techniques, setting the new state of the art result on the ImageNet dataset. The success of deep convolutional networks for large-scale object recognition Krizhevsky et al. (2012) ; Simonyan & Zisserman (2014) ; Szegedy et al. (2015) ; He et al. (2016) has spurred interest in utilizing them to automatically detect and localize objects in natural images. Pioneering this direction, Simonyan et al. (2013) and Springenberg et al. (2014) demonstrated that the gradient of the class-specific score of a given classifier could be used for extracting a saliency map of an image. Such classifier-dependent saliency maps can be utilized to analyze the inner workings of a specific network. However, as only the part of the image that is used by a given model is highlighted, these methods are not identifying all ""evidence"" in a given image. They also tend to be noisy, covering many irrelevant pixels and missing many relevant ones. Therefore, much of the recent work has focused on introducing regularization techniques of correcting such classifier-dependent saliency maps. For instance, Selvaraju et al. (2017) propose averaging multiple saliency maps created for perturbed images to obtain a smooth saliency map. We argue, however, that applying tricks and tweaks on top of methods that were designed to analyze inner workings of a given classifier is not a principled way to get saliency maps that focus on all useful evidence. In this work, we aim to find saliency maps indicating pixels which aid classification, i.e. we want to find pixels in the input image such that if they were masked, it would confuse an unknown classifier. Assuming we were given a classifier, a naive approximate solution would be to train a generative model to output a mask (a saliency map) confusing that classifier. That can be achieved using a simple GAN-like approach (Goodfellow et al., 2014) where the classifier acts as a fixed discriminator. Unfortunately, as we prove experimentally, this solution suffers from the same issues as prior approaches. We argue that the strong dependence on a given classifier lies at the center of the problem. To tackle this directly we propose to train a saliency mapping that is not strongly coupled with any specific classifier. Our approach, a class-agnostic saliency map extraction, can be formulated as a practical algorithm that realizes our goal. Our focus on classifier-agnostic saliency maps is not our objective per se, it is a remedy that resolves the core problem. The proposed approach results in a neural network based saliency mapping that only depends on an input image. We qualitatively find that it extracts higher quality saliency maps compared to classifier-dependent methods, as can be seen in Fig. 2 . Extracted saliency maps show all the evidence without using any symptom-masking methods: difficult to tune regularization penalties (such as total variation), exotic activation functions, complex training procedures or image preprocessing tricks (such as superpixels), etc. We also evaluate our method quantitatively by using the extracted saliency maps for object localization. We observe that the proposed approach outperforms the existing weakly-supervised techniques setting the new state of the art result on the ImageNet dataset and closely approaches the localization performance of a strongly supervised model. Furthermore, we experimentally validate that the proposed approach works reasonably well even for classes unseen during training. Our method has many potential applications, in which being classifier-agnostic is of primary importance. For instance, in medical image analysis, where we are interested not only in class prediction but also in indicating which part of the image is important to classification. Importantly, however, it is criticial to indicate all parts of the image, which can influence diagnosis, not just ones used by a specific classifier. In this paper, we proposed a new framework for classifier-agnostic saliency map extraction which aims at finding a saliency mapping that works for all possible classifiers weighted by their posterior probabilities. We designed a practical algorithm that amounts to simultaneously training a classifier and a saliency mapping using stochastic gradient descent. We qualitatively observed that the proposed approach extracts saliency maps that cover all the relevant pixels in an image and that the masked-out images cannot be easily recovered by inpainting, unlike for classifier-dependent approaches. We further observed that the proposed saliency map extraction procedure outperforms all existing weakly supervised approaches to object localization and can also be used on images containing objects from previously unseen classes, paving a way toward class-agnostic saliency map extraction.",1015,0.659,610,1.6639344262295082,"Extracting saliency maps, indicate parts important classification requires many tricks satisfactory performance when classifier-dependent methods Instead propose classifier-agnostic saliency map extraction finds all parts any classifier not given in advance We observe the proposed approach extracts higher quality saliency maps outperforms existing weakly-supervised localization techniques setting the new state the art result on the ImageNet dataset The success deep convolutional networks for Krizhevsky (2012 ; Simonyan & Zisserman Szegedy (2015 ; He et (2016 has spurred interest utilizing them automatically localize objects natural images Pioneering this direction Simonyan et (2013 and Springenberg et al (2014 demonstrated the gradient the class-specific score could extracting a saliency map Such classifier-dependent saliency maps utilized analyze the inner workings a specific network However only the part used a given model highlighted these methods identifying all ""evidence They also tend noisy covering many irrelevant pixels missing many relevant ones Therefore much introducing regularization techniques of correcting such classifier-dependent saliency maps For instance Selvaraju et (2017 propose averaging multiple saliency maps created perturbed images obtain We argue, applying tricks tweaks top methods analyze inner workings a given classifier get saliency maps focus all useful evidence In this work aim find saliency maps indicating pixels which aid classification we such if masked confuse an unknown classifier Assuming given a classifier a naive approximate solution train output a maska saliency map confusing That can achieved a simple GAN-like approachGoodfellow acts a fixed discriminator Unfortunately as prove experimentally this solution suffers prior approaches We argue the strong dependence a given classifier lies To tackle directly propose train a saliency mapping strongly coupled Our approach, a class-agnostic saliency map extraction formulated a practical algorithm realizes Our focus classifier-agnostic saliency maps our objective per it a remedy resolves proposed approach results a neural network based saliency mapping only depends We qualitatively find it extracts higher quality saliency maps compared classifier-dependent methods can 2 . Extracted saliency maps show all the evidence without any symptom-masking methods: difficult tune regularization penaltiessuch total variation exotic activation functions complex training procedures image preprocessing tricks superpixels We also evaluate our method quantitatively the extracted saliency maps object localization We observe the proposed approach outperforms setting the new state on the ImageNet dataset closely approaches the localization performance a strongly supervised model Furthermore experimentally validate the proposed approach reasonably even classes unseen during training Our method has many potential applications in which being classifier For instance medical image analysis where not class prediction indicating which part important classification. Importantly however criticial indicate all parts influence diagnosis used a specific classifier In proposed classifier-agnostic saliency map extraction which aims finding works weighted We designed a practical algorithm amounts simultaneously training a saliency mapping using We qualitatively observed the proposed approach extracts saliency maps cover all the relevant pixels the masked-out images easily recovered inpainting unlike for classifier-dependent approaches We further observed the proposed saliency map extraction procedure outperforms all existing weakly supervised approaches object localization can on images containing objects previously unseen classes paving toward",0.01,0.3957257550757154
"Unsupervised image-to-image translation has gained considerable attention due to the recent impressive progress based on generative adversarial networks (GANs). However, previous methods often fail in challenging cases, in particular, when an image has multiple target instances and a translation task involves significant changes in shape, e.g., translating pants to skirts in fashion images. To tackle the issues, we propose a novel method, coined instance-aware GAN (InstaGAN), that incorporates the instance information (e.g., object segmentation masks) and improves multi-instance transfiguration. The proposed method translates both an image and the corresponding set of instance attributes while maintaining the permutation invariance property of the instances. To this end, we introduce a context preserving loss that encourages the network to learn the identity function outside of target instances. We also propose a sequential mini-batch inference/training technique that handles multiple instances with a limited GPU memory and enhances the network to generalize better for multiple instances. Our comparative evaluation demonstrates the effectiveness of the proposed method on different image datasets, in particular, in the aforementioned challenging cases. Code and results are available in https://github.com/sangwoomo/instagan Cross-domain generation arises in many machine learning tasks, including neural machine translation BID2 BID21 , image synthesis BID33 BID48 , text style transfer BID34 , and video generation BID3 BID39 BID6 . In particular, the unpaired (or unsupervised) image-to-image translation has achieved an impressive progress based on variants of generative adversarial networks (GANs) BID27 BID7 BID0 BID23 , and has also drawn considerable attention due to its practical applications including colorization , super-resolution BID22 , semantic manipulation BID40 , and domain adaptation BID5 BID35 BID15 . Previous methods on this line of research, however, often fail on challenging tasks, in particular, when the translation task involves significant changes in shape of instances or the images to translate contains multiple target instances BID10 . Our goal is to extend image-to-image translation towards such challenging tasks, which can strengthen its applicability up to the next level, e.g., changing pants to skirts in fashion images for a customer to decide which one is better to buy. To this end, we propose a novel method that incorporates the instance information of multiple target objectsin the framework of generative adversarial networks (GAN); hence we called it instance-aware GAN (InstaGAN) . In this work, we use the object segmentation masks for instance information, which may be a good representation for instance shapes, as it contains object boundaries while ignoring other details such as color. Using the information, our method shows impressive results for multi-instance transfiguration tasks, as shown in FIG0 .Our main contribution is three-fold: an instance-augmented neural architecture, a context preserving loss, and a sequential mini-batch inference/training technique. First , we propose a neural network architecture that translates both an image and the corresponding set of instance attributes. Our architecture can translate an arbitrary number of instance attributes conditioned by the input, and is designed to be permutation-invariant to the order of instances. Second , we propose a context preserv- ), and our proposed method, InstaGAN. Our method shows better results for multi-instance transfiguration problems.ing loss that encourages the network to focus on target instances in translation and learn an identity function outside of them. Namely, it aims at preserving the background context while transforming the target instances. Finally, we propose a sequential mini-batch inference/training technique, i.e., translating the mini-batches of instance attributes sequentially, instead of doing the entire set at once. It allows to handle a large number of instance attributes with a limited GPU memory, and thus enhances the network to generalize better for images with many instances. Furthermore, it improves the translation quality of images with even a few instances because it acts as data augmentation during training by producing multiple intermediate samples. All the aforementioned contributions are dedicated to how to incorporates the instance information (e.g., segmentation masks) for image-to-image translation. However, we believe that our approach is applicable to numerous other cross-domain generation tasks where set-structured side information is available.To the best of our knowledge, we are the first to report image-to-image translation results for multiinstance transfiguration tasks. A few number of recent methods BID27 BID10 show some transfiguration results but only for images with a single instance often in a clear background. Unlike the previous results in a simple setting, our focus is on the harmony of instances naturally rendered with the background. On the other hand, CycleGAN show some results for multi-instance cases, but report only a limited performance for transfiguration tasks. At a high level, the significance of our work is also on discovering that the instance information is effective for shape-transforming image-to-image translation, which we think would be influential to other related research in the future. Mask contrast-GAN and Attention-GAN (Mejjati et al., 2018) use segmentation masks or predicted attentions, but only to attach the background to the (translated) cropped instances. They do not allow to transform the shapes of the instances. To the contrary, our method learns how to preserve the background by optimizing the context preserving loss, thus facilitating the shape transformation. We have proposed a novel method incorporating the set of instance attributes for image-to-image translation. The experiments on different datasets have shown successful image-to-image translation on the challenging tasks of multi-instance transfiguration, including new tasks, e.g., translating jeans to skirt in fashion images. We remark that our ideas utilizing the set-structured side information have potential to be applied to other cross-domain generations tasks, e.g., neural machine translation or video generation. Investigating new tasks and new information could be an interesting research direction in the future.",1166,0.853,707,1.6492220650636493,"Unsupervised imageto translation has gained the recent impressive progress based However previous methods often challenging cases in an image multiple target instances a translation task involves significant changes shape translating pants skirts fashion images To tackle propose coined instanceaware GAN (InstaGAN incorporates the instance information ( object segmentation masks improves multi-instance transfiguration The proposed method translates both an image the corresponding set instance attributes while the permutation invariance property To this end introduce a context preserving loss that encourages the network learn the identity function outside target instances We also propose a sequential mini-batch inference/training technique handles multiple instances with a limited GPU memory enhances to generalize better Our comparative evaluation demonstrates the proposed method different image datasets the aforementioned challenging cases Code and results https://github.com/sangwoomo/instagan Cross-domain generation arises many machine learning tasks neural machine translation BID2 BID21 , image synthesis text style transfer video generation In particular unpaired ( imageto translation has achieved an impressive progress based variants BID27 BID7 BID0 BID23 , drawn due including colorization , superresolution BID22 semantic manipulation BID40 domain adaptation Previous methods on this line, often on challenging tasks in the translation task significant changes shape instances the images translate contains multiple target instances BID10 . Our goal extend image translation towards such challenging tasks strengthen its applicability up changing pants skirts fashion images for decide To this end propose incorporates the instance information multiple target objectsin); hence called (InstaGAN In this work the object segmentation masks instance information, a good representation instance shapes as contains object boundaries while ignoring color Using, our method impressive results multi-instance transfiguration tasks FIG0 .Our main contribution three an instance-augmented neural architecture a context preserving loss a sequential mini-batch inference/training technique First , propose translates both an image the corresponding set instance attributes Our architecture can translate instance attributes conditioned is designed permutation Second , propose a context preserv- ), our proposed method InstaGAN Our method shows better results multi-instance transfiguration problems.ing loss that encourages the network focus target instances translation learn an identity function outside them Namely aims preserving the background context while transforming the target instances Finally propose a sequential mini-batch inference/training technique translating instance attributes sequentially instead doing at It allows to handle instance attributes a limited GPU memory thus enhances the network to generalize better for images Furthermore improves images even a few instances because acts data augmentation during training by producing multiple intermediate samples All the aforementioned contributions dedicated how incorporates the instance information ( segmentation masks for image translation However we applicable numerous other cross-domain generation tasks set-structured side information availableTo the image translation results multiinstance transfiguration tasks A few number recent methods BID27 BID10 show some transfiguration results images a single instance often Unlike the previous results a simple setting our focus the harmony instances naturally rendered On CycleGAN show some results multi-instance cases report transfiguration tasks At the significance our work also on discovering that the instance information effective shape imageto translation think would influential other related research Mask contrast-GAN and Attention-GAN (Mejjati 2018 use segmentation masks or predicted attentions to attach the background the (translated) cropped instances They do allow to transform the shapes the instances To our method learns preserve the background by optimizing the context preserving loss thus facilitating the shape transformation We proposed incorporating the set instance attributes imageto translation The experiments different datasets successful imageto translation on the challenging tasks multi-instance transfiguration new tasks translating jeans skirt fashion images We remark our ideas utilizing the set-structured side information have potential other cross-domain generations tasks neural machine translation video generation Investigating new tasks new information could an interesting research direction",0.01,0.3582399514390256
"Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime  where classical learning theory would instead predict that they would severely overfit.   While many proposals for some kind of implicit regularization have been made to rationalise this success, there is no consensus for the fundamental reason why DNNs do not strongly overfit.   In this paper, we provide a new explanation. By applying a very general probability-complexity bound recently derived from  algorithmic information theory (AIT), we argue that the parameter-function map of many DNNs should be exponentially biased towards simple functions. We then provide clear evidence for this strong simplicity bias in a model DNN for Boolean functions, as well as in much larger fully connected and convolutional networks trained on CIFAR10 and MNIST.
 As the target functions in many real problems are expected to be highly structured, this intrinsic simplicity bias helps explain why deep networks generalize well on real world problems.
 This picture also facilitates a novel PAC-Bayes approach where the prior is taken over the DNN input-output function space, rather than  the more conventional prior over parameter space.   If we assume that the training algorithm samples parameters close to uniformly within the zero-error region then the PAC-Bayes theorem can be used to guarantee good expected generalization for target functions producing high-likelihood training sets.   By exploiting recently discovered connections between DNNs and Gaussian processes to estimate the marginal likelihood,  we produce relatively tight generalization PAC-Bayes error bounds which correlate well with the true error on realistic datasets such as MNIST and CIFAR10 and for architectures including convolutional and fully connected networks. Deep learning is a machine learning paradigm based on very large, expressive and composable models, which most often require similarly large data sets to train. The name comes from the main component in the models: deep neural networks (DNNs) with many layers of representation. These models have been remarkably successful in domains ranging from image recognition and synthesis, to natural language processing, and reinforcement learning (Mnih et al. (2015) ; LeCun et al. (2015) ; BID7 ; BID12 ). There has been work on understanding the expressive power of certain classes of deep networks ), their learning dynamics BID0 ; ), and generalization properties (Kawaguchi et al. (2017) ; BID5 ; BID1 ). However, a full theoretical understanding of many of these properties is still lacking.DNNs are typically overparametrized, with many more parameters than training examples. Classical learning theory suggests that overparamterized models lead to overfitting, and so poorer generalization performance. By contrast, for deep learning there is good evidence that increasing the number of parameters leads to improved generalization (see e.g. BID2 ). For a typical supervised learning scenario, classical learning theory provides bounds on the generalization error (f ) for target function f that typically scale as the complexity of the hypothesis class H. Complexity measures include simply the number of functions in H, the VC dimension, and the Rademacher complexity BID15 ). Since neural networks are highly expressive, typical measures of C(H) will be extremely large, leading to trivial bounds.Many empirical schemes such as dropout BID18 ), weight decay (Krogh & Hertz (1992) ), early stopping (Morgan & Bourlard (1990) ), have been proposed as sources of regularization that effectively lower C(H). However, in an important recent paper BID27 ), it was explicitly demonstrated that these regularization methods are not necessary to obtain good generalization. Moreover, by randomly labelling images in the well known CIFAR10 data set (Krizhevsky & Hinton (2009) ), these authors showed that DNNs are sufficiently expressive to memorize a data set in not much more time than it takes to train on uncorrupted CIFAR10 data. By showing that it is relatively easy to train DNNs to find functions f that do not generalize at all, this work sharpened the question as to why DNNs generalize so well when presented with uncorrupted training data. This study stimulated much recent work, see e.g. (Kawaguchi et al. (2017) ; Arora et al. (2018) ; Morcos et al. (2018) ; BID1 ; Dziugaite & Roy (2017; ; Neyshabur et al. (2017a; ), but there is no consensus as to why DNNs generalize so well.Because DNNs have so many parameters, minimizing the loss function L to find a minimal training set error is a challenging numerical problem. The most popular methods for performing such optimization rely on some version of stochastic gradient descent (SGD). In addition, many authors have also argued that SGD may exploit certain features of the loss-function to find solutions that generalize particularly well BID17 ; BID28 ) However, while SGD is typically superior to other standard minimization methods in terms of optimization performance, there is no consensus in the field on how much of the remarkable generalization performance of DNNs is linked to SGD (Krueger et al. (2017) ). In fact DNNs generalize well when other optimization methods are used (from variants of SGD, like Adam (Kingma & Ba (2014) ), to gradient-free methods )). For example, in recent papers BID23 ; BID29 ; Keskar et al. (2016) simple gradient descent (GD) was shown to lead to differences in generalization with SGD of at most a few percent. Of course in practical applications such small improvements in generalization performance can be important. However, the question we want to address in this paper is the broader one of Why do DNNs generalize at all, given that they are so highly expressive and overparameterized? . While SGD is important for optimization, and may aid generalization, it does not appear to be the fundamental source of generalization in DNNs.Another longstanding family of arguments focuses on the local curvature of a stationary point of the loss function, typically quantified in terms of products of eigenvalues of the local Hessian matrix. Flatter stationary points (often simply called minima) are associated with better generalization performance (Hochreiter & Schmidhuber (1997) ; Hinton & van Camp (1993) ). Part of the intuition is that flatter minima are associated with simpler functions (Hochreiter & Schmidhuber (1997) ; BID23 ), which should generalize better. Recent work (Dinh et al. (2017) ) has pointed out that flat minima can be transformed to sharp minima under suitable re-scaling of parameters, so care must be taken in how flatness is defined. In an important recent paper BID23 ) an attack data set was used to vary the generalization performance of a standard DNN from a few percent error to nearly 100% error. This performance correlates closely with a robust measure of the flatness of the minima (see also BID29 for a similar correlation over a much smaller range, but with evidence that SGD leads to slightly flatter minima than simple GD does). The authors also conjectured that this large difference in local flatness would be reflected in large differences between the volume V good of the basin of attraction for solutions that generalize well and V bad for solutions that generalize badly. If these volumes differ sufficiently, then this may help explain why SGD and other methods such as GD converge to good solutions; these are simply much easier to find than bad ones. Although this line of argument provides a tantalizing suggestion for why DNNs generalize well in spite of being heavily overparameterized, it still begs the fundamental question of Why do solutions vary so much in flatness or associated properties such as basin volume?In this paper we build on recent applications of algorithmic information theory (AIT) (Dingle et al. (2018) ) to suggest that the large observed differences in flatness observed by BID23 ) can be correlated with measures of descriptional complexity. We then apply a connection between Gaussian processes and DNNS to empirically demonstrate for several different standard architectures that the probability of obtaining a function f in DNNs upon a random choice of parameters varies over many orders of magnitude. This bias allows us to apply a classical result from PAC-Bayes theory to help explain why DNNs generalize so well. In this paper, we present an argument that we think offers a first-order explanation of generalization in highly overparameterized DNNs. First, PAC-Bayes shows how priors which are sufficiently biased towards the true distribution can result in generalization in highly expressive models, e.g. even if there are many more parameters than data points. Second, the huge bias towards simple functions in the parameter-function map strongly suggests that neural networks have a similarly biased prior. The number of parameters in a fully expressive DNN does not strongly affect the bias. Third, since real-world problems tend to be far from random, using these same complexity measures, we expect the prior to be biased towards the right class of solutions for real-world datasets and problems. Figure 4: Average probability of finding a function for a variant of SGD, versus average probability of finding a function when using the Gaussian process approximation. This is done for a randomly chosen, but fixed, target Boolean function of Lempel-Ziv complexity 84.0. See Appendix D for details. The Gaussian process parameters are σ w = 10.0, and σ b = 10.0. For advSGD, we have removed functions which only appared once in the whole sample, to avoid finite-size effects. In the captions, ρ refers to the 2-tailed Pearson correlation coefficient, and p to its corresponding p value.To demonstrate the bias in the parameter-function map, we used both direct sampling for a small network and an equivalence with Gaussian processes for larger networks. We also used arguments from AIT to show that functions f that obtain with higher P (f ) are likely to be simple. However, a more complete understanding of this bias is still called for.We also demonstrated how to make this approach quantitative, approximating neural networks as Gaussian processes to calculate PAC-Bayesian bounds on the generalization error.It should be noted that our approach is not yet able to explain the effects that different tricks used in practice have on generalization. However, most of these improvements tend to be of the order of a few percent in the accuracy. The aim of this paper is to explain the bulk of the generalization, which classical learning theory would predict to be poor in this highly overparametrized regime. It is still an open question whether our approach can be extended to explain some of the tricks used in practice, as well as to methods other than neural networks (Belkin et al. (2018) ) that may also have simple parameter-function maps. To stimulate work in improving our bounds, we summarize here the main potential sources of error for our bounds:1. The probability that the training algorithm (like SGD) finds a particular function in the zero-error region can be approximated by the probability that the function obtains upon i.i.d. sampling of parameters.2. Gaussian processes model neural networks with i.i.d.-sampled parameters well even for finite widths.3. Expectation-propagation gives a good approximation of the Gaussian process marginal likelihood.",2339,1.366,1348,1.7351632047477745,"Deep neural networks generalize remarkably without explicit regularization even where classical learning theory would instead predict they severely While many proposals some kind implicit regularization rationalise this success for the fundamental reason DNNs do strongly overfit In. By applying a very general probability-complexity bound recently derived algorithmic information theory argue the parameter-function map many DNNs should exponentially biased simple functions We then provide clear evidence this strong simplicity bias a model DNN for Boolean functions much larger fully connected and convolutional networks trained CIFAR10 As the target functions many real problems expected highly structured this intrinsic simplicity bias helps deep networks generalize on This picture also facilitates a novel PAC-Bayes approach where prior is taken over the DNN input-output function space rather more prior over parameter space If assume the training algorithm samples parameters close uniformly within the zero-error region the PAC-Bayes theorem guarantee good expected generalization target functions producing By exploiting recently discovered connections DNNs Gaussian processes to estimate the marginal likelihood, produce relatively tight generalization PAC-Bayes error bounds which correlate on realistic datasets such and for architectures including Deep learning based very large, expressive and composable models most require similarly large data sets train The name comes the main component the models deep neural networks with representation These models remarkably domains image recognition synthesisMnih et al (2015 ; LeCun et (2015 ; BID7 ; There work understanding the expressive power certain classes deep networks ), their learning dynamics BID0 ; ), generalization propertiesKawaguchi (2017 ; BID5 ; However a full theoretical understanding manyDNNs typically overparametrized training examples Classical learning theory suggests overparamterized models lead poorer performance By contrast for deep learning there good evidence increasing parameters leads BID2 For a typical supervised learning scenario classical learning theory boundsf ) target function f that typically scale as the hypothesis class H. Complexity measures include simply functions H, the VC dimension the Rademacher complexity BID15 ). Since neural networks highly expressive, typical measures C(H will extremely large leading trivial boundsMany empirical schemes such dropout BID18 ), weight decayKrogh & Hertz (1992 early stopping (Morgan Bourlard have sources regularization that However an important recent paper BID27 ), explicitly these regularization methods obtain Moreover by randomly labelling images the well known CIFAR10 data Hinton ( DNNs sufficiently expressive memorize a data not much more time it train on By showing relatively train DNNs find functions f that generalize at this work sharpened as generalize presented uncorrupted training data This study stimulated much recent work see (2017 ; Arora et (2018 ; Morcos (2018) ; BID1 ; Dziugaite & Roy; ; Neyshabur et al (2017a; ), but DNNs generalize soBecause minimizing the loss function L to find a minimal training set error a challenging numerical problem The most popular methods performing such optimization rely some version In addition many authors also SGD may exploit certain features the loss-function find solutions generalize particularly BID17 ; BID28 ) However while typically superior other standard minimization methods optimization performance the remarkable generalization performance linked (2017 ). In fact DNNs generalize well other optimization methodsfrom variants SGD Adam (Kingma Ba (2014 gradient-free methods ) For example recent papers BID23 ; Keskar (2016) simple gradient descentGD was shown lead differences generalization with SGD of Of in practical applications such small improvements generalization performance important However the question we want broader one Why DNNs generalize at given highly expressive overparameterized . While SGD important optimization and may aid generalization appear the fundamental sourceAnother longstanding family arguments focuses the local curvature a stationary point of the loss function typically quantified products the local Hessian matrix Flatter stationary pointsoften simply minima associated better generalization performance ( ; Hinton van Camp Part the intuition flatter minima associated simpler functionsHochreiter & ( ; BID23 should generalize better Recent work (Dinh et (2017 ) has pointed flat minima transformed under suitable re parameters care how flatness In an important recent paper BID23 ) an attack data vary the generalization performance a standard DNN from a few percent error This performance correlates a robust measure the flatness BID29 for over, evidence SGD leads than simple GD does The authors also conjectured this large difference local flatness reflected large differences the volume V good the basin attraction solutions generalize well and V If these volumes differ sufficiently help SGD and other methods such GD converge good solutions; these simply much find bad ones Although this line argument provides a tantalizing suggestion why DNNs generalize spite being heavily still begs Why solutions vary flatness or associated properties such basin volume?In build recent applications algorithmic information theory (Dingle (2018 ) to suggest the large observed differences flatness observed BID23 ) can correlated measures descriptional complexity We then apply a connection Gaussian processes DNNS empirically demonstrate for several different standard architectures the probability obtaining f upon a random choice parameters varies over many orders This bias allows apply a classical result PAC-Bayes theory help DNNs generalize so In an argument we think offers generalization highly overparameterized DNNs First PAC-Bayes shows priors which sufficiently biased result highly expressive models even data points Second the huge bias simple functions the parameter-function map strongly neural networks similarly prior The number parameters a fully expressive DNN does strongly the bias Third since real-world problems tend far using these same complexity measures, expect prior biased the right class solutions and problems Figure Average probability finding a function a variant SGD, versus when This done randomly, fixed target Boolean function Lempel-Ziv complexity 84.0 See Appendix D The Gaussian process parameters � w advSGD removed functions only appared once to finite-size effects In the captions �� refers p toTo demonstrate the bias the parameter-function map both direct sampling for a small network an equivalence with Gaussian processes We also used arguments AIT to that functions f that obtain with higher P (f ) likely simple However a more complete understanding this bias still calledWe also demonstrated how to make this approach quantitative approximating neural networks as Gaussian processes to calculate PAC-Bayesian bounds the generalization errorIt yet able different tricks used practice However most these improvements tend of the accuracy The aim the bulk, classical learning theory would predict poor this highly overparametrized regime It still our approach extended explain some the tricks practice methods other neural networksBelkin (2018 ) that may also have simple parameter-function maps To stimulate work improving our bounds summarize here the main potential sources error bounds:1 The probability the training algorithm (like SGD finds the zero-error region can obtains upon i.i.d sampling parameters.2. Gaussian processes model well even gives marginal likelihood",0.01,0.5772104246482039
"We establish a theoretical link between evolutionary algorithms and variational parameter optimization of probabilistic generative models with binary hidden variables.
 While the novel approach is independent of the actual generative model, here we use two such models to investigate its applicability and scalability: a noisy-OR Bayes Net (as a standard example of binary data) and Binary Sparse Coding (as a model for continuous data).

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

 As a proof of concept, we apply the novel evolutionary EM approach to the optimization of the parameters of noisy-OR Bayes nets and binary sparse coding on artificial and real data (natural image patches). Using point mutations and single-point cross-over for the evolutionary algorithm, we find that scalable variational EM algorithms are obtained which efficiently improve the data likelihood. In general we believe that, with the link established here, standard as well as recent results in the field of evolutionary optimization can be leveraged to address the difficult problem of parameter optimization in generative models. Evolutionary algorithms (EA) have been introduced (e.g. BID3 BID23 as a technique for function optimization using methods inspired by biological evolutionary processes such as mutation, recombination, and selection. As such EAs are of interest as tools to solve Machine Learning problems, and they have been frequently applied to a number of tasks such as clustering BID21 BID9 , reinforcement learning BID25 , and hierarchical unsupervised BID16 or deep supervised learning (e.g., BID32 BID32 BID33 BID22 for recent examples). In some of these tasks EAs have been investigated as alternatives to standard procedures BID9 ), but most frequently EAs are used to solve specific sub-problems. For example, for classification with Deep Neural Networks (DNNs LeCun et al., 2015; BID27 , EAs are frequently applied to solve the sub-problem of selecting the best DNN architectures for a given task (e.g. BID32 BID33 or more generally to find the best hyper-parameters of a DNN (e.g. BID12 BID22 .Inspired by these previous contributions, we here ask if EAs and learning algorithms can be linked more tightly. To address this question we make use of the theoretical framework of probabilistic generative models and expectation maximization (EM Dempster et al., 1977) approaches for parameter optimization. The probabilistic approach in combination with EM is appealing as it establishes a very general unifying framework able to encompass diverse algorithms from clustering and dimensionality reduction BID24 BID34 over feature learning and sparse coding BID18 to deep learning approaches BID20 . However, for most generative data models, EM is computationally intractable and requires approximations. Variational EM is a very prominent such approximation and is continuously further developed to become more efficient, more accurate and more autonomously applicable. Variational EM seeks to approximately solve optimization problems of functions with potentially many local optima in potentially very high dimensional spaces. The key observation exploited in this study is that a variational EM algorithm can be formulated such that latent states serve as variational parameters. If the latent states are then considered as genomes of individuals, EAs emerge as a very natural choice for optimization in the variational loop of EM. The training of generative models is a very intensively studied branch of Machine Learning. If EM is applied for training, most non-elementary models require approximations. For this reason, sophisticated and mathematically grounded approaches such as sampling or variational EM have been developed in order to derive sufficiently precise and efficient learning algorithms.Evolutionary algorithms (EAs) have also been applied in conjunction with EM. BID21 , for instance, have used EAs for clustering with Gaussian mixture models (GMMs). However, the GMM parameters are updated by their approach relatively conventionally using EM, while EAs are used to select the best GMM models for the clustering problem (using a min. description length criterion). Such a use of EAs is similar to DNN optimization where EAs optimize DNN hyperparameters in an outer optimization loop BID32 BID12 BID22 Suganuma et al., 2017, etc) , while the DNNs themselves are optimized using standard error-minimization algorithms. Still other approaches have used EAs to directly optimize, e.g., a clustering objective. But in these cases EAs replace EM approaches for optimization (compare Hruschka et al., 2009) . In contrast to all such previous applications, we have here shown that EAs and EM can be combined directly and intimately: Alg. 1 defines EAs as an integral part of EM, and as such EAs address the key optimization problem arising in the training of generative models.We see the main contribution of our study in the establishment of this close theoretical link between EAs and EM. This novel link will make it possible to leverage an extensive body of knowledge and experience from the community of evolutionary approaches for learning algorithms. Our numerical experiments are a proof of concept which shows that EAs are indeed able to train generative models with large hidden spaces and local optima. For this purpose we used very basic EAs with elementary selection, mutation, cross-over operators.EAs more specialized to the specific optimization problems arising in the training of generative models have great potentials in future improvements of accuracy and scalability, we believe. In our experiments, we have only just started to exploit the abilities of EAs for learning algorithms. Still, our results represent, to the knowledge of the authors, the first examples of noisy-OR or sparse coding models trained with EAs (although both models have been studied very extensively before). Most importantly, we have pointed out a novel mathematically grounded way how EAs can be used for generative models with binary latents in general. The approach here established is, moreover, not only very generically formulated using the models' joint probabilities but it is also very straightforward to apply.",1326,0.84,789,1.6806083650190113,"We establish a theoretical link evolutionary algorithms variational parameter optimization of binary hidden variables While the novel approach independent the actual generative model here two such models investigate a noisy-OR Bayes Netas a standard example binary data Binary Sparse Coding Learning of first formulated approximate maximum likelihood optimization variational expectation maximizationEM We choose truncated posteriors variational distributions discrete latent states serve In the variational E-step the latent states then optimized according a tractable free-energy objective . Given a data point show evolutionary algorithms the variational optimization loop by (A)~considering the bit-vectors the latent states as genomes individuals by the (log) joint probabilities given the used generative model As a proof apply the novel evolutionary EM approach the optimization the parameters noisy-OR Bayes nets binary sparse coding on artificial and real datanatural image patches Using point mutations single-point cross for the evolutionary algorithm scalable variational EM algorithms obtained which efficiently improve the data likelihood In general we believe, the link established here standard as recent results evolutionary optimization address parameter optimization Evolutionary algorithms (EA introduced ( BID3 BID23 as a technique function optimization using methods inspired biological evolutionary processes mutation. As such EAs of interest as tools solve Machine Learning problems frequently applied tasks BID21 BID9 , reinforcement or deep supervised learning for recent examples In some these tasks EAs investigated alternatives standard procedures BID9 ), most frequently solve specific sub For example for classification with Deep Neural Networks LeCun BID27 , EAs are frequently applied solve the sub selecting architectures more generally to .Inspired these previous contributions here ask learning algorithms linked more To address make the theoretical framework expectation maximization (EM Dempster et al 1977 approaches parameter optimization The probabilistic approach in combination EM is appealing establishes a very general unifying framework able encompass diverse algorithms from clustering and dimensionality reduction BID24 BID34 over feature learning sparse coding to approaches . However for most generative data models EM is Variational EM is a very prominent such approximation continuously further become autonomously applicable Variational EM seeks approximately solve optimization problems functions potentially many local optima potentially very high dimensional spaces The key observation exploited a variational EM algorithm formulated such that latent states serve variational parameters If the latent states then considered genomes individuals EAs emerge a very natural choice optimization the variational loop EM. The training generative models a very intensively studied branch If EM is applied for training most non-elementary models For sophisticated and mathematically grounded approaches such sampling variational EM have derive sufficiently precise and efficient learningEvolutionary algorithms applied conjunction BID21 , for have used EAs clustering with Gaussian mixture modelsGMMs However the GMM parameters updated by their approach relatively conventionally using EM, EAs select the clustering problemusing a min. description length criterion Such a use EAs similar DNN optimization where optimize an outer optimization loop BID32 BID12 Suganuma etc) , while standard error-minimization algorithms Still other approaches used EAs directly optimize, a clustering objective But these cases EAs replace EM approaches optimization (compare Hruschka . In contrast all such previous applications here shown EAs EM can directly intimately: Alg. 1 defines EAs an integral part EM as address the key optimization problem arising the trainingWe see the main contribution our study the establishment this close theoretical link This novel link make leverage an extensive body evolutionary approaches for learning algorithms Our numerical experiments a proof which EAs indeed train large hidden spaces local optima For this purpose very basic EAs elementary selection, mutation, cross-over operatorsEAs more specialized the specific optimization problems arising the training have great potentials future improvements accuracy we In our experiments have only just exploit the abilities EAs for learning algorithms Still, our results represent, the knowledge noisy-OR or sparse coding models trained EAsalthough both models studied very before Most importantly pointed a novel mathematically grounded way how EAs with binary latents general The approach here established, moreover very generically formulated using the models' joint probabilities it straightforward",0.01,0.4382094861551254
"While deep neural networks have achieved groundbreaking prediction results in many tasks, there is a class of data where existing architectures are not optimal -- sequences of probability distributions. Performing forward prediction on sequences of distributions has many important applications. However, there are two main challenges in designing a network model for this task. First, neural networks are unable to encode distributions compactly as each node encodes just a real value. A recent work of Distribution Regression Network (DRN) solved this problem with a novel network that encodes an entire distribution in a single node, resulting in improved accuracies while using much fewer parameters than neural networks. However, despite its compact distribution representation, DRN does not address the second challenge, which is the need to model time dependencies in a sequence of distributions. In this paper, we propose our Recurrent Distribution Regression Network (RDRN) which adopts a recurrent architecture for DRN. The combination of compact distribution representation and shared weights architecture across time steps makes RDRN suitable for modeling the time dependencies in a distribution sequence. Compared to neural networks and DRN, RDRN achieves the best prediction performance while keeping the network compact. Deep neural networks have achieved state-of-the-art results in many tasks by designing the network architecture according to the data type. For instance, the convolutional neural network (CNN) uses local filters to capture the features in an image and max pooling to reduce the image representation size. By using a series of convolution and max pooling layers, CNN extracts the semantic meaning of the image. The recurrent architecture of recurrent neural networks (RNN) when unrolled, presents a shared weight structure which is designed to model time dependencies in a data sequence. However, among the major network architectures, the multilayer perceptron, convolutional neural network and recurrent neural network, there is no architecture suitable for representing sequences of probability distributions. Specifically, we address the task of forward prediction on distribution sequences.There are two main challenges in designing a network for sequences of probability distributions. First, conventional neural networks are unable to represent distributions compactly. Since each node encodes only a real value, a distribution has to be decomposed to smaller parts that are represented by separate nodes. When the distribution has been decomposed into separate nodes, the notion of distribution is no longer captured explicitly. Similarly, for image data, the fully-connected multilayer perceptron (MLP), unlike convolutional neural networks, fails to capture the notion of an image. A recently proposed network, Distribution Regression Network (DRN) BID8 , has solved this problem. DRN uses a novel representation of encoding an entire distribution in a single node, allowing DRN to use more compact models while achieving superior performance for distribution regression. It has been shown that DRN can achieve better accuracies with 500 times fewer parameters compared to MLP. However, despite the strengths of DRN, it is a feedforward network and hence it does not address a second problem, which is the need to model time dependencies in a distribution sequence.We address these two challenges and propose a recurrent extension of DRN, named the Recurrent Distribution Regression Network (RDRN). In the hidden states of RDRN, each node represents a distribution, thus containing much richer information while using fewer weights compared to the real-valued hidden states in RNN. This compact representation consequently results in better generalization performance. Compared to DRN, the shared weights in RDRN captures time dependencies better and results in better prediction performance. By having both compact distribution representations and modeling of time dependencies, RDRN is able to achieve superior prediction performance compared to the other methods. Neural network models work well by designing the architecture according to the data type. However, among the conventional neural network architectures, there is none that is designed for time-varying probability distributions. There are two key challenges in learning from distribution sequences. First, we require a suitable representation for probability distributions. Conventional neural networks, however, do not have suitable representations for distributions. As each node encodes only a real value, the distribution has to be split into smaller parts which are then represented by independent nodes. Hence, the neural network is agnostic to the distribution nature of the input data. A recently proposed Distribution Regression Network (DRN) addresses this issue. DRN has a novel network representation where each node encodes a distribution, showing improved accuracies compared to neural networks. However, a second challenge remains, which is to model the time dependencies in the distribution sequence. Both the recurrent neural network (RNN) and the Distribution Regression Network address only either one of the challenges. In this work, we propose our Recurrent Distribution Regression Network (RDRN) which extends DRN with a recurrent architecture. By having an explicit distribution representation in each node and shared weights across time steps, RDRN performs forward prediction on distribution sequences most effectively, achieving better prediction accuracies than RNN, DRN and other regression methods.",997,0.719,585,1.7042735042735042,"While deep neural networks achieved groundbreaking prediction results many tasks a class data where existing architectures optimal -- sequences probability distributions Performing forward prediction sequences distributions has many important applications However two main challenges designing a network model this task First neural networks unable encode distributions compactly as each node just a real value A recent work Distribution Regression Network solved an entire distribution resulting improved accuracies while using neural networks However despite its compact distribution representation DRN address the second challenge, model time dependencies a sequence distributions In our Recurrent Distribution Regression Network which adopts DRN The combination compact distribution representation shared weights architecture across time steps RDRN suitable modeling dependencies a distribution sequence Compared neural networks DRN RDRN achieves the best prediction performance while keeping compact Deep neural networks achieved state results by designing the network architecture according the data type For instance local filters capture max pooling the image representation size By using a series convolution and max pooling layers CNN extracts the semantic meaning The recurrent architecture when unrolled presents a shared weight structure designed model time dependencies a data sequence However among the major network architectures the multilayer perceptron there no architecture suitable representing sequences probability distributions Specifically address the task forward prediction on distribution sequencesThere designing a network sequences First conventional neural networks unable represent distributions compactly Since each node encodes only a real value a distribution has smaller parts represented separate nodes When the distribution has decomposed separate nodes the notion distribution no captured explicitly Similarly for image data the fully-connected multilayer perceptron unlike fails the notion A recently proposed network, Distribution Regression Network (DRN) BID8 , solved DRN uses a novel representation encoding an entire distribution allowing use more compact models while achieving distribution regression It shown DRN achieve better accuracies 500 times fewer parameters MLP However despite the strengths DRN a feedforward network hence address a second problem model time dependencies a distribution sequenceWe address and propose a recurrent extension named In the hidden states RDRN each node represents a distribution thus containing much richer information while using fewer weights compared in This compact representation consequently results better generalization performance Compared DRN the shared weights RDRN captures time dependencies better results By having both compact distribution representations modeling time dependencies RDRN achieve superior prediction performance compared Neural network models work by designing the architecture according the data type However among conventional neural none designed There two key challenges learning from distribution sequences First require a suitable representation probability distributions Conventional neural networks suitable representations distributions As each node encodes only a real value the distribution has split which represented independent nodes Hence the neural network agnostic the distribution nature A recently proposed Distribution Regression Network addresses DRN has a novel network representation where a distribution showing improved accuracies neural networks However a second challenge remains model the time dependencies the distribution sequence Both the recurrent neural network the Distribution Regression Network address only either one the challenges In this work propose our Recurrent Distribution Regression Network which extends DRN By having an explicit distribution representation each node and shared weights across time steps RDRN performs forward prediction distribution sequences most effectively achieving DRN",0.01,0.49850618177917244
