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--- /dev/null +++ b/parse/train/BJgqQ6NYvB/images/d70f3138595d7ee2a1719b713d86d53da07cd9c555245e286159689880f1dc4a.jpg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8bb7a8c9cdded081b0cef84b39f2cea2f6c2d13be311e0588bb377cdb9164e2f +size 13656 diff --git a/parse/train/BJh6Ztuxl/BJh6Ztuxl.md b/parse/train/BJh6Ztuxl/BJh6Ztuxl.md new file mode 100644 index 0000000000000000000000000000000000000000..044cf11c0a515606bc59b5d72fd9932b35143455 --- /dev/null +++ b/parse/train/BJh6Ztuxl/BJh6Ztuxl.md @@ -0,0 +1,316 @@ +# FINE-GRAINED ANALYSIS OF SENTENCE EMBEDDINGS USING AUXILIARY PREDICTION TASKS + +Yossi Adi $^ { 1 , 2 }$ , Einat Kermany2, Yonatan Belinkov3, Ofer Lavi2, Yoav Goldberg1 + +1Bar-Ilan University, Ramat-Gan, Israel +{yoav.goldberg, yossiadidrum}@gmail.com +2IBM Haifa Research Lab, Haifa, Israel +{einatke, oferl}@il.ibm.com +3MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA, USA belinkov@mit.edu + +# ABSTRACT + +There is a lot of research interest in encoding variable length sentences into fixed length vectors, in a way that preserves the sentence meanings. Two common methods include representations based on averaging word vectors, and representations based on the hidden states of recurrent neural networks such as LSTMs. The sentence vectors are used as features for subsequent machine learning tasks or for pre-training in the context of deep learning. However, not much is known about the properties that are encoded in these sentence representations and about the language information they capture. + +We propose a framework that facilitates better understanding of the encoded representations. We define prediction tasks around isolated aspects of sentence structure (namely sentence length, word content, and word order), and score representations by the ability to train a classifier to solve each prediction task when using the representation as input. We demonstrate the potential contribution of the approach by analyzing different sentence representation mechanisms. The analysis sheds light on the relative strengths of different sentence embedding methods with respect to these low level prediction tasks, and on the effect of the encoded vector’s dimensionality on the resulting representations. + +# 1 INTRODUCTION + +While sentence embeddings or sentence representations play a central role in recent deep learning approaches to NLP, little is known about the information that is captured by different sentence embedding learning mechanisms. We propose a methodology facilitating fine-grained measurement of some of the information encoded in sentence embeddings, as well as performing fine-grained comparison of different sentence embedding methods. + +In sentence embeddings, sentences, which are variable-length sequences of discrete symbols, are encoded into fixed length continuous vectors that are then used for further prediction tasks. A simple and common approach is producing word-level vectors using, e.g., word2vec (Mikolov et al., 2013a;b), and summing or averaging the vectors of the words participating in the sentence. This continuous-bag-of-words (CBOW) approach disregards the word order in the sentence.1 + +Another approach is the encoder-decoder architecture, producing models also known as sequenceto-sequence models (Sutskever et al., 2014; Cho et al., 2014; Bahdanau et al., 2014, inter alia). In this architecture, an encoder network (e.g. an LSTM) is used to produce a vector representation of the sentence, which is then fed as input into a decoder network that uses it to perform some prediction task (e.g. recreate the sentence, or produce a translation of it). The encoder and decoder networks are trained jointly in order to perform the final task. + +Some systems (for example in machine translation) train the system end-to-end, and use the trained system for prediction (Bahdanau et al., 2014). Such systems do not generally care about the encoded vectors, which are used merely as intermediate values. However, another common case is to train an encoder-decoder network and then throw away the decoder and use the trained encoder as a general mechanism for obtaining sentence representations. For example, an encoder-decoder network can be trained as an auto-encoder, where the encoder creates a vector representation, and the decoder attempts to recreate the original sentence (Li et al., 2015). Similarly, Kiros et al. (2015) train a network to encode a sentence such that the decoder can recreate its neighboring sentences in the text. Such networks do not require specially labeled data, and can be trained on large amounts of unannotated text. As the decoder needs information about the sentence in order to perform well, it is clear that the encoded vectors capture a non-trivial amount of information about the sentence, making the encoder appealing to use as a general purpose, stand-alone sentence encoding mechanism. The sentence encodings can then be used as input for other prediction tasks for which less training data is available (Dai & Le, 2015). In this work we focus on these “general purpose” sentence encodings. + +The resulting sentence representations are opaque, and there is currently no good way of comparing different representations short of using them as input for different high-level semantic tasks (e.g. sentiment classification, entailment recognition, document retrieval, question answering, sentence similarity, etc.) and measuring how well they perform on these tasks. This is the approach taken by Li et al. (2015), Hill et al. (2016) and Kiros et al. (2015). This method of comparing sentence embeddings leaves a lot to be desired: the comparison is at a very coarse-grained level, does not tell us much about the kind of information that is encoded in the representation, and does not help us form generalizable conclusions. + +Our Contribution We take a first step towards opening the black box of vector embeddings for sentences. We propose a methodology that facilitates comparing sentence embeddings on a much finer-grained level, and demonstrate its use by analyzing and comparing different sentence representations. We analyze sentence representation methods that are based on LSTM auto-encoders and the simple CBOW representation produced by averaging word2vec word embeddings. For each of CBOW and LSTM auto-encoder, we compare different numbers of dimensions, exploring the effect of the dimensionality on the resulting representation. We also provide some comparison to the skip-thought embeddings of Kiros et al. (2015). + +In this work, we focus on what are arguably the three most basic characteristics of a sequence: its length, the items within it, and their order. We investigate different sentence representations based on the capacity to which they encode these aspects. Our analysis of these low-level properties leads to interesting, actionable insights, exposing relative strengths and weaknesses of the different representations. + +Limitations Focusing on low-level sentence properties also has limitations: The tasks focus on measuring the preservation of surface aspects of the sentence and do not measure syntactic and semantic generalization abilities; the tasks are not directly related to any specific downstream application (although the properties we test are important factors in many tasks – knowing that a model is good at predicting length and word order is likely advantageous for syntactic parsing, while models that excel at word content are good for text classification tasks). Dealing with these limitations requires a complementary set of auxiliary tasks, which is outside the scope of this study and is left for future work. + +The study also suffers from the general limitations of empirical work: we do not prove general theorems but rather measure behaviors on several data points and attempt to draw conclusions from these measurements. There is always the risk that our conclusions only hold for the datasets on which we measured, and will not generalize. However, we do consider our large sample of sentences from Wikipedia to be representative of the English language, at least in terms of the three basic sentence properties that we study. + +Summary of Findings Our analysis reveals the following insights regarding the different sentence embedding methods: + +• Sentence representations based on averaged word vectors are surprisingly effective, and encode a non-trivial amount of information regarding sentence length. The information they contain can also be used to reconstruct a non-trivial amount of the original word order in a probabilistic manner (due to regularities in the natural language data). + +• LSTM auto-encoders are very effective at encoding word order and word content. • Increasing the number of dimensions benefits some tasks more than others. • Adding more hidden units sometimes degrades the encoders’ ability to encode word content. This degradation is not correlated with the BLEU scores of the decoder, suggesting that BLEU over the decoder output is sub-optimal for evaluating the encoders’ quality. • LSTM encoders trained as auto-encoders do not rely on ordering patterns in the training sentences when encoding novel sentences, while the skip-thought encoders do rely on such patterns. + +# 2 RELATED WORK + +Word-level distributed representations have been analyzed rather extensively, both empirically and theoretically, for example by Baroni et al. (2014), Levy & Goldberg (2014) and Levy et al. (2015). In contrast, the analysis of sentence-level representations has been much more limited. Commonly used approaches is to either compare the performance of the sentence embeddings on down-stream tasks (Hill et al., 2016), or to analyze models, specifically trained for predefined task (Schmaltz et al., 2016; Sutskever et al., 2011). + +While the resulting analysis reveals differences in performance of different models, it does not adequately explain what kind of linguistic properties of the sentence they capture. Other studies analyze the hidden units learned by neural networks when training a sentence representation model (Elman, 1991; Karpathy et al., 2015; Kad´ ar et al., 2016). This approach often associates certain linguistic ´ aspects with certain hidden units. Kad´ ar et al. (2016) propose a methodology for quantifying the ´ contribution of each input word to a resulting GRU-based encoding. These methods depend on the specific learning model and cannot be applied to arbitrary representations. Moreover, it is still not clear what is captured by the final sentence embeddings. + +Our work is orthogonal and complementary to the previous efforts: we analyze the resulting sentence embeddings by devising auxiliary prediction tasks for core sentence properties. The methodology we purpose is general and can be applied to any sentence representation model. + +# 3 APPROACH + +We aim to inspect and compare encoded sentence vectors in a task-independent manner. The main idea of our method is to focus on isolated aspects of sentence structure, and design experiments to measure to what extent each aspect is captured in a given representation. + +In each experiment, we formulate a prediction task. Given a sentence representation method, we create training data and train a classifier to predict a specific sentence property (e.g. their length) based on their vector representations. We then measure how well we can train a model to perform the task. The basic premise is that if we cannot train a classifier to predict some property of a sentence based on its vector representation, then this property is not encoded in the representation (or rather, not encoded in a useful way, considering how the representation is likely to be used). + +The experiments in this work focus on low-level properties of sentences – the sentence length, the identities of words in a sentence, and the order of the words. We consider these to be the core elements of sentence structure. Generalizing the approach to higher-level semantic and syntactic properties holds great potential, which we hope will be explored in future work, by us or by others. + +# 3.1 THE PREDICTION TASKS + +We now turn to describe the specific prediction tasks. We use lower case italics $( s , w )$ to refer to sentences and words, and boldface to refer to their corresponding vector representations (s, w). When more than one element is considered, they are distinguished by indices $( w _ { 1 } , w _ { 2 } , \mathbf { w _ { 1 } } , \mathbf { w _ { 2 } } )$ . + +Our underlying corpus for generating the classification instances consists of 200,000 Wikipedia sentences, where 150,000 sentences are used to generate training examples, and 25,000 sentences are used for each of the test and development examples. These sentences are a subset of the training set that was used to train the original sentence encoders. The idea behind this setup is to test the models on what are presumably their best embeddings. + +Length Task This task measures to what extent the sentence representation encodes its length. Given a sentence representation $\mathbf { s } \in \mathbb { R } ^ { k }$ , the goal of the classifier is to predict the length (number of words) in the original sentence $s$ . The task is formulated as multiclass classification, with eight output classes corresponding to binned lengths.2 The resulting dataset is reasonably balanced, with a majority class (lengths 5-8 words) of 5,182 test instances and a minority class (34-70) of 1,084 test instances. Predicting the majority class results in classification accuracy of $2 0 . 1 \%$ . + +Word-content Task This task measures to what extent the sentence representation encodes the identities of words within it. Given a sentence representation $\mathbf { s } \in \mathbb { R } ^ { k }$ and a word representation $\mathbf { w } \in \mathbb { R } ^ { d }$ , the goal of the classifier is to determine whether $w$ appears in the $s$ , with access to neither $w$ nor $s$ . This is formulated as a binary classification task, where the input is the concatenation of s and w. + +To create a dataset for this task, we need to provide positive and negative examples. Obtaining positive examples is straightforward: we simply pick a random word from each sentence. For negative examples, we could pick a random word from the entire corpus. However, we found that such a dataset tends to push models to memorize words as either positive or negative words, instead of finding their relation to the sentence representation. Therefore, for each sentence we pick as a negative example a word that appears as a positive example somewhere in our dataset, but does not appear in the given sentence. This forces the models to learn a relationship between word and sentence representations. We generate one positive and one negative example from each sentence. The dataset is balanced, with a baseline accuracy of $50 \%$ . + +Word-order Task This task measures to what extent the sentence representation encodes word order. Given a sentence representation $\mathbf { s } \in \mathbb { R } ^ { k }$ and the representations of two words that appear in the sentence, $\mathbf { w } _ { 1 } , \mathbf { w } _ { 2 } \in \mathbb { R } ^ { { \bar { d } } }$ , the goal of the classifier is to predict whether $w _ { 1 }$ appears before or after $w _ { 2 }$ in the original sentence $s$ . Again, the model has no access to the original sentence and the two words. This is formulated as a binary classification task, where the input is a concatenation of the three vectors s, $\mathbf { w } _ { 1 }$ and $\mathbf { w } _ { 2 }$ . + +For each sentence in the corpus, we simply pick two random words from the sentence as a positive example. For negative examples, we flip the order of the words. We generate one positive and one negative example from each sentence. The dataset is balanced, with a baseline accuracy of $50 \%$ . + +# 4 SENTENCE REPRESENTATION MODELS + +Given a sentence $s = \{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \}$ we aim to find a sentence representation s using an encoder: + +$$ +\mathrm { E N C } : s = \{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \} \mapsto \mathbf { s } \in \mathbb { R } ^ { k } +$$ + +The encoding process usually assumes a vector representation $\mathbf { w } _ { i } \in \mathbb { R } ^ { d }$ for each word in the vocabulary. In general, the word and sentence embedding dimensions, $d$ and $k$ , need not be the same. The word vectors can be learned together with other encoder parameters or pre-trained. Below we describe different instantiations of ENC. + +Continuous Bag-of-words (CBOW) This simple yet effective text representation consists of performing element-wise averaging of word vectors that are obtained using a word-embedding method such as word2vec. + +Despite its obliviousness to word order, CBOW has proven useful in different tasks (Hill et al., 2016) and is easy to compute, making it an important model class to consider. + +Encoder-Decoder (ED) The encoder-decoder framework has been successfully used in a number of sequence-to-sequence learning tasks (Sutskever et al., 2014; Bahdanau et al., 2014; Dai & Le, 2015; Li et al., 2015). After the encoding phase, a decoder maps the sentence representation back to the sequence of words: + +$$ +\mathtt { D E C } : \mathbf { s } \in \mathbb { R } ^ { k } \mapsto s = \{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \} +$$ + +![](images/28e6a935890943d42b298369f4f746ec45d819f218a69ca5e4f43d7c67269071.jpg) +Figure 1: Task accuracy vs. embedding size for different models; ED BLEU scores given for reference. + +Here we investigate the specific case of an auto-encoder, where the entire encoding-decoding process can be trained end-to-end from a corpus of raw texts. The sentence representation is the final output vector of the encoder. We use a long short-term memory (LSTM) recurrent neural network (Hochreiter & Schmidhuber, 1997; Graves et al., 2013) for both encoder and decoder. The LSTM decoder is similar to the LSTM encoder but with different weights. + +# 5 EXPERIMENTAL SETUP + +The bag-of-words (CBOW) and encoder-decoder models are trained on 1 million sentences from a 2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use NLTK (Bird, 2006) for tokenization, and constrain sentence lengths to be between 5 and 70 words. For both models we control the embedding size $k$ and train word and sentence vectors of sizes $k \in \{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \}$ . More details about the experimental setup are available in the Appendix. + +# 6 RESULTS + +In this section we provide a detailed description of our experimental results along with their analysis. For each of the three main tests – length, content and order – we investigate the performance of different sentence representation models across embedding size. + +# 6.1 LENGTH EXPERIMENTS + +We begin by investigating how well the different representations encode sentence length. Figure 1a shows the performance of the different models on the length task, as well as the BLEU obtained by the LSTM encoder-decoder (ED). + +With enough dimensions, the LSTM embeddings are very good at capturing sentence length, obtaining accuracies between $82 \%$ and $87 \%$ . Length prediction ability is not perfectly correlated with BLEU scores: from 300 dimensions onward the length prediction accuracies of the LSTM remain relatively stable, while the BLEU score of the encoder-decoder model increases as more dimensions are added. + +Somewhat surprisingly, the CBOW model also encodes a fair amount of length information, with length prediction accuracies of $45 \%$ to $65 \%$ , way above the $20 \%$ baseline. This is remarkable, as the CBOW representation consists of averaged word vectors, and we did not expect it to encode length at all. We return to CBOW’s exceptional performance in Section 7. + +# 6.2 WORD CONTENT EXPERIMENTS + +To what extent do the different sentence representations encode the identities of the words in the sentence? Figure 1b visualizes the performance of our models on the word content test. + +All the representations encode some amount of word information, and clearly outperform the random baseline of $50 \%$ . Some trends are worth noting. While the capacity of the LSTM encoder to preserve word identities generally increases when adding dimensions, the performance peaks at 750 dimensions and drops afterwards. This stands in contrast to the BLEU score of the respective encoder-decoder models. We hypothesize that this occurs because a sizable part of the auto-encoder performance comes from the decoder, which also improves as we add more dimensions. At 1000 dimensions, the decoder’s language model may be strong enough to allow the representation produced by the encoder to be less informative with regard to word content. + +CBOW representations with low dimensional vectors (100 and 300 dimensions) perform exceptionally well, outperforming the more complex, sequence-aware models by a wide margin. If your task requires access to word identities, it is worth considering this simple representation. Interestingly, CBOW scores drop at higher dimensions. + +# 6.3 WORD ORDER EXPERIMENTS + +Figure 1c shows the performance of the different models on the order test. The LSTM encoders are very capable of encoding word order, with LSTM-1000 allowing the recovery of word order in $91 \%$ of the cases. Similar to the length test, LSTM order prediction accuracy is only loosely correlated with BLEU scores. It is worth noting that increasing the representation size helps the LSTM-encoder to better encode order information. + +Surprisingly, the CBOW encodings manage to reach an accuracy of $70 \%$ on the word order task, $20 \%$ above the baseline. This is remarkable as, by definition, the CBOW encoder does not attempt to preserve word order information. One way to explain this is by considering distribution patterns of words in natural language sentences: some words tend to appear before others. In the next section we analyze the effect of natural language on the different models. + +# 7 IMPORTANCE OF “NATURAL LANGUAGENESS” + +Natural language imposes many constraints on sentence structure. To what extent do the different encoders rely on specific properties of word distributions in natural language sentences when encoding sentences? + +To account for this, we perform additional experiments in which we attempt to control for the effect of natural language. + +How can CBOW encode sentence length? Is the ability of CBOW embeddings to encode length related to specific words being indicative of longer or shorter sentences? To control for this, we created a synthetic dataset where each word in each sentence is replaced by a random word from the dictionary and re-ran the length test for the CBOW embeddings using this dataset. As Figure 2a shows, this only leads to a slight decrease in accuracy, indicating that the identity of the words is not the main component in CBOW’s success at predicting length. + +![](images/e82d67756d02b673c9f625bf59ad4d67cc57469760268bc810c6082a021e2cf1.jpg) +(a) Length accuracy for different CBOW sizes on natural and synthetic (random words) sentences. + +![](images/99d2d39164f58bedacce7e357432eda8f8225f5272edfca5fd0629fdcfc12507.jpg) +(b) Average embedding norm vs. sentence length for CBOW with an embedding size of 300. + +An alternative explanation for CBOW’s ability to encode sentence length is given by considering the norms of the sentence embeddings. Indeed, Figure 2b shows that the embedding norm decreases as sentences grow longer. We believe this is one of the main reasons for the strong CBOW results. + +While the correlation between the number of averaged vectors and the resulting norm surprised us, in retrospect it is an expected behavior that has sound mathematical foundations. To understand the behavior, consider the different word vectors to be random variables, with the values in each dimension centered roughly around zero. Both central limit theorem and Hoeffding‘s inequality tell us that as we add more samples, the expected average of the values will better approximate the true mean, causing the norm of the average vector to decrease. We expect the correlation between the sentence length and its norm to be more pronounced with shorter sentences (above some number of samples we will already be very close to the true mean, and the norm will not decrease further), a behavior which we indeed observe in practice. + +How does CBOW encode word order? The surprisingly strong performance of the CBOW model on the order task made us hypothesize that much of the word order information is captured in general natural language word order statistics. + +To investigate this, we re-run the word order tests, but this time drop the sentence embedding in training and testing time, learning from the word-pairs alone. In other words, we feed the network as input two word embeddings and ask which word comes first in the sentence. This test isolates general word order statistics of language from information that is contained in the sentence embedding (Fig. 3). + +The difference between including and removing the sentence embeddings when using the CBOW model is minor, while the LSTM-ED suffers a significant drop. Clearly, the LSTMED model encodes word order, while the prediction ability of CBOW is mostly explained by general language statistics. However, CBOW does benefit from the sentence to some extent: we observe a gain of ${ \sim } 3 \%$ accuracy points when the CBOW tests are allowed access to the sentence representation. This may be explained by higher order statistics of correlation between word order patterns and the occurrences of specific words. + +![](images/140826fd2b77809f6dcea513cd5b657687e4e1698e2815c2dba2787703048c6e.jpg) +Figure 3: Order accuracy w/ and w/o sentence representation for ED and CBOW models. + +# How important is English word order for en + +coding sentences? To what extent are the models trained to rely on natural language word order when encoding sentences? To control for this, we create a synthetic dataset, PERMUTED, in which the word order in each sentence is randomly permuted. Then, we repeat the length, content and order experiments using the PERMUTED dataset (we still use the original sentence encoders that are trained on non-permuted sentences). While the permuted sentence representation is the same for CBOW, it is completely different when generated by the encoder-decoder. + +Results are presented in Fig. 4. When considering CBOW embeddings, word order accuracy drops to chance level, as expected, while results on the other tests remain the same. Moving to the LSTM encoder-decoder, the results on all three tests are comparable to the ones using non-permuted sentences. These results are somewhat surprising since the models were originally trained on “real”, non-permuted sentences. This indicates that the LSTM encoder-decoder is a general-purpose sequence encoder that for the most part does not rely on word ordering properties of natural language when encoding sentences. The small and consistent drop in word order accuracy on the permuted sentences can be attributed to the encoder relying on natural language word order to some extent, but can also be explained by the word order prediction task becoming harder due to the inability to use general word order statistics. The results suggest that a trained encoder will transfer well across different natural language domains, as long as the vocabularies remain stable. When considering the decoder’s BLEU score on the permuted dataset (not shown), we do see a dramatic decrease in accuracy. For example, LSTM encoder-decoder with 1000 dimensions drops from 32.5 to 8.2 BLEU score. These results suggest that the decoder, which is thrown away, contains most of the language-specific information. + +![](images/e9af8c8bd91c7b7fed7ecfbb6beeda8b61833cac7aed0ea51520dfe929cd5cee.jpg) +Figure 4: Results for length, content and order tests on natural and permuted sentences. + +# 8 SKIP-THOUGHT VECTORS + +In addition to the experiments on CBOW and LSTM-encoders, we also experiment with the skipthought vectors model (Kiros et al., 2015). This model extends the idea of the auto-encoder to neighboring sentences. + +Given a sentence $s _ { i }$ , it first encodes it using an RNN, similar to the auto-encoder model. However, instead of predicting the original sentence, skip-thought predicts the preceding and following sentences, $s _ { i - 1 }$ and $s _ { i + 1 }$ . The encoder and decoder are implemented with gated recurrent units (Cho et al., 2014). + +Here, we deviate from the controlled environment and use the author’s provided model3 with the recommended embeddings size of 4800. This makes the direct comparison of the models “unfair”. However, our aim is not to decide which is the “best” model but rather to show how our method can be used to measure the kinds of information captured by different representations. + +Table 1 summarizes the performance of the skip-thought embeddings in each of the prediction tasks on both the PERMUTED and original dataset. + +
LengthWord contentWordorder
Original82.1%79.7%81.1%
Permuted68.2%76.4%76.5%
+ +Table 1: Classification accuracy for the prediction tasks using skip-thought embeddings. + +The performance of the skip-thought embeddings is well above the baselines and roughly similar for all tasks. Its performance is similar to the higher-dimensional encoder-decoder models, except in the order task where it lags somewhat behind. However, we note that the results are not directly comparable as skip-thought was trained on a different corpus. + +The more interesting finding is its performance on the PERMUTED sentences. In this setting we see a large drop. In contrast to the LSTM encoder-decoder, skip-thought’s ability to predict length and word content does degrade significantly on the permuted sentences, suggesting that the encoding process of the skip-thought model is indeed specialized towards natural language texts. + +# 9 CONCLUSION + +We presented a methodology for performing fine-grained analysis of sentence embeddings using auxiliary prediction tasks. Our analysis reveals some properties of sentence embedding methods: + +• CBOW is surprisingly effective – in addition to being very strong at content, it is also predictive of length, and can be used to reconstruct a non-trivial amount of the original word order. 300 dimensions perform best, with greatly degraded word-content prediction performance on higher dimensions. +• With enough dimensions, LSTM auto-encoders are very effective at encoding word order and word content information. Increasing the dimensionality of the LSTM encoder does not significantly improve its ability to encode length, but does increase its ability to encode content and order information. 500 dimensional embeddings are already quite effective for encoding word order, with little gains beyond that. Word content accuracy peaks at 750 dimensions and drops at 1000, suggesting that larger is not always better. + +• The trained LSTM encoder (when trained with an auto-encoder objective) does not rely on ordering patterns in the training sentences when encoding novel sequences. + +In contrast, the skip-thought encoder does rely on such patterns. Its performance on the other tasks is similar to the higher-dimensional LSTM encoder, which is impressive considering it was trained on a different corpus. + +• Finally, the encoder-decoder’s ability to recreate sentences (BLEU) is not entirely indicative of the quality of the encoder at representing aspects such as word identity and order. This suggests that BLEU is sub-optimal for model selection. + +# REFERENCES + +Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014. + +Marco Baroni, Georgiana Dinu, and German Kruszewski. 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Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701, 2012. + +# APPENDIX I: EXPERIMENTAL SETUP + +Sentence Encoders The bag-of-words (CBOW) and encoder-decoder models are trained on 1 million sentences from a 2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use NLTK (Bird, 2006) for tokenization, and constrain sentence lengths to be between 5 and 70 words. + +For the CBOW model, we train Skip-gram word vectors (Mikolov et al., 2013a), with hierarchicalsoftmax and a window size of 5 words, using the Gensim implementation.4 We control for the embedding size $k$ and train word vectors of sizes $k \in \{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \}$ . + +For the encoder-decoder models, we use an in-house implementation using the Torch7 toolkit (Collobert et al., 2011). The decoder is trained as a language model, attempting to predict the correct word at each time step using a negative-log-likelihood objective (cross-entropy loss over the softmax layer). We use one layer of LSTM cells for the encoder and decoder using the implementation in Leonard et al. (2015). ´ + +We use the same size for word and sentence representations (i.e. $d \ = \ k$ ), and train models of sizes $k \in \{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \}$ . We follow previous work on sequence-to-sequence learning (Sutskever et al., 2014; Li et al., 2015) in reversing the input sentences and clipping gradients. Word vectors are initialized to random values. + +We evaluate the encoder-decoder models using BLEU scores (Papineni et al., 2002), a popular machine translation evaluation metric that is also used to evaluate auto-encoder models (Li et al., 2015). BLEU score measures how well the original sentence is recreated, and can be thought of as a proxy for the quality of the encoded representation. We compare it with the performance of the models on the three prediction tasks. The results of the higher-dimensional models are comparable to those found in the literature, which serves as a sanity check for the quality of the learned models. + +Auxiliary Task Classifier For the auxiliary task predictors, we use multi-layer perceptrons with a single hidden layer and ReLU activation, which were carefully tuned for each of the tasks. We experimented with several network architectures prior to arriving at this configuration. + +Further details regarding the training and architectures of both the sentence encoders and auxiliary task classifiers are available in the Appendix. + +# APPENDIX II: TECHNICAL DETAILS + +ENCODER DECODER + +Parameters of the encoder-decoder were tuned on a dedicated validation set. We experienced with different learning rates (0.1, 0.01, 0.001), dropout-rates (0.1, 0.2, 0.3, 0.5) (Hinton et al., 2012) and optimization techniques (AdaGrad (Duchi et al., 2011), AdaDelta (Zeiler, 2012), Adam (Kingma & Ba, 2014) and RMSprop (Tieleman & Hinton, 2012)). We also experimented with different batch sizes (8, 16, 32), and found improvement in runtime but no significant improvement in performance. + +Based on the tuned parameters, we trained the encoder-decoder models on a single GPU (NVIDIA Tesla K40), with mini-batches of 32 sentences, learning rate of 0.01, dropout rate of 0.1, and the AdaGrad optimizer; training takes approximately 10 days and is stopped after 5 epochs with no loss improvement on a validation set. + +# PREDICTION TASKS + +Parameters for the predictions tasks as well as classifier architecture were tuned on a dedicated validation set. We experimented with one, two and three layer feed-forward networks using ReLU (Nair & Hinton, 2010; Glorot et al., 2011), tanh and sigmoid activation functions. We tried different hidden layer sizes: the same as the input size, twice the input size and one and a half times the input size. We tried different learning rates (0.1, 0.01, 0.001), dropout rates (0.1, 0.3, 0.5, 0.8) and different optimization techniques (AdaGrad, AdaDelta and Adam). + +Our best tuned classifier, which we use for all experiments, is a feed-forward network with one hidden layer and a ReLU activation function. We set the size of the hidden layer to be the same size as the input vector. We place a softmax layer on top whose size varies according to the specific task, and apply dropout before the softmax layer. We optimize the log-likelihood using AdaGrad. We use a dropout rate of 0.8 and a learning rate of 0.01. Training is stopped after 5 epochs with no loss improvement on the development set. Training was done on a single GPU (NVIDIA Tesla K40). + +# 10 ADDITIONAL EXPERIMENTS - CONTENT TASK + +How well do the models preserve content when we increase the sentence length? In Fig. 5 we plot content prediction accuracy vs. sentence length for different models. + +![](images/8a2f0243ec8ee281bff85c440c131dec3d455bbb04308d04d68ae81b98dd8e95.jpg) +Figure 5: Content accuracy vs. sentence length for selected models. + +As expected, all models suffer a drop in content accuracy on longer sentences. The degradation is roughly linear in the sentence length. For the encoder-decoder, models with fewer dimensions seem to degrade slower. + +# APPENDIX III: SIGNIFICANCE TESTS + +In this section we report the significance tests we conduct in order to evaluate our findings. In order to do so, we use the paired t-test (Rubin, 1973). + +All the results reported in the summery of findings are highly significant (p-value $\ll 0 . 0 0 0 1$ ). The ones we found to be not significant $\mathrm { { \dot { p } } }$ -value $\gg 0 . 0 3$ ) are the ones which their accuracy does not have much of a difference, i.e ED with size 500 and ED with size 750 tested on the word order task (p-value $= 0 . 1 1$ ), or CBOW with dimensions 750 and 1000 (p-value ${ \ : = } 0 . 3$ ). + +Table 2: P-values for ED vs. CBOW over the different dimensions and tasks. For example, in the row where dim equals 100, we compute the p-value of ED compared to CBOW with embed size of 100 on all three tasks. + +
Dim.LengthWordcontentWordorder
1001.77e-1470.01.83e-296
3000.00.00.0
5000.00.00.0
7500.00.00.0
10000.00.00.0
+ +
Dim.LengthWord contentWord order
100 vs.3000.08.56e-1900.0
300 vs. 5007.3e-714.20e-055.48e-56
500 vs. 7503.64e-1754.46e-650.11
750 vs. 10001.37e-1112.35e-2434.32e-61
+ +Table 3: P-values for ED models over the different dimensions and tasks. + +
Dim.LengthWord contentWord order
100 vs.3000.00.01.5e-33
300 vs. 5001.47e-2150.03.06e-64
500 vs. 7500.680.0320.05
750 vs.10004.44e-320.30.08
+ +Table 4: P-values for CBOW models over the different dimensions and tasks. \ No newline at end of file diff --git a/parse/train/BJh6Ztuxl/BJh6Ztuxl_content_list.json b/parse/train/BJh6Ztuxl/BJh6Ztuxl_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..973328f4bf7f2cc9753426dc5a140d846343e875 --- /dev/null +++ b/parse/train/BJh6Ztuxl/BJh6Ztuxl_content_list.json @@ -0,0 +1,1771 @@ +[ + { + "type": "text", + "text": "FINE-GRAINED ANALYSIS OF SENTENCE EMBEDDINGS USING AUXILIARY PREDICTION TASKS ", + "text_level": 1, + "bbox": [ + 176, + 99, + 818, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yossi Adi $^ { 1 , 2 }$ , Einat Kermany2, Yonatan Belinkov3, Ofer Lavi2, Yoav Goldberg1 ", + "bbox": [ + 184, + 169, + 730, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Bar-Ilan University, Ramat-Gan, Israel \n{yoav.goldberg, yossiadidrum}@gmail.com \n2IBM Haifa Research Lab, Haifa, Israel \n{einatke, oferl}@il.ibm.com \n3MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA, USA belinkov@mit.edu ", + "bbox": [ + 184, + 198, + 750, + 282 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 320, + 544, + 335 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There is a lot of research interest in encoding variable length sentences into fixed length vectors, in a way that preserves the sentence meanings. Two common methods include representations based on averaging word vectors, and representations based on the hidden states of recurrent neural networks such as LSTMs. The sentence vectors are used as features for subsequent machine learning tasks or for pre-training in the context of deep learning. However, not much is known about the properties that are encoded in these sentence representations and about the language information they capture. ", + "bbox": [ + 233, + 348, + 764, + 459 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a framework that facilitates better understanding of the encoded representations. We define prediction tasks around isolated aspects of sentence structure (namely sentence length, word content, and word order), and score representations by the ability to train a classifier to solve each prediction task when using the representation as input. We demonstrate the potential contribution of the approach by analyzing different sentence representation mechanisms. The analysis sheds light on the relative strengths of different sentence embedding methods with respect to these low level prediction tasks, and on the effect of the encoded vector’s dimensionality on the resulting representations. ", + "bbox": [ + 233, + 462, + 764, + 585 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 609, + 336, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While sentence embeddings or sentence representations play a central role in recent deep learning approaches to NLP, little is known about the information that is captured by different sentence embedding learning mechanisms. We propose a methodology facilitating fine-grained measurement of some of the information encoded in sentence embeddings, as well as performing fine-grained comparison of different sentence embedding methods. ", + "bbox": [ + 174, + 640, + 825, + 709 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In sentence embeddings, sentences, which are variable-length sequences of discrete symbols, are encoded into fixed length continuous vectors that are then used for further prediction tasks. A simple and common approach is producing word-level vectors using, e.g., word2vec (Mikolov et al., 2013a;b), and summing or averaging the vectors of the words participating in the sentence. This continuous-bag-of-words (CBOW) approach disregards the word order in the sentence.1 ", + "bbox": [ + 174, + 717, + 823, + 786 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Another approach is the encoder-decoder architecture, producing models also known as sequenceto-sequence models (Sutskever et al., 2014; Cho et al., 2014; Bahdanau et al., 2014, inter alia). In this architecture, an encoder network (e.g. an LSTM) is used to produce a vector representation of the sentence, which is then fed as input into a decoder network that uses it to perform some prediction task (e.g. recreate the sentence, or produce a translation of it). The encoder and decoder networks are trained jointly in order to perform the final task. ", + "bbox": [ + 173, + 792, + 825, + 877 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some systems (for example in machine translation) train the system end-to-end, and use the trained system for prediction (Bahdanau et al., 2014). Such systems do not generally care about the encoded vectors, which are used merely as intermediate values. However, another common case is to train an encoder-decoder network and then throw away the decoder and use the trained encoder as a general mechanism for obtaining sentence representations. For example, an encoder-decoder network can be trained as an auto-encoder, where the encoder creates a vector representation, and the decoder attempts to recreate the original sentence (Li et al., 2015). Similarly, Kiros et al. (2015) train a network to encode a sentence such that the decoder can recreate its neighboring sentences in the text. Such networks do not require specially labeled data, and can be trained on large amounts of unannotated text. As the decoder needs information about the sentence in order to perform well, it is clear that the encoded vectors capture a non-trivial amount of information about the sentence, making the encoder appealing to use as a general purpose, stand-alone sentence encoding mechanism. The sentence encodings can then be used as input for other prediction tasks for which less training data is available (Dai & Le, 2015). In this work we focus on these “general purpose” sentence encodings. ", + "bbox": [ + 174, + 103, + 825, + 297 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The resulting sentence representations are opaque, and there is currently no good way of comparing different representations short of using them as input for different high-level semantic tasks (e.g. sentiment classification, entailment recognition, document retrieval, question answering, sentence similarity, etc.) and measuring how well they perform on these tasks. This is the approach taken by Li et al. (2015), Hill et al. (2016) and Kiros et al. (2015). This method of comparing sentence embeddings leaves a lot to be desired: the comparison is at a very coarse-grained level, does not tell us much about the kind of information that is encoded in the representation, and does not help us form generalizable conclusions. ", + "bbox": [ + 174, + 305, + 825, + 416 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our Contribution We take a first step towards opening the black box of vector embeddings for sentences. We propose a methodology that facilitates comparing sentence embeddings on a much finer-grained level, and demonstrate its use by analyzing and comparing different sentence representations. We analyze sentence representation methods that are based on LSTM auto-encoders and the simple CBOW representation produced by averaging word2vec word embeddings. For each of CBOW and LSTM auto-encoder, we compare different numbers of dimensions, exploring the effect of the dimensionality on the resulting representation. We also provide some comparison to the skip-thought embeddings of Kiros et al. (2015). ", + "bbox": [ + 174, + 433, + 825, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we focus on what are arguably the three most basic characteristics of a sequence: its length, the items within it, and their order. We investigate different sentence representations based on the capacity to which they encode these aspects. Our analysis of these low-level properties leads to interesting, actionable insights, exposing relative strengths and weaknesses of the different representations. ", + "bbox": [ + 174, + 551, + 825, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Limitations Focusing on low-level sentence properties also has limitations: The tasks focus on measuring the preservation of surface aspects of the sentence and do not measure syntactic and semantic generalization abilities; the tasks are not directly related to any specific downstream application (although the properties we test are important factors in many tasks – knowing that a model is good at predicting length and word order is likely advantageous for syntactic parsing, while models that excel at word content are good for text classification tasks). Dealing with these limitations requires a complementary set of auxiliary tasks, which is outside the scope of this study and is left for future work. ", + "bbox": [ + 173, + 637, + 825, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The study also suffers from the general limitations of empirical work: we do not prove general theorems but rather measure behaviors on several data points and attempt to draw conclusions from these measurements. There is always the risk that our conclusions only hold for the datasets on which we measured, and will not generalize. However, we do consider our large sample of sentences from Wikipedia to be representative of the English language, at least in terms of the three basic sentence properties that we study. ", + "bbox": [ + 174, + 755, + 823, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Summary of Findings Our analysis reveals the following insights regarding the different sentence embedding methods: ", + "bbox": [ + 173, + 854, + 823, + 882 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• Sentence representations based on averaged word vectors are surprisingly effective, and encode a non-trivial amount of information regarding sentence length. The information they contain can also be used to reconstruct a non-trivial amount of the original word order in a probabilistic manner (due to regularities in the natural language data). ", + "bbox": [ + 176, + 895, + 821, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 179, + 103, + 823, + 132 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "• LSTM auto-encoders are very effective at encoding word order and word content. • Increasing the number of dimensions benefits some tasks more than others. • Adding more hidden units sometimes degrades the encoders’ ability to encode word content. This degradation is not correlated with the BLEU scores of the decoder, suggesting that BLEU over the decoder output is sub-optimal for evaluating the encoders’ quality. • LSTM encoders trained as auto-encoders do not rely on ordering patterns in the training sentences when encoding novel sentences, while the skip-thought encoders do rely on such patterns. ", + "bbox": [ + 173, + 137, + 826, + 251 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 271, + 344, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Word-level distributed representations have been analyzed rather extensively, both empirically and theoretically, for example by Baroni et al. (2014), Levy & Goldberg (2014) and Levy et al. (2015). In contrast, the analysis of sentence-level representations has been much more limited. Commonly used approaches is to either compare the performance of the sentence embeddings on down-stream tasks (Hill et al., 2016), or to analyze models, specifically trained for predefined task (Schmaltz et al., 2016; Sutskever et al., 2011). ", + "bbox": [ + 174, + 303, + 825, + 387 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While the resulting analysis reveals differences in performance of different models, it does not adequately explain what kind of linguistic properties of the sentence they capture. Other studies analyze the hidden units learned by neural networks when training a sentence representation model (Elman, 1991; Karpathy et al., 2015; Kad´ ar et al., 2016). This approach often associates certain linguistic ´ aspects with certain hidden units. Kad´ ar et al. (2016) propose a methodology for quantifying the ´ contribution of each input word to a resulting GRU-based encoding. These methods depend on the specific learning model and cannot be applied to arbitrary representations. Moreover, it is still not clear what is captured by the final sentence embeddings. ", + "bbox": [ + 174, + 393, + 825, + 506 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work is orthogonal and complementary to the previous efforts: we analyze the resulting sentence embeddings by devising auxiliary prediction tasks for core sentence properties. The methodology we purpose is general and can be applied to any sentence representation model. ", + "bbox": [ + 176, + 512, + 825, + 554 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 APPROACH", + "text_level": 1, + "bbox": [ + 174, + 575, + 299, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We aim to inspect and compare encoded sentence vectors in a task-independent manner. The main idea of our method is to focus on isolated aspects of sentence structure, and design experiments to measure to what extent each aspect is captured in a given representation. ", + "bbox": [ + 174, + 607, + 825, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In each experiment, we formulate a prediction task. Given a sentence representation method, we create training data and train a classifier to predict a specific sentence property (e.g. their length) based on their vector representations. We then measure how well we can train a model to perform the task. The basic premise is that if we cannot train a classifier to predict some property of a sentence based on its vector representation, then this property is not encoded in the representation (or rather, not encoded in a useful way, considering how the representation is likely to be used). ", + "bbox": [ + 174, + 655, + 823, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The experiments in this work focus on low-level properties of sentences – the sentence length, the identities of words in a sentence, and the order of the words. We consider these to be the core elements of sentence structure. Generalizing the approach to higher-level semantic and syntactic properties holds great potential, which we hope will be explored in future work, by us or by others. ", + "bbox": [ + 174, + 747, + 823, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 THE PREDICTION TASKS ", + "text_level": 1, + "bbox": [ + 174, + 820, + 387, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We now turn to describe the specific prediction tasks. We use lower case italics $( s , w )$ to refer to sentences and words, and boldface to refer to their corresponding vector representations (s, w). When more than one element is considered, they are distinguished by indices $( w _ { 1 } , w _ { 2 } , \\mathbf { w _ { 1 } } , \\mathbf { w _ { 2 } } )$ . ", + "bbox": [ + 176, + 847, + 823, + 888 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our underlying corpus for generating the classification instances consists of 200,000 Wikipedia sentences, where 150,000 sentences are used to generate training examples, and 25,000 sentences are used for each of the test and development examples. These sentences are a subset of the training set that was used to train the original sentence encoders. The idea behind this setup is to test the models on what are presumably their best embeddings. ", + "bbox": [ + 176, + 895, + 821, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 823, + 146 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Length Task This task measures to what extent the sentence representation encodes its length. Given a sentence representation $\\mathbf { s } \\in \\mathbb { R } ^ { k }$ , the goal of the classifier is to predict the length (number of words) in the original sentence $s$ . The task is formulated as multiclass classification, with eight output classes corresponding to binned lengths.2 The resulting dataset is reasonably balanced, with a majority class (lengths 5-8 words) of 5,182 test instances and a minority class (34-70) of 1,084 test instances. Predicting the majority class results in classification accuracy of $2 0 . 1 \\%$ . ", + "bbox": [ + 173, + 150, + 825, + 234 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Word-content Task This task measures to what extent the sentence representation encodes the identities of words within it. Given a sentence representation $\\mathbf { s } \\in \\mathbb { R } ^ { k }$ and a word representation $\\mathbf { w } \\in \\mathbb { R } ^ { d }$ , the goal of the classifier is to determine whether $w$ appears in the $s$ , with access to neither $w$ nor $s$ . This is formulated as a binary classification task, where the input is the concatenation of s and w. ", + "bbox": [ + 174, + 238, + 825, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To create a dataset for this task, we need to provide positive and negative examples. Obtaining positive examples is straightforward: we simply pick a random word from each sentence. For negative examples, we could pick a random word from the entire corpus. However, we found that such a dataset tends to push models to memorize words as either positive or negative words, instead of finding their relation to the sentence representation. Therefore, for each sentence we pick as a negative example a word that appears as a positive example somewhere in our dataset, but does not appear in the given sentence. This forces the models to learn a relationship between word and sentence representations. We generate one positive and one negative example from each sentence. The dataset is balanced, with a baseline accuracy of $50 \\%$ . ", + "bbox": [ + 174, + 314, + 825, + 439 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Word-order Task This task measures to what extent the sentence representation encodes word order. Given a sentence representation $\\mathbf { s } \\in \\mathbb { R } ^ { k }$ and the representations of two words that appear in the sentence, $\\mathbf { w } _ { 1 } , \\mathbf { w } _ { 2 } \\in \\mathbb { R } ^ { { \\bar { d } } }$ , the goal of the classifier is to predict whether $w _ { 1 }$ appears before or after $w _ { 2 }$ in the original sentence $s$ . Again, the model has no access to the original sentence and the two words. This is formulated as a binary classification task, where the input is a concatenation of the three vectors s, $\\mathbf { w } _ { 1 }$ and $\\mathbf { w } _ { 2 }$ . ", + "bbox": [ + 174, + 444, + 825, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each sentence in the corpus, we simply pick two random words from the sentence as a positive example. For negative examples, we flip the order of the words. We generate one positive and one negative example from each sentence. The dataset is balanced, with a baseline accuracy of $50 \\%$ . ", + "bbox": [ + 174, + 534, + 825, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 SENTENCE REPRESENTATION MODELS ", + "text_level": 1, + "bbox": [ + 174, + 595, + 529, + 612 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a sentence $s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\}$ we aim to find a sentence representation s using an encoder: ", + "bbox": [ + 174, + 626, + 823, + 642 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/028c40eb38c89033d23dedb8550c9222de08e33b01c5f48311d315854d242bac.jpg", + "text": "$$\n\\mathrm { E N C } : s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\} \\mapsto \\mathbf { s } \\in \\mathbb { R } ^ { k }\n$$", + "text_format": "latex", + "bbox": [ + 367, + 645, + 629, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The encoding process usually assumes a vector representation $\\mathbf { w } _ { i } \\in \\mathbb { R } ^ { d }$ for each word in the vocabulary. In general, the word and sentence embedding dimensions, $d$ and $k$ , need not be the same. The word vectors can be learned together with other encoder parameters or pre-trained. Below we describe different instantiations of ENC. ", + "bbox": [ + 174, + 666, + 825, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Continuous Bag-of-words (CBOW) This simple yet effective text representation consists of performing element-wise averaging of word vectors that are obtained using a word-embedding method such as word2vec. ", + "bbox": [ + 174, + 737, + 825, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Despite its obliviousness to word order, CBOW has proven useful in different tasks (Hill et al., 2016) and is easy to compute, making it an important model class to consider. ", + "bbox": [ + 173, + 786, + 821, + 815 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Encoder-Decoder (ED) The encoder-decoder framework has been successfully used in a number of sequence-to-sequence learning tasks (Sutskever et al., 2014; Bahdanau et al., 2014; Dai & Le, 2015; Li et al., 2015). After the encoding phase, a decoder maps the sentence representation back to the sequence of words: ", + "bbox": [ + 174, + 829, + 825, + 885 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/e604f5fc4aed2abefe6dc577ec27e0803c75745cbb4691ec7ccf3d02ac2319c0.jpg", + "text": "$$\n\\mathtt { D E C } : \\mathbf { s } \\in \\mathbb { R } ^ { k } \\mapsto s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\}\n$$", + "text_format": "latex", + "bbox": [ + 367, + 883, + 629, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/28e6a935890943d42b298369f4f746ec45d819f218a69ca5e4f43d7c67269071.jpg", + "image_caption": [ + "Figure 1: Task accuracy vs. embedding size for different models; ED BLEU scores given for reference. " + ], + "image_footnote": [], + "bbox": [ + 202, + 101, + 794, + 222 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here we investigate the specific case of an auto-encoder, where the entire encoding-decoding process can be trained end-to-end from a corpus of raw texts. The sentence representation is the final output vector of the encoder. We use a long short-term memory (LSTM) recurrent neural network (Hochreiter & Schmidhuber, 1997; Graves et al., 2013) for both encoder and decoder. The LSTM decoder is similar to the LSTM encoder but with different weights. ", + "bbox": [ + 174, + 275, + 825, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5 EXPERIMENTAL SETUP ", + "text_level": 1, + "bbox": [ + 176, + 366, + 398, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The bag-of-words (CBOW) and encoder-decoder models are trained on 1 million sentences from a 2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use NLTK (Bird, 2006) for tokenization, and constrain sentence lengths to be between 5 and 70 words. For both models we control the embedding size $k$ and train word and sentence vectors of sizes $k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}$ . More details about the experimental setup are available in the Appendix. ", + "bbox": [ + 174, + 397, + 825, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6 RESULTS ", + "text_level": 1, + "bbox": [ + 174, + 488, + 281, + 503 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section we provide a detailed description of our experimental results along with their analysis. For each of the three main tests – length, content and order – we investigate the performance of different sentence representation models across embedding size. ", + "bbox": [ + 176, + 520, + 825, + 563 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.1 LENGTH EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 580, + 379, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We begin by investigating how well the different representations encode sentence length. Figure 1a shows the performance of the different models on the length task, as well as the BLEU obtained by the LSTM encoder-decoder (ED). ", + "bbox": [ + 174, + 607, + 825, + 648 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With enough dimensions, the LSTM embeddings are very good at capturing sentence length, obtaining accuracies between $82 \\%$ and $87 \\%$ . Length prediction ability is not perfectly correlated with BLEU scores: from 300 dimensions onward the length prediction accuracies of the LSTM remain relatively stable, while the BLEU score of the encoder-decoder model increases as more dimensions are added. ", + "bbox": [ + 174, + 656, + 825, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Somewhat surprisingly, the CBOW model also encodes a fair amount of length information, with length prediction accuracies of $45 \\%$ to $65 \\%$ , way above the $20 \\%$ baseline. This is remarkable, as the CBOW representation consists of averaged word vectors, and we did not expect it to encode length at all. We return to CBOW’s exceptional performance in Section 7. ", + "bbox": [ + 174, + 732, + 825, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6.2 WORD CONTENT EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 806, + 437, + 820 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To what extent do the different sentence representations encode the identities of the words in the sentence? Figure 1b visualizes the performance of our models on the word content test. ", + "bbox": [ + 176, + 832, + 823, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All the representations encode some amount of word information, and clearly outperform the random baseline of $50 \\%$ . Some trends are worth noting. While the capacity of the LSTM encoder to preserve word identities generally increases when adding dimensions, the performance peaks at 750 dimensions and drops afterwards. This stands in contrast to the BLEU score of the respective encoder-decoder models. We hypothesize that this occurs because a sizable part of the auto-encoder performance comes from the decoder, which also improves as we add more dimensions. At 1000 dimensions, the decoder’s language model may be strong enough to allow the representation produced by the encoder to be less informative with regard to word content. ", + "bbox": [ + 176, + 867, + 823, + 922 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 823, + 159 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CBOW representations with low dimensional vectors (100 and 300 dimensions) perform exceptionally well, outperforming the more complex, sequence-aware models by a wide margin. If your task requires access to word identities, it is worth considering this simple representation. Interestingly, CBOW scores drop at higher dimensions. ", + "bbox": [ + 174, + 166, + 825, + 222 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.3 WORD ORDER EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 241, + 419, + 255 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 1c shows the performance of the different models on the order test. The LSTM encoders are very capable of encoding word order, with LSTM-1000 allowing the recovery of word order in $91 \\%$ of the cases. Similar to the length test, LSTM order prediction accuracy is only loosely correlated with BLEU scores. It is worth noting that increasing the representation size helps the LSTM-encoder to better encode order information. ", + "bbox": [ + 174, + 267, + 825, + 337 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Surprisingly, the CBOW encodings manage to reach an accuracy of $70 \\%$ on the word order task, $20 \\%$ above the baseline. This is remarkable as, by definition, the CBOW encoder does not attempt to preserve word order information. One way to explain this is by considering distribution patterns of words in natural language sentences: some words tend to appear before others. In the next section we analyze the effect of natural language on the different models. ", + "bbox": [ + 174, + 344, + 825, + 414 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "7 IMPORTANCE OF “NATURAL LANGUAGENESS”", + "text_level": 1, + "bbox": [ + 174, + 435, + 591, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Natural language imposes many constraints on sentence structure. To what extent do the different encoders rely on specific properties of word distributions in natural language sentences when encoding sentences? ", + "bbox": [ + 176, + 468, + 823, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To account for this, we perform additional experiments in which we attempt to control for the effect of natural language. ", + "bbox": [ + 173, + 517, + 823, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How can CBOW encode sentence length? Is the ability of CBOW embeddings to encode length related to specific words being indicative of longer or shorter sentences? To control for this, we created a synthetic dataset where each word in each sentence is replaced by a random word from the dictionary and re-ran the length test for the CBOW embeddings using this dataset. As Figure 2a shows, this only leads to a slight decrease in accuracy, indicating that the identity of the words is not the main component in CBOW’s success at predicting length. ", + "bbox": [ + 173, + 551, + 825, + 636 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e82d67756d02b673c9f625bf59ad4d67cc57469760268bc810c6082a021e2cf1.jpg", + "image_caption": [ + "(a) Length accuracy for different CBOW sizes on natural and synthetic (random words) sentences. " + ], + "image_footnote": [], + "bbox": [ + 245, + 651, + 467, + 768 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/99d2d39164f58bedacce7e357432eda8f8225f5272edfca5fd0629fdcfc12507.jpg", + "image_caption": [ + "(b) Average embedding norm vs. sentence length for CBOW with an embedding size of 300. " + ], + "image_footnote": [], + "bbox": [ + 529, + 651, + 753, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "An alternative explanation for CBOW’s ability to encode sentence length is given by considering the norms of the sentence embeddings. Indeed, Figure 2b shows that the embedding norm decreases as sentences grow longer. We believe this is one of the main reasons for the strong CBOW results. ", + "bbox": [ + 176, + 833, + 825, + 875 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While the correlation between the number of averaged vectors and the resulting norm surprised us, in retrospect it is an expected behavior that has sound mathematical foundations. To understand the behavior, consider the different word vectors to be random variables, with the values in each dimension centered roughly around zero. Both central limit theorem and Hoeffding‘s inequality tell us that as we add more samples, the expected average of the values will better approximate the true mean, causing the norm of the average vector to decrease. We expect the correlation between the sentence length and its norm to be more pronounced with shorter sentences (above some number of samples we will already be very close to the true mean, and the norm will not decrease further), a behavior which we indeed observe in practice. ", + "bbox": [ + 176, + 882, + 825, + 922 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 825, + 188 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "How does CBOW encode word order? The surprisingly strong performance of the CBOW model on the order task made us hypothesize that much of the word order information is captured in general natural language word order statistics. ", + "bbox": [ + 176, + 191, + 821, + 233 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To investigate this, we re-run the word order tests, but this time drop the sentence embedding in training and testing time, learning from the word-pairs alone. In other words, we feed the network as input two word embeddings and ask which word comes first in the sentence. This test isolates general word order statistics of language from information that is contained in the sentence embedding (Fig. 3). ", + "bbox": [ + 174, + 241, + 825, + 310 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The difference between including and removing the sentence embeddings when using the CBOW model is minor, while the LSTM-ED suffers a significant drop. Clearly, the LSTMED model encodes word order, while the prediction ability of CBOW is mostly explained by general language statistics. However, CBOW does benefit from the sentence to some extent: we observe a gain of ${ \\sim } 3 \\%$ accuracy points when the CBOW tests are allowed access to the sentence representation. This may be explained by higher order statistics of correlation between word order patterns and the occurrences of specific words. ", + "bbox": [ + 174, + 318, + 483, + 511 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/140826fd2b77809f6dcea513cd5b657687e4e1698e2815c2dba2787703048c6e.jpg", + "image_caption": [ + "Figure 3: Order accuracy w/ and w/o sentence representation for ED and CBOW models. " + ], + "image_footnote": [], + "bbox": [ + 532, + 337, + 787, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "How important is English word order for en", + "text_level": 1, + "bbox": [ + 176, + 517, + 480, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "coding sentences? To what extent are the models trained to rely on natural language word order when encoding sentences? To control for this, we create a synthetic dataset, PERMUTED, in which the word order in each sentence is randomly permuted. Then, we repeat the length, content and order experiments using the PERMUTED dataset (we still use the original sentence encoders that are trained on non-permuted sentences). While the permuted sentence representation is the same for CBOW, it is completely different when generated by the encoder-decoder. ", + "bbox": [ + 174, + 531, + 825, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results are presented in Fig. 4. When considering CBOW embeddings, word order accuracy drops to chance level, as expected, while results on the other tests remain the same. Moving to the LSTM encoder-decoder, the results on all three tests are comparable to the ones using non-permuted sentences. These results are somewhat surprising since the models were originally trained on “real”, non-permuted sentences. This indicates that the LSTM encoder-decoder is a general-purpose sequence encoder that for the most part does not rely on word ordering properties of natural language when encoding sentences. The small and consistent drop in word order accuracy on the permuted sentences can be attributed to the encoder relying on natural language word order to some extent, but can also be explained by the word order prediction task becoming harder due to the inability to use general word order statistics. The results suggest that a trained encoder will transfer well across different natural language domains, as long as the vocabularies remain stable. When considering the decoder’s BLEU score on the permuted dataset (not shown), we do see a dramatic decrease in accuracy. For example, LSTM encoder-decoder with 1000 dimensions drops from 32.5 to 8.2 BLEU score. These results suggest that the decoder, which is thrown away, contains most of the language-specific information. ", + "bbox": [ + 173, + 621, + 825, + 747 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e9af8c8bd91c7b7fed7ecfbb6beeda8b61833cac7aed0ea51520dfe929cd5cee.jpg", + "image_caption": [ + "Figure 4: Results for length, content and order tests on natural and permuted sentences. " + ], + "image_footnote": [], + "bbox": [ + 204, + 770, + 794, + 895 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 825, + 188 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8 SKIP-THOUGHT VECTORS ", + "text_level": 1, + "bbox": [ + 176, + 208, + 423, + 224 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In addition to the experiments on CBOW and LSTM-encoders, we also experiment with the skipthought vectors model (Kiros et al., 2015). This model extends the idea of the auto-encoder to neighboring sentences. ", + "bbox": [ + 176, + 239, + 823, + 281 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Given a sentence $s _ { i }$ , it first encodes it using an RNN, similar to the auto-encoder model. However, instead of predicting the original sentence, skip-thought predicts the preceding and following sentences, $s _ { i - 1 }$ and $s _ { i + 1 }$ . The encoder and decoder are implemented with gated recurrent units (Cho et al., 2014). ", + "bbox": [ + 174, + 287, + 825, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Here, we deviate from the controlled environment and use the author’s provided model3 with the recommended embeddings size of 4800. This makes the direct comparison of the models “unfair”. However, our aim is not to decide which is the “best” model but rather to show how our method can be used to measure the kinds of information captured by different representations. ", + "bbox": [ + 173, + 351, + 825, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1 summarizes the performance of the skip-thought embeddings in each of the prediction tasks on both the PERMUTED and original dataset. ", + "bbox": [ + 173, + 414, + 823, + 443 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c18a1ce9500889fafc393fd1472a6ffbdeb91fd88a710b256a87ac6bcd9a206c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
LengthWord contentWordorder
Original82.1%79.7%81.1%
Permuted68.2%76.4%76.5%
", + "bbox": [ + 321, + 457, + 673, + 498 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1: Classification accuracy for the prediction tasks using skip-thought embeddings. ", + "bbox": [ + 233, + 510, + 761, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The performance of the skip-thought embeddings is well above the baselines and roughly similar for all tasks. Its performance is similar to the higher-dimensional encoder-decoder models, except in the order task where it lags somewhat behind. However, we note that the results are not directly comparable as skip-thought was trained on a different corpus. ", + "bbox": [ + 173, + 549, + 825, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The more interesting finding is its performance on the PERMUTED sentences. In this setting we see a large drop. In contrast to the LSTM encoder-decoder, skip-thought’s ability to predict length and word content does degrade significantly on the permuted sentences, suggesting that the encoding process of the skip-thought model is indeed specialized towards natural language texts. ", + "bbox": [ + 174, + 612, + 825, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "9 CONCLUSION ", + "text_level": 1, + "bbox": [ + 174, + 688, + 320, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We presented a methodology for performing fine-grained analysis of sentence embeddings using auxiliary prediction tasks. Our analysis reveals some properties of sentence embedding methods: ", + "bbox": [ + 174, + 713, + 823, + 742 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "• CBOW is surprisingly effective – in addition to being very strong at content, it is also predictive of length, and can be used to reconstruct a non-trivial amount of the original word order. 300 dimensions perform best, with greatly degraded word-content prediction performance on higher dimensions. \n• With enough dimensions, LSTM auto-encoders are very effective at encoding word order and word content information. Increasing the dimensionality of the LSTM encoder does not significantly improve its ability to encode length, but does increase its ability to encode content and order information. 500 dimensional embeddings are already quite effective for encoding word order, with little gains beyond that. Word content accuracy peaks at 750 dimensions and drops at 1000, suggesting that larger is not always better. ", + "bbox": [ + 174, + 755, + 825, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "• The trained LSTM encoder (when trained with an auto-encoder objective) does not rely on ordering patterns in the training sentences when encoding novel sequences. ", + "bbox": [ + 171, + 103, + 821, + 132 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In contrast, the skip-thought encoder does rely on such patterns. Its performance on the other tasks is similar to the higher-dimensional LSTM encoder, which is impressive considering it was trained on a different corpus. ", + "bbox": [ + 181, + 135, + 821, + 176 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "• Finally, the encoder-decoder’s ability to recreate sentences (BLEU) is not entirely indicative of the quality of the encoder at representing aspects such as word identity and order. This suggests that BLEU is sub-optimal for model selection. 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We use NLTK (Bird, 2006) for tokenization, and constrain sentence lengths to be between 5 and 70 words. ", + "bbox": [ + 174, + 135, + 825, + 176 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "For the CBOW model, we train Skip-gram word vectors (Mikolov et al., 2013a), with hierarchicalsoftmax and a window size of 5 words, using the Gensim implementation.4 We control for the embedding size $k$ and train word vectors of sizes $k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}$ . ", + "bbox": [ + 174, + 184, + 825, + 226 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "For the encoder-decoder models, we use an in-house implementation using the Torch7 toolkit (Collobert et al., 2011). The decoder is trained as a language model, attempting to predict the correct word at each time step using a negative-log-likelihood objective (cross-entropy loss over the softmax layer). We use one layer of LSTM cells for the encoder and decoder using the implementation in Leonard et al. (2015). ´ ", + "bbox": [ + 174, + 233, + 825, + 303 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "We use the same size for word and sentence representations (i.e. $d \\ = \\ k$ ), and train models of sizes $k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}$ . We follow previous work on sequence-to-sequence learning (Sutskever et al., 2014; Li et al., 2015) in reversing the input sentences and clipping gradients. Word vectors are initialized to random values. ", + "bbox": [ + 174, + 309, + 825, + 364 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "We evaluate the encoder-decoder models using BLEU scores (Papineni et al., 2002), a popular machine translation evaluation metric that is also used to evaluate auto-encoder models (Li et al., 2015). BLEU score measures how well the original sentence is recreated, and can be thought of as a proxy for the quality of the encoded representation. We compare it with the performance of the models on the three prediction tasks. The results of the higher-dimensional models are comparable to those found in the literature, which serves as a sanity check for the quality of the learned models. ", + "bbox": [ + 174, + 372, + 825, + 455 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Auxiliary Task Classifier For the auxiliary task predictors, we use multi-layer perceptrons with a single hidden layer and ReLU activation, which were carefully tuned for each of the tasks. We experimented with several network architectures prior to arriving at this configuration. ", + "bbox": [ + 174, + 473, + 825, + 515 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Further details regarding the training and architectures of both the sentence encoders and auxiliary task classifiers are available in the Appendix. ", + "bbox": [ + 176, + 522, + 823, + 551 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "APPENDIX II: TECHNICAL DETAILS ", + "text_level": 1, + "bbox": [ + 176, + 573, + 472, + 589 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "ENCODER DECODER ", + "bbox": [ + 176, + 607, + 318, + 621 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Parameters of the encoder-decoder were tuned on a dedicated validation set. We experienced with different learning rates (0.1, 0.01, 0.001), dropout-rates (0.1, 0.2, 0.3, 0.5) (Hinton et al., 2012) and optimization techniques (AdaGrad (Duchi et al., 2011), AdaDelta (Zeiler, 2012), Adam (Kingma & Ba, 2014) and RMSprop (Tieleman & Hinton, 2012)). We also experimented with different batch sizes (8, 16, 32), and found improvement in runtime but no significant improvement in performance. ", + "bbox": [ + 174, + 632, + 825, + 703 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Based on the tuned parameters, we trained the encoder-decoder models on a single GPU (NVIDIA Tesla K40), with mini-batches of 32 sentences, learning rate of 0.01, dropout rate of 0.1, and the AdaGrad optimizer; training takes approximately 10 days and is stopped after 5 epochs with no loss improvement on a validation set. ", + "bbox": [ + 176, + 709, + 825, + 765 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "PREDICTION TASKS ", + "text_level": 1, + "bbox": [ + 176, + 785, + 313, + 799 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Parameters for the predictions tasks as well as classifier architecture were tuned on a dedicated validation set. We experimented with one, two and three layer feed-forward networks using ReLU (Nair & Hinton, 2010; Glorot et al., 2011), tanh and sigmoid activation functions. We tried different hidden layer sizes: the same as the input size, twice the input size and one and a half times the input size. We tried different learning rates (0.1, 0.01, 0.001), dropout rates (0.1, 0.3, 0.5, 0.8) and different optimization techniques (AdaGrad, AdaDelta and Adam). ", + "bbox": [ + 174, + 813, + 825, + 895 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Our best tuned classifier, which we use for all experiments, is a feed-forward network with one hidden layer and a ReLU activation function. We set the size of the hidden layer to be the same size as the input vector. We place a softmax layer on top whose size varies according to the specific task, and apply dropout before the softmax layer. We optimize the log-likelihood using AdaGrad. We use a dropout rate of 0.8 and a learning rate of 0.01. Training is stopped after 5 epochs with no loss improvement on the development set. Training was done on a single GPU (NVIDIA Tesla K40). ", + "bbox": [ + 173, + 103, + 825, + 188 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "10 ADDITIONAL EXPERIMENTS - CONTENT TASK ", + "text_level": 1, + "bbox": [ + 176, + 207, + 602, + 223 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "How well do the models preserve content when we increase the sentence length? In Fig. 5 we plot content prediction accuracy vs. sentence length for different models. ", + "bbox": [ + 174, + 238, + 825, + 266 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/8a2f0243ec8ee281bff85c440c131dec3d455bbb04308d04d68ae81b98dd8e95.jpg", + "image_caption": [ + "Figure 5: Content accuracy vs. sentence length for selected models. " + ], + "image_footnote": [], + "bbox": [ + 346, + 281, + 650, + 443 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "As expected, all models suffer a drop in content accuracy on longer sentences. The degradation is roughly linear in the sentence length. For the encoder-decoder, models with fewer dimensions seem to degrade slower. ", + "bbox": [ + 174, + 487, + 825, + 529 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "APPENDIX III: SIGNIFICANCE TESTS ", + "text_level": 1, + "bbox": [ + 176, + 547, + 482, + 565 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In this section we report the significance tests we conduct in order to evaluate our findings. In order to do so, we use the paired t-test (Rubin, 1973). ", + "bbox": [ + 173, + 579, + 823, + 608 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "All the results reported in the summery of findings are highly significant (p-value $\\ll 0 . 0 0 0 1$ ). The ones we found to be not significant $\\mathrm { { \\dot { p } } }$ -value $\\gg 0 . 0 3$ ) are the ones which their accuracy does not have much of a difference, i.e ED with size 500 and ED with size 750 tested on the word order task (p-value $= 0 . 1 1$ ), or CBOW with dimensions 750 and 1000 (p-value ${ \\ : = } 0 . 3$ ). ", + "bbox": [ + 176, + 614, + 823, + 671 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/e8cf86dc65b2e6769898ec6f61a7bb023639c41bb10218c50aa02354b00b8e20.jpg", + "table_caption": [ + "Table 2: P-values for ED vs. CBOW over the different dimensions and tasks. For example, in the row where dim equals 100, we compute the p-value of ED compared to CBOW with embed size of 100 on all three tasks. " + ], + "table_footnote": [], + "table_body": "
Dim.LengthWordcontentWordorder
1001.77e-1470.01.83e-296
3000.00.00.0
5000.00.00.0
7500.00.00.0
10000.00.00.0
", + "bbox": [ + 331, + 684, + 663, + 763 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/2c372fcc94fbc381c62cbfcd2faaf60422e180ca46deb8bc4b77596070b89bc8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dim.LengthWord contentWord order
100 vs.3000.08.56e-1900.0
300 vs. 5007.3e-714.20e-055.48e-56
500 vs. 7503.64e-1754.46e-650.11
750 vs. 10001.37e-1112.35e-2434.32e-61
", + "bbox": [ + 308, + 829, + 687, + 895 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "Table 3: P-values for ED models over the different dimensions and tasks. ", + "bbox": [ + 277, + 906, + 720, + 920 + ], + "page_idx": 11 + }, + { + "type": "table", + "img_path": "images/c4339b1508fd6d14b345b14e037aa1fc698b19329d98d84de8851ecb3cd7f1c7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Dim.LengthWord contentWord order
100 vs.3000.00.01.5e-33
300 vs. 5001.47e-2150.03.06e-64
500 vs. 7500.680.0320.05
750 vs.10004.44e-320.30.08
", + "bbox": [ + 308, + 101, + 687, + 167 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Table 4: P-values for CBOW models over the different dimensions and tasks. 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Two common", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 299, + 469, + 311 + ], + "spans": [ + { + "bbox": [ + 141, + 299, + 469, + 311 + ], + "score": 1.0, + "content": "methods include representations based on averaging word vectors, and represen-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 142, + 309, + 469, + 320 + ], + "spans": [ + { + "bbox": [ + 142, + 309, + 469, + 320 + ], + "score": 1.0, + "content": "tations based on the hidden states of recurrent neural networks such as LSTMs.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 142, + 320, + 469, + 332 + ], + "spans": [ + { + "bbox": [ + 142, + 320, + 469, + 332 + ], + "score": 1.0, + "content": "The sentence vectors are used as features for subsequent machine learning tasks", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 331, + 470, + 344 + ], + "spans": [ + { + "bbox": [ + 141, + 331, + 470, + 344 + ], + "score": 1.0, + "content": "or for pre-training in the context of deep learning. However, not much is known", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 142, + 342, + 470, + 354 + ], + "spans": [ + { + "bbox": [ + 142, + 342, + 470, + 354 + ], + "score": 1.0, + "content": "about the properties that are encoded in these sentence representations and about", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 353, + 298, + 366 + ], + "spans": [ + { + "bbox": [ + 141, + 353, + 298, + 366 + ], + "score": 1.0, + "content": "the language information they capture.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13.5, + "bbox_fs": [ + 141, + 276, + 470, + 366 + ] + }, + { + "type": "text", + "bbox": [ + 143, + 366, + 468, + 464 + ], + "lines": [ + { + "bbox": [ + 142, + 365, + 469, + 379 + ], + "spans": [ + { + "bbox": [ + 142, + 365, + 469, + 379 + ], + "score": 1.0, + "content": "We propose a framework that facilitates better understanding of the encoded rep-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 377, + 469, + 389 + ], + "spans": [ + { + "bbox": [ + 141, + 377, + 469, + 389 + ], + "score": 1.0, + "content": "resentations. We define prediction tasks around isolated aspects of sentence struc-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 388, + 469, + 400 + ], + "spans": [ + { + "bbox": [ + 141, + 388, + 469, + 400 + ], + "score": 1.0, + "content": "ture (namely sentence length, word content, and word order), and score repre-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 399, + 469, + 410 + ], + "spans": [ + { + "bbox": [ + 141, + 399, + 469, + 410 + ], + "score": 1.0, + "content": "sentations by the ability to train a classifier to solve each prediction task when", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 410, + 470, + 421 + ], + "spans": [ + { + "bbox": [ + 141, + 410, + 470, + 421 + ], + "score": 1.0, + "content": "using the representation as input. 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The analy-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 432, + 469, + 443 + ], + "spans": [ + { + "bbox": [ + 141, + 432, + 469, + 443 + ], + "score": 1.0, + "content": "sis sheds light on the relative strengths of different sentence embedding methods", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 142, + 443, + 470, + 455 + ], + "spans": [ + { + "bbox": [ + 142, + 443, + 470, + 455 + ], + "score": 1.0, + "content": "with respect to these low level prediction tasks, and on the effect of the encoded", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 453, + 368, + 466 + ], + "spans": [ + { + "bbox": [ + 141, + 453, + 368, + 466 + ], + "score": 1.0, + "content": "vector’s dimensionality on the resulting representations.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22, + "bbox_fs": [ + 141, + 365, + 470, + 466 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 483, + 206, + 495 + ], + "lines": [ + { + "bbox": [ + 105, + 482, + 208, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 208, + 498 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 507, + 505, + 562 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "score": 1.0, + "content": "While sentence embeddings or sentence representations play a central role in recent deep learning", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 517, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 505, + 532 + ], + "score": 1.0, + "content": "approaches to NLP, little is known about the information that is captured by different sentence em-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 528, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 505, + 542 + ], + "score": 1.0, + "content": "bedding learning mechanisms. 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A", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 603 + ], + "score": 1.0, + "content": "simple and common approach is producing word-level vectors using, e.g., word2vec (Mikolov et al.,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "2013a;b), and summing or averaging the vectors of the words participating in the sentence. This", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 612, + 459, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 459, + 624 + ], + "score": 1.0, + "content": "continuous-bag-of-words (CBOW) approach disregards the word order in the sentence.1", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35, + "bbox_fs": [ + 105, + 567, + 506, + 624 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 628, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 106, + 628, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 505, + 641 + ], + "score": 1.0, + "content": "Another approach is the encoder-decoder architecture, producing models also known as sequence-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 639, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 651 + ], + "score": 1.0, + "content": "to-sequence models (Sutskever et al., 2014; Cho et al., 2014; Bahdanau et al., 2014, inter alia). In", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "this architecture, an encoder network (e.g. an LSTM) is used to produce a vector representation", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 661, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 661, + 505, + 673 + ], + "score": 1.0, + "content": "of the sentence, which is then fed as input into a decoder network that uses it to perform some", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "score": 1.0, + "content": "prediction task (e.g. recreate the sentence, or produce a translation of it). The encoder and decoder", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 684, + 353, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 684, + 353, + 695 + ], + "score": 1.0, + "content": "networks are trained jointly in order to perform the final task.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 628, + 505, + 695 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 236 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Some systems (for example in machine translation) train the system end-to-end, and use the trained", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "system for prediction (Bahdanau et al., 2014). Such systems do not generally care about the encoded", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "vectors, which are used merely as intermediate values. However, another common case is to train an", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "encoder-decoder network and then throw away the decoder and use the trained encoder as a general", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 505, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 139 + ], + "score": 1.0, + "content": "mechanism for obtaining sentence representations. For example, an encoder-decoder network can", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "be trained as an auto-encoder, where the encoder creates a vector representation, and the decoder", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "score": 1.0, + "content": "attempts to recreate the original sentence (Li et al., 2015). Similarly, Kiros et al. (2015) train a net-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 160, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 160, + 505, + 171 + ], + "score": 1.0, + "content": "work to encode a sentence such that the decoder can recreate its neighboring sentences in the text.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 169, + 506, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 506, + 183 + ], + "score": 1.0, + "content": "Such networks do not require specially labeled data, and can be trained on large amounts of unanno-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 182, + 505, + 193 + ], + "spans": [ + { + "bbox": [ + 106, + 182, + 505, + 193 + ], + "score": 1.0, + "content": "tated text. As the decoder needs information about the sentence in order to perform well, it is clear", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "score": 1.0, + "content": "that the encoded vectors capture a non-trivial amount of information about the sentence, making", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 203, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 505, + 216 + ], + "score": 1.0, + "content": "the encoder appealing to use as a general purpose, stand-alone sentence encoding mechanism. The", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 215, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 226 + ], + "score": 1.0, + "content": "sentence encodings can then be used as input for other prediction tasks for which less training data", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 224, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 505, + 239 + ], + "score": 1.0, + "content": "is available (Dai & Le, 2015). 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This is the approach taken", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 285, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 299 + ], + "score": 1.0, + "content": "by Li et al. (2015), Hill et al. (2016) and Kiros et al. (2015). This method of comparing sentence", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 297, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 505, + 309 + ], + "score": 1.0, + "content": "embeddings leaves a lot to be desired: the comparison is at a very coarse-grained level, does not tell", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 307, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 506, + 321 + ], + "score": 1.0, + "content": "us much about the kind of information that is encoded in the representation, and does not help us", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 319, + 236, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 319, + 236, + 330 + ], + "score": 1.0, + "content": "form generalizable conclusions.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 17.5 + }, + { + "type": "text", + "bbox": [ + 107, + 343, + 505, + 431 + ], + "lines": [ + { + "bbox": [ + 105, + 342, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 506, + 356 + ], + "score": 1.0, + "content": "Our Contribution We take a first step towards opening the black box of vector embeddings for", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "score": 1.0, + "content": "sentences. We propose a methodology that facilitates comparing sentence embeddings on a much", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 365, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 378 + ], + "score": 1.0, + "content": "finer-grained level, and demonstrate its use by analyzing and comparing different sentence repre-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 376, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 505, + 388 + ], + "score": 1.0, + "content": "sentations. We analyze sentence representation methods that are based on LSTM auto-encoders and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 387, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 506, + 400 + ], + "score": 1.0, + "content": "the simple CBOW representation produced by averaging word2vec word embeddings. For each of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 397, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 506, + 411 + ], + "score": 1.0, + "content": "CBOW and LSTM auto-encoder, we compare different numbers of dimensions, exploring the ef-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 408, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 408, + 506, + 422 + ], + "score": 1.0, + "content": "fect of the dimensionality on the resulting representation. We also provide some comparison to the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 420, + 298, + 432 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 298, + 432 + ], + "score": 1.0, + "content": "skip-thought embeddings of Kiros et al. 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Our analysis of these low-level properties", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 469, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 506, + 483 + ], + "score": 1.0, + "content": "leads to interesting, actionable insights, exposing relative strengths and weaknesses of the different", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 481, + 172, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 172, + 493 + ], + "score": 1.0, + "content": "representations.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 106, + 505, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 105, + 504, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 506, + 518 + ], + "score": 1.0, + "content": "Limitations Focusing on low-level sentence properties also has limitations: The tasks focus on", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "measuring the preservation of surface aspects of the sentence and do not measure syntactic and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "semantic generalization abilities; the tasks are not directly related to any specific downstream appli-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "cation (although the properties we test are important factors in many tasks – knowing that a model", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "is good at predicting length and word order is likely advantageous for syntactic parsing, while mod-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "els that excel at word content are good for text classification tasks). Dealing with these limitations", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 570, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 104, + 570, + 506, + 583 + ], + "score": 1.0, + "content": "requires a complementary set of auxiliary tasks, which is outside the scope of this study and is left", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 582, + 172, + 593 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 172, + 593 + ], + "score": 1.0, + "content": "for future work.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 598, + 504, + 664 + ], + "lines": [ + { + "bbox": [ + 106, + 598, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 598, + 505, + 611 + ], + "score": 1.0, + "content": "The study also suffers from the general limitations of empirical work: we do not prove general", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 609, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 505, + 621 + ], + "score": 1.0, + "content": "theorems but rather measure behaviors on several data points and attempt to draw conclusions from", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 621, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 632 + ], + "score": 1.0, + "content": "these measurements. There is always the risk that our conclusions only hold for the datasets on", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 631, + 505, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 631, + 505, + 643 + ], + "score": 1.0, + "content": "which we measured, and will not generalize. However, we do consider our large sample of sentences", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 641, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 506, + 655 + ], + "score": 1.0, + "content": "from Wikipedia to be representative of the English language, at least in terms of the three basic", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 653, + 243, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 243, + 666 + ], + "score": 1.0, + "content": "sentence properties that we study.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45.5 + }, + { + "type": "text", + "bbox": [ + 106, + 677, + 504, + 699 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "Summary of Findings Our analysis reveals the following insights regarding the different sentence", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 688, + 193, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 193, + 700 + ], + "score": 1.0, + "content": "embedding methods:", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 49.5 + }, + { + "type": "text", + "bbox": [ + 108, + 709, + 503, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "• Sentence representations based on averaged word vectors are surprisingly effective, and encode", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 115, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 115, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "a non-trivial amount of information regarding sentence length. The information they contain", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 51.5 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 13, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 236 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "Some systems (for example in machine translation) train the system end-to-end, and use the trained", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "system for prediction (Bahdanau et al., 2014). 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For example, an encoder-decoder network can", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "be trained as an auto-encoder, where the encoder creates a vector representation, and the decoder", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "score": 1.0, + "content": "attempts to recreate the original sentence (Li et al., 2015). Similarly, Kiros et al. 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The", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 215, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 226 + ], + "score": 1.0, + "content": "sentence encodings can then be used as input for other prediction tasks for which less training data", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 224, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 505, + 239 + ], + "score": 1.0, + "content": "is available (Dai & Le, 2015). 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For each of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 397, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 506, + 411 + ], + "score": 1.0, + "content": "CBOW and LSTM auto-encoder, we compare different numbers of dimensions, exploring the ef-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 408, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 408, + 506, + 422 + ], + "score": 1.0, + "content": "fect of the dimensionality on the resulting representation. We also provide some comparison to the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 420, + 298, + 432 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 298, + 432 + ], + "score": 1.0, + "content": "skip-thought embeddings of Kiros et al. (2015).", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25.5, + "bbox_fs": [ + 104, + 342, + 506, + 432 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 437, + 505, + 491 + ], + "lines": [ + { + "bbox": [ + 105, + 436, + 505, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 505, + 449 + ], + "score": 1.0, + "content": "In this work, we focus on what are arguably the three most basic characteristics of a sequence:", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 448, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 460 + ], + "score": 1.0, + "content": "its length, the items within it, and their order. We investigate different sentence representations", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "based on the capacity to which they encode these aspects. Our analysis of these low-level properties", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 469, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 506, + 483 + ], + "score": 1.0, + "content": "leads to interesting, actionable insights, exposing relative strengths and weaknesses of the different", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 481, + 172, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 172, + 493 + ], + "score": 1.0, + "content": "representations.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 436, + 506, + 493 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 505, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 105, + 504, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 506, + 518 + ], + "score": 1.0, + "content": "Limitations Focusing on low-level sentence properties also has limitations: The tasks focus on", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "measuring the preservation of surface aspects of the sentence and do not measure syntactic and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "semantic generalization abilities; the tasks are not directly related to any specific downstream appli-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "cation (although the properties we test are important factors in many tasks – knowing that a model", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "is good at predicting length and word order is likely advantageous for syntactic parsing, while mod-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "els that excel at word content are good for text classification tasks). Dealing with these limitations", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 104, + 570, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 104, + 570, + 506, + 583 + ], + "score": 1.0, + "content": "requires a complementary set of auxiliary tasks, which is outside the scope of this study and is left", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 582, + 172, + 593 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 172, + 593 + ], + "score": 1.0, + "content": "for future work.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38.5, + "bbox_fs": [ + 104, + 504, + 506, + 593 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 598, + 504, + 664 + ], + "lines": [ + { + "bbox": [ + 106, + 598, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 598, + 505, + 611 + ], + "score": 1.0, + "content": "The study also suffers from the general limitations of empirical work: we do not prove general", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 609, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 505, + 621 + ], + "score": 1.0, + "content": "theorems but rather measure behaviors on several data points and attempt to draw conclusions from", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 621, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 632 + ], + "score": 1.0, + "content": "these measurements. There is always the risk that our conclusions only hold for the datasets on", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 631, + 505, + 643 + ], + "spans": [ + { + "bbox": [ + 106, + 631, + 505, + 643 + ], + "score": 1.0, + "content": "which we measured, and will not generalize. However, we do consider our large sample of sentences", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 641, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 506, + 655 + ], + "score": 1.0, + "content": "from Wikipedia to be representative of the English language, at least in terms of the three basic", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 653, + 243, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 243, + 666 + ], + "score": 1.0, + "content": "sentence properties that we study.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 598, + 506, + 666 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 677, + 504, + 699 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "Summary of Findings Our analysis reveals the following insights regarding the different sentence", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 688, + 193, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 193, + 700 + ], + "score": 1.0, + "content": "embedding methods:", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 49.5, + "bbox_fs": [ + 105, + 677, + 505, + 700 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 709, + 503, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "• Sentence representations based on averaged word vectors are surprisingly effective, and encode", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 115, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 115, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "a non-trivial amount of information regarding sentence length. The information they contain", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 116, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 116, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "can also be used to reconstruct a non-trivial amount of the original word order in a probabilistic", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 344, + 106 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 344, + 106 + ], + "score": 1.0, + "content": "manner (due to regularities in the natural language data).", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 51.5, + "bbox_fs": [ + 106, + 709, + 505, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 110, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 116, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 116, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "can also be used to reconstruct a non-trivial amount of the original word order in a probabilistic", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 344, + 106 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 344, + 106 + ], + "score": 1.0, + "content": "manner (due to regularities in the natural language data).", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 106, + 109, + 506, + 199 + ], + "lines": [ + { + "bbox": [ + 105, + 109, + 444, + 121 + ], + "spans": [ + { + "bbox": [ + 105, + 109, + 444, + 121 + ], + "score": 1.0, + "content": "• LSTM auto-encoders are very effective at encoding word order and word content.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 124, + 418, + 136 + ], + "spans": [ + { + "bbox": [ + 106, + 124, + 418, + 136 + ], + "score": 1.0, + "content": "• Increasing the number of dimensions benefits some tasks more than others.", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 139, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 106, + 139, + 505, + 151 + ], + "score": 1.0, + "content": "• Adding more hidden units sometimes degrades the encoders’ ability to encode word content. This", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 150, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 115, + 150, + 505, + 163 + ], + "score": 1.0, + "content": "degradation is not correlated with the BLEU scores of the decoder, suggesting that BLEU over", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 161, + 398, + 174 + ], + "spans": [ + { + "bbox": [ + 115, + 161, + 398, + 174 + ], + "score": 1.0, + "content": "the decoder output is sub-optimal for evaluating the encoders’ quality.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "• LSTM encoders trained as auto-encoders do not rely on ordering patterns in the training sentences", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 187, + 477, + 200 + ], + "spans": [ + { + "bbox": [ + 116, + 187, + 477, + 200 + ], + "score": 1.0, + "content": "when encoding novel sentences, while the skip-thought encoders do rely on such patterns.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 108, + 215, + 211, + 228 + ], + "lines": [ + { + "bbox": [ + 104, + 214, + 213, + 231 + ], + "spans": [ + { + "bbox": [ + 104, + 214, + 213, + 231 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 240, + 505, + 307 + ], + "lines": [ + { + "bbox": [ + 106, + 241, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 505, + 254 + ], + "score": 1.0, + "content": "Word-level distributed representations have been analyzed rather extensively, both empirically and", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "theoretically, for example by Baroni et al. (2014), Levy & Goldberg (2014) and Levy et al. (2015).", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 262, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 505, + 276 + ], + "score": 1.0, + "content": "In contrast, the analysis of sentence-level representations has been much more limited. Commonly", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 273, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 505, + 286 + ], + "score": 1.0, + "content": "used approaches is to either compare the performance of the sentence embeddings on down-stream", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "tasks (Hill et al., 2016), or to analyze models, specifically trained for predefined task (Schmaltz", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 296, + 250, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 296, + 250, + 308 + ], + "score": 1.0, + "content": "et al., 2016; Sutskever et al., 2011).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 505, + 401 + ], + "lines": [ + { + "bbox": [ + 106, + 313, + 504, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 504, + 325 + ], + "score": 1.0, + "content": "While the resulting analysis reveals differences in performance of different models, it does not ade-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "quately explain what kind of linguistic properties of the sentence they capture. Other studies analyze", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "the hidden units learned by neural networks when training a sentence representation model (Elman,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "1991; Karpathy et al., 2015; Kad´ ar et al., 2016). This approach often associates certain linguistic ´", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "score": 1.0, + "content": "aspects with certain hidden units. Kad´ ar et al. (2016) propose a methodology for quantifying the ´", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "contribution of each input word to a resulting GRU-based encoding. These methods depend on the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "score": 1.0, + "content": "specific learning model and cannot be applied to arbitrary representations. Moreover, it is still not", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 389, + 334, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 334, + 403 + ], + "score": 1.0, + "content": "clear what is captured by the final sentence embeddings.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 108, + 406, + 505, + 439 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "Our work is orthogonal and complementary to the previous efforts: we analyze the resulting sentence", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 415, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 432 + ], + "score": 1.0, + "content": "embeddings by devising auxiliary prediction tasks for core sentence properties. The methodology", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 428, + 425, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 425, + 441 + ], + "score": 1.0, + "content": "we purpose is general and can be applied to any sentence representation model.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 107, + 456, + 183, + 468 + ], + "lines": [ + { + "bbox": [ + 104, + 454, + 185, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 454, + 185, + 471 + ], + "score": 1.0, + "content": "3 APPROACH", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 481, + 505, + 514 + ], + "lines": [ + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "score": 1.0, + "content": "We aim to inspect and compare encoded sentence vectors in a task-independent manner. The main", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "score": 1.0, + "content": "idea of our method is to focus on isolated aspects of sentence structure, and design experiments to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 504, + 397, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 397, + 515 + ], + "score": 1.0, + "content": "measure to what extent each aspect is captured in a given representation.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 519, + 504, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 520, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 505, + 532 + ], + "score": 1.0, + "content": "In each experiment, we formulate a prediction task. Given a sentence representation method, we", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "create training data and train a classifier to predict a specific sentence property (e.g. their length)", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "based on their vector representations. We then measure how well we can train a model to perform the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "task. The basic premise is that if we cannot train a classifier to predict some property of a sentence", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 564, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 576 + ], + "score": 1.0, + "content": "based on its vector representation, then this property is not encoded in the representation (or rather,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 575, + 446, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 446, + 587 + ], + "score": 1.0, + "content": "not encoded in a useful way, considering how the representation is likely to be used).", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 107, + 592, + 504, + 636 + ], + "lines": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "score": 1.0, + "content": "The experiments in this work focus on low-level properties of sentences – the sentence length, the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 603, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 506, + 615 + ], + "score": 1.0, + "content": "identities of words in a sentence, and the order of the words. We consider these to be the core", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 614, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 505, + 626 + ], + "score": 1.0, + "content": "elements of sentence structure. Generalizing the approach to higher-level semantic and syntactic", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 625, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 504, + 637 + ], + "score": 1.0, + "content": "properties holds great potential, which we hope will be explored in future work, by us or by others.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5 + }, + { + "type": "title", + "bbox": [ + 107, + 650, + 237, + 661 + ], + "lines": [ + { + "bbox": [ + 105, + 648, + 238, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 238, + 663 + ], + "score": 1.0, + "content": "3.1 THE PREDICTION TASKS", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 108, + 671, + 504, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 670, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 670, + 443, + 684 + ], + "score": 1.0, + "content": "We now turn to describe the specific prediction tasks. 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This", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 150, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 115, + 150, + 505, + 163 + ], + "score": 1.0, + "content": "degradation is not correlated with the BLEU scores of the decoder, suggesting that BLEU over", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 161, + 398, + 174 + ], + "spans": [ + { + "bbox": [ + 115, + 161, + 398, + 174 + ], + "score": 1.0, + "content": "the decoder output is sub-optimal for evaluating the encoders’ quality.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "• LSTM encoders trained as auto-encoders do not rely on ordering patterns in the training sentences", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 116, + 187, + 477, + 200 + ], + "spans": [ + { + "bbox": [ + 116, + 187, + 477, + 200 + ], + "score": 1.0, + "content": "when encoding novel sentences, while the skip-thought encoders do rely on such patterns.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 109, + 505, + 200 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 215, + 211, + 228 + ], + "lines": [ + { + "bbox": [ + 104, + 214, + 213, + 231 + ], + "spans": [ + { + "bbox": [ + 104, + 214, + 213, + 231 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 240, + 505, + 307 + ], + "lines": [ + { + "bbox": [ + 106, + 241, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 505, + 254 + ], + "score": 1.0, + "content": "Word-level distributed representations have been analyzed rather extensively, both empirically and", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "theoretically, for example by Baroni et al. (2014), Levy & Goldberg (2014) and Levy et al. (2015).", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 262, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 505, + 276 + ], + "score": 1.0, + "content": "In contrast, the analysis of sentence-level representations has been much more limited. Commonly", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 273, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 505, + 286 + ], + "score": 1.0, + "content": "used approaches is to either compare the performance of the sentence embeddings on down-stream", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "tasks (Hill et al., 2016), or to analyze models, specifically trained for predefined task (Schmaltz", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 296, + 250, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 296, + 250, + 308 + ], + "score": 1.0, + "content": "et al., 2016; Sutskever et al., 2011).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 241, + 506, + 308 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 505, + 401 + ], + "lines": [ + { + "bbox": [ + 106, + 313, + 504, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 504, + 325 + ], + "score": 1.0, + "content": "While the resulting analysis reveals differences in performance of different models, it does not ade-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "quately explain what kind of linguistic properties of the sentence they capture. Other studies analyze", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "the hidden units learned by neural networks when training a sentence representation model (Elman,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "1991; Karpathy et al., 2015; Kad´ ar et al., 2016). This approach often associates certain linguistic ´", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "score": 1.0, + "content": "aspects with certain hidden units. Kad´ ar et al. (2016) propose a methodology for quantifying the ´", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "contribution of each input word to a resulting GRU-based encoding. These methods depend on the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 506, + 391 + ], + "score": 1.0, + "content": "specific learning model and cannot be applied to arbitrary representations. Moreover, it is still not", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 389, + 334, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 334, + 403 + ], + "score": 1.0, + "content": "clear what is captured by the final sentence embeddings.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 313, + 506, + 403 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 406, + 505, + 439 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "Our work is orthogonal and complementary to the previous efforts: we analyze the resulting sentence", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 415, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 432 + ], + "score": 1.0, + "content": "embeddings by devising auxiliary prediction tasks for core sentence properties. The methodology", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 428, + 425, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 425, + 441 + ], + "score": 1.0, + "content": "we purpose is general and can be applied to any sentence representation model.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 406, + 505, + 441 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 456, + 183, + 468 + ], + "lines": [ + { + "bbox": [ + 104, + 454, + 185, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 454, + 185, + 471 + ], + "score": 1.0, + "content": "3 APPROACH", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 481, + 505, + 514 + ], + "lines": [ + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 505, + 494 + ], + "score": 1.0, + "content": "We aim to inspect and compare encoded sentence vectors in a task-independent manner. The main", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 505 + ], + "score": 1.0, + "content": "idea of our method is to focus on isolated aspects of sentence structure, and design experiments to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 504, + 397, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 397, + 515 + ], + "score": 1.0, + "content": "measure to what extent each aspect is captured in a given representation.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 481, + 505, + 515 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 519, + 504, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 520, + 505, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 505, + 532 + ], + "score": 1.0, + "content": "In each experiment, we formulate a prediction task. Given a sentence representation method, we", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "create training data and train a classifier to predict a specific sentence property (e.g. their length)", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "based on their vector representations. We then measure how well we can train a model to perform the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "task. The basic premise is that if we cannot train a classifier to predict some property of a sentence", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 564, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 576 + ], + "score": 1.0, + "content": "based on its vector representation, then this property is not encoded in the representation (or rather,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 575, + 446, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 446, + 587 + ], + "score": 1.0, + "content": "not encoded in a useful way, considering how the representation is likely to be used).", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 520, + 505, + 587 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 592, + 504, + 636 + ], + "lines": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "score": 1.0, + "content": "The experiments in this work focus on low-level properties of sentences – the sentence length, the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 603, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 506, + 615 + ], + "score": 1.0, + "content": "identities of words in a sentence, and the order of the words. We consider these to be the core", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 614, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 505, + 626 + ], + "score": 1.0, + "content": "elements of sentence structure. Generalizing the approach to higher-level semantic and syntactic", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 625, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 504, + 637 + ], + "score": 1.0, + "content": "properties holds great potential, which we hope will be explored in future work, by us or by others.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 591, + 506, + 637 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 650, + 237, + 661 + ], + "lines": [ + { + "bbox": [ + 105, + 648, + 238, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 238, + 663 + ], + "score": 1.0, + "content": "3.1 THE PREDICTION TASKS", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 108, + 671, + 504, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 670, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 670, + 443, + 684 + ], + "score": 1.0, + "content": "We now turn to describe the specific prediction tasks. 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The idea behind this setup is to test the", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 328, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 328, + 118 + ], + "score": 1.0, + "content": "models on what are presumably their best embeddings.", + "type": "text", + "cross_page": true + } + ], + "index": 2 + } + ], + "index": 45.5, + "bbox_fs": [ + 106, + 709, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "are used for each of the test and development examples. These sentences are a subset of the training", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "set that was used to train the original sentence encoders. The idea behind this setup is to test the", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 328, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 328, + 118 + ], + "score": 1.0, + "content": "models on what are presumably their best embeddings.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 119, + 505, + 186 + ], + "lines": [ + { + "bbox": [ + 106, + 119, + 504, + 130 + ], + "spans": [ + { + "bbox": [ + 106, + 119, + 504, + 130 + ], + "score": 1.0, + "content": "Length Task This task measures to what extent the sentence representation encodes its length.", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 128, + 506, + 143 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 237, + 143 + ], + "score": 1.0, + "content": "Given a sentence representation", + "type": "text" + }, + { + "bbox": [ + 237, + 129, + 269, + 141 + ], + "score": 0.91, + "content": "\\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 128, + 506, + 143 + ], + "score": 1.0, + "content": ", the goal of the classifier is to predict the length (number", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 140, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 105, + 140, + 244, + 154 + ], + "score": 1.0, + "content": "of words) in the original sentence", + "type": "text" + }, + { + "bbox": [ + 245, + 144, + 251, + 151 + ], + "score": 0.71, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 251, + 140, + 505, + 154 + ], + "score": 1.0, + "content": ". The task is formulated as multiclass classification, with eight", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 151, + 506, + 164 + ], + "spans": [ + { + "bbox": [ + 105, + 151, + 506, + 164 + ], + "score": 1.0, + "content": "output classes corresponding to binned lengths.2 The resulting dataset is reasonably balanced, with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 162, + 505, + 175 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 505, + 175 + ], + "score": 1.0, + "content": "a majority class (lengths 5-8 words) of 5,182 test instances and a minority class (34-70) of 1,084 test", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 174, + 437, + 186 + ], + "spans": [ + { + "bbox": [ + 106, + 174, + 406, + 186 + ], + "score": 1.0, + "content": "instances. Predicting the majority class results in classification accuracy of", + "type": "text" + }, + { + "bbox": [ + 407, + 174, + 433, + 185 + ], + "score": 0.87, + "content": "2 0 . 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 174, + 437, + 186 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 243 + ], + "lines": [ + { + "bbox": [ + 106, + 188, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 200 + ], + "score": 1.0, + "content": "Word-content Task This task measures to what extent the sentence representation encodes the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 361, + 212 + ], + "score": 1.0, + "content": "identities of words within it. Given a sentence representation", + "type": "text" + }, + { + "bbox": [ + 362, + 199, + 394, + 210 + ], + "score": 0.75, + "content": "\\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 198, + 505, + 212 + ], + "score": 1.0, + "content": "and a word representation", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 506, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 140, + 221 + ], + "score": 0.88, + "content": "\\mathbf { w } \\in \\mathbb { R } ^ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 209, + 338, + 223 + ], + "score": 1.0, + "content": ", the goal of the classifier is to determine whether", + "type": "text" + }, + { + "bbox": [ + 339, + 212, + 348, + 220 + ], + "score": 0.7, + "content": "w", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 209, + 406, + 223 + ], + "score": 1.0, + "content": "appears in the", + "type": "text" + }, + { + "bbox": [ + 407, + 212, + 412, + 220 + ], + "score": 0.68, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 209, + 506, + 223 + ], + "score": 1.0, + "content": ", with access to neither", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 221, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 115, + 231 + ], + "score": 0.7, + "content": "w", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 221, + 132, + 234 + ], + "score": 1.0, + "content": "nor", + "type": "text" + }, + { + "bbox": [ + 133, + 224, + 138, + 231 + ], + "score": 0.64, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 221, + 506, + 234 + ], + "score": 1.0, + "content": ". This is formulated as a binary classification task, where the input is the concatenation of s", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 232, + 138, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 138, + 244 + ], + "score": 1.0, + "content": "and w.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 249, + 505, + 348 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 506, + 263 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 263 + ], + "score": 1.0, + "content": "To create a dataset for this task, we need to provide positive and negative examples. Obtaining", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "score": 1.0, + "content": "positive examples is straightforward: we simply pick a random word from each sentence. For", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 271, + 506, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 284 + ], + "score": 1.0, + "content": "negative examples, we could pick a random word from the entire corpus. However, we found that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "such a dataset tends to push models to memorize words as either positive or negative words, instead", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 292, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 506, + 306 + ], + "score": 1.0, + "content": "of finding their relation to the sentence representation. Therefore, for each sentence we pick as a", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 304, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 506, + 317 + ], + "score": 1.0, + "content": "negative example a word that appears as a positive example somewhere in our dataset, but does", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "score": 1.0, + "content": "not appear in the given sentence. This forces the models to learn a relationship between word and", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 325, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 340 + ], + "score": 1.0, + "content": "sentence representations. We generate one positive and one negative example from each sentence.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 337, + 338, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 337, + 315, + 349 + ], + "score": 1.0, + "content": "The dataset is balanced, with a baseline accuracy of", + "type": "text" + }, + { + "bbox": [ + 315, + 337, + 334, + 348 + ], + "score": 0.87, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 337, + 338, + 349 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 352, + 505, + 418 + ], + "lines": [ + { + "bbox": [ + 106, + 352, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 505, + 363 + ], + "score": 1.0, + "content": "Word-order Task This task measures to what extent the sentence representation encodes word", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 362, + 506, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 263, + 375 + ], + "score": 1.0, + "content": "order. Given a sentence representation", + "type": "text" + }, + { + "bbox": [ + 263, + 362, + 295, + 373 + ], + "score": 0.9, + "content": "\\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 362, + 506, + 375 + ], + "score": 1.0, + "content": "and the representations of two words that appear in", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 372, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 160, + 386 + ], + "score": 1.0, + "content": "the sentence,", + "type": "text" + }, + { + "bbox": [ + 160, + 373, + 215, + 385 + ], + "score": 0.93, + "content": "\\mathbf { w } _ { 1 } , \\mathbf { w } _ { 2 } \\in \\mathbb { R } ^ { { \\bar { d } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 372, + 399, + 386 + ], + "score": 1.0, + "content": ", the goal of the classifier is to predict whether", + "type": "text" + }, + { + "bbox": [ + 399, + 375, + 412, + 385 + ], + "score": 0.87, + "content": "w _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 372, + 506, + 386 + ], + "score": 1.0, + "content": "appears before or after", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 384, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 119, + 396 + ], + "score": 0.84, + "content": "w _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 384, + 217, + 397 + ], + "score": 1.0, + "content": "in the original sentence", + "type": "text" + }, + { + "bbox": [ + 218, + 387, + 223, + 394 + ], + "score": 0.56, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 384, + 506, + 397 + ], + "score": 1.0, + "content": ". Again, the model has no access to the original sentence and the two", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "score": 1.0, + "content": "words. This is formulated as a binary classification task, where the input is a concatenation of the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 406, + 220, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 169, + 419 + ], + "score": 1.0, + "content": "three vectors s,", + "type": "text" + }, + { + "bbox": [ + 169, + 408, + 183, + 417 + ], + "score": 0.84, + "content": "\\mathbf { w } _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 406, + 201, + 419 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 202, + 408, + 215, + 417 + ], + "score": 0.86, + "content": "\\mathbf { w } _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 406, + 220, + 419 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25.5 + }, + { + "type": "text", + "bbox": [ + 107, + 423, + 505, + 457 + ], + "lines": [ + { + "bbox": [ + 105, + 423, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 437 + ], + "score": 1.0, + "content": "For each sentence in the corpus, we simply pick two random words from the sentence as a positive", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 435, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 505, + 446 + ], + "score": 1.0, + "content": "example. For negative examples, we flip the order of the words. We generate one positive and one", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 446, + 493, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 469, + 458 + ], + "score": 1.0, + "content": "negative example from each sentence. The dataset is balanced, with a baseline accuracy of", + "type": "text" + }, + { + "bbox": [ + 469, + 446, + 488, + 456 + ], + "score": 0.88, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 446, + 493, + 458 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30 + }, + { + "type": "title", + "bbox": [ + 107, + 472, + 324, + 485 + ], + "lines": [ + { + "bbox": [ + 105, + 471, + 324, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 324, + 486 + ], + "score": 1.0, + "content": "4 SENTENCE REPRESENTATION MODELS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 496, + 504, + 509 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 176, + 510 + ], + "score": 1.0, + "content": "Given a sentence", + "type": "text" + }, + { + "bbox": [ + 176, + 497, + 265, + 509 + ], + "score": 0.92, + "content": "s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 496, + 505, + 510 + ], + "score": 1.0, + "content": "we aim to find a sentence representation s using an encoder:", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 511, + 385, + 525 + ], + "lines": [ + { + "bbox": [ + 225, + 511, + 385, + 525 + ], + "spans": [ + { + "bbox": [ + 225, + 511, + 385, + 525 + ], + "score": 0.9, + "content": "\\mathrm { E N C } : s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\} \\mapsto \\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "interline_equation", + "image_path": "028c40eb38c89033d23dedb8550c9222de08e33b01c5f48311d315854d242bac.jpg" + } + ] + } + ], + "index": 34, + "virtual_lines": [ + { + "bbox": [ + 225, + 511, + 385, + 525 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 528, + 505, + 572 + ], + "lines": [ + { + "bbox": [ + 105, + 527, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 362, + 542 + ], + "score": 1.0, + "content": "The encoding process usually assumes a vector representation", + "type": "text" + }, + { + "bbox": [ + 362, + 528, + 401, + 540 + ], + "score": 0.92, + "content": "\\mathbf { w } _ { i } \\in \\mathbb { R } ^ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 527, + 505, + 542 + ], + "score": 1.0, + "content": "for each word in the vo-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 380, + 551 + ], + "score": 1.0, + "content": "cabulary. In general, the word and sentence embedding dimensions,", + "type": "text" + }, + { + "bbox": [ + 381, + 540, + 387, + 550 + ], + "score": 0.79, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 540, + 405, + 551 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 405, + 540, + 412, + 549 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 540, + 505, + 551 + ], + "score": 1.0, + "content": ", need not be the same.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "The word vectors can be learned together with other encoder parameters or pre-trained. Below we", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 561, + 268, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 268, + 573 + ], + "score": 1.0, + "content": "describe different instantiations of ENC.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 107, + 584, + 505, + 617 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 597 + ], + "score": 1.0, + "content": "Continuous Bag-of-words (CBOW) This simple yet effective text representation consists of per-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "forming element-wise averaging of word vectors that are obtained using a word-embedding method", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 606, + 182, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 182, + 618 + ], + "score": 1.0, + "content": "such as word2vec.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 106, + 623, + 503, + 646 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 505, + 636 + ], + "score": 1.0, + "content": "Despite its obliviousness to word order, CBOW has proven useful in different tasks (Hill et al., 2016)", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 634, + 393, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 393, + 646 + ], + "score": 1.0, + "content": "and is easy to compute, making it an important model class to consider.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5 + }, + { + "type": "text", + "bbox": [ + 107, + 657, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 105, + 657, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 657, + 505, + 669 + ], + "score": 1.0, + "content": "Encoder-Decoder (ED) The encoder-decoder framework has been successfully used in a number", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 668, + 506, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 506, + 681 + ], + "score": 1.0, + "content": "of sequence-to-sequence learning tasks (Sutskever et al., 2014; Bahdanau et al., 2014; Dai & Le,", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "score": 1.0, + "content": "2015; Li et al., 2015). After the encoding phase, a decoder maps the sentence representation back to", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 690, + 200, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 690, + 200, + 702 + ], + "score": 1.0, + "content": "the sequence of words:", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5 + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 700, + 385, + 715 + ], + "lines": [ + { + "bbox": [ + 225, + 700, + 385, + 715 + ], + "spans": [ + { + "bbox": [ + 225, + 700, + 385, + 715 + ], + "score": 0.92, + "content": "\\mathtt { D E C } : \\mathbf { s } \\in \\mathbb { R } ^ { k } \\mapsto s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\}", + "type": "interline_equation", + "image_path": "e604f5fc4aed2abefe6dc577ec27e0803c75745cbb4691ec7ccf3d02ac2319c0.jpg" + } + ] + } + ], + "index": 48, + "virtual_lines": [ + { + "bbox": [ + 225, + 700, + 385, + 715 + ], + "spans": [], + "index": 48 + } + ] + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 116, + 721, + 419, + 732 + ], + "lines": [ + { + "bbox": [ + 119, + 719, + 418, + 734 + ], + "spans": [ + { + "bbox": [ + 119, + 719, + 418, + 734 + ], + "score": 1.0, + "content": "2We use the bins (5-8), (9-12), (13-16), (17-20), (21-25), (26-29), (30-33), (34-70).", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "4", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 116 + ], + "lines": [], + "index": 1, + "bbox_fs": [ + 105, + 82, + 505, + 118 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 119, + 505, + 186 + ], + "lines": [ + { + "bbox": [ + 106, + 119, + 504, + 130 + ], + "spans": [ + { + "bbox": [ + 106, + 119, + 504, + 130 + ], + "score": 1.0, + "content": "Length Task This task measures to what extent the sentence representation encodes its length.", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 128, + 506, + 143 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 237, + 143 + ], + "score": 1.0, + "content": "Given a sentence representation", + "type": "text" + }, + { + "bbox": [ + 237, + 129, + 269, + 141 + ], + "score": 0.91, + "content": "\\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 128, + 506, + 143 + ], + "score": 1.0, + "content": ", the goal of the classifier is to predict the length (number", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 140, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 105, + 140, + 244, + 154 + ], + "score": 1.0, + "content": "of words) in the original sentence", + "type": "text" + }, + { + "bbox": [ + 245, + 144, + 251, + 151 + ], + "score": 0.71, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 251, + 140, + 505, + 154 + ], + "score": 1.0, + "content": ". The task is formulated as multiclass classification, with eight", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 151, + 506, + 164 + ], + "spans": [ + { + "bbox": [ + 105, + 151, + 506, + 164 + ], + "score": 1.0, + "content": "output classes corresponding to binned lengths.2 The resulting dataset is reasonably balanced, with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 162, + 505, + 175 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 505, + 175 + ], + "score": 1.0, + "content": "a majority class (lengths 5-8 words) of 5,182 test instances and a minority class (34-70) of 1,084 test", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 174, + 437, + 186 + ], + "spans": [ + { + "bbox": [ + 106, + 174, + 406, + 186 + ], + "score": 1.0, + "content": "instances. Predicting the majority class results in classification accuracy of", + "type": "text" + }, + { + "bbox": [ + 407, + 174, + 433, + 185 + ], + "score": 0.87, + "content": "2 0 . 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 174, + 437, + 186 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 119, + 506, + 186 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 243 + ], + "lines": [ + { + "bbox": [ + 106, + 188, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 200 + ], + "score": 1.0, + "content": "Word-content Task This task measures to what extent the sentence representation encodes the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 361, + 212 + ], + "score": 1.0, + "content": "identities of words within it. Given a sentence representation", + "type": "text" + }, + { + "bbox": [ + 362, + 199, + 394, + 210 + ], + "score": 0.75, + "content": "\\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 198, + 505, + 212 + ], + "score": 1.0, + "content": "and a word representation", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 506, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 140, + 221 + ], + "score": 0.88, + "content": "\\mathbf { w } \\in \\mathbb { R } ^ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 209, + 338, + 223 + ], + "score": 1.0, + "content": ", the goal of the classifier is to determine whether", + "type": "text" + }, + { + "bbox": [ + 339, + 212, + 348, + 220 + ], + "score": 0.7, + "content": "w", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 209, + 406, + 223 + ], + "score": 1.0, + "content": "appears in the", + "type": "text" + }, + { + "bbox": [ + 407, + 212, + 412, + 220 + ], + "score": 0.68, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 209, + 506, + 223 + ], + "score": 1.0, + "content": ", with access to neither", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 221, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 115, + 231 + ], + "score": 0.7, + "content": "w", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 221, + 132, + 234 + ], + "score": 1.0, + "content": "nor", + "type": "text" + }, + { + "bbox": [ + 133, + 224, + 138, + 231 + ], + "score": 0.64, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 221, + 506, + 234 + ], + "score": 1.0, + "content": ". This is formulated as a binary classification task, where the input is the concatenation of s", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 232, + 138, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 138, + 244 + ], + "score": 1.0, + "content": "and w.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 188, + 506, + 244 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 249, + 505, + 348 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 506, + 263 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 263 + ], + "score": 1.0, + "content": "To create a dataset for this task, we need to provide positive and negative examples. Obtaining", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "score": 1.0, + "content": "positive examples is straightforward: we simply pick a random word from each sentence. For", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 271, + 506, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 284 + ], + "score": 1.0, + "content": "negative examples, we could pick a random word from the entire corpus. However, we found that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "such a dataset tends to push models to memorize words as either positive or negative words, instead", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 292, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 506, + 306 + ], + "score": 1.0, + "content": "of finding their relation to the sentence representation. Therefore, for each sentence we pick as a", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 304, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 506, + 317 + ], + "score": 1.0, + "content": "negative example a word that appears as a positive example somewhere in our dataset, but does", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "score": 1.0, + "content": "not appear in the given sentence. This forces the models to learn a relationship between word and", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 325, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 340 + ], + "score": 1.0, + "content": "sentence representations. We generate one positive and one negative example from each sentence.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 337, + 338, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 337, + 315, + 349 + ], + "score": 1.0, + "content": "The dataset is balanced, with a baseline accuracy of", + "type": "text" + }, + { + "bbox": [ + 315, + 337, + 334, + 348 + ], + "score": 0.87, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 337, + 338, + 349 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 247, + 506, + 349 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 352, + 505, + 418 + ], + "lines": [ + { + "bbox": [ + 106, + 352, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 505, + 363 + ], + "score": 1.0, + "content": "Word-order Task This task measures to what extent the sentence representation encodes word", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 362, + 506, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 263, + 375 + ], + "score": 1.0, + "content": "order. Given a sentence representation", + "type": "text" + }, + { + "bbox": [ + 263, + 362, + 295, + 373 + ], + "score": 0.9, + "content": "\\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 362, + 506, + 375 + ], + "score": 1.0, + "content": "and the representations of two words that appear in", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 372, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 160, + 386 + ], + "score": 1.0, + "content": "the sentence,", + "type": "text" + }, + { + "bbox": [ + 160, + 373, + 215, + 385 + ], + "score": 0.93, + "content": "\\mathbf { w } _ { 1 } , \\mathbf { w } _ { 2 } \\in \\mathbb { R } ^ { { \\bar { d } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 372, + 399, + 386 + ], + "score": 1.0, + "content": ", the goal of the classifier is to predict whether", + "type": "text" + }, + { + "bbox": [ + 399, + 375, + 412, + 385 + ], + "score": 0.87, + "content": "w _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 372, + 506, + 386 + ], + "score": 1.0, + "content": "appears before or after", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 384, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 119, + 396 + ], + "score": 0.84, + "content": "w _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 384, + 217, + 397 + ], + "score": 1.0, + "content": "in the original sentence", + "type": "text" + }, + { + "bbox": [ + 218, + 387, + 223, + 394 + ], + "score": 0.56, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 384, + 506, + 397 + ], + "score": 1.0, + "content": ". Again, the model has no access to the original sentence and the two", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 505, + 407 + ], + "score": 1.0, + "content": "words. This is formulated as a binary classification task, where the input is a concatenation of the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 406, + 220, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 169, + 419 + ], + "score": 1.0, + "content": "three vectors s,", + "type": "text" + }, + { + "bbox": [ + 169, + 408, + 183, + 417 + ], + "score": 0.84, + "content": "\\mathbf { w } _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 184, + 406, + 201, + 419 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 202, + 408, + 215, + 417 + ], + "score": 0.86, + "content": "\\mathbf { w } _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 406, + 220, + 419 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 352, + 506, + 419 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 423, + 505, + 457 + ], + "lines": [ + { + "bbox": [ + 105, + 423, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 437 + ], + "score": 1.0, + "content": "For each sentence in the corpus, we simply pick two random words from the sentence as a positive", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 435, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 505, + 446 + ], + "score": 1.0, + "content": "example. For negative examples, we flip the order of the words. We generate one positive and one", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 446, + 493, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 469, + 458 + ], + "score": 1.0, + "content": "negative example from each sentence. The dataset is balanced, with a baseline accuracy of", + "type": "text" + }, + { + "bbox": [ + 469, + 446, + 488, + 456 + ], + "score": 0.88, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 489, + 446, + 493, + 458 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 423, + 506, + 458 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 472, + 324, + 485 + ], + "lines": [ + { + "bbox": [ + 105, + 471, + 324, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 324, + 486 + ], + "score": 1.0, + "content": "4 SENTENCE REPRESENTATION MODELS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 496, + 504, + 509 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 176, + 510 + ], + "score": 1.0, + "content": "Given a sentence", + "type": "text" + }, + { + "bbox": [ + 176, + 497, + 265, + 509 + ], + "score": 0.92, + "content": "s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 496, + 505, + 510 + ], + "score": 1.0, + "content": "we aim to find a sentence representation s using an encoder:", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33, + "bbox_fs": [ + 106, + 496, + 505, + 510 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 511, + 385, + 525 + ], + "lines": [ + { + "bbox": [ + 225, + 511, + 385, + 525 + ], + "spans": [ + { + "bbox": [ + 225, + 511, + 385, + 525 + ], + "score": 0.9, + "content": "\\mathrm { E N C } : s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\} \\mapsto \\mathbf { s } \\in \\mathbb { R } ^ { k }", + "type": "interline_equation", + "image_path": "028c40eb38c89033d23dedb8550c9222de08e33b01c5f48311d315854d242bac.jpg" + } + ] + } + ], + "index": 34, + "virtual_lines": [ + { + "bbox": [ + 225, + 511, + 385, + 525 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 528, + 505, + 572 + ], + "lines": [ + { + "bbox": [ + 105, + 527, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 362, + 542 + ], + "score": 1.0, + "content": "The encoding process usually assumes a vector representation", + "type": "text" + }, + { + "bbox": [ + 362, + 528, + 401, + 540 + ], + "score": 0.92, + "content": "\\mathbf { w } _ { i } \\in \\mathbb { R } ^ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 402, + 527, + 505, + 542 + ], + "score": 1.0, + "content": "for each word in the vo-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 540, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 380, + 551 + ], + "score": 1.0, + "content": "cabulary. In general, the word and sentence embedding dimensions,", + "type": "text" + }, + { + "bbox": [ + 381, + 540, + 387, + 550 + ], + "score": 0.79, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 540, + 405, + 551 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 405, + 540, + 412, + 549 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 540, + 505, + 551 + ], + "score": 1.0, + "content": ", need not be the same.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "The word vectors can be learned together with other encoder parameters or pre-trained. Below we", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 561, + 268, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 268, + 573 + ], + "score": 1.0, + "content": "describe different instantiations of ENC.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 527, + 505, + 573 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 584, + 505, + 617 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 597 + ], + "score": 1.0, + "content": "Continuous Bag-of-words (CBOW) This simple yet effective text representation consists of per-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "forming element-wise averaging of word vectors that are obtained using a word-embedding method", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 606, + 182, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 182, + 618 + ], + "score": 1.0, + "content": "such as word2vec.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 583, + 505, + 618 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 623, + 503, + 646 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 505, + 636 + ], + "score": 1.0, + "content": "Despite its obliviousness to word order, CBOW has proven useful in different tasks (Hill et al., 2016)", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 634, + 393, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 393, + 646 + ], + "score": 1.0, + "content": "and is easy to compute, making it an important model class to consider.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 106, + 622, + 505, + 646 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 657, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 105, + 657, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 657, + 505, + 669 + ], + "score": 1.0, + "content": "Encoder-Decoder (ED) The encoder-decoder framework has been successfully used in a number", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 668, + 506, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 506, + 681 + ], + "score": 1.0, + "content": "of sequence-to-sequence learning tasks (Sutskever et al., 2014; Bahdanau et al., 2014; Dai & Le,", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 692 + ], + "score": 1.0, + "content": "2015; Li et al., 2015). After the encoding phase, a decoder maps the sentence representation back to", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 690, + 200, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 690, + 200, + 702 + ], + "score": 1.0, + "content": "the sequence of words:", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 657, + 506, + 702 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 700, + 385, + 715 + ], + "lines": [ + { + "bbox": [ + 225, + 700, + 385, + 715 + ], + "spans": [ + { + "bbox": [ + 225, + 700, + 385, + 715 + ], + "score": 0.92, + "content": "\\mathtt { D E C } : \\mathbf { s } \\in \\mathbb { R } ^ { k } \\mapsto s = \\{ w _ { 1 } , w _ { 2 } , . . . , w _ { N } \\}", + "type": "interline_equation", + "image_path": "e604f5fc4aed2abefe6dc577ec27e0803c75745cbb4691ec7ccf3d02ac2319c0.jpg" + } + ] + } + ], + "index": 48, + "virtual_lines": [ + { + "bbox": [ + 225, + 700, + 385, + 715 + ], + "spans": [], + "index": 48 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 124, + 80, + 486, + 176 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 124, + 80, + 486, + 176 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 124, + 80, + 486, + 176 + ], + "spans": [ + { + "bbox": [ + 124, + 80, + 486, + 176 + ], + "score": 0.968, + "type": "image", + "image_path": "28e6a935890943d42b298369f4f746ec45d819f218a69ca5e4f43d7c67269071.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 124, + 80, + 486, + 112.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 124, + 112.0, + 486, + 144.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 124, + 144.0, + 486, + 176.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 114, + 185, + 493, + 196 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 116, + 183, + 495, + 198 + ], + "spans": [ + { + "bbox": [ + 116, + 183, + 495, + 198 + ], + "score": 1.0, + "content": "Figure 1: Task accuracy vs. embedding size for different models; ED BLEU scores given for reference.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 218, + 505, + 273 + ], + "lines": [ + { + "bbox": [ + 106, + 218, + 504, + 230 + ], + "spans": [ + { + "bbox": [ + 106, + 218, + 504, + 230 + ], + "score": 1.0, + "content": "Here we investigate the specific case of an auto-encoder, where the entire encoding-decoding process", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 228, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 505, + 241 + ], + "score": 1.0, + "content": "can be trained end-to-end from a corpus of raw texts. The sentence representation is the final output", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 240, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 505, + 253 + ], + "score": 1.0, + "content": "vector of the encoder. We use a long short-term memory (LSTM) recurrent neural network (Hochre-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "score": 1.0, + "content": "iter & Schmidhuber, 1997; Graves et al., 2013) for both encoder and decoder. The LSTM decoder", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 261, + 341, + 274 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 341, + 274 + ], + "score": 1.0, + "content": "is similar to the LSTM encoder but with different weights.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6 + }, + { + "type": "title", + "bbox": [ + 108, + 290, + 244, + 303 + ], + "lines": [ + { + "bbox": [ + 105, + 289, + 245, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 245, + 304 + ], + "score": 1.0, + "content": "5 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 315, + 505, + 370 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 506, + 327 + ], + "score": 1.0, + "content": "The bag-of-words (CBOW) and encoder-decoder models are trained on 1 million sentences from a", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 326, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 505, + 338 + ], + "score": 1.0, + "content": "2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use NLTK (Bird, 2006) for tok-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "score": 1.0, + "content": "enization, and constrain sentence lengths to be between 5 and 70 words. For both models we control", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 186, + 361 + ], + "score": 1.0, + "content": "the embedding size", + "type": "text" + }, + { + "bbox": [ + 186, + 349, + 194, + 358 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 348, + 374, + 361 + ], + "score": 1.0, + "content": "and train word and sentence vectors of sizes", + "type": "text" + }, + { + "bbox": [ + 374, + 348, + 501, + 360 + ], + "score": 0.89, + "content": "k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 348, + 505, + 361 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 359, + 398, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 398, + 372 + ], + "score": 1.0, + "content": "More details about the experimental setup are available in the Appendix.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 107, + 387, + 172, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 385, + 174, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 174, + 402 + ], + "score": 1.0, + "content": "6 RESULTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 108, + 412, + 505, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "In this section we provide a detailed description of our experimental results along with their analysis.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "score": 1.0, + "content": "For each of the three main tests – length, content and order – we investigate the performance of", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 434, + 365, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 365, + 447 + ], + "score": 1.0, + "content": "different sentence representation models across embedding size.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17 + }, + { + "type": "title", + "bbox": [ + 108, + 460, + 232, + 471 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 233, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 233, + 472 + ], + "score": 1.0, + "content": "6.1 LENGTH EXPERIMENTS", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 481, + 505, + 514 + ], + "lines": [ + { + "bbox": [ + 106, + 481, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 505, + 493 + ], + "score": 1.0, + "content": "We begin by investigating how well the different representations encode sentence length. Figure 1a", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 491, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 505, + 505 + ], + "score": 1.0, + "content": "shows the performance of the different models on the length task, as well as the BLEU obtained by", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 503, + 244, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 244, + 515 + ], + "score": 1.0, + "content": "the LSTM encoder-decoder (ED).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 520, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 106, + 519, + 504, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 504, + 532 + ], + "score": 1.0, + "content": "With enough dimensions, the LSTM embeddings are very good at capturing sentence length, ob-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 530, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 216, + 543 + ], + "score": 1.0, + "content": "taining accuracies between", + "type": "text" + }, + { + "bbox": [ + 217, + 531, + 236, + 541 + ], + "score": 0.86, + "content": "82 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 236, + 530, + 254, + 543 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 254, + 531, + 273, + 541 + ], + "score": 0.87, + "content": "87 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 274, + 530, + 505, + 543 + ], + "score": 1.0, + "content": ". Length prediction ability is not perfectly correlated with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "BLEU scores: from 300 dimensions onward the length prediction accuracies of the LSTM remain", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "relatively stable, while the BLEU score of the encoder-decoder model increases as more dimensions", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 564, + 150, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 150, + 575 + ], + "score": 1.0, + "content": "are added.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 580, + 505, + 624 + ], + "lines": [ + { + "bbox": [ + 106, + 580, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 505, + 592 + ], + "score": 1.0, + "content": "Somewhat surprisingly, the CBOW model also encodes a fair amount of length information, with", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 592, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 230, + 604 + ], + "score": 1.0, + "content": "length prediction accuracies of", + "type": "text" + }, + { + "bbox": [ + 231, + 592, + 250, + 602 + ], + "score": 0.88, + "content": "45 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 592, + 261, + 604 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 261, + 592, + 280, + 602 + ], + "score": 0.87, + "content": "65 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 592, + 342, + 604 + ], + "score": 1.0, + "content": ", way above the", + "type": "text" + }, + { + "bbox": [ + 343, + 592, + 362, + 602 + ], + "score": 0.87, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 592, + 505, + 604 + ], + "score": 1.0, + "content": "baseline. This is remarkable, as the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "score": 1.0, + "content": "CBOW representation consists of averaged word vectors, and we did not expect it to encode length", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 614, + 376, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 376, + 625 + ], + "score": 1.0, + "content": "at all. We return to CBOW’s exceptional performance in Section 7.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 29.5 + }, + { + "type": "title", + "bbox": [ + 108, + 639, + 268, + 650 + ], + "lines": [ + { + "bbox": [ + 106, + 639, + 270, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 639, + 270, + 651 + ], + "score": 1.0, + "content": "6.2 WORD CONTENT EXPERIMENTS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 108, + 659, + 504, + 682 + ], + "lines": [ + { + "bbox": [ + 107, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "To what extent do the different sentence representations encode the identities of the words in the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 671, + 457, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 457, + 683 + ], + "score": 1.0, + "content": "sentence? Figure 1b visualizes the performance of our models on the word content test.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 108, + 687, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "All the representations encode some amount of word information, and clearly outperform the ran-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 175, + 711 + ], + "score": 1.0, + "content": "dom baseline of", + "type": "text" + }, + { + "bbox": [ + 176, + 699, + 195, + 709 + ], + "score": 0.86, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". Some trends are worth noting. While the capacity of the LSTM encoder", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 104, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "to preserve word identities generally increases when adding dimensions, the performance peaks at", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "750 dimensions and drops afterwards. This stands in contrast to the BLEU score of the respective", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 36.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 124, + 80, + 486, + 176 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 124, + 80, + 486, + 176 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 124, + 80, + 486, + 176 + ], + "spans": [ + { + "bbox": [ + 124, + 80, + 486, + 176 + ], + "score": 0.968, + "type": "image", + "image_path": "28e6a935890943d42b298369f4f746ec45d819f218a69ca5e4f43d7c67269071.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 124, + 80, + 486, + 112.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 124, + 112.0, + 486, + 144.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 124, + 144.0, + 486, + 176.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 114, + 185, + 493, + 196 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 116, + 183, + 495, + 198 + ], + "spans": [ + { + "bbox": [ + 116, + 183, + 495, + 198 + ], + "score": 1.0, + "content": "Figure 1: Task accuracy vs. embedding size for different models; ED BLEU scores given for reference.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 218, + 505, + 273 + ], + "lines": [ + { + "bbox": [ + 106, + 218, + 504, + 230 + ], + "spans": [ + { + "bbox": [ + 106, + 218, + 504, + 230 + ], + "score": 1.0, + "content": "Here we investigate the specific case of an auto-encoder, where the entire encoding-decoding process", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 228, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 505, + 241 + ], + "score": 1.0, + "content": "can be trained end-to-end from a corpus of raw texts. The sentence representation is the final output", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 240, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 505, + 253 + ], + "score": 1.0, + "content": "vector of the encoder. We use a long short-term memory (LSTM) recurrent neural network (Hochre-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 505, + 263 + ], + "score": 1.0, + "content": "iter & Schmidhuber, 1997; Graves et al., 2013) for both encoder and decoder. The LSTM decoder", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 261, + 341, + 274 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 341, + 274 + ], + "score": 1.0, + "content": "is similar to the LSTM encoder but with different weights.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 218, + 505, + 274 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 290, + 244, + 303 + ], + "lines": [ + { + "bbox": [ + 105, + 289, + 245, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 245, + 304 + ], + "score": 1.0, + "content": "5 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 315, + 505, + 370 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 506, + 327 + ], + "score": 1.0, + "content": "The bag-of-words (CBOW) and encoder-decoder models are trained on 1 million sentences from a", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 326, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 505, + 338 + ], + "score": 1.0, + "content": "2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use NLTK (Bird, 2006) for tok-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "score": 1.0, + "content": "enization, and constrain sentence lengths to be between 5 and 70 words. For both models we control", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 348, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 186, + 361 + ], + "score": 1.0, + "content": "the embedding size", + "type": "text" + }, + { + "bbox": [ + 186, + 349, + 194, + 358 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 348, + 374, + 361 + ], + "score": 1.0, + "content": "and train word and sentence vectors of sizes", + "type": "text" + }, + { + "bbox": [ + 374, + 348, + 501, + 360 + ], + "score": 0.89, + "content": "k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 348, + 505, + 361 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 359, + 398, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 398, + 372 + ], + "score": 1.0, + "content": "More details about the experimental setup are available in the Appendix.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 316, + 506, + 372 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 387, + 172, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 385, + 174, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 174, + 402 + ], + "score": 1.0, + "content": "6 RESULTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 108, + 412, + 505, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "In this section we provide a detailed description of our experimental results along with their analysis.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 505, + 436 + ], + "score": 1.0, + "content": "For each of the three main tests – length, content and order – we investigate the performance of", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 434, + 365, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 365, + 447 + ], + "score": 1.0, + "content": "different sentence representation models across embedding size.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 412, + 505, + 447 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 460, + 232, + 471 + ], + "lines": [ + { + "bbox": [ + 106, + 460, + 233, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 460, + 233, + 472 + ], + "score": 1.0, + "content": "6.1 LENGTH EXPERIMENTS", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 481, + 505, + 514 + ], + "lines": [ + { + "bbox": [ + 106, + 481, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 505, + 493 + ], + "score": 1.0, + "content": "We begin by investigating how well the different representations encode sentence length. Figure 1a", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 491, + 505, + 505 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 505, + 505 + ], + "score": 1.0, + "content": "shows the performance of the different models on the length task, as well as the BLEU obtained by", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 503, + 244, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 503, + 244, + 515 + ], + "score": 1.0, + "content": "the LSTM encoder-decoder (ED).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 481, + 505, + 515 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 520, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 106, + 519, + 504, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 519, + 504, + 532 + ], + "score": 1.0, + "content": "With enough dimensions, the LSTM embeddings are very good at capturing sentence length, ob-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 530, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 216, + 543 + ], + "score": 1.0, + "content": "taining accuracies between", + "type": "text" + }, + { + "bbox": [ + 217, + 531, + 236, + 541 + ], + "score": 0.86, + "content": "82 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 236, + 530, + 254, + 543 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 254, + 531, + 273, + 541 + ], + "score": 0.87, + "content": "87 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 274, + 530, + 505, + 543 + ], + "score": 1.0, + "content": ". Length prediction ability is not perfectly correlated with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "BLEU scores: from 300 dimensions onward the length prediction accuracies of the LSTM remain", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "relatively stable, while the BLEU score of the encoder-decoder model increases as more dimensions", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 564, + 150, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 150, + 575 + ], + "score": 1.0, + "content": "are added.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 519, + 505, + 575 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 580, + 505, + 624 + ], + "lines": [ + { + "bbox": [ + 106, + 580, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 505, + 592 + ], + "score": 1.0, + "content": "Somewhat surprisingly, the CBOW model also encodes a fair amount of length information, with", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 592, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 230, + 604 + ], + "score": 1.0, + "content": "length prediction accuracies of", + "type": "text" + }, + { + "bbox": [ + 231, + 592, + 250, + 602 + ], + "score": 0.88, + "content": "45 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 250, + 592, + 261, + 604 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 261, + 592, + 280, + 602 + ], + "score": 0.87, + "content": "65 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 592, + 342, + 604 + ], + "score": 1.0, + "content": ", way above the", + "type": "text" + }, + { + "bbox": [ + 343, + 592, + 362, + 602 + ], + "score": 0.87, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 592, + 505, + 604 + ], + "score": 1.0, + "content": "baseline. This is remarkable, as the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "score": 1.0, + "content": "CBOW representation consists of averaged word vectors, and we did not expect it to encode length", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 614, + 376, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 376, + 625 + ], + "score": 1.0, + "content": "at all. We return to CBOW’s exceptional performance in Section 7.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 29.5, + "bbox_fs": [ + 105, + 580, + 505, + 625 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 639, + 268, + 650 + ], + "lines": [ + { + "bbox": [ + 106, + 639, + 270, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 639, + 270, + 651 + ], + "score": 1.0, + "content": "6.2 WORD CONTENT EXPERIMENTS", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 108, + 659, + 504, + 682 + ], + "lines": [ + { + "bbox": [ + 107, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 107, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "To what extent do the different sentence representations encode the identities of the words in the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 671, + 457, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 457, + 683 + ], + "score": 1.0, + "content": "sentence? Figure 1b visualizes the performance of our models on the word content test.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 660, + 505, + 683 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 687, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "All the representations encode some amount of word information, and clearly outperform the ran-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 175, + 711 + ], + "score": 1.0, + "content": "dom baseline of", + "type": "text" + }, + { + "bbox": [ + 176, + 699, + 195, + 709 + ], + "score": 0.86, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". Some trends are worth noting. While the capacity of the LSTM encoder", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 104, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "to preserve word identities generally increases when adding dimensions, the performance peaks at", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "750 dimensions and drops afterwards. This stands in contrast to the BLEU score of the respective", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "encoder-decoder models. We hypothesize that this occurs because a sizable part of the auto-encoder", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 105 + ], + "score": 1.0, + "content": "performance comes from the decoder, which also improves as we add more dimensions. At 1000 di-", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "mensions, the decoder’s language model may be strong enough to allow the representation produced", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 116, + 371, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 371, + 128 + ], + "score": 1.0, + "content": "by the encoder to be less informative with regard to word content.", + "type": "text", + "cross_page": true + } + ], + "index": 3 + } + ], + "index": 36.5, + "bbox_fs": [ + 104, + 688, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 126 + ], + "lines": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "encoder-decoder models. We hypothesize that this occurs because a sizable part of the auto-encoder", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 105 + ], + "score": 1.0, + "content": "performance comes from the decoder, which also improves as we add more dimensions. At 1000 di-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "mensions, the decoder’s language model may be strong enough to allow the representation produced", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 116, + 371, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 371, + 128 + ], + "score": 1.0, + "content": "by the encoder to be less informative with regard to word content.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 107, + 132, + 505, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 131, + 504, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 504, + 145 + ], + "score": 1.0, + "content": "CBOW representations with low dimensional vectors (100 and 300 dimensions) perform exception-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 505, + 155 + ], + "score": 1.0, + "content": "ally well, outperforming the more complex, sequence-aware models by a wide margin. If your task", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "requires access to word identities, it is worth considering this simple representation. Interestingly,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 274, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 274, + 178 + ], + "score": 1.0, + "content": "CBOW scores drop at higher dimensions.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5 + }, + { + "type": "title", + "bbox": [ + 108, + 191, + 257, + 202 + ], + "lines": [ + { + "bbox": [ + 106, + 191, + 258, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 258, + 203 + ], + "score": 1.0, + "content": "6.3 WORD ORDER EXPERIMENTS", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 212, + 505, + 267 + ], + "lines": [ + { + "bbox": [ + 105, + 212, + 505, + 224 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 505, + 224 + ], + "score": 1.0, + "content": "Figure 1c shows the performance of the different models on the order test. The LSTM encoders are", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 223, + 504, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 484, + 236 + ], + "score": 1.0, + "content": "very capable of encoding word order, with LSTM-1000 allowing the recovery of word order in", + "type": "text" + }, + { + "bbox": [ + 484, + 223, + 504, + 234 + ], + "score": 0.85, + "content": "91 \\%", + "type": "inline_equation" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 234, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 105, + 234, + 505, + 247 + ], + "score": 1.0, + "content": "of the cases. Similar to the length test, LSTM order prediction accuracy is only loosely correlated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 245, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 505, + 258 + ], + "score": 1.0, + "content": "with BLEU scores. It is worth noting that increasing the representation size helps the LSTM-encoder", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 256, + 248, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 248, + 268 + ], + "score": 1.0, + "content": "to better encode order information.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 273, + 505, + 328 + ], + "lines": [ + { + "bbox": [ + 105, + 272, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 385, + 285 + ], + "score": 1.0, + "content": "Surprisingly, the CBOW encodings manage to reach an accuracy of", + "type": "text" + }, + { + "bbox": [ + 386, + 273, + 406, + 284 + ], + "score": 0.86, + "content": "70 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 272, + 505, + 285 + ], + "score": 1.0, + "content": "on the word order task,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 283, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 126, + 295 + ], + "score": 0.84, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 283, + 505, + 297 + ], + "score": 1.0, + "content": "above the baseline. This is remarkable as, by definition, the CBOW encoder does not attempt", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "score": 1.0, + "content": "to preserve word order information. One way to explain this is by considering distribution patterns", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 305, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 505, + 318 + ], + "score": 1.0, + "content": "of words in natural language sentences: some words tend to appear before others. In the next section", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 317, + 369, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 369, + 329 + ], + "score": 1.0, + "content": "we analyze the effect of natural language on the different models.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16 + }, + { + "type": "title", + "bbox": [ + 107, + 345, + 362, + 358 + ], + "lines": [ + { + "bbox": [ + 104, + 344, + 363, + 360 + ], + "spans": [ + { + "bbox": [ + 104, + 344, + 363, + 360 + ], + "score": 1.0, + "content": "7 IMPORTANCE OF “NATURAL LANGUAGENESS”", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 108, + 371, + 504, + 404 + ], + "lines": [ + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "score": 1.0, + "content": "Natural language imposes many constraints on sentence structure. To what extent do the differ-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 382, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 505, + 394 + ], + "score": 1.0, + "content": "ent encoders rely on specific properties of word distributions in natural language sentences when", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 393, + 191, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 191, + 405 + ], + "score": 1.0, + "content": "encoding sentences?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 410, + 504, + 432 + ], + "lines": [ + { + "bbox": [ + 106, + 410, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 505, + 422 + ], + "score": 1.0, + "content": "To account for this, we perform additional experiments in which we attempt to control for the effect", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 189, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 189, + 434 + ], + "score": 1.0, + "content": "of natural language.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 106, + 437, + 505, + 504 + ], + "lines": [ + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "How can CBOW encode sentence length? Is the ability of CBOW embeddings to encode length", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 447, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 506, + 461 + ], + "score": 1.0, + "content": "related to specific words being indicative of longer or shorter sentences? To control for this, we", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "score": 1.0, + "content": "created a synthetic dataset where each word in each sentence is replaced by a random word from", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "the dictionary and re-ran the length test for the CBOW embeddings using this dataset. As Figure 2a", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 481, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 506, + 494 + ], + "score": 1.0, + "content": "shows, this only leads to a slight decrease in accuracy, indicating that the identity of the words is not", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 493, + 353, + 504 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 353, + 504 + ], + "score": 1.0, + "content": "the main component in CBOW’s success at predicting length.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5 + }, + { + "type": "image", + "bbox": [ + 150, + 516, + 286, + 609 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 150, + 516, + 286, + 609 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 150, + 516, + 286, + 609 + ], + "spans": [ + { + "bbox": [ + 150, + 516, + 286, + 609 + ], + "score": 0.963, + "type": "image", + "image_path": "e82d67756d02b673c9f625bf59ad4d67cc57469760268bc810c6082a021e2cf1.jpg" + } + ] + } + ], + "index": 32.0, + "virtual_lines": [ + { + "bbox": [ + 150, + 516, + 286, + 562.5 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 150, + 562.5, + 286, + 609.0 + ], + "spans": [], + "index": 33 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 147, + 616, + 289, + 646 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 147, + 615, + 290, + 627 + ], + "spans": [ + { + "bbox": [ + 147, + 615, + 290, + 627 + ], + "score": 1.0, + "content": "(a) Length accuracy for different", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 147, + 625, + 290, + 637 + ], + "spans": [ + { + "bbox": [ + 147, + 625, + 290, + 637 + ], + "score": 1.0, + "content": "CBOW sizes on natural and synthetic", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 148, + 636, + 248, + 647 + ], + "spans": [ + { + "bbox": [ + 148, + 636, + 248, + 647 + ], + "score": 1.0, + "content": "(random words) sentences.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36 + } + ], + "index": 34.0 + }, + { + "type": "image", + "bbox": [ + 324, + 516, + 461, + 609 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 324, + 516, + 461, + 609 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 324, + 516, + 461, + 609 + ], + "spans": [ + { + "bbox": [ + 324, + 516, + 461, + 609 + ], + "score": 0.964, + "type": "image", + "image_path": "99d2d39164f58bedacce7e357432eda8f8225f5272edfca5fd0629fdcfc12507.jpg" + } + ] + } + ], + "index": 33.0, + "virtual_lines": [ + { + "bbox": [ + 324, + 516, + 461, + 562.5 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 324, + 562.5, + 461, + 609.0 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 321, + 616, + 462, + 646 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 321, + 616, + 463, + 627 + ], + "spans": [ + { + "bbox": [ + 321, + 616, + 463, + 627 + ], + "score": 1.0, + "content": "(b) Average embedding norm vs. sen-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 321, + 626, + 463, + 636 + ], + "spans": [ + { + "bbox": [ + 321, + 626, + 463, + 636 + ], + "score": 1.0, + "content": "tence length for CBOW with an em-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 320, + 636, + 397, + 647 + ], + "spans": [ + { + "bbox": [ + 320, + 636, + 397, + 647 + ], + "score": 1.0, + "content": "bedding size of 300.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39 + } + ], + "index": 36.0 + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "An alternative explanation for CBOW’s ability to encode sentence length is given by considering the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "norms of the sentence embeddings. Indeed, Figure 2b shows that the embedding norm decreases as", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 681, + 489, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 489, + 694 + ], + "score": 1.0, + "content": "sentences grow longer. We believe this is one of the main reasons for the strong CBOW results.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "While the correlation between the number of averaged vectors and the resulting norm surprised us,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "in retrospect it is an expected behavior that has sound mathematical foundations. To understand", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "the behavior, consider the different word vectors to be random variables, with the values in each", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 126 + ], + "lines": [], + "index": 1.5, + "bbox_fs": [ + 105, + 83, + 506, + 128 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 132, + 505, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 131, + 504, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 504, + 145 + ], + "score": 1.0, + "content": "CBOW representations with low dimensional vectors (100 and 300 dimensions) perform exception-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 505, + 155 + ], + "score": 1.0, + "content": "ally well, outperforming the more complex, sequence-aware models by a wide margin. If your task", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "requires access to word identities, it is worth considering this simple representation. Interestingly,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 274, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 274, + 178 + ], + "score": 1.0, + "content": "CBOW scores drop at higher dimensions.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 131, + 505, + 178 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 191, + 257, + 202 + ], + "lines": [ + { + "bbox": [ + 106, + 191, + 258, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 258, + 203 + ], + "score": 1.0, + "content": "6.3 WORD ORDER EXPERIMENTS", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 212, + 505, + 267 + ], + "lines": [ + { + "bbox": [ + 105, + 212, + 505, + 224 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 505, + 224 + ], + "score": 1.0, + "content": "Figure 1c shows the performance of the different models on the order test. The LSTM encoders are", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 223, + 504, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 484, + 236 + ], + "score": 1.0, + "content": "very capable of encoding word order, with LSTM-1000 allowing the recovery of word order in", + "type": "text" + }, + { + "bbox": [ + 484, + 223, + 504, + 234 + ], + "score": 0.85, + "content": "91 \\%", + "type": "inline_equation" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 234, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 105, + 234, + 505, + 247 + ], + "score": 1.0, + "content": "of the cases. Similar to the length test, LSTM order prediction accuracy is only loosely correlated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 245, + 505, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 505, + 258 + ], + "score": 1.0, + "content": "with BLEU scores. It is worth noting that increasing the representation size helps the LSTM-encoder", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 256, + 248, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 248, + 268 + ], + "score": 1.0, + "content": "to better encode order information.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 212, + 505, + 268 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 273, + 505, + 328 + ], + "lines": [ + { + "bbox": [ + 105, + 272, + 505, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 385, + 285 + ], + "score": 1.0, + "content": "Surprisingly, the CBOW encodings manage to reach an accuracy of", + "type": "text" + }, + { + "bbox": [ + 386, + 273, + 406, + 284 + ], + "score": 0.86, + "content": "70 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 272, + 505, + 285 + ], + "score": 1.0, + "content": "on the word order task,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 283, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 126, + 295 + ], + "score": 0.84, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 283, + 505, + 297 + ], + "score": 1.0, + "content": "above the baseline. This is remarkable as, by definition, the CBOW encoder does not attempt", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 505, + 307 + ], + "score": 1.0, + "content": "to preserve word order information. One way to explain this is by considering distribution patterns", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 305, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 505, + 318 + ], + "score": 1.0, + "content": "of words in natural language sentences: some words tend to appear before others. In the next section", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 317, + 369, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 317, + 369, + 329 + ], + "score": 1.0, + "content": "we analyze the effect of natural language on the different models.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 272, + 505, + 329 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 345, + 362, + 358 + ], + "lines": [ + { + "bbox": [ + 104, + 344, + 363, + 360 + ], + "spans": [ + { + "bbox": [ + 104, + 344, + 363, + 360 + ], + "score": 1.0, + "content": "7 IMPORTANCE OF “NATURAL LANGUAGENESS”", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 108, + 371, + 504, + 404 + ], + "lines": [ + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "score": 1.0, + "content": "Natural language imposes many constraints on sentence structure. To what extent do the differ-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 382, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 505, + 394 + ], + "score": 1.0, + "content": "ent encoders rely on specific properties of word distributions in natural language sentences when", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 393, + 191, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 191, + 405 + ], + "score": 1.0, + "content": "encoding sentences?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 371, + 505, + 405 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 410, + 504, + 432 + ], + "lines": [ + { + "bbox": [ + 106, + 410, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 106, + 410, + 505, + 422 + ], + "score": 1.0, + "content": "To account for this, we perform additional experiments in which we attempt to control for the effect", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 189, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 189, + 434 + ], + "score": 1.0, + "content": "of natural language.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 410, + 505, + 434 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 437, + 505, + 504 + ], + "lines": [ + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 106, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "How can CBOW encode sentence length? Is the ability of CBOW embeddings to encode length", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 447, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 506, + 461 + ], + "score": 1.0, + "content": "related to specific words being indicative of longer or shorter sentences? To control for this, we", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "score": 1.0, + "content": "created a synthetic dataset where each word in each sentence is replaced by a random word from", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "the dictionary and re-ran the length test for the CBOW embeddings using this dataset. As Figure 2a", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 481, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 506, + 494 + ], + "score": 1.0, + "content": "shows, this only leads to a slight decrease in accuracy, indicating that the identity of the words is not", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 493, + 353, + 504 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 353, + 504 + ], + "score": 1.0, + "content": "the main component in CBOW’s success at predicting length.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 437, + 506, + 504 + ] + }, + { + "type": "image", + "bbox": [ + 150, + 516, + 286, + 609 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 150, + 516, + 286, + 609 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 150, + 516, + 286, + 609 + ], + "spans": [ + { + "bbox": [ + 150, + 516, + 286, + 609 + ], + "score": 0.963, + "type": "image", + "image_path": "e82d67756d02b673c9f625bf59ad4d67cc57469760268bc810c6082a021e2cf1.jpg" + } + ] + } + ], + "index": 32.0, + "virtual_lines": [ + { + "bbox": [ + 150, + 516, + 286, + 562.5 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 150, + 562.5, + 286, + 609.0 + ], + "spans": [], + "index": 33 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 147, + 616, + 289, + 646 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 147, + 615, + 290, + 627 + ], + "spans": [ + { + "bbox": [ + 147, + 615, + 290, + 627 + ], + "score": 1.0, + "content": "(a) Length accuracy for different", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 147, + 625, + 290, + 637 + ], + "spans": [ + { + "bbox": [ + 147, + 625, + 290, + 637 + ], + "score": 1.0, + "content": "CBOW sizes on natural and synthetic", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 148, + 636, + 248, + 647 + ], + "spans": [ + { + "bbox": [ + 148, + 636, + 248, + 647 + ], + "score": 1.0, + "content": "(random words) sentences.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36 + } + ], + "index": 34.0 + }, + { + "type": "image", + "bbox": [ + 324, + 516, + 461, + 609 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 324, + 516, + 461, + 609 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 324, + 516, + 461, + 609 + ], + "spans": [ + { + "bbox": [ + 324, + 516, + 461, + 609 + ], + "score": 0.964, + "type": "image", + "image_path": "99d2d39164f58bedacce7e357432eda8f8225f5272edfca5fd0629fdcfc12507.jpg" + } + ] + } + ], + "index": 33.0, + "virtual_lines": [ + { + "bbox": [ + 324, + 516, + 461, + 562.5 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 324, + 562.5, + 461, + 609.0 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 321, + 616, + 462, + 646 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 321, + 616, + 463, + 627 + ], + "spans": [ + { + "bbox": [ + 321, + 616, + 463, + 627 + ], + "score": 1.0, + "content": "(b) Average embedding norm vs. sen-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 321, + 626, + 463, + 636 + ], + "spans": [ + { + "bbox": [ + 321, + 626, + 463, + 636 + ], + "score": 1.0, + "content": "tence length for CBOW with an em-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 320, + 636, + 397, + 647 + ], + "spans": [ + { + "bbox": [ + 320, + 636, + 397, + 647 + ], + "score": 1.0, + "content": "bedding size of 300.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39 + } + ], + "index": 36.0 + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "An alternative explanation for CBOW’s ability to encode sentence length is given by considering the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "norms of the sentence embeddings. Indeed, Figure 2b shows that the embedding norm decreases as", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 681, + 489, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 489, + 694 + ], + "score": 1.0, + "content": "sentences grow longer. We believe this is one of the main reasons for the strong CBOW results.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 659, + 505, + 694 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "While the correlation between the number of averaged vectors and the resulting norm surprised us,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "in retrospect it is an expected behavior that has sound mathematical foundations. To understand", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 732 + ], + "score": 1.0, + "content": "the behavior, consider the different word vectors to be random variables, with the values in each", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "dimension centered roughly around zero. Both central limit theorem and Hoeffding‘s inequality tell", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "us that as we add more samples, the expected average of the values will better approximate the true", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 116 + ], + "score": 1.0, + "content": "mean, causing the norm of the average vector to decrease. We expect the correlation between the", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "sentence length and its norm to be more pronounced with shorter sentences (above some number of", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "samples we will already be very close to the true mean, and the norm will not decrease further), a", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 293, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 293, + 149 + ], + "score": 1.0, + "content": "behavior which we indeed observe in practice.", + "type": "text", + "cross_page": true + } + ], + "index": 5 + } + ], + "index": 45, + "bbox_fs": [ + 106, + 698, + 505, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "dimension centered roughly around zero. Both central limit theorem and Hoeffding‘s inequality tell", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "us that as we add more samples, the expected average of the values will better approximate the true", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 116 + ], + "score": 1.0, + "content": "mean, causing the norm of the average vector to decrease. We expect the correlation between the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "sentence length and its norm to be more pronounced with shorter sentences (above some number of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "samples we will already be very close to the true mean, and the norm will not decrease further), a", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 293, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 293, + 149 + ], + "score": 1.0, + "content": "behavior which we indeed observe in practice.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 108, + 152, + 503, + 185 + ], + "lines": [ + { + "bbox": [ + 105, + 152, + 505, + 165 + ], + "spans": [ + { + "bbox": [ + 105, + 152, + 505, + 165 + ], + "score": 1.0, + "content": "How does CBOW encode word order? The surprisingly strong performance of the CBOW model", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 163, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 505, + 177 + ], + "score": 1.0, + "content": "on the order task made us hypothesize that much of the word order information is captured in general", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 175, + 261, + 187 + ], + "spans": [ + { + "bbox": [ + 106, + 175, + 261, + 187 + ], + "score": 1.0, + "content": "natural language word order statistics.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 191, + 505, + 246 + ], + "lines": [ + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "score": 1.0, + "content": "To investigate this, we re-run the word order tests, but this time drop the sentence embedding in", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 203, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 505, + 214 + ], + "score": 1.0, + "content": "training and testing time, learning from the word-pairs alone. In other words, we feed the network as", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 213, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 505, + 226 + ], + "score": 1.0, + "content": "input two word embeddings and ask which word comes first in the sentence. This test isolates general", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 222, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 505, + 239 + ], + "score": 1.0, + "content": "word order statistics of language from information that is contained in the sentence embedding (Fig.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 235, + 120, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 120, + 248 + ], + "score": 1.0, + "content": "3).", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 252, + 296, + 405 + ], + "lines": [ + { + "bbox": [ + 106, + 251, + 297, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 297, + 264 + ], + "score": 1.0, + "content": "The difference between including and remov-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 263, + 297, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 297, + 276 + ], + "score": 1.0, + "content": "ing the sentence embeddings when using the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 273, + 297, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 297, + 286 + ], + "score": 1.0, + "content": "CBOW model is minor, while the LSTM-ED", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 284, + 297, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 297, + 297 + ], + "score": 1.0, + "content": "suffers a significant drop. Clearly, the LSTM-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 295, + 297, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 297, + 308 + ], + "score": 1.0, + "content": "ED model encodes word order, while the pre-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 306, + 297, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 297, + 319 + ], + "score": 1.0, + "content": "diction ability of CBOW is mostly explained by", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 318, + 297, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 297, + 329 + ], + "score": 1.0, + "content": "general language statistics. 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To what extent are the models trained to rely on natural language word order", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 432, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 432, + 505, + 443 + ], + "score": 1.0, + "content": "when encoding sentences? To control for this, we create a synthetic dataset, PERMUTED, in which", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "the word order in each sentence is randomly permuted. Then, we repeat the length, content and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "score": 1.0, + "content": "order experiments using the PERMUTED dataset (we still use the original sentence encoders that are", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 465, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 506, + 477 + ], + "score": 1.0, + "content": "trained on non-permuted sentences). While the permuted sentence representation is the same for", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 476, + 403, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 403, + 487 + ], + "score": 1.0, + "content": "CBOW, it is completely different when generated by the encoder-decoder.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 106, + 492, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 106, + 493, + 504, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 504, + 505 + ], + "score": 1.0, + "content": "Results are presented in Fig. 4. When considering CBOW embeddings, word order accuracy drops", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "score": 1.0, + "content": "to chance level, as expected, while results on the other tests remain the same. Moving to the LSTM", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "score": 1.0, + "content": "encoder-decoder, the results on all three tests are comparable to the ones using non-permuted sen-", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "tences. These results are somewhat surprising since the models were originally trained on “real”,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "non-permuted sentences. This indicates that the LSTM encoder-decoder is a general-purpose se-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 104, + 546, + 506, + 561 + ], + "spans": [ + { + "bbox": [ + 104, + 546, + 506, + 561 + ], + "score": 1.0, + "content": "quence encoder that for the most part does not rely on word ordering properties of natural language", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 559, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 505, + 570 + ], + "score": 1.0, + "content": "when encoding sentences. The small and consistent drop in word order accuracy on the permuted", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "score": 1.0, + "content": "sentences can be attributed to the encoder relying on natural language word order to some extent,", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 579, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 505, + 593 + ], + "score": 1.0, + "content": "but can also be explained by the word order prediction task becoming harder due to the inability to", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 49 + }, + { + "type": "image", + "bbox": [ + 125, + 610, + 486, + 709 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 125, + 610, + 486, + 709 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 125, + 610, + 486, + 709 + ], + "spans": [ + { + "bbox": [ + 125, + 610, + 486, + 709 + ], + "score": 0.973, + "type": "image", + "image_path": "e9af8c8bd91c7b7fed7ecfbb6beeda8b61833cac7aed0ea51520dfe929cd5cee.jpg" + } + ] + } + ], + "index": 55, + "virtual_lines": [ + { + "bbox": [ + 125, + 610, + 486, + 643.0 + ], + "spans": [], + "index": 54 + }, + { + "bbox": [ + 125, + 643.0, + 486, + 676.0 + ], + "spans": [], + "index": 55 + }, + { + "bbox": [ + 125, + 676.0, + 486, + 709.0 + ], + "spans": [], + "index": 56 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 145, + 718, + 465, + 729 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 145, + 717, + 465, + 730 + ], + "spans": [ + { + "bbox": [ + 145, + 717, + 465, + 730 + ], + "score": 1.0, + "content": "Figure 4: Results for length, content and order tests on natural and permuted sentences.", + "type": "text" + } + ], + "index": 57 + } + ], + "index": 57 + } + ], + "index": 56.0 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [], + "index": 2.5, + "bbox_fs": [ + 105, + 82, + 506, + 149 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 108, + 152, + 503, + 185 + ], + "lines": [ + { + "bbox": [ + 105, + 152, + 505, + 165 + ], + "spans": [ + { + "bbox": [ + 105, + 152, + 505, + 165 + ], + "score": 1.0, + "content": "How does CBOW encode word order? The surprisingly strong performance of the CBOW model", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 163, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 505, + 177 + ], + "score": 1.0, + "content": "on the order task made us hypothesize that much of the word order information is captured in general", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 175, + 261, + 187 + ], + "spans": [ + { + "bbox": [ + 106, + 175, + 261, + 187 + ], + "score": 1.0, + "content": "natural language word order statistics.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 152, + 505, + 187 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 191, + 505, + 246 + ], + "lines": [ + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "score": 1.0, + "content": "To investigate this, we re-run the word order tests, but this time drop the sentence embedding in", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 203, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 505, + 214 + ], + "score": 1.0, + "content": "training and testing time, learning from the word-pairs alone. In other words, we feed the network as", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 213, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 505, + 226 + ], + "score": 1.0, + "content": "input two word embeddings and ask which word comes first in the sentence. This test isolates general", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 222, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 505, + 239 + ], + "score": 1.0, + "content": "word order statistics of language from information that is contained in the sentence embedding (Fig.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 235, + 120, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 120, + 248 + ], + "score": 1.0, + "content": "3).", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 191, + 505, + 248 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 252, + 296, + 405 + ], + "lines": [ + { + "bbox": [ + 106, + 251, + 297, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 297, + 264 + ], + "score": 1.0, + "content": "The difference between including and remov-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 263, + 297, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 297, + 276 + ], + "score": 1.0, + "content": "ing the sentence embeddings when using the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 273, + 297, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 297, + 286 + ], + "score": 1.0, + "content": "CBOW model is minor, while the LSTM-ED", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 284, + 297, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 297, + 297 + ], + "score": 1.0, + "content": "suffers a significant drop. Clearly, the LSTM-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 295, + 297, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 297, + 308 + ], + "score": 1.0, + "content": "ED model encodes word order, while the pre-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 306, + 297, + 319 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 297, + 319 + ], + "score": 1.0, + "content": "diction ability of CBOW is mostly explained by", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 318, + 297, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 297, + 329 + ], + "score": 1.0, + "content": "general language statistics. However, CBOW", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 328, + 297, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 328, + 297, + 340 + ], + "score": 1.0, + "content": "does benefit from the sentence to some extent:", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 340, + 297, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 203, + 352 + ], + "score": 1.0, + "content": "we observe a gain of", + "type": "text" + }, + { + "bbox": [ + 204, + 340, + 226, + 351 + ], + "score": 0.87, + "content": "{ \\sim } 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 340, + 297, + 352 + ], + "score": 1.0, + "content": "accuracy points", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 351, + 297, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 297, + 362 + ], + "score": 1.0, + "content": "when the CBOW tests are allowed access to the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 362, + 297, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 362, + 297, + 373 + ], + "score": 1.0, + "content": "sentence representation. This may be explained", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 373, + 297, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 297, + 384 + ], + "score": 1.0, + "content": "by higher order statistics of correlation between", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 383, + 297, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 297, + 396 + ], + "score": 1.0, + "content": "word order patterns and the occurrences of spe-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 395, + 155, + 406 + ], + "spans": [ + { + "bbox": [ + 106, + 395, + 155, + 406 + ], + "score": 1.0, + "content": "cific words.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 251, + 297, + 406 + ] + }, + { + "type": "image", + "bbox": [ + 326, + 267, + 482, + 373 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 326, + 267, + 482, + 373 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 326, + 267, + 482, + 373 + ], + "spans": [ + { + "bbox": [ + 326, + 267, + 482, + 373 + ], + "score": 0.957, + "type": "image", + "image_path": "140826fd2b77809f6dcea513cd5b657687e4e1698e2815c2dba2787703048c6e.jpg" + } + ] + } + ], + "index": 31.5, + "virtual_lines": [ + { + "bbox": [ + 326, + 267, + 482, + 280.25 + ], + "spans": [], + "index": 28 + }, + { + "bbox": [ + 326, + 280.25, + 482, + 293.5 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 326, + 293.5, + 482, + 306.75 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 326, + 306.75, + 482, + 320.0 + ], + "spans": [], + "index": 31 + }, + { + "bbox": [ + 326, + 320.0, + 482, + 333.25 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 326, + 333.25, + 482, + 346.5 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 326, + 346.5, + 482, + 359.75 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 326, + 359.75, + 482, + 373.0 + ], + "spans": [], + "index": 35 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 304, + 385, + 504, + 405 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 504, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 504, + 396 + ], + "score": 1.0, + "content": "Figure 3: Order accuracy w/ and w/o sentence repre-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 395, + 440, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 440, + 405 + ], + "score": 1.0, + "content": "sentation for ED and CBOW models.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5 + } + ], + "index": 34.0 + }, + { + "type": "title", + "bbox": [ + 108, + 410, + 294, + 421 + ], + "lines": [ + { + "bbox": [ + 106, + 409, + 297, + 423 + ], + "spans": [ + { + "bbox": [ + 106, + 409, + 297, + 423 + ], + "score": 1.0, + "content": "How important is English word order for en-", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 421, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 421, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 505, + 432 + ], + "score": 1.0, + "content": "coding sentences? 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Then, we repeat the length, content and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "score": 1.0, + "content": "order experiments using the PERMUTED dataset (we still use the original sentence encoders that are", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 465, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 506, + 477 + ], + "score": 1.0, + "content": "trained on non-permuted sentences). While the permuted sentence representation is the same for", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 476, + 403, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 403, + 487 + ], + "score": 1.0, + "content": "CBOW, it is completely different when generated by the encoder-decoder.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 421, + 506, + 487 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 492, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 106, + 493, + 504, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 504, + 505 + ], + "score": 1.0, + "content": "Results are presented in Fig. 4. When considering CBOW embeddings, word order accuracy drops", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "score": 1.0, + "content": "to chance level, as expected, while results on the other tests remain the same. Moving to the LSTM", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 505, + 527 + ], + "score": 1.0, + "content": "encoder-decoder, the results on all three tests are comparable to the ones using non-permuted sen-", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "tences. These results are somewhat surprising since the models were originally trained on “real”,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "non-permuted sentences. This indicates that the LSTM encoder-decoder is a general-purpose se-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 104, + 546, + 506, + 561 + ], + "spans": [ + { + "bbox": [ + 104, + 546, + 506, + 561 + ], + "score": 1.0, + "content": "quence encoder that for the most part does not rely on word ordering properties of natural language", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 559, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 505, + 570 + ], + "score": 1.0, + "content": "when encoding sentences. The small and consistent drop in word order accuracy on the permuted", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "score": 1.0, + "content": "sentences can be attributed to the encoder relying on natural language word order to some extent,", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 579, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 505, + 593 + ], + "score": 1.0, + "content": "but can also be explained by the word order prediction task becoming harder due to the inability to", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "use general word order statistics. The results suggest that a trained encoder will transfer well across", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "different natural language domains, as long as the vocabularies remain stable. When considering", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 505, + 117 + ], + "score": 1.0, + "content": "the decoder’s BLEU score on the permuted dataset (not shown), we do see a dramatic decrease", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 116, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 116, + 505, + 127 + ], + "score": 1.0, + "content": "in accuracy. For example, LSTM encoder-decoder with 1000 dimensions drops from 32.5 to 8.2", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "BLEU score. These results suggest that the decoder, which is thrown away, contains most of the", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 231, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 231, + 150 + ], + "score": 1.0, + "content": "language-specific information.", + "type": "text", + "cross_page": true + } + ], + "index": 5 + } + ], + "index": 49, + "bbox_fs": [ + 104, + 493, + 506, + 593 + ] + }, + { + "type": "image", + "bbox": [ + 125, + 610, + 486, + 709 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 125, + 610, + 486, + 709 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 125, + 610, + 486, + 709 + ], + "spans": [ + { + "bbox": [ + 125, + 610, + 486, + 709 + ], + "score": 0.973, + "type": "image", + "image_path": "e9af8c8bd91c7b7fed7ecfbb6beeda8b61833cac7aed0ea51520dfe929cd5cee.jpg" + } + ] + } + ], + "index": 55, + "virtual_lines": [ + { + "bbox": [ + 125, + 610, + 486, + 643.0 + ], + "spans": [], + "index": 54 + }, + { + "bbox": [ + 125, + 643.0, + 486, + 676.0 + ], + "spans": [], + "index": 55 + }, + { + "bbox": [ + 125, + 676.0, + 486, + 709.0 + ], + "spans": [], + "index": 56 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 145, + 718, + 465, + 729 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 145, + 717, + 465, + 730 + ], + "spans": [ + { + "bbox": [ + 145, + 717, + 465, + 730 + ], + "score": 1.0, + "content": "Figure 4: Results for length, content and order tests on natural and permuted sentences.", + "type": "text" + } + ], + "index": 57 + } + ], + "index": 57 + } + ], + "index": 56.0 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "use general word order statistics. The results suggest that a trained encoder will transfer well across", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "different natural language domains, as long as the vocabularies remain stable. When considering", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 505, + 117 + ], + "score": 1.0, + "content": "the decoder’s BLEU score on the permuted dataset (not shown), we do see a dramatic decrease", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 116, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 116, + 505, + 127 + ], + "score": 1.0, + "content": "in accuracy. For example, LSTM encoder-decoder with 1000 dimensions drops from 32.5 to 8.2", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 140 + ], + "score": 1.0, + "content": "BLEU score. These results suggest that the decoder, which is thrown away, contains most of the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 231, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 231, + 150 + ], + "score": 1.0, + "content": "language-specific information.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 165, + 259, + 178 + ], + "lines": [ + { + "bbox": [ + 105, + 163, + 261, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 163, + 261, + 180 + ], + "score": 1.0, + "content": "8 SKIP-THOUGHT VECTORS", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 108, + 190, + 504, + 223 + ], + "lines": [ + { + "bbox": [ + 105, + 189, + 504, + 203 + ], + "spans": [ + { + "bbox": [ + 105, + 189, + 504, + 203 + ], + "score": 1.0, + "content": "In addition to the experiments on CBOW and LSTM-encoders, we also experiment with the skip-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 201, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 106, + 201, + 505, + 213 + ], + "score": 1.0, + "content": "thought vectors model (Kiros et al., 2015). This model extends the idea of the auto-encoder to", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 212, + 201, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 201, + 226 + ], + "score": 1.0, + "content": "neighboring sentences.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 228, + 505, + 273 + ], + "lines": [ + { + "bbox": [ + 105, + 228, + 506, + 242 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 177, + 242 + ], + "score": 1.0, + "content": "Given a sentence", + "type": "text" + }, + { + "bbox": [ + 177, + 231, + 186, + 240 + ], + "score": 0.84, + "content": "s _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 228, + 506, + 242 + ], + "score": 1.0, + "content": ", it first encodes it using an RNN, similar to the auto-encoder model. However,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 240, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 505, + 252 + ], + "score": 1.0, + "content": "instead of predicting the original sentence, skip-thought predicts the preceding and following sen-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 251, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 137, + 264 + ], + "score": 1.0, + "content": "tences,", + "type": "text" + }, + { + "bbox": [ + 137, + 253, + 156, + 262 + ], + "score": 0.89, + "content": "s _ { i - 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 251, + 175, + 264 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 176, + 252, + 195, + 263 + ], + "score": 0.9, + "content": "s _ { i + 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 251, + 505, + 264 + ], + "score": 1.0, + "content": ". The encoder and decoder are implemented with gated recurrent units (Cho", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 262, + 159, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 159, + 273 + ], + "score": 1.0, + "content": "et al., 2014).", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + }, + { + "type": "text", + "bbox": [ + 106, + 278, + 505, + 323 + ], + "lines": [ + { + "bbox": [ + 105, + 278, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 278, + 505, + 290 + ], + "score": 1.0, + "content": "Here, we deviate from the controlled environment and use the author’s provided model3 with the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 290, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 505, + 301 + ], + "score": 1.0, + "content": "recommended embeddings size of 4800. This makes the direct comparison of the models “unfair”.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 301, + 504, + 312 + ], + "spans": [ + { + "bbox": [ + 106, + 301, + 504, + 312 + ], + "score": 1.0, + "content": "However, our aim is not to decide which is the “best” model but rather to show how our method can", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 311, + 435, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 435, + 324 + ], + "score": 1.0, + "content": "be used to measure the kinds of information captured by different representations.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 106, + 328, + 504, + 351 + ], + "lines": [ + { + "bbox": [ + 106, + 327, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 341 + ], + "score": 1.0, + "content": "Table 1 summarizes the performance of the skip-thought embeddings in each of the prediction tasks", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 339, + 288, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 288, + 352 + ], + "score": 1.0, + "content": "on both the PERMUTED and original dataset.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5 + }, + { + "type": "table", + "bbox": [ + 197, + 362, + 412, + 395 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 197, + 362, + 412, + 395 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 197, + 362, + 412, + 395 + ], + "spans": [ + { + "bbox": [ + 197, + 362, + 412, + 395 + ], + "score": 0.97, + "html": "
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Its performance is similar to the higher-dimensional encoder-decoder models, except", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 457, + 504, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 504, + 469 + ], + "score": 1.0, + "content": "in the order task where it lags somewhat behind. However, we note that the results are not directly", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 468, + 355, + 481 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 355, + 481 + ], + "score": 1.0, + "content": "comparable as skip-thought was trained on a different corpus.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 107, + 485, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 484, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "The more interesting finding is its performance on the PERMUTED sentences. In this setting we see", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 496, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 508 + ], + "score": 1.0, + "content": "a large drop. In contrast to the LSTM encoder-decoder, skip-thought’s ability to predict length and", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "score": 1.0, + "content": "word content does degrade significantly on the permuted sentences, suggesting that the encoding", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 519, + 456, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 456, + 531 + ], + "score": 1.0, + "content": "process of the skip-thought model is indeed specialized towards natural language texts.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5 + }, + { + "type": "title", + "bbox": [ + 107, + 545, + 196, + 558 + ], + "lines": [ + { + "bbox": [ + 104, + 542, + 198, + 562 + ], + "spans": [ + { + "bbox": [ + 104, + 542, + 198, + 562 + ], + "score": 1.0, + "content": "9 CONCLUSION", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 565, + 504, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 564, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 579 + ], + "score": 1.0, + "content": "We presented a methodology for performing fine-grained analysis of sentence embeddings using", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 576, + 494, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 494, + 589 + ], + "score": 1.0, + "content": "auxiliary prediction tasks. 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This suggests", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 165, + 302, + 178 + ], + "spans": [ + { + "bbox": [ + 116, + 165, + 302, + 178 + ], + "score": 1.0, + "content": "that BLEU is sub-optimal for model selection.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "title", + "bbox": [ + 107, + 193, + 176, + 205 + ], + "lines": [ + { + "bbox": [ + 106, + 194, + 176, + 207 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 176, + 207 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 212, + 504, + 234 + ], + "lines": [ + { + "bbox": [ + 105, + 211, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 105, + 211, + 505, + 225 + ], + "score": 1.0, + "content": "Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. 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COURSERA: Neural networks for", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 115, + 577, + 216, + 589 + ], + "spans": [ + { + "bbox": [ + 115, + 577, + 216, + 589 + ], + "score": 1.0, + "content": "machine learning, 2012.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5, + "bbox_fs": [ + 106, + 566, + 505, + 589 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 596, + 505, + 620 + ], + "lines": [ + { + "bbox": [ + 104, + 594, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 104, + 594, + 506, + 609 + ], + "score": 1.0, + "content": "Matthew D Zeiler. Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 114, + 606, + 143, + 619 + ], + "spans": [ + { + "bbox": [ + 114, + 606, + 143, + 619 + ], + "score": 1.0, + "content": "2012.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5, + "bbox_fs": [ + 104, + 594, + 506, + 619 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 293, + 94 + ], + "lines": [ + { + "bbox": [ + 107, + 81, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 107, + 81, + 295, + 95 + ], + "score": 1.0, + "content": "APPENDIX I: EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 107, + 505, + 140 + ], + "lines": [ + { + "bbox": [ + 105, + 107, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 107, + 505, + 119 + ], + "score": 1.0, + "content": "Sentence Encoders The bag-of-words (CBOW) and encoder-decoder models are trained on 1", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 118, + 505, + 131 + ], + "spans": [ + { + "bbox": [ + 105, + 118, + 505, + 131 + ], + "score": 1.0, + "content": "million sentences from a 2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 129, + 503, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 129, + 503, + 142 + ], + "score": 1.0, + "content": "NLTK (Bird, 2006) for tokenization, and constrain sentence lengths to be between 5 and 70 words.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 107, + 146, + 505, + 179 + ], + "lines": [ + { + "bbox": [ + 105, + 145, + 505, + 158 + ], + "spans": [ + { + "bbox": [ + 105, + 145, + 505, + 158 + ], + "score": 1.0, + "content": "For the CBOW model, we train Skip-gram word vectors (Mikolov et al., 2013a), with hierarchical-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 156, + 505, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 156, + 505, + 169 + ], + "score": 1.0, + "content": "softmax and a window size of 5 words, using the Gensim implementation.4 We control for the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 168, + 434, + 180 + ], + "spans": [ + { + "bbox": [ + 106, + 168, + 171, + 180 + ], + "score": 1.0, + "content": "embedding size", + "type": "text" + }, + { + "bbox": [ + 171, + 168, + 178, + 178 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 168, + 303, + 180 + ], + "score": 1.0, + "content": "and train word vectors of sizes", + "type": "text" + }, + { + "bbox": [ + 304, + 168, + 429, + 180 + ], + "score": 0.89, + "content": "k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 168, + 434, + 180 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 185, + 505, + 240 + ], + "lines": [ + { + "bbox": [ + 106, + 185, + 504, + 197 + ], + "spans": [ + { + "bbox": [ + 106, + 185, + 504, + 197 + ], + "score": 1.0, + "content": "For the encoder-decoder models, we use an in-house implementation using the Torch7 toolkit (Col-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 195, + 505, + 209 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 505, + 209 + ], + "score": 1.0, + "content": "lobert et al., 2011). The decoder is trained as a language model, attempting to predict the correct", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 206, + 505, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 206, + 505, + 220 + ], + "score": 1.0, + "content": "word at each time step using a negative-log-likelihood objective (cross-entropy loss over the softmax", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 217, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 217, + 505, + 231 + ], + "score": 1.0, + "content": "layer). We use one layer of LSTM cells for the encoder and decoder using the implementation in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 228, + 196, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 196, + 241 + ], + "score": 1.0, + "content": "Leonard et al. (2015). ´", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 505, + 289 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 382, + 258 + ], + "score": 1.0, + "content": "We use the same size for word and sentence representations (i.e.", + "type": "text" + }, + { + "bbox": [ + 382, + 246, + 414, + 256 + ], + "score": 0.88, + "content": "d \\ = \\ k", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 244, + 506, + 258 + ], + "score": 1.0, + "content": "), and train models of", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 129, + 269 + ], + "score": 1.0, + "content": "sizes", + "type": "text" + }, + { + "bbox": [ + 129, + 257, + 259, + 268 + ], + "score": 0.89, + "content": "k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 257, + 505, + 269 + ], + "score": 1.0, + "content": ". We follow previous work on sequence-to-sequence learn-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "score": 1.0, + "content": "ing (Sutskever et al., 2014; Li et al., 2015) in reversing the input sentences and clipping gradients.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 278, + 293, + 291 + ], + "spans": [ + { + "bbox": [ + 106, + 278, + 293, + 291 + ], + "score": 1.0, + "content": "Word vectors are initialized to random values.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 295, + 505, + 361 + ], + "lines": [ + { + "bbox": [ + 106, + 295, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 505, + 308 + ], + "score": 1.0, + "content": "We evaluate the encoder-decoder models using BLEU scores (Papineni et al., 2002), a popular ma-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 307, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 505, + 318 + ], + "score": 1.0, + "content": "chine translation evaluation metric that is also used to evaluate auto-encoder models (Li et al., 2015).", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 331 + ], + "score": 1.0, + "content": "BLEU score measures how well the original sentence is recreated, and can be thought of as a proxy", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "score": 1.0, + "content": "for the quality of the encoded representation. We compare it with the performance of the models", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "score": 1.0, + "content": "on the three prediction tasks. The results of the higher-dimensional models are comparable to those", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 350, + 472, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 472, + 363 + ], + "score": 1.0, + "content": "found in the literature, which serves as a sanity check for the quality of the learned models.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 107, + 375, + 505, + 408 + ], + "lines": [ + { + "bbox": [ + 106, + 375, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 388 + ], + "score": 1.0, + "content": "Auxiliary Task Classifier For the auxiliary task predictors, we use multi-layer perceptrons with", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "score": 1.0, + "content": "a single hidden layer and ReLU activation, which were carefully tuned for each of the tasks. We", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 398, + 453, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 453, + 410 + ], + "score": 1.0, + "content": "experimented with several network architectures prior to arriving at this configuration.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 108, + 414, + 504, + 437 + ], + "lines": [ + { + "bbox": [ + 105, + 413, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 428 + ], + "score": 1.0, + "content": "Further details regarding the training and architectures of both the sentence encoders and auxiliary", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 426, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 288, + 437 + ], + "score": 1.0, + "content": "task classifiers are available in the Appendix.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25.5 + }, + { + "type": "title", + "bbox": [ + 108, + 454, + 289, + 467 + ], + "lines": [ + { + "bbox": [ + 107, + 455, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 107, + 455, + 290, + 469 + ], + "score": 1.0, + "content": "APPENDIX II: TECHNICAL DETAILS", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 108, + 481, + 195, + 492 + ], + "lines": [ + { + "bbox": [ + 106, + 480, + 196, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 196, + 493 + ], + "score": 1.0, + "content": "ENCODER DECODER", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 501, + 505, + 557 + ], + "lines": [ + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "score": 1.0, + "content": "Parameters of the encoder-decoder were tuned on a dedicated validation set. We experienced with", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 513, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 106, + 513, + 505, + 525 + ], + "score": 1.0, + "content": "different learning rates (0.1, 0.01, 0.001), dropout-rates (0.1, 0.2, 0.3, 0.5) (Hinton et al., 2012) and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 523, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 505, + 537 + ], + "score": 1.0, + "content": "optimization techniques (AdaGrad (Duchi et al., 2011), AdaDelta (Zeiler, 2012), Adam (Kingma &", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 535, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 505, + 548 + ], + "score": 1.0, + "content": "Ba, 2014) and RMSprop (Tieleman & Hinton, 2012)). We also experimented with different batch", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 545, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 506, + 560 + ], + "score": 1.0, + "content": "sizes (8, 16, 32), and found improvement in runtime but no significant improvement in performance.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 108, + 562, + 505, + 606 + ], + "lines": [ + { + "bbox": [ + 106, + 563, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 505, + 575 + ], + "score": 1.0, + "content": "Based on the tuned parameters, we trained the encoder-decoder models on a single GPU (NVIDIA", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 573, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 505, + 586 + ], + "score": 1.0, + "content": "Tesla K40), with mini-batches of 32 sentences, learning rate of 0.01, dropout rate of 0.1, and the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "score": 1.0, + "content": "AdaGrad optimizer; training takes approximately 10 days and is stopped after 5 epochs with no loss", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 596, + 239, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 239, + 608 + ], + "score": 1.0, + "content": "improvement on a validation set.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35.5 + }, + { + "type": "title", + "bbox": [ + 108, + 622, + 192, + 633 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 193, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 193, + 635 + ], + "score": 1.0, + "content": "PREDICTION TASKS", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 644, + 505, + 709 + ], + "lines": [ + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "Parameters for the predictions tasks as well as classifier architecture were tuned on a dedicated vali-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "dation set. We experimented with one, two and three layer feed-forward networks using ReLU (Nair", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "& Hinton, 2010; Glorot et al., 2011), tanh and sigmoid activation functions. We tried different hid-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "den layer sizes: the same as the input size, twice the input size and one and a half times the input", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "size. We tried different learning rates (0.1, 0.01, 0.001), dropout rates (0.1, 0.3, 0.5, 0.8) and differ-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 698, + 354, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 354, + 711 + ], + "score": 1.0, + "content": "ent optimization techniques (AdaGrad, AdaDelta and Adam).", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5 + } + ], + "page_idx": 10, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 120, + 722, + 244, + 731 + ], + "lines": [ + { + "bbox": [ + 119, + 720, + 244, + 733 + ], + "spans": [ + { + "bbox": [ + 119, + 720, + 244, + 733 + ], + "score": 1.0, + "content": "4https://radimrehurek.com/gensim", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 13 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 293, + 94 + ], + "lines": [ + { + "bbox": [ + 107, + 81, + 295, + 95 + ], + "spans": [ + { + "bbox": [ + 107, + 81, + 295, + 95 + ], + "score": 1.0, + "content": "APPENDIX I: EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 107, + 505, + 140 + ], + "lines": [ + { + "bbox": [ + 105, + 107, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 107, + 505, + 119 + ], + "score": 1.0, + "content": "Sentence Encoders The bag-of-words (CBOW) and encoder-decoder models are trained on 1", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 118, + 505, + 131 + ], + "spans": [ + { + "bbox": [ + 105, + 118, + 505, + 131 + ], + "score": 1.0, + "content": "million sentences from a 2012 Wikipedia dump with vocabulary size of 50,000 tokens. We use", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 129, + 503, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 129, + 503, + 142 + ], + "score": 1.0, + "content": "NLTK (Bird, 2006) for tokenization, and constrain sentence lengths to be between 5 and 70 words.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 107, + 505, + 142 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 146, + 505, + 179 + ], + "lines": [ + { + "bbox": [ + 105, + 145, + 505, + 158 + ], + "spans": [ + { + "bbox": [ + 105, + 145, + 505, + 158 + ], + "score": 1.0, + "content": "For the CBOW model, we train Skip-gram word vectors (Mikolov et al., 2013a), with hierarchical-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 156, + 505, + 169 + ], + "spans": [ + { + "bbox": [ + 105, + 156, + 505, + 169 + ], + "score": 1.0, + "content": "softmax and a window size of 5 words, using the Gensim implementation.4 We control for the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 168, + 434, + 180 + ], + "spans": [ + { + "bbox": [ + 106, + 168, + 171, + 180 + ], + "score": 1.0, + "content": "embedding size", + "type": "text" + }, + { + "bbox": [ + 171, + 168, + 178, + 178 + ], + "score": 0.77, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 168, + 303, + 180 + ], + "score": 1.0, + "content": "and train word vectors of sizes", + "type": "text" + }, + { + "bbox": [ + 304, + 168, + 429, + 180 + ], + "score": 0.89, + "content": "k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 168, + 434, + 180 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 145, + 505, + 180 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 185, + 505, + 240 + ], + "lines": [ + { + "bbox": [ + 106, + 185, + 504, + 197 + ], + "spans": [ + { + "bbox": [ + 106, + 185, + 504, + 197 + ], + "score": 1.0, + "content": "For the encoder-decoder models, we use an in-house implementation using the Torch7 toolkit (Col-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 195, + 505, + 209 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 505, + 209 + ], + "score": 1.0, + "content": "lobert et al., 2011). The decoder is trained as a language model, attempting to predict the correct", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 206, + 505, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 206, + 505, + 220 + ], + "score": 1.0, + "content": "word at each time step using a negative-log-likelihood objective (cross-entropy loss over the softmax", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 217, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 217, + 505, + 231 + ], + "score": 1.0, + "content": "layer). We use one layer of LSTM cells for the encoder and decoder using the implementation in", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 228, + 196, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 196, + 241 + ], + "score": 1.0, + "content": "Leonard et al. (2015). ´", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 185, + 505, + 241 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 245, + 505, + 289 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 382, + 258 + ], + "score": 1.0, + "content": "We use the same size for word and sentence representations (i.e.", + "type": "text" + }, + { + "bbox": [ + 382, + 246, + 414, + 256 + ], + "score": 0.88, + "content": "d \\ = \\ k", + "type": "inline_equation" + }, + { + "bbox": [ + 414, + 244, + 506, + 258 + ], + "score": 1.0, + "content": "), and train models of", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 257, + 505, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 129, + 269 + ], + "score": 1.0, + "content": "sizes", + "type": "text" + }, + { + "bbox": [ + 129, + 257, + 259, + 268 + ], + "score": 0.89, + "content": "k \\in \\{ 1 0 0 , 3 0 0 , 5 0 0 , 7 5 0 , 1 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 257, + 505, + 269 + ], + "score": 1.0, + "content": ". We follow previous work on sequence-to-sequence learn-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 505, + 280 + ], + "score": 1.0, + "content": "ing (Sutskever et al., 2014; Li et al., 2015) in reversing the input sentences and clipping gradients.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 278, + 293, + 291 + ], + "spans": [ + { + "bbox": [ + 106, + 278, + 293, + 291 + ], + "score": 1.0, + "content": "Word vectors are initialized to random values.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 244, + 506, + 291 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 295, + 505, + 361 + ], + "lines": [ + { + "bbox": [ + 106, + 295, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 505, + 308 + ], + "score": 1.0, + "content": "We evaluate the encoder-decoder models using BLEU scores (Papineni et al., 2002), a popular ma-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 307, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 505, + 318 + ], + "score": 1.0, + "content": "chine translation evaluation metric that is also used to evaluate auto-encoder models (Li et al., 2015).", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 331 + ], + "score": 1.0, + "content": "BLEU score measures how well the original sentence is recreated, and can be thought of as a proxy", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 340 + ], + "score": 1.0, + "content": "for the quality of the encoded representation. We compare it with the performance of the models", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 340, + 505, + 351 + ], + "score": 1.0, + "content": "on the three prediction tasks. The results of the higher-dimensional models are comparable to those", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 350, + 472, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 472, + 363 + ], + "score": 1.0, + "content": "found in the literature, which serves as a sanity check for the quality of the learned models.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 295, + 505, + 363 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 375, + 505, + 408 + ], + "lines": [ + { + "bbox": [ + 106, + 375, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 388 + ], + "score": 1.0, + "content": "Auxiliary Task Classifier For the auxiliary task predictors, we use multi-layer perceptrons with", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "score": 1.0, + "content": "a single hidden layer and ReLU activation, which were carefully tuned for each of the tasks. We", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 398, + 453, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 453, + 410 + ], + "score": 1.0, + "content": "experimented with several network architectures prior to arriving at this configuration.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 375, + 505, + 410 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 414, + 504, + 437 + ], + "lines": [ + { + "bbox": [ + 105, + 413, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 428 + ], + "score": 1.0, + "content": "Further details regarding the training and architectures of both the sentence encoders and auxiliary", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 426, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 288, + 437 + ], + "score": 1.0, + "content": "task classifiers are available in the Appendix.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 413, + 505, + 437 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 454, + 289, + 467 + ], + "lines": [ + { + "bbox": [ + 107, + 455, + 290, + 469 + ], + "spans": [ + { + "bbox": [ + 107, + 455, + 290, + 469 + ], + "score": 1.0, + "content": "APPENDIX II: TECHNICAL DETAILS", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 108, + 481, + 195, + 492 + ], + "lines": [ + { + "bbox": [ + 106, + 480, + 196, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 196, + 493 + ], + "score": 1.0, + "content": "ENCODER DECODER", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28, + "bbox_fs": [ + 106, + 480, + 196, + 493 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 501, + 505, + 557 + ], + "lines": [ + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 505, + 514 + ], + "score": 1.0, + "content": "Parameters of the encoder-decoder were tuned on a dedicated validation set. We experienced with", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 513, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 106, + 513, + 505, + 525 + ], + "score": 1.0, + "content": "different learning rates (0.1, 0.01, 0.001), dropout-rates (0.1, 0.2, 0.3, 0.5) (Hinton et al., 2012) and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 523, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 505, + 537 + ], + "score": 1.0, + "content": "optimization techniques (AdaGrad (Duchi et al., 2011), AdaDelta (Zeiler, 2012), Adam (Kingma &", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 535, + 505, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 505, + 548 + ], + "score": 1.0, + "content": "Ba, 2014) and RMSprop (Tieleman & Hinton, 2012)). We also experimented with different batch", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 545, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 506, + 560 + ], + "score": 1.0, + "content": "sizes (8, 16, 32), and found improvement in runtime but no significant improvement in performance.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 502, + 506, + 560 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 562, + 505, + 606 + ], + "lines": [ + { + "bbox": [ + 106, + 563, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 505, + 575 + ], + "score": 1.0, + "content": "Based on the tuned parameters, we trained the encoder-decoder models on a single GPU (NVIDIA", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 573, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 505, + 586 + ], + "score": 1.0, + "content": "Tesla K40), with mini-batches of 32 sentences, learning rate of 0.01, dropout rate of 0.1, and the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "score": 1.0, + "content": "AdaGrad optimizer; training takes approximately 10 days and is stopped after 5 epochs with no loss", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 596, + 239, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 239, + 608 + ], + "score": 1.0, + "content": "improvement on a validation set.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 563, + 505, + 608 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 622, + 192, + 633 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 193, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 193, + 635 + ], + "score": 1.0, + "content": "PREDICTION TASKS", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 644, + 505, + 709 + ], + "lines": [ + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "Parameters for the predictions tasks as well as classifier architecture were tuned on a dedicated vali-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "dation set. We experimented with one, two and three layer feed-forward networks using ReLU (Nair", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "& Hinton, 2010; Glorot et al., 2011), tanh and sigmoid activation functions. We tried different hid-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 688 + ], + "score": 1.0, + "content": "den layer sizes: the same as the input size, twice the input size and one and a half times the input", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "size. We tried different learning rates (0.1, 0.01, 0.001), dropout rates (0.1, 0.3, 0.5, 0.8) and differ-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 698, + 354, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 354, + 711 + ], + "score": 1.0, + "content": "ent optimization techniques (AdaGrad, AdaDelta and Adam).", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 644, + 505, + 711 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 505, + 95 + ], + "score": 1.0, + "content": "Our best tuned classifier, which we use for all experiments, is a feed-forward network with one", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "hidden layer and a ReLU activation function. We set the size of the hidden layer to be the same size", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "as the input vector. We place a softmax layer on top whose size varies according to the specific task,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 127 + ], + "score": 1.0, + "content": "and apply dropout before the softmax layer. We optimize the log-likelihood using AdaGrad. We", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 126, + 506, + 139 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 506, + 139 + ], + "score": 1.0, + "content": "use a dropout rate of 0.8 and a learning rate of 0.01. Training is stopped after 5 epochs with no loss", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 493, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 493, + 150 + ], + "score": 1.0, + "content": "improvement on the development set. Training was done on a single GPU (NVIDIA Tesla K40).", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 164, + 369, + 177 + ], + "lines": [ + { + "bbox": [ + 106, + 163, + 369, + 179 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 369, + 179 + ], + "score": 1.0, + "content": "10 ADDITIONAL EXPERIMENTS - CONTENT TASK", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 211 + ], + "lines": [ + { + "bbox": [ + 106, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 505, + 201 + ], + "score": 1.0, + "content": "How well do the models preserve content when we increase the sentence length? In Fig. 5 we plot", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 200, + 381, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 381, + 212 + ], + "score": 1.0, + "content": "content prediction accuracy vs. sentence length for different models.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "image", + "bbox": [ + 212, + 223, + 398, + 351 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 212, + 223, + 398, + 351 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 212, + 223, + 398, + 351 + ], + "spans": [ + { + "bbox": [ + 212, + 223, + 398, + 351 + ], + "score": 0.971, + "type": "image", + "image_path": "8a2f0243ec8ee281bff85c440c131dec3d455bbb04308d04d68ae81b98dd8e95.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 212, + 223, + 398, + 237.22222222222223 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 212, + 237.22222222222223, + 398, + 251.44444444444446 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 212, + 251.44444444444446, + 398, + 265.6666666666667 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 212, + 265.6666666666667, + 398, + 279.8888888888889 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 212, + 279.8888888888889, + 398, + 294.11111111111114 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 212, + 294.11111111111114, + 398, + 308.33333333333337 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 212, + 308.33333333333337, + 398, + 322.5555555555556 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 212, + 322.5555555555556, + 398, + 336.7777777777778 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 212, + 336.7777777777778, + 398, + 351.00000000000006 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 180, + 363, + 430, + 375 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 180, + 362, + 430, + 376 + ], + "spans": [ + { + "bbox": [ + 180, + 362, + 430, + 376 + ], + "score": 1.0, + "content": "Figure 5: Content accuracy vs. sentence length for selected models.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 386, + 505, + 419 + ], + "lines": [ + { + "bbox": [ + 106, + 385, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 506, + 399 + ], + "score": 1.0, + "content": "As expected, all models suffer a drop in content accuracy on longer sentences. The degradation is", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "score": 1.0, + "content": "roughly linear in the sentence length. For the encoder-decoder, models with fewer dimensions seem", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 408, + 182, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 182, + 420 + ], + "score": 1.0, + "content": "to degrade slower.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "title", + "bbox": [ + 108, + 434, + 295, + 448 + ], + "lines": [ + { + "bbox": [ + 107, + 434, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 107, + 434, + 296, + 449 + ], + "score": 1.0, + "content": "APPENDIX III: SIGNIFICANCE TESTS", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 459, + 504, + 482 + ], + "lines": [ + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "score": 1.0, + "content": "In this section we report the significance tests we conduct in order to evaluate our findings. In order", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 471, + 298, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 471, + 298, + 482 + ], + "score": 1.0, + "content": "to do so, we use the paired t-test (Rubin, 1973).", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 108, + 487, + 504, + 532 + ], + "lines": [ + { + "bbox": [ + 106, + 487, + 506, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 436, + 501 + ], + "score": 1.0, + "content": "All the results reported in the summery of findings are highly significant (p-value", + "type": "text" + }, + { + "bbox": [ + 437, + 488, + 479, + 498 + ], + "score": 0.74, + "content": "\\ll 0 . 0 0 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 479, + 487, + 506, + 501 + ], + "score": 1.0, + "content": "). The", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 499, + 506, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 257, + 511 + ], + "score": 1.0, + "content": "ones we found to be not significant", + "type": "text" + }, + { + "bbox": [ + 258, + 500, + 264, + 510 + ], + "score": 0.31, + "content": "\\mathrm { { \\dot { p } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 499, + 290, + 511 + ], + "score": 1.0, + "content": "-value", + "type": "text" + }, + { + "bbox": [ + 290, + 499, + 323, + 509 + ], + "score": 0.8, + "content": "\\gg 0 . 0 3", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 499, + 506, + 511 + ], + "score": 1.0, + "content": ") are the ones which their accuracy does not", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 510, + 506, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 506, + 522 + ], + "score": 1.0, + "content": "have much of a difference, i.e ED with size 500 and ED with size 750 tested on the word order task", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 520, + 398, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 140, + 533 + ], + "score": 1.0, + "content": "(p-value", + "type": "text" + }, + { + "bbox": [ + 140, + 520, + 164, + 531 + ], + "score": 0.49, + "content": "= 0 . 1 1", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 520, + 371, + 533 + ], + "score": 1.0, + "content": "), or CBOW with dimensions 750 and 1000 (p-value", + "type": "text" + }, + { + "bbox": [ + 372, + 521, + 391, + 531 + ], + "score": 0.69, + "content": "{ \\ : = } 0 . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 391, + 520, + 398, + 533 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5 + }, + { + "type": "table", + "bbox": [ + 203, + 542, + 406, + 605 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 203, + 542, + 406, + 605 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 203, + 542, + 406, + 605 + ], + "spans": [ + { + "bbox": [ + 203, + 542, + 406, + 605 + ], + "score": 0.975, + "html": "
Dim.LengthWordcontentWordorder
1001.77e-1470.01.83e-296
3000.00.00.0
5000.00.00.0
7500.00.00.0
10000.00.00.0
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Dim.LengthWord contentWord order
100 vs.3000.08.56e-1900.0
300 vs. 5007.3e-714.20e-055.48e-56
500 vs. 7503.64e-1754.46e-650.11
750 vs. 10001.37e-1112.35e-2434.32e-61
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Training is stopped after 5 epochs with no loss", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 493, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 493, + 150 + ], + "score": 1.0, + "content": "improvement on the development set. Training was done on a single GPU (NVIDIA Tesla K40).", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5, + "bbox_fs": [ + 105, + 81, + 506, + 150 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 164, + 369, + 177 + ], + "lines": [ + { + "bbox": [ + 106, + 163, + 369, + 179 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 369, + 179 + ], + "score": 1.0, + "content": "10 ADDITIONAL EXPERIMENTS - CONTENT TASK", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 211 + ], + "lines": [ + { + "bbox": [ + 106, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 189, + 505, + 201 + ], + "score": 1.0, + "content": "How well do the models preserve content when we increase the sentence length? In Fig. 5 we plot", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 200, + 381, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 381, + 212 + ], + "score": 1.0, + "content": "content prediction accuracy vs. sentence length for different models.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 189, + 505, + 212 + ] + }, + { + "type": "image", + "bbox": [ + 212, + 223, + 398, + 351 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 212, + 223, + 398, + 351 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 212, + 223, + 398, + 351 + ], + "spans": [ + { + "bbox": [ + 212, + 223, + 398, + 351 + ], + "score": 0.971, + "type": "image", + "image_path": "8a2f0243ec8ee281bff85c440c131dec3d455bbb04308d04d68ae81b98dd8e95.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 212, + 223, + 398, + 237.22222222222223 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 212, + 237.22222222222223, + 398, + 251.44444444444446 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 212, + 251.44444444444446, + 398, + 265.6666666666667 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 212, + 265.6666666666667, + 398, + 279.8888888888889 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 212, + 279.8888888888889, + 398, + 294.11111111111114 + ], + "spans": [], + "index": 13 + }, + { + "bbox": [ + 212, + 294.11111111111114, + 398, + 308.33333333333337 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 212, + 308.33333333333337, + 398, + 322.5555555555556 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 212, + 322.5555555555556, + 398, + 336.7777777777778 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 212, + 336.7777777777778, + 398, + 351.00000000000006 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 180, + 363, + 430, + 375 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 180, + 362, + 430, + 376 + ], + "spans": [ + { + "bbox": [ + 180, + 362, + 430, + 376 + ], + "score": 1.0, + "content": "Figure 5: Content accuracy vs. sentence length for selected models.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 386, + 505, + 419 + ], + "lines": [ + { + "bbox": [ + 106, + 385, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 506, + 399 + ], + "score": 1.0, + "content": "As expected, all models suffer a drop in content accuracy on longer sentences. The degradation is", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 505, + 409 + ], + "score": 1.0, + "content": "roughly linear in the sentence length. For the encoder-decoder, models with fewer dimensions seem", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 408, + 182, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 182, + 420 + ], + "score": 1.0, + "content": "to degrade slower.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20, + "bbox_fs": [ + 106, + 385, + 506, + 420 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 434, + 295, + 448 + ], + "lines": [ + { + "bbox": [ + 107, + 434, + 296, + 449 + ], + "spans": [ + { + "bbox": [ + 107, + 434, + 296, + 449 + ], + "score": 1.0, + "content": "APPENDIX III: SIGNIFICANCE TESTS", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 106, + 459, + 504, + 482 + ], + "lines": [ + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 505, + 472 + ], + "score": 1.0, + "content": "In this section we report the significance tests we conduct in order to evaluate our findings. 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The", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 499, + 506, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 257, + 511 + ], + "score": 1.0, + "content": "ones we found to be not significant", + "type": "text" + }, + { + "bbox": [ + 258, + 500, + 264, + 510 + ], + "score": 0.31, + "content": "\\mathrm { { \\dot { p } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 499, + 290, + 511 + ], + "score": 1.0, + "content": "-value", + "type": "text" + }, + { + "bbox": [ + 290, + 499, + 323, + 509 + ], + "score": 0.8, + "content": "\\gg 0 . 0 3", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 499, + 506, + 511 + ], + "score": 1.0, + "content": ") are the ones which their accuracy does not", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 510, + 506, + 522 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 506, + 522 + ], + "score": 1.0, + "content": "have much of a difference, i.e ED with size 500 and ED with size 750 tested on the word order task", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 520, + 398, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 140, + 533 + ], + "score": 1.0, + "content": "(p-value", + "type": "text" + }, + { + "bbox": [ + 140, + 520, + 164, + 531 + ], + "score": 0.49, + "content": "= 0 . 1 1", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 520, + 371, + 533 + ], + "score": 1.0, + "content": "), or CBOW with dimensions 750 and 1000 (p-value", + "type": "text" + }, + { + "bbox": [ + 372, + 521, + 391, + 531 + ], + "score": 0.69, + "content": "{ \\ : = } 0 . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 391, + 520, + 398, + 533 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 487, + 506, + 533 + ] + }, + { + "type": "table", + "bbox": [ + 203, + 542, + 406, + 605 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 203, + 542, + 406, + 605 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 203, + 542, + 406, + 605 + ], + "spans": [ + { + "bbox": [ + 203, + 542, + 406, + 605 + ], + "score": 0.975, + "html": "
Dim.LengthWordcontentWordorder
1001.77e-1470.01.83e-296
3000.00.00.0
5000.00.00.0
7500.00.00.0
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Dim.LengthWord contentWord order
100 vs.3000.08.56e-1900.0
300 vs. 5007.3e-714.20e-055.48e-56
500 vs. 7503.64e-1754.46e-650.11
750 vs. 10001.37e-1112.35e-2434.32e-61
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Dim.LengthWord contentWord order
100 vs.3000.00.01.5e-33
300 vs. 5001.47e-2150.03.06e-64
500 vs. 7500.680.0320.05
750 vs.10004.44e-320.30.08
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Dim.LengthWord contentWord order
100 vs.3000.00.01.5e-33
300 vs. 5001.47e-2150.03.06e-64
500 vs. 7500.680.0320.05
750 vs.10004.44e-320.30.08