"We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of computationally intensive matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-the-art results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a protein-protein interaction dataset (wherein test graphs remain unseen during training). Convolutional Neural Networks (CNNs) have been successfully applied to tackle problems such as image classification BID17 , semantic segmentation BID21 or machine translation BID13 , where the underlying data representation has a grid-like structure. These architectures efficiently reuse their local filters, with learnable parameters, by applying them to all the input positions.However, many interesting tasks involve data that can not be represented in a grid-like structure and that instead lies in an irregular domain. This is the case of 3D meshes, social networks, telecommunication networks, biological networks or brain connectomes. Such data can usually be represented in the form of graphs.There have been several attempts in the literature to extend neural networks to deal with arbitrarily structured graphs. Early work used recursive neural networks to process data represented in graph domains as directed acyclic graphs BID12 BID35 . Graph Neural Networks (GNNs) were introduced in BID15 and BID33 as a generalization of recursive neural networks that can directly deal with a more general class of graphs, e.g. cyclic, directed and undirected graphs. GNNs consist of an iterative process, which propagates the node states until equilibrium; followed by a neural network, which produces an output for each node based on its state. This idea was adopted and improved by , which propose to use gated recurrent units BID6 in the propagation step.Nevertheless, there is an increasing interest in generalizing convolutions to the graph domain. Advances in this direction are often categorized as spectral approaches and non-spectral approaches.On one hand, spectral approaches work with a spectral representation of the graphs and have been successfully applied in the context of node classification. In BID4 , the convolution operation is defined in the Fourier domain by computing the eigendecomposition of the graph Laplacian, resulting in potentially intense computations and non-spatially localized filters. These issues were addressed by subsequent works. BID18 introduced a parameterization of the spectral filters with smooth coefficients in order to make them spatially localized. Later, BID8 proposed to approximate the filters by means of a Chebyshev expansion of the graph Laplacian, removing the need to compute the eigenvectors of the Laplacian and yielding spatially localized filters. Finally, BID23 simplified the previous method by restricting the filters to operate in a 1-step neighborhood around each node. However, in all of the aforementioned spectral approaches, the learned filters depend on the Laplacian eigenbasis, which depends on the graph structure. Thus, a model trained on a specific structure can not be directly applied to a graph with a different structure.On the other hand, we have non-spectral approaches BID11 BID1 BID16 , which define convolutions directly on the graph, operating on groups of spatially close neighbors. One of the challenges of these approaches is to define an operator which works with different sized neighborhoods and maintains the weight sharing property of CNNs. In some cases, this requires learning a specific weight matrix for each node degree BID11 , using the powers of a transition matrix to define the neighborhood while learning weights for each input channel and neighborhood degree BID1 , or extracting and normalizing neighborhoods containing a fixed number of nodes BID29 . BID28 presented mixture model CNNs (MoNet), a spatial approach which provides a unified generalization of CNN architectures to graphs. More recently, BID16 introduced GraphSAGE, a method for computing node representations in an inductive manner. This technique operates by sampling a fixed-size neighborhood of each node, and then performing a specific aggregator over it (such as the mean over all the sampled neighbors' feature vectors, or the result of feeding them through a recurrent neural network). This approach has yielded impressive performance across several large-scale inductive benchmarks.Attention mechanisms have become almost a de facto standard in many sequence-based tasks BID2 BID13 . One of the benefits of attention mechanisms is that they allow for dealing with variable sized inputs, focusing on the most relevant parts of the input to make decisions. When an attention mechanism is used to compute a representation of a single sequence, it is commonly referred to as self-attention or intra-attention. Together with Recurrent Neural Networks (RNNs) or convolutions, self-attention has proven to be useful for tasks such as machine reading BID5 and learning sentence representations BID25 . However, BID38 showed that not only self-attention can improve a method based on RNNs or convolutions, but also that it is sufficient for constructing a powerful model obtaining state-of-the-art performance on the machine translation task.Inspired by this recent work, we introduce an attention-based architecture to perform node classification of graph-structured data. The idea is to compute the hidden representations of each node in the graph, by attending over its neighbors, following a self-attention strategy. The attention architecture has several interesting properties: (1) the operation is efficient, since it is parallelizable across nodeneighbor pairs; (2) it can be applied to graph nodes having different degrees by specifying arbitrary weights to the neighbors; and (3) the model is directly applicable to inductive learning problems, including tasks where the model has to generalize to completely unseen graphs. We validate the proposed approach on four challenging benchmarks: Cora, Citeseer and Pubmed citation networks as well as an inductive protein-protein interaction dataset, achieving or matching state-of-the-art results that highlight the potential of attention-based models when dealing with arbitrarily structured graphs.It is worth noting that, as BID23 and BID1 , our work can also be reformulated as a particular instance of MoNet BID28 . Moreover, our approach of sharing a neural network computation across edges is reminiscent of the formulation of relational networks BID32 and VAIN BID20 , wherein relations between objects or agents are aggregated pair-wise, by employing a shared mechanism. Similarly, our proposed attention model can be connected to the works by BID10 and BID9 , which use a neighborhood attention operation to compute attention coefficients between different objects in an environment. Other related approaches include locally linear embedding (LLE) BID31 and memory networks BID40 . LLE selects a fixed number of neighbors around each data point, and learns a weight coefficient for each neighbor to reconstruct each point as a weighted sum of its neighbors. A second optimization step extracts the point's feature embedding. Memory networks also share some connections with our work, in particular, if we interpret the neighborhood of a node as the memory, which is used to compute the node features by attending over its values, and then is updated by storing the new features in the same position. We have presented graph attention networks (GATs), novel convolution-style neural networks that operate on graph-structured data, leveraging masked self-attentional layers. The graph attentional layer utilized throughout these networks is computationally efficient (does not require computationally intensive matrix operations, and is parallelizable across all nodes in the graph), allows for (implicitly) assigning different importances to different nodes within a neighborhood while dealing with different sized neighborhoods, and does not depend on knowing the entire graph structure upfrontthus addressing many of the theoretical issues with previous spectral-based approaches. Our models leveraging attention have successfully achieved or matched state-of-the-art performance across four well-established node classification benchmarks, both transductive and inductive (especially, with completely unseen graphs used for testing).There are several potential improvements and extensions to graph attention networks that could be addressed as future work, such as overcoming the practical problems described in subsection 2.2 to be able to handle larger batch sizes. A particularly interesting research direction would be taking advantage of the attention mechanism to perform a thorough analysis on the model interpretability. Moreover, extending the method to perform graph classification instead of node classification would also be relevant from the application perspective. Finally, extending the model to incorporate edge features (possibly indicating relationship among nodes) would allow us to tackle a larger variety of problems.",1783,0.89,1073,1.6616961789375582,"We present graph attention networks novel neural network operate leveraging masked self-attentional layers address the shortcomings prior methods based graph convolutions or By stacking layers in which nodes able attend over their neighborhoods' features enable ( specifying different weights without computationally intensive matrix operation inversion depending knowing the graph structure upfront In this way address several key challenges spectral-based graph neural networks simultaneously make our model readily inductive as transductive problems Our GAT models achieved or matched state results across four established transductive graph benchmarks the Cora, Citeseer and Pubmed citation network datasets as a protein-protein interaction datasetwherein test graphs remain unseen during training successfully tackle image classification BID17 , semantic segmentation BID21 or machine translation BID13 where the underlying data representation These architectures efficiently reuse their local filters with learnable parameters by applying all the input positionsHowever many interesting tasks involve data and instead lies an irregular domain This the case 3D meshes social networks telecommunication networks biological networks or brain connectomes Such data usually represented graphsThere have extend neural networks deal arbitrarily structured graphs Early work used recursive neural networks process represented graph domains as directed acyclic graphs BID12 BID35 . Graph Neural Networks were introduced BID15 as directly deal a more general class graphs GNNs consist propagates the node states until equilibrium; followed produces for based This idea adopted and improved , propose gated recurrent units BID6 in the propagation stepNevertheless an increasing interest convolutions the graph domain Advances this direction often categorized spectral approachesOn work a spectral representation the graphs have successfully node classification In BID4 , the convolution operation defined the Fourier domain computing the eigendecomposition resulting potentially intense computations non-spatially localized filters These issues subsequent works BID18 introduced a parameterization the spectral filters with smooth coefficients make spatially localized Later BID8 proposed approximate the filters means a Chebyshev expansion removing compute yielding spatially localized filters Finally BID23 simplified the previous method restricting the filters operate a 1-step neighborhood around However all the aforementioned spectral approaches the learned filters depend the Laplacian eigenbasis depends the graph structure Thus a model trained a specific structure not directly a graph withOn we non-spectral approaches BID11 BID1 BID16 define convolutions directly operating groups spatially close neighbors One these approaches define an operator works different sized neighborhoods maintains the weight sharing property CNNs requires learning a specific weight matrix each node degree BID11 , using the powers a transition matrix while learning each input channel neighborhood degree or extracting and normalizing neighborhoods containing BID29 BID28 presented mixture model CNNsMoNet a spatial approach a unified generalization architectures graphs More recently BID16 introduced GraphSAGE computing node representations an inductive manner This technique operates sampling a fixed-size neighborhood each node performing a specific aggregator over ( the mean over all the sampled neighbors' feature vectors the result feeding through This approach yielded impressive performance across several large-scale inductive benchmarksAttention mechanisms become many sequence-based tasks BID2 BID13 . One attention mechanisms dealing variable sized inputs focusing When an attention mechanism used compute a representation a single sequence commonly self-attention or intra Together Recurrent Neural Networks or convolutions self-attention has proven tasks machine reading BID5 learning sentence representations BID25 . However BID38 showed not only self-attention can a method based RNNs or convolutions sufficient constructing a powerful model obtaining state performance the machine translation taskInspired introduce an attention-based architecture perform node classification The idea compute the hidden representations each node by attending over its neighbors following a self-attention strategy The attention architecture several interesting properties ( the operation efficient since parallelizable across nodeneighbor pairs graph nodes having different degrees by specifying arbitrary weights to the neighbors the model directly applicable inductive learning problems including tasks generalize completely unseen graphs We validate the proposed approach on four challenging benchmarks Cora, Citeseer and Pubmed citation networks as an inductive protein-protein interaction dataset achieving or matching state that highlight attention-based models when dealing arbitrarily structured graphsIt worth, BID23 and , can reformulated a particular instance MoNet BID28 Moreover our approach of sharing a neural network computation across edges reminiscent the formulation relational networks BID32 VAIN BID20 , wherein relations objects or agents pair- by employing a shared mechanism Similarly our proposed attention model can connected the works by BID10 , use a neighborhood attention operation compute attention coefficients between different objects Other related approaches locally linear embedding (LLE BID31 and memory networks BID40 . LLE selects a fixed number neighbors around learns a weight coefficient reconstruct each point A second optimization step extracts the point's feature embedding Memory networks also share some connections our work in if interpret the neighborhood, used compute the node features by attending over its values is updated storing We presented graph attention networks novel convolution-style neural networks operate leveraging masked self-attentional layers The graph attentional layer utilized throughout these networks computationallydoes parallelizable allows ( assigning different importances a neighborhood while dealing different sized neighborhoods does depend knowing upfrontthus addressing previous spectral-based approaches Our models leveraging attention have successfully achieved or matched state four well node classification benchmarks both transductiveespecially, with completely unseen graphs used testing).There several potential improvements extensions graph attention networks addressed future work, overcoming the practical problems described subsection to be handle larger batch sizes A particularly interesting research direction would taking the attention mechanism to perform on the model interpretability Moreover extending the method perform graph classification instead node classification relevant from Finally extending the model incorporate edge features (possibly indicating relationship among nodes tackle a larger variety",0.01,0.3900228976260837
"While bigger and deeper neural network architectures continue to advance the state-of-the-art for many computer vision tasks, real-world adoption of these networks is impeded by hardware and speed constraints. Conventional model compression methods attempt to address this problem by modifying the architecture manually or using pre-defined heuristics. Since the space of all reduced architectures is very large, modifying the architecture of a deep neural network in this way is a difficult task. In this paper, we tackle this issue by introducing a principled method for learning reduced network architectures in a data-driven way using reinforcement learning. Our approach takes a larger 'teacher' network as input and outputs a compressed 'student' network derived from the 'teacher' network. In the first stage of our method, a recurrent policy network aggressively removes layers from the large 'teacher' model. In the second stage, another  recurrent policy network carefully reduces the size of each remaining layer. The resulting network is then evaluated to obtain a reward -- a score based on the accuracy and compression of the network. Our approach uses this reward signal with policy gradients to train the policies to find a locally optimal student network. Our experiments show that we can achieve compression rates of more than 10x for models such as ResNet-34 while maintaining similar performance to the input 'teacher' network. We also present a valuable transfer learning result which shows that policies which are pre-trained on smaller 'teacher' networks can be used to rapidly speed up training on larger 'teacher' networks. While carefully hand-designed deep convolutional networks continue to increase in size and in performance, they also require significant power, memory and computational resources, often to the point of prohibiting their deployment on smaller devices. As a result, researchers have developed model compression techniques based on Knowledge Distillation to compress a large (teacher) network to a smaller (student) network using various training techniques (e.g., soft output matching, hint layer matching, uncertainty modeling). Unfortunately, state-of-the-art knowledge distillation methods share a common feature: they require carefully hand-designed architectures for the student model. Hand-designing networks is a tedious sequential process, often loosely guided by a sequence of trial-and-error based decisions to identify a smaller network architecture. This process makes it very difficult to know if the resulting network is optimal. Clearly, there is a need to develop more principled methods of identifying optimal student architectures. Towards a more principled approach to network architecture compression, we present a reinforcement learning approach to identify a compressed high-performance architecture (student) given knowledge distilled from a larger high-performing model (teacher). We make a key conceptual assumption that formulates the sequential process of converting a teacher network to a student network as a Markov Decision Process (MDP). Under this model, a state s represents the network architecture. Clearly, the domain of the state S is very large since it contains every possible reduced architecture of the teacher network. A deterministic transition in this state space, T (s |s, a), is determined by selecting the action a, e.g., removing a convolutional filter or reducing the size of a fully connected layer. Each action will transform one architecture s to another architecture s . Under the MDP, the strategy for selecting an action given a certain state is represented by the policy π(a|s), which stochastically maps a state to an action. The process of reinforcement learning is used to learn an optimal policy based on a reward function r(s) defined over the state space. In our work, we define the reward function based on the accuracy and the compression rate of the specified architecture s.A straightforward application of reinforcement learning to this problem can be very slow depending on the definition of the action space. For example, an action could be defined as removing a single filter from every layer of a convolutional neural network. Since the search space is exponential in the size of the action space and sequence length, it certainly does not scale to modern networks that have hundreds of layers.Our proposed approach addresses the problem of scalability in part, by introducing a two-stage action selection mechanism which first selects a macro-scale ""layer removal"" action, followed by a micro-scale ""layer shrinkage"" action. In this way we enable our reinforcement learning process to efficiently explore the space of reduced networks. Each network architecture that is generated by our policy is then trained with Knowledge Distillation BID12 . FIG0 illustrates our proposed approach.To the best of our knowledge, this is the first paper to provide a principled approach to the task of network compression, where the architecture of the student network is obtained via reinforcement learning. To facilitate reinforcement learning, we propose a reward function that encodes both the compression rate and the accuracy of the student model. In particular, we propose a novel formulation of the compression reward term based on a relaxation of a constrained optimization problem, which encodes the hardware-based computational budget items in the form of linear constraints.We demonstrate the effectiveness of our approach over several network architectures and several visual learning tasks of varying difficulty (MNIST, SVHN, CIFAR-10, CIFAR-100, Caltech-256). We also demonstrate that the compression policies exhibit generalization across networks with similar architectures. In particular, we use a policy trained on a ResNet-18 model on a ResNet-34 model and show that it greatly accelerates the reinforcement learning process. We introduced a novel method for compressing neural networks. Our approach employs a two-stage layer removal and layer shrinkage procedure to learn how to compress large neural networks. By leveraging signals for accuracy and compression as supervision, our method efficiently learns to search the space of model architectures. We show that our method performs well over a variety of datasets and architectures. We also observe generalization capabilities of our method through transfer learning, allowing our procedure to be made even more efficient. Our method is also able to incorporate other practical constraints, such as power or inference time, thus showing potential for application in a real world setting.",1194,0.694,700,1.7057142857142857,"While bigger and deeper neural network architectures continue advance the state for real-world adoption impeded hardware and speed constraints Conventional model compression methods attempt address modifying manually or Since the space of all reduced architectures very modifying in In tackle introducing a principled method learning reduced network Our approach takes a larger 'teacher' network as input derived In our method a recurrent policy network aggressively removes layers the large 'teacher' model In the second stage another recurrent policy network carefully reduces each remaining layer The resulting network then evaluated obtain a reward -- a score compression Our approach uses this reward signal with policy gradients train the policies find a locally optimal student network Our experiments we achieve compression rates models such ResNet-34 while the input 'teacher' network We also present a valuable transfer learning result which policies pretrained smaller 'teacher' networks rapidly speed training While carefully hand-designed deep convolutional networks continue increase in performance require significant power memory often prohibiting smaller devices As researchers model compression techniques based Knowledge Distillation a large (teacher) network using various training techniquese.g., soft output matching hint layer matching uncertainty modeling Unfortunately stateof knowledge distillation methods share carefully hand-designed architectures the student model Hand-designing networks a tedious sequential process often loosely guided to a smaller network architecture This process makes know the resulting network optimal Clearly develop more principled methods identifying optimal student architectures network architecture compression present identify a compressed high-performance architecturestudent given knowledge distilled a larger high-performing model We make a key conceptual assumption formulates the sequential process converting a teacher network as a Markov Decision Process Under this model a state s represents the network architecture Clearly the domain the state S is very large since every possible reduced architecture the teacher network A deterministic transition this state space T (s |s a determined selecting the action a, removing reducing a fully connected layer Each action transform one architecture s to . Under the MDP the strategy selecting an action given a certain state represented the policy ��a|s stochastically maps The process reinforcement learning used an optimal policy based a reward function r(s defined over In our work define the reward function based the accuracy the compression rate the specified architecture s.A straightforward application reinforcement learning very slow depending the definition the action space For example an action could defined removing a single filter every layer Since the search space exponential the action space sequence length certainly scale modern networks hundreds layersOur proposed approach addresses part, introducing a two-stage action selection mechanism which first a macro-scale ""layer removal"" action In this way enable our reinforcement learning process efficiently explore the space reduced networks Each network architecture that generated our policy then trained Knowledge Distillation BID12 . FIG0 illustrates our proposed approachTo the the task network compression where the architecture the student network obtained To facilitate reinforcement learning propose a reward function both the compression rate the student model In particular propose the compression reward term based a relaxation a constrained optimization problem encodes the hardware-based computational budget items linear constraintsWe demonstrate the effectiveness over several network architectures several visual learning tasks ofMNIST SVHN Caltech-256 We also demonstrate the compression policies exhibit generalization networks similar architectures In particular use a policy trained a ResNet-18 model on show greatly We introduced compressing neural networks Our approach employs a two-stage layer removal layer shrinkage procedure learn compress large neural networks By leveraging signals for accuracy compression as supervision our method efficiently learns search the space model architectures We show our method performs over a variety datasets architectures We also observe generalization capabilities our method through transfer learning allowing our procedure made even Our method also able incorporate other practical constraints power or inference time thus showing potential application real setting",0.01,0.5021771663046105
"Recent advances in conditional image generation tasks, such as image-to-image translation and image inpainting, are largely accounted to the success of conditional GAN models, which are often optimized by the joint use of the GAN loss with the reconstruction loss. However, we reveal that this training recipe shared by almost all existing methods causes one critical side effect: lack of diversity in output samples. In order to accomplish both training stability and multimodal output generation, we propose novel training schemes with a new set of losses named moment reconstruction losses that simply replace the reconstruction loss. We show that our approach is applicable to any conditional generation tasks by performing thorough experiments on image-to-image translation, super-resolution and image inpainting using Cityscapes and CelebA dataset. Quantitative evaluations also confirm that our methods achieve a great diversity in outputs while retaining or even improving the visual fidelity of generated samples. Recently, active research has led to a huge progress on conditional image generation, whose typical tasks include image-to-image translation BID11 ), image inpainting BID31 ), super-resolution BID18 ) and video prediction BID27 ). At the core of such advances is the success of conditional GANs BID28 ), which improve GANs by allowing the generator to take an additional code or condition to control the modes of the data being generated. However, training GANs, including conditional GANs, is highly unstable and easy to collapse BID8 ). To mitigate such instability, almost all previous models in conditional image generation exploit the reconstruction loss such as 1 / 2 loss in addition to the GAN loss. Indeed, using these two types of losses is synergetic in that the GAN loss complements the weakness of the reconstruction loss that output samples are blurry and lack high-frequency structure, while the reconstruction loss offers the training stability required for convergence.In spite of its success, we argue that it causes one critical side effect; the reconstruction loss aggravates the mode collapse, one of notorious problems of GANs. In conditional generation tasks, which are to intrinsically learn one-to-many mappings, the model is expected to generate diverse outputs from a single conditional input, depending on some stochastic variables (e.g. many realistic street scene images for a single segmentation map BID11 ). Nevertheless, such stochastic input rarely generates any diversity in the output, and surprisingly many previous methods omit a random noise source in their models. Most papers rarely mention the necessity of random noise, and a few others report that the model completely ignores the noise even if it is fed into the model. For example, BID11 state that the generator simply learns to ignore the noise, and even dropout fails to incur meaningful output variation.The objective of this paper is to propose a new set of losses named moment reconstruction losses that can replace the reconstruction loss with losing neither the visual fidelity nor diversity in output samples. The core idea is to use maximum likelihood estimation (MLE) loss (e.g. 1 / 2 loss) to predict conditional statistics of the real data distribution instead of applying it directly to the generator as done in most existing algorithms. Then, we assist GAN training by enforcing the generated distribution to match its statistics to the statistics of the real distribution.In summary, our major contributions are three-fold. First, we show that there is a significant mismatch between the GAN loss and the reconstruction loss, thereby the model cannot achieve the optimality w.r.t. both losses. Second, we propose two novel loss functions that enable the model to accomplish both training stability and multimodal output generation. Our methods simply replace the reconstruction loss, and thus are applicable to any conditional generation tasks. Finally, we show the effectiveness and generality of our methods through extensive experiments on three generation tasks, including image-to-image translation, super-resolution and image inpainting, where our methods outperform recent strong baselines in terms of realism and diversity. In this work, we pointed out that there is a mismatch between the GAN loss and the conventional reconstruction losses. As alternatives, we proposed a set of novel loss functions named MR loss and proxy MR loss that enable conditional GAN models to accomplish both stability of training and multimodal generation. Empirically, we showed that our loss functions were successfully integrated with multiple state-of-the-art models for image translation, super-resolution and image inpainting tasks, for which our method generated realistic image samples of high visual fidelity and variability on Cityscapes and CelebA dataset.There are numerous possible directions beyond this work. First, there are other conditional generation tasks that we did not cover, such as text-to-image synthesis, text-to-speech synthesis and video prediction, for which our methods can be directly applied to generate diverse, high-quality samples. Second, in terms of statistics matching, our methods can be extended to explore other higher order statistics or covariance. Third, using the statistics of high-level features may capture additional correlations that cannot be represented with pixel-level statistics.",973,0.466,599,1.6243739565943238,"Recent advances conditional image generation tasksto translation inpainting largely accounted to the success conditional GAN models optimized the joint use the GAN loss with the reconstruction loss However we reveal this training recipe shared almost all existing methods causes one critical side effect lack diversity output samples In order accomplish both training stability multimodal output generation propose novel training schemes losses named moment reconstruction losses simply We show our approach applicable any conditional generation tasks by performing thorough experiments imageto translation super inpainting Cityscapes CelebA dataset Quantitative evaluations also confirm our methods achieve a great diversity outputs while retaining or the visual fidelity generated samples Recently active research led a huge progress conditional image generation whose typical tasksto translation BID11 ), inpainting super video prediction At such advances the success conditional GANs BID28 ), improve the generator take an additional code or condition control the modes However training GANs including conditional GANs highly unstable easy collapse BID8 ). To mitigate such instability almost all previous models in conditional image generation exploit the reconstruction loss such 1 / 2 loss addition Indeed using these two types losses synergetic the GAN loss complements the weakness the reconstruction loss that output samples blurry lack high-frequency structure offers the training stability convergenceIn spite its success argue causes one critical side effect; aggravates the mode collapse one notorious problems conditional generation tasks which to intrinsically learn expected diverse outputs depending some stochastic variables (e.g. many realistic street scene images for a single segmentation map BID11 Nevertheless such stochastic input rarely generates any diversity surprisingly many previous methods omit a random noise source Most papers rarely the necessity random noise a few others report the model completely even fed For example BID11 state the generator simply learns ignore even dropout fails incur meaningful output variationThe objective propose losses named moment reconstruction losses replace the reconstruction loss losing neither the visual fidelity diversity output samples The core idea maximum likelihood estimation (MLE) loss ( conditional statistics the real data distribution instead applying the generator as done most existing algorithms Then assist GAN training enforcing the generated distribution to match its statistics to the real distributionIn summary our major contributions three First show the GAN loss the reconstruction loss thereby the model achieve both losses Second propose two novel loss functions enable the model accomplish both training stability multimodal output generation Our methods simply replace the reconstruction loss, thus are applicable any conditional generation tasks Finally show the effectiveness generality our methods through extensive experiments three generation tasks imageto translation super inpainting where recent strong baselines realism diversity In this work pointed the GAN loss the conventional reconstruction losses As alternatives proposed novel loss functions named MR loss proxy MR loss enable conditional GAN models accomplish both stability of training multimodal generation we showed our loss functions successfully integrated multiple state models image translation superresolution and image inpainting tasks for our method generated realistic image samples high visual fidelity variability on Cityscapes CelebA datasetThere numerous possible directions beyond First there other conditional generation tasks did cover textimage synthesis video prediction for our methods directly generate Second terms statistics matching our methods can extended explore other higher order statistics or covariance Third using the statistics high-level features may capture additional correlations represented pixel-level statistics",0.01,0.29492915419012383
"Generative models are important tools to capture and investigate the properties of complex empirical data. Recent developments such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) use two very similar, but \textit{reverse}, deep convolutional architectures, one to generate and one to extract information from data. Does learning the parameters of both architectures obey the same rules? We exploit the causality principle of independence of mechanisms to quantify how the weights of successive layers adapt to each other. Using the recently introduced Spectral Independence Criterion, we quantify the dependencies between the kernels of successive convolutional layers and show that those are more independent for the generative process than for information extraction, in line with results from the field of causal inference. In addition, our experiments on generation of human faces suggest that more independence between successive layers of generators results in improved performance of these architectures.
 Deep generative models have proven powerful in learning to design realistic images in a variety of complex domains (handwritten digits, human faces, interior scenes). In particular, two approaches have recently emerged: Generative Adversarial Networks (GANs) BID8 , which train an image generator by having it fool a discriminator that should tell apart real from artificially generated images; and Variational Autoencoders (VAEs) BID15 BID21 ) that learn both a mapping from latent variables to the data (the decoder) and the converse mapping from the data to the latent variables (the encoder), such that correspondences between latent variables and data features can be easily investigated. Although these architecture have been lately the subject of extensive investigations, understanding why and how they work, and how they can be improved, remains elusive.An interesting feature of GANs and VAEs is that they both involve the learning of two deep subnetworks. These sub-networks have a ""mirrored"" architecture, as they both consist in a hierarchy of convolutional layers, but information flows in opposite ways: generators and decoders map latent variables to the data space, while discriminators and encoders extract information from the same space. Interestingly, this difference could be framed in a causal perspective, with information flowing in the causal direction in the case of generators (from the putative causes of variations in the observed data), while extracting high level properties from the observations (with encoders or discriminators) would operate in the anti-causal direction.Generative models in machine learning are usually not required to be causal, as modeling the data distribution is considered to be the goal to achieve. However, the idea that a generative model able to capture the causal structure of the data by disentangling the contribution of independent factors should perform better has been suggested in the literature BID0 BID17 and evidence supports that this can help the learning procedure BID1 . Although many approaches have been implemented on specific examples, principles and automated ways of learning disentangled representations from data remains largely an open problem both for learning representations (targeting supervised learning applications) and for fitting good generative models. GANs have for example recently been a subject of intensive work in this direction, leading to algorithms disentangling high level properties of the data such as InfoGans BID2 or conditional GANs BID18 . However such models require supervision (e.g. feeding digit labels as additional inputs) to disentangle factors of interest. Unsupervised learning of disentangled representations has been addressed in various frameworks including Restricted Boltzmann Machines BID6 , tensor analyzers BID26 and Lie groups BID4 . A recent attempt to address unsupervised learning in VAEs is β-VAE BID10 which introduces and adjustable parameter β in the VAE objective to strengthen the data compression constraint with respect to reconstruction error.While the above approaches envision the disentangling of representations as finding subsets of latent variables that relate to different properties of the generated data, parameters of the network can be also considered as factors affecting the generated data. Ideally, to ensure modularity of deep generative models, different layers should encode different aspects of the data in their parameters. Intuitively for deep convolutional networks, different layers should encode image features at different scales. The idea that successive layers can be used as modules encoding different levels of details has for example been exploited to build high-resolution generative models by training iteratively a GAN with an increasing number of layers BID14 . Enforcing modularity of trained neural architecture may not only allow to adapt them to the task at hand with minimum additional training, but also to better understand the structure and function of these highly complex black-box systems. However, to the best of our knowledge, assessing how independent (or disentangled) are the properties encoded by the weights distributed across the structure of deep networks has not been addressed quantitatively in the literature.We propose that the coupling between high dimensional parameters can be quantified and exploited in a causal framework to infer whether the layered architecture disentangles different aspects of the data. This hypothesis relies on recent work exploiting the postulate of Independence of Cause and Mechanism stating that Nature chooses independently the properties of a cause and those of the mechanism that generate effects from the cause BID13 . Several methods relying on this principle have been proposed in the literature in association to different model classes BID28 BID5 BID24 BID23 . Among these methods, the Spectral Independence Criterion (SIC) BID24 can be used in the context of linear dynamical systems, which involve a convolution mechanism.In this paper, we show how SIC can be adapted to investigate the coupling between the parameters of successive convolutional layers. Empirical investigation shows that SIC is approximately valid between successive layers of generative models, and suggests SIC violations indicate deficiencies in the learning algorithm or the architecture of the network. Interestingly, and in line with theoretical predictions BID24 , SIC tends to be more satisfied for generative sub-networks (mapping latent variables to data), than for the part of the system that map the anti-causal direction (data to latent variables). In addition, comparison of different generative models indicates that more independence between layers is associated to better performance of the model. Overall, our study suggests that quantifying Independence of Mechanisms in deep architecture can help analyze and design better generative models. In this work, we derived a measure of independence between the weights learned by convolutional layers of deep networks. The results suggest that generative models that map latent variables to data tend to have more independence between successive layers than discriminative or encoding networks. This is in line with theoretical predictions about independence of mechanisms for causal and anti-causal systems. In addition, our results suggest the dependency between successive layers relates to the bad performance of the trained generative models. Moreover, the SDR analysis also indicates which layers should be modified to improve the performance. Enforcing independence during training may thus help diagnose and improve generative models. Finally, we speculate that independence between successive layers, by favoring modularity of the network, may help build architectures that can be easily adapted to new purposes. In particular, separation of spatial scales in such models may help build networks in which one can intervene on one scale without affecting others, with applications such as style transfer BID7 . One specific feature of our approach is that this quantitative measure of the network performance in not statistical and as such requires neither extensive sampling form the fitted generative distribution nor from real datasets to be computed: only the parameters of the model are used. This is in strong contrast with state-ofthe-art approaches such as the Fréchet Inception Distance (FID) BID9 , and makes the approach easy to apply to any neural network equipped with convolutional layers.",1529,0.718,883,1.7315968289920725,"Generative models capture investigate complex empirical data Recent developments such Generative Adversarial Networks Variational Auto-Encoders use two very, \textit{reverse to generate extract Does learning the parameters both architectures obey We exploit the causality principle independence mechanisms quantify the weights successive layers adapt Using the recently introduced Spectral Independence Criterion quantify the dependencies the kernels show those are more independent for information extraction line results the field causal inference In addition our experiments on generation human faces suggest more independence between successive layers generators results improved performance these architectures Deep generative models proven powerful learning design realistic images complex domainshandwritten digits interior scenes In particular two approaches recently Generative Adversarial Networks (GANs) BID8 , train an image generator having fool that should tell apart real from ) learn both a mapping latent variables (the decoder the converse mapping such correspondences data features easily investigated Although these architecture have lately extensive investigations understanding whyAn interesting feature GANs and VAEs both involve the learning two deep subnetworks These sub a ""mirrored"" architecture as both consist in a hierarchy convolutional layers information opposite ways generators map latent variables the data space discriminators extract Interestingly this difference could framed a causal perspective information flowing in generatorsfrom the putative causes variations extracting high level propertieswith encoders or discriminators operateGenerative models in not required causal modeling the data distribution considered the goal to However the idea a generative model able capture by the contribution independent factors should perform has BID0 BID17 evidence supports can help the learning procedure . Although many approaches implemented on specific examples principles automated ways learning disentangled representations data remains both learning representations (targeting supervised learning applications fitting good generative models GANs for example recently a subject intensive work this direction leading algorithms disentangling high level properties such InfoGans BID2 or conditional GANs BID18 . However such models require supervision ( feeding digit labels as additional inputs factors Unsupervised learning disentangled representations has addressed various frameworks Restricted Boltzmann Machines BID6 , tensor analyzers BID26 and Lie groups A recent attempt address unsupervised learning VAEs β-VAE BID10 which introduces and adjustable parameter β in to strengthen the data compression constraint with respect reconstruction errorWhile the above approaches envision representations as finding subsets latent variables relate different properties parameters the network also factors Ideally to ensure modularity deep generative models different layers encode different aspects their parameters Intuitively for deep convolutional networks different layers should encode image features The idea successive layers can used modules encoding different levels details for example exploited build by training iteratively a GAN with layers BID14 . Enforcing modularity trained neural architecture may adapt them with minimum additional training better these highly complex black-box systems However to assessing independent ( disentangled are the properties encoded the weights distributed deep networks has addressed quantitativelyWe the coupling high dimensional parameters can exploited a causal framework infer the layered architecture different aspects This hypothesis relies recent work exploiting the postulate Independence Cause Mechanism stating Nature chooses independently the properties a cause those generate effects from BID13 . Several methods relying this principle in association to different model classes BID28 BID5 BID24 BID23 . Among these methods Spectral Independence BID24 can linear dynamical systems involve a convolution mechanismIn adapted investigate the parameters shows SIC approximately valid between successive layers generative models suggests SIC violations indicate deficiencies or the architecture Interestingly and line theoretical predictions BID24 , SIC tends satisfied for generative sub (mapping latent variables data the part map the anti-causal directiondata In addition comparison different generative models indicates more independence layers associated to Overall our study quantifying Independence Mechanisms deep architecture analyze design better generative models In this work derived independence the weights learned convolutional layers deep networks The results suggest generative models that map latent variables data tend more independence between successive layers or encoding networks This in line theoretical predictions independence mechanisms In addition our results the dependency successive layers relates the bad performance the trained generative models Moreover the SDR analysis which layers should modified Enforcing independence during training may thus help diagnose improve generative models Finally speculate that independence between successive layers, by favoring modularity build architectures new purposes In particular separation spatial scales in such models build networks one can intervene with applications style transfer BID7 . One specific feature our approach this quantitative measure the network performance in not statistical and as requires neither extensive sampling form the fitted generative distribution from real datasets computed: This in strong contrast state-ofthe-art approaches Fréchet Inception Distance BID9 , makes easy any neural network equipped",0.01,0.5681236125610228
"Many deep reinforcement learning approaches use graphical state representations,
 this means visually distinct games that share the same underlying structure cannot
 effectively share knowledge. This paper outlines a new approach for learning
 underlying game state embeddings irrespective of the visual rendering of the game
 state. We utilise approaches from multi-task learning and domain adaption in
 order to place visually distinct game states on a shared embedding manifold. We