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sha256:96674fdccdce295ca45ab8079c65a9cd391f47c2e17ae3a95690f2ca5552f9df +size 25716 diff --git a/parse/train/Hk8N3Sclg/Hk8N3Sclg.md b/parse/train/Hk8N3Sclg/Hk8N3Sclg.md new file mode 100644 index 0000000000000000000000000000000000000000..04c642384e11049e5a2922776cb2c3acac71e87a --- /dev/null +++ b/parse/train/Hk8N3Sclg/Hk8N3Sclg.md @@ -0,0 +1,238 @@ +# MULTI-AGENT COOPERATIONAND THE EMERGENCE OF (NATURAL) LANGUAGE + +Angeliki Lazaridou1∗, Alexander Peysakhovich2, Marco Baroni2,3 1Google DeepMind, 2Facebook AI Research, 3University of Trento angeliki@google.com, {alexpeys,mbaroni}@fb.com + +# ABSTRACT + +The current mainstream approach to train natural language systems is to expose them to large amounts of text. This passive learning is problematic if we are interested in developing interactive machines, such as conversational agents. We propose a framework for language learning that relies on multi-agent communication. We study this learning in the context of referential games. In these games, a sender and a receiver see a pair of images. The sender is told one of them is the target and is allowed to send a message from a fixed, arbitary vocabulary to the receiver. The receiver must rely on this message to identify the target. Thus, the agents develop their own language interactively out of the need to communicate. We show that two networks with simple configurations are able to learn to coordinate in the referential game. We further explore how to make changes to the game environment to cause the “word meanings” induced in the game to better reflect intuitive semantic properties of the images. In addition, we present a simple strategy for grounding the agents’ code into natural language. Both of these are necessary steps towards developing machines that are able to communicate with humans productively. + +# 1 INTRODUCTION + +I tried to break it to him gently [...] the only way to learn an unknown language is to interact with a native speaker [...] asking questions, holding a conversation, that sort of thing [...] If you want to learn the aliens’ language, someone [...] will have to talk with an alien. Recordings alone aren’t sufficient. + +Ted Chiang, Story of Your Life + +One of the main aims of AI is to develop agents that can cooperate with others to achieve goals (Wooldridge, 2009). Such coordination requires communication. If the coordination partners are to include humans, the most obvious channel of communication is natural language. Thus, handling natural-language-based communication is a key step toward the development of AI that can thrive in a world populated by other agents. + +Given the success of deep learning models in related domains such as image captioning or machine translation (e.g., Sutskever et al., 2014; Xu et al., 2015), it would seem reasonable to cast the problem of training conversational agents as an instance of supervised learning (Vinyals & Le, 2015). However, training on “canned” conversations does not allow learners to experience the interactive aspects of communication. Supervised approaches, which focus on the structure of language, are an excellent way to learn general statistical associations between sequences of symbols. However, they do not capture the functional aspects of communication, i.e., that humans use words to coordinate with others and make things happen (Austin, 1962; Clark, 1996; Wittgenstein, 1953). + +This paper introduces the first steps of a research program based on multi-agent coordination communication games. These games place agents in simple environments where they need to develop a language to coordinate and earn payoffs. Importantly, the agents start as blank slates, but, by playing a game together, they can develop and bootstrap knowledge on top of each others, leading to the emergence of a language. + +The central problem of our program, then, is the following: How do we design environments that foster the development of a language that is portable to new situations and to new communication partners (in particular humans)? + +We start from the most basic challenge of using a language in order to refer to things in the context of a two-agent game. We focus on two questions. First, whether tabula rasa agents succeed in communication. Second, what features of the environment lead to the development of codes resembling human language. + +We assess this latter question in two ways. First, we consider whether the agents associate general conceptual properties, such as broad object categories (as opposed to low-level visual properties), to the symbols they learn to use. Second, we examine whether the agents’ “word usage” is partially interpretable by humans in an online experiment. + +Other researchers have proposed communication-based environments for the development of coordination-capable AI. Work in multi-agent systems has focused on the design of pre-programmed communication systems to solve specific tasks (e.g., robot soccer, Stone & Veloso 1998). Most related to our work, Sukhbaatar et al. (2016) and Foerster et al. (2016) show that neural networks can evolve communication in the context of games without a pre-coded protocol. We pursue the same question, but further ask how we can change our environment to make the emergent language more interpretable. + +Others (e.g., the SHRLDU program of Winograd 1971 or the game in Wang et al. 2016) propose building a communicating AI by putting humans in the loop from the very beginning. This approach has benefits but faces serious scalability issues, as active human intervention is required at each step. An attractive component of our game-based paradigm is that humans may be added as players, but do not need to be there all the time. + +A third branch of research focuses on “Wizard-of-Oz” environments, where agents learn to play games by interacting with a complex scripted environment (Mikolov et al., 2015). This approach gives the designer tight control over the learning curriculum, but imposes a heavy engineering burden on developers. We also stress the importance of the environment (game setup), but we focus on simpler environments with multiple agents that force them to get smarter by bootstrapping on top of each other. + +We leverage ideas from work in linguistics, cognitive science and game theory on the emergence of language (Wagner et al., 2003; Skyrms, 2010; Crawford & Sobel, 1982; Crawford, 1998). Our game is a variation of Lewis’ signaling game (Lewis, 1969). There is a rich tradition of linguistic and cognitive studies using similar setups (e.g., Briscoe, 2002; Cangelosi & Parisi, 2002; Spike et al., 2016; Steels & Loetzsch, 2012). What distinguishes us from this literature is our aim to, eventually, develop practical AI. This motivates our focus on more realistic input data (a large collection of noisy natural images) and on trying to align the agents’ language with human intuitions. + +Lewis’ classic games have been studied extensively in game theory under the name of “cheap talk”. These games have been used as models to study the evolution of language both theoretically and experimentally (Crawford, 1998; Blume et al., 1998; Crawford & Sobel, 1982). A major question in game theory is whether equilibrium actually occurs in a game as convergence in learning is not guaranteed (Fudenberg & Peysakhovich, 2014; Roth & Erev, 1995). And, if an equilibrium is reached, which one it will be (since they are typically not unique). This is particularly true for cheap talk games, which exhibit Nash equilibria in which precise language emerges, others where vague language emerges and others where no language emerges at all (Crawford & Sobel, 1982). In addition, because in these games language has no ex-ante meaning and only emerges in the context of the equilibrium, some of the emergent languages may not be very natural. Our results speak to both the convergence question and the question of what features of the game cause the appearance of different types of languages. Thus, our results are also of interest to game theorists. + +An evolutionary perspective has recently been advocated as a way to mitigate the data hunger of traditional supervised approaches (Goodfellow et al., 2014; Silver et al., 2016). This research confirms that learning can be bootstrapped from competition between agents. We focus, however, on cooperation between agents as a way to foster learning while reducing the need for annotated data. + +# 2 GENERAL FRAMEWORK + +Our general framework includes K players, each parametrized by $\theta _ { k }$ , a collection of tasks/games that the players have to perform, a communication protocol $V$ that enables the players to communicate with each other, and payoffs assigned to the players as a deterministic function of a well-defined goal. In this paper we focus on a particular version of this: referential games. These games are structured as follows. + +1. There is a set of images represented by vectors $\{ i _ { 1 } , \dotsc , i _ { N } \}$ , two images are drawn at random from this set, call them $( i _ { L } , i _ { R } )$ , one of them is chosen to be the “target” $t \in \{ L , R \}$ +2. There are two players, a sender and a receiver, each seeing the images - the sender receives input $\theta _ { S } ( i _ { L } , i _ { R } , t )$ +3. There is a vocabulary $V$ of size $K$ and the sender chooses one symbol to send to the receiver, we call this the sender’s policy $s ( \theta _ { S } ( i _ { L } , i _ { R } , t ) ) \in V$ +4. The receiver does not know the target, but sees the sender’s symbol and tries to guess the target image. We call this the receiver’s policy $r ( i _ { L } , i _ { R } , s ( \theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \in \{ L , \bar { R } \}$ +5. If $r ( i _ { L } , i _ { R } , s ( \theta _ { S } ( i _ { L } , i _ { R } , t ) ) = t$ , that is, if the receiver guesses the target, both players receive a payoff of 1 (win), otherwise they receive a payoff of 0 (lose). + +Many extensions to the basic referential game explored here are possible. There can be more images, or a more sophisticated communication protocol (e.g., communication of a sequence of symbols or multi-step communication requiring back-and-forth interaction1), rotation of the sender and receiver roles, having a human occasionally playing one of the roles, etc. + +# 3 EXPERIMENTAL SETUP + +Images We use the McRae et al.’s (2005) set of 463 base-level concrete concepts (e.g., cat, apple, car. . . ) spanning across 20 general categories (e.g., animal, fruit/vegetable, vehicle. . . ). We randomly sample 100 images of each concept from ImageNet (Deng et al., 2009). To create target/distractor pairs, we randomly sample two concepts, one image for each concept and whether the first or second image will serve as target. We apply to each image a forward-pass through the pretrained VGG ConvNet (Simonyan & Zisserman, 2014), and represent it with the activations from either the top 1000-D softmax layer (sm) or the second-to-last 4096-D fully connected layer $( f c )$ . + +Agent Players Both sender and receiver are simple feed-forward networks. For the sender, we experiment with the two architectures depicted in Figure 1. Both sender architectures take as input the target (marked with a green square in Figure 1) and distractor representations, always in this order, so that they are implicitly informed of which image is the target (the receiver, instead, sees the two images in random order). + +The agnostic sender is a generic neural network that maps the original image vectors onto a “gamespecific” embedding space (in the sense that the embedding is learned while playing the game) followed by a sigmoid nonlinearity. Fully-connected weights are applied to the embedding concatenation to produce scores over vocabulary symbols. + +The informed sender also first embeds the images into a “game-specific” space. It then applies 1-D convolutions (“filters”) on the image embeddings by treating them as different channels. The informed sender uses convolutions with kernel size 2x1 applied dimension-by-dimension to the two image embeddings (in Figure 1, there are 4 such filters). This is followed by the sigmoid nonlinearity. The resulting feature maps are combined through another filter (kernel size $f \mathrm { x } 1$ , where $f$ is the number of filters on the image embeddings), to produce scores for the vocabulary symbols. Intuitively, the informed sender has an inductive bias towards combining the two images dimensionby-dimension whereas the agnostic sender does not (though we note the agnostic architecture nests the informed one). + +![](images/922b96f905d5c5ad3d20244a196d7b3b633b7d9cf1391770bbbb062b580fc805.jpg) +Figure 1: Architectures of agent players. + +For both senders, motivated by the discrete nature of language, we enforce a strong communication bottleneck that discretizes the communication protocol. Activations on the top (vocabulary) layer are converted to a Gibbs distribution (with temperature parameter $\tau$ ), and then a single symbol $s$ is sampled from the resulting probability distribution. + +The receiver takes as input the target and distractor image vectors in random order, as well as the symbol produced by the sender (as a one-hot vector over the vocabulary). It embeds the images and the symbol into its own “game-specific” space. It then computes dot products between the symbol and image embeddings. Ideally, dot similarity should be higher for the image that is better denoted by the symbol. The two dot products are converted to a Gibbs distribution (with temperature $\tau$ ) and the receiver “points” to an image by sampling from the resulting distribution. + +General Training Details We set the following hyperparameters without tuning: embedding dimensionality: 50, number of filters applied to embeddings by informed sender: 20, temperature of Gibbs distributions: 10. We explore two vocabulary sizes: 10 and 100 symbols. + +The sender and receiver parameters $\theta = \langle \theta _ { R } , \theta _ { S } \rangle$ are learned while playing the game. No weights are shared and the only supervision used is communication success, i.e., whether the receiver pointed at the right referent. + +This setup is naturally modeled with Reinforcement Learning (Sutton & Barto, 1998). As outlined in Section 2, the sender follows policy $s ( \theta _ { S } ( i _ { L } , i _ { R } , t ) ) \ \in \ V$ and the receiver policy $r ( i _ { L } , i _ { R } , s ( \theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \ \in \ \{ \{ L , { R } \}$ . The loss function that the two agents must minimize is $- { \bf E } _ { \widetilde { r } } [ R ( \widetilde { r } ) ]$ where $R$ is the reward function returning 1 iff $r ( i _ { L } , i _ { R } , s ( \theta _ { S } ( \bar { i } _ { L } , i _ { R } , t ) ) = t$ . Parameters are updated through the Reinforce rule (Williams, 1992). We apply mini-batch updates, with a batch size of 32 and for a total of $5 0 \mathrm { k }$ iterations (games). At test time, we compile a set of $1 0 \mathrm { k }$ games using the same method as for the training games. + +We now turn to our main questions. The first is whether the agents can learn to successfully coordinate in a reasonable amount of time. The second is whether the agents’ language can be thought of as “natural language”, i.e., symbols are assigned to meanings that make intuitive sense in terms of our conceptualization of the world. + +# 4 LEARNING TO COMMUNICATE + +Our first question is whether agents converge to successful communication at all. We see that they do: agents almost perfectly coordinate in the 1k rounds following the 10k training games for every architecture and parameter choice (Table 1). + +We see, though, some differences between different sender architectures. Figure 2 (left) shows performance on a sample of the test set as a function of the first 5,000 rounds of training. The agents + +![](images/8b7ccb74f6ae2d5d2910b3273bff3233f9d817f0ba835a8d414dbe490337ebfa.jpg) +Figure 2: Left: Communication success as a function of training iterations, we see that informed senders converge faster than agnostic ones. Right: Spectrum of an example symbol usage matrix: the first few dimensions do capture only partial variance, suggesting that the usage of more symbols by the informed sender is not just due to synonymy. + +
idsendervisrepvocsizeusedsymbolscommsuccess(%)purity (%)obs-chancepurity (%)
1informedsm10058100462723
2informedfc1003810041
34567informedinformedagnosticagnosticinformedsm101010035
fc101010032
sm100299211515
fc1029921
agnosticsm102992015
8agnosticfc1002991915
+ +Table 1: Playing the referential game: test results after 50K training games. Used symbols column reports number of distinct vocabulary symbols that were produced at least once in the test phase. See text for explanation of comm success and purity. All purity values are highly significant $( p < 0 . 0 0 1 )$ compared to simulated chance symbol assignment when matching observed symbol usage. The obschance purity column reports the difference between observed and expected purity under chance. + +converge to coordination quite fast, but the informed sender reaches higher levels more quickly than the agnostic one. + +The informed sender makes use of more symbols from the available vocabulary, while the agnostic sender constantly uses a compact 2-symbol vocabulary. This suggests that the informed sender is using more varied and word-like symbols (recall that the images depict 463 distinct objects, so we would expect a natural-language-endowed sender to use a wider array of symbols to discriminate among them). However, it could also be the case that the informed sender vocabulary simply contains higher redundancy/synonymy. To check this, we construct a (sampled) matrix where rows are game image pairs, columns are symbols, and entries represent how often that symbol is used for that pair. We then decompose the matrix through SVD. If the sender is indeed just using a strategy with few effective symbols but high synonymy, then we should expect a 1- or 2-dimensional decomposition. Figure 2 (right) plots the normalized spectrum of this matrix. While there is some redundancy in the matrix (thus potentially implying there is synonymy in the usage), the language still requires multiple dimensions to summarize (cross-validated SVD suggests 50 dimensions). + +We now turn to investigating the semantic properties of the emergent communication protocol. Recall that the vocabulary that agents use is arbitrary and has no initial meaning. One way to understand its emerging semantics is by looking at the relationship between symbols and the sets of images they refer to. + +![](images/2ca860e20014c9fd162e1ab3ea2256686254b0b07c3b8026c618d83be37358a3.jpg) +Figure 3: t-SNE plots of object fc vectors color-coded by majority symbols assigned to them by informed sender. Object class names shown for a random subset. Left: configuration of 4th row of Table 1. Right: 2nd row of Table 2. + +The objects in our images were categorized into 20 broader categories (such as weapon and mammal) by McRae et al. (2005). If the agents converged to higher level semantic meanings for the symbols, we would expect that objects belonging to the same category would activate the same symbols, e.g., that, say, when the target images depict bayonets and guns, the sender would use the same symbol to refer to them, whereas cows and guns should not share a symbol. + +To quantify this, we form clusters by grouping objects by the symbols that are most often activated when target images contain them. We then assess the quality of the resulting clusters by measuring their purity with respect to the McRae categories. Purity (Zhao & Karypis, 2003) is a standard measure of cluster “quality”. The purity of a clustering solution is the proportion of category labels in the clusters that agree with the respective cluster majority category. This number reaches $100 \%$ for perfect clustering and we always compare the observed purity to the score that would be obtained from a random permutation of symbol assignments to objects. Table 1 shows that purity, while far from perfect, is significantly above chance in all cases. We confirm moreover that the informed sender is producing symbols that are more semantically natural than those of the agnostic one. + +Still, surprisingly, purity is significantly above chance even when the latter is only using two symbols. From our qualitative evaluations, in this case the agents converge to a (noisy) characterization of objects as “living-vs-non-living” which, intriguingly, has been recognized as the most basic one in the human semantic system (Caramazza & Shelton, 1998). + +Rather than using hard clusters, we can also ask whether symbol usage reflects the semantics of the visual space. To do so we construct vector representations for each object (defined by its ImageNet label) by averaging the CNN fc representations of all category images in our data-set (see Section 3 above). Note that the fc layer, being near the top of a deep CNN, is expected to capture highlevel visual properties of objects (Zeiler & Fergus, 2014). Moreover, since we average across many specific images, our vectors should capture rather general, high-level properties of objects. + +We map these average object vectors to 2 dimensions via t-SNE mapping (Van der Maaten & Hinton, 2008) and we color-code them by the majority symbol the sender used for images containing the corresponding object. Figure 3 (left) shows the results for the current experiment. We see that objects that are close in CNN space (thus, presumably, visually similar) are associated to the same symbol (same color). However, there still appears to be quite a bit of variation. + +# 4.1 OBJECT-LEVEL REFERENCE + +We established that our agents can solve the coordination problem, and we have at least tentative evidence that they do so by developing symbol meanings that align with our semantic intuition. We + +
idsendervis repvoc sizeused symbolscomm success(%)purity (%)obs-chance purity (%)
1informedfc100431004521
2informedfc10101003719
3agnosticfc100292237
4agnosticfc103982812
+ +Table 2: Playing the referential game with image-level targets: test results after 50K training plays. +Columns as in Table 1. All purity values significant at $p < 0 . 0 0 1$ . + +turn now to a simple way to tweak the game setup in order to encourage the agents to further pursue high-level semantics. + +The strategy is to remove some aspects of “common knowledge” from the game. Common knowledge, in game-theoretic parlance, are facts that everyone knows, everyone knows that everyone knows, and so on (Brandenburger et al., 2014). Coordination can only occur if the basis of the coordination is common knowledge (Rubinstein, 1989), therefore if we remove some facts from common knowledge, we will preclude our agents from coordinating on them. In our case, we want to remove facts pertaining to the details of the input images, thus forcing the agents to coordinate on more abstract properties. We can remove all low-level common knowledge by letting the agents play only using class-level properties of the objects. We achieve this by modifying the game to show the agents different pairs of images but maintaining the ImageNet class of both the target and distractor (e.g., if the target is dog, the sender is shown a picture of a Chihuahua and the receiver that of a Boston Terrier). + +Table 2 reports results for various configurations. We see that the agents are still able to coordinate. Moreover, we observe a small increase in symbol usage purity, as expected since agents can now only coordinate on general properties of object classes, rather than on the specific properties of each image. This effect is clearer in Figure 3 (right), when we repeat t-SNE based visualization of the relationship that emerges between visual embeddings and the words used to refer to them in this new experiment. + +# 5 GROUNDING AGENTS’ COMMUNICATION IN HUMAN LANGUAGE + +The results in Section 4 show communication robustly arising in our game, and that we can change the environment to nudge agents to develop symbol meanings which are more closely related to the visual or class-based semantics of the images. Still, we would like agents to converge on a language fully understandable by humans, as our ultimate goal is to develop conversational machines. To do this, we will need to ground the communication. + +Taking inspiration from AlphaGo (Silver et al., 2016), an AI that reached the Go master level by combining interactive learning in games of self-play with passive supervised learning from a large set of human games, we combine the usual referential game, in which agents interactively develop their communication protocol, with a supervised image labeling task, where the sender must learn to assign objects their conventional names. This way, the sender will naturally be encouraged to use such names with their conventional meaning to discriminate target images when playing the game, making communication more transparent to humans. + +In this experiment, the sender switches, equiprobably, between game playing and a supervised image classification task using ImageNet classes. Note that the supervised objective does not aim at improving agents’ coordination performance. Instead, supervision provides them with basic grounding in natural language (in the form of image-label associations), while concurrent interactive game playing should teach them how to effectively use this grounding to communicate. + +We use the informed sender, fc image representations and a vocabulary size of 100. Supervised training is based on 100 labels that are a subset of the object names in our data-set (see Section 3 above). When predicting object names, the sender uses the usual game-embedding layer coupled with a softmax layer of dimensionality 100 corresponding to the object names. Importantly, the game-embedding layers used in object classification and the reference game are shared. Consequently, we hope that, when playing, the sender will produce symbols aligned with object names acquired in the supervised phase. + +![](images/9dc46da9c68bda1e70a2c5179f3650cd669ccc0cfa553e9eb6447eb64e195bad.jpg) +Figure 4: Example pairs from the ReferItGame set, with word produced by sender. Target images framed in green. + +The supervised objective has no negative effect on communication success: the agents are still able to reach full coordination after 10k training trials (corresponding to $5 \mathrm { k }$ trials of reference game playing). The sender uses many more symbols after training than in any previous experiment (88) and symbol purity dramatically increases to $70 \%$ (the obs-chance purity difference also increases to $3 7 \%$ ). + +Even more importantly, many symbols have now become directly interpretable, thanks to their direct correspondence to labels. Considering the 632 image pairs where the target gold standard label corresponds to one of the labels that were used in the supervised phase, in $47 \%$ of these cases the sender produced exactly the symbol corresponding to the correct supervised label for the target image (chance: $1 \%$ ). + +For image pairs where the target image belongs to one of the directly supervised categories, it is not surprising that the sender adopted the “conventional” supervised label to signal the target . However, a very interesting effect of supervision is that it improves the interpretability of the code even when agents must communicate about images that do not contain objects in the supervised category set. This emerged in a follow-up experiment in which, during training, the sender was again exposed (with equal probability) to the same supervised classification task as above, but now the agents played the referential game on a different dataset of images derived from ReferItGame (Kazemzadeh et al., 2014). In its general format, the ReferItGame contains annotations of bounding boxes in real images with referring expressions produced by humans when playing the game. For our purposes, we constructed $1 0 \mathrm { k }$ pairs by randomly sampling two bounding boxes, to act as target and distractor. Again, the agents converged to perfect communication after 15k trials, and this time used all 100 available symbols in some trial. + +We then asked whether this language was human-interpretable. For each symbol used by the trained sender, we randomly extracted 3 image pairs in which the sender picked that symbol and the receiver pointed at the right target (for two symbols, only 2 pairs matched these criteria, leading to a set of 298 image pairs). We annotated each pair with the word corresponding to the symbol in the supervised set. Out of the 298 pairs, only 25 $( 8 \% )$ included one of the 100 words among the corresponding referring expressions in ReferItGame. So, in the large majority of cases, the sender had been faced with a pair not (saliently) containing the categories used in the supervised phase of its training, and it had to produce a word that could, at best, only indirectly refer to what is depicted in the target image. We then tested whether this code would be understandable by humans. In essence, it is as if we replaced the trained agent receiver with a human. + +We prepared a crowdsourced survey using the CrowdFlower platform. For each pair, human participants were shown the two images and the sender-emitted word (that is, the ImageNet label associated to the symbol produced by the sender; see examples in Figure 4). The participants were asked to pick the picture that they thought was most related to the word. We collected 10 ratings for each pair. + +We found that in $68 \%$ of the cases the subjects were able to guess the right image. A logistic regression predicting subject image choice from ground-truth target images, with subjects and words as random effects, confirmed the highly significant correlation between the true and guessed images $( z ~ = ~ 1 6 . 7 5$ , $p \ < \ 0 . 0 0 0 1 $ ). Thus, while far from perfect, we find that supervised learning on a separate data set does provide some grounding for communication with humans, that generalizes beyond the conventional word denotations learned in the supervised phase. + +Looking at the results qualitatively, we found that very often sender-subject communication succeeded when the sender established a sort of “metonymic” link between the words in its possession and the contents of an image. Figure 4 shows an example where the sender produced dolphin to refer to a picture showing a stretch of sea, and fence for a patch of land. Similar semantic shifts are a core characteristic of natural language (e.g., Pustejovsky, 1995), and thus subjects were, in many cases, able to successfully play the referential game with our sender (10/10 subjects guessed the dolphin target, and 8/10 the fence). This is very encouraging. Although the language developed in referential games will be initially very limited, if both agents and humans possess the sort of flexibility displayed in this last experiment, the noisy but shared common ground might suffice to establish basic communication. + +# 6 DISCUSSION + +Our results confirmed that fairly simple neural-network agents can learn to coordinate in a referential game in which they need to communicate about a large number of real pictures. They also suggest that the meanings agents come to assign to symbols in this setup capture general conceptual properties of the objects depicted in the image, rather than low-level visual properties. We also showed a path to grounding the communication in natural language by mixing the game with a supervised task. + +In future work, encouraged by our preliminary experiments with object naming, we want to study how to ensure that the emergent communication stays close to human natural language. Predictive learning should be retained as an important building block of intelligent agents, focusing on teaching them structural properties of language (e.g., lexical choice, syntax or style). However, it is also important to learn the function-driven facets of language, such as how to hold a conversation, and interactive games are a potentially fruitful method to achieve this goal. + +# REFERENCES + +John Langshaw Austin. How to do things with words. Harvard University Press, Cambridge, MA, 1962. + +Andreas Blume, Douglas V DeJong, Yong-Gwan Kim, and Geoffrey B Sprinkle. Experimental evidence on the evolution of meaning of messages in sender-receiver games. The American Economic Review, 88(5):1323–1340, 1998. + +Adam Brandenburger, Eddie Dekel, et al. Hierarchies of beliefs and common knowledge. The Language of Game Theory: Putting Epistemics into the Mathematics of Games, 5:31, 2014. + +Ted Briscoe (ed.). Linguistic evolution through language acquisition. Cambridge University Press, Cambridge, UK, 2002. + +Angelo Cangelosi and Domenico Parisi (eds.). Simulating the evolution of language. Springer, New York, 2002. + +Alfonso Caramazza and Jennifer Shelton. Domain-specific knowledge systems in the brain the animate-inanimate distinction. Journal of Cognitive Neuroscience, 10(1):1–34, 1998. + +Herbert H Clark. Using language. 1996. Cambridge University Press: Cambridge), 952:274–296, 1996. + +Vincent Crawford. A survey of experiments on communication via cheap talk. Journal of Economic theory, 78(2):286–298, 1998. + +Vincent P Crawford and Joel Sobel. Strategic information transmission. Econometrica: Journal of the Econometric Society, pp. 1431–1451, 1982. + +Jia Deng, Wei Dong, Richard Socher, Lia-Ji Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In Proceedings of CVPR, pp. 248–255, Miami Beach, FL, 2009. + +Jakob N. Foerster, Yannis M. Assael, Nando de Freitas, and Shimon Whiteson. 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In EMNLP, pp. 787–798, 2014. + +David Lewis. Convention. Harvard University Press, Cambridge, MA, 1969. + +Ken McRae, George Cree, Mark Seidenberg, and Chris McNorgan. Semantic feature production norms for a large set of living and nonliving things. Behavior Research Methods, 37(4):547–559, 2005. + +Tomas Mikolov, Armand Joulin, and Marco Baroni. A roadmap towards machine intelligence. arXiv preprint arXiv:1511.08130, 2015. + +James Pustejovsky. The Generative Lexicon. MIT Press, Cambridge, MA, 1995. + +Alvin E Roth and Ido Erev. Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term. Games and economic behavior, 8(1):164–212, 1995. + +Ariel Rubinstein. The electronic mail game: Strategic behavior under ‘almost common knowledge’. The American Economic Review, pp. 385–391, 1989. + +David Silver, Aja Huang, Christopher Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the game of Go with deep neural networks and tree search. Nature, 529:484–503, 2016. + +Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556, 2014. + +Brian Skyrms. Signals: Evolution, learning, and information. Oxford University Press, 2010. + +Matthew Spike, Kevin Stadler, Simon Kirby, and Kenny Smith. Minimal requirements for the emergence of learned signaling. Cognitive Science, 2016. In press. + +Luc Steels and Martin Loetzsch. The grounded naming game. In Luc Steels (ed.), Experiments in Cultural Language Evolution, pp. 41–59. John Benjamins, Amsterdam, 2012. + +Peter Stone and Manuela Veloso. Towards collaborative and adversarial learning: A case study in robotic soccer. International Journal of Human-Computer Studies, 48(1):83–104, 1998. + +Sainbayar Sukhbaatar, Arthur Szlam, and Rob Fergus. Learning multiagent communication with backpropagation. arXiv preprint arXiv:1605.07736, 2016. + +Ilya Sutskever, Oriol Vinyals, and Quoc Le. Sequence to sequence learning with neural networks. In Proceedings of NIPS, pp. 3104–3112, Montreal, Canada, 2014. + +Richard Sutton and Andrew Barto. Reinforcement Learning: An Introduction. MIT Press, Cambridge, MA, 1998. + +Laurens Van der Maaten and Geoffrey Hinton. Visualizing data using t-SNE. Journal of Machine Learning Research, 9(2579-2605), 2008. + +Oriol Vinyals and Quoc Le. A neural conversational model. In Proceedings of the ICML Deep Learning Workshop, Lille, France, 2015. Published online: https://sites.google.com/ site/deeplearning2015/accepted-papers. + +Kyle Wagner, James A Reggia, Juan Uriagereka, and Gerald S Wilkinson. Progress in the simulation of emergent communication and language. Adaptive Behavior, 11(1):37–69, 2003. + +S. I. Wang, P. Liang, and C. Manning. Learning language games through interaction. In Association for Computational Linguistics (ACL), 2016. + +Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning, 8(3-4):229–256, 1992. + +Terry Winograd. Procedures as a representation for data in a computer program for understanding natural language. Technical Report AI 235, Massachusetts Institute of Technology, 1971. + +Ludwig Wittgenstein. Philosophical Investigations. Blackwell, Oxford, UK, 1953. Translated by G.E.M. Anscombe. + +Michael Wooldridge. An introduction to multiagent systems. John Wiley & Sons, 2009. + +Kelvin Xu, Jimmy Ba, Ryan Kiros, Kyunghyun Cho, Aaron Courville, Ruslan Salakhudinov, Rich Zemel, and Yoshua Bengio. Show, attend and tell: Neural image caption generation with visual attention. In Proceedings of ICML, pp. 2048–2057, Lille, France, 2015. + +Matthew Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In Proceedings of ECCV (Part 1), pp. 818–833, Zurich, Switzerland, 2014. + +Ying Zhao and George Karypis. Criterion functions for document clustering: Experiments and analysis. Technical Report 01-40, University of Minnesota Department of Computer Science, 2003. \ No newline at end of file diff --git a/parse/train/Hk8N3Sclg/Hk8N3Sclg_content_list.json b/parse/train/Hk8N3Sclg/Hk8N3Sclg_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2bea879e57bc6632c5acb96ba3cdd2acbf8b1523 --- /dev/null +++ b/parse/train/Hk8N3Sclg/Hk8N3Sclg_content_list.json @@ -0,0 +1,1321 @@ +[ + { + "type": "text", + "text": "MULTI-AGENT COOPERATIONAND THE EMERGENCE OF (NATURAL) LANGUAGE", + "text_level": 1, + "bbox": [ + 176, + 99, + 774, + 147 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Angeliki Lazaridou1∗, Alexander Peysakhovich2, Marco Baroni2,3 1Google DeepMind, 2Facebook AI Research, 3University of Trento angeliki@google.com, {alexpeys,mbaroni}@fb.com ", + "bbox": [ + 184, + 172, + 642, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 252, + 544, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The current mainstream approach to train natural language systems is to expose them to large amounts of text. This passive learning is problematic if we are interested in developing interactive machines, such as conversational agents. We propose a framework for language learning that relies on multi-agent communication. We study this learning in the context of referential games. In these games, a sender and a receiver see a pair of images. The sender is told one of them is the target and is allowed to send a message from a fixed, arbitary vocabulary to the receiver. The receiver must rely on this message to identify the target. Thus, the agents develop their own language interactively out of the need to communicate. We show that two networks with simple configurations are able to learn to coordinate in the referential game. We further explore how to make changes to the game environment to cause the “word meanings” induced in the game to better reflect intuitive semantic properties of the images. In addition, we present a simple strategy for grounding the agents’ code into natural language. Both of these are necessary steps towards developing machines that are able to communicate with humans productively. ", + "bbox": [ + 233, + 284, + 764, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 529, + 336, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "I tried to break it to him gently [...] the only way to learn an unknown language is to interact with a native speaker [...] asking questions, holding a conversation, that sort of thing [...] If you want to learn the aliens’ language, someone [...] will have to talk with an alien. Recordings alone aren’t sufficient. ", + "bbox": [ + 232, + 554, + 764, + 609 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ted Chiang, Story of Your Life ", + "bbox": [ + 235, + 612, + 433, + 626 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "One of the main aims of AI is to develop agents that can cooperate with others to achieve goals (Wooldridge, 2009). Such coordination requires communication. If the coordination partners are to include humans, the most obvious channel of communication is natural language. Thus, handling natural-language-based communication is a key step toward the development of AI that can thrive in a world populated by other agents. ", + "bbox": [ + 174, + 638, + 823, + 707 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given the success of deep learning models in related domains such as image captioning or machine translation (e.g., Sutskever et al., 2014; Xu et al., 2015), it would seem reasonable to cast the problem of training conversational agents as an instance of supervised learning (Vinyals & Le, 2015). However, training on “canned” conversations does not allow learners to experience the interactive aspects of communication. Supervised approaches, which focus on the structure of language, are an excellent way to learn general statistical associations between sequences of symbols. However, they do not capture the functional aspects of communication, i.e., that humans use words to coordinate with others and make things happen (Austin, 1962; Clark, 1996; Wittgenstein, 1953). ", + "bbox": [ + 174, + 714, + 825, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper introduces the first steps of a research program based on multi-agent coordination communication games. These games place agents in simple environments where they need to develop a language to coordinate and earn payoffs. Importantly, the agents start as blank slates, but, by playing a game together, they can develop and bootstrap knowledge on top of each others, leading to the emergence of a language. ", + "bbox": [ + 176, + 833, + 823, + 904 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The central problem of our program, then, is the following: How do we design environments that foster the development of a language that is portable to new situations and to new communication partners (in particular humans)? ", + "bbox": [ + 176, + 103, + 823, + 146 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We start from the most basic challenge of using a language in order to refer to things in the context of a two-agent game. We focus on two questions. First, whether tabula rasa agents succeed in communication. Second, what features of the environment lead to the development of codes resembling human language. ", + "bbox": [ + 174, + 152, + 823, + 208 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We assess this latter question in two ways. First, we consider whether the agents associate general conceptual properties, such as broad object categories (as opposed to low-level visual properties), to the symbols they learn to use. Second, we examine whether the agents’ “word usage” is partially interpretable by humans in an online experiment. ", + "bbox": [ + 174, + 215, + 825, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Other researchers have proposed communication-based environments for the development of coordination-capable AI. Work in multi-agent systems has focused on the design of pre-programmed communication systems to solve specific tasks (e.g., robot soccer, Stone & Veloso 1998). Most related to our work, Sukhbaatar et al. (2016) and Foerster et al. (2016) show that neural networks can evolve communication in the context of games without a pre-coded protocol. We pursue the same question, but further ask how we can change our environment to make the emergent language more interpretable. ", + "bbox": [ + 174, + 279, + 825, + 376 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Others (e.g., the SHRLDU program of Winograd 1971 or the game in Wang et al. 2016) propose building a communicating AI by putting humans in the loop from the very beginning. This approach has benefits but faces serious scalability issues, as active human intervention is required at each step. An attractive component of our game-based paradigm is that humans may be added as players, but do not need to be there all the time. ", + "bbox": [ + 174, + 382, + 825, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A third branch of research focuses on “Wizard-of-Oz” environments, where agents learn to play games by interacting with a complex scripted environment (Mikolov et al., 2015). This approach gives the designer tight control over the learning curriculum, but imposes a heavy engineering burden on developers. We also stress the importance of the environment (game setup), but we focus on simpler environments with multiple agents that force them to get smarter by bootstrapping on top of each other. ", + "bbox": [ + 174, + 459, + 825, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We leverage ideas from work in linguistics, cognitive science and game theory on the emergence of language (Wagner et al., 2003; Skyrms, 2010; Crawford & Sobel, 1982; Crawford, 1998). Our game is a variation of Lewis’ signaling game (Lewis, 1969). There is a rich tradition of linguistic and cognitive studies using similar setups (e.g., Briscoe, 2002; Cangelosi & Parisi, 2002; Spike et al., 2016; Steels & Loetzsch, 2012). What distinguishes us from this literature is our aim to, eventually, develop practical AI. This motivates our focus on more realistic input data (a large collection of noisy natural images) and on trying to align the agents’ language with human intuitions. ", + "bbox": [ + 173, + 549, + 825, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Lewis’ classic games have been studied extensively in game theory under the name of “cheap talk”. These games have been used as models to study the evolution of language both theoretically and experimentally (Crawford, 1998; Blume et al., 1998; Crawford & Sobel, 1982). A major question in game theory is whether equilibrium actually occurs in a game as convergence in learning is not guaranteed (Fudenberg & Peysakhovich, 2014; Roth & Erev, 1995). And, if an equilibrium is reached, which one it will be (since they are typically not unique). This is particularly true for cheap talk games, which exhibit Nash equilibria in which precise language emerges, others where vague language emerges and others where no language emerges at all (Crawford & Sobel, 1982). In addition, because in these games language has no ex-ante meaning and only emerges in the context of the equilibrium, some of the emergent languages may not be very natural. Our results speak to both the convergence question and the question of what features of the game cause the appearance of different types of languages. Thus, our results are also of interest to game theorists. ", + "bbox": [ + 173, + 655, + 825, + 820 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An evolutionary perspective has recently been advocated as a way to mitigate the data hunger of traditional supervised approaches (Goodfellow et al., 2014; Silver et al., 2016). This research confirms that learning can be bootstrapped from competition between agents. We focus, however, on cooperation between agents as a way to foster learning while reducing the need for annotated data. ", + "bbox": [ + 176, + 829, + 823, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 GENERAL FRAMEWORK ", + "text_level": 1, + "bbox": [ + 176, + 102, + 405, + 118 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our general framework includes K players, each parametrized by $\\theta _ { k }$ , a collection of tasks/games that the players have to perform, a communication protocol $V$ that enables the players to communicate with each other, and payoffs assigned to the players as a deterministic function of a well-defined goal. In this paper we focus on a particular version of this: referential games. These games are structured as follows. ", + "bbox": [ + 174, + 133, + 825, + 204 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "1. There is a set of images represented by vectors $\\{ i _ { 1 } , \\dotsc , i _ { N } \\}$ , two images are drawn at random from this set, call them $( i _ { L } , i _ { R } )$ , one of them is chosen to be the “target” $t \\in \\{ L , R \\}$ \n2. There are two players, a sender and a receiver, each seeing the images - the sender receives input $\\theta _ { S } ( i _ { L } , i _ { R } , t )$ \n3. There is a vocabulary $V$ of size $K$ and the sender chooses one symbol to send to the receiver, we call this the sender’s policy $s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) \\in V$ \n4. The receiver does not know the target, but sees the sender’s symbol and tries to guess the target image. We call this the receiver’s policy $r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \\in \\{ L , \\bar { R } \\}$ \n5. If $r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) = t$ , that is, if the receiver guesses the target, both players receive a payoff of 1 (win), otherwise they receive a payoff of 0 (lose). ", + "bbox": [ + 210, + 218, + 825, + 382 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Many extensions to the basic referential game explored here are possible. There can be more images, or a more sophisticated communication protocol (e.g., communication of a sequence of symbols or multi-step communication requiring back-and-forth interaction1), rotation of the sender and receiver roles, having a human occasionally playing one of the roles, etc. ", + "bbox": [ + 174, + 396, + 825, + 453 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 EXPERIMENTAL SETUP ", + "text_level": 1, + "bbox": [ + 176, + 473, + 398, + 489 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Images We use the McRae et al.’s (2005) set of 463 base-level concrete concepts (e.g., cat, apple, car. . . ) spanning across 20 general categories (e.g., animal, fruit/vegetable, vehicle. . . ). We randomly sample 100 images of each concept from ImageNet (Deng et al., 2009). To create target/distractor pairs, we randomly sample two concepts, one image for each concept and whether the first or second image will serve as target. We apply to each image a forward-pass through the pretrained VGG ConvNet (Simonyan & Zisserman, 2014), and represent it with the activations from either the top 1000-D softmax layer (sm) or the second-to-last 4096-D fully connected layer $( f c )$ . ", + "bbox": [ + 173, + 506, + 825, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Agent Players Both sender and receiver are simple feed-forward networks. For the sender, we experiment with the two architectures depicted in Figure 1. Both sender architectures take as input the target (marked with a green square in Figure 1) and distractor representations, always in this order, so that they are implicitly informed of which image is the target (the receiver, instead, sees the two images in random order). ", + "bbox": [ + 174, + 621, + 825, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The agnostic sender is a generic neural network that maps the original image vectors onto a “gamespecific” embedding space (in the sense that the embedding is learned while playing the game) followed by a sigmoid nonlinearity. Fully-connected weights are applied to the embedding concatenation to produce scores over vocabulary symbols. ", + "bbox": [ + 174, + 696, + 825, + 753 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The informed sender also first embeds the images into a “game-specific” space. It then applies 1-D convolutions (“filters”) on the image embeddings by treating them as different channels. The informed sender uses convolutions with kernel size 2x1 applied dimension-by-dimension to the two image embeddings (in Figure 1, there are 4 such filters). This is followed by the sigmoid nonlinearity. The resulting feature maps are combined through another filter (kernel size $f \\mathrm { x } 1$ , where $f$ is the number of filters on the image embeddings), to produce scores for the vocabulary symbols. Intuitively, the informed sender has an inductive bias towards combining the two images dimensionby-dimension whereas the agnostic sender does not (though we note the agnostic architecture nests the informed one). ", + "bbox": [ + 174, + 760, + 825, + 885 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/922b96f905d5c5ad3d20244a196d7b3b633b7d9cf1391770bbbb062b580fc805.jpg", + "image_caption": [ + "Figure 1: Architectures of agent players. " + ], + "image_footnote": [], + "bbox": [ + 171, + 108, + 818, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For both senders, motivated by the discrete nature of language, we enforce a strong communication bottleneck that discretizes the communication protocol. Activations on the top (vocabulary) layer are converted to a Gibbs distribution (with temperature parameter $\\tau$ ), and then a single symbol $s$ is sampled from the resulting probability distribution. ", + "bbox": [ + 174, + 368, + 825, + 424 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The receiver takes as input the target and distractor image vectors in random order, as well as the symbol produced by the sender (as a one-hot vector over the vocabulary). It embeds the images and the symbol into its own “game-specific” space. It then computes dot products between the symbol and image embeddings. Ideally, dot similarity should be higher for the image that is better denoted by the symbol. The two dot products are converted to a Gibbs distribution (with temperature $\\tau$ ) and the receiver “points” to an image by sampling from the resulting distribution. ", + "bbox": [ + 174, + 431, + 825, + 515 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "General Training Details We set the following hyperparameters without tuning: embedding dimensionality: 50, number of filters applied to embeddings by informed sender: 20, temperature of Gibbs distributions: 10. We explore two vocabulary sizes: 10 and 100 symbols. ", + "bbox": [ + 176, + 532, + 825, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The sender and receiver parameters $\\theta = \\langle \\theta _ { R } , \\theta _ { S } \\rangle$ are learned while playing the game. No weights are shared and the only supervision used is communication success, i.e., whether the receiver pointed at the right referent. ", + "bbox": [ + 174, + 580, + 825, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This setup is naturally modeled with Reinforcement Learning (Sutton & Barto, 1998). As outlined in Section 2, the sender follows policy $s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) \\ \\in \\ V$ and the receiver policy $r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \\ \\in \\ \\{ \\{ L , { R } \\}$ . The loss function that the two agents must minimize is $- { \\bf E } _ { \\widetilde { r } } [ R ( \\widetilde { r } ) ]$ where $R$ is the reward function returning 1 iff $r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( \\bar { i } _ { L } , i _ { R } , t ) ) = t$ . Parameters are updated through the Reinforce rule (Williams, 1992). We apply mini-batch updates, with a batch size of 32 and for a total of $5 0 \\mathrm { k }$ iterations (games). At test time, we compile a set of $1 0 \\mathrm { k }$ games using the same method as for the training games. ", + "bbox": [ + 173, + 630, + 825, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now turn to our main questions. The first is whether the agents can learn to successfully coordinate in a reasonable amount of time. The second is whether the agents’ language can be thought of as “natural language”, i.e., symbols are assigned to meanings that make intuitive sense in terms of our conceptualization of the world. ", + "bbox": [ + 176, + 734, + 825, + 791 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 LEARNING TO COMMUNICATE ", + "text_level": 1, + "bbox": [ + 176, + 813, + 457, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our first question is whether agents converge to successful communication at all. We see that they do: agents almost perfectly coordinate in the 1k rounds following the 10k training games for every architecture and parameter choice (Table 1). ", + "bbox": [ + 174, + 847, + 823, + 888 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We see, though, some differences between different sender architectures. Figure 2 (left) shows performance on a sample of the test set as a function of the first 5,000 rounds of training. The agents ", + "bbox": [ + 174, + 895, + 821, + 924 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8b7ccb74f6ae2d5d2910b3273bff3233f9d817f0ba835a8d414dbe490337ebfa.jpg", + "image_caption": [ + "Figure 2: Left: Communication success as a function of training iterations, we see that informed senders converge faster than agnostic ones. Right: Spectrum of an example symbol usage matrix: the first few dimensions do capture only partial variance, suggesting that the usage of more symbols by the informed sender is not just due to synonymy. " + ], + "image_footnote": [], + "bbox": [ + 178, + 103, + 816, + 320 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/b2a75e6fff100b8d69afded2e6e53b9215d234e57ee9e150f93a0471610416bd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
idsendervisrepvocsizeusedsymbolscommsuccess(%)purity (%)obs-chancepurity (%)
1informedsm10058100462723
2informedfc1003810041
34567informedinformedagnosticagnosticinformedsm101010035
fc101010032
sm100299211515
fc1029921
agnosticsm102992015
8agnosticfc1002991915
", + "bbox": [ + 243, + 412, + 754, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1: Playing the referential game: test results after 50K training games. Used symbols column reports number of distinct vocabulary symbols that were produced at least once in the test phase. See text for explanation of comm success and purity. All purity values are highly significant $( p < 0 . 0 0 1 )$ compared to simulated chance symbol assignment when matching observed symbol usage. The obschance purity column reports the difference between observed and expected purity under chance. ", + "bbox": [ + 173, + 553, + 825, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "converge to coordination quite fast, but the informed sender reaches higher levels more quickly than the agnostic one. ", + "bbox": [ + 174, + 659, + 821, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The informed sender makes use of more symbols from the available vocabulary, while the agnostic sender constantly uses a compact 2-symbol vocabulary. This suggests that the informed sender is using more varied and word-like symbols (recall that the images depict 463 distinct objects, so we would expect a natural-language-endowed sender to use a wider array of symbols to discriminate among them). However, it could also be the case that the informed sender vocabulary simply contains higher redundancy/synonymy. To check this, we construct a (sampled) matrix where rows are game image pairs, columns are symbols, and entries represent how often that symbol is used for that pair. We then decompose the matrix through SVD. If the sender is indeed just using a strategy with few effective symbols but high synonymy, then we should expect a 1- or 2-dimensional decomposition. Figure 2 (right) plots the normalized spectrum of this matrix. While there is some redundancy in the matrix (thus potentially implying there is synonymy in the usage), the language still requires multiple dimensions to summarize (cross-validated SVD suggests 50 dimensions). ", + "bbox": [ + 173, + 694, + 825, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now turn to investigating the semantic properties of the emergent communication protocol. Recall that the vocabulary that agents use is arbitrary and has no initial meaning. One way to understand its emerging semantics is by looking at the relationship between symbols and the sets of images they refer to. ", + "bbox": [ + 174, + 867, + 823, + 922 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2ca860e20014c9fd162e1ab3ea2256686254b0b07c3b8026c618d83be37358a3.jpg", + "image_caption": [ + "Figure 3: t-SNE plots of object fc vectors color-coded by majority symbols assigned to them by informed sender. Object class names shown for a random subset. Left: configuration of 4th row of Table 1. Right: 2nd row of Table 2. " + ], + "image_footnote": [], + "bbox": [ + 200, + 108, + 799, + 327 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The objects in our images were categorized into 20 broader categories (such as weapon and mammal) by McRae et al. (2005). If the agents converged to higher level semantic meanings for the symbols, we would expect that objects belonging to the same category would activate the same symbols, e.g., that, say, when the target images depict bayonets and guns, the sender would use the same symbol to refer to them, whereas cows and guns should not share a symbol. ", + "bbox": [ + 174, + 420, + 825, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To quantify this, we form clusters by grouping objects by the symbols that are most often activated when target images contain them. We then assess the quality of the resulting clusters by measuring their purity with respect to the McRae categories. Purity (Zhao & Karypis, 2003) is a standard measure of cluster “quality”. The purity of a clustering solution is the proportion of category labels in the clusters that agree with the respective cluster majority category. This number reaches $100 \\%$ for perfect clustering and we always compare the observed purity to the score that would be obtained from a random permutation of symbol assignments to objects. Table 1 shows that purity, while far from perfect, is significantly above chance in all cases. We confirm moreover that the informed sender is producing symbols that are more semantically natural than those of the agnostic one. ", + "bbox": [ + 174, + 497, + 825, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Still, surprisingly, purity is significantly above chance even when the latter is only using two symbols. From our qualitative evaluations, in this case the agents converge to a (noisy) characterization of objects as “living-vs-non-living” which, intriguingly, has been recognized as the most basic one in the human semantic system (Caramazza & Shelton, 1998). ", + "bbox": [ + 174, + 628, + 823, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Rather than using hard clusters, we can also ask whether symbol usage reflects the semantics of the visual space. To do so we construct vector representations for each object (defined by its ImageNet label) by averaging the CNN fc representations of all category images in our data-set (see Section 3 above). Note that the fc layer, being near the top of a deep CNN, is expected to capture highlevel visual properties of objects (Zeiler & Fergus, 2014). Moreover, since we average across many specific images, our vectors should capture rather general, high-level properties of objects. ", + "bbox": [ + 174, + 693, + 823, + 776 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We map these average object vectors to 2 dimensions via t-SNE mapping (Van der Maaten & Hinton, 2008) and we color-code them by the majority symbol the sender used for images containing the corresponding object. Figure 3 (left) shows the results for the current experiment. We see that objects that are close in CNN space (thus, presumably, visually similar) are associated to the same symbol (same color). However, there still appears to be quite a bit of variation. ", + "bbox": [ + 174, + 782, + 823, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1 OBJECT-LEVEL REFERENCE ", + "text_level": 1, + "bbox": [ + 176, + 871, + 405, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We established that our agents can solve the coordination problem, and we have at least tentative evidence that they do so by developing symbol meanings that align with our semantic intuition. We ", + "bbox": [ + 174, + 895, + 823, + 924 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/58fa7af64b181601b7e3223fb31404fb081b1e6bdef5c26d86c04fabeed1d690.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
idsendervis repvoc sizeused symbolscomm success(%)purity (%)obs-chance purity (%)
1informedfc100431004521
2informedfc10101003719
3agnosticfc100292237
4agnosticfc103982812
", + "bbox": [ + 245, + 99, + 753, + 180 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2: Playing the referential game with image-level targets: test results after 50K training plays. \nColumns as in Table 1. All purity values significant at $p < 0 . 0 0 1$ . ", + "bbox": [ + 173, + 189, + 823, + 218 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "turn now to a simple way to tweak the game setup in order to encourage the agents to further pursue high-level semantics. ", + "bbox": [ + 174, + 251, + 823, + 280 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The strategy is to remove some aspects of “common knowledge” from the game. Common knowledge, in game-theoretic parlance, are facts that everyone knows, everyone knows that everyone knows, and so on (Brandenburger et al., 2014). Coordination can only occur if the basis of the coordination is common knowledge (Rubinstein, 1989), therefore if we remove some facts from common knowledge, we will preclude our agents from coordinating on them. In our case, we want to remove facts pertaining to the details of the input images, thus forcing the agents to coordinate on more abstract properties. We can remove all low-level common knowledge by letting the agents play only using class-level properties of the objects. We achieve this by modifying the game to show the agents different pairs of images but maintaining the ImageNet class of both the target and distractor (e.g., if the target is dog, the sender is shown a picture of a Chihuahua and the receiver that of a Boston Terrier). ", + "bbox": [ + 174, + 286, + 825, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2 reports results for various configurations. We see that the agents are still able to coordinate. Moreover, we observe a small increase in symbol usage purity, as expected since agents can now only coordinate on general properties of object classes, rather than on the specific properties of each image. This effect is clearer in Figure 3 (right), when we repeat t-SNE based visualization of the relationship that emerges between visual embeddings and the words used to refer to them in this new experiment. ", + "bbox": [ + 174, + 446, + 825, + 530 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5 GROUNDING AGENTS’ COMMUNICATION IN HUMAN LANGUAGE ", + "text_level": 1, + "bbox": [ + 176, + 559, + 741, + 575 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results in Section 4 show communication robustly arising in our game, and that we can change the environment to nudge agents to develop symbol meanings which are more closely related to the visual or class-based semantics of the images. Still, we would like agents to converge on a language fully understandable by humans, as our ultimate goal is to develop conversational machines. To do this, we will need to ground the communication. ", + "bbox": [ + 174, + 595, + 825, + 665 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Taking inspiration from AlphaGo (Silver et al., 2016), an AI that reached the Go master level by combining interactive learning in games of self-play with passive supervised learning from a large set of human games, we combine the usual referential game, in which agents interactively develop their communication protocol, with a supervised image labeling task, where the sender must learn to assign objects their conventional names. This way, the sender will naturally be encouraged to use such names with their conventional meaning to discriminate target images when playing the game, making communication more transparent to humans. ", + "bbox": [ + 174, + 672, + 825, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this experiment, the sender switches, equiprobably, between game playing and a supervised image classification task using ImageNet classes. Note that the supervised objective does not aim at improving agents’ coordination performance. Instead, supervision provides them with basic grounding in natural language (in the form of image-label associations), while concurrent interactive game playing should teach them how to effectively use this grounding to communicate. ", + "bbox": [ + 174, + 777, + 823, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We use the informed sender, fc image representations and a vocabulary size of 100. Supervised training is based on 100 labels that are a subset of the object names in our data-set (see Section 3 above). When predicting object names, the sender uses the usual game-embedding layer coupled with a softmax layer of dimensionality 100 corresponding to the object names. Importantly, the game-embedding layers used in object classification and the reference game are shared. Consequently, we hope that, when playing, the sender will produce symbols aligned with object names acquired in the supervised phase. ", + "bbox": [ + 176, + 854, + 823, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9dc46da9c68bda1e70a2c5179f3650cd669ccc0cfa553e9eb6447eb64e195bad.jpg", + "image_caption": [ + "Figure 4: Example pairs from the ReferItGame set, with word produced by sender. Target images framed in green. " + ], + "image_footnote": [], + "bbox": [ + 241, + 102, + 756, + 212 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 296, + 823, + 324 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The supervised objective has no negative effect on communication success: the agents are still able to reach full coordination after 10k training trials (corresponding to $5 \\mathrm { k }$ trials of reference game playing). The sender uses many more symbols after training than in any previous experiment (88) and symbol purity dramatically increases to $70 \\%$ (the obs-chance purity difference also increases to $3 7 \\%$ ). ", + "bbox": [ + 174, + 332, + 825, + 401 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Even more importantly, many symbols have now become directly interpretable, thanks to their direct correspondence to labels. Considering the 632 image pairs where the target gold standard label corresponds to one of the labels that were used in the supervised phase, in $47 \\%$ of these cases the sender produced exactly the symbol corresponding to the correct supervised label for the target image (chance: $1 \\%$ ). ", + "bbox": [ + 174, + 409, + 825, + 478 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For image pairs where the target image belongs to one of the directly supervised categories, it is not surprising that the sender adopted the “conventional” supervised label to signal the target . However, a very interesting effect of supervision is that it improves the interpretability of the code even when agents must communicate about images that do not contain objects in the supervised category set. This emerged in a follow-up experiment in which, during training, the sender was again exposed (with equal probability) to the same supervised classification task as above, but now the agents played the referential game on a different dataset of images derived from ReferItGame (Kazemzadeh et al., 2014). In its general format, the ReferItGame contains annotations of bounding boxes in real images with referring expressions produced by humans when playing the game. For our purposes, we constructed $1 0 \\mathrm { k }$ pairs by randomly sampling two bounding boxes, to act as target and distractor. Again, the agents converged to perfect communication after 15k trials, and this time used all 100 available symbols in some trial. ", + "bbox": [ + 174, + 486, + 825, + 651 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We then asked whether this language was human-interpretable. For each symbol used by the trained sender, we randomly extracted 3 image pairs in which the sender picked that symbol and the receiver pointed at the right target (for two symbols, only 2 pairs matched these criteria, leading to a set of 298 image pairs). We annotated each pair with the word corresponding to the symbol in the supervised set. Out of the 298 pairs, only 25 $( 8 \\% )$ included one of the 100 words among the corresponding referring expressions in ReferItGame. So, in the large majority of cases, the sender had been faced with a pair not (saliently) containing the categories used in the supervised phase of its training, and it had to produce a word that could, at best, only indirectly refer to what is depicted in the target image. We then tested whether this code would be understandable by humans. In essence, it is as if we replaced the trained agent receiver with a human. ", + "bbox": [ + 174, + 660, + 825, + 797 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We prepared a crowdsourced survey using the CrowdFlower platform. For each pair, human participants were shown the two images and the sender-emitted word (that is, the ImageNet label associated to the symbol produced by the sender; see examples in Figure 4). The participants were asked to pick the picture that they thought was most related to the word. We collected 10 ratings for each pair. ", + "bbox": [ + 174, + 805, + 825, + 875 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We found that in $68 \\%$ of the cases the subjects were able to guess the right image. A logistic regression predicting subject image choice from ground-truth target images, with subjects and words as random effects, confirmed the highly significant correlation between the true and guessed images $( z ~ = ~ 1 6 . 7 5$ , $p \\ < \\ 0 . 0 0 0 1 $ ). Thus, while far from perfect, we find that supervised learning on a separate data set does provide some grounding for communication with humans, that generalizes beyond the conventional word denotations learned in the supervised phase. ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 823, + 145 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Looking at the results qualitatively, we found that very often sender-subject communication succeeded when the sender established a sort of “metonymic” link between the words in its possession and the contents of an image. Figure 4 shows an example where the sender produced dolphin to refer to a picture showing a stretch of sea, and fence for a patch of land. Similar semantic shifts are a core characteristic of natural language (e.g., Pustejovsky, 1995), and thus subjects were, in many cases, able to successfully play the referential game with our sender (10/10 subjects guessed the dolphin target, and 8/10 the fence). This is very encouraging. Although the language developed in referential games will be initially very limited, if both agents and humans possess the sort of flexibility displayed in this last experiment, the noisy but shared common ground might suffice to establish basic communication. ", + "bbox": [ + 173, + 154, + 825, + 291 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "6 DISCUSSION ", + "text_level": 1, + "bbox": [ + 174, + 313, + 310, + 329 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our results confirmed that fairly simple neural-network agents can learn to coordinate in a referential game in which they need to communicate about a large number of real pictures. They also suggest that the meanings agents come to assign to symbols in this setup capture general conceptual properties of the objects depicted in the image, rather than low-level visual properties. We also showed a path to grounding the communication in natural language by mixing the game with a supervised task. ", + "bbox": [ + 174, + 344, + 825, + 428 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "In future work, encouraged by our preliminary experiments with object naming, we want to study how to ensure that the emergent communication stays close to human natural language. Predictive learning should be retained as an important building block of intelligent agents, focusing on teaching them structural properties of language (e.g., lexical choice, syntax or style). However, it is also important to learn the function-driven facets of language, such as how to hold a conversation, and interactive games are a potentially fruitful method to achieve this goal. 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", + "bbox": [ + 176, + 532, + 825, + 574 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/parse/train/Hk8N3Sclg/Hk8N3Sclg_middle.json b/parse/train/Hk8N3Sclg/Hk8N3Sclg_middle.json new file mode 100644 index 0000000000000000000000000000000000000000..368a3d1d25d28f02412298eef713309497aceb53 --- /dev/null +++ b/parse/train/Hk8N3Sclg/Hk8N3Sclg_middle.json @@ -0,0 +1,26262 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 79, + 474, + 117 + ], + "lines": [ + { + "bbox": [ + 105, + 78, + 330, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 78, + 330, + 97 + ], + "score": 1.0, + "content": "MULTI-AGENT COOPERATION", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 99, + 476, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 99, + 476, + 118 + ], + "score": 1.0, + "content": "AND THE EMERGENCE OF (NATURAL) LANGUAGE", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 113, + 137, + 393, + 172 + ], + "lines": [ + { + "bbox": [ + 111, + 136, + 395, + 150 + ], + "spans": [ + { + "bbox": [ + 111, + 136, + 395, + 150 + ], + "score": 1.0, + "content": "Angeliki Lazaridou1∗, Alexander Peysakhovich2, Marco Baroni2,3", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 147, + 384, + 162 + ], + "spans": [ + { + "bbox": [ + 111, + 147, + 384, + 162 + ], + "score": 1.0, + "content": "1Google DeepMind, 2Facebook AI Research, 3University of Trento", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 113, + 161, + 381, + 173 + ], + "spans": [ + { + "bbox": [ + 113, + 161, + 381, + 173 + ], + "score": 1.0, + "content": "angeliki@google.com, {alexpeys,mbaroni}@fb.com", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 278, + 200, + 333, + 213 + ], + "lines": [ + { + "bbox": [ + 277, + 200, + 335, + 214 + ], + "spans": [ + { + "bbox": [ + 277, + 200, + 335, + 214 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 143, + 225, + 468, + 399 + ], + "lines": [ + { + "bbox": [ + 142, + 224, + 469, + 236 + ], + "spans": [ + { + "bbox": [ + 142, + 224, + 469, + 236 + ], + "score": 1.0, + "content": "The current mainstream approach to train natural language systems is to expose", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 235, + 469, + 248 + ], + "spans": [ + { + "bbox": [ + 141, + 235, + 469, + 248 + ], + "score": 1.0, + "content": "them to large amounts of text. 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Both of these are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 378, + 469, + 389 + ], + "spans": [ + { + "bbox": [ + 141, + 378, + 469, + 389 + ], + "score": 1.0, + "content": "necessary steps towards developing machines that are able to communicate with", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 389, + 230, + 401 + ], + "spans": [ + { + "bbox": [ + 141, + 389, + 230, + 401 + ], + "score": 1.0, + "content": "humans productively.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 13.5 + }, + { + "type": "title", + "bbox": [ + 108, + 419, + 206, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 418, + 208, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 208, + 435 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 142, + 439, + 468, + 483 + ], + "lines": [ + { + "bbox": [ + 140, + 438, + 469, + 453 + ], + "spans": [ + { + "bbox": [ + 140, + 438, + 469, + 453 + ], + "score": 1.0, + "content": "I tried to break it to him gently [...] the only way to learn an unknown language", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 450, + 469, + 463 + ], + "spans": [ + { + "bbox": [ + 141, + 450, + 469, + 463 + ], + "score": 1.0, + "content": "is to interact with a native speaker [...] asking questions, holding a conversation,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 461, + 469, + 474 + ], + "spans": [ + { + "bbox": [ + 141, + 461, + 469, + 474 + ], + "score": 1.0, + "content": "that sort of thing [...] If you want to learn the aliens’ language, someone [...] will", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 472, + 387, + 484 + ], + "spans": [ + { + "bbox": [ + 141, + 472, + 387, + 484 + ], + "score": 1.0, + "content": "have to talk with an alien. Recordings alone aren’t sufficient.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 144, + 485, + 265, + 496 + ], + "lines": [ + { + "bbox": [ + 141, + 484, + 266, + 499 + ], + "spans": [ + { + "bbox": [ + 141, + 484, + 266, + 499 + ], + "score": 1.0, + "content": "Ted Chiang, Story of Your Life", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 506, + 504, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "One of the main aims of AI is to develop agents that can cooperate with others to achieve goals", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 515, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 506, + 530 + ], + "score": 1.0, + "content": "(Wooldridge, 2009). Such coordination requires communication. If the coordination partners are to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 525, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 542 + ], + "score": 1.0, + "content": "include humans, the most obvious channel of communication is natural language. Thus, handling", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "score": 1.0, + "content": "natural-language-based communication is a key step toward the development of AI that can thrive", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 550, + 256, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 256, + 562 + ], + "score": 1.0, + "content": "in a world populated by other agents.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 566, + 505, + 654 + ], + "lines": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "Given the success of deep learning models in related domains such as image captioning or machine", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "translation (e.g., Sutskever et al., 2014; Xu et al., 2015), it would seem reasonable to cast the prob-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 589, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 505, + 601 + ], + "score": 1.0, + "content": "lem of training conversational agents as an instance of supervised learning (Vinyals & Le, 2015).", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "score": 1.0, + "content": "However, training on “canned” conversations does not allow learners to experience the interactive", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "aspects of communication. Supervised approaches, which focus on the structure of language, are an", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "excellent way to learn general statistical associations between sequences of symbols. However, they", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "do not capture the functional aspects of communication, i.e., that humans use words to coordinate", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 642, + 448, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 448, + 655 + ], + "score": 1.0, + "content": "with others and make things happen (Austin, 1962; Clark, 1996; Wittgenstein, 1953).", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 504, + 716 + ], + "lines": [ + { + "bbox": [ + 106, + 659, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 505, + 672 + ], + "score": 1.0, + "content": "This paper introduces the first steps of a research program based on multi-agent coordination com-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 670, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 506, + 684 + ], + "score": 1.0, + "content": "munication games. These games place agents in simple environments where they need to develop a", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 681, + 506, + 696 + ], + "spans": [ + { + "bbox": [ + 104, + 681, + 506, + 696 + ], + "score": 1.0, + "content": "language to coordinate and earn payoffs. 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This passive learning is problematic if we are in-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 246, + 470, + 259 + ], + "spans": [ + { + "bbox": [ + 141, + 246, + 470, + 259 + ], + "score": 1.0, + "content": "terested in developing interactive machines, such as conversational agents. We", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 257, + 470, + 270 + ], + "spans": [ + { + "bbox": [ + 141, + 257, + 470, + 270 + ], + "score": 1.0, + "content": "propose a framework for language learning that relies on multi-agent communi-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 268, + 470, + 281 + ], + "spans": [ + { + "bbox": [ + 141, + 268, + 470, + 281 + ], + "score": 1.0, + "content": "cation. We study this learning in the context of referential games. In these games,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 279, + 470, + 292 + ], + "spans": [ + { + "bbox": [ + 141, + 279, + 470, + 292 + ], + "score": 1.0, + "content": "a sender and a receiver see a pair of images. The sender is told one of them is", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 290, + 469, + 303 + ], + "spans": [ + { + "bbox": [ + 141, + 290, + 469, + 303 + ], + "score": 1.0, + "content": "the target and is allowed to send a message from a fixed, arbitary vocabulary to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 300, + 470, + 314 + ], + "spans": [ + { + "bbox": [ + 141, + 300, + 470, + 314 + ], + "score": 1.0, + "content": "the receiver. The receiver must rely on this message to identify the target. Thus,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 312, + 470, + 325 + ], + "spans": [ + { + "bbox": [ + 141, + 312, + 470, + 325 + ], + "score": 1.0, + "content": "the agents develop their own language interactively out of the need to communi-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 323, + 469, + 335 + ], + "spans": [ + { + "bbox": [ + 141, + 323, + 469, + 335 + ], + "score": 1.0, + "content": "cate. We show that two networks with simple configurations are able to learn to", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 334, + 470, + 347 + ], + "spans": [ + { + "bbox": [ + 141, + 334, + 470, + 347 + ], + "score": 1.0, + "content": "coordinate in the referential game. We further explore how to make changes to the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 345, + 470, + 358 + ], + "spans": [ + { + "bbox": [ + 141, + 345, + 470, + 358 + ], + "score": 1.0, + "content": "game environment to cause the “word meanings” induced in the game to better re-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 356, + 469, + 369 + ], + "spans": [ + { + "bbox": [ + 141, + 356, + 469, + 369 + ], + "score": 1.0, + "content": "flect intuitive semantic properties of the images. In addition, we present a simple", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 367, + 470, + 379 + ], + "spans": [ + { + "bbox": [ + 141, + 367, + 470, + 379 + ], + "score": 1.0, + "content": "strategy for grounding the agents’ code into natural language. Both of these are", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 378, + 469, + 389 + ], + "spans": [ + { + "bbox": [ + 141, + 378, + 469, + 389 + ], + "score": 1.0, + "content": "necessary steps towards developing machines that are able to communicate with", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 389, + 230, + 401 + ], + "spans": [ + { + "bbox": [ + 141, + 389, + 230, + 401 + ], + "score": 1.0, + "content": "humans productively.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 13.5, + "bbox_fs": [ + 141, + 224, + 470, + 401 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 419, + 206, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 418, + 208, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 208, + 435 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 142, + 439, + 468, + 483 + ], + "lines": [ + { + "bbox": [ + 140, + 438, + 469, + 453 + ], + "spans": [ + { + "bbox": [ + 140, + 438, + 469, + 453 + ], + "score": 1.0, + "content": "I tried to break it to him gently [...] the only way to learn an unknown language", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 450, + 469, + 463 + ], + "spans": [ + { + "bbox": [ + 141, + 450, + 469, + 463 + ], + "score": 1.0, + "content": "is to interact with a native speaker [...] asking questions, holding a conversation,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 461, + 469, + 474 + ], + "spans": [ + { + "bbox": [ + 141, + 461, + 469, + 474 + ], + "score": 1.0, + "content": "that sort of thing [...] If you want to learn the aliens’ language, someone [...] will", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 472, + 387, + 484 + ], + "spans": [ + { + "bbox": [ + 141, + 472, + 387, + 484 + ], + "score": 1.0, + "content": "have to talk with an alien. Recordings alone aren’t sufficient.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 24.5, + "bbox_fs": [ + 140, + 438, + 469, + 484 + ] + }, + { + "type": "text", + "bbox": [ + 144, + 485, + 265, + 496 + ], + "lines": [ + { + "bbox": [ + 141, + 484, + 266, + 499 + ], + "spans": [ + { + "bbox": [ + 141, + 484, + 266, + 499 + ], + "score": 1.0, + "content": "Ted Chiang, Story of Your Life", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27, + "bbox_fs": [ + 141, + 484, + 266, + 499 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 506, + 504, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "One of the main aims of AI is to develop agents that can cooperate with others to achieve goals", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 515, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 506, + 530 + ], + "score": 1.0, + "content": "(Wooldridge, 2009). Such coordination requires communication. If the coordination partners are to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 525, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 542 + ], + "score": 1.0, + "content": "include humans, the most obvious channel of communication is natural language. Thus, handling", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 551 + ], + "score": 1.0, + "content": "natural-language-based communication is a key step toward the development of AI that can thrive", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 550, + 256, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 256, + 562 + ], + "score": 1.0, + "content": "in a world populated by other agents.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 505, + 506, + 562 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 566, + 505, + 654 + ], + "lines": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "Given the success of deep learning models in related domains such as image captioning or machine", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "translation (e.g., Sutskever et al., 2014; Xu et al., 2015), it would seem reasonable to cast the prob-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 589, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 505, + 601 + ], + "score": 1.0, + "content": "lem of training conversational agents as an instance of supervised learning (Vinyals & Le, 2015).", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 612 + ], + "score": 1.0, + "content": "However, training on “canned” conversations does not allow learners to experience the interactive", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "aspects of communication. Supervised approaches, which focus on the structure of language, are an", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "excellent way to learn general statistical associations between sequences of symbols. However, they", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "do not capture the functional aspects of communication, i.e., that humans use words to coordinate", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 642, + 448, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 448, + 655 + ], + "score": 1.0, + "content": "with others and make things happen (Austin, 1962; Clark, 1996; Wittgenstein, 1953).", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 565, + 506, + 655 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 504, + 716 + ], + "lines": [ + { + "bbox": [ + 106, + 659, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 505, + 672 + ], + "score": 1.0, + "content": "This paper introduces the first steps of a research program based on multi-agent coordination com-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 670, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 506, + 684 + ], + "score": 1.0, + "content": "munication games. These games place agents in simple environments where they need to develop a", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 681, + 506, + 696 + ], + "spans": [ + { + "bbox": [ + 104, + 681, + 506, + 696 + ], + "score": 1.0, + "content": "language to coordinate and earn payoffs. Importantly, the agents start as blank slates, but, by play-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 693, + 505, + 706 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 505, + 706 + ], + "score": 1.0, + "content": "ing a game together, they can develop and bootstrap knowledge on top of each others, leading to the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 703, + 211, + 718 + ], + "spans": [ + { + "bbox": [ + 105, + 703, + 211, + 718 + ], + "score": 1.0, + "content": "emergence of a language.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43, + "bbox_fs": [ + 104, + 659, + 506, + 718 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "The central problem of our program, then, is the following: How do we design environments that", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "foster the development of a language that is portable to new situations and to new communication", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 237, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 237, + 116 + ], + "score": 1.0, + "content": "partners (in particular humans)?", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 107, + 121, + 504, + 165 + ], + "lines": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "score": 1.0, + "content": "We start from the most basic challenge of using a language in order to refer to things in the context", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "score": 1.0, + "content": "of a two-agent game. We focus on two questions. First, whether tabula rasa agents succeed in com-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 506, + 156 + ], + "score": 1.0, + "content": "munication. Second, what features of the environment lead to the development of codes resembling", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 177, + 168 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 177, + 168 + ], + "score": 1.0, + "content": "human language.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 107, + 171, + 505, + 216 + ], + "lines": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "score": 1.0, + "content": "We assess this latter question in two ways. First, we consider whether the agents associate general", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "conceptual properties, such as broad object categories (as opposed to low-level visual properties),", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 194, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 505, + 205 + ], + "score": 1.0, + "content": "to the symbols they learn to use. Second, we examine whether the agents’ “word usage” is partially", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 304, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 304, + 217 + ], + "score": 1.0, + "content": "interpretable by humans in an online experiment.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 107, + 221, + 505, + 298 + ], + "lines": [ + { + "bbox": [ + 106, + 221, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 506, + 233 + ], + "score": 1.0, + "content": "Other researchers have proposed communication-based environments for the development of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "score": 1.0, + "content": "coordination-capable AI. Work in multi-agent systems has focused on the design of pre-programmed", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 243, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 506, + 256 + ], + "score": 1.0, + "content": "communication systems to solve specific tasks (e.g., robot soccer, Stone & Veloso 1998). Most re-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "score": 1.0, + "content": "lated to our work, Sukhbaatar et al. (2016) and Foerster et al. (2016) show that neural networks can", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "evolve communication in the context of games without a pre-coded protocol. We pursue the same", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "question, but further ask how we can change our environment to make the emergent language more", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 286, + 162, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 162, + 299 + ], + "score": 1.0, + "content": "interpretable.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 303, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "Others (e.g., the SHRLDU program of Winograd 1971 or the game in Wang et al. 2016) propose", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "score": 1.0, + "content": "building a communicating AI by putting humans in the loop from the very beginning. This approach", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 325, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 505, + 339 + ], + "score": 1.0, + "content": "has benefits but faces serious scalability issues, as active human intervention is required at each step.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 336, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 350 + ], + "score": 1.0, + "content": "An attractive component of our game-based paradigm is that humans may be added as players, but", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 347, + 249, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 249, + 360 + ], + "score": 1.0, + "content": "do not need to be there all the time.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 364, + 505, + 430 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 378 + ], + "score": 1.0, + "content": "A third branch of research focuses on “Wizard-of-Oz” environments, where agents learn to play", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 375, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 506, + 389 + ], + "score": 1.0, + "content": "games by interacting with a complex scripted environment (Mikolov et al., 2015). This approach", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "score": 1.0, + "content": "gives the designer tight control over the learning curriculum, but imposes a heavy engineering burden", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 397, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 505, + 410 + ], + "score": 1.0, + "content": "on developers. We also stress the importance of the environment (game setup), but we focus on", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "simpler environments with multiple agents that force them to get smarter by bootstrapping on top of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 419, + 152, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 152, + 431 + ], + "score": 1.0, + "content": "each other.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25.5 + }, + { + "type": "text", + "bbox": [ + 106, + 435, + 505, + 514 + ], + "lines": [ + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "score": 1.0, + "content": "We leverage ideas from work in linguistics, cognitive science and game theory on the emergence of", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "score": 1.0, + "content": "language (Wagner et al., 2003; Skyrms, 2010; Crawford & Sobel, 1982; Crawford, 1998). Our game", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "score": 1.0, + "content": "is a variation of Lewis’ signaling game (Lewis, 1969). There is a rich tradition of linguistic and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "cognitive studies using similar setups (e.g., Briscoe, 2002; Cangelosi & Parisi, 2002; Spike et al.,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 479, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 493 + ], + "score": 1.0, + "content": "2016; Steels & Loetzsch, 2012). What distinguishes us from this literature is our aim to, eventually,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 491, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 506, + 504 + ], + "score": 1.0, + "content": "develop practical AI. This motivates our focus on more realistic input data (a large collection of", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 502, + 460, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 460, + 515 + ], + "score": 1.0, + "content": "noisy natural images) and on trying to align the agents’ language with human intuitions.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 106, + 519, + 505, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 518, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 531 + ], + "score": 1.0, + "content": "Lewis’ classic games have been studied extensively in game theory under the name of “cheap talk”.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 529, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 505, + 543 + ], + "score": 1.0, + "content": "These games have been used as models to study the evolution of language both theoretically and", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 541, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 505, + 553 + ], + "score": 1.0, + "content": "experimentally (Crawford, 1998; Blume et al., 1998; Crawford & Sobel, 1982). A major question", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "in game theory is whether equilibrium actually occurs in a game as convergence in learning is", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 562, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 562, + 505, + 576 + ], + "score": 1.0, + "content": "not guaranteed (Fudenberg & Peysakhovich, 2014; Roth & Erev, 1995). And, if an equilibrium", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 574, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 505, + 586 + ], + "score": 1.0, + "content": "is reached, which one it will be (since they are typically not unique). This is particularly true for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "score": 1.0, + "content": "cheap talk games, which exhibit Nash equilibria in which precise language emerges, others where", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "vague language emerges and others where no language emerges at all (Crawford & Sobel, 1982). In", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "score": 1.0, + "content": "addition, because in these games language has no ex-ante meaning and only emerges in the context", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 617, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 631 + ], + "score": 1.0, + "content": "of the equilibrium, some of the emergent languages may not be very natural. Our results speak to", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "score": 1.0, + "content": "both the convergence question and the question of what features of the game cause the appearance", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 639, + 452, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 452, + 653 + ], + "score": 1.0, + "content": "of different types of languages. Thus, our results are also of interest to game theorists.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 108, + 657, + 504, + 700 + ], + "lines": [ + { + "bbox": [ + 106, + 657, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 506, + 668 + ], + "score": 1.0, + "content": "An evolutionary perspective has recently been advocated as a way to mitigate the data hunger of", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "score": 1.0, + "content": "traditional supervised approaches (Goodfellow et al., 2014; Silver et al., 2016). This research con-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "score": 1.0, + "content": "firms that learning can be bootstrapped from competition between agents. We focus, however, on", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 690, + 502, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 690, + 502, + 702 + ], + "score": 1.0, + "content": "cooperation between agents as a way to foster learning while reducing the need for annotated data.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49.5 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "The central problem of our program, then, is the following: How do we design environments that", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "foster the development of a language that is portable to new situations and to new communication", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 237, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 237, + 116 + ], + "score": 1.0, + "content": "partners (in particular humans)?", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 105, + 82, + 505, + 116 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 121, + 504, + 165 + ], + "lines": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 506, + 134 + ], + "score": 1.0, + "content": "We start from the most basic challenge of using a language in order to refer to things in the context", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 505, + 144 + ], + "score": 1.0, + "content": "of a two-agent game. We focus on two questions. First, whether tabula rasa agents succeed in com-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 506, + 156 + ], + "score": 1.0, + "content": "munication. Second, what features of the environment lead to the development of codes resembling", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 177, + 168 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 177, + 168 + ], + "score": 1.0, + "content": "human language.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5, + "bbox_fs": [ + 105, + 120, + 506, + 168 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 171, + 505, + 216 + ], + "lines": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 183 + ], + "score": 1.0, + "content": "We assess this latter question in two ways. First, we consider whether the agents associate general", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 505, + 195 + ], + "score": 1.0, + "content": "conceptual properties, such as broad object categories (as opposed to low-level visual properties),", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 194, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 505, + 205 + ], + "score": 1.0, + "content": "to the symbols they learn to use. Second, we examine whether the agents’ “word usage” is partially", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 304, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 304, + 217 + ], + "score": 1.0, + "content": "interpretable by humans in an online experiment.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5, + "bbox_fs": [ + 105, + 171, + 505, + 217 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 221, + 505, + 298 + ], + "lines": [ + { + "bbox": [ + 106, + 221, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 106, + 221, + 506, + 233 + ], + "score": 1.0, + "content": "Other researchers have proposed communication-based environments for the development of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 245 + ], + "score": 1.0, + "content": "coordination-capable AI. Work in multi-agent systems has focused on the design of pre-programmed", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 243, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 506, + 256 + ], + "score": 1.0, + "content": "communication systems to solve specific tasks (e.g., robot soccer, Stone & Veloso 1998). Most re-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 266 + ], + "score": 1.0, + "content": "lated to our work, Sukhbaatar et al. (2016) and Foerster et al. (2016) show that neural networks can", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "evolve communication in the context of games without a pre-coded protocol. We pursue the same", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "score": 1.0, + "content": "question, but further ask how we can change our environment to make the emergent language more", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 286, + 162, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 162, + 299 + ], + "score": 1.0, + "content": "interpretable.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 221, + 506, + 299 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 303, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "Others (e.g., the SHRLDU program of Winograd 1971 or the game in Wang et al. 2016) propose", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 327 + ], + "score": 1.0, + "content": "building a communicating AI by putting humans in the loop from the very beginning. This approach", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 325, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 505, + 339 + ], + "score": 1.0, + "content": "has benefits but faces serious scalability issues, as active human intervention is required at each step.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 336, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 350 + ], + "score": 1.0, + "content": "An attractive component of our game-based paradigm is that humans may be added as players, but", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 347, + 249, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 249, + 360 + ], + "score": 1.0, + "content": "do not need to be there all the time.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 303, + 505, + 360 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 364, + 505, + 430 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 378 + ], + "score": 1.0, + "content": "A third branch of research focuses on “Wizard-of-Oz” environments, where agents learn to play", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 375, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 506, + 389 + ], + "score": 1.0, + "content": "games by interacting with a complex scripted environment (Mikolov et al., 2015). This approach", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "score": 1.0, + "content": "gives the designer tight control over the learning curriculum, but imposes a heavy engineering burden", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 397, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 505, + 410 + ], + "score": 1.0, + "content": "on developers. We also stress the importance of the environment (game setup), but we focus on", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "simpler environments with multiple agents that force them to get smarter by bootstrapping on top of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 419, + 152, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 152, + 431 + ], + "score": 1.0, + "content": "each other.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 363, + 506, + 431 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 435, + 505, + 514 + ], + "lines": [ + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 506, + 449 + ], + "score": 1.0, + "content": "We leverage ideas from work in linguistics, cognitive science and game theory on the emergence of", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "score": 1.0, + "content": "language (Wagner et al., 2003; Skyrms, 2010; Crawford & Sobel, 1982; Crawford, 1998). Our game", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "score": 1.0, + "content": "is a variation of Lewis’ signaling game (Lewis, 1969). There is a rich tradition of linguistic and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "cognitive studies using similar setups (e.g., Briscoe, 2002; Cangelosi & Parisi, 2002; Spike et al.,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 479, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 493 + ], + "score": 1.0, + "content": "2016; Steels & Loetzsch, 2012). What distinguishes us from this literature is our aim to, eventually,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 491, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 506, + 504 + ], + "score": 1.0, + "content": "develop practical AI. This motivates our focus on more realistic input data (a large collection of", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 502, + 460, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 502, + 460, + 515 + ], + "score": 1.0, + "content": "noisy natural images) and on trying to align the agents’ language with human intuitions.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 435, + 506, + 515 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 519, + 505, + 650 + ], + "lines": [ + { + "bbox": [ + 105, + 518, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 531 + ], + "score": 1.0, + "content": "Lewis’ classic games have been studied extensively in game theory under the name of “cheap talk”.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 529, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 529, + 505, + 543 + ], + "score": 1.0, + "content": "These games have been used as models to study the evolution of language both theoretically and", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 541, + 505, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 505, + 553 + ], + "score": 1.0, + "content": "experimentally (Crawford, 1998; Blume et al., 1998; Crawford & Sobel, 1982). A major question", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "in game theory is whether equilibrium actually occurs in a game as convergence in learning is", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 562, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 562, + 505, + 576 + ], + "score": 1.0, + "content": "not guaranteed (Fudenberg & Peysakhovich, 2014; Roth & Erev, 1995). And, if an equilibrium", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 574, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 505, + 586 + ], + "score": 1.0, + "content": "is reached, which one it will be (since they are typically not unique). This is particularly true for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 505, + 598 + ], + "score": 1.0, + "content": "cheap talk games, which exhibit Nash equilibria in which precise language emerges, others where", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "vague language emerges and others where no language emerges at all (Crawford & Sobel, 1982). In", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "score": 1.0, + "content": "addition, because in these games language has no ex-ante meaning and only emerges in the context", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 617, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 631 + ], + "score": 1.0, + "content": "of the equilibrium, some of the emergent languages may not be very natural. Our results speak to", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "score": 1.0, + "content": "both the convergence question and the question of what features of the game cause the appearance", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 639, + 452, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 452, + 653 + ], + "score": 1.0, + "content": "of different types of languages. Thus, our results are also of interest to game theorists.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 518, + 506, + 653 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 657, + 504, + 700 + ], + "lines": [ + { + "bbox": [ + 106, + 657, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 506, + 668 + ], + "score": 1.0, + "content": "An evolutionary perspective has recently been advocated as a way to mitigate the data hunger of", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 680 + ], + "score": 1.0, + "content": "traditional supervised approaches (Goodfellow et al., 2014; Silver et al., 2016). This research con-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "score": 1.0, + "content": "firms that learning can be bootstrapped from competition between agents. We focus, however, on", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 690, + 502, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 690, + 502, + 702 + ], + "score": 1.0, + "content": "cooperation between agents as a way to foster learning while reducing the need for annotated data.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49.5, + "bbox_fs": [ + 105, + 657, + 506, + 702 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 248, + 94 + ], + "lines": [ + { + "bbox": [ + 104, + 78, + 250, + 96 + ], + "spans": [ + { + "bbox": [ + 104, + 78, + 250, + 96 + ], + "score": 1.0, + "content": "2 GENERAL FRAMEWORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 162 + ], + "lines": [ + { + "bbox": [ + 106, + 107, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 107, + 365, + 119 + ], + "score": 1.0, + "content": "Our general framework includes K players, each parametrized by", + "type": "text" + }, + { + "bbox": [ + 365, + 108, + 376, + 118 + ], + "score": 0.88, + "content": "\\theta _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 107, + 505, + 119 + ], + "score": 1.0, + "content": ", a collection of tasks/games that", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 118, + 505, + 130 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 330, + 130 + ], + "score": 1.0, + "content": "the players have to perform, a communication protocol", + "type": "text" + }, + { + "bbox": [ + 330, + 118, + 340, + 128 + ], + "score": 0.74, + "content": "V", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 118, + 505, + 130 + ], + "score": 1.0, + "content": "that enables the players to communicate", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 129, + 505, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 129, + 505, + 141 + ], + "score": 1.0, + "content": "with each other, and payoffs assigned to the players as a deterministic function of a well-defined", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 139, + 506, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 139, + 506, + 153 + ], + "score": 1.0, + "content": "goal. In this paper we focus on a particular version of this: referential games. These games are", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 150, + 194, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 194, + 163 + ], + "score": 1.0, + "content": "structured as follows.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 129, + 173, + 505, + 303 + ], + "lines": [ + { + "bbox": [ + 130, + 172, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 130, + 172, + 343, + 186 + ], + "score": 1.0, + "content": "1. There is a set of images represented by vectors", + "type": "text" + }, + { + "bbox": [ + 343, + 173, + 395, + 185 + ], + "score": 0.93, + "content": "\\{ i _ { 1 } , \\dotsc , i _ { N } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 172, + 505, + 186 + ], + "score": 1.0, + "content": ", two images are drawn at", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 184, + 504, + 198 + ], + "spans": [ + { + "bbox": [ + 141, + 184, + 267, + 198 + ], + "score": 1.0, + "content": "random from this set, call them", + "type": "text" + }, + { + "bbox": [ + 267, + 184, + 299, + 196 + ], + "score": 0.92, + "content": "( i _ { L } , i _ { R } )", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 184, + 458, + 198 + ], + "score": 1.0, + "content": ", one of them is chosen to be the “target”", + "type": "text" + }, + { + "bbox": [ + 458, + 184, + 504, + 196 + ], + "score": 0.93, + "content": "t \\in \\{ L , R \\}", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 128, + 199, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 128, + 199, + 505, + 214 + ], + "score": 1.0, + "content": "2. There are two players, a sender and a receiver, each seeing the images - the sender receives", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 142, + 211, + 216, + 223 + ], + "spans": [ + { + "bbox": [ + 142, + 212, + 165, + 223 + ], + "score": 1.0, + "content": "input", + "type": "text" + }, + { + "bbox": [ + 165, + 211, + 216, + 223 + ], + "score": 0.93, + "content": "\\theta _ { S } ( i _ { L } , i _ { R } , t )", + "type": "inline_equation" + } + ], + "index": 9 + }, + { + "bbox": [ + 128, + 226, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 128, + 226, + 236, + 239 + ], + "score": 1.0, + "content": "3. There is a vocabulary", + "type": "text" + }, + { + "bbox": [ + 237, + 227, + 246, + 237 + ], + "score": 0.72, + "content": "V", + "type": "inline_equation" + }, + { + "bbox": [ + 247, + 226, + 280, + 239 + ], + "score": 1.0, + "content": "of size", + "type": "text" + }, + { + "bbox": [ + 280, + 227, + 291, + 237 + ], + "score": 0.8, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 226, + 505, + 239 + ], + "score": 1.0, + "content": "and the sender chooses one symbol to send to the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 140, + 237, + 387, + 250 + ], + "spans": [ + { + "bbox": [ + 140, + 237, + 304, + 250 + ], + "score": 1.0, + "content": "receiver, we call this the sender’s policy", + "type": "text" + }, + { + "bbox": [ + 304, + 238, + 387, + 250 + ], + "score": 0.91, + "content": "s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) \\in V", + "type": "inline_equation" + } + ], + "index": 11 + }, + { + "bbox": [ + 128, + 253, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 128, + 253, + 505, + 266 + ], + "score": 1.0, + "content": "4. The receiver does not know the target, but sees the sender’s symbol and tries to guess the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 264, + 475, + 278 + ], + "spans": [ + { + "bbox": [ + 141, + 264, + 329, + 278 + ], + "score": 1.0, + "content": "target image. We call this the receiver’s policy", + "type": "text" + }, + { + "bbox": [ + 330, + 264, + 475, + 277 + ], + "score": 0.92, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \\in \\{ L , \\bar { R } \\}", + "type": "inline_equation" + } + ], + "index": 13 + }, + { + "bbox": [ + 128, + 279, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 128, + 279, + 153, + 294 + ], + "score": 1.0, + "content": "5. If", + "type": "text" + }, + { + "bbox": [ + 153, + 280, + 275, + 293 + ], + "score": 0.92, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) = t", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 279, + 505, + 294 + ], + "score": 1.0, + "content": ", that is, if the receiver guesses the target, both players", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 142, + 292, + 425, + 304 + ], + "spans": [ + { + "bbox": [ + 142, + 292, + 425, + 304 + ], + "score": 1.0, + "content": "receive a payoff of 1 (win), otherwise they receive a payoff of 0 (lose).", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 107, + 314, + 505, + 359 + ], + "lines": [ + { + "bbox": [ + 105, + 313, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 328 + ], + "score": 1.0, + "content": "Many extensions to the basic referential game explored here are possible. There can be more images,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 325, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 338 + ], + "score": 1.0, + "content": "or a more sophisticated communication protocol (e.g., communication of a sequence of symbols or", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "multi-step communication requiring back-and-forth interaction1), rotation of the sender and receiver", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 348, + 365, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 365, + 360 + ], + "score": 1.0, + "content": "roles, having a human occasionally playing one of the roles, etc.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5 + }, + { + "type": "title", + "bbox": [ + 108, + 375, + 244, + 388 + ], + "lines": [ + { + "bbox": [ + 105, + 374, + 245, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 245, + 390 + ], + "score": 1.0, + "content": "3 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 401, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 415 + ], + "score": 1.0, + "content": "Images We use the McRae et al.’s (2005) set of 463 base-level concrete concepts (e.g., cat, ap-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "ple, car. . . ) spanning across 20 general categories (e.g., animal, fruit/vegetable, vehicle. . . ). We", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "score": 1.0, + "content": "randomly sample 100 images of each concept from ImageNet (Deng et al., 2009). To create tar-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 104, + 434, + 505, + 447 + ], + "score": 1.0, + "content": "get/distractor pairs, we randomly sample two concepts, one image for each concept and whether the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "score": 1.0, + "content": "first or second image will serve as target. We apply to each image a forward-pass through the pre-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "trained VGG ConvNet (Simonyan & Zisserman, 2014), and represent it with the activations from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 466, + 495, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 475, + 480 + ], + "score": 1.0, + "content": "either the top 1000-D softmax layer (sm) or the second-to-last 4096-D fully connected layer", + "type": "text" + }, + { + "bbox": [ + 475, + 467, + 490, + 479 + ], + "score": 0.6, + "content": "( f c )", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 466, + 495, + 480 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 492, + 505, + 547 + ], + "lines": [ + { + "bbox": [ + 105, + 491, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 506, + 504 + ], + "score": 1.0, + "content": "Agent Players Both sender and receiver are simple feed-forward networks. For the sender, we", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "score": 1.0, + "content": "experiment with the two architectures depicted in Figure 1. Both sender architectures take as input", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 514, + 505, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 505, + 526 + ], + "score": 1.0, + "content": "the target (marked with a green square in Figure 1) and distractor representations, always in this", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "score": 1.0, + "content": "order, so that they are implicitly informed of which image is the target (the receiver, instead, sees", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 535, + 241, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 241, + 548 + ], + "score": 1.0, + "content": "the two images in random order).", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 552, + 505, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "The agnostic sender is a generic neural network that maps the original image vectors onto a “game-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "specific” embedding space (in the sense that the embedding is learned while playing the game)", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 574, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 505, + 587 + ], + "score": 1.0, + "content": "followed by a sigmoid nonlinearity. Fully-connected weights are applied to the embedding concate-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 586, + 310, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 310, + 597 + ], + "score": 1.0, + "content": "nation to produce scores over vocabulary symbols.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 107, + 602, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 106, + 603, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 505, + 614 + ], + "score": 1.0, + "content": "The informed sender also first embeds the images into a “game-specific” space. It then applies", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 613, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 506, + 626 + ], + "score": 1.0, + "content": "1-D convolutions (“filters”) on the image embeddings by treating them as different channels. The", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 625, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 625, + 505, + 636 + ], + "score": 1.0, + "content": "informed sender uses convolutions with kernel size 2x1 applied dimension-by-dimension to the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "score": 1.0, + "content": "two image embeddings (in Figure 1, there are 4 such filters). This is followed by the sigmoid", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 646, + 457, + 659 + ], + "score": 1.0, + "content": "nonlinearity. The resulting feature maps are combined through another filter (kernel size", + "type": "text" + }, + { + "bbox": [ + 457, + 646, + 474, + 658 + ], + "score": 0.89, + "content": "f \\mathrm { x } 1", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 646, + 506, + 659 + ], + "score": 1.0, + "content": ", where", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 657, + 504, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 114, + 669 + ], + "score": 0.85, + "content": "f", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 658, + 504, + 669 + ], + "score": 1.0, + "content": "is the number of filters on the image embeddings), to produce scores for the vocabulary symbols.", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "Intuitively, the informed sender has an inductive bias towards combining the two images dimension-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "score": 1.0, + "content": "by-dimension whereas the agnostic sender does not (though we note the agnostic architecture nests", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 689, + 182, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 182, + 703 + ], + "score": 1.0, + "content": "the informed one).", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 41 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 711, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 119, + 709, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 119, + 709, + 506, + 724 + ], + "score": 1.0, + "content": "1For example, Jorge et al. (2016) explore agents playing a “Guess Who” game to learn about the emergence", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 720, + 276, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 276, + 734 + ], + "score": 1.0, + "content": "of question-asking and answering in language.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 248, + 94 + ], + "lines": [ + { + "bbox": [ + 104, + 78, + 250, + 96 + ], + "spans": [ + { + "bbox": [ + 104, + 78, + 250, + 96 + ], + "score": 1.0, + "content": "2 GENERAL FRAMEWORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 162 + ], + "lines": [ + { + "bbox": [ + 106, + 107, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 107, + 365, + 119 + ], + "score": 1.0, + "content": "Our general framework includes K players, each parametrized by", + "type": "text" + }, + { + "bbox": [ + 365, + 108, + 376, + 118 + ], + "score": 0.88, + "content": "\\theta _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 107, + 505, + 119 + ], + "score": 1.0, + "content": ", a collection of tasks/games that", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 118, + 505, + 130 + ], + "spans": [ + { + "bbox": [ + 106, + 118, + 330, + 130 + ], + "score": 1.0, + "content": "the players have to perform, a communication protocol", + "type": "text" + }, + { + "bbox": [ + 330, + 118, + 340, + 128 + ], + "score": 0.74, + "content": "V", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 118, + 505, + 130 + ], + "score": 1.0, + "content": "that enables the players to communicate", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 129, + 505, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 129, + 505, + 141 + ], + "score": 1.0, + "content": "with each other, and payoffs assigned to the players as a deterministic function of a well-defined", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 139, + 506, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 139, + 506, + 153 + ], + "score": 1.0, + "content": "goal. In this paper we focus on a particular version of this: referential games. These games are", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 150, + 194, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 194, + 163 + ], + "score": 1.0, + "content": "structured as follows.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 107, + 506, + 163 + ] + }, + { + "type": "list", + "bbox": [ + 129, + 173, + 505, + 303 + ], + "lines": [ + { + "bbox": [ + 130, + 172, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 130, + 172, + 343, + 186 + ], + "score": 1.0, + "content": "1. There is a set of images represented by vectors", + "type": "text" + }, + { + "bbox": [ + 343, + 173, + 395, + 185 + ], + "score": 0.93, + "content": "\\{ i _ { 1 } , \\dotsc , i _ { N } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 172, + 505, + 186 + ], + "score": 1.0, + "content": ", two images are drawn at", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 184, + 504, + 198 + ], + "spans": [ + { + "bbox": [ + 141, + 184, + 267, + 198 + ], + "score": 1.0, + "content": "random from this set, call them", + "type": "text" + }, + { + "bbox": [ + 267, + 184, + 299, + 196 + ], + "score": 0.92, + "content": "( i _ { L } , i _ { R } )", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 184, + 458, + 198 + ], + "score": 1.0, + "content": ", one of them is chosen to be the “target”", + "type": "text" + }, + { + "bbox": [ + 458, + 184, + 504, + 196 + ], + "score": 0.93, + "content": "t \\in \\{ L , R \\}", + "type": "inline_equation" + } + ], + "index": 7 + }, + { + "bbox": [ + 128, + 199, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 128, + 199, + 505, + 214 + ], + "score": 1.0, + "content": "2. 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There is a vocabulary", + "type": "text" + }, + { + "bbox": [ + 237, + 227, + 246, + 237 + ], + "score": 0.72, + "content": "V", + "type": "inline_equation" + }, + { + "bbox": [ + 247, + 226, + 280, + 239 + ], + "score": 1.0, + "content": "of size", + "type": "text" + }, + { + "bbox": [ + 280, + 227, + 291, + 237 + ], + "score": 0.8, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 226, + 505, + 239 + ], + "score": 1.0, + "content": "and the sender chooses one symbol to send to the", + "type": "text" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 140, + 237, + 387, + 250 + ], + "spans": [ + { + "bbox": [ + 140, + 237, + 304, + 250 + ], + "score": 1.0, + "content": "receiver, we call this the sender’s policy", + "type": "text" + }, + { + "bbox": [ + 304, + 238, + 387, + 250 + ], + "score": 0.91, + "content": "s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) \\in V", + "type": "inline_equation" + } + ], + "index": 11, + "is_list_end_line": true + }, + { + "bbox": [ + 128, + 253, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 128, + 253, + 505, + 266 + ], + "score": 1.0, + "content": "4. The receiver does not know the target, but sees the sender’s symbol and tries to guess the", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 264, + 475, + 278 + ], + "spans": [ + { + "bbox": [ + 141, + 264, + 329, + 278 + ], + "score": 1.0, + "content": "target image. We call this the receiver’s policy", + "type": "text" + }, + { + "bbox": [ + 330, + 264, + 475, + 277 + ], + "score": 0.92, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \\in \\{ L , \\bar { R } \\}", + "type": "inline_equation" + } + ], + "index": 13, + "is_list_end_line": true + }, + { + "bbox": [ + 128, + 279, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 128, + 279, + 153, + 294 + ], + "score": 1.0, + "content": "5. If", + "type": "text" + }, + { + "bbox": [ + 153, + 280, + 275, + 293 + ], + "score": 0.92, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) = t", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 279, + 505, + 294 + ], + "score": 1.0, + "content": ", that is, if the receiver guesses the target, both players", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 142, + 292, + 425, + 304 + ], + "spans": [ + { + "bbox": [ + 142, + 292, + 425, + 304 + ], + "score": 1.0, + "content": "receive a payoff of 1 (win), otherwise they receive a payoff of 0 (lose).", + "type": "text" + } + ], + "index": 15, + "is_list_end_line": true + } + ], + "index": 10.5, + "bbox_fs": [ + 128, + 172, + 505, + 304 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 314, + 505, + 359 + ], + "lines": [ + { + "bbox": [ + 105, + 313, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 328 + ], + "score": 1.0, + "content": "Many extensions to the basic referential game explored here are possible. There can be more images,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 325, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 338 + ], + "score": 1.0, + "content": "or a more sophisticated communication protocol (e.g., communication of a sequence of symbols or", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "multi-step communication requiring back-and-forth interaction1), rotation of the sender and receiver", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 348, + 365, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 365, + 360 + ], + "score": 1.0, + "content": "roles, having a human occasionally playing one of the roles, etc.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 313, + 506, + 360 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 375, + 244, + 388 + ], + "lines": [ + { + "bbox": [ + 105, + 374, + 245, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 245, + 390 + ], + "score": 1.0, + "content": "3 EXPERIMENTAL SETUP", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 401, + 505, + 478 + ], + "lines": [ + { + "bbox": [ + 105, + 400, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 505, + 415 + ], + "score": 1.0, + "content": "Images We use the McRae et al.’s (2005) set of 463 base-level concrete concepts (e.g., cat, ap-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "ple, car. . . ) spanning across 20 general categories (e.g., animal, fruit/vegetable, vehicle. . . ). We", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "score": 1.0, + "content": "randomly sample 100 images of each concept from ImageNet (Deng et al., 2009). To create tar-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 104, + 434, + 505, + 447 + ], + "score": 1.0, + "content": "get/distractor pairs, we randomly sample two concepts, one image for each concept and whether the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "score": 1.0, + "content": "first or second image will serve as target. We apply to each image a forward-pass through the pre-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 468 + ], + "score": 1.0, + "content": "trained VGG ConvNet (Simonyan & Zisserman, 2014), and represent it with the activations from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 466, + 495, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 475, + 480 + ], + "score": 1.0, + "content": "either the top 1000-D softmax layer (sm) or the second-to-last 4096-D fully connected layer", + "type": "text" + }, + { + "bbox": [ + 475, + 467, + 490, + 479 + ], + "score": 0.6, + "content": "( f c )", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 466, + 495, + 480 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24, + "bbox_fs": [ + 104, + 400, + 505, + 480 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 492, + 505, + 547 + ], + "lines": [ + { + "bbox": [ + 105, + 491, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 506, + 504 + ], + "score": 1.0, + "content": "Agent Players Both sender and receiver are simple feed-forward networks. For the sender, we", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 505, + 515 + ], + "score": 1.0, + "content": "experiment with the two architectures depicted in Figure 1. Both sender architectures take as input", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 514, + 505, + 526 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 505, + 526 + ], + "score": 1.0, + "content": "the target (marked with a green square in Figure 1) and distractor representations, always in this", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 505, + 537 + ], + "score": 1.0, + "content": "order, so that they are implicitly informed of which image is the target (the receiver, instead, sees", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 535, + 241, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 241, + 548 + ], + "score": 1.0, + "content": "the two images in random order).", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 491, + 506, + 548 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 552, + 505, + 597 + ], + "lines": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "The agnostic sender is a generic neural network that maps the original image vectors onto a “game-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "specific” embedding space (in the sense that the embedding is learned while playing the game)", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 574, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 505, + 587 + ], + "score": 1.0, + "content": "followed by a sigmoid nonlinearity. Fully-connected weights are applied to the embedding concate-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 586, + 310, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 310, + 597 + ], + "score": 1.0, + "content": "nation to produce scores over vocabulary symbols.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 552, + 506, + 597 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 602, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 106, + 603, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 603, + 505, + 614 + ], + "score": 1.0, + "content": "The informed sender also first embeds the images into a “game-specific” space. It then applies", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 613, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 506, + 626 + ], + "score": 1.0, + "content": "1-D convolutions (“filters”) on the image embeddings by treating them as different channels. The", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 625, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 625, + 505, + 636 + ], + "score": 1.0, + "content": "informed sender uses convolutions with kernel size 2x1 applied dimension-by-dimension to the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "score": 1.0, + "content": "two image embeddings (in Figure 1, there are 4 such filters). This is followed by the sigmoid", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 646, + 457, + 659 + ], + "score": 1.0, + "content": "nonlinearity. The resulting feature maps are combined through another filter (kernel size", + "type": "text" + }, + { + "bbox": [ + 457, + 646, + 474, + 658 + ], + "score": 0.89, + "content": "f \\mathrm { x } 1", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 646, + 506, + 659 + ], + "score": 1.0, + "content": ", where", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 657, + 504, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 114, + 669 + ], + "score": 0.85, + "content": "f", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 658, + 504, + 669 + ], + "score": 1.0, + "content": "is the number of filters on the image embeddings), to produce scores for the vocabulary symbols.", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "Intuitively, the informed sender has an inductive bias towards combining the two images dimension-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 692 + ], + "score": 1.0, + "content": "by-dimension whereas the agnostic sender does not (though we note the agnostic architecture nests", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 689, + 182, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 182, + 703 + ], + "score": 1.0, + "content": "the informed one).", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 603, + 506, + 703 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 105, + 86, + 501, + 248 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 105, + 86, + 501, + 248 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 86, + 501, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 86, + 501, + 248 + ], + "score": 0.964, + "type": "image", + "image_path": "922b96f905d5c5ad3d20244a196d7b3b633b7d9cf1391770bbbb062b580fc805.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 105, + 86, + 501, + 140.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 105, + 140.0, + 501, + 194.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 105, + 194.0, + 501, + 248.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 224, + 259, + 386, + 270 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 222, + 257, + 388, + 273 + ], + "spans": [ + { + "bbox": [ + 222, + 257, + 388, + 273 + ], + "score": 1.0, + "content": "Figure 1: Architectures of agent players.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 292, + 505, + 336 + ], + "lines": [ + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "score": 1.0, + "content": "For both senders, motivated by the discrete nature of language, we enforce a strong communication", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "score": 1.0, + "content": "bottleneck that discretizes the communication protocol. Activations on the top (vocabulary) layer", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 315, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 371, + 326 + ], + "score": 1.0, + "content": "are converted to a Gibbs distribution (with temperature parameter", + "type": "text" + }, + { + "bbox": [ + 372, + 316, + 379, + 324 + ], + "score": 0.66, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 315, + 488, + 326 + ], + "score": 1.0, + "content": "), and then a single symbol", + "type": "text" + }, + { + "bbox": [ + 489, + 316, + 495, + 324 + ], + "score": 0.69, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 315, + 506, + 326 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 325, + 313, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 313, + 338 + ], + "score": 1.0, + "content": "sampled from the resulting probability distribution.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 342, + 505, + 408 + ], + "lines": [ + { + "bbox": [ + 106, + 342, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 342, + 505, + 354 + ], + "score": 1.0, + "content": "The receiver takes as input the target and distractor image vectors in random order, as well as the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 353, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 365 + ], + "score": 1.0, + "content": "symbol produced by the sender (as a one-hot vector over the vocabulary). It embeds the images and", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 363, + 506, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 506, + 377 + ], + "score": 1.0, + "content": "the symbol into its own “game-specific” space. It then computes dot products between the symbol", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "and image embeddings. Ideally, dot similarity should be higher for the image that is better denoted", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 386, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 477, + 398 + ], + "score": 1.0, + "content": "by the symbol. The two dot products are converted to a Gibbs distribution (with temperature", + "type": "text" + }, + { + "bbox": [ + 477, + 388, + 484, + 396 + ], + "score": 0.72, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 386, + 505, + 398 + ], + "score": 1.0, + "content": ") and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 397, + 416, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 416, + 410 + ], + "score": 1.0, + "content": "the receiver “points” to an image by sampling from the resulting distribution.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 108, + 422, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 106, + 421, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 505, + 435 + ], + "score": 1.0, + "content": "General Training Details We set the following hyperparameters without tuning: embedding di-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "mensionality: 50, number of filters applied to embeddings by informed sender: 20, temperature of", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 444, + 425, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 425, + 456 + ], + "score": 1.0, + "content": "Gibbs distributions: 10. We explore two vocabulary sizes: 10 and 100 symbols.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 460, + 505, + 494 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 252, + 474 + ], + "score": 1.0, + "content": "The sender and receiver parameters", + "type": "text" + }, + { + "bbox": [ + 252, + 461, + 307, + 473 + ], + "score": 0.93, + "content": "\\theta = \\langle \\theta _ { R } , \\theta _ { S } \\rangle", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 460, + 505, + 474 + ], + "score": 1.0, + "content": "are learned while playing the game. No weights", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "score": 1.0, + "content": "are shared and the only supervision used is communication success, i.e., whether the receiver pointed", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 483, + 188, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 188, + 495 + ], + "score": 1.0, + "content": "at the right referent.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 499, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 106, + 500, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 505, + 512 + ], + "score": 1.0, + "content": "This setup is naturally modeled with Reinforcement Learning (Sutton & Barto, 1998). As out-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 306, + 523 + ], + "score": 1.0, + "content": "lined in Section 2, the sender follows policy", + "type": "text" + }, + { + "bbox": [ + 307, + 511, + 400, + 523 + ], + "score": 0.91, + "content": "s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) \\ \\in \\ V", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 510, + 505, + 523 + ], + "score": 1.0, + "content": "and the receiver policy", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 522, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 258, + 534 + ], + "score": 0.9, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \\ \\in \\ \\{ \\{ L , { R } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 522, + 505, + 534 + ], + "score": 1.0, + "content": ". The loss function that the two agents must minimize is", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 531, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 107, + 533, + 153, + 545 + ], + "score": 0.91, + "content": "- { \\bf E } _ { \\widetilde { r } } [ R ( \\widetilde { r } ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 531, + 182, + 546 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 183, + 533, + 192, + 543 + ], + "score": 0.76, + "content": "R", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 531, + 347, + 546 + ], + "score": 1.0, + "content": "is the reward function returning 1 iff", + "type": "text" + }, + { + "bbox": [ + 347, + 532, + 467, + 545 + ], + "score": 0.93, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( \\bar { i } _ { L } , i _ { R } , t ) ) = t", + "type": "inline_equation" + }, + { + "bbox": [ + 467, + 531, + 505, + 546 + ], + "score": 1.0, + "content": ". Param-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 543, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 505, + 556 + ], + "score": 1.0, + "content": "eters are updated through the Reinforce rule (Williams, 1992). We apply mini-batch updates, with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 555, + 504, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 253, + 567 + ], + "score": 1.0, + "content": "a batch size of 32 and for a total of", + "type": "text" + }, + { + "bbox": [ + 254, + 555, + 270, + 565 + ], + "score": 0.42, + "content": "5 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 555, + 488, + 567 + ], + "score": 1.0, + "content": "iterations (games). At test time, we compile a set of", + "type": "text" + }, + { + "bbox": [ + 488, + 555, + 504, + 565 + ], + "score": 0.43, + "content": "1 0 \\mathrm { k }", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 565, + 333, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 333, + 579 + ], + "score": 1.0, + "content": "games using the same method as for the training games.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 108, + 582, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 504, + 594 + ], + "score": 1.0, + "content": "We now turn to our main questions. The first is whether the agents can learn to successfully coordi-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 593, + 506, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 506, + 605 + ], + "score": 1.0, + "content": "nate in a reasonable amount of time. The second is whether the agents’ language can be thought of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 605, + 506, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 616 + ], + "score": 1.0, + "content": "as “natural language”, i.e., symbols are assigned to meanings that make intuitive sense in terms of", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 616, + 248, + 626 + ], + "spans": [ + { + "bbox": [ + 106, + 616, + 248, + 626 + ], + "score": 1.0, + "content": "our conceptualization of the world.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5 + }, + { + "type": "title", + "bbox": [ + 108, + 644, + 280, + 657 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 282, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 282, + 659 + ], + "score": 1.0, + "content": "4 LEARNING TO COMMUNICATE", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 671, + 504, + 704 + ], + "lines": [ + { + "bbox": [ + 105, + 669, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 506, + 684 + ], + "score": 1.0, + "content": "Our first question is whether agents converge to successful communication at all. We see that they", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 680, + 505, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 505, + 695 + ], + "score": 1.0, + "content": "do: agents almost perfectly coordinate in the 1k rounds following the 10k training games for every", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 693, + 285, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 285, + 705 + ], + "score": 1.0, + "content": "architecture and parameter choice (Table 1).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 503, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "We see, though, some differences between different sender architectures. Figure 2 (left) shows", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "performance on a sample of the test set as a function of the first 5,000 rounds of training. The agents", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 35.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 105, + 86, + 501, + 248 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 105, + 86, + 501, + 248 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 86, + 501, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 86, + 501, + 248 + ], + "score": 0.964, + "type": "image", + "image_path": "922b96f905d5c5ad3d20244a196d7b3b633b7d9cf1391770bbbb062b580fc805.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 105, + 86, + 501, + 140.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 105, + 140.0, + 501, + 194.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 105, + 194.0, + 501, + 248.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 224, + 259, + 386, + 270 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 222, + 257, + 388, + 273 + ], + "spans": [ + { + "bbox": [ + 222, + 257, + 388, + 273 + ], + "score": 1.0, + "content": "Figure 1: Architectures of agent players.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 292, + 505, + 336 + ], + "lines": [ + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "score": 1.0, + "content": "For both senders, motivated by the discrete nature of language, we enforce a strong communication", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 315 + ], + "score": 1.0, + "content": "bottleneck that discretizes the communication protocol. Activations on the top (vocabulary) layer", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 315, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 371, + 326 + ], + "score": 1.0, + "content": "are converted to a Gibbs distribution (with temperature parameter", + "type": "text" + }, + { + "bbox": [ + 372, + 316, + 379, + 324 + ], + "score": 0.66, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 315, + 488, + 326 + ], + "score": 1.0, + "content": "), and then a single symbol", + "type": "text" + }, + { + "bbox": [ + 489, + 316, + 495, + 324 + ], + "score": 0.69, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 315, + 506, + 326 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 325, + 313, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 313, + 338 + ], + "score": 1.0, + "content": "sampled from the resulting probability distribution.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 292, + 506, + 338 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 342, + 505, + 408 + ], + "lines": [ + { + "bbox": [ + 106, + 342, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 342, + 505, + 354 + ], + "score": 1.0, + "content": "The receiver takes as input the target and distractor image vectors in random order, as well as the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 353, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 365 + ], + "score": 1.0, + "content": "symbol produced by the sender (as a one-hot vector over the vocabulary). It embeds the images and", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 363, + 506, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 506, + 377 + ], + "score": 1.0, + "content": "the symbol into its own “game-specific” space. It then computes dot products between the symbol", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "and image embeddings. Ideally, dot similarity should be higher for the image that is better denoted", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 386, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 477, + 398 + ], + "score": 1.0, + "content": "by the symbol. The two dot products are converted to a Gibbs distribution (with temperature", + "type": "text" + }, + { + "bbox": [ + 477, + 388, + 484, + 396 + ], + "score": 0.72, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 386, + 505, + 398 + ], + "score": 1.0, + "content": ") and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 397, + 416, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 416, + 410 + ], + "score": 1.0, + "content": "the receiver “points” to an image by sampling from the resulting distribution.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5, + "bbox_fs": [ + 105, + 342, + 506, + 410 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 422, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 106, + 421, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 421, + 505, + 435 + ], + "score": 1.0, + "content": "General Training Details We set the following hyperparameters without tuning: embedding di-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "mensionality: 50, number of filters applied to embeddings by informed sender: 20, temperature of", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 444, + 425, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 425, + 456 + ], + "score": 1.0, + "content": "Gibbs distributions: 10. We explore two vocabulary sizes: 10 and 100 symbols.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 421, + 506, + 456 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 460, + 505, + 494 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 252, + 474 + ], + "score": 1.0, + "content": "The sender and receiver parameters", + "type": "text" + }, + { + "bbox": [ + 252, + 461, + 307, + 473 + ], + "score": 0.93, + "content": "\\theta = \\langle \\theta _ { R } , \\theta _ { S } \\rangle", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 460, + 505, + 474 + ], + "score": 1.0, + "content": "are learned while playing the game. No weights", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "score": 1.0, + "content": "are shared and the only supervision used is communication success, i.e., whether the receiver pointed", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 483, + 188, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 188, + 495 + ], + "score": 1.0, + "content": "at the right referent.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 460, + 505, + 495 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 499, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 106, + 500, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 505, + 512 + ], + "score": 1.0, + "content": "This setup is naturally modeled with Reinforcement Learning (Sutton & Barto, 1998). As out-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 306, + 523 + ], + "score": 1.0, + "content": "lined in Section 2, the sender follows policy", + "type": "text" + }, + { + "bbox": [ + 307, + 511, + 400, + 523 + ], + "score": 0.91, + "content": "s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) \\ \\in \\ V", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 510, + 505, + 523 + ], + "score": 1.0, + "content": "and the receiver policy", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 522, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 258, + 534 + ], + "score": 0.9, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( i _ { L } , i _ { R } , t ) ) ) \\ \\in \\ \\{ \\{ L , { R } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 522, + 505, + 534 + ], + "score": 1.0, + "content": ". The loss function that the two agents must minimize is", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 531, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 107, + 533, + 153, + 545 + ], + "score": 0.91, + "content": "- { \\bf E } _ { \\widetilde { r } } [ R ( \\widetilde { r } ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 531, + 182, + 546 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 183, + 533, + 192, + 543 + ], + "score": 0.76, + "content": "R", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 531, + 347, + 546 + ], + "score": 1.0, + "content": "is the reward function returning 1 iff", + "type": "text" + }, + { + "bbox": [ + 347, + 532, + 467, + 545 + ], + "score": 0.93, + "content": "r ( i _ { L } , i _ { R } , s ( \\theta _ { S } ( \\bar { i } _ { L } , i _ { R } , t ) ) = t", + "type": "inline_equation" + }, + { + "bbox": [ + 467, + 531, + 505, + 546 + ], + "score": 1.0, + "content": ". Param-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 543, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 505, + 556 + ], + "score": 1.0, + "content": "eters are updated through the Reinforce rule (Williams, 1992). We apply mini-batch updates, with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 555, + 504, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 253, + 567 + ], + "score": 1.0, + "content": "a batch size of 32 and for a total of", + "type": "text" + }, + { + "bbox": [ + 254, + 555, + 270, + 565 + ], + "score": 0.42, + "content": "5 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 555, + 488, + 567 + ], + "score": 1.0, + "content": "iterations (games). At test time, we compile a set of", + "type": "text" + }, + { + "bbox": [ + 488, + 555, + 504, + 565 + ], + "score": 0.43, + "content": "1 0 \\mathrm { k }", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 565, + 333, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 333, + 579 + ], + "score": 1.0, + "content": "games using the same method as for the training games.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 500, + 505, + 579 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 582, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 504, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 504, + 594 + ], + "score": 1.0, + "content": "We now turn to our main questions. The first is whether the agents can learn to successfully coordi-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 593, + 506, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 506, + 605 + ], + "score": 1.0, + "content": "nate in a reasonable amount of time. 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We see that they", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 680, + 505, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 505, + 695 + ], + "score": 1.0, + "content": "do: agents almost perfectly coordinate in the 1k rounds following the 10k training games for every", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 693, + 285, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 285, + 705 + ], + "score": 1.0, + "content": "architecture and parameter choice (Table 1).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 669, + 506, + 705 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 503, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "We see, though, some differences between different sender architectures. Figure 2 (left) shows", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "performance on a sample of the test set as a function of the first 5,000 rounds of training. 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Right: Spectrum of an example symbol usage matrix:", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "the first few dimensions do capture only partial variance, suggesting that the usage of more symbols", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 298, + 315, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 315, + 312 + ], + "score": 1.0, + "content": "by the informed sender is not just due to synonymy.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "table", + "bbox": [ + 149, + 327, + 462, + 430 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 149, + 327, + 462, + 430 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 149, + 327, + 462, + 430 + ], + "spans": [ + { + "bbox": [ + 149, + 327, + 462, + 430 + ], + "score": 0.978, + "html": "