 present our results in the context of deep reinforcement learning agents. Games have often been used in order to experiment with new approaches with Artificial Intelligence (AI) research. Games provide flexibility to simulate a range of problems such as fully observable vs partially observable, stochastic vs discrete and noisy vs noise free environments. This first started with digital versions of board games being used such as backgammon and chess. More recently video games have begun to provide a plethora of digital environments and tasks for benchmarking AI systems. These new systems use neural networks and are usually trained using the raw pixel values of game frames, meaning the networks have to interpret these pixels into game states that can then be used to learn an optimal policy for play. Due to the fact that they use these raw pixel values they are sensitive to changes in the visuals of the game used, this results in very little knowledge transfer between visually distinct games BID25 resulting in the networks learning each game individually without any representation overlap. Games are usually very visually distinct as concepts are often abstract, especially for puzzle games. Early video games were often like this because it is very computationally expensive to create games that accurately imitate the real world, whereas more modern games may take a more abstract representation due to the financial expense.Learning representations has long been an important area of AI research. It has led to many new approaches to producing representations for many applications, such as word embeddings BID1 and style transfer BID6 . In the case of word embeddings networks can be used to solve various tasks such as predicting the context within which each word appears, the outputs of one of the hidden layers can then be used in order represent that word. This then results in word embeddings that place words that appear in similar contexts within close proximity to each other in the embedding space BID1 ). These resulting embeddings can then be used in order to solve more complex tasks without the system having to train from raw input. This could be seen as a form of knowledge transfer as the knowledge of the meaning of words has been encoded into its embedding and can then be used with new networks working on new tasks without the need to learn this mapping between words and their context again BID27 .In our work we improve knowledge representation across tasks that have underlying similarities but are represented in a visually distinct way. The architecture we propose in this paper learns representations that are independent of the visual differences of the games. This will result in the strategic elements of the game playing network to share knowledge between visually distinct games.In order to achieve this we use and extend work that has been done around domain adaption. Domain adaption seeks to produce shared representation between two separate domains a source domain and a target, such as high resolution product photos and images taken with a low resolution webcam BID5 . We present a method for using similar techniques in the domain of reinforcement learning allowing an agent to learn domain independent representations for a group of similar games that are visually distinct. This paper will first ground our work in the context of both learning representations and reinforcement learning. We will then outline the environment that the networks were trained in along with the desired outcomes. We will finally present the resulting representations and outline future work to extend this approach.2 RELATED WORK 2.1 AI AND GAMES Games provide a good benchmark for AI as they require high level reasoning and planning BID32 BID18 . This means that they have often been used to signify advances in the state of the art such as with Deep Blue the chess playing AI that beat Gary Kasparov BID2 and AlphaGo the go playing agent that beat Lee Sedol . Games also provide a nice interface for agents to be able to either look into the internal state of the games, as needed for methods such as Monte carlo tree search (MCTS) , or can provide visual representations of state that can be used by agents . Games also allow agents to process experiences much faster than would be possible in the real world. This means data hungry methods are still able to learn in a relatively short period of time BID13 ).There has also been a significant amount of research into other areas of game playing, such as competitions aimed at agents passing a form of Turing Test in order to rank agents based on their ability to mimic human play BID9 ). Most of these systems have revolved around using data from human play in order to achieve this goal BID24 BID14 . There have also been competitions organised in order to assess agents ability to generalise across a variety of games, the General Game Playing Competition BID7 focusing on playing multiple board games, and the General Video Game Playing Competition that assess agents performance across a broad range of video games. Other work has also started that uses modified versions of game engines in order to provide environments to teach AI, these include Project Malmo that uses the popular Minecraft Game in order to provide an experimentation platform for AI agents BID11 , and OpenArena, a modified version of the ID Tech 3 engine used by Quake 3, in order to train and benchmark AI at a range of tasks including path finding in a Labyrinth and laser tag BID10 ).There has also been some work in using neural evolution to evolve a network to control an agent in an first-person shooter (FPS) environment BID22 . Others have investigated the use of hierarchical approaches in the design of AI agents for FPS games BID28 that use networks in a hierarchical fashion to deconstruct the tasks into sub-skills. As our results show it is possible for our system to separate game states from raw pixel values despite the renderings of the game being so distinct. It also effectively separates out states that require a different task to be completed, with the game states that contain pickups being in a distinct but related space to the states that require the player to now head towards the goal. This shows that the learned embeddings are capturing a lot about how the game is played irrespective of how the frame is rendered. We show that this is possible in the context of deep reinforcement learning for domain adaptions to be successfully achieved using adversarial networks. Our network also manages to deal with more visually diverse inputs than was possible with a network that fully shares its parameters. As the results have shown the single shared convolutional layers did not have the capacity to deal with the differences between the visual representations of the game. We have shown that it is possible to use adversarial networks along with separate convolutional layers in order to produce shared embedding spaces for visually distinct inputs.",1364,0.691,759,1.7971014492753623,"Many deep reinforcement learning approaches graphical state representations this means visually distinct games share cannot effectively share knowledge This paper outlines learning underlying game state embeddings irrespective the visual rendering We utilise approaches multi-task learning and domain adaption place visually distinct game states a shared embedding manifold We present deep reinforcement learning agents Games have often used order experiment with Games provide flexibility simulate problems such fully observable vs partially discrete noisy This first started digital versions board games being such chess More recently video games begun provide digital environments tasks benchmarking AI systems These new systems use usually trained the raw pixel values game frames meaning the networks interpret into game states learn an optimal policy play Due they use these raw pixel values they sensitive changes the visuals used results very little knowledge transfer visually distinct games BID25 resulting the networks learning each game without any representation overlap Games usually very visually distinct as concepts abstract especially Early video games often like because is computationally accurately imitate whereas may a more abstract representation due the financial expenseLearning representations has long It led many new approaches producing representations many applications BID1 style transfer In word embeddings networks can solve various tasks predicting the context within the outputs one the hidden layers represent This then results word embeddings place words similar contexts close proximity BID1 These resulting embeddings order solve without the system train from raw input This could seen knowledge transfer as the meaning has encoded its embedding and can with new networks working new tasks without this mapping between again BID27 .In our work improve knowledge representation across tasks underlying similarities but represented The architecture we propose learns representations independent the visual differences the games This will result the strategic elements the game playing network to share knowledge visually distinct gamesIn use and extend work around domain adaption Domain adaption seeks produce shared representation a source domain, such high resolution product photos images taken BID5 . We present using similar techniques allowing an agent domain independent representations similar games visually This paper will first ground our work both learning representations We will then outline the environment the networks were trained along the desired outcomes We will finally present the resulting representations and outline future work extend approach.2 RELATED WORK 2.1 AI AND GAMES Games provide a good benchmark AI as require planning BID32 BID18 . This means they often signify advances the state such with Deep Blue the chess playing AI beat BID2 AlphaGo the go playing agent . Games also provide a nice interface agents be either look the internal state as needed methods Monte carlo tree search , can provide visual representations state . Games also allow agents process experiences much would This means data hungry methods still able learn in BID13 ).There has other areas game playing competitions aimed agents passing a form rank agents mimic human play BID9 Most these systems revolved using data human play achieve BID24 BID14 . There also competitions organised order assess agents ability generalise across games the General Game Playing Competition BID7 focusing playing multiple board games Video that assess agents performance Other work started that modified versions game engines in environments teach AI these Project Malmo that the popular Minecraft Game in provide an experimentation platform AI agents BID11 , OpenArena the ID Tech 3 engine Quake train benchmark at tasks including path finding in Labyrinth laser tag BID10 ).There using neural evolution evolve a network control BID22 Others investigated hierarchical approaches AI agents FPS games BID28 that networks in deconstruct the tasks into As our results it our system separate game states raw pixel values despite the renderings so distinct It also effectively separates out states require a different task with the game states that contain pickups in a distinct but related space to now head This shows the learned embeddings capturing about irrespective the frame We show this deep reinforcement learning for domain adaptions to successfully achieved Our network also manages deal more visually diverse inputs was a network fully shares its parameters As the results have the single shared convolutional layers did deal the differences the visual representations the game We shown it adversarial networks along separate convolutional layers shared embedding spaces visually distinct inputs",0.01,0.7350236298698348
"We study discrete time dynamical systems governed by the state equation $h_{t+1}=ϕ(Ah_t+Bu_t)$. Here A,B are weight matrices, ϕ is an activation function, and $u_t$ is the input data. This relation is the backbone of recurrent neural networks (e.g. LSTMs) which have broad applications in sequential learning tasks. We utilize stochastic gradient descent to learn the weight matrices from a finite input/state trajectory $(u_t,h_t)_{t=0}^N$. We prove that SGD estimate linearly converges to the ground truth weights while using near-optimal sample size. Our results apply to increasing activations whose derivatives are bounded away from zero. The analysis is based on i) an SGD convergence result with nonlinear activations and ii) careful statistical characterization of the state vector. Numerical experiments verify the fast convergence of SGD on ReLU and leaky ReLU in consistence with our theory. A wide range of problems involve sequential data with a natural temporal ordering. Examples include natural language processing, time series prediction, system identification, and control design, among others. State-of-the-art algorithms for sequential problems often stem from dynamical systems theory and are tailored to learn from temporally dependent data. Linear models and algorithms; such as Kalman filter, PID controller, and linear dynamical systems, have a long history and are utilized in control theory since 1960's with great success (Brown et al. (1992) ; Ho & Kalman (1966) ; Åström & Hägglund (1995) ). More recently, nonlinear models such as recurrent neural networks (RNN) found applications in complex tasks such as machine translation and speech recognition (Bahdanau et al. (2014) ; Graves et al. (2013) ; Hochreiter & Schmidhuber (1997) ). Unlike feedforward neural networks, RNNs are dynamical systems that use their internal state to process inputs. The goal of this work is to shed light on the inner workings of RNNs from a theoretical point of view. In particular, we focus on the RNN state equation which is characterized by a nonlinear activation function φ, state weight matrix A, and input weight matrix B as follows h t+1 = φ(Ah t + Bu t ),(1.1)Here h t is the state vector and u t is the input data at timestamp t. This equation is the source of dynamic behavior of RNNs and distinguishes RNN from feedforward networks. The weight matrices A and B govern the dynamics of the state equation and are inferred from data. We will explore the statistical and computational efficiency of stochastic gradient descent (SGD) for learning these weight matrices.Contributions: Suppose we are given a finite trajectory of input/state pairs (u t , h t ) N t=0 generated from the state equation (1.1). We consider a least-squares regression obtained from N equations; with inputs (u t , h t ) N t=1 and outputs (h t+1 ) N t=1 . For a class of activation functions including leaky ReLU and for stable systems 1 , we show that SGD linearly converges to the ground truth weight matrices while requiring near-optimal trajectory length N . In particular, the required sample size is O(n + p) where n and p are the dimensions of the state and input vectors respectively. The results are extended to unstable systems when the samples are collected from multiple independent RNN trajectories rather than a single trajectory. Our theory applies to increasing activation functions whose derivatives are bounded away from zero, which includes leaky ReLU, and Gaussian input data. Numerical experiments on ReLU and leaky ReLU corroborate our theory and demonstrate that SGD converges faster as the activation slope increases. To obtain our results, we i) characterize the statistical properties of the state vector (e.g. well-conditioned covariance) and ii) derive a novel SGD convergence result with nonlinear activations; which may be of independent interest. As a whole, this paper provides a step towards foundational understanding of RNN training via SGD. This work showed that SGD can learn the nonlinear dynamical system (1.1); which is characterized by weight matrices and an activation function. This problem is of interest for recurrent neural networks as well as nonlinear system identification. We showed that efficient learning is possible with optimal sample complexity and good computational performance. Our results apply to strictly increasing activations such as Leaky ReLU. We empirically showed that Leaky ReLU converges faster than ReLU and requires less samples; in consistence with our theory. We list a few unanswered problems that would provide further insights into recurrent neural networks.• Covariance of the state-vector: Our results depend on the covariance of the state-vector and requires it to be positive definite. One might be able to improve the current bounds on the condition number and relax the assumptions on the activation function. Deriving similar performance bounds for ReLU is particularly interesting.• Hidden state: For RNNs, the state vector is hidden and is observed through an additional equation (2.1); which further complicates the optimization landscape. Even for linear dynamical systems, learning the (A, B, C, D) system ((1.1), (2.1)) is a non-trivial task Ho & Kalman (1966); Hardt et al. (2016) . What can be said when we add the nonlinear activations?• Classification task: In this work, we used normally distributed input and least-squares regression for our theoretical guarantees. More realistic input distributions might provide better insight into contemporary problems, such as natural language processing; where the goal is closer to classification (e.g. finding the best translation from another language).",1178,0.701,669,1.7608370702541105,"We study discrete time dynamical systems governed the state equation Here A,B are weight matrices �� an activation function $u_t$ This relation the backbone recurrent neural networks broad applications sequential learning tasks We utilize learn the weight matrices a finite input/state trajectory $(u_t We prove SGD estimate linearly ground truth weights while Our results apply increasing activations whose derivatives bounded away zero The analysis i) an SGD convergence result nonlinear activations careful statistical characterization the state vector Numerical experiments verify the fast convergence SGD on ReLU leaky ReLU consistence with our theory A wide range problems involve sequential data with a natural temporal ordering Examples include natural language processing time series prediction system identification control design State algorithms sequential problems often stem dynamical systems theory tailored learn temporally dependent data Linear models algorithms; such Kalman filter PID controller linear dynamical systems utilized control theory since 1960 with (Brown (1992 ; Ho & Kalman1966 � More recently nonlinear models found applications complex tasks machine translationBahdanau et (2014 ; Graves (2013 ; Hochreiter &1997 Unlike feedforward neural networks dynamical systems use their internal state inputs The goal shed RNNs from In particular focus the RNN state equation characterized a nonlinear activation function �� state weight matrix A input weight as follows h t+1 = ��Ah t + Bu t(1.1)Here h t at timestamp t. This equation the source dynamic behavior distinguishes feedforward networks The weight matrices A govern the state equation inferred data We will explore the statistical and computational efficiency learning these weight matricesContributions Suppose a finite trajectory input/state pairsu t N t=0 generated the state equation We consider obtained N equations; with inputs (u t h N t=1 For a class activation functions including leaky ReLU for stable systems 1 , SGD linearly the ground truth weight matrices while requiring near-optimal trajectory length N . In particular the required sample size O(n + p and the state and input vectors The results extended unstable systems when the samples collected multiple independent RNN trajectories rather Our theory applies increasing activation functions whose derivatives bounded away zero which includes leaky ReLU Gaussian input data Numerical experiments ReLU leaky ReLU corroborate SGD converges faster as the activation slope To obtain our results i) characterize the state vector derive a novel SGD convergence result nonlinear activations; which may of independent interest As a whole this paper towards foundational understanding RNN training via SGD This work showed SGD learn1.1 which characterized weight matrices an activation function This problem of for recurrent neural networks nonlinear system identification We showed efficient learning optimal sample complexity good computational performance Our results apply strictly increasing activations such Leaky ReLU We empirically showed Leaky ReLU converges faster and requires less samples; in consistence with our theory We list a few unanswered problems would provide further insights recurrent networks.• the state-vector: Our results depend requires it positive definite One might improve the current bounds the condition number relax the activation function Deriving similar performance bounds ReLU particularly interesting.• Hidden state For RNNs hidden observed through an additional equation which further the optimization landscape Even for linear dynamical systems learning (( Ho & Kalman1966 Hardt (2016 . What can when add the nonlinear activations?• Classification task In normally for our theoretical guarantees More realistic input distributions might provide contemporary problems; where closer classification ( finding",0.01,0.6426251782771885
"Although deep neural networks show their extraordinary power in various tasks, they are not feasible for deploying such large models on embedded systems due to high computational cost and storage space limitation. The recent work knowledge distillation (KD) aims at transferring model knowledge from a well-trained teacher model to a small and fast student model which can significantly help extending the usage of large deep neural networks on portable platform. In this paper, we show that, by properly defining the neuron manifold of deep neuron network (DNN), we can significantly improve the performance of student DNN networks through approximating neuron manifold of powerful teacher network. To make this, we propose several novel methods for learning neuron manifold from DNN model. Empowered with neuron manifold knowledge, our experiments show the great improvement across a variety of DNN architectures and training data. Compared with other KD methods, our Neuron Manifold Transfer (NMT) has best transfer ability of the learned features. In recent years, deep neural networks become more and more popular in computer vision and neural language processing. A well-trained learning model shows its power on tasks such as image classification, object detection, pattern recognizing, live stream analyzing, etc. We also have the promise that given enough data, deeper and wider neural networks can achieve better performance than the shallow networks BID0 ). However, these larger but well-trained networks also bring in high computational cost, and leave large amount of memory footprints which make these models very hard to travel and reproduce BID7 ). Due to this drawback, a massive amount of trainable data gathered by small devices such as mobiles, cameras, smart sensors, etc. is unable to be utilized in the local environment which can cause time-sensitive prediction delay and other impractical issues.To address the above issues, recently, there are extensive works proposed to mitigate the problem of model compression to reduce the computational burden on embedded system. Back to the date 2006, Buciluǎ et al. first proposed to train a neural network to mimic the output of a complex and large ensemble. This method uses ensemble to label the unlabeled data and trains the neural network with the data labeled by the ensemble, thus mimicking the function which learned by the ensemble and achieves similar accuracy. Based on the idea of (Buciluǎ,Geoffrey et al.) originally introduced a student-teacher paradigm in transferring the knowledge from a deeper and wider network (teacher) to a shallow network (student). They call this student-teacher paradigm as knowledge distillation (KD). By properly defining the knowledge of teacher as softened softmax (soft target), the student learns to mimic soft target distribution for each class. Thanks to Hinton's pioneer work, a series of subsequent works have sprung up by utilizing different forms of knowledge. BID22 regard the spatial attention maps of a convolution neural network as network knowledge. However, an implicit assumption that they make is that the absolute value of a hidden neuron activation can be used as an indication about the importance of that neuron w.r.t. the specific input which limited their application only fit for image classification tasks. Another assumption that has been widely used is from BID0 that deeper networks always learn better representation. Based on that, FitNets BID13 ) tries to learn a thin deep network using a shallow one with more parameters. They believe that the convolution regressor is the network knowledge which can inherit from the teacher to its student. In 2017, researcher from TuSimple ( TuSimple et al. (2015) , using softmax as knowledge, the student network mimics teacher's softmax and minimize the loss on soft target. Middle one, mentioned in BID22 , named as attention transfer, an additional regularizer has been applied known as attention map, student needs to learn the attention map and soft target. The right part is our neuron manifold transfer, where we take neuron manifold as knowledge, and it reduces the computational and space cost.(2015 )) introduces two new definitions of network knowledge, BID8 takes the advantage of Maximum Mean Discrepancy (MMD) to minimize the distance metric in probability distributions, and they regard network knowledge as class distribution. BID4 propose to transfer the cross sample similarities between the student and teacher to improve the performance of transferred networks. We notice that in the DarkRank the network knowledge is defined as cross sample similarities.By reviewing extensive KD works, we notice that the key point in knowledge transfer is how we define the network knowledge, and in fact, a well-defined network knowledge can greatly improve the performance of the distilled network. Moreover, in our perspective, a perfect knowledge transfer method must allow us to transfer one neural network architecture into another, while preserving other generalization. A perfect transfer method, however, would use little observations to train, optimally use the limited samples at its disposal. Unfortunately , to our best knowledge, due to the complexity of large DNN, simply mimicking the teacher logit or a part of teacher features properties is far away to be benefited. Therefore, if we look back and consider the essence of DNN training, we notice that, another point of view to look at the distribution of neuron features is the shape of that feature. Here, the shape of neuron features include the actual value and the relative distance between two features. That is, during the process of knowledge transfer, student network not only learns the numerical information but also inherits the geometric properties. Therefore, in order to track the change of large DNN feature knowledge, a manifold approximation technique is vying for our attention. Manifold learning has been widely used in Topological Data Analysis (TDA) BID3 ), and this technique can project the high dimensional data to a lower dimensional manifold and preserving both numerical feature properties and geometric properties. In previous works, feature mapping causes computational resource waste, and class distribution matching is limited the usage. However, using the neuron manifold information, we not only collect as much as possible feature properties which can greatly represent feature, but also preserve inter-neuron characteristics (spatial relation). Since manifold projection can greatly reduce the dimension of teacher feature, we compress the teacher model and make student model more reliable. To summarize, the contributions of this paper are three folds:• We introduce a new type of knowledge that is the d-dimensional smooth sub-manifold of teacher feature maps called neuron manifold.• We formalize manifold space in feature map, and implement in details.• We test our proposed method on various metric learning tasks. Our method can significantly improve the performance of student networks. And it can be applied jointly with existing methods for a better transferring performance.We test our method on MNIST, CIFAR-10, and CIFAR-100 datasets and show that our Neuron Manifold Transfer (NMT) improves the students performance notably. In this paper, we propose a novel method for knowledge transfer and we define a new type network knowledge named neuron manifold. By utilizing the state of art technique in Topological Data Analysis, we extract the DNN's feature properties and its geometric properties. We test our NMT on various dataset and the results are quite promising, thus further confirming that our knowledge transfer method could indeed learn better feature representations. They can be successfully transferred to high level vision task in the future. We believe that our novel view will facilitate the further design of knowledge transfer methods. In our future work, we plan to explore more applications of our NMT methods, especially in various regression problems, such as super resolution and optical flow prediction, etc.",1499,0.859,901,1.6637069922308545,"Although deep neural networks show their extraordinary power various tasks feasible deploying such large models due The recent work knowledge distillation (KD aims transferring model knowledge a well-trained teacher model which significantly help extending the usage large deep neural networks on portable platform In properly defining the neuron manifold deep neuron network significantly student DNN networks through approximating neuron manifold powerful teacher network To, propose several novel methods learning neuron manifold DNN model Empowered neuron manifold knowledge our experiments the great improvement across DNN architectures training data Compared other KD methods our Neuron Manifold Transfer ( best transfer ability the learned features In deep neural networks become A well-trained learning model shows its power on tasks image classification pattern recognizing live stream analyzing etc We also the promise given enough data deeper and wider neural networks achieve the shallow networks BID0 ). However these larger but well-trained networks also bring high computational cost leave large amount memory footprints these models travel and reproduce BID7 ). Due this drawback massive trainable data gathered small devices smart sensors is unable be utilized the local environment which time-sensitive prediction delay other impractical issuesTo recently there extensive works proposed mitigate model compression to embedded system Back the date 2006 Bucilu� et first proposed train mimic the output a complex and large ensemble This method ensemble to label trains labeled which learned by achieves Based (Bucilu��,Geoffrey et originally a student-teacher paradigm transferring a deeper and wider network They call this student-teacher paradigm as knowledge distillation (KD By properly defining the knowledge teacher as softened softmax (soft target mimic soft target distribution for Thanks Hinton's pioneer work a series subsequent works sprung by utilizing different forms knowledge BID22 regard the spatial attention maps a convolution neural network network knowledge However an implicit assumption they make the absolute value a hidden neuron activation about the specific input which limited their application only fit for image classification tasks Another assumption from BID0 deeper networks always learn better representation Based that FitNets BID13 ) tries learn a thin deep network shallow one with more parameters They believe the convolution regressor the network knowledge which inherit the teacher its student In 2017, researcher from TuSimple ( TuSimple et al (2015 , using softmax as knowledge, the student network mimics teacher's softmax minimize on soft target Middle one mentioned BID22 , named as attention transfer an additional regularizer has applied known attention map student needs learn soft target The right part our neuron manifold transfer take neuron manifold knowledge it reduces the computational and space cost.(2015 )) introduces network knowledge BID8 takes the advantage Maximum Mean Discrepancy minimize metric probability distributions they regard class distribution BID4 propose transfer the cross sample similarities the student improve transferred networks We notice the DarkRank the network knowledge defined cross sample similaritiesBy reviewing extensive KD works notice the key point knowledge transfer how greatly the distilled network Moreover our perspective a perfect knowledge transfer method must one neural network architecture while other generalization A perfect transfer method however use little observations train, optimally use the limited samples at Unfortunately , to due large DNN, simply mimicking the teacher logit or a part teacher features properties far away to benefited Therefore the essence DNN training notice another point to look the distribution neuron features the shape Here the shape neuron features include the actual value That during knowledge transfer student network not learns the numerical information inherits the geometric properties Therefore track large DNN feature knowledge a manifold approximation technique vying Manifold learning has widely Topological Data AnalysisTDA) BID3 ), project the high dimensional data preserving both numerical feature properties In previous works feature mapping causes computational resource waste class distribution matching limited the usage. However using the neuron manifold information not collect as possible feature properties which greatly represent feature, preservespatial relation Since manifold projection can greatly teacher feature compress student model reliable To summarize the contributions three folds:• We introduce knowledge the d smooth submanifold teacher feature maps called neuron manifold.• formalize manifold space feature map implement in details.• test various metric learning tasks Our method can significantly student networks And can applied jointly existing methods a better transferring performanceWe test MNIST our Neuron Manifold Transfer ( improves the students performance notably In knowledge transfer we define a new type network knowledge named neuron manifold By utilizing art technique Topological Data Analysis extract the DNN's feature properties its geometric properties We test our NMT on various dataset thus further confirming our knowledge transfer method could learn better feature representations They can successfully transferred high level vision task in We believe our novel view will facilitate the further design knowledge transfer methods In our future work more applications our NMT methods various regression problems super resolution optical flow prediction etc",0.01,0.39514627322927853
"We present a simple and general method to train a single neural network executable at different widths (number of channels in a layer), permitting instant and adaptive accuracy-efficiency trade-offs at runtime. Instead of training individual networks with different width configurations, we train a shared network with switchable batch normalization. At runtime, the network can adjust its width on the fly according to on-device benchmarks and resource constraints, rather than downloading and offloading different models. Our trained networks, named slimmable neural networks, achieve similar (and in many cases better) ImageNet classification accuracy than individually trained models of MobileNet v1, MobileNet v2, ShuffleNet and ResNet-50 at different widths respectively. We also demonstrate better performance of slimmable models compared with individual ones across a wide range of applications including COCO bounding-box object detection, instance segmentation and person keypoint detection without tuning hyper-parameters. Lastly we visualize and discuss the learned features of slimmable networks. Code and models are available at: https://github.com/JiahuiYu/slimmable_networks Recently deep neural networks are prevailing in applications on mobile phones, augmented reality devices and autonomous cars. Many of these applications require a short response time. Towards this goal, manually designed lightweight networks BID51 BID50 are proposed with low computational complexities and small memory footprints. Automated neural architecture search methods ) also integrate on-device latency into search objectives by running models on a specific phone. However, at runtime these networks are not re-configurable to adapt across different devices given a same response time budget. For example, there were over 24,000 unique Android devices in 2015 2 . These devices have drastically different runtimes for the same neural network BID19 , as shown in TAB0 . In practice, given the same response time constraint, high-end phones can achieve higher accuracy by running larger models, while low-end phones have to sacrifice accuracy to reduce latency. Although a global hyper-parameter, width multiplier, is provided in lightweight networks BID51 BID50 to trade off between latency and accuracy, it is inflexible and has many constraints. First, models with different width multipliers need to be trained, benchmarked and deployed individually. A big offline table needs to be maintained to document the allocation of different models to different devices, according to time and energy budget. Second, even on a same device, the computational budget varies (for example, excessive consumption of background apps reduces the available computing capacity), and the energy budget varies (for example, a mobile phone may be in low-power or power-saving mode). Third, when switching to a larger or smaller model, the cost of time and data for downloading and offloading models is not negligible. Recently dynamic neural networks are introduced to allow selective inference paths. BID29 introduce controller modules whose outputs control whether to execute other modules. It has low theoretical computational complexity but is nontrivial to optimize and deploy on mobiles since dynamic conditions prohibit layer fusing and memory optimization. adapt early-exits into networks and connect them with dense connectivity. and propose to selectively choose the blocks in a deep residual network to execute during inference. Nevertheless, in contrast to width (number of channels), reducing depth cannot reduce memory footprint in inference, which is commonly constrained on mobiles.The question remains: Given budgets of resources, how to instantly, adaptively and efficiently trade off between accuracy and latency for neural networks at runtime? In this work we introduce slimmable neural networks, a new class of networks executable at different widths, as a general solution to trade off between accuracy and latency on the fly. FIG0 shows an example of a slimmable network that can switch between four model variants with different numbers of active channels. The parameters of all model variants are shared and the active channels in different layers can be adjusted. For brevity, we denote a model variant in a slimmable network as a switch, the number of active channels in a switch as its width. 0.25× represents that the width in all layers are scaled by 0.25 of the full model. In contrast to other solutions above, slimmable networks have several advantages: (1) For different conditions, a single model is trained, benchmarked and deployed. (2) A near-optimal trade-off can be achieved by running the model on a target device and adjusting active channels accordingly. (3) The solution is generally applicable to (normal, group, depthwise-separable, dilated) convolutions, fully-connected layers, pooling layers and many other building blocks of neural networks. It is also generally applicable to different tasks including classification, detection, identification, image restoration and more. (4) In practice, it is straightforward to deploy on mobiles with existing runtime libraries. After switching to a new configuration, the slimmable network becomes a normal network to run without additional runtime and memory cost.However, neural networks naturally run as a whole and usually the number of channels cannot be adjusted dynamically. Empirically training neural networks with multiple switches has an extremely low testing accuracy around 0.1% for 1000-class ImageNet classification. We conjecture it is mainly due to the problem that accumulating different number of channels results in different feature mean and variance. This discrepancy of feature mean and variance across different switches leads to inaccurate statistics of shared Batch Normalization layers BID20 , an important training stabilizer. To this end, we propose a simple and effective approach, switchable batch normalization, that privatizes batch normalization for different switches of a slimmable network. The variables of moving averaged means and variances can independently accumulate feature statistics of each switch. Moreover, Batch Normalization usually comes with two additional learnable scale and bias parameter to ensure same representation space BID20 . These two parameters may able to act as conditional parameters for different switches, since the computation graph of a slimmable network depends on the width configuration. It is noteworthy that the scale and bias can be merged into variables of moving mean and variance after training, thus by default we also use independent scale and bias as they come for free. Importantly, batch normalization layers usually have negligible size (less than 1%) in a model. BID10 BID53 BID22 and BID16 implanted earlyexiting prediction branches to reduce the average execution depth. The computation graph of these methods are conditioned on network input, and lower theoretical computational complexity can be achieved.Conditional Normalization. Many real-world problems require conditional input. Feature-wise transformation BID7 ) is a prevalent approach to integrate different sources of information, where conditional scales and biases are applied across the network. It is commonly implemented in the form of conditional normalization layers, such as batch normalization or layer normalization BID2 . Conditional normalization is widely used in tasks including style transfer BID6 BID25 BID18 BID26 , image recognition BID24 BID45 and many others BID34 a) . We introduced slimmable networks that permit instant and adaptive accuracy-efficiency trade-offs at runtime. Switchable batch normalization is proposed to facilitate robust training of slimmable networks. Compared with individually trained models with same width configurations, slimmable networks have similar or better performances on tasks of classification, object detection, instance segmentation and keypoints detection. The proposed slimmable networks and slimmable training could be further applied to unsupervised learning and reinforcement learning, and may help to related fields such as network pruning and model distillation.end, we mainly conduct COCO experiments based on another detection framework: MMDetection , which has hyper-parameter settings with same pytorch-style ResNet-50. With same hyper-parameter settings (i.e., RCNN R50 FPN 1 ×), we fine-tune both individual ResNet-50 models and slimmable ResNet-50 on tasks of object detection and instance segmentation. Our reproduced results on ResNet-50 1.0× is consistent with official models in MMDetection ). For keypoint detection task, we conduct experiment on Detectron framework by modifying caffe-style ResNet-50 to pytorch-style and training on 4 GPUs without other modification of hyper-parameters. We have released code (training and testing) and pretrained models on both ImageNet classification task and COCO detection tasks.",1654,0.992,969,1.7069143446852426,"We present train executable at different widthsnumber channels permitting instant and adaptive accuracy-efficiency trade-offs at runtime Instead training individual networks different width configurations train switchable batch normalization At runtime adjust its width on according on benchmarks resource rather downloading offloading different models Our trained networks named slimmable neural networks achieve ( ImageNet individually trained models MobileNet v1 and ResNet-50 at respectively We also demonstrate better performance slimmable models compared individual ones across COCO bounding-box object detection instance segmentation person keypoint detection without tuning hyper Lastly visualize discuss the learned features slimmable networks Code and models Recently deep neural networks prevailing applications on augmented autonomous Many this goal manually designed lightweight networks BID51 BID50 proposed with low computational complexities small memory footprints Automated neural architecture search methods ) also integrate on latency search objectives running models a specific phone However at runtime these networks re adapt across given a same response time budget For 2 . These devices drastically different runtimes BID19 , TAB0 . In practice given the same response time constraint high-end phones achieve higher accuracy running larger models sacrifice accuracy reduce Although a global hyper width multiplier provided lightweight networks BID51 BID50 to trade latency accuracy many constraints First models different width multipliers trained benchmarked deployed individually A big offline table needs maintained document the allocation different models according time and energy budget Second even on a same device the computational budget varies ( excessive consumption background apps reduces in Third when switching time data downloading and offloading models negligible Recently dynamic neural networks introduced allow selective inference paths BID29 introduce controller modules whose outputs whether execute other modules It low theoretical computational complexity optimize deploy mobiles since dynamic conditions prohibit layer fusing and memory optimization adapt early-exits into networks connect dense connectivity and propose selectively choose the blocks a deep residual network execute during inference Nevertheless contrast width (number channels reducing depth inference commonly constrained on mobilesThe question Given budgets resources to instantly, trade accuracy latency neural networks at In introduce slimmable neural networks executable at different widths trade latency FIG0 shows a slimmable network switch four model variants active channels The parameters all model variants shared the active channels different layers adjusted For brevity denote a model variant a slimmable network the number active channels its width 0.25× represents that the width all layers are scaled of In contrast other solutions above slimmable networks For different conditions a single model trained benchmarked deployed can running a target device active channels (3 The solution generally applicable (normal, group depthwise-separable fully-connected layers pooling many building It generally applicable different tasks including classification detection image restoration more (4 practice straightforward deploy on mobiles existing runtime libraries After switching the slimmable network becomes to without additional runtime and memory costHowever neural networks naturally as usually the number channels adjusted dynamically training neural networks multiple switches has an extremely low testing accuracy around 1000-class ImageNet classification We conjecture it mainly accumulating different number channels results different feature mean This discrepancy of feature mean across different switches leads inaccurate statistics shared Batch Normalization layers BID20 , an important training stabilizer To propose switchable batch normalization privatizes different switches of a slimmable network The variables moving averaged means independently accumulate feature statistics each switch Moreover Batch Normalization usually comes two additional learnable scale and bias parameter to same representation space BID20 . These two parameters able act conditional parameters different switches since the computation graph a slimmable network the width configuration It noteworthy the scale bias can merged variables moving mean after training thus by default also independent scale bias as they come for free Importantly batch normalization layers usually negligible size a model BID10 BID53 BID22 and implanted earlyexiting prediction branches reduce the average execution depth The computation graph these methods conditioned network input lower theoretical computational complexityConditional Normalization Many real-world problems require conditional input Feature-wise transformation BID7 ) a prevalent approach integrate different sources where conditional scales biases across It commonly implemented conditional normalization layers BID2 Conditional normalization widely tasks including style transfer BID6 BID25 BID18 BID26 , and a . We introduced slimmable networks permit instant and adaptive accuracy-efficiency trade-offs at runtime Switchable batch normalization proposed robust training slimmable networks Compared individually trained models same width configurations slimmable networks similar or better performances tasks classification instance segmentation keypoints The proposed slimmable networks could further applied related fields network pruning model distillation.end, we mainly conduct COCO experiments based another detection framework MMDetection , hyper-parameter settings with same pytorch-style ResNet-50. With same hyper-parameter settings RCNN R50 FPN 1 ×), fine both individual ResNet-50 models slimmable on tasks object detection instance segmentation Our reproduced results on ResNet-50 1.0× is official models MMDetection ). For keypoint detection task conduct experiment Detectron framework modifying caffe-style ResNet-50 to pytorch-style training 4 GPUs without other modification hyper We released code (training pretrained both ImageNet classification task COCO detection tasks",0.01,0.5052348111265802
"Measuring visual (dis)similarity between two or more instances within a data distribution is a fundamental task in many applications, specially in image retrieval. Theoretically, non-metric distances are able to generate a more complex and accurate similarity model than metric distances, provided that the non-linear data distribution is precisely captured by the similarity model. In this work, we analyze a simple approach for deep learning networks to be used as an approximation of non-metric similarity functions and we study how these models generalize across different image retrieval datasets. For humans, deciding whether two images are visually similar or not is, to some extent, a natural task. However, in computer vision, this is a challenging problem and algorithms do not always succeed in matching pictures that contain similar-looking elements. This is mainly because of the well-known semantic gap problem, which refers to the difference or gap between low-level image pixels and high-level semantic concepts. Estimating visual similarity is a fundamental task that seeks to break this semantic gap by accurately evaluating how alike two or more pictures are. Visual similarity is crucial for many computer vision areas including image retrieval, image classification and object recognition, among others.Given a query image, content-based image retrieval systems rank pictures in a dataset according to how similar they are with respect to the input. This can be broken into two fundamental tasks: 1) computing meaningful image representations that capture the most salient visual information from pixels and 2) measuring accurate visual similarity between these image representations to rank images according to a similarity score.In the last years, several methods to represent visual information from raw pixels in images have been proposed, first by designing handcrafted features such as SIFT BID22 , then by compacting these local features into a single global image descriptor using different techniques such as Fisher Vectors BID28 and more recently by extracting deep image representations from neural networks BID1 ). However, once two images are described by feature vectors, visual similarity is commonly measured by computing a standard metric between them. Although regular distance metrics, such as Euclidean distance or cosine similarity, are fast and easy to implement, they do not take into account the possible interdependency within the dataset, which means that even if a strong nonlinear data dependency is occurring in the visual collection, they might not be able to capture it. This suggests that learning a similarity estimation directly from visual data can improve the performance on image retrieval tasks, provided that the likely nonlinearity dependencies within the dataset are precisely learned by the similarity function.Visual similarity learning is closely related to distance metric learning. Traditionally, distance metric learning algorithms were based on linear metrics such as the Mahalanobis distance. However, if the visual data presents any nonlinear interdependency, better results are expected when using nonlinear approaches. According to some studies BID41 , standard metric axioms are not valid for human perception of visual similarity and hence, visual similarity functions should not necessarily satisfy distance metric conditions. Deep learning-based similarity learning methods are mostly focused on learning an optimal mapping from pixels to a linear space in which Euclidean distance can be applied. Instead, we propose a simple approach based on neural networks to learn a non-metric similarity score in the feature space. Figure 1: System overview. The feature extraction block computes visual representations of images whereas the visual similarity block estimates a similarity score using a neural network. Figure 1 shows an overview of the proposed approach. By training a deep learning model, we can estimate a visual similarity function that outperforms methods based on standard metric computations. One convolutional neural network extracts image representations from input images, while a second neural network computes the visual similarity score. The visual similarity neural network is trained using both pairs of similar and dissimilar images in three stages. The output score of the similarity network can be directly applied as a similarity estimation to rank images in an image retrieval task. Experimental results on standard datasets show that our network is able to discriminate when a pair of images is similar or dissimilar and improve standard metrics score on top of that. Four different configurations A-D for the similarity neural network are proposed. We compare the performance of each one during Stage 1, when the network is trained with the standard cosine similarity measurement. If s l is the network score and y l is the cosine similarity of the l-th pair with l = 1.. L, we evaluate each network by computing the mean squared error, MSE, and the correlation coefficient, ρ, as: DISPLAYFORM0 where µ s and σ s are the mean and standard deviation of the vector of network scores s, and µ y and σ y are the mean and standard deviation of the vectors of cosine similarities y.Results are shown in TAB0 . Unsurprisingly, the configuration with bigger number of parameters, C, achieves the best MSE and ρ results, both in training and validation sets. However, the performance of networks B and D is very close to the performance of network C. As network B requires only 21 million parameters and network C requires 76 million parameters, we keep configuration B as our default architecture for the rest of the experiments. We have presented a method for learning visual similarity directly from visual data. Instead of using a rigid metric distance, such as the standard cosine similarity, we propose to train a neural network model to learn a similarity estimation between a pair of visual representations previously extracted from input images. Our method outperforms state-of-the-art approaches based on rigid distances in standard image retrieval collection of images and experimental results showed that learning a nonmetric visual similarity function is beneficial in image retrieval tasks provided that a small subset of images of the same domain are available during training. Standard image retrieval techniques that are commonly applied after cosine similarity computation, such as query expansion or image re-ranking, might also be applied on top of the similarity network. Finally, we end with an open question, which is the subject of planned future work, concerning efficient computation of exact or approximate K-nearest neighbours based on the learned network similarity function.",1201,0.645,706,1.7011331444759208,"Measuring visual (dis)similarity within a data distribution specially image retrieval Theoretically non-metric distances able generate a more complex and accurate similarity model provided the non-linear data distribution precisely captured In this work analyze a simple approach deep learning networks be an approximation non-metric similarity functions and we study generalize different image retrieval datasets For humans deciding two images visually, a natural task However computer vision this algorithms do succeed matching pictures that contain This mainly the well-known semantic gap problem refers or gap low-level image pixels Estimating visual similarity seeks break this semantic gap accurately evaluating how alike Visual similarity crucial many computer vision areas including image retrieval amongGiven a query image content-based image retrieval systems rank pictures a dataset how respect This can broken two fundamental tasks computing meaningful image representations that capture pixels measuring accurate visual similarity rank images according a similarity scoreIn the last years several methods to represent in images first designing handcrafted features SIFT BID22 , compacting these local features a single global image descriptor using different techniques Fisher Vectors BID28 more extracting deep image representations BID1 ). However once two images described feature vectors visual similarity commonly measured computing a standard metric between Although regular distance metrics, or cosine similarity fast within the dataset even a strong nonlinear data dependency occurring the visual collection they might This suggests learning a similarity estimation directly visual data on image retrieval tasks provided the likely nonlinearity dependencies within precisely learned byVisual similarity learning closely distance metric learning distance metric learning algorithms linear metrics However if the visual data presents any nonlinear interdependency better results when using According some studies BID41 , standard metric axioms valid human perception visual similarity hence visual similarity functions should necessarily satisfy distance metric conditions Deep learning-based similarity learning methods mostly focused learning an optimal mapping from pixels a linear space in can applied Instead propose based neural networks a non-metric similarity score the feature space Figure System overview The feature extraction block computes visual representations images whereas the visual similarity block estimates using Figure shows the proposed approach By training a deep learning model estimate a visual similarity function outperforms methods standard metric computations One convolutional neural network extracts image representations input images the visual similarity score The visual similarity neural network trained using both pairs similar and dissimilar images three stages The output score the similarity network can directly applied as a similarity estimation to rank images an image retrieval task Experimental results on standard datasets our network able discriminate when a pair images similar and improve standard metrics score on top Four different configurations A-D for the similarity neural network are proposed We compare each one during Stage when the network trained the standard cosine similarity measurement If s l is the network score y l the cosine similarity with l =.. L, we evaluate each network by computing, MSE as: DISPLAYFORM0 where µ s and �� s the vector network scores s µ cosine similarities y.Results TAB0 . Unsurprisingly the configuration with bigger number parameters C, achieves the best MSE and �� results both training and validation sets However the performance networks B very close As network B requires only 21 million parameters keep configuration B our default architecture the experiments We presented learning visual similarity directly Instead using a rigid metric distance such the standard cosine similarity propose train learn a similarity estimation between visual representations previously extracted input images Our method outperforms state approaches based rigid distances standard image retrieval collection of experimental results showed learning a nonmetric visual similarity function beneficial provided a small subset of available during Standard image retrieval techniques that applied after cosine similarity computation query expansion image reranking might applied on top the similarity network Finally end the subject planned future work concerning efficient computation exact or approximate K-nearest neighbours based the learned network similarity function",0.01,0.4905048209239249
"Training a model to perform a task typically requires a large amount of data from the domains in which the task will be applied.
 However, it is often the case that data are abundant in some domains but scarce in others. Domain adaptation deals with the challenge of adapting a model trained from a data-rich source domain to perform well in a data-poor target domain. In general, this requires learning plausible mappings between domains. CycleGAN is a powerful framework that efficiently learns to map inputs from one domain to another using adversarial training and a cycle-consistency constraint. However, the conventional approach of enforcing cycle-consistency via reconstruction may be overly restrictive in cases where one or more domains have limited training data. In this paper, we propose an augmented cyclic adversarial learning model that enforces the cycle-consistency constraint via an external task specific model, which encourages the preservation of task-relevant content as opposed to exact reconstruction. We explore digit classification in a low-resource setting in supervised, semi and unsupervised situation, as well as high resource unsupervised. In low-resource supervised setting, the results show that our approach improves absolute performance by 14% and 4% when adapting SVHN to MNIST and vice versa, respectively, which outperforms unsupervised domain adaptation methods that require high-resource unlabeled target domain.   Moreover, using only few unsupervised target data, our approach can still outperforms many high-resource unsupervised models. Our model also outperforms on USPS to MNIST and synthetic digit to SVHN for high resource unsupervised adaptation. In speech domains, we similarly adopt a speech recognition model from each domain as the task specific model. Our approach improves absolute performance of speech recognition by 2% for female speakers in the TIMIT dataset, where the majority of training samples are from male voices. Domain adaptation BID18 BID36 BID1 aims to generalize a model from source domain to a target domain. Typically, the source domain has a large amount of training data, whereas the data are scarce in the target domain. This challenge is typically addressed by learning a mapping between domains, which allows data from the source domain to enrich the available data for training in the target domain. One way of learning such mappings is through Generative Adversarial Networks (GANs BID8 with cycle-consistency constraint (CycleGAN Zhu et al., 2017) , which enforces that mapping of an example from the source to the target and then back to the source domain would result in the same example (and vice versa for a target example). Due to this constraint, CycleGAN learns to preserve the 'content' 1 from the source domain while only transferring the 'style' to match the distribution of the target domain. This is a powerful constraint, and various works BID37 BID12 have demonstrated its effectiveness in learning cross domain mappings.Enforcing cycle-consistency is appealing as a technique for preserving semantic information of the data with respect to a task, but implementing it through reconstruction may be too restrictive when data are imbalanced across domains. This is because the reconstruction error encourages exact match of samples from the reverse mapping, which may in turn encourage the forward-mapping to keep the sample close to the original domain. Normally, the adversarial objectives would counter this effect; however, when data from the target domain are scarce, it is very difficult to learn a powerful discriminator that can capture meaningful properties of the target distribution. Therefore, the resulting mappings learned is likely to be sub-optimal. Importantly, for the learned mapping to be meaningful, it is not necessary to have the exact reconstruction. As long as the 'semantic' information is preserved and the 'style' matches the corresponding distribution, it would be a valid mapping.To address this issue, we propose an augmented cyclic adversarial learning model (ACAL) for domain adaptation. In particular, we replace the reconstruction objective with a task specific model. The model learns to preserve the 'semantic' information from the data samples in a particular domain by minimizing the loss of the mapped samples for the task specific model. On the other hand, the task specific model also serves as an additional source of information for the corresponding domain and hence supplements the discriminator in that domain to facilitate better modeling of the distribution. The task specific model can also be viewed as an implicit way of disentangling the information essential to the task from the 'style' information that relates to the data distribution of different domain. We show that our approach improves the performance by 40% as compared to the baseline on digit domain adaptation. We improve the phoneme error rate by ∼ 5% on TIMIT dataset, when adapting the model trained on one speech from one gender to the other. In this paper, we propose to use augmented cycle-consistency adversarial learning for domain adaptation and introduce a task specific model to facilitate learning domain related mappings. We enforce cycle-consistency using a task specific loss instead of the conventional reconstruction objective. Additionally, we use the task specific model as an additional source of information for the discriminator in the corresponding domain. We demonstrate the effectiveness of our proposed approach by evaluating on two domain adaptation tasks, and in both cases we achieve significant performance improvement as compared to the baseline.By extending the definition of task-specific model to unsupervised learning, such as reconstruction loss using autoencoder, or self-supervision, our proposed method would work on all settings of domain adaptation. Such unsupervised task can be speech modeling using wavenet BID35 , or language modeling using recurrent or transformer networks BID27 .",1116,0.605,659,1.6934749620637328,"Training a model typically data from the domains will applied However often data abundant some domains scarce Domain adaptation deals the challenge a model trained from a data-rich source domain perform In general this requires learning plausible mappings domains CycleGAN efficiently learns map inputs one domain adversarial training a cycle-consistency constraint However the conventional approach enforcing cycle-consistency via reconstruction may overly cases limited training data In an augmented cyclic adversarial learning model enforces via an external task specific model encourages the preservation as exact reconstruction We explore digit classification supervised, semi and unsupervised situation high resource. In low-resource supervised setting the results our approach improves absolute performance adapting SVHN MNIST vice which outperforms unsupervised domain adaptation methods that high-resource unlabeled target domain Moreover using only few unsupervised target data our approach still outperforms Our model also on USPS to MNIST and synthetic digit to SVHN high resource unsupervised adaptation In speech domains we similarly adopt a speech recognition model from each domain the task specific model Our approach improves absolute performance speech recognition 2% female speakers the TIMIT dataset where the majority training samples male voices Domain adaptation BID18 BID36 BID1 aims generalize a model from source domain Typically the source domain has training data whereas are scarce This challenge typically addressed learning a mapping domains data enrich training in One way learning such mappings Generative Adversarial NetworksGANs BID8 with cycle-consistency constraint (CycleGAN Zhu 2017 , enforces that mapping an example from and would result vice a target example Due this constraint CycleGAN learns preserve the 'content 1 from the source domain while only transferring match the distribution This a powerful constraint various works BID37 BID12 have demonstrated its effectiveness learning cross domain mappingsEnforcing cycle-consistency appealing preserving semantic information of with a task implementing through reconstruction may restrictive when data imbalanced This because the reconstruction error encourages exact match samples the reverse mapping in encourage keep close Normally the adversarial objectives would counter this effect; data the target domain scarce very learn a powerful discriminator capture meaningful properties the target distribution Therefore the resulting mappings learned is likely sub Importantly for the learned mapping to meaningful the exact reconstruction As long the 'semantic' information preserved the 'style matches the corresponding distribution would a valid mappingTo address propose an augmented cyclic adversarial learning modelACAL domain adaptation In particular replace the reconstruction objective a task specific model The model learns preserve the 'semantic' information the data samples a particular domain minimizing the mapped samples for the task specific model On the task specific model also serves the corresponding domain hence supplements in facilitate better modeling The task specific model can viewed an implicit way essential the 'style' information relates the data distribution different domain We show our approach improves by as on digit domain adaptation We improve the phoneme error rate ∼ 5 on TIMIT dataset when adapting trained one speech from one gender In augmented cycle-consistency adversarial learning for domain adaptation introduce a task specific model facilitate domain related mappings We enforce cycle-consistency using a task specific loss instead the conventional reconstruction objective Additionally use the task specific model as the discriminator in the corresponding domain We demonstrate our proposed approach evaluating on two domain adaptation tasks and in achieve asBy extending task-specific model such reconstruction loss using or would work all settings Such unsupervised task can speech modeling using wavenet BID35 , or language modeling recurrent or transformer networks",0.01,0.4709924449782198
"Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can also be used to inform machine learning on graphs. However, learning structural representations of nodes is a challenging unsupervised-learning task, which typically involves manually specifying and tailoring topological features for each node. Here we develop GraphWave, a method that represents each node’s local network neighborhood via a low-dimensional embedding by leveraging spectral graph wavelet diffusion patterns. We prove that nodes with similar local network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network. Our method scales linearly with the number of edges and does not require any hand-tailoring of topological features. We evaluate performance on both synthetic and real-world datasets, obtaining improvements of up to 71% over state-of-the-art baselines. Structural role discovery in graphs focuses on identifying nodes which have topologically similar local neighborhoods (i.e., similar local structural roles) while residing in potentially distant areas of the network FIG0 ). Such alternative definition of node similarity is very different than more traditional notions BID21 BID7 BID30 BID19 BID15 BID8 BID6 , which all assume some notion of ""smoothness"" over the graph and thus consider nodes residing in close network proximity to be similar. Such structural role information about the nodes can be used for a variety of tasks, including as input to machine learning problems, or even to identify key nodes in a system (principal ""influencers"" in a social network, critical hubs in contagion graphs, etc.).When structural roles of nodes are defined over a discrete space, they correspond to different topologies of local network neighborhoods (e.g., edge of a chain, center of a star, a bridge between two clusters). However , such discrete roles must be pre-defined, requiring domain expertise and manual inspection of the graph structure. A more powerful and robust method for identifying structural similarity involves learning a continuous vector-valued structural signature χ a of each node a in an unsupervised way. This motivates a natural definition of structural similarity in terms of closeness of topological signatures: For any > 0, nodes a and b are defined to be -structurally similar with respect to a given distance if: dist(χ a , χ b ) ≤ . Thus, a robust structural similarity metric must introduce both an appropriate signature and an adequate distance metric.While several methods have been proposed for structural role discovery in graphs, existing approaches are extremely sensitive to small perturbations in the topology and typically lack one or more desirable properties. They often require manually hand-labeling topological features BID12 , rely on non-scalable heuristics BID22 , and/or return a single similarity score instead of a multidimensional structural signature BID13 .Here we address the problem of structure learning on graphs by developing GRAPHWAVE. Building upon techniques from graph signal processing BID4 BID10 BID26 , our approach learns a structural embedding for each node based on the diffusion of a spectral graph wavelet centered at that node. Intuitively, each node propagates a unit of energy over the graph and characterizes its neighboring topology based on the response of the network to While raw spectral graph wavelet signatures/coefficients Ψ of a and b might be very different, we treat them as probability distributions and show that the coefficient distributions are indeed similar.this probe. In contrast to prior work that characterizes the wavelet diffusion as a function of the wavelet scaling parameter, we study how the wavelet diffuses through the network at a given scale as a function of the initial source node. We prove that the coefficients of this wavelet directly relate to graph topological properties. Hence, these coefficients contain all the necessary information to recover structurally similar nodes, without requiring the hand-labeling of features. However, the wavelets are, by design, localized on the graph. Therefore to compare structural signatures for nodes that are far away from each other, typical graph signal processing methods (using metrics like correlation between wavelets or 2 distance) cannot be used without specifying an exact one-to-one mapping between nodes for every pairwise comparison, a computationally intractable task.To overcome this challenge, we propose a novel way of treating the wavelets as probability distributions over the graph. This way the structural information is contained in how the diffusion spreads over the network rather than where it spreads. In order to provide vector-valued signatures which can then be used as input to any machine learning algorithm, we embed these wavelet distributions using the empirical characteristic function BID18 . The advantage of empirical characteristic functions is that they capture all the moments of a given distribution. This allows GRAPHWAVE to be robust to small perturbations in the local edge structure, as we prove mathematically. Computational complexity of GRAPHWAVE is linear in the number of edges, thus allowing it to scale to large (sparse) networks. Finally, we compare GRAPHWAVE to several state-of-the-art baselines on both real and synthetic datasets, obtaining improvements of up to 71% and demonstrating how our approach is a useful tool for characterizing structural signatures in graphs.Summary of contributions. The main contributions of our paper are as follows:• We develop a novel use of spectral graph wavelets by treating them as probability distributions and characterizing the distributions using empirical characteristic functions.• We leverage these insights to develop a scalable method (GRAPHWAVE) for learning node embeddings based on structural similarity in graphs.• We prove that GRAPHWAVE accurately recovers structurally similar nodes.Further related work. Prior work on discovering nodes with similar structural roles has typically relied on explicit featurization of nodes. These methods generate an exhaustive listing of each node's local topological properties (e.g., node degree, number of triangles it participates in, number of k-cliques, its PageRank score) before computing node similarities based on such heuristic representations. A notable example of such approaches is RolX BID12 , which aims to recover a soft-clustering of nodes into a predetermined number of K distinct roles using recursive feature extraction BID11 . Similarly, struc2vec BID22 uses a heuristic to construct a multilayered graph based on topological metrics and simulates random walks on the graph to capture structural information. In contrast, our approach does not rely on heuristics (we mathematically prove its efficacy) and does not require explicit manual feature engineering or hand-tuning of parameters.Another line of related work are graph diffusion kernels BID4 which have been utilized for various graph modeling purposes BID17 BID2 BID24 BID29 . However, to the best of our knowledge, our paper is the first to apply graph diffusion kernels for determining structural roles in graphs. Kernels have been shown to efficiently capture geometrical properties and have been successfully used for shape detection in the image processing community BID28 BID20 BID0 . However, in contrast to shape-matching problems, GRAPHWAVE considers these kernels as probability distributions over real-world graphs. This is because the graphs that we consider are highly irregular (as opposed to the Euclidean and manifold graphs ). Therefore, traditional wavelet methods, which typically analyze node diffusions across specific nodes that occur in regular and predictable patterns, do not apply. Instead, by treating wavelets as distributions, GRAPHWAVE characterizes the shape of the diffusion, rather than the specific nodes where the diffusion occurs. This key insight allows us to uncover structural signatures and to discover structurally similar nodes. We have developed a new method for learning structural signatures in graphs. Our approach, GRAPHWAVE, uses spectral graph wavelets to generate a structural embedding for each node, which we accomplish by treating the wavelets as a distributions and evaluating the resulting characteristic functions. Considering the wavelets as distributions instead of vectors is a key insight needed to capture structural similarity in graphs.Our method provides mathematical guarantees on the optimality of learned structural signatures. Using spectral graph theory, we prove that structurally equivalent/similar nodes have nearidentical/similar structural signatures in GRAPHWAVE. Experiments on real and synthetic networks provide empirical evidence for our analytical results and yield large gains in performance over stateof-the-art baselines. For future work, these signatures could be used for transfer learning, leveraging data from a well-explored region of the graph to infer knowledge about less-explored regions.",1694,0.85,975,1.7374358974358974,"Nodes residing a graph similar structural roles within their local network topology The identification such roles provides networks can machine learning on graphs However learning structural representations nodes typically manually specifying tailoring topological features Here develop GraphWave represents each node��s local network neighborhood via by leveraging spectral graph wavelet diffusion patterns We prove nodes similar local network neighborhoods will similar GraphWave embeddings even reside Our method scales edges does topological features We evaluate performance obtaining improvements state baselines Structural role discovery graphs focuses identifying nodes which topologically similar local neighborhoods while residing potentially distant areas FIG0 Such alternative definition node similarity very more traditional notions , all some notion "" over the graph consider residing close network proximity Such structural role information about the nodes as input even key nodes (principal ""influencers critical hubs contagion graphs etc.).When structural roles of defined over a discrete space correspond different topologies local network neighborhoods edge of a chain center a star a bridge However , such discrete roles must pre requiring domain expertise manual inspection the graph structure A more powerful and robust method identifying structural similarity involves learning a continuous vector-valued structural signature �� a each node a This motivates a natural definition structural similarity closeness topological signatures For > 0 nodes a defined -structurally with a given distance if: dist(� . Thus a robust structural similarity metric must introduce both an appropriate signature distance metricWhile several methods structural role discovery graphs existing approaches extremely sensitive typically They often require manually hand-labeling topological features BID12 , rely return a single similarity score instead address structure learning on graphs developing GRAPHWAVE. Building upon techniques graph signal BID4 BID10 BID26 , learns structural embedding for based the diffusion a spectral graph wavelet centered Intuitively each node propagates a unit energy over characterizes its neighboring topology based the response While raw spectral graph wavelet signatures/coefficients �� of and might very we treat probability distributions show the coefficient distributions indeed similar.this probe. In contrast prior work the wavelet diffusion as the wavelet scaling parameter study diffuses as the initial source node We prove the coefficients this wavelet directly graph topological properties Hence these coefficients contain recover structurally similar nodes without the hand-labeling features However the wavelets, localized on the graph Therefore to compare structural signatures nodes far each other, typical graph signal processing methodsusing metrics correlation between wavelets 2 distance without specifying for every pairwise comparisonTo overcome treating probability distributions over This way the structural information contained how the diffusion spreads rather spreads In order provide vector-valued signatures which then input embed these wavelet distributions using the empirical characteristic function BID18 The advantage empirical characteristic functions capture all the moments a given distribution This allows GRAPHWAVE robust the local edge structure we prove mathematically Computational complexity GRAPHWAVE linear edges thus allowing it scale large (sparse) networks Finally compare GRAPHWAVE several state baselines on both real and synthetic datasets obtaining improvements demonstrating how our approach characterizing structural signatures graphsSummary contributions. The main contributions our paper develop spectral graph wavelets by treating probability distributions empirical characteristic leverage these insights (GRAPHWAVE learning node embeddings based structural similarity prove accurately recoversFurther related work. Prior work discovering nodes similar structural roles typically explicit featurization These methods generate an exhaustive listing each node's local topological properties number triangles it participates kcliques its PageRank score before computing node similarities based such heuristic representations A notable example such approaches RolX BID12 , aims recover a soft-clustering nodes into a predetermined number K distinct roles using recursive feature extraction BID11 Similarly struc2vec BID22 uses a heuristic construct based topological metrics simulates random walks capture structural information In contrast our approach does heuristicswe mathematically prove its efficacy explicit manual feature engineering parametersAnother line related work are graph diffusion kernels BID4 which utilized various graph modeling purposes . However to our paper apply graph diffusion kernels for determining structural roles graphs Kernels have shown efficiently capture geometrical properties have successfully shape detection BID28 BID20 BID0 . However contrast shape-matching problems GRAPHWAVE considers these kernels probability distributions over This because the graphs that consider highly irregularas the Euclidean and manifold graphs Therefore traditional wavelet methods typically analyze node diffusions across specific nodes that occur regular and predictable patterns apply Instead by treating wavelets distributions GRAPHWAVE characterizes the diffusion, rather the specific nodes where This key insight allows uncover structural signatures and to discover structurally similar nodes We developed learning structural signatures graphs Our approach, GRAPHWAVE uses spectral graph wavelets structural embedding for accomplish treating a distributions evaluating the resulting characteristic functions Considering the wavelets as distributions instead vectors a key insight needed capture structural similarity graphsOur method provides mathematical guarantees learned structural signatures Using spectral graph theory prove structurally equivalent/similar nodes nearidentical/similar structural signatures GRAPHWAVE Experiments real and synthetic networks provide our analytical results yield large gains stateof- baselines For future work these signatures could transfer learning leveraging a well-explored region the graph infer knowledge",0.01,0.5830010459409448
"Driving simulators play an important role in vehicle research. However, existing virtual reality simulators do not give users a true sense of presence. UniNet is our driving simulator, designed to allow users to interact with and visualize simulated traffic in mixed reality. It is powered by SUMO and Unity. UniNet's modular architecture allows us to investigate interdisciplinary research topics such as vehicular ad-hoc networks, human-computer interaction, and traffic management. We accomplish this by giving users the ability to observe and interact with simulated traffic in a high fidelity driving simulator. We present a user study that subjectively measures user's sense of presence in UniNet. Our findings suggest that our novel mixed reality system does increase this sensation. Many driving simulators have been developed, with most of them being used for driver training or research in the field of driver safety [44] . However, these simulators often present limited features in regards to traffic simulation, and user presence [11, 25, 26] . The need for high-quality Virtual Reality (VR) driving simulators with a focus on user presence is long overdue. In addition to this, a driving simulator with traffic simulation is a strong tool for Vehicular Ad-Hoc Network (VANET) research, which is made possible by our choice of traffic generation software. Network simulation is commonly used in networking research, to evaluate the performance of communication protocols and algorithms. Existing simulation tools for vehicular networks focus exclusively on network simulation. A driving simulator that combines network simulation, application prototyping, and testing would be beneficial Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. to VANET researchers. For instance, one could evaluate the performance of a communication protocol or application by using a realistic virtual environment with thousands of vehicles and interacting with them before deploying their research in the real world, which is costly, and at times, unsafe. In addition to a modular simulator with VANET capabilities, we introduce a system for Mixed Reality (MR). Our system introduces the user as their own avatar in a virtual environment, by using stereoscopic cameras and passthrough VR technology. We designed the system to be compatible with existing VR systems, and most VR systems can easily upgrade to our proposed immersion configuration. In this paper, we describe UniNet -a driving simulator that combines realistic vehicle dynamics [42] with a high performance traffic flow simulation platform Simulation of Urban MObility (SUMO) [27] . We discuss the systems we have built within Unity [40] , which connect external applications for a high quality driving experience. In our user study, we followed a within-subjects experimental design, to test if UniNet's MR immersion system improved the user's sense of presence in the virtual environment. We are able to show that the MR configuration is more immersive, however the results are primarily subjective, and come from the questionnaires we chose to include in our study. Our study produced two types of results for each participant. Subjective results, and behavioural results based on reactions to vehicle collision events. Our analysis of the subjective results supported our hypothesis, however we could not draw any conclusions from the behavioural results. Insko writes that, due to presence being a subjective sensation, subjective means of measuring presence have become the most popular [20] . Therefore our inability to corroborate the results from our questionnaires with the behavioural measurements taken, does not disprove our hypothesis. The in-simulator portion of the study contained four trials, designed to compare four configurations of UniNet, and instigate visceral reactions which we measured as reaction times. The reason we chose to compare four configurations, was to compare common existing options for VR simulations, and a non-VR control with our technology. In summary, here is a brief description of why we chose these four immersion configurations. As the market for VR continues to grow, the development of MR technology should grow with it. The reality-virtuality continuum is defined by the mixed-reality area between reality and virtuality, and UniNet was designed to fit within this range. This thesis focused on the effect of user presence in a MR driving simulator, and the construction of a physical product. The user study investigated the effect of our MR immersion configuration, on user presence. The user study hypothesized that our MR configuration would increase the user's sense of presence in the virtual environment, when compared to traditional VR and non-VR configurations. Participants were presented with four trials to complete in UniNet, and each trial finished with a vehicle collision event to create a behavioural response from participants. The subjective results were significant, and in favor of our study's hypothesis. Prior to the study, we designed and tested the hardware and software for UniNet. Unity and SUMO are the primary systems controlling player vehicles and NPC vehicles respectively. Our technology is built to work with the Oculus Rift, using commercially available stereoscopic cameras mounted to the front face of the HMD. Our software creates a passthrough VR experience with this hardware configuration. When combined with the green screen chamber constructed for UniNet, our technology fits on the reality-virtuality continuum as a unique mixed reality experience.",1129,0.776,658,1.71580547112462,"Driving simulators play vehicle research However existing virtual reality simulators give presence UniNet our driving simulator interact and visualize simulated traffic mixed reality It powered SUMO Unity UniNet's modular architecture us investigate interdisciplinary research topics vehicular ad-hoc networks traffic management We accomplish giving users observe simulated traffic a high fidelity driving simulator We present a user study subjectively user's sense presence UniNet Our findings our novel mixed reality system does increase this sensation Many driving simulators with most used driver training research in [44 However these simulators often present limited features regards traffic simulation user presence [11 25 . The need high-quality Virtual Reality driving with a focus user presence long In addition this a driving simulator with traffic simulation a strong tool Vehicular Ad- Network research made our choice traffic generation software Network simulation commonly networking research to evaluate communication protocols algorithms Existing simulation tools vehicular networks focus exclusively network simulation A driving simulator combines network simulation application prototyping testing would beneficial Permission to make digital or hard copies granted provided copies copies bear this notice on Copyrights components owned than must honored Abstracting with credit permitted To copy otherwise or to post servers to lists requires prior specific permission a fee Request permissions to VANET researchers For instance one could evaluate a communication protocol or application a realistic virtual environment thousands vehicles interacting before deploying their research in costly at unsafe In addition a modular simulator with VANET capabilities introduce Mixed Reality Our system introduces the user as by stereoscopic cameras passthrough VR technology We designed compatible existing VR systems can easily upgrade our proposed immersion configuration In this paper UniNet -a driving simulator combines realistic vehicle dynamics [42 a high performance traffic flow simulation platform Simulation of Urban MObility27 We discuss the systems within Unity [40 which connect external applications for a high quality driving experience In our user study followed to UniNet's MR immersion system improved presence We able show the MR configuration more immersive however primarily subjective come the questionnaires chose Our study produced two types results each participant Subjective results, and behavioural results based reactions vehicle collision events Our analysis the subjective results supported, however we could draw the behavioural results Insko writes, due presence being a subjective sensation subjective means of measuring presence have [20 Therefore our inability corroborate the behavioural measurements taken, does in-simulator portion the study contained four trials designed four configurations UniNet and instigate visceral reactions which we measured reaction times The reason chose compare four configurations, was compare common existing options VR simulations a non-VR control with our technology In summary here why chose these four immersion configurations As the market VR continues the development MR technology should grow with The reality-virtuality continuum defined the mixed-reality area between UniNet was fit within This thesis focused user presence a MR driving simulator the construction a physical product The user study investigated our MR immersion configuration, on user presence The user study hypothesized our MR configuration the user's sense presence when traditional VR and Participants presented four trials complete UniNet finished a vehicle collision event to create a behavioural response from The subjective results significant in favor our study's hypothesis Prior the study designed the hardware UniNet Unity and SUMO the primary systems controlling player vehicles NPC vehicles respectively Our technology using commercially available stereoscopic cameras mounted Our software creates a passthrough VR experience this hardware configuration When combined the green screen chamber constructed UniNet our technology fits on the reality-virtuality continuum as a unique mixed reality experience",0.01,0.5278886201282862
"We consider the problem of improving kernel approximation via feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. We propose to use more efficient numerical integration technique to obtain better estimates of the integrals compared to the state-of-the-art methods. Our approach allows to use information about the integrand to enhance approximation and facilitates fast computations. We derive the convergence behavior and conduct an extensive empirical study that supports our hypothesis. Kernel methods proved to be an efficient technique in numerous real-world problems. The core idea of kernel methods is the kernel trick -compute an inner product in a high-dimensional (or even infinite-dimensional) feature space by means of a kernel function k:k(x, y) = ψ(x ), ψ(y ) ,where ψ : X → F is a non-linear feature map transporting elements of input space X into a feature space F. It is a common knowledge that kernel methods incur space and time complexity infeasible to be used with large-scale datasets directly. For example, kernel regression has O(N 3 + N d 2 ) training time, O(N 2 ) memory, O(N d) prediction time complexity for N data points in original d-dimensional space X . One of the most successful techniques to handle this problem BID18 ) introduces a low-dimensional randomized approximation to feature maps: DISPLAYFORM0 This is essentially carried out by using Monte-Carlo sampling to approximate scalar product in (1). A randomized D-dimensional mappingΨ(·) applied to the original data input allows employing standard linear methods, i.e. reverting the kernel trick. In doing so one reduces the complexity to that of linear methods, e.g. D-dimensional approximation admits O(N D 2 ) training time, O(N D) memory and O(N ) prediction time.It is well known that as D → ∞, the inner product in (2) converges to exact kernel k(x, y). Recent research BID22 ; BID9 ; BID4 ) aims to improve the convergence of approximation so that a smaller D can be used to obtain the same quality of approximation.This paper considers kernels that allow the following integral representation k(x, y) = E q(w) g xy (w) ≈ E p(w) f xy (w) = I(f xy ), p(w ) = 1 (2π) d/2 e − w 2 2 ,where q(w) is a density associated with a kernel, e.g. the popular Gaussian kernel has q(w) = p(w), so the exact equality holds with g xy (w) = f xy (w) = φ(w x) φ(w y), where φ(·) = [cos (·), sin( ·)] .The class of kernels admitting the form in (3) covers shift-invariant kernels (e.g. radial basis function (RBF) kernels) and Pointwise Nonlinear Gaussian (PNG) kernels. They are widely used in practice and have interesting connections with neural networks BID3 BID21 ).The main challenge for the construction of low-dimensional feature maps is the approximation of the expectation in (3) which is d-dimensional integral with Gaussian weight. While standard MonteCarlo rule is easy to implement, there are better quadrature rules for such kind of integrals. For example, BID22 apply quasi-Monte Carlo (QMC) rules and obtain better quality kernel matrix approximations compared to random Fourier features of BID18 .Unlike other research studies we refrain from using simple Monte Carlo estimate of the integral, instead, we propose to use specific quadrature rules. We now list our contributions:1. We propose to use advanced quadrature rules to improve kernel approximation accuracy. We also provide an analytical estimate of the error for the used quadrature rules. 2. We note that for kernels with specific integrand f xy (w) in (3) one can improve on its properties. For example , for kernels with even function f xy (w) we derive the reduced quadrature rule which gives twice smaller embedded dimension D with the same accuracy. This applies, for example, to any RBF kernel. 3. We use structured orthogonal matrices (so-called butterfly matrices ) when designing quadrature rule that allow fast matrix by vector multiplications. As a result, we speed up the approximation of the kernel function and reduce memory requirements. 4. We demonstrate our approach on a set of regression and classification problems. Empirical results show that the proposed approach has a better quality of approximation of kernel function as well as better quality of classification and regression when using different kernels. In this work we proposed to apply advanced integration rule that allowed us to achieve higher quality of kernel approximation. Our derivation of the variance of the error implies the dependence of the error on the scale of data, which in case of Gaussian kernel can be interpreted as width of the kernel. However, as we have seen earlier, accuracy on the final task has no direct dependence on the approximation quality, so we can only speculate whether better approximated wide kernels deliver better accuracy compared to the poorer approximated narrow ones. It is interesting to explore this connection in the future work.To speed up the computations we employed butterfly orthogonal matrices yielding the computational complexity O(d log d). Although the procedure we used to generate butterfly matrices claims to produce uniformly random orthogonal matrices, we found that it is not always so. However, the comparison of the method H (uses properly distributed orthogonal matrices) with method B (sometimes fails to do so) did not reveal any differences. We also leave it for the future investigation.Our experimental study confirms that for many kernels on the most datasets the proposed approach delivers better kernel approximation. Additionally, the empirical results showed that the quality of the final task (classification/regression) is also higher than the state-of-the-art baselines. The connection between the final score and the kernel approximation error is to be explored as well.",1196,0.653,683,1.7510980966325036,"We consider the problem improving kernel approximation via feature maps These maps arise Monte Carlo approximation integral representations kernel functions scale up kernel methods larger datasets We propose more efficient numerical integration technique obtain better estimates compared state Our approach allows to information the integrand enhance approximation facilitates We derive the convergence behavior conduct that supports Kernel methods proved an efficient technique The core idea kernel methods the kernel trick -compute an inner product in means k: �� ), )where : X → F transporting elements input space X It a common knowledge kernel methods incur space complexity infeasible be directly For example kernel regression has O(N 3 + N d 2 ) training time memory) prediction time complexity for N data points original d-dimensional space X . One handle BID18 ) introduces a low-dimensional randomized approximation feature: DISPLAYFORM0 This essentially carried approximate scalar product in ( A randomized D-dimensional mapping��· applied the original data input allows employing standard linear methods reverting the kernel trick In doing one reduces to that linear methods admits O(N D 2 ) training timeIt well as D → � the inner product in ( exact kernel k(x Recent research BID22 ; ) aims improve the convergence approximation so a smaller D canThis paper considers kernels allow the following integral representation k(x E q(w I(f ) 1 (2π d/2 e − w 2 2 ,where a density associated has the exact equality holds with g ��· [cos (·), sin( · .The class admitting the form in ( covers (e.g. radial basis function They widely practice interesting connections neural networks BID3 BID21 ).The main challenge the construction low-dimensional feature maps the approximation the expectation in ( which d-dimensional integral Gaussian weight While standard MonteCarlo rule easy better quadrature rules such kind integrals For example BID22 apply quasiMonte rules obtain better quality kernel matrix approximations compared random Fourier features of BID18 .Unlike other research studies we refrain simple Monte Carlo estimate integral, instead propose specific quadrature rules We now list our contributions:1 We propose advanced quadrature rules improve kernel approximation accuracy We also provide an analytical estimate the error the used quadrature rules 2 We note for kernels specific integrand f xy (w in (3 one improve its properties For example , for kernels even function f xy (w we derive the reduced quadrature rule which twice smaller embedded dimension D with the same accuracy This applies, any RBF kernel 3 We use structured orthogonal matrices ) when designing quadrature rule that allow fast matrix by vector multiplications As speed the approximation memory requirements 4 We demonstrate our approach on a set regression and classification problems the proposed approach a better quality approximation of kernel function classification regression when In this work proposed apply advanced integration rule that allowed achieve higher quality kernel approximation Our derivation the variance the error implies the dependence data case Gaussian kernel can interpreted width However earlier accuracy on the final task no direct dependence the approximation quality better approximated wide kernels deliver compared It interesting explore this connection the future workTo speed employed butterfly orthogonal matrices yielding the computational complexity O(d log Although the procedure we generate butterfly matrices claims produce always so However the comparison the method H (uses properly distributed method Bsometimes fails did We also leave for the future investigationOur experimental study confirms for many kernels on the most datasets the proposed approach delivers better kernel approximation Additionally the empirical results showed the quality the final taskclassification/regression also higher state baselines The connection the final score the kernel approximation error to explored",0.01,0.6178111291462006
"Human world knowledge is both structured and flexible. When people see an object, they represent it not as a pixel array but as a meaningful arrangement of semantic parts. Moreover, when people refer to an object, they provide descriptions that are not merely true but also relevant in the current context. Here, we combine these two observations in order to learn fine-grained correspondences between language and contextually relevant geometric properties of 3D objects. To do this, we employed an interactive communication task with human participants to construct a large dataset containing natural utterances referring to 3D objects from ShapeNet in a wide variety of contexts. Using this dataset, we developed neural listener and speaker models with strong capacity for generalization. By performing targeted lesions of visual and linguistic input, we discovered that the neural listener depends heavily on part-related words and associates these words correctly with the corresponding geometric properties of objects, suggesting that it has learned task-relevant structure linking the two input modalities. We further show that a neural speaker that is `listener-aware' --- that plans its utterances according to how an imagined listener would interpret its words in context --- produces more discriminative referring expressions than an `listener-unaware' speaker, as measured by human performance in identifying the correct object. Human world knowledge is both structured and flexible. For example, when people see a chair, they represent it not as a pixel array but as a semantically meaningful combination of parts, such as arms, legs, seat, and back. How to obtain and flexibly deploy such structured knowledge remains an outstanding problem in machine learning (Lake et al., 2017) . One promising approach is to harness the rich conceptual and relational structure latent in language (Andreas et al., 2017) . Natural languages have been optimized across human history to solve the problem of efficiently communicating those aspects of the world most relevant to current goals (Kirby et al., 2015; Gibson et al., 2017) . Consequently, language reflects the structured nature of our world knowledge: we not only conceive of a chair in terms of its semantic parts, but can combine multiple words to refer to its 'curved back' or 'cushioned seat', and provide more informative descriptions if the context requires it, e.g., refer to a different distinguishing part if all the chairs have a cushioned seat.Our goal is to leverage these insights to develop systems that can make fine-grained distinctions between complex object geometries across a wide variety of contexts. Our approach is to leverage natural language produced by people in an interactive communication task to develop neural network models of the speaker and listener roles in this task. We find that the resulting representations learned by these models exhibit structure that is crucial for robust communication: first, they capture taskrelevant correspondences between individual parts of objects and individual tokens of language, and second, they have strong capacity to generalize to novel contexts, objects, utterances, and other related object classes.We make the following contributions:close context far context Figure 1 : Constructing ""close"" and ""far"" contexts by exploiting the latent neighborhood structure of 3D chairs. Orange is a high indegree seed chair, dark gray its selected distractors in each context. Taken together, our results show that natural language, derived from communication in context, provides a strong objective for learning to make fine-grained distinctions between objects with an emphasis on their shared part-structure. An exciting future application of this work would be to leverage these techniques for improving unsupervised part segmentation and 3D shape retrieval, as well as context-aware shape synthesis, providing an advance over existing context-unaware synthesis techniques (Chen et al., 2018) . ACKNOWLEDGMENTS 9 APPENDIX",753,0.365,462,1.62987012987013,"Human world knowledge both structured flexible When people see an object represent not a pixel array a meaningful arrangement semantic parts Moreover when people refer an object provide descriptions merely true relevant Here, combine these two observations learn fine-grained correspondences language and contextually relevant geometric properties To do employed an interactive communication task with human participants construct natural utterances referring 3D objects from ShapeNet in Using this dataset developed neural listener strong capacity By performing targeted lesions visual and linguistic input discovered the neural listener depends part-related words associates correctly the corresponding geometric properties objects suggesting it task-relevant structure linking We further show a neural speaker `listener --- plans how an imagined listener interpret its words in context produces more discriminative referring expressions human performance identifying the correct object Human world knowledge both structured flexible For example people see a chair represent it not a pixel array a semantically meaningful combination parts arms seat How obtain and flexibly deploy such structured knowledge remains an outstanding problem (Lake et al 2017 . One promising approach harness the rich conceptual and relational structure latent language (Andreas et 2017 . Natural languages optimized across human history solve efficiently those aspects most current goals ( 2015 Gibson) . language reflects the structured nature our world knowledge: not conceive a chair terms its semantic parts can combine multiple words refer its 'curved back' or 'cushioned seat provide more informative descriptions if requires refer a different distinguishing part if all the chairsOur goal leverage systems make complex object geometries across Our approach leverage natural language produced people an interactive communication task develop neural network models the speaker listener roles this task We find the resulting representations learned these models exhibit structure crucial robust communication: first capture taskrelevant correspondences individual parts objects individual tokens language have strong capacity generalize objects utterances other related object classesWe makeclose context far context Figure : Constructing ""close by exploiting the latent neighborhood structure 3D chairs Orange a high indegree seed chair dark gray its selected distractors in each context Taken our results natural language, derived communication in context provides a strong objective learning make objects with an emphasis their shared part-structure An exciting future application this work would leverage these techniques improving unsupervised part segmentation and 3D shape retrieval, as well as context-aware shape synthesis providing an advance over existing context-unaware synthesis techniques ( 2018 . 9 APPENDIX",0.0,0.30893292080837365
"Object-based factorizations provide a useful level of abstraction for interacting with the world. Building explicit object representations, however, often requires supervisory signals that are difficult to obtain in practice. We present a paradigm for learning object-centric representations for physical scene understanding without direct supervision of object properties. Our model, Object-Oriented Prediction and Planning (O2P2), jointly learns a perception function to map from image observations to object representations, a pairwise physics interaction function to predict the time evolution of a collection of objects, and a rendering function to map objects back to pixels. For evaluation, we consider not only the accuracy of the physical predictions of the model, but also its utility for downstream tasks that require an actionable representation of intuitive physics. After training our model on an image prediction task, we can use its learned representations to build block towers more complicated than those observed during training. Consider the castle made out of toy blocks in Figure 1a . Can you imagine how each block was placed, one-by-one, to build this structure? Humans possess a natural physical intuition that aids in the performance of everyday tasks. This physical intuition can be acquired, and refined, through experience. Despite being a core focus of the earliest days of artificial intelligence and computer vision research BID19 BID28 , a similar level of physical scene understanding remains elusive for machines.Cognitive scientists argue that humans' ability to interpret the physical world derives from a richly structured apparatus. In particular, the perceptual grouping of the world into objects and their relations constitutes core knowledge in cognition BID24 . While it is appealing to apply such an insight to contemporary machine learning methods, it is not straightforward to do so. A fundamental challenge is the design of an interface between the raw, often high-dimensional observation space and a structured, object-factorized representation. Existing works that have investigated the benefit of using objects have either assumed that an interface to an idealized object space already exists or that supervision is available to learn a mapping between raw inputs and relevant object properties (for instance, category, position, and orientation).Assuming access to training labels for all object properties is prohibitive for at least two reasons. The most apparent concern is that curating supervision for all object properties of interest is difficult to scale for even a modest number of properties. More subtly , a representation based on semantic a) b)Figure 1: (a) A toy block castle. (b) Our method's build of the observed castle, using its learned object representations as a guide during planning. The second uses ground-truth labels of object properties to supervise a learning algorithm that can map to the space of a traditional or learned physics engine. (c) O2P2, like (b), employs an object factorization and the functional structure of a physics engine, but like (a), does not assume access to supervision of object properties. Without object-level supervision, we must jointly learn a perception function to map from images to objects, a physics engine to simulate a collection of objects, and a rendering engine to map a set of objects back to a single composite image prediction. In all three approaches , we highlight the key supervision in orange.attributes can be limiting or even ill-defined. For example, while the size of an object in absolute terms is unambiguous, its orientation must be defined with respect to a canonical, class-specific orientation. Object categorization poses another problem, as treating object identity as a classification problem inherently limits a system to a predefined vocabulary.In this paper, we propose Object-Oriented Prediction and Planning (O2P2), in which we train an object representation suitable for physical interactions without supervision of object attributes. Instead of direct supervision , we demonstrate that segments or proposal regions in video frames, without correspondence between frames, are sufficient supervision to allow a model to reason effectively about intuitive physics. We jointly train a perception module, an object-factorized physics engine, and a neural renderer on a physics prediction task with pixel generation objective. We evaluate our learned model not only on the quality of its predictions, but also on its ability to use the learned representations for tasks that demand a sophisticated physical understanding. We introduced a method of learning object-centric representations suitable for physical interactions. These representations did not assume the usual supervision of object properties in the form of position, orientation, velocity, or shape labels. Instead, we relied only on segment proposals and a factorized structure in a learned physics engine to guide the training of such representations. We demonstrated that this approach is appropriate for a standard physics prediction task. More importantly, we showed that this method gives rise to object representations that can be used for difficult planning problems, in which object configurations differ from those seen during training, without further adaptation. We evaluated our model on a block tower matching task and found that it outperformed object-agnostic approaches that made comparisons in pixel-space directly.",972,0.586,617,1.5753646677471638,"Object-based factorizations provide a useful level interacting Building explicit object representations however often supervisory signals difficult We present a paradigm learning object-centric representations physical scene understanding without direct supervision object properties Our model, Object-Oriented Prediction and Planning (O2P2 jointly learns a perception function map from image observations object representations a pairwise physics interaction function the time evolution a collection back pixels For evaluation consider the physical predictions its utility downstream tasks an actionable representation intuitive physics After training our model an image prediction task can its learned representations block towers more complicated observed Consider the castle made toy blocks in Figure 1a . Can each block was placed one- build this structure Humans possess a natural physical intuition aids This physical intuition acquired, refined Despite a core focus the earliest days artificial intelligence and computer vision research BID19 BID28 , a similar level physical scene understanding machinesCognitive scientists argue interpret derives a richly structured apparatus In particular the perceptual grouping the world objects their relations constitutes core knowledge cognition BID24 While appealing apply such an insight contemporary machine learning methods straightforward A fundamental challenge the design an interface the raw, often high-dimensional observation space a structured, object-factorized representation Existing works that investigated the benefit objects have either assumed an interface an idealized object space already that supervision available learn a mapping raw inputs relevant object properties category position orientation).Assuming access training labels prohibitive for The most apparent concern curating supervision all object properties interest scale for properties More subtly , a representation based semantic a) b)Figure (a) A toy block castle (b) Our method's build of the observed castle, using its learned object representations during planning second uses ground-truth labels of object properties supervise a learning algorithm map the space a traditional or learned physics engine (c) O2P2 like ( employs an object factorization and the functional structure a physics engine like assume access supervision object properties Without object-level supervision we jointly learn a perception function map from images a physics engine simulate a collection map back a single composite image prediction In all three approaches , highlight the key supervision in orange.attributes can limiting ill For example while the size absolute terms unambiguous its orientation must with a canonical, class-specific orientation Object categorization poses treating object identity inherently limits a system a predefined vocabularyIn Object-Oriented Prediction PlanningO2P2 in train suitable physical interactions without supervision object attributes Instead direct supervision , demonstrate segments or proposal regions video frames, without correspondence sufficient supervision allow a model reason effectively intuitive physics We jointly train a perception module an object-factorized physics engine on a physics prediction task with pixel generation objective We evaluate our learned model not use the learned representations tasks demand a sophisticated physical understanding We introduced a method learning object-centric representations suitable physical interactions These representations did assume the usual supervision object properties position velocity shape labels Instead relied only segment proposals a factorized structure in a learned physics engine guide the training such representations We demonstrated this approach appropriate a standard physics prediction task More importantly showed this method gives rise object representations difficult planning problems in object configurations differ seen during training without further adaptation We evaluated our model a block tower matching task object-agnostic approaches that made comparisons in pixel-space directly",0.01,0.170057792116597
"We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and sufficient conditions for a critical point of the risk function to be a global minimum. Surprisingly, our conditions provide an efficiently checkable test for global optimality, while such tests are typically intractable in nonconvex optimization. We further extend these results to deep nonlinear neural networks and prove similar sufficient conditions for global optimality, albeit in a more limited function space setting. Since the advent of AlexNet BID10 , deep neural networks have surged in popularity, and have redefined the state-of-the-art across many application areas of machine learning and artificial intelligence, such as computer vision, speech recognition, and natural language processing. However, a concrete theoretical understanding of why deep neural networks work well in practice remains elusive. From the perspective of optimization, a significant barrier is imposed by the nonconvexity of training neural networks. Moreover, it was proved by BID2 that training even a 3-node neural network to global optimality is NP-Hard in the worst case, so there is little hope that neural networks have properties that make global optimization tractable.Despite the difficulties of optimizing weights in neural networks, the empirical successes suggest that the local minima of their loss surfaces could be close to global minima; and several papers have recently appeared in the literature attempting to provide a theoretical justification for the success of these models. For example, by relating neural networks to spherical spin-glass models from statistical physics, BID3 provided some empirical evidence that the increase of size of neural networks makes local minima close to global minima.Another line of results BID16 BID14 BID15 BID13 provides conditions under which a critical point of the empirical risk is a global minimum. Such results roughly involve proving that if full rank conditions of certain matrices (as well as some additional technical conditions) are satisfied, derivative of the risk being zero implies loss being zero. However, these results are obtained under restrictive assumptions; for example, BID13 require the width of one of the hidden layers to be as large as the number of training examples. BID14 and BID15 require the product of widths of two adjacent layers to be at least as large as the number of training examples, meaning that the number of parameters in the model must grow rapidly as we have more training data available. Another recent paper BID4 provides a sufficient condition for global optimality when the neural network is composed of subnetworks with identical architectures connected in parallel and a regularizer is designed to control the number of parallel architectures.Towards obtaining a more precise characterization of the loss-surfaces, a valuable conceptual simplification of deep nonlinear networks is deep linear neural networks, in which all activation functions are linear and the output of the entire network is a chained product of weight matrices with the input vector. Although at first sight a deep linear model may appear overly simplistic, even its opti-mization is nonconvex, and only recently theoretical results on this problem have started emerging. Interestingly, already in 1989, BID0 showed that some shallow linear neural networks have no local minima. More recently, BID8 extended this result to deep linear networks and proved that any local minimum is also global while any other critical point is a saddle point. Subsequently, BID11 provided a simpler proof that any local minimum is also global, with fewer assumptions than BID8 . Motivated by the success of deep residual networks BID6 b) , BID5 investigated loss surfaces of deep linear residual networks and showed every critical point is a global minimum in a near-identity region; subsequently, Bartlett et al. (2017) extended this result to a nonlinear function space setting.",774,0.37,468,1.6538461538461537,"We study the error landscape deep linear and nonlinear neural networks the squared error loss Minimizing the loss a deep linear neural network despite our understanding this loss surface For deep linear networks present necessary and sufficient conditions a critical point the risk function a global minimum Surprisingly our conditions provide an efficiently checkable test global optimality while such tests typically nonconvex optimization We further extend these results deep nonlinear neural networks prove similar sufficient conditions global optimality albeit a more limited function space setting Since AlexNet BID10 , deep neural networks surged redefined the state across many application areas of However a concrete theoretical understanding why well practice From the perspective optimization a significant barrier imposed training neural networks Moreover proved BID2 training even a 3-node neural network global optimality NPHard so there little hope have properties global optimization tractableDespite optimizing weights the empirical successes suggest the local minima their loss surfaces could close; several papers recently appeared attempting provide the success For example by relating neural networks spherical spin-glass models from statistical physics BID3 provided some empirical evidence the increase size makes local minima closeAnother line results provides conditions under a critical point the empirical risk a global minimum Such results roughly involve proving if full rank conditions certain matricesas some additional technical conditions derivative of the risk being zero implies loss being However these results obtained under restrictive assumptions; BID13 require the width one of the hidden layers as training examples BID14 and require the product of widths two adjacent layers as training examples meaning parameters grow rapidly we have Another recent paper BID4 provides a sufficient condition global optimality when the neural network composed identical architectures connected a regularizer is designed control parallel architecturesTowards obtaining the loss-surfaces a valuable conceptual simplification deep nonlinear networks deep linear neural networks all activation functions linear a chained product weight matrices Although at a deep linear model overly even its opti-mization nonconvex only recently theoretical results on started emerging Interestingly already 1989 BID0 showed some shallow linear neural networks have no local minima More recently BID8 extended this result deep linear networks proved any local minimum also global while any other critical point a saddle point Subsequently BID11 provided a simpler proof any local minimum is also global fewer assumptions . Motivated deep residual networks BID6 b) , investigated loss surfaces deep linear residual networks showed every critical point a global minimum in a near-identity region; subsequently Bartlett (2017 extended this result a nonlinear function space setting",0.0,0.3700217233888486
"Recurrent auto-encoder model can summarise sequential data through an encoder structure into a fixed-length vector and then reconstruct into its original sequential form through the decoder structure. The summarised information can be used to represent time series features. In this paper, we propose relaxing the dimensionality of the decoder output so that it performs partial reconstruction. The fixed-length vector can therefore represent features only in the selected dimensions. In addition, we propose using rolling fixed window approach to generate samples. The change of time series features over time can be summarised as a smooth trajectory path. The fixed-length vectors are further analysed through additional visualisation and unsupervised clustering techniques. 

 This proposed method can be applied in large-scale industrial processes for sensors signal analysis purpose where clusters of the vector representations can be used to reflect the operating states of selected aspects of the industrial system. Successive context vectors generated by windowing approach are always highly correlated, thus form a smooth trajectory in high-dimensional space. Additional dimensionality reduction techniques can be applied visualise the change of features as a smooth trajectory. One of the key contributions of this study is that, the context vectors form distinct neighbourhoods which can be identified through unsupervised clustering algorithms such as K-means. The clusters can be optionally labelled manually to identify operating state (e.g. healthy vs. faulty). Alarm can be triggered when the context vector travels beyond the boundary of a predefined neighbourhood. Moreover, this enables us to find the clusters of unlabelled time series data. Clusters of the vector representation can be used by operators and engineers to aid diagnostics and maintenance.Another contribution of this study is that dimensionality of the output sequence can be relaxed, thus allowing the recurrent auto-encoder to perform partial reconstruction. Although it is clearly easier for the model to partially reconstruct the original sequence, such simple improvement allows users to define different sets of sensors of particular interest. By limiting the number of sensors to include in the output dimension, the context vector can be used to reflect the underlying states of specific aspects of the large-scale industrial process. This ultimately generates more actionable insights and enables users to diagnose the induatrial system. We have demonstrated the use of partial reconstruction by through two examples which graphically show the effects of it.This proposed method performs multidimensional time series clustering, which can natively scale up to very high dimensionality as it is based on recurrent auto-encoder model. We have applied the method to an industrial sensor dataset with P = 158 and empirically show that it can summarise multidimensional time series data effectively.The model can be generalised to any multi-sensor multi-state processes for operating state recognition. We also recognise that the cost of collecting labelled time series data can be very expensive. This study established that recurrent auto-encoder model can be used to analyse unlabelled and un-bounded time series data. This opens up further possibilities for analysing IoT and industrial sensors data given that these domains are predominately overwhelmed with unbounded and unlabelled time series data. Nevertheless, the proposed approach has not included any categorical sensor measurements (e.g. open/closed, tripped/healthy, start/stop... etc). Future research can focus on incorporating categorical measurements alongside real-valued measurements.",650,0.441,370,1.7567567567567568,Recurrent auto-encoder model can summarise sequential data through into reconstruct into its original sequential form through The summarised information can represent time series features In relaxing the decoder output so performs partial reconstruction The fixed-length vector can therefore represent features only the selected dimensions In addition propose using rolling fixed window approach generate samples The change time series features over time can a smooth trajectory path The fixed-length vectors further analysed through additional visualisation This proposed method can for sensors signal analysis purpose where clusters the vector representations reflect the operating states selected aspects Successive context vectors generated windowing approach always highly thus form a smooth trajectory Additional dimensionality reduction techniques visualise features as a smooth trajectory One the context vectors form distinct neighbourhoods which such The clusters can optionally labelled manually to operating state healthy faulty). Alarm can the context vector travels a predefined neighbourhood Moreover this enables find the clusters unlabelled time series data Clusters the vector representation can by operators engineers aid maintenanceAnother contribution dimensionality the output sequence relaxed the recurrent auto-encoder partial reconstruction Although clearly easier the model partially reconstruct such simple improvement allows users define different sets sensors of particular interest By limiting sensors include in the output dimension the context vector reflect the underlying states specific aspects This ultimately generates more actionable insights enables diagnose the induatrial system We demonstrated partial reconstruction through two examples which graphically itThis proposed method performs time natively as based recurrent auto-encoder model We applied an industrial sensor dataset P = 158 empirically summarise effectivelyThe model generalised any multi-sensor multi-state processes for operating state recognition We also recognise the cost collecting labelled time series data This study established recurrent auto-encoder model can analyse This opens analysing IoT and industrial sensors data given these domains predominately overwhelmed unbounded and unlabelled time series data Nevertheless the proposed approach included any categorical sensor measurements open/ trippedhealthy start... etc Future research can incorporating categorical measurements alongside,0.0,0.6322288979783552
"We view molecule optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be optimized in different ways, there are multiple viable translations for each input graph. A key challenge is therefore to model diverse translation outputs. Our primary contributions include a junction tree encoder-decoder for learning diverse graph translations along with a novel adversarial training method for aligning distributions of molecules. Diverse output distributions in our model are explicitly realized by low-dimensional latent vectors that modulate the translation process. We evaluate our model on multiple molecule optimization tasks and show that our model outperforms previous state-of-the-art baselines by a significant margin. 