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Used symbols column", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "score": 1.0, + "content": "reports number of distinct vocabulary symbols that were produced at least once in the test phase. See", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 460, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 457, + 473 + ], + "score": 1.0, + "content": "text for explanation of comm success and purity. All purity values are highly significant", + "type": "text" + }, + { + "bbox": [ + 457, + 460, + 502, + 471 + ], + "score": 0.86, + "content": "( p < 0 . 0 0 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 460, + 505, + 473 + ], + "score": 0.0, + "content": "", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "score": 1.0, + "content": "compared to simulated chance symbol assignment when matching observed symbol usage. The obs-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 482, + 496, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 496, + 495 + ], + "score": 1.0, + "content": "chance purity column reports the difference between observed and expected purity under chance.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 522, + 503, + 545 + ], + "lines": [ + { + "bbox": [ + 105, + 521, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 505, + 536 + ], + "score": 1.0, + "content": "converge to coordination quite fast, but the informed sender reaches higher levels more quickly than", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 532, + 177, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 177, + 547 + ], + "score": 1.0, + "content": "the agnostic one.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 106, + 550, + 505, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "The informed sender makes use of more symbols from the available vocabulary, while the agnostic", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "sender constantly uses a compact 2-symbol vocabulary. This suggests that the informed sender is", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 571, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 506, + 585 + ], + "score": 1.0, + "content": "using more varied and word-like symbols (recall that the images depict 463 distinct objects, so we", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "would expect a natural-language-endowed sender to use a wider array of symbols to discriminate", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "among them). However, it could also be the case that the informed sender vocabulary simply con-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "score": 1.0, + "content": "tains higher redundancy/synonymy. To check this, we construct a (sampled) matrix where rows are", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 617, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 628 + ], + "score": 1.0, + "content": "game image pairs, columns are symbols, and entries represent how often that symbol is used for that", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "pair. We then decompose the matrix through SVD. If the sender is indeed just using a strategy with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "few effective symbols but high synonymy, then we should expect a 1- or 2-dimensional decomposi-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 648, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 104, + 648, + 505, + 662 + ], + "score": 1.0, + "content": "tion. Figure 2 (right) plots the normalized spectrum of this matrix. While there is some redundancy", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 104, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "in the matrix (thus potentially implying there is synonymy in the usage), the language still requires", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 671, + 437, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 437, + 683 + ], + "score": 1.0, + "content": "multiple dimensions to summarize (cross-validated SVD suggests 50 dimensions).", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "We now turn to investigating the semantic properties of the emergent communication protocol. Re-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "call that the vocabulary that agents use is arbitrary and has no initial meaning. One way to understand", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "its emerging semantics is by looking at the relationship between symbols and the sets of images they", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 719, + 142, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 142, + 733 + ], + "score": 1.0, + "content": "refer to.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 82, + 500, + 254 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 82, + 500, + 254 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 82, + 500, + 254 + ], + "spans": [ + { + "bbox": [ + 109, + 82, + 500, + 254 + ], + "score": 0.962, + "type": "image", + "image_path": "8b7ccb74f6ae2d5d2910b3273bff3233f9d817f0ba835a8d414dbe490337ebfa.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 82, + 500, + 139.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 139.33333333333334, + 500, + 196.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 196.66666666666669, + 500, + 254.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 264, + 505, + 309 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 264, + 506, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 506, + 278 + ], + "score": 1.0, + "content": "Figure 2: Left: Communication success as a function of training iterations, we see that informed", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "senders converge faster than agnostic ones. Right: Spectrum of an example symbol usage matrix:", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "the first few dimensions do capture only partial variance, suggesting that the usage of more symbols", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 298, + 315, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 315, + 312 + ], + "score": 1.0, + "content": "by the informed sender is not just due to synonymy.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "table", + "bbox": [ + 149, + 327, + 462, + 430 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 149, + 327, + 462, + 430 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 149, + 327, + 462, + 430 + ], + "spans": [ + { + "bbox": [ + 149, + 327, + 462, + 430 + ], + "score": 0.978, + "html": "
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Used symbols column", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 506, + 461 + ], + "score": 1.0, + "content": "reports number of distinct vocabulary symbols that were produced at least once in the test phase. See", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 460, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 457, + 473 + ], + "score": 1.0, + "content": "text for explanation of comm success and purity. All purity values are highly significant", + "type": "text" + }, + { + "bbox": [ + 457, + 460, + 502, + 471 + ], + "score": 0.86, + "content": "( p < 0 . 0 0 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 460, + 505, + 473 + ], + "score": 0.0, + "content": "", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "score": 1.0, + "content": "compared to simulated chance symbol assignment when matching observed symbol usage. The obs-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 482, + 496, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 496, + 495 + ], + "score": 1.0, + "content": "chance purity column reports the difference between observed and expected purity under chance.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 437, + 506, + 495 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 522, + 503, + 545 + ], + "lines": [ + { + "bbox": [ + 105, + 521, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 505, + 536 + ], + "score": 1.0, + "content": "converge to coordination quite fast, but the informed sender reaches higher levels more quickly than", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 532, + 177, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 177, + 547 + ], + "score": 1.0, + "content": "the agnostic one.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 521, + 505, + 547 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 550, + 505, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 505, + 563 + ], + "score": 1.0, + "content": "The informed sender makes use of more symbols from the available vocabulary, while the agnostic", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "sender constantly uses a compact 2-symbol vocabulary. This suggests that the informed sender is", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 571, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 506, + 585 + ], + "score": 1.0, + "content": "using more varied and word-like symbols (recall that the images depict 463 distinct objects, so we", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "would expect a natural-language-endowed sender to use a wider array of symbols to discriminate", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "among them). However, it could also be the case that the informed sender vocabulary simply con-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "score": 1.0, + "content": "tains higher redundancy/synonymy. To check this, we construct a (sampled) matrix where rows are", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 617, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 628 + ], + "score": 1.0, + "content": "game image pairs, columns are symbols, and entries represent how often that symbol is used for that", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 104, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "pair. We then decompose the matrix through SVD. If the sender is indeed just using a strategy with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "few effective symbols but high synonymy, then we should expect a 1- or 2-dimensional decomposi-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 648, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 104, + 648, + 505, + 662 + ], + "score": 1.0, + "content": "tion. Figure 2 (right) plots the normalized spectrum of this matrix. While there is some redundancy", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 659, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 104, + 659, + 505, + 673 + ], + "score": 1.0, + "content": "in the matrix (thus potentially implying there is synonymy in the usage), the language still requires", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 671, + 437, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 437, + 683 + ], + "score": 1.0, + "content": "multiple dimensions to summarize (cross-validated SVD suggests 50 dimensions).", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22.5, + "bbox_fs": [ + 104, + 550, + 506, + 683 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "We now turn to investigating the semantic properties of the emergent communication protocol. Re-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "call that the vocabulary that agents use is arbitrary and has no initial meaning. One way to understand", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "its emerging semantics is by looking at the relationship between symbols and the sets of images they", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 719, + 142, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 142, + 733 + ], + "score": 1.0, + "content": "refer to.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 687, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 86, + 489, + 259 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 86, + 489, + 259 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 86, + 489, + 259 + ], + "spans": [ + { + "bbox": [ + 123, + 86, + 489, + 259 + ], + "score": 0.973, + "type": "image", + "image_path": "2ca860e20014c9fd162e1ab3ea2256686254b0b07c3b8026c618d83be37358a3.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 123, + 86, + 489, + 143.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 123, + 143.66666666666666, + 489, + 201.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 123, + 201.33333333333331, + 489, + 259.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 108, + 280, + 504, + 313 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 279, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 293 + ], + "score": 1.0, + "content": "Figure 3: t-SNE plots of object fc vectors color-coded by majority symbols assigned to them by", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 291, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 303 + ], + "score": 1.0, + "content": "informed sender. Object class names shown for a random subset. Left: configuration of 4th row of", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 302, + 253, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 253, + 314 + ], + "score": 1.0, + "content": "Table 1. Right: 2nd row of Table 2.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 333, + 505, + 389 + ], + "lines": [ + { + "bbox": [ + 106, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "The objects in our images were categorized into 20 broader categories (such as weapon and mammal)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "by McRae et al. (2005). If the agents converged to higher level semantic meanings for the symbols,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 354, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 104, + 354, + 506, + 370 + ], + "score": 1.0, + "content": "we would expect that objects belonging to the same category would activate the same symbols, e.g.,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 366, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 379 + ], + "score": 1.0, + "content": "that, say, when the target images depict bayonets and guns, the sender would use the same symbol", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 378, + 377, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 377, + 389 + ], + "score": 1.0, + "content": "to refer to them, whereas cows and guns should not share a symbol.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 394, + 505, + 493 + ], + "lines": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "score": 1.0, + "content": "To quantify this, we form clusters by grouping objects by the symbols that are most often activated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 403, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 419 + ], + "score": 1.0, + "content": "when target images contain them. We then assess the quality of the resulting clusters by measuring", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 416, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 505, + 429 + ], + "score": 1.0, + "content": "their purity with respect to the McRae categories. Purity (Zhao & Karypis, 2003) is a standard", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 427, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 505, + 440 + ], + "score": 1.0, + "content": "measure of cluster “quality”. The purity of a clustering solution is the proportion of category labels", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 437, + 504, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 479, + 451 + ], + "score": 1.0, + "content": "in the clusters that agree with the respective cluster majority category. This number reaches", + "type": "text" + }, + { + "bbox": [ + 480, + 438, + 504, + 449 + ], + "score": 0.86, + "content": "100 \\%", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 448, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 506, + 462 + ], + "score": 1.0, + "content": "for perfect clustering and we always compare the observed purity to the score that would be obtained", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "score": 1.0, + "content": "from a random permutation of symbol assignments to objects. Table 1 shows that purity, while far", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "score": 1.0, + "content": "from perfect, is significantly above chance in all cases. We confirm moreover that the informed", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 482, + 484, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 484, + 495 + ], + "score": 1.0, + "content": "sender is producing symbols that are more semantically natural than those of the agnostic one.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 498, + 504, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 498, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 505, + 512 + ], + "score": 1.0, + "content": "Still, surprisingly, purity is significantly above chance even when the latter is only using two sym-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "score": 1.0, + "content": "bols. From our qualitative evaluations, in this case the agents converge to a (noisy) characterization", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 520, + 506, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 506, + 534 + ], + "score": 1.0, + "content": "of objects as “living-vs-non-living” which, intriguingly, has been recognized as the most basic one", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 532, + 353, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 353, + 543 + ], + "score": 1.0, + "content": "in the human semantic system (Caramazza & Shelton, 1998).", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 549, + 504, + 615 + ], + "lines": [ + { + "bbox": [ + 105, + 548, + 506, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 506, + 561 + ], + "score": 1.0, + "content": "Rather than using hard clusters, we can also ask whether symbol usage reflects the semantics of the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "visual space. To do so we construct vector representations for each object (defined by its ImageNet", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 570, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 506, + 583 + ], + "score": 1.0, + "content": "label) by averaging the CNN fc representations of all category images in our data-set (see Section", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 104, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "3 above). Note that the fc layer, being near the top of a deep CNN, is expected to capture high-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 591, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 605 + ], + "score": 1.0, + "content": "level visual properties of objects (Zeiler & Fergus, 2014). Moreover, since we average across many", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 604, + 469, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 469, + 616 + ], + "score": 1.0, + "content": "specific images, our vectors should capture rather general, high-level properties of objects.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5 + }, + { + "type": "text", + "bbox": [ + 107, + 620, + 504, + 676 + ], + "lines": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "We map these average object vectors to 2 dimensions via t-SNE mapping (Van der Maaten & Hinton,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 630, + 506, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 506, + 644 + ], + "score": 1.0, + "content": "2008) and we color-code them by the majority symbol the sender used for images containing the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 641, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 104, + 641, + 506, + 655 + ], + "score": 1.0, + "content": "corresponding object. Figure 3 (left) shows the results for the current experiment. We see that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 652, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 652, + 506, + 667 + ], + "score": 1.0, + "content": "objects that are close in CNN space (thus, presumably, visually similar) are associated to the same", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 664, + 423, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 664, + 423, + 677 + ], + "score": 1.0, + "content": "symbol (same color). However, there still appears to be quite a bit of variation.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 108, + 690, + 248, + 700 + ], + "lines": [ + { + "bbox": [ + 106, + 689, + 250, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 250, + 701 + ], + "score": 1.0, + "content": "4.1 OBJECT-LEVEL REFERENCE", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "We established that our agents can solve the coordination problem, and we have at least tentative", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "evidence that they do so by developing symbol meanings that align with our semantic intuition. We", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 123, + 86, + 489, + 259 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 86, + 489, + 259 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 86, + 489, + 259 + ], + "spans": [ + { + "bbox": [ + 123, + 86, + 489, + 259 + ], + "score": 0.973, + "type": "image", + "image_path": "2ca860e20014c9fd162e1ab3ea2256686254b0b07c3b8026c618d83be37358a3.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 123, + 86, + 489, + 143.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 123, + 143.66666666666666, + 489, + 201.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 123, + 201.33333333333331, + 489, + 259.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 108, + 280, + 504, + 313 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 279, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 293 + ], + "score": 1.0, + "content": "Figure 3: t-SNE plots of object fc vectors color-coded by majority symbols assigned to them by", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 291, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 303 + ], + "score": 1.0, + "content": "informed sender. Object class names shown for a random subset. Left: configuration of 4th row of", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 302, + 253, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 253, + 314 + ], + "score": 1.0, + "content": "Table 1. Right: 2nd row of Table 2.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 333, + 505, + 389 + ], + "lines": [ + { + "bbox": [ + 106, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 106, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "The objects in our images were categorized into 20 broader categories (such as weapon and mammal)", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "by McRae et al. (2005). If the agents converged to higher level semantic meanings for the symbols,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 354, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 104, + 354, + 506, + 370 + ], + "score": 1.0, + "content": "we would expect that objects belonging to the same category would activate the same symbols, e.g.,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 366, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 505, + 379 + ], + "score": 1.0, + "content": "that, say, when the target images depict bayonets and guns, the sender would use the same symbol", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 378, + 377, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 377, + 389 + ], + "score": 1.0, + "content": "to refer to them, whereas cows and guns should not share a symbol.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8, + "bbox_fs": [ + 104, + 333, + 506, + 389 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 394, + 505, + 493 + ], + "lines": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "score": 1.0, + "content": "To quantify this, we form clusters by grouping objects by the symbols that are most often activated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 403, + 506, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 419 + ], + "score": 1.0, + "content": "when target images contain them. We then assess the quality of the resulting clusters by measuring", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 416, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 505, + 429 + ], + "score": 1.0, + "content": "their purity with respect to the McRae categories. Purity (Zhao & Karypis, 2003) is a standard", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 427, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 505, + 440 + ], + "score": 1.0, + "content": "measure of cluster “quality”. The purity of a clustering solution is the proportion of category labels", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 437, + 504, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 479, + 451 + ], + "score": 1.0, + "content": "in the clusters that agree with the respective cluster majority category. This number reaches", + "type": "text" + }, + { + "bbox": [ + 480, + 438, + 504, + 449 + ], + "score": 0.86, + "content": "100 \\%", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 448, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 506, + 462 + ], + "score": 1.0, + "content": "for perfect clustering and we always compare the observed purity to the score that would be obtained", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "score": 1.0, + "content": "from a random permutation of symbol assignments to objects. Table 1 shows that purity, while far", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 505, + 484 + ], + "score": 1.0, + "content": "from perfect, is significantly above chance in all cases. We confirm moreover that the informed", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 482, + 484, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 484, + 495 + ], + "score": 1.0, + "content": "sender is producing symbols that are more semantically natural than those of the agnostic one.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 394, + 506, + 495 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 498, + 504, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 498, + 505, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 505, + 512 + ], + "score": 1.0, + "content": "Still, surprisingly, purity is significantly above chance even when the latter is only using two sym-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 506, + 523 + ], + "score": 1.0, + "content": "bols. From our qualitative evaluations, in this case the agents converge to a (noisy) characterization", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 520, + 506, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 506, + 534 + ], + "score": 1.0, + "content": "of objects as “living-vs-non-living” which, intriguingly, has been recognized as the most basic one", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 532, + 353, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 353, + 543 + ], + "score": 1.0, + "content": "in the human semantic system (Caramazza & Shelton, 1998).", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 498, + 506, + 543 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 549, + 504, + 615 + ], + "lines": [ + { + "bbox": [ + 105, + 548, + 506, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 506, + 561 + ], + "score": 1.0, + "content": "Rather than using hard clusters, we can also ask whether symbol usage reflects the semantics of the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "visual space. To do so we construct vector representations for each object (defined by its ImageNet", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 570, + 506, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 506, + 583 + ], + "score": 1.0, + "content": "label) by averaging the CNN fc representations of all category images in our data-set (see Section", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 104, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 104, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "3 above). Note that the fc layer, being near the top of a deep CNN, is expected to capture high-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 591, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 605 + ], + "score": 1.0, + "content": "level visual properties of objects (Zeiler & Fergus, 2014). Moreover, since we average across many", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 604, + 469, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 469, + 616 + ], + "score": 1.0, + "content": "specific images, our vectors should capture rather general, high-level properties of objects.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5, + "bbox_fs": [ + 104, + 548, + 506, + 616 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 620, + 504, + 676 + ], + "lines": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "We map these average object vectors to 2 dimensions via t-SNE mapping (Van der Maaten & Hinton,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 630, + 506, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 506, + 644 + ], + "score": 1.0, + "content": "2008) and we color-code them by the majority symbol the sender used for images containing the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 641, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 104, + 641, + 506, + 655 + ], + "score": 1.0, + "content": "corresponding object. Figure 3 (left) shows the results for the current experiment. We see that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 652, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 652, + 506, + 667 + ], + "score": 1.0, + "content": "objects that are close in CNN space (thus, presumably, visually similar) are associated to the same", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 664, + 423, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 664, + 423, + 677 + ], + "score": 1.0, + "content": "symbol (same color). 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In our case, we want", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 283, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 506, + 295 + ], + "score": 1.0, + "content": "to remove facts pertaining to the details of the input images, thus forcing the agents to coordinate on", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 293, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 505, + 307 + ], + "score": 1.0, + "content": "more abstract properties. We can remove all low-level common knowledge by letting the agents play", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "score": 1.0, + "content": "only using class-level properties of the objects. 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We see that the agents are still able to coordinate.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 365, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 378 + ], + "score": 1.0, + "content": "Moreover, we observe a small increase in symbol usage purity, as expected since agents can now", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 376, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 505, + 389 + ], + "score": 1.0, + "content": "only coordinate on general properties of object classes, rather than on the specific properties of each", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 387, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 505, + 400 + ], + "score": 1.0, + "content": "image. This effect is clearer in Figure 3 (right), when we repeat t-SNE based visualization of the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 398, + 504, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 504, + 409 + ], + "score": 1.0, + "content": "relationship that emerges between visual embeddings and the words used to refer to them in this", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 410, + 175, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 175, + 421 + ], + "score": 1.0, + "content": "new experiment.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5 + }, + { + "type": "title", + "bbox": [ + 108, + 443, + 454, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 442, + 457, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 457, + 458 + ], + "score": 1.0, + "content": "5 GROUNDING AGENTS’ COMMUNICATION IN HUMAN LANGUAGE", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 472, + 505, + 527 + ], + "lines": [ + { + "bbox": [ + 106, + 472, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 472, + 505, + 485 + ], + "score": 1.0, + "content": "The results in Section 4 show communication robustly arising in our game, and that we can change", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "the environment to nudge agents to develop symbol meanings which are more closely related to the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 494, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "visual or class-based semantics of the images. 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All purity values significant at", + "type": "text" + }, + { + "bbox": [ + 324, + 162, + 366, + 173 + ], + "score": 0.9, + "content": "p < 0 . 0 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 160, + 370, + 174 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true, + "is_list_end_line": true + } + ], + "index": 3.5, + "bbox_fs": [ + 105, + 149, + 505, + 174 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 199, + 504, + 222 + ], + "lines": [ + { + "bbox": [ + 105, + 198, + 505, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 213 + ], + "score": 1.0, + "content": "turn now to a simple way to tweak the game setup in order to encourage the agents to further pursue", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 210, + 193, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 193, + 223 + ], + "score": 1.0, + "content": "high-level semantics.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 198, + 505, + 223 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 227, + 505, + 348 + ], + "lines": [ + { + "bbox": [ + 105, + 227, + 505, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 505, + 240 + ], + "score": 1.0, + "content": "The strategy is to remove some aspects of “common knowledge” from the game. Common knowl-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 239, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 505, + 251 + ], + "score": 1.0, + "content": "edge, in game-theoretic parlance, are facts that everyone knows, everyone knows that everyone", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 250, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 250, + 505, + 261 + ], + "score": 1.0, + "content": "knows, and so on (Brandenburger et al., 2014). Coordination can only occur if the basis of the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 261, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 106, + 261, + 505, + 272 + ], + "score": 1.0, + "content": "coordination is common knowledge (Rubinstein, 1989), therefore if we remove some facts from", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 272, + 506, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 506, + 284 + ], + "score": 1.0, + "content": "common knowledge, we will preclude our agents from coordinating on them. In our case, we want", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 283, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 506, + 295 + ], + "score": 1.0, + "content": "to remove facts pertaining to the details of the input images, thus forcing the agents to coordinate on", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 293, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 505, + 307 + ], + "score": 1.0, + "content": "more abstract properties. We can remove all low-level common knowledge by letting the agents play", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 317 + ], + "score": 1.0, + "content": "only using class-level properties of the objects. We achieve this by modifying the game to show the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 315, + 506, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 506, + 328 + ], + "score": 1.0, + "content": "agents different pairs of images but maintaining the ImageNet class of both the target and distractor", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 326, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 506, + 339 + ], + "score": 1.0, + "content": "(e.g., if the target is dog, the sender is shown a picture of a Chihuahua and the receiver that of a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 336, + 173, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 173, + 349 + ], + "score": 1.0, + "content": "Boston Terrier).", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 227, + 506, + 349 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 354, + 505, + 420 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "score": 1.0, + "content": "Table 2 reports results for various configurations. We see that the agents are still able to coordinate.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 365, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 378 + ], + "score": 1.0, + "content": "Moreover, we observe a small increase in symbol usage purity, as expected since agents can now", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 376, + 505, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 505, + 389 + ], + "score": 1.0, + "content": "only coordinate on general properties of object classes, rather than on the specific properties of each", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 387, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 505, + 400 + ], + "score": 1.0, + "content": "image. This effect is clearer in Figure 3 (right), when we repeat t-SNE based visualization of the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 398, + 504, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 504, + 409 + ], + "score": 1.0, + "content": "relationship that emerges between visual embeddings and the words used to refer to them in this", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 410, + 175, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 175, + 421 + ], + "score": 1.0, + "content": "new experiment.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 353, + 505, + 421 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 443, + 454, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 442, + 457, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 457, + 458 + ], + "score": 1.0, + "content": "5 GROUNDING AGENTS’ COMMUNICATION IN HUMAN LANGUAGE", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 472, + 505, + 527 + ], + "lines": [ + { + "bbox": [ + 106, + 472, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 472, + 505, + 485 + ], + "score": 1.0, + "content": "The results in Section 4 show communication robustly arising in our game, and that we can change", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "the environment to nudge agents to develop symbol meanings which are more closely related to the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 494, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "visual or class-based semantics of the images. Still, we would like agents to converge on a language", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 504, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 518 + ], + "score": 1.0, + "content": "fully understandable by humans, as our ultimate goal is to develop conversational machines. To do", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 516, + 301, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 301, + 528 + ], + "score": 1.0, + "content": "this, we will need to ground the communication.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 472, + 505, + 528 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 533, + 505, + 610 + ], + "lines": [ + { + "bbox": [ + 105, + 532, + 505, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 547 + ], + "score": 1.0, + "content": "Taking inspiration from AlphaGo (Silver et al., 2016), an AI that reached the Go master level by", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 506, + 558 + ], + "score": 1.0, + "content": "combining interactive learning in games of self-play with passive supervised learning from a large", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "set of human games, we combine the usual referential game, in which agents interactively develop", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 578 + ], + "score": 1.0, + "content": "their communication protocol, with a supervised image labeling task, where the sender must learn", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "to assign objects their conventional names. This way, the sender will naturally be encouraged to use", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 505, + 601 + ], + "score": 1.0, + "content": "such names with their conventional meaning to discriminate target images when playing the game,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 599, + 319, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 319, + 612 + ], + "score": 1.0, + "content": "making communication more transparent to humans.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 532, + 506, + 612 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 616, + 504, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 615, + 504, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 504, + 629 + ], + "score": 1.0, + "content": "In this experiment, the sender switches, equiprobably, between game playing and a supervised im-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 639 + ], + "score": 1.0, + "content": "age classification task using ImageNet classes. Note that the supervised objective does not aim at", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "improving agents’ coordination performance. Instead, supervision provides them with basic ground-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "score": 1.0, + "content": "ing in natural language (in the form of image-label associations), while concurrent interactive game", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 659, + 433, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 433, + 673 + ], + "score": 1.0, + "content": "playing should teach them how to effectively use this grounding to communicate.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 615, + 506, + 673 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 677, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "We use the informed sender, fc image representations and a vocabulary size of 100. Supervised", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "training is based on 100 labels that are a subset of the object names in our data-set (see Section 3", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "above). When predicting object names, the sender uses the usual game-embedding layer coupled", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 708, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 708, + 506, + 723 + ], + "score": 1.0, + "content": "with a softmax layer of dimensionality 100 corresponding to the object names. Importantly, the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "game-embedding layers used in object classification and the reference game are shared. Conse-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 235, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 505, + 249 + ], + "score": 1.0, + "content": "quently, we hope that, when playing, the sender will produce symbols aligned with object names", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 246, + 241, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 241, + 259 + ], + "score": 1.0, + "content": "acquired in the supervised phase.", + "type": "text", + "cross_page": true + } + ], + "index": 6 + } + ], + "index": 44, + "bbox_fs": [ + 105, + 676, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 148, + 81, + 463, + 168 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 148, + 81, + 463, + 168 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 148, + 81, + 463, + 168 + ], + "spans": [ + { + "bbox": [ + 148, + 81, + 463, + 168 + ], + "score": 0.964, + "type": "image", + "image_path": "9dc46da9c68bda1e70a2c5179f3650cd669ccc0cfa553e9eb6447eb64e195bad.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 148, + 81, + 463, + 110.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 148, + 110.0, + 463, + 139.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 148, + 139.0, + 463, + 168.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 181, + 504, + 204 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 179, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 179, + 506, + 196 + ], + "score": 1.0, + "content": "Figure 4: Example pairs from the ReferItGame set, with word produced by sender. Target images", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 191, + 175, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 175, + 205 + ], + "score": 1.0, + "content": "framed in green.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 107, + 235, + 504, + 257 + ], + "lines": [ + { + "bbox": [ + 106, + 235, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 505, + 249 + ], + "score": 1.0, + "content": "quently, we hope that, when playing, the sender will produce symbols aligned with object names", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 246, + 241, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 241, + 259 + ], + "score": 1.0, + "content": "acquired in the supervised phase.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 263, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "score": 1.0, + "content": "The supervised objective has no negative effect on communication success: the agents are still able", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 273, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 390, + 287 + ], + "score": 1.0, + "content": "to reach full coordination after 10k training trials (corresponding to", + "type": "text" + }, + { + "bbox": [ + 390, + 275, + 402, + 285 + ], + "score": 0.62, + "content": "5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 273, + 505, + 287 + ], + "score": 1.0, + "content": "trials of reference game", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "playing). The sender uses many more symbols after training than in any previous experiment (88)", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 295, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 282, + 309 + ], + "score": 1.0, + "content": "and symbol purity dramatically increases to", + "type": "text" + }, + { + "bbox": [ + 282, + 296, + 302, + 307 + ], + "score": 0.85, + "content": "70 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 295, + 506, + 309 + ], + "score": 1.0, + "content": "(the obs-chance purity difference also increases to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 305, + 135, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 126, + 318 + ], + "score": 0.82, + "content": "3 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 305, + 135, + 321 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 324, + 505, + 379 + ], + "lines": [ + { + "bbox": [ + 106, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 106, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "Even more importantly, many symbols have now become directly interpretable, thanks to their direct", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "correspondence to labels. Considering the 632 image pairs where the target gold standard label", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 346, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 410, + 358 + ], + "score": 1.0, + "content": "corresponds to one of the labels that were used in the supervised phase, in", + "type": "text" + }, + { + "bbox": [ + 410, + 346, + 430, + 357 + ], + "score": 0.87, + "content": "47 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 346, + 505, + 358 + ], + "score": 1.0, + "content": "of these cases the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "sender produced exactly the symbol corresponding to the correct supervised label for the target", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 367, + 191, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 170, + 380 + ], + "score": 1.0, + "content": "image (chance:", + "type": "text" + }, + { + "bbox": [ + 170, + 368, + 185, + 379 + ], + "score": 0.8, + "content": "1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 367, + 191, + 380 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 385, + 505, + 516 + ], + "lines": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "For image pairs where the target image belongs to one of the directly supervised categories, it is not", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 396, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 409 + ], + "score": 1.0, + "content": "surprising that the sender adopted the “conventional” supervised label to signal the target . However,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 407, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 419 + ], + "score": 1.0, + "content": "a very interesting effect of supervision is that it improves the interpretability of the code even when", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "agents must communicate about images that do not contain objects in the supervised category set.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 428, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 505, + 442 + ], + "score": 1.0, + "content": "This emerged in a follow-up experiment in which, during training, the sender was again exposed", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 439, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 452 + ], + "score": 1.0, + "content": "(with equal probability) to the same supervised classification task as above, but now the agents", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 451, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 505, + 462 + ], + "score": 1.0, + "content": "played the referential game on a different dataset of images derived from ReferItGame (Kazemzadeh", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 461, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 474 + ], + "score": 1.0, + "content": "et al., 2014). In its general format, the ReferItGame contains annotations of bounding boxes in real", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "score": 1.0, + "content": "images with referring expressions produced by humans when playing the game. For our purposes,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 483, + 504, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 169, + 496 + ], + "score": 1.0, + "content": "we constructed", + "type": "text" + }, + { + "bbox": [ + 169, + 484, + 186, + 494 + ], + "score": 0.25, + "content": "1 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 483, + 504, + 496 + ], + "score": 1.0, + "content": "pairs by randomly sampling two bounding boxes, to act as target and distractor.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "Again, the agents converged to perfect communication after 15k trials, and this time used all 100", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 506, + 235, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 235, + 518 + ], + "score": 1.0, + "content": "available symbols in some trial.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 505, + 632 + ], + "lines": [ + { + "bbox": [ + 106, + 522, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 506, + 535 + ], + "score": 1.0, + "content": "We then asked whether this language was human-interpretable. For each symbol used by the trained", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "sender, we randomly extracted 3 image pairs in which the sender picked that symbol and the receiver", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "pointed at the right target (for two symbols, only 2 pairs matched these criteria, leading to a set of 298", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "image pairs). We annotated each pair with the word corresponding to the symbol in the supervised", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 249, + 579 + ], + "score": 1.0, + "content": "set. Out of the 298 pairs, only 25", + "type": "text" + }, + { + "bbox": [ + 249, + 566, + 270, + 577 + ], + "score": 0.79, + "content": "( 8 \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "included one of the 100 words among the corresponding", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 589 + ], + "score": 1.0, + "content": "referring expressions in ReferItGame. So, in the large majority of cases, the sender had been faced", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 601 + ], + "score": 1.0, + "content": "with a pair not (saliently) containing the categories used in the supervised phase of its training, and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "score": 1.0, + "content": "it had to produce a word that could, at best, only indirectly refer to what is depicted in the target", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 609, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 506, + 622 + ], + "score": 1.0, + "content": "image. We then tested whether this code would be understandable by humans. In essence, it is as if", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 320, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 320, + 634 + ], + "score": 1.0, + "content": "we replaced the trained agent receiver with a human.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 107, + 638, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 637, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 505, + 650 + ], + "score": 1.0, + "content": "We prepared a crowdsourced survey using the CrowdFlower platform. For each pair, human partici-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "pants were shown the two images and the sender-emitted word (that is, the ImageNet label associated", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "to the symbol produced by the sender; see examples in Figure 4). The participants were asked to", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "pick the picture that they thought was most related to the word. We collected 10 ratings for each", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 682, + 126, + 694 + ], + "spans": [ + { + "bbox": [ + 104, + 682, + 126, + 694 + ], + "score": 1.0, + "content": "pair.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 180, + 712 + ], + "score": 1.0, + "content": "We found that in", + "type": "text" + }, + { + "bbox": [ + 181, + 699, + 201, + 709 + ], + "score": 0.87, + "content": "68 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "of the cases the subjects were able to guess the right image. A logistic", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "regression predicting subject image choice from ground-truth target images, with subjects and words", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "as random effects, confirmed the highly significant correlation between the true and guessed images", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2017", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 148, + 81, + 463, + 168 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 148, + 81, + 463, + 168 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 148, + 81, + 463, + 168 + ], + "spans": [ + { + "bbox": [ + 148, + 81, + 463, + 168 + ], + "score": 0.964, + "type": "image", + "image_path": "9dc46da9c68bda1e70a2c5179f3650cd669ccc0cfa553e9eb6447eb64e195bad.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 148, + 81, + 463, + 110.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 148, + 110.0, + 463, + 139.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 148, + 139.0, + 463, + 168.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 181, + 504, + 204 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 179, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 179, + 506, + 196 + ], + "score": 1.0, + "content": "Figure 4: Example pairs from the ReferItGame set, with word produced by sender. Target images", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 191, + 175, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 175, + 205 + ], + "score": 1.0, + "content": "framed in green.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + } + ], + "index": 2.25 + }, + { + "type": "text", + "bbox": [ + 107, + 235, + 504, + 257 + ], + "lines": [], + "index": 5.5, + "bbox_fs": [ + 106, + 235, + 505, + 259 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 263, + 505, + 318 + ], + "lines": [ + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 275 + ], + "score": 1.0, + "content": "The supervised objective has no negative effect on communication success: the agents are still able", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 273, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 273, + 390, + 287 + ], + "score": 1.0, + "content": "to reach full coordination after 10k training trials (corresponding to", + "type": "text" + }, + { + "bbox": [ + 390, + 275, + 402, + 285 + ], + "score": 0.62, + "content": "5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 273, + 505, + 287 + ], + "score": 1.0, + "content": "trials of reference game", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 506, + 298 + ], + "score": 1.0, + "content": "playing). The sender uses many more symbols after training than in any previous experiment (88)", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 295, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 282, + 309 + ], + "score": 1.0, + "content": "and symbol purity dramatically increases to", + "type": "text" + }, + { + "bbox": [ + 282, + 296, + 302, + 307 + ], + "score": 0.85, + "content": "70 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 295, + 506, + 309 + ], + "score": 1.0, + "content": "(the obs-chance purity difference also increases to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 305, + 135, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 126, + 318 + ], + "score": 0.82, + "content": "3 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 127, + 305, + 135, + 321 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 263, + 506, + 321 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 324, + 505, + 379 + ], + "lines": [ + { + "bbox": [ + 106, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 106, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "Even more importantly, many symbols have now become directly interpretable, thanks to their direct", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "correspondence to labels. Considering the 632 image pairs where the target gold standard label", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 346, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 410, + 358 + ], + "score": 1.0, + "content": "corresponds to one of the labels that were used in the supervised phase, in", + "type": "text" + }, + { + "bbox": [ + 410, + 346, + 430, + 357 + ], + "score": 0.87, + "content": "47 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 346, + 505, + 358 + ], + "score": 1.0, + "content": "of these cases the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "sender produced exactly the symbol corresponding to the correct supervised label for the target", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 367, + 191, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 170, + 380 + ], + "score": 1.0, + "content": "image (chance:", + "type": "text" + }, + { + "bbox": [ + 170, + 368, + 185, + 379 + ], + "score": 0.8, + "content": "1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 367, + 191, + 380 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 324, + 505, + 380 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 385, + 505, + 516 + ], + "lines": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "For image pairs where the target image belongs to one of the directly supervised categories, it is not", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 396, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 409 + ], + "score": 1.0, + "content": "surprising that the sender adopted the “conventional” supervised label to signal the target . However,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 407, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 419 + ], + "score": 1.0, + "content": "a very interesting effect of supervision is that it improves the interpretability of the code even when", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 431 + ], + "score": 1.0, + "content": "agents must communicate about images that do not contain objects in the supervised category set.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 428, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 505, + 442 + ], + "score": 1.0, + "content": "This emerged in a follow-up experiment in which, during training, the sender was again exposed", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 439, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 452 + ], + "score": 1.0, + "content": "(with equal probability) to the same supervised classification task as above, but now the agents", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 451, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 505, + 462 + ], + "score": 1.0, + "content": "played the referential game on a different dataset of images derived from ReferItGame (Kazemzadeh", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 461, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 474 + ], + "score": 1.0, + "content": "et al., 2014). In its general format, the ReferItGame contains annotations of bounding boxes in real", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 486 + ], + "score": 1.0, + "content": "images with referring expressions produced by humans when playing the game. For our purposes,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 483, + 504, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 169, + 496 + ], + "score": 1.0, + "content": "we constructed", + "type": "text" + }, + { + "bbox": [ + 169, + 484, + 186, + 494 + ], + "score": 0.25, + "content": "1 0 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 483, + 504, + 496 + ], + "score": 1.0, + "content": "pairs by randomly sampling two bounding boxes, to act as target and distractor.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "Again, the agents converged to perfect communication after 15k trials, and this time used all 100", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 506, + 235, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 235, + 518 + ], + "score": 1.0, + "content": "available symbols in some trial.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 385, + 506, + 518 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 505, + 632 + ], + "lines": [ + { + "bbox": [ + 106, + 522, + 506, + 535 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 506, + 535 + ], + "score": 1.0, + "content": "We then asked whether this language was human-interpretable. For each symbol used by the trained", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "sender, we randomly extracted 3 image pairs in which the sender picked that symbol and the receiver", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "pointed at the right target (for two symbols, only 2 pairs matched these criteria, leading to a set of 298", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "image pairs). We annotated each pair with the word corresponding to the symbol in the supervised", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 249, + 579 + ], + "score": 1.0, + "content": "set. Out of the 298 pairs, only 25", + "type": "text" + }, + { + "bbox": [ + 249, + 566, + 270, + 577 + ], + "score": 0.79, + "content": "( 8 \\% )", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "included one of the 100 words among the corresponding", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 577, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 589 + ], + "score": 1.0, + "content": "referring expressions in ReferItGame. So, in the large majority of cases, the sender had been faced", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 588, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 588, + 506, + 601 + ], + "score": 1.0, + "content": "with a pair not (saliently) containing the categories used in the supervised phase of its training, and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "score": 1.0, + "content": "it had to produce a word that could, at best, only indirectly refer to what is depicted in the target", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 609, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 506, + 622 + ], + "score": 1.0, + "content": "image. We then tested whether this code would be understandable by humans. In essence, it is as if", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 621, + 320, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 320, + 634 + ], + "score": 1.0, + "content": "we replaced the trained agent receiver with a human.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 522, + 506, + 634 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 638, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 637, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 505, + 650 + ], + "score": 1.0, + "content": "We prepared a crowdsourced survey using the CrowdFlower platform. For each pair, human partici-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 661 + ], + "score": 1.0, + "content": "pants were shown the two images and the sender-emitted word (that is, the ImageNet label associated", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "to the symbol produced by the sender; see examples in Figure 4). The participants were asked to", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "pick the picture that they thought was most related to the word. We collected 10 ratings for each", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 682, + 126, + 694 + ], + "spans": [ + { + "bbox": [ + 104, + 682, + 126, + 694 + ], + "score": 1.0, + "content": "pair.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41, + "bbox_fs": [ + 104, + 637, + 505, + 694 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 180, + 712 + ], + "score": 1.0, + "content": "We found that in", + "type": "text" + }, + { + "bbox": [ + 181, + 699, + 201, + 709 + ], + "score": 0.87, + "content": "68 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "of the cases the subjects were able to guess the right image. A logistic", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "regression predicting subject image choice from ground-truth target images, with subjects and words", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "as random effects, confirmed the highly significant correlation between the true and guessed images", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 109, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 109, + 83, + 156, + 93 + ], + "score": 0.82, + "content": "( z ~ = ~ 1 6 . 7 5", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 157, + 81, + 161, + 96 + ], + "score": 1.0, + "content": ",", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 162, + 83, + 214, + 94 + ], + "score": 0.83, + "content": "p \\ < \\ 0 . 0 0 0 1 ", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 215, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "). Thus, while far from perfect, we find that supervised learning on a", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "separate data set does provide some grounding for communication with humans, that generalizes", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 407, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 407, + 117 + ], + "score": 1.0, + "content": "beyond the conventional word denotations learned in the supervised phase.", + "type": "text", + "cross_page": true + } + ], + "index": 2 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 698, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 115 + ], + "lines": [ + { + "bbox": [ + 109, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 109, + 83, + 156, + 93 + ], + "score": 0.82, + "content": "( z ~ = ~ 1 6 . 7 5", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 81, + 161, + 96 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 162, + 83, + 214, + 94 + ], + "score": 0.83, + "content": "p \\ < \\ 0 . 0 0 0 1 ", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "). Thus, while far from perfect, we find that supervised learning on a", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "separate data set does provide some grounding for communication with humans, that generalizes", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 407, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 407, + 117 + ], + "score": 1.0, + "content": "beyond the conventional word denotations learned in the supervised phase.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 122, + 505, + 231 + ], + "lines": [ + { + "bbox": [ + 105, + 121, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 505, + 134 + ], + "score": 1.0, + "content": "Looking at the results qualitatively, we found that very often sender-subject communication suc-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "ceeded when the sender established a sort of “metonymic” link between the words in its possession", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 142, + 506, + 157 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 506, + 157 + ], + "score": 1.0, + "content": "and the contents of an image. Figure 4 shows an example where the sender produced dolphin to", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 506, + 166 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 506, + 166 + ], + "score": 1.0, + "content": "refer to a picture showing a stretch of sea, and fence for a patch of land. Similar semantic shifts", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "are a core characteristic of natural language (e.g., Pustejovsky, 1995), and thus subjects were, in", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 177, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 505, + 188 + ], + "score": 1.0, + "content": "many cases, able to successfully play the referential game with our sender (10/10 subjects guessed", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 506, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 201 + ], + "score": 1.0, + "content": "the dolphin target, and 8/10 the fence). This is very encouraging. Although the language developed", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "in referential games will be initially very limited, if both agents and humans possess the sort of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "flexibility displayed in this last experiment, the noisy but shared common ground might suffice to", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 220, + 234, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 220, + 234, + 232 + ], + "score": 1.0, + "content": "establish basic communication.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 7.5 + }, + { + "type": "title", + "bbox": [ + 107, + 248, + 190, + 261 + ], + "lines": [ + { + "bbox": [ + 105, + 246, + 192, + 263 + ], + "spans": [ + { + "bbox": [ + 105, + 246, + 192, + 263 + ], + "score": 1.0, + "content": "6 DISCUSSION", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 273, + 505, + 339 + ], + "lines": [ + { + "bbox": [ + 106, + 273, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 505, + 286 + ], + "score": 1.0, + "content": "Our results confirmed that fairly simple neural-network agents can learn to coordinate in a referential", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 285, + 506, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 298 + ], + "score": 1.0, + "content": "game in which they need to communicate about a large number of real pictures. They also suggest", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 295, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 505, + 309 + ], + "score": 1.0, + "content": "that the meanings agents come to assign to symbols in this setup capture general conceptual prop-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 307, + 505, + 319 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 505, + 319 + ], + "score": 1.0, + "content": "erties of the objects depicted in the image, rather than low-level visual properties. We also showed", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 318, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 505, + 330 + ], + "score": 1.0, + "content": "a path to grounding the communication in natural language by mixing the game with a supervised", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 328, + 128, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 128, + 340 + ], + "score": 1.0, + "content": "task.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 107, + 345, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 105, + 345, + 504, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 504, + 358 + ], + "score": 1.0, + "content": "In future work, encouraged by our preliminary experiments with object naming, we want to study", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "score": 1.0, + "content": "how to ensure that the emergent communication stays close to human natural language. Predictive", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 366, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 366, + 505, + 381 + ], + "score": 1.0, + "content": "learning should be retained as an important building block of intelligent agents, focusing on teaching", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 378, + 505, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 391 + ], + "score": 1.0, + "content": "them structural properties of language (e.g., lexical choice, syntax or style). However, it is also", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "score": 1.0, + "content": "important to learn the function-driven facets of language, such as how to hold a conversation, and", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 401, + 390, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 390, + 412 + ], + "score": 1.0, + "content": "interactive games are a potentially fruitful method to achieve this goal.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5 + }, + { + "type": "title", + "bbox": [ + 107, + 429, + 175, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 176, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 176, + 442 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 448, + 504, + 471 + ], + "lines": [ + { + "bbox": [ + 104, + 447, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 104, + 447, + 505, + 461 + ], + "score": 1.0, + "content": "John Langshaw Austin. 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Springer, New", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 116, + 594, + 167, + 608 + ], + "spans": [ + { + "bbox": [ + 116, + 594, + 167, + 608 + ], + "score": 1.0, + "content": "York, 2002.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 105, + 615, + 504, + 639 + ], + "lines": [ + { + "bbox": [ + 106, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "Alfonso Caramazza and Jennifer Shelton. Domain-specific knowledge systems in the brain the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 115, + 626, + 459, + 639 + ], + "spans": [ + { + "bbox": [ + 115, + 626, + 459, + 639 + ], + "score": 1.0, + "content": "animate-inanimate distinction. 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sha256:87879bc2dcf3d5c54b46dab505e8b88d9b2e6451b20ee4dd6f41db728bc32e9e +size 32082 diff --git a/parse/train/Hkn7CBaTW/Hkn7CBaTW.md b/parse/train/Hkn7CBaTW/Hkn7CBaTW.md new file mode 100644 index 0000000000000000000000000000000000000000..1adb4899513b0f068a997097844e1fc2db522fbb --- /dev/null +++ b/parse/train/Hkn7CBaTW/Hkn7CBaTW.md @@ -0,0 +1,492 @@ +# LEARNING HOW TO EXPLAIN NEURAL NETWORKS: PATTERNNET AND PATTERNATTRIBUTION + +Pieter-Jan Kindermans∗ Google Brain pikinder@google.com + +Kristof T. Schutt & Maximilian Alber ¨ +TU Berlin +{kristof.schuett,maximilian.alber}@tu-berlin.de + +# Klaus-Robert Muller ¨ † + +TU Berlin klaus-robert.mueller@tu-berlin.de + +Dumitru Erhan & Been Kim Google Brain {dumitru,beenkim}@google.com + +# Sven Dahne ¨ ‡ + +TU Berlin sven.daehne@tu-berlin.de + +# ABSTRACT + +DeConvNet, Guided BackProp, LRP, were invented to better understand deep neural networks. We show that these methods do not produce the theoretically correct explanation for a linear model. Yet they are used on multi-layer networks with millions of parameters. This is a cause for concern since linear models are simple neural networks. We argue that explanation methods for neural nets should work reliably in the limit of simplicity, the linear models. Based on our analysis of linear models we propose a generalization that yields two explanation techniques (PatternNet and PatternAttribution) that are theoretically sound for linear models and produce improved explanations for deep networks. + +# 1 INTRODUCTION + +Deep learning made a huge impact on a wide variety of applications (Krizhevsky et al., 2012; Sutskever et al., 2014; LeCun et al., 2015; Schmidhuber, 2015; Mnih et al., 2015; Silver et al., 2016) and recent neural network classifiers have become excellent at detecting relevant signals (e.g., the presence of a cat) contained in input data points such as images by filtering out all other, nonrelevant and distracting components also present in the data. This separation of signal and distractors is achieved by passing the input through many layers with millions of parameters and nonlinear activation functions in between, until finally at the output layer, these models yield a highly condensed version of the signal, e.g. a single number indicating the probability of a cat being in the image. + +While deep neural networks learn efficient and powerful representations, they are often considered a ‘black-box’. In order to better understand classifier decisions and to gain insight into how these models operate, a variety techniques have been proposed (Simonyan et al., 2014; Yosinski et al., 2015; Nguyen et al., 2016; Baehrens et al., 2010; Bach et al., 2015; Montavon et al., 2017; Zeiler & Fergus, 2014; Springenberg et al., 2015; Zintgraf et al., 2017; Sundararajan et al., 2017; Smilkov et al., 2017). These methods for explaining classifier decisions operate under the assumption that it is possible to propagate the condensed output signal back through the classifier to arrive at something that shows how the relevant signal was encoded in the input and thereby explains the classifier decision. Simply put, if the classifier detected a cat, the visualization should point to the cat-relevant aspects of the input image from the perspective of the network. Techniques that are based on this principle include saliency maps from network gradients (Baehrens et al., 2010; Simonyan et al., 2014), DeConvNet (Zeiler & Fergus, 2014, DCN), Guided BackProp (Springenberg et al., 2015, GBP), + +![](images/4d83e01158e9f8a863d901e0e6ac69cef72b6c29330d69f35b721d2d995ef1cd.jpg) +Figure 1: Illustration of explanation approaches. Function and signal approximators visualize the explanation using the original color channels. The attribution is visualized as a heat map of pixelwise contributions to the output + +Layer-wise Relevance Propagation (Bach et al., 2015, LRP) and the Deep Taylor Decomposition (Montavon et al., 2017, DTD), Integrated Gradients (Sundararajan et al., 2017) and SmoothGrad (Smilkov et al., 2017). + +The merit of explanation methods is often demonstrated by applying them to state-of-the-art deep learning models in the context of high dimensional real world data, such as ImageNet, where the provided explanation is intuitive to humans. Unfortunately, theoretical analysis as well as quantitative empirical evaluations of these methods are lacking. + +Deep neural networks are essentially a composition of linear transformations connected with nonlinear activation functions. Since approaches, such as DeConvNet, Guided BackProp, and LRP, back-propagate the explanations in a layer-wise fashion, it is crucial that the individual linear layers are handled correctly. In this work we show that these gradient-based methods fail to recover the signal even for a single-layer architecture, i.e. a linear model. We argue that therefore they cannot be expected to reliably explain a deep neural network and demonstrate this with quantitative and qualitative experiments. In particular, we provide the following key contributions: + +• We analyze the performance of existing explanation approaches in the controlled setting of a linear model (Sections 2 and 3). +• We categorize explanation methods into three groups – functions, signals and attribution (see Fig. 1) – that require fundamentally different interpretations and are complementary in terms of information about the neural network (Section 3). +• We propose two novel explanation methods – PatternNet and PatternAttribution – that alleviate shortcomings of current approaches, as discovered during our analysis, and improve explanations in real-world deep neural networks visually and quantitatively (Sections 4 and 5). + +This presents a step towards a thorough analysis of explanation methods and suggests qualitatively and measurably improved explanations. These are crucial requirements for reliable explanation techniques, in particular in domains, where explanations are not necessarily intuitive, e.g. in health and the sciences Schutt et al. (2017). ¨ + +Notation and scope Scalars are lowercase letters $( i )$ , column vectors are bold $( \pmb { u } )$ , element-wise multiplication is $( \odot )$ . The covariance between $\textbf { \em u }$ and $\textbf { { v } }$ is $\boldsymbol { \mathbf { \rho } } _ { \mathbf { 0 } } \mathbf { v } [ \pmb { u } , \pmb { v } ]$ , the covariance of $\textbf { \em u }$ and $i$ is $\mathrm { c o v } [ \bar { \boldsymbol { u } } , i ]$ . The variance of a scalar random variable $i$ is $\sigma _ { i } ^ { 2 }$ . Estimates of random variables will have a hat $( \hat { u } )$ . We analyze neural networks excluding the final soft-max output layer. To allow for analytical treatment, we only consider networks with linear neurons optionally followed by a rectified linear unit (ReLU), max-pooling or soft-max. We analyze linear neurons and nonlinearities independently such that every neuron has its own weight vector. These restrictions are similar to those in the saliency map (Simonyan et al., 2014), DCN (Zeiler & Fergus, 2014), GBP (Springenberg et al., 2015), LRP (Bach et al., 2015) and DTD (Montavon et al., 2017). Without loss of generality, biases are considered constant neurons to enhance clarity. + +![](images/fadc0d3e80752b97d7b31564914d142aeb247209fdb0365ffc20487b5064a4a4.jpg) +Figure 2: For linear models, i.e., a simple neural network, the weight vector does not explain the signal it detects Haufe et al. (2014). The data ${ \pmb x } = y { \pmb a } _ { s } + \epsilon { \pmb a } _ { d }$ is color-coded w.r.t. the output $\mathbf { \Psi } y = \pmb { w } ^ { T } \mathbf { \em x }$ . Only the signal $\mathit { s } = y \mathbf { a } _ { s }$ contributes to $y$ . The weight vector $\pmb { w }$ does not agree with the signal direction, since its primary objective is canceling the distractor. Therefore, rotations of the basis vector $\mathbf { \mu } _ { a _ { d } }$ of the distractor with constant signal $\pmb { s }$ lead to rotations of the weight vector (right). + +# 2 UNDERSTANDING LINEAR MODELS + +In this section, we analyze explanation methods for deep neural network, starting with the simplest neural network setting: a purely linear model and data sampled from a linear generative model. This setup allows us to (i) fully control how signal and distractor components are encoded in the input data and (ii) analytically track how the resulting explanation relates to the known signal component. This analysis allows us then to highlight shortcomings of current explanation approaches that carry over to deep neural networks. + +Consider the following toy example (see Fig. 2) where we generate data $_ { \textbf { \em x } }$ as: + +$$ +\begin{array} { r l r l r l r l } { x = s + d } & { } & & { \quad s = a _ { s } y , } & { \quad } & { \mathrm { ~ w i t h ~ } a _ { s } = \left( 1 , 0 \right) ^ { T } , } & { } & { \quad y \in [ - 1 , 1 ] } \\ & { } & & { \quad d = a _ { d } \epsilon , } & { } & & { \mathrm { ~ w i t h ~ } a _ { d } = \left( 1 , 1 \right) ^ { T } , } & { } & { \epsilon \sim \mathcal { N } \left( \mu , \sigma ^ { 2 } \right) . } \end{array} +$$ + +We train a linear regression model to extract $y$ from $_ { \textbf { \em x } }$ . By construction, $\pmb { s }$ is the signal in our data, i.e., the part of $_ { \textbf { \em x } }$ containing information about $y$ . Using the terminology of Haufe et al. (2014) the distractor $^ d$ obfuscates the signal making the detection task more difficult. To optimally extract $y$ , our model has to be able to filter out the distractor $^ d$ . This is why the weight vector is also called the filter. In the example, $\mathbf { \boldsymbol { w } } = \left[ 1 , - 1 \right] ^ { T }$ fulfills this convex task. + +From this example, we can make several observations: The optimal weight vector $\textbf { \em w }$ does not align, in general, with the signal direction $\mathbf { \delta } _ \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathbf { \delta } \mathrm { \delta } \mathbf { \delta } \mathbf { \delta } \mathrm { \delta } \mathbf { \delta } \mathrm { \delta } \mathbf { \delta } \mathrm { \delta } \mathbf { \delta } \mathrm { \delta } \mathbf { \delta } \mathrm { \delta } \mathrm { \delta } \mathbf { \delta } \mathrm { \delta } \mathrm { \delta } \mathbf { \delta } \mathrm { \delta } \mathrm { \delta } \mathrm { \delta } \mathrm { \delta } \mathrm \mathbf { \delta } \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm { \delta } \mathrm \mathrm \mathrm { \delta } \mathrm \mathrm \mathrm { \delta } \mathrm \mathrm \delta \mathrm \mathrm { \delta } \delta \mathrm \mathrm \delta \mathrm \mathrm \mathrm { \delta } \delta \delta \mathrm \delta \mathrm \mathrm \delta \mathrm \delta \mathrm \delta \mathrm \delta \mathrm \delta \mathrm \delta \mathrm \delta \delta \mathrm \delta \delta \delta \mathrm \delta \delta \delta \delta \delta \delta \mathrm \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta \delta$ , but tries to filter the contribution of the distractor (see Fig. 2). This is optimally solved when the weight vector is orthogonal to the distractor ${ \pmb w } ^ { T } { \pmb d } = 0$ . Therefore, when the direction of the distractor $\mathbf { \delta } _ { \mathbf { \alpha } \mathbf { \delta } \mathbf { \alpha } \mathbf { \textit { a } } }$ changes, $\textbf { \em w }$ must follow, as illustrated on the right hand side of the figure. On the other hand, a change in signal direction $\mathbf { \delta } _ { a _ { s } }$ can be compensated for by a change in sign and magnitude of $\pmb { w }$ such that $\mathbf { \bar { w } } ^ { T } \pmb { a } _ { s } \equiv 1$ , but the direction stays constant. + +The fact that the direction of the weight vector in a linear model is largely determined by the distractor implies that given only the weight vector, we cannot know what part of the input produces the output $y$ . On the contrary, the direction $\mathbf { \delta } _ { a _ { s } }$ must be learned from data. + +Now assume that we have additive isotropic Gaussian noise. The mean of the noise can easily be compensated for with a bias change. Therefore, we only have to consider the zero-mean case. Since isotropic Gaussian noise does not contain any correlations or structure, the only way to remove it is by averaging over different measurements. It is not possible to cancel it out effectively by using a well-chosen weight vector. However, it is well known that adding Gaussian noise shrinks the weight vector and corresponds to L2 regularization. In the absence of a structured distractor, the smallest weight vector $\textbf { \em w }$ such that ${ \pmb w } ^ { T } { \pmb a } _ { s } = 1$ is the one in the direction of the signal. Therefore in practice both these effects influence the actual weight vector. + +As already indicated above, deep neural networks are essentially a composition of linear layers and non-linear activation functions. In the next section, we will show that gradient-based methods, e.g., DeConvNet, Guided BackProp, and LRP, are not able to distinguish signal from distractor in a linear model and therefore back-propagate sub-optimal explanations in deeper networks. This analysis allows us to develop improved layer-wise explanation techniques and to demonstrate quantitative and qualitative better explanations for deep neural networks. + +Terminology Throughout this manuscript we will use the following terminology: The filter $\pmb { w }$ tells us how to extract the output $y$ optimally from data $_ { \textbf { \em x } }$ . The pattern $\mathbf { \delta } _ { a _ { s } }$ is the direction in the data along which the desired output $y$ varies. Both constitute the signal $\textbf { \em s } = \textbf { \em a } _ { s } y$ , i.e., the contributing part of $_ { \textbf { \em x } }$ . The distractor $^ d$ is the component of the data that does not contain information about the desired output. + +# 3 OVERVIEW OF EXPLANATION APPROACHES AND THEIR BEHAVIOR + +In this section, we take a look at a subset of explanation methods for individual classifier decisions and discuss how they are connected to our analysis of linear models in the previous section. Fig. 1 gives an overview of the different types of explanation methods which can be divided into function, signal and attribution visualizations. These three groups all present different information about the network and complement each other. + +Functions – gradients, saliency map Explaining the function in input space corresponds to describing the operations the model uses to extract $y$ from $_ { \textbf { \em x } }$ . Since deep neural networks are highly nonlinear, this can only be approximated. The saliency map estimates how moving along a particular direction in input space influences $y$ (i.e., sensitivity analysis) where the direction is given by the model gradient (Baehrens et al., 2010; Simonyan et al., 2014). In case of a linear model $y = \dot { \pmb { w } } ^ { T } \pmb { x }$ , the saliency map reduces to analyzing the weights $\partial y / \partial x = w$ . Since it is mostly determined by the distractor, as demonstrated above, it is not representing the signal. It tells us how to extract the signal, not what the signal is in a deep neural network. + +Signal – DeConvNet, Guided BackProp, PatternNet The signal $\pmb { s }$ detected by the neural network is the component of the data that caused the networks activations. Zeiler & Fergus (2014) formulated the goal of these methods as ”[...] to map these activities back to the input pixel space, showing what input pattern originally caused a given activation in the feature maps”. + +In a linear model, the signal corresponds to $\mathbf { \boldsymbol { s } } = \mathbf { \boldsymbol { a } } _ { s } \boldsymbol { y }$ . The pattern $\mathbf { \delta } _ { \mathbf { \alpha } \mathbf { \delta } _ { a _ { s } } }$ contains the signal direction, i.e., it tells us where a change of the output variable is expected to be measurable in the input (Haufe et al., 2014). Attempts to visualize the signal for deep neural networks were made using DeConvNet (Zeiler & Fergus, 2014) and Guided BackProp (Springenberg et al., 2015). These use the same algorithm as the saliency map, but treat the rectifiers differently (see Fig. 1): DeConvNet leaves out the rectifiers from the forward pass, but adds additional ReLUs after each deconvolution, while Guided BackProp uses the ReLUs from the forward pass as well as additional ones. The back-projections for the linear components of the network correspond to a superposition of what are assumed to be the signal directions of each neuron. For this reason, these projections must be seen as an approximation of the features that activated the higher layer neuron. It is not a reconstruction in input space (Zeiler & Fergus, 2014). + +For the simplest of neural networks – the linear model – these visualizations reduce to the gradient1. They show the filter $\pmb { w }$ and neither the pattern $\mathbf { \delta } _ { a _ { s } }$ , nor the signal $\pmb { s }$ . Hence, DeConvNet and Guided BackProp do not guarantee to produce the detected signal for a linear model, which is proven by our toy example in Fig. 2. Since they do produce compelling visualizations, we will later investigate whether the direction of the filter $\pmb { w }$ coincides with the direction of the signal $\pmb { s }$ . We will show that this is not the case and propose a new approach, PatternNet (see Fig. 1), to estimate the correct direction that improves upon the DeConvNet and Guided BackProp visualizations. + +Attribution – LRP, Deep Taylor Decomposition, PatternAttribution Finally, we can look at how much the signal dimensions contribute to the output through the layers. This will be referred to as the attribution. For a linear model, the optimal attribution would be obtained by element-wise multiplying the signal with the weight vector: $\mathbf { \boldsymbol { r } } ^ { i n p u t } = \mathbf { \boldsymbol { w } } \odot \mathbf { \boldsymbol { a } } y$ , with $\odot$ the element-wise multiplication. Bach et al. (2015) introduced layer-wise relevance propagation (LRP) as a decomposition of pixel-wise contributions (called relevances). Montavon et al. (2017) extended this idea and proposed the deep Taylor decomposition (DTD). The key idea of DTD is to decompose the activation of a neuron in terms of contributions from its inputs. This is achieved using a first-order Taylor expansion around a root point $\scriptstyle { \mathbf { { \mathit { x } } } } _ { 0 }$ with ${ \pmb w } ^ { T } { \pmb x } _ { 0 } = 0$ . The relevance of the selected output neuron $i$ is initialized with its output from the forward pass. The relevance from neuron $i$ in layer $l$ is re-distributed towards its input as: + +$$ +r _ { i } ^ { o u t p u t } = y , \qquad r _ { j \neq i } ^ { o u t p u t } = 0 , \qquad r ^ { l - 1 , i } = \frac { w \odot ( x - x _ { 0 } ) } { w ^ { T } x } r _ { i } ^ { l } . +$$ + +To obtain the relevance for neuron $i$ in layer $l - 1$ the incoming relevances from all connected neurons $j$ in layer $l$ are summed + +$$ +r _ { i } ^ { l - 1 } = \sum _ { j } r _ { i } ^ { l - 1 , j } . +$$ + +Here we can safely assume that ${ \pmb w } ^ { T } { \pmb x } > 0$ because a non-active ReLU unit from the forward pass stops the re-distribution in the backward pass. This is identical to how a ReLU stops the propagation of the gradient. The difficulty in the application of the deep Taylor decomposition is the choice of the root point $\scriptstyle { \pmb x } _ { 0 }$ , for which many options are available. It is important to recognize at this point that selecting a root point for the DTD corresponds to estimating the distractor $\scriptstyle { \pmb { x } } _ { 0 } = { \pmb { d } }$ and, by that, the signal $\hat { \pmb { s } } = \pmb { x } - \pmb { x } _ { 0 }$ . PatternAttribution is a DTD extension that learns from data how to set the root point. + +Summarizing, the function extracts the signal from the data by removing the distractor. The attribution of output values to input dimensions shows how much an individual component of the signal contributes to the output, which is what LRP calls relevance. + +# 4 LEARNING TO ESTIMATE THE SIGNAL + +Visualizing the function has proven to be straightforward (Baehrens et al., 2010; Simonyan et al., 2014). In contrast, visualizing the signal (Haufe et al., 2014; Zeiler & Fergus, 2014; Springenberg et al., 2015) and the attribution (Bach et al., 2015; Montavon et al., 2017; Sundararajan et al., 2017) is more difficult. It requires a good estimate of what is the signal and what is the distractor. In the following section we first propose a quality measure for neuron-wise signal estimators. This allows us to evaluate existing approaches and, finally, derive signal estimators that optimize this criterion. These estimators will then be used to explain the signal (PatternNet) and the attribution (PatternAttribution). All mentioned techniques as well as our proposed signal estimators treat neurons independently, i.e., the full explanation will be a superposition of neuron-wise explanations. + +# 4.1 QUALITY CRITERION FOR SIGNAL ESTIMATORS + +Recall that the input data $_ { \textbf { \em x } }$ comprises both signal and distractor: ${ \pmb x } = { \pmb s } + { \pmb d }$ , and that the signal contributes to the output but the distractor does not. Assuming the filter $\textbf { \em w }$ has been trained sufficiently well to extract $y$ , we have + +$$ +\begin{array} { r } { \boldsymbol { w } ^ { T } \boldsymbol { x } = \boldsymbol { y } , \quad \boldsymbol { w } ^ { T } \boldsymbol { s } = \boldsymbol { y } , \quad \boldsymbol { w } ^ { T } \boldsymbol { d } = 0 . } \end{array} +$$ + +Note that estimating the signal based on these conditions alone is an ill-posed problem. We could limit ourselves to linear estimators of the form $\hat { \pmb { s } } = \pmb { u } ( \pmb { w } ^ { T } \pmb { u } ) ^ { - 1 } \pmb { y }$ , with $\textbf { \em u }$ a random vector such that $\pmb { w } ^ { T } \pmb { u } \neq 0$ . For such an estimator, the signal estimate $\hat { \pmb { s } } = \pmb { u } \left( \pmb { w } ^ { T } \pmb { u } \right) ^ { - 1 } \ b { y }$ satisfies $\mathbf { \boldsymbol { w } } ^ { T } \hat { \mathbf { \boldsymbol { s } } } = \boldsymbol { y }$ . This implies the existence of an infinite number of possible rules for the DTD as well as infinitely many back-projections for the DeConvNet family. + +To alleviate this issue, we introduce the following quality measure $\rho$ for a signal estimator $S ( { \pmb x } ) = \hat { \pmb s }$ that will be written with explicit variances and covariances using the shorthands $\hat { \pmb { d } } = \pmb { x } - \pmb { S } ( \pmb { x } )$ and + +$$ +y = \pmb { w } ^ { T } \pmb { x } \colon +$$ + +$$ +\rho ( S ) = 1 - \operatorname* { m a x } _ { \pmb { v } } c o r r \left( \pmb { w } ^ { T } \pmb { x } , \pmb { v } ^ { T } \left( \pmb { x } - S ( \pmb { x } ) \right) \right) = 1 - \operatorname* { m a x } _ { \pmb { v } } \frac { \pmb { v } ^ { T } \mathrm { c o v } [ \hat { d } , y ] } { \sqrt { \sigma _ { \pmb { v } ^ { T } \hat { d } } ^ { 2 } \sigma _ { y } ^ { 2 } } } . +$$ + +This criterion introduces an additional constraint by measuring how much information about $y$ can be reconstructed from the residuals $\mathbf { \Delta } \mathbf { x } - \hat { \mathbf { \mu } } _ { s }$ using a linear projection. The best signal estimators remove most of the information iinvariant to scaling, we constrain ${ \pmb v } ^ { T } \hat { \pmb d }$ residuals and thto have varian $\sigma _ { v ^ { T } \hat { d } } ^ { 2 } = \sigma _ { y } ^ { 2 }$ $\rho ( S )$ . Since the correlding the optimal $\textbf { { v } }$ ion isfor a fixed amounts to a least-squares regression from $\hat { \ b { d } }$ to $y$ . This enables us to assess the quality of signal estimators efficiently. + +# 4.2 EXISTING SIGNAL ESTIMATORS + +Let us now discuss two signal estimators that have been used in previous approaches. + +$S _ { x }$ – the identity estimator The naive approach to signal estimation is to assume the entire data is signal and there are no distractors: + +$$ +S _ { x } ( { \pmb x } ) = { \pmb x } . +$$ + +With this being plugged into the deep Taylor framework, we obtain the $z$ -rule (Montavon et al., 2017) which is equivalent to LRP (Bach et al., 2015). For a linear model, this corresponds to $\mathbf { \Delta } \mathbf { \mathbf { \mathit { r } } } = \mathbf { \mathit { w } } \odot \mathbf { \mathbf { \mathit { x } } }$ as the attribution. It can be shown that for ReLU and max-pooling networks, the $z$ -rule reduces to the element-wise multiplication of the input and the saliency map (Shrikumar et al., 2016; Kindermans et al., 2016). This means that for a whole network, the assumed signal is simply the original input image. It also implies that, if there are distractors present in the data, they are included in the attribution: + +$$ +\pmb { r } = \pmb { w } \odot \pmb { x } = \pmb { w } \odot \pmb { s } + \pmb { w } \odot \pmb { d } . +$$ + +When moving through the layers by applying the filters $\pmb { w }$ during the forward pass, the contributions from the distractor $^ d$ are cancelled out. However, they cannot be cancelled in the backward pass by the element-wise multiplication. The distractor contributions $\omega \odot d$ that are included in the LRP explanation cause the noisy nature of the visualizations based on the $z$ -rule. + +$S _ { w }$ – the filter based estimator The implicit assumption made by DeConvNet and Guided BackProp is that the detected signal varies in the direction of the weight vector $\pmb { w }$ . This weight vector has to be normalized in order to be a valid signal estimator. In the deep Taylor decomposition framework this corresponds to the $w ^ { 2 }$ -rule and results in the following signal estimator: + +$$ +S _ { \pmb { w } } ( \pmb { x } ) = \frac { \pmb { w } } { \pmb { w } ^ { T } \pmb { w } } \pmb { w } ^ { T } \pmb { x } . +$$ + +For a linear model, this produces an attribution of the form $\frac { { \pmb w } \odot { \pmb w } } { { \pmb w } ^ { T } . { \pmb w } } \textcircled { y }$ . This estimator does not reconstruct the proper signal in the toy example of section 2. Empirically it is also sub-optimal in our experiment in Fig. 3. + +# 4.3 PATTERNNET AND PATTERNATTRIBUTION + +We suggest to learn the signal estimator $S$ from data by optimizing the previously established criterion. A signal estimator $S$ is optimal with respect to Eq. (1) if the correlation is zero for all possible ${ \pmb v } \colon \forall { \pmb v } , \mathrm { c o v } [ y , \hat { \pmb d } ] { \pmb v } = { \bf 0 }$ . This is the case when there is no covariance between $y$ and $\hat { \ b { d } }$ . Because of linearity of the covariance and since $\hat { \pmb { d } } = \pmb { x } - \pmb { S } ( \pmb { x } )$ the above condition leads to + +$$ +\mathrm { c o v } [ y , \hat { d } ] = { \bf 0 } \Rightarrow \mathrm { c o v } [ { \pmb x } , y ] = \mathrm { c o v } [ S ( { \pmb x } ) , y ] . +$$ + +It is important to recognize that the covariance is a summarizing statistic and consequently the problem can still be solved in multiple ways. We will present two possible solutions to this problem. Note that when optimizing the estimator, the contribution from the bias neuron will be considered 0 since it does not covary with the output $y$ . + +$S _ { a }$ – The linear estimator A linear neuron can only extract linear signals $\pmb { s }$ from its input $_ { \textbf { \em x } }$ . Therefore, we could assume a linear dependency between $\pmb { s }$ and $y$ , yielding a signal estimator: + +$$ +\begin{array} { r } { S _ { \pmb { a } } ( \pmb { x } ) = \pmb { a } \pmb { w } ^ { T } \pmb { x } . } \end{array} +$$ + +Plugging this into Eq. (2) and optimising for $^ { a }$ yields + +$$ +\operatorname { c o v } [ { \pmb x } , { \pmb y } ] = \operatorname { c o v } [ { \pmb a } { \pmb w } ^ { T } { \pmb x } , { \pmb y } ] = { \pmb a } \mathrm { c o v } [ { \pmb y } , { \pmb y } ] \Rightarrow { \pmb a } = \frac { \mathrm { c o v } [ { \pmb x } , { \pmb y } ] } { \sigma _ { y } ^ { 2 } } . +$$ + +Note that this solution is equivalent to the approach commonly used in neuro-imaging (Haufe et al., 2014) despite different derivation. With this approach we can recover the signal of our toy example in section 2. It is equivalent to the filter-based approach only if the distractors are orthogonal to the signal. We found that the linear estimator works well for the convolutional layers. However, when using this signal estimator with ReLUs in the dense layers, there is still a considerable correlation left in the distractor component (see Fig. 3). + +$S _ { a _ { + - } }$ – The two-component estimator To move beyond the linear signal estimator, it is crucial to understand how the rectifier influences the training. Since the gate of the ReLU closes for negative activations, the weights only need to filter the distractor component of neurons with $y > 0$ . Since this allows the neural network to apply filters locally, we cannot assume a global distractor component. We rather need to distinguish between the positive and negative regime: + +$$ +\pmb { x } = \left\{ \begin{array} { l l } { \pmb { s } _ { + } + \pmb { d } _ { + } } & { \mathrm { i f } \ y > 0 } \\ { \pmb { s } _ { - } + \pmb { d } _ { - } } & { \mathrm { o t h e r w i s e } } \end{array} \right. +$$ + +Even though signal and distractor of the negative regime are canceled by the following ReLU, we still need to make this distinction in order to approximate the signal. Otherwise, information about whether a neuron fired would be retained in the distractor. Thus, we propose the two-component signal estimator: + +$$ +\begin{array} { r } { S _ { \boldsymbol { a } + - } ( \boldsymbol { x } ) = \left\{ \begin{array} { l l } { \boldsymbol { a } _ { + } \boldsymbol { w } ^ { T } \boldsymbol { x } , \quad \mathrm { i f } \ \boldsymbol { w } ^ { T } \boldsymbol { x } > 0 } \\ { \boldsymbol { a } _ { - } \boldsymbol { w } ^ { T } \boldsymbol { x } , \quad \mathrm { o t h e r w i s e } } \end{array} \right. } \end{array} +$$ + +Next, we derive expressions for the patterns ${ \pmb a } _ { + }$ and $\mathbf { \delta } \mathbf { a } _ { - }$ . We denote expectations over $_ { \textbf { \em x } }$ within the positive and negative regime with $\bar { \mathbb { E } _ { + } } \left[ x \right]$ and $\mathbb { E } _ { - } \left[ { \pmb x } \right]$ , respectively. Let $\pi _ { + }$ be the expected ratio of inputs $_ { \textbf { \em x } }$ with $\mathbf { \Sigma } \mathbf { w } ^ { T } \mathbf { x } > 0$ . The covariance of data/signal and output become: + +$$ +\begin{array} { r l r } { \mathrm { c o v } [ { \pmb x } , { y } ] = } & { } & { \pi _ { + } \left( \mathbb { E } _ { + } \left[ { \pmb x } { \pmb y } \right] - \mathbb { E } _ { + } \left[ { \pmb x } \right] \mathbb { E } \left[ { \pmb y } \right] \right) + \frac { } { } \left( 1 - \pi _ { + } \right) \left( \mathbb { E } _ { - } \left[ { \pmb x } { \pmb y } \right] - \mathbb { E } _ { - } \left[ { \pmb x } \right] \mathbb { E } \left[ { \pmb y } \right] \right) } \\ { \mathrm { c o v } [ { \pmb s } , { y } ] = } & { } & { \pi _ { + } \left( \mathbb { E } _ { + } \left[ { \pmb s } { \pmb y } \right] - \mathbb { E } _ { + } \left[ { \pmb s } \right] \mathbb { E } \left[ { \pmb y } \right] \right) + \frac { } { } \left( 1 - \pi _ { + } \right) \left( \mathbb { E } _ { - } \left[ { \pmb s } { \pmb y } \right] - \mathbb { E } _ { - } \left[ { \pmb s } \right] \mathbb { E } \left[ { \pmb y } \right] \right) } \end{array} +$$ + +Assuming both covariances are equal, we can treat the positive and negative regime separately using Eq. (2) to optimize the signal estimator: + +$$ +\begin{array} { r l r } { { \mathbb E } _ { + } \left[ { \pmb x } { \pmb y } \right] - { \mathbb E } _ { + } \left[ { \pmb x } \right] { \mathbb E } \left[ { \pmb y } \right] } & { = } & { { \mathbb E } _ { + } \left[ { \pmb s } { \pmb y } \right] - { \mathbb E } _ { + } \left[ { \pmb s } \right] { \mathbb E } \left[ { \pmb y } \right] } \end{array} +$$ + +Plugging in Eq. (5) and solving for ${ \pmb a } _ { + }$ yields the required parameter $( a _ { - }$ analogous). + +$$ +\begin{array} { r l r } { \pmb { a } _ { + } } & { = } & { \frac { \mathbb { E } _ { + } \left[ \pmb { x } \pmb { y } \right] - \mathbb { E } _ { + } \left[ \pmb { x } \right] \mathbb { E } \left[ \pmb { y } \right] } { \pmb { w } ^ { T } \mathbb { E } _ { + } \left[ \pmb { x } \pmb { y } \right] - \pmb { w } ^ { T } \mathbb { E } _ { + } \left[ \pmb { x } \right] \mathbb { E } \left[ \pmb { y } \right] } } \end{array} +$$ + +The solution for $S _ { a + - }$ reduces to the linear estimator when the relation between input and output is linear. Therefore, it solves our introductory linear example correctly. + +PatternNet and PatternAttribution Based on the presented analysis, we propose PatternNet and PatternAttribution as illustrated in Fig. 1. PatternNet yields a layer-wise back-projection of the estimated signal to input space. The signal estimator is approximated as a superposition of neuron-wise, nonlinear signal estimators $S _ { a + - }$ in each layer. It is equal to the computation of the gradient where during the backward pass the weights of the network are replaced by the informative directions. In Fig. 1, a visual improvement over DeConvNet and Guided Backprop is apparent. + +PatternAttribution exposes the attribution ${ \pmb w } \odot { \pmb a } _ { + }$ and improves upon the layer-wise relevance propagation (LRP) framework (Bach et al., 2015). It can be seen as a root point estimator for the DeepTaylor Decomposition (DTD). Here, the explanation consists of neuron-wise contributions of the estimated signal to the classification score. By ignoring the distractor, PatternAttribution can reduce the noise and produces much clearer heat maps. By working out the back-projection steps in the Deep-Taylor Decomposition with the proposed root point selection method, it becomes obvious that PatternAttribution is also analogous to the backpropagation operation. In this case, the weights are replaced during the backward pass by ${ \pmb w } \odot { \pmb a } _ { + }$ . + +![](images/9c4bfa0b68162a0e16416f5555faa6fa77e72b7690d63e5a5bd97481ad920da0.jpg) +Figure 3: Evaluating $\rho ( S )$ for VGG-16 on ImageNet. Higher values are better. The gradient $( S _ { w } )$ , linear estimator $( S _ { a } )$ and nonlinear estimator $( S _ { a _ { + - } } )$ are compared. An estimator using random directions is the baseline. The network has 5 blocks with 2/3 convolutional layers and 1 max-pooling layer each, followed by 3 dense layers. + +![](images/d8e47053480d3957b47a181537b3935694502e6013c570f2ac522e4d8be5dfd1.jpg) +Figure 4: Image degradation experiment on all 50.000 images in the ImageNet validation set. The effect on the classifier output is measured. A steeper decrease is better. + +# 5 EXPERIMENTS AND DISCUSSION + +To evaluate the quality of the explanations, we focus on the task of image classification. Nevertheless, our method is not restricted to networks operating on image inputs. We used Theano (Bergstra et al., 2010) and Lasagne (Dieleman et al., 2015) for our implementation. We restrict the analysis to the well-known ImageNet dataset (Russakovsky et al., 2015) using the pre-trained VGG-16 model (Simonyan & Zisserman, 2015). Images were rescaled and cropped to $2 2 4 \mathbf { x } 2 2 4$ pixels. The signal estimators are trained on the first half of the training dataset. + +The vector $\pmb { v }$ , used to measure the quality of the signal estimator $\rho ( { \pmb x } )$ in Eq. (1), is optimized on the second half of the training dataset. This enables us to test the signal estimators for generalization. All the results presented here were obtained using the official validation set of 50000 samples. The validation set was not used for training the signal estimators, nor for training the vector $\pmb { v }$ to measure the quality. Consequently our results are obtained on previously unseen data. + +The linear and the two component signal estimators are obtained by solving their respective closed form solutions (Eq. (4) and Eq. (8)). With a highly parallelized implementation using 4 GPUs this could be done in 3-4 hours. This can be considered reasonable given that several days are required to train the actual network. The quality of a signal estimator is assessed with Eq. (1). Solving it with the closed form solution is computationally prohibitive since it must be repeated for every single weight vector in the network. Therefore we optimize the equivalent least-squares problem using stochastic mini-batch gradient descent with ADAM Kingma & Ba (2015) until convergence. This was implemented on a NVIDIA Tesla K40 and took about 24 hours per optimized signal estimator. + +After learning to explain, individual explanations are computationally cheap since they can be implemented as a back-propagation pass with a modified weight vector. As a result, our method produces explanations at least as fast as the work by Dabkowski & Gal (2017) on real time saliency. However, our method has the advantage that it is not only applicable to image models but is a generalization of the theory commonly used in neuroimaging Haufe et al. (2014). + +![](images/b372c59547081ace17a88655dd8b643c962e0a2010955da9560f3fc9f8db8ad9.jpg) +Figure 5: Top: signal. Bottom: attribution. For the trivial estimator $S _ { x }$ the original input is the signal. This is not informative w.r.t. how the network operates. + +Measuring the quality of signal estimators In Fig. 3 we present the results from the correlation measure $\rho ( { \pmb x } )$ , where higher values are better. We use random directions as baseline signal estimators. Clearly, this approach removes almost no correlation. The filter-based estimator $S _ { w }$ succeeds in removing some of the information in the first layer. This indicates that the filters are similar to the patterns in this layer. However, the gradient removes much less information in the higher layers. Overall, it does not perform much better than the random estimator. This implies that the weights do not correspond to the detected stimulus in a neural network. Hence the implicit assumptions about the signal made by DeConvNet and Guided BackProp is not valid. The optimized estimators remove much more of the correlations across the board. For convolutional layers, $S _ { a }$ and $S _ { a + - }$ perform comparably in all but one layer. The two component estimator $S _ { a + - }$ is best in the dense layers. + +Image degradation The first experiment was a direct measurement of the quality of the signal estimators of individual neurons. The second one is an indirect measurement of the quality, but it considers the whole network. We measure how the prediction (after the soft-max) for the initially selected class changes as a function of corrupting more and more patches based on the ordering assigned by the attribution (see Samek et al., 2016). This is also related to the work by Zintgraf et al. (2017). In this experiment, we split the image in non-overlapping patches of $9 \mathrm { x } 9$ pixels. We compute the attribution and sum all the values within a patch. We sort the patches in decreasing order based on the aggregate heat map value. In step $n = 1 . . 1 0 0$ we replace the first $n$ patches with the their mean per color channel to remove the information in this patch. Then, we measure how this influences the classifiers output. We use the estimators from the previous experiment to obtain the function-signal attribution heat maps for evaluation. A steeper decay indicates a better heat map. + +Results are shown in Fig. 4. The baseline, in which the patches are randomly ordered, performs worst. The linear optimized estimator $S _ { a }$ performs quite poorly, followed by the filter-based estimator $S _ { w }$ . The trivial signal estimator $S _ { x }$ performs just slightly better. However, the two component model $S _ { a + - }$ leads to the fastest decrease in confidence in the original prediction by a large margin. Its excellent quantitative performance is also backed up by the visualizations discussed next. + +Qualitative evaluation In Fig. 5, we compare all signal estimators on a single input image. For the trivial estimator $S _ { x }$ , the signal is by definition the original input image and, thus, includes the distractor. Therefore, its noisy attribution heat map shows contributions that cancel each other in the neural network. The $S _ { w }$ estimator captures some of the structure. The optimized estimator $S _ { a }$ results in slightly more structure but struggles on color information and produces dense heat maps. The two component model $S _ { a + - }$ on the right captures the original input during signal estimation and produces a crisp heat map of the attribution. + +Fig. 6 shows the visualizations for six randomly selected images from ImageNet. PatternNet is able to recover a signal close to the original without having to resort to the inclusion of additional rectifiers in contrast to DeConvNet and Guided BackProp. We argue that this is due to the fact that the optimization of the pattern allows for capturing the important directions in input space. This contrasts with the commonly used methods DeConvNet, Guided BackProp, LRP and DTD, for which the correlation experiment indicates that their implicit signal estimator cannot capture the true signal in the data. Overall, the proposed approach produces the most crisp visualization in addition to being measurably better, as shown in the previous section. Additonally, we also contrast our methods to the prediction-differences analysis by Zintgraf et al. (2017) in the supplementary material. + +![](images/cb30d37d6dbeabf075edf5246d5726ad4db711f47c218a2fd6889841b22072a4.jpg) +Figure 6: Visualization of random images from ImageNet (validation set). In the leftmost shows column the ground truth, the predicted label and the classifier’s confidence. Methods should only be compared within their group. PatternNet, Guided Backprop, DeConvNet and the Gradient (saliency map) are back-projections to input space with the original color channels. They are normalized using $\begin{array} { r } { x _ { n o r m } = \frac { \bar { x } } { 2 \operatorname* { m a x } | x | } + \frac { 1 } { 2 } } \end{array}$ to maximize contrast. LRP and PatternAttribution are heat maps showing pixel-wise contributions. + +Relation to previous methods Our method can be thought of as a generalization of the work by Haufe et al. (2014), making it applicable on deep neural networks. Remarkably, our proposed approach can solve the toy example in section 2 optimally while none of the previously published methods for deep learning are able to solve this (Bach et al., 2015; Montavon et al., 2017; Smilkov et al., 2017; Sundararajan et al., 2017; Zintgraf et al., 2017; Dabkowski & Gal, 2017; Zeiler & Fergus, 2014; Springenberg et al., 2015). Our method shares the idea that to explain a model properly one has to learn how to explain it with Zintgraf et al. (2017) and Dabkowski & Gal (2017). Furthermore, since our approach is after training just as expensive as a single back-propagation step, it can be applied in a real-time context, which is also possible for the work done by Dabkowski & Gal (2017) but not for Zintgraf et al. (2017). + +# 6 CONCLUSION + +Understanding and explaining nonlinear methods is an important challenge in machine learning. Algorithms for visualizing nonlinear models have emerged but theoretical contributions are scarce. We have shown that the direction of the model gradient does not necessarily provide an estimate for the signal in the data. Instead it reflects the relation between the signal direction and the distracting noise contributions ( Fig. 2). This implies that popular explanation approaches for neural networks (DeConvNet, Guided BackProp, LRP) do not provide the correct explanation, even for a simple linear model. Our reasoning can be extended to nonlinear models. We have proposed an objective function for neuron-wise explanations. This can be optimized to correct the signal visualizations (PatternNet) and the decomposition methods (PatternAttribution) by taking the data distribution into account. We have demonstrated that our methods constitute a theoretical, qualitative and quantitative improvement towards understanding deep neural networks. + +# ACKNOWLEDGMENTS + +This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement NO 657679, the BMBF for the Berlin Big Data Center BBDC (01IS14013A), a hardware donation from NVIDIA. We thank Sander Dieleman, Jonas Degraeve, Ira Korshunova, Stefan Chmiela, Malte Esders, Sarah Hooker, Vincent Vanhoucke for their comments to improve this manuscript. We are grateful to Chris Olah and Gregoire Montavon for the valuable discussions. + +# REFERENCES + +Sebastian Bach, Alexander Binder, Gregoire Montavon, Frederick Klauschen, Klaus-Robert M ´ uller, ¨ and Wojciech Samek. 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In ICLR, 2015. + +Mukund Sundararajan, Ankur Taly, and Qiqi Yan. Axiomatic attribution for deep networks. In ICML 2017, 2017. + +Ilya Sutskever, Oriol Vinyals, and Quoc V Le. Sequence to sequence learning with neural networks. In Advances in neural information processing systems, pp. 3104–3112, 2014. + +Jason Yosinski, Jeff Clune, Thomas Fuchs, and Hod Lipson. Understanding neural networks through deep visualization. In ICML Workshop on Deep Learning, 2015. + +Matthew D Zeiler and Rob Fergus. Visualizing and understanding convolutional networks. In European Conference on Computer Vision, pp. 818–833. Springer, 2014. + +Luisa M Zintgraf, Taco S Cohen, Tameem Adel, and Max Welling. Visualizing deep neural network decisions: Prediction difference analysis. In ICLR, 2017. + +# A ALGORITHMS + +In this section we will give an overview of the visualization algorithms to clarify their actual implementation for ReLu networks. This shows the similarities and the differences between all approaches. For all visualization approaches, the back-projection through a max-pooling layer is only through the path that was active in the forward pass. + +A.1.1 GRADIENT WITH RESPECT TO THE INPUT + +Initialization To compute the gradient of an output neuron w.r.t. to the input, we can initialize the gradient at the output neuron with a single 1, for the non-selected output neurons we initialize it at 0. + +$$ +g _ { i } ^ { o u t p u t } = y , \qquad g _ { j \neq i } ^ { o u t p u t } = 0 . +$$ + +Linear or convolutional layer If it is a linear layer, the gradients from neuron $i$ in layer $l$ can be projected back to its input along the weight vector + +$$ +\begin{array} { r } { \pmb { g } ^ { l - 1 , i } = \pmb { w g } _ { i } ^ { l } . } \end{array} +$$ + +The gradient of neuron $i$ at layer $l - 1$ is the sum of all incoming gradients from the layer above: + +$$ +g _ { i } ^ { l - 1 } = \sum _ { j } g _ { i } ^ { l - 1 , j } . +$$ + +ReLu layer To propagate through a ReLu, the propagation is blocked if the ReLu was not active in the forward pass. + +$$ +g _ { i } ^ { l - 1 } = { \left\{ \begin{array} { l l } { g _ { i } ^ { l } } & { x _ { i } ^ { l } > 0 } \\ { 0 } & { { \mathrm { o t h e r w i s e } } } \end{array} \right. } +$$ + +# A.2 SIGNAL VISUALIZATION + +# A.2.1 DECONVNET + +The DeConvNet visualization is highly similar to the computation of the gradient. The key difference is how the ReLu’s are treated. + +Initialization To compute the visualization of the signal of an output neuron w.r.t. to the input, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. + +$$ +s _ { i } ^ { o u t p u t } = y , \qquad s _ { j \neq i } ^ { o u t p u t } = 0 . +$$ + +Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input along the weight vector. + +$$ +\begin{array} { r } { \pmb { s } ^ { l - 1 , i } = \pmb { w s } _ { i } ^ { l } . } \end{array} +$$ + +The signal of neuron $i$ at layer $l - 1$ is the sum of all incoming signals from the layer above: + +$$ +s _ { i } ^ { l - 1 } = \sum _ { j } s _ { i } ^ { l - 1 , j } . +$$ + +ReLu layer To propagate through a ReLu, the propagation is blocked if the signal is negative + +$$ +s _ { i } ^ { l - 1 } = \left\{ \begin{array} { l l } { s _ { i } ^ { l } } & { s _ { i } ^ { l } > 0 } \\ { 0 } & { \mathrm { o t h e r w i s e } } \end{array} \right. +$$ + +# A.2.2 GUIDED BACKPROPAGATION + +The Guided Backpropagation visualization is highly similar to the computation of the gradient. and to DeConvNet. The only difference is how the ReLu’s are treated. + +Initialization To compute the visualization of the signal of an output neuron w.r.t. to the input, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. + +$$ +s _ { i } ^ { o u t p u t } = y , \qquad s _ { j \neq i } ^ { o u t p u t } = 0 . +$$ + +Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input along the weight vector + +$$ +\begin{array} { r } { \pmb { s } ^ { l - 1 , i } = \pmb { w s } _ { i } ^ { l } . } \end{array} +$$ + +The signal of neuron $i$ at layer $l - 1$ is the sum of all incoming signals from the layer above: + +$$ +s _ { i } ^ { l - 1 } = \sum _ { j } s _ { i } ^ { l - 1 , j } . +$$ + +ReLu layer To propagate through a ReLu, the propagation is blocked if the signal is negative or if the neuron was not active in the forward pass + +$$ +s _ { i } ^ { l - 1 } = \left\{ \begin{array} { l l } { s _ { i } ^ { l } } & { s _ { i } ^ { l } > 0 \mathrm { a n d } x _ { i } ^ { l } > 0 } \\ { 0 } & { \mathrm { o t h e r w i s e } } \end{array} \right. +$$ + +# A.2.3 PATTERNNET + +The PatternNet computation is analogous to the gradient computation. The key difference is that during the backward pass patterns are used instead of weights. + +Initialization To compute the visualization of the signal of an output neuron w.r.t. to the input, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. + +$$ +s _ { i } ^ { o u t p u t } = y , \qquad s _ { j \neq i } ^ { o u t p u t } = 0 . +$$ + +Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input along the pattern vector. + +$$ +\pmb { s } ^ { l - 1 , i } = \pmb { a } s _ { i } ^ { l } . +$$ + +In our case where we use the $S _ { a + - } ( x )$ estimator, this vector is always the positive components ${ \pmb a } _ { + }$ since non-active ReLu’s block the propagation. + +The signal of neuron $i$ at layer $l - 1$ is the sum of all incoming signals from the layer above: + +$$ +s _ { i } ^ { l - 1 } = \sum _ { j } s _ { i } ^ { l - 1 , j } . +$$ + +ReLu layer To propagate through a ReLu, the propagation is blocked if the neuron was not active in the forward pass + +$$ +s _ { i } ^ { l - 1 } = \left\{ \begin{array} { l l } { s _ { i } ^ { l } } & { x _ { i } ^ { l } > 0 } \\ { 0 } & { \mathrm { o t h e r w i s e } } \end{array} \right. +$$ + +# A.3 ATTRIBUTION VISUALIZATION + +# A.3.1 DEEP-TAYLOR DECOMPOSITION + +Initialization To compute the attribution of an output neuron, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. + +$$ +r _ { i } ^ { o u t p u t } = y , \qquad r _ { j \neq i } ^ { o u t p u t } = 0 . +$$ + +Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input w.r.t. a reference point $\scriptstyle { \mathbf { { \mathit { x } } } } _ { 0 }$ + +$$ +\pmb { r } ^ { l - 1 , i } = \frac { \pmb { w } \odot ( \pmb { x } - \pmb { x } _ { 0 } ) } { \pmb { w } ^ { T } \pmb { x } } r _ { i } ^ { l } . +$$ + +In this work we use the $S _ { a + - } ( x )$ estimator. Since a non-active ReLu blocks the propagation, we only have to use the positive component $\mathbf { \pmb { a } } _ { + }$ . + +The attribution of neuron $i$ at layer $l - 1$ is the sum of all incoming attributions from the layer above: + +$$ +r _ { i } ^ { l - 1 } = \sum _ { j } r _ { i } ^ { l - 1 , j } . +$$ + +ReLu layer To propagate through a ReLu, the propagation is blocked if the ReLu was not active in the forward pass. + +$$ +r _ { i } ^ { l - 1 } = { \left\{ \begin{array} { l l } { r _ { i } ^ { l } } & { x _ { i } ^ { l } > 0 } \\ { 0 } & { { \mathrm { o t h e r w i s e } } } \end{array} \right. } +$$ + +# A.3.2 LRP + +LRP corresponds to $\mathbf { \delta x } _ { 0 } = \mathbf { \delta 0 }$ . This allows us to re-write the distribution rule for the linear and convolutional layers as: + +$$ +r ^ { l - 1 , i } = \frac { { \pmb w } \odot { \pmb x } } { { \pmb w } ^ { T } { \pmb x } } r _ { i } ^ { l } . +$$ + +Division by zero is not an issue since the propagation is blocked at the ReLu if ${ \pmb w } ^ { T } { \pmb x } < = 0$ + +# A.3.3 PATTERNATTRIBUTION WITH $S _ { a + - } ( x )$ + +PatternAttributions corresponds to ${ \pmb x } _ { 0 } = { \pmb x } - S _ { { \pmb a } + - } ( { \pmb x } )$ . Because propagation is blocked at the ReLu if ${ \pmb w } ^ { T } { \pmb x } < = 0$ , we can always use $\pmb { x } _ { 0 } = \pmb { x } - \pmb { a } _ { + } \pmb { w } ^ { T } \pmb { x } .