 The goal of drug discovery is to design molecules with desirable chemical properties. The task is challenging since the chemical space is vast and often difficult to navigate. One of the prevailing approaches, known as matched molecular pair analysis (MMPA) BID16 BID11 , learns rules for generating ""molecular paraphrases"" that are likely to improve target chemical properties. The setup is analogous to machine translation: MMPA takes as input molecular pairs {(X, Y )}, where Y is a paraphrase of X with better chemical properties. However, current MMPA methods distill the matched pairs into graph transformation rules rather than treating it as a general translation problem over graphs based on parallel data.In this paper, we formulate molecular optimization as graph-to-graph translation. Given a corpus of molecular pairs, our goal is to learn to translate input molecular graphs into better graphs. The proposed translation task involves many challenges. While several methods are available to encode graphs BID12 BID32 , generating graphs as output is more challenging without resorting to a domain-specific graph linearization. In addition, the target molecular paraphrases are diverse since multiple strategies can be applied to improve a molecule. Therefore, our goal is to learn multimodal output distributions over graphs.To this end, we propose junction tree encoder-decoder, a refined graph-to-graph neural architecture that decodes molecular graphs with neural attention. To capture diverse outputs, we introduce stochastic latent codes into the decoding process and guide these codes to capture meaningful molecular variations. The basic learning problem can be cast as a variational autoencoder, where the posterior over the latent codes is inferred from input molecular pair (X, Y ). Further, to avoid invalid translations, we propose a novel adversarial training method to align the distribution of graphs generated from the model using randomly selected latent codes with the observed distribution of valid targets. Specifically, we perform adversarial regularization on the level of the hidden states created as part of the graph generation. We evaluate our model on three molecular optimization tasks, with target properties ranging from drug likeness to biological activity. 1 As baselines, we utilize state-of-the-art graph generation methods BID23 BID47 and MMPA BID9 . We demonstrate that our model excels in discovering molecules with desired properties, outperforming the baselines across 2 RELATED WORK Molecular Generation/Optimization Prior work on molecular optimization approached the graph translation task through generative modeling BID14 BID42 BID28 BID8 BID23 BID39 BID31 and reinforcement learning BID17 BID36 BID37 BID47 . Earlier approaches represented molecules as SMILES strings BID46 , while more recent methods represented them as graphs. Most of these methods coupled a molecule generator with a property predictor and solved the optimization problem through Bayesian optimization or reinforcement learning. In contrast, our model is trained to translate a molecular graph into a better graph through supervised learning, which is more sample efficient.Our approach is closely related to matched molecular pair analysis (MMPA) BID16 BID11 in drug de novo design, where the matched pairs are hard-coded into graph transformation rules. MMPA's main drawback is that large numbers of rules have to be realized (e.g. millions) to cover all the complex transformation patterns. In contrast, our approach uses neural networks to learn such transformations, which does not require the rules to be explicitly realized.Graph Neural Networks Our work is related to graph encoders and decoders. Previous work on graph encoders includes convolutional BID40 BID4 BID20 BID12 BID35 BID10 BID27 and recurrent architectures BID32 BID7 . Graph encoders have been applied to social network analysis BID26 BID19 and chemistry BID24 BID13 BID41 . Recently proposed graph decoders BID44 BID33 BID23 BID48 BID34 focus on learning generative models of graphs. While our model builds on BID23 to generate graphs, we contribute new techniques to learn multimodal graph-to-graph mappings.Image/Text Style Translation Our work is closely related to image-to-image translation BID21 , which was later extended by to learn multimodal mappings. Our adversarial training technique is inspired by recent text style transfer methods BID43 BID49 ) that adversarially regularize the continuous representation of discrete structures to enable end-to-end training. Our technical contribution is a novel adversarial regularization over graphs that constrains their scaffold structures in a continuous manner. In conclusion, we have evaluated various graph-to-graph translation models for molecular optimization. By combining the variational junction tree encoder-decoder with adversarial training, we can generate better and more diverse molecules than the baselines.",1063,0.628,632,1.6819620253164558,"We view molecule optimization graphto translation The goal learn map from one molecular graph better properties based an available corpus paired molecules Since molecules optimized multiple viable translations each input graph A key challenge therefore model diverse translation outputs Our primary contributions a junction tree encoder-decoder learning diverse graph translations along aligning distributions molecules Diverse output distributions our model explicitly realized low-dimensional latent vectors the translation process We evaluate our model multiple molecule optimization tasks state baselines The goal drug discovery design The task challenging since the chemical space vast often One the prevailing approaches, known matched molecular pair analysis BID16 BID11 learns rules generating likely improve target chemical properties The setup analogous machine translation MMPA takes as molecular pairs {(X ) with better chemical properties However current MMPA methods distill the matched pairs graph transformation rules rather treating a general translation problem over graphs based parallel dataIn formulate molecular optimization graph Given a corpus molecular pairs our goal learn translate input molecular graphs better graphs The proposed translation task involves many challenges While several methods encode graphs BID12 BID32 , generating as output without a domain-specific graph linearization In the target molecular paraphrases diverse since multiple strategies improve a molecule Therefore our goal learn multimodal output distributions graphsTo propose junction tree encoder-decoder refined graphto neural architecture molecular graphs neural attention To capture diverse outputs introduce stochastic latent codes into guide capture meaningful molecular variations The basic learning problem can cast posterior over the latent codes inferred input molecular pair (X Further to invalid translations propose a novel adversarial training method align the distribution graphs generated using randomly selected latent codes valid targets Specifically perform adversarial regularization the level the hidden states created as the graph generation We evaluate our model three molecular optimization tasks target properties ranging drug likeness biological activity 1 As baselines utilize state graph generation BID23 BID47 MMPA BID9 We demonstrate our model excels discovering molecules desired properties outperforming the baselines across 2 RELATED WORK Molecular Generation/ Prior work molecular optimization approached the graph translation task through and reinforcement . Earlier approaches represented molecules as SMILES strings BID46 , while graphs Most these methods coupled a molecule generator a property predictor solved through or In contrast our model trained translate a molecular graph a better graph through supervised learning sampleOur approach closely matched molecular pair analysisMMPA BID16 BID11 in drug de novo design hard graph transformation rules MMPA's main drawback large numbers rules realized () cover all the complex transformation patterns In contrast our approach uses such transformations does the rules realizedGraph Neural Networks Our work related graph Previous work graph encoders includes and recurrent architectures . Graph encoders applied social network analysis BID26 BID19 . Recently proposed graph decoders BID44 BID33 BID23 BID48 BID34 focus learning generative models graphs While our model builds BID23 to generate graphs contribute new techniques learn multimodal graphtoImage/Text Style Translation Our work closely imageimage BID21 , later to learn Our adversarial training technique inspired recent text style transfer methods BID43 BID49 ) adversarially regularize the continuous representation discrete structures enable end training Our technical contribution a novel adversarial regularization over graphs their scaffold structures In conclusion evaluated various graphto translation molecular optimization By combining the variational junction tree encoder-decoder adversarial training better and more diverse molecules the baselines",0.01,0.4416584936617205
"Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be sub-optimal for specific classes of problems. In contrast to existing hand-crafted solutions, we propose an approach to learn a fast iterative solver tailored to a specific domain. We achieve this goal by learning to modify the updates of an existing solver using a deep neural network. Crucially, our approach is proven to preserve strong correctness and convergence guarantees. After training on a single geometry, our model generalizes to a wide variety of geometries and boundary conditions, and achieves 2-3 times speedup compared to state-of-the-art solvers. Partial differential equations (PDEs) are ubiquitous tools for modeling physical phenomena, such as heat, electrostatics, and quantum mechanics. Traditionally, PDEs are solved with hand-crafted approaches that iteratively update and improve a candidate solution until convergence. Decades of research and engineering went into designing update rules with fast convergence properties.The performance of existing solvers varies greatly across application domains, with no method uniformly dominating the others. Generic solvers are typically effective, but could be far from optimal for specific domains. In addition, high performing update rules could be too complex to design by hand. In recent years, we have seen that for many classical problems, complex updates learned from data or experience can out-perform hand-crafted ones. For example, for Markov chain Monte Carlo, learned proposal distributions lead to orders of magnitude speedups compared to handdesigned ones BID20 BID12 . Other domains that benefited significantly include learned optimizers BID1 and learned data structures BID9 . Our goal is to bring similar benefits to PDE solvers.Hand-designed solvers are relatively simple to analyze and are guaranteed to be correct in a large class of problems. The main challenge is how to provide the same guarantees with a potentially much more complex learned solver. To achieve this goal, we build our learned iterator on top of an existing standard iterative solver to inherit its desirable properties. The iterative solver updates the solution at each step, and we learn a parameterized function to modify this update. This function class is chosen so that for any choice of parameters, the fixed point of the original iterator is preserved. This guarantees correctness, and training can be performed to enhance convergence speed. Because of this design, we only train on a single problem instance; our model correctly generalizes to a variety of different geometries and boundary conditions with no observable loss of performance. As a result, our approach provides: (i) theoretical guarantees of convergence to the correct stationary solution, (ii) faster convergence than existing solvers, and (iii) generalizes to geometries and boundary conditions very different from the ones seen at training time. This is in stark contrast with existing deep learning approaches for PDE solving BID21 BID6 that are limited to specific geometries and boundary conditions, and offer no guarantee of correctness.Our approach applies to any PDE with existing linear iterative solvers. As an example application, we solve the 2D Poisson equations. Our method achieves a 2-3× speedup on number of multiplyadd operations when compared to standard iterative solvers, even on domains that are significantly different from our training set. Moreover, compared with state-of-the-art solvers implemented in FEniCS BID13 , our method achieves faster performance in terms of wall clock CPU time. Our method is also simple as opposed to deeply optimized solvers such as our baseline in FEniCS (minimal residual method + algebraic multigrid preconditioner). Finally, since we utilize standard convolutional networks which can be easily parallelized on GPU, our approach leads to an additional 30× speedup when run on GPU. We presented a method to learn an iterative solver for PDEs that improves on an existing standard solver. The correct solution is theoretically guaranteed to be the fixed point of our iterator. We show that our model, trained on simple domains, can generalize to different grid sizes, geometries and boundary conditions. It converges correctly and achieves significant speedups compared to standard solvers, including highly optimized ones implemented in FEniCS.A PROOFS Theorem 1. For a linear iterator Ψ(u) = T u + c, Ψ converges to a unique stable fixed point from any initialization if and only if the spectral radius ρ(T ) < 1.Proof. Suppose ρ(T ) < 1, then (I−T ) −1 must exist because all eigenvalues of I−T must be strictly positive. Let u * = (I − T ) −1 c; this u * is a stationary point of the iterator Ψ, i.e. u * = T u * + c. For DISPLAYFORM0 Since ρ(T ) < 1, we know BID11 , which means the error e k → 0. Therefore, Ψ converges to u * from any u 0 . DISPLAYFORM1 Now suppose ρ(T ) ≥ 1. Let λ 1 be the largest absolute eigenvalue where ρ(T ) = |λ 1 | ≥ 1, and v 1 be its corresponding eigenvector. We select initialization u 0 = u * + v 1 , then e 0 = v 1 . Because |λ 1 | ≥ 1, we have |λ k 1 | ≥ 1, then T k e 0 = λ k 1 v 1 → k→∞ 0 However we know that under a different initializationû 0 = u * , we haveê 0 = 0, so T kê0 = 0. Therefore the iteration cannot converge to the same fixed point from different initializations u 0 and u 0 .Proposition 1 If M is a full rank diagonal matrix, and u * ∈ R n 2 ×n 2 satisfies Eq. (7) , then u * satisfies Eq. (4).Proof of Proposition 1. Let u * be a fixed point of Eq. (7) then The latter equation is equivalent to GM −1 (Au * − f ) = 0. If M is a full rank diagonal matrix, this implies G(Au * − f ) = 0, which is GAu * = Gf . Therefore, u * satisfies Eq.(4).Theorem 2. For fixed G, f, b, n, the spectral norm of Φ H (u; G, f, b, n) is a convex function of H, and the set of H such that the spectral norm of Φ H (u; G, f, b, n) < 1 is a convex open set.Proof. As before, denote Ψ(u) = T u + c. Observe that Φ H (u; G, f, b, n) = T u + c + GH(T u + c − u) = (T + GHT − GH)u + GHc + cThe spectral norm · 2 is convex with respect to its argument, and (T + GHT − GH) is linear in H. Thus, T + GHT − GH 2 is convex in H as well. Thus, under the condition that T + GHT − GH 2 < 1, the set of H must be convex because it is a sub-level set of the convex function T + GHT − GH 2 .To prove that it is open, observe that · 2 is a continuous function, so T + GHT − GH 2 is a continuous map from H to the spectral radius of Φ H . If we consider the set of H such that T + GHT − GH 2 < 1, this set is the preimage of (− , 1) for any > 0. As (− , 1) is open, its preimage must be open. Proposition 2. For fixed A, G, n and fixed H, if for some f 0 , b 0 , Φ H (u; G, f 0 , b 0 , n) is valid for the PDE problem (A, G, f 0 , b 0 , n), then for all f and b, the iterator Φ H (u; G, f, b, n) is valid for the PDE problem (A, G, f, b, n).Proof. From Theorem 1 and Lemma 1, our iterator is valid if and only if ρ(T + GHT − GH) < 1. The iterator T + GHT − GH only depends on A, G, and is independent of the constant c in Eq. (18). Thus, the validity of the iterator is independent with f and b. Thus, if the iterator is valid for some f 0 and b 0 , then it is valid for any choice of f and b.",1835,1.002,1080,1.6990740740740742,"Partial differential equations widely across Decades engineering went designing fast iterative solution methods Existing solvers general purpose may sub specific classes In contrast existing hand-crafted solutions propose learn a fast iterative solver tailored We achieve learning modify the updates an existing solver Crucially our approach proven preserve strong correctness convergence guarantees After training a single geometry our model generalizes boundary conditions achieves 2-3 times speedup state solvers Partial differential equations ubiquitous tools heat electrostatics PDEs solved hand-crafted approaches iteratively update a candidate solution until convergence Decades engineering went designing update rules with fast convergence propertiesThe performance existing solvers varies across application domains no method uniformly dominating the others Generic solvers typically effective could far specific domains In addition high performing update rules could too complex design by In we that for many classical problems complex updates learned data or experience For example for Markov chain Monte Carlo learned proposal distributions lead orders compared handdesigned ones BID20 BID12 . Other domains benefited significantly include learned optimizers BID1 learned data structures BID9 . Our goal similar benefits PDE solversHand-designed solvers relatively analyze are guaranteed correct a large class The main challenge how provide the same guarantees with a potentially much more complex learned solver To achieve build our learned iterator on an existing standard iterative solver to inherit its desirable properties The iterative solver updates the solution at we learn a parameterized function modify this update This function class chosen so for any choice parameters the fixed point the original iterator preserved This guarantees correctness training can to enhance convergence speed Because this design only train a single problem instance; our model correctly generalizes boundary conditions with no observable loss As our approach provides: (i) theoretical guarantees convergence the correct stationary solution faster convergence existing solvers generalizes boundary conditions very different seen at training time This in existing deep learning approaches for PDE solving BID21 BID6 that limited boundary conditions offer no guarantee correctnessOur approach applies existing linear iterative solvers As an example application solve the 2D Poisson equations Our method achieves number multiplyadd operations when compared standard iterative solvers even domains significantly different our training set Moreover compared state solvers implemented FEniCS BID13 , our method achieves faster performance terms wall clock CPU time Our method also simple as opposed to deeply optimized solvers such our baseline in FEniCS (minimal residual method + algebraic multigrid preconditioner Finally since utilize standard convolutional networks which easily on GPU our approach leads an additional 30× speedup run We presented learn an solver PDEs improves The correct solution theoretically guaranteed the fixed point our iterator We show our model, trained simple domains different grid sizes boundary conditions It converges correctly achieves significant speedups compared standard solvers including highly optimized ones implemented FEniCS.A PROOFS Theorem 1 For a linear iterator ��u T u + c, �� converges a unique stable fixed point from any initialization if only if the spectral radius ��T ) 1.Proof Suppose ��T ) < (I−T −1 must exist because strictly Let u * = (I − T −1 c; this u a stationary point of the iterator �� = T u For DISPLAYFORM0 Since ��(T ) < know BID11 , the error e k → 0 Therefore, �� converges u * from any u 0 DISPLAYFORM1 Now suppose ��T ) ≥ Let � 1 the largest absolute eigenvalue where(T ) = |λ ≥ v its corresponding eigenvector We select initialization u 0 = u * + v then e . Because |λ 1 ≥ k then T k e 0 v → k→� 0 However know under a different initializationû 0 u * , haveê Therefore the iteration converge from different initializations u 0 .Proposition If M a full rank diagonal matrix u * � R n 2 ×n satisfies7 satisfies4).Proof Proposition Let u * be a fixed point Eq7 then The latter equation equivalent GM −1 (Au * − f If M is a full rank diagonal matrix this implies G(Au * − f ) GAu = Gf Therefore u * satisfies Eq.(4).Theorem For fixed G, f n the spectral norm �� Hu; G H the set H such < a convex open setProof As before, denote ��u T u c. Observe �� Hu; G, f = T u + c + GH(T u + GHT − GHc cThe spectral norm · 2 convex its argument ( linear H. Thus T + GHT − GH 2 is convex H as Thus under T + GHT − GH 2 < the set H must convex because a sub-level set the convex function T .To prove it open observe · 2 a continuous map from the spectral radius �� H If we consider the set H such that T + GHT − GH 2 < this set the preimage (− , 1 for any > As (− , 1 open its preimage must Proposition For fixed A, G n fixed H if for some f 0 b 0 , �� H (u; G f n valid the PDE problemA and the iterator �� H n).Proof From Theorem 1 and Lemma our iterator valid �T + GHT − GH The iterator T + GHT − GH only depends A is independent the constant c in Eq18 Thus the validity the iterator independent with f Thus the iterator valid some f 0 b any choice and",0.01,0.48525849044796715
"Variational Bayesian neural networks (BNN) perform variational inference over weights, but it is difficult to specify meaningful priors and approximating posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes is equal to the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which approximates the functional ELBO using finite measurement sets and the spectral Stein gradient estimator. With fBNNs, we can specify priors which entail rich structure, including Gaussian processes and implicit stochastic processes. Empirically, we find that fBNNs extrapolate well using various structured priors, provide reliable uncertainty estimates, and can scale to large datasets. Bayesian neural networks (BNNs) BID22 BID40 have the potential to combine the scalability, flexibility, and predictive performance of neural networks with principled Bayesian uncertainty modelling. However, the practical effectiveness of BNNs is limited by our ability to specify meaningful prior distributions and by the intractability of posterior inference. Choosing a meaningful prior distribution over network weights is difficult because the weights have a complicated relationship to the function computed by the network. Stochastic variational inference is appealing because the update rules resemble ordinary backprop BID15 BID4 , but fitting accurate posterior distributions is difficult due to strong and complicated posterior dependencies BID34 BID51 .In a classic result, BID40 showed that under certain assumptions, as the width of a shallow BNN was increased, the limiting distribution is a Gaussian process (GP). BID31 recently extended this result to deep BNNs. Deep Gaussian Processes (DGP) BID5 BID49 have close connections to BNNs due to similar deep structures. However , the relationship of finite BNNs to GPs is unclear, and practical variational BNN approximations fail to match the predictions of the corresponding GP. Furthermore , because the previous analyses related specific BNN architectures to specific GP kernels, it's not clear how to design BNN architectures for a given kernel. Given the rich variety of structural assumptions that GP kernels can represent BID45 BID33 , there remains a significant gap in expressive power between BNNs and GPs (not to mention stochastic processes more broadly).In this paper , we perform variational inference directly on the distribution of functions. Specifically , we introduce functional variational BNNs (fBNNs), where a BNN is trained to produce a distribution of functions with small KL divergence to the true posterior over functions. We prove that the KL divergence between stochastic processes can be expressed as the supremum of marginal KL divergences at finite sets of points. Based on this , we present functional ELBO (fELBO) training objective. Then we introduce a GAN-like minimax formulation and a sampling-based approximation for functional variational inference. To approximate the marginal KL divergence gradients, we adopt the recently proposed spectral Stein gradient estimator (SSGE) BID52 . Here a × b represents a hidden layers of b units. Red dots are 20 training points. The blue curve is the mean of final prediction, and the shaded areas represent standard derivations. We compare fBNNs and Bayes-by-Backprop (BBB). For BBB, which performs weight-space inference , varying the network size leads to drastically different predictions. For fBNNs, which perform functionspace inference , we observe consistent predictions for the larger networks. Note that the 1 × 100 factorized Gaussian fBNNs network is not expressive enough to generate diverse predictions.Our fBNNs make it possible to specify stochastic process priors which encode richly structured dependencies between function values. This includes stochastic processes with explicit densities, such as GPs which can model various structures like smoothness and periodicity BID33 . We can also use stochastic processes with implicit densities, such as distributions over piecewise linear or piecewise constant functions. Furthermore, in contrast with GPs, fBNNs efficiently yield explicit posterior samples of the function. This enables fBNNs to be used in settings that require explicit minimization of sampled functions, such as Thompson sampling BID57 BID48 or predictive entropy search BID21 BID59 .One desideratum of Bayesian models is that they behave gracefully as their capacity is increased BID44 . Unfortunately, ordinary BNNs don't meet this basic requirement : unless the asymptotic regime is chosen very carefully (e.g. BID40 ), BNN priors may have undesirable behaviors as more units or layers are added. Furthermore, larger BNNs entail more difficult posterior inference and larger description length for the posterior, causing degeneracy for large networks, as shown in FIG0 . In contrast, the prior of fBNNs is defined directly over the space of functions, thus the BNN can be made arbitrarily large without changing the functional variational inference problem. Hence, the predictions behave well as the capacity increases.Empirically , we demonstrate that fBNNs generate sensible extrapolations for both explicit periodic priors and implicit piecewise priors. We show fBNNs outperform competing approaches on both small scale and large scale regression datasets. fBNNs' reliable uncertainty estimates enable state-of-art performance on the contextual bandits benchmark of BID46 . In this paper we investigated variational inference between stochastic processes. We proved that the KL divergence between stochastic processes equals the supremum of KL divergence for marginal distributions over all finite measurement sets. Then we presented two practical functional variational inference approaches: adversarial and sampling-based. Adopting BNNs as the variational posterior yields our functional variational Bayesian neural networks. Empirically, we demonstrated that fBNNs extrapolate well over various structures, estimate reliable uncertainties, and scale to large datasets.",1182,0.695,741,1.5951417004048583,"Variational Bayesian neural networks perform over weights specify meaningful priors approximating posteriors We introduce functional variational Bayesian neural networks maximize an Evidence Lower BOund (ELBO defined directly functions We prove the KL divergence equal the supremum marginal KL divergences over all finite sets inputs Based introduce a practical training objective the functional ELBO using finite measurement sets the spectral Stein gradient estimator With fBNNs specify priors which entail rich structure including Gaussian processes we find fBNNs extrapolate well using various structured priors provide reliable uncertainty estimates scale Bayesian neural networks BID22 BID40 have combine the scalability predictive performance principled Bayesian uncertainty modelling However the practical effectiveness BNNs our ability specify meaningful prior distributions by posterior inference Choosing a meaningful prior distribution over network weights the function computed Stochastic variational inference appealing the update rules resemble ordinary backprop BID15 BID4 fitting accurate posterior distributions strong and complicated posterior dependencies BID34 .In a classic result showed under as the width a shallow BNN the limiting distribution isGP BID31 recently extended this result deep BNNs Deep Gaussian Processes BID5 BID49 have close connections due similar deep structures However , the relationship finite BNNs GPs practical variational BNN approximations fail match the corresponding GP Furthermore , because the previous analyses related specific BNN architectures specific GP kernels's design Given the rich variety structural assumptions GP kernels represent BID45 BID33 there remains expressive power BNNs GPsnot more broadly).In , perform directly functions Specifically , introduce functional variational BNNs trained functions small KL divergence to the true posterior over functions We prove the KL divergence the supremum marginal KL divergences at finite sets points Based , present functional ELBO (fELBO) training objective Then introduce a GAN-like minimax formulation a sampling-based approximation functional variational inference To approximate the marginal KL divergence gradients adopt the recently proposed spectral Stein gradient estimatorSSGE BID52 Here a × b represents a hidden layers b units Red dots 20 training points The blue curve final prediction standard derivations We compare fBNNs BayesbyBackprop ( For BBB which performs weight-space inference , varying leads drastically different predictions For fBNNs which perform functionspace inference , observe consistent predictions the larger networks Note the 1 × 100 factorized Gaussian fBNNs network expressive diverse predictions make specify stochastic process priors which encode richly structured dependencies function values This includes stochastic processes with explicit densities GPs which model various structures like smoothness and periodicity BID33 . We stochastic processes with implicit densities distributions piecewise linear or constant functions Furthermore contrast GPs fBNNs efficiently yield explicit posterior samples the function This enables fBNNs settings explicit minimization sampled functions Thompson sampling BID57 BID48 predictive entropy search BID21 BID59 .One desideratum Bayesian models behave gracefully their capacity BID44 Unfortunately ordinary BNNs meet : unless chosen very undesirable behaviors as more units or layers Furthermore larger BNNs entail more difficult posterior inference larger description length, causing degeneracy for large networks FIG0 . In contrast prior of fBNNs defined directly over functions thus made arbitrarily the functional variational inference problem Hence the predictions behave well the capacity increasesEmpirically , demonstrate that fBNNs generate sensible extrapolations both explicit periodic priors We show fBNNs outperform competing approaches on both small scale fBNNs' reliable uncertainty estimates enable stateart performance on the contextual bandits benchmark of BID46 . In investigated variational inference between We proved the KL divergence equals the supremum KL divergence marginal distributions over all finite measurement sets Then presented two practical functional variational inference adversarial sampling BNNs the variational posterior yields our functional variational Bayesian neural networks we demonstrated fBNNs extrapolate well various structures estimate reliable uncertainties scale large datasets",0.01,0.22044793373731217
"Words are not created equal. In fact, they form an aristocratic graph with a latent hierarchical structure that the next generation of unsupervised learned word embeddings should reveal. In this paper, justified by the notion of delta-hyperbolicity or tree-likeliness of a space, we propose to embed words in a Cartesian product of hyperbolic spaces which we theoretically connect to the Gaussian word embeddings and their Fisher geometry. This connection allows us to introduce a novel principled hypernymy score for word embeddings. Moreover, we adapt the well-known Glove algorithm to learn unsupervised word embeddings in this type of Riemannian manifolds. We further explain how to solve the analogy task using the Riemannian parallel transport that generalizes vector arithmetics to this new type of geometry. Empirically, based on extensive experiments, we prove that our embeddings, trained unsupervised, are the first to simultaneously outperform strong and popular baselines on the tasks of similarity, analogy and hypernymy detection. In particular, for word hypernymy, we obtain new state-of-the-art on fully unsupervised WBLESS classification accuracy. Word embeddings are ubiquitous nowadays as first layers in neural network and deep learning models for natural language processing. They are essential in order to move from the discrete word space to the continuous space where differentiable loss functions can be optimized. The popular models of Glove BID31 , Word2Vec BID25 or FastText BID6 , provide efficient ways to learn word vectors fully unsupervised from raw text corpora, solely based on word co-occurrence statistics. These models are then successfully applied to word similarity and other downstream tasks and, surprisingly (or not BID1 ), exhibit a linear algebraic structure that is also useful to solve word analogy.However, unsupervised word embeddings still largely suffer from revealing asymmetric word relations including the latent hierarchical structure of words. This is currently one of the key limitations in automatic text understanding, e.g. for tasks such as textual entailment BID9 . To address this issue, BID36 BID27 propose to move from point embeddings to probability density functions, the simplest being Gaussian or Elliptical distributions. Their intuition is that the variance of such a distribution should encode the generality/specificity of the respective word. However, this method results in losing the arithmetic properties of point embeddings (e.g. for analogy reasoning) and becomes unclear how to properly use them in downstream tasks. To this end, we propose to take the best from both worlds: we embed words as points in a Cartesian product of hyperbolic spaces and, additionally, explain how they are bijectively mapped to Gaussian embeddings with diagonal covariance matrices, where the hyperbolic distance between two points becomes the Fisher distance between the corresponding probability distribution functions (PDFs). This allows us to derive a novel principled is-a score on top of word embeddings that can be leveraged for hypernymy detection. We learn these word embeddings unsupervised from raw text by generalizing the Glove method. Moreover, the linear arithmetic property used for solving word analogy has a mathematical grounded correspondence in this new space based on the established notion of parallel transport in Riemannian manifolds. In addition, these hyperbolic embeddings outperform Euclidean Glove on word similarity benchmarks. We thus describe, to our knowledge, the first word embedding model that competitively addresses the above three tasks simultaneously. Finally, these word vectors can also be used in downstream tasks as explained by BID17 .We provide additional reasons for choosing the hyperbolic geometry to embed words. We explain the notion of average δ-hyperbolicity of a graph, a geometric quantity that measures its ""democracy"" BID8 . A small hyperbolicity constant implies ""aristocracy"", namely the existence of a small set of nodes that ""influence"" most of the paths in the graph. It is known that real-world graphs are mainly complex networks (e.g. scale-free exhibiting power-law node degree distributions) which in turn are better embedded in a tree-like space, i.e. hyperbolic BID20 . Since , intuitively, words form an ""aristocratic"" community (few generic ones from different topics and many more specific ones) and since a significant subset of them exhibits a hierarchical structure (e.g. WordNet BID26 ), it is naturally to learn hyperbolic word embeddings. Moreover , we empirically measure very low average δ-hyperbolicity constants of some variants of the word log-co-occurrence graph (used by the Glove method), providing additional quantitative reasons for why spaces of negative curvature (i.e. hyperbolic) are better suited for word representations. We propose to adapt the GloVe algorithm to hyperbolic spaces and to leverage a connection between statistical manifolds of Gaussian distributions and hyperbolic geometry, in order to better interpret entailment relations between hyperbolic embeddings. We justify the choice of products of hyperbolic spaces via this connection to Gaussian distributions and via computations of the hyperbolicity of the symbolic data upon which GloVe is based. Empirically we present the first model that can simultaneously obtain state-of-the-art results or close on the three tasks of word similarity, analogy and hypernymy detection.",1064,0.549,633,1.6808846761453398,"Words created In fact they form an aristocratic graph a latent hierarchical structure the next generation unsupervised learned word embeddings reveal In justified delta-hyperbolicity or tree-likeliness a space embed words a Cartesian product which theoretically connect their Fisher geometry This connection allows introduce a novel principled hypernymy score Moreover adapt the well-known Glove algorithm learn this type Riemannian manifolds We further solve the analogy task the Riemannian parallel transport that vector arithmetics this new type geometry based extensive experiments prove our embeddings, trained simultaneously strong and popular baselines the tasks similarity analogy hypernymy detection In particular for word hypernymy obtain new state on fully unsupervised WBLESS classification accuracy Word embeddings ubiquitous nowadays as first layers neural network and They essential order move the discrete word space differentiable loss functions optimized The popular models Glove BID31 , Word2Vec BID25 or provide efficient ways learn word vectors fully raw text corpora solely co These models then successfully applied word similarity other downstream tasks and, surprisingly ( BID1 exhibit also useful solve word analogyHowever still largely suffer revealing asymmetric word relations including the latent hierarchical structure This currently one the key limitations automatic text understanding tasks textual entailment BID9 . To address BID36 BID27 propose move point embeddings probability density functions the simplest being Gaussian or Elliptical distributions Their intuition the variance encode the generality/specificity the respective word However this method results losing the arithmetic properties point embeddings for analogy reasoning becomes unclear properly downstream tasks To this end propose take best from both worlds we embed words as points, additionally explain bijectively mapped with becomes the Fisher distance the corresponding probability distribution functionsPDFs This allows derive novel principled is-a score top hypernymy detection We learn these word embeddings unsupervised raw text by generalizing the Glove method Moreover the linear arithmetic property used solving word analogy a mathematical grounded correspondence in this new space based the established notion parallel transport In these hyperbolic embeddings outperform Euclidean Glove on word similarity benchmarks We thus describe, to word embedding model that competitively addresses the above three tasks simultaneously Finally these word vectors downstream tasks explained BID17 .We provide additional reasons choosing the hyperbolic geometry embed words We explain the notion average ��-hyperbolicity of a graph a geometric quantity measures its ""democracy"" BID8 . A small hyperbolicity constant implies ""aristocracy nodes most the paths It known real-world graphs mainly complex networks (e.g. scale-free exhibiting power-law node degree distributions in better embedded . Since , intuitively words form an ""aristocratic"" communityfew generic ones from different topics since a significant subset exhibits WordNet BID26 naturally to learn Moreover , empirically measure very low average ��-hyperbolicity constants some variants the word log-co-occurrence graphused the Glove method providing additional quantitative reasons spaces better word representations We propose adapt the GloVe algorithm hyperbolic spaces leverage a connection statistical manifolds better interpret entailment relations We justify products of hyperbolic spaces via this connection Gaussian distributions via computations the symbolic data upon GloVe we present simultaneously obtain state results or close on the three tasks word similarity analogy hypernymy detection",0.01,0.4389135026285801
"Answering questions about a text frequently requires aggregating information from multiple places in that text. End-to-end neural network models, the dominant approach in the current literature, can theoretically learn how to distill and manipulate representations of the text without explicit supervision about how to do so. We investigate a canonical architecture for this task, the memory network, and analyze how effective it really is in the context of three multi-hop reasoning settings. In a simple synthetic setting, the path-finding task of the bAbI dataset, the model fails to learn the correct reasoning without additional supervision of its attention mechanism. However, with this supervision, it can perform well. On a real text dataset, WikiHop, the memory network gives nearly state-of-the-art performance, but does so without using its multi-hop capabilities. A tougher anonymized version of the WikiHop dataset is qualitatively similar to bAbI: the model fails to perform well unless it has additional supervision. We hypothesize that many ""multi-hop"" architectures do not truly learn this reasoning as advertised, though they could learn this reasoning if appropriately supervised. Question answering from text is a key challenge problem for NLP that tests whether models can extract information based on a query. Recent new datasets BID22 BID9 BID8 BID21 and new models BID24 BID25 have dramatically advanced the state-of-the-art in this area. However, some QA tasks, such as SQuAD, only simple pattern matching to solve BID29 . One thread of recent work has emphasized multi-hop reasoning in particular BID13 BID11 BID30 , particularly work on memory networks BID28 BID13 . Memory networks define a generic model class that attends to a text passage using the question and a memory cell iteratively to gather information in the different parts of the passage. Many existing reading comprehension models use memory net-like structures and iterative attention over the document, showing improvement in a variety of tasks and settings BID8 BID17 BID27 BID4 BID25 BID20 .We tackle two main questions in this paper. First , are memory networks effective? Second , do they behave as advertised (selecting a sequence of relevant passage excerpts through their computation)? We examine the behavior of memory network-like models across three different tasks. These include one purely synthetic setting, the bAbI path-finding task , and two forms of a more realistic multi-hop reasoning dataset constructed from Wikipedia BID30 . In each case, we apply memory networks to the problem, and can observe their performance and behavior. Exploiting the properties of these particular datasets, we can use heuristics capturing how humans might solve this problem to derive a pseudogold ""reasoning chain."" We then compare the model's reasoning chain with this pseudogold to see whether the model is following a similar chain of reasoning.Our results show that memory networks generally do not learn to do reasoning in the right way, but can do well when using additional supervision to guide how they reason. On bAbI and in a Figure 1 : Computation flow of our hierarchical memory network on an example from WikiHop BID30 . The question is encoded to produce a query q 1 , which produces sentencelevel attention α and word-level attention β for each sentence. This attention computes a passage representation m 1 from which we form the query q 2 for the next step of inference.""masked"" form of the WikiHop task (where entities are anonymized), the memory network performs badly when applied in the standard way. However, when we explicitly supervise the model with pseudogold chains, the model can perform dramatically better with no other changes to its structure or parameterization. On the standard WikHop dataset, our memory network model can achieve nearly state-of-the-art performance, but we show that this is not due to multi-hop reasoning: it barely outperforms a baseline that does not make use of the text at all, calling into question what is being learned. However, additional supervision on the attention can still yield improvement, making our final system close in performance to much more sophisticated state-of-the-art models.Our observations can be summarized as follows:• In both synthetic and more realistic settings, memory networks fail to learn multi-hop reasoning from task supervision alone. This is true even though there exist settings of the parameters that do fit the data, as we can see by their success when more heavily supervised.• When the attention of memory networks is additionally supervised during training, they can do well at text question answering. This supervision qualitatively changes the model's performance with respect to multi-hop reasoning.• When memory networks and related models perform well on multi-hop reasoning tasks, they may be doing so through other means and not actually performing multi-hop reasoning, as we see on the standard WikiHop setting. In this paper, we explore how the memory network behaves on the task of multi-hop reasoning. Experimental results on bAbI and WikiHop show that additional supervision beyond the downstream answers to the questions is needed to learn generalizable multi-hop reasoning. However, when incorporating this supervision, our memory network model can learn to do this and achieves strong results on the WikiHop dataset.",1024,0.564,609,1.6814449917898193," a text frequently requires aggregating End neural models the dominant approach can theoretically learn distill representations the text without explicit supervision about We investigate a canonical architecture this task the memory network analyze effective really three multi-hop reasoning settings In a simple synthetic setting the path-finding task the bAbI dataset, the model fails learn the correct reasoning without additional supervision its attention mechanism However with this supervision perform On a real text dataset WikiHop, the memory network gives nearly state does its multi-hop capabilities A tougher anonymized version the WikiHop dataset qualitatively bAbI: the model fails perform unless additional supervision We hypothesize many ""multi-hop"" architectures do truly learn this reasoning as advertised though appropriately supervised Question answering from text is a key challenge problem NLP that tests models extract based a query Recent new datasets BID22 BID9 and new models have dramatically advanced However, some QA tasks SQuAD only simple pattern to solve BID29 . One thread recent work emphasized multi-hop reasoning particular BID13 BID11 BID30 , particularly work memory networks Memory networks define a generic model class attends a text passage the question a memory cell iteratively to gather in Many existing reading comprehension models memory net-like structures iterative attention over the document showing improvement settings BID8 BID17 .We tackle First , are memory networks effective Second , do they behave advertised (selecting a sequence relevant passage excerpts through their computation We examine memory network-like models across These include one purely synthetic setting the bAbI path-finding task , two forms a more realistic multi-hop reasoning dataset constructed Wikipedia BID30 . In each case apply memory networks can observe Exploiting the properties these particular datasets capturing how humans might solve to derive a pseudogold ""reasoning chain compare followingOur results memory networks generally learn do can well additional supervision guide how reason On bAbI and a Figure : Computation flow our hierarchical memory network on an example from WikiHop BID30 . The question encoded to produce q 1 produces sentencelevel attention α for This attention computes a passage representation m 1 which form the query q inference.""masked"" form the WikiHop taskwhere entities anonymized the memory network performs badly applied However explicitly supervise the model with pseudogold chains perform dramatically no other changes parameterization On the standard WikHop dataset our memory network model achieve nearly state show due multi-hop reasoning barely a baseline that make the text at calling learned However additional supervision on the attention can yield improvement making our final system close in performance much state modelsOur observations can both synthetic and more realistic settings memory networks fail learn multi-hop reasoning task supervision alone This true exist settings of the parameters do fit their success when more heavily supervised.• When the attention memory networks additionally supervised during do well text question answering This supervision qualitatively with multi-hop reasoning.• When memory networks related models perform doing through actually on the standard WikiHop setting In the memory network behaves the task multi-hop reasoning Experimental results bAbI WikiHop show additional supervision beyond the downstream answers learn generalizable multi-hop reasoning However incorporating this supervision our memory network model learn do this and achieves strong results the WikiHop dataset",0.01,0.44034113766191973
"Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be optimized with a discriminator or an encoder. The embedding is Lipschitz continuous to deformations so that generators transform linear interpolations between input white noise vectors into deformations between output images. This embedding is computed with a wavelet Scattering transform. Numerical experiments demonstrate that the resulting Scattering generators have similar properties as GANs or VAEs, without learning a discriminative network or an encoder. Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) allow training generative networks to synthesize images of remarkable quality and complexity from Gaussian white noise. This work shows that one can train generative networks having similar properties to those obtained with GANs or VAEs without learning a discriminator or an encoder. The generator is a deep convolutional network that inverts a predefined embedding operator. To reproduce relevant properties of GAN image synthesis the embedding operator is chosen to be Lipschitz continuous to deformations, and it is implemented with a wavelet Scattering transform. Defining image generators as the solution of an inverse problem provides a mathematical framework, which is closer to standard probabilistic models such as Gaussian autoregressive models.GANs were introduced by BID6 as an unsupervised learning framework to estimate implicit generative models of complex data (such as natural images) by training a generative model (the generator) and a discriminative model (the discriminator) simultaneously. An implicit generative model of the random vector X consists in an operator G which transforms a Gaussian white noise random vector Z into a model X = G(Z) of X. The operator G is called a generative network or generator when it is a deep convolutional network. BID17 introduced deep convolutional architectures for the generator and the discriminator, which result in high-quality image synthesis. They also showed that linearly modifying the vector z results in a progressive deformation of the imagex = G(z). BID6 and BID0 argue that GANs select the generator G by minimizing the Jensen-Shannon divergence or the Wasserstein distance calculated from empirical estimations of these distances with generated and training images. However, BID1 prove that this explanation fails to pass the curse of dimensionality since estimates of Jensen-Shannon or Wasserstein distances do not generalize with a number of training examples which is polynomial on the dimension of the images. Therefore, the reason behind the generalization capacities of generative networks remains an open problem.VAEs, introduced by BID8 , provide an alternative approach to GANs, by optimizing G together with its inverse on the training samples, instead of using a discriminator. The inverse Φ is an embedding operator (the encoder) that is trained to transform X into a Gaussian white noise Z. Therefore, the loss function to train a VAE is based on probabilistic distances which also suffer from the same dimensionality curse shown in BID1 . Furthermore, a significant disadvantage of VAEs is that the resulting generative models produce blurred images compared with GANs.Generative Latent Optimization (GLO) was introduced in BID2 to eliminate the need for a GAN discriminator while restoring sharper images than VAEs. GLO still uses an autoencoder computational structure, where the latent space variables z are optimized together with the generator G. Despite good results, linear variations of the embedding space variables are not mapped as clearly into image deformations as in GANs, which reduces the quality of generated images.GANs and VAEs raise many questions. Where are the deformation properties coming from? What are the characteristics of the embedding operator Φ? Why do these algorithms seem to generalize despite the curse of dimensionality? Learning a stable embedding which maps X into a Gaussian white noise is intractable without strong prior information BID1 . This paper shows that this prior information is available for image generation and that one can predefine the embedding up to a linear operator. The embedding must be Lipschitz continuous to translations and deformations so that modifications of the input noise result in deformations of X. Lipschitz continuity to deformations requires separating the signal variations at different scales, which leads to the use of wavelet transforms. We concentrate on wavelet Scattering transforms BID12 , which linearize translations and provide appropriate Gaussianization. We then define the generative model as an inversion of the Scattering embedding on training data, with a deep convolutional network. The inversion is regularized by the architecture of the generative network, which is the same as the generator of a DCGAN BID17 . Experiments in Section 4 show that these generative Scattering networks have similar properties as GAN generators, and the synthesized images have the same quality as the ones obtained with VAEs or GLOs. This paper shows that most properties of GANs and VAEs can be reproduced with an embedding computed with a Scattering transform, which avoids using a discriminator as in GANs or learning the embedding as in VAEs or GLOs. It also provides a mathematical framework to analyze the statistical properties of these generators through the resolution of an inverse problem, regularized by the convolutional network architecture and the sparsity of the obtained activations. Because the embedding function is known, numerical results can be evaluated on training as well as test samples.We report preliminary numerical results with no hyperparameter optimization. The architecture of the convolutional generator may be adapted to the properties of the Scattering operator S j as j increases. Also, the paper uses a ""plain"" Scattering transform which does not take into account interactions between angle and scale variables, which may also improve the representation as explained in BID15 .",1180,0.628,677,1.742983751846381,"Generative Adversarial Nets impressive image generations from Gaussian white noise but the underlying mathematics We compute deep convolutional network generators a fixed embedding operator Therefore they do require optimized a discriminator embedding is Lipschitz continuous to deformations so generators transform linear interpolations input white noise vectors deformations between This embedding computed a wavelet Scattering transform Numerical experiments demonstrate the resulting Scattering generators GANs VAEs without learning a discriminative network Variational Auto-Encoders allow training generative networks synthesize images remarkable quality Gaussian white noise This work shows one train generative networks having obtained GANs VAEs without learning The generator inverts predefined embedding operator To reproduce relevant properties GAN image synthesis the embedding operator chosen Lipschitz continuous to deformations it implemented a wavelet Scattering transform Defining image generators the solution an inverse problem provides, closer suchGANs were BID6 estimate complex datasuch natural images trainingthe generator simultaneously An implicit generative model the random vector X consists an operator G transforms a Gaussian white noise random vector Z of The operator G is called a generative network or generator when BID17 introduced deep convolutional architectures the generator result They also showed linearly modifying the vector z results the imagex = G(z BID6 and argue GANs select the generator G by minimizing the Jensen-Shannon divergence or the Wasserstein distance calculated empirical estimations these distances with generated and training images However BID1 prove this explanation fails pass the curse dimensionality since estimates Jensen-Shannon or Wasserstein distances with a number training examples which is on the images Therefore the reason behind the generalization capacities generative networks remainsVAEs introduced BID8 , GANs optimizing G together its inverse on the training samples instead The inverse �� an embedding operator trained transform X Z. Therefore the loss function to train a VAE based probabilistic distances which also suffer the same dimensionality curse shown BID1 . Furthermore a significant disadvantage VAEs the resulting generative models produce blurred images compared GANsGenerative Latent Optimization BID2 eliminate while restoring sharper images than still uses the latent space variables z are optimized together the generator G. Despite good results linear variations the embedding space variables mapped as clearly into image deformations GANs reduces generated imagesGANs and VAEs raise Where the deformation properties coming What the embedding operator �� Why these algorithms seem generalize despite the curse dimensionality Learning stable embedding which maps X into a Gaussian white noise without strong prior information BID1 . This paper this prior information available image generation that one predefine embedding up a linear operator embedding must Lipschitz continuous to translations deformations so modifications the input noise result X. Lipschitz continuity to deformations requires separating the signal variations at leads wavelet transforms We concentrate wavelet Scattering transforms BID12 , linearize translations provide appropriate Gaussianization We then define the Scattering embedding on training data The inversion regularized the architecture the generative network a DCGAN BID17 . Experiments Section show these generative Scattering networks GAN generators the synthesized images VAEs GLOs most properties reproduced embedding computed avoids using as in learning as analyze through the resolution an inverse problem regularized the obtained activations Because the embedding function known numerical results evaluated training as test samplesWe report with The architecture the convolutional generator may adapted the properties the Scattering operator S j as j increases Also the paper uses a ""plain"" Scattering transform account interactions angle and scale variables also improve as explained BID15 .",0.01,0.5971364915496983
"Recurrent neural networks (RNNs) can model natural language by sequentially ''reading'' input tokens and outputting a distributed representation of each token. Due to the sequential nature of RNNs, inference time is linearly dependent on the input length, and all inputs are read regardless of their importance. Efforts to speed up this inference, known as ''neural speed reading'', either ignore or skim over part of the input. We present Structural-Jump-LSTM: the first neural speed reading model to both skip and jump text during inference. The model consists of a standard LSTM and two agents: one capable of skipping single words when reading, and one capable of exploiting punctuation structure (sub-sentence separators (,:), sentence end symbols (.!?), or end of text markers) to jump ahead after reading a word.
 A comprehensive experimental evaluation of our model against all five state-of-the-art neural reading models shows that 
 Structural-Jump-LSTM achieves the best overall floating point operations (FLOP) reduction (hence is faster), while keeping the same accuracy or even improving it compared to a vanilla LSTM that reads the whole text. Recurrent neural networks (RNNs) are a popular model for processing sequential data. The Gated Recurrent Unit (GRU) BID4 and Long Short Term Memory (LSTM) BID7 are RNN units developed for learning long term dependencies by reducing the problem of vanishing gradients during training. However, both GRU and LSTM incur fairly expensive computational costs, with e.g. LSTM requiring the computation of 4 fully connected layers for each input it reads, independently of the input's importance for the overall task.Based on the idea that not all inputs are equally important, and that relevant information can be spread throughout the input sequence, attention mechanisms were developed BID0 to help the network focus on important parts of the input. With soft attention, all inputs are read, but the attention mechanism is fully differentiable. In comparison, hard attention completely ignores part of the input sequence. Hard attention mechanisms have been considered in many areas, ranging from computer vision BID14 BID1 where the model learns what parts of the image it should focus on, to natural language processing (NLP), such as text classification and question answering BID22 BID1 BID23 , where the model learns which part of a document it can ignore. With hard attention, the RNN has fewer state updates, and therefore fewer floating point operations (FLOPs) are needed for inference. This is often denoted as speed reading: obtaining the same accuracy while using (far) fewer FLOPs BID22 BID19 BID8 BID5 . Prior work on speed reading processes text as chunks of either individual words or blocks of contiguous words. If the chunk being read is important enough, a full state update is performed; if not, the chunk is either ignored or a very limited amount of computations are done. This is followed by an action aiming to speed up the reading, e.g. skipping or jumping forward in text.Inspired by human speed reading, we contribute an RNN speed reading model that ignores unimportant words in important sections, while also being able to jump past unimportant sections of the text. Our model, called Structural-Jump-LSTM 1 , both skips and jumps over dynamically defined chunks of text as follows: (a) it can skip individual words, after reading them, but before updating the RNN state; (b) it uses the punctuation structure of the text to define dynamically spaced jumps to the next sub-sentence separator (,;), end of sentence symbol (.!?), or the end of the text.An extensive experimental evaluation against all state-of-the-art speed reading models BID19 BID22 BID5 BID8 , shows that our Structural-Jump-LSTM of dynamically spaced jumps and word level skipping leads to large FLOP reductions while maintaining the same or better reading accuracy than a vanilla LSTM that reads the full text. We presented Structural-Jump-LSTM, a recurrent neural network for speed reading. StructuralJump-LSTM is inspired by human speed reading, and can skip irrelevant words in important sections, while also jumping past unimportant parts of a text. It uses the dynamically spaced punctuation structure of text to determine whether to jump to the next word, the next sub-sentence separator (,;), next end of sentence (.!?), or to the end of the text. In addition, it allows skipping a word after observing it without updating the state of the RNN. Through an extensive experimental evaluation against all five state-of-the-art baselines, Structural-Jump-LSTM obtains the overall largest reduction in floating point operations, while maintaining the same accuracy or even improving it over a vanilla LSTM model that reads the full text. We contribute the first ever neural speed reading model that both skips and jumps over dynamically defined chunks of text without loss of effectiveness and with notable gains in efficiency. Future work includes investigating other reward functions, where most of the reward is not awarded in the end, and whether this would improve agent training by having a stronger signal spread throughout the text.",1027,0.488,586,1.7525597269624573,"Recurrent neural networks model by sequentially ''reading input tokens a distributed representation Due the sequential nature RNNs inference time linearly all inputs read regardless their importance speed this inference known ''neural speed reading either ignore skim part We present Structural-Jump-LSTM: the first neural speed reading model both skip text during inference The model consists two agents capable skipping single words when reading exploiting punctuation structure (,:) sentence end symbols!? end text markers jump ahead after reading A comprehensive experimental evaluation our model against all five state neural reading models shows Structural-Jump-LSTM achieves the best overall floating point operations (FLOP) reductionhence is faster keeping or even improving compared a vanilla that reads Recurrent neural networks processing sequential data The Gated Recurrent Unit (GRU) BID4 and Long Short Term Memory RNN units developed learning long term dependencies by reducing the problem vanishing gradients during However both GRU LSTM incur fairly expensive computational costs with requiring the computation 4 fully connected layers it reads independentlyBased the idea and relevant information spread throughout attention mechanisms were BID0 help focus important parts With soft attention all inputs read the attention mechanism fully differentiable In comparison hard attention completely part the input sequence Hard attention mechanisms considered ranging computer vision BID14 BID1 where the model learns what parts such text classification question BID22 , can ignore With hard attention the RNN fewer state updates therefore fewer floating point operations are inference This often denoted speed reading: obtaining the same accuracy while (far) fewer FLOPs BID22 BID19 BID8 BID5 . Prior work speed reading processes text as chunks either individual words blocks contiguous words If the chunk being read important a full state update performed; either a very limited amount computations This followed an action aiming speed the reading skipping or jumping forward textInspired human speed reading contribute an RNN speed reading model ignores unimportant words important sections being jump past of Our model, called Structural-Jump-LSTM 1 both skips over dynamically defined chunks text as follows ( it can skip individual words after reading updating the RNN state uses the punctuation structure define dynamically spaced jumps,;) end sentence symbol (.!?An extensive experimental evaluation against all state speed reading models BID19 BID22 BID5 BID8 , shows of dynamically spaced jumps and word level skipping leads large FLOP reductions while or reading reads We presented Structural-Jump-LSTM speed reading StructuralJump-LSTM inspired human speed reading can skip irrelevant words important sections jumping past It uses the dynamically spaced punctuation structure text determine jump,;) next end (.!? In addition allows skipping a word after observing without updating the RNN Through an extensive experimental evaluation against all five state baselines Structural-Jump-LSTM obtains the overall largest reduction floating point operations while or even improving over reads We contribute the first ever neural speed reading model that both skips jumps dynamically defined chunks without loss effectiveness and notable gains Future work includes investigating other reward functions where most not awarded whether agent training by having a stronger signal spread throughout the text",0.01,0.621535234809486
"One of the key challenges of session-based recommender systems is to enhance users’ purchase intentions. In this paper, we formulate the sequential interactions between user sessions and a recommender agent as a Markov Decision Process (MDP). In practice, the purchase reward is delayed and sparse, and may be buried by clicks, making it an impoverished signal for policy learning. Inspired by the prediction error minimization (PEM) and embodied cognition, we propose a simple architecture to augment reward, namely Imagination Reconstruction Network (IRN). Specifically, IRN enables the agent to explore its environment and learn predictive representations via three key components. The imagination core generates predicted trajectories, i.e., imagined items that users may purchase. The trajectory manager controls the granularity of imagined trajectories using the planning strategies, which balances the long-term rewards and short-term rewards. To optimize the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of simulated trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using model-free algorithms. Empirically, IRN promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance compared to several baselines. Somewhat surprisingly, IRN using only the purchase reward achieves excellent next-click prediction performance, demonstrating that the agent can ""guess what you like"" via internal planning. A good recommender system can enhance both satisfaction for users and profit for content providers BID7 . In many real-world scenarios, the recommender systems make recommendations based only on the current browsing session, given the absence of user profiles (because the user is new or not tracked or not logged in, till the final purchase step). A session is a group of sequential interactions between a user and the system within a short period of time. To model this phenomenon, Recurrent Neural Networks (RNNs) were recently employed as session-based recommenders BID9 BID12 . For instance, GRU4Rec BID9 utilizes the session-parallel mini-batch training to handle the variable lengths of sessions, and predicts the next action given the sequence of items in the current session. However, these approaches primarily focus on next-click prediction and model the session data via sequential classification, and thus cannot distinguish the different effects of user clicks and purchases.In this paper, we consider the session-based recommendation as a Markov Decision Process (MDP), which can take into account both the click reward and the purchase reward (see FIG0 , and leverage Reinforcement Learning (RL) to learn the recommendation strategy. In practice, several challenges need to be addressed. First, the recommender systems involve large numbers of discrete actions (i.e., items), making current RL algorithms difficult to apply . This requires the agent to explore its environment for action feature learning and develop an ability to generalize over unseen actions. Second, we found it difficult to specify the click reward and the purchase reward; the policy may be biased by long sessions that contain many user clicks, as RL algorithms maximize the accumulated reward. Besides, real-world recommender systems require quick adaptation to user interest and robustness to the cold-start scenario (i.e., enhancing the purchase performance of short sessions). Therefore, we will be particularly interested in a case where only the purchase is used as reward (click sequences are used as inputs of the imagination core for Under review as a conference paper at ICLR 2019 exploration). 1 However, the purchase reward is delayed and sparse (one session may contain only one purchase), making it a difficult signal for policy learning.To augment reward and encourage exploration, we present the Imagination Reconstruction Network (IRN), which is inspired by the prediction error minimization (PEM) BID10 BID5 BID14 and embodied cognition BID2 BID1 BID23 BID3 from the neuroscience literature. The PEM is an increasingly influential theory that stresses the importance of brain-body-world interactions in cognitive processes, involving perception, action and learning. In particular, IRN can be regarded as a proof-of-concept for the PEM from the recommendation perspective, following the ideas in BID1 and BID23 -the brain utilizes active sensorimotor predictions (or counterfactual predictions) to represent states of affairs in the world in an action-oriented manner. Specifically, the imagination core of IRN that predicts the future trajectories (i.e., a set of imagined items that user may purchase) conditioned on actions sampled from the imagination policy, can be considered as the generative model of the brain that simulates sensorimotor predictions. To update the action policy, the imagination-augmented executor minimizes the intrinsic imagination error of predicted trajectories by self-supervised reconstruction, while maximizing the extrinsic reward using RL, with shared input state or output action representations for predictive learning. This simulates the active perception (a key aspect of embodied cognition) of the body under the PEM framework, which adapts the agent to possible changes that arise from the ongoing exploratory action. Note that the imagination policy imitates the action policy through distillation or a delayed target network, and thus IRN constructs a loop between brain and body, encouraging the agent to perform actions that can reduce the error in the agent's ability to predict the future events BID20 . IRN equips the agent with a planning module, trajectory manager, that controls the granularity of imagined trajectories using the planning strategies (e.g., breadth-n and depth-m). Besides, IRN is a combination of model-based planning and self-supervised RL, as the imagined trajectories provide dense training signals for auxiliary task learning (see section 2).The key contributions of this paper are summarized as follows:• We formulate the session-based recommendation as a MDP, and leverage deep RL to learn the optimal recommendation policy, and also discuss several challenges when RL is applied.• We consider a special case where only the purchase is used as reward, and then propose the IRN architecture to optimize the sparser but more business-critical purchase signals, which draws inspiration from the theories of cognition science.• We present a self-supervised reconstruction method for predictive learning, which minimizes the imagination error of simulated trajectories over time. IRN achieves excellent click and purchase performance even without any external reward (predictive perception BID23 ).• We conduct a comprehensive set of experiments to demonstrate the effectiveness of IRN. Compared to several baselines, IRN improves data efficiency, promotes quicker adaptation to user interest, and shows improved robustness to the cold-start scenario and ultimately higher purchase performance. These are highly valuable properties in an industrial context.",1311,0.629,771,1.7003891050583657,"One session-based recommender systems enhance users�� purchase intentions In formulate the sequential interactions user sessions a recommender agent as In practice the purchase reward delayed sparse may buried clicks making an impoverished signal policy learning Inspired the prediction error minimization embodied cognition augment reward, namely Imagination Reconstruction Network Speci���cally IRN enables the agent explore learn predictive representations via three key components The imagination core generates predicted trajectories imagined items users purchase The trajectory manager controls imagined trajectories the planning strategies, balances To optimize the action policy the imagination-augmented executor minimizes the intrinsic imagination error simulated trajectories self-supervised reconstruction while using IRN promotes quicker adaptation user interest shows improved robustness the cold-start scenario ultimately higher purchase performance several baselines IRN using only the purchase reward achieves excellent next-click prediction performance demonstrating the agent "" via internal planning A good recommender system enhance both satisfaction for profit content providers BID7 . In the recommender systems make recommendations only the current browsing session given user profilesbecause new tracked or till the final purchase step A session is sequential interactions within To model this phenomenon recently employed session-based recommenders BID9 BID12 . For instance GRU4Rec BID9 utilizes the session-parallel mini-batch training handle the variable lengths sessions predicts given items However these approaches primarily next-click prediction model the session data via sequential classification distinguish user clicks purchasesIn consider the session-based recommendation as take both the click reward FIG0 , leverage Reinforcement Learning ( the recommendation strategy. In practice several challenges need First the recommender systems involve large numbers discrete actions making current RL algorithms apply . This requires the agent explore its environment action feature learning develop generalize over unseen actions Second found it specify the click reward and; the policy may biased long sessions contain many user clicks RL algorithms maximize the accumulated reward Besides real-world recommender systems require quick adaptation user interest robustness the cold-start scenario enhancing the purchase performance short sessions Therefore particularly a case only the purchase is used reward (click sequences used inputs of the imagination core Under review as a conference paper at ICLR 2019 exploration 1 However the purchase reward delayed sparseone session may contain making signal policy learningTo augment reward and encourage exploration present the Imagination Reconstruction Network inspired the prediction error minimization BID10 BID5 BID14 embodied cognition from The PEM an increasingly influential theory stresses brain-body-world interactions involving perception action In particular IRN can regarded a proof the PEM from the recommendation perspective following BID1 BID23 -the brain utilizes active sensorimotor predictionsor represent states Specifically, the imagination core IRN that predicts ( imagined items user purchase conditioned actions sampled the imagination policy can To update the action policy the imagination-augmented executor minimizes the intrinsic imagination error predicted trajectories self-supervised reconstruction while using RL, with shared input state or output action representations for predictive learning This simulates the active perception (a key aspect embodied cognition under the PEM framework adapts the agent possible changes that the ongoing exploratory action Note the imagination policy imitates through distillation or a delayed target network IRN constructs a loop between brain encouraging the agent reduce the error predict BID20 . IRN equips the agent a planning module trajectory manager that controls the granularity imagined trajectories using the planning strategies ( breadth-n andm Besides IRN a combination model-based planning and self-supervised RL the imagined trajectories provide dense training signals auxiliary task learning section 2).The key contributions summarized as formulate the session-based recommendation as a MDP leverage deep RL the optimal recommendation policy also discuss several challenges when RL consider only the purchase is used reward propose the IRN architecture optimize the sparser but more business-critical purchase signals draws inspiration the theories cognition predictive learning the imagination error simulated trajectories over IRN achieves excellent click purchase performance even any external rewardpredictive perception BID23 ).• We conduct Compared several baselines IRN improves data efficiency promotes quicker adaptation user interest shows improved the cold-start scenario and ultimately higher purchase performance These highly valuable properties",0.01,0.488609073858583
"The question why deep learning algorithms generalize so well has attracted increasing
 research interest. However, most of the well-established approaches,
 such as hypothesis capacity, stability or sparseness, have not provided complete
 explanations (Zhang et al., 2016; Kawaguchi et al., 2017). In this work, we focus
 on the robustness approach (Xu & Mannor, 2012), i.e., if the error of a hypothesis
 will not change much due to perturbations of its training examples, then it
 will also generalize well. As most deep learning algorithms are stochastic (e.g.,
 Stochastic Gradient Descent, Dropout, and Bayes-by-backprop), we revisit the robustness
 arguments of Xu & Mannor, and introduce a new approach – ensemble
 robustness – that concerns the robustness of a population of hypotheses. Through
 the lens of ensemble robustness, we reveal that a stochastic learning algorithm can
 generalize well as long as its sensitiveness to adversarial perturbations is bounded
 in average over training examples. Moreover, an algorithm may be sensitive to
 some adversarial examples (Goodfellow et al., 2015) but still generalize well. To
 support our claims, we provide extensive simulations for different deep learning
 algorithms and different network architectures exhibiting a strong correlation between
 ensemble robustness and the ability to generalize. Deep Neural Networks (DNNs) have been successfully applied in many artificial intelligence tasks, providing state-of-the-art performance and a remarkably small generalization error. On the other hand, DNNs often have far more trainable model parameters than the number of samples they are trained on and were shown to have a large enough capacity to memorize the training data BID26 . The findings of Zhang et al. suggest that classical explanations for generalization cannot be applied directly to DNNs and motivated researchers to look for new complexity measures and explanations for the generalization deep neural networks BID2 BID16 BID0 BID13 . However, in this work, we focus on a different approach to study generalization of DNNs, i.e., the connection between the robustness of a deep learning algorithm and its generalization performance. Xu & Mannor have shown that if an algorithm is robust (i.e., its empirical loss does not change dramatically for perturbed samples), its generalization performance can also be guaranteed. However, in the context of DNNs, practitioners observe contradicting evidence between these two attributes. On the one hand, DNNs generalize well, and on the other, they are fragile to adversarial perturbation on the inputs BID21 BID8 . Nevertheless, algorithms that try to improve the robustness of learning algorithms have been shown to improve the generalization of deep neural networks. Two examples are adversarial training, i.e., generating adversarial examples and training on them BID21 BID8 BID18 , and Parseval regularization BID5 , i.e., minimizing the Lifshitz constant of the network to guarantee low robustness. While these meth-ods minimize the robustness implicitly, their empirical success Indicates a connection between the robustness of an algorithm and its ability to generalize.To solve this contradiction, we revisit the robustness argument in BID23 and present ensemble robustness, to characterize the generalization performance of deep learning algorithms. Our proposed approach is not intended to give tight bounds for general deep learning algorithms, but rather to pave the way for addressing the question: how can deep learning perform so well while being fragile to adversarial examples? Answering this question is difficult, yet we present evidence in both theory and simulation suggesting that ensemble robustness explains the generalization performance of deep learning algorithms.Ensemble robustness concerns the fact that a randomized algorithm (e.g., Stochastic Gradient Descent (SGD), Dropout BID19 , Bayes-by-backprop BID3 , etc. ) produces a distribution of hypotheses instead of a deterministic one. Therefore, ensemble robustness takes into consideration robustness of the population of the hypotheses: even though some hypotheses may be sensitive to perturbation on inputs, an algorithm can still generalize well as long as most of the hypotheses sampled from the distribution are robust on average. BID13 took a different approach and claimed that deep neural networks could generalize well despite nonrobustness. However, our definition of ensemble robustness together with our empirical findings suggest that deep learning methods are typically robust although being fragile to adversarial examples.Through ensemble robustness, we prove that the following holds with a high probability: randomized learning algorithms can generalize well as long as its output hypothesis has bounded sensitiveness to perturbation in average (see Theorem 1). Specified for deep learning algorithms, we reveal that if hypotheses from different runs of a deep learning method perform consistently well in terms of robustness, the performance of such deep learning method can be confidently expected. Moreover, each hypothesis may be sensitive to some adversarial examples as long as it is robust on average.Although ensemble robustness may be difficult to compute analytically, we demonstrate an empirical estimate of ensemble robustness and investigate the role of ensemble robustness via extensive simulations. The results provide supporting evidence for our claim: ensemble robustness consistently explains the generalization performance of deep neural networks. Furthermore, ensemble robustness is measured solely on training data, potentially allowing one to use the testing examples for training and selecting the best model based on its ensemble robustness. BID23 proposed to consider model robustness for estimating generalization performance for deterministic algorithms, such as for SVM BID25 and Lasso BID24 . They suggest using robust optimization to construct learning algorithms, i.e., minimizing the empirical loss concerning the adversarial perturbed training examples. In this paper, we investigated the generalization ability of stochastic deep learning algorithm based on their ensemble robustness; i.e., the property that if a testing sample is similar to a training sample, then its loss is close to the training error. We established both theoretically and experimentally evidence that ensemble robustness of an algorithm, measured on the training set, indicates its generalization performance well. Moreover, our theory and experiments suggest that DNNs may be robust (and generalize) while being fragile to specific adversarial examples. Measuring ensemble robustness of stochastic deep learning algorithms may be computationally prohibitive as one needs to sample several output hypotheses of the algorithm. Thus, we demonstrated that by learning the probability distribution of the weights of a neural network explicitly, e.g., via variational methods such as Bayes-by-backprop, we can still observe a positive correlation between robustness and generalization while using fewer computations, making ensemble robustness feasible to measure.As a direct consequence, one can potentially measure the generalization error of an algorithm without using testing examples. In future work, we plan to further investigate if ensemble robustness can be used for model selection instead of cross-validation (and hence, increasing the training set size), in particular in problems that have a small training set. A different direction is to study the resilience of deep learning methods to adversarial attacks BID17 . BID20 recently showed that ensemble methods are useful as a mean to defense against adversarial attacks. However, they only considered implicit ensemble methods which are computationally prohibitive. As our simulations show that explicit ensembles are robust as well, we believe that they are likely to be a useful defense strategy while reducing computational cost. Finally, Theorem 2 suggests that a randomized algorithm can tolerate the non-robustness of some hypotheses to certain samples; this may help to explain Proposition 1 in BID13 : ""For any dataset, there exist arbitrarily unstable non-robust algorithms such that has a small generalization gap"". We leave this intuition for future work.",1533,0.746,855,1.792982456140351,"The question why deep learning algorithms generalize so has attracted increasing research interest However most the well-established approaches, hypothesis capacity stability or sparseness provided complete explanations (Zhang 2016 Kawaguchi In this work focus the robustness approach (Xu & Mannor if the error will change much due its training examples also generalize As most deep learning algorithms stochastic Dropout Bayesbybackprop revisit the robustness arguments Xu & Mannor introduce – ensemble robustness concerns a population hypotheses Through ensemble robustness reveal generalize well as long its sensitiveness bounded in average over training examples Moreover an algorithm may sensitive some adversarial examplesGoodfellow 2015 still generalize To support our claims provide extensive simulations different deep learning algorithms different network exhibiting ensemble robustness the ability generalize Deep Neural Networks successfully many artificial intelligence tasks providing state performance a remarkably small generalization error On DNNs often far more trainable model parameters the number samples were shown a large enough capacity memorize BID26 . The findings Zhang suggest that classical explanations generalization applied directly DNNs motivated researchers look new complexity measures and explanations deep neural BID2 BID16 BID0 BID13 . However in this work study generalization DNNs the robustness Xu & Mannor have shown if an algorithm robust ( its empirical loss does dramatically for perturbed samples its generalization performance also guaranteed However in DNNs practitioners observe contradicting evidence between these two attributes On DNNs generalize well on fragile to adversarial perturbation on the inputs BID21 BID8 . Nevertheless algorithms try improve learning algorithms deep neural networks Two examples adversarial training generating training on BID21 BID8 , Parseval regularization minimizing the Lifshitz constant of the network to guarantee low robustness While these meth-ods minimize the robustness implicitly their empirical success Indicates a connection an algorithm generalizeTo solve revisit BID23 present ensemble robustness, to characterize deep learning Our proposed approach not intended give tight bounds general deep learning pave addressing perform so while being fragile adversarial examples Answering difficult yet we present evidence in both theory simulation suggesting ensemble robustness explains the generalization performanceEnsemble robustness concerns randomized algorithm Dropout BID19 , Bayesbybackprop BID3. ) produces a distribution hypotheses instead deterministic one Therefore ensemble robustness takes the hypotheses: even sensitive on inputs an algorithm well as most sampled from on average BID13 took claimed deep neural networks generalize well despite nonrobustness However our definition ensemble robustness together deep learning methods typically robust although being fragile to adversarial examplesThrough prove the following holds with randomized learning algorithms as its output hypothesis has bounded sensitiveness in average (see Theorem Specified for deep learning algorithms we reveal if hypotheses from different runs perform consistently terms robustness confidently expected Moreover each hypothesis may sensitive some adversarial examples as long robust on averageAlthough ensemble robustness difficult compute demonstrate an empirical estimate and investigate via extensive simulations The results provide supporting evidence our claim: ensemble robustness consistently explains the generalization performance Furthermore ensemble robustness measured solely training data potentially one use the testing examples training selecting based BID23 proposed consider model robustness estimating generalization performance deterministic algorithms such for SVM BID25 Lasso BID24 They suggest using robust optimization construct learning minimizing the empirical loss concerning adversarial perturbed training examples In this paper investigated the generalization ability stochastic deep learning algorithm their ensemble robustness; property if a testing sample similar its loss close We established both theoretically and experimentally evidence ensemble robustness an algorithm, measured on the training set indicates its generalization performance well Moreover our theory and experiments DNNs robust ( generalize while being fragile to specific adversarial examples Measuring ensemble robustness may as one needs sample several output hypotheses of Thus demonstrated by learning the probability distribution the weights explicitly variational methodsbybackprop, still observe robustness while fewer computations making ensemble feasible to measureAs one potentially measure testing examples In future work further if ensemble robustness model selection instead crossand increasing in problems A different direction study the resilience deep learning methods BID17 . BID20 recently showed ensemble methods useful as a mean defense However they only considered implicit ensemble methods which As our simulations explicit ensembles robust as believe they a useful defense strategy while reducing computational cost Finally Theorem suggests a randomized algorithm tolerate non some hypotheses to certain samples; may help Proposition BID13 : ""For any dataset exist arbitrarily unstable non-robust algorithms such has a small generalization gap We leave this intuition future work",0.01,0.7245287972526057
"Deep autoregressive models have shown state-of-the-art performance in density estimation for natural images on large-scale datasets such as ImageNet.   However, such models require many thousands of gradient-based weight updates and unique image examples for training. Ideally, the models would rapidly learn visual concepts from only a handful of examples, similar to the manner in which humans learns across many vision tasks.   In this paper, we show how 1) neural attention and 2) meta learning techniques can be used in combination with autoregressive models to enable effective few-shot density estimation. Our proposed modifications to PixelCNN result in state-of-the art few-shot density estimation on the Omniglot dataset.   Furthermore, we visualize the learned attention policy and find that it learns intuitive algorithms for simple tasks such as image mirroring on ImageNet and handwriting on Omniglot without supervision. Finally, we extend the model to natural images and demonstrate few-shot image generation on the Stanford Online Products dataset. Contemporary machine learning systems are still far behind humans in their ability to rapidly learn new visual concepts from only a few examples BID14 . This setting, called few-shot learning, has been studied using deep neural networks and many other approaches in the context of discriminative models, for example ; BID21 . However, comparatively little attention has been devoted to the task of few-shot image density estimation; that is, the problem of learning a model of a probability distribution from a small number of examples. Below we motivate our study of few-shot autoregressive models, their connection to meta-learning, and provide a comparison of multiple approaches to conditioning in neural density models. In this paper we adapted PixelCNN to the task of few-shot density estimation. Comparing to several strong baselines, we showed that Attention PixelCNN achieves state-of-the-art results on Omniglot and also promising results on natural images. The model is very simple and fast to train. By looking at the attention weights, we see that it learns sensible algorithms for generation tasks such as image mirroring and handwritten character drawing. In the Meta PixelCNN model, we also showed that recently proposed methods for gradient-based meta learning can also be used for few-shot density estimation, and also achieve state-of-the-art results in terms of likelihood on Omniglot.",456,0.274,283,1.6113074204946995,"Deep autoregressive models shown state density estimation natural images on However such models require many thousands gradient-based weight updates unique image examples training Ideally the models rapidly learn visual concepts only a handful examples similar the manner humans learns across many vision tasks In this paper how 1) neural attention meta learning techniques combination with enable effective few-shot density estimation Our proposed modifications PixelCNN result state fewshot density estimation on the Omniglot dataset Furthermore visualize the learned attention policy find learns intuitive algorithms simple tasks image mirroring on ImageNet handwriting on Omniglot without supervision Finally extend the model natural images demonstrate few-shot image generation on the Stanford Online Products dataset Contemporary machine learning systems still far humans rapidly new visual concepts from BID14 . This setting, called few-shot learning studied using discriminative models for ; BID21 . However comparatively little attention devoted the task few-shot image density estimation learning a model a probability distribution examples Below we motivate our study few-shot autoregressive models their connection meta-learning provide multiple approaches conditioning neural density models In this paper adapted PixelCNN the task few-shot density estimation Comparing to several strong baselines showed Attention PixelCNN achieves state results Omniglot also promising natural images The model very fast train By looking the attention weights it learns sensible algorithms generation tasks such image mirroring handwritten character drawing In the Meta PixelCNN model also showed recently proposed methods gradient-based meta learning few-shot density estimation also achieve state terms likelihood on Omniglot",0.0,0.26163676822159043
"Neural networks exhibit good generalization behavior in the
 over-parameterized regime, where the number of network parameters
 exceeds the number of observations. Nonetheless,
 current generalization bounds for neural networks fail to explain this
 phenomenon. In an attempt to bridge this gap, we study the problem of
 learning a two-layer over-parameterized neural network, when the data is generated by a linearly separable function. In the case where the network has Leaky
 ReLU activations, we provide both optimization and generalization guarantees for over-parameterized networks.
 Specifically, we prove convergence rates of SGD to a global
 minimum and provide generalization guarantees for this global minimum
 that are independent of the network size. 