$ + +This allows us to re-write the distribution rule for the linear and convolutional layers as: + +$$ +\pmb { r } ^ { l - 1 , i } = \frac { \pmb { w } \odot \left( \pmb { x } - \pmb { x } + \pmb { a } _ { + } \pmb { w } ^ { T } \pmb { x } \right) } { \pmb { w } ^ { T } \pmb { x } } r _ { i } ^ { l } . +$$ + +This can be simplified to + +$$ +r ^ { l - 1 , i } = { \pmb w } \odot { \pmb a } _ { + } r _ { i } ^ { l } +$$ + +since division by zero is not an issue because the propagation is blocked at the ReLu if ${ \pmb w } ^ { T } { \pmb x } < = 0$ . + +# B QUALITATIVE COMPARISON TO PREDICTION-DIFFERENCES ANALYSIS + +To create the Predictive-Differences analysis visualizations Zintgraf et al. (2017), we used the opensource code provided by the authors with the default parameter settings provided for VGG. + +![](images/ff933e0a2064a6b03a92b2dc89030693194cb4c132c5bb99ffa4a9512decaddb.jpg) +Figure 7: Visualization of random images from ImageNet (validation set). In the leftmost shows column the ground truth, the predicted label and the classifier’s confidence. Comparison between the proposed methods PatternNet and PatternAttribution to the Prediction-Differences approach by Zintgraf et al. (2017). \ No newline at end of file diff --git a/parse/train/Hkn7CBaTW/Hkn7CBaTW_content_list.json b/parse/train/Hkn7CBaTW/Hkn7CBaTW_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2cc0a063e914715ed0997aea6ccf726b8a66be2f --- /dev/null +++ b/parse/train/Hkn7CBaTW/Hkn7CBaTW_content_list.json @@ -0,0 +1,2379 @@ +[ + { + "type": "text", + "text": "LEARNING HOW TO EXPLAIN NEURAL NETWORKS: PATTERNNET AND PATTERNATTRIBUTION ", + "text_level": 1, + "bbox": [ + 176, + 101, + 781, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pieter-Jan Kindermans∗ Google Brain pikinder@google.com ", + "bbox": [ + 183, + 170, + 372, + 212 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Kristof T. Schutt & Maximilian Alber ¨ \nTU Berlin \n{kristof.schuett,maximilian.alber}@tu-berlin.de ", + "bbox": [ + 388, + 170, + 848, + 213 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Klaus-Robert Muller ¨ † ", + "text_level": 1, + "bbox": [ + 184, + 233, + 338, + 247 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "TU Berlin klaus-robert.mueller@tu-berlin.de ", + "bbox": [ + 183, + 250, + 508, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dumitru Erhan & Been Kim Google Brain {dumitru,beenkim}@google.com ", + "bbox": [ + 540, + 233, + 815, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sven Dahne ¨ ‡ ", + "text_level": 1, + "bbox": [ + 184, + 296, + 274, + 310 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "TU Berlin sven.daehne@tu-berlin.de ", + "bbox": [ + 184, + 313, + 421, + 338 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 376, + 544, + 390 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "DeConvNet, Guided BackProp, LRP, were invented to better understand deep neural networks. We show that these methods do not produce the theoretically correct explanation for a linear model. Yet they are used on multi-layer networks with millions of parameters. This is a cause for concern since linear models are simple neural networks. We argue that explanation methods for neural nets should work reliably in the limit of simplicity, the linear models. Based on our analysis of linear models we propose a generalization that yields two explanation techniques (PatternNet and PatternAttribution) that are theoretically sound for linear models and produce improved explanations for deep networks. ", + "bbox": [ + 233, + 406, + 764, + 531 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 558, + 336, + 574 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning made a huge impact on a wide variety of applications (Krizhevsky et al., 2012; Sutskever et al., 2014; LeCun et al., 2015; Schmidhuber, 2015; Mnih et al., 2015; Silver et al., 2016) and recent neural network classifiers have become excellent at detecting relevant signals (e.g., the presence of a cat) contained in input data points such as images by filtering out all other, nonrelevant and distracting components also present in the data. This separation of signal and distractors is achieved by passing the input through many layers with millions of parameters and nonlinear activation functions in between, until finally at the output layer, these models yield a highly condensed version of the signal, e.g. a single number indicating the probability of a cat being in the image. ", + "bbox": [ + 174, + 589, + 825, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While deep neural networks learn efficient and powerful representations, they are often considered a ‘black-box’. In order to better understand classifier decisions and to gain insight into how these models operate, a variety techniques have been proposed (Simonyan et al., 2014; Yosinski et al., 2015; Nguyen et al., 2016; Baehrens et al., 2010; Bach et al., 2015; Montavon et al., 2017; Zeiler & Fergus, 2014; Springenberg et al., 2015; Zintgraf et al., 2017; Sundararajan et al., 2017; Smilkov et al., 2017). These methods for explaining classifier decisions operate under the assumption that it is possible to propagate the condensed output signal back through the classifier to arrive at something that shows how the relevant signal was encoded in the input and thereby explains the classifier decision. Simply put, if the classifier detected a cat, the visualization should point to the cat-relevant aspects of the input image from the perspective of the network. Techniques that are based on this principle include saliency maps from network gradients (Baehrens et al., 2010; Simonyan et al., 2014), DeConvNet (Zeiler & Fergus, 2014, DCN), Guided BackProp (Springenberg et al., 2015, GBP), ", + "bbox": [ + 173, + 707, + 825, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d83e01158e9f8a863d901e0e6ac69cef72b6c29330d69f35b721d2d995ef1cd.jpg", + "image_caption": [ + "Figure 1: Illustration of explanation approaches. Function and signal approximators visualize the explanation using the original color channels. The attribution is visualized as a heat map of pixelwise contributions to the output " + ], + "image_footnote": [], + "bbox": [ + 179, + 99, + 821, + 281 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Layer-wise Relevance Propagation (Bach et al., 2015, LRP) and the Deep Taylor Decomposition (Montavon et al., 2017, DTD), Integrated Gradients (Sundararajan et al., 2017) and SmoothGrad (Smilkov et al., 2017). ", + "bbox": [ + 174, + 363, + 825, + 406 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The merit of explanation methods is often demonstrated by applying them to state-of-the-art deep learning models in the context of high dimensional real world data, such as ImageNet, where the provided explanation is intuitive to humans. Unfortunately, theoretical analysis as well as quantitative empirical evaluations of these methods are lacking. ", + "bbox": [ + 174, + 412, + 825, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep neural networks are essentially a composition of linear transformations connected with nonlinear activation functions. Since approaches, such as DeConvNet, Guided BackProp, and LRP, back-propagate the explanations in a layer-wise fashion, it is crucial that the individual linear layers are handled correctly. In this work we show that these gradient-based methods fail to recover the signal even for a single-layer architecture, i.e. a linear model. We argue that therefore they cannot be expected to reliably explain a deep neural network and demonstrate this with quantitative and qualitative experiments. In particular, we provide the following key contributions: ", + "bbox": [ + 174, + 476, + 825, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• We analyze the performance of existing explanation approaches in the controlled setting of a linear model (Sections 2 and 3). \n• We categorize explanation methods into three groups – functions, signals and attribution (see Fig. 1) – that require fundamentally different interpretations and are complementary in terms of information about the neural network (Section 3). \n• We propose two novel explanation methods – PatternNet and PatternAttribution – that alleviate shortcomings of current approaches, as discovered during our analysis, and improve explanations in real-world deep neural networks visually and quantitatively (Sections 4 and 5). ", + "bbox": [ + 215, + 585, + 825, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This presents a step towards a thorough analysis of explanation methods and suggests qualitatively and measurably improved explanations. These are crucial requirements for reliable explanation techniques, in particular in domains, where explanations are not necessarily intuitive, e.g. in health and the sciences Schutt et al. (2017). ¨ ", + "bbox": [ + 176, + 738, + 825, + 795 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Notation and scope Scalars are lowercase letters $( i )$ , column vectors are bold $( \\pmb { u } )$ , element-wise multiplication is $( \\odot )$ . The covariance between $\\textbf { \\em u }$ and $\\textbf { { v } }$ is $\\boldsymbol { \\mathbf { \\rho } } _ { \\mathbf { 0 } } \\mathbf { v } [ \\pmb { u } , \\pmb { v } ]$ , the covariance of $\\textbf { \\em u }$ and $i$ is $\\mathrm { c o v } [ \\bar { \\boldsymbol { u } } , i ]$ . The variance of a scalar random variable $i$ is $\\sigma _ { i } ^ { 2 }$ . Estimates of random variables will have a hat $( \\hat { u } )$ . We analyze neural networks excluding the final soft-max output layer. To allow for analytical treatment, we only consider networks with linear neurons optionally followed by a rectified linear unit (ReLU), max-pooling or soft-max. We analyze linear neurons and nonlinearities independently such that every neuron has its own weight vector. These restrictions are similar to those in the saliency map (Simonyan et al., 2014), DCN (Zeiler & Fergus, 2014), GBP (Springenberg et al., 2015), LRP (Bach et al., 2015) and DTD (Montavon et al., 2017). Without loss of generality, biases are considered constant neurons to enhance clarity. ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fadc0d3e80752b97d7b31564914d142aeb247209fdb0365ffc20487b5064a4a4.jpg", + "image_caption": [ + "Figure 2: For linear models, i.e., a simple neural network, the weight vector does not explain the signal it detects Haufe et al. (2014). The data ${ \\pmb x } = y { \\pmb a } _ { s } + \\epsilon { \\pmb a } _ { d }$ is color-coded w.r.t. the output $\\mathbf { \\Psi } y = \\pmb { w } ^ { T } \\mathbf { \\em x }$ . Only the signal $\\mathit { s } = y \\mathbf { a } _ { s }$ contributes to $y$ . The weight vector $\\pmb { w }$ does not agree with the signal direction, since its primary objective is canceling the distractor. Therefore, rotations of the basis vector $\\mathbf { \\mu } _ { a _ { d } }$ of the distractor with constant signal $\\pmb { s }$ lead to rotations of the weight vector (right). " + ], + "image_footnote": [], + "bbox": [ + 178, + 101, + 820, + 229 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 349, + 823, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2 UNDERSTANDING LINEAR MODELS ", + "text_level": 1, + "bbox": [ + 174, + 400, + 498, + 416 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we analyze explanation methods for deep neural network, starting with the simplest neural network setting: a purely linear model and data sampled from a linear generative model. This setup allows us to (i) fully control how signal and distractor components are encoded in the input data and (ii) analytically track how the resulting explanation relates to the known signal component. This analysis allows us then to highlight shortcomings of current explanation approaches that carry over to deep neural networks. ", + "bbox": [ + 174, + 431, + 825, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider the following toy example (see Fig. 2) where we generate data $_ { \\textbf { \\em x } }$ as: ", + "bbox": [ + 173, + 522, + 687, + 537 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/b72a99c8d0bd8bc7ec4633301981ea18169ce3a5a566901154edf1d1428a2bc9.jpg", + "text": "$$\n\\begin{array} { r l r l r l r l } { x = s + d } & { } & & { \\quad s = a _ { s } y , } & { \\quad } & { \\mathrm { ~ w i t h ~ } a _ { s } = \\left( 1 , 0 \\right) ^ { T } , } & { } & { \\quad y \\in [ - 1 , 1 ] } \\\\ & { } & & { \\quad d = a _ { d } \\epsilon , } & { } & & { \\mathrm { ~ w i t h ~ } a _ { d } = \\left( 1 , 1 \\right) ^ { T } , } & { } & { \\epsilon \\sim \\mathcal { N } \\left( \\mu , \\sigma ^ { 2 } \\right) . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 235, + 544, + 763, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We train a linear regression model to extract $y$ from $_ { \\textbf { \\em x } }$ . By construction, $\\pmb { s }$ is the signal in our data, i.e., the part of $_ { \\textbf { \\em x } }$ containing information about $y$ . Using the terminology of Haufe et al. (2014) the distractor $^ d$ obfuscates the signal making the detection task more difficult. To optimally extract $y$ , our model has to be able to filter out the distractor $^ d$ . This is why the weight vector is also called the filter. In the example, $\\mathbf { \\boldsymbol { w } } = \\left[ 1 , - 1 \\right] ^ { T }$ fulfills this convex task. ", + "bbox": [ + 173, + 593, + 825, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "From this example, we can make several observations: The optimal weight vector $\\textbf { \\em w }$ does not align, in general, with the signal direction $\\mathbf { \\delta } _ \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\delta \\mathrm \\mathrm { \\delta } \\delta \\mathrm \\mathrm \\delta \\mathrm \\mathrm \\mathrm { \\delta } \\delta \\delta \\mathrm \\delta \\mathrm \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\delta \\mathrm \\delta \\delta \\delta \\mathrm \\delta \\delta \\delta \\delta \\delta \\delta \\mathrm \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta$ , but tries to filter the contribution of the distractor (see Fig. 2). This is optimally solved when the weight vector is orthogonal to the distractor ${ \\pmb w } ^ { T } { \\pmb d } = 0$ . Therefore, when the direction of the distractor $\\mathbf { \\delta } _ { \\mathbf { \\alpha } \\mathbf { \\delta } \\mathbf { \\alpha } \\mathbf { \\textit { a } } }$ changes, $\\textbf { \\em w }$ must follow, as illustrated on the right hand side of the figure. On the other hand, a change in signal direction $\\mathbf { \\delta } _ { a _ { s } }$ can be compensated for by a change in sign and magnitude of $\\pmb { w }$ such that $\\mathbf { \\bar { w } } ^ { T } \\pmb { a } _ { s } \\equiv 1$ , but the direction stays constant. ", + "bbox": [ + 173, + 672, + 825, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The fact that the direction of the weight vector in a linear model is largely determined by the distractor implies that given only the weight vector, we cannot know what part of the input produces the output $y$ . On the contrary, the direction $\\mathbf { \\delta } _ { a _ { s } }$ must be learned from data. ", + "bbox": [ + 174, + 762, + 825, + 805 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Now assume that we have additive isotropic Gaussian noise. The mean of the noise can easily be compensated for with a bias change. Therefore, we only have to consider the zero-mean case. Since isotropic Gaussian noise does not contain any correlations or structure, the only way to remove it is by averaging over different measurements. It is not possible to cancel it out effectively by using a well-chosen weight vector. However, it is well known that adding Gaussian noise shrinks the weight vector and corresponds to L2 regularization. In the absence of a structured distractor, the smallest weight vector $\\textbf { \\em w }$ such that ${ \\pmb w } ^ { T } { \\pmb a } _ { s } = 1$ is the one in the direction of the signal. Therefore in practice both these effects influence the actual weight vector. ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As already indicated above, deep neural networks are essentially a composition of linear layers and non-linear activation functions. In the next section, we will show that gradient-based methods, e.g., DeConvNet, Guided BackProp, and LRP, are not able to distinguish signal from distractor in a linear model and therefore back-propagate sub-optimal explanations in deeper networks. This analysis allows us to develop improved layer-wise explanation techniques and to demonstrate quantitative and qualitative better explanations for deep neural networks. ", + "bbox": [ + 174, + 103, + 825, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Terminology Throughout this manuscript we will use the following terminology: The filter $\\pmb { w }$ tells us how to extract the output $y$ optimally from data $_ { \\textbf { \\em x } }$ . The pattern $\\mathbf { \\delta } _ { a _ { s } }$ is the direction in the data along which the desired output $y$ varies. Both constitute the signal $\\textbf { \\em s } = \\textbf { \\em a } _ { s } y$ , i.e., the contributing part of $_ { \\textbf { \\em x } }$ . The distractor $^ d$ is the component of the data that does not contain information about the desired output. ", + "bbox": [ + 174, + 207, + 825, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 OVERVIEW OF EXPLANATION APPROACHES AND THEIR BEHAVIOR ", + "text_level": 1, + "bbox": [ + 173, + 303, + 751, + 318 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we take a look at a subset of explanation methods for individual classifier decisions and discuss how they are connected to our analysis of linear models in the previous section. Fig. 1 gives an overview of the different types of explanation methods which can be divided into function, signal and attribution visualizations. These three groups all present different information about the network and complement each other. ", + "bbox": [ + 174, + 337, + 825, + 406 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Functions – gradients, saliency map Explaining the function in input space corresponds to describing the operations the model uses to extract $y$ from $_ { \\textbf { \\em x } }$ . Since deep neural networks are highly nonlinear, this can only be approximated. The saliency map estimates how moving along a particular direction in input space influences $y$ (i.e., sensitivity analysis) where the direction is given by the model gradient (Baehrens et al., 2010; Simonyan et al., 2014). In case of a linear model $y = \\dot { \\pmb { w } } ^ { T } \\pmb { x }$ , the saliency map reduces to analyzing the weights $\\partial y / \\partial x = w$ . Since it is mostly determined by the distractor, as demonstrated above, it is not representing the signal. It tells us how to extract the signal, not what the signal is in a deep neural network. ", + "bbox": [ + 174, + 426, + 825, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Signal – DeConvNet, Guided BackProp, PatternNet The signal $\\pmb { s }$ detected by the neural network is the component of the data that caused the networks activations. Zeiler & Fergus (2014) formulated the goal of these methods as ”[...] to map these activities back to the input pixel space, showing what input pattern originally caused a given activation in the feature maps”. ", + "bbox": [ + 174, + 559, + 825, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a linear model, the signal corresponds to $\\mathbf { \\boldsymbol { s } } = \\mathbf { \\boldsymbol { a } } _ { s } \\boldsymbol { y }$ . The pattern $\\mathbf { \\delta } _ { \\mathbf { \\alpha } \\mathbf { \\delta } _ { a _ { s } } }$ contains the signal direction, i.e., it tells us where a change of the output variable is expected to be measurable in the input (Haufe et al., 2014). Attempts to visualize the signal for deep neural networks were made using DeConvNet (Zeiler & Fergus, 2014) and Guided BackProp (Springenberg et al., 2015). These use the same algorithm as the saliency map, but treat the rectifiers differently (see Fig. 1): DeConvNet leaves out the rectifiers from the forward pass, but adds additional ReLUs after each deconvolution, while Guided BackProp uses the ReLUs from the forward pass as well as additional ones. The back-projections for the linear components of the network correspond to a superposition of what are assumed to be the signal directions of each neuron. For this reason, these projections must be seen as an approximation of the features that activated the higher layer neuron. It is not a reconstruction in input space (Zeiler & Fergus, 2014). ", + "bbox": [ + 174, + 621, + 825, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the simplest of neural networks – the linear model – these visualizations reduce to the gradient1. They show the filter $\\pmb { w }$ and neither the pattern $\\mathbf { \\delta } _ { a _ { s } }$ , nor the signal $\\pmb { s }$ . Hence, DeConvNet and Guided BackProp do not guarantee to produce the detected signal for a linear model, which is proven by our toy example in Fig. 2. Since they do produce compelling visualizations, we will later investigate whether the direction of the filter $\\pmb { w }$ coincides with the direction of the signal $\\pmb { s }$ . We will show that this is not the case and propose a new approach, PatternNet (see Fig. 1), to estimate the correct direction that improves upon the DeConvNet and Guided BackProp visualizations. ", + "bbox": [ + 174, + 781, + 825, + 878 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attribution – LRP, Deep Taylor Decomposition, PatternAttribution Finally, we can look at how much the signal dimensions contribute to the output through the layers. This will be referred to as the attribution. For a linear model, the optimal attribution would be obtained by element-wise multiplying the signal with the weight vector: $\\mathbf { \\boldsymbol { r } } ^ { i n p u t } = \\mathbf { \\boldsymbol { w } } \\odot \\mathbf { \\boldsymbol { a } } y$ , with $\\odot$ the element-wise multiplication. Bach et al. (2015) introduced layer-wise relevance propagation (LRP) as a decomposition of pixel-wise contributions (called relevances). Montavon et al. (2017) extended this idea and proposed the deep Taylor decomposition (DTD). The key idea of DTD is to decompose the activation of a neuron in terms of contributions from its inputs. This is achieved using a first-order Taylor expansion around a root point $\\scriptstyle { \\mathbf { { \\mathit { x } } } } _ { 0 }$ with ${ \\pmb w } ^ { T } { \\pmb x } _ { 0 } = 0$ . The relevance of the selected output neuron $i$ is initialized with its output from the forward pass. The relevance from neuron $i$ in layer $l$ is re-distributed towards its input as: ", + "bbox": [ + 173, + 103, + 825, + 256 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/b25ae5056eefef3f85942556900ea8eacfecf3645672fb5addc26c0d0e379d07.jpg", + "text": "$$\nr _ { i } ^ { o u t p u t } = y , \\qquad r _ { j \\neq i } ^ { o u t p u t } = 0 , \\qquad r ^ { l - 1 , i } = \\frac { w \\odot ( x - x _ { 0 } ) } { w ^ { T } x } r _ { i } ^ { l } .\n$$", + "text_format": "latex", + "bbox": [ + 274, + 263, + 722, + 295 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To obtain the relevance for neuron $i$ in layer $l - 1$ the incoming relevances from all connected neurons $j$ in layer $l$ are summed ", + "bbox": [ + 171, + 301, + 825, + 329 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/73621359c316d3d4829bce90aed25007171642f906cb23475d93d08b8cb11b55.jpg", + "text": "$$\nr _ { i } ^ { l - 1 } = \\sum _ { j } r _ { i } ^ { l - 1 , j } .\n$$", + "text_format": "latex", + "bbox": [ + 436, + 328, + 562, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here we can safely assume that ${ \\pmb w } ^ { T } { \\pmb x } > 0$ because a non-active ReLU unit from the forward pass stops the re-distribution in the backward pass. This is identical to how a ReLU stops the propagation of the gradient. The difficulty in the application of the deep Taylor decomposition is the choice of the root point $\\scriptstyle { \\pmb x } _ { 0 }$ , for which many options are available. It is important to recognize at this point that selecting a root point for the DTD corresponds to estimating the distractor $\\scriptstyle { \\pmb { x } } _ { 0 } = { \\pmb { d } }$ and, by that, the signal $\\hat { \\pmb { s } } = \\pmb { x } - \\pmb { x } _ { 0 }$ . PatternAttribution is a DTD extension that learns from data how to set the root point. ", + "bbox": [ + 173, + 367, + 825, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Summarizing, the function extracts the signal from the data by removing the distractor. The attribution of output values to input dimensions shows how much an individual component of the signal contributes to the output, which is what LRP calls relevance. ", + "bbox": [ + 174, + 473, + 825, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 LEARNING TO ESTIMATE THE SIGNAL ", + "text_level": 1, + "bbox": [ + 174, + 537, + 516, + 553 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visualizing the function has proven to be straightforward (Baehrens et al., 2010; Simonyan et al., 2014). In contrast, visualizing the signal (Haufe et al., 2014; Zeiler & Fergus, 2014; Springenberg et al., 2015) and the attribution (Bach et al., 2015; Montavon et al., 2017; Sundararajan et al., 2017) is more difficult. It requires a good estimate of what is the signal and what is the distractor. In the following section we first propose a quality measure for neuron-wise signal estimators. This allows us to evaluate existing approaches and, finally, derive signal estimators that optimize this criterion. These estimators will then be used to explain the signal (PatternNet) and the attribution (PatternAttribution). All mentioned techniques as well as our proposed signal estimators treat neurons independently, i.e., the full explanation will be a superposition of neuron-wise explanations. ", + "bbox": [ + 173, + 568, + 825, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1 QUALITY CRITERION FOR SIGNAL ESTIMATORS ", + "text_level": 1, + "bbox": [ + 174, + 712, + 542, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recall that the input data $_ { \\textbf { \\em x } }$ comprises both signal and distractor: ${ \\pmb x } = { \\pmb s } + { \\pmb d }$ , and that the signal contributes to the output but the distractor does not. Assuming the filter $\\textbf { \\em w }$ has been trained sufficiently well to extract $y$ , we have ", + "bbox": [ + 174, + 738, + 825, + 780 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/e7d09f49ef0fbbe9039ad145b622d49cb7717966d43992239755abdc0890bfbd.jpg", + "text": "$$\n\\begin{array} { r } { \\boldsymbol { w } ^ { T } \\boldsymbol { x } = \\boldsymbol { y } , \\quad \\boldsymbol { w } ^ { T } \\boldsymbol { s } = \\boldsymbol { y } , \\quad \\boldsymbol { w } ^ { T } \\boldsymbol { d } = 0 . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 367, + 785, + 629, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that estimating the signal based on these conditions alone is an ill-posed problem. We could limit ourselves to linear estimators of the form $\\hat { \\pmb { s } } = \\pmb { u } ( \\pmb { w } ^ { T } \\pmb { u } ) ^ { - 1 } \\pmb { y }$ , with $\\textbf { \\em u }$ a random vector such that $\\pmb { w } ^ { T } \\pmb { u } \\neq 0$ . For such an estimator, the signal estimate $\\hat { \\pmb { s } } = \\pmb { u } \\left( \\pmb { w } ^ { T } \\pmb { u } \\right) ^ { - 1 } \\ b { y }$ satisfies $\\mathbf { \\boldsymbol { w } } ^ { T } \\hat { \\mathbf { \\boldsymbol { s } } } = \\boldsymbol { y }$ . This implies the existence of an infinite number of possible rules for the DTD as well as infinitely many back-projections for the DeConvNet family. ", + "bbox": [ + 174, + 811, + 825, + 887 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To alleviate this issue, we introduce the following quality measure $\\rho$ for a signal estimator $S ( { \\pmb x } ) = \\hat { \\pmb s }$ that will be written with explicit variances and covariances using the shorthands $\\hat { \\pmb { d } } = \\pmb { x } - \\pmb { S } ( \\pmb { x } )$ and ", + "bbox": [ + 173, + 892, + 823, + 924 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/1dae6d2be042669e1185ea2c754a6d49a234f17cfcc5cf4d2fae7983f250cff2.jpg", + "text": "$$\ny = \\pmb { w } ^ { T } \\pmb { x } \\colon\n$$", + "text_format": "latex", + "bbox": [ + 173, + 102, + 245, + 119 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/e0b280e91657c8d29470f2a1326d5513f35acdd2e418d3eed270c4ba16a37c64.jpg", + "text": "$$\n\\rho ( S ) = 1 - \\operatorname* { m a x } _ { \\pmb { v } } c o r r \\left( \\pmb { w } ^ { T } \\pmb { x } , \\pmb { v } ^ { T } \\left( \\pmb { x } - S ( \\pmb { x } ) \\right) \\right) = 1 - \\operatorname* { m a x } _ { \\pmb { v } } \\frac { \\pmb { v } ^ { T } \\mathrm { c o v } [ \\hat { d } , y ] } { \\sqrt { \\sigma _ { \\pmb { v } ^ { T } \\hat { d } } ^ { 2 } \\sigma _ { y } ^ { 2 } } } .\n$$", + "text_format": "latex", + "bbox": [ + 258, + 126, + 740, + 172 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This criterion introduces an additional constraint by measuring how much information about $y$ can be reconstructed from the residuals $\\mathbf { \\Delta } \\mathbf { x } - \\hat { \\mathbf { \\mu } } _ { s }$ using a linear projection. The best signal estimators remove most of the information iinvariant to scaling, we constrain ${ \\pmb v } ^ { T } \\hat { \\pmb d }$ residuals and thto have varian $\\sigma _ { v ^ { T } \\hat { d } } ^ { 2 } = \\sigma _ { y } ^ { 2 }$ $\\rho ( S )$ . Since the correlding the optimal $\\textbf { { v } }$ ion isfor a fixed amounts to a least-squares regression from $\\hat { \\ b { d } }$ to $y$ . This enables us to assess the quality of signal estimators efficiently. ", + "bbox": [ + 173, + 178, + 826, + 271 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2 EXISTING SIGNAL ESTIMATORS ", + "text_level": 1, + "bbox": [ + 176, + 287, + 434, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Let us now discuss two signal estimators that have been used in previous approaches. ", + "bbox": [ + 173, + 314, + 730, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$S _ { x }$ – the identity estimator The naive approach to signal estimation is to assume the entire data is signal and there are no distractors: ", + "bbox": [ + 174, + 344, + 821, + 373 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/7293ad93e9b4502ba4d927df2424160dcbad8bb9e8cea4ef77827a6b0a185850.jpg", + "text": "$$\nS _ { x } ( { \\pmb x } ) = { \\pmb x } .\n$$", + "text_format": "latex", + "bbox": [ + 457, + 373, + 540, + 391 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "With this being plugged into the deep Taylor framework, we obtain the $z$ -rule (Montavon et al., 2017) which is equivalent to LRP (Bach et al., 2015). For a linear model, this corresponds to $\\mathbf { \\Delta } \\mathbf { \\mathbf { \\mathit { r } } } = \\mathbf { \\mathit { w } } \\odot \\mathbf { \\mathbf { \\mathit { x } } }$ as the attribution. It can be shown that for ReLU and max-pooling networks, the $z$ -rule reduces to the element-wise multiplication of the input and the saliency map (Shrikumar et al., 2016; Kindermans et al., 2016). This means that for a whole network, the assumed signal is simply the original input image. It also implies that, if there are distractors present in the data, they are included in the attribution: ", + "bbox": [ + 173, + 395, + 825, + 492 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/a60da33747453bbd841cf0bb504651991b7911dbb045537eb85199eaf7427bb7.jpg", + "text": "$$\n\\pmb { r } = \\pmb { w } \\odot \\pmb { x } = \\pmb { w } \\odot \\pmb { s } + \\pmb { w } \\odot \\pmb { d } .\n$$", + "text_format": "latex", + "bbox": [ + 392, + 493, + 604, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When moving through the layers by applying the filters $\\pmb { w }$ during the forward pass, the contributions from the distractor $^ d$ are cancelled out. However, they cannot be cancelled in the backward pass by the element-wise multiplication. The distractor contributions $\\omega \\odot d$ that are included in the LRP explanation cause the noisy nature of the visualizations based on the $z$ -rule. ", + "bbox": [ + 174, + 513, + 825, + 569 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$S _ { w }$ – the filter based estimator The implicit assumption made by DeConvNet and Guided BackProp is that the detected signal varies in the direction of the weight vector $\\pmb { w }$ . This weight vector has to be normalized in order to be a valid signal estimator. In the deep Taylor decomposition framework this corresponds to the $w ^ { 2 }$ -rule and results in the following signal estimator: ", + "bbox": [ + 174, + 585, + 825, + 642 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/310de1955c2d2e26897b63a4f5cab5e1d1fa562287b0ee2d2f7191972f55e90a.jpg", + "text": "$$\nS _ { \\pmb { w } } ( \\pmb { x } ) = \\frac { \\pmb { w } } { \\pmb { w } ^ { T } \\pmb { w } } \\pmb { w } ^ { T } \\pmb { x } .\n$$", + "text_format": "latex", + "bbox": [ + 423, + 648, + 575, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For a linear model, this produces an attribution of the form $\\frac { { \\pmb w } \\odot { \\pmb w } } { { \\pmb w } ^ { T } . { \\pmb w } } \\textcircled { y }$ . This estimator does not reconstruct the proper signal in the toy example of section 2. Empirically it is also sub-optimal in our experiment in Fig. 3. ", + "bbox": [ + 173, + 684, + 825, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3 PATTERNNET AND PATTERNATTRIBUTION ", + "text_level": 1, + "bbox": [ + 173, + 744, + 508, + 760 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We suggest to learn the signal estimator $S$ from data by optimizing the previously established criterion. A signal estimator $S$ is optimal with respect to Eq. (1) if the correlation is zero for all possible ${ \\pmb v } \\colon \\forall { \\pmb v } , \\mathrm { c o v } [ y , \\hat { \\pmb d } ] { \\pmb v } = { \\bf 0 }$ . This is the case when there is no covariance between $y$ and $\\hat { \\ b { d } }$ . Because of linearity of the covariance and since $\\hat { \\pmb { d } } = \\pmb { x } - \\pmb { S } ( \\pmb { x } )$ the above condition leads to ", + "bbox": [ + 173, + 771, + 825, + 833 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/7f5a4b684c062604fdd22da11b23bc767fdfdb281ba3f08896b90160da6cf789.jpg", + "text": "$$\n\\mathrm { c o v } [ y , \\hat { d } ] = { \\bf 0 } \\Rightarrow \\mathrm { c o v } [ { \\pmb x } , y ] = \\mathrm { c o v } [ S ( { \\pmb x } ) , y ] .\n$$", + "text_format": "latex", + "bbox": [ + 356, + 840, + 642, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "It is important to recognize that the covariance is a summarizing statistic and consequently the problem can still be solved in multiple ways. We will present two possible solutions to this problem. Note that when optimizing the estimator, the contribution from the bias neuron will be considered 0 since it does not covary with the output $y$ . ", + "bbox": [ + 174, + 867, + 825, + 924 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$S _ { a }$ – The linear estimator A linear neuron can only extract linear signals $\\pmb { s }$ from its input $_ { \\textbf { \\em x } }$ . Therefore, we could assume a linear dependency between $\\pmb { s }$ and $y$ , yielding a signal estimator: ", + "bbox": [ + 169, + 103, + 823, + 132 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/5578591e74a0e03d02d72254b68cba0aeab5e108662390256d8a47d0acc4e90f.jpg", + "text": "$$\n\\begin{array} { r } { S _ { \\pmb { a } } ( \\pmb { x } ) = \\pmb { a } \\pmb { w } ^ { T } \\pmb { x } . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 439, + 132, + 557, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Plugging this into Eq. (2) and optimising for $^ { a }$ yields ", + "bbox": [ + 174, + 151, + 524, + 166 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/23d9fa8b0c1b1e69bbfecbdad8c8e62ae5789ee431dfd0d716a925fb03a028e0.jpg", + "text": "$$\n\\operatorname { c o v } [ { \\pmb x } , { \\pmb y } ] = \\operatorname { c o v } [ { \\pmb a } { \\pmb w } ^ { T } { \\pmb x } , { \\pmb y } ] = { \\pmb a } \\mathrm { c o v } [ { \\pmb y } , { \\pmb y } ] \\Rightarrow { \\pmb a } = \\frac { \\mathrm { c o v } [ { \\pmb x } , { \\pmb y } ] } { \\sigma _ { y } ^ { 2 } } .\n$$", + "text_format": "latex", + "bbox": [ + 302, + 166, + 696, + 202 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note that this solution is equivalent to the approach commonly used in neuro-imaging (Haufe et al., 2014) despite different derivation. With this approach we can recover the signal of our toy example in section 2. It is equivalent to the filter-based approach only if the distractors are orthogonal to the signal. We found that the linear estimator works well for the convolutional layers. However, when using this signal estimator with ReLUs in the dense layers, there is still a considerable correlation left in the distractor component (see Fig. 3). ", + "bbox": [ + 173, + 202, + 825, + 286 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$S _ { a _ { + - } }$ – The two-component estimator To move beyond the linear signal estimator, it is crucial to understand how the rectifier influences the training. Since the gate of the ReLU closes for negative activations, the weights only need to filter the distractor component of neurons with $y > 0$ . Since this allows the neural network to apply filters locally, we cannot assume a global distractor component. We rather need to distinguish between the positive and negative regime: ", + "bbox": [ + 173, + 299, + 825, + 369 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/03c2b918810fe3dfa27c47f2e8b231d138547f168e015c751b1fae1335693dc5.jpg", + "text": "$$\n\\pmb { x } = \\left\\{ \\begin{array} { l l } { \\pmb { s } _ { + } + \\pmb { d } _ { + } } & { \\mathrm { i f } \\ y > 0 } \\\\ { \\pmb { s } _ { - } + \\pmb { d } _ { - } } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$", + "text_format": "latex", + "bbox": [ + 403, + 371, + 589, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Even though signal and distractor of the negative regime are canceled by the following ReLU, we still need to make this distinction in order to approximate the signal. Otherwise, information about whether a neuron fired would be retained in the distractor. Thus, we propose the two-component signal estimator: ", + "bbox": [ + 174, + 407, + 825, + 463 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/2ffa4483f412bc6e35f44147511080e5b175671bf5b61f0dc40029f89ea3e14e.jpg", + "text": "$$\n\\begin{array} { r } { S _ { \\boldsymbol { a } + - } ( \\boldsymbol { x } ) = \\left\\{ \\begin{array} { l l } { \\boldsymbol { a } _ { + } \\boldsymbol { w } ^ { T } \\boldsymbol { x } , \\quad \\mathrm { i f } \\ \\boldsymbol { w } ^ { T } \\boldsymbol { x } > 0 } \\\\ { \\boldsymbol { a } _ { - } \\boldsymbol { w } ^ { T } \\boldsymbol { x } , \\quad \\mathrm { o t h e r w i s e } } \\end{array} \\right. } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 359, + 462, + 620, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next, we derive expressions for the patterns ${ \\pmb a } _ { + }$ and $\\mathbf { \\delta } \\mathbf { a } _ { - }$ . We denote expectations over $_ { \\textbf { \\em x } }$ within the positive and negative regime with $\\bar { \\mathbb { E } _ { + } } \\left[ x \\right]$ and $\\mathbb { E } _ { - } \\left[ { \\pmb x } \\right]$ , respectively. Let $\\pi _ { + }$ be the expected ratio of inputs $_ { \\textbf { \\em x } }$ with $\\mathbf { \\Sigma } \\mathbf { w } ^ { T } \\mathbf { x } > 0$ . The covariance of data/signal and output become: ", + "bbox": [ + 173, + 506, + 823, + 546 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/6bf36795903aa07f5d4fb841069959b6212a83d69e2c0c6041454c6df22fc1f2.jpg", + "text": "$$\n\\begin{array} { r l r } { \\mathrm { c o v } [ { \\pmb x } , { y } ] = } & { } & { \\pi _ { + } \\left( \\mathbb { E } _ { + } \\left[ { \\pmb x } { \\pmb y } \\right] - \\mathbb { E } _ { + } \\left[ { \\pmb x } \\right] \\mathbb { E } \\left[ { \\pmb y } \\right] \\right) + \\frac { } { } \\left( 1 - \\pi _ { + } \\right) \\left( \\mathbb { E } _ { - } \\left[ { \\pmb x } { \\pmb y } \\right] - \\mathbb { E } _ { - } \\left[ { \\pmb x } \\right] \\mathbb { E } \\left[ { \\pmb y } \\right] \\right) } \\\\ { \\mathrm { c o v } [ { \\pmb s } , { y } ] = } & { } & { \\pi _ { + } \\left( \\mathbb { E } _ { + } \\left[ { \\pmb s } { \\pmb y } \\right] - \\mathbb { E } _ { + } \\left[ { \\pmb s } \\right] \\mathbb { E } \\left[ { \\pmb y } \\right] \\right) + \\frac { } { } \\left( 1 - \\pi _ { + } \\right) \\left( \\mathbb { E } _ { - } \\left[ { \\pmb s } { \\pmb y } \\right] - \\mathbb { E } _ { - } \\left[ { \\pmb s } \\right] \\mathbb { E } \\left[ { \\pmb y } \\right] \\right) } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 200, + 547, + 777, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Assuming both covariances are equal, we can treat the positive and negative regime separately using Eq. (2) to optimize the signal estimator: ", + "bbox": [ + 181, + 584, + 821, + 611 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/297fe70479f0f78a51c56cff0e538420831f6185ef9eef62392254602a78e4d9.jpg", + "text": "$$\n\\begin{array} { r l r } { { \\mathbb E } _ { + } \\left[ { \\pmb x } { \\pmb y } \\right] - { \\mathbb E } _ { + } \\left[ { \\pmb x } \\right] { \\mathbb E } \\left[ { \\pmb y } \\right] } & { = } & { { \\mathbb E } _ { + } \\left[ { \\pmb s } { \\pmb y } \\right] - { \\mathbb E } _ { + } \\left[ { \\pmb s } \\right] { \\mathbb E } \\left[ { \\pmb y } \\right] } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 325, + 612, + 673, + 630 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Plugging in Eq. (5) and solving for ${ \\pmb a } _ { + }$ yields the required parameter $( a _ { - }$ analogous). ", + "bbox": [ + 174, + 631, + 728, + 645 + ], + "page_idx": 6 + }, + { + "type": "equation", + "img_path": "images/47323f463de64411135ad259331aed678503eaa517a346b726db51122bb5d637.jpg", + "text": "$$\n\\begin{array} { r l r } { \\pmb { a } _ { + } } & { = } & { \\frac { \\mathbb { E } _ { + } \\left[ \\pmb { x } \\pmb { y } \\right] - \\mathbb { E } _ { + } \\left[ \\pmb { x } \\right] \\mathbb { E } \\left[ \\pmb { y } \\right] } { \\pmb { w } ^ { T } \\mathbb { E } _ { + } \\left[ \\pmb { x } \\pmb { y } \\right] - \\pmb { w } ^ { T } \\mathbb { E } _ { + } \\left[ \\pmb { x } \\right] \\mathbb { E } \\left[ \\pmb { y } \\right] } } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 357, + 645, + 638, + 679 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The solution for $S _ { a + - }$ reduces to the linear estimator when the relation between input and output is linear. Therefore, it solves our introductory linear example correctly. ", + "bbox": [ + 174, + 680, + 821, + 708 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PatternNet and PatternAttribution Based on the presented analysis, we propose PatternNet and PatternAttribution as illustrated in Fig. 1. PatternNet yields a layer-wise back-projection of the estimated signal to input space. The signal estimator is approximated as a superposition of neuron-wise, nonlinear signal estimators $S _ { a + - }$ in each layer. It is equal to the computation of the gradient where during the backward pass the weights of the network are replaced by the informative directions. In Fig. 1, a visual improvement over DeConvNet and Guided Backprop is apparent. ", + "bbox": [ + 173, + 720, + 825, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PatternAttribution exposes the attribution ${ \\pmb w } \\odot { \\pmb a } _ { + }$ and improves upon the layer-wise relevance propagation (LRP) framework (Bach et al., 2015). It can be seen as a root point estimator for the DeepTaylor Decomposition (DTD). Here, the explanation consists of neuron-wise contributions of the estimated signal to the classification score. By ignoring the distractor, PatternAttribution can reduce the noise and produces much clearer heat maps. By working out the back-projection steps in the Deep-Taylor Decomposition with the proposed root point selection method, it becomes obvious that PatternAttribution is also analogous to the backpropagation operation. In this case, the weights are replaced during the backward pass by ${ \\pmb w } \\odot { \\pmb a } _ { + }$ . ", + "bbox": [ + 174, + 811, + 825, + 924 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c4bfa0b68162a0e16416f5555faa6fa77e72b7690d63e5a5bd97481ad920da0.jpg", + "image_caption": [ + "Figure 3: Evaluating $\\rho ( S )$ for VGG-16 on ImageNet. Higher values are better. The gradient $( S _ { w } )$ , linear estimator $( S _ { a } )$ and nonlinear estimator $( S _ { a _ { + - } } )$ are compared. An estimator using random directions is the baseline. The network has 5 blocks with 2/3 convolutional layers and 1 max-pooling layer each, followed by 3 dense layers. " + ], + "image_footnote": [], + "bbox": [ + 194, + 58, + 815, + 210 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d8e47053480d3957b47a181537b3935694502e6013c570f2ac522e4d8be5dfd1.jpg", + "image_caption": [ + "Figure 4: Image degradation experiment on all 50.000 images in the ImageNet validation set. The effect on the classifier output is measured. A steeper decrease is better. " + ], + "image_footnote": [], + "bbox": [ + 334, + 297, + 660, + 459 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5 EXPERIMENTS AND DISCUSSION ", + "text_level": 1, + "bbox": [ + 176, + 531, + 473, + 546 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the quality of the explanations, we focus on the task of image classification. Nevertheless, our method is not restricted to networks operating on image inputs. We used Theano (Bergstra et al., 2010) and Lasagne (Dieleman et al., 2015) for our implementation. We restrict the analysis to the well-known ImageNet dataset (Russakovsky et al., 2015) using the pre-trained VGG-16 model (Simonyan & Zisserman, 2015). Images were rescaled and cropped to $2 2 4 \\mathbf { x } 2 2 4$ pixels. The signal estimators are trained on the first half of the training dataset. ", + "bbox": [ + 174, + 568, + 825, + 652 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The vector $\\pmb { v }$ , used to measure the quality of the signal estimator $\\rho ( { \\pmb x } )$ in Eq. (1), is optimized on the second half of the training dataset. This enables us to test the signal estimators for generalization. All the results presented here were obtained using the official validation set of 50000 samples. The validation set was not used for training the signal estimators, nor for training the vector $\\pmb { v }$ to measure the quality. Consequently our results are obtained on previously unseen data. ", + "bbox": [ + 174, + 659, + 825, + 728 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The linear and the two component signal estimators are obtained by solving their respective closed form solutions (Eq. (4) and Eq. (8)). With a highly parallelized implementation using 4 GPUs this could be done in 3-4 hours. This can be considered reasonable given that several days are required to train the actual network. The quality of a signal estimator is assessed with Eq. (1). Solving it with the closed form solution is computationally prohibitive since it must be repeated for every single weight vector in the network. Therefore we optimize the equivalent least-squares problem using stochastic mini-batch gradient descent with ADAM Kingma & Ba (2015) until convergence. This was implemented on a NVIDIA Tesla K40 and took about 24 hours per optimized signal estimator. ", + "bbox": [ + 174, + 734, + 825, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "After learning to explain, individual explanations are computationally cheap since they can be implemented as a back-propagation pass with a modified weight vector. As a result, our method produces explanations at least as fast as the work by Dabkowski & Gal (2017) on real time saliency. However, our method has the advantage that it is not only applicable to image models but is a generalization of the theory commonly used in neuroimaging Haufe et al. (2014). ", + "bbox": [ + 174, + 854, + 823, + 924 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b372c59547081ace17a88655dd8b643c962e0a2010955da9560f3fc9f8db8ad9.jpg", + "image_caption": [ + "Figure 5: Top: signal. Bottom: attribution. For the trivial estimator $S _ { x }$ the original input is the signal. This is not informative w.r.t. how the network operates. " + ], + "image_footnote": [], + "bbox": [ + 338, + 99, + 661, + 261 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Measuring the quality of signal estimators In Fig. 3 we present the results from the correlation measure $\\rho ( { \\pmb x } )$ , where higher values are better. We use random directions as baseline signal estimators. Clearly, this approach removes almost no correlation. The filter-based estimator $S _ { w }$ succeeds in removing some of the information in the first layer. This indicates that the filters are similar to the patterns in this layer. However, the gradient removes much less information in the higher layers. Overall, it does not perform much better than the random estimator. This implies that the weights do not correspond to the detected stimulus in a neural network. Hence the implicit assumptions about the signal made by DeConvNet and Guided BackProp is not valid. The optimized estimators remove much more of the correlations across the board. For convolutional layers, $S _ { a }$ and $S _ { a + - }$ perform comparably in all but one layer. The two component estimator $S _ { a + - }$ is best in the dense layers. ", + "bbox": [ + 173, + 332, + 825, + 472 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Image degradation The first experiment was a direct measurement of the quality of the signal estimators of individual neurons. The second one is an indirect measurement of the quality, but it considers the whole network. We measure how the prediction (after the soft-max) for the initially selected class changes as a function of corrupting more and more patches based on the ordering assigned by the attribution (see Samek et al., 2016). This is also related to the work by Zintgraf et al. (2017). In this experiment, we split the image in non-overlapping patches of $9 \\mathrm { x } 9$ pixels. We compute the attribution and sum all the values within a patch. We sort the patches in decreasing order based on the aggregate heat map value. In step $n = 1 . . 1 0 0$ we replace the first $n$ patches with the their mean per color channel to remove the information in this patch. Then, we measure how this influences the classifiers output. We use the estimators from the previous experiment to obtain the function-signal attribution heat maps for evaluation. A steeper decay indicates a better heat map. ", + "bbox": [ + 174, + 488, + 825, + 641 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Results are shown in Fig. 4. The baseline, in which the patches are randomly ordered, performs worst. The linear optimized estimator $S _ { a }$ performs quite poorly, followed by the filter-based estimator $S _ { w }$ . The trivial signal estimator $S _ { x }$ performs just slightly better. However, the two component model $S _ { a + - }$ leads to the fastest decrease in confidence in the original prediction by a large margin. Its excellent quantitative performance is also backed up by the visualizations discussed next. ", + "bbox": [ + 174, + 648, + 825, + 718 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Qualitative evaluation In Fig. 5, we compare all signal estimators on a single input image. For the trivial estimator $S _ { x }$ , the signal is by definition the original input image and, thus, includes the distractor. Therefore, its noisy attribution heat map shows contributions that cancel each other in the neural network. The $S _ { w }$ estimator captures some of the structure. The optimized estimator $S _ { a }$ results in slightly more structure but struggles on color information and produces dense heat maps. The two component model $S _ { a + - }$ on the right captures the original input during signal estimation and produces a crisp heat map of the attribution. ", + "bbox": [ + 174, + 736, + 825, + 833 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Fig. 6 shows the visualizations for six randomly selected images from ImageNet. PatternNet is able to recover a signal close to the original without having to resort to the inclusion of additional rectifiers in contrast to DeConvNet and Guided BackProp. We argue that this is due to the fact that the optimization of the pattern allows for capturing the important directions in input space. This contrasts with the commonly used methods DeConvNet, Guided BackProp, LRP and DTD, for which the correlation experiment indicates that their implicit signal estimator cannot capture the true signal in the data. Overall, the proposed approach produces the most crisp visualization in addition to being measurably better, as shown in the previous section. Additonally, we also contrast our methods to the prediction-differences analysis by Zintgraf et al. (2017) in the supplementary material. ", + "bbox": [ + 174, + 840, + 825, + 924 + ], + "page_idx": 8 + }, + { + "type": "image", + "img_path": "images/cb30d37d6dbeabf075edf5246d5726ad4db711f47c218a2fd6889841b22072a4.jpg", + "image_caption": [ + "Figure 6: Visualization of random images from ImageNet (validation set). In the leftmost shows column the ground truth, the predicted label and the classifier’s confidence. Methods should only be compared within their group. PatternNet, Guided Backprop, DeConvNet and the Gradient (saliency map) are back-projections to input space with the original color channels. They are normalized using $\\begin{array} { r } { x _ { n o r m } = \\frac { \\bar { x } } { 2 \\operatorname* { m a x } | x | } + \\frac { 1 } { 2 } } \\end{array}$ to maximize contrast. LRP and PatternAttribution are heat maps showing pixel-wise contributions. " + ], + "image_footnote": [], + "bbox": [ + 181, + 101, + 813, + 407 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 535, + 823, + 590 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Relation to previous methods Our method can be thought of as a generalization of the work by Haufe et al. (2014), making it applicable on deep neural networks. Remarkably, our proposed approach can solve the toy example in section 2 optimally while none of the previously published methods for deep learning are able to solve this (Bach et al., 2015; Montavon et al., 2017; Smilkov et al., 2017; Sundararajan et al., 2017; Zintgraf et al., 2017; Dabkowski & Gal, 2017; Zeiler & Fergus, 2014; Springenberg et al., 2015). Our method shares the idea that to explain a model properly one has to learn how to explain it with Zintgraf et al. (2017) and Dabkowski & Gal (2017). Furthermore, since our approach is after training just as expensive as a single back-propagation step, it can be applied in a real-time context, which is also possible for the work done by Dabkowski & Gal (2017) but not for Zintgraf et al. (2017). ", + "bbox": [ + 173, + 607, + 825, + 746 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6 CONCLUSION ", + "text_level": 1, + "bbox": [ + 174, + 766, + 318, + 782 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Understanding and explaining nonlinear methods is an important challenge in machine learning. Algorithms for visualizing nonlinear models have emerged but theoretical contributions are scarce. We have shown that the direction of the model gradient does not necessarily provide an estimate for the signal in the data. Instead it reflects the relation between the signal direction and the distracting noise contributions ( Fig. 2). This implies that popular explanation approaches for neural networks (DeConvNet, Guided BackProp, LRP) do not provide the correct explanation, even for a simple linear model. Our reasoning can be extended to nonlinear models. We have proposed an objective function for neuron-wise explanations. This can be optimized to correct the signal visualizations (PatternNet) and the decomposition methods (PatternAttribution) by taking the data distribution into account. We have demonstrated that our methods constitute a theoretical, qualitative and quantitative improvement towards understanding deep neural networks. ", + "bbox": [ + 174, + 797, + 825, + 924 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "", + "bbox": [ + 171, + 103, + 823, + 132 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "ACKNOWLEDGMENTS ", + "text_level": 1, + "bbox": [ + 176, + 150, + 326, + 162 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement NO 657679, the BMBF for the Berlin Big Data Center BBDC (01IS14013A), a hardware donation from NVIDIA. We thank Sander Dieleman, Jonas Degraeve, Ira Korshunova, Stefan Chmiela, Malte Esders, Sarah Hooker, Vincent Vanhoucke for their comments to improve this manuscript. We are grateful to Chris Olah and Gregoire Montavon for the valuable discussions. ", + "bbox": [ + 174, + 172, + 825, + 256 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 174, + 279, + 285, + 292 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Sebastian Bach, Alexander Binder, Gregoire Montavon, Frederick Klauschen, Klaus-Robert M ´ uller, ¨ and Wojciech Samek. On pixel-wise explanations for non-linear classifier decisions by layer-wise relevance propagation. PloS one, 10(7):e0130140, 2015. ", + "bbox": [ + 176, + 301, + 823, + 344 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "David Baehrens, Timon Schroeter, Stefan Harmeling, Motoaki Kawanabe, Katja Hansen, and KlausRobert Muller. 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Visualizing deep neural network decisions: Prediction difference analysis. In ICLR, 2017. ", + "bbox": [ + 173, + 775, + 823, + 804 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A ALGORITHMS ", + "text_level": 1, + "bbox": [ + 176, + 835, + 326, + 851 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "In this section we will give an overview of the visualization algorithms to clarify their actual implementation for ReLu networks. This shows the similarities and the differences between all approaches. For all visualization approaches, the back-projection through a max-pooling layer is only through the path that was active in the forward pass. ", + "bbox": [ + 174, + 867, + 823, + 924 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "A.1.1 GRADIENT WITH RESPECT TO THE INPUT ", + "bbox": [ + 174, + 128, + 514, + 143 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Initialization To compute the gradient of an output neuron w.r.t. to the input, we can initialize the gradient at the output neuron with a single 1, for the non-selected output neurons we initialize it at 0. ", + "bbox": [ + 173, + 154, + 823, + 193 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/f6fe2c4a75e7f2c4f7b92b7497f7ca4b7866c0f6d2958fd51b7c1ae35781ccd0.jpg", + "text": "$$\ng _ { i } ^ { o u t p u t } = y , \\qquad g _ { j \\neq i } ^ { o u t p u t } = 0 .\n$$", + "text_format": "latex", + "bbox": [ + 388, + 191, + 609, + 214 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Linear or convolutional layer If it is a linear layer, the gradients from neuron $i$ in layer $l$ can be projected back to its input along the weight vector ", + "bbox": [ + 169, + 227, + 825, + 255 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/a2be3ff605e20523929c2019a53c5b1f637deb89a5e387abbbb8cc8adbff3114.jpg", + "text": "$$\n\\begin{array} { r } { \\pmb { g } ^ { l - 1 , i } = \\pmb { w g } _ { i } ^ { l } . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 449, + 261, + 547, + 280 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The gradient of neuron $i$ at layer $l - 1$ is the sum of all incoming gradients from the layer above: ", + "bbox": [ + 169, + 286, + 805, + 301 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/759c898f308445544ce8ec3dbecbb7c7ac84be4b6ec4ea9bb8a65c962f16bac5.jpg", + "text": "$$\ng _ { i } ^ { l - 1 } = \\sum _ { j } g _ { i } ^ { l - 1 , j } .\n$$", + "text_format": "latex", + "bbox": [ + 434, + 306, + 562, + 342 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "ReLu layer To propagate through a ReLu, the propagation is blocked if the ReLu was not active in the forward pass. ", + "bbox": [ + 173, + 354, + 825, + 382 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/d2267460e6dfa0262641412ecf1e609778cc396978f1724098389e2703d63d55.jpg", + "text": "$$\ng _ { i } ^ { l - 1 } = { \\left\\{ \\begin{array} { l l } { g _ { i } ^ { l } } & { x _ { i } ^ { l } > 0 } \\\\ { 0 } & { { \\mathrm { o t h e r w i s e } } } \\end{array} \\right. }\n$$", + "text_format": "latex", + "bbox": [ + 416, + 381, + 578, + 417 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A.2 SIGNAL VISUALIZATION ", + "text_level": 1, + "bbox": [ + 174, + 434, + 387, + 448 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A.2.1 DECONVNET ", + "text_level": 1, + "bbox": [ + 176, + 458, + 328, + 473 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The DeConvNet visualization is highly similar to the computation of the gradient. The key difference is how the ReLu’s are treated. ", + "bbox": [ + 174, + 483, + 823, + 512 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Initialization To compute the visualization of the signal of an output neuron w.r.t. to the input, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. ", + "bbox": [ + 174, + 526, + 823, + 568 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/f55a76fb95c61540e15e65a5e01eeb4394f18a90249447208236a4eef0200232.jpg", + "text": "$$\ns _ { i } ^ { o u t p u t } = y , \\qquad s _ { j \\neq i } ^ { o u t p u t } = 0 .\n$$", + "text_format": "latex", + "bbox": [ + 390, + 565, + 607, + 588 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input along the weight vector. ", + "bbox": [ + 171, + 599, + 826, + 628 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/2b71861d064a8c35dc13134a2e828e201ca456de5a110d66e73e901a13ab94fa.jpg", + "text": "$$\n\\begin{array} { r } { \\pmb { s } ^ { l - 1 , i } = \\pmb { w s } _ { i } ^ { l } . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 450, + 633, + 547, + 654 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The signal of neuron $i$ at layer $l - 1$ is the sum of all incoming signals from the layer above: ", + "bbox": [ + 168, + 660, + 776, + 675 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/b8caeea92369adc715abf14b36e12400c0bf1a2a56fd0d00db7baed7d20bb556.jpg", + "text": "$$\ns _ { i } ^ { l - 1 } = \\sum _ { j } s _ { i } ^ { l - 1 , j } .\n$$", + "text_format": "latex", + "bbox": [ + 436, + 680, + 562, + 715 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "ReLu layer To propagate through a ReLu, the propagation is blocked if the signal is negative ", + "bbox": [ + 171, + 728, + 799, + 744 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/298479b37686d049360d878e02281e4b27e25c933ab3a0da14b907bf70c97704.jpg", + "text": "$$\ns _ { i } ^ { l - 1 } = \\left\\{ \\begin{array} { l l } { s _ { i } ^ { l } } & { s _ { i } ^ { l } > 0 } \\\\ { 0 } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$", + "text_format": "latex", + "bbox": [ + 418, + 750, + 578, + 786 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "A.2.2 GUIDED BACKPROPAGATION ", + "text_level": 1, + "bbox": [ + 174, + 799, + 431, + 815 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "The Guided Backpropagation visualization is highly similar to the computation of the gradient. and to DeConvNet. The only difference is how the ReLu’s are treated. ", + "bbox": [ + 173, + 824, + 825, + 853 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Initialization To compute the visualization of the signal of an output neuron w.r.t. to the input, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. ", + "bbox": [ + 171, + 867, + 823, + 907 + ], + "page_idx": 12 + }, + { + "type": "equation", + "img_path": "images/091438fc35a18f873e591c5b37a7eed050775c9ff52c63095605c99f9e2c8de9.jpg", + "text": "$$\ns _ { i } ^ { o u t p u t } = y , \\qquad s _ { j \\neq i } ^ { o u t p u t } = 0 .\n$$", + "text_format": "latex", + "bbox": [ + 390, + 905, + 607, + 928 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input along the weight vector ", + "bbox": [ + 169, + 103, + 825, + 132 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/191c107fdea5c7b75152346d1001ca1f185e0f1dbabc04dfeeb18adb233d7d76.jpg", + "text": "$$\n\\begin{array} { r } { \\pmb { s } ^ { l - 1 , i } = \\pmb { w s } _ { i } ^ { l } . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 450, + 133, + 547, + 154 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The signal of neuron $i$ at layer $l - 1$ is the sum of all incoming signals from the layer above: ", + "bbox": [ + 169, + 162, + 776, + 178 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/4c4a542c76148b44dcba7f2bd9a0878a361b0697aa940ecadc01e9a7fe3c3a9e.jpg", + "text": "$$\ns _ { i } ^ { l - 1 } = \\sum _ { j } s _ { i } ^ { l - 1 , j } .\n$$", + "text_format": "latex", + "bbox": [ + 436, + 179, + 562, + 214 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "ReLu layer To propagate through a ReLu, the propagation is blocked if the signal is negative or if the neuron was not active in the forward pass ", + "bbox": [ + 173, + 223, + 823, + 252 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/b4a508f80aed35b104942bd8f98b0aa04f3d5e994e79935eea459b2fd1d89e99.jpg", + "text": "$$\ns _ { i } ^ { l - 1 } = \\left\\{ \\begin{array} { l l } { s _ { i } ^ { l } } & { s _ { i } ^ { l } > 0 \\mathrm { a n d } x _ { i } ^ { l } > 0 } \\\\ { 0 } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$", + "text_format": "latex", + "bbox": [ + 385, + 255, + 611, + 291 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.2.3 PATTERNNET ", + "text_level": 1, + "bbox": [ + 174, + 300, + 326, + 315 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The PatternNet computation is analogous to the gradient computation. The key difference is that during the backward pass patterns are used instead of weights. ", + "bbox": [ + 173, + 324, + 823, + 354 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Initialization To compute the visualization of the signal of an output neuron w.r.t. to the input, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. ", + "bbox": [ + 173, + 367, + 823, + 409 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/760219775bfbc6a3086ffbee9dd798f86c3232291348c3690827b3a55449c08b.jpg", + "text": "$$\ns _ { i } ^ { o u t p u t } = y , \\qquad s _ { j \\neq i } ^ { o u t p u t } = 0 .\n$$", + "text_format": "latex", + "bbox": [ + 390, + 406, + 607, + 429 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input along the pattern vector. ", + "bbox": [ + 169, + 440, + 823, + 468 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/bee0ffdadf98cb7d2f0635c6ef7b92f57bcea185b2062a77f0f4190e12991884.jpg", + "text": "$$\n\\pmb { s } ^ { l - 1 , i } = \\pmb { a } s _ { i } ^ { l } .\n$$", + "text_format": "latex", + "bbox": [ + 452, + 470, + 545, + 489 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In our case where we use the $S _ { a + - } ( x )$ estimator, this vector is always the positive components ${ \\pmb a } _ { + }$ since non-active ReLu’s block the propagation. ", + "bbox": [ + 171, + 492, + 821, + 521 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The signal of neuron $i$ at layer $l - 1$ is the sum of all incoming signals from the layer above: ", + "bbox": [ + 173, + 526, + 779, + 542 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/02871598bc1cd3f1c75af47b08915e0ef5a0d0427a2c183f539db17cf9973e3e.jpg", + "text": "$$\ns _ { i } ^ { l - 1 } = \\sum _ { j } s _ { i } ^ { l - 1 , j } .\n$$", + "text_format": "latex", + "bbox": [ + 436, + 544, + 560, + 579 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "ReLu layer To propagate through a ReLu, the propagation is blocked if the neuron was not active in the forward pass ", + "bbox": [ + 171, + 588, + 823, + 616 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/c4078e6325056a7e43cf3aaca99bd4dcb56d5fb7377381119836a0cfb28bca1a.jpg", + "text": "$$\ns _ { i } ^ { l - 1 } = \\left\\{ \\begin{array} { l l } { s _ { i } ^ { l } } & { x _ { i } ^ { l } > 0 } \\\\ { 0 } & { \\mathrm { o t h e r w i s e } } \\end{array} \\right.\n$$", + "text_format": "latex", + "bbox": [ + 418, + 614, + 578, + 651 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.3 ATTRIBUTION VISUALIZATION ", + "text_level": 1, + "bbox": [ + 176, + 665, + 429, + 680 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "A.3.1 DEEP-TAYLOR DECOMPOSITION ", + "text_level": 1, + "bbox": [ + 174, + 690, + 457, + 707 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Initialization To compute the attribution of an output neuron, we can initialize it at the output neuron with the output value $y$ , for the non-selected output neurons we initialize it at 0. ", + "bbox": [ + 173, + 715, + 823, + 744 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/ba7c2a11bd71af31dfb10e794218605c54bc30a3aba575b2d67201651674533c.jpg", + "text": "$$\nr _ { i } ^ { o u t p u t } = y , \\qquad r _ { j \\neq i } ^ { o u t p u t } = 0 .\n$$", + "text_format": "latex", + "bbox": [ + 388, + 746, + 607, + 768 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "Linear or convolutional layer If it is a linear layer, the signal from neuron $i$ in layer $l$ can be projected back to its input w.r.t. a reference point $\\scriptstyle { \\mathbf { { \\mathit { x } } } } _ { 0 }$ ", + "bbox": [ + 171, + 776, + 823, + 806 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/5114ec7a43b3e37115fea7e0823177de0fd30573e596d069308e28756b72c8cd.jpg", + "text": "$$\n\\pmb { r } ^ { l - 1 , i } = \\frac { \\pmb { w } \\odot ( \\pmb { x } - \\pmb { x } _ { 0 } ) } { \\pmb { w } ^ { T } \\pmb { x } } r _ { i } ^ { l } .\n$$", + "text_format": "latex", + "bbox": [ + 408, + 808, + 589, + 839 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "In this work we use the $S _ { a + - } ( x )$ estimator. Since a non-active ReLu blocks the propagation, we only have to use the positive component $\\mathbf { \\pmb { a } } _ { + }$ . ", + "bbox": [ + 174, + 840, + 823, + 871 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "The attribution of neuron $i$ at layer $l - 1$ is the sum of all incoming attributions from the layer above: ", + "bbox": [ + 174, + 876, + 821, + 891 + ], + "page_idx": 13 + }, + { + "type": "equation", + "img_path": "images/2fba011f6813907d7a3952ffced8dcbb8a7b82af74945138790d035825a5f725.jpg", + "text": "$$\nr _ { i } ^ { l - 1 } = \\sum _ { j } r _ { i } ^ { l - 1 , j } .\n$$", + "text_format": "latex", + "bbox": [ + 436, + 893, + 560, + 928 + ], + "page_idx": 13 + }, + { + "type": "text", + "text": "ReLu layer To propagate through a ReLu, the propagation is blocked if the ReLu was not active in the forward pass. ", + "bbox": [ + 169, + 102, + 826, + 131 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/57c8ce57efa4f50f3807216a9e434a6c213700996fc537c0ac4c1893d39c06c8.jpg", + "text": "$$\nr _ { i } ^ { l - 1 } = { \\left\\{ \\begin{array} { l l } { r _ { i } ^ { l } } & { x _ { i } ^ { l } > 0 } \\\\ { 0 } & { { \\mathrm { o t h e r w i s e } } } \\end{array} \\right. }\n$$", + "text_format": "latex", + "bbox": [ + 416, + 131, + 576, + 166 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "A.3.2 LRP ", + "text_level": 1, + "bbox": [ + 174, + 179, + 266, + 194 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "LRP corresponds to $\\mathbf { \\delta x } _ { 0 } = \\mathbf { \\delta 0 }$ . This allows us to re-write the distribution rule for the linear and convolutional layers as: ", + "bbox": [ + 171, + 204, + 825, + 232 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/0d3794ab2add0daea40039e77b2524202af33fbf5452dce3f6a5d2e49d04d7a1.jpg", + "text": "$$\nr ^ { l - 1 , i } = \\frac { { \\pmb w } \\odot { \\pmb x } } { { \\pmb w } ^ { T } { \\pmb x } } r _ { i } ^ { l } .\n$$", + "text_format": "latex", + "bbox": [ + 433, + 231, + 563, + 260 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "Division by zero is not an issue since the propagation is blocked at the ReLu if ${ \\pmb w } ^ { T } { \\pmb x } < = 0$ ", + "bbox": [ + 173, + 263, + 772, + 280 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "A.3.3 PATTERNATTRIBUTION WITH $S _ { a + - } ( x )$ ", + "text_level": 1, + "bbox": [ + 173, + 292, + 503, + 309 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "PatternAttributions corresponds to ${ \\pmb x } _ { 0 } = { \\pmb x } - S _ { { \\pmb a } + - } ( { \\pmb x } )$ . Because propagation is blocked at the ReLu if ${ \\pmb w } ^ { T } { \\pmb x } < = 0$ , we can always use $\\pmb { x } _ { 0 } = \\pmb { x } - \\pmb { a } _ { + } \\pmb { w } ^ { T } \\pmb { x } .$ ", + "bbox": [ + 174, + 318, + 825, + 347 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "This allows us to re-write the distribution rule for the linear and convolutional layers as: ", + "bbox": [ + 173, + 353, + 750, + 368 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/c9696dd50f7e9cee47803e9245a2ff5b72dc89fe17485e70c25f97aa4e578fc8.jpg", + "text": "$$\n\\pmb { r } ^ { l - 1 , i } = \\frac { \\pmb { w } \\odot \\left( \\pmb { x } - \\pmb { x } + \\pmb { a } _ { + } \\pmb { w } ^ { T } \\pmb { x } \\right) } { \\pmb { w } ^ { T } \\pmb { x } } r _ { i } ^ { l } .\n$$", + "text_format": "latex", + "bbox": [ + 370, + 373, + 625, + 407 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "This can be simplified to ", + "bbox": [ + 174, + 412, + 338, + 428 + ], + "page_idx": 14 + }, + { + "type": "equation", + "img_path": "images/5bfcdb54e7b4f5f45a41d4ba11e1e20a3ebc9d8d79feb9cd87c17758e44f70a0.jpg", + "text": "$$\nr ^ { l - 1 , i } = { \\pmb w } \\odot { \\pmb a } _ { + } r _ { i } ^ { l }\n$$", + "text_format": "latex", + "bbox": [ + 431, + 425, + 566, + 444 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "since division by zero is not an issue because the propagation is blocked at the ReLu if ${ \\pmb w } ^ { T } { \\pmb x } < = 0$ . ", + "bbox": [ + 173, + 446, + 823, + 463 + ], + "page_idx": 14 + }, + { + "type": "text", + "text": "B QUALITATIVE COMPARISON TO PREDICTION-DIFFERENCES ANALYSIS ", + "text_level": 1, + "bbox": [ + 169, + 102, + 789, + 118 + ], + "page_idx": 15 + }, + { + "type": "text", + "text": "To create the Predictive-Differences analysis visualizations Zintgraf et al. (2017), we used the opensource code provided by the authors with the default parameter settings provided for VGG. ", + "bbox": [ + 173, + 133, + 820, + 162 + ], + "page_idx": 15 + }, + { + "type": "image", + "img_path": "images/ff933e0a2064a6b03a92b2dc89030693194cb4c132c5bb99ffa4a9512decaddb.jpg", + "image_caption": [ + "Figure 7: Visualization of random images from ImageNet (validation set). In the leftmost shows column the ground truth, the predicted label and the classifier’s confidence. Comparison between the proposed methods PatternNet and PatternAttribution to the Prediction-Differences approach by Zintgraf et al. (2017). 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We show that these methods do not produce the theoretically correct", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 142, + 344, + 469, + 356 + ], + "spans": [ + { + "bbox": [ + 142, + 344, + 469, + 356 + ], + "score": 1.0, + "content": "explanation for a linear model. Yet they are used on multi-layer networks with", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 356, + 469, + 366 + ], + "spans": [ + { + "bbox": [ + 142, + 356, + 469, + 366 + ], + "score": 1.0, + "content": "millions of parameters. This is a cause for concern since linear models are simple", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 367, + 469, + 377 + ], + "spans": [ + { + "bbox": [ + 141, + 367, + 469, + 377 + ], + "score": 1.0, + "content": "neural networks. We argue that explanation methods for neural nets should work", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 377, + 470, + 389 + ], + "spans": [ + { + "bbox": [ + 141, + 377, + 470, + 389 + ], + "score": 1.0, + "content": "reliably in the limit of simplicity, the linear models. Based on our analysis of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 388, + 469, + 401 + ], + "spans": [ + { + "bbox": [ + 141, + 388, + 469, + 401 + ], + "score": 1.0, + "content": "linear models we propose a generalization that yields two explanation techniques", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 142, + 400, + 469, + 411 + ], + "spans": [ + { + "bbox": [ + 142, + 400, + 469, + 411 + ], + "score": 1.0, + "content": "(PatternNet and PatternAttribution) that are theoretically sound for linear models", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 142, + 411, + 363, + 423 + ], + "spans": [ + { + "bbox": [ + 142, + 411, + 363, + 423 + ], + "score": 1.0, + "content": "and produce improved explanations for deep networks.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22, + "bbox_fs": [ + 141, + 322, + 470, + 423 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 442, + 206, + 455 + ], + "lines": [ + { + "bbox": [ + 105, + 441, + 208, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 208, + 458 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 467, + 505, + 555 + ], + "lines": [ + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "Deep learning made a huge impact on a wide variety of applications (Krizhevsky et al., 2012;", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 477, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 506, + 491 + ], + "score": 1.0, + "content": "Sutskever et al., 2014; LeCun et al., 2015; Schmidhuber, 2015; Mnih et al., 2015; Silver et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 487, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 506, + 502 + ], + "score": 1.0, + "content": "2016) and recent neural network classifiers have become excellent at detecting relevant signals (e.g.,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "the presence of a cat) contained in input data points such as images by filtering out all other, non-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 505, + 524 + ], + "score": 1.0, + "content": "relevant and distracting components also present in the data. This separation of signal and distractors", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 521, + 505, + 535 + ], + "spans": [ + { + "bbox": [ + 104, + 521, + 505, + 535 + ], + "score": 1.0, + "content": "is achieved by passing the input through many layers with millions of parameters and nonlinear ac-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 533, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 545 + ], + "score": 1.0, + "content": "tivation functions in between, until finally at the output layer, these models yield a highly condensed", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 543, + 490, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 490, + 558 + ], + "score": 1.0, + "content": "version of the signal, e.g. a single number indicating the probability of a cat being in the image.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31.5, + "bbox_fs": [ + 104, + 467, + 506, + 558 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 560, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 560, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 506, + 573 + ], + "score": 1.0, + "content": "While deep neural networks learn efficient and powerful representations, they are often considered a", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 571, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 571, + 505, + 584 + ], + "score": 1.0, + "content": "‘black-box’. 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In particular, we provide the following key contributions:", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 378, + 506, + 456 + ] + }, + { + "type": "list", + "bbox": [ + 132, + 464, + 505, + 574 + ], + "lines": [ + { + "bbox": [ + 132, + 465, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 132, + 465, + 506, + 478 + ], + "score": 1.0, + "content": "• We analyze the performance of existing explanation approaches in the controlled setting of", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 476, + 281, + 488 + ], + "spans": [ + { + "bbox": [ + 141, + 476, + 281, + 488 + ], + "score": 1.0, + "content": "a linear model (Sections 2 and 3).", + "type": "text" + } + ], + "index": 21, + "is_list_end_line": true + }, + { + "bbox": [ + 131, + 492, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 131, + 492, + 505, + 506 + ], + "score": 1.0, + "content": "• We categorize explanation methods into three groups – functions, signals and attribution", + "type": "text" + } + ], + "index": 22, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 503, + 504, + 516 + ], + "spans": [ + { + "bbox": [ + 141, + 503, + 504, + 516 + ], + "score": 1.0, + "content": "(see Fig. 1) – that require fundamentally different interpretations and are complementary", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 142, + 515, + 388, + 527 + ], + "spans": [ + { + "bbox": [ + 142, + 515, + 388, + 527 + ], + "score": 1.0, + "content": "in terms of information about the neural network (Section 3).", + "type": "text" + } + ], + "index": 24, + "is_list_end_line": true + }, + { + "bbox": [ + 134, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 134, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "• We propose two novel explanation methods – PatternNet and PatternAttribution – that alle-", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 141, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "viate shortcomings of current approaches, as discovered during our analysis, and improve", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 553, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 141, + 553, + 505, + 565 + ], + "score": 1.0, + "content": "explanations in real-world deep neural networks visually and quantitatively (Sections 4 and", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 564, + 157, + 577 + ], + "spans": [ + { + "bbox": [ + 141, + 564, + 157, + 577 + ], + "score": 1.0, + "content": "5).", + "type": "text" + } + ], + "index": 28, + "is_list_end_line": true + } + ], + "index": 24, + "bbox_fs": [ + 131, + 465, + 506, + 577 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 585, + 505, + 630 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 505, + 598 + ], + "score": 1.0, + "content": "This presents a step towards a thorough analysis of explanation methods and suggests qualitatively", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 597, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 597, + 505, + 608 + ], + "score": 1.0, + "content": "and measurably improved explanations. 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Without loss of generality,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 289, + 338, + 301 + ], + "spans": [ + { + "bbox": [ + 106, + 289, + 338, + 301 + ], + "score": 1.0, + "content": "biases are considered constant neurons to enhance clarity.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + }, + { + "type": "title", + "bbox": [ + 107, + 317, + 305, + 330 + ], + "lines": [ + { + "bbox": [ + 104, + 316, + 306, + 334 + ], + "spans": [ + { + "bbox": [ + 104, + 316, + 306, + 334 + ], + "score": 1.0, + "content": "2 UNDERSTANDING LINEAR MODELS", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 342, + 505, + 409 + ], + "lines": [ + { + "bbox": [ + 106, + 343, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 505, + 354 + ], + "score": 1.0, + "content": "In this section, we analyze explanation methods for deep neural network, starting with the simplest", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "score": 1.0, + "content": "neural network setting: a purely linear model and data sampled from a linear generative model. This", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 364, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 505, + 378 + ], + "score": 1.0, + "content": "setup allows us to (i) fully control how signal and distractor components are encoded in the input", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "score": 1.0, + "content": "data and (ii) analytically track how the resulting explanation relates to the known signal component.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "score": 1.0, + "content": "This analysis allows us then to highlight shortcomings of current explanation approaches that carry", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 398, + 227, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 227, + 409 + ], + "score": 1.0, + "content": "over to deep neural networks.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 106, + 414, + 421, + 426 + ], + "lines": [ + { + "bbox": [ + 106, + 413, + 421, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 413, + 398, + 429 + ], + "score": 1.0, + "content": "Consider the following toy example (see Fig. 2) where we generate data", + "type": "text" + }, + { + "bbox": [ + 398, + 417, + 406, + 424 + ], + "score": 0.75, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 413, + 421, + 429 + ], + "score": 1.0, + "content": "as:", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "interline_equation", + "bbox": [ + 144, + 431, + 467, + 466 + ], + "lines": [ + { + "bbox": [ + 144, + 431, + 467, + 466 + ], + "spans": [ + { + "bbox": [ + 144, + 431, + 467, + 466 + ], + "score": 0.91, + "content": "\\begin{array} { r l r l r l r l } { x = s + d } & { } & & { \\quad s = a _ { s } y , } & { \\quad } & { \\mathrm { ~ w i t h ~ } a _ { s } = \\left( 1 , 0 \\right) ^ { T } , } & { } & { \\quad y \\in [ - 1 , 1 ] } \\\\ & { } & & { \\quad d = a _ { d } \\epsilon , } & { } & & { \\mathrm { ~ w i t h ~ } a _ { d } = \\left( 1 , 1 \\right) ^ { T } , } & { } & { \\epsilon \\sim \\mathcal { N } \\left( \\mu , \\sigma ^ { 2 } \\right) . } \\end{array}", + "type": "interline_equation", + "image_path": "b72a99c8d0bd8bc7ec4633301981ea18169ce3a5a566901154edf1d1428a2bc9.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 144, + 431, + 467, + 442.6666666666667 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 144, + 442.6666666666667, + 467, + 454.33333333333337 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 144, + 454.33333333333337, + 467, + 466.00000000000006 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 106, + 469, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 286, + 484 + ], + "score": 1.0, + "content": "We train a linear regression model to extract", + "type": "text" + }, + { + "bbox": [ + 286, + 473, + 293, + 482 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 469, + 316, + 484 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 317, + 473, + 324, + 480 + ], + "score": 0.73, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 469, + 398, + 484 + ], + "score": 1.0, + "content": ". By construction,", + "type": "text" + }, + { + "bbox": [ + 398, + 473, + 405, + 480 + ], + "score": 0.67, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 469, + 505, + 484 + ], + "score": 1.0, + "content": "is the signal in our data,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 482, + 505, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 168, + 494 + ], + "score": 1.0, + "content": "i.e., the part of", + "type": "text" + }, + { + "bbox": [ + 168, + 483, + 176, + 491 + ], + "score": 0.72, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 482, + 296, + 494 + ], + "score": 1.0, + "content": "containing information about", + "type": "text" + }, + { + "bbox": [ + 297, + 483, + 303, + 493 + ], + "score": 0.77, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 482, + 505, + 494 + ], + "score": 1.0, + "content": ". Using the terminology of Haufe et al. (2014) the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 490, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 104, + 490, + 148, + 507 + ], + "score": 1.0, + "content": "distractor", + "type": "text" + }, + { + "bbox": [ + 149, + 493, + 156, + 502 + ], + "score": 0.78, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 490, + 495, + 507 + ], + "score": 1.0, + "content": "obfuscates the signal making the detection task more difficult. To optimally extract", + "type": "text" + }, + { + "bbox": [ + 495, + 495, + 501, + 504 + ], + "score": 0.77, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 490, + 506, + 507 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 502, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 306, + 516 + ], + "score": 1.0, + "content": "our model has to be able to filter out the distractor", + "type": "text" + }, + { + "bbox": [ + 306, + 504, + 314, + 513 + ], + "score": 0.66, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 502, + 506, + 516 + ], + "score": 1.0, + "content": ". This is why the weight vector is also called the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 514, + 351, + 529 + ], + "spans": [ + { + "bbox": [ + 104, + 515, + 195, + 529 + ], + "score": 1.0, + "content": "filter. In the example,", + "type": "text" + }, + { + "bbox": [ + 195, + 514, + 252, + 528 + ], + "score": 0.94, + "content": "\\mathbf { \\boldsymbol { w } } = \\left[ 1 , - 1 \\right] ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 515, + 351, + 529 + ], + "score": 1.0, + "content": "fulfills this convex task.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 106, + 533, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 105, + 532, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 433, + 546 + ], + "score": 1.0, + "content": "From this example, we can make several observations: The optimal weight vector", + "type": "text" + }, + { + "bbox": [ + 433, + 536, + 443, + 543 + ], + "score": 0.58, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 532, + 505, + 546 + ], + "score": 1.0, + "content": "does not align,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 543, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 258, + 556 + ], + "score": 1.0, + "content": "in general, with the signal direction", + "type": "text" + }, + { + "bbox": [ + 259, + 546, + 271, + 555 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\delta \\mathrm \\mathrm { \\delta } \\delta \\mathrm \\mathrm \\delta \\mathrm \\mathrm \\mathrm { \\delta } \\delta \\delta \\mathrm \\delta \\mathrm \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\delta \\mathrm \\delta \\delta \\delta \\mathrm \\delta \\delta \\delta \\delta \\delta \\delta \\mathrm \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 543, + 505, + 556 + ], + "score": 1.0, + "content": ", but tries to filter the contribution of the distractor (see", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 555, + 506, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 459, + 567 + ], + "score": 1.0, + "content": "Fig. 2). This is optimally solved when the weight vector is orthogonal to the distractor", + "type": "text" + }, + { + "bbox": [ + 460, + 555, + 501, + 565 + ], + "score": 0.91, + "content": "{ \\pmb w } ^ { T } { \\pmb d } = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 555, + 506, + 567 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 566, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 291, + 578 + ], + "score": 1.0, + "content": "Therefore, when the direction of the distractor", + "type": "text" + }, + { + "bbox": [ + 291, + 567, + 304, + 577 + ], + "score": 0.88, + "content": "\\mathbf { \\delta } _ { \\mathbf { \\alpha } \\mathbf { \\delta } \\mathbf { \\alpha } \\mathbf { \\textit { a } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 566, + 342, + 578 + ], + "score": 1.0, + "content": "changes,", + "type": "text" + }, + { + "bbox": [ + 342, + 568, + 352, + 576 + ], + "score": 0.61, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 566, + 506, + 578 + ], + "score": 1.0, + "content": "must follow, as illustrated on the right", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 394, + 590 + ], + "score": 1.0, + "content": "hand side of the figure. 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On the contrary, the direction", + "type": "text" + }, + { + "bbox": [ + 279, + 628, + 291, + 638 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 627, + 402, + 639 + ], + "score": 1.0, + "content": "must be learned from data.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Now assume that we have additive isotropic Gaussian noise. The mean of the noise can easily be", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "compensated for with a bias change. Therefore, we only have to consider the zero-mean case. Since", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "isotropic Gaussian noise does not contain any correlations or structure, the only way to remove it is", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "by averaging over different measurements. It is not possible to cancel it out effectively by using a", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "well-chosen weight vector. However, it is well known that adding Gaussian noise shrinks the weight", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "vector and corresponds to L2 regularization. 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Therefore in practice", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 720, + 317, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 317, + 733 + ], + "score": 1.0, + "content": "both these effects influence the actual weight vector.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38.5 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 109, + 80, + 502, + 182 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 109, + 80, + 502, + 182 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 80, + 502, + 181 + ], + "spans": [ + { + "bbox": [ + 109, + 80, + 502, + 181 + ], + "score": 0.963, + "type": "image", + "image_path": "fadc0d3e80752b97d7b31564914d142aeb247209fdb0365ffc20487b5064a4a4.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 109, + 80, + 502, + 114.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 109, + 114.0, + 502, + 148.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 109, + 148.0, + 502, + 182.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 189, + 505, + 245 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 190, + 504, + 201 + ], + "spans": [ + { + "bbox": [ + 106, + 190, + 504, + 201 + ], + "score": 1.0, + "content": "Figure 2: For linear models, i.e., a simple neural network, the weight vector does not explain the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 200, + 506, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 301, + 214 + ], + "score": 1.0, + "content": "signal it detects Haufe et al. (2014). The data", + "type": "text" + }, + { + "bbox": [ + 302, + 201, + 372, + 212 + ], + "score": 0.9, + "content": "{ \\pmb x } = y { \\pmb a } _ { s } + \\epsilon { \\pmb a } _ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 200, + 506, + 214 + ], + "score": 1.0, + "content": "is color-coded w.r.t. the output", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 210, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 107, + 210, + 148, + 223 + ], + "score": 0.92, + "content": "\\mathbf { \\Psi } y = \\pmb { w } ^ { T } \\mathbf { \\em x }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 210, + 217, + 225 + ], + "score": 1.0, + "content": ". Only the signal", + "type": "text" + }, + { + "bbox": [ + 217, + 213, + 253, + 223 + ], + "score": 0.9, + "content": "\\mathit { s } = y \\mathbf { a } _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 210, + 311, + 225 + ], + "score": 1.0, + "content": "contributes to", + "type": "text" + }, + { + "bbox": [ + 311, + 214, + 318, + 223 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 210, + 398, + 225 + ], + "score": 1.0, + "content": ". The weight vector", + "type": "text" + }, + { + "bbox": [ + 398, + 213, + 408, + 222 + ], + "score": 0.59, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 408, + 210, + 506, + 225 + ], + "score": 1.0, + "content": "does not agree with the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 222, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 235 + ], + "score": 1.0, + "content": "signal direction, since its primary objective is canceling the distractor. Therefore, rotations of the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 234, + 504, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 156, + 246 + ], + "score": 1.0, + "content": "basis vector", + "type": "text" + }, + { + "bbox": [ + 156, + 235, + 168, + 244 + ], + "score": 0.86, + "content": "\\mathbf { \\mu } _ { a _ { d } }", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 234, + 316, + 246 + ], + "score": 1.0, + "content": "of the distractor with constant signal", + "type": "text" + }, + { + "bbox": [ + 317, + 235, + 323, + 243 + ], + "score": 0.7, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 324, + 234, + 504, + 246 + ], + "score": 1.0, + "content": "lead to rotations of the weight vector (right).", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 106, + 277, + 504, + 300 + ], + "lines": [], + "index": 8.5, + "bbox_fs": [ + 105, + 276, + 505, + 301 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 317, + 305, + 330 + ], + "lines": [ + { + "bbox": [ + 104, + 316, + 306, + 334 + ], + "spans": [ + { + "bbox": [ + 104, + 316, + 306, + 334 + ], + "score": 1.0, + "content": "2 UNDERSTANDING LINEAR MODELS", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 342, + 505, + 409 + ], + "lines": [ + { + "bbox": [ + 106, + 343, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 505, + 354 + ], + "score": 1.0, + "content": "In this section, we analyze explanation methods for deep neural network, starting with the simplest", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "score": 1.0, + "content": "neural network setting: a purely linear model and data sampled from a linear generative model. This", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 364, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 505, + 378 + ], + "score": 1.0, + "content": "setup allows us to (i) fully control how signal and distractor components are encoded in the input", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 388 + ], + "score": 1.0, + "content": "data and (ii) analytically track how the resulting explanation relates to the known signal component.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 505, + 400 + ], + "score": 1.0, + "content": "This analysis allows us then to highlight shortcomings of current explanation approaches that carry", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 398, + 227, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 227, + 409 + ], + "score": 1.0, + "content": "over to deep neural networks.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 343, + 505, + 409 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 414, + 421, + 426 + ], + "lines": [ + { + "bbox": [ + 106, + 413, + 421, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 413, + 398, + 429 + ], + "score": 1.0, + "content": "Consider the following toy example (see Fig. 2) where we generate data", + "type": "text" + }, + { + "bbox": [ + 398, + 417, + 406, + 424 + ], + "score": 0.75, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 413, + 421, + 429 + ], + "score": 1.0, + "content": "as:", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17, + "bbox_fs": [ + 106, + 413, + 421, + 429 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 144, + 431, + 467, + 466 + ], + "lines": [ + { + "bbox": [ + 144, + 431, + 467, + 466 + ], + "spans": [ + { + "bbox": [ + 144, + 431, + 467, + 466 + ], + "score": 0.91, + "content": "\\begin{array} { r l r l r l r l } { x = s + d } & { } & & { \\quad s = a _ { s } y , } & { \\quad } & { \\mathrm { ~ w i t h ~ } a _ { s } = \\left( 1 , 0 \\right) ^ { T } , } & { } & { \\quad y \\in [ - 1 , 1 ] } \\\\ & { } & & { \\quad d = a _ { d } \\epsilon , } & { } & & { \\mathrm { ~ w i t h ~ } a _ { d } = \\left( 1 , 1 \\right) ^ { T } , } & { } & { \\epsilon \\sim \\mathcal { N } \\left( \\mu , \\sigma ^ { 2 } \\right) . } \\end{array}", + "type": "interline_equation", + "image_path": "b72a99c8d0bd8bc7ec4633301981ea18169ce3a5a566901154edf1d1428a2bc9.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 144, + 431, + 467, + 442.6666666666667 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 144, + 442.6666666666667, + 467, + 454.33333333333337 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 144, + 454.33333333333337, + 467, + 466.00000000000006 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 470, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 106, + 469, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 286, + 484 + ], + "score": 1.0, + "content": "We train a linear regression model to extract", + "type": "text" + }, + { + "bbox": [ + 286, + 473, + 293, + 482 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 469, + 316, + 484 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 317, + 473, + 324, + 480 + ], + "score": 0.73, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 469, + 398, + 484 + ], + "score": 1.0, + "content": ". By construction,", + "type": "text" + }, + { + "bbox": [ + 398, + 473, + 405, + 480 + ], + "score": 0.67, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 469, + 505, + 484 + ], + "score": 1.0, + "content": "is the signal in our data,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 482, + 505, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 168, + 494 + ], + "score": 1.0, + "content": "i.e., the part of", + "type": "text" + }, + { + "bbox": [ + 168, + 483, + 176, + 491 + ], + "score": 0.72, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 176, + 482, + 296, + 494 + ], + "score": 1.0, + "content": "containing information about", + "type": "text" + }, + { + "bbox": [ + 297, + 483, + 303, + 493 + ], + "score": 0.77, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 482, + 505, + 494 + ], + "score": 1.0, + "content": ". Using the terminology of Haufe et al. (2014) the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 490, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 104, + 490, + 148, + 507 + ], + "score": 1.0, + "content": "distractor", + "type": "text" + }, + { + "bbox": [ + 149, + 493, + 156, + 502 + ], + "score": 0.78, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 490, + 495, + 507 + ], + "score": 1.0, + "content": "obfuscates the signal making the detection task more difficult. To optimally extract", + "type": "text" + }, + { + "bbox": [ + 495, + 495, + 501, + 504 + ], + "score": 0.77, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 490, + 506, + 507 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 502, + 506, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 306, + 516 + ], + "score": 1.0, + "content": "our model has to be able to filter out the distractor", + "type": "text" + }, + { + "bbox": [ + 306, + 504, + 314, + 513 + ], + "score": 0.66, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 502, + 506, + 516 + ], + "score": 1.0, + "content": ". This is why the weight vector is also called the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 514, + 351, + 529 + ], + "spans": [ + { + "bbox": [ + 104, + 515, + 195, + 529 + ], + "score": 1.0, + "content": "filter. In the example,", + "type": "text" + }, + { + "bbox": [ + 195, + 514, + 252, + 528 + ], + "score": 0.94, + "content": "\\mathbf { \\boldsymbol { w } } = \\left[ 1 , - 1 \\right] ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 515, + 351, + 529 + ], + "score": 1.0, + "content": "fulfills this convex task.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23, + "bbox_fs": [ + 104, + 469, + 506, + 529 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 533, + 505, + 600 + ], + "lines": [ + { + "bbox": [ + 105, + 532, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 433, + 546 + ], + "score": 1.0, + "content": "From this example, we can make several observations: The optimal weight vector", + "type": "text" + }, + { + "bbox": [ + 433, + 536, + 443, + 543 + ], + "score": 0.58, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 532, + 505, + 546 + ], + "score": 1.0, + "content": "does not align,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 543, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 258, + 556 + ], + "score": 1.0, + "content": "in general, with the signal direction", + "type": "text" + }, + { + "bbox": [ + 259, + 546, + 271, + 555 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm { \\delta } \\mathrm \\mathbf { \\delta } \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\mathrm { \\delta } \\mathrm \\mathrm \\delta \\mathrm \\mathrm { \\delta } \\delta \\mathrm \\mathrm \\delta \\mathrm \\mathrm \\mathrm { \\delta } \\delta \\delta \\mathrm \\delta \\mathrm \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\mathrm \\delta \\delta \\mathrm \\delta \\delta \\delta \\mathrm \\delta \\delta \\delta \\delta \\delta \\delta \\mathrm \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 543, + 505, + 556 + ], + "score": 1.0, + "content": ", but tries to filter the contribution of the distractor (see", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 555, + 506, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 459, + 567 + ], + "score": 1.0, + "content": "Fig. 2). This is optimally solved when the weight vector is orthogonal to the distractor", + "type": "text" + }, + { + "bbox": [ + 460, + 555, + 501, + 565 + ], + "score": 0.91, + "content": "{ \\pmb w } ^ { T } { \\pmb d } = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 555, + 506, + 567 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 566, + 506, + 578 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 291, + 578 + ], + "score": 1.0, + "content": "Therefore, when the direction of the distractor", + "type": "text" + }, + { + "bbox": [ + 291, + 567, + 304, + 577 + ], + "score": 0.88, + "content": "\\mathbf { \\delta } _ { \\mathbf { \\alpha } \\mathbf { \\delta } \\mathbf { \\alpha } \\mathbf { \\textit { a } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 566, + 342, + 578 + ], + "score": 1.0, + "content": "changes,", + "type": "text" + }, + { + "bbox": [ + 342, + 568, + 352, + 576 + ], + "score": 0.61, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 566, + 506, + 578 + ], + "score": 1.0, + "content": "must follow, as illustrated on the right", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 577, + 506, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 394, + 590 + ], + "score": 1.0, + "content": "hand side of the figure. On the other hand, a change in signal direction", + "type": "text" + }, + { + "bbox": [ + 394, + 579, + 406, + 588 + ], + "score": 0.84, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 577, + 506, + 590 + ], + "score": 1.0, + "content": "can be compensated for", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 587, + 484, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 258, + 601 + ], + "score": 1.0, + "content": "by a change in sign and magnitude of", + "type": "text" + }, + { + "bbox": [ + 258, + 590, + 268, + 598 + ], + "score": 0.76, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 588, + 307, + 601 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 308, + 587, + 352, + 599 + ], + "score": 0.93, + "content": "\\mathbf { \\bar { w } } ^ { T } \\pmb { a } _ { s } \\equiv 1", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 588, + 484, + 601 + ], + "score": 1.0, + "content": ", but the direction stays constant.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 532, + 506, + 601 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 604, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "The fact that the direction of the weight vector in a linear model is largely determined by the dis-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 617, + 504, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 504, + 627 + ], + "score": 1.0, + "content": "tractor implies that given only the weight vector, we cannot know what part of the input produces", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 627, + 402, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 149, + 639 + ], + "score": 1.0, + "content": "the output", + "type": "text" + }, + { + "bbox": [ + 149, + 629, + 156, + 639 + ], + "score": 0.72, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 156, + 627, + 279, + 639 + ], + "score": 1.0, + "content": ". On the contrary, the direction", + "type": "text" + }, + { + "bbox": [ + 279, + 628, + 291, + 638 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 627, + 402, + 639 + ], + "score": 1.0, + "content": "must be learned from data.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33, + "bbox_fs": [ + 106, + 605, + 505, + 639 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Now assume that we have additive isotropic Gaussian noise. The mean of the noise can easily be", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "compensated for with a bias change. Therefore, we only have to consider the zero-mean case. Since", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "isotropic Gaussian noise does not contain any correlations or structure, the only way to remove it is", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "by averaging over different measurements. It is not possible to cancel it out effectively by using a", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "well-chosen weight vector. However, it is well known that adding Gaussian noise shrinks the weight", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "vector and corresponds to L2 regularization. In the absence of a structured distractor, the smallest", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 163, + 722 + ], + "score": 1.0, + "content": "weight vector", + "type": "text" + }, + { + "bbox": [ + 164, + 711, + 173, + 720 + ], + "score": 0.71, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 710, + 213, + 722 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 213, + 709, + 258, + 721 + ], + "score": 0.92, + "content": "{ \\pmb w } ^ { T } { \\pmb a } _ { s } = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "is the one in the direction of the signal. Therefore in practice", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 720, + 317, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 317, + 733 + ], + "score": 1.0, + "content": "both these effects influence the actual weight vector.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 643, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 94 + ], + "score": 1.0, + "content": "As already indicated above, deep neural networks are essentially a composition of linear layers and", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 92, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 92, + 506, + 108 + ], + "score": 1.0, + "content": "non-linear activation functions. In the next section, we will show that gradient-based methods, e.g.,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "score": 1.0, + "content": "DeConvNet, Guided BackProp, and LRP, are not able to distinguish signal from distractor in a linear", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "model and therefore back-propagate sub-optimal explanations in deeper networks. This analysis", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "allows us to develop improved layer-wise explanation techniques and to demonstrate quantitative", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 350, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 350, + 149 + ], + "score": 1.0, + "content": "and qualitative better explanations for deep neural networks.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 164, + 505, + 220 + ], + "lines": [ + { + "bbox": [ + 106, + 164, + 504, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 164, + 494, + 178 + ], + "score": 1.0, + "content": "Terminology Throughout this manuscript we will use the following terminology: The filter", + "type": "text" + }, + { + "bbox": [ + 494, + 166, + 504, + 175 + ], + "score": 0.28, + "content": "\\pmb { w }", + "type": "inline_equation" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 174, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 237, + 189 + ], + "score": 1.0, + "content": "tells us how to extract the output", + "type": "text" + }, + { + "bbox": [ + 237, + 178, + 244, + 187 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 174, + 326, + 189 + ], + "score": 1.0, + "content": "optimally from data", + "type": "text" + }, + { + "bbox": [ + 326, + 178, + 334, + 186 + ], + "score": 0.66, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 174, + 387, + 189 + ], + "score": 1.0, + "content": ". The pattern", + "type": "text" + }, + { + "bbox": [ + 387, + 178, + 399, + 187 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 174, + 505, + 189 + ], + "score": 1.0, + "content": "is the direction in the data", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 234, + 200 + ], + "score": 1.0, + "content": "along which the desired output", + "type": "text" + }, + { + "bbox": [ + 234, + 189, + 241, + 198 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 186, + 379, + 200 + ], + "score": 1.0, + "content": "varies. Both constitute the signal", + "type": "text" + }, + { + "bbox": [ + 380, + 188, + 417, + 198 + ], + "score": 0.89, + "content": "\\textbf { \\em s } = \\textbf { \\em a } _ { s } y", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 186, + 505, + 200 + ], + "score": 1.0, + "content": ", i.e., the contributing", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 196, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 135, + 210 + ], + "score": 1.0, + "content": "part of", + "type": "text" + }, + { + "bbox": [ + 135, + 199, + 143, + 208 + ], + "score": 0.72, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 196, + 207, + 210 + ], + "score": 1.0, + "content": ". The distractor", + "type": "text" + }, + { + "bbox": [ + 207, + 198, + 215, + 208 + ], + "score": 0.78, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 196, + 506, + 210 + ], + "score": 1.0, + "content": "is the component of the data that does not contain information about the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 207, + 168, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 207, + 168, + 222 + ], + "score": 1.0, + "content": "desired output.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 106, + 240, + 460, + 252 + ], + "lines": [ + { + "bbox": [ + 104, + 239, + 461, + 255 + ], + "spans": [ + { + "bbox": [ + 104, + 239, + 461, + 255 + ], + "score": 1.0, + "content": "3 OVERVIEW OF EXPLANATION APPROACHES AND THEIR BEHAVIOR", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 267, + 505, + 322 + ], + "lines": [ + { + "bbox": [ + 105, + 267, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 505, + 279 + ], + "score": 1.0, + "content": "In this section, we take a look at a subset of explanation methods for individual classifier decisions", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 279, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 505, + 290 + ], + "score": 1.0, + "content": "and discuss how they are connected to our analysis of linear models in the previous section. Fig. 1", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 289, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 104, + 289, + 506, + 303 + ], + "score": 1.0, + "content": "gives an overview of the different types of explanation methods which can be divided into function,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 299, + 506, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 506, + 313 + ], + "score": 1.0, + "content": "signal and attribution visualizations. These three groups all present different information about the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 311, + 255, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 255, + 323 + ], + "score": 1.0, + "content": "network and complement each other.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 338, + 505, + 426 + ], + "lines": [ + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "score": 1.0, + "content": "Functions – gradients, saliency map Explaining the function in input space corresponds to de-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 349, + 504, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 304, + 361 + ], + "score": 1.0, + "content": "scribing the operations the model uses to extract", + "type": "text" + }, + { + "bbox": [ + 304, + 352, + 311, + 361 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 349, + 335, + 361 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 335, + 352, + 342, + 360 + ], + "score": 0.66, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 349, + 504, + 361 + ], + "score": 1.0, + "content": ". Since deep neural networks are highly", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 361, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 373 + ], + "score": 1.0, + "content": "nonlinear, this can only be approximated. The saliency map estimates how moving along a particu-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 372, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 257, + 384 + ], + "score": 1.0, + "content": "lar direction in input space influences", + "type": "text" + }, + { + "bbox": [ + 257, + 373, + 264, + 383 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 372, + 505, + 384 + ], + "score": 1.0, + "content": "(i.e., sensitivity analysis) where the direction is given by the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 381, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 459, + 396 + ], + "score": 1.0, + "content": "model gradient (Baehrens et al., 2010; Simonyan et al., 2014). In case of a linear model", + "type": "text" + }, + { + "bbox": [ + 460, + 382, + 501, + 394 + ], + "score": 0.93, + "content": "y = \\dot { \\pmb { w } } ^ { T } \\pmb { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 381, + 506, + 396 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 312, + 406 + ], + "score": 1.0, + "content": "the saliency map reduces to analyzing the weights", + "type": "text" + }, + { + "bbox": [ + 313, + 393, + 365, + 405 + ], + "score": 0.91, + "content": "\\partial y / \\partial x = w", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 393, + 505, + 406 + ], + "score": 1.0, + "content": ". Since it is mostly determined by", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 404, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 505, + 417 + ], + "score": 1.0, + "content": "the distractor, as demonstrated above, it is not representing the signal. It tells us how to extract the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 416, + 326, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 326, + 427 + ], + "score": 1.0, + "content": "signal, not what the signal is in a deep neural network.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20.5 + }, + { + "type": "text", + "bbox": [ + 107, + 443, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 443, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 385, + 454 + ], + "score": 1.0, + "content": "Signal – DeConvNet, Guided BackProp, PatternNet The signal", + "type": "text" + }, + { + "bbox": [ + 385, + 445, + 392, + 453 + ], + "score": 0.57, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 443, + 505, + 454 + ], + "score": 1.0, + "content": "detected by the neural net-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "score": 1.0, + "content": "work is the component of the data that caused the networks activations. Zeiler & Fergus (2014)", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 464, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 478 + ], + "score": 1.0, + "content": "formulated the goal of these methods as ”[...] to map these activities back to the input pixel space,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 475, + 446, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 446, + 488 + ], + "score": 1.0, + "content": "showing what input pattern originally caused a given activation in the feature maps”.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5 + }, + { + "type": "text", + "bbox": [ + 107, + 492, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 104, + 491, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 104, + 491, + 283, + 506 + ], + "score": 1.0, + "content": "In a linear model, the signal corresponds to", + "type": "text" + }, + { + "bbox": [ + 284, + 495, + 320, + 504 + ], + "score": 0.89, + "content": "\\mathbf { \\boldsymbol { s } } = \\mathbf { \\boldsymbol { a } } _ { s } \\boldsymbol { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 491, + 374, + 506 + ], + "score": 1.0, + "content": ". The pattern", + "type": "text" + }, + { + "bbox": [ + 374, + 495, + 386, + 504 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ { \\mathbf { \\alpha } \\mathbf { \\delta } _ { a _ { s } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 491, + 506, + 506 + ], + "score": 1.0, + "content": "contains the signal direction,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 503, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 505, + 516 + ], + "score": 1.0, + "content": "i.e., it tells us where a change of the output variable is expected to be measurable in the input", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "score": 1.0, + "content": "(Haufe et al., 2014). Attempts to visualize the signal for deep neural networks were made using", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "DeConvNet (Zeiler & Fergus, 2014) and Guided BackProp (Springenberg et al., 2015). These use", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 536, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 505, + 549 + ], + "score": 1.0, + "content": "the same algorithm as the saliency map, but treat the rectifiers differently (see Fig. 1): DeConvNet", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 548, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 548, + 505, + 559 + ], + "score": 1.0, + "content": "leaves out the rectifiers from the forward pass, but adds additional ReLUs after each deconvolution,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "score": 1.0, + "content": "while Guided BackProp uses the ReLUs from the forward pass as well as additional ones. The", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 569, + 505, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 505, + 582 + ], + "score": 1.0, + "content": "back-projections for the linear components of the network correspond to a superposition of what are", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 580, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 505, + 593 + ], + "score": 1.0, + "content": "assumed to be the signal directions of each neuron. For this reason, these projections must be seen", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 592, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 505, + 604 + ], + "score": 1.0, + "content": "as an approximation of the features that activated the higher layer neuron. It is not a reconstruction", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 602, + 264, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 264, + 614 + ], + "score": 1.0, + "content": "in input space (Zeiler & Fergus, 2014).", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 619, + 505, + 696 + ], + "lines": [ + { + "bbox": [ + 104, + 618, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 104, + 618, + 505, + 631 + ], + "score": 1.0, + "content": "For the simplest of neural networks – the linear model – these visualizations reduce to the gradient1.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 630, + 506, + 643 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 188, + 643 + ], + "score": 1.0, + "content": "They show the filter", + "type": "text" + }, + { + "bbox": [ + 189, + 632, + 198, + 640 + ], + "score": 0.47, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 630, + 292, + 643 + ], + "score": 1.0, + "content": "and neither the pattern", + "type": "text" + }, + { + "bbox": [ + 292, + 632, + 304, + 641 + ], + "score": 0.86, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 630, + 365, + 643 + ], + "score": 1.0, + "content": ", nor the signal", + "type": "text" + }, + { + "bbox": [ + 366, + 632, + 372, + 640 + ], + "score": 0.31, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 630, + 506, + 643 + ], + "score": 1.0, + "content": ". Hence, DeConvNet and Guided", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "BackProp do not guarantee to produce the detected signal for a linear model, which is proven by our", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 653, + 506, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 506, + 664 + ], + "score": 1.0, + "content": "toy example in Fig. 2. Since they do produce compelling visualizations, we will later investigate", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 663, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 663, + 241, + 675 + ], + "score": 1.0, + "content": "whether the direction of the filter", + "type": "text" + }, + { + "bbox": [ + 242, + 664, + 252, + 673 + ], + "score": 0.55, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 663, + 419, + 675 + ], + "score": 1.0, + "content": "coincides with the direction of the signal", + "type": "text" + }, + { + "bbox": [ + 419, + 665, + 425, + 673 + ], + "score": 0.48, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 663, + 505, + 675 + ], + "score": 1.0, + "content": ". We will show that", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 673, + 507, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 507, + 688 + ], + "score": 1.0, + "content": "this is not the case and propose a new approach, PatternNet (see Fig. 1), to estimate the correct", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 685, + 438, + 698 + ], + "spans": [ + { + "bbox": [ + 105, + 685, + 438, + 698 + ], + "score": 1.0, + "content": "direction that improves upon the DeConvNet and Guided BackProp visualizations.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 43 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 711, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 119, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 119, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "1In tensorflow terminoloy: linear model on MNIST can be seen as a convolutional neural network with", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 721, + 260, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 260, + 733 + ], + "score": 1.0, + "content": "VALID padding and a 28 by 28 filter size.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 149 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 94 + ], + "score": 1.0, + "content": "As already indicated above, deep neural networks are essentially a composition of linear layers and", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 92, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 92, + 506, + 108 + ], + "score": 1.0, + "content": "non-linear activation functions. In the next section, we will show that gradient-based methods, e.g.,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 505, + 116 + ], + "score": 1.0, + "content": "DeConvNet, Guided BackProp, and LRP, are not able to distinguish signal from distractor in a linear", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "model and therefore back-propagate sub-optimal explanations in deeper networks. This analysis", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 126, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 106, + 126, + 505, + 138 + ], + "score": 1.0, + "content": "allows us to develop improved layer-wise explanation techniques and to demonstrate quantitative", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 350, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 350, + 149 + ], + "score": 1.0, + "content": "and qualitative better explanations for deep neural networks.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 2.5, + "bbox_fs": [ + 104, + 83, + 506, + 149 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 164, + 505, + 220 + ], + "lines": [ + { + "bbox": [ + 106, + 164, + 504, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 164, + 494, + 178 + ], + "score": 1.0, + "content": "Terminology Throughout this manuscript we will use the following terminology: The filter", + "type": "text" + }, + { + "bbox": [ + 494, + 166, + 504, + 175 + ], + "score": 0.28, + "content": "\\pmb { w }", + "type": "inline_equation" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 174, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 237, + 189 + ], + "score": 1.0, + "content": "tells us how to extract the output", + "type": "text" + }, + { + "bbox": [ + 237, + 178, + 244, + 187 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 174, + 326, + 189 + ], + "score": 1.0, + "content": "optimally from data", + "type": "text" + }, + { + "bbox": [ + 326, + 178, + 334, + 186 + ], + "score": 0.66, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 174, + 387, + 189 + ], + "score": 1.0, + "content": ". The pattern", + "type": "text" + }, + { + "bbox": [ + 387, + 178, + 399, + 187 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 174, + 505, + 189 + ], + "score": 1.0, + "content": "is the direction in the data", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 186, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 234, + 200 + ], + "score": 1.0, + "content": "along which the desired output", + "type": "text" + }, + { + "bbox": [ + 234, + 189, + 241, + 198 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 186, + 379, + 200 + ], + "score": 1.0, + "content": "varies. Both constitute the signal", + "type": "text" + }, + { + "bbox": [ + 380, + 188, + 417, + 198 + ], + "score": 0.89, + "content": "\\textbf { \\em s } = \\textbf { \\em a } _ { s } y", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 186, + 505, + 200 + ], + "score": 1.0, + "content": ", i.e., the contributing", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 196, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 135, + 210 + ], + "score": 1.0, + "content": "part of", + "type": "text" + }, + { + "bbox": [ + 135, + 199, + 143, + 208 + ], + "score": 0.72, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 196, + 207, + 210 + ], + "score": 1.0, + "content": ". The distractor", + "type": "text" + }, + { + "bbox": [ + 207, + 198, + 215, + 208 + ], + "score": 0.78, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 196, + 506, + 210 + ], + "score": 1.0, + "content": "is the component of the data that does not contain information about the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 207, + 168, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 207, + 168, + 222 + ], + "score": 1.0, + "content": "desired output.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 164, + 506, + 222 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 240, + 460, + 252 + ], + "lines": [ + { + "bbox": [ + 104, + 239, + 461, + 255 + ], + "spans": [ + { + "bbox": [ + 104, + 239, + 461, + 255 + ], + "score": 1.0, + "content": "3 OVERVIEW OF EXPLANATION APPROACHES AND THEIR BEHAVIOR", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 267, + 505, + 322 + ], + "lines": [ + { + "bbox": [ + 105, + 267, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 505, + 279 + ], + "score": 1.0, + "content": "In this section, we take a look at a subset of explanation methods for individual classifier decisions", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 279, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 505, + 290 + ], + "score": 1.0, + "content": "and discuss how they are connected to our analysis of linear models in the previous section. Fig. 1", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 289, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 104, + 289, + 506, + 303 + ], + "score": 1.0, + "content": "gives an overview of the different types of explanation methods which can be divided into function,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 299, + 506, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 506, + 313 + ], + "score": 1.0, + "content": "signal and attribution visualizations. These three groups all present different information about the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 311, + 255, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 255, + 323 + ], + "score": 1.0, + "content": "network and complement each other.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14, + "bbox_fs": [ + 104, + 267, + 506, + 323 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 338, + 505, + 426 + ], + "lines": [ + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 352 + ], + "score": 1.0, + "content": "Functions – gradients, saliency map Explaining the function in input space corresponds to de-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 349, + 504, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 304, + 361 + ], + "score": 1.0, + "content": "scribing the operations the model uses to extract", + "type": "text" + }, + { + "bbox": [ + 304, + 352, + 311, + 361 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 349, + 335, + 361 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 335, + 352, + 342, + 360 + ], + "score": 0.66, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 349, + 504, + 361 + ], + "score": 1.0, + "content": ". Since deep neural networks are highly", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 361, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 505, + 373 + ], + "score": 1.0, + "content": "nonlinear, this can only be approximated. The saliency map estimates how moving along a particu-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 372, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 372, + 257, + 384 + ], + "score": 1.0, + "content": "lar direction in input space influences", + "type": "text" + }, + { + "bbox": [ + 257, + 373, + 264, + 383 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 372, + 505, + 384 + ], + "score": 1.0, + "content": "(i.e., sensitivity analysis) where the direction is given by the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 381, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 459, + 396 + ], + "score": 1.0, + "content": "model gradient (Baehrens et al., 2010; Simonyan et al., 2014). In case of a linear model", + "type": "text" + }, + { + "bbox": [ + 460, + 382, + 501, + 394 + ], + "score": 0.93, + "content": "y = \\dot { \\pmb { w } } ^ { T } \\pmb { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 381, + 506, + 396 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 393, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 312, + 406 + ], + "score": 1.0, + "content": "the saliency map reduces to analyzing the weights", + "type": "text" + }, + { + "bbox": [ + 313, + 393, + 365, + 405 + ], + "score": 0.91, + "content": "\\partial y / \\partial x = w", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 393, + 505, + 406 + ], + "score": 1.0, + "content": ". Since it is mostly determined by", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 404, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 505, + 417 + ], + "score": 1.0, + "content": "the distractor, as demonstrated above, it is not representing the signal. It tells us how to extract the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 416, + 326, + 427 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 326, + 427 + ], + "score": 1.0, + "content": "signal, not what the signal is in a deep neural network.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 338, + 506, + 427 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 443, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 443, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 443, + 385, + 454 + ], + "score": 1.0, + "content": "Signal – DeConvNet, Guided BackProp, PatternNet The signal", + "type": "text" + }, + { + "bbox": [ + 385, + 445, + 392, + 453 + ], + "score": 0.57, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 392, + 443, + 505, + 454 + ], + "score": 1.0, + "content": "detected by the neural net-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 454, + 505, + 465 + ], + "score": 1.0, + "content": "work is the component of the data that caused the networks activations. Zeiler & Fergus (2014)", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 464, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 506, + 478 + ], + "score": 1.0, + "content": "formulated the goal of these methods as ”[...] to map these activities back to the input pixel space,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 475, + 446, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 446, + 488 + ], + "score": 1.0, + "content": "showing what input pattern originally caused a given activation in the feature maps”.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 443, + 506, + 488 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 492, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 104, + 491, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 104, + 491, + 283, + 506 + ], + "score": 1.0, + "content": "In a linear model, the signal corresponds to", + "type": "text" + }, + { + "bbox": [ + 284, + 495, + 320, + 504 + ], + "score": 0.89, + "content": "\\mathbf { \\boldsymbol { s } } = \\mathbf { \\boldsymbol { a } } _ { s } \\boldsymbol { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 491, + 374, + 506 + ], + "score": 1.0, + "content": ". The pattern", + "type": "text" + }, + { + "bbox": [ + 374, + 495, + 386, + 504 + ], + "score": 0.85, + "content": "\\mathbf { \\delta } _ { \\mathbf { \\alpha } \\mathbf { \\delta } _ { a _ { s } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 491, + 506, + 506 + ], + "score": 1.0, + "content": "contains the signal direction,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 503, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 503, + 505, + 516 + ], + "score": 1.0, + "content": "i.e., it tells us where a change of the output variable is expected to be measurable in the input", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "score": 1.0, + "content": "(Haufe et al., 2014). Attempts to visualize the signal for deep neural networks were made using", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "DeConvNet (Zeiler & Fergus, 2014) and Guided BackProp (Springenberg et al., 2015). These use", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 536, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 505, + 549 + ], + "score": 1.0, + "content": "the same algorithm as the saliency map, but treat the rectifiers differently (see Fig. 1): DeConvNet", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 548, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 106, + 548, + 505, + 559 + ], + "score": 1.0, + "content": "leaves out the rectifiers from the forward pass, but adds additional ReLUs after each deconvolution,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 505, + 571 + ], + "score": 1.0, + "content": "while Guided BackProp uses the ReLUs from the forward pass as well as additional ones. The", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 569, + 505, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 505, + 582 + ], + "score": 1.0, + "content": "back-projections for the linear components of the network correspond to a superposition of what are", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 580, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 505, + 593 + ], + "score": 1.0, + "content": "assumed to be the signal directions of each neuron. For this reason, these projections must be seen", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 592, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 505, + 604 + ], + "score": 1.0, + "content": "as an approximation of the features that activated the higher layer neuron. It is not a reconstruction", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 602, + 264, + 614 + ], + "spans": [ + { + "bbox": [ + 106, + 602, + 264, + 614 + ], + "score": 1.0, + "content": "in input space (Zeiler & Fergus, 2014).", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 34, + "bbox_fs": [ + 104, + 491, + 506, + 614 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 619, + 505, + 696 + ], + "lines": [ + { + "bbox": [ + 104, + 618, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 104, + 618, + 505, + 631 + ], + "score": 1.0, + "content": "For the simplest of neural networks – the linear model – these visualizations reduce to the gradient1.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 630, + 506, + 643 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 188, + 643 + ], + "score": 1.0, + "content": "They show the filter", + "type": "text" + }, + { + "bbox": [ + 189, + 632, + 198, + 640 + ], + "score": 0.47, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 630, + 292, + 643 + ], + "score": 1.0, + "content": "and neither the pattern", + "type": "text" + }, + { + "bbox": [ + 292, + 632, + 304, + 641 + ], + "score": 0.86, + "content": "\\mathbf { \\delta } _ { a _ { s } }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 630, + 365, + 643 + ], + "score": 1.0, + "content": ", nor the signal", + "type": "text" + }, + { + "bbox": [ + 366, + 632, + 372, + 640 + ], + "score": 0.31, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 630, + 506, + 643 + ], + "score": 1.0, + "content": ". Hence, DeConvNet and Guided", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "BackProp do not guarantee to produce the detected signal for a linear model, which is proven by our", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 653, + 506, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 506, + 664 + ], + "score": 1.0, + "content": "toy example in Fig. 2. Since they do produce compelling visualizations, we will later investigate", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 663, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 663, + 241, + 675 + ], + "score": 1.0, + "content": "whether the direction of the filter", + "type": "text" + }, + { + "bbox": [ + 242, + 664, + 252, + 673 + ], + "score": 0.55, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 663, + 419, + 675 + ], + "score": 1.0, + "content": "coincides with the direction of the signal", + "type": "text" + }, + { + "bbox": [ + 419, + 665, + 425, + 673 + ], + "score": 0.48, + "content": "\\pmb { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 663, + 505, + 675 + ], + "score": 1.0, + "content": ". We will show that", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 673, + 507, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 507, + 688 + ], + "score": 1.0, + "content": "this is not the case and propose a new approach, PatternNet (see Fig. 1), to estimate the correct", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 685, + 438, + 698 + ], + "spans": [ + { + "bbox": [ + 105, + 685, + 438, + 698 + ], + "score": 1.0, + "content": "direction that improves upon the DeConvNet and Guided BackProp visualizations.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 43, + "bbox_fs": [ + 104, + 618, + 507, + 698 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 203 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "Attribution – LRP, Deep Taylor Decomposition, PatternAttribution Finally, we can look at", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "how much the signal dimensions contribute to the output through the layers. This will be referred", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 504, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 504, + 117 + ], + "score": 1.0, + "content": "to as the attribution. 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This is identical to how a ReLU stops the propagation", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 313, + 506, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 328 + ], + "score": 1.0, + "content": "of the gradient. The difficulty in the application of the deep Taylor decomposition is the choice of", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 326, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 162, + 338 + ], + "score": 1.0, + "content": "the root point", + "type": "text" + }, + { + "bbox": [ + 162, + 327, + 174, + 337 + ], + "score": 0.88, + "content": "\\scriptstyle { \\pmb x } _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 326, + 506, + 338 + ], + "score": 1.0, + "content": ", for which many options are available. It is important to recognize at this point that", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 405, + 349 + ], + "score": 1.0, + "content": "selecting a root point for the DTD corresponds to estimating the distractor", + "type": "text" + }, + { + "bbox": [ + 405, + 337, + 437, + 348 + ], + "score": 0.92, + "content": "\\scriptstyle { \\pmb { x } } _ { 0 } = { \\pmb { d } }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 336, + 505, + 349 + ], + "score": 1.0, + "content": "and, by that, the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 348, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 133, + 360 + ], + "score": 1.0, + "content": "signal", + "type": "text" + }, + { + "bbox": [ + 133, + 348, + 183, + 359 + ], + "score": 0.91, + "content": "\\hat { \\pmb { s } } = \\pmb { x } - \\pmb { x } _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 348, + 506, + 360 + ], + "score": 1.0, + "content": ". PatternAttribution is a DTD extension that learns from data how to set the root", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 359, + 133, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 359, + 133, + 371 + ], + "score": 1.0, + "content": "point.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 375, + 505, + 409 + ], + "lines": [ + { + "bbox": [ + 106, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "Summarizing, the function extracts the signal from the data by removing the distractor. The attri-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 386, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 505, + 398 + ], + "score": 1.0, + "content": "bution of output values to input dimensions shows how much an individual component of the signal", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 398, + 352, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 352, + 410 + ], + "score": 1.0, + "content": "contributes to the output, which is what LRP calls relevance.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24 + }, + { + "type": "title", + "bbox": [ + 107, + 426, + 316, + 438 + ], + "lines": [ + { + "bbox": [ + 105, + 425, + 318, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 318, + 440 + ], + "score": 1.0, + "content": "4 LEARNING TO ESTIMATE THE SIGNAL", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 450, + 505, + 550 + ], + "lines": [ + { + "bbox": [ + 106, + 450, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 464 + ], + "score": 1.0, + "content": "Visualizing the function has proven to be straightforward (Baehrens et al., 2010; Simonyan et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 459, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 104, + 459, + 506, + 477 + ], + "score": 1.0, + "content": "2014). In contrast, visualizing the signal (Haufe et al., 2014; Zeiler & Fergus, 2014; Springenberg", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "et al., 2015) and the attribution (Bach et al., 2015; Montavon et al., 2017; Sundararajan et al., 2017)", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "is more difficult. It requires a good estimate of what is the signal and what is the distractor. In the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 494, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 506, + 508 + ], + "score": 1.0, + "content": "following section we first propose a quality measure for neuron-wise signal estimators. 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All mentioned techniques as well as our proposed signal estimators treat neurons", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 538, + 474, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 474, + 552 + ], + "score": 1.0, + "content": "independently, i.e., the full explanation will be a superposition of neuron-wise explanations.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31 + }, + { + "type": "title", + "bbox": [ + 107, + 564, + 332, + 576 + ], + "lines": [ + { + "bbox": [ + 105, + 564, + 333, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 333, + 577 + ], + "score": 1.0, + "content": "4.1 QUALITY CRITERION FOR SIGNAL ESTIMATORS", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 585, + 505, + 618 + ], + "lines": [ + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 207, + 597 + ], + "score": 1.0, + "content": "Recall that the input data", + "type": "text" + }, + { + "bbox": [ + 207, + 587, + 215, + 595 + ], + "score": 0.75, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 585, + 364, + 597 + ], + "score": 1.0, + "content": "comprises both signal and distractor:", + "type": "text" + }, + { + "bbox": [ + 365, + 586, + 407, + 596 + ], + "score": 0.91, + "content": "{ \\pmb x } = { \\pmb s } + { \\pmb d }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 585, + 505, + 597 + ], + "score": 1.0, + "content": ", and that the signal con-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 596, + 504, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 380, + 608 + ], + "score": 1.0, + "content": "tributes to the output but the distractor does not. Assuming the filter", + "type": "text" + }, + { + "bbox": [ + 380, + 598, + 389, + 606 + ], + "score": 0.72, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 596, + 504, + 608 + ], + "score": 1.0, + "content": "has been trained sufficiently", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 607, + 211, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 166, + 618 + ], + "score": 1.0, + "content": "well to extract", + "type": "text" + }, + { + "bbox": [ + 166, + 609, + 172, + 618 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 607, + 211, + 618 + ], + "score": 1.0, + "content": ", we have", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38 + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 622, + 385, + 637 + ], + "lines": [ + { + "bbox": [ + 225, + 622, + 385, + 637 + ], + "spans": [ + { + "bbox": [ + 225, + 622, + 385, + 637 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\boldsymbol { w } ^ { T } \\boldsymbol { x } = \\boldsymbol { y } , \\quad \\boldsymbol { w } ^ { T } \\boldsymbol { s } = \\boldsymbol { y } , \\quad \\boldsymbol { w } ^ { T } \\boldsymbol { d } = 0 . } \\end{array}", + "type": "interline_equation", + "image_path": "e7d09f49ef0fbbe9039ad145b622d49cb7717966d43992239755abdc0890bfbd.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 225, + 622, + 385, + 637 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "Note that estimating the signal based on these conditions alone is an ill-posed problem. We could", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 294, + 666 + ], + "score": 1.0, + "content": "limit ourselves to linear estimators of the form", + "type": "text" + }, + { + "bbox": [ + 295, + 654, + 366, + 667 + ], + "score": 0.92, + "content": "\\hat { \\pmb { s } } = \\pmb { u } ( \\pmb { w } ^ { T } \\pmb { u } ) ^ { - 1 } \\pmb { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 654, + 390, + 666 + ], + "score": 1.0, + "content": ", with", + "type": "text" + }, + { + "bbox": [ + 390, + 657, + 398, + 664 + ], + "score": 0.74, + "content": "\\textbf { \\em u }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "a random vector such that", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 666, + 507, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 149, + 680 + ], + "score": 0.9, + "content": "\\pmb { w } ^ { T } \\pmb { u } \\neq 0", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 667, + 325, + 682 + ], + "score": 1.0, + "content": ". For such an estimator, the signal estimate", + "type": "text" + }, + { + "bbox": [ + 325, + 666, + 403, + 681 + ], + "score": 0.92, + "content": "\\hat { \\pmb { s } } = \\pmb { u } \\left( \\pmb { w } ^ { T } \\pmb { u } \\right) ^ { - 1 } \\ b { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 667, + 438, + 682 + ], + "score": 1.0, + "content": "satisfies", + "type": "text" + }, + { + "bbox": [ + 438, + 667, + 479, + 680 + ], + "score": 0.92, + "content": "\\mathbf { \\boldsymbol { w } } ^ { T } \\hat { \\mathbf { \\boldsymbol { s } } } = \\boldsymbol { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 667, + 507, + 682 + ], + "score": 1.0, + "content": ". This", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "score": 1.0, + "content": "implies the existence of an infinite number of possible rules for the DTD as well as infinitely many", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 691, + 284, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 284, + 703 + ], + "score": 1.0, + "content": "back-projections for the DeConvNet family.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43 + }, + { + "type": "text", + "bbox": [ + 106, + 707, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 707, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 106, + 707, + 370, + 720 + ], + "score": 1.0, + "content": "To alleviate this issue, we introduce the following quality measure", + "type": "text" + }, + { + "bbox": [ + 370, + 710, + 376, + 719 + ], + "score": 0.81, + "content": "\\rho", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 707, + 463, + 720 + ], + "score": 1.0, + "content": "for a signal estimator", + "type": "text" + }, + { + "bbox": [ + 463, + 707, + 504, + 720 + ], + "score": 0.93, + "content": "S ( { \\pmb x } ) = \\hat { \\pmb s }", + "type": "inline_equation" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 719, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 427, + 733 + ], + "score": 1.0, + "content": "that will be written with explicit variances and covariances using the shorthands", + "type": "text" + }, + { + "bbox": [ + 427, + 719, + 487, + 732 + ], + "score": 0.92, + "content": "\\hat { \\pmb { d } } = \\pmb { x } - \\pmb { S } ( \\pmb { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46.5 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 763 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 203 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "Attribution – LRP, Deep Taylor Decomposition, PatternAttribution Finally, we can look at", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "how much the signal dimensions contribute to the output through the layers. 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This is identical to how a ReLU stops the propagation", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 313, + 506, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 328 + ], + "score": 1.0, + "content": "of the gradient. The difficulty in the application of the deep Taylor decomposition is the choice of", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 326, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 162, + 338 + ], + "score": 1.0, + "content": "the root point", + "type": "text" + }, + { + "bbox": [ + 162, + 327, + 174, + 337 + ], + "score": 0.88, + "content": "\\scriptstyle { \\pmb x } _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 326, + 506, + 338 + ], + "score": 1.0, + "content": ", for which many options are available. It is important to recognize at this point that", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 405, + 349 + ], + "score": 1.0, + "content": "selecting a root point for the DTD corresponds to estimating the distractor", + "type": "text" + }, + { + "bbox": [ + 405, + 337, + 437, + 348 + ], + "score": 0.92, + "content": "\\scriptstyle { \\pmb { x } } _ { 0 } = { \\pmb { d } }", + "type": "inline_equation" + }, + { + "bbox": [ + 438, + 336, + 505, + 349 + ], + "score": 1.0, + "content": "and, by that, the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 348, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 348, + 133, + 360 + ], + "score": 1.0, + "content": "signal", + "type": "text" + }, + { + "bbox": [ + 133, + 348, + 183, + 359 + ], + "score": 0.91, + "content": "\\hat { \\pmb { s } } = \\pmb { x } - \\pmb { x } _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 348, + 506, + 360 + ], + "score": 1.0, + "content": ". PatternAttribution is a DTD extension that learns from data how to set the root", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 359, + 133, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 359, + 133, + 371 + ], + "score": 1.0, + "content": "point.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19, + "bbox_fs": [ + 104, + 292, + 506, + 371 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 375, + 505, + 409 + ], + "lines": [ + { + "bbox": [ + 106, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "Summarizing, the function extracts the signal from the data by removing the distractor. The attri-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 386, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 106, + 386, + 505, + 398 + ], + "score": 1.0, + "content": "bution of output values to input dimensions shows how much an individual component of the signal", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 398, + 352, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 352, + 410 + ], + "score": 1.0, + "content": "contributes to the output, which is what LRP calls relevance.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 375, + 505, + 410 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 426, + 316, + 438 + ], + "lines": [ + { + "bbox": [ + 105, + 425, + 318, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 318, + 440 + ], + "score": 1.0, + "content": "4 LEARNING TO ESTIMATE THE SIGNAL", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 450, + 505, + 550 + ], + "lines": [ + { + "bbox": [ + 106, + 450, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 505, + 464 + ], + "score": 1.0, + "content": "Visualizing the function has proven to be straightforward (Baehrens et al., 2010; Simonyan et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 459, + 506, + 477 + ], + "spans": [ + { + "bbox": [ + 104, + 459, + 506, + 477 + ], + "score": 1.0, + "content": "2014). In contrast, visualizing the signal (Haufe et al., 2014; Zeiler & Fergus, 2014; Springenberg", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "et al., 2015) and the attribution (Bach et al., 2015; Montavon et al., 2017; Sundararajan et al., 2017)", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "is more difficult. It requires a good estimate of what is the signal and what is the distractor. In the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 494, + 506, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 506, + 508 + ], + "score": 1.0, + "content": "following section we first propose a quality measure for neuron-wise signal estimators. This allows", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 506, + 504, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 504, + 518 + ], + "score": 1.0, + "content": "us to evaluate existing approaches and, finally, derive signal estimators that optimize this criterion.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "These estimators will then be used to explain the signal (PatternNet) and the attribution (Patter-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 528, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 505, + 540 + ], + "score": 1.0, + "content": "nAttribution). All mentioned techniques as well as our proposed signal estimators treat neurons", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 538, + 474, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 474, + 552 + ], + "score": 1.0, + "content": "independently, i.e., the full explanation will be a superposition of neuron-wise explanations.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31, + "bbox_fs": [ + 104, + 450, + 506, + 552 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 564, + 332, + 576 + ], + "lines": [ + { + "bbox": [ + 105, + 564, + 333, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 333, + 577 + ], + "score": 1.0, + "content": "4.1 QUALITY CRITERION FOR SIGNAL ESTIMATORS", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 585, + 505, + 618 + ], + "lines": [ + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 207, + 597 + ], + "score": 1.0, + "content": "Recall that the input data", + "type": "text" + }, + { + "bbox": [ + 207, + 587, + 215, + 595 + ], + "score": 0.75, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 585, + 364, + 597 + ], + "score": 1.0, + "content": "comprises both signal and distractor:", + "type": "text" + }, + { + "bbox": [ + 365, + 586, + 407, + 596 + ], + "score": 0.91, + "content": "{ \\pmb x } = { \\pmb s } + { \\pmb d }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 585, + 505, + 597 + ], + "score": 1.0, + "content": ", and that the signal con-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 596, + 504, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 380, + 608 + ], + "score": 1.0, + "content": "tributes to the output but the distractor does not. Assuming the filter", + "type": "text" + }, + { + "bbox": [ + 380, + 598, + 389, + 606 + ], + "score": 0.72, + "content": "\\textbf { \\em w }", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 596, + 504, + 608 + ], + "score": 1.0, + "content": "has been trained sufficiently", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 607, + 211, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 166, + 618 + ], + "score": 1.0, + "content": "well to extract", + "type": "text" + }, + { + "bbox": [ + 166, + 609, + 172, + 618 + ], + "score": 0.79, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 607, + 211, + 618 + ], + "score": 1.0, + "content": ", we have", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 585, + 505, + 618 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 622, + 385, + 637 + ], + "lines": [ + { + "bbox": [ + 225, + 622, + 385, + 637 + ], + "spans": [ + { + "bbox": [ + 225, + 622, + 385, + 637 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\boldsymbol { w } ^ { T } \\boldsymbol { x } = \\boldsymbol { y } , \\quad \\boldsymbol { w } ^ { T } \\boldsymbol { s } = \\boldsymbol { y } , \\quad \\boldsymbol { w } ^ { T } \\boldsymbol { d } = 0 . } \\end{array}", + "type": "interline_equation", + "image_path": "e7d09f49ef0fbbe9039ad145b622d49cb7717966d43992239755abdc0890bfbd.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 225, + 622, + 385, + 637 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "Note that estimating the signal based on these conditions alone is an ill-posed problem. We could", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 294, + 666 + ], + "score": 1.0, + "content": "limit ourselves to linear estimators of the form", + "type": "text" + }, + { + "bbox": [ + 295, + 654, + 366, + 667 + ], + "score": 0.92, + "content": "\\hat { \\pmb { s } } = \\pmb { u } ( \\pmb { w } ^ { T } \\pmb { u } ) ^ { - 1 } \\pmb { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 654, + 390, + 666 + ], + "score": 1.0, + "content": ", with", + "type": "text" + }, + { + "bbox": [ + 390, + 657, + 398, + 664 + ], + "score": 0.74, + "content": "\\textbf { \\em u }", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "a random vector such that", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 666, + 507, + 682 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 149, + 680 + ], + "score": 0.9, + "content": "\\pmb { w } ^ { T } \\pmb { u } \\neq 0", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 667, + 325, + 682 + ], + "score": 1.0, + "content": ". 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This", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "score": 1.0, + "content": "implies the existence of an infinite number of possible rules for the DTD as well as infinitely many", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 691, + 284, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 284, + 703 + ], + "score": 1.0, + "content": "back-projections for the DeConvNet family.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43, + "bbox_fs": [ + 105, + 644, + 507, + 703 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 707, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 707, + 504, + 720 + ], + "spans": [ + { + "bbox": [ + 106, + 707, + 370, + 720 + ], + "score": 1.0, + "content": "To alleviate this issue, we introduce the following quality measure", + "type": "text" + }, + { + "bbox": [ + 370, + 710, + 376, + 719 + ], + "score": 0.81, + "content": "\\rho", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 707, + 463, + 720 + ], + "score": 1.0, + "content": "for a signal estimator", + "type": "text" + }, + { + "bbox": [ + 463, + 707, + 504, + 720 + ], + "score": 0.93, + "content": "S ( { \\pmb x } ) = \\hat { \\pmb s }", + "type": "inline_equation" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 719, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 427, + 733 + ], + "score": 1.0, + "content": "that will be written with explicit variances and covariances using the shorthands", + "type": "text" + }, + { + "bbox": [ + 427, + 719, + 487, + 732 + ], + "score": 0.92, + "content": "\\hat { \\pmb { d } } = \\pmb { x } - \\pmb { S } ( \\pmb { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46.5, + "bbox_fs": [ + 106, + 707, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "interline_equation", + "bbox": [ + 106, + 81, + 150, + 95 + ], + "lines": [ + { + "bbox": [ + 106, + 81, + 150, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 81, + 150, + 95 + ], + "score": 0.37, + "content": "y = \\pmb { w } ^ { T } \\pmb { x } \\colon", + "type": "interline_equation", + "image_path": "1dae6d2be042669e1185ea2c754a6d49a234f17cfcc5cf4d2fae7983f250cff2.jpg" + } + ] + } + ], + "index": 0, + "virtual_lines": [ + { + "bbox": [ + 106, + 81, + 150, + 95 + ], + "spans": [], + "index": 0 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 158, + 100, + 453, + 137 + ], + "lines": [ + { + "bbox": [ + 158, + 100, + 453, + 137 + ], + "spans": [ + { + "bbox": [ + 158, + 100, + 453, + 137 + ], + "score": 0.92, + "content": "\\rho ( S ) = 1 - \\operatorname* { m a x } _ { \\pmb { v } } c o r r \\left( \\pmb { w } ^ { T } \\pmb { x } , \\pmb { v } ^ { T } \\left( \\pmb { x } - S ( \\pmb { x } ) \\right) \\right) = 1 - \\operatorname* { m a x } _ { \\pmb { v } } \\frac { \\pmb { v } ^ { T } \\mathrm { c o v } [ \\hat { d } , y ] } { \\sqrt { \\sigma _ { \\pmb { v } ^ { T } \\hat { d } } ^ { 2 } \\sigma _ { y } ^ { 2 } } } .", + "type": "interline_equation", + "image_path": "e0b280e91657c8d29470f2a1326d5513f35acdd2e418d3eed270c4ba16a37c64.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 158, + 100, + 453, + 112.33333333333333 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 158, + 112.33333333333333, + 453, + 124.66666666666666 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 158, + 124.66666666666666, + 453, + 137.0 + ], + "spans": [], + "index": 3 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 141, + 506, + 215 + ], + "lines": [ + { + "bbox": [ + 106, + 141, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 106, + 141, + 480, + 155 + ], + "score": 1.0, + "content": "This criterion introduces an additional constraint by measuring how much information about", + "type": "text" + }, + { + "bbox": [ + 481, + 145, + 488, + 154 + ], + "score": 0.8, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 141, + 505, + 155 + ], + "score": 1.0, + "content": "can", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 153, + 506, + 165 + ], + "spans": [ + { + "bbox": [ + 106, + 153, + 255, + 165 + ], + "score": 1.0, + "content": "be reconstructed from the residuals", + "type": "text" + }, + { + "bbox": [ + 255, + 154, + 283, + 164 + ], + "score": 0.89, + "content": "\\mathbf { \\Delta } \\mathbf { x } - \\hat { \\mathbf { \\mu } } _ { s }", + "type": "inline_equation" + }, + { + "bbox": [ + 283, + 153, + 506, + 165 + ], + "score": 1.0, + "content": "using a linear projection. The best signal estimators", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 99, + 164, + 506, + 200 + ], + "spans": [ + { + "bbox": [ + 99, + 164, + 244, + 200 + ], + "score": 1.0, + "content": "remove most of the information iinvariant to scaling, we constrain", + "type": "text" + }, + { + "bbox": [ + 244, + 175, + 264, + 187 + ], + "score": 0.91, + "content": "{ \\pmb v } ^ { T } \\hat { \\pmb d }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 164, + 326, + 200 + ], + "score": 1.0, + "content": "residuals and thto have varian", + "type": "text" + }, + { + "bbox": [ + 335, + 176, + 384, + 191 + ], + "score": 0.94, + "content": "\\sigma _ { v ^ { T } \\hat { d } } ^ { 2 } = \\sigma _ { y } ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 164, + 404, + 176 + ], + "score": 0.92, + "content": "\\rho ( S )", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 164, + 474, + 200 + ], + "score": 1.0, + "content": ". Since the correlding the optimal", + "type": "text" + }, + { + "bbox": [ + 474, + 179, + 481, + 187 + ], + "score": 0.71, + "content": "\\textbf { { v } }", + "type": "inline_equation" + }, + { + "bbox": [ + 482, + 164, + 506, + 200 + ], + "score": 1.0, + "content": "ion isfor a", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 129, + 205 + ], + "score": 1.0, + "content": "fixed", + "type": "text" + }, + { + "bbox": [ + 151, + 191, + 326, + 205 + ], + "score": 1.0, + "content": "amounts to a least-squares regression from", + "type": "text" + }, + { + "bbox": [ + 327, + 191, + 335, + 202 + ], + "score": 0.83, + "content": "\\hat { \\ b { d } }", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 191, + 346, + 205 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 346, + 194, + 353, + 204 + ], + "score": 0.78, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 191, + 505, + 205 + ], + "score": 1.0, + "content": ". This enables us to assess the quality", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 203, + 231, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 231, + 216 + ], + "score": 1.0, + "content": "of signal estimators efficiently.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6 + }, + { + "type": "title", + "bbox": [ + 108, + 228, + 266, + 240 + ], + "lines": [ + { + "bbox": [ + 106, + 228, + 268, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 268, + 241 + ], + "score": 1.0, + "content": "4.2 EXISTING SIGNAL ESTIMATORS", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 249, + 447, + 262 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 449, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 449, + 264 + ], + "score": 1.0, + "content": "Let us now discuss two signal estimators that have been used in previous approaches.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 273, + 503, + 296 + ], + "lines": [ + { + "bbox": [ + 106, + 274, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 106, + 275, + 119, + 285 + ], + "score": 0.85, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 274, + 505, + 287 + ], + "score": 1.0, + "content": "– the identity estimator The naive approach to signal estimation is to assume the entire data", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 285, + 255, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 255, + 298 + ], + "score": 1.0, + "content": "is signal and there are no distractors:", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5 + }, + { + "type": "interline_equation", + "bbox": [ + 280, + 296, + 331, + 310 + ], + "lines": [ + { + "bbox": [ + 280, + 296, + 331, + 310 + ], + "spans": [ + { + "bbox": [ + 280, + 296, + 331, + 310 + ], + "score": 0.91, + "content": "S _ { x } ( { \\pmb x } ) = { \\pmb x } .", + "type": "interline_equation", + "image_path": "7293ad93e9b4502ba4d927df2424160dcbad8bb9e8cea4ef77827a6b0a185850.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 280, + 296, + 331, + 310 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 313, + 505, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 312, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 404, + 326 + ], + "score": 1.0, + "content": "With this being plugged into the deep Taylor framework, we obtain the", + "type": "text" + }, + { + "bbox": [ + 405, + 315, + 411, + 323 + ], + "score": 0.79, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 312, + 506, + 326 + ], + "score": 1.0, + "content": "-rule (Montavon et al.,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "score": 1.0, + "content": "2017) which is equivalent to LRP (Bach et al., 2015). For a linear model, this corresponds to", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 107, + 336, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 107, + 336, + 154, + 346 + ], + "score": 0.88, + "content": "\\mathbf { \\Delta } \\mathbf { \\mathbf { \\mathit { r } } } = \\mathbf { \\mathit { w } } \\odot \\mathbf { \\mathbf { \\mathit { x } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 336, + 478, + 347 + ], + "score": 1.0, + "content": "as the attribution. It can be shown that for ReLU and max-pooling networks, the", + "type": "text" + }, + { + "bbox": [ + 479, + 337, + 485, + 345 + ], + "score": 0.8, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 336, + 505, + 347 + ], + "score": 1.0, + "content": "-rule", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 347, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 359 + ], + "score": 1.0, + "content": "reduces to the element-wise multiplication of the input and the saliency map (Shrikumar et al., 2016;", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 356, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 370 + ], + "score": 1.0, + "content": "Kindermans et al., 2016). This means that for a whole network, the assumed signal is simply the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 368, + 506, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 506, + 380 + ], + "score": 1.0, + "content": "original input image. 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The distractor contributions", + "type": "text" + }, + { + "bbox": [ + 356, + 429, + 386, + 440 + ], + "score": 0.9, + "content": "\\omega \\odot d", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 429, + 506, + 441 + ], + "score": 1.0, + "content": "that are included in the LRP", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 441, + 410, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 381, + 452 + ], + "score": 1.0, + "content": "explanation cause the noisy nature of the visualizations based on the", + "type": "text" + }, + { + "bbox": [ + 381, + 442, + 387, + 450 + ], + "score": 0.8, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 441, + 410, + 452 + ], + "score": 1.0, + "content": "-rule.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 107, + 464, + 505, + 509 + ], + "lines": [ + { + "bbox": [ + 107, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 107, + 465, + 121, + 475 + ], + "score": 0.87, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 122, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "– the filter based estimator The implicit assumption made by DeConvNet and Guided Back-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 399, + 487 + ], + "score": 1.0, + "content": "Prop is that the detected signal varies in the direction of the weight vector", + "type": "text" + }, + { + "bbox": [ + 399, + 477, + 408, + 485 + ], + "score": 0.69, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 475, + 505, + 487 + ], + "score": 1.0, + "content": ". This weight vector has", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "to be normalized in order to be a valid signal estimator. 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Empirically it is also sub-optimal in our", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 565, + 195, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 195, + 577 + ], + "score": 1.0, + "content": "experiment in Fig. 3.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 106, + 590, + 311, + 602 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 311, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 311, + 603 + ], + "score": 1.0, + "content": "4.3 PATTERNNET AND PATTERNATTRIBUTION", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 106, + 611, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 610, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 268, + 624 + ], + "score": 1.0, + "content": "We suggest to learn the signal estimator", + "type": "text" + }, + { + "bbox": [ + 268, + 612, + 276, + 622 + ], + "score": 0.83, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 610, + 505, + 624 + ], + "score": 1.0, + "content": "from data by optimizing the previously established crite-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 203, + 635 + ], + "score": 1.0, + "content": "rion. A signal estimator", + "type": "text" + }, + { + "bbox": [ + 204, + 623, + 212, + 632 + ], + "score": 0.83, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "is optimal with respect to Eq. (1) if the correlation is zero for all possible", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 633, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 198, + 648 + ], + "score": 0.9, + "content": "{ \\pmb v } \\colon \\forall { \\pmb v } , \\mathrm { c o v } [ y , \\hat { \\pmb d } ] { \\pmb v } = { \\bf 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 635, + 420, + 648 + ], + "score": 1.0, + "content": ". 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Since the correlding the optimal", + "type": "text" + }, + { + "bbox": [ + 474, + 179, + 481, + 187 + ], + "score": 0.71, + "content": "\\textbf { { v } }", + "type": "inline_equation" + }, + { + "bbox": [ + 482, + 164, + 506, + 200 + ], + "score": 1.0, + "content": "ion isfor a", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 191, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 191, + 129, + 205 + ], + "score": 1.0, + "content": "fixed", + "type": "text" + }, + { + "bbox": [ + 151, + 191, + 326, + 205 + ], + "score": 1.0, + "content": "amounts to a least-squares regression from", + "type": "text" + }, + { + "bbox": [ + 327, + 191, + 335, + 202 + ], + "score": 0.83, + "content": "\\hat { \\ b { d } }", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 191, + 346, + 205 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 346, + 194, + 353, + 204 + ], + "score": 0.78, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 191, + 505, + 205 + ], + "score": 1.0, + "content": ". This enables us to assess the quality", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 203, + 231, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 231, + 216 + ], + "score": 1.0, + "content": "of signal estimators efficiently.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6, + "bbox_fs": [ + 99, + 141, + 506, + 216 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 228, + 266, + 240 + ], + "lines": [ + { + "bbox": [ + 106, + 228, + 268, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 268, + 241 + ], + "score": 1.0, + "content": "4.2 EXISTING SIGNAL ESTIMATORS", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 249, + 447, + 262 + ], + "lines": [ + { + "bbox": [ + 105, + 247, + 449, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 449, + 264 + ], + "score": 1.0, + "content": "Let us now discuss two signal estimators that have been used in previous approaches.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 247, + 449, + 264 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 273, + 503, + 296 + ], + "lines": [ + { + "bbox": [ + 106, + 274, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 106, + 275, + 119, + 285 + ], + "score": 0.85, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 274, + 505, + 287 + ], + "score": 1.0, + "content": "– the identity estimator The naive approach to signal estimation is to assume the entire data", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 285, + 255, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 255, + 298 + ], + "score": 1.0, + "content": "is signal and there are no distractors:", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 274, + 505, + 298 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 280, + 296, + 331, + 310 + ], + "lines": [ + { + "bbox": [ + 280, + 296, + 331, + 310 + ], + "spans": [ + { + "bbox": [ + 280, + 296, + 331, + 310 + ], + "score": 0.91, + "content": "S _ { x } ( { \\pmb x } ) = { \\pmb x } .", + "type": "interline_equation", + "image_path": "7293ad93e9b4502ba4d927df2424160dcbad8bb9e8cea4ef77827a6b0a185850.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 280, + 296, + 331, + 310 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 313, + 505, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 312, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 404, + 326 + ], + "score": 1.0, + "content": "With this being plugged into the deep Taylor framework, we obtain the", + "type": "text" + }, + { + "bbox": [ + 405, + 315, + 411, + 323 + ], + "score": 0.79, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 312, + 506, + 326 + ], + "score": 1.0, + "content": "-rule (Montavon et al.,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 337 + ], + "score": 1.0, + "content": "2017) which is equivalent to LRP (Bach et al., 2015). For a linear model, this corresponds to", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 107, + 336, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 107, + 336, + 154, + 346 + ], + "score": 0.88, + "content": "\\mathbf { \\Delta } \\mathbf { \\mathbf { \\mathit { r } } } = \\mathbf { \\mathit { w } } \\odot \\mathbf { \\mathbf { \\mathit { x } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 336, + 478, + 347 + ], + "score": 1.0, + "content": "as the attribution. It can be shown that for ReLU and max-pooling networks, the", + "type": "text" + }, + { + "bbox": [ + 479, + 337, + 485, + 345 + ], + "score": 0.8, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 336, + 505, + 347 + ], + "score": 1.0, + "content": "-rule", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 347, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 359 + ], + "score": 1.0, + "content": "reduces to the element-wise multiplication of the input and the saliency map (Shrikumar et al., 2016;", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 356, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 370 + ], + "score": 1.0, + "content": "Kindermans et al., 2016). This means that for a whole network, the assumed signal is simply the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 368, + 506, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 506, + 380 + ], + "score": 1.0, + "content": "original input image. It also implies that, if there are distractors present in the data, they are included", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 378, + 178, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 178, + 391 + ], + "score": 1.0, + "content": "in the attribution:", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 312, + 506, + 391 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 240, + 391, + 370, + 402 + ], + "lines": [ + { + "bbox": [ + 240, + 391, + 370, + 402 + ], + "spans": [ + { + "bbox": [ + 240, + 391, + 370, + 402 + ], + "score": 0.9, + "content": "\\pmb { r } = \\pmb { w } \\odot \\pmb { x } = \\pmb { w } \\odot \\pmb { s } + \\pmb { w } \\odot \\pmb { d } .", + "type": "interline_equation", + "image_path": "a60da33747453bbd841cf0bb504651991b7911dbb045537eb85199eaf7427bb7.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 240, + 391, + 370, + 402 + ], + "spans": [], + "index": 21 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 407, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 327, + 420 + ], + "score": 1.0, + "content": "When moving through the layers by applying the filters", + "type": "text" + }, + { + "bbox": [ + 327, + 409, + 337, + 417 + ], + "score": 0.77, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 337, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "during the forward pass, the contributions", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 183, + 430 + ], + "score": 1.0, + "content": "from the distractor", + "type": "text" + }, + { + "bbox": [ + 183, + 419, + 191, + 428 + ], + "score": 0.8, + "content": "^ d", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "are cancelled out. However, they cannot be cancelled in the backward pass by", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 429, + 506, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 356, + 441 + ], + "score": 1.0, + "content": "the element-wise multiplication. The distractor contributions", + "type": "text" + }, + { + "bbox": [ + 356, + 429, + 386, + 440 + ], + "score": 0.9, + "content": "\\omega \\odot d", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 429, + 506, + 441 + ], + "score": 1.0, + "content": "that are included in the LRP", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 441, + 410, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 381, + 452 + ], + "score": 1.0, + "content": "explanation cause the noisy nature of the visualizations based on the", + "type": "text" + }, + { + "bbox": [ + 381, + 442, + 387, + 450 + ], + "score": 0.8, + "content": "z", + "type": "inline_equation" + }, + { + "bbox": [ + 388, + 441, + 410, + 452 + ], + "score": 1.0, + "content": "-rule.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 407, + 506, + 452 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 464, + 505, + 509 + ], + "lines": [ + { + "bbox": [ + 107, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 107, + 465, + 121, + 475 + ], + "score": 0.87, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 122, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "– the filter based estimator The implicit assumption made by DeConvNet and Guided Back-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 399, + 487 + ], + "score": 1.0, + "content": "Prop is that the detected signal varies in the direction of the weight vector", + "type": "text" + }, + { + "bbox": [ + 399, + 477, + 408, + 485 + ], + "score": 0.69, + "content": "\\pmb { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 475, + 505, + 487 + ], + "score": 1.0, + "content": ". This weight vector has", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "to be normalized in order to be a valid signal estimator. In the deep Taylor decomposition framework", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 497, + 413, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 199, + 510 + ], + "score": 1.0, + "content": "this corresponds to the", + "type": "text" + }, + { + "bbox": [ + 199, + 497, + 213, + 507 + ], + "score": 0.89, + "content": "w ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 497, + 413, + 510 + ], + "score": 1.0, + "content": "-rule and results in the following signal estimator:", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 464, + 505, + 510 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 259, + 514, + 352, + 537 + ], + "lines": [ + { + "bbox": [ + 259, + 514, + 352, + 537 + ], + "spans": [ + { + "bbox": [ + 259, + 514, + 352, + 537 + ], + "score": 0.93, + "content": "S _ { \\pmb { w } } ( \\pmb { x } ) = \\frac { \\pmb { w } } { \\pmb { w } ^ { T } \\pmb { w } } \\pmb { w } ^ { T } \\pmb { x } .", + "type": "interline_equation", + "image_path": "310de1955c2d2e26897b63a4f5cab5e1d1fa562287b0ee2d2f7191972f55e90a.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 259, + 514, + 352, + 537 + ], + "spans": [], + "index": 30 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 542, + 505, + 577 + ], + "lines": [ + { + "bbox": [ + 106, + 536, + 509, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 347, + 563 + ], + "score": 1.0, + "content": "For a linear model, this produces an attribution of the form", + "type": "text" + }, + { + "bbox": [ + 347, + 542, + 375, + 556 + ], + "score": 0.92, + "content": "\\frac { { \\pmb w } \\odot { \\pmb w } } { { \\pmb w } ^ { T } . { \\pmb w } } \\textcircled { y }", + "type": "inline_equation" + }, + { + "bbox": [ + 375, + 536, + 509, + 563 + ], + "score": 1.0, + "content": ". This estimator does not recon-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "struct the proper signal in the toy example of section 2. Empirically it is also sub-optimal in our", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 565, + 195, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 195, + 577 + ], + "score": 1.0, + "content": "experiment in Fig. 3.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 536, + 509, + 577 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 590, + 311, + 602 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 311, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 311, + 603 + ], + "score": 1.0, + "content": "4.3 PATTERNNET AND PATTERNATTRIBUTION", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 106, + 611, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 610, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 268, + 624 + ], + "score": 1.0, + "content": "We suggest to learn the signal estimator", + "type": "text" + }, + { + "bbox": [ + 268, + 612, + 276, + 622 + ], + "score": 0.83, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 610, + 505, + 624 + ], + "score": 1.0, + "content": "from data by optimizing the previously established crite-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 203, + 635 + ], + "score": 1.0, + "content": "rion. A signal estimator", + "type": "text" + }, + { + "bbox": [ + 204, + 623, + 212, + 632 + ], + "score": 0.83, + "content": "S", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "is optimal with respect to Eq. (1) if the correlation is zero for all possible", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 633, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 198, + 648 + ], + "score": 0.9, + "content": "{ \\pmb v } \\colon \\forall { \\pmb v } , \\mathrm { c o v } [ y , \\hat { \\pmb d } ] { \\pmb v } = { \\bf 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 635, + 420, + 648 + ], + "score": 1.0, + "content": ". This is the case when there is no covariance between", + "type": "text" + }, + { + "bbox": [ + 420, + 638, + 427, + 647 + ], + "score": 0.78, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 635, + 445, + 648 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 446, + 633, + 453, + 645 + ], + "score": 0.82, + "content": "\\hat { \\ b { d } }", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 635, + 505, + 648 + ], + "score": 1.0, + "content": ". 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Let", + "type": "text" + }, + { + "bbox": [ + 393, + 413, + 407, + 423 + ], + "score": 0.88, + "content": "\\pi _ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "be the expected ratio of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 421, + 409, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 422, + 133, + 435 + ], + "score": 1.0, + "content": "inputs", + "type": "text" + }, + { + "bbox": [ + 133, + 424, + 141, + 432 + ], + "score": 0.77, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 422, + 163, + 435 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 163, + 421, + 204, + 433 + ], + "score": 0.92, + "content": "\\mathbf { \\Sigma } \\mathbf { w } ^ { T } \\mathbf { x } > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 422, + 409, + 435 + ], + "score": 1.0, + "content": ". 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In", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 627, + 431, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 431, + 640 + ], + "score": 1.0, + "content": "Fig. 1, a visual improvement over DeConvNet and Guided Backprop is apparent.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 272, + 658 + ], + "score": 1.0, + "content": "PatternAttribution exposes the attribution", + "type": "text" + }, + { + "bbox": [ + 273, + 645, + 305, + 655 + ], + "score": 0.91, + "content": "{ \\pmb w } \\odot { \\pmb a } _ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 305, + 643, + 505, + 658 + ], + "score": 1.0, + "content": "and improves upon the layer-wise relevance prop-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 655, + 504, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 504, + 668 + ], + "score": 1.0, + "content": "agation (LRP) framework (Bach et al., 2015). 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However, when", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 204, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 217 + ], + "score": 1.0, + "content": "using this signal estimator with ReLUs in the dense layers, there is still a considerable correlation", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 287, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 287, + 228 + ], + "score": 1.0, + "content": "left in the distractor component (see Fig. 3).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 8.5, + "bbox_fs": [ + 105, + 160, + 505, + 228 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 237, + 505, + 293 + ], + "lines": [ + { + "bbox": [ + 106, + 236, + 507, + 251 + ], + "spans": [ + { + "bbox": [ + 106, + 238, + 130, + 251 + ], + "score": 0.87, + "content": "S _ { a _ { + - } }", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 236, + 507, + 251 + ], + "score": 1.0, + "content": "– The two-component estimator To move beyond the linear signal estimator, it is crucial to", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 249, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 505, + 261 + ], + "score": 1.0, + "content": "understand how the rectifier influences the training. 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Let", + "type": "text" + }, + { + "bbox": [ + 393, + 413, + 407, + 423 + ], + "score": 0.88, + "content": "\\pi _ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 407, + 412, + 506, + 424 + ], + "score": 1.0, + "content": "be the expected ratio of", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 421, + 409, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 422, + 133, + 435 + ], + "score": 1.0, + "content": "inputs", + "type": "text" + }, + { + "bbox": [ + 133, + 424, + 141, + 432 + ], + "score": 0.77, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 422, + 163, + 435 + ], + "score": 1.0, + "content": "with", + "type": "text" + }, + { + "bbox": [ + 163, + 421, + 204, + 433 + ], + "score": 0.92, + "content": "\\mathbf { \\Sigma } \\mathbf { w } ^ { T } \\mathbf { x } > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 422, + 409, + 435 + ], + "score": 1.0, + "content": ". 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(1), is optimized on the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 534, + 504, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 504, + 546 + ], + "score": 1.0, + "content": "second half of the training dataset. This enables us to test the signal estimators for generalization.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 545, + 505, + 556 + ], + "score": 1.0, + "content": "All the results presented here were obtained using the official validation set of 50000 samples. The", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 555, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 451, + 568 + ], + "score": 1.0, + "content": "validation set was not used for training the signal estimators, nor for training the vector", + "type": "text" + }, + { + "bbox": [ + 451, + 557, + 459, + 565 + ], + "score": 0.72, + "content": "\\pmb { v }", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 555, + 505, + 568 + ], + "score": 1.0, + "content": "to measure", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 565, + 415, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 415, + 579 + ], + "score": 1.0, + "content": "the quality. Consequently our results are obtained on previously unseen data.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27, + "bbox_fs": [ + 106, + 522, + 505, + 579 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 505, + 671 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "The linear and the two component signal estimators are obtained by solving their respective closed", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "form solutions (Eq. (4) and Eq. (8)). With a highly parallelized implementation using 4 GPUs this", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "could be done in 3-4 hours. This can be considered reasonable given that several days are required", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "to train the actual network. The quality of a signal estimator is assessed with Eq. (1). Solving it with", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "the closed form solution is computationally prohibitive since it must be repeated for every single", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 637, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 506, + 651 + ], + "score": 1.0, + "content": "weight vector in the network. Therefore we optimize the equivalent least-squares problem using", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 648, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 505, + 662 + ], + "score": 1.0, + "content": "stochastic mini-batch gradient descent with ADAM Kingma & Ba (2015) until convergence. This", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 660, + 504, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 504, + 673 + ], + "score": 1.0, + "content": "was implemented on a NVIDIA Tesla K40 and took about 24 hours per optimized signal estimator.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 582, + 506, + 673 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 677, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 676, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 504, + 689 + ], + "score": 1.0, + "content": "After learning to explain, individual explanations are computationally cheap since they can be imple-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "mented as a back-propagation pass with a modified weight vector. As a result, our method produces", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 697, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 697, + 506, + 713 + ], + "score": 1.0, + "content": "explanations at least as fast as the work by Dabkowski & Gal (2017) on real time saliency. However,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "our method has the advantage that it is not only applicable to image models but is a generalization", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 720, + 374, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 374, + 734 + ], + "score": 1.0, + "content": "of the theory commonly used in neuroimaging Haufe et al. (2014).", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 676, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 207, + 79, + 405, + 207 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 207, + 79, + 405, + 207 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 207, + 79, + 405, + 207 + ], + "spans": [ + { + "bbox": [ + 207, + 79, + 405, + 207 + ], + "score": 0.94, + "type": "image", + "image_path": "b372c59547081ace17a88655dd8b643c962e0a2010955da9560f3fc9f8db8ad9.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 207, + 79, + 405, + 93.22222222222223 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 207, + 93.22222222222223, + 405, + 107.44444444444446 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 207, + 107.44444444444446, + 405, + 121.66666666666669 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 207, + 121.66666666666669, + 405, + 135.8888888888889 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 207, + 135.8888888888889, + 405, + 150.11111111111114 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 207, + 150.11111111111114, + 405, + 164.33333333333337 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 207, + 164.33333333333337, + 405, + 178.5555555555556 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 207, + 178.5555555555556, + 405, + 192.77777777777783 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 207, + 192.77777777777783, + 405, + 207.00000000000006 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 217, + 504, + 240 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 216, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 392, + 231 + ], + "score": 1.0, + "content": "Figure 5: Top: signal. Bottom: attribution. For the trivial estimator", + "type": "text" + }, + { + "bbox": [ + 392, + 218, + 404, + 229 + ], + "score": 0.89, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 216, + 505, + 231 + ], + "score": 1.0, + "content": "the original input is the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 229, + 359, + 242 + ], + "spans": [ + { + "bbox": [ + 106, + 229, + 359, + 242 + ], + "score": 1.0, + "content": "signal. This is not informative w.r.t. how the network operates.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + } + ], + "index": 6.75 + }, + { + "type": "text", + "bbox": [ + 106, + 263, + 505, + 374 + ], + "lines": [ + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "score": 1.0, + "content": "Measuring the quality of signal estimators In Fig. 3 we present the results from the correlation", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 274, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 142, + 287 + ], + "score": 1.0, + "content": "measure", + "type": "text" + }, + { + "bbox": [ + 142, + 275, + 163, + 286 + ], + "score": 0.94, + "content": "\\rho ( { \\pmb x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 274, + 505, + 287 + ], + "score": 1.0, + "content": ", where higher values are better. We use random directions as baseline signal estima-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 285, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 451, + 298 + ], + "score": 1.0, + "content": "tors. Clearly, this approach removes almost no correlation. The filter-based estimator", + "type": "text" + }, + { + "bbox": [ + 451, + 286, + 465, + 297 + ], + "score": 0.89, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 285, + 505, + 298 + ], + "score": 1.0, + "content": "succeeds", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "score": 1.0, + "content": "in removing some of the information in the first layer. This indicates that the filters are similar to", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 308, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 505, + 320 + ], + "score": 1.0, + "content": "the patterns in this layer. However, the gradient removes much less information in the higher layers.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 318, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 505, + 331 + ], + "score": 1.0, + "content": "Overall, it does not perform much better than the random estimator. This implies that the weights do", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "score": 1.0, + "content": "not correspond to the detected stimulus in a neural network. Hence the implicit assumptions about", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "the signal made by DeConvNet and Guided BackProp is not valid. The optimized estimators remove", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 350, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 410, + 365 + ], + "score": 1.0, + "content": "much more of the correlations across the board. For convolutional layers,", + "type": "text" + }, + { + "bbox": [ + 411, + 351, + 424, + 362 + ], + "score": 0.89, + "content": "S _ { a }", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 350, + 443, + 365 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 443, + 351, + 469, + 363 + ], + "score": 0.91, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 350, + 505, + 365 + ], + "score": 1.0, + "content": "perform", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 362, + 490, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 357, + 375 + ], + "score": 1.0, + "content": "comparably in all but one layer. The two component estimator", + "type": "text" + }, + { + "bbox": [ + 357, + 362, + 383, + 374 + ], + "score": 0.92, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 362, + 490, + 375 + ], + "score": 1.0, + "content": "is best in the dense layers.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 387, + 505, + 508 + ], + "lines": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "score": 1.0, + "content": "Image degradation The first experiment was a direct measurement of the quality of the signal", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "score": 1.0, + "content": "estimators of individual neurons. The second one is an indirect measurement of the quality, but it", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 408, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 422 + ], + "score": 1.0, + "content": "considers the whole network. We measure how the prediction (after the soft-max) for the initially", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "selected class changes as a function of corrupting more and more patches based on the ordering", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 431, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 506, + 443 + ], + "score": 1.0, + "content": "assigned by the attribution (see Samek et al., 2016). This is also related to the work by Zintgraf", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 441, + 456 + ], + "score": 1.0, + "content": "et al. (2017). In this experiment, we split the image in non-overlapping patches of", + "type": "text" + }, + { + "bbox": [ + 441, + 442, + 458, + 453 + ], + "score": 0.63, + "content": "9 \\mathrm { x } 9", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "pixels. We", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 452, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 467 + ], + "score": 1.0, + "content": "compute the attribution and sum all the values within a patch. We sort the patches in decreasing", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 463, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 318, + 478 + ], + "score": 1.0, + "content": "order based on the aggregate heat map value. In step", + "type": "text" + }, + { + "bbox": [ + 318, + 465, + 365, + 475 + ], + "score": 0.88, + "content": "n = 1 . . 1 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 463, + 443, + 478 + ], + "score": 1.0, + "content": "we replace the first", + "type": "text" + }, + { + "bbox": [ + 444, + 466, + 451, + 474 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 463, + 505, + 478 + ], + "score": 1.0, + "content": "patches with", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 475, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 505, + 488 + ], + "score": 1.0, + "content": "the their mean per color channel to remove the information in this patch. Then, we measure how", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "this influences the classifiers output. We use the estimators from the previous experiment to obtain", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "score": 1.0, + "content": "the function-signal attribution heat maps for evaluation. A steeper decay indicates a better heat map.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 514, + 505, + 569 + ], + "lines": [ + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "score": 1.0, + "content": "Results are shown in Fig. 4. The baseline, in which the patches are randomly ordered, performs", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 258, + 538 + ], + "score": 1.0, + "content": "worst. The linear optimized estimator", + "type": "text" + }, + { + "bbox": [ + 258, + 525, + 271, + 536 + ], + "score": 0.89, + "content": "S _ { a }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "performs quite poorly, followed by the filter-based estima-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 535, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 120, + 549 + ], + "score": 1.0, + "content": "tor", + "type": "text" + }, + { + "bbox": [ + 120, + 536, + 135, + 547 + ], + "score": 0.89, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 535, + 252, + 549 + ], + "score": 1.0, + "content": ". The trivial signal estimator", + "type": "text" + }, + { + "bbox": [ + 252, + 536, + 265, + 547 + ], + "score": 0.89, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 535, + 505, + 549 + ], + "score": 1.0, + "content": "performs just slightly better. However, the two component", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 547, + 504, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 134, + 560 + ], + "score": 1.0, + "content": "model", + "type": "text" + }, + { + "bbox": [ + 134, + 547, + 159, + 559 + ], + "score": 0.91, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 547, + 504, + 560 + ], + "score": 1.0, + "content": "leads to the fastest decrease in confidence in the original prediction by a large margin.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 558, + 477, + 571 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 477, + 571 + ], + "score": 1.0, + "content": "Its excellent quantitative performance is also backed up by the visualizations discussed next.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 583, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "Qualitative evaluation In Fig. 5, we compare all signal estimators on a single input image. For", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 188, + 606 + ], + "score": 1.0, + "content": "the trivial estimator", + "type": "text" + }, + { + "bbox": [ + 189, + 594, + 201, + 605 + ], + "score": 0.89, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 594, + 505, + 606 + ], + "score": 1.0, + "content": ", the signal is by definition the original input image and, thus, includes the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "distractor. Therefore, its noisy attribution heat map shows contributions that cancel each other in", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 615, + 504, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 206, + 629 + ], + "score": 1.0, + "content": "the neural network. The", + "type": "text" + }, + { + "bbox": [ + 207, + 616, + 221, + 627 + ], + "score": 0.88, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 221, + 615, + 491, + 629 + ], + "score": 1.0, + "content": "estimator captures some of the structure. The optimized estimator", + "type": "text" + }, + { + "bbox": [ + 491, + 616, + 504, + 627 + ], + "score": 0.86, + "content": "S _ { a }", + "type": "inline_equation" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 625, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 505, + 640 + ], + "score": 1.0, + "content": "results in slightly more structure but struggles on color information and produces dense heat maps.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 218, + 651 + ], + "score": 1.0, + "content": "The two component model", + "type": "text" + }, + { + "bbox": [ + 218, + 638, + 244, + 650 + ], + "score": 0.91, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "on the right captures the original input during signal estimation", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 649, + 301, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 301, + 662 + ], + "score": 1.0, + "content": "and produces a crisp heat map of the attribution.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "Fig. 6 shows the visualizations for six randomly selected images from ImageNet. PatternNet is", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "able to recover a signal close to the original without having to resort to the inclusion of additional", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "rectifiers in contrast to DeConvNet and Guided BackProp. We argue that this is due to the fact", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "that the optimization of the pattern allows for capturing the important directions in input space.", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "This contrasts with the commonly used methods DeConvNet, Guided BackProp, LRP and DTD,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "for which the correlation experiment indicates that their implicit signal estimator cannot capture", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 46.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 207, + 79, + 405, + 207 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 207, + 79, + 405, + 207 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 207, + 79, + 405, + 207 + ], + "spans": [ + { + "bbox": [ + 207, + 79, + 405, + 207 + ], + "score": 0.94, + "type": "image", + "image_path": "b372c59547081ace17a88655dd8b643c962e0a2010955da9560f3fc9f8db8ad9.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 207, + 79, + 405, + 93.22222222222223 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 207, + 93.22222222222223, + 405, + 107.44444444444446 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 207, + 107.44444444444446, + 405, + 121.66666666666669 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 207, + 121.66666666666669, + 405, + 135.8888888888889 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 207, + 135.8888888888889, + 405, + 150.11111111111114 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 207, + 150.11111111111114, + 405, + 164.33333333333337 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 207, + 164.33333333333337, + 405, + 178.5555555555556 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 207, + 178.5555555555556, + 405, + 192.77777777777783 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 207, + 192.77777777777783, + 405, + 207.00000000000006 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 217, + 504, + 240 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 216, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 392, + 231 + ], + "score": 1.0, + "content": "Figure 5: Top: signal. Bottom: attribution. For the trivial estimator", + "type": "text" + }, + { + "bbox": [ + 392, + 218, + 404, + 229 + ], + "score": 0.89, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 216, + 505, + 231 + ], + "score": 1.0, + "content": "the original input is the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 229, + 359, + 242 + ], + "spans": [ + { + "bbox": [ + 106, + 229, + 359, + 242 + ], + "score": 1.0, + "content": "signal. This is not informative w.r.t. how the network operates.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + } + ], + "index": 6.75 + }, + { + "type": "text", + "bbox": [ + 106, + 263, + 505, + 374 + ], + "lines": [ + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "score": 1.0, + "content": "Measuring the quality of signal estimators In Fig. 3 we present the results from the correlation", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 274, + 505, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 142, + 287 + ], + "score": 1.0, + "content": "measure", + "type": "text" + }, + { + "bbox": [ + 142, + 275, + 163, + 286 + ], + "score": 0.94, + "content": "\\rho ( { \\pmb x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 274, + 505, + 287 + ], + "score": 1.0, + "content": ", where higher values are better. We use random directions as baseline signal estima-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 285, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 451, + 298 + ], + "score": 1.0, + "content": "tors. Clearly, this approach removes almost no correlation. The filter-based estimator", + "type": "text" + }, + { + "bbox": [ + 451, + 286, + 465, + 297 + ], + "score": 0.89, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 285, + 505, + 298 + ], + "score": 1.0, + "content": "succeeds", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "score": 1.0, + "content": "in removing some of the information in the first layer. This indicates that the filters are similar to", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 308, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 505, + 320 + ], + "score": 1.0, + "content": "the patterns in this layer. However, the gradient removes much less information in the higher layers.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 318, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 505, + 331 + ], + "score": 1.0, + "content": "Overall, it does not perform much better than the random estimator. This implies that the weights do", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 505, + 342 + ], + "score": 1.0, + "content": "not correspond to the detected stimulus in a neural network. Hence the implicit assumptions about", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 353 + ], + "score": 1.0, + "content": "the signal made by DeConvNet and Guided BackProp is not valid. The optimized estimators remove", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 350, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 410, + 365 + ], + "score": 1.0, + "content": "much more of the correlations across the board. For convolutional layers,", + "type": "text" + }, + { + "bbox": [ + 411, + 351, + 424, + 362 + ], + "score": 0.89, + "content": "S _ { a }", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 350, + 443, + 365 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 443, + 351, + 469, + 363 + ], + "score": 0.91, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 350, + 505, + 365 + ], + "score": 1.0, + "content": "perform", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 362, + 490, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 357, + 375 + ], + "score": 1.0, + "content": "comparably in all but one layer. The two component estimator", + "type": "text" + }, + { + "bbox": [ + 357, + 362, + 383, + 374 + ], + "score": 0.92, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 362, + 490, + 375 + ], + "score": 1.0, + "content": "is best in the dense layers.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 263, + 506, + 375 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 387, + 505, + 508 + ], + "lines": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 505, + 401 + ], + "score": 1.0, + "content": "Image degradation The first experiment was a direct measurement of the quality of the signal", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "score": 1.0, + "content": "estimators of individual neurons. The second one is an indirect measurement of the quality, but it", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 408, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 422 + ], + "score": 1.0, + "content": "considers the whole network. We measure how the prediction (after the soft-max) for the initially", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 433 + ], + "score": 1.0, + "content": "selected class changes as a function of corrupting more and more patches based on the ordering", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 431, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 506, + 443 + ], + "score": 1.0, + "content": "assigned by the attribution (see Samek et al., 2016). This is also related to the work by Zintgraf", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 441, + 456 + ], + "score": 1.0, + "content": "et al. (2017). In this experiment, we split the image in non-overlapping patches of", + "type": "text" + }, + { + "bbox": [ + 441, + 442, + 458, + 453 + ], + "score": 0.63, + "content": "9 \\mathrm { x } 9", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "pixels. We", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 452, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 467 + ], + "score": 1.0, + "content": "compute the attribution and sum all the values within a patch. We sort the patches in decreasing", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 463, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 318, + 478 + ], + "score": 1.0, + "content": "order based on the aggregate heat map value. In step", + "type": "text" + }, + { + "bbox": [ + 318, + 465, + 365, + 475 + ], + "score": 0.88, + "content": "n = 1 . . 1 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 463, + 443, + 478 + ], + "score": 1.0, + "content": "we replace the first", + "type": "text" + }, + { + "bbox": [ + 444, + 466, + 451, + 474 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 463, + 505, + 478 + ], + "score": 1.0, + "content": "patches with", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 475, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 505, + 488 + ], + "score": 1.0, + "content": "the their mean per color channel to remove the information in this patch. Then, we measure how", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "this influences the classifiers output. We use the estimators from the previous experiment to obtain", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "score": 1.0, + "content": "the function-signal attribution heat maps for evaluation. A steeper decay indicates a better heat map.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 387, + 506, + 510 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 514, + 505, + 569 + ], + "lines": [ + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 505, + 527 + ], + "score": 1.0, + "content": "Results are shown in Fig. 4. The baseline, in which the patches are randomly ordered, performs", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 258, + 538 + ], + "score": 1.0, + "content": "worst. The linear optimized estimator", + "type": "text" + }, + { + "bbox": [ + 258, + 525, + 271, + 536 + ], + "score": 0.89, + "content": "S _ { a }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "performs quite poorly, followed by the filter-based estima-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 535, + 505, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 120, + 549 + ], + "score": 1.0, + "content": "tor", + "type": "text" + }, + { + "bbox": [ + 120, + 536, + 135, + 547 + ], + "score": 0.89, + "content": "S _ { w }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 535, + 252, + 549 + ], + "score": 1.0, + "content": ". The trivial signal estimator", + "type": "text" + }, + { + "bbox": [ + 252, + 536, + 265, + 547 + ], + "score": 0.89, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 535, + 505, + 549 + ], + "score": 1.0, + "content": "performs just slightly better. However, the two component", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 547, + 504, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 134, + 560 + ], + "score": 1.0, + "content": "model", + "type": "text" + }, + { + "bbox": [ + 134, + 547, + 159, + 559 + ], + "score": 0.91, + "content": "S _ { a + - }", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 547, + 504, + 560 + ], + "score": 1.0, + "content": "leads to the fastest decrease in confidence in the original prediction by a large margin.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 558, + 477, + 571 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 477, + 571 + ], + "score": 1.0, + "content": "Its excellent quantitative performance is also backed up by the visualizations discussed next.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 513, + 505, + 571 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 583, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "Qualitative evaluation In Fig. 5, we compare all signal estimators on a single input image. For", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 188, + 606 + ], + "score": 1.0, + "content": "the trivial estimator", + "type": "text" + }, + { + "bbox": [ + 189, + 594, + 201, + 605 + ], + "score": 0.89, + "content": "S _ { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 594, + 505, + 606 + ], + "score": 1.0, + "content": ", the signal is by definition the original input image and, thus, includes the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "distractor. 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Fur-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 558, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 558, + 506, + 570 + ], + "score": 1.0, + "content": "thermore, since our approach is after training just as expensive as a single back-propagation step, it", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 569, + 505, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 505, + 582 + ], + "score": 1.0, + "content": "can be applied in a real-time context, which is also possible for the work done by Dabkowski & Gal", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 580, + 268, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 268, + 592 + ], + "score": 1.0, + "content": "(2017) but not for Zintgraf et al. 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Instead it reflects the relation between the signal direction and the distracting", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "noise contributions ( Fig. 2). This implies that popular explanation approaches for neural networks", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 686, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 505, + 702 + ], + "score": 1.0, + "content": "(DeConvNet, Guided BackProp, LRP) do not provide the correct explanation, even for a simple", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "linear model. Our reasoning can be extended to nonlinear models. 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NetworkBitWidthStraight-through estimator
identityvanilla ReLUclipped ReLU
MNISTLeNet522.6× 10-2/98.495.1 ×10 3/99.245.4×10 -3/99.23
46.0 × 10-3/98.989.0×10 4/99.328.8×10 -4/99.24
CIFAR10VGG1120.19/86.580.10/88.690.02/90.92
43.1 × 10-2/90.191.5 × 10-/92.011.3 × 10-/92.08
ResNet2021.56/46.521.50/48.050.24/88.39
41.38/54.160.25/86.590.04/91.24
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\\left[ \\mathbf { Z } _ { i } \\mathbf { 1 } _ { \\{ \\mathbf { Z } _ { j } ^ { \\top } w > 0 \\} } \\right] - \\displaystyle \\sum _ { i = 1 } ^ { m } \\sum _ { j = 1 } ^ { m } v _ { i } ^ { * } v _ { j } \\mathbb { E } \\left[ \\mathbf { Z } _ { i } \\mathbf { 1 } _ { \\{ \\mathbf { Z } _ { j } ^ { \\top } w ^ { * } > 0 \\} } \\right] } \\\\ & { \\quad \\quad \\quad = \\displaystyle \\frac { 1 } { \\sqrt { 2 \\pi } } \\left( \\| v \\| ^ { 2 } \\frac { w } { \\| w \\| } - ( v ^ { \\top } v ^ { * } ) w ^ { * } \\right) . } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 410, + 1718, + 1289, + 1718, + 1289, + 2035, + 410, + 2035 + ], + "score": 0.94, + "latex": "\\begin{array} { r l } & { \\quad \\left. \\mathbb { E } _ { \\mathbf { Z } } \\Big [ g _ { \\mathrm { i d } } ( v , w ; \\mathbf { Z } ) \\Big ] , \\frac { \\partial f } { \\partial w } ( v , w ) \\right. = \\frac { ( v ^ { \\top } v ^ { * } ) ^ { 2 } } { ( \\sqrt { 2 \\pi } ) ^ { 3 } \\| w \\| } \\frac { ( w ^ { * } ) ^ { \\top } \\Big ( I _ { n } - \\frac { w w ^ { \\top } } { \\| w \\| ^ { 2 } } \\Big ) w ^ { * } } { \\Big \\| \\Big ( I _ { n } - \\frac { w w ^ { \\top } } { \\| w \\| ^ { 2 } } \\Big ) w ^ { * } \\Big \\| } } \\\\ & { = \\frac { ( v ^ { \\top } v ^ { * } ) ^ { 2 } } { ( \\sqrt { 2 \\pi } ) ^ { 3 } \\| w \\| } \\frac { 1 - \\frac { ( w ^ { \\top } w ^ { * } ) ^ { 2 } } { \\| w \\| ^ { 2 } } } { \\sqrt { 1 - \\frac { ( w ^ { \\top } w ^ { * } ) ^ { 2 } } { \\| w \\| ^ { 2 } } } } = \\frac { ( v ^ { \\top } v ^ { * } ) ^ { 2 } } { ( \\sqrt { 2 \\pi } ) ^ { 3 } \\| w \\| } \\sqrt { 1 - \\frac { ( w ^ { \\top } w ^ { * } ) ^ { 2 } } { \\| w \\| ^ { 2 } } } } \\\\ & { = \\frac { ( v ^ { \\top } v ^ { * } ) ^ { 2 } } { ( \\sqrt { 2 \\pi } ) ^ { 3 } \\| w \\| } \\sin ( \\theta ( w , w ^ { * } ) ) . } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 529, + 1583, + 1167, + 1583, + 1167, + 1661, + 529, + 1661 + ], + "score": 0.94, + "latex": "\\mathbb { E } _ { \\mathbf { Z } } \\Big [ g _ { \\mathrm { i d } } ( \\boldsymbol { v } , \\boldsymbol { w } ; \\mathbf { Z } ) \\Big ] = \\frac { 1 } { \\sqrt { 2 \\pi } } \\left( \\| \\boldsymbol { v } \\| ^ { 2 } \\frac { \\boldsymbol { w } } { \\| \\boldsymbol { w } \\| } - ( \\boldsymbol { v } ^ { \\top } \\boldsymbol { v } ^ { * } ) \\boldsymbol { w } ^ { * } \\right) ." + }, + { + "category_id": 13, + "poly": [ + 519, + 230, + 597, + 230, + 597, + 262, + 519, + 262 + ], + "score": 0.93, + "latex": "\\mu ^ { \\prime } = 1" + }, + { + "category_id": 13, + "poly": [ + 368, + 1660, + 617, + 1660, + 617, + 1716, + 368, + 1716 + ], + "score": 0.93, + "latex": "\\begin{array} { r } { \\bigg ( I _ { n } - \\frac { w w ^ { \\top } } { \\| w \\| ^ { 2 } } \\bigg ) w = \\mathbf { 0 } _ { n } } \\end{array}" + }, + { + "category_id": 14, + "poly": [ + 597, + 1446, + 1104, + 1446, + 1104, + 1566, + 597, + 1566 + ], + "score": 0.93, + "latex": "{ \\frac { \\partial f } { \\partial \\mathbf { w } } } ( \\mathbf { v } , 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/dev/null +++ b/parse/train/rJIN_4lA-/images/fd6e41510f8d1d96b14ca8d9cc70977165b62565258761d9d777b38bee2da4a7.jpg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:40b74e7bb848969e47bbce3631b7900a52e80740cf93025928d089c5089946b7 +size 5299 diff --git a/parse/train/rkQkBnJAb/rkQkBnJAb.md b/parse/train/rkQkBnJAb/rkQkBnJAb.md new file mode 100644 index 0000000000000000000000000000000000000000..04fc4cf89f705c50a51fe33a6e460dc08b994b9e --- /dev/null +++ b/parse/train/rkQkBnJAb/rkQkBnJAb.md @@ -0,0 +1,273 @@ +# IMPROVING GANS USING OPTIMAL TRANSPORT + +Tim Salimans∗ OpenAI tim@openai.com + +Han Zhang∗† +Rutgers University +han.zhang@cs.rutgers.edu + +Alec Radford OpenAI alec@openai.com + +Dimitris Metaxas Rutgers University dnm@cs.rutgers.edu + +# ABSTRACT + +We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. Experimentally we show OT-GAN to be highly stable when trained with large mini-batches, and we present state-of-the-art results on several popular benchmark problems for image generation. + +# 1 INTRODUCTION + +Generative modeling is a major sub-field of Machine Learning that studies the problem of how to learn models that generate images, audio, video, text or other data. Applications of generative models include image compression, generating speech from text, planning in reinforcement learning, semi-supervised and unsupervised representation learning, and many others. Since generative models can be trained on unlabeled data, which is almost endlessly available, they have enormous potential in the development of artificial intelligence. + +The central problem in generative modeling is how to train a generative model such that the distribution of its generated data will match the distribution of the training data. Generative adversarial nets (GANs) represent an advance in solving this problem, using a neural network discriminator or critic to distinguish between generated data and training data. The critic defines a distance between the model distribution and the data distribution which the generative model can optimize to produce data that more closely resembles the training data. + +A closely related approach to measuring the distance between the distributions of generated data and training data is provided by optimal transport theory. By framing the problem as optimally transporting one set of data points to another, it represents an alternative method of specifying a metric over probability distributions and provides another objective for training generative models. The dual problem of optimal transport is closely related to GANs, as discussed in the next section. However, the primal formulation of optimal transport has the advantage that it allows for closed form solutions and can thus more easily be used to define tractable training objectives that can be evaluated in practice without making approximations. A complication in using primal form optimal transport is that it may give biased gradients when used with mini-batches (see Bellemare et al., 2017) and may therefore be inconsistent as a technique for statistical estimation. + +In this paper we present OT-GAN, a variant of generative adversarial nets incorporating primal form optimal transport into its critic. We derive and justify our model by defining a new metric over probability distributions, which we call Mini-batch Energy Distance, combining optimal transport in primal form with an energy distance defined in an adversarially learned feature space. This combination results in a highly discriminative metric with unbiased mini-batch gradients. + +In Section 2 we provide the preliminaries required to understand our work, and we put our contribution into context by discussing the relevant literature. Section 3 presents our main theoretical contribution: Minibatch energy distance. We apply this new distance metric to the problem of learning generative models in Section 4, and show state-of-the-art results in Section 5. Finally, Section 6 concludes by discussing the strengths and weaknesses of the proposed method, as well as directions for future work. + +# 2 GANS AND OPTIMAL TRANSPORT + +Generative adversarial nets (Goodfellow et al., 2014) were originally motivated using game theory: A generator $g$ and a discriminator $d$ play a zero-sum game where the generator maps noise $\mathbf { z }$ to simulated images $\mathbf { y } = g ( \mathbf { z } )$ and where the discriminator tries to distinguish the simulated images y from images $\mathbf { x }$ drawn from the distribution of training data $p$ . The discriminator takes in each image $\mathbf { x }$ and y and outputs an estimated probability that the given image is real rather than generated. The discriminator is rewarded for putting high probability on the correct classification, and the generator is rewarded for fooling the discriminator. The goal of training is then to find a pair of $( g , d )$ for which this game is at a Nash equilibrium. At such an equilibrium, the generator minimizes its loss, or negative game value, which can be defined as + +$$ +L _ { g } = \operatorname* { s u p } _ { d } \mathbb { E } _ { \mathbf { x } \sim p } \log [ d ( \mathbf { x } ) ] + \mathbb { E } _ { \mathbf { y } \sim g } \log [ 1 - d ( \mathbf { y } ) ] +$$ + +Arjovsky et al. (2017) re-interpret GANs in the framework of optimal transport theory. Specifically, they propose the Earth-Mover distance or Wasserstein- $^ { l }$ distance as a good objective for generative modeling: + +$$ +D _ { \mathrm { E M D } } ( p , g ) = \operatorname* { i n f } _ { \gamma \in \Pi ( p , g ) } \mathbb { E } _ { \mathbf { x } , \mathbf { y } \sim \gamma } c ( \mathbf { x } , \mathbf { y } ) , +$$ + +where $\Pi ( p , g )$ is the set of all joint distributions $\gamma ( \mathbf { x } , \mathbf { y } )$ with marginals $p ( \mathbf { x } ) , g ( \mathbf { y } )$ , and where $c ( \mathbf { x } , \mathbf { y } )$ is a cost function that Arjovsky et al. (2017) take to be the Euclidean distance. If the $p ( \mathbf { x } )$ and $g ( \mathbf { y } )$ distributions are interpreted as piles of earth, the Earth-Mover distance $D _ { \mathrm { E M D } } ( p , g )$ can be interpreted as the minimum amount of “mass” that $\gamma$ has to transport to turn the generator distribution $g ( \mathbf { y } )$ into the data distribution $p ( \mathbf { x } )$ . For the right choice of cost $c$ , this quantity is a metric in the mathematical sense, meaning that $D _ { \mathrm { E M D } } ( p , g ) \geq 0$ and $D _ { \mathrm { E M D } } ( p , g ) = 0$ if and only if $p = g$ . Minimizing the Earth-Mover distance in $g$ is thus a valid method for deriving a statistically consistent estimator of $p$ , provided $p$ is in the model class of our generator $g$ . + +Unfortunately, the minimization over $\gamma$ in Equation 2 is generally intractable, so Arjovsky et al. (2017) turn to the dual formulation of this optimal transport problem: + +$$ +D _ { \mathrm { E M D } } ( p , g ) = \operatorname* { s u p } _ { \| f \| _ { L } \leq 1 } \mathbb { E } _ { \mathbf { x } \sim p } f ( \mathbf { x } ) - \mathbb { E } _ { \mathbf { y } \sim g } f ( \mathbf { y } ) , +$$ + +where we have replaced the minimization over $\gamma$ with a maximization over the set of 1-Lipschitz functions. This optimization problem is generally still intractable, but Arjovsky et al. (2017) argue that it is well approximated by using the class of neural network GAN discriminators or critics described earlier in place of the class of 1-Lipschitz functions, provided we bound the norm of their gradient with respect to the image input. Making this substitution, the objective becomes quite similar to that of our original GAN formulation in Equation 1. + +In followup work Gulrajani et al. (2017) propose a different method of bounding the gradients in the class of allowed critics, and provide strong empirical results supporting this interpretation of GANs. In spite of their success, however, we should note that GANs are still only able to solve this optimal transport problem approximately. The optimization with respect to the critic cannot be performed perfectly, and the class of obtainable critics only very roughly corresponds to the class of 1-Lipschitz functions. The connection between GANs and dual form optimal transport is further explored by Bousquet et al. (2017) and Genevay et al. (2017a), who extend the analysis to different optimal transport costs and to a broader model class including latent variables. + +An alternative approach to generative modeling is chosen by Genevay et al. (2017b) who instead chose to approximate the primal formulation of optimal transport. They start by taking an entropically smoothed generalization of the Earth Mover distance, called the Sinkhorn distance (Cuturi, + +$$ +D _ { \mathrm { S i n k h o r n } } ( p , g ) = \operatorname* { i n f } _ { \gamma \in \Pi _ { \beta } ( p , g ) } \mathbb { E } _ { \mathbf { x } , \mathbf { y } \sim \gamma } c ( \mathbf { x } , \mathbf { y } ) , +$$ + +where the set of allowed joint distribution $\Pi _ { \beta }$ is now restricted to distributions with entropy of at least some constant $\beta$ . Genevay et al. (2017b) then approximate this distance by evaluating it on mini-batches of data $\mathbf { X } , \mathbf { Y }$ consisting of $K$ data vectors $\mathbf x , \mathbf y$ . The cost function $c$ then gives rise to a $K \times K$ transport cost matrix $C$ , where $C _ { i , j } = c ( \mathbf { x } _ { i } , \mathbf { y } _ { j } )$ tells us how expensive it is to transport the $i$ - th data vector $\mathbf { x } _ { i }$ in mini-batch $\mathbf { X }$ to the $j$ -th data vector $\mathbf { y } _ { j }$ in mini-batch $\mathbf { Y }$ . Similarly, the coupling distribution $\gamma$ is replaced by a $K \times K$ matrix $M$ of soft matchings between these $i , j$ elements, which is restricted to the set of matrices $\mathcal { M }$ with all positive entries, with all rows and columns summing to one, and with sufficient entropy $- \operatorname { T r } [ M \log ( M ^ { \mathrm { T } } ) ] \geq \alpha$ . The resulting distance, evaluated on a minibatch, is then + +$$ +{ \mathcal { W } } _ { c } ( X , Y ) = \operatorname* { i n f } _ { M \in { \mathcal { M } } } \mathrm { T r } [ M C ^ { \mathrm { T } } ] . +$$ + +In practice, the minimization over the soft matchings $M$ can be found efficiently on the GPU using the Sinkhorn algorithm. Consequently, Genevay et al. (2017b) call their method of using Equation 5 in generative modeling Sinkhorn AutoDiff. + +The great advantage of this mini-batch Sinkhorn distance is that it is fully tractable, eliminating the instabilities often experienced with GANs due to imperfect optimization of the critic. However, a disadvantage is that the expectation of Equation 5 over mini-batches is no longer a valid metric over probability distributions. Viewed another way, the gradients of Equation 5, for fixed mini-batch size, are not unbiased estimators of the gradients of our original optimal transport problem in Equation 4. For this reason, Bellemare et al. (2017) propose to instead use the Energy Distance, also called Cramer Distance, as the basis of generative modeling: + +$$ +D _ { \mathrm { E D } } ( p , g ) = \sqrt { 2 \mathbb { E } [ \left\| \mathbf { x } - \mathbf { y } \right\| ] - \mathbb { E } [ \left\| \mathbf { x } - \mathbf { x } ^ { \prime } \right\| ] - \mathbb { E } [ \left\| \mathbf { y } - \mathbf { y } ^ { \prime } \right\| ] } , +$$ + +where $\mathbf { x } , \mathbf { x } ^ { \prime }$ are independent samples from data distribution $p$ and $\mathbf { y } , \mathbf { y } ^ { \prime }$ independent samples from the generator dsitribution $g$ . In Cramer $G A N$ they propose training the generator by minimizing this distance metric, evaluated in a latent space which is learned by the GAN critic. + +In the next section we propose a new metric for generative modeling, combining the insights of GANs and optimal transport. Although our work was performed concurrently to that by Genevay et al. (2017b) and Bellemare et al. (2017), it can be understood most easily as forming a synthesis of the ideas used in Sinkhorn AutoDiff and Cramer GAN. + +# 3 MINI-BATCH ENERGY DISTANCE + +As discussed in the last section, most previous work in generative modeling can be interpreted as minimizing a distance $D ( g , p )$ between a generator distribution $g ( \mathbf { x } )$ and the data distribution $p ( \mathbf { x } )$ , where the distributions are defined over a single vector $\mathbf { x }$ which we here take to be an image. However, in practice deep learning typically works with mini-batches of images $\mathbf { X }$ rather than individual images. For example, a GAN generator is typically implemented as a high dimensional function $G ( \mathbf { Z } )$ that turns a mini-batch of random noise $\mathbf { Z }$ into a mini-batch of images $\mathbf { X }$ , which the GAN discriminator then compares to a mini-batch of images from the training data. The central insight of Mini-batch GAN (Salimans et al., 2016) is that it is strictly more powerful to work with the distributions over mini-batches $g ( \mathbf { X } ) , p ( \mathbf { X } )$ than with the distributions over individual images. Here we further pursue this insight and propose a new distance over mini-batch distributions $\bar { D [ { g ( \mathbf { X } ) , p ( \mathbf { X } ) } ] }$ which we call the Mini-batch Energy Distance. This new distance combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. + +In order to derive our new distance function, we start by generalizing the energy distance given in Equation 6 to general non-Euclidean distance functions $d$ . Doing so gives us the generalized energy distance: + +$$ +D _ { \mathtt { G E D } } ( p , g ) = { \sqrt { 2 \mathbb { E } [ d ( \mathbf { X } , \mathbf { Y } ) ] - \mathbb { E } [ d ( \mathbf { X } , \mathbf { X } ^ { \prime } ) ] - \mathbb { E } [ d ( \mathbf { Y } , \mathbf { Y } ^ { \prime } ) ] } } , +$$ + +where $\mathbf { X } , \mathbf { X } ^ { \prime }$ are independent samples from distribution $p$ and $\mathbf { Y } , \mathbf { Y } ^ { \prime }$ independent samples from $g$ . This distance is typically defined for individual samples, but it is valid for general random objects, including mini-batches like we assume here. The energy distance $D _ { \mathrm { G E D } } ( \bar { p } , g )$ is a metric, in the mathematical sense, as long as the distance function $d$ is a metric (Klebanov et al., 2005). Under this condition, meaning that $d$ satisfies the triangle inequality and several other conditions, we have that $D ( p , g ) \geq 0$ , and $\bar { D } ( p , g ) = 0$ if and only if $p = g$ . + +Using individual samples $\mathbf x , \mathbf y$ instead of minibatches $\mathbf { X } , \mathbf { Y }$ , Sejdinovic et al. (2013) showed that such generalizations of the energy distance can equivalently be viewed as a form of maximum mean discrepancy, where the MMD kernel $k$ is related to the distance function $d$ by $d ( { \bf x } , { \bf x } ^ { \prime } ) \equiv k ( { \bf x } , { \bf x } ) +$ $k ( \mathbf { x } ^ { \prime } , \mathbf { \bar { x } } ^ { \prime } ) - 2 k ( \mathbf { x } , \mathbf { x } ^ { \prime } )$ . We find the energy distance perspective more intuitive here and follow Cramer GAN in using this perspective instead. + +We are free to choose any metric $d$ for use in Equation 7, but not all choices will be equally discriminative when used for generative modeling. Here, we choose $d$ to be the entropy-regularized Wasserstein distance, or Sinkhorn distance, as defined for mini-batches in Equation 5. Although the average over mini-batch Sinkhorn distances is not a valid metric over probability distributions $p , g$ , resulting in the biased gradients problem discussed in Section 2, the Sinkhorn distance is a valid metric between individual mini-batches, which is all we require for use inside the generalized energy distance. + +Putting everything together, we arrive at our final distance function over distributions, which we call the Minibatch Energy Distance. Like with the Cramer distance, we typically work with the squared distance, which we define as + +$$ +D _ { \mathrm { M E D } } ^ { 2 } ( p , g ) = 2 \mathbb { E } [ \mathcal { W } _ { c } ( \mathbf { X } , \mathbf { Y } ) ] - \mathbb { E } [ \mathcal { W } _ { c } ( \mathbf { X } , \mathbf { X } ^ { \prime } ) ] - \mathbb { E } [ \mathcal { W } _ { c } ( \mathbf { Y } , \mathbf { Y } ^ { \prime } ) ] , +$$ + +where $\mathbf { X }$ , $\mathbf { X } ^ { \prime }$ are independently sampled mini-batches from distribution $p$ and $\mathbf { Y } , \mathbf { Y } ^ { \prime }$ are independent mini-batches from $g$ . We include the subscript $c$ to make explicit that this distance depends on the choice of transport cost function $c$ , which we will learn adversarially as discussed in Section 4. + +In comparison with the original Sinkhorn distance (Equation 5 the loss function for training $g$ implied by this metric adds a repulsive term − $\mathbf { \nabla } \cdot \mathcal { W } _ { c } ( \mathbf { Y } , \mathbf { Y } ^ { \prime } )$ to the attractive term ${ \mathcal W } _ { c } ( { \bf X } , { \bf Y } )$ . Like with the energy distance used by Cramer GAN, this is what makes the resulting mini-batch gradients unbiased and the objective statistically consistent. However, unlike the plain energy distance, the mini-batch energy distance $D _ { \mathrm { M E D } } ^ { 2 } ( p , \bar { g } )$ still incorporates the primal form optimal transport of the Sinkhorn distance, which in Section 5 we show leads to much stronger discriminative power and more stable generative modeling. + +In concurrent work, Genevay et al. (2018) independently propose a very similar loss function to (8), but using a single sample from the data and generator distributions. We obtained best results using two independently sampled minibatches from each distribution. + +# 4 OPTIMAL TRANSPORT GAN (OT-GAN) + +In the last section we defined the mini-batch energy distance which we propose using for training generative models. However, we left undefined the transport cost function $c ( \mathbf { x } , \mathbf { y } )$ on which it depends. One possibility would be to choose $c$ to be some fixed function over vectors, like Euclidean distance, but we found this to perform poorly in preliminary experiments. Although minimizing the mini-batch energy distance $\bar { D } _ { M E D } ^ { 2 } ( \bar { p } , g )$ guarantees statistical consistency for simple fixed cost functions $c$ like Euclidean distance, the resulting statistical efficiency is generally poor in high dimensions. This means that there typically exist many bad distributions distributions $g$ for which $D _ { M E D } ^ { 2 } ( p , g )$ is so close to zero that we cannot tell $p$ and $g$ apart without requiring an enormous sample size. To solve this we propose learning the cost function adversarially, so that it can adapt to the generator distribution $g$ and thereby become more discriminative. In practice we implement this by defining $c$ to be the cosine distance between vectors $v _ { \eta } ( \mathbf { x } )$ and $v _ { \eta } ( \mathbf { y } )$ , where $v _ { \eta }$ is a deep neural network that maps the images in our mini-batch into a learned latent space. That is we define the transport cost to be + +$$ +c _ { \eta } ( \mathbf x , \mathbf y ) = 1 - \frac { v _ { \eta } ( \mathbf x ) \cdot v _ { \eta } ( \mathbf y ) } { \| v _ { \eta } ( \mathbf x ) \| _ { 2 } \| v _ { \eta } ( \mathbf y ) \| _ { 2 } } , +$$ + +where we choose $\eta$ to maximize the resulting minibatch energy distance. + +In practice, training our generative model $g _ { \boldsymbol { \theta } }$ and our adversarial transport cost $c _ { \eta }$ is done by alternating gradient descent as is standard practice in GANs (Goodfellow et al., 2014). Here we choose to update the generator more often than we update our critic. This is contrary to standard practice (e.g. Arjovsky et al., 2017) and ensures our cost function $c$ does not become degenerate. If $c$ were to assign zero transport cost to two non-identical regions in image space, the generator would quickly adjust to take advantage of this. Similar to how a quickly adapting critic controls the generator in standard GANs, this works the other way around in our case. Contrary to standard GANs, our generator has a well defined and statistically consistent training objective even when the critic is not updated, as long as the cost function $c$ is not degenerate. We also investigated forcing $v _ { \eta }$ to be one-to-one by parameterizing it using a RevNet Gomez et al. (2017), thereby ensuring $c$ cannot degenerate, but this proved unnecessary if the generator is updated often enough. + +Our full training procedure is described in Algorithm 1, and is visually depicted in Figure 1. Here we compute the matching matrix $M$ in ${ \mathcal { W } } _ { c }$ using the Sinkhorn algorithm. Unlike Genevay et al. (2017b) we do not backpropagate through this algorithm. Ignoring the gradient flow through the matchings $M$ is justified by the envelope theorem (see e.g. Carter, 2001): Since $M$ is chosen to minimize ${ \mathcal { W } } _ { c }$ , the gradient of ${ \mathcal { W } } _ { c }$ with respect to this variable is zero (when projected into the allowed space $\mathcal { M }$ ). Algorithm 1 assumes we use standard SGD for optimization, but we are free to use other optimizers. In our experiments we use Adam (Kingma & Ba, 2014). + +Our algorithm for training generative models can be generalized to include conditional generation of images given some side information $s$ , such as a text-description of the image or a label. When generating an image y we simply draw $s$ from the training data and condition the generator on it. The rest of the algorithm is identical to Algorithm 1 but with $( \mathbf { Y } , S )$ in place of $\mathbf { Y }$ , and similar substitutions for $\breve { \mathbf { X } } , \mathbf { X } ^ { \prime } , \mathbf { Y } ^ { \prime }$ . The full algorithm for conditional generation is detailed in Algorithm 2 in the appendix. + +Require: $n _ { g e n }$ , the number of iterations of the generator per critic iteration +Require: $\eta _ { 0 }$ , initial critic parameters. $\theta _ { 0 }$ , initial generator parameters +1: for $t = 1$ to $N$ do +2: Sample $\mathbf { X } , \mathbf { X } ^ { \prime }$ two independent mini-batches from real data, and $\mathbf { Y } , \mathbf { Y } ^ { \prime }$ two independent mini-batches from the generated samples +3: ${ \mathcal { L } } = \mathcal { W } _ { c } ( \mathbf { X } , \mathbf { Y } ) + \mathcal { W } _ { c } ( \mathbf { \tilde { X } } , \mathbf { Y } ^ { \prime } ) + \mathcal { W } _ { c } \mathbf { \tilde { ( X ' , Y ) } } + \mathcal { W } _ { c } ( \mathbf { X } ^ { \prime } , \mathbf { Y } ^ { \prime } ) - 2 \mathcal { W } _ { c } ( \mathbf { X } , \mathbf { X } ^ { \prime } ) - 2 \mathcal { W } _ { c } ( \mathbf { Y } , \mathbf { Y } ^ { \prime } )$ +4: if $t$ mod $n _ { g e n } + 1 = 0$ then +5: $\eta \eta + \alpha \cdot \nabla _ { \eta } \mathcal { L }$ +6: else +7: $\theta \theta - \alpha \cdot \nabla _ { \theta } \mathcal { L }$ +8: end if +9: end for + +![](images/1e58273fd7719f4bfa348121cdbe49a29a843f422b7306bcbedd5a9726afdbb0.jpg) +Figure 1: Illustration of OT-GAN. Mini-batches from the generator and training data are embedded into a learned feature space via the critic. A transport cost matrix is calculated between the two mini-batches of features. Soft matching aligns features across mini-batches and aligned features are compared. The figure only illustrates the distance calculation between one pair of mini-batches whereas several are computed. + +# 5 EXPERIMENTS + +In this section, we demonstrate the improved stability and consistency of the proposed method on five different datasets with increasing complexity. + +# 5.1 MIXTURE OF GAUSSIAN DATASET + +One advantage of OT-GAN compared to regular GAN is that for any setting of the transport cost $c$ , i.e. any fixed critic, the objective is statistically consistent for training the generator $g$ . Even if we stop updating the critic, the generator should thus never diverge. With a bad fixed cost function $c$ the signal for learning $g$ may be very weak, but at least it should never point in the wrong direction. We investigate whether this theoretical property holds in practice by examining a simple toy example. We train generative models using different types of GAN on a 2D mixture of 8 Gaussians, with means arranged on a circle. The goal for the generator is to recover all 8 modes. For the proposed method and all the baseline methods, the architectures are simple MLPs with ReLU activations. A similar experimental setting has been considered in (Metz et al., 2017; Li et al., 2017) to demonstrate the mode coverage behavior of various GAN models. There, GANs using mini-batch features, DAN-S (Li et al., 2017), are shown to capture all the 8 modes when training converges. To test the consistency of GAN models, we stop updating the discriminator after $1 5 \mathrm { k }$ iterations and visualize the generator distribution for an additional 25K iterations. As shown in Figure 2, mode collapse occurs in a mini-batch feature GAN after a few thousand iterations training with a fixed discriminator. However, using the mini-batch energy distance, the generator does not diverge and the generated samples still cover all 8 modes of the data. + +![](images/1687b47c7688836cb6bf32cf7cfdd10ff315315751109cb91d4da734f7b693bc.jpg) +Figure 2: Results for consistency when fixing the critic on data generated from 8 Gaussian mixtures. The first column shows the data distribution. The top row shows the training results of OT-GAN using mini-batch energy distance. The bottom row shows the training result with the original GAN loss (DAN-S). The latter collapses to 3 out of 8 modes after fixing the discriminator, while OT-GAN remains consistent. + +# 5.2 CIFAR-10 + +CIFAR-10 is a well-studied dataset of $3 2 \times 3 2$ color images for generative models (Krizhevsky, 2009). We use this data set to investigate the importance of the different design decisions made with OT-GAN, and we compare the visual quality of its generated samples with other state-of-theart GAN models. Our model and the other reported results are trained in an unsupervised manner. We choose “inception score” (Salimans et al., 2016) as numerical assessment to compare the visual quality of samples generated by different models. Our generator and critic are standard convnets, similar to those used by DCGAN (Radford et al., 2015), but without any batch normalization, layer normalization, or other stabilizing additions. Appendix B contains additional architecture and training details. + +We first investigate the effect of batch size on training stability and sample quality. As shown in Figure 3, training is not very stable when the batch size is small (i.e. 200). As batch size increases, training becomes more stable and the inception score of samples increases. Unlike previous methods, our objective (the minibatch energy distance, Section 3) depends on the chosen minibatch size: Larger minibatches are more likely to cover many modes of the data distribution, thereby not only yielding lower variance estimates but also making our distance metric more discriminative. To reach the large batch sizes needed for optimal performance we make use of multi GPU training. In this work we only use up to 8 GPUs per experiment, but we anticipate more GPUs to be useful when using larger models. + +In Figure 4 we present the samples generated by our model trained with a batch size of 8000. In addition, we also compare with the sample quality of other state-of-the-art GAN models in Table 1. OT-GAN achieves a score of $8 . 4 7 \pm . 1 2$ , outperforming all baseline models. + +To evaluate the importance of using optimal transport in OT-GAN, we repeat our CIFAR-10 experiment with random matching of samples. Our minibatch energy distance objective remains valid when we match samples randomly rather than using optimal transport. In this case the minibatch energy distance reduces to the regular (generalized) energy distance. We repeat our CIFAR-10 experiment and train a generator with the same architecture and hyperparameters as above, but with random matching of samples instead of optimal transport. The highest resulting Inception score achieved during the training process is 4.64 using this approach, as compared to 8.47 with optimal transport. Figure 5 shows a random sample from the resulting model. + +
MethodInception score
Real Data11.95 ± .12
DCGAN6.16±.07
Improved GAN6.86±.06
DenoisingFM7.72±.13
WGAN-GP7.86± .07
OT-GAN8.47±.12
+ +Table 1: Inception scores on CIFAR-10. All the models are trained in an unsupervised manner. + +![](images/a54c9124dd2c9ce0fbf6f3b48b53066b7a43bbea3a067d23c1d5ead9061ec014.jpg) +Figure 3: CIFAR-10 inception score over the course of training for different batch sizes. + +![](images/2bf7a927be164f1ae5be549e065c1add2c85346abe9fed718132083af632ff1f.jpg) +Figure 4: Samples generated by OT-GAN on CIFAR-10, without using labels. + +![](images/41ab2c798337bfae4bf37c8b841670c515c8340fa9046e2edb009ce8972bd7d0.jpg) +Figure 5: Samples generated without using optimal transport. + +# 5.3 IMAGENET DOGS + +To illustrate the ability of OT-GAN in generating high quality images on more complex data sets, we train OT-GAN to generate $1 2 8 \times 1 2 8$ images on the dog subset of ImageNet (Russakovsky et al., 2015). A smaller batch size of 2048 is used due to GPU memory contraints. As shown in Figure 6, the samples generated by OT-GAN contain less nonsensical images, and the sample quality is significantly better than that of a tuned DCGAN variant which still suffers from mode collapse. The superior image quality is confirmed by the inception score achieved by OT-GAN $( 8 . 9 7 { \scriptstyle \pm 0 . 0 9 } )$ on this dataset, which outperforms that of DCGAN(8.19±0.11) + +![](images/f014376b44941bf3c6b56a596486ceca17208002ae78bcc958f676fc2b5e1b13.jpg) +Figure 6: ImageNet Dog subset samples generated by OT-GAN (left) and DCGAN (right). + +# 5.4 CONDITIONAL GENERATION OF BIRDS + +To further demonstrate the effectiveness of the proposed method on conditional image synthesis, we compare OT-GAN with state-of-the-art models on text-to-image generation (Reed et al., 2016b;a; Zhang et al., 2017). As shown in Table 2, the images generated by OT-GAN with batch size 2048 also achieve the best inception score here. Example images generated by our conditional generative model on the CUB test set are presented in Figure 7. + +Table 2: Inception scores by state-of-the-art methods (Reed et al., 2016b;a; Zhang et al., 2017) and the proposed OT-GAN on the CUB test set. Higher inception scores mean better image quality. + +
MethodGAN-INT-CLSGAWWNStackGANOT-GAN
Inception Score2.88± .043.62 ± .073.70±.043.84 ± .05
+ +![](images/60dfbeabf4e67698c3c1e31fa5a3ee4ca6acba57bf8cfac62732229ae9d9f4eb.jpg) +Figure 7: Bird example images generated by conditional OT-GAN + +# 6 DISCUSSION + +We have presented OT-GAN, a new variant of GANs where the generator is trained to minimize a novel distance metric over probability distributions. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. OT-GAN was shown to be uniquely stable when trained with large mini-batches and to achieve state-of-the-art results on several common benchmarks. + +One downside of OT-GAN, as currently proposed, is that it requires large amounts of computation and memory. We achieve the best results when using very large mini-batches, which increases the time required for each update of the parameters. All experiments in this paper, except for the mixture of Gaussians toy example, were performed using 8 GPUs and trained for several days. In future work we hope to make the method more computationally efficient, as well as to scale up our approach to multi-machine training to enable generation of even more challenging and high resolution image data sets. + +A unique property of OT-GAN is that the mini-batch energy distance remains a valid training objective even when we stop training the critic. Our implementation of OT-GAN updates the generative model more often than the critic, where GANs typically do this the other way around (see e.g. Gulrajani et al., 2017). As a result we learn a relatively stable transport cost function $c ( \mathbf { x } , \mathbf { y } )$ , describing how (dis)similar two images are, as well as an image embedding function $v _ { \eta } ( \mathbf { x } )$ capturing the geometry of the training data. Preliminary experiments suggest these learned functions can be used successfully for unsupervised learning and other applications, which we plan to investigate further in future work. + +# REFERENCES + +Martin Arjovsky, Soumith Chintala, and Leon Bottou. Wasserstein gan. ´ arXiv preprint arXiv:1701.07875, 2017. +Marc G Bellemare, Ivo Danihelka, Will Dabney, Shakir Mohamed, Balaji Lakshminarayanan, Stephan Hoyer, and Remi Munos. The cramer distance as a solution to biased wasserstein gradients. ´ arXiv preprint arXiv:1705.10743, 2017. +Olivier Bousquet, Sylvain Gelly, Ilya Tolstikhin, Carl-Johann Simon-Gabriel, and Bernhard Schoelkopf. From optimal transport to generative modeling: the vegan cookbook. arXiv preprint arXiv:1705.07642, 2017. +Michael Carter. Foundations of mathematical economics. MIT Press, 2001. +Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems, pp. 2292–2300, 2013. +Yann N Dauphin, Angela Fan, Michael Auli, and David Grangier. Language modeling with gated convolutional networks. arXiv preprint arXiv:1612.08083, 2016. +Aude Genevay, Gabriel Peyre, and Marco Cuturi. Gan and vae from an optimal transport point of view. ´ arXiv preprint arXiv:1706.01807, 2017a. +Aude Genevay, Gabriel Peyre, and Marco Cuturi. Sinkhorn-autodiff: Tractable wasserstein learning of genera- ´ tive models. arXiv preprint arXiv:1706.00292, 2017b. +Aude Genevay, Gabriel Peyre, and Marco Cuturi. Learning generative models with sinkhorn divergences. ´ AISTATS Proceedings, 2018. +Aidan N Gomez, Mengye Ren, Raquel Urtasun, and Roger B Grosse. The reversible residual network: Backpropagation without storing activations. In Advances in Neural Information Processing Systems, pp. 2211– 2221, 2017. +Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pp. 2672–2680, 2014. +Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville. Improved training of wasserstein gans. arXiv preprint arXiv:1704.00028, 2017. +Diederik Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. +Lev Borisovich Klebanov, Viktor Benes, and Ivan Saxl. ˇ N-distances and their applications. Charles University in Prague, the Karolinum Press, 2005. +Alex Krizhevsky. Learning multiple layers of features from tiny images. Technical report, 2009. +Chengtao Li, David Alvarez-Melis, Keyulu Xu, Stefanie Jegelka, and Suvrit Sra. Distributional adversarial networks. arXiv:1706.09549, 2017. +Luke Metz, Ben Poole, David Pfau, and Jascha Sohl-Dickstein. Unrolled generative adversarial networks. In ICLR, 2017. +Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434, 2015. +Scott Reed, Zeynep Akata, Santosh Mohan, Samuel Tenka, Bernt Schiele, and Honglak Lee. Learning what and where to draw. In NIPS, 2016a. +Scott Reed, Zeynep Akata, Xinchen Yan, Lajanugen Logeswaran, Bernt Schiele, and Honglak Lee. Generative adversarial text-to-image synthesis. In ICML, 2016b. +Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. ImageNet Large Scale Visual Recognition Challenge. International Journal of Computer Vision (IJCV), 115(3):211–252, 2015. doi: 10.1007/s11263-015-0816-y. +Tim Salimans and Diederik P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016. +Tim Salimans, Ian J. Goodfellow, Wojciech Zaremba, Vicki Cheung, Alec Radford, and Xi Chen. Improved techniques for training gans. In NIPS, 2016. +Dino Sejdinovic, Bharath Sriperumbudur, Arthur Gretton, and Kenji Fukumizu. Equivalence of distance-based and rkhs-based statistics in hypothesis testing. The Annals of Statistics, pp. 2263–2291, 2013. +Wenling Shang, Kihyuk Sohn, Diogo Almeida, and Honglak Lee. Understanding and improving convolutional neural networks via concatenated rectified linear units. In International Conference on Machine Learning, pp. 2217–2225, 2016. +Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris Metaxas. Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. In ICCV, 2017. + +A CONDITIONAL GENERATION + +Algorithm 2 Conditional Optimal Transport GAN (OT-GAN) training algorithm with step size α, using minibatch SGD for simplicity + +Require: $n _ { g e n }$ , the number of iterations of the generator per critic iteration +Require: $\eta _ { 0 }$ , initial critic parameters. $\theta _ { 0 }$ , initial generator parameters +1: for $t = 1$ to $N$ do +2: Sample $( \mathbf { X } , S )$ , $( \mathbf { X } ^ { \prime } , S ^ { \prime } )$ two independent mini-batches from real data, with side information, and $( \mathbf { Y } , S ) , ( \mathbf { Y } ^ { \prime } , S ^ { \prime } )$ two independent mini-batches from the generator, re-using the same side information +3: $\begin{array} { r l r } { \mathcal { L } } & { { } = } & { \mathcal { W } _ { c } [ ( { \bf X } , S ) , ( { \bf Y } ^ { \prime } , S ^ { \prime } ) ] ~ + ~ \mathcal { W } _ { c } [ ( { \bf X } ^ { \prime } , S ^ { \prime } ) , ( { \bf Y } , S ) ] ~ - ~ \mathcal { W } _ { c } [ ( { \bf X } , S ) , ( { \bf X } ^ { \prime } , S ^ { \prime } ) ] ~ - ~ \mathcal { W } _ { c } [ ( { \bf X } , S ) , ( { \bf X } ^ { \prime } , S ^ { \prime } ) ] ~ } \end{array}$ $\mathcal { W } _ { c } [ ( \mathbf { Y } , S ) , ( \mathbf { Y } ^ { \prime } , S ^ { \prime } ) ]$ +4: if $t$ mod $n _ { g e n } + 1 = 0$ then +5: $\eta \eta + \alpha \cdot \nabla _ { \eta } \mathcal { L }$ +6: else +7: $\theta \theta - \alpha \cdot \nabla _ { \theta } \mathcal { L }$ +8: end if +9: end for + +# B CIFAR-10 ARCHITECTURE AND TRAINING DETAILS + +The generator and critic are implemented as convolutional networks. Their architectures are loosely based on DCGAN with various modifications. Weight normalization and data-dependent initialization (Salimans & Kingma, 2016) are used for both. The generator maps latent codes sampled from a 100 dimensional uniform distribution between $^ { - 1 }$ and 1 to $3 2 \times 3 2$ color images. The main module of the generator is a $2 \mathbf { x } 2$ nearest-neighbor upsampling operation followed by a convolution with a $5 \times 5$ kernel using gated linear units (Dauphin et al., 2016). The main module of the critic is a convolution with a $5 \times 5$ kernel and stride 2 using the concatenated ReLU activation function (Shang et al., 2016). Notably, the generator and critic do not use an activation normalization technique such as batch or layer normalization. We train the model using Adam with a learning rate of $3 \times 1 0 ^ { - 4 }$ , $\beta _ { 1 } = 0 . 5$ , $\beta _ { 2 } = 0 . 9 9 9$ . We update the generator 3 times for every critic update. OT-GAN includes two additional hyperparameters for the Sinkhorn algorithm, the number of iterations to run the algorithm and $\textstyle { \frac { 1 } { \lambda } }$ which is the entropy penalty of alignments. Initial tuning found a value of 500 to work well for both. + +Table 3: Generator architecture for CIFAR-10. + +
operationactivationkernelstrideoutput shape
Z linear reshape 2x NN upsample convolution 2x NN upsample convolutionGLU100 16384
1024×4×4
GLU5×511024×8×8 512×8×8
512 ×16 × 16
GLU5×51256×1 16 ×16
2x NN upsample256 × 32 × 32
convolutionGLU5×51128 × 32 × 32
convolutiontanh5×513 × 32× 32
+ +Table 4: Critic architecture for CIFAR-10. + +
operationactivationkernelstride output shape
convolutionCReLU5×51256× 32×32512 ×16×161024×8×82048×4×43276832768
convolutionconvolutionconvolutionreshape12 normalizeCReLUCReLUCReLU5×5２２2
5×55×5
+ +# C ADVERSARIALLY LEARNING THE TRANSPORT COST FUNCTION + +To illustrate the importance of learning the transport cost function adversarially, we repeat our CIFAR-10 experiment using cosine distance defined in the original feature space: + +$$ +c ( \mathbf { x } , \mathbf { y } ) = 1 - { \frac { \mathbf { x } \cdot \mathbf { y } } { \| \mathbf { x } \| _ { 2 } \| \mathbf { y } \| _ { 2 } } } , +$$ + +where x, y are original image pixel values. In this case, only the transport cost function is a fixed distance function, but all the rest experiment settings are the same as those of OT-GAN. The highest inception score during the training process is 4.93, as compared to 8.47 when learning cost function adversarially using another neural network. The generated samples are shown in Figure 8. + +![](images/b73148457d2daeac3ccdd99d209d8eeebb6514005247c6dd560417366a7d254e.jpg) +Figure 8: CIFAR-10 Samples generated without adversarially learning the cost function. + +# D MODEL COLLAPSE AND SAMPLE DIVERSITY + +To further investigate sample diversity and mode collapse in GANs, we train the same generator using DCGAN and OT-GAN on the Imagenet dog data set for a large number of epochs. For DCGAN we observe mode collapse starting to occur after about 900 epochs, as indicated in figure 9. The model does not recover from this if we continue training. We have observed similar behavior for many other types of GAN. For OT-GAN we continued to train for 13000 epochs on this data set but never observed any mode collapse or reduction in sample diversity. + +![](images/d695e9bb1e93fa6444466b1317a36d31e797fae6fa95c3932de83ad4d5357d5b.jpg) +Figure 9: Imagenet dog samples generated with DCGAN (left) after 900 epochs and OT-GAN (right) after 13000 epochs. When training long enough, DCGAN suffers from mode collapse as indicated by the highlighted samples. We did not observe any mode collapse for OT-GAN, even when training for many more epochs. \ No newline at end of file diff --git a/parse/train/rkQkBnJAb/rkQkBnJAb_content_list.json b/parse/train/rkQkBnJAb/rkQkBnJAb_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..56387f8befbfb43ce65d66ae710c09542c43c760 --- /dev/null +++ b/parse/train/rkQkBnJAb/rkQkBnJAb_content_list.json @@ -0,0 +1,1203 @@ +[ + { + "type": "text", + "text": "IMPROVING GANS USING OPTIMAL TRANSPORT ", + "text_level": 1, + "bbox": [ + 171, + 98, + 761, + 121 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tim Salimans∗ OpenAI tim@openai.com ", + "bbox": [ + 184, + 145, + 325, + 188 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Han Zhang∗† \nRutgers University \nhan.zhang@cs.rutgers.edu ", + "bbox": [ + 375, + 143, + 612, + 188 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Alec Radford OpenAI alec@openai.com ", + "bbox": [ + 665, + 145, + 813, + 188 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dimitris Metaxas Rutgers University dnm@cs.rutgers.edu ", + "bbox": [ + 183, + 208, + 362, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 287, + 544, + 303 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present Optimal Transport GAN (OT-GAN), a variant of generative adversarial nets minimizing a new metric measuring the distance between the generator distribution and the data distribution. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. Experimentally we show OT-GAN to be highly stable when trained with large mini-batches, and we present state-of-the-art results on several popular benchmark problems for image generation. ", + "bbox": [ + 233, + 320, + 764, + 445 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 478, + 336, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generative modeling is a major sub-field of Machine Learning that studies the problem of how to learn models that generate images, audio, video, text or other data. Applications of generative models include image compression, generating speech from text, planning in reinforcement learning, semi-supervised and unsupervised representation learning, and many others. Since generative models can be trained on unlabeled data, which is almost endlessly available, they have enormous potential in the development of artificial intelligence. ", + "bbox": [ + 174, + 512, + 825, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The central problem in generative modeling is how to train a generative model such that the distribution of its generated data will match the distribution of the training data. Generative adversarial nets (GANs) represent an advance in solving this problem, using a neural network discriminator or critic to distinguish between generated data and training data. The critic defines a distance between the model distribution and the data distribution which the generative model can optimize to produce data that more closely resembles the training data. ", + "bbox": [ + 174, + 603, + 825, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A closely related approach to measuring the distance between the distributions of generated data and training data is provided by optimal transport theory. By framing the problem as optimally transporting one set of data points to another, it represents an alternative method of specifying a metric over probability distributions and provides another objective for training generative models. The dual problem of optimal transport is closely related to GANs, as discussed in the next section. However, the primal formulation of optimal transport has the advantage that it allows for closed form solutions and can thus more easily be used to define tractable training objectives that can be evaluated in practice without making approximations. A complication in using primal form optimal transport is that it may give biased gradients when used with mini-batches (see Bellemare et al., 2017) and may therefore be inconsistent as a technique for statistical estimation. ", + "bbox": [ + 174, + 693, + 825, + 832 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper we present OT-GAN, a variant of generative adversarial nets incorporating primal form optimal transport into its critic. We derive and justify our model by defining a new metric over probability distributions, which we call Mini-batch Energy Distance, combining optimal transport in primal form with an energy distance defined in an adversarially learned feature space. This combination results in a highly discriminative metric with unbiased mini-batch gradients. ", + "bbox": [ + 176, + 839, + 821, + 881 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 171, + 103, + 823, + 132 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In Section 2 we provide the preliminaries required to understand our work, and we put our contribution into context by discussing the relevant literature. Section 3 presents our main theoretical contribution: Minibatch energy distance. We apply this new distance metric to the problem of learning generative models in Section 4, and show state-of-the-art results in Section 5. Finally, Section 6 concludes by discussing the strengths and weaknesses of the proposed method, as well as directions for future work. ", + "bbox": [ + 174, + 138, + 825, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 GANS AND OPTIMAL TRANSPORT ", + "text_level": 1, + "bbox": [ + 174, + 241, + 493, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Generative adversarial nets (Goodfellow et al., 2014) were originally motivated using game theory: A generator $g$ and a discriminator $d$ play a zero-sum game where the generator maps noise $\\mathbf { z }$ to simulated images $\\mathbf { y } = g ( \\mathbf { z } )$ and where the discriminator tries to distinguish the simulated images y from images $\\mathbf { x }$ drawn from the distribution of training data $p$ . The discriminator takes in each image $\\mathbf { x }$ and y and outputs an estimated probability that the given image is real rather than generated. The discriminator is rewarded for putting high probability on the correct classification, and the generator is rewarded for fooling the discriminator. The goal of training is then to find a pair of $( g , d )$ for which this game is at a Nash equilibrium. At such an equilibrium, the generator minimizes its loss, or negative game value, which can be defined as ", + "bbox": [ + 173, + 271, + 825, + 397 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/bc0bb279681edbe0e5aa30776d8c73db7dfadf1dda2ec43816cec675956e8a49.jpg", + "text": "$$\nL _ { g } = \\operatorname* { s u p } _ { d } \\mathbb { E } _ { \\mathbf { x } \\sim p } \\log [ d ( \\mathbf { x } ) ] + \\mathbb { E } _ { \\mathbf { y } \\sim g } \\log [ 1 - d ( \\mathbf { y } ) ]\n$$", + "text_format": "latex", + "bbox": [ + 338, + 400, + 658, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Arjovsky et al. (2017) re-interpret GANs in the framework of optimal transport theory. Specifically, they propose the Earth-Mover distance or Wasserstein- $^ { l }$ distance as a good objective for generative modeling: ", + "bbox": [ + 176, + 428, + 823, + 468 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/5b2537e553fe3a9ba555c237c26959fcb0ec30661f389bb77a11ae085eabc273.jpg", + "text": "$$\nD _ { \\mathrm { E M D } } ( p , g ) = \\operatorname* { i n f } _ { \\gamma \\in \\Pi ( p , g ) } \\mathbb { E } _ { \\mathbf { x } , \\mathbf { y } \\sim \\gamma } c ( \\mathbf { x } , \\mathbf { y } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 367, + 468, + 629, + 492 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\Pi ( p , g )$ is the set of all joint distributions $\\gamma ( \\mathbf { x } , \\mathbf { y } )$ with marginals $p ( \\mathbf { x } ) , g ( \\mathbf { y } )$ , and where $c ( \\mathbf { x } , \\mathbf { y } )$ is a cost function that Arjovsky et al. (2017) take to be the Euclidean distance. If the $p ( \\mathbf { x } )$ and $g ( \\mathbf { y } )$ distributions are interpreted as piles of earth, the Earth-Mover distance $D _ { \\mathrm { E M D } } ( p , g )$ can be interpreted as the minimum amount of “mass” that $\\gamma$ has to transport to turn the generator distribution $g ( \\mathbf { y } )$ into the data distribution $p ( \\mathbf { x } )$ . For the right choice of cost $c$ , this quantity is a metric in the mathematical sense, meaning that $D _ { \\mathrm { E M D } } ( p , g ) \\geq 0$ and $D _ { \\mathrm { E M D } } ( p , g ) = 0$ if and only if $p = g$ . Minimizing the Earth-Mover distance in $g$ is thus a valid method for deriving a statistically consistent estimator of $p$ , provided $p$ is in the model class of our generator $g$ . ", + "bbox": [ + 173, + 493, + 825, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unfortunately, the minimization over $\\gamma$ in Equation 2 is generally intractable, so Arjovsky et al. (2017) turn to the dual formulation of this optimal transport problem: ", + "bbox": [ + 176, + 612, + 820, + 640 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/b87a4c96db769c4d62dc9c8cf2ae6c01e43e045d40aa8f4ad52855f285e613d0.jpg", + "text": "$$\nD _ { \\mathrm { E M D } } ( p , g ) = \\operatorname* { s u p } _ { \\| f \\| _ { L } \\leq 1 } \\mathbb { E } _ { \\mathbf { x } \\sim p } f ( \\mathbf { x } ) - \\mathbb { E } _ { \\mathbf { y } \\sim g } f ( \\mathbf { y } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 339, + 642, + 656, + 671 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where we have replaced the minimization over $\\gamma$ with a maximization over the set of 1-Lipschitz functions. This optimization problem is generally still intractable, but Arjovsky et al. (2017) argue that it is well approximated by using the class of neural network GAN discriminators or critics described earlier in place of the class of 1-Lipschitz functions, provided we bound the norm of their gradient with respect to the image input. Making this substitution, the objective becomes quite similar to that of our original GAN formulation in Equation 1. ", + "bbox": [ + 174, + 672, + 825, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In followup work Gulrajani et al. (2017) propose a different method of bounding the gradients in the class of allowed critics, and provide strong empirical results supporting this interpretation of GANs. In spite of their success, however, we should note that GANs are still only able to solve this optimal transport problem approximately. The optimization with respect to the critic cannot be performed perfectly, and the class of obtainable critics only very roughly corresponds to the class of 1-Lipschitz functions. The connection between GANs and dual form optimal transport is further explored by Bousquet et al. (2017) and Genevay et al. (2017a), who extend the analysis to different optimal transport costs and to a broader model class including latent variables. ", + "bbox": [ + 173, + 762, + 825, + 875 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An alternative approach to generative modeling is chosen by Genevay et al. (2017b) who instead chose to approximate the primal formulation of optimal transport. They start by taking an entropically smoothed generalization of the Earth Mover distance, called the Sinkhorn distance (Cuturi, ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 217, + 117 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/0bdd32a18c45d2369250c4172e9858a12c411df32e28dbcc32ad815c0cf5b06f.jpg", + "text": "$$\nD _ { \\mathrm { S i n k h o r n } } ( p , g ) = \\operatorname* { i n f } _ { \\gamma \\in \\Pi _ { \\beta } ( p , g ) } \\mathbb { E } _ { \\mathbf { x } , \\mathbf { y } \\sim \\gamma } c ( \\mathbf { x } , \\mathbf { y } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 356, + 116, + 640, + 142 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the set of allowed joint distribution $\\Pi _ { \\beta }$ is now restricted to distributions with entropy of at least some constant $\\beta$ . Genevay et al. (2017b) then approximate this distance by evaluating it on mini-batches of data $\\mathbf { X } , \\mathbf { Y }$ consisting of $K$ data vectors $\\mathbf x , \\mathbf y$ . The cost function $c$ then gives rise to a $K \\times K$ transport cost matrix $C$ , where $C _ { i , j } = c ( \\mathbf { x } _ { i } , \\mathbf { y } _ { j } )$ tells us how expensive it is to transport the $i$ - th data vector $\\mathbf { x } _ { i }$ in mini-batch $\\mathbf { X }$ to the $j$ -th data vector $\\mathbf { y } _ { j }$ in mini-batch $\\mathbf { Y }$ . Similarly, the coupling distribution $\\gamma$ is replaced by a $K \\times K$ matrix $M$ of soft matchings between these $i , j$ elements, which is restricted to the set of matrices $\\mathcal { M }$ with all positive entries, with all rows and columns summing to one, and with sufficient entropy $- \\operatorname { T r } [ M \\log ( M ^ { \\mathrm { T } } ) ] \\geq \\alpha$ . The resulting distance, evaluated on a minibatch, is then ", + "bbox": [ + 173, + 143, + 825, + 268 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/ff6f5825b316fbb031805417dc8971553e8b6f751bb959d4bad1c7b805f885b1.jpg", + "text": "$$\n{ \\mathcal { W } } _ { c } ( X , Y ) = \\operatorname* { i n f } _ { M \\in { \\mathcal { M } } } \\mathrm { T r } [ M C ^ { \\mathrm { T } } ] .\n$$", + "text_format": "latex", + "bbox": [ + 397, + 265, + 602, + 290 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In practice, the minimization over the soft matchings $M$ can be found efficiently on the GPU using the Sinkhorn algorithm. Consequently, Genevay et al. (2017b) call their method of using Equation 5 in generative modeling Sinkhorn AutoDiff. ", + "bbox": [ + 174, + 292, + 825, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The great advantage of this mini-batch Sinkhorn distance is that it is fully tractable, eliminating the instabilities often experienced with GANs due to imperfect optimization of the critic. However, a disadvantage is that the expectation of Equation 5 over mini-batches is no longer a valid metric over probability distributions. Viewed another way, the gradients of Equation 5, for fixed mini-batch size, are not unbiased estimators of the gradients of our original optimal transport problem in Equation 4. For this reason, Bellemare et al. (2017) propose to instead use the Energy Distance, also called Cramer Distance, as the basis of generative modeling: ", + "bbox": [ + 173, + 340, + 825, + 440 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/778d8579934dbf9de2a0e90a2bf2d115bc2277087a396108f16bc7ac0ea52cae.jpg", + "text": "$$\nD _ { \\mathrm { E D } } ( p , g ) = \\sqrt { 2 \\mathbb { E } [ \\left\\| \\mathbf { x } - \\mathbf { y } \\right\\| ] - \\mathbb { E } [ \\left\\| \\mathbf { x } - \\mathbf { x } ^ { \\prime } \\right\\| ] - \\mathbb { E } [ \\left\\| \\mathbf { y } - \\mathbf { y } ^ { \\prime } \\right\\| ] } ,\n$$", + "text_format": "latex", + "bbox": [ + 297, + 444, + 699, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf { x } , \\mathbf { x } ^ { \\prime }$ are independent samples from data distribution $p$ and $\\mathbf { y } , \\mathbf { y } ^ { \\prime }$ independent samples from the generator dsitribution $g$ . In Cramer $G A N$ they propose training the generator by minimizing this distance metric, evaluated in a latent space which is learned by the GAN critic. ", + "bbox": [ + 174, + 469, + 825, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the next section we propose a new metric for generative modeling, combining the insights of GANs and optimal transport. Although our work was performed concurrently to that by Genevay et al. (2017b) and Bellemare et al. (2017), it can be understood most easily as forming a synthesis of the ideas used in Sinkhorn AutoDiff and Cramer GAN. ", + "bbox": [ + 173, + 518, + 825, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 MINI-BATCH ENERGY DISTANCE ", + "text_level": 1, + "bbox": [ + 174, + 594, + 480, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As discussed in the last section, most previous work in generative modeling can be interpreted as minimizing a distance $D ( g , p )$ between a generator distribution $g ( \\mathbf { x } )$ and the data distribution $p ( \\mathbf { x } )$ , where the distributions are defined over a single vector $\\mathbf { x }$ which we here take to be an image. However, in practice deep learning typically works with mini-batches of images $\\mathbf { X }$ rather than individual images. For example, a GAN generator is typically implemented as a high dimensional function $G ( \\mathbf { Z } )$ that turns a mini-batch of random noise $\\mathbf { Z }$ into a mini-batch of images $\\mathbf { X }$ , which the GAN discriminator then compares to a mini-batch of images from the training data. The central insight of Mini-batch GAN (Salimans et al., 2016) is that it is strictly more powerful to work with the distributions over mini-batches $g ( \\mathbf { X } ) , p ( \\mathbf { X } )$ than with the distributions over individual images. Here we further pursue this insight and propose a new distance over mini-batch distributions $\\bar { D [ { g ( \\mathbf { X } ) , p ( \\mathbf { X } ) } ] }$ which we call the Mini-batch Energy Distance. This new distance combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. ", + "bbox": [ + 173, + 625, + 825, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to derive our new distance function, we start by generalizing the energy distance given in Equation 6 to general non-Euclidean distance functions $d$ . Doing so gives us the generalized energy distance: ", + "bbox": [ + 173, + 813, + 825, + 854 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/3fe32891ca4c06790481cf033894725a497c07ca6cfca96730273a91ef8fa26f.jpg", + "text": "$$\nD _ { \\mathtt { G E D } } ( p , g ) = { \\sqrt { 2 \\mathbb { E } [ d ( \\mathbf { X } , \\mathbf { Y } ) ] - \\mathbb { E } [ d ( \\mathbf { X } , \\mathbf { X } ^ { \\prime } ) ] - \\mathbb { E } [ d ( \\mathbf { Y } , \\mathbf { Y } ^ { \\prime } ) ] } } ,\n$$", + "text_format": "latex", + "bbox": [ + 292, + 852, + 704, + 878 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf { X } , \\mathbf { X } ^ { \\prime }$ are independent samples from distribution $p$ and $\\mathbf { Y } , \\mathbf { Y } ^ { \\prime }$ independent samples from $g$ . This distance is typically defined for individual samples, but it is valid for general random objects, including mini-batches like we assume here. The energy distance $D _ { \\mathrm { G E D } } ( \\bar { p } , g )$ is a metric, in the mathematical sense, as long as the distance function $d$ is a metric (Klebanov et al., 2005). Under this condition, meaning that $d$ satisfies the triangle inequality and several other conditions, we have that $D ( p , g ) \\geq 0$ , and $\\bar { D } ( p , g ) = 0$ if and only if $p = g$ . ", + "bbox": [ + 174, + 881, + 825, + 924 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 103, + 823, + 147 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using individual samples $\\mathbf x , \\mathbf y$ instead of minibatches $\\mathbf { X } , \\mathbf { Y }$ , Sejdinovic et al. (2013) showed that such generalizations of the energy distance can equivalently be viewed as a form of maximum mean discrepancy, where the MMD kernel $k$ is related to the distance function $d$ by $d ( { \\bf x } , { \\bf x } ^ { \\prime } ) \\equiv k ( { \\bf x } , { \\bf x } ) +$ $k ( \\mathbf { x } ^ { \\prime } , \\mathbf { \\bar { x } } ^ { \\prime } ) - 2 k ( \\mathbf { x } , \\mathbf { x } ^ { \\prime } )$ . We find the energy distance perspective more intuitive here and follow Cramer GAN in using this perspective instead. ", + "bbox": [ + 173, + 152, + 825, + 223 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We are free to choose any metric $d$ for use in Equation 7, but not all choices will be equally discriminative when used for generative modeling. Here, we choose $d$ to be the entropy-regularized Wasserstein distance, or Sinkhorn distance, as defined for mini-batches in Equation 5. Although the average over mini-batch Sinkhorn distances is not a valid metric over probability distributions $p , g$ , resulting in the biased gradients problem discussed in Section 2, the Sinkhorn distance is a valid metric between individual mini-batches, which is all we require for use inside the generalized energy distance. ", + "bbox": [ + 173, + 228, + 825, + 327 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Putting everything together, we arrive at our final distance function over distributions, which we call the Minibatch Energy Distance. Like with the Cramer distance, we typically work with the squared distance, which we define as ", + "bbox": [ + 174, + 333, + 825, + 376 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/af1a341e2e2ef472b3c441e8f5a17e96be4872691b71245f9cb3d2279985dab9.jpg", + "text": "$$\nD _ { \\mathrm { M E D } } ^ { 2 } ( p , g ) = 2 \\mathbb { E } [ \\mathcal { W } _ { c } ( \\mathbf { X } , \\mathbf { Y } ) ] - \\mathbb { E } [ \\mathcal { W } _ { c } ( \\mathbf { X } , \\mathbf { X } ^ { \\prime } ) ] - \\mathbb { E } [ \\mathcal { W } _ { c } ( \\mathbf { Y } , \\mathbf { Y } ^ { \\prime } ) ] ,\n$$", + "text_format": "latex", + "bbox": [ + 276, + 382, + 720, + 401 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf { X }$ , $\\mathbf { X } ^ { \\prime }$ are independently sampled mini-batches from distribution $p$ and $\\mathbf { Y } , \\mathbf { Y } ^ { \\prime }$ are independent mini-batches from $g$ . We include the subscript $c$ to make explicit that this distance depends on the choice of transport cost function $c$ , which we will learn adversarially as discussed in Section 4. ", + "bbox": [ + 174, + 407, + 825, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In comparison with the original Sinkhorn distance (Equation 5 the loss function for training $g$ implied by this metric adds a repulsive term − $\\mathbf { \\nabla } \\cdot \\mathcal { W } _ { c } ( \\mathbf { Y } , \\mathbf { Y } ^ { \\prime } )$ to the attractive term ${ \\mathcal W } _ { c } ( { \\bf X } , { \\bf Y } )$ . Like with the energy distance used by Cramer GAN, this is what makes the resulting mini-batch gradients unbiased and the objective statistically consistent. However, unlike the plain energy distance, the mini-batch energy distance $D _ { \\mathrm { M E D } } ^ { 2 } ( p , \\bar { g } )$ still incorporates the primal form optimal transport of the Sinkhorn distance, which in Section 5 we show leads to much stronger discriminative power and more stable generative modeling. ", + "bbox": [ + 173, + 457, + 825, + 555 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In concurrent work, Genevay et al. (2018) independently propose a very similar loss function to (8), but using a single sample from the data and generator distributions. We obtained best results using two independently sampled minibatches from each distribution. ", + "bbox": [ + 174, + 561, + 825, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4 OPTIMAL TRANSPORT GAN (OT-GAN) ", + "text_level": 1, + "bbox": [ + 174, + 623, + 540, + 641 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the last section we defined the mini-batch energy distance which we propose using for training generative models. However, we left undefined the transport cost function $c ( \\mathbf { x } , \\mathbf { y } )$ on which it depends. One possibility would be to choose $c$ to be some fixed function over vectors, like Euclidean distance, but we found this to perform poorly in preliminary experiments. Although minimizing the mini-batch energy distance $\\bar { D } _ { M E D } ^ { 2 } ( \\bar { p } , g )$ guarantees statistical consistency for simple fixed cost functions $c$ like Euclidean distance, the resulting statistical efficiency is generally poor in high dimensions. This means that there typically exist many bad distributions distributions $g$ for which $D _ { M E D } ^ { 2 } ( p , g )$ is so close to zero that we cannot tell $p$ and $g$ apart without requiring an enormous sample size. To solve this we propose learning the cost function adversarially, so that it can adapt to the generator distribution $g$ and thereby become more discriminative. In practice we implement this by defining $c$ to be the cosine distance between vectors $v _ { \\eta } ( \\mathbf { x } )$ and $v _ { \\eta } ( \\mathbf { y } )$ , where $v _ { \\eta }$ is a deep neural network that maps the images in our mini-batch into a learned latent space. That is we define the transport cost to be ", + "bbox": [ + 173, + 656, + 825, + 837 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/cf88758a29e8032ac3e154ad749a606988d6ef49661782d14f28df9658d17a8b.jpg", + "text": "$$\nc _ { \\eta } ( \\mathbf x , \\mathbf y ) = 1 - \\frac { v _ { \\eta } ( \\mathbf x ) \\cdot v _ { \\eta } ( \\mathbf y ) } { \\| v _ { \\eta } ( \\mathbf x ) \\| _ { 2 } \\| v _ { \\eta } ( \\mathbf y ) \\| _ { 2 } } ,\n$$", + "text_format": "latex", + "bbox": [ + 379, + 835, + 617, + 871 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we choose $\\eta$ to maximize the resulting minibatch energy distance. ", + "bbox": [ + 176, + 875, + 650, + 888 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In practice, training our generative model $g _ { \\boldsymbol { \\theta } }$ and our adversarial transport cost $c _ { \\eta }$ is done by alternating gradient descent as is standard practice in GANs (Goodfellow et al., 2014). Here we choose to update the generator more often than we update our critic. This is contrary to standard practice (e.g. Arjovsky et al., 2017) and ensures our cost function $c$ does not become degenerate. If $c$ were to assign zero transport cost to two non-identical regions in image space, the generator would quickly adjust to take advantage of this. Similar to how a quickly adapting critic controls the generator in standard GANs, this works the other way around in our case. Contrary to standard GANs, our generator has a well defined and statistically consistent training objective even when the critic is not updated, as long as the cost function $c$ is not degenerate. We also investigated forcing $v _ { \\eta }$ to be one-to-one by parameterizing it using a RevNet Gomez et al. (2017), thereby ensuring $c$ cannot degenerate, but this proved unnecessary if the generator is updated often enough. ", + "bbox": [ + 173, + 895, + 826, + 924 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "", + "bbox": [ + 173, + 103, + 825, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our full training procedure is described in Algorithm 1, and is visually depicted in Figure 1. Here we compute the matching matrix $M$ in ${ \\mathcal { W } } _ { c }$ using the Sinkhorn algorithm. Unlike Genevay et al. (2017b) we do not backpropagate through this algorithm. Ignoring the gradient flow through the matchings $M$ is justified by the envelope theorem (see e.g. Carter, 2001): Since $M$ is chosen to minimize ${ \\mathcal { W } } _ { c }$ , the gradient of ${ \\mathcal { W } } _ { c }$ with respect to this variable is zero (when projected into the allowed space $\\mathcal { M }$ ). Algorithm 1 assumes we use standard SGD for optimization, but we are free to use other optimizers. In our experiments we use Adam (Kingma & Ba, 2014). ", + "bbox": [ + 174, + 236, + 825, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our algorithm for training generative models can be generalized to include conditional generation of images given some side information $s$ , such as a text-description of the image or a label. When generating an image y we simply draw $s$ from the training data and condition the generator on it. The rest of the algorithm is identical to Algorithm 1 but with $( \\mathbf { Y } , S )$ in place of $\\mathbf { Y }$ , and similar substitutions for $\\breve { \\mathbf { X } } , \\mathbf { X } ^ { \\prime } , \\mathbf { Y } ^ { \\prime }$ . The full algorithm for conditional generation is detailed in Algorithm 2 in the appendix. ", + "bbox": [ + 173, + 340, + 825, + 424 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Require: $n _ { g e n }$ , the number of iterations of the generator per critic iteration \nRequire: $\\eta _ { 0 }$ , initial critic parameters. $\\theta _ { 0 }$ , initial generator parameters \n1: for $t = 1$ to $N$ do \n2: Sample $\\mathbf { X } , \\mathbf { X } ^ { \\prime }$ two independent mini-batches from real data, and $\\mathbf { Y } , \\mathbf { Y } ^ { \\prime }$ two independent mini-batches from the generated samples \n3: ${ \\mathcal { L } } = \\mathcal { W } _ { c } ( \\mathbf { X } , \\mathbf { Y } ) + \\mathcal { W } _ { c } ( \\mathbf { \\tilde { X } } , \\mathbf { Y } ^ { \\prime } ) + \\mathcal { W } _ { c } \\mathbf { \\tilde { ( X ' , Y ) } } + \\mathcal { W } _ { c } ( \\mathbf { X } ^ { \\prime } , \\mathbf { Y } ^ { \\prime } ) - 2 \\mathcal { W } _ { c } ( \\mathbf { X } , \\mathbf { X } ^ { \\prime } ) - 2 \\mathcal { W } _ { c } ( \\mathbf { Y } , \\mathbf { Y } ^ { \\prime } )$ \n4: if $t$ mod $n _ { g e n } + 1 = 0$ then \n5: $\\eta \\eta + \\alpha \\cdot \\nabla _ { \\eta } \\mathcal { L }$ \n6: else \n7: $\\theta \\theta - \\alpha \\cdot \\nabla _ { \\theta } \\mathcal { L }$ \n8: end if \n9: end for ", + "bbox": [ + 174, + 477, + 825, + 643 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1e58273fd7719f4bfa348121cdbe49a29a843f422b7306bcbedd5a9726afdbb0.jpg", + "image_caption": [ + "Figure 1: Illustration of OT-GAN. Mini-batches from the generator and training data are embedded into a learned feature space via the critic. A transport cost matrix is calculated between the two mini-batches of features. Soft matching aligns features across mini-batches and aligned features are compared. The figure only illustrates the distance calculation between one pair of mini-batches whereas several are computed. " + ], + "image_footnote": [], + "bbox": [ + 202, + 672, + 795, + 842 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 174, + 102, + 326, + 117 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we demonstrate the improved stability and consistency of the proposed method on five different datasets with increasing complexity. ", + "bbox": [ + 176, + 132, + 823, + 161 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1 MIXTURE OF GAUSSIAN DATASET ", + "text_level": 1, + "bbox": [ + 176, + 176, + 449, + 191 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "One advantage of OT-GAN compared to regular GAN is that for any setting of the transport cost $c$ , i.e. any fixed critic, the objective is statistically consistent for training the generator $g$ . Even if we stop updating the critic, the generator should thus never diverge. With a bad fixed cost function $c$ the signal for learning $g$ may be very weak, but at least it should never point in the wrong direction. We investigate whether this theoretical property holds in practice by examining a simple toy example. We train generative models using different types of GAN on a 2D mixture of 8 Gaussians, with means arranged on a circle. The goal for the generator is to recover all 8 modes. For the proposed method and all the baseline methods, the architectures are simple MLPs with ReLU activations. A similar experimental setting has been considered in (Metz et al., 2017; Li et al., 2017) to demonstrate the mode coverage behavior of various GAN models. There, GANs using mini-batch features, DAN-S (Li et al., 2017), are shown to capture all the 8 modes when training converges. To test the consistency of GAN models, we stop updating the discriminator after $1 5 \\mathrm { k }$ iterations and visualize the generator distribution for an additional 25K iterations. As shown in Figure 2, mode collapse occurs in a mini-batch feature GAN after a few thousand iterations training with a fixed discriminator. However, using the mini-batch energy distance, the generator does not diverge and the generated samples still cover all 8 modes of the data. ", + "bbox": [ + 174, + 204, + 825, + 424 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1687b47c7688836cb6bf32cf7cfdd10ff315315751109cb91d4da734f7b693bc.jpg", + "image_caption": [ + "Figure 2: Results for consistency when fixing the critic on data generated from 8 Gaussian mixtures. The first column shows the data distribution. The top row shows the training results of OT-GAN using mini-batch energy distance. The bottom row shows the training result with the original GAN loss (DAN-S). The latter collapses to 3 out of 8 modes after fixing the discriminator, while OT-GAN remains consistent. " + ], + "image_footnote": [], + "bbox": [ + 205, + 438, + 790, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2 CIFAR-10 ", + "text_level": 1, + "bbox": [ + 174, + 640, + 290, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CIFAR-10 is a well-studied dataset of $3 2 \\times 3 2$ color images for generative models (Krizhevsky, 2009). We use this data set to investigate the importance of the different design decisions made with OT-GAN, and we compare the visual quality of its generated samples with other state-of-theart GAN models. Our model and the other reported results are trained in an unsupervised manner. We choose “inception score” (Salimans et al., 2016) as numerical assessment to compare the visual quality of samples generated by different models. Our generator and critic are standard convnets, similar to those used by DCGAN (Radford et al., 2015), but without any batch normalization, layer normalization, or other stabilizing additions. Appendix B contains additional architecture and training details. ", + "bbox": [ + 173, + 666, + 825, + 791 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first investigate the effect of batch size on training stability and sample quality. As shown in Figure 3, training is not very stable when the batch size is small (i.e. 200). As batch size increases, training becomes more stable and the inception score of samples increases. Unlike previous methods, our objective (the minibatch energy distance, Section 3) depends on the chosen minibatch size: Larger minibatches are more likely to cover many modes of the data distribution, thereby not only yielding lower variance estimates but also making our distance metric more discriminative. To reach the large batch sizes needed for optimal performance we make use of multi GPU training. In this work we only use up to 8 GPUs per experiment, but we anticipate more GPUs to be useful when using larger models. ", + "bbox": [ + 173, + 797, + 825, + 924 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Figure 4 we present the samples generated by our model trained with a batch size of 8000. In addition, we also compare with the sample quality of other state-of-the-art GAN models in Table 1. OT-GAN achieves a score of $8 . 4 7 \\pm . 1 2$ , outperforming all baseline models. ", + "bbox": [ + 173, + 103, + 823, + 146 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the importance of using optimal transport in OT-GAN, we repeat our CIFAR-10 experiment with random matching of samples. Our minibatch energy distance objective remains valid when we match samples randomly rather than using optimal transport. In this case the minibatch energy distance reduces to the regular (generalized) energy distance. We repeat our CIFAR-10 experiment and train a generator with the same architecture and hyperparameters as above, but with random matching of samples instead of optimal transport. The highest resulting Inception score achieved during the training process is 4.64 using this approach, as compared to 8.47 with optimal transport. Figure 5 shows a random sample from the resulting model. ", + "bbox": [ + 173, + 152, + 825, + 265 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2b68ae8cd3d000b7202969fab78806360cc6d1ccd329fd34095c8213d5ce3802.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInception score
Real Data11.95 ± .12
DCGAN6.16±.07
Improved GAN6.86±.06
DenoisingFM7.72±.13
WGAN-GP7.86± .07
OT-GAN8.47±.12
", + "bbox": [ + 406, + 276, + 589, + 353 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1: Inception scores on CIFAR-10. All the models are trained in an unsupervised manner. ", + "bbox": [ + 183, + 369, + 805, + 385 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a54c9124dd2c9ce0fbf6f3b48b53066b7a43bbea3a067d23c1d5ead9061ec014.jpg", + "image_caption": [ + "Figure 3: CIFAR-10 inception score over the course of training for different batch sizes. " + ], + "image_footnote": [], + "bbox": [ + 341, + 406, + 655, + 568 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2bf7a927be164f1ae5be549e065c1add2c85346abe9fed718132083af632ff1f.jpg", + "image_caption": [ + "Figure 4: Samples generated by OT-GAN on CIFAR-10, without using labels. " + ], + "image_footnote": [], + "bbox": [ + 174, + 621, + 501, + 875 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/41ab2c798337bfae4bf37c8b841670c515c8340fa9046e2edb009ce8972bd7d0.jpg", + "image_caption": [ + "Figure 5: Samples generated without using optimal transport. " + ], + "image_footnote": [], + "bbox": [ + 531, + 621, + 856, + 875 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3 IMAGENET DOGS ", + "text_level": 1, + "bbox": [ + 176, + 103, + 338, + 117 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To illustrate the ability of OT-GAN in generating high quality images on more complex data sets, we train OT-GAN to generate $1 2 8 \\times 1 2 8$ images on the dog subset of ImageNet (Russakovsky et al., 2015). A smaller batch size of 2048 is used due to GPU memory contraints. As shown in Figure 6, the samples generated by OT-GAN contain less nonsensical images, and the sample quality is significantly better than that of a tuned DCGAN variant which still suffers from mode collapse. The superior image quality is confirmed by the inception score achieved by OT-GAN $( 8 . 9 7 { \\scriptstyle \\pm 0 . 0 9 } )$ on this dataset, which outperforms that of DCGAN(8.19±0.11) ", + "bbox": [ + 174, + 128, + 825, + 227 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f014376b44941bf3c6b56a596486ceca17208002ae78bcc958f676fc2b5e1b13.jpg", + "image_caption": [ + "Figure 6: ImageNet Dog subset samples generated by OT-GAN (left) and DCGAN (right). " + ], + "image_footnote": [], + "bbox": [ + 196, + 239, + 802, + 467 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4 CONDITIONAL GENERATION OF BIRDS ", + "text_level": 1, + "bbox": [ + 176, + 515, + 478, + 529 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To further demonstrate the effectiveness of the proposed method on conditional image synthesis, we compare OT-GAN with state-of-the-art models on text-to-image generation (Reed et al., 2016b;a; Zhang et al., 2017). As shown in Table 2, the images generated by OT-GAN with batch size 2048 also achieve the best inception score here. Example images generated by our conditional generative model on the CUB test set are presented in Figure 7. ", + "bbox": [ + 174, + 540, + 826, + 611 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/efde24e554bca4af5862c3fa8b2e4d16b0d99c0c032ce55e3722142ddb0feb67.jpg", + "table_caption": [ + "Table 2: Inception scores by state-of-the-art methods (Reed et al., 2016b;a; Zhang et al., 2017) and the proposed OT-GAN on the CUB test set. Higher inception scores mean better image quality. " + ], + "table_footnote": [], + "table_body": "
MethodGAN-INT-CLSGAWWNStackGANOT-GAN
Inception Score2.88± .043.62 ± .073.70±.043.84 ± .05
", + "bbox": [ + 259, + 623, + 736, + 652 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/60dfbeabf4e67698c3c1e31fa5a3ee4ca6acba57bf8cfac62732229ae9d9f4eb.jpg", + "image_caption": [ + "Figure 7: Bird example images generated by conditional OT-GAN " + ], + "image_footnote": [], + "bbox": [ + 192, + 717, + 818, + 840 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6 DISCUSSION ", + "text_level": 1, + "bbox": [ + 174, + 102, + 310, + 117 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We have presented OT-GAN, a new variant of GANs where the generator is trained to minimize a novel distance metric over probability distributions. This metric, which we call mini-batch energy distance, combines optimal transport in primal form with an energy distance defined in an adversarially learned feature space, resulting in a highly discriminative distance function with unbiased mini-batch gradients. OT-GAN was shown to be uniquely stable when trained with large mini-batches and to achieve state-of-the-art results on several common benchmarks. ", + "bbox": [ + 174, + 133, + 823, + 217 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "One downside of OT-GAN, as currently proposed, is that it requires large amounts of computation and memory. We achieve the best results when using very large mini-batches, which increases the time required for each update of the parameters. All experiments in this paper, except for the mixture of Gaussians toy example, were performed using 8 GPUs and trained for several days. In future work we hope to make the method more computationally efficient, as well as to scale up our approach to multi-machine training to enable generation of even more challenging and high resolution image data sets. ", + "bbox": [ + 174, + 223, + 825, + 320 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "A unique property of OT-GAN is that the mini-batch energy distance remains a valid training objective even when we stop training the critic. Our implementation of OT-GAN updates the generative model more often than the critic, where GANs typically do this the other way around (see e.g. Gulrajani et al., 2017). As a result we learn a relatively stable transport cost function $c ( \\mathbf { x } , \\mathbf { y } )$ , describing how (dis)similar two images are, as well as an image embedding function $v _ { \\eta } ( \\mathbf { x } )$ capturing the geometry of the training data. Preliminary experiments suggest these learned functions can be used successfully for unsupervised learning and other applications, which we plan to investigate further in future work. ", + "bbox": [ + 174, + 328, + 825, + 439 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 174, + 460, + 285, + 474 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Martin Arjovsky, Soumith Chintala, and Leon Bottou. Wasserstein gan. ´ arXiv preprint arXiv:1701.07875, 2017. \nMarc G Bellemare, Ivo Danihelka, Will Dabney, Shakir Mohamed, Balaji Lakshminarayanan, Stephan Hoyer, and Remi Munos. The cramer distance as a solution to biased wasserstein gradients. ´ arXiv preprint arXiv:1705.10743, 2017. \nOlivier Bousquet, Sylvain Gelly, Ilya Tolstikhin, Carl-Johann Simon-Gabriel, and Bernhard Schoelkopf. From optimal transport to generative modeling: the vegan cookbook. arXiv preprint arXiv:1705.07642, 2017. \nMichael Carter. Foundations of mathematical economics. MIT Press, 2001. \nMarco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. In Advances in Neural Information Processing Systems, pp. 2292–2300, 2013. \nYann N Dauphin, Angela Fan, Michael Auli, and David Grangier. Language modeling with gated convolutional networks. arXiv preprint arXiv:1612.08083, 2016. \nAude Genevay, Gabriel Peyre, and Marco Cuturi. Gan and vae from an optimal transport point of view. ´ arXiv preprint arXiv:1706.01807, 2017a. \nAude Genevay, Gabriel Peyre, and Marco Cuturi. Sinkhorn-autodiff: Tractable wasserstein learning of genera- ´ tive models. arXiv preprint arXiv:1706.00292, 2017b. \nAude Genevay, Gabriel Peyre, and Marco Cuturi. Learning generative models with sinkhorn divergences. ´ AISTATS Proceedings, 2018. \nAidan N Gomez, Mengye Ren, Raquel Urtasun, and Roger B Grosse. The reversible residual network: Backpropagation without storing activations. 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", + "bbox": [ + 171, + 478, + 826, + 926 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 171, + 97, + 826, + 626 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "A CONDITIONAL GENERATION ", + "bbox": [ + 178, + 103, + 444, + 117 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Algorithm 2 Conditional Optimal Transport GAN (OT-GAN) training algorithm with step size α, using minibatch SGD for simplicity ", + "bbox": [ + 173, + 170, + 823, + 200 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Require: $n _ { g e n }$ , the number of iterations of the generator per critic iteration \nRequire: $\\eta _ { 0 }$ , initial critic parameters. $\\theta _ { 0 }$ , initial generator parameters \n1: for $t = 1$ to $N$ do \n2: Sample $( \\mathbf { X } , S )$ , $( \\mathbf { X } ^ { \\prime } , S ^ { \\prime } )$ two independent mini-batches from real data, with side information, and $( \\mathbf { Y } , S ) , ( \\mathbf { Y } ^ { \\prime } , S ^ { \\prime } )$ two independent mini-batches from the generator, re-using the same side information \n3: $\\begin{array} { r l r } { \\mathcal { L } } & { { } = } & { \\mathcal { W } _ { c } [ ( { \\bf X } , S ) , ( { \\bf Y } ^ { \\prime } , S ^ { \\prime } ) ] ~ + ~ \\mathcal { W } _ { c } [ ( { \\bf X } ^ { \\prime } , S ^ { \\prime } ) , ( { \\bf Y } , S ) ] ~ - ~ \\mathcal { W } _ { c } [ ( { \\bf X } , S ) , ( { \\bf X } ^ { \\prime } , S ^ { \\prime } ) ] ~ - ~ \\mathcal { W } _ { c } [ ( { \\bf X } , S ) , ( { \\bf X } ^ { \\prime } , S ^ { \\prime } ) ] ~ } \\end{array}$ $\\mathcal { W } _ { c } [ ( \\mathbf { Y } , S ) , ( \\mathbf { Y } ^ { \\prime } , S ^ { \\prime } ) ]$ \n4: if $t$ mod $n _ { g e n } + 1 = 0$ then \n5: $\\eta \\eta + \\alpha \\cdot \\nabla _ { \\eta } \\mathcal { L }$ \n6: else \n7: $\\theta \\theta - \\alpha \\cdot \\nabla _ { \\theta } \\mathcal { L }$ \n8: end if \n9: end for ", + "bbox": [ + 176, + 205, + 854, + 401 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "B CIFAR-10 ARCHITECTURE AND TRAINING DETAILS ", + "text_level": 1, + "bbox": [ + 174, + 473, + 640, + 488 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "The generator and critic are implemented as convolutional networks. Their architectures are loosely based on DCGAN with various modifications. Weight normalization and data-dependent initialization (Salimans & Kingma, 2016) are used for both. The generator maps latent codes sampled from a 100 dimensional uniform distribution between $^ { - 1 }$ and 1 to $3 2 \\times 3 2$ color images. The main module of the generator is a $2 \\mathbf { x } 2$ nearest-neighbor upsampling operation followed by a convolution with a $5 \\times 5$ kernel using gated linear units (Dauphin et al., 2016). The main module of the critic is a convolution with a $5 \\times 5$ kernel and stride 2 using the concatenated ReLU activation function (Shang et al., 2016). Notably, the generator and critic do not use an activation normalization technique such as batch or layer normalization. We train the model using Adam with a learning rate of $3 \\times 1 0 ^ { - 4 }$ , $\\beta _ { 1 } = 0 . 5$ , $\\beta _ { 2 } = 0 . 9 9 9$ . We update the generator 3 times for every critic update. OT-GAN includes two additional hyperparameters for the Sinkhorn algorithm, the number of iterations to run the algorithm and $\\textstyle { \\frac { 1 } { \\lambda } }$ which is the entropy penalty of alignments. Initial tuning found a value of 500 to work well for both. ", + "bbox": [ + 173, + 516, + 825, + 696 + ], + "page_idx": 10 + }, + { + "type": "table", + "img_path": "images/811019152da8015d4029e7cfca0ab2afd379d8f0bc29fbaf1436cae21254df18.jpg", + "table_caption": [ + "Table 3: Generator architecture for CIFAR-10. " + ], + "table_footnote": [], + "table_body": "
operationactivationkernelstrideoutput shape
Z linear reshape 2x NN upsample convolution 2x NN upsample convolutionGLU100 16384
1024×4×4
GLU5×511024×8×8 512×8×8
512 ×16 × 16
GLU5×51256×1 16 ×16
2x NN upsample256 × 32 × 32
convolutionGLU5×51128 × 32 × 32
convolutiontanh5×513 × 32× 32
", + "bbox": [ + 274, + 742, + 723, + 897 + ], + "page_idx": 10 + }, + { + "type": "table", + "img_path": "images/94c2d4c10f595f497ed08d27ce8b81b493553f9c50fa6412dc6f2a8313ee9069.jpg", + "table_caption": [ + "Table 4: Critic architecture for CIFAR-10. " + ], + "table_footnote": [], + "table_body": "
operationactivationkernelstride output shape
convolutionCReLU5×51256× 32×32512 ×16×161024×8×82048×4×43276832768
convolutionconvolutionconvolutionreshape12 normalizeCReLUCReLUCReLU5×5２２2
5×55×5
", + "bbox": [ + 289, + 114, + 709, + 215 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "C ADVERSARIALLY LEARNING THE TRANSPORT COST FUNCTION ", + "text_level": 1, + "bbox": [ + 174, + 266, + 728, + 281 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "To illustrate the importance of learning the transport cost function adversarially, we repeat our CIFAR-10 experiment using cosine distance defined in the original feature space: ", + "bbox": [ + 173, + 296, + 821, + 325 + ], + "page_idx": 11 + }, + { + "type": "equation", + "img_path": "images/d1f43d8e888a52cd0f0a6786f99292ea22057a38a7c82a37487f8b29875dac8a.jpg", + "text": "$$\nc ( \\mathbf { x } , \\mathbf { y } ) = 1 - { \\frac { \\mathbf { x } \\cdot \\mathbf { y } } { \\| \\mathbf { x } \\| _ { 2 } \\| \\mathbf { y } \\| _ { 2 } } } ,\n$$", + "text_format": "latex", + "bbox": [ + 408, + 330, + 588, + 362 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "where x, y are original image pixel values. In this case, only the transport cost function is a fixed distance function, but all the rest experiment settings are the same as those of OT-GAN. The highest inception score during the training process is 4.93, as compared to 8.47 when learning cost function adversarially using another neural network. The generated samples are shown in Figure 8. ", + "bbox": [ + 174, + 368, + 825, + 424 + ], + "page_idx": 11 + }, + { + "type": "image", + "img_path": "images/b73148457d2daeac3ccdd99d209d8eeebb6514005247c6dd560417366a7d254e.jpg", + "image_caption": [ + "Figure 8: CIFAR-10 Samples generated without adversarially learning the cost function. " + ], + "image_footnote": [], + "bbox": [ + 351, + 436, + 647, + 664 + ], + "page_idx": 11 + }, + { + "type": "text", + "text": "D MODEL COLLAPSE AND SAMPLE DIVERSITY ", + "text_level": 1, + "bbox": [ + 173, + 103, + 575, + 117 + ], + "page_idx": 12 + }, + { + "type": "text", + "text": "To further investigate sample diversity and mode collapse in GANs, we train the same generator using DCGAN and OT-GAN on the Imagenet dog data set for a large number of epochs. For DCGAN we observe mode collapse starting to occur after about 900 epochs, as indicated in figure 9. The model does not recover from this if we continue training. We have observed similar behavior for many other types of GAN. For OT-GAN we continued to train for 13000 epochs on this data set but never observed any mode collapse or reduction in sample diversity. ", + "bbox": [ + 174, + 133, + 825, + 217 + ], + "page_idx": 12 + }, + { + "type": "image", + "img_path": "images/d695e9bb1e93fa6444466b1317a36d31e797fae6fa95c3932de83ad4d5357d5b.jpg", + "image_caption": [ + "Figure 9: Imagenet dog samples generated with DCGAN (left) after 900 epochs and OT-GAN (right) after 13000 epochs. When training long enough, DCGAN suffers from mode collapse as indicated by the highlighted samples. We did not observe any mode collapse for OT-GAN, even when training for many more epochs. 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Since generative", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "score": 1.0, + "content": "models can be trained on unlabeled data, which is almost endlessly available, they have enormous", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 461, + 320, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 320, + 473 + ], + "score": 1.0, + "content": "potential in the development of artificial intelligence.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5 + }, + { + "type": "text", + "bbox": [ + 107, + 478, + 505, + 544 + ], + "lines": [ + { + "bbox": [ + 106, + 477, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 490 + ], + "score": 1.0, + "content": "The central problem in generative modeling is how to train a generative model such that the distri-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 489, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 500 + ], + "score": 1.0, + "content": "bution of its generated data will match the distribution of the training data. 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A complication in using primal form optimal", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 637, + 506, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 506, + 650 + ], + "score": 1.0, + "content": "transport is that it may give biased gradients when used with mini-batches (see Bellemare et al.,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 649, + 428, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 428, + 660 + ], + "score": 1.0, + "content": "2017) and may therefore be inconsistent as a technique for statistical estimation.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 40.5 + }, + { + "type": "text", + "bbox": [ + 108, + 665, + 503, + 698 + ], + "lines": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "score": 1.0, + "content": "In this paper we present OT-GAN, a variant of generative adversarial nets incorporating primal form", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 676, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 504, + 689 + ], + "score": 1.0, + "content": "optimal transport into its critic. 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This metric, which we call mini-batch en-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 288, + 469, + 300 + ], + "spans": [ + { + "bbox": [ + 141, + 288, + 469, + 300 + ], + "score": 1.0, + "content": "ergy distance, combines optimal transport in primal form with an energy distance", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 298, + 470, + 311 + ], + "spans": [ + { + "bbox": [ + 141, + 298, + 470, + 311 + ], + "score": 1.0, + "content": "defined in an adversarially learned feature space, resulting in a highly discrimi-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 309, + 470, + 322 + ], + "spans": [ + { + "bbox": [ + 141, + 309, + 470, + 322 + ], + "score": 1.0, + "content": "native distance function with unbiased mini-batch gradients. Experimentally we", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 320, + 469, + 333 + ], + "spans": [ + { + "bbox": [ + 141, + 320, + 469, + 333 + ], + "score": 1.0, + "content": "show OT-GAN to be highly stable when trained with large mini-batches, and we", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 331, + 469, + 345 + ], + "spans": [ + { + "bbox": [ + 141, + 331, + 469, + 345 + ], + "score": 1.0, + "content": "present state-of-the-art results on several popular benchmark problems for image", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 344, + 189, + 353 + ], + "spans": [ + { + "bbox": [ + 141, + 344, + 189, + 353 + ], + "score": 1.0, + "content": "generation.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 18, + "bbox_fs": [ + 141, + 254, + 470, + 353 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 379, + 206, + 392 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 208, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 208, + 395 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 406, + 505, + 472 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "Generative modeling is a major sub-field of Machine Learning that studies the problem of how", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 416, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 416, + 505, + 430 + ], + "score": 1.0, + "content": "to learn models that generate images, audio, video, text or other data. Applications of generative", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 427, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 505, + 441 + ], + "score": 1.0, + "content": "models include image compression, generating speech from text, planning in reinforcement learn-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 439, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 505, + 451 + ], + "score": 1.0, + "content": "ing, semi-supervised and unsupervised representation learning, and many others. Since generative", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "score": 1.0, + "content": "models can be trained on unlabeled data, which is almost endlessly available, they have enormous", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 461, + 320, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 320, + 473 + ], + "score": 1.0, + "content": "potential in the development of artificial intelligence.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 406, + 505, + 473 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 478, + 505, + 544 + ], + "lines": [ + { + "bbox": [ + 106, + 477, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 505, + 490 + ], + "score": 1.0, + "content": "The central problem in generative modeling is how to train a generative model such that the distri-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 489, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 500 + ], + "score": 1.0, + "content": "bution of its generated data will match the distribution of the training data. Generative adversarial", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 500, + 506, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 512 + ], + "score": 1.0, + "content": "nets (GANs) represent an advance in solving this problem, using a neural network discriminator or", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 523 + ], + "score": 1.0, + "content": "critic to distinguish between generated data and training data. The critic defines a distance between", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 521, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 505, + 534 + ], + "score": 1.0, + "content": "the model distribution and the data distribution which the generative model can optimize to produce", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 533, + 308, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 308, + 545 + ], + "score": 1.0, + "content": "data that more closely resembles the training data.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 477, + 506, + 545 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 549, + 505, + 659 + ], + "lines": [ + { + "bbox": [ + 106, + 550, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 561 + ], + "score": 1.0, + "content": "A closely related approach to measuring the distance between the distributions of generated data", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 560, + 504, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 504, + 573 + ], + "score": 1.0, + "content": "and training data is provided by optimal transport theory. By framing the problem as optimally", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 570, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 506, + 586 + ], + "score": 1.0, + "content": "transporting one set of data points to another, it represents an alternative method of specifying a", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "metric over probability distributions and provides another objective for training generative models.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 593, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 605 + ], + "score": 1.0, + "content": "The dual problem of optimal transport is closely related to GANs, as discussed in the next section.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "score": 1.0, + "content": "However, the primal formulation of optimal transport has the advantage that it allows for closed", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "form solutions and can thus more easily be used to define tractable training objectives that can be", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 626, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 505, + 639 + ], + "score": 1.0, + "content": "evaluated in practice without making approximations. A complication in using primal form optimal", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 637, + 506, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 506, + 650 + ], + "score": 1.0, + "content": "transport is that it may give biased gradients when used with mini-batches (see Bellemare et al.,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 649, + 428, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 428, + 660 + ], + "score": 1.0, + "content": "2017) and may therefore be inconsistent as a technique for statistical estimation.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 550, + 506, + 660 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 665, + 503, + 698 + ], + "lines": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "score": 1.0, + "content": "In this paper we present OT-GAN, a variant of generative adversarial nets incorporating primal form", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 676, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 504, + 689 + ], + "score": 1.0, + "content": "optimal transport into its critic. 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This", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 465, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 465, + 105 + ], + "score": 1.0, + "content": "combination results in a highly discriminative metric with unbiased mini-batch gradients.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 110, + 505, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "In Section 2 we provide the preliminaries required to understand our work, and we put our con-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "score": 1.0, + "content": "tribution into context by discussing the relevant literature. 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Specifically,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 350, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 350, + 326, + 363 + ], + "score": 1.0, + "content": "they propose the Earth-Mover distance or Wasserstein-", + "type": "text" + }, + { + "bbox": [ + 326, + 351, + 332, + 360 + ], + "score": 0.29, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 350, + 505, + 363 + ], + "score": 1.0, + "content": "distance as a good objective for generative", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 360, + 150, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 150, + 374 + ], + "score": 1.0, + "content": "modeling:", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 371, + 385, + 390 + ], + "lines": [ + { + "bbox": [ + 225, + 371, + 385, + 390 + ], + "spans": [ + { + "bbox": [ + 225, + 371, + 385, + 390 + ], + "score": 0.94, + "content": "D _ { \\mathrm { E M D } } ( p , g ) = \\operatorname* { i n f } _ { \\gamma \\in \\Pi ( p , g ) } \\mathbb { E } _ { \\mathbf { x } , \\mathbf { y } \\sim \\gamma } c ( \\mathbf { x } , \\mathbf { y } ) ,", + "type": "interline_equation", + "image_path": "5b2537e553fe3a9ba555c237c26959fcb0ec30661f389bb77a11ae085eabc273.jpg" + } + ] + } + ], + "index": 22, + "virtual_lines": [ + { + "bbox": [ + 225, + 371, + 385, + 390 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 391, + 505, + 480 + ], + "lines": [ + { + "bbox": [ + 105, + 391, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 135, + 405 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 135, + 392, + 165, + 403 + ], + "score": 0.92, + "content": "\\Pi ( p , g )", + "type": "inline_equation" + }, + { + "bbox": [ + 166, + 391, + 312, + 405 + ], + "score": 1.0, + "content": "is the set of all joint distributions", + "type": "text" + }, + { + "bbox": [ + 312, + 392, + 343, + 403 + ], + "score": 0.93, + "content": "\\gamma ( \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 391, + 410, + 405 + ], + "score": 1.0, + "content": "with marginals", + "type": "text" + }, + { + "bbox": [ + 411, + 392, + 454, + 403 + ], + "score": 0.92, + "content": "p ( \\mathbf { x } ) , g ( \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 391, + 505, + 405 + ], + "score": 1.0, + "content": ", and where", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 402, + 504, + 415 + ], + "spans": [ + { + "bbox": [ + 107, + 403, + 136, + 414 + ], + "score": 0.91, + "content": "c ( \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 402, + 483, + 415 + ], + "score": 1.0, + "content": "is a cost function that Arjovsky et al. 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If the", + "type": "text" + }, + { + "bbox": [ + 484, + 402, + 504, + 415 + ], + "score": 0.9, + "content": "p ( \\mathbf { x } )", + "type": "inline_equation" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 414, + 504, + 426 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 123, + 426 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 123, + 414, + 144, + 426 + ], + "score": 0.9, + "content": "g ( \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 414, + 428, + 426 + ], + "score": 1.0, + "content": "distributions are interpreted as piles of earth, the Earth-Mover distance", + "type": "text" + }, + { + "bbox": [ + 428, + 414, + 475, + 426 + ], + "score": 0.93, + "content": "D _ { \\mathrm { E M D } } ( p , g )", + "type": "inline_equation" + }, + { + "bbox": [ + 476, + 414, + 504, + 426 + ], + "score": 1.0, + "content": "can be", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 425, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 312, + 437 + ], + "score": 1.0, + "content": "interpreted as the minimum amount of “mass” that", + "type": "text" + }, + { + "bbox": [ + 312, + 426, + 319, + 436 + ], + "score": 0.83, + "content": "\\gamma", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 425, + 505, + 437 + ], + "score": 1.0, + "content": "has to transport to turn the generator distribu-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 124, + 448 + ], + "score": 1.0, + "content": "tion", + "type": "text" + }, + { + "bbox": [ + 124, + 436, + 144, + 448 + ], + "score": 0.91, + "content": "g ( \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 145, + 436, + 244, + 448 + ], + "score": 1.0, + "content": "into the data distribution", + "type": "text" + }, + { + "bbox": [ + 245, + 435, + 264, + 447 + ], + "score": 0.9, + "content": "p ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 436, + 377, + 448 + ], + "score": 1.0, + "content": ". 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The optimization with respect to the critic cannot be", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 104, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 104, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "performed perfectly, and the class of obtainable critics only very roughly corresponds to the class", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "of 1-Lipschitz functions. The connection between GANs and dual form optimal transport is further", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 671, + 506, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 506, + 683 + ], + "score": 1.0, + "content": "explored by Bousquet et al. (2017) and Genevay et al. 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Consequently, Genevay et al. (2017b) call their method of using Equation 5", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 278, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 278, + 267 + ], + "score": 1.0, + "content": "in generative modeling Sinkhorn AutoDiff.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 505, + 349 + ], + "lines": [ + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "score": 1.0, + "content": "The great advantage of this mini-batch Sinkhorn distance is that it is fully tractable, eliminating the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "instabilities often experienced with GANs due to imperfect optimization of the critic. However, a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 293, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 506, + 306 + ], + "score": 1.0, + "content": "disadvantage is that the expectation of Equation 5 over mini-batches is no longer a valid metric over", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 104, + 304, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 104, + 304, + 506, + 317 + ], + "score": 1.0, + "content": "probability distributions. Viewed another way, the gradients of Equation 5, for fixed mini-batch size,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 314, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 104, + 314, + 505, + 328 + ], + "score": 1.0, + "content": "are not unbiased estimators of the gradients of our original optimal transport problem in Equation 4.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 325, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 505, + 339 + ], + "score": 1.0, + "content": "For this reason, Bellemare et al. 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Although our work was performed concurrently to that by Genevay", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 434, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 505, + 445 + ], + "score": 1.0, + "content": "et al. (2017b) and Bellemare et al. (2017), it can be understood most easily as forming a synthesis", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 444, + 340, + 456 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 340, + 456 + ], + "score": 1.0, + "content": "of the ideas used in Sinkhorn AutoDiff and Cramer GAN.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27.5 + }, + { + "type": "title", + "bbox": [ + 107, + 471, + 294, + 484 + ], + "lines": [ + { + "bbox": [ + 104, + 469, + 295, + 486 + ], + "spans": [ + { + "bbox": [ + 104, + 469, + 295, + 486 + ], + "score": 1.0, + "content": "3 MINI-BATCH ENERGY DISTANCE", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 106, + 495, + 505, + 640 + ], + "lines": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "score": 1.0, + "content": "As discussed in the last section, most previous work in generative modeling can be interpreted as", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 507, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 196, + 520 + ], + "score": 1.0, + "content": "minimizing a distance", + "type": "text" + }, + { + "bbox": [ + 196, + 507, + 228, + 519 + ], + "score": 0.93, + "content": "D ( g , p )", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 507, + 361, + 520 + ], + "score": 1.0, + "content": "between a generator distribution", + "type": "text" + }, + { + "bbox": [ + 361, + 507, + 381, + 519 + ], + "score": 0.92, + "content": "g ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 507, + 481, + 520 + ], + "score": 1.0, + "content": "and the data distribution", + "type": "text" + }, + { + "bbox": [ + 482, + 507, + 501, + 519 + ], + "score": 0.9, + "content": "p ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 507, + 505, + 520 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 518, + 504, + 530 + ], + "spans": [ + { + "bbox": [ + 106, + 518, + 327, + 530 + ], + "score": 1.0, + "content": "where the distributions are defined over a single vector", + "type": "text" + }, + { + "bbox": [ + 327, + 520, + 335, + 528 + ], + "score": 0.57, + "content": "\\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 518, + 504, + 530 + ], + "score": 1.0, + "content": "which we here take to be an image. How-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 529, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 406, + 541 + ], + "score": 1.0, + "content": "ever, in practice deep learning typically works with mini-batches of images", + "type": "text" + }, + { + "bbox": [ + 406, + 529, + 416, + 540 + ], + "score": 0.37, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 529, + 505, + 541 + ], + "score": 1.0, + "content": "rather than individual", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "score": 1.0, + "content": "images. 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The central insight of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "score": 1.0, + "content": "Mini-batch GAN (Salimans et al., 2016) is that it is strictly more powerful to work with the distri-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 213, + 596 + ], + "score": 1.0, + "content": "butions over mini-batches", + "type": "text" + }, + { + "bbox": [ + 213, + 584, + 261, + 596 + ], + "score": 0.93, + "content": "g ( \\mathbf { X } ) , p ( \\mathbf { X } )", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "than with the distributions over individual images. 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How-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 529, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 406, + 541 + ], + "score": 1.0, + "content": "ever, in practice deep learning typically works with mini-batches of images", + "type": "text" + }, + { + "bbox": [ + 406, + 529, + 416, + 540 + ], + "score": 0.37, + "content": "\\mathbf { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 529, + 505, + 541 + ], + "score": 1.0, + "content": "rather than individual", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "score": 1.0, + "content": "images. 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The central insight of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "score": 1.0, + "content": "Mini-batch GAN (Salimans et al., 2016) is that it is strictly more powerful to work with the distri-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 213, + 596 + ], + "score": 1.0, + "content": "butions over mini-batches", + "type": "text" + }, + { + "bbox": [ + 213, + 584, + 261, + 596 + ], + "score": 0.93, + "content": "g ( \\mathbf { X } ) , p ( \\mathbf { X } )", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "than with the distributions over individual images. Here we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 593, + 504, + 609 + ], + "spans": [ + { + "bbox": [ + 104, + 593, + 441, + 609 + ], + "score": 1.0, + "content": "further pursue this insight and propose a new distance over mini-batch distributions", + "type": "text" + }, + { + "bbox": [ + 442, + 595, + 504, + 607 + ], + "score": 0.92, + "content": "\\bar { D [ { g ( \\mathbf { X } ) , p ( \\mathbf { X } ) } ] }", + "type": "inline_equation" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 619 + ], + "score": 1.0, + "content": "which we call the Mini-batch Energy Distance. This new distance combines optimal transport in", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 616, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 506, + 630 + ], + "score": 1.0, + "content": "primal form with an energy distance defined in an adversarially learned feature space, resulting in a", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 627, + 409, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 409, + 641 + ], + "score": 1.0, + "content": "highly discriminative distance function with unbiased mini-batch gradients.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 37, + "bbox_fs": [ + 104, + 495, + 506, + 641 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 644, + 505, + 677 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "In order to derive our new distance function, we start by generalizing the energy distance given in", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 654, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 329, + 669 + ], + "score": 1.0, + "content": "Equation 6 to general non-Euclidean distance functions", + "type": "text" + }, + { + "bbox": [ + 329, + 657, + 335, + 665 + ], + "score": 0.81, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 654, + 505, + 669 + ], + "score": 1.0, + "content": ". Doing so gives us the generalized energy", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 666, + 146, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 146, + 680 + ], + "score": 1.0, + "content": "distance:", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 644, + 505, + 680 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 179, + 675, + 431, + 696 + ], + "lines": [ + { + "bbox": [ + 179, + 675, + 431, + 696 + ], + "spans": [ + { + "bbox": [ + 179, + 675, + 431, + 696 + ], + "score": 0.93, + "content": "D _ { \\mathtt { G E D } } ( p , g ) = { \\sqrt { 2 \\mathbb { E } [ d ( \\mathbf { X } , \\mathbf { Y } ) ] - \\mathbb { E } [ d ( \\mathbf { X } , \\mathbf { X } ^ { \\prime } ) ] - \\mathbb { E } [ d ( \\mathbf { Y } , \\mathbf { Y } ^ { \\prime } ) ] } } ,", + "type": "interline_equation", + "image_path": "3fe32891ca4c06790481cf033894725a497c07ca6cfca96730273a91ef8fa26f.jpg" + } + ] + } + ], + "index": 47, + "virtual_lines": [ + { + "bbox": [ + 179, + 675, + 431, + 696 + ], + "spans": [], + "index": 47 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 698, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 696, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 696, + 133, + 713 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 698, + 159, + 710 + ], + "score": 0.84, + "content": "\\mathbf { X } , \\mathbf { X } ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 696, + 333, + 713 + ], + "score": 1.0, + "content": "are independent samples from distribution", + "type": "text" + }, + { + "bbox": [ + 333, + 701, + 340, + 710 + ], + "score": 0.77, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 696, + 358, + 713 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 358, + 698, + 385, + 710 + ], + "score": 0.86, + "content": "\\mathbf { Y } , \\mathbf { Y } ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 385, + 696, + 495, + 713 + ], + "score": 1.0, + "content": "independent samples from", + "type": "text" + }, + { + "bbox": [ + 495, + 702, + 501, + 711 + ], + "score": 0.73, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 696, + 505, + 713 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "score": 1.0, + "content": "This distance is typically defined for individual samples, but it is valid for general random objects,", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 380, + 733 + ], + "score": 1.0, + "content": "including mini-batches like we assume here. The energy distance", + "type": "text" + }, + { + "bbox": [ + 381, + 720, + 427, + 732 + ], + "score": 0.95, + "content": "D _ { \\mathrm { G E D } } ( \\bar { p } , g )", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "is a metric, in the", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 321, + 95 + ], + "score": 1.0, + "content": "mathematical sense, as long as the distance function", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 322, + 83, + 329, + 92 + ], + "score": 0.78, + "content": "d", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 329, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "is a metric (Klebanov et al., 2005). Under", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 221, + 106 + ], + "score": 1.0, + "content": "this condition, meaning that", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 221, + 94, + 227, + 104 + ], + "score": 0.81, + "content": "d", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 228, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "satisfies the triangle inequality and several other conditions, we have", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 330, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 124, + 118 + ], + "score": 1.0, + "content": "that", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 124, + 104, + 174, + 117 + ], + "score": 0.93, + "content": "D ( p , g ) \\geq 0", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 174, + 103, + 195, + 118 + ], + "score": 1.0, + "content": ", and", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 195, + 104, + 245, + 117 + ], + "score": 0.93, + "content": "\\bar { D } ( p , g ) = 0", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 246, + 103, + 300, + 118 + ], + "score": 1.0, + "content": "if and only if", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 300, + 106, + 325, + 116 + ], + "score": 0.9, + "content": "p = g", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 326, + 103, + 330, + 118 + ], + "score": 1.0, + "content": ".", + "type": "text", + "cross_page": true + } + ], + "index": 2 + } + ], + "index": 49, + "bbox_fs": [ + 105, + 696, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 117 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 321, + 95 + ], + "score": 1.0, + "content": "mathematical sense, as long as the distance function", + "type": "text" + }, + { + "bbox": [ + 322, + 83, + 329, + 92 + ], + "score": 0.78, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "is a metric (Klebanov et al., 2005). Under", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 221, + 106 + ], + "score": 1.0, + "content": "this condition, meaning that", + "type": "text" + }, + { + "bbox": [ + 221, + 94, + 227, + 104 + ], + "score": 0.81, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "satisfies the triangle inequality and several other conditions, we have", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 330, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 124, + 118 + ], + "score": 1.0, + "content": "that", + "type": "text" + }, + { + "bbox": [ + 124, + 104, + 174, + 117 + ], + "score": 0.93, + "content": "D ( p , g ) \\geq 0", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 103, + 195, + 118 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 195, + 104, + 245, + 117 + ], + "score": 0.93, + "content": "\\bar { D } ( p , g ) = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 103, + 300, + 118 + ], + "score": 1.0, + "content": "if and only if", + "type": "text" + }, + { + "bbox": [ + 300, + 106, + 325, + 116 + ], + "score": 0.9, + "content": "p = g", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 103, + 330, + 118 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 177 + ], + "lines": [ + { + "bbox": [ + 106, + 121, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 212, + 133 + ], + "score": 1.0, + "content": "Using individual samples", + "type": "text" + }, + { + "bbox": [ + 212, + 123, + 231, + 133 + ], + "score": 0.72, + "content": "\\mathbf x , \\mathbf y", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 122, + 326, + 133 + ], + "score": 1.0, + "content": "instead of minibatches", + "type": "text" + }, + { + "bbox": [ + 327, + 121, + 350, + 133 + ], + "score": 0.79, + "content": "\\mathbf { X } , \\mathbf { Y }", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 122, + 505, + 133 + ], + "score": 1.0, + "content": ", Sejdinovic et al. (2013) showed that", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 506, + 145 + ], + "score": 1.0, + "content": "such generalizations of the energy distance can equivalently be viewed as a form of maximum mean", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 143, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 255, + 155 + ], + "score": 1.0, + "content": "discrepancy, where the MMD kernel", + "type": "text" + }, + { + "bbox": [ + 255, + 144, + 262, + 153 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 144, + 397, + 155 + ], + "score": 1.0, + "content": "is related to the distance function", + "type": "text" + }, + { + "bbox": [ + 397, + 144, + 404, + 154 + ], + "score": 0.78, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 144, + 417, + 155 + ], + "score": 1.0, + "content": "by", + "type": "text" + }, + { + "bbox": [ + 418, + 143, + 505, + 155 + ], + "score": 0.92, + "content": "d ( { \\bf x } , { \\bf x } ^ { \\prime } ) \\equiv k ( { \\bf x } , { \\bf x } ) +", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 154, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 154, + 190, + 166 + ], + "score": 0.92, + "content": "k ( \\mathbf { x } ^ { \\prime } , \\mathbf { \\bar { x } } ^ { \\prime } ) - 2 k ( \\mathbf { x } , \\mathbf { x } ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 154, + 506, + 167 + ], + "score": 1.0, + "content": ". We find the energy distance perspective more intuitive here and follow Cramer", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 262, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 262, + 178 + ], + "score": 1.0, + "content": "GAN in using this perspective instead.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 181, + 505, + 259 + ], + "lines": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 182, + 244, + 194 + ], + "score": 1.0, + "content": "We are free to choose any metric", + "type": "text" + }, + { + "bbox": [ + 245, + 183, + 252, + 192 + ], + "score": 0.79, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 182, + 505, + 194 + ], + "score": 1.0, + "content": "for use in Equation 7, but not all choices will be equally dis-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 376, + 205 + ], + "score": 1.0, + "content": "criminative when used for generative modeling. Here, we choose", + "type": "text" + }, + { + "bbox": [ + 377, + 194, + 384, + 203 + ], + "score": 0.77, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 193, + 505, + 205 + ], + "score": 1.0, + "content": "to be the entropy-regularized", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 203, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 505, + 217 + ], + "score": 1.0, + "content": "Wasserstein distance, or Sinkhorn distance, as defined for mini-batches in Equation 5. Although", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 215, + 505, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 227 + ], + "score": 1.0, + "content": "the average over mini-batch Sinkhorn distances is not a valid metric over probability distributions", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 226, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 122, + 238 + ], + "score": 0.85, + "content": "p , g", + "type": "inline_equation" + }, + { + "bbox": [ + 123, + 226, + 506, + 239 + ], + "score": 1.0, + "content": ", resulting in the biased gradients problem discussed in Section 2, the Sinkhorn distance is a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 237, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 506, + 249 + ], + "score": 1.0, + "content": "valid metric between individual mini-batches, which is all we require for use inside the generalized", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 249, + 174, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 174, + 260 + ], + "score": 1.0, + "content": "energy distance.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 505, + 298 + ], + "lines": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "Putting everything together, we arrive at our final distance function over distributions, which we call", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 275, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 505, + 288 + ], + "score": 1.0, + "content": "the Minibatch Energy Distance. 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(2018) independently propose a very similar loss function to (8),", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 455, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 469 + ], + "score": 1.0, + "content": "but using a single sample from the data and generator distributions. We obtained best results using", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 468, + 362, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 362, + 480 + ], + "score": 1.0, + "content": "two independently sampled minibatches from each distribution.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30 + }, + { + "type": "title", + "bbox": [ + 107, + 494, + 331, + 508 + ], + "lines": [ + { + "bbox": [ + 104, + 492, + 331, + 512 + ], + "spans": [ + { + "bbox": [ + 104, + 492, + 331, + 512 + ], + "score": 1.0, + "content": "4 OPTIMAL TRANSPORT GAN (OT-GAN)", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 106, + 520, + 505, + 663 + ], + "lines": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "score": 1.0, + "content": "In the last section we defined the mini-batch energy distance which we propose using for training", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 531, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 409, + 545 + ], + "score": 1.0, + "content": "generative models. However, we left undefined the transport cost function", + "type": "text" + }, + { + "bbox": [ + 410, + 532, + 439, + 544 + ], + "score": 0.92, + "content": "c ( \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 531, + 506, + 545 + ], + "score": 1.0, + "content": "on which it de-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 542, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 104, + 542, + 279, + 556 + ], + "score": 1.0, + "content": "pends. One possibility would be to choose", + "type": "text" + }, + { + "bbox": [ + 280, + 545, + 286, + 552 + ], + "score": 0.7, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 542, + 506, + 556 + ], + "score": 1.0, + "content": "to be some fixed function over vectors, like Euclidean", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 552, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 568 + ], + "score": 1.0, + "content": "distance, but we found this to perform poorly in preliminary experiments. 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Here we choose", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 49.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 8 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 117 + ], + "lines": [], + "index": 1, + "bbox_fs": [ + 105, + 82, + 505, + 118 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 177 + ], + "lines": [ + { + "bbox": [ + 106, + 121, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 212, + 133 + ], + "score": 1.0, + "content": "Using individual samples", + "type": "text" + }, + { + "bbox": [ + 212, + 123, + 231, + 133 + ], + "score": 0.72, + "content": "\\mathbf x , \\mathbf y", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 122, + 326, + 133 + ], + "score": 1.0, + "content": "instead of minibatches", + "type": "text" + }, + { + "bbox": [ + 327, + 121, + 350, + 133 + ], + "score": 0.79, + "content": "\\mathbf { X } , \\mathbf { Y }", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 122, + 505, + 133 + ], + "score": 1.0, + "content": ", Sejdinovic et al. (2013) showed that", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 506, + 145 + ], + "score": 1.0, + "content": "such generalizations of the energy distance can equivalently be viewed as a form of maximum mean", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 143, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 255, + 155 + ], + "score": 1.0, + "content": "discrepancy, where the MMD kernel", + "type": "text" + }, + { + "bbox": [ + 255, + 144, + 262, + 153 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 144, + 397, + 155 + ], + "score": 1.0, + "content": "is related to the distance function", + "type": "text" + }, + { + "bbox": [ + 397, + 144, + 404, + 154 + ], + "score": 0.78, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 144, + 417, + 155 + ], + "score": 1.0, + "content": "by", + "type": "text" + }, + { + "bbox": [ + 418, + 143, + 505, + 155 + ], + "score": 0.92, + "content": "d ( { \\bf x } , { \\bf x } ^ { \\prime } ) \\equiv k ( { \\bf x } , { \\bf x } ) +", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 154, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 154, + 190, + 166 + ], + "score": 0.92, + "content": "k ( \\mathbf { x } ^ { \\prime } , \\mathbf { \\bar { x } } ^ { \\prime } ) - 2 k ( \\mathbf { x } , \\mathbf { x } ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 154, + 506, + 167 + ], + "score": 1.0, + "content": ". We find the energy distance perspective more intuitive here and follow Cramer", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 262, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 262, + 178 + ], + "score": 1.0, + "content": "GAN in using this perspective instead.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 121, + 506, + 178 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 181, + 505, + 259 + ], + "lines": [ + { + "bbox": [ + 106, + 182, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 182, + 244, + 194 + ], + "score": 1.0, + "content": "We are free to choose any metric", + "type": "text" + }, + { + "bbox": [ + 245, + 183, + 252, + 192 + ], + "score": 0.79, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 182, + 505, + 194 + ], + "score": 1.0, + "content": "for use in Equation 7, but not all choices will be equally dis-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 376, + 205 + ], + "score": 1.0, + "content": "criminative when used for generative modeling. Here, we choose", + "type": "text" + }, + { + "bbox": [ + 377, + 194, + 384, + 203 + ], + "score": 0.77, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 193, + 505, + 205 + ], + "score": 1.0, + "content": "to be the entropy-regularized", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 203, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 505, + 217 + ], + "score": 1.0, + "content": "Wasserstein distance, or Sinkhorn distance, as defined for mini-batches in Equation 5. Although", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 215, + 505, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 227 + ], + "score": 1.0, + "content": "the average over mini-batch Sinkhorn distances is not a valid metric over probability distributions", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 226, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 228, + 122, + 238 + ], + "score": 0.85, + "content": "p , g", + "type": "inline_equation" + }, + { + "bbox": [ + 123, + 226, + 506, + 239 + ], + "score": 1.0, + "content": ", resulting in the biased gradients problem discussed in Section 2, the Sinkhorn distance is a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 237, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 506, + 249 + ], + "score": 1.0, + "content": "valid metric between individual mini-batches, which is all we require for use inside the generalized", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 249, + 174, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 174, + 260 + ], + "score": 1.0, + "content": "energy distance.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 182, + 506, + 260 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 505, + 298 + ], + "lines": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "Putting everything together, we arrive at our final distance function over distributions, which we call", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 275, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 505, + 288 + ], + "score": 1.0, + "content": "the Minibatch Energy Distance. 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Like with", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "score": 1.0, + "content": "the energy distance used by Cramer GAN, this is what makes the resulting mini-batch gradients", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 395, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 505, + 408 + ], + "score": 1.0, + "content": "unbiased and the objective statistically consistent. However, unlike the plain energy distance, the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 405, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 104, + 405, + 219, + 421 + ], + "score": 1.0, + "content": "mini-batch energy distance", + "type": "text" + }, + { + "bbox": [ + 219, + 406, + 266, + 418 + ], + "score": 0.93, + "content": "D _ { \\mathrm { M E D } } ^ { 2 } ( p , \\bar { g } )", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 405, + 506, + 421 + ], + "score": 1.0, + "content": "still incorporates the primal form optimal transport of the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 416, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 505, + 430 + ], + "score": 1.0, + "content": "Sinkhorn distance, which in Section 5 we show leads to much stronger discriminative power and", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 428, + 241, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 241, + 442 + ], + "score": 1.0, + "content": "more stable generative modeling.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25, + "bbox_fs": [ + 104, + 362, + 506, + 442 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 505, + 479 + ], + "lines": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "score": 1.0, + "content": "In concurrent work, Genevay et al. (2018) independently propose a very similar loss function to (8),", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 455, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 469 + ], + "score": 1.0, + "content": "but using a single sample from the data and generator distributions. We obtained best results using", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 468, + 362, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 362, + 480 + ], + "score": 1.0, + "content": "two independently sampled minibatches from each distribution.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 445, + 505, + 480 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 494, + 331, + 508 + ], + "lines": [ + { + "bbox": [ + 104, + 492, + 331, + 512 + ], + "spans": [ + { + "bbox": [ + 104, + 492, + 331, + 512 + ], + "score": 1.0, + "content": "4 OPTIMAL TRANSPORT GAN (OT-GAN)", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 106, + 520, + 505, + 663 + ], + "lines": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 505, + 534 + ], + "score": 1.0, + "content": "In the last section we defined the mini-batch energy distance which we propose using for training", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 531, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 409, + 545 + ], + "score": 1.0, + "content": "generative models. However, we left undefined the transport cost function", + "type": "text" + }, + { + "bbox": [ + 410, + 532, + 439, + 544 + ], + "score": 0.92, + "content": "c ( \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 531, + 506, + 545 + ], + "score": 1.0, + "content": "on which it de-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 542, + 506, + 556 + ], + "spans": [ + { + "bbox": [ + 104, + 542, + 279, + 556 + ], + "score": 1.0, + "content": "pends. One possibility would be to choose", + "type": "text" + }, + { + "bbox": [ + 280, + 545, + 286, + 552 + ], + "score": 0.7, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 542, + 506, + 556 + ], + "score": 1.0, + "content": "to be some fixed function over vectors, like Euclidean", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 552, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 568 + ], + "score": 1.0, + "content": "distance, but we found this to perform poorly in preliminary experiments. Although minimizing", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 561, + 507, + 581 + ], + "spans": [ + { + "bbox": [ + 104, + 561, + 231, + 581 + ], + "score": 1.0, + "content": "the mini-batch energy distance", + "type": "text" + }, + { + "bbox": [ + 232, + 564, + 285, + 577 + ], + "score": 0.93, + "content": "\\bar { D } _ { M E D } ^ { 2 } ( \\bar { p } , g )", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 561, + 507, + 581 + ], + "score": 1.0, + "content": "guarantees statistical consistency for simple fixed cost", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 574, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 146, + 588 + ], + "score": 1.0, + "content": "functions", + "type": "text" + }, + { + "bbox": [ + 147, + 577, + 153, + 585 + ], + "score": 0.67, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 574, + 505, + 588 + ], + "score": 1.0, + "content": "like Euclidean distance, the resulting statistical efficiency is generally poor in high di-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 587, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 454, + 599 + ], + "score": 1.0, + "content": "mensions. This means that there typically exist many bad distributions distributions", + "type": "text" + }, + { + "bbox": [ + 454, + 588, + 461, + 598 + ], + "score": 0.79, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 587, + 505, + 599 + ], + "score": 1.0, + "content": "for which", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 596, + 507, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 597, + 160, + 610 + ], + "score": 0.93, + "content": "D _ { M E D } ^ { 2 } ( p , g )", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 596, + 318, + 612 + ], + "score": 1.0, + "content": "is so close to zero that we cannot tell", + "type": "text" + }, + { + "bbox": [ + 319, + 599, + 326, + 609 + ], + "score": 0.8, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 596, + 345, + 612 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 345, + 599, + 352, + 609 + ], + "score": 0.78, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 596, + 507, + 612 + ], + "score": 1.0, + "content": "apart without requiring an enormous", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 608, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 506, + 622 + ], + "score": 1.0, + "content": "sample size. To solve this we propose learning the cost function adversarially, so that it can adapt to", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 619, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 209, + 632 + ], + "score": 1.0, + "content": "the generator distribution", + "type": "text" + }, + { + "bbox": [ + 209, + 621, + 216, + 631 + ], + "score": 0.8, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 619, + 505, + 632 + ], + "score": 1.0, + "content": "and thereby become more discriminative. In practice we implement this", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 630, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 630, + 154, + 644 + ], + "score": 1.0, + "content": "by defining", + "type": "text" + }, + { + "bbox": [ + 154, + 633, + 160, + 640 + ], + "score": 0.72, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 630, + 329, + 644 + ], + "score": 1.0, + "content": "to be the cosine distance between vectors", + "type": "text" + }, + { + "bbox": [ + 329, + 631, + 353, + 642 + ], + "score": 0.92, + "content": "v _ { \\eta } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 630, + 372, + 644 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 372, + 631, + 396, + 643 + ], + "score": 0.91, + "content": "v _ { \\eta } ( \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 630, + 427, + 644 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 428, + 632, + 439, + 642 + ], + "score": 0.86, + "content": "v _ { \\eta }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 630, + 505, + 644 + ], + "score": 1.0, + "content": "is a deep neural", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 641, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 506, + 654 + ], + "score": 1.0, + "content": "network that maps the images in our mini-batch into a learned latent space. That is we define the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 653, + 185, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 653, + 185, + 664 + ], + "score": 1.0, + "content": "transport cost to be", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 39, + "bbox_fs": [ + 104, + 519, + 507, + 664 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 232, + 662, + 378, + 690 + ], + "lines": [ + { + "bbox": [ + 232, + 662, + 378, + 690 + ], + "spans": [ + { + "bbox": [ + 232, + 662, + 378, + 690 + ], + "score": 0.95, + "content": "c _ { \\eta } ( \\mathbf x , \\mathbf y ) = 1 - \\frac { v _ { \\eta } ( \\mathbf x ) \\cdot v _ { \\eta } ( \\mathbf y ) } { \\| v _ { \\eta } ( \\mathbf x ) \\| _ { 2 } \\| v _ { \\eta } ( \\mathbf y ) \\| _ { 2 } } ,", + "type": "interline_equation", + "image_path": "cf88758a29e8032ac3e154ad749a606988d6ef49661782d14f28df9658d17a8b.jpg" + } + ] + } + ], + "index": 46.5, + "virtual_lines": [ + { + "bbox": [ + 232, + 662, + 378, + 676.0 + ], + "spans": [], + "index": 46 + }, + { + "bbox": [ + 232, + 676.0, + 378, + 690.0 + ], + "spans": [], + "index": 47 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 693, + 398, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 691, + 399, + 707 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 177, + 707 + ], + "score": 1.0, + "content": "where we choose", + "type": "text" + }, + { + "bbox": [ + 178, + 695, + 184, + 704 + ], + "score": 0.79, + "content": "\\eta", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 691, + 399, + 707 + ], + "score": 1.0, + "content": "to maximize the resulting minibatch energy distance.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 48, + "bbox_fs": [ + 106, + 691, + 399, + 707 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 709, + 506, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 276, + 722 + ], + "score": 1.0, + "content": "In practice, training our generative model", + "type": "text" + }, + { + "bbox": [ + 276, + 711, + 286, + 721 + ], + "score": 0.82, + "content": "g _ { \\boldsymbol { \\theta } }", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 709, + 425, + 722 + ], + "score": 1.0, + "content": "and our adversarial transport cost", + "type": "text" + }, + { + "bbox": [ + 425, + 712, + 435, + 722 + ], + "score": 0.85, + "content": "c _ { \\eta }", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "is done by alter-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "nating gradient descent as is standard practice in GANs (Goodfellow et al., 2014). Here we choose", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "to update the generator more often than we update our critic. This is contrary to standard practice", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 333, + 106 + ], + "score": 1.0, + "content": "(e.g. Arjovsky et al., 2017) and ensures our cost function", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 333, + 96, + 339, + 104 + ], + "score": 0.59, + "content": "c", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 340, + 93, + 466, + 106 + ], + "score": 1.0, + "content": "does not become degenerate. If", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 466, + 95, + 472, + 104 + ], + "score": 0.64, + "content": "c", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 473, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "were to", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "score": 1.0, + "content": "assign zero transport cost to two non-identical regions in image space, the generator would quickly", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "adjust to take advantage of this. Similar to how a quickly adapting critic controls the generator", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "score": 1.0, + "content": "in standard GANs, this works the other way around in our case. Contrary to standard GANs, our", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "generator has a well defined and statistically consistent training objective even when the critic is", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 276, + 161 + ], + "score": 1.0, + "content": "not updated, as long as the cost function", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 277, + 151, + 283, + 158 + ], + "score": 0.68, + "content": "c", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 283, + 148, + 481, + 161 + ], + "score": 1.0, + "content": "is not degenerate. 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(2017), thereby ensuring", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 469, + 162, + 475, + 169 + ], + "score": 0.48, + "content": "c", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 475, + 159, + 505, + 172 + ], + "score": 1.0, + "content": "cannot", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 430, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 430, + 183 + ], + "score": 1.0, + "content": "degenerate, but this proved unnecessary if the generator is updated often enough.", + "type": "text", + "cross_page": true + } + ], + "index": 8 + } + ], + "index": 49.5, + "bbox_fs": [ + 105, + 709, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 182 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "to update the generator more often than we update our critic. This is contrary to standard practice", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 333, + 106 + ], + "score": 1.0, + "content": "(e.g. Arjovsky et al., 2017) and ensures our cost function", + "type": "text" + }, + { + "bbox": [ + 333, + 96, + 339, + 104 + ], + "score": 0.59, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 93, + 466, + 106 + ], + "score": 1.0, + "content": "does not become degenerate. 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Contrary to standard GANs, our", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 506, + 150 + ], + "score": 1.0, + "content": "generator has a well defined and statistically consistent training objective even when the critic is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 276, + 161 + ], + "score": 1.0, + "content": "not updated, as long as the cost function", + "type": "text" + }, + { + "bbox": [ + 277, + 151, + 283, + 158 + ], + "score": 0.68, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 283, + 148, + 481, + 161 + ], + "score": 1.0, + "content": "is not degenerate. 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(2017), thereby ensuring", + "type": "text" + }, + { + "bbox": [ + 469, + 162, + 475, + 169 + ], + "score": 0.48, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 159, + 505, + 172 + ], + "score": 1.0, + "content": "cannot", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 430, + 183 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 430, + 183 + ], + "score": 1.0, + "content": "degenerate, but this proved unnecessary if the generator is updated often enough.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 187, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 106, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 106, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "Our full training procedure is described in Algorithm 1, and is visually depicted in Figure 1. Here we", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 224, + 212 + ], + "score": 1.0, + "content": "compute the matching matrix", + "type": "text" + }, + { + "bbox": [ + 224, + 198, + 236, + 208 + ], + "score": 0.63, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 236, + 198, + 246, + 212 + ], + "score": 1.0, + "content": "in", + "type": "text" + }, + { + "bbox": [ + 247, + 198, + 263, + 209 + ], + "score": 0.9, + "content": "{ \\mathcal { W } } _ { c }", + "type": "inline_equation" + }, + { + "bbox": [ + 263, + 198, + 505, + 212 + ], + "score": 1.0, + "content": "using the Sinkhorn algorithm. Unlike Genevay et al. (2017b)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "we do not backpropagate through this algorithm. 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As shown in Figure 2, mode collapse occurs", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "in a mini-batch feature GAN after a few thousand iterations training with a fixed discriminator.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "score": 1.0, + "content": "However, using the mini-batch energy distance, the generator does not diverge and the generated", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 326, + 279, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 279, + 338 + ], + "score": 1.0, + "content": "samples still cover all 8 modes of the data.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 11.5 + }, + { + "type": "image", + "bbox": [ + 126, + 347, + 484, + 435 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 126, + 347, + 484, + 435 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 126, + 347, + 484, + 435 + ], + "spans": [ + { + "bbox": [ + 126, + 347, + 484, + 435 + ], + "score": 0.813, + "type": "image", + "image_path": "1687b47c7688836cb6bf32cf7cfdd10ff315315751109cb91d4da734f7b693bc.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 126, + 347, + 484, + 376.3333333333333 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 126, + 376.3333333333333, + 484, + 405.66666666666663 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 126, + 405.66666666666663, + 484, + 434.99999999999994 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 442, + 505, + 497 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 442, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 505, + 454 + ], + "score": 1.0, + "content": "Figure 2: Results for consistency when fixing the critic on data generated from 8 Gaussian mixtures.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "The first column shows the data distribution. The top row shows the training results of OT-GAN", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "using mini-batch energy distance. The bottom row shows the training result with the original GAN", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "loss (DAN-S). The latter collapses to 3 out of 8 modes after fixing the discriminator, while OT-GAN", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 487, + 185, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 185, + 497 + ], + "score": 1.0, + "content": "remains consistent.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + } + ], + "index": 23.0 + }, + { + "type": "title", + "bbox": [ + 107, + 507, + 178, + 519 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 179, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 179, + 521 + ], + "score": 1.0, + "content": "5.2 CIFAR-10", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 105, + 527, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 268, + 541 + ], + "score": 1.0, + "content": "CIFAR-10 is a well-studied dataset of", + "type": "text" + }, + { + "bbox": [ + 269, + 528, + 298, + 539 + ], + "score": 0.88, + "content": "3 2 \\times 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 527, + 505, + 541 + ], + "score": 1.0, + "content": "color images for generative models (Krizhevsky,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "score": 1.0, + "content": "2009). We use this data set to investigate the importance of the different design decisions made", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "with OT-GAN, and we compare the visual quality of its generated samples with other state-of-the-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 561, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 504, + 574 + ], + "score": 1.0, + "content": "art GAN models. Our model and the other reported results are trained in an unsupervised manner.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "We choose “inception score” (Salimans et al., 2016) as numerical assessment to compare the visual", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "quality of samples generated by different models. Our generator and critic are standard convnets,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 593, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 506, + 607 + ], + "score": 1.0, + "content": "similar to those used by DCGAN (Radford et al., 2015), but without any batch normalization, layer", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "score": 1.0, + "content": "normalization, or other stabilizing additions. Appendix B contains additional architecture and train-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 153, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 153, + 630 + ], + "score": 1.0, + "content": "ing details.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "We first investigate the effect of batch size on training stability and sample quality. As shown in", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "Figure 3, training is not very stable when the batch size is small (i.e. 200). As batch size increases,", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 655, + 504, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 504, + 667 + ], + "score": 1.0, + "content": "training becomes more stable and the inception score of samples increases. Unlike previous meth-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "ods, our objective (the minibatch energy distance, Section 3) depends on the chosen minibatch size:", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "Larger minibatches are more likely to cover many modes of the data distribution, thereby not only", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "yielding lower variance estimates but also making our distance metric more discriminative. To reach", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "the large batch sizes needed for optimal performance we make use of multi GPU training. In this", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "work we only use up to 8 GPUs per experiment, but we anticipate more GPUs to be useful when", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 721, + 190, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 190, + 733 + ], + "score": 1.0, + "content": "using larger models.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 42 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 81, + 200, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 201, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 201, + 96 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 108, + 105, + 504, + 128 + ], + "lines": [ + { + "bbox": [ + 105, + 104, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 119 + ], + "score": 1.0, + "content": "In this section, we demonstrate the improved stability and consistency of the proposed method on", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 115, + 307, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 307, + 129 + ], + "score": 1.0, + "content": "five different datasets with increasing complexity.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1.5, + "bbox_fs": [ + 105, + 104, + 505, + 129 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 140, + 275, + 152 + ], + "lines": [ + { + "bbox": [ + 106, + 140, + 277, + 153 + ], + "spans": [ + { + "bbox": [ + 106, + 140, + 277, + 153 + ], + "score": 1.0, + "content": "5.1 MIXTURE OF GAUSSIAN DATASET", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 162, + 505, + 336 + ], + "lines": [ + { + "bbox": [ + 106, + 160, + 506, + 175 + ], + "spans": [ + { + "bbox": [ + 106, + 160, + 496, + 175 + ], + "score": 1.0, + "content": "One advantage of OT-GAN compared to regular GAN is that for any setting of the transport cost", + "type": "text" + }, + { + "bbox": [ + 496, + 164, + 501, + 171 + ], + "score": 0.62, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 160, + 506, + 175 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 172, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 446, + 185 + ], + "score": 1.0, + "content": "i.e. any fixed critic, the objective is statistically consistent for training the generator", + "type": "text" + }, + { + "bbox": [ + 447, + 174, + 453, + 184 + ], + "score": 0.75, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 172, + 505, + 185 + ], + "score": 1.0, + "content": ". Even if we", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 183, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 483, + 195 + ], + "score": 1.0, + "content": "stop updating the critic, the generator should thus never diverge. With a bad fixed cost function", + "type": "text" + }, + { + "bbox": [ + 484, + 185, + 490, + 193 + ], + "score": 0.71, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 183, + 505, + 195 + ], + "score": 1.0, + "content": "the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 194, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 181, + 208 + ], + "score": 1.0, + "content": "signal for learning", + "type": "text" + }, + { + "bbox": [ + 182, + 196, + 189, + 205 + ], + "score": 0.76, + "content": "g", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 194, + 505, + 208 + ], + "score": 1.0, + "content": "may be very weak, but at least it should never point in the wrong direction. We", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "investigate whether this theoretical property holds in practice by examining a simple toy example.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "We train generative models using different types of GAN on a 2D mixture of 8 Gaussians, with", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 228, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 239 + ], + "score": 1.0, + "content": "means arranged on a circle. The goal for the generator is to recover all 8 modes. For the proposed", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 238, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 505, + 250 + ], + "score": 1.0, + "content": "method and all the baseline methods, the architectures are simple MLPs with ReLU activations. A", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 249, + 505, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 505, + 261 + ], + "score": 1.0, + "content": "similar experimental setting has been considered in (Metz et al., 2017; Li et al., 2017) to demonstrate", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 259, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 273 + ], + "score": 1.0, + "content": "the mode coverage behavior of various GAN models. There, GANs using mini-batch features,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 270, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 284 + ], + "score": 1.0, + "content": "DAN-S (Li et al., 2017), are shown to capture all the 8 modes when training converges. To test the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 282, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 381, + 294 + ], + "score": 1.0, + "content": "consistency of GAN models, we stop updating the discriminator after", + "type": "text" + }, + { + "bbox": [ + 381, + 282, + 397, + 293 + ], + "score": 0.58, + "content": "1 5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 282, + 505, + 294 + ], + "score": 1.0, + "content": "iterations and visualize the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 293, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 505, + 306 + ], + "score": 1.0, + "content": "generator distribution for an additional 25K iterations. As shown in Figure 2, mode collapse occurs", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "in a mini-batch feature GAN after a few thousand iterations training with a fixed discriminator.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "score": 1.0, + "content": "However, using the mini-batch energy distance, the generator does not diverge and the generated", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 326, + 279, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 279, + 338 + ], + "score": 1.0, + "content": "samples still cover all 8 modes of the data.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 160, + 506, + 338 + ] + }, + { + "type": "image", + "bbox": [ + 126, + 347, + 484, + 435 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 126, + 347, + 484, + 435 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 126, + 347, + 484, + 435 + ], + "spans": [ + { + "bbox": [ + 126, + 347, + 484, + 435 + ], + "score": 0.813, + "type": "image", + "image_path": "1687b47c7688836cb6bf32cf7cfdd10ff315315751109cb91d4da734f7b693bc.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 126, + 347, + 484, + 376.3333333333333 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 126, + 376.3333333333333, + 484, + 405.66666666666663 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 126, + 405.66666666666663, + 484, + 434.99999999999994 + ], + "spans": [], + "index": 22 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 442, + 505, + 497 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 442, + 505, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 442, + 505, + 454 + ], + "score": 1.0, + "content": "Figure 2: Results for consistency when fixing the critic on data generated from 8 Gaussian mixtures.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "The first column shows the data distribution. The top row shows the training results of OT-GAN", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "using mini-batch energy distance. The bottom row shows the training result with the original GAN", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "loss (DAN-S). The latter collapses to 3 out of 8 modes after fixing the discriminator, while OT-GAN", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 487, + 185, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 185, + 497 + ], + "score": 1.0, + "content": "remains consistent.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + } + ], + "index": 23.0 + }, + { + "type": "title", + "bbox": [ + 107, + 507, + 178, + 519 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 179, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 179, + 521 + ], + "score": 1.0, + "content": "5.2 CIFAR-10", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 106, + 528, + 505, + 627 + ], + "lines": [ + { + "bbox": [ + 105, + 527, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 268, + 541 + ], + "score": 1.0, + "content": "CIFAR-10 is a well-studied dataset of", + "type": "text" + }, + { + "bbox": [ + 269, + 528, + 298, + 539 + ], + "score": 0.88, + "content": "3 2 \\times 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 527, + 505, + 541 + ], + "score": 1.0, + "content": "color images for generative models (Krizhevsky,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "score": 1.0, + "content": "2009). We use this data set to investigate the importance of the different design decisions made", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 505, + 563 + ], + "score": 1.0, + "content": "with OT-GAN, and we compare the visual quality of its generated samples with other state-of-the-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 561, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 504, + 574 + ], + "score": 1.0, + "content": "art GAN models. Our model and the other reported results are trained in an unsupervised manner.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "We choose “inception score” (Salimans et al., 2016) as numerical assessment to compare the visual", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 506, + 596 + ], + "score": 1.0, + "content": "quality of samples generated by different models. Our generator and critic are standard convnets,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 593, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 506, + 607 + ], + "score": 1.0, + "content": "similar to those used by DCGAN (Radford et al., 2015), but without any batch normalization, layer", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "score": 1.0, + "content": "normalization, or other stabilizing additions. Appendix B contains additional architecture and train-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 153, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 153, + 630 + ], + "score": 1.0, + "content": "ing details.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 527, + 506, + 630 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 632, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "We first investigate the effect of batch size on training stability and sample quality. As shown in", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "score": 1.0, + "content": "Figure 3, training is not very stable when the batch size is small (i.e. 200). As batch size increases,", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 655, + 504, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 504, + 667 + ], + "score": 1.0, + "content": "training becomes more stable and the inception score of samples increases. Unlike previous meth-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "ods, our objective (the minibatch energy distance, Section 3) depends on the chosen minibatch size:", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "Larger minibatches are more likely to cover many modes of the data distribution, thereby not only", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "yielding lower variance estimates but also making our distance metric more discriminative. To reach", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "the large batch sizes needed for optimal performance we make use of multi GPU training. In this", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "work we only use up to 8 GPUs per experiment, but we anticipate more GPUs to be useful when", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 721, + 190, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 190, + 733 + ], + "score": 1.0, + "content": "using larger models.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 632, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 95 + ], + "score": 1.0, + "content": "In Figure 4 we present the samples generated by our model trained with a batch size of 8000. In", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "addition, we also compare with the sample quality of other state-of-the-art GAN models in Table 1.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 413, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 223, + 117 + ], + "score": 1.0, + "content": "OT-GAN achieves a score of", + "type": "text" + }, + { + "bbox": [ + 223, + 105, + 267, + 115 + ], + "score": 0.85, + "content": "8 . 4 7 \\pm . 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 104, + 413, + 117 + ], + "score": 1.0, + "content": ", outperforming all baseline models.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 210 + ], + "lines": [ + { + "bbox": [ + 105, + 120, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 505, + 134 + ], + "score": 1.0, + "content": "To evaluate the importance of using optimal transport in OT-GAN, we repeat our CIFAR-10 exper-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "score": 1.0, + "content": "iment with random matching of samples. Our minibatch energy distance objective remains valid", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "when we match samples randomly rather than using optimal transport. In this case the minibatch", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 504, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 504, + 167 + ], + "score": 1.0, + "content": "energy distance reduces to the regular (generalized) energy distance. We repeat our CIFAR-10 ex-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 166, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 166, + 505, + 178 + ], + "score": 1.0, + "content": "periment and train a generator with the same architecture and hyperparameters as above, but with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "random matching of samples instead of optimal transport. The highest resulting Inception score", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 506, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 200 + ], + "score": 1.0, + "content": "achieved during the training process is 4.64 using this approach, as compared to 8.47 with optimal", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 385, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 385, + 210 + ], + "score": 1.0, + "content": "transport. Figure 5 shows a random sample from the resulting model.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + }, + { + "type": "table", + "bbox": [ + 249, + 219, + 361, + 280 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 249, + 219, + 361, + 280 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 249, + 219, + 361, + 280 + ], + "spans": [ + { + "bbox": [ + 249, + 219, + 361, + 280 + ], + "score": 0.97, + "html": "
MethodInception score
Real Data11.95 ± .12
DCGAN6.16±.07
Improved GAN6.86±.06
DenoisingFM7.72±.13
WGAN-GP7.86± .07
OT-GAN8.47±.12
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In", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 506, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 506, + 106 + ], + "score": 1.0, + "content": "addition, we also compare with the sample quality of other state-of-the-art GAN models in Table 1.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 413, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 223, + 117 + ], + "score": 1.0, + "content": "OT-GAN achieves a score of", + "type": "text" + }, + { + "bbox": [ + 223, + 105, + 267, + 115 + ], + "score": 0.85, + "content": "8 . 4 7 \\pm . 1 2", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 104, + 413, + 117 + ], + "score": 1.0, + "content": ", outperforming all baseline models.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 105, + 82, + 506, + 117 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 210 + ], + "lines": [ + { + "bbox": [ + 105, + 120, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 120, + 505, + 134 + ], + "score": 1.0, + "content": "To evaluate the importance of using optimal transport in OT-GAN, we repeat our CIFAR-10 exper-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "score": 1.0, + "content": "iment with random matching of samples. Our minibatch energy distance objective remains valid", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 143, + 505, + 156 + ], + "score": 1.0, + "content": "when we match samples randomly rather than using optimal transport. In this case the minibatch", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 504, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 504, + 167 + ], + "score": 1.0, + "content": "energy distance reduces to the regular (generalized) energy distance. We repeat our CIFAR-10 ex-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 166, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 166, + 505, + 178 + ], + "score": 1.0, + "content": "periment and train a generator with the same architecture and hyperparameters as above, but with", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "random matching of samples instead of optimal transport. The highest resulting Inception score", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 506, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 200 + ], + "score": 1.0, + "content": "achieved during the training process is 4.64 using this approach, as compared to 8.47 with optimal", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 385, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 385, + 210 + ], + "score": 1.0, + "content": "transport. Figure 5 shows a random sample from the resulting model.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5, + "bbox_fs": [ + 105, + 120, + 506, + 210 + ] + }, + { + "type": "table", + "bbox": [ + 249, + 219, + 361, + 280 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 249, + 219, + 361, + 280 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 249, + 219, + 361, + 280 + ], + "spans": [ + { + "bbox": [ + 249, + 219, + 361, + 280 + ], + "score": 0.97, + "html": "
MethodInception score
Real Data11.95 ± .12
DCGAN6.16±.07
Improved GAN6.86±.06
DenoisingFM7.72±.13
WGAN-GP7.86± .07
OT-GAN8.47±.12
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A smaller batch size of 2048 is used due to GPU memory contraints. As shown in Figure 6,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 135, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 135, + 505, + 150 + ], + "score": 1.0, + "content": "the samples generated by OT-GAN contain less nonsensical images, and the sample quality is sig-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 146, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 146, + 505, + 160 + ], + "score": 1.0, + "content": "nificantly better than that of a tuned DCGAN variant which still suffers from mode collapse. The", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 158, + 505, + 170 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 426, + 170 + ], + "score": 1.0, + "content": "superior image quality is confirmed by the inception score achieved by OT-GAN", + "type": "text" + }, + { + "bbox": [ + 426, + 158, + 474, + 169 + ], + "score": 0.45, + "content": "( 8 . 9 7 { \\scriptstyle \\pm 0 . 0 9 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 158, + 505, + 170 + ], + "score": 1.0, + "content": "on this", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 168, + 333, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 168, + 333, + 182 + ], + "score": 1.0, + "content": "dataset, which outperforms that of DCGAN(8.19±0.11)", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 120, + 190, + 491, + 370 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 120, + 190, + 491, + 370 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 120, + 190, + 491, + 370 + ], + "spans": [ + { + "bbox": [ + 120, + 190, + 491, + 370 + ], + "score": 0.976, + "type": "image", + "image_path": "f014376b44941bf3c6b56a596486ceca17208002ae78bcc958f676fc2b5e1b13.jpg" + } + ] + } + ], + "index": 9, + "virtual_lines": [ + { + "bbox": [ + 120, + 190, + 491, + 250.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 120, + 250.0, + 491, + 310.0 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 120, + 310.0, + 491, + 370.0 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 122, + 376, + 487, + 388 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 375, + 487, + 390 + ], + "spans": [ + { + "bbox": [ + 122, + 375, + 487, + 390 + ], + "score": 1.0, + "content": "Figure 6: ImageNet Dog subset samples generated by OT-GAN (left) and DCGAN (right).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + } + ], + "index": 10.0 + }, + { + "type": "title", + "bbox": [ + 108, + 408, + 293, + 419 + ], + "lines": [ + { + "bbox": [ + 106, + 408, + 294, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 294, + 420 + ], + "score": 1.0, + "content": "5.4 CONDITIONAL GENERATION OF BIRDS", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 428, + 506, + 484 + ], + "lines": [ + { + "bbox": [ + 106, + 427, + 506, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 506, + 442 + ], + "score": 1.0, + "content": "To further demonstrate the effectiveness of the proposed method on conditional image synthesis, we", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 439, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 505, + 452 + ], + "score": 1.0, + "content": "compare OT-GAN with state-of-the-art models on text-to-image generation (Reed et al., 2016b;a;", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 450, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 506, + 464 + ], + "score": 1.0, + "content": "Zhang et al., 2017). As shown in Table 2, the images generated by OT-GAN with batch size 2048", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 461, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 506, + 474 + ], + "score": 1.0, + "content": "also achieve the best inception score here. Example images generated by our conditional generative", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 473, + 317, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 317, + 484 + ], + "score": 1.0, + "content": "model on the CUB test set are presented in Figure 7.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 159, + 494, + 451, + 517 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 159, + 494, + 451, + 517 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 159, + 494, + 451, + 517 + ], + "spans": [ + { + "bbox": [ + 159, + 494, + 451, + 517 + ], + "score": 0.956, + "html": "
MethodGAN-INT-CLSGAWWNStackGANOT-GAN
Inception Score2.88± .043.62 ± .073.70±.043.84 ± .05
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MethodGAN-INT-CLSGAWWNStackGANOT-GAN
Inception Score2.88± .043.62 ± .073.70±.043.84 ± .05
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Preliminary experiments suggest these learned functions can be used", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 326, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 506, + 340 + ], + "score": 1.0, + "content": "successfully for unsupervised learning and other applications, which we plan to investigate further", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 337, + 168, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 168, + 349 + ], + "score": 1.0, + "content": "in future work.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 17.5 + }, + { + "type": "title", + "bbox": [ + 107, + 365, + 175, + 376 + ], + "lines": [ + { + "bbox": [ + 106, + 364, + 176, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 364, + 176, + 378 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 105, + 379, + 506, + 734 + ], + "lines": [ + { + "bbox": [ + 105, + 381, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 395 + ], + "score": 1.0, + "content": "Martin Arjovsky, Soumith Chintala, and Leon Bottou. 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As a result we learn a relatively stable transport cost function", + "type": "text" + }, + { + "bbox": [ + 428, + 294, + 457, + 306 + ], + "score": 0.92, + "content": "c ( \\mathbf { x } , \\mathbf { y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 457, + 293, + 506, + 308 + ], + "score": 1.0, + "content": ", describing", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 304, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 407, + 318 + ], + "score": 1.0, + "content": "how (dis)similar two images are, as well as an image embedding function", + "type": "text" + }, + { + "bbox": [ + 408, + 305, + 432, + 317 + ], + "score": 0.92, + "content": "v _ { \\eta } ( \\mathbf { x } )", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 304, + 506, + 318 + ], + "score": 1.0, + "content": "capturing the ge-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 315, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 506, + 329 + ], + "score": 1.0, + "content": "ometry of the training data. Preliminary experiments suggest these learned functions can be used", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 326, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 506, + 340 + ], + "score": 1.0, + "content": "successfully for unsupervised learning and other applications, which we plan to investigate further", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 337, + 168, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 168, + 349 + ], + "score": 1.0, + "content": "in future work.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 17.5, + "bbox_fs": [ + 104, + 260, + 506, + 349 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 365, + 175, + 376 + ], + "lines": [ + { + "bbox": [ + 106, + 364, + 176, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 364, + 176, + 378 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "list", + "bbox": [ + 105, + 379, + 506, + 734 + ], + "lines": [ + { + "bbox": [ + 105, + 381, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 395 + ], + "score": 1.0, + "content": "Martin Arjovsky, Soumith Chintala, and Leon Bottou. 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For OT-GAN we continued to train for 13000 epochs on this data set but", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 161, + 376, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 376, + 174 + ], + "score": 1.0, + "content": "never observed any mode collapse or reduction in sample diversity.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3.5, + "bbox_fs": [ + 105, + 106, + 506, + 174 + ] + }, + { + "type": "image", + "bbox": [ + 118, + 184, + 493, + 361 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 118, + 184, + 493, + 361 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 118, + 184, + 493, + 361 + ], + "spans": [ + { + "bbox": [ + 118, + 184, + 493, + 361 + ], + "score": 0.977, + "type": "image", + "image_path": "d695e9bb1e93fa6444466b1317a36d31e797fae6fa95c3932de83ad4d5357d5b.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 118, + 184, + 493, + 243.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 118, + 243.0, + 493, + 302.0 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 118, + 302.0, + 493, + 361.0 + ], + "spans": [], + "index": 9 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 371, + 505, + 415 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 370, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 505, + 384 + ], + "score": 1.0, + "content": "Figure 9: Imagenet dog samples generated with DCGAN (left) after 900 epochs and OT-GAN (right)", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 381, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 506, + 394 + ], + "score": 1.0, + "content": "after 13000 epochs. When training long enough, DCGAN suffers from mode collapse as indicated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 392, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 406 + ], + "score": 1.0, + "content": "by the highlighted samples. We did not observe any mode collapse for OT-GAN, even when training", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 404, + 200, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 404, + 200, + 416 + ], + "score": 1.0, + "content": "for many more epochs.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + } + ], + "index": 9.75 + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/train/rkQkBnJAb/rkQkBnJAb_model.json b/parse/train/rkQkBnJAb/rkQkBnJAb_model.json new file mode 100644 index 0000000000000000000000000000000000000000..164e50064bdd1345fe919db213f8c797167d0544 --- /dev/null +++ b/parse/train/rkQkBnJAb/rkQkBnJAb_model.json @@ -0,0 +1,17500 @@ +[ + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 398, + 707, + 1302, + 707, + 1302, + 983, + 398, + 983 + ], + "score": 0.982 + }, + { + "category_id": 1, + "poly": [ + 298, + 1527, + 1404, + 1527, + 1404, + 1832, + 298, + 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MethodInception score
Real Data11.95 ± .12
DCGAN6.16±.07
Improved GAN6.86±.06
DenoisingFM7.72±.13
WGAN-GP7.86± .07
OT-GAN8.47±.12
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MethodGAN-INT-CLSGAWWNStackGANOT-GAN
Inception Score2.88± .043.62 ± .073.70±.043.84 ± .05
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operationactivationkernelstrideoutput shape
Z linear reshape 2x NN upsample convolution 2x NN upsample convolutionGLU100 16384
1024×4×4
GLU5×511024×8×8 512×8×8
512 ×16 × 16
GLU5×51256×1 16 ×16
2x NN upsample256 × 32 × 32
convolutionGLU5×51128 × 32 × 32
convolutiontanh5×513 × 32× 32
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convolutionCReLU5×51256× 32×32512 ×16×161024×8×82048×4×43276832768
convolutionconvolutionconvolutionreshape12 normalizeCReLUCReLUCReLU5×5２２2
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a/parse/train/u8X280hw1Mt/images/fdfd6c31f01e27b1dfb0e51ca6e92e790e469956ce43071b7216e43f4d0af5b3.jpg b/parse/train/u8X280hw1Mt/images/fdfd6c31f01e27b1dfb0e51ca6e92e790e469956ce43071b7216e43f4d0af5b3.jpg new file mode 100644 index 0000000000000000000000000000000000000000..b8e2d82f31a2449e2746ddc993e0ed3d3e9e595e --- /dev/null +++ b/parse/train/u8X280hw1Mt/images/fdfd6c31f01e27b1dfb0e51ca6e92e790e469956ce43071b7216e43f4d0af5b3.jpg @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c4926cead656a589193ac3f5ed1748710720827d0ab4d858c2f7ba958cc09a5d +size 11545 diff --git a/parse/train/wZrOOO9XBn/wZrOOO9XBn.md b/parse/train/wZrOOO9XBn/wZrOOO9XBn.md new file mode 100644 index 0000000000000000000000000000000000000000..02a36638519bd0d8dc5d01ca81d9ed19dd74a41b --- /dev/null +++ b/parse/train/wZrOOO9XBn/wZrOOO9XBn.md @@ -0,0 +1,323 @@ +# Lossy Compression for Lossless Prediction + +Yann Dubois Vector Institute yanndubois96@gmail.com + +Benjamin Bloem-Reddy The University of British Columbia benbr@stat.ubc.ca + +Karen Ullrich Facebook AI Research karenu@fb.com + +Chris J. Maddison University of Toronto Vector Institute cmaddis@cs.toronto.edu + +# Abstract + +Most data is automatically collected and only ever “seen” by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations. Based on our theory, we design unsupervised objectives for training neural compressors. Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than $1 0 0 0 \times$ on ImageNet) compared to JPEG on 8 datasets, without decreasing downstream classification performance. + +# 1 Introduction + +Progress in important areas requires processing huge amounts of data. For climate prediction, models are still data-limited [1], despite the Natl. Center for Computational Sciences storing 32 million gigabytes (GB) of climate data [2]. For autonomous driving, capturing a realistic range of rare events with current methods requires around 3 trillion GB of data.1 At these scales, data are only processed by task-specific algorithms, and storing data in human-readable formats can be prohibitive. We need compressors that retain only the information needed for algorithmic execution of downstream tasks. + +Existing lossy compressors are not up to the challenge, because they aim to reconstruct the data for human perception [5–10]. However, much of perceptual information is not needed to perform the tasks that we care about. Consider classifying images, which can require about 1 MB to store. Classification is typically invariant under small image transformations, such as rescalings or rotations, and could instead be performed using a representation that discards such information (see Fig. 1). The amount of unnecessary perceptual information is likely substantial, as illustrated by the fact that typical image classification can be performed using a detailed caption, which requires only about $1 \mathrm { k B }$ to store $1 0 0 0 \times$ fewer bits). + +![](images/228aa771e17e279691c98492f9ac7e7cf20a7f3bf05378f39656e5e370197397.jpg) +Figure 1: Our unsupervised coder improves compression by only keeping information necessary for typical tasks. (left) source augmented MNIST digit; (center) a neural perceptual compressor achieves 130 bit-rate; (right) our invariant compressor achieves 48 bit-rate. + +Our goal is to quantify the bit-rate needed to ensure high performance on a collection of prediction tasks. In the simple case of a single supervised task, the minimum bit-rate is achieved by compressing predicted labels, and essentially corresponds to the Information Bottleneck (IB; [11]). Our challenge, instead, is to ensure good performance on any future tasks of interest, which will rarely be completely known at compression time, or might be too large to enumerate. + +We overcome this challenge by focusing on sets of tasks that are invariant under user-defined transformations (e.g., translation, brightness, cropping), as is the case for many tasks of interest to humans [12, 13]. This structure allows us to characterize a worst-case invariant task, which bounds the relative predictive performance on all invariant tasks. As a result, the bit-rate required to perform well on all invariant tasks is exactly the rate to compress the worst-case labels. At a high level, the worst-case task is to recognize which examples are transformed versions of one another, and rate savings come from discarding information from those transformations. + +We also provide two unsupervised neural compressors to target the optimal rates. One is similar to a variational autoencoder [14] that reconstructs canonical examples (Fig. 1). Our second is a simple modification of contrastive self-supervised learning (SSL; [15]), which allows us to convert pre-trained SSL models into powerful, generic compressors. Our contributions are: + +• We formalize the notion of compression for downstream predictive tasks. +• We characterize the bits needed for high performance on any task invariant to augmentations. +• We provide unsupervised objectives to train compressors that approximate the optimal rates. +• We show that our compressor outperforms JPEG by orders of magnitude on 8 datasets on which it was never trained (i.e., zero-shot). E.g., on ImageNet [16], it decreases the bit-rate by $1 0 0 0 \times$ . + +# 2 Rate-distortion theory background + +The goal of lossy compression theory is to find the number of bits (bit-rate) required to store outcomes $x$ of a random variable (r.v.) $X$ , so that it can be reconstructed within a certain tolerance. This is accomplished in Shannon’s [17] rate-distortion (RD) theory by mapping $X$ into a r.v. $Z$ with low mutual information $\operatorname { I } [ X ; Z ]$ . Specifically, given a distortion measure $\mathrm { D } [ X , Z ]$ , the RD theory characterizes the minimal achievable bit-rate for a distortion threshold $\delta$ by + +$$ +R a t e ( \delta ) = \operatorname* { m i n } _ { p ( Z | X ) } \operatorname { I } [ X ; Z ] \quad { \mathrm { ~ s u c h ~ t h a t ~ } } \quad \operatorname { D } [ X , Z ] \leq \delta . +$$ + +In lossy compression, $Z$ is usually a reconstruction of $X$ , i.e., it aims to faithfully approximate $X$ . As a result, typical distortions, e.g., the mean squared error (MSE), assume that the sample spaces $\mathcal { X } , \mathcal { Z }$ of both r.v.s are the same. This assumption is not required. Indeed, any distortion $d : \mathcal { X } \times \mathcal { Z } \to \mathbb { R } _ { \ge 0 }$ of the form $\mathrm { D } [ X , Z ] = \mathrm { E } _ { p ( X , Z ) } [ d ( X ^ { ' } , Z ) ]$ , where there exists a $z \in Z$ such that $\mathrm { D } [ X , z ]$ is finite, is a valid choice [18]. This shows that RD theory can be used outside of reconstructions. In the following we refer to $Z$ as a compressed representation of $X$ to distinguish it from a reconstruction. + +# 3 Minimal bit-rate for high predictive performance + +In this section, we characterize the bit-rate needed to represent $X$ to ensure high performance on downstream tasks. Our argument has three high-level steps: (i) define a distortion that controls downstream performance when predicting from $Z$ instead of $X$ ; (ii) simplify and validate this distortion when desired tasks satisfy an invariance condition; (iii) apply RD theory with the valid distortion. For simplicity, our presentation is relatively informal; formal proofs are in Apps. A and B. + +# 3.1 A distortion for worst-case predictive performance + +Suppose $X$ is an image. Potential downstream tasks might include $Y _ { \mathrm { d o g } }$ , whether the image displays a dog; or $Y _ { \mathrm { h d } }$ , whether the image is hand-drawn. Formally, these and other downstream tasks are expressed as $\mathcal { T } = \{ Y _ { \mathrm { d o g } } , Y _ { \mathrm { h d } } , . . . \}$ , a set of random variables that are jointly distributed with $X$ . Let $\mathrm { R } [ Y | X ]$ denote the Bayes (best possible) risk when predicting $Y$ from $X$ . For ease of presentation in the main paper, we consider only classification tasks $\tau$ and Bayes risk of the standard log loss $\begin{array} { r } { \mathrm { R } [ Y | X ] : = \bar { \operatorname* { i n f } _ { q } \mathrm { E } } _ { p ( X , Y ) } [ - \log q ( \dot { Y } | X ) ] } \end{array}$ . We deal with MSE and regression in Appx. B.6. + +![](images/9108ffa9cd994dbe365806d6efeca48befc210b4d5e08d0166cef74a1bc15cc0.jpg) +Figure 2: Maximal invariants $M ( X )$ are representatives of equivalence classes. Example $M \mathrm { s }$ include the: (a) Euclidean norm for rotations; (b) unit vector for scaling; (c) $f$ when equivalence classes are pre-images by $f$ ; (d) empirical measure for permutations; (e) canonical graph for graph isomorphisms; (f) unaugmented input for data augmentations. + +In this setting, a meaningful distortion $\mathrm { D } _ { \tau } [ X , Z ]$ quantifies the difference between predicting any $Y \in \tau$ from the compressed $Z$ , as opposed to using $X$ . This is the worst-case excess risk, + +$$ +\operatorname { D } _ { \tau } [ X , Z ] : = \operatorname* { s u p } _ { Y \in { \mathcal { T } } } \quad \operatorname { R } [ Y \mid Z ] - \operatorname { R } [ Y \mid X ] . +$$ + +If $\mathrm { D } _ { \tau } [ X , Z ] = 0$ , it is possible to achieve lossless prediction: performing as well using $Z$ as using $X$ . More generally, bounding $\mathrm { D } _ { \tau }$ by $\delta$ ensures that $\mathrm { R } [ Y | Z ] - \mathrm { R } [ Y | X ] \leq \delta$ for all tasks in $\tau$ . However, there are two issues that need to be addressed before Eq. (2) can be used. First, it is not clear whether $\mathrm { D } _ { \tau }$ is a valid distortion for RD theory. Second, the worst excess-risk $\mathrm { D } _ { \tau }$ assumes access to all downstream tasks of interest $\tau$ during compression, which is unrealistic in general. + +# 3.2 Invariant tasks + +The tasks that we care about are not arbitrary, and often share structure. One such structure is invariance to certain pre-specified transformations of input data. For example, computer vision tasks are often invariant to mild transformations such as brightness changes. Such invariance structure is common in realistic tasks, as seen by the wide-spread use of data augmentations [13] in machine learning (ML), which encourage predictions to be the same for an unaugmented $x$ and an augmented $x ^ { + }$ . Motivated by this we focus on sets of invariant tasks $\tau$ . + +We consider a general notion of invariance, namely invariance specified by an equivalence relation $\sim$ on $\mathcal { X }$ .2 The equivalence induces a partition of $\mathcal { X }$ into disjoint equivalence classes, and we are interested in tasks whose conditional distributions are constant within these classes. + +Definition 1. The set of invariant tasks of interest with respect to an equivalence $( \mathcal { X } , \sim )$ , denoted $\mathcal { T } _ { \sim }$ , is all random variables $Y$ such that $x \sim x ^ { + } \implies p ( Y | x ) = p ( Y | x ^ { + } )$ for any $x , x ^ { + } \in \mathcal { X }$ . + +# 3.3 Rate-distortion theory for invariant task prediction + +The key to simplifying $\mathrm { D } _ { \tau _ { \sim } }$ is the existence of a (non-unique) worst-case invariant task, denoted $M ( X )$ . Such task contains all and only information to which tasks $Y \in \mathcal { T } _ { \sim }$ are not invariant; we call them maximal invariants. A maximal invariant $M ( \bullet )$ with respect to $\sim$ is any function satisfying3 + +$$ +x \sim x ^ { + } \iff M ( x ) = M ( x ^ { + } ) \quad { \mathrm { f o r ~ a n y ~ } } x , x ^ { + } \in \mathcal { X } . +$$ + +A maximal invariant removes all information that tasks are invariant to, as it maps equivalent inputs to the same output, i.e., $M ( x ) = M ( x ^ { + } )$ . Yet, it retains the minimal information needed to perform invariant tasks, by mapping non-equivalent inputs $x \not \sim x ^ { - }$ to different outputs $M ( x ) \neq { \overline { { M } } } ( x ^ { - } )$ . In other words, $M ( x )$ indexes the equivalence classes. For example, the Euclidean norm is a maximal invariant for rotation invariance, as all vectors that are rotated versions of one another can be characterized by their radial coordinate. For data augmentations, the canonical (unaugmented) version of the input is a maximal invariant. Other examples are shown in Fig. 2. + +We prove in Appx. B.2 that under weak regularity conditions, maximal invariant tasks exist in $\mathcal { T } _ { \sim }$ , and that they achieve the supremum in Eq. (2). This allows us to show that $\mathrm { D } _ { \tau _ { \sim } }$ reduces to the Bayes risk of predicting $M ( X )$ from $Z$ and that it is a valid distortion measure. Crucially, this allows us to quantify downstream performance without enumerating invariant tasks. + +Proposition 1. Let $( \mathcal { X } , \sim )$ be an equivalence relation and $M$ a maximal invariant that takes at most countably many values, with $\mathrm { H } [ M ( \bar { X } ) ] < \infty$ . Then $\mathrm { D } _ { \tau _ { \sim } }$ (2) with log loss is a valid distortion and + +$$ +\mathrm { D } _ { \tau _ { \sim } } [ X , Z ] = \mathrm { R } [ M ( X ) | Z ] \ . +$$ + +Here we used $\operatorname { R } [ M ( X ) | X ] = 0$ , as $M$ is a deterministic function. Also, note that the countable requirement holds when tasks are invariant to some rounding of the input, as is typically the case due to floating-point storage. We accommodate the uncountable case for squared-error loss in Appx. B.6. + +With a valid distortion in hand, we invoke the RD theorem with $\mathrm { D } _ { \tau _ { \sim } }$ to obtain our “Rate-Invariance” (RI) theorem. The RI theorem characterizes the bit-rate needed to store $X$ while ensuring small log-loss on invariant tasks. We obtain analogous results for squared-error loss. + +Theorem 2 (Rate-Invariance). Assume the conditions of Prop. 1. Let $\delta \geq 0$ , and $R a t e ( \delta )$ denote the minimum achievable bit-rate for transmitting $Z$ such that for any $Y \in \mathcal { T } _ { \sim }$ we have $\mathrm { R } [ \dot { Y } | Z ] -$ $\mathrm { R } [ Y | X ] \leq \delta$ . Then $R a t e ( \delta ) = 0$ if $\delta \geq \mathrm { H } [ M ( \bar { X } ) ]$ and otherwise it is finite and + +![](images/cb8ccf92de6e597a10d0adc453be47c4173aa7e0fb6ecca9ffa8de99785a3aca.jpg) + +To ensure lossless prediction, i.e., $R a t e ( 0 )$ , our theorem states that we require a bit-rate of $\mathrm { H } [ M ( { \bar { X } } ) ]$ . Intuitively, this is because $M ( X )$ contains the minimal information needed to predict losslessly any $Y \in \tau _ { \sim }$ .4 Furthermore, the theorem relates compression and prediction by showing that allowing a $\delta$ decrease in log-loss performance on all tasks can save exactly $\delta$ bits. Intuitively, this is a linear relationship, because expected log-loss is measured in bits. On the right of Eq. (5) we further decompose $\mathrm { H } [ M ( X ) ]$ into two terms to provide another interpretation: (i) $\mathrm { H } [ X ]$ , which, for discrete $X$ , is the bit-rate required to losslessly compress $X$ , and (ii) $\mathrm { H } [ X | M ( X ) ]$ , which quantifies the information removed due to the invariance of desired tasks. Importantly, removing this information does not impact the best possible predictive performance. See Fig. 3. + +![](images/5ec6bce1f3417baafb6ede7024f058c61fc0939e9b65007e3138dad6df7de2a2.jpg) +Figure 3: Rate-Invariance function. + +The bit-rate gains can be substantial, depending on the invariances. Consider compressing a sequence of $n$ i.i.d. fair coin flips. Suppose one is only interested in predicting permutation invariant labels. Then instead of compressing the entire sequence in $\operatorname { H } [ X ^ { n } ] = n \operatorname { H } [ X ] = n$ bits, one could compress the number of heads, which is a maximal invariant for permutation invariance, in ${ \mathcal { O } } ( \log n )$ bits.5 As more interesting examples, we recover in Appx. B.4 results from (i) unlabeled graph compression [20]; (ii) multiset compression [21]; (iii) single task compression (IB; [11]). The equivalence $\sim$ can be induced by any transformations, such as transforming an image to its caption. We use this idea in Sec. 5.3 to obtain ${ \mathrm { > } } 1 0 0 0 \times$ compression on ImageNet without sacrificing predictive performance. + +![](images/92ee44f90fed57f5b1bc8cdcd797bb90169e242082ce1cc774d494daba369015.jpg) +Figure 4: Our unsupervised objectives for invariant image compression under data augmentation use the same encoder, but differ in their approximation to the invariance distortion. Both models encode the augmented data, pass the representation through an entropy bottleneck which ensures that they are compressed, and use a distortion to retain the information about the identity of the original data. The models differ in how they retain that information: (VIC) by reconstructing unaugmented inputs; (BINCE) by recognizing which inputs come from the same original data. + +# 4 Unsupervised training of invariant neural compressors + +In this section, we design practical, invariant neural compressors that bound optimal rates. Derivations are in Appx. C. In particular, we are interested in the arg min encoders $p ( Z | X )$ of the RD function (Eq. (1)) under the invariance distortion $\mathrm { D } _ { \tau _ { \sim } }$ . To accomplish this, we can optimize the following equivalent (i.e., it induces the same RI function) Lagrangian, where $\beta$ takes the role of $\delta$ , 6 + +$$ +\begin{array} { r l } { \underset { p ( Z | X ) } { \operatorname { a r g m i n } } } & { { } \operatorname { I } [ X ; Z ] + \beta \cdot \operatorname { R } [ M ( X ) \mid Z ] . } \end{array} +$$ + +In ML, the maximal invariant $M$ is often not available. Instead, invariances are implicitly specified by sampling a random augmentation from $A$ , applying it to a datapoint $X$ , and asking that the model’s prediction be invariant between $X$ and $A ( X )$ . For example, invariance to cropping can be enforced by randomly cropping images while retaining the original label. We show in Appx. C, that in such case, we can treat the augmented $A ( X )$ as the new source, $Z$ as the representation of $A ( X )$ , and the unaugmented $X$ as the maximal invariant task $M ( A ( X ) )$ . Indeed, $\operatorname { R } [ M ( A ( X ) ) | Z ]$ is equal to $\mathrm { R } [ X | Z ]$ up to a constant, so we can rewrite Eq. (6) as the following equivalent objective, + +$$ +\begin{array} { r l } { \operatorname { a r g m i n } } & { \operatorname { I } [ A ( X ) ; Z ] \ + \ \beta \cdot \operatorname { R } [ X \mid Z ] . } \end{array} +$$ + +Such reformulation is possible if random augmentations retain the invariance structure $X \sim A ( X )$ but “erase” enough information about equivalent inputs, specifically, if $X \bot \bot A ( X ) \mid M ( X )$ . We discuss the second requirement in Appx. C but note that it will likely not be a practical issue if the dataset is small compared to the support $\left| \mathcal { D } \right| \ll \left| \mathcal { X } \right|$ . With this, we have an objective whose r.v.s. are easy to sample from. However, both terms in Eq. (7) are still challenging to estimate. + +In the following, we develop two practical variational bounds to Eq. (7), which can be optimized by stochastic gradient descent [23] over the encoder’s parameters. Both approximations use the standard lossy neural compression bound $\begin{array} { r } { \operatorname { I } [ Z ; A ( X ) ] \bar { \le } \operatorname { H } [ Z ] \le \operatorname* { m i n } _ { \theta } \operatorname { E } _ { p ( Z ) } [ - \log q _ { \theta } ( Z ) ] } \end{array}$ where $q _ { \theta } ( Z )$ is called an entropy model (or a prior) [24, 25]. This has the advantage that the learned $q _ { \theta }$ can be used for entropy coding $Z$ [26, 27]. See Ballé et al. [28] for possible entropy models. Our two approximations differ in how they upper bound $\mathrm { R } [ X \mid Z ]$ . The first uses a reconstruction loss, which attempts to reconstruct the unaugmented input $x \in \mathcal { D }$ from $A ( x )$ . The second uses a discrimination loss, which attempts to recognize which examples are augmented versions of the input. + +# 4.1 Variational Invariant Compressor (VIC) + +Our first model is a modified neural compressor in which inputs are augmented but target reconstructions are not. We refer to it as a variational invariant compressor (VIC). See Fig. 4 for an illustration. VIC has an encoder $p _ { \varphi } ( Z | A ( X ) )$ , an entropy model $q _ { \theta } ( Z )$ , and a decoder $q _ { \phi } ( X | Z )$ . Given a data sample $x \in \mathcal { D }$ , we apply a random augmentation $A ( x )$ , and encode it to get a representation $Z$ . The decoder then attempts to reconstruct the unaugmented $x$ from $Z$ . This leads to the objective, + +$$ +{ \mathcal { L } } _ { \mathrm { v l c } } ( \phi , \theta , \varphi ) : = - \sum _ { x \in { \mathcal { D } } } \operatorname { E } _ { p ( A ) p _ { \varphi } ( Z \mid A ( x ) ) } [ \log q _ { \theta } ( Z ) + \beta \cdot \log q _ { \phi } ( x \mid Z ) ] . +$$ + +The term $\log q _ { \theta } ( Z )$ is an entropy bottleneck, which bounds the rate $\operatorname { I } [ A ( X ) ; Z ]$ and ensures that unnecessary information is removed. The term $\log q _ { \phi } ( x | Z )$ bounds the distortion $\mathrm { R } [ X | Z ] \leq$ $\operatorname { E } _ { p ( X , Z ) } [ - \log q _ { \phi } ( X \mid Z ) ]$ and ensures that VIC preserves the information needed for invariant tasks. + +# 4.2 Bottleneck InfoNCE (BINCE) + +Our second compressor retains all predictive information without reconstructing the data. It has two components: an entropy bottleneck and an InfoNCE [15] objective, which is the standard in contrastive SSL. We refer to this as the bottleneck InfoNCE (BINCE), see Fig. 4. BINCE has an advantage over VIC in that it avoids the problem of reconstructing possibly high dimensional data. + +Algorithm 1 shows how to train BINCE, where each call to $A$ returns an independent augmentation of its input. As with VIC, for every datapoint $x \in \mathcal { D }$ , we obtain a representation $Z$ by applying an augmentation $A ( x )$ and passing it through the encoder $p _ { \varphi } ( Z | A ( X ) )$ . We then sample a “positive” example $Z ^ { + }$ by encoding a different augmented version of the same underlying datapoint $x$ . Finally, we sample $n$ “negative” examples $Z _ { i } ^ { - }$ by encoding augmentations $A ( x _ { i } ^ { - } )$ of datapoints $x _ { i } ^ { - } \in \mathcal { D }$ that are different from $x$ . This results in a sequence $z =$ $( Z ^ { + } , Z _ { 1 } ^ { - } , \ldots , Z _ { n } ^ { - } )$ . For conciseness we will denote the above sampling procedure as $p _ { \varphi } ( Z , Z \mid A , \mathcal { D } , x )$ . The final loss uses a discriminator $f _ { \psi }$ that is optimized to score the equivalence of two representation, + +# Algorithm 1 BINCE’s forward pass for $x$ + +Require: $p _ { \varphi } , q _ { \theta } , f _ { \psi } , \mathcal { D } , A , \beta , n , x$ + +1: $\tilde { x } \mathrm { s a m p l e } ( A ( x ) )$ . Augment +2: $z \gets \mathrm { s a m p l e } ( p _ { \varphi } ( Z | \tilde { x } ) )$ . Encode +3: rate_ $\mathrm { l o s s } - \log q _ { \theta } ( z )$ +4: $\{ x _ { i } ^ { - } \} _ { i = 1 } ^ { n } \operatorname { s e l e c t } ( { \mathcal { D } } \setminus \{ x \} ) ~ i$ $n$ times +5: $\tilde { \mathbf { x } } \gets \mathrm { s a m p l e } ( [ A ( x ) , A ( x _ { 1 } ^ { - } ) , \ldots , A ( x _ { n } ^ { - } ) ] )$ +6: $\mathbf { z } \gets \mathrm { s a m p l e } ( p _ { \varphi } ( Z | \tilde { \mathbf { x } } ) )$ +7: z+ ← z[0] +8: softmax ← ψ (Pz0∈z exp fψ(z0,z)) +9: distortion_loss ← − log(softmax) +10: return rate_loss $+ \beta \cdot$ distortion_loss + +$$ +\mathcal { L } _ { \mathrm { { s u r c e } } } ( \varphi , \theta , \psi ) : = - \sum _ { x \in \mathcal { D } } \mathrm { E } _ { p ( A ) p _ { \varphi } ( Z , Z | A , \mathcal { D } , x ) } \left[ \log q _ { \theta } ( Z ) + \beta \cdot \log \frac { \exp f _ { \psi } ( Z ^ { + } , Z ) } { \sum _ { Z ^ { \prime } \in \mathbb { Z } } \exp f _ { \psi } ( Z ^ { \prime } , Z ) } \right] . +$$ + +BINCE retains the necessary information by classifying (as seen by the softmax) which $Z$ is associated with an equivalent example $X$ . Both VIC and BINCE give rise to efficient compressors by passing $X$ through $p _ { \varphi } ( Z | X )$ and entropy coding using $q _ { \theta } ( Z )$ . In theory they can both recover the optimal rate for lossless predictions, i.e., $\mathrm { H } [ M ( X ) ]$ , in the limit of infinite samples $( | \mathcal { D } | , n )$ and unconstrained variational families. In practice, BINCE has the advantage over VIC of (i) not requiring a high dimensional decoder; and (ii) giving (for suitable $f _ { \psi }$ ) representations that are approximately linearly separable [29–31] and thus easy to predict from [15, 32]. The disadvantages of BINCE are that it (i) does not provide to reconstructions diminishes interpretability; and (ii) has a high bias, unless the number of negative samples $n$ is large [33, 34], which is computationally intensive. + +# 5 Experiments + +We evaluated our framework focusing on two questions: (i) What compression rates can our framework achieve at what cost? (ii) Can we train a general purpose predictive image compressor? For all experiments, we train the compressors, freeze them, train the downstream predictors, and finally evaluate both on a test set. For classical compressors, standard neural compressors (VC) and our VIC, we used either reconstructions $\tilde { X }$ as inputs to the predictors or representations $Z$ . As BINCE does not provide reconstructions, we predicted from the compressed $Z$ using a multi-layer perceptron (MLP). We used ResNet18 [35] for encoders and image predictors. For entropy models we used Ballé et al.’s [28] hyperprior, which uses uniform quantization. We optimized hyper-parameters on validation using random search. For classification tasks, we report classification error instead of log-loss. The former is more standard and gave similar results (see Appx. F.2). For experimental details see Appx. E. For additional results see Appx. F. Code is at github.com/YannDubs/lossyless. + +# 5.1 Building intuition with toy experiments + +To build an visual intuition, we compressed samples from a 2D banana source distribution [36], assuming rotation invariant tasks, e.g., classifying whether points are in the unit circle. We also compressed MNIST digits as in Fig. 1. Digits are augmented (rotations, translations, shearing, scaling) both at train and test time to ensure that our invariance assumption still holds. + +![](images/6919e6f58eb4eca1ba90304ab55c81cc42f56b53a7aa00c4e3157d80046883ee.jpg) +Figure 5: Compression rates of a Banana source [36] can be decreased when downstream tasks are rotation invariant. (Left) Our invariant compressor (VIC, blue) outperforms neural compressors (VC, orange). 5 runs with standard errors in gray. (Right) VIC quantizes the space using disks to remove unnecessary angular information. Pink lines are quantization boundaries, dots are code vectors with size proportional to learned probabilities. Low rates correspond to low $\beta$ in Eq. (7). + +Where do our rate gains come from? For rotation invariant tasks, our method (VIC) discards unnecessary angular information by learning disk-shaped quantizations (Fig. 5, bottom right). Specifically, VIC retains only radial information by mapping all randomly rotated points (disks) back to maximal invariants (pink dots). In contrast, standard neural compressors (VC) attempt to reconstruct all information, which requires a finer partition (Fig. 5, top right). As a result (Fig. 5a), VIC needs a smaller bit-rate $y$ -axis) for the same desired performance $( \mathrm { D } _ { \tau _ { \sim } }$ , $x$ -axis). The area under the RD curve (AURD) for VIC is $3 5 . 8 { \pm } 4 . 2 $ against $4 8 . 1 { \pm } 0 . 3 $ for VC, i.e., expected bit-rate gains are around $7 0 \%$ . Similar gains are achieved for augmented MNIST in Fig. 6 by reconstructing canonical digits. + +![](images/4444126e4d93d8d0691113b395d75bc5be911978be1e8ca385d5ac3e21dd53b8.jpg) +Figure 6: (Left) By reconstructing prototypical digits our VIC (blue) achieves higher compression of augmented MNIST digits than standard neural compressors (VC, orange) without hindering downstream classification. 5 runs. (Right) The source examples (first row) as well as reconstructions for the non-invariant (second row) and invariant compressor (last row). + +Can we recover the optimal bit-rate? We investigated whether our losses can achieve the optimal bit-rate for lossy prediction by using supervised augmentations, i.e., $A ( x )$ randomly samples a train example $x ^ { + }$ that has the same label. For MNIST the single-task optimal bit-rate is $\mathrm { H } \bar { \vert } Y \vert = \mathrm { \bar { l o g } } ( 1 0 ) \approx$ 3.3 bits. VIC and BINCE respectively achieve 5.7 and 5.9 bits, which shows that our losses are relatively good despite practical approximations. Details in Appx. F.2. + +What is the impact of the choice of augmentations? The choice of augmentation $A$ implicitly defines the desired task-set $\tau$ , i.e., $\tau$ is the set of all tasks for which $A$ does not remove information. As a result Theorem 2 can be rewritten as $R a t e ( \delta ) = \operatorname { I } [ X ; A ( X ) ] - \delta$ , so the rate decreases when $A$ removes more information from $X$ . To illustrate this we trained our VIC using three augmentation sets on MNIST, all of which keep the true label invariant but progressively discard more $X$ information. VIC respectively achieves a rate of 185.3, 79.0, and 5.7 bits, which shows the importance of using augmentations that remove $X$ information. Details and BINCE results are in Appx. F.2. + +# 5.2 Evaluating our methods with controlled experiments + +To investigate our methods, we compressed the STL10 dataset [37]. We augment (flipping, color jittering, cropping) the train and test set, to ensure that the task invariance assumptions are satisfied. We focus on more realistic settings in the next section. In each experiment, we sampled 100 combinations of hyper-parameters to ensure equal computational budget across models and baselines. + +Table 1: Invariant compressors (BINCE, VIC) outperform classical (PNG, JPEG, WebP) and neural (VC) compressors on STL10. BINCE achieves lossless prediction but compresses $1 2 1 \times$ better. + +
PNG [38]JPEG [39]WebP [40]vcxVIC XVIC ZBINCE
Decrease in test acc.00.71.121.025.116.10.0
Compression gains1×3×13×63×269×175×121×
+ +How do our BINCE and VIC compare to standard compressors? In Table 1 we compare compressors at the lowest downstream error that they achieved. As benchmark, we use PNG’s lossless compression. Predicting from PNG corresponds to standard image classification, and obtains a rate of $1 . 4 2 \mathrm { e 4 }$ bits per image for $8 0 . 8 \%$ accuracy. Classical lossy methods (JPEG, WebP) achieved up to $1 3 \times$ bit-rate gains with little drop in performance. In comparison, our BINCE method achieved $1 2 1 \times$ compression gains with no impact on predictions. Both our invariant (VIC) and standard (VC) neural compressors significantly decreased classification accuracy, which we believe can be explained by the encoders architecture (ResNet18) that we use for consistency (see Appx. F.3). + +Should we predict from representations $Z$ or reconstructions $X ?$ In Table 1 we analyzed the impact of predicting from $Z$ instead of $\tilde { X }$ for VIC and see that this increases accuracy by $9 \%$ . In contrast, predicting from $Z$ for VC decreases performance by $1 2 \%$ (see Appx. F.3). This suggests that invariant reconstructions $\tilde { X }$ might not be easy to predict from with standard image predictors. + +Are we learning invariant compressors? Invariant compressors should provide RD curves that are robust to test distribution shift in the desired augmentations. We thus trained our VIC by applying the augmentations $5 0 \%$ of the time but varying that probability $p$ at test time. In Appx. F.3 we show that this distribution shift have negligible influence on RD curves. + +# 5.3 A zero-shot compressor using pre-trained self-supervised models + +BINCE includes a standard contrastive SSL loss. So, we investigated whether existing pre-trained SSL models [32, 41] can be used to build generic compressors. In particular, we investigated whether CLIP [41] could be quickly turned into a powerful task-centric compressor for computer vision. In the introduction, we motivated large compression gains by noting that typical image classification tasks can be predicted from detailed captions instead of images (around $1 0 0 0 \times$ more bits). CLIP is a vision transformer [42] pre-trained on 400M pairs of images and text $( x _ { i m a g e } , x _ { t e x t } ^ { + } )$ using a contrastive loss. The “augmentation” $A$ is then a function that maps $x _ { i m a g e }$ to its associated $\boldsymbol { x } _ { t e x t } ^ { + }$ and vis-versa. This will partition the images and texts into sets, each of which are associated directly or by transitivity in CLIP’s dataset. This suggests that CLIP is retaining the image information that corresponds to a detailed caption, and may be turned into a generic compressor for image classification. + +CLIP can essentially be seen as a BINCE model with an image-to-text augmentation, but without an entropy bottleneck. (For details about the CLIP-BINCE relation see Appx. C.5.) We thus constructed an approximation of our desired image-to-text BINCE compressor by two simple steps. First, we downloaded and froze CLIP’s parameters. Second, we trained, on the small MSCOCO dataset [43], an entropy bottleneck to compress CLIP’s representation. The latter step can be done by training any lossy compressor on CLIP’s representations, we did so using Ballé et al.’s [28] hyperprior entropy model with a learned rounded precision. We then evaluated our resulting compressor on 8 datasets (various classification tasks and image shapes) that were never seen during training (zero-shot), by training an MLP for downstream predictions on each dataset. One can see this as a multi-task setting (each dataset is a distinct task). We investigate the case of multiple labels per images in Appx. F.5. + +Can we use pretrained SSL to obtain a generic compressor? Table 2 shows that we can exploit existing state-of-the-art (SOTA) SSL models to get a powerful image compressor, which achieves $1 0 0 0 \times$ bit-rate gains on ImageNet compared to JPEG (at the quality level used for storing ImageNet). The bit-rate gains ( $1 ^ { \mathrm { s t } }$ row) are significant across all zero-shot datasets, even for biological tissues (PCam; [44]). Importantly, these gains come at little cost in test performance. Indeed, the test accuracies of MLPs from our representations ( $2 ^ { \mathrm { n d } }$ row) is similar to a near SOTA model trained on the uncompressed images $3 ^ { \mathrm { r d } }$ row is from Radford et al. [41]). These results are not surprising as JPEG is optimized to retain perceptual rather than classification information. Note that the large variance in rate gains come from JPEG rates due to different images shapes (see Table 3). + +Table 2: Converting a pretrained SSL model into a zero-shot compressor achieves substantial bit-rate gains while allowing test accuracies similar to supervised models predicting from raw images. + +
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
Rate gains vs JPEG1104×35×64×131×7×109×150×126×
Our Acc. [%]76.398.780.979.695.288.389.593.4
Supervised Acc. [%]76.199.082.649.196.781.890.494.5
+ +Our CLIP compressor retains all the information needed to get 0 error for those tasks. Table 2 provides the test performance for MLPs, while our theory discusses Bayes risk, which is independent of specific predictors and generalization. We estimated the excess Bayes risk for our datasets by counting the images (in train and test) that get compressed to the same $Z$ but have different labels. We found that we are in the lossless prediction regime for those datasets. + +Table 3: Our entropy bottleneck (EB) on CLIP improves compression of representations up to $1 7 \times$ with little impact on predictions. The same compressor is used across datasets. Rates are per image. + +
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
JPEG1.49e64.71e49.60e41.92e51.05e41.54e51.81e51.69e5
CLIP1.52e41.52e41.52e41.52e41.52e41.52e41.52e41.52e4
Brr+EB high β2.47e32.46e32.61e32.59e32.53e32.39e32.33e32.46e3
+EB β1.35e31.34e31.49e31.47e31.41e31.27e31.21e31.34e3
+EB low β9.63e29.52e21.09e31.07e31.02e38.89e28.35e29.53e2
CLIP76.598.684.580.895.388.589.793.2
+EB high β76.698.782.780.495.388.589.693.5
Trrs sss+EB β76.398.780.979.695.288.389.593.4
+EB low β76.098.780.178.994.887.688.692.9
+ +What is the effect of the entropy bottleneck? In Table 3 we compare the pretrained CLIP, to our CLIP compressor with an entropy bottleneck (EB) trained at different values for $\beta$ . When trained with a high $\beta$ , our EB improves bit-rates by an average of $6 \times$ without impacting predictions. For our compressor from Table 2 $\mathbf { ( C L I P + E B \ } \beta \mathbf { \Lambda }$ ) the gains increase to $1 1 \times$ with little predictive impact. The sacrifice in predictions is more clear for $1 6 \times$ bit-rate gains (low $\beta$ ). This shows that CLIP’s raw representations retain unnecessary information as it not explicitly trained to discard information. + +How would end-to-end BINCE compare to staggered training? Compression gains can likely be larger by end-to-end training of BINCE, which would require access to CLIP’s original dataset.7 To get an idea of potential gains we compared end-to-end and staggered BINCE on augmented MNIST in Appx. F.2. We found significant rate improvements (358 to 131 bits) for similar test accuracy. + +Our CLIP compressor is simple to use. In Appx. E.7, we provide a minimal script (150 lines) to train a generic compressor in less than five minutes on a single GPU. The script contains an efficient entropy coder for our model (200 images/second), which shows its practicality. As usual in SSL, the compressed representations are also more computationally efficient to work with than standard compressors. In our minimal script we achieve the desired performance $9 8 . 7 \%$ on STL) using a linear model that is trained in one second, which is $1 0 0 0 \times$ faster than the baseline in Table 2. This shows that our pipeline can improve computational efficiency in addition to storage efficiency. + +What augmentations to use for SSL compression? Table 4 compares two ResNet50 pretrained with contrastive learning using invariance to text-image (CLIP) or standard image augmentations (SimCLR [32]) such as cropping or flipping. We see that CLIP’s augmentation usually give better compression and downstream performance, which shows the importance of the choice of augmentations. This also supports our motivation of using text-image augmentations, which are likely label-preserving for a vast amount of tasks but discard large amounts of unnecessary information. + +Table 4: Text-image invariance is better than invariance to standard augmentations for image classification. CLIP and SimCLR are both ResNet50 pretrained with InfoNCE but different augmentations. + +
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
3CLIP+EB21081962194924212111199118671968
SimCLR+EB28112732276927512950207728392502
ACLIP+EB63.292.078.668.065.574.181.883.0
SimCLR+EB62.891.981.429.678.660.078.979.0
+ +# 6 Related work + +In Appx. D we discuss more related work, including invariances in compression and the link to SSL. + +Task-centric compression. To our knowledge, our paper is the first to formalize compression only for predictions. IB [11] uses a task-centric distortion, but is not used for compression as it requires supervised training, so there are no advantages compared to compressing predicted labels. Some authors used heuristics to bypass the supervised issue, e.g., focusing on low frequencies for classification [45] or high frequencies for segmentation [46]. Other authors have incorporated predictive errors to perceptual distortions [47, 48], but cannot compress without the perceptual distortion for the same reason as IB. One exception is Weber et al.’s [49] compressor, which (when removing their perceptual distortion) minimizes MSE in the hidden layers of a pretrained classifier. Even more related is Singh et al.’s [50] work on compressing pretrained features for transfer learning, which is practice is similar to our compression of SSL features. Their work do not provide theoretical justifications, and are constrained to tasks that are similar to those used for pretraining. + +# 7 Discussion and Outlook + +Given the ever increasing amount of data that is processed by task-specific algorithms, it is necessary to rethink the current task-agnostic compression paradigm. We formalized the first compression framework for retaining only the information necessary for high performance on desired tasks. Using our theory, we provide two unsupervised objectives for training neural compressors. Experimentally, we show that these compressors can achieve bit-rates that are orders of magnitude $1 0 0 0 \times$ on ImageNet) smaller than standard image compressors without losing predictive performance. + +There are a number of caveats that should be addressed. First, to achieve better rates, our theory requires an irrecoverable loss of information. This can be an issue if the set of desired tasks changes. For example, if one uses text-image invariances then it may be impossible to perform image segmentation from the compressed representations. One solution would be to keep an original copy and use invariant compression for duplicated data, e.g., for the thousands copies of ImageNet. A second issue is the interpretability of the compressed representations. This can be partially addressed by reconstructing prototypical data as in Fig. 1 (post-hoc decoders could be trained for BINCE). A third caveat is that the compressed representations may be harder to learn from, e.g., neural networks may struggle to predict from representations even if the information is retained. Although our experiments actually showed the opposite, this should be addressed theoretically, e.g., using decodable information [51, 52]. Finally, successful use of our framework requires access to labelpreserving augmentations $A$ that discard significant information about $X$ . Finding such an $A$ may be challenging for some tasks. Given that augmentations are ubiquitous in ML, the community will hopefully continue developing task-specific augmentations which we could take advantage of. + +Nevertheless, we achieved orders of magnitude improvements in compression for predictions, and we believe that our improvements are just the beginning. For example, many tasks can be answered by referencing a detailed natural language description of the data. In these cases, the improvements can be very large, potentially $1 \mathbf { M } \times$ for videos.8 In the long-term, we hope that abandoning perceptual reconstructions will enable individuals to process data at scales that are currently only possible at large institutions, and our society to take advantage of large data sources in a more sustainable way. + +# Acknowledgments and Disclosure of Funding + +We would like to thank Alex Alemi, David Duvenaud, Andriy Mnih, Emile Mathieu, Jonah Philion, Yangjun Ruan, and Ilya Sutskever for their helpful feedback and encouragements. Resources used in preparing this research were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR, and companies sponsoring the Vector Institute. BBR acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC): RGPIN-2020-04995, RGPAS-2020-00095, DGECR-2020-00343. + +# References + +[1] D. Rolnick, P. L. Donti, L. H. Kaack, K. 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OpenReview.net, 2020. [Online]. Available: https://openreview.net/forum?id=r1eBeyHFDH [52] Y. Dubois, D. Kiela, D. J. Schwab, and R. Vedantam, “Learning Optimal Representations with the Decodable Information Bottleneck,” in Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS +2020, December 6-12, 2020, virtual, H. Larochelle, M. Ranzato, R. Hadsell, M.-F. Balcan, and H.-T. Lin, Eds., 2020. [Online]. Available: https://proceedings.neurips.cc/paper/2020/hash/ d8ea5f53c1b1eb087ac2e356253395d8-Abstract.html + +# Checklist + +1. For all authors... + +(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] +(b) Did you describe the limitations of your work? [Yes] In Sec. 7. +(c) Did you discuss any potential negative societal impacts of your work? [Yes] In Sec. 7 we mention the potential decrease in interpretability. +(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] + +2. If you are including theoretical results... + +(a) Did you state the full set of assumptions of all theoretical results? [Yes] See Appx. A.2. +(b) Did you include complete proofs of all theoretical results? [Yes] See Appx. B. + +3. If you ran experiments... + +(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] The code to train our main compressor is in Appx. E.7, the code to replicate all our results is at anonymous. +(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] The most important training details can be found at Appx. E. Minor hyperparameters can be found in our code at anonymous. +(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [Yes] We report error bars for MNIST (Appx. F.2) and Banana (Appx. F.1). For larger experiments we sampled a fixed number of hyperparameters for each model and baseline (see Appx. E), and report the best result. +(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [No] + +4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... + +(a) If your work uses existing assets, did you cite the creators? [Yes] In Appx. E. +(b) Did you mention the license of the assets? [No] +(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] Our clip compressor in Appx. E.7 and our code at anonymous. +(d) Did you discuss whether and how consent was obtained from people whose data you’re using/curating? [No] We do not propose any new dataset. The main possible issues come from the CLIP dataset [41], for which the data collection procedure is discussed in details in their paper. +(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [No] We do not propose any new dataset. The main possible issues come from the CLIP dataset [41], for which the data collection procedure is discussed in details in their paper. \ No newline at end of file diff --git a/parse/train/wZrOOO9XBn/wZrOOO9XBn_content_list.json b/parse/train/wZrOOO9XBn/wZrOOO9XBn_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..2c211e95a87bacd689f9b7357245f3a88f3e608b --- /dev/null +++ b/parse/train/wZrOOO9XBn/wZrOOO9XBn_content_list.json @@ -0,0 +1,1361 @@ +[ + { + "type": "text", + "text": "Lossy Compression for Lossless Prediction ", + "text_level": 1, + "bbox": [ + 238, + 122, + 758, + 147 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yann Dubois Vector Institute yanndubois96@gmail.com ", + "bbox": [ + 246, + 200, + 437, + 243 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Benjamin Bloem-Reddy The University of British Columbia benbr@stat.ubc.ca ", + "bbox": [ + 516, + 200, + 753, + 242 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Karen Ullrich Facebook AI Research karenu@fb.com ", + "bbox": [ + 274, + 263, + 426, + 305 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chris J. Maddison University of Toronto Vector Institute cmaddis@cs.toronto.edu ", + "bbox": [ + 532, + 263, + 723, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 356, + 535, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most data is automatically collected and only ever “seen” by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations. Based on our theory, we design unsupervised objectives for training neural compressors. Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than $1 0 0 0 \\times$ on ImageNet) compared to JPEG on 8 datasets, without decreasing downstream classification performance. ", + "bbox": [ + 232, + 388, + 766, + 513 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Introduction ", + "text_level": 1, + "bbox": [ + 174, + 541, + 310, + 558 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Progress in important areas requires processing huge amounts of data. For climate prediction, models are still data-limited [1], despite the Natl. Center for Computational Sciences storing 32 million gigabytes (GB) of climate data [2]. For autonomous driving, capturing a realistic range of rare events with current methods requires around 3 trillion GB of data.1 At these scales, data are only processed by task-specific algorithms, and storing data in human-readable formats can be prohibitive. We need compressors that retain only the information needed for algorithmic execution of downstream tasks. ", + "bbox": [ + 174, + 571, + 825, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing lossy compressors are not up to the challenge, because they aim to reconstruct the data for human perception [5–10]. However, much of perceptual information is not needed to perform the tasks that we care about. Consider classifying images, which can require about 1 MB to store. Classification is typically invariant under small image transformations, such as rescalings or rotations, and could instead be performed using a representation that discards such information (see Fig. 1). The amount of unnecessary perceptual information is likely substantial, as illustrated by the fact that typical image classification can be performed using a detailed caption, which requires only about $1 \\mathrm { k B }$ to store $1 0 0 0 \\times$ fewer bits). ", + "bbox": [ + 174, + 661, + 517, + 853 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/228aa771e17e279691c98492f9ac7e7cf20a7f3bf05378f39656e5e370197397.jpg", + "image_caption": [ + "Figure 1: Our unsupervised coder improves compression by only keeping information necessary for typical tasks. (left) source augmented MNIST digit; (center) a neural perceptual compressor achieves 130 bit-rate; (right) our invariant compressor achieves 48 bit-rate. " + ], + "image_footnote": [], + "bbox": [ + 531, + 664, + 820, + 756 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Our goal is to quantify the bit-rate needed to ensure high performance on a collection of prediction tasks. In the simple case of a single supervised task, the minimum bit-rate is achieved by compressing predicted labels, and essentially corresponds to the Information Bottleneck (IB; [11]). Our challenge, instead, is to ensure good performance on any future tasks of interest, which will rarely be completely known at compression time, or might be too large to enumerate. ", + "bbox": [ + 174, + 90, + 825, + 161 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We overcome this challenge by focusing on sets of tasks that are invariant under user-defined transformations (e.g., translation, brightness, cropping), as is the case for many tasks of interest to humans [12, 13]. This structure allows us to characterize a worst-case invariant task, which bounds the relative predictive performance on all invariant tasks. As a result, the bit-rate required to perform well on all invariant tasks is exactly the rate to compress the worst-case labels. At a high level, the worst-case task is to recognize which examples are transformed versions of one another, and rate savings come from discarding information from those transformations. ", + "bbox": [ + 173, + 166, + 825, + 265 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also provide two unsupervised neural compressors to target the optimal rates. One is similar to a variational autoencoder [14] that reconstructs canonical examples (Fig. 1). Our second is a simple modification of contrastive self-supervised learning (SSL; [15]), which allows us to convert pre-trained SSL models into powerful, generic compressors. Our contributions are: ", + "bbox": [ + 173, + 270, + 825, + 327 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "• We formalize the notion of compression for downstream predictive tasks. \n• We characterize the bits needed for high performance on any task invariant to augmentations. \n• We provide unsupervised objectives to train compressors that approximate the optimal rates. \n• We show that our compressor outperforms JPEG by orders of magnitude on 8 datasets on which it was never trained (i.e., zero-shot). E.g., on ImageNet [16], it decreases the bit-rate by $1 0 0 0 \\times$ . ", + "bbox": [ + 173, + 332, + 825, + 402 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 Rate-distortion theory background ", + "text_level": 1, + "bbox": [ + 173, + 421, + 498, + 438 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The goal of lossy compression theory is to find the number of bits (bit-rate) required to store outcomes $x$ of a random variable (r.v.) $X$ , so that it can be reconstructed within a certain tolerance. This is accomplished in Shannon’s [17] rate-distortion (RD) theory by mapping $X$ into a r.v. $Z$ with low mutual information $\\operatorname { I } [ X ; Z ]$ . Specifically, given a distortion measure $\\mathrm { D } [ X , Z ]$ , the RD theory characterizes the minimal achievable bit-rate for a distortion threshold $\\delta$ by ", + "bbox": [ + 173, + 450, + 825, + 520 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/9d93b4a56ae41ec0e3fc397175910e336a79b5625f1b3ffd4618889c0a7ed46e.jpg", + "text": "$$\nR a t e ( \\delta ) = \\operatorname* { m i n } _ { p ( Z | X ) } \\operatorname { I } [ X ; Z ] \\quad { \\mathrm { ~ s u c h ~ t h a t ~ } } \\quad \\operatorname { D } [ X , Z ] \\leq \\delta .\n$$", + "text_format": "latex", + "bbox": [ + 316, + 544, + 681, + 569 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In lossy compression, $Z$ is usually a reconstruction of $X$ , i.e., it aims to faithfully approximate $X$ . As a result, typical distortions, e.g., the mean squared error (MSE), assume that the sample spaces $\\mathcal { X } , \\mathcal { Z }$ of both r.v.s are the same. This assumption is not required. Indeed, any distortion $d : \\mathcal { X } \\times \\mathcal { Z } \\to \\mathbb { R } _ { \\ge 0 }$ of the form $\\mathrm { D } [ X , Z ] = \\mathrm { E } _ { p ( X , Z ) } [ d ( X ^ { ' } , Z ) ]$ , where there exists a $z \\in Z$ such that $\\mathrm { D } [ X , z ]$ is finite, is a valid choice [18]. This shows that RD theory can be used outside of reconstructions. In the following we refer to $Z$ as a compressed representation of $X$ to distinguish it from a reconstruction. ", + "bbox": [ + 173, + 592, + 825, + 678 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3 Minimal bit-rate for high predictive performance ", + "text_level": 1, + "bbox": [ + 173, + 695, + 616, + 713 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we characterize the bit-rate needed to represent $X$ to ensure high performance on downstream tasks. Our argument has three high-level steps: (i) define a distortion that controls downstream performance when predicting from $Z$ instead of $X$ ; (ii) simplify and validate this distortion when desired tasks satisfy an invariance condition; (iii) apply RD theory with the valid distortion. For simplicity, our presentation is relatively informal; formal proofs are in Apps. A and B. ", + "bbox": [ + 174, + 726, + 825, + 796 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1 A distortion for worst-case predictive performance ", + "text_level": 1, + "bbox": [ + 173, + 806, + 565, + 821 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Suppose $X$ is an image. Potential downstream tasks might include $Y _ { \\mathrm { d o g } }$ , whether the image displays a dog; or $Y _ { \\mathrm { h d } }$ , whether the image is hand-drawn. Formally, these and other downstream tasks are expressed as $\\mathcal { T } = \\{ Y _ { \\mathrm { d o g } } , Y _ { \\mathrm { h d } } , . . . \\}$ , a set of random variables that are jointly distributed with $X$ . Let $\\mathrm { R } [ Y | X ]$ denote the Bayes (best possible) risk when predicting $Y$ from $X$ . For ease of presentation in the main paper, we consider only classification tasks $\\tau$ and Bayes risk of the standard log loss $\\begin{array} { r } { \\mathrm { R } [ Y | X ] : = \\bar { \\operatorname* { i n f } _ { q } \\mathrm { E } } _ { p ( X , Y ) } [ - \\log q ( \\dot { Y } | X ) ] } \\end{array}$ . We deal with MSE and regression in Appx. B.6. ", + "bbox": [ + 174, + 827, + 825, + 912 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9108ffa9cd994dbe365806d6efeca48befc210b4d5e08d0166cef74a1bc15cc0.jpg", + "image_caption": [ + "Figure 2: Maximal invariants $M ( X )$ are representatives of equivalence classes. Example $M \\mathrm { s }$ include the: (a) Euclidean norm for rotations; (b) unit vector for scaling; (c) $f$ when equivalence classes are pre-images by $f$ ; (d) empirical measure for permutations; (e) canonical graph for graph isomorphisms; (f) unaugmented input for data augmentations. " + ], + "image_footnote": [], + "bbox": [ + 196, + 92, + 805, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this setting, a meaningful distortion $\\mathrm { D } _ { \\tau } [ X , Z ]$ quantifies the difference between predicting any $Y \\in \\tau$ from the compressed $Z$ , as opposed to using $X$ . This is the worst-case excess risk, ", + "bbox": [ + 174, + 411, + 823, + 440 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/d61030e5a566b6a43b4aa6f108357f7cf870257551c6b3d296486261463b9ca5.jpg", + "text": "$$\n\\operatorname { D } _ { \\tau } [ X , Z ] : = \\operatorname* { s u p } _ { Y \\in { \\mathcal { T } } } \\quad \\operatorname { R } [ Y \\mid Z ] - \\operatorname { R } [ Y \\mid X ] .\n$$", + "text_format": "latex", + "bbox": [ + 354, + 448, + 643, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "If $\\mathrm { D } _ { \\tau } [ X , Z ] = 0$ , it is possible to achieve lossless prediction: performing as well using $Z$ as using $X$ . More generally, bounding $\\mathrm { D } _ { \\tau }$ by $\\delta$ ensures that $\\mathrm { R } [ Y | Z ] - \\mathrm { R } [ Y | X ] \\leq \\delta$ for all tasks in $\\tau$ . However, there are two issues that need to be addressed before Eq. (2) can be used. First, it is not clear whether $\\mathrm { D } _ { \\tau }$ is a valid distortion for RD theory. Second, the worst excess-risk $\\mathrm { D } _ { \\tau }$ assumes access to all downstream tasks of interest $\\tau$ during compression, which is unrealistic in general. ", + "bbox": [ + 173, + 482, + 825, + 553 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2 Invariant tasks ", + "text_level": 1, + "bbox": [ + 174, + 564, + 318, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The tasks that we care about are not arbitrary, and often share structure. One such structure is invariance to certain pre-specified transformations of input data. For example, computer vision tasks are often invariant to mild transformations such as brightness changes. Such invariance structure is common in realistic tasks, as seen by the wide-spread use of data augmentations [13] in machine learning (ML), which encourage predictions to be the same for an unaugmented $x$ and an augmented $x ^ { + }$ . Motivated by this we focus on sets of invariant tasks $\\tau$ . ", + "bbox": [ + 174, + 584, + 825, + 669 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider a general notion of invariance, namely invariance specified by an equivalence relation $\\sim$ on $\\mathcal { X }$ .2 The equivalence induces a partition of $\\mathcal { X }$ into disjoint equivalence classes, and we are interested in tasks whose conditional distributions are constant within these classes. ", + "bbox": [ + 173, + 674, + 825, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1. The set of invariant tasks of interest with respect to an equivalence $( \\mathcal { X } , \\sim )$ , denoted $\\mathcal { T } _ { \\sim }$ , is all random variables $Y$ such that $x \\sim x ^ { + } \\implies p ( Y | x ) = p ( Y | x ^ { + } )$ for any $x , x ^ { + } \\in \\mathcal { X }$ . ", + "bbox": [ + 171, + 729, + 825, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3 Rate-distortion theory for invariant task prediction ", + "text_level": 1, + "bbox": [ + 173, + 770, + 570, + 786 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The key to simplifying $\\mathrm { D } _ { \\tau _ { \\sim } }$ is the existence of a (non-unique) worst-case invariant task, denoted $M ( X )$ . Such task contains all and only information to which tasks $Y \\in \\mathcal { T } _ { \\sim }$ are not invariant; we call them maximal invariants. A maximal invariant $M ( \\bullet )$ with respect to $\\sim$ is any function satisfying3 ", + "bbox": [ + 176, + 791, + 826, + 834 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/4a9138c0deaada2706d5575cef88635b1199839f85d06835a9f9764d7b61a43a.jpg", + "text": "$$\nx \\sim x ^ { + } \\iff M ( x ) = M ( x ^ { + } ) \\quad { \\mathrm { f o r ~ a n y ~ } } x , x ^ { + } \\in \\mathcal { X } .\n$$", + "text_format": "latex", + "bbox": [ + 320, + 842, + 678, + 859 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A maximal invariant removes all information that tasks are invariant to, as it maps equivalent inputs to the same output, i.e., $M ( x ) = M ( x ^ { + } )$ . Yet, it retains the minimal information needed to perform invariant tasks, by mapping non-equivalent inputs $x \\not \\sim x ^ { - }$ to different outputs $M ( x ) \\neq { \\overline { { M } } } ( x ^ { - } )$ . In other words, $M ( x )$ indexes the equivalence classes. For example, the Euclidean norm is a maximal invariant for rotation invariance, as all vectors that are rotated versions of one another can be characterized by their radial coordinate. For data augmentations, the canonical (unaugmented) version of the input is a maximal invariant. Other examples are shown in Fig. 2. ", + "bbox": [ + 173, + 90, + 826, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We prove in Appx. B.2 that under weak regularity conditions, maximal invariant tasks exist in $\\mathcal { T } _ { \\sim }$ , and that they achieve the supremum in Eq. (2). This allows us to show that $\\mathrm { D } _ { \\tau _ { \\sim } }$ reduces to the Bayes risk of predicting $M ( X )$ from $Z$ and that it is a valid distortion measure. Crucially, this allows us to quantify downstream performance without enumerating invariant tasks. ", + "bbox": [ + 173, + 194, + 825, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 1. Let $( \\mathcal { X } , \\sim )$ be an equivalence relation and $M$ a maximal invariant that takes at most countably many values, with $\\mathrm { H } [ M ( \\bar { X } ) ] < \\infty$ . Then $\\mathrm { D } _ { \\tau _ { \\sim } }$ (2) with log loss is a valid distortion and ", + "bbox": [ + 173, + 263, + 825, + 292 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/98d782cef09afa364b2f4eccba15917dcffd1f4c559f303c4291c2abe4e3db74.jpg", + "text": "$$\n\\mathrm { D } _ { \\tau _ { \\sim } } [ X , Z ] = \\mathrm { R } [ M ( X ) | Z ] \\ .\n$$", + "text_format": "latex", + "bbox": [ + 398, + 294, + 594, + 310 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here we used $\\operatorname { R } [ M ( X ) | X ] = 0$ , as $M$ is a deterministic function. Also, note that the countable requirement holds when tasks are invariant to some rounding of the input, as is typically the case due to floating-point storage. We accommodate the uncountable case for squared-error loss in Appx. B.6. ", + "bbox": [ + 173, + 318, + 825, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With a valid distortion in hand, we invoke the RD theorem with $\\mathrm { D } _ { \\tau _ { \\sim } }$ to obtain our “Rate-Invariance” (RI) theorem. The RI theorem characterizes the bit-rate needed to store $X$ while ensuring small log-loss on invariant tasks. We obtain analogous results for squared-error loss. ", + "bbox": [ + 174, + 366, + 825, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 2 (Rate-Invariance). Assume the conditions of Prop. 1. Let $\\delta \\geq 0$ , and $R a t e ( \\delta )$ denote the minimum achievable bit-rate for transmitting $Z$ such that for any $Y \\in \\mathcal { T } _ { \\sim }$ we have $\\mathrm { R } [ \\dot { Y } | Z ] -$ $\\mathrm { R } [ Y | X ] \\leq \\delta$ . Then $R a t e ( \\delta ) = 0$ if $\\delta \\geq \\mathrm { H } [ M ( \\bar { X } ) ]$ and otherwise it is finite and ", + "bbox": [ + 174, + 421, + 823, + 464 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cb8ccf92de6e597a10d0adc453be47c4173aa7e0fb6ecca9ffa8de99785a3aca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 187, + 468, + 790, + 516 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure lossless prediction, i.e., $R a t e ( 0 )$ , our theorem states that we require a bit-rate of $\\mathrm { H } [ M ( { \\bar { X } } ) ]$ . Intuitively, this is because $M ( X )$ contains the minimal information needed to predict losslessly any $Y \\in \\tau _ { \\sim }$ .4 Furthermore, the theorem relates compression and prediction by showing that allowing a $\\delta$ decrease in log-loss performance on all tasks can save exactly $\\delta$ bits. Intuitively, this is a linear relationship, because expected log-loss is measured in bits. On the right of Eq. (5) we further decompose $\\mathrm { H } [ M ( X ) ]$ into two terms to provide another interpretation: (i) $\\mathrm { H } [ X ]$ , which, for discrete $X$ , is the bit-rate required to losslessly compress $X$ , and (ii) $\\mathrm { H } [ X | M ( X ) ]$ , which quantifies the information removed due to the invariance of desired tasks. Importantly, removing this information does not impact the best possible predictive performance. See Fig. 3. ", + "bbox": [ + 174, + 526, + 550, + 734 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5ec6bce1f3417baafb6ede7024f058c61fc0939e9b65007e3138dad6df7de2a2.jpg", + "image_caption": [ + "Figure 3: Rate-Invariance function. " + ], + "image_footnote": [], + "bbox": [ + 566, + 537, + 795, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The bit-rate gains can be substantial, depending on the invariances. Consider compressing a sequence of $n$ i.i.d. fair coin flips. Suppose one is only interested in predicting permutation invariant labels. Then instead of compressing the entire sequence in $\\operatorname { H } [ X ^ { n } ] = n \\operatorname { H } [ X ] = n$ bits, one could compress the number of heads, which is a maximal invariant for permutation invariance, in ${ \\mathcal { O } } ( \\log n )$ bits.5 As more interesting examples, we recover in Appx. B.4 results from (i) unlabeled graph compression [20]; (ii) multiset compression [21]; (iii) single task compression (IB; [11]). The equivalence $\\sim$ can be induced by any transformations, such as transforming an image to its caption. We use this idea in Sec. 5.3 to obtain ${ \\mathrm { > } } 1 0 0 0 \\times$ compression on ImageNet without sacrificing predictive performance. ", + "bbox": [ + 173, + 739, + 825, + 852 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/92ee44f90fed57f5b1bc8cdcd797bb90169e242082ce1cc774d494daba369015.jpg", + "image_caption": [ + "Figure 4: Our unsupervised objectives for invariant image compression under data augmentation use the same encoder, but differ in their approximation to the invariance distortion. Both models encode the augmented data, pass the representation through an entropy bottleneck which ensures that they are compressed, and use a distortion to retain the information about the identity of the original data. The models differ in how they retain that information: (VIC) by reconstructing unaugmented inputs; (BINCE) by recognizing which inputs come from the same original data. " + ], + "image_footnote": [], + "bbox": [ + 184, + 89, + 825, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4 Unsupervised training of invariant neural compressors ", + "text_level": 1, + "bbox": [ + 176, + 308, + 663, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we design practical, invariant neural compressors that bound optimal rates. Derivations are in Appx. C. In particular, we are interested in the arg min encoders $p ( Z | X )$ of the RD function (Eq. (1)) under the invariance distortion $\\mathrm { D } _ { \\tau _ { \\sim } }$ . To accomplish this, we can optimize the following equivalent (i.e., it induces the same RI function) Lagrangian, where $\\beta$ takes the role of $\\delta$ , 6 ", + "bbox": [ + 173, + 338, + 825, + 393 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/34c4bfa58ca1f5d7a7a3b4b6da7498b50ed7e176f9c1d974ec6d185b8e73fa6e.jpg", + "text": "$$\n\\begin{array} { r l } { \\underset { p ( Z | X ) } { \\operatorname { a r g m i n } } } & { { } \\operatorname { I } [ X ; Z ] + \\beta \\cdot \\operatorname { R } [ M ( X ) \\mid Z ] . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 362, + 395, + 632, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In ML, the maximal invariant $M$ is often not available. Instead, invariances are implicitly specified by sampling a random augmentation from $A$ , applying it to a datapoint $X$ , and asking that the model’s prediction be invariant between $X$ and $A ( X )$ . For example, invariance to cropping can be enforced by randomly cropping images while retaining the original label. We show in Appx. C, that in such case, we can treat the augmented $A ( X )$ as the new source, $Z$ as the representation of $A ( X )$ , and the unaugmented $X$ as the maximal invariant task $M ( A ( X ) )$ . Indeed, $\\operatorname { R } [ M ( A ( X ) ) | Z ]$ is equal to $\\mathrm { R } [ X | Z ]$ up to a constant, so we can rewrite Eq. (6) as the following equivalent objective, ", + "bbox": [ + 173, + 424, + 825, + 521 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/efcfacb0d34bee00eaf2488530e6ff8bab114a89a06ca74a413a0e46170e0be2.jpg", + "text": "$$\n\\begin{array} { r l } { \\operatorname { a r g m i n } } & { \\operatorname { I } [ A ( X ) ; Z ] \\ + \\ \\beta \\cdot \\operatorname { R } [ X \\mid Z ] . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 359, + 522, + 635, + 550 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Such reformulation is possible if random augmentations retain the invariance structure $X \\sim A ( X )$ but “erase” enough information about equivalent inputs, specifically, if $X \\bot \\bot A ( X ) \\mid M ( X )$ . We discuss the second requirement in Appx. C but note that it will likely not be a practical issue if the dataset is small compared to the support $\\left| \\mathcal { D } \\right| \\ll \\left| \\mathcal { X } \\right|$ . With this, we have an objective whose r.v.s. are easy to sample from. However, both terms in Eq. (7) are still challenging to estimate. ", + "bbox": [ + 173, + 551, + 825, + 622 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the following, we develop two practical variational bounds to Eq. (7), which can be optimized by stochastic gradient descent [23] over the encoder’s parameters. Both approximations use the standard lossy neural compression bound $\\begin{array} { r } { \\operatorname { I } [ Z ; A ( X ) ] \\bar { \\le } \\operatorname { H } [ Z ] \\le \\operatorname* { m i n } _ { \\theta } \\operatorname { E } _ { p ( Z ) } [ - \\log q _ { \\theta } ( Z ) ] } \\end{array}$ where $q _ { \\theta } ( Z )$ is called an entropy model (or a prior) [24, 25]. This has the advantage that the learned $q _ { \\theta }$ can be used for entropy coding $Z$ [26, 27]. See Ballé et al. [28] for possible entropy models. Our two approximations differ in how they upper bound $\\mathrm { R } [ X \\mid Z ]$ . The first uses a reconstruction loss, which attempts to reconstruct the unaugmented input $x \\in \\mathcal { D }$ from $A ( x )$ . The second uses a discrimination loss, which attempts to recognize which examples are augmented versions of the input. ", + "bbox": [ + 173, + 627, + 825, + 741 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1 Variational Invariant Compressor (VIC) ", + "text_level": 1, + "bbox": [ + 173, + 751, + 495, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our first model is a modified neural compressor in which inputs are augmented but target reconstructions are not. We refer to it as a variational invariant compressor (VIC). See Fig. 4 for an illustration. VIC has an encoder $p _ { \\varphi } ( Z | A ( X ) )$ , an entropy model $q _ { \\theta } ( Z )$ , and a decoder $q _ { \\phi } ( X | Z )$ . Given a data sample $x \\in \\mathcal { D }$ , we apply a random augmentation $A ( x )$ , and encode it to get a representation $Z$ . The decoder then attempts to reconstruct the unaugmented $x$ from $Z$ . This leads to the objective, ", + "bbox": [ + 173, + 772, + 826, + 842 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/8fa2bbeadebb4e0bbb0e553cdd3c194cecf12d2f6adcc91cc1766fdfb3957c36.jpg", + "text": "$$\n{ \\mathcal { L } } _ { \\mathrm { v l c } } ( \\phi , \\theta , \\varphi ) : = - \\sum _ { x \\in { \\mathcal { D } } } \\operatorname { E } _ { p ( A ) p _ { \\varphi } ( Z \\mid A ( x ) ) } [ \\log q _ { \\theta } ( Z ) + \\beta \\cdot \\log q _ { \\phi } ( x \\mid Z ) ] .\n$$", + "text_format": "latex", + "bbox": [ + 264, + 843, + 732, + 877 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The term $\\log q _ { \\theta } ( Z )$ is an entropy bottleneck, which bounds the rate $\\operatorname { I } [ A ( X ) ; Z ]$ and ensures that unnecessary information is removed. The term $\\log q _ { \\phi } ( x | Z )$ bounds the distortion $\\mathrm { R } [ X | Z ] \\leq$ $\\operatorname { E } _ { p ( X , Z ) } [ - \\log q _ { \\phi } ( X \\mid Z ) ]$ and ensures that VIC preserves the information needed for invariant tasks. ", + "bbox": [ + 174, + 90, + 825, + 133 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2 Bottleneck InfoNCE (BINCE) ", + "text_level": 1, + "bbox": [ + 176, + 146, + 419, + 161 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our second compressor retains all predictive information without reconstructing the data. It has two components: an entropy bottleneck and an InfoNCE [15] objective, which is the standard in contrastive SSL. We refer to this as the bottleneck InfoNCE (BINCE), see Fig. 4. BINCE has an advantage over VIC in that it avoids the problem of reconstructing possibly high dimensional data. ", + "bbox": [ + 173, + 167, + 825, + 223 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Algorithm 1 shows how to train BINCE, where each call to $A$ returns an independent augmentation of its input. As with VIC, for every datapoint $x \\in \\mathcal { D }$ , we obtain a representation $Z$ by applying an augmentation $A ( x )$ and passing it through the encoder $p _ { \\varphi } ( Z | A ( X ) )$ . We then sample a “positive” example $Z ^ { + }$ by encoding a different augmented version of the same underlying datapoint $x$ . Finally, we sample $n$ “negative” examples $Z _ { i } ^ { - }$ by encoding augmentations $A ( x _ { i } ^ { - } )$ of datapoints $x _ { i } ^ { - } \\in \\mathcal { D }$ that are different from $x$ . This results in a sequence $z =$ $( Z ^ { + } , Z _ { 1 } ^ { - } , \\ldots , Z _ { n } ^ { - } )$ . For conciseness we will denote the above sampling procedure as $p _ { \\varphi } ( Z , Z \\mid A , \\mathcal { D } , x )$ . The final loss uses a discriminator $f _ { \\psi }$ that is optimized to score the equivalence of two representation, ", + "bbox": [ + 174, + 229, + 517, + 438 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Algorithm 1 BINCE’s forward pass for $x$ ", + "text_level": 1, + "bbox": [ + 532, + 234, + 803, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Require: $p _ { \\varphi } , q _ { \\theta } , f _ { \\psi } , \\mathcal { D } , A , \\beta , n , x$ ", + "bbox": [ + 531, + 257, + 743, + 270 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "1: $\\tilde { x } \\mathrm { s a m p l e } ( A ( x ) )$ . Augment \n2: $z \\gets \\mathrm { s a m p l e } ( p _ { \\varphi } ( Z | \\tilde { x } ) )$ . Encode \n3: rate_ $\\mathrm { l o s s } - \\log q _ { \\theta } ( z )$ \n4: $\\{ x _ { i } ^ { - } \\} _ { i = 1 } ^ { n } \\operatorname { s e l e c t } ( { \\mathcal { D } } \\setminus \\{ x \\} ) ~ i$ $n$ times \n5: $\\tilde { \\mathbf { x } } \\gets \\mathrm { s a m p l e } ( [ A ( x ) , A ( x _ { 1 } ^ { - } ) , \\ldots , A ( x _ { n } ^ { - } ) ] )$ \n6: $\\mathbf { z } \\gets \\mathrm { s a m p l e } ( p _ { \\varphi } ( Z | \\tilde { \\mathbf { x } } ) )$ \n7: z+ ← z[0] \n8: softmax ← ψ (Pz0∈z exp fψ(z0,z)) \n9: distortion_loss ← − log(softmax) \n10: return rate_loss $+ \\beta \\cdot$ distortion_loss ", + "bbox": [ + 534, + 270, + 823, + 426 + ], + "page_idx": 5 + }, + { + "type": "equation", + "img_path": "images/ab4418a9c151ec169592f74555c1198d4a8879d2627ee97b070e84899c415b0b.jpg", + "text": "$$\n\\mathcal { L } _ { \\mathrm { { s u r c e } } } ( \\varphi , \\theta , \\psi ) : = - \\sum _ { x \\in \\mathcal { D } } \\mathrm { E } _ { p ( A ) p _ { \\varphi } ( Z , Z | A , \\mathcal { D } , x ) } \\left[ \\log q _ { \\theta } ( Z ) + \\beta \\cdot \\log \\frac { \\exp f _ { \\psi } ( Z ^ { + } , Z ) } { \\sum _ { Z ^ { \\prime } \\in \\mathbb { Z } } \\exp f _ { \\psi } ( Z ^ { \\prime } , Z ) } \\right] .\n$$", + "text_format": "latex", + "bbox": [ + 189, + 446, + 787, + 487 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BINCE retains the necessary information by classifying (as seen by the softmax) which $Z$ is associated with an equivalent example $X$ . Both VIC and BINCE give rise to efficient compressors by passing $X$ through $p _ { \\varphi } ( Z | X )$ and entropy coding using $q _ { \\theta } ( Z )$ . In theory they can both recover the optimal rate for lossless predictions, i.e., $\\mathrm { H } [ M ( X ) ]$ , in the limit of infinite samples $( | \\mathcal { D } | , n )$ and unconstrained variational families. In practice, BINCE has the advantage over VIC of (i) not requiring a high dimensional decoder; and (ii) giving (for suitable $f _ { \\psi }$ ) representations that are approximately linearly separable [29–31] and thus easy to predict from [15, 32]. The disadvantages of BINCE are that it (i) does not provide to reconstructions diminishes interpretability; and (ii) has a high bias, unless the number of negative samples $n$ is large [33, 34], which is computationally intensive. ", + "bbox": [ + 173, + 494, + 825, + 621 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5 Experiments ", + "text_level": 1, + "bbox": [ + 174, + 638, + 312, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluated our framework focusing on two questions: (i) What compression rates can our framework achieve at what cost? (ii) Can we train a general purpose predictive image compressor? For all experiments, we train the compressors, freeze them, train the downstream predictors, and finally evaluate both on a test set. For classical compressors, standard neural compressors (VC) and our VIC, we used either reconstructions $\\tilde { X }$ as inputs to the predictors or representations $Z$ . As BINCE does not provide reconstructions, we predicted from the compressed $Z$ using a multi-layer perceptron (MLP). We used ResNet18 [35] for encoders and image predictors. For entropy models we used Ballé et al.’s [28] hyperprior, which uses uniform quantization. We optimized hyper-parameters on validation using random search. For classification tasks, we report classification error instead of log-loss. The former is more standard and gave similar results (see Appx. F.2). For experimental details see Appx. E. For additional results see Appx. F. Code is at github.com/YannDubs/lossyless. ", + "bbox": [ + 173, + 669, + 826, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1 Building intuition with toy experiments ", + "text_level": 1, + "bbox": [ + 174, + 834, + 486, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To build an visual intuition, we compressed samples from a 2D banana source distribution [36], assuming rotation invariant tasks, e.g., classifying whether points are in the unit circle. We also compressed MNIST digits as in Fig. 1. Digits are augmented (rotations, translations, shearing, scaling) both at train and test time to ensure that our invariance assumption still holds. ", + "bbox": [ + 176, + 856, + 826, + 911 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6919e6f58eb4eca1ba90304ab55c81cc42f56b53a7aa00c4e3157d80046883ee.jpg", + "image_caption": [ + "Figure 5: Compression rates of a Banana source [36] can be decreased when downstream tasks are rotation invariant. (Left) Our invariant compressor (VIC, blue) outperforms neural compressors (VC, orange). 5 runs with standard errors in gray. (Right) VIC quantizes the space using disks to remove unnecessary angular information. Pink lines are quantization boundaries, dots are code vectors with size proportional to learned probabilities. Low rates correspond to low $\\beta$ in Eq. (7). " + ], + "image_footnote": [], + "bbox": [ + 215, + 90, + 784, + 279 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Where do our rate gains come from? For rotation invariant tasks, our method (VIC) discards unnecessary angular information by learning disk-shaped quantizations (Fig. 5, bottom right). Specifically, VIC retains only radial information by mapping all randomly rotated points (disks) back to maximal invariants (pink dots). In contrast, standard neural compressors (VC) attempt to reconstruct all information, which requires a finer partition (Fig. 5, top right). As a result (Fig. 5a), VIC needs a smaller bit-rate $y$ -axis) for the same desired performance $( \\mathrm { D } _ { \\tau _ { \\sim } }$ , $x$ -axis). The area under the RD curve (AURD) for VIC is $3 5 . 8 { \\pm } 4 . 2 $ against $4 8 . 1 { \\pm } 0 . 3 $ for VC, i.e., expected bit-rate gains are around $7 0 \\%$ . Similar gains are achieved for augmented MNIST in Fig. 6 by reconstructing canonical digits. ", + "bbox": [ + 173, + 371, + 825, + 483 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4444126e4d93d8d0691113b395d75bc5be911978be1e8ca385d5ac3e21dd53b8.jpg", + "image_caption": [ + "Figure 6: (Left) By reconstructing prototypical digits our VIC (blue) achieves higher compression of augmented MNIST digits than standard neural compressors (VC, orange) without hindering downstream classification. 5 runs. (Right) The source examples (first row) as well as reconstructions for the non-invariant (second row) and invariant compressor (last row). " + ], + "image_footnote": [], + "bbox": [ + 183, + 497, + 821, + 662 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Can we recover the optimal bit-rate? We investigated whether our losses can achieve the optimal bit-rate for lossy prediction by using supervised augmentations, i.e., $A ( x )$ randomly samples a train example $x ^ { + }$ that has the same label. For MNIST the single-task optimal bit-rate is $\\mathrm { H } \\bar { \\vert } Y \\vert = \\mathrm { \\bar { l o g } } ( 1 0 ) \\approx$ 3.3 bits. VIC and BINCE respectively achieve 5.7 and 5.9 bits, which shows that our losses are relatively good despite practical approximations. Details in Appx. F.2. ", + "bbox": [ + 173, + 738, + 825, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "What is the impact of the choice of augmentations? The choice of augmentation $A$ implicitly defines the desired task-set $\\tau$ , i.e., $\\tau$ is the set of all tasks for which $A$ does not remove information. As a result Theorem 2 can be rewritten as $R a t e ( \\delta ) = \\operatorname { I } [ X ; A ( X ) ] - \\delta$ , so the rate decreases when $A$ removes more information from $X$ . To illustrate this we trained our VIC using three augmentation sets on MNIST, all of which keep the true label invariant but progressively discard more $X$ information. VIC respectively achieves a rate of 185.3, 79.0, and 5.7 bits, which shows the importance of using augmentations that remove $X$ information. Details and BINCE results are in Appx. F.2. ", + "bbox": [ + 173, + 814, + 825, + 911 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2 Evaluating our methods with controlled experiments ", + "text_level": 1, + "bbox": [ + 173, + 90, + 578, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To investigate our methods, we compressed the STL10 dataset [37]. We augment (flipping, color jittering, cropping) the train and test set, to ensure that the task invariance assumptions are satisfied. We focus on more realistic settings in the next section. In each experiment, we sampled 100 combinations of hyper-parameters to ensure equal computational budget across models and baselines. ", + "bbox": [ + 174, + 112, + 826, + 167 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/bfaf95455bea4d182488b8baf70d0b989091927010c8a79d52ac9e75b91da9c6.jpg", + "table_caption": [ + "Table 1: Invariant compressors (BINCE, VIC) outperform classical (PNG, JPEG, WebP) and neural (VC) compressors on STL10. BINCE achieves lossless prediction but compresses $1 2 1 \\times$ better. " + ], + "table_footnote": [], + "table_body": "
PNG [38]JPEG [39]WebP [40]vcxVIC XVIC ZBINCE
Decrease in test acc.00.71.121.025.116.10.0
Compression gains1×3×13×63×269×175×121×
", + "bbox": [ + 179, + 209, + 815, + 265 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "How do our BINCE and VIC compare to standard compressors? In Table 1 we compare compressors at the lowest downstream error that they achieved. As benchmark, we use PNG’s lossless compression. Predicting from PNG corresponds to standard image classification, and obtains a rate of $1 . 4 2 \\mathrm { e 4 }$ bits per image for $8 0 . 8 \\%$ accuracy. Classical lossy methods (JPEG, WebP) achieved up to $1 3 \\times$ bit-rate gains with little drop in performance. In comparison, our BINCE method achieved $1 2 1 \\times$ compression gains with no impact on predictions. Both our invariant (VIC) and standard (VC) neural compressors significantly decreased classification accuracy, which we believe can be explained by the encoders architecture (ResNet18) that we use for consistency (see Appx. F.3). ", + "bbox": [ + 173, + 279, + 825, + 390 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Should we predict from representations $Z$ or reconstructions $X ?$ In Table 1 we analyzed the impact of predicting from $Z$ instead of $\\tilde { X }$ for VIC and see that this increases accuracy by $9 \\%$ . In contrast, predicting from $Z$ for VC decreases performance by $1 2 \\%$ (see Appx. F.3). This suggests that invariant reconstructions $\\tilde { X }$ might not be easy to predict from with standard image predictors. ", + "bbox": [ + 174, + 396, + 825, + 457 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Are we learning invariant compressors? Invariant compressors should provide RD curves that are robust to test distribution shift in the desired augmentations. We thus trained our VIC by applying the augmentations $5 0 \\%$ of the time but varying that probability $p$ at test time. In Appx. F.3 we show that this distribution shift have negligible influence on RD curves. ", + "bbox": [ + 174, + 462, + 825, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3 A zero-shot compressor using pre-trained self-supervised models ", + "text_level": 1, + "bbox": [ + 176, + 530, + 661, + 545 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "BINCE includes a standard contrastive SSL loss. So, we investigated whether existing pre-trained SSL models [32, 41] can be used to build generic compressors. In particular, we investigated whether CLIP [41] could be quickly turned into a powerful task-centric compressor for computer vision. In the introduction, we motivated large compression gains by noting that typical image classification tasks can be predicted from detailed captions instead of images (around $1 0 0 0 \\times$ more bits). CLIP is a vision transformer [42] pre-trained on 400M pairs of images and text $( x _ { i m a g e } , x _ { t e x t } ^ { + } )$ using a contrastive loss. The “augmentation” $A$ is then a function that maps $x _ { i m a g e }$ to its associated $\\boldsymbol { x } _ { t e x t } ^ { + }$ and vis-versa. This will partition the images and texts into sets, each of which are associated directly or by transitivity in CLIP’s dataset. This suggests that CLIP is retaining the image information that corresponds to a detailed caption, and may be turned into a generic compressor for image classification. ", + "bbox": [ + 173, + 550, + 825, + 691 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "CLIP can essentially be seen as a BINCE model with an image-to-text augmentation, but without an entropy bottleneck. (For details about the CLIP-BINCE relation see Appx. C.5.) We thus constructed an approximation of our desired image-to-text BINCE compressor by two simple steps. First, we downloaded and froze CLIP’s parameters. Second, we trained, on the small MSCOCO dataset [43], an entropy bottleneck to compress CLIP’s representation. The latter step can be done by training any lossy compressor on CLIP’s representations, we did so using Ballé et al.’s [28] hyperprior entropy model with a learned rounded precision. We then evaluated our resulting compressor on 8 datasets (various classification tasks and image shapes) that were never seen during training (zero-shot), by training an MLP for downstream predictions on each dataset. One can see this as a multi-task setting (each dataset is a distinct task). We investigate the case of multiple labels per images in Appx. F.5. ", + "bbox": [ + 174, + 696, + 825, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Can we use pretrained SSL to obtain a generic compressor? Table 2 shows that we can exploit existing state-of-the-art (SOTA) SSL models to get a powerful image compressor, which achieves $1 0 0 0 \\times$ bit-rate gains on ImageNet compared to JPEG (at the quality level used for storing ImageNet). The bit-rate gains ( $1 ^ { \\mathrm { s t } }$ row) are significant across all zero-shot datasets, even for biological tissues (PCam; [44]). Importantly, these gains come at little cost in test performance. Indeed, the test accuracies of MLPs from our representations ( $2 ^ { \\mathrm { n d } }$ row) is similar to a near SOTA model trained on the uncompressed images $3 ^ { \\mathrm { r d } }$ row is from Radford et al. [41]). These results are not surprising as JPEG is optimized to retain perceptual rather than classification information. Note that the large variance in rate gains come from JPEG rates due to different images shapes (see Table 3). ", + "bbox": [ + 174, + 842, + 825, + 911 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c99ee8045364b6ede58dbb0f36bc982e9db0665f8022b50a624f9c5b1a2d0f94.jpg", + "table_caption": [ + "Table 2: Converting a pretrained SSL model into a zero-shot compressor achieves substantial bit-rate gains while allowing test accuracies similar to supervised models predicting from raw images. " + ], + "table_footnote": [], + "table_body": "
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
Rate gains vs JPEG1104×35×64×131×7×109×150×126×
Our Acc. [%]76.398.780.979.695.288.389.593.4
Supervised Acc. [%]76.199.082.649.196.781.890.494.5
", + "bbox": [ + 183, + 117, + 812, + 191 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "", + "bbox": [ + 176, + 214, + 825, + 270 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our CLIP compressor retains all the information needed to get 0 error for those tasks. Table 2 provides the test performance for MLPs, while our theory discusses Bayes risk, which is independent of specific predictors and generalization. We estimated the excess Bayes risk for our datasets by counting the images (in train and test) that get compressed to the same $Z$ but have different labels. We found that we are in the lossless prediction regime for those datasets. ", + "bbox": [ + 173, + 276, + 825, + 347 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/ac0424fe22e10dbaa28ef2f1f175f4779cda844ebcaa59b55cbf9b0dc9d4c7f4.jpg", + "table_caption": [ + "Table 3: Our entropy bottleneck (EB) on CLIP improves compression of representations up to $1 7 \\times$ with little impact on predictions. The same compressor is used across datasets. Rates are per image. " + ], + "table_footnote": [], + "table_body": "
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
JPEG1.49e64.71e49.60e41.92e51.05e41.54e51.81e51.69e5
CLIP1.52e41.52e41.52e41.52e41.52e41.52e41.52e41.52e4
Brr+EB high β2.47e32.46e32.61e32.59e32.53e32.39e32.33e32.46e3
+EB β1.35e31.34e31.49e31.47e31.41e31.27e31.21e31.34e3
+EB low β9.63e29.52e21.09e31.07e31.02e38.89e28.35e29.53e2
CLIP76.598.684.580.895.388.589.793.2
+EB high β76.698.782.780.495.388.589.693.5
Trrs sss+EB β76.398.780.979.695.288.389.593.4
+EB low β76.098.780.178.994.887.688.692.9
", + "bbox": [ + 174, + 387, + 821, + 536 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "What is the effect of the entropy bottleneck? In Table 3 we compare the pretrained CLIP, to our CLIP compressor with an entropy bottleneck (EB) trained at different values for $\\beta$ . When trained with a high $\\beta$ , our EB improves bit-rates by an average of $6 \\times$ without impacting predictions. For our compressor from Table 2 $\\mathbf { ( C L I P + E B \\ } \\beta \\mathbf { \\Lambda }$ ) the gains increase to $1 1 \\times$ with little predictive impact. The sacrifice in predictions is more clear for $1 6 \\times$ bit-rate gains (low $\\beta$ ). This shows that CLIP’s raw representations retain unnecessary information as it not explicitly trained to discard information. ", + "bbox": [ + 173, + 549, + 825, + 633 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "How would end-to-end BINCE compare to staggered training? Compression gains can likely be larger by end-to-end training of BINCE, which would require access to CLIP’s original dataset.7 To get an idea of potential gains we compared end-to-end and staggered BINCE on augmented MNIST in Appx. F.2. We found significant rate improvements (358 to 131 bits) for similar test accuracy. ", + "bbox": [ + 174, + 640, + 825, + 695 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Our CLIP compressor is simple to use. In Appx. E.7, we provide a minimal script (150 lines) to train a generic compressor in less than five minutes on a single GPU. The script contains an efficient entropy coder for our model (200 images/second), which shows its practicality. As usual in SSL, the compressed representations are also more computationally efficient to work with than standard compressors. In our minimal script we achieve the desired performance $9 8 . 7 \\%$ on STL) using a linear model that is trained in one second, which is $1 0 0 0 \\times$ faster than the baseline in Table 2. This shows that our pipeline can improve computational efficiency in addition to storage efficiency. ", + "bbox": [ + 173, + 702, + 825, + 799 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "What augmentations to use for SSL compression? Table 4 compares two ResNet50 pretrained with contrastive learning using invariance to text-image (CLIP) or standard image augmentations (SimCLR [32]) such as cropping or flipping. We see that CLIP’s augmentation usually give better compression and downstream performance, which shows the importance of the choice of augmentations. This also supports our motivation of using text-image augmentations, which are likely label-preserving for a vast amount of tasks but discard large amounts of unnecessary information. ", + "bbox": [ + 174, + 804, + 823, + 888 + ], + "page_idx": 8 + }, + { + "type": "table", + "img_path": "images/f8bca2852f082708e268465e44c247d8a60d35fa24114f6a7a44743c19258166.jpg", + "table_caption": [ + "Table 4: Text-image invariance is better than invariance to standard augmentations for image classification. CLIP and SimCLR are both ResNet50 pretrained with InfoNCE but different augmentations. " + ], + "table_footnote": [], + "table_body": "
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
3CLIP+EB21081962194924212111199118671968
SimCLR+EB28112732276927512950207728392502
ACLIP+EB63.292.078.668.065.574.181.883.0
SimCLR+EB62.891.981.429.678.660.078.979.0
", + "bbox": [ + 194, + 117, + 799, + 204 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "6 Related work ", + "text_level": 1, + "bbox": [ + 174, + 227, + 318, + 244 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "In Appx. D we discuss more related work, including invariances in compression and the link to SSL. ", + "bbox": [ + 176, + 257, + 823, + 271 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Task-centric compression. To our knowledge, our paper is the first to formalize compression only for predictions. IB [11] uses a task-centric distortion, but is not used for compression as it requires supervised training, so there are no advantages compared to compressing predicted labels. Some authors used heuristics to bypass the supervised issue, e.g., focusing on low frequencies for classification [45] or high frequencies for segmentation [46]. Other authors have incorporated predictive errors to perceptual distortions [47, 48], but cannot compress without the perceptual distortion for the same reason as IB. One exception is Weber et al.’s [49] compressor, which (when removing their perceptual distortion) minimizes MSE in the hidden layers of a pretrained classifier. Even more related is Singh et al.’s [50] work on compressing pretrained features for transfer learning, which is practice is similar to our compression of SSL features. Their work do not provide theoretical justifications, and are constrained to tasks that are similar to those used for pretraining. ", + "bbox": [ + 174, + 277, + 825, + 429 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "7 Discussion and Outlook ", + "text_level": 1, + "bbox": [ + 176, + 449, + 401, + 467 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Given the ever increasing amount of data that is processed by task-specific algorithms, it is necessary to rethink the current task-agnostic compression paradigm. We formalized the first compression framework for retaining only the information necessary for high performance on desired tasks. Using our theory, we provide two unsupervised objectives for training neural compressors. Experimentally, we show that these compressors can achieve bit-rates that are orders of magnitude $1 0 0 0 \\times$ on ImageNet) smaller than standard image compressors without losing predictive performance. ", + "bbox": [ + 174, + 478, + 825, + 563 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "There are a number of caveats that should be addressed. First, to achieve better rates, our theory requires an irrecoverable loss of information. This can be an issue if the set of desired tasks changes. For example, if one uses text-image invariances then it may be impossible to perform image segmentation from the compressed representations. One solution would be to keep an original copy and use invariant compression for duplicated data, e.g., for the thousands copies of ImageNet. A second issue is the interpretability of the compressed representations. This can be partially addressed by reconstructing prototypical data as in Fig. 1 (post-hoc decoders could be trained for BINCE). A third caveat is that the compressed representations may be harder to learn from, e.g., neural networks may struggle to predict from representations even if the information is retained. Although our experiments actually showed the opposite, this should be addressed theoretically, e.g., using decodable information [51, 52]. Finally, successful use of our framework requires access to labelpreserving augmentations $A$ that discard significant information about $X$ . Finding such an $A$ may be challenging for some tasks. Given that augmentations are ubiquitous in ML, the community will hopefully continue developing task-specific augmentations which we could take advantage of. ", + "bbox": [ + 174, + 568, + 825, + 761 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Nevertheless, we achieved orders of magnitude improvements in compression for predictions, and we believe that our improvements are just the beginning. For example, many tasks can be answered by referencing a detailed natural language description of the data. In these cases, the improvements can be very large, potentially $1 \\mathbf { M } \\times$ for videos.8 In the long-term, we hope that abandoning perceptual reconstructions will enable individuals to process data at scales that are currently only possible at large institutions, and our society to take advantage of large data sources in a more sustainable way. ", + "bbox": [ + 174, + 768, + 825, + 852 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Acknowledgments and Disclosure of Funding ", + "text_level": 1, + "bbox": [ + 174, + 88, + 553, + 107 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "We would like to thank Alex Alemi, David Duvenaud, Andriy Mnih, Emile Mathieu, Jonah Philion, Yangjun Ruan, and Ilya Sutskever for their helpful feedback and encouragements. Resources used in preparing this research were provided, in part, by the Province of Ontario, the Government of Canada through CIFAR, and companies sponsoring the Vector Institute. BBR acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC): RGPIN-2020-04995, RGPAS-2020-00095, DGECR-2020-00343. ", + "bbox": [ + 174, + 118, + 826, + 202 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "References ", + "text_level": 1, + "bbox": [ + 174, + 222, + 266, + 238 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "[1] D. Rolnick, P. L. Donti, L. H. Kaack, K. Kochanski, A. Lacoste, K. Sankaran, A. S. Ross, N. Milojevic-Dupont, N. Jaques, A. Waldman-Brown, A. Luccioni, T. Maharaj, E. D. Sherwin, S. K. Mukkavilli, K. P. Körding, C. P. Gomes, A. Y. $\\mathrm { N g }$ , D. Hassabis, J. C. Platt, F. Creutzig, J. T. Chayes, and Y. Bengio, “Tackling Climate Change with Machine Learning,” CoRR, vol. abs/1906.05433, 2019, _eprint: 1906.05433. [Online]. Available: http://arxiv.org/abs/1906.05433 \n[2] M. Z. Zgurovsky and Y. P. Zaychenko, Big Data: Conceptual Analysis and Applications. Springer, 2020. \n[3] N. 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We need", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "score": 1.0, + "content": "compressors that retain only the information needed for algorithmic execution of downstream tasks.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5 + }, + { + "type": "text", + "bbox": [ + 107, + 524, + 317, + 676 + ], + "lines": [ + { + "bbox": [ + 106, + 524, + 318, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 318, + 536 + ], + "score": 1.0, + "content": "Existing lossy compressors are not up to the chal-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 535, + 318, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 318, + 547 + ], + "score": 1.0, + "content": "lenge, because they aim to reconstruct the data for hu-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 546, + 317, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 317, + 558 + ], + "score": 1.0, + "content": "man perception [5–10]. 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We need", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 506, + 520 + ], + "score": 1.0, + "content": "compressors that retain only the information needed for algorithmic execution of downstream tasks.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 452, + 506, + 520 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 524, + 317, + 676 + ], + "lines": [ + { + "bbox": [ + 106, + 524, + 318, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 318, + 536 + ], + "score": 1.0, + "content": "Existing lossy compressors are not up to the chal-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 535, + 318, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 535, + 318, + 547 + ], + "score": 1.0, + "content": "lenge, because they aim to reconstruct the data for hu-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 546, + 317, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 317, + 558 + ], + "score": 1.0, + "content": "man perception [5–10]. However, much of perceptual", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 556, + 317, + 569 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 317, + 569 + ], + "score": 1.0, + "content": "information is not needed to perform the tasks that", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 568, + 317, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 317, + 579 + ], + "score": 1.0, + "content": "we care about. Consider classifying images, which", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 577, + 318, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 318, + 592 + ], + "score": 1.0, + "content": "can require about 1 MB to store. 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Indeed, any distortion", + "type": "text" + }, + { + "bbox": [ + 428, + 493, + 504, + 504 + ], + "score": 0.87, + "content": "d : \\mathcal { X } \\times \\mathcal { Z } \\to \\mathbb { R } _ { \\ge 0 }", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 502, + 507, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 153, + 517 + ], + "score": 1.0, + "content": "of the form", + "type": "text" + }, + { + "bbox": [ + 153, + 503, + 272, + 516 + ], + "score": 0.91, + "content": "\\mathrm { D } [ X , Z ] = \\mathrm { E } _ { p ( X , Z ) } [ d ( X ^ { ' } , Z ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 502, + 356, + 517 + ], + "score": 1.0, + "content": ", where there exists a", + "type": "text" + }, + { + "bbox": [ + 357, + 504, + 382, + 513 + ], + "score": 0.9, + "content": "z \\in Z", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 502, + 421, + 517 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 421, + 504, + 453, + 515 + ], + "score": 0.89, + "content": "\\mathrm { D } [ X , z ]", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 502, + 507, + 517 + ], + "score": 1.0, + "content": "is finite, is a", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 512, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 506, + 528 + ], + "score": 1.0, + "content": "valid choice [18]. This shows that RD theory can be used outside of reconstructions. In the following", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 525, + 466, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 152, + 537 + ], + "score": 1.0, + "content": "we refer to", + "type": "text" + }, + { + "bbox": [ + 152, + 526, + 160, + 535 + ], + "score": 0.84, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 161, + 525, + 300, + 537 + ], + "score": 1.0, + "content": "as a compressed representation of", + "type": "text" + }, + { + "bbox": [ + 300, + 526, + 310, + 535 + ], + "score": 0.86, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 525, + 466, + 537 + ], + "score": 1.0, + "content": "to distinguish it from a reconstruction.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5 + }, + { + "type": "title", + "bbox": [ + 106, + 551, + 377, + 565 + ], + "lines": [ + { + "bbox": [ + 103, + 549, + 379, + 569 + ], + "spans": [ + { + "bbox": [ + 103, + 549, + 379, + 569 + ], + "score": 1.0, + "content": "3 Minimal bit-rate for high predictive performance", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 575, + 505, + 631 + ], + "lines": [ + { + "bbox": [ + 106, + 576, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 365, + 587 + ], + "score": 1.0, + "content": "In this section, we characterize the bit-rate needed to represent", + "type": "text" + }, + { + "bbox": [ + 366, + 576, + 376, + 585 + ], + "score": 0.84, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 576, + 505, + 587 + ], + "score": 1.0, + "content": "to ensure high performance on", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 586, + 504, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 504, + 598 + ], + "score": 1.0, + "content": "downstream tasks. 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This structure allows us to characterize a worst-case invariant task, which bounds", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "the relative predictive performance on all invariant tasks. As a result, the bit-rate required to perform", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "well on all invariant tasks is exactly the rate to compress the worst-case labels. 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E.g., on ImageNet [16], it decreases the bit-rate by", + "type": "text" + }, + { + "bbox": [ + 458, + 307, + 486, + 318 + ], + "score": 0.87, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 307, + 490, + 320 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18, + "bbox_fs": [ + 103, + 261, + 506, + 320 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 334, + 305, + 347 + ], + "lines": [ + { + "bbox": [ + 104, + 332, + 306, + 351 + ], + "spans": [ + { + "bbox": [ + 104, + 332, + 306, + 351 + ], + "score": 1.0, + "content": "2 Rate-distortion theory background", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 357, + 505, + 412 + ], + "lines": [ + { + "bbox": [ + 106, + 358, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 505, + 370 + ], + "score": 1.0, + "content": "The goal of lossy compression theory is to find the number of bits (bit-rate) required to store outcomes", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 369, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 107, + 371, + 113, + 378 + ], + "score": 0.71, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 369, + 228, + 380 + ], + "score": 1.0, + "content": "of a random variable (r.v.)", + "type": "text" + }, + { + "bbox": [ + 229, + 369, + 239, + 379 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 369, + 505, + 380 + ], + "score": 1.0, + "content": ", so that it can be reconstructed within a certain tolerance. 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Indeed, any distortion", + "type": "text" + }, + { + "bbox": [ + 428, + 493, + 504, + 504 + ], + "score": 0.87, + "content": "d : \\mathcal { X } \\times \\mathcal { Z } \\to \\mathbb { R } _ { \\ge 0 }", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 502, + 507, + 517 + ], + "spans": [ + { + "bbox": [ + 105, + 502, + 153, + 517 + ], + "score": 1.0, + "content": "of the form", + "type": "text" + }, + { + "bbox": [ + 153, + 503, + 272, + 516 + ], + "score": 0.91, + "content": "\\mathrm { D } [ X , Z ] = \\mathrm { E } _ { p ( X , Z ) } [ d ( X ^ { ' } , Z ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 502, + 356, + 517 + ], + "score": 1.0, + "content": ", where there exists a", + "type": "text" + }, + { + "bbox": [ + 357, + 504, + 382, + 513 + ], + "score": 0.9, + "content": "z \\in Z", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 502, + 421, + 517 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 421, + 504, + 453, + 515 + ], + "score": 0.89, + "content": "\\mathrm { D } [ X , z ]", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 502, + 507, + 517 + ], + "score": 1.0, + "content": "is finite, is a", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 512, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 506, + 528 + ], + "score": 1.0, + "content": "valid choice [18]. This shows that RD theory can be used outside of reconstructions. In the following", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 525, + 466, + 537 + ], + "spans": [ + { + "bbox": [ + 106, + 525, + 152, + 537 + ], + "score": 1.0, + "content": "we refer to", + "type": "text" + }, + { + "bbox": [ + 152, + 526, + 160, + 535 + ], + "score": 0.84, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 161, + 525, + 300, + 537 + ], + "score": 1.0, + "content": "as a compressed representation of", + "type": "text" + }, + { + "bbox": [ + 300, + 526, + 310, + 535 + ], + "score": 0.86, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 525, + 466, + 537 + ], + "score": 1.0, + "content": "to distinguish it from a reconstruction.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5, + "bbox_fs": [ + 104, + 470, + 507, + 537 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 551, + 377, + 565 + ], + "lines": [ + { + "bbox": [ + 103, + 549, + 379, + 569 + ], + "spans": [ + { + "bbox": [ + 103, + 549, + 379, + 569 + ], + "score": 1.0, + "content": "3 Minimal bit-rate for high predictive performance", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 575, + 505, + 631 + ], + "lines": [ + { + "bbox": [ + 106, + 576, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 365, + 587 + ], + "score": 1.0, + "content": "In this section, we characterize the bit-rate needed to represent", + "type": "text" + }, + { + "bbox": [ + 366, + 576, + 376, + 585 + ], + "score": 0.84, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 576, + 505, + 587 + ], + "score": 1.0, + "content": "to ensure high performance on", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 586, + 504, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 586, + 504, + 598 + ], + "score": 1.0, + "content": "downstream tasks. 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For simplicity, our presentation is relatively informal; formal proofs are in Apps. 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For ease of presentation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 334, + 713 + ], + "score": 1.0, + "content": "in the main paper, we consider only classification tasks", + "type": "text" + }, + { + "bbox": [ + 334, + 701, + 343, + 710 + ], + "score": 0.84, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "and Bayes risk of the standard log loss", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 709, + 471, + 725 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 272, + 724 + ], + "score": 0.91, + "content": "\\begin{array} { r } { \\mathrm { R } [ Y | X ] : = \\bar { \\operatorname* { i n f } _ { q } \\mathrm { E } } _ { p ( X , Y ) } [ - \\log q ( \\dot { Y } | X ) ] } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 709, + 471, + 725 + ], + "score": 1.0, + "content": ". 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Second, the worst excess-risk", + "type": "text" + }, + { + "bbox": [ + 452, + 416, + 467, + 427 + ], + "score": 0.88, + "content": "\\mathrm { D } _ { \\tau }", + "type": "inline_equation" + }, + { + "bbox": [ + 468, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "assumes", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 426, + 491, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 426, + 273, + 438 + ], + "score": 1.0, + "content": "access to all downstream tasks of interest", + "type": "text" + }, + { + "bbox": [ + 273, + 427, + 283, + 437 + ], + "score": 0.81, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 283, + 426, + 491, + 438 + ], + "score": 1.0, + "content": "during compression, which is unrealistic in general.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 107, + 447, + 195, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 446, + 195, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 195, + 460 + ], + "score": 1.0, + "content": "3.2 Invariant tasks", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 463, + 505, + 530 + ], + "lines": [ + { + "bbox": [ + 106, + 464, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 505, + 475 + ], + "score": 1.0, + "content": "The tasks that we care about are not arbitrary, and often share structure. One such structure is", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "score": 1.0, + "content": "invariance to certain pre-specified transformations of input data. For example, computer vision tasks", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "are often invariant to mild transformations such as brightness changes. Such invariance structure is", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 497, + 504, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 504, + 509 + ], + "score": 1.0, + "content": "common in realistic tasks, as seen by the wide-spread use of data augmentations [13] in machine", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 508, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 423, + 519 + ], + "score": 1.0, + "content": "learning (ML), which encourage predictions to be the same for an unaugmented", + "type": "text" + }, + { + "bbox": [ + 423, + 509, + 430, + 517 + ], + "score": 0.77, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 508, + 505, + 519 + ], + "score": 1.0, + "content": "and an augmented", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 107, + 517, + 349, + 531 + ], + "spans": [ + { + "bbox": [ + 107, + 519, + 120, + 528 + ], + "score": 0.87, + "content": "x ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 517, + 335, + 531 + ], + "score": 1.0, + "content": ". Motivated by this we focus on sets of invariant tasks", + "type": "text" + }, + { + "bbox": [ + 335, + 519, + 344, + 529 + ], + "score": 0.83, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 517, + 349, + 531 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 106, + 534, + 505, + 568 + ], + "lines": [ + { + "bbox": [ + 105, + 533, + 505, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 547 + ], + "score": 1.0, + "content": "We consider a general notion of invariance, namely invariance specified by an equivalence relation", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 545, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 547, + 116, + 556 + ], + "score": 0.67, + "content": "\\sim", + "type": "inline_equation" + }, + { + "bbox": [ + 117, + 545, + 130, + 558 + ], + "score": 1.0, + "content": "on", + "type": "text" + }, + { + "bbox": [ + 130, + 546, + 140, + 555 + ], + "score": 0.77, + "content": "\\mathcal { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 545, + 309, + 558 + ], + "score": 1.0, + "content": ".2 The equivalence induces a partition of", + "type": "text" + }, + { + "bbox": [ + 309, + 546, + 319, + 555 + ], + "score": 0.82, + "content": "\\mathcal { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 545, + 505, + 558 + ], + "score": 1.0, + "content": "into disjoint equivalence classes, and we are", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 556, + 442, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 442, + 569 + ], + "score": 1.0, + "content": "interested in tasks whose conditional distributions are constant within these classes.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 105, + 578, + 505, + 602 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 437, + 591 + ], + "score": 1.0, + "content": "Definition 1. The set of invariant tasks of interest with respect to an equivalence", + "type": "text" + }, + { + "bbox": [ + 437, + 578, + 466, + 590 + ], + "score": 0.9, + "content": "( \\mathcal { X } , \\sim )", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 577, + 505, + 591 + ], + "score": 1.0, + "content": ", denoted", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 107, + 588, + 489, + 602 + ], + "spans": [ + { + "bbox": [ + 107, + 591, + 119, + 600 + ], + "score": 0.81, + "content": "\\mathcal { T } _ { \\sim }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 588, + 215, + 602 + ], + "score": 1.0, + "content": ", is all random variables", + "type": "text" + }, + { + "bbox": [ + 216, + 590, + 225, + 599 + ], + "score": 0.77, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 588, + 264, + 602 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 264, + 589, + 409, + 601 + ], + "score": 0.91, + "content": "x \\sim x ^ { + } \\implies p ( Y | x ) = p ( Y | x ^ { + } )", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 588, + 441, + 602 + ], + "score": 1.0, + "content": "for any", + "type": "text" + }, + { + "bbox": [ + 441, + 590, + 485, + 601 + ], + "score": 0.91, + "content": "x , x ^ { + } \\in \\mathcal { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 588, + 489, + 602 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25.5 + }, + { + "type": "title", + "bbox": [ + 106, + 610, + 349, + 623 + ], + "lines": [ + { + "bbox": [ + 105, + 609, + 349, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 349, + 624 + ], + "score": 1.0, + "content": "3.3 Rate-distortion theory for invariant task prediction", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 108, + 627, + 506, + 661 + ], + "lines": [ + { + "bbox": [ + 106, + 627, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 202, + 640 + ], + "score": 1.0, + "content": "The key to simplifying", + "type": "text" + }, + { + "bbox": [ + 203, + 628, + 221, + 639 + ], + "score": 0.89, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 627, + 506, + 640 + ], + "score": 1.0, + "content": "is the existence of a (non-unique) worst-case invariant task, denoted", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 107, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 107, + 640, + 135, + 650 + ], + "score": 0.91, + "content": "M ( X )", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 638, + 371, + 650 + ], + "score": 1.0, + "content": ". 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The set of invariant tasks of interest with respect to an equivalence", + "type": "text" + }, + { + "bbox": [ + 437, + 578, + 466, + 590 + ], + "score": 0.9, + "content": "( \\mathcal { X } , \\sim )", + "type": "inline_equation" + }, + { + "bbox": [ + 466, + 577, + 505, + 591 + ], + "score": 1.0, + "content": ", denoted", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 107, + 588, + 489, + 602 + ], + "spans": [ + { + "bbox": [ + 107, + 591, + 119, + 600 + ], + "score": 0.81, + "content": "\\mathcal { T } _ { \\sim }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 588, + 215, + 602 + ], + "score": 1.0, + "content": ", is all random variables", + "type": "text" + }, + { + "bbox": [ + 216, + 590, + 225, + 599 + ], + "score": 0.77, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 588, + 264, + 602 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 264, + 589, + 409, + 601 + ], + "score": 0.91, + "content": "x \\sim x ^ { + } \\implies p ( Y | x ) = p ( Y | x ^ { + } )", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 588, + 441, + 602 + ], + "score": 1.0, + "content": "for any", + "type": "text" + }, + { + "bbox": [ + 441, + 590, + 485, + 601 + ], + "score": 0.91, + "content": "x , x ^ { + } \\in \\mathcal { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 588, + 489, + 602 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 577, + 505, + 602 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 610, + 349, + 623 + ], + "lines": [ + { + "bbox": [ + 105, + 609, + 349, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 349, + 624 + ], + "score": 1.0, + "content": "3.3 Rate-distortion theory for invariant task prediction", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 108, + 627, + 506, + 661 + ], + "lines": [ + { + "bbox": [ + 106, + 627, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 202, + 640 + ], + "score": 1.0, + "content": "The key to simplifying", + "type": "text" + }, + { + "bbox": [ + 203, + 628, + 221, + 639 + ], + "score": 0.89, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 627, + 506, + 640 + ], + "score": 1.0, + "content": "is the existence of a (non-unique) worst-case invariant task, denoted", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 107, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 107, + 640, + 135, + 650 + ], + "score": 0.91, + "content": "M ( X )", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 638, + 371, + 650 + ], + "score": 1.0, + "content": ". Such task contains all and only information to which tasks", + "type": "text" + }, + { + "bbox": [ + 372, + 639, + 404, + 649 + ], + "score": 0.91, + "content": "Y \\in \\mathcal { T } _ { \\sim }", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "are not invariant; we call", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 649, + 501, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 295, + 662 + ], + "score": 1.0, + "content": "them maximal invariants. A maximal invariant", + "type": "text" + }, + { + "bbox": [ + 296, + 649, + 322, + 662 + ], + "score": 0.92, + "content": "M ( \\bullet )", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 649, + 384, + 662 + ], + "score": 1.0, + "content": "with respect to", + "type": "text" + }, + { + "bbox": [ + 385, + 651, + 394, + 659 + ], + "score": 0.79, + "content": "\\sim", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 649, + 501, + 662 + ], + "score": 1.0, + "content": "is any function satisfying3", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 106, + 627, + 506, + 662 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 196, + 667, + 415, + 681 + ], + "lines": [ + { + "bbox": [ + 196, + 667, + 415, + 681 + ], + "spans": [ + { + "bbox": [ + 196, + 667, + 415, + 681 + ], + "score": 0.88, + "content": "x \\sim x ^ { + } \\iff M ( x ) = M ( x ^ { + } ) \\quad { \\mathrm { f o r ~ a n y ~ } } x , x ^ { + } \\in \\mathcal { X } .", + "type": "interline_equation", + "image_path": "4a9138c0deaada2706d5575cef88635b1199839f85d06835a9f9764d7b61a43a.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 196, + 667, + 415, + 681 + ], + "spans": [], + "index": 31 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 72, + 506, + 150 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "score": 1.0, + "content": "A maximal invariant removes all information that tasks are invariant to, as it maps equivalent inputs", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 201, + 95 + ], + "score": 1.0, + "content": "to the same output, i.e.,", + "type": "text" + }, + { + "bbox": [ + 202, + 83, + 271, + 96 + ], + "score": 0.93, + "content": "M ( x ) = M ( x ^ { + } )", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 83, + 505, + 95 + ], + "score": 1.0, + "content": ". Yet, it retains the minimal information needed to perform", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 94, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 313, + 107 + ], + "score": 1.0, + "content": "invariant tasks, by mapping non-equivalent inputs", + "type": "text" + }, + { + "bbox": [ + 314, + 95, + 348, + 106 + ], + "score": 0.91, + "content": "x \\not \\sim x ^ { - }", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 95, + 432, + 107 + ], + "score": 1.0, + "content": "to different outputs", + "type": "text" + }, + { + "bbox": [ + 432, + 94, + 503, + 106 + ], + "score": 0.93, + "content": "M ( x ) \\neq { \\overline { { M } } } ( x ^ { - } )", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 95, + 506, + 107 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 106, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 174, + 118 + ], + "score": 1.0, + "content": "In other words,", + "type": "text" + }, + { + "bbox": [ + 175, + 106, + 200, + 118 + ], + "score": 0.92, + "content": "M ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 106, + 506, + 118 + ], + "score": 1.0, + "content": "indexes the equivalence classes. For example, the Euclidean norm is a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "score": 1.0, + "content": "maximal invariant for rotation invariance, as all vectors that are rotated versions of one another can", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "score": 1.0, + "content": "be characterized by their radial coordinate. For data augmentations, the canonical (unaugmented)", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 138, + 426, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 426, + 150 + ], + "score": 1.0, + "content": "version of the input is a maximal invariant. Other examples are shown in Fig. 2.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 106, + 154, + 505, + 199 + ], + "lines": [ + { + "bbox": [ + 105, + 154, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 489, + 167 + ], + "score": 1.0, + "content": "We prove in Appx. B.2 that under weak regularity conditions, maximal invariant tasks exist in", + "type": "text" + }, + { + "bbox": [ + 490, + 155, + 502, + 165 + ], + "score": 0.86, + "content": "\\mathcal { T } _ { \\sim }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 154, + 506, + 167 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 165, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 166, + 401, + 177 + ], + "score": 1.0, + "content": "and that they achieve the supremum in Eq. (2). This allows us to show that", + "type": "text" + }, + { + "bbox": [ + 401, + 165, + 420, + 177 + ], + "score": 0.91, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 166, + 505, + 177 + ], + "score": 1.0, + "content": "reduces to the Bayes", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 177, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 177, + 189 + ], + "score": 1.0, + "content": "risk of predicting", + "type": "text" + }, + { + "bbox": [ + 177, + 177, + 205, + 189 + ], + "score": 0.92, + "content": "M ( X )", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 177, + 228, + 189 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 229, + 177, + 238, + 187 + ], + "score": 0.79, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 238, + 177, + 505, + 189 + ], + "score": 1.0, + "content": "and that it is a valid distortion measure. Crucially, this allows us to", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 187, + 394, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 394, + 200 + ], + "score": 1.0, + "content": "quantify downstream performance without enumerating invariant tasks.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 106, + 209, + 505, + 232 + ], + "lines": [ + { + "bbox": [ + 106, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 186, + 222 + ], + "score": 1.0, + "content": "Proposition 1. Let", + "type": "text" + }, + { + "bbox": [ + 187, + 209, + 216, + 221 + ], + "score": 0.92, + "content": "( \\mathcal { X } , \\sim )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 209, + 339, + 222 + ], + "score": 1.0, + "content": "be an equivalence relation and", + "type": "text" + }, + { + "bbox": [ + 340, + 210, + 352, + 219 + ], + "score": 0.83, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "a maximal invariant that takes at most", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 500, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 223, + 232 + ], + "score": 1.0, + "content": "countably many values, with", + "type": "text" + }, + { + "bbox": [ + 224, + 220, + 288, + 232 + ], + "score": 0.92, + "content": "\\mathrm { H } [ M ( \\bar { X } ) ] < \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 220, + 315, + 232 + ], + "score": 1.0, + "content": ". Then", + "type": "text" + }, + { + "bbox": [ + 315, + 220, + 334, + 232 + ], + "score": 0.89, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 220, + 500, + 232 + ], + "score": 1.0, + "content": "(2) with log loss is a valid distortion and", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5 + }, + { + "type": "interline_equation", + "bbox": [ + 244, + 233, + 364, + 246 + ], + "lines": [ + { + "bbox": [ + 244, + 233, + 364, + 246 + ], + "spans": [ + { + "bbox": [ + 244, + 233, + 364, + 246 + ], + "score": 0.76, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } } [ X , Z ] = \\mathrm { R } [ M ( X ) | Z ] \\ .", + "type": "interline_equation", + "image_path": "98d782cef09afa364b2f4eccba15917dcffd1f4c559f303c4291c2abe4e3db74.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 244, + 233, + 364, + 246 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 252, + 505, + 286 + ], + "lines": [ + { + "bbox": [ + 105, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 165, + 264 + ], + "score": 1.0, + "content": "Here we used", + "type": "text" + }, + { + "bbox": [ + 165, + 252, + 241, + 264 + ], + "score": 0.91, + "content": "\\operatorname { R } [ M ( X ) | X ] = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 252, + 257, + 264 + ], + "score": 1.0, + "content": ", as", + "type": "text" + }, + { + "bbox": [ + 258, + 253, + 269, + 263 + ], + "score": 0.83, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "is a deterministic function. Also, note that the countable", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "score": 1.0, + "content": "requirement holds when tasks are invariant to some rounding of the input, as is typically the case due", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 274, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 274, + 506, + 286 + ], + "score": 1.0, + "content": "to floating-point storage. We accommodate the uncountable case for squared-error loss in Appx. B.6.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 290, + 505, + 324 + ], + "lines": [ + { + "bbox": [ + 105, + 289, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 359, + 303 + ], + "score": 1.0, + "content": "With a valid distortion in hand, we invoke the RD theorem with", + "type": "text" + }, + { + "bbox": [ + 360, + 291, + 378, + 302 + ], + "score": 0.9, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 289, + 506, + 303 + ], + "score": 1.0, + "content": "to obtain our “Rate-Invariance”", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 301, + 505, + 314 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 405, + 314 + ], + "score": 1.0, + "content": "(RI) theorem. The RI theorem characterizes the bit-rate needed to store", + "type": "text" + }, + { + "bbox": [ + 405, + 302, + 415, + 312 + ], + "score": 0.83, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 416, + 301, + 505, + 314 + ], + "score": 1.0, + "content": "while ensuring small", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 313, + 421, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 421, + 325 + ], + "score": 1.0, + "content": "log-loss on invariant tasks. We obtain analogous results for squared-error loss.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 334, + 504, + 368 + ], + "lines": [ + { + "bbox": [ + 105, + 333, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 392, + 347 + ], + "score": 1.0, + "content": "Theorem 2 (Rate-Invariance). Assume the conditions of Prop. 1. 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In practice, however,", + "type": "text" + }, + { + "bbox": [ + 383, + 711, + 409, + 722 + ], + "score": 0.92, + "content": "P ( X ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 410, + 711, + 460, + 723 + ], + "score": 1.0, + "content": "will rarely be", + "type": "text" + }, + { + "bbox": [ + 460, + 713, + 469, + 720 + ], + "score": 0.77, + "content": "\\sim", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "invariant.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 741, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 72, + 506, + 150 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "score": 1.0, + "content": "A maximal invariant removes all information that tasks are invariant to, as it maps equivalent inputs", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 201, + 95 + ], + "score": 1.0, + "content": "to the same output, i.e.,", + "type": "text" + }, + { + "bbox": [ + 202, + 83, + 271, + 96 + ], + "score": 0.93, + "content": "M ( x ) = M ( x ^ { + } )", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 83, + 505, + 95 + ], + "score": 1.0, + "content": ". Yet, it retains the minimal information needed to perform", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 94, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 106, + 95, + 313, + 107 + ], + "score": 1.0, + "content": "invariant tasks, by mapping non-equivalent inputs", + "type": "text" + }, + { + "bbox": [ + 314, + 95, + 348, + 106 + ], + "score": 0.91, + "content": "x \\not \\sim x ^ { - }", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 95, + 432, + 107 + ], + "score": 1.0, + "content": "to different outputs", + "type": "text" + }, + { + "bbox": [ + 432, + 94, + 503, + 106 + ], + "score": 0.93, + "content": "M ( x ) \\neq { \\overline { { M } } } ( x ^ { - } )", + "type": "inline_equation" + }, + { + "bbox": [ + 503, + 95, + 506, + 107 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 106, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 174, + 118 + ], + "score": 1.0, + "content": "In other words,", + "type": "text" + }, + { + "bbox": [ + 175, + 106, + 200, + 118 + ], + "score": 0.92, + "content": "M ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 106, + 506, + 118 + ], + "score": 1.0, + "content": "indexes the equivalence classes. For example, the Euclidean norm is a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 506, + 129 + ], + "score": 1.0, + "content": "maximal invariant for rotation invariance, as all vectors that are rotated versions of one another can", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "score": 1.0, + "content": "be characterized by their radial coordinate. For data augmentations, the canonical (unaugmented)", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 138, + 426, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 426, + 150 + ], + "score": 1.0, + "content": "version of the input is a maximal invariant. Other examples are shown in Fig. 2.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 72, + 506, + 150 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 154, + 505, + 199 + ], + "lines": [ + { + "bbox": [ + 105, + 154, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 489, + 167 + ], + "score": 1.0, + "content": "We prove in Appx. B.2 that under weak regularity conditions, maximal invariant tasks exist in", + "type": "text" + }, + { + "bbox": [ + 490, + 155, + 502, + 165 + ], + "score": 0.86, + "content": "\\mathcal { T } _ { \\sim }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 154, + 506, + 167 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 165, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 166, + 401, + 177 + ], + "score": 1.0, + "content": "and that they achieve the supremum in Eq. (2). This allows us to show that", + "type": "text" + }, + { + "bbox": [ + 401, + 165, + 420, + 177 + ], + "score": 0.91, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 166, + 505, + 177 + ], + "score": 1.0, + "content": "reduces to the Bayes", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 177, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 177, + 189 + ], + "score": 1.0, + "content": "risk of predicting", + "type": "text" + }, + { + "bbox": [ + 177, + 177, + 205, + 189 + ], + "score": 0.92, + "content": "M ( X )", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 177, + 228, + 189 + ], + "score": 1.0, + "content": "from", + "type": "text" + }, + { + "bbox": [ + 229, + 177, + 238, + 187 + ], + "score": 0.79, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 238, + 177, + 505, + 189 + ], + "score": 1.0, + "content": "and that it is a valid distortion measure. Crucially, this allows us to", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 187, + 394, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 394, + 200 + ], + "score": 1.0, + "content": "quantify downstream performance without enumerating invariant tasks.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5, + "bbox_fs": [ + 105, + 154, + 506, + 200 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 209, + 505, + 232 + ], + "lines": [ + { + "bbox": [ + 106, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 186, + 222 + ], + "score": 1.0, + "content": "Proposition 1. Let", + "type": "text" + }, + { + "bbox": [ + 187, + 209, + 216, + 221 + ], + "score": 0.92, + "content": "( \\mathcal { X } , \\sim )", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 209, + 339, + 222 + ], + "score": 1.0, + "content": "be an equivalence relation and", + "type": "text" + }, + { + "bbox": [ + 340, + 210, + 352, + 219 + ], + "score": 0.83, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "a maximal invariant that takes at most", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 220, + 500, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 223, + 232 + ], + "score": 1.0, + "content": "countably many values, with", + "type": "text" + }, + { + "bbox": [ + 224, + 220, + 288, + 232 + ], + "score": 0.92, + "content": "\\mathrm { H } [ M ( \\bar { X } ) ] < \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 220, + 315, + 232 + ], + "score": 1.0, + "content": ". Then", + "type": "text" + }, + { + "bbox": [ + 315, + 220, + 334, + 232 + ], + "score": 0.89, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 220, + 500, + 232 + ], + "score": 1.0, + "content": "(2) with log loss is a valid distortion and", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 209, + 505, + 232 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 244, + 233, + 364, + 246 + ], + "lines": [ + { + "bbox": [ + 244, + 233, + 364, + 246 + ], + "spans": [ + { + "bbox": [ + 244, + 233, + 364, + 246 + ], + "score": 0.76, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } } [ X , Z ] = \\mathrm { R } [ M ( X ) | Z ] \\ .", + "type": "interline_equation", + "image_path": "98d782cef09afa364b2f4eccba15917dcffd1f4c559f303c4291c2abe4e3db74.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 244, + 233, + 364, + 246 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 252, + 505, + 286 + ], + "lines": [ + { + "bbox": [ + 105, + 252, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 165, + 264 + ], + "score": 1.0, + "content": "Here we used", + "type": "text" + }, + { + "bbox": [ + 165, + 252, + 241, + 264 + ], + "score": 0.91, + "content": "\\operatorname { R } [ M ( X ) | X ] = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 252, + 257, + 264 + ], + "score": 1.0, + "content": ", as", + "type": "text" + }, + { + "bbox": [ + 258, + 253, + 269, + 263 + ], + "score": 0.83, + "content": "M", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 252, + 505, + 264 + ], + "score": 1.0, + "content": "is a deterministic function. Also, note that the countable", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 276 + ], + "score": 1.0, + "content": "requirement holds when tasks are invariant to some rounding of the input, as is typically the case due", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 274, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 274, + 506, + 286 + ], + "score": 1.0, + "content": "to floating-point storage. We accommodate the uncountable case for squared-error loss in Appx. B.6.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 252, + 506, + 286 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 290, + 505, + 324 + ], + "lines": [ + { + "bbox": [ + 105, + 289, + 506, + 303 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 359, + 303 + ], + "score": 1.0, + "content": "With a valid distortion in hand, we invoke the RD theorem with", + "type": "text" + }, + { + "bbox": [ + 360, + 291, + 378, + 302 + ], + "score": 0.9, + "content": "\\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 289, + 506, + 303 + ], + "score": 1.0, + "content": "to obtain our “Rate-Invariance”", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 301, + 505, + 314 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 405, + 314 + ], + "score": 1.0, + "content": "(RI) theorem. The RI theorem characterizes the bit-rate needed to store", + "type": "text" + }, + { + "bbox": [ + 405, + 302, + 415, + 312 + ], + "score": 0.83, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 416, + 301, + 505, + 314 + ], + "score": 1.0, + "content": "while ensuring small", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 313, + 421, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 421, + 325 + ], + "score": 1.0, + "content": "log-loss on invariant tasks. We obtain analogous results for squared-error loss.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 289, + 506, + 325 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 334, + 504, + 368 + ], + "lines": [ + { + "bbox": [ + 105, + 333, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 392, + 347 + ], + "score": 1.0, + "content": "Theorem 2 (Rate-Invariance). Assume the conditions of Prop. 1. Let", + "type": "text" + }, + { + "bbox": [ + 393, + 335, + 418, + 345 + ], + "score": 0.89, + "content": "\\delta \\geq 0", + "type": "inline_equation" + }, + { + "bbox": [ + 418, + 333, + 439, + 347 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 439, + 334, + 474, + 346 + ], + "score": 0.74, + "content": "R a t e ( \\delta )", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 333, + 506, + 347 + ], + "score": 1.0, + "content": "denote", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 345, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 345, + 307, + 357 + ], + "score": 1.0, + "content": "the minimum achievable bit-rate for transmitting", + "type": "text" + }, + { + "bbox": [ + 308, + 346, + 316, + 355 + ], + "score": 0.81, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 345, + 388, + 357 + ], + "score": 1.0, + "content": "such that for any", + "type": "text" + }, + { + "bbox": [ + 388, + 346, + 420, + 356 + ], + "score": 0.91, + "content": "Y \\in \\mathcal { T } _ { \\sim }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 345, + 458, + 357 + ], + "score": 1.0, + "content": "we have", + "type": "text" + }, + { + "bbox": [ + 459, + 345, + 505, + 357 + ], + "score": 0.91, + "content": "\\mathrm { R } [ \\dot { Y } | Z ] -", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 356, + 429, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 162, + 368 + ], + "score": 0.92, + "content": "\\mathrm { R } [ Y | X ] \\leq \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 356, + 189, + 368 + ], + "score": 1.0, + "content": ". Then", + "type": "text" + }, + { + "bbox": [ + 190, + 356, + 242, + 368 + ], + "score": 0.92, + "content": "R a t e ( \\delta ) = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 356, + 252, + 368 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 253, + 356, + 312, + 368 + ], + "score": 0.94, + "content": "\\delta \\geq \\mathrm { H } [ M ( \\bar { X } ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 356, + 429, + 368 + ], + "score": 1.0, + "content": "and otherwise it is finite and", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 333, + 506, + 368 + ] + }, + { + "type": "image", + "bbox": [ + 115, + 371, + 484, + 409 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 371, + 484, + 409 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 115, + 371, + 484, + 409 + ], + "spans": [ + { + "bbox": [ + 115, + 371, + 484, + 409 + ], + "score": 0.923, + "type": "image", + "image_path": "cb8ccf92de6e597a10d0adc453be47c4173aa7e0fb6ecca9ffa8de99785a3aca.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 115, + 371, + 484, + 383.6666666666667 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 115, + 383.6666666666667, + 484, + 396.33333333333337 + ], + "spans": [], + "index": 24 + }, + { + "bbox": [ + 115, + 396.33333333333337, + 484, + 409.00000000000006 + ], + "spans": [], + "index": 25 + } + ] + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 417, + 337, + 582 + ], + "lines": [ + { + "bbox": [ + 106, + 417, + 337, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 246, + 430 + ], + "score": 1.0, + "content": "To ensure lossless prediction, i.e.,", + "type": "text" + }, + { + "bbox": [ + 246, + 417, + 281, + 429 + ], + "score": 0.5, + "content": "R a t e ( 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 417, + 337, + 430 + ], + "score": 1.0, + "content": ", our theorem", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 426, + 338, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 245, + 442 + ], + "score": 1.0, + "content": "states that we require a bit-rate of", + "type": "text" + }, + { + "bbox": [ + 245, + 428, + 286, + 440 + ], + "score": 0.9, + "content": "\\mathrm { H } [ M ( { \\bar { X } } ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 426, + 338, + 442 + ], + "score": 1.0, + "content": ". 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For example, invariance to cropping can be enforced", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 369, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 381 + ], + "score": 1.0, + "content": "by randomly cropping images while retaining the original label. We show in Appx. 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This has the advantage that the learned", + "type": "text" + }, + { + "bbox": [ + 477, + 533, + 488, + 543 + ], + "score": 0.8, + "content": "q _ { \\theta }", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 531, + 506, + 545 + ], + "score": 1.0, + "content": "can", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 218, + 555 + ], + "score": 1.0, + "content": "be used for entropy coding", + "type": "text" + }, + { + "bbox": [ + 218, + 543, + 227, + 552 + ], + "score": 0.7, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 542, + 506, + 555 + ], + "score": 1.0, + "content": "[26, 27]. See Ballé et al. [28] for possible entropy models. Our two", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 552, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 104, + 552, + 295, + 566 + ], + "score": 1.0, + "content": "approximations differ in how they upper bound", + "type": "text" + }, + { + "bbox": [ + 296, + 553, + 332, + 565 + ], + "score": 0.92, + "content": "\\mathrm { R } [ X \\mid Z ]", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 552, + 506, + 566 + ], + "score": 1.0, + "content": ". 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We refer to it as a variational invariant compressor (VIC). See Fig. 4 for an illustration.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 634, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 189, + 647 + ], + "score": 1.0, + "content": "VIC has an encoder", + "type": "text" + }, + { + "bbox": [ + 189, + 634, + 243, + 646 + ], + "score": 0.92, + "content": "p _ { \\varphi } ( Z | A ( X ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 634, + 321, + 647 + ], + "score": 1.0, + "content": ", an entropy model", + "type": "text" + }, + { + "bbox": [ + 321, + 634, + 346, + 646 + ], + "score": 0.91, + "content": "q _ { \\theta } ( Z )", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 634, + 409, + 647 + ], + "score": 1.0, + "content": ", and a decoder", + "type": "text" + }, + { + "bbox": [ + 409, + 634, + 447, + 646 + ], + "score": 0.93, + "content": "q _ { \\phi } ( X | Z )", + "type": "inline_equation" + }, + { + "bbox": [ + 447, + 634, + 506, + 647 + ], + "score": 1.0, + "content": ". 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The disadvantages of BINCE are that it", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "(i) does not provide to reconstructions diminishes interpretability; and (ii) has a high bias, unless the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 480, + 441, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 220, + 493 + ], + "score": 1.0, + "content": "number of negative samples", + "type": "text" + }, + { + "bbox": [ + 221, + 482, + 228, + 490 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 480, + 441, + 493 + ], + "score": 1.0, + "content": "is large [33, 34], which is computationally intensive.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 42 + }, + { + "type": "title", + "bbox": [ + 107, + 506, + 191, + 520 + ], + "lines": [ + { + "bbox": [ + 103, + 504, + 193, + 524 + ], + "spans": [ + { + "bbox": [ + 103, + 504, + 193, + 524 + ], + "score": 1.0, + "content": "5 Experiments", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 47 + }, + { + "type": "text", + "bbox": [ + 106, + 530, + 506, + 653 + ], + "lines": [ + { + "bbox": [ + 105, + 530, + 507, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 507, + 544 + ], + "score": 1.0, + "content": "We evaluated our framework focusing on two questions: (i) What compression rates can our frame-", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 541, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 505, + 554 + ], + "score": 1.0, + "content": "work achieve at what cost? 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The disadvantages of BINCE are that it", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "(i) does not provide to reconstructions diminishes interpretability; and (ii) has a high bias, unless the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 480, + 441, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 220, + 493 + ], + "score": 1.0, + "content": "number of negative samples", + "type": "text" + }, + { + "bbox": [ + 221, + 482, + 228, + 490 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 480, + 441, + 493 + ], + "score": 1.0, + "content": "is large [33, 34], which is computationally intensive.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 42, + "bbox_fs": [ + 104, + 393, + 506, + 493 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 506, + 191, + 520 + ], + "lines": [ + { + "bbox": [ + 103, + 504, + 193, + 524 + ], + "spans": [ + { + "bbox": [ + 103, + 504, + 193, + 524 + ], + "score": 1.0, + "content": "5 Experiments", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 47 + }, + { + "type": "text", + "bbox": [ + 106, + 530, + 506, + 653 + ], + "lines": [ + { + "bbox": [ + 105, + 530, + 507, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 507, + 544 + ], + "score": 1.0, + "content": "We evaluated our framework focusing on two questions: (i) What compression rates can our frame-", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 541, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 505, + 554 + ], + "score": 1.0, + "content": "work achieve at what cost? 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For classical compressors, standard neural compressors (VC) and our VIC,", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 574, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 226, + 588 + ], + "score": 1.0, + "content": "we used either reconstructions", + "type": "text" + }, + { + "bbox": [ + 227, + 574, + 237, + 585 + ], + "score": 0.85, + "content": "\\tilde { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 574, + 412, + 588 + ], + "score": 1.0, + "content": "as inputs to the predictors or representations", + "type": "text" + }, + { + "bbox": [ + 412, + 576, + 421, + 586 + ], + "score": 0.65, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 574, + 506, + 588 + ], + "score": 1.0, + "content": ". 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E.", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 105, + 640, + 446, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 446, + 654 + ], + "score": 1.0, + "content": "For additional results see Appx. F. Code is at github.com/YannDubs/lossyless.", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 53, + "bbox_fs": [ + 105, + 530, + 507, + 654 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 661, + 298, + 673 + ], + "lines": [ + { + "bbox": [ + 105, + 659, + 299, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 299, + 677 + ], + "score": 1.0, + "content": "5.1 Building intuition with toy experiments", + "type": "text" + } + ], + "index": 59 + } + ], + "index": 59 + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 506, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 678, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 506, + 690 + ], + "score": 1.0, + "content": "To build an visual intuition, we compressed samples from a 2D banana source distribution [36],", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 105, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "assuming rotation invariant tasks, e.g., classifying whether points are in the unit circle. We also", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 106, + 701, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 701, + 506, + 712 + ], + "score": 1.0, + "content": "compressed MNIST digits as in Fig. 1. Digits are augmented (rotations, translations, shearing,", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 106, + 711, + 451, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 451, + 723 + ], + "score": 1.0, + "content": "scaling) both at train and test time to ensure that our invariance assumption still holds.", + "type": "text" + } + ], + "index": 63 + } + ], + "index": 61.5, + "bbox_fs": [ + 105, + 678, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 132, + 72, + 480, + 221 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 132, + 72, + 480, + 221 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 132, + 72, + 480, + 221 + ], + "spans": [ + { + "bbox": [ + 132, + 72, + 480, + 221 + ], + "score": 0.974, + "type": "image", + "image_path": "6919e6f58eb4eca1ba90304ab55c81cc42f56b53a7aa00c4e3157d80046883ee.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 132, + 72, + 480, + 121.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 132, + 121.66666666666666, + 480, + 171.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 132, + 171.33333333333331, + 480, + 220.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 227, + 506, + 283 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 227, + 506, + 240 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 506, + 240 + ], + "score": 1.0, + "content": "Figure 5: Compression rates of a Banana source [36] can be decreased when downstream tasks are", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 239, + 506, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 506, + 252 + ], + "score": 1.0, + "content": "rotation invariant. (Left) Our invariant compressor (VIC, blue) outperforms neural compressors (VC,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 249, + 506, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 506, + 263 + ], + "score": 1.0, + "content": "orange). 5 runs with standard errors in gray. (Right) VIC quantizes the space using disks to remove", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "score": 1.0, + "content": "unnecessary angular information. Pink lines are quantization boundaries, dots are code vectors with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 271, + 441, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 389, + 285 + ], + "score": 1.0, + "content": "size proportional to learned probabilities. Low rates correspond to low", + "type": "text" + }, + { + "bbox": [ + 390, + 272, + 397, + 283 + ], + "score": 0.85, + "content": "\\beta", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 271, + 441, + 285 + ], + "score": 1.0, + "content": "in Eq. (7).", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 106, + 294, + 505, + 383 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 505, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 505, + 307 + ], + "score": 1.0, + "content": "Where do our rate gains come from? For rotation invariant tasks, our method (VIC) discards", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 305, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 305, + 506, + 317 + ], + "score": 1.0, + "content": "unnecessary angular information by learning disk-shaped quantizations (Fig. 5, bottom right). Specif-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 316, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 506, + 329 + ], + "score": 1.0, + "content": "ically, VIC retains only radial information by mapping all randomly rotated points (disks) back to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 327, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 506, + 339 + ], + "score": 1.0, + "content": "maximal invariants (pink dots). In contrast, standard neural compressors (VC) attempt to reconstruct", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 338, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 351 + ], + "score": 1.0, + "content": "all information, which requires a finer partition (Fig. 5, top right). As a result (Fig. 5a), VIC needs", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 348, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 104, + 348, + 180, + 362 + ], + "score": 1.0, + "content": "a smaller bit-rate", + "type": "text" + }, + { + "bbox": [ + 181, + 350, + 187, + 360 + ], + "score": 0.71, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 188, + 348, + 350, + 362 + ], + "score": 1.0, + "content": "-axis) for the same desired performance", + "type": "text" + }, + { + "bbox": [ + 350, + 349, + 372, + 361 + ], + "score": 0.87, + "content": "( \\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 348, + 376, + 362 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 376, + 351, + 383, + 359 + ], + "score": 0.68, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 348, + 506, + 362 + ], + "score": 1.0, + "content": "-axis). The area under the RD", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 359, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 209, + 373 + ], + "score": 1.0, + "content": "curve (AURD) for VIC is", + "type": "text" + }, + { + "bbox": [ + 209, + 360, + 249, + 370 + ], + "score": 0.79, + "content": "3 5 . 8 { \\pm } 4 . 2 ", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 359, + 280, + 373 + ], + "score": 1.0, + "content": "against", + "type": "text" + }, + { + "bbox": [ + 280, + 360, + 320, + 370 + ], + "score": 0.84, + "content": "4 8 . 1 { \\pm } 0 . 3 ", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 359, + 506, + 373 + ], + "score": 1.0, + "content": "for VC, i.e., expected bit-rate gains are around", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 370, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 126, + 381 + ], + "score": 0.87, + "content": "7 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 370, + 506, + 384 + ], + "score": 1.0, + "content": ". Similar gains are achieved for augmented MNIST in Fig. 6 by reconstructing canonical digits.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 11.5 + }, + { + "type": "image", + "bbox": [ + 112, + 394, + 503, + 525 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 112, + 394, + 503, + 525 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 112, + 394, + 503, + 525 + ], + "spans": [ + { + "bbox": [ + 112, + 394, + 503, + 525 + ], + "score": 0.971, + "type": "image", + "image_path": "4444126e4d93d8d0691113b395d75bc5be911978be1e8ca385d5ac3e21dd53b8.jpg" + } + ] + } + ], + "index": 17, + "virtual_lines": [ + { + "bbox": [ + 112, + 394, + 503, + 437.6666666666667 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 112, + 437.6666666666667, + 503, + 481.33333333333337 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 112, + 481.33333333333337, + 503, + 525.0 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 533, + 505, + 577 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "Figure 6: (Left) By reconstructing prototypical digits our VIC (blue) achieves higher compression", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 543, + 505, + 557 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 505, + 557 + ], + "score": 1.0, + "content": "of augmented MNIST digits than standard neural compressors (VC, orange) without hindering", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "downstream classification. 5 runs. (Right) The source examples (first row) as well as reconstructions", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 565, + 391, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 391, + 578 + ], + "score": 1.0, + "content": "for the non-invariant (second row) and invariant compressor (last row).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5 + } + ], + "index": 18.75 + }, + { + "type": "text", + "bbox": [ + 106, + 585, + 505, + 641 + ], + "lines": [ + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "score": 1.0, + "content": "Can we recover the optimal bit-rate? We investigated whether our losses can achieve the