 Therefore, our result clearly shows that the use of SGD for optimization both finds a global minimum, and avoids overfitting despite the high capacity of the model. This is the first theoretical demonstration that SGD can avoid overfitting, when learning over-specified neural network classifiers. Neural networks have achieved remarkable performance in many machine learning tasks. Although recently there have been numerous theoretical contributions to understand their success, it is still largely unexplained and remains a mystery. In particular, it is not known why in the overparameterized setting, in which there are far more parameters than training points, stochastic gradient descent (SGD) can learn networks that generalize well, as been observed in practice BID15 BID26 .In such over-parameterized settings, the loss function can contain multiple global minima that generalize poorly. Therefore , learning can in principle lead to models with low training error, but high test error. However, as often observed in practice, SGD is in fact able to find models with low training error and good generalization performance. This suggests that the optimization procedure, which depends on the optimization method (SGD) and the training data, introduces some form of inductive bias which directs it towards a low complexity solution. Thus, in order to explain the success of neural networks, it is crucial to characterize this inductive bias and understand what are the guarantees for generalization of over-parameterized neural networks.In this work, we address these problems in a binary classification setting where SGD optimizes a two-layer over-parameterized network with the goal of learning a linearly separable function. We study a relatively simple case of SGD where the weights of the second layer are fixed throughout the training process, and only the weights of the first layer are updated. Clearly, an over-parameterized network is not necessary for classifying linearly separable data, since this is possible with linear classifiers (e.g., with the Perceptron algorithm) which also have good generalization guarantees BID20 . But, the key question which we address here is whether a large network will overfit in such a case or not. As we shall see, it turns out that although the networks we consider are rich enough to considerably overfit the data, this does not happen when SGD is used for optimization. In other words, SGD introduces an inductive bias which allows it to learn over-parameterized networks that can generalize well. Therefore, this setting serves as a good test bed for studying the effect of over-paramaterization. Understanding the performance of over-parameterized neural networks is essential for explaining the success of deep learning models in practice. Despite a plethora of theoretical results for generalization of neural networks, none of them give guarantees for over-parameterized networks. In this work, we give the first provable guarantees for the generalization performance of over-parameterized networks, in a setting where the data is linearly separable and the network has Leaky ReLU activations. We show that SGD compresses its output when learning over-parameterized networks, and thus exhibits good generalization performance.The analysis for networks with Leaky ReLU activations does not hold for networks with ReLU activations, since in this case the loss contains spurious local minima. However, due to the success of over-parameterized networks with ReLU activations in practice, it is likely that similar results hold here as well. It would be very interesting to provide convergence guarantees and generalization bounds for this case. Another direction for future work is to show that similar results hold under different assumptions on the data.",870,0.458,495,1.7575757575757576,"Neural networks exhibit good generalization behavior the over-parameterized regime network parameters exceeds observations Nonetheless current generalization bounds for neural networks fail explain In bridge study the problem learning a two-layer over-parameterized neural network when generated a linearly separable function In where the network Leaky ReLU activations provide both optimization and generalization guarantees Specifically prove convergence rates SGD to a global minimum provide generalization guarantees that independent the network size Therefore our result clearly SGD for optimization both finds a global minimum, avoids despite the high capacity This the first theoretical demonstration SGD avoid overfitting when learning over-specified neural network classifiers Neural networks achieved Although recently there numerous theoretical contributions understand their success largely unexplained and remains In particular known why in the overparameterized setting in there far more parameters training points learn networks generalize been practice BID15 BID26 .In such over contain multiple global minima generalize poorly Therefore , learning can in models low training error high test error However as often observed practice SGD in able find models low training error good generalization performance This suggests the optimization procedure, dependsSGD introduces some form inductive bias which directs it a low complexity solution Thus explain the success neural networks crucial characterize this inductive bias understand are the guaranteesIn address a binary classification setting where SGD optimizes learning a linearly separable function We study a relatively simple case SGD where the weights the second layer fixed throughout updated Clearly an over-parameterized network necessary classifying linearly separable data this possible with which also good guarantees BID20 . But, the key question which we address a large network will overfit in or As shall turns although the networks we consider are rich considerably overfit this happen SGD optimization In SGD introduces an inductive bias which allows learn over-parameterized networks that generalize well Therefore this setting serves studying over-paramaterization Understanding the performance essential explaining the success practice Despite a plethora theoretical results for generalization none give guarantees over-parameterized networks In this work give the first provable guarantees the generalization performance over-parameterized networks a setting linearly has Leaky ReLU activations We show SGD compresses its output when learning over-parameterized networks exhibits good generalization performanceThe analysis for networks Leaky ReLU activations does hold in contains spurious local minima However due the success over-parameterized networks with ReLU activations practice similar results hold here It would very provide convergence guarantees generalization bounds this case Another direction future work show similar results hold under on the data",0.01,0.634315640108544
"A central challenge in reinforcement learning is discovering effective policies for tasks where rewards are sparsely distributed. We postulate that in the absence of useful reward signals, an effective exploration strategy should seek out {\it decision states}. These states lie at critical junctions in the state space from where the agent can transition to new, potentially unexplored regions. We propose to learn about decision states from prior experience. By training a goal-conditioned model with an information bottleneck, we can identify decision states by examining where the model accesses the goal state through the bottleneck. We find that this simple mechanism effectively identifies decision states, even in partially observed settings. In effect, the model learns the sensory cues that correlate with potential subgoals. In new environments, this model can then identify novel subgoals for further exploration, guiding the agent through a sequence of potential decision  states and through new regions of the state space.",181,0.127,105,1.723809523809524,A central challenge reinforcement learning discovering effective policies tasks rewards sparsely We postulate useful reward signals an effective exploration strategy {\it decision states These states lie the state space from the agent transition We propose learn decision states prior experience By training a goal-conditioned model an information bottleneck identify decision states by examining where accesses through We find this simple mechanism effectively identifies decision states even partially observed settings In effect the model learns the sensory cues correlate potential subgoals In new environments this model then identify novel subgoals guiding potential decision states through new regions,0.0,0.5482822431410416
"Many applications in machine learning require optimizing a function whose true gradient is unknown, but where surrogate gradient information (directions that may be correlated with, but not necessarily identical to, the true gradient) is available instead. This arises when an approximate gradient is easier to compute than the full gradient (e.g. in meta-learning or unrolled optimization), or when a true gradient is intractable and is replaced with a surrogate (e.g. in certain reinforcement learning applications or training networks with discrete variables). We propose Guided Evolutionary Strategies, a method for optimally using surrogate gradient directions along with random search. We define a search distribution for evolutionary strategies that is elongated along a subspace spanned by the surrogate gradients. This allows us to estimate a descent direction which can then be passed to a first-order optimizer. We analytically and numerically characterize the tradeoffs that result from tuning how strongly the search distribution is stretched along the guiding subspace, and use this to derive a setting of the hyperparameters that works well across problems. Finally, we apply our method to example problems including truncated unrolled optimization and training neural networks with discrete variables, demonstrating improvement over both standard evolutionary strategies and first-order methods (that directly follow the surrogate gradient). We provide a demo of Guided ES at: redacted URL Optimization in machine learning often involves minimizing a cost function where the gradient of the cost with respect to model parameters is known. When gradient information is available, firstorder methods such as gradient descent are popular due to their ease of implementation, memory efficiency, and convergence guarantees (Sra et al., 2012) . When gradient information is not available, however, we turn to zeroth-order optimization methods, including random search methods such as evolutionary strategies (Rechenberg, 1973; Nesterov & Spokoiny, 2011; Salimans et al., 2017) .However , what if only partial gradient information is available? That is , what if one has access to surrogate gradients that are correlated with the true gradient, but may be biased in some unknown fashion? Naïvely , there are two extremal approaches to optimization with surrogate gradients. On one hand, you could ignore the surrogate gradient information entirely and perform zeroth-order optimization, using methods such as evolutionary strategies to estimate a descent direction. These methods exhibit poor convergence properties when the parameter dimension is large BID5 . On the other hand, you could directly feed the surrogate gradients to a first-order optimization algorithm. However , bias in the surrogate gradients will interfere with optimizing the target problem (Tucker et al., 2017) . Ideally , we would like a method that combines the complementary strengths of these two approaches: we would like to combine the unbiased descent direction estimated with evolutionary strategies with the low-variance estimate given by the surrogate gradient. In this work, we propose a method for doing this called guided evolutionary strategies (Guided ES).The critical assumption underlying Guided ES is that we have access to surrogate gradient information, but not the true gradient. This scenario arises in a wide variety of machine learning problems, which typically fall into two categories: cases where the true gradient is unknown or not defined, and cases where the true gradient is hard or expensive to compute. Examples of the former include: models with discrete stochastic variables (where straight through estimators (Bengio et al., Figure 1: (a) Schematic of guided evolutionary strategies. We perform a random search using a distribution (white contours) elongated along a subspace (white arrow) which we are given instead of the true gradient (blue arrow). (b) Comparison of different algorithms on a quadratic loss, where a bias is explicitly added to the gradient to mimic situations where the true gradient is unknown. The loss (left) and correlation between surrogate and true gradient (right) are shown during optimization. See §4.1 for experimental details.2013 ; van den Oord et al., 2017) or Concrete/Gumble-Softmax methods (Maddison et al., 2016; BID12 are commonly used) and learned models in reinforcement learning (e.g. for Q functions (Watkins & Dayan, 1992; Mnih et al., 2013; or value estimation (Mnih et al., 2016) ). For the latter, examples include optimization using truncated backprop through time (Rumelhart et al., 1985; Williams & Peng, 1990; Wu et al., 2018) . Surrogate gradients also arise in situations where the gradients are explicitly modified during training, as in feedback alignment BID17 and related methods (Nøkland, 2016; BID6 .The key idea in Guided ES is to keep track of a low-dimensional subspace, defined by the recent history of surrogate gradients during optimization, which we call the guiding subspace. We then perform a finite difference random search (as in evolutionary strategies) preferentially within this subspace. By concentrating our search samples in a low-dimensional subspace where the true gradient has non-negative support, we dramatically reduce the variance of the search direction.Our contributions in this work are:• a new method for combining surrogate gradient information with random search,• an analysis of the bias-variance tradeoff underlying the technique ( §3.3),• a scheme for choosing optimal hyperparameters for the method ( §3.4), and• applications to example problems ( §4). We have introduced guided evolutionary strategies (Guided ES), an optimization algorithm which combines the benefits of first-order methods and random search, when we have access to surrogate gradients that are correlated with the true gradient. We analyzed the bias-variance tradeoff inherent in our method analytically, and demonstrated the generality of the technique by applying it to unrolled optimization, synthetic gradients, and training neural networks with discrete variables.",1185,0.563,697,1.7001434720229556,"Many applications in machine learning require optimizing a function whose true gradient unknown where surrogate gradient information (directions that correlated, instead This arises an approximate gradient easier meta-learning or unrolled optimization intractable replaced surrogate ( certain reinforcement learning applications or training networks with discrete variables We propose Guided Evolutionary Strategies optimally using surrogate gradient directions along with random search We define a search distribution evolutionary strategies is elongated along a subspace spanned the surrogate gradients This allows estimate a descent direction which then passed We analytically and characterize result tuning how strongly the search distribution stretched along the guiding subspace use derive a setting works across problems Finally apply our method example problems including truncated unrolled optimization training neural networks discrete variables demonstrating improvement both standard evolutionary strategiesthat directly follow the surrogate gradient We provide a demo Guided ES at: redacted URL Optimization machine learning often minimizing a cost function where with model parameters known When gradient information available firstorder methods popular due memory efficiency convergence guarantees (Sra et) . When gradient information not however turn zeroth-order optimization methods including random search methods evolutionary strategiesRechenberg 1973 Nesterov & Spokoiny 2011 Salimans 2017 .However , what That , what if one has access surrogate gradients correlated the true gradient may biased some unknown fashion Naïvely , there two extremal approaches optimization with surrogate gradients On ignore the surrogate gradient information entirely perform zeroth-order optimization using methods evolutionary strategies estimate a descent direction These methods exhibit poor convergence properties the parameter dimension large BID5 . On you directly feed the surrogate gradients However , bias the surrogate gradients will interfere optimizing the target problemTucker 2017 Ideally , a method combines the complementary strengths we the unbiased descent direction estimated evolutionary strategies with given the surrogate gradient In this work propose doing this called guided evolutionary strategiesGuided ES).The critical assumption underlying access surrogate gradient information true This scenario arises machine learning problems which typically fall cases the true gradient unknown not defined hard or expensive Examples former models discrete stochastic variableswhere straight through estimators (Bengio Figure: ( Schematic guided evolutionary strategies. We perform a distribution (white contours elongated along a subspacewhite arrow which we are given instead the true gradient (b) Comparison different algorithms on a quadratic loss, a bias explicitly added mimic situations unknown The loss (left correlation surrogate and true gradient during optimization See § experimental details.2013 ; van Oord 2017) or Concrete/GumbleSoftmax methodsMaddison BID12 are commonly learned models in for Q functions ( Dayan 1992 Mnih or value estimation For latter examples optimization using truncated backprop through timeRumelhart et al 1985 Williams Peng 2018 . Surrogate gradients also arise situations explicitly modified during training feedback alignment BID17 and related methods (Nøkland 2016 BID6 .The key idea Guided ES keep a low-dimensional subspace defined the recent history surrogate gradients during optimization we the guiding subspace We then perform a finite difference random search (as evolutionary strategies preferentially within this subspace By concentrating our search samples where the true gradient has non-negative support dramatically the search directionOur contributions a new method combining surrogate gradient information random search,• underlying the technique §3.3),• a scheme choosing and• applications to example problems We introduced guided evolutionary strategies (Guided ES an optimization algorithm combines random search when we access surrogate gradients correlated We analyzed the bias-variance tradeoff inherent our method analytically demonstrated the technique applying unrolled optimization, synthetic gradients training discrete variables",0.01,0.48798322246544046
"Point clouds are an important type of geometric data and have widespread use in computer graphics and vision. However, learning representations for point clouds is particularly challenging due to their nature as being an unordered collection of points irregularly distributed in 3D space. Graph convolution, a generalization of the convolution operation for data defined over graphs, has been recently shown to be very successful at extracting localized features from point clouds in supervised or semi-supervised tasks such as classification or segmentation. This paper studies the unsupervised problem of a generative model exploiting graph convolution. We focus on the generator of a GAN and define methods for graph convolution when the graph is not known in advance as it is the very output of the generator. The proposed architecture learns to generate localized features that approximate graph embeddings of the output geometry. We also study the problem of defining an upsampling layer in the graph-convolutional generator, such that it learns to exploit a self-similarity prior on the data distribution to sample more effectively. Convolutional neural networks are at the core of highly successful models in image generation and understanding. This success is due to the ability of the convolution operation to exploit the principles of locality, stationarity and compositionality that hold true for many data of interest. In particular, feature locality and weight sharing across the data domain greatly reduce the number of parameters in the model, simplifying training and countering overfitting. However, while images are defined on an underlying regular grid structure, several other types of data naturally lie on irregular or nonEuclidean domains . Examples include problems in 3D models BID3 BID17 , computational biology BID1 BID7 or social network graphs BID14 . Defining convolutional architectures on these domains is key to exploit useful priors on the data to obtain more powerful representations.Graph convolution is emerging as one of the most successful approaches to deal with data where the irregular domain can be represented as a graph. In this case, the data are defined as vectors on the nodes of a graph. Defining a convolution-like operation for this kind of data is not trivial, as even simple notions such as shifts are undefined. The literature has identified two main approaches to define graph convolution, namely spectral or spatial. In the former case BID13 BID6 BID14 , the convolution operator is defined in the spectral domain through the graph Fourier transform BID24 . Fast polynomial approximations BID6 exist that allow an efficient implementation of the operation. This spectral approach has been successfully used in semi-supervised classification BID14 and link prediction BID23 . However, the main drawback of these techniques is that the structure of the graph is supposed to be fixed and it is not clear how to handle the case where the graph structure varies. The latter class of methods BID25 BID26 defines the convolution operator using a spatial approach by means of local aggregations, i.e., weighted combinations of the vectors restricted to a neighborhood. Since this kind of convolution is defined at a neighborhood level, the operation remains well defined even when the graph varies.Point clouds are a challenging data type due to the irregular positioning of the points and the fact that a point cloud is an unordered set of points, and therefore any permutation of its members, while changing the representation, does not change its semantic meaning. Some works have addressed supervised problems on point clouds such as classification or segmentation, either through voxelization BID19 BID27 , where the irregular point structure is approximated with a regular 3D grid, or by networks like PointNet BID21 b) that address the problem of permutation invariance by processing each point identically and independently before applying a globally symmetric operation. The most recent approaches BID25 BID26 build graphs in the Euclidean space of the point cloud and use graph convolution operations. This approach has shown multiple advantages in i) reducing the degrees of freedom in the learned models by enforcing some kind of weight sharing, ii) extracting localized features that successfully capture dependencies among neighboring points. Generative models are powerful tools in unsupervised learning aiming at capturing the data distribution. However, so far little work has been done on generative models for point clouds. Generative models of point clouds can be useful for many tasks that range from data augmentation to shape completion or inpainting partial data thanks to the features learned by the model. Generative Adversarial Networks (GANs) have been shown on images to provide better approximations of the data distribution than variational autoencoders (VAEs) BID15 , being able to generate sharper images and to capture semantic properties in their latent space. For this reason, it is interesting to study them for unordered point sets. In the first work on the topic, BID0 studied some GAN architectures to generate point clouds. Such architectures use the PointNet approach to deal with the permutation problem at the discriminator and employ a dense generator. However, this means that they are unable to learn localized features or exploit weight sharing. This paper studies a generative model for point clouds based on graph convolution. In particular, we focus on the GAN generator which is not well explored by the graph convolution literature. This poses a unique challenge: how can one apply a localized operation (the graph convolution) without knowing the domain (the graph) in advance because it is the very output of the generator? We show that the proposed architecture learns domain and features simultaneously and promotes the features to be graph embeddings, i.e. representations in a vector space of the local dependencies between a point and its neighbors. Such localized features learned by the generator provide a flexible and descriptive model. Moreover, we address the problem of upsampling at the generator. While downsampling based on graph coarsening is a staple in (semi-)supervised problems using graph convolution, it is not obvious how to properly upsample the intermediate layers of a graph-convolutional GAN generator. We propose a method exploiting non-local self-similarities in the data distribution. We presented a GAN using graph convolutional layers to generate 3D point clouds. In particular, we showed how constructing nearest neighbor graphs from generator features to implement the graph convolution operation promotes the features to be localized and to approximate a graph embedding of the output geometry. We also proposed an upsampling scheme for the generator that exploits self-similarities in the samples to be generated. The main drawback of the current method is the rather high complexity of the graph convolution operation. Future work will focus on reducing the overall complexity, e.g., in the graph construction operation, and study new upsampling schemes.",1305,0.767,751,1.7376830892143809,"Point clouds geometric data widespread use vision However learning representations point clouds particularly being irregularly Graph convolution data defined over graphs recently shown successful extracting localized features point clouds such classification This paper studies the unsupervised problem a generative model exploiting graph convolution We focus the generator a GAN and define methods graph convolution when known as the very output The proposed architecture learns generate localized features that approximate graph embeddings the output geometry We also study the problem defining an upsampling layer the graph-convolutional generator such learns exploit prior on the data distribution to sample effectively at highly successful models image generation understanding This success the convolution operation exploit the principles locality stationarity compositionality that hold many data of In particular feature locality weight sharing across the data domain greatly parameters training countering However while images defined on an underlying regular grid structure several other types naturally lie irregular or nonEuclidean domains . Examples include problems 3D models BID3 BID17 , computational biology or social network graphs Defining convolutional architectures on these domains key exploit useful priors on to obtain more powerful representationsGraph convolution emerging deal where the irregular domain In are defined vectors on the nodes Defining a convolution-like operation this kind even simple notions shifts undefined The literature identified define graph convolution spectral or spatial In the former case BID13 BID6 , the convolution operator the spectral domain through the graph Fourier BID24 Fast polynomial approximations BID6 exist that an efficient implementation the operation This spectral approach successfully semi-supervised classification BID14 link prediction However the main drawback these techniques the structure supposed fixed clear handle the case varies The latter class methods BID25 BID26 defines the convolution operator using a spatial approach by means local aggregations weighted combinations restricted a neighborhood Since this kind convolution defined at a neighborhood level the operation remains well even the graph variesPoint clouds a challenging data type due the irregular positioning any permutation its members, while changing Some works addressed supervised problems on point clouds such classification either voxelization BID19 BID27 , where the irregular point structure approximated networks like PointNet b) address permutation invariance by processing identically independently before a globally symmetric operation The most recent approaches BID25 BID26 build graphs in of the point cloud use graph convolution operations This approach shown multiple advantages i) the degrees the learned models by enforcing some kind weight sharing extracting localized features successfully dependencies among neighboring points. Generative models aiming capturing the data distribution However so far little work generative models point clouds Generative models point clouds many tasks range data augmentation shape completion or inpainting partial data thanks learned on images provide the data distribution thanVAEs) BID15 , being sharper images capture semantic properties their latent space For interesting study them unordered point sets In the first work BID0 studied some GAN architectures generate point clouds Such architectures use the PointNet approach deal at the discriminator and employ a dense generator However means they unable learn localized features exploit weight sharing This paper studies point clouds based graph convolution In particular focus the GAN generator not well explored the graph convolution literature This poses apply a localized operationthe graph convolution without knowing the domain ( advance because the very output the generator We show the proposed architecture learns domain and features simultaneously promotes the features graph embeddings the local dependencies a point Such localized features learned the generator provide a flexible and descriptive model Moreover address upsampling at the generator While downsampling based graph coarsening (semi-)supervised problems using obvious properly upsample the intermediate layers a graph-convolutional GAN generator We propose exploiting We presented a GAN using graph convolutional layers In particular showed constructing nearest neighbor graphs generator features to implement the graph convolution operation promotes the features localized approximate a graph embedding of the output geometry We also proposed an upsampling scheme the generator exploits self-similarities the samples be The main drawback the rather high complexity the graph convolution operation Future work reducing, in the graph construction operation study new upsampling schemes",0.01,0.5836308688744883
"Memorization in over-parameterized neural networks can severely hurt generalization in the presence of mislabeled examples. However, mislabeled examples are to hard avoid in extremely large datasets. We address this problem using the implicit regularization effect of stochastic gradient descent with large learning rates, which we find to be able to separate clean and mislabeled examples with remarkable success using loss statistics. We leverage this to identify and on-the-fly discard mislabeled examples using a threshold on their losses. This leads to On-the-fly Data Denoising (ODD), a simple yet effective algorithm that is robust to mislabeled examples, while introducing almost zero computational overhead. Empirical results demonstrate the effectiveness of ODD on several datasets containing artificial and real-world mislabeled examples. Over-parametrized deep neural networks have remarkable generalization properties while achieving near-zero training error (Zhang et al., 2016) . However, the ability to fit the entire training set is highly undesirable, as a small portion of mislabeled examples in the dataset could severely hurt generalization (Zhang et al., 2016; BID0 . Meanwhile, an exponential growth in training data size is required to linearly improve generalization in vision tasks BID31 ; this progress could be hindered if there are mislabeled examples within the dataset.Mislabeled examples are to be expected in large datasets that contain millions of examples. Webbased supervision produces noisy labels BID17 BID21 ; whereas human labeled datasets sacrifice accuracy for scalability BID16 . Therefore, algorithms that are robust to various levels of mislabeled examples are warranted in order to further improve generalization for very large labeled datasets.In this paper, we propose On-the-fly Data Denoising (ODD), a simple and robust method for training with noisy examples based on the implicit regularization effect of stochastic gradient descent. First, we train residual networks with large learning rate schedules and use the resulting losses to separate clean examples from mislabeled ones. This is done by identifying examples whose losses exceed a certain threshold. Reasonable thresholds can be derived from the loss distribution for uniform label noise which does not depend on the amount of mislabeled examples in the dataset. Finally, we remove these examples from the dataset and continue training until convergence. Empirically, ODD performs significantly better than previous methods in datasets containing artificial noise (Sections 4.1 and 4.2) or real-world mislabeled examples (Section 4.3), while achieving equal or better accuracy than the state-of-the-art on clean datasets (Sections 4.1 and 4.2). We further conduct ablation studies to demonstrate that ODD is robust w.r.t hyperparameters and artificial noise levels (Section 4.4). Our method is also able to detect mislabeled examples in the CIFAR-100 dataset without any additional supervision ( FIG0 ). We have proposed ODD, a straightforward method for robust training with mislabeled examples. ODD utilizes the implicit regularization effect of stochastic gradient descent to prune examples that potentially harm generalization. Empirical results demonstrate that ODD is able to significantly outperform related methods on a wide range of datasets with artificial and real-world mislabeled examples, maintain competitiveness with ERM on clean datasets, as well as detecting mislabeled examples automatically in CIFAR-100.The implicit regularization of stochastic gradient descent opens up other research directions for implementing robust algorithms. For example, we could consider using a smaller network to remove examples, removing examples not only once but multiple times, retraining from scratch with the denoised dataset, or other data-augmentation approaches such as mixup (Zhang et al., 2017) . Moreover, it would be interesting to understand the implicit regularization over mislabeled examples from a theoretical viewpoint. A ADDITIONAL EXPERIMENTAL RESULTS",766,0.42,439,1.744874715261959,Memorization in over-parameterized neural networks severely hurt mislabeled examples However mislabeled examples to hard avoid extremely large datasets We address the implicit regularization effect with large learning rates find able separate clean and mislabeled examples remarkable success using loss statistics We leverage this to identify on discard mislabeled examples using a threshold on their losses This leads On Data Denoising robust mislabeled examples while introducing almost zero computational overhead demonstrate ODD on several datasets containing artificial and mislabeled examples Over-parametrized deep neural networks remarkable generalization properties while achieving . However the ability fit the entire training set highly undesirable a small portion mislabeled examples in severely hurt generalizationZhang BID0 . Meanwhile an exponential growth training data size required linearly improve vision tasks BID31 ; this progress could hindered mislabeled examples withinMislabeled examples to millions examples Webbased supervision produces noisy labels BID17 BID21 ; whereas human labeled datasets sacrifice accuracy . Therefore algorithms robust various levels mislabeled examples warranted further for very large labeled datasetsIn On Data Denoising training with noisy examples based the implicit regularization effect First train residual networks large learning rate schedules use the resulting losses separate clean examples mislabeled ones This done identifying examples whose losses exceed Reasonable thresholds can derived the loss distribution uniform label noise which does mislabeled examples Finally remove these examples continue training until convergence ODD performs significantly previous methods datasets containing artificial noiseSections real-world mislabeled examples while achieving the state on clean datasets We further conduct ablation studies demonstrate ODD robust w.r.t hyperparameters artificial noise levelsSection Our method also able mislabeled examples without any additional supervision FIG0 We proposed ODD a straightforward method robust training mislabeled examples ODD utilizes the implicit regularization effect prune examples potentially harm generalization demonstrate ODD able significantly related methods on datasets with artificial and real-world mislabeled examples maintain competitiveness ERM on clean datasets as detecting automatically CIFAR-100.The implicit regularization opens other research directions implementing robust algorithms For example consider a smaller network remove examples removing examples not once retraining from scratch with the denoised dataset other data-augmentation approaches such mixup (Zhang 2017 . Moreover interesting understand the implicit regularization over mislabeled examples from a theoretical viewpoint,0.0,0.6019545001943617
"Binarized Neural Networks (BNNs) have recently attracted significant interest due to their computational efficiency. Concurrently, it has been shown that neural networks may be overly sensitive to ``attacks"" -- tiny adversarial changes in the input -- which may be detrimental to their use in safety-critical domains. Designing attack algorithms that effectively fool trained models is a key step towards learning robust neural networks.
 The discrete, non-differentiable nature of BNNs, which distinguishes them from their full-precision counterparts, poses a challenge to gradient-based attacks. In this work, we study the problem of attacking a BNN through the lens of combinatorial and integer optimization. We propose a Mixed Integer Linear Programming (MILP) formulation of the problem. While exact and flexible, the MILP quickly becomes intractable as the network and perturbation space grow. To address this issue, we propose IProp, a decomposition-based algorithm that solves a sequence of much smaller MILP problems. Experimentally, we evaluate both proposed methods against the standard gradient-based attack (PGD) on MNIST and Fashion-MNIST, and show that IProp performs favorably compared to PGD, while scaling beyond the limits of the MILP. The success of neural networks in vision, text and speech tasks has led to their widespread deployment in commercial systems and devices. However, these models can often be fooled by minimal perturbations to their inputs, posing serious security and safety threats BID13 . A great deal of current research addresses the ""robustification"" of neural networks using adversarially generated examples BID19 BID22 , a variant of standard gradient-based training that uses adversarial training examples to defend against possible attacks. Recent work has also formulated the problem of ""adversarial learning"" as a robust optimization problem BID22 BID17 BID29 , where one seeks the best model parameters with respect to the loss function as measured on the worst-case adversarial perturbation of each point in the training dataset. Attack algorithms may thus be used to augment the training dataset with adversarial examples during training, resulting in more robust models BID19 . These new advances further motivate the need to develop effective methods for generating adversarial examples for neural networks.In this work, we focus on designing effective attacks against Binarized Neural Networks (BNNs) BID8 . BNNs are neural networks with weights in {−1, +1} and the sign function non-linearity, and are especially pertinent in low-power or hardware-constrained settings, where they have the potential to be used at an unprecedented scale if deployed to smartphones and other edge devices. This makes attacking, and consequently robustifying BNNs, a task of major importance. However, the discrete, non-differentiable structure of a BNN renders less effective the typical attack algorithms that rely on gradient information. As strong attacks are crucial to effective adversarial training, we are motivated to address this problem in the hope of generating better attacks.The goal of adversarial attacks is to modify an input slightly, so that the neural network predicts a different class than what it would have predicted for the original input. More formally, the task of generating an optimal adversarial example is the following: Given:-A (clean) data point x ∈ R n ;-A trained BNN model with parameters w, that outputs a value f c (x; w) for a class c ∈ C; -prediction, the class predicted for data point x, arg max c∈C f c (x; w); -target, the class we would like to predict for a slightly perturbed version of x; -, the maximum amount of perturbation allowed in any of the n dimensions of the input x. We developed combinatorial search methods for generating adversarial examples that fool trained Binarized Neural Networks, based on a Mixed Integer Linear Programming (MILP) model and a target propagation-driven iterative algorithm IProp. To our knowledge, this is the first such integer optimization-based attack for BNNs, a type of neural networks that is inherently discrete. Our MILP model results show that standard (PGD) attack methods often are suboptimal in generating good adversarial examples when the perturbation budget is limited. The ultimate goal is to ""attack to protect"", i.e. to generate perturbations that can be used during adversarial training, resulting in BNNs that are robust to a class of perturbation. Unfortunately, our MILP model cannot be solved quickly enough to be incorporated into adversarial training. On the other hand, through extensive experiments we have shown that our iterative algorithm IProp is able to scale-up this solving process while maintaining good performance compared to the PGD attack. With these contributions, we believe we have laid the foundations for improved attacks and potentially robust training of BNNs. This work is a good example of successful cross fertilization of ideas and methods from discrete optimization and machine learning, a growing synergistic area of research, both in terms of using discrete optimization for ML as was done here BID11 BID2 , as well as using ML in discrete optimization tasks BID14 BID28 BID16 BID18 BID9 . We believe that target propagation ideas such as in IProp can be potentially extended for the problem of training BNNs, a challenging task to this day. The same can be said about hard-threshold networks, as hinted to by BID11 . We implemented the method of ""simultaneous perturbation stochastic approximation"" (SPSA) BID30 , which was recently used in BID33 as an example of a gradient-free attack. Our implementation of SPSA follows BID33 and uses the Adam optimization method with learning rate 0.01, a stochastic sample of perturbations (referred to as ""batch size"" in BID33 ) of size 100, and an iteration limit of 100. As with PGD, SPSA is run with random restarts every 100 iterations until the time limit of 180 seconds is reached. FIG10 shows the flip prediction rates for IProp (same as in FIG3 in the main text) and SPSA. Generally, SPSA performs worse than IProp and PGD.",1244,0.626,749,1.6608811748998664,"Binarized Neural Networks attracted Concurrently it shown neural networks may overly ``attacks"" -- tiny adversarial changes -- detrimental their use safety-critical domains Designing attack algorithms effectively fool trained models learning robust neural networks The discrete, non-differentiable nature BNNs distinguishes poses gradient-based attacks In this work study the problem attacking a BNN through combinatorial and integer optimization We propose a Mixed Integer Linear Programming (MILP) formulation While exact and flexible, the MILP quickly the network and perturbation space grow To address propose IProp solves a sequence much smaller MILP problems Experimentally evaluate both proposed methods against the standard gradient-based attackPGD MNIST Fashion-MNIST IProp performs favorably scaling beyond the MILP The success neural networks vision text their widespread deployment commercial systems devices However these models can often fooled minimal perturbations their inputs posing BID13 . A great deal current research addresses the ""robustification using adversarially generated examples BID19 BID22 , a variant standard gradient-based training defend possible attacks Recent work also formulated the problem a robust optimization problem BID22 BID17 BID29 , one seeks the best model parameters as measured on each point Attack algorithms may thus augment the training dataset with adversarial examples during resulting BID19 . These new advances further motivate effective methods generating adversarial examplesIn focus designing effective attacks Binarized Neural Networks BID8 . BNNs neural networks weights {−1 the sign function non especially pertinent low-power or hardware-constrained settings at if deployed smartphones other edge devices This makes attacking, consequently robustifying BNNs However the discrete, non-differentiable structure a BNN renders less effective the typical attack algorithms rely gradient information As strong attacks are crucial effective adversarial training motivated address the hope generating better attacksThe goal adversarial attacks modify an input slightly predicts a different class than for More formally the task generating an optimal adversarial example following Given:-A (clean) data point x �� R n ; trained BNN model parameters w that outputs f c;; -prediction, the class predicted for arg max c��C f c -target we would a slightly perturbed version, the maximum amount allowed any of the n dimensions We developed combinatorial search methods generating adversarial examples fool trained Binarized Neural Networks based a Mixed Integer Linear Programming (MILP) model a target propagation-driven iterative algorithm IProp To our knowledge the first such integer optimization-based attack for BNNs a type neural networks inherently discrete Our MILP model results show standard (PGD) attack methods often are generating good adversarial examples when the perturbation budget limited The ultimate goal ""attack to protect generate perturbations during adversarial training resulting BNNs robust a class Unfortunately our MILP model solved quickly to incorporated adversarial training On through extensive experiments we our iterative algorithm IProp scale- this solving process while compared the PGD attack With these contributions believe laid improved attacks potentially robust training BNNs successful cross fertilization ideas methods from discrete optimization a growing synergistic area both terms using discrete optimization ML as was here BID11 BID2 , as using ML discrete optimization tasks . We believe target propagation ideas such in IProp can potentially extended for the problem training BNNs a challenging task to this day same can hard-threshold networks hinted to BID11 . We implemented the method ""simultaneous perturbation stochastic approximation BID30 , recently used BID33 as a gradient-free attack Our implementation SPSA follows BID33 and uses the Adam optimization method with learning ratereferred ""batch size ) size 100 an iteration limit As with PGD SPSA run with random restarts every 100 iterations until 180 seconds FIG10 the flip prediction rates IProp (same in the main text SPSA Generally SPSA performs worse IProp PGD",0.01,0.38794633894351693
"Highly regularized LSTMs achieve impressive results on several benchmark datasets in language modeling. We propose a new regularization method based on decoding the last token in the context using the predicted distribution of the next token. This biases the model towards retaining more contextual information, in turn improving its ability to predict the next token. With negligible overhead in the number of parameters and training time, our Past Decode Regularization (PDR) method achieves a word level perplexity of 55.6 on the Penn Treebank and 63.5 on the WikiText-2 datasets using a single softmax. We also show gains by using PDR in combination with a mixture-of-softmaxes, achieving a word level perplexity of 53.8 and 60.5 on these datasets. In addition, our method achieves 1.169 bits-per-character on the Penn Treebank Character dataset for character level language modeling. These results constitute a new state-of-the-art in their respective settings. Language modeling is a fundamental task in natural language processing. Given a sequence of tokens, its joint probability distribution can be modeled using the auto-regressive conditional factorization. This leads to a convenient formulation where a language model has to predict the next token given a sequence of tokens as context. Recurrent neural networks are an effective way to compute distributed representations of the context by sequentially operating on the embeddings of the tokens. These representations can then be used to predict the next token as a probability distribution over a fixed vocabulary using a linear decoder followed by Softmax.Starting from the work of BID16 , there has been a long list of works that seek to improve language modeling performance using more sophisticated recurrent neural networks (RNNs) BID26 ; BID27 ; BID28 ; BID17 ). However, in more recent work vanilla LSTMs BID7 ) with relatively large number of parameters have been shown to achieve state-of-the-art performance on several standard benchmark datasets both in word-level and character-level perplexity BID14 b) ; BID12 ; BID25 ). A key component in these models is the use of several forms of regularization e.g. variational dropout on the token embeddings BID3 ), dropout on the hidden-to-hidden weights in the LSTM BID24 ), norm regularization on the outputs of the LSTM and classical dropout BID23 ). By carefully tuning the hyperparameters associated with these regularizers combined with optimization algorithms like NT-ASGD (a variant of the Averaged SGD), it is possible to achieve very good performance. Each of these regularizations address different parts of the LSTM model and are general techniques that could be applied to any other sequence modeling problem.In this paper, we propose a regularization technique that is specific to language modeling. One unique aspect of language modeling using LSTMs (or any RNN) is that at each time step t, the model takes as input a particular token x t from a vocabulary W and using the hidden state of the LSTM (which encodes the context till x t ) predicts a probability distribution w t+1 on the next token x t+1 over the same vocabulary as output. Since x t can be mapped to a trivial probability distribution over W , this operation can be interpreted as transforming distributions over W BID9 ). Clearly, the output distribution is dependent on and is a function of x t and the context further in the past and encodes information about it. We ask the following question -How much information is it possible to decode about the input distribution (and hence x t ) from the output distribution w t+1 ? In general, it is impossible to decode x t unambiguously. Even if the language model is perfect and correctly predicts x t+1 with probability 1, there could be many tokens preceding it. However, in this case the number of possibilities for x t will be limited, as dictated by the bigram statistics of the corpus and the language in general. We argue that biasing the language model such that it is possible to decode more information about the past tokens from the predicted next token distribution is beneficial. We incorporate this intuition into a regularization term in the loss function of the language model.The symmetry in the inputs and outputs of the language model at each step lends itself to a simple decoding operation. It can be cast as a (pseudo) language modeling problem in ""reverse"", where the future prediction w t+1 acts as the input and the last token x t acts as the target of prediction. The token embedding matrix and weights of the linear decoder of the main language model can be reused in the past decoding operation. We only need a few extra parameters to model the nonlinear transformation performed by the LSTM, which we do by using a simple stateless layer. We compute the cross-entropy loss between the decoded distribution for the past token and x t and add it to the main loss function after suitable weighting. The extra parameters used in the past decoding are discarded during inference time. We call our method Past Decode Regularization or PDR for short.We conduct extensive experiments on four benchmark datasets for word level and character level language modeling by combining PDR with existing LSTM based language models and achieve new state-of-the-art performance on three of them.",1049,0.559,612,1.7140522875816993,"Highly regularized LSTMs achieve impressive results several benchmark datasets in language modeling We propose decoding the last token using the predicted distribution This biases towards retaining more contextual information in turn improving the next token With negligible overhead in the number parameters training time our Past Decode Regularization achieves a word level perplexity 55.6 on the Penn Treebank and the WikiText-2 datasets using We also show gains by PDR in combination a mixture-softmaxes, achieving a word level perplexity 53.8 and these datasets In addition our method achieves 1.169 bits- Penn Treebank Character dataset character level language modeling These results constitute a new state their respective settings Language modeling Given a sequence tokens its joint probability distribution modeled the auto-regressive conditional factorization This leads a convenient formulation where a language model has predict the next token given as context Recurrent neural networks compute distributed representations the context by sequentially operating the tokens These representations can then predict the next token as a fixed vocabulary using a linear decoder followed SoftmaxStarting the work BID16 , there works seek language modeling performance BID26 ; However more recent work vanilla LSTMs BID7 ) with relatively large number parameters have achieve state several standard benchmark datasets both word-level and character-level perplexity BID14 b) ; A key component these models several forms regularization variational dropout on the token embeddings BID3 ), the hidden-to-hidden weights norm regularization the outputs classical By carefully tuning associated these regularizers combined optimization algorithms like NT-ASGDa variant Each these regularizations address different parts general techniques could any other sequence modeling problemIn language modeling One unique aspect language modeling using (or any RNN at t takes as a particular token x t a vocabulary W using the hidden state encodes till predicts w t+1 on next token over as output Since x t can mapped a trivial probability distribution over W this operation interpreted transforming distributions W BID9 ). Clearly the output distribution dependent and x t the context further in the past and encodes information it We ask -How much information it decode about the input distribution x t w In general impossible decode x t unambiguously Even the language model perfect correctly predicts x t+1 with could many tokens preceding However the number possibilities x t will dictated the bigram statistics the corpus the language in We argue biasing the language model such possible decode more information the past tokens from the predicted next token distribution beneficial We incorporate this intuition a regularization term the loss function the language modelThe symmetry the inputs at lends a simple decoding operation It can cast a (pseudo) language modeling problem ""reverse the future prediction w t+1 acts the last token x t prediction The token embedding matrix and weights the linear decoder of the main language model reused the past decoding operation We only model the nonlinear transformation performed do a simple stateless layer We compute between the decoded distribution for the past token and x t add after suitable weighting The extra parameters used the past decoding discarded during inference time We call our method Past Decode Regularization orWe conduct extensive experiments four benchmark datasets word level character level language modeling by achieve new state three",0.01,0.523421662493946
"The assumption that data samples are independently identically distributed is the backbone of many learning algorithms. Nevertheless, datasets often exhibit rich structures in practice, and we argue that there exist some unknown orders within the data instances. Aiming to find such orders, we introduce a novel Generative Markov Network (GMN) which we use to extract the order of data instances automatically. Specifically, we assume that the instances are sampled from a Markov chain. Our goal is to learn the transitional operator of the chain as well as the generation order by maximizing the generation probability under all possible data permutations. One of our key ideas is to use neural networks as a soft lookup table for approximating the possibly huge, but discrete transition matrix. This strategy allows us to amortize the space complexity with a single model and make the transitional operator generalizable to unseen instances. To ensure the learned Markov chain is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training.   Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover orders among data instances and also perform comparably well to state-of-the-art methods on the one-shot recognition benchmark task. Recent advances in deep neural networks offer great potentials for machines to learn automatically without humans interventions. For instance, Convolutional Neural Networks (CNNs) BID16 provided an automated way for learning image feature representations. Compared to hand-crafted ones such as SIFT and SURF, these hierarchical deep features demonstrate superior performance in recognition BID35 and transfer learning BID7 problems. Another example would be learning to learn for automatic parameter estimation. BID0 proposed to update model parameters without any pre-defined update rule such as stochastic gradient descent (SGD) or ADAM . Surprisingly, this update-rule-free framework showed better performance and faster convergence on both object recognition and image style transformation tasks. In our paper, we investigate the following novel question: given an unordered dataset where instances may be exhibiting some implicit order, can we order a dataset automatically according to this order?We argue that such order often exists even when we are dealing with the data that are naturally thought of as being i.i.d. sampled from a common though complex distribution. For example, let's consider a dataset consisting of the joint locations on the body of the same person taken on different days. The data i.i.d. assumption is justified since postures of a person took on different days are likely unrelated. However , we can arrange the data instances such that the joints follow an articulated motion or a set of motions in a way that makes each pose highly predictable given the previous ones. Although this arrangement depends on the person as ballerinas' poses might obey different dynamics than the poses of tennis players, the simultaneous inference on the pose dynamics can lead to a robust model that explains the correlations among joints. To put it differently, if we reshuffle the frames of a video clip, the data can now be modeled by an i.i.d. model. Nevertheless , reconstructing the order leads to an alternative model where transitions between the frames are easier to fit the links between the latent structures and observations. The ballerina 's dancing, if sampled very sparsely, can be thought of as a reshuffled video sequence that needs to be reordered such that a temporal model can generate it.One naive and obvious way to find the order in a dataset is to perform sorting based on a predefined distance metric; e.g., the Euclidean distance between image pixel values. However, the distance metrics have to be predefined differently and empirically according to distinct types/characteristics of the datasets at hand. A proper distance metric for one domain may not be a good one for other domains. For instance, p distance is a good measure for DNA/RNA sequences BID23 while it does not characterize the semantic distances between images. We argue that the key component of the ordering problem lies in the discovery of proper distance metric in an automatic and adaptive way.To approach this problem, we propose to learn a distance-metric-free model to discover the ordering in the dataset. More specifically, we model the data by treating them as if they were generated from a Markov chain. We propose to simultaneously train the transitional operator and find the best order by a joint optimization over the parameter space as well as all possible permutations. We term our model Generative Markov Networks (GMNs). One of the key ideas in the design of GMNs is to use neural networks as a soft lookup table to approximate the possibly huge but discrete transition matrix. This strategy allows GMNs to amortize the space complexity using a unified model. Furthermore, due to the differentiable property of neural networks, the transitional operator of GMNs can also generalize on unseen but similar data instances. As an additional contribution, to ensure the Markov chain learned by GMNs is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training.One related task is one-shot recognition which has only one labeled data per category in the target domain. Most of the work in this area considered learning a specific distance metric BID15 BID33 BID28 or category-separation metric BID24 for the data. During the inference phase, they computed either the smallest distance or highest class prediction score between the support and query instances. Alternatively, from a generative modeling perspective, we can first generate the Markov chain for the support instances, then we fit the query instances into the Markov chain and decide the labels with the highest log-likelihood.Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover implicit orders among data instances and also perform comparably well to state-of-the-art methods on the benchmark one-shot recognition task. In this section we give a detailed description on how to implement the transitional operator where the state can be both discrete or continuous. At the first step, to prevent our GMNs from simply memorizing all the training data and their transitions, we introduce stochastic latent variables z 2 R z via Variational Bayes Inference BID34 . The evidence lower bound (ELBO) of the log likelihood for the transitional operator (i.e., log T (s 0 |s; ✓)) becomes: DISPLAYFORM0 where T (s 0 |s; ✓) has been replaced by a distribution P(s 0 |s, z; ) parametrized by , which allows us to make the dependence of s on z. Moreover, KL is the KL-divergence, Q(z|s; ) is an encoder function parametrized by that encodes latent code z given current state s, and P(z) is a fixed prior which we take its form as Gaussian distribution N (0, I). We use reparametrized trick to draw Q(z|s; ) from Gaussian N µ Q, (s), 2 Q, (s)I where µ Q, (s) and Q, (s) are learnable functions.Next, we consider two types of distribution family for P(s 0 |s, z; ✓): Bernoulli and Gaussian. If s 2 {0, 1} p (i.e., a binary image), we define log P(s 0 |s, z; ) as: DISPLAYFORM1 where is element-wise multiplication and g (s, z) : DISPLAYFORM2 If s 2 R p (i.e., a real-valued feature vector), we choose P(s 0 |s, z; ) to be fixed variance factored DISPLAYFORM3 ⌘ , where µ P, (s, z) : R p+z ! R p and P is a fixed variance. We simply choose P in all the experiments. log P(s 0 |s, z; ✓) can thus be defined as DISPLAYFORM4 where const. is not related to the optimization of .For simplicity, we specify ✓ = { [ }. Therefore , the model parameters update for ✓ in (2) refers to the updates for and . In this paper, we argue that data i.i.d. assumption is not always the case in most of the datasets. Often, data instances are exhibiting some implicit orders which may benefit our understanding and analysis of the dataset. To observe the implicit orders, we propose a novel Generative Markov Network which considers a Markov chain data generation scheme. Specifically, we simultaneously learn the transitional operator as a generative model in the Markov chain as well as find the optimal orders of the data under all possible permutations. In lots of experiments, we show that our model is able to observe implicit orders from unordered datasets and also perform well on the one-shot recognition task.",1743,0.934,990,1.7606060606060605,"The assumption data samples independently identically the backbone many learning algorithms Nevertheless datasets often exhibit rich structures practice argue exist some unknown orders the data instances Aiming find such orders we introduce a novel Generative Markov Network extract data instances automatically Specifically assume the instances sampled Our goal learn the transitional operator the chain as the generation order by maximizing the generation probability under all possible data permutations One our key ideas a soft lookup table approximating possibly huge, discrete transition matrix This strategy amortize the space complexity with make the transitional operator unseen instances To ensure the learned Markov chain ergodic propose a greedy batch-wise permutation scheme fast training evaluate the learned Markov chain by showing GMNs able discover orders among data instances also perform comparably state on the one-shot recognition benchmark task Recent advances offer great potentials machines automatically without humans interventions For instance Convolutional BID16 provided learning image feature representations Compared hand-crafted ones such SIFT SURF these hierarchical deep features demonstrate recognition BID35 transfer BID7 problems Another example would learning learn for automatic parameter estimation BID0 proposed update model parameters without any pre-defined update rule such ADAM . Surprisingly this update-rule-free framework showed faster convergence both object recognition image style transformation tasks In our paper investigate the following novel question given an unordered dataset where instances may exhibiting some implicit order order automatically according argue such order often exists even naturally thought i.i.d sampled a common though complex distribution For example let the joint locations on the body taken The data i.i.d. assumption justified since postures took different days likely unrelated However , arrange the data instances such the joints follow an articulated motion or motions each pose highly predictable given the previous ones Although this arrangement depends as ballerinas' poses might obey different dynamics the simultaneous inference on the pose dynamics a robust model joints To put differently reshuffle the frames now modeled Nevertheless , reconstructing the order leads transitions the frames easier fit the links the latent structures observations The ballerina 's dancing if sampled very thought a reshuffled video sequence needs such a temporal model generateOne naive and obvious way find the order a dataset perform sorting based distance image pixel values However the distance metrics to predefined differently empirically according distinct types/ the datasets at A proper distance metric one domain may For instance p distance DNA/RNA sequences BID23 while it characterize the semantic distances images We argue the key component the ordering problem the discovery proper distance metric an automatic and adaptive wayTo approach learn discover the dataset More specifically model treating them generated We propose simultaneously train the transitional operator find by a joint optimization over as We term our model Generative Markov Networks One GMNs neural networks a soft lookup table approximate the possibly huge but discrete transition matrix This strategy GMNs the space complexity using a unified model Furthermore due the differentiable property neural networks the transitional operator GMNs on unseen but similar data instances As an additional contribution to the Markov chain learned by GMNs ergodic propose a greedy batch-wise permutation scheme fast trainingOne related task one-shot recognition which only one labeled data per category Most considered learning a specific distance metric BID15 BID33 BID28 or category-separation metric BID24 for During the inference phase they computed either smallest distance highest class prediction score between the support query instances Alternatively from first generate the support instances fit the query instances decide the labels withEmpirically evaluate showing GMNs able discover implicit orders among data instances also perform comparably state on the benchmark one-shot recognition task In give on implement the transitional operator where both discrete At to prevent our GMNs simply memorizing their transitions introduce stochastic latent variables z 2 R z via Variational Bayes Inference BID34 The evidence lower bound (ELBO the log likelihood the transitional operator; ✓ becomes: DISPLAYFORM0 where has replaced a distribution z; , allows make the dependence s z. Moreover KL is the KL-divergence Q(z|s; that encodes latent code z given current state s fixed prior which we take its form N0 I We use reparametrized trick to draw Q(z|s; Gaussian N µ Q, (s 2 Qs)I where and learnable functionsNext consider two types distribution family P(s 0 |s z; ✓): If s 2 { p define log P(s 0 |s, z; DISPLAYFORM1 where is element-wise multiplication g (s : If 2 R p choose to be fixed variance factored , where µ P, ( R p+z ! and is. We simply choose P in all the experiments log P(s 0 |s, z; ✓ can thus DISPLAYFORM4 where const. is related the optimization .For simplicity specify ✓ = { [ }. Therefore , the model parameters update for ✓ ( refers and In data i.i.d. assumption always most Often data instances exhibiting some implicit orders which benefit analysis To observe the implicit orders propose a novel Generative Markov Network which considers Specifically simultaneously learn the transitional operator as as find the optimal orders under In lots experiments show our model observe implicit orders from unordered datasets also perform",0.01,0.6420365859902427
"We present a Neural Program Search, an algorithm to generate programs from natural language description and a small number of input / output examples. The algorithm combines methods from Deep Learning and Program Synthesis fields by designing rich domain-specific language (DSL) and defining efficient search algorithm guided by a Seq2Tree model on it. To evaluate the quality of the approach we also present a semi-synthetic dataset of descriptions with test examples and corresponding programs. We show that our algorithm significantly outperforms sequence-to-sequence model with attention baseline. The ability to synthesize a program from user intent (specification) is considered as one of the central problems in artificial intelligence BID9 ). Significant progress has been made recently in both program synthesis from examples (e.g. BID1 , BID22 , BID6 ) and program synthesis from descriptions (e.g. BID4 , BID28 , BID17 , BID18 ).Programming by example techniques such as Flash Fill BID11 ) and BlinkFill BID25 ) were developed to help users perform data transformation tasks using examples instead of writing programs. These methods rely on a small domain-specific language (DSL) and then develop algorithms to efficiently search the space of programs. Two shortcomings of these approaches are that DSL limits types of programs that can be synthesized, and that large engineering effort is needed to fine-tune such systems.Program synthesis from description has not been applied widely in practice yet. One of the challenges is that the natural language is very ambiguous, yet there are very strict requirements for the synthesized programs (see BID27 and BID23 for some discussion). In this paper we present Neural Program Search that learns from both description and examples and has high accuracy and speed to be applicable in practice.We specifically consider a problem of synthesizing programs from a short description and several input / output pairs. By combining description and sample tests we address both limitations of programming by example and natural language program inference. We propose LISP-inspired DSL that is capable of representing solutions to many simple problems similar to those given as data transformation homework assignments, but is rather concise, making it more tractable to search in the space of programs in this DSL.We propose a combination of two techniques -search in the programs space that is guided by a deep learning model. This way we can use the latest advances in natural language understanding with the precision of the search techniques. We use a Seq2Tree model BID0 ) that consists of a sequence encoder that reads the problem statement and a tree decoder augmented with attention that computes probabilities of each symbol in an AST tree node one node at a time. We then run a tree beam search that uses those probabilities to compute a number of most likely trees, and chooses one that is consistent with the given input/output pairs.To evaluate the proposed model we have created a partially synthetic dataset AlgoLISP consisting of problem statements, solutions in our DSL and tests. We show that search guided by deep learning models achieves significantly better results than either of the two techniques separately. We have presented an algorithm for program synthesis from textual specification and a sample of input / output pairs, that combines deep learning network for understanding language and general programming patterns with conventional search technique that allows to find correct program in discrete space which neural models struggle with. We presented a semi-synthetic dataset to empirically evaluate learning of program composition and usage of programing constructs. Our empirical results show improvement using combination of structured tree decoding and search over attentional sequence to sequence model.There remain some limitations, however. Our training data currently is semi-generated and contains only limited set of types of problems. It is prohibitively expensive to collect a human annotated set with large quantity of tasks per each problem type, so finding a way to learn from few examples per problem type is crucial. Additionally, in many practical use cases there will be no input / output examples, requiring interaction with the user to resolve ambiguity and improved techniques for structural output decoding in neural networks.",779,0.404,437,1.7826086956521738,"We present a Neural Program Search programs natural language description a small number input / output examples The algorithm combines methods Program Synthesis fields by designing defining efficient search algorithm guided a Seq2Tree model on it To evaluate the approach also present descriptions test examples corresponding programs We show our algorithm significantly sequenceto model attention baseline The ability a program user intent (specification considered artificial intelligence BID9 ). Significant progress recently both program synthesis from examples ( , descriptions.Programming by example techniques Flash Fill BID11 ) BlinkFill BID25 were users perform data transformation tasks examples instead writing These methods rely then develop algorithms efficiently search the space programs Two shortcomings these approaches DSL limits types programs synthesized that large engineering effortProgram synthesis from description has not applied widely practice yet One the natural language ambiguous yet very strict requirements the synthesized programs ( BID27 and some discussion In Neural Program Search that learns both description examples has be applicable practiceWe specifically consider synthesizing programs several input / output pairs By combining description sample tests we address both limitations programming by example and natural language program inference We propose LISP-inspired DSL that representing solutions similar given as data transformation homework assignments rather concise making search the space programs this DSL.We -search the programs space that guided This way the latest advances natural language understanding with the precision the search techniques We use a Seq2Tree model BID0 ) consists a sequence encoder reads the problem statement augmented attention that probabilities each symbol an AST tree node one node We then run a tree beam search those probabilities most likely trees chooses consistentTo evaluate created a partially synthetic dataset AlgoLISP consisting problem statements solutions in our DSL tests We show search guided achieves either separately We presented program synthesis from textual specification a sample input / output pairs that combines deep learning network for understanding language general programming patterns conventional search technique that find correct program discrete space which neural models struggle We presented learning program composition usage programing constructs Our empirical results improvement using combination structured tree decoding search over attentional sequence to sequence modelThere remain Our training data currently semigenerated contains only limited set types problems It collect a human annotated set with large quantity tasks per each problem type finding learn few examples per Additionally many practical use cases there no input / output examples requiring interaction resolve ambiguity improved techniques structural output decoding in",0.01,0.6980973669573614
"Generative adversarial training can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions, typically  neural networks. The discriminator set should be large enough to be able to uniquely identify the true distribution (discriminative), and also be small enough to go beyond memorizing samples (generalizable). In this paper, we show that a discriminator set is guaranteed to be discriminative whenever its linear span is dense in the set of bounded continuous functions. This is a very mild condition satisfied even by neural networks with a single neuron. Further, we develop generalization bounds between the learned distribution and true distribution under different evaluation metrics. When evaluated with neural distance, our bounds show that generalization is guaranteed as long as the discriminator set is small enough, regardless of the size of the generator or hypothesis set. When evaluated with KL divergence, our bound provides an explanation on the counter-intuitive behaviors of testing likelihood in GAN training. Our analysis sheds lights on understanding the practical performance of GANs. Generative adversarial networks (GANs) BID14 and their variants can be generally understood as minimizing certain moment matching loss defined by a set of discriminator functions. Mathematically, GANs minimize the integral probability metric (IPM) BID31 , that is, DISPLAYFORM0 whereμ m is the empirical measure of the observed data, and F and G are the sets of discriminators and generators, respectively.1. Wasserstain GAN (W-GAN) BID1 . F = Lip 1 (X) := {f : ||f || Lip ≤ 1}, corresponding to the Wasserstain-1 distance. 2. MMD-GAN BID27 BID13 BID25 . F is taken as the unit ball in a Reproducing Kernel Hilbert Space (RKHS), corresponding to the Maximum Mean Discrepency (MMD). 3. Energy-based GANs BID45 . F is taken as the set of continuous functions bounded between 0 and M for some constant M > 0, corresponding to the total variation distance BID1 .4. When the KL divergence is used as the evaluation metric, our bound (Corollary 3.5) suggests that the generator and discriminator sets have to be compatible in that the log density ratios of the generators and the true distributions should exist and be included inside the linear span of the discriminator set. The strong condition that log-density ratio should exist partially explains the counter-intuitive behavior of testing likelihood in flow GANs (e.g., BID11 BID15 . 5. We extend our analysis to study neural f -divergences that are the learning objective of f -GANs, and establish similar results on the discrimination and generalization properties of neural fdivergences; see Appedix B. Different from neural distance, a neural f -divergence is discriminative if linear span of its discriminators without the output activation function is dense in the bounded continuous function space. We studied the discrimination and generalization properties of GANs with parameterized discriminator class such as neural networks. A neural distance is guaranteed to be discriminative whenever the linear span of its discriminator set is dense in the bounded continuous function space. On the other hand, a neural divergence is discriminative whenever the linear span of features defined by the last linear layer of its discriminators is dense in the bounded continuous function space. We also provided generalization bounds for GANs in different evaluation metrics. In terms of neural distance, our bounds show that generalization is guaranteed as long as the discriminator set is small enough, regardless of the size of the generator or hypothesis set. This raises an interesting discriminationgeneralization balance in GANs. Fortunately, several GAN methods in practice already choose their discriminator set at the sweet point, where both the discrimination and generalization hold. Finally, our generalization bound in KL divergence provides an explanation on the counter-intuitive behaviors of testing likelihood in GAN training.There are several directions that we would like to explore in the future. First of all, in this paper, we do not talk about methods to compute the neural distance/divergence. This is typically a non-concave maximization problem and is extremely difficult to solve. Many methods have been proposed to solve this kind of minimax problems, but both stable training methods and theoretical analysis of these algorithms are still missing. Secondly, our generalization bound depends purely on the discriminator set. It is possible to obtain sharper bounds by incorporating structural information from the generator set. Finally, we would like to extend our analysis to conditional GANs (see, e.g., BID30",925,0.585,583,1.5866209262435678,"Generative adversarial training generally minimizing certain moment matching loss defined The discriminator set should large uniquely the true distribution also go memorizing samplesgeneralizable In a discriminator set guaranteed whenever its linear span dense in bounded continuous functions This a very mild condition satisfied even neural networks Further develop generalization bounds between the learned distribution true distribution under different evaluation metrics When evaluated neural distance our bounds show generalization guaranteed as regardless hypothesis set When evaluated KL divergence our bound provides an explanation on the counter-intuitive behaviors testing likelihood GAN training Our analysis sheds lights understanding the practical performance GANs Generative adversarial networks (GANs) BID14 their variants generally minimizing certain moment matching loss defined Mathematically GANs minimize the integral probability metricIPM) BID31 , that is, DISPLAYFORM0 whereμ m the empirical measure F and the sets discriminators generators. Wasserstain GAN . F = Lip 1X {f : ||f || Lip ≤ corresponding the Wasserstain-1 distance 2 MMD-GAN BID27 BID13 BID25 . F is taken the unit ball a Reproducing Kernel Hilbert Space (RKHS corresponding the Maximum Mean Discrepency 3 Energy-based GANs BID45 . F is taken the set continuous functions bounded between M for some constant M > corresponding the total variation distance BID1 .4 When the KL divergence used the evaluation metric our bound (Corollary suggests the generator and discriminator sets compatible the log density ratios the true distributions should exist and included inside the linear span The strong condition log-density ratio should exist partially testing likelihood flow GANs BID11 BID15 . 5 We extend our analysis study neural f -divergences the learning objective f -GANs establish similar results the discrimination and generalization properties; Appedix B. Different neural distance a neural f -divergence discriminative if linear span its discriminators without the output activation function dense the bounded continuous function space We studied the discrimination and generalization properties GANs parameterized discriminator class such neural networks A neural distance guaranteed whenever the linear span its discriminator set dense in the bounded continuous function space On a neural divergence discriminative whenever the linear span features defined the last linear layer its discriminators dense the bounded continuous function space We also provided generalization bounds GANs different evaluation metrics In terms neural distance our bounds show generalization guaranteed as the discriminator set regardless hypothesis set This raises an interesting discriminationgeneralization balance GANs Fortunately several GAN methods in already choose their discriminator set at the sweet point hold Finally our generalization bound in KL divergence provides on testing likelihood GAN trainingThere several directions would First in this paper do talk methods compute the neural distance/divergence This typically a non-concave maximization problem and extremely Many methods this kind minimax problems both stable training methods theoretical analysis Secondly our generalization bound depends purely the discriminator set It obtain sharper bounds incorporating structural information the generator set Finally would extend our analysis conditional GANs, BID30",0.01,0.19873774980137626
"Normalization layers are a staple in state-of-the-art deep neural network architectures. They are widely believed to stabilize training, enable higher learning rate, accelerate convergence and improve generalization, though the reason for their effectiveness is still an active research topic. In this work, we challenge the commonly-held beliefs by showing that none of the perceived benefits is unique to normalization. Specifically, we propose fixed-update initialization (Fixup), an initialization motivated by solving the exploding and vanishing gradient problem at the beginning of training via properly rescaling a standard initialization. We find training residual networks with Fixup to be as stable as training with normalization -- even for networks with 10,000 layers. Furthermore, with proper regularization, Fixup enables residual networks without normalization to achieve state-of-the-art performance in image classification and machine translation. Artificial intelligence applications have witnessed major advances in recent years. At the core of this revolution is the development of novel neural network models and their training techniques. For example, since the landmark work of BID13 , most of the state-of-the-art image recognition systems are built upon a deep stack of network blocks consisting of convolutional layers and additive skip connections, with some normalization mechanism (e.g., batch normalization BID16 ) to facilitate training and generalization. Besides image classification, various normalization techniques (Ulyanov et al., 2016; BID0 BID26 Wu & He, 2018) have been found essential to achieving good performance on other tasks, such as machine translation (Vaswani et al., 2017) and generative modeling (Zhu et al., 2017) . They are widely believed to have multiple benefits for training very deep neural networks, including stabilizing learning, enabling higher learning rate, accelerating convergence, and improving generalization.• Training without normalization. We propose Fixup, a method that rescales the standard initialization of residual branches by adjusting for the network architecture. Fixup enables training very deep residual networks stably at maximal learning rate without normalization. In the remaining of this paper, we first analyze the exploding gradient problem of residual networks at initialization in Section 2. To solve this problem, we develop Fixup in Section 3. In Section 4 we quantify the properties of Fixup and compare it against state-of-the-art normalization methods on real world benchmarks. A comparison with related work is presented in Section 5. In this work, we study how to train a deep residual network reliably without normalization. Our theory in Section 2 suggests that the exploding gradient problem at initialization in a positively homogeneous network such as ResNet is directly linked to the blowup of logits. In Section 3 we develop Fixup initialization to ensure the whole network as well as each residual branch gets updates of proper scale, based on a top-down analysis. Extensive experiments on real world datasets demonstrate that Fixup matches normalization techniques in training deep residual networks, and achieves state-of-the-art test performance with proper regularization.Our work opens up new possibilities for both theory and applications. Can we analyze the training dynamics of Fixup, which may potentially be simpler than analyzing models with batch normalization is? Could we apply or extend the initialization scheme to other applications of deep learning? It would also be very interesting to understand the regularization benefits of various normalization methods, and to develop better regularizers to further improve the test performance of Fixup. Proof of Theorem 1. We use f i→j to denote the composition DISPLAYFORM0 . Note that z is p.h. with respect to the input of each network block, i.e. f i→L ((1 + )x i−1 ) = (1 + )f i→L (x i−1 ) for > −1. This allows us to compute the gradient of the cross-entropy loss with respect to the scaling factor at = 0 as DISPLAYFORM1 Since the gradient L 2 norm ∂ /∂xi−1 must be greater than the directional derivative DISPLAYFORM2 xi−1 ), y), defining = t / xi−1 we have DISPLAYFORM3",819,0.469,452,1.8119469026548674,"Normalization layers a staple state deep neural They widely stabilize training enable higher learning rate accelerate convergence though the reason an active research topic In this work challenge by showing none is unique normalization Specifically propose fixed-update initializationFixup motivated solving the exploding and vanishing gradient problem at training via properly rescaling a standard initialization We find training residual networks with Fixup as stable training with normalization -- networks Furthermore with proper regularization Fixup enables residual networks without normalization achieve state image classification and machine translation Artificial intelligence applications witnessed At this revolution novel neural network models their training techniques For example since the landmark work BID13 , most state- image a deep stack network blocks consisting additive skip connections some normalization mechanism training Besides image classification various normalization techniques 2016 BID0 BID26 Wu He found essential achieving good performance other tasks machine translationVaswani generative modeling . They widely multiple benefits training very deep neural networks stabilizing learning enabling accelerating convergence generalization.• Training without normalization We propose Fixup rescales the standard initialization residual branches adjusting for the network architecture Fixup enables training very deep residual networks stably at maximal learning rate without normalization In the remaining of first analyze the exploding gradient problem residual networks at initialization Section To solve develop Fixup in Section In Section we quantify Fixup compare state normalization on real benchmarks A comparison with related work Section In this work study train a deep residual network reliably without normalization Our theory in Section suggests the exploding gradient problem at initialization in a positively homogeneous network such ResNet directly the blowup logits In Section we develop Fixup initialization to the whole network as each residual branch updates of proper scale based Extensive experiments real world datasets demonstrate Fixup matches normalization techniques training deep residual networks achieves state test proper regularizationOur work opens both theory applications Can analyze the training dynamics Fixup may potentially simpler analyzing models batch normalization is Could apply or extend the initialization scheme of It would also very understand the regularization benefits various normalization methods develop better regularizers further the test performance Fixup Proof Theorem We use f i→j denote the composition DISPLAYFORM0 Note z is p.h with respect the input each network block (( )x for > −1 This allows compute the gradient with at = as DISPLAYFORM1 Since the gradient L 2 norm �� /��xi−1 must directional derivative ), y), defining we",0.01,0.7728485407735411
"Designing a metric manually for unsupervised sequence generation tasks, such as text generation, is essentially difficult. In a such situation, learning a metric of a sequence from data is one possible solution. The previous study, SeqGAN, proposed the framework for unsupervised sequence generation, in which a metric is learned from data, and a generator is optimized with regard to the learned metric with policy gradient, inspired by generative adversarial nets (GANs) and reinforcement learning. In this paper, we make two proposals to learn better metric than SeqGAN's: partial reward function and expert-based reward function training. The partial reward function is a reward function for a partial sequence of a certain length. SeqGAN employs a reward function for completed sequence only. By combining long-scale and short-scale partial reward functions, we expect a learned metric to be able to evaluate a partial correctness as well as a coherence of a sequence, as a whole. In expert-based reward function training, a reward function is trained to discriminate between an expert (or true) sequence and a fake sequence that is produced by editing an expert sequence. Expert-based reward function training is not a kind of GAN frameworks. This makes the optimization of the generator easier. We examine the effect of the partial reward function and expert-based reward function training on synthetic data and real text data, and show improvements over SeqGAN and the model trained with MLE. Specifically, whereas SeqGAN gains 0.42 improvement of NLL over MLE on synthetic data, our best model gains 3.02 improvement, and whereas SeqGAN gains 0.029 improvement of BLEU over MLE, our best model gains 0.250 improvement. Generating sequential data is one of the main areas of research in machine learning. Recently, sequential generative model with recurrent neural networks (RNNs) have shown great success in several sequence generation tasks BID7 BID20 . The most common training method of RNNs is maximum log likelihood estimation (MLE). Although MLE provides stable training, a trained RNN generator suffers from the discrepancy of training mode and inference mode, called exposure bias BID3 . Exposure bias occurs because, at the inference, the generator predicts the next token given the tokens that the generator itself has generated so far, though the generator is trained to predict the next token given previous true tokens. To alleviate exposure bias, sequence training methods with reinforcement learning (RL) have been proposed BID17 . By using the methods of RL, the RNN generator can be optimized w.r.t. a task specific metric such as BLEU BID16 , rather than the log likelihood. The application of RL methods to sequence generation tasks is increasing importance recently BID23 BID14 . Throughout this paper, we use the term ""metric"" as a total reward for a sequence.If we have a good metric of a sequence, we can expect that a good sequence generator would be obtained by using a method of RL. However, as BID0 pointed out, it is generally difficult to manually specify a task specific metric for RL. It is especially difficult to manually design a proper metric for unsupervised sequence generation tasks, such as text generation or music generation (imagine how hard it is to manually design the metric of the naturalness of a sentence, or the beauty of music). One of the solutions for designing a metric for those tasks is to learn a metric from data. BID24 proposed SeqGAN, which a metric of sequence is learned from data, and a generator is optimized w.r.t. the metric. Inspired by generative adversarial nets (GANs) BID6 and RL, SeqGAN employs a discriminator which is trained to discriminate between a true sequence and a generated sequence, and a generator is trained with policy gradient BID21 by treating the discriminator as the reward function. Because SeqGAN learns a metric from data and optimizes a generator in RL manner, we can see SeqGAN as the study of inverse reinforcement learning (IRL).In this study, we also consider unsupervised sequence generation as a task of IRL, and we aim to learn the better metric than SeqGAN's. We state two proposals for this purpose: partial reward function and expert-based reward function training.The partial reward function is the reward function for a partial sequence of a certain length. SeqGAN only uses a reward function for completed sequence. As a background of its proposal, we have an assumption that it is too much of a burden on a reward function employed in SeqGAN to evaluate a coherence of sequence as well as a partial correctness comprehensively. By employing the partial reward function, we aim to make a metric that can evaluate both a coherence and a partial correctness of a sequence. Empirically, we show that the partial reward function can correctly evaluate a partial mistake of a sequence which a reward function for a completed sequence can not evaluate.In expert-based reward function training, we train the reward function without the generator's samples. The reward function is trained to discriminate between an expert sequence and a fake sequence that is produced by editing expert one. Unlike SeqGAN, expert-based reward function is not a kind of GAN frameworks. Although GAN framework has an advantage that a reward function is simultaneously trained with a generator's performance, the training of the generator frequently fails because of an instability of the GAN framework. Expert-based reward function training prioritizes executing stable training of the generator over taking an advantage of GAN framework.We conducted experiments based on synthetic data and real text data to investigate the effectiveness of partial reward function and expert-based reward function training. As an evaluation method, we employ oracle negative log likelihood (NLL) in synthetic data, and BLEU BID16 in text data. We show that the models with our proposals outperform SeqGAN in both experiments. Specifically, whereas SeqGAN gains 0.42 improvement of NLL over MLE on synthetic data, our best model gains 3.02 improvement, and whereas SeqGAN gains 0.029 improvement of BLEU over MLE, our best model gains 0.250 improvement. We stated two proposals for a learning better metric: partial reward function and expert-based reward function training. We showed that the partial reward function returns an accurate reward for a partial sequence, and benefits sequence generation training. By using partial functions of different scales, one can compose a reward function that can evaluate both coherence and the partial correctness of a sequence. We also showed that expert-based reward function training is effective compared to adversarial training. We demonstrated that a generator is well optimized w.r.t. the metric that is trained with expert-based reward function training.The balance of short-term reward and long-term reward is a difficult problem. When prioritizing short-term reward too much, the generator produces a sequence that is partially correct but not coherent, and vice versa. In our study, this balance is tuned by the hyperparameter α Di . Unfortunately, the tuning of α Di is difficult. Even validating the goodness of selected α Di is difficult because there is usually no true metric for the generated sequence (except for the special case such as oracle test). Therefore, we have to validate the selected α Di by seeing the generated sentences. This is a fundamental problem of IRL. IRL learns a reward from expert, but a goodness of a learned reward function can be evaluated by a behavior of policy, and an evaluation of a learned policy is done by a human (with a bias), or a surrogate manually designed metric. One practical strategy to balance a partial correctness and a coherence is to separate a generation process into two stages. We first produce a coherent sequence by using the generator learned with only long-term reward, and then use a short-term reward function to make a modification to partial mistakes of the produced sequence.As the generator is improving, it is desirable to update the reward function to a more strict one. A GAN framework is a good method in this sense, but as experimental results showed, it is difficult to train. One idea to update the reward function is to decrease a probability to change a token of expert in expert-based reward function training. If we decrease a probability, the reward function would become more strict. By decreasing a probability as the generator is improving, the generator might generate a more sophisticated sequence.We believe that our proposals in this paper can be applied to GAN-based sequence generation. The partial reward function can be applied to GAN-based text generator directly. In fact, BID18 used similar technique in the image generation with GAN. Expert-based reward function might make GAN training stable. The edited expert sequences have a lot of variety. There is a technique that uses the past generator's samples to ensure the variety of the samples for the training of the discriminator to stabilize GAN training, as we can see in BID18 , and the edited expert can be also applied for this purpose.A GENERATED SENTENCES Model name Generated sentence MLE us light sweet crude futures to enter the [crossover] segment ,"" said nick ross , daimlerchrysler and damaged property finance the reserve chairman united said the us sought bankruptcy protection in the us on monday , kill bill: volume 2 his previous two companies holes has been picking up in the past year . ""we are bringing a small third but the uk has been on hold of many of users to get their hands at least . icstis , ""if you work i were struggling . ""people's spending offer have to bring across the uk opened a 5bn) earlier "" the intel researchers have leveraged the company's ""most affordable media use , reaching the firm , the operating system unless voluntary fit will fund the animation prices , should remain also in novel ways that p2p is a human according to the stability pact to rises and confirm that thrives in succession . tourism said this tactic of creating vedomosti newspaper said mr irish and mark all the caribbean said the ability of the $2 , amid allegations of the virus-fighting program , updated monthly or just also brings me that had been compressed into recession -are a PG L(SeqGAN) these are pooled in london , draw about its future while it is the richest part of the digital images identity theft are being people to jump in sound to the neat business which can walk along at the show a apple of financial mail messages that has already has got given the chicago data , or or their semi-conductor after leaving weather , video games in over the third . stuff has telling parliament: level time checking for gadget there are combining automatic syncing worldwide , and you will give people the state pension age of of large and just been wiped out . the federal reserve is struggling with treasury and organisations have said you play online in a hydroelectric-power generator the airline said in the election , you would then its broadcasting attraction ,"" said research , a number of stagnation and more than 1 million copies of the personal firewalls ,"" he said . ""it is us lawyers claimed that the mac mini and is being piloted by the royal national hi-tech crime unit yuganskneftegas (yugansk) ""it will be disruptive to music , employment for mobile firm , almost three-quarters of job creation , the airline PG L exp ""a literate and qualified turkish population ,"" insisted the year to meet he has been security to be . however the game on be done in the us in the us -it will play games on the net , the success is set to the company's and court ,"" he said , it plans the market by the uk an ex-chief financial advice , that is the biggest category said a problem in europe was not enough . people yukos claims that it would the banning of a market . it will make up of work recently about security there were originally had to be seen in the way . it were also falling demand at 20% of the however , which will continue to make 50gb of high-quality data , which is one of its investment can come the game maker you can be done in the year . ""skype's success at spreading on the launch of sony's russian newspapers has been done -its own fuelled by lower prices than up to 100% . ""we will be mr ghosn will devote 40% of the directive will put up to google's funds . but on the network is PG S exp they would retaliate by seeking injunctions in the company , said they had been seen as they will be used they will be able to add to be used to spot in the world's largest car maker , said they they will be able to be recycled at 1 . 4% in october . 3bn . however , he said however , prices fell as part of the service . they need to invest in the cost of more than however , he said he would be to raise awareness of the 14 . but it is part of the this is likely to be seen in the us government , you go from the deal . but he said however , the company , which is part of the euro last week after new york times on the mobile they will be able to prevent conflicts to take their office . but they are looking for bargains , which more than 1 . 4% in the company , which is part of the industry will be able to invest the deal has been seen as they will be able to prevent conflicts . but they had been sidelined in PG SL exp (α S = 0.3) at a mere £20 , metal slug 3 is as cheap , but it is not the second time when the global entertainment industry was more than two to the uk exported , according to the uk-based journal screen that it is not the firm of england is expected to go on a broadband connection , with a single threat according to figures to come to meet , it said it would also reduce its customers , according to prevail if the end of the year , microsoft , which is expected by to $4 . 35bn , said it two of the most important costs . "" spanish , it would be failed to do a new record for it is expected to make an advisor to work , said it would allow broadband connections by the trading national users navigated around the dollar of 572 ,900 points to build the risks , and it is so far , it is not about stealing to the growing efforts in new york in the south following an apple ipod , ""it's for the most important for us crude oil company in early february , according to the report . at PG SL exp (α S = 1.0) according to the report , the company has not been being announced it will go from the decision to discuss one of the two companies will be able to go with other digital entertainment , with other companies like the it will be able to be part of its efforts . ""we're on the outlook for its core businesses , ""we want to go on the technology ,"" he said . ""we're in december , in a europe -on yukos has been made in december to graphics out of its efforts in 2005 , and paramount will go for their aim is to launch a new rental subscription service , this proves , the company will be able to more than 50% of the economy is part of its efforts to transfer files as a threat of the russian meanwhile , the decision for bt is available in december , the largest us giant earned $630m (£481 . 5m) the company announced it will see the study of the decision for digital images and technology from two companies , people will have to think of the report that it has been working with other carmakers . 5bn in january",3129,1.643,1789,1.7490217998882056,"Designing metric manually unsupervised sequence generation tasks essentially difficult a such situation learning a metric a sequence from data The previous study SeqGAN proposed the framework a metric learned a generator optimized regard with policy gradient inspired make learn better metric than SeqGAN's: partial reward function expert-based reward function training The partial reward function SeqGAN employs a reward function completed sequence only By combining long-scale and short-scale partial reward functions expect a learned metric evaluate a partial correctness as expert-based reward function training discriminate an expert (or true) sequence produced editing Expert-based reward function training a kind GAN frameworks This makes the optimization the generator easier We examine the partial reward function expert-based reward function training synthetic data real text data improvements SeqGAN trained MLE Specifically whereas SeqGAN gains 0.42 improvement NLL MLE on synthetic data our best model whereas BLEU Generating sequential data Recently sequential generative model with several sequence BID7 BID20 . RNNs maximum log likelihood estimation Although MLE provides stable training a trained RNN generator suffers the discrepancy inference mode called exposure bias BID3 Exposure bias occurs, the inference, the generator predicts the next token given itself so though trained previous true tokens To alleviate exposure bias sequence training methods with reinforcement learningRL BID17 . By using RL optimized a task specific metric BLEU BID16 rather the log likelihood The application RL methods sequence generation tasks increasing importance recently BID23 . Throughout a total reward a sequenceIf expect obtained RL However BID0 generally difficult manually specify a task specific metric RL It especially manually design a proper metric unsupervised sequence generation tasks manually the naturalness One designing a metric for those tasks learn data BID24 proposed SeqGAN a metric sequence learned data a generator optimized w.r.t the metric Inspired generative adversarial nets (GANs) BID6 RL SeqGAN employs which a true sequence is with policy gradient BID21 by treating the reward function Because SeqGAN learns a metric a generator RL manner the study also consider aim better metric than We state two proposals this purpose partial reward function expert-based reward function training a partial sequence a certain length SeqGAN only a reward function completed sequence As a background of its proposal we an assumption too a reward function employed SeqGAN evaluate sequence as a partial correctness comprehensively By employing the partial reward function aim a metric evaluate both a coherence a partial correctness show the partial reward function correctly evaluate a partial mistake which a reward forIn expert-based reward function training without the generator's samples The reward function trained discriminate an expert sequence produced editing expert one Unlike SeqGAN, expert-based reward function a kind GAN frameworks Although GAN framework an advantage that a reward function simultaneously trained a generator's performance frequently an instability Expert-based reward function training prioritizes executing stable training of the generator taking an advantage GAN frameworkWe conducted experiments synthetic data real text data partial reward function and As an evaluation method employ oracle negative log likelihood synthetic data BLEU BID16 We show the models our proposals SeqGAN both experiments Specifically whereas SeqGAN gains 0.42 improvement NLL MLE on synthetic data our best model whereas BLEU We stated two proposals a learning better metric: partial reward function We showed the partial reward function returns an accurate reward benefits sequence generation training By using partial functions different scales compose a reward function evaluate both coherence the partial correctness We showed expert-based reward function training compared We demonstrated a generator the metric trained expert-based reward function trainingThe balance When prioritizing too the generator produces partially correct coherent our study this balance tuned α Di . Unfortunately the tuning α Di is Even validating the goodness selected α Di is usually no true metric the generated sequenceexcept such oracle test Therefore validate the selected α Di by seeing the generated sentences This IRL IRL learns a reward expert a goodness a learned reward function evaluated of policy an evaluation done (with a surrogate manually designed metric One practical strategy balance a partial correctness separate a generation process We first produce a coherent sequence by the generator learned only long-term reward a modification partial mistakesAs improving desirable update strict A GAN framework a good method in as experimental results train One idea update the reward function decrease a probability change of expert expert-based reward function training If decrease a probability the reward function would strict By decreasing a probability as the generator improving generateWe believe our proposals The partial reward function GAN-based text generator directly fact BID18 used similar technique the image generation with GAN Expert-based reward function might GAN training stable The edited expert sequences variety There a technique the past generator's samples ensure the variety for the training to stabilize GAN training BID18 , the edited expert can also appliedA GENERATED SENTENCES Model name Generated sentence MLE us light sweet crude futures to enter the [crossover] segment ,"" said nick ross daimlerchrysler damaged property finance the reserve chairman united said the us sought bankruptcy protection the us on kill bill: volume 2 his previous two companies holes has picking .we bringing a small third but the uk has on hold of many users at least . icstis , ""if work i were struggling .people's spending offer have bring across the uk opened a 5bn) earlier "" the intel researchers leveraged the company's ""most affordable media use , reaching the firm , the operating system unless voluntary fit will fund the animation prices , should remain also novel ways p2p is a human according the stability pact to rises confirm thrives succession . tourism said this tactic creating vedomosti newspaper said mr irish mark all the caribbean said the ability $ , amid allegations the virus-fighting program , updated monthly or just also brings me that had compressed recession -are PG L(SeqGAN these pooled london draw about its future while the richest part the digital images identity theft are people to jump sound the neat business which walk along the show a apple financial mail messages has got given the chicago data , or or their semi after leaving weather , video games over third . stuff has telling parliament level time checking gadget there combining automatic worldwide , give people the state pension age of large just been wiped the federal reserve struggling treasury organisations have you play online a hydroelectric-power generator the airline said the election , you then its broadcasting attraction research , a number stagnation more than 1 million copies the personal firewallsit us lawyers claimed the mac mini is the royal national hi-tech crime unit yuganskneftegas ""it disruptive music , employment for mobile firm almost three airline PG L exp ""a literate and qualified turkish population insisted year to meet he security to be . however on be done the us in -it play games , the success set the company and court ,"" , it plans the market by an ex-chief financial advice that the biggest category said a problem was . people yukos claims the banning a market . it up of work recently about security there were originally had seen . it were also falling demand 20% however , will make 50gb , one its investment can come the game maker you done .skype's success at spreading on the launch sony's russian newspapers done -its own fuelled lower prices than .we mr ghosn will devote 40% the directive will put google's funds . but on the network PG S exp they retaliate seeking , said they seen as they will used they add be spot in they recycled 1 . 4% october . 3bn . however , however prices fell part . they need invest the cost more however , he he to raise awareness 14 . but part the this likely seen the us government , you go the deal . but however , , part the euro last after new york times on the mobile they prevent conflicts to take their office . but looking bargains , more 1 . 4% the company , part will the deal has seen they prevent conflicts . but sidelined PG SL exp (α S at mere £ , metal slug 3 is as , when the global entertainment industry more two the uk exported , according the uk-based journal screen that it the firm england is expected go a broadband connection a single threat according figures to meet , it reduce , prevail if end microsoft by $ . 35bn , said two of . spanish , it failed a new record it expected make an advisor work , said it allow broadband connections the trading national users navigated around the dollar of 572 ,900 points build the risks so , about stealing to the growing efforts new york the south following an apple ipod ""it for most for us crude oil company early february according at PG SL exp (α S according , the company being announced it go from the decision discuss one will other digital entertainment , the it part its effortswe on the outlook its core businesses , ""we go the technology ,""we december , in a europe -on yukos has made graphics out its efforts 2005 paramount will go their aim launch a new rental subscription service this proves , is part transfer files as a threat russian meanwhile the decision bt available the largest us giant earned630481 . 5m) the company see the study the decision digital images technology , people will think that other carmakers 5bn january",0.02,0.6125209074631667
"One of the most successful techniques in generative models has been decomposing a complicated generation task into a series of simpler generation tasks.   For example, generating an image at a low resolution and then learning to refine that into a high resolution image often improves results substantially.   Here we explore a novel strategy for decomposing generation for complicated objects in which we first generate latent variables which describe a subset of the observed variables, and then map from these latent variables to the observed space.   We show that this allows us to achieve decoupled training of complicated generative models and present both theoretical and experimental results supporting the benefit of such an approach.   Learning useful intermediate representations in a hierarchical manner has been a driving factor in the recent success of deep learning BID11 . When ample amounts of labelled data are available, supervised learning methods are successful in learning useful intermediate representations BID20 BID14 ). However, the task is significantly more challenging in the context of unsupervised learning. One such approach to unsupervised learning is to learn a generative model of high-dimensional observed variables with low-dimensional latent variables, such that the latent variables capture the salient features of the data, which could then be used for other upstream tasks.Recent work by BID22 argues why hierarchical latent variables models are often not able to take advantage of the hierarchy, and only the lowest-level latent variables learn any useful representations. We posit that this is possibly because the vanilla hierarchical latent variable structure by itself only adds a very weak prior (that of devoting more processing to higher-level latent variables). When parameterizing the conditional distributions with powerful deep neural networks, this could admit a local optima in which all factors of variation are sub-optimally explained by the lowest-level latent variable. Notably, this phenomenon was also common in supervised training of deep neural networks, before BID6 introduced batch normalization, which successfully disentangles the learning dynamics at each layer, as if each layer has an independent objective function.For example, the resolution-based hierarchy is well suited to images because lower resolution images capture some factors of variation (such as objects) but discards other factors of variation (such as texture and details), giving the low and high level models distinct responsibilities. However, this decomposition is a strong prior and may not work well or apply to other types of data (for example, it is not clear how it would apply to language or video). This motivates the need for an unsupervised method for learning hierarchical latent variables with a requisite but general prior to facilitate disentangled learning dynamics in each level.Our proposed approach, which we call Locally Disentangled Factors (LDF), has the following desired features:• Decoupled level-wise training objectives which significantly accelerate training.• A graphical model based on spatial locality which aids in credit assignment, and can be thought of as a generalization to resolution-based hierarchies.• Vastly reduced memory consumption which allows training generative models on large objects, such as videos, where this is known to be a prohibitive limitation.• Applicable to variable-length objects, such as videos and text.2 PROPOSED APPROACH We have proposed Locally Disentangled Factors (LDF), a powerful new approach to decomposing the training of generative models. We have shown that LDF is able to successfully generate joint distributions over complicated objects, even though the discriminators and gradient flow are entirely local within the hierarchy. We have also shown that this allows for decoupled training and improved ability to learn from small amounts of data from the joint distribution. While our method assumes a more general prior than resolution-hierarchy style approaches, it still leaves the decision of what the local factors would be on the practitioner. Finding methods that enjoy the same computational and sample-complexity benefits with fewer assumptions about the data is an interesting research direction.",763,0.332,429,1.7785547785547786,One the most successful techniques generative models decomposing a complicated generation task For example generating at learning refine into often improves results substantially Here explore a novel strategy decomposing generation for complicated objects which first generate latent variables which describe a subset the observed variables map from the observed space We show this allows achieve decoupled training complicated generative models present supporting the benefit Learning useful intermediate representations a hierarchical manner has a driving factor BID11 . When ample amounts labelled data supervised learning methods successful learning useful intermediate representations BID20 BID14 ). However the task significantly One such approach unsupervised learning learn high-dimensional observed variables with capture which could other upstream tasksRecent work BID22 argues why hierarchical latent variables models often able take the hierarchy learn any useful representations We posit this possibly the vanilla hierarchical latent variable structure by only adds very weak prior (that devoting more processing When parameterizing the conditional distributions with powerful deep neural networks this could admit a local optima all factors variation sub explained Notably this phenomenon common supervised training deep neural networks before BID6 introduced batch normalization successfully the learning dynamics at as if has an independent objective functionFor the resolution-based hierarchy well images because lower resolution images capture some factors variation objects) discards texture details giving the low and high level models distinct responsibilities However this decomposition strong prior and may work or apply data it language or video This motivates the need an unsupervised method learning hierarchical latent variables with requisite but general prior to facilitate disentangled learning dynamics each levelOur proposed approach Locally Disentangled Factors desired Decoupled level training objectives which significantly accelerate A graphical model based spatial locality which aids credit assignment can thought training generative models on large objects videos where this known Applicable variable-length objects videos text.2 PROPOSED APPROACH We decomposing the training We shown LDF successfully generate joint distributions complicated objects even the discriminators gradient flow entirely local within the hierarchy We also shown this allows decoupled training improved ability learn small amounts from the joint distribution While our method assumes more prior than resolution-hierarchy style approaches still leaves the decision the local factors would on the practitioner Finding methods enjoy the same computational and sample-complexity benefits with fewer assumptions an interesting research direction,0.01,0.6877683423664601
"Visual grounding of language is an active research field aiming at enriching text-based representations with visual information. In this paper, we propose a new way to leverage visual knowledge for sentence representations. Our approach transfers the structure of a visual representation space to the textual space by using two complementary sources of information: (1) the cluster information: the implicit knowledge that two sentences associated with the same visual content describe the same underlying reality and (2) the perceptual information contained within the structure of the visual space. We use a joint approach to encourage beneficial interactions during training between textual, perceptual, and cluster information. We demonstrate the quality of the learned representations on semantic relatedness, classification, and cross-modal retrieval tasks. Building linguistic vectors that represent semantics is a long-standing issue in Artificial Intelligence. Distributional Semantic Models BID36 BID41 are well-known recent efforts in this direction, making use of the distributional hypothesis BID16 on text corpora to learn word embeddings. At another granularity level, having high-quality general-purpose sentence representations is crucial for all models that encode sentences into semantic vectors, such as the ones used in machine translation BID0 or question answering BID42 . Moreover, encoding semantics of sentences is paramount because sentences describe relationships between objects and thus convey complex and high-level knowledge better than individual words, which mostly refer to a single concept BID38 .Relying only on text can lead to biased representations and unrealistic predictions (e.g., text-based models could predict that ""the sky is green"" BID1 ). Besides , it has been shown that human understanding of language is grounded in physical reality and perceptual experience (FincherKiefer, 2001 ). To overcome this limitation, one emerging approach is the visual grounding of language, which consists of leveraging visual information, usually from images, to enhance word representations. Two methods showing substantial improvements have emerged: (1) the sequential technique combines textual and visual representations that were separately learned BID3 BID44 , and (2) the joint method learns a common multimodal representation from multiple sources simultaneously BID29 . In the case of words, the latter has proven to produce representations that perform better on intrinsic and downstream tasks.While there exist numerous approaches to learning sentence representations from text corpora only, and to learning multimodal word embeddings, the problem of the visual grounding of sentences is quite new to the research community. To the best of our knowledge, the only work in the field is BID26 . The authors propose a sequential model: linguistic vectors, learned from a purely textual corpus, are concatenated with grounded vectors, which were independently learned from a captioning dataset. However, the two sources are considered separately, which might prevent beneficial interactions between textual and visual modalities during training.We propose a joint model to learn multimodal sentence representations, based on the assumption that the meaning of a sentence is simultaneously grounded in its textual and visual contexts. In our case, the textual context of a sentence consists of adjacent sentences in a text corpus. Within a distinct dataset, the visual context is learned from a paired video and its associated captions. Indeed, we propose to use videos instead of images because of their temporal aspect, since sentences often describe actions grounded in time. The key challenge is to capture visual information. Usually, to transfer information from the visual space to the textual one, one space is projected onto the other BID26 BID29 . However, as pointed out by BID9 , projections are not sufficient to transfer neighborhood structure between modalities. In our work, we rather propose to exploit the visual space by preserving the overall structure, i.e. conserving the similarities between related elements across spaces. More precisely, we take visual context into account by distinguishing two types of complementary information sources. First, the cluster information , which consists in the implicit knowledge that sentences associated with the same video refer to the same underlying reality. Second, the perceptual information , which is the high-level information extracted from a video using a pre-trained CNN.Regarding these considerations, we formulate three Research Questions (RQ):• RQ1: Is perceptual information useful to improve sentence representations?• RQ2: Are cluster and perceptual information complementary, and does their combination compete with previous models based on projections between visual and textual spaces?• RQ3: Is a joint approach better suited than a sequential one regarding the multimodal acquisition of textual and visual knowledge?Our contribution is threefold: (1) We propose a joint multimodal framework for learning grounded sentence representations; (2) We show that cluster and perceptual information are complementary sources of information; (3) To the best of our knowledge, obtained results achieve state-of-the-art performances on multimodal sentence representations. In this paper, we proposed a joint multimodal model to learn sentence representations and our learned grounded sentence embeddings show state-of-the-art performances. Besides, our main findings are the following: (1) Both perceptual and cluster information are useful to learn sentence representations, in a complementary way. (2) Preserving the structure of the visual space, by modeling textual similarities on visual ones, outperforms a strategy based on projecting one space into the other. (3) A joint approach is more appropriate than a sequential method to learn multimodal representation for sentences. As future work, we would investigate the contribution of the temporal knowledge contained in videos for sentence grounding.",1070,0.554,607,1.7627677100494235,"Visual grounding language an active research field aiming enriching text-based representations with In this paper leverage visual knowledge sentence representations Our approach transfers the structure a visual representation space the textual space by two complementary sources cluster information: the implicit knowledge two sentences associated describe contained We use a joint approach encourage beneficial interactions during training between textual, perceptual, and cluster information We demonstrate the quality the learned representations on semantic relatedness classification Building linguistic vectors that represent semantics Artificial Intelligence Distributional Semantic Models BID36 BID41 are well-known recent efforts this direction making the distributional hypothesis BID16 on text corpora learn At another granularity level having high-quality general-purpose sentence representations crucial all models encode sentences into semantic vectors machine translation BID0 or question answering BID42 Moreover encoding semantics sentences paramount because sentences describe relationships thus convey better individual words mostly refer BID38 .Relying text can biased representations unrealistic predictions, text-based models could that ""the sky green"" BID1 Besides , shown human understanding language grounded physical reality perceptual experienceFincherKiefer To overcome one emerging approach the visual grounding language consists leveraging usually images enhance word representations Two methods showing substantial improvements have emerged combines textual and visual representations that were separately learned BID3 BID44 , learns simultaneously BID29 In words latter proven produce representations perform intrinsic and downstream tasksWhile exist numerous approaches learning sentence representations text corpora only and to learning the visual grounding quite new to To the only work is BID26 . The authors propose a sequential model: linguistic vectors learned a purely textual corpus grounded vectors were independently a captioning dataset However the two sources are considered separately might prevent beneficial interactions textual and visual modalities during trainingWe propose a joint model learn multimodal sentence representations the meaning simultaneously grounded In our case the textual context consists adjacent sentences a text corpus Within a distinct dataset the visual context learned a paired video and Indeed we propose videos instead because their temporal aspect sentences describe actions grounded The key challenge capture visual information Usually to transfer information the visual space textual one space projected the other BID26 BID29 . However as pointed BID9 , projections sufficient transfer neighborhood structure between modalities In our work rather propose exploit the visual space preserving conserving the similarities related elements across spaces More precisely take visual context by distinguishing complementary information sources First, the cluster information , consists in the implicit knowledge sentences associated the same video refer the same underlying reality Second perceptual information , extracted using a pre-trained CNN.Regarding these considerations formulate three Research Questions useful improve cluster and perceptual information complementary, their combination compete previous models based projections between a joint approach better regarding textual and visual knowledge?Our contribution threefold learning grounded sentence representations show complementary sources To obtained results achieve state performances In this paper proposed learn sentence representations our learned grounded sentence embeddings show state performances Besides our main findings Both perceptual and cluster information useful learn sentence representations in a complementary way (2 Preserving the structure the visual space modeling textual similarities on visual ones outperforms a strategy projecting one space (3) A joint approach more a sequential method learn multimodal representation for sentences As future work, we would investigate the contribution the temporal knowledge contained videos for sentence grounding",0.01,0.647544278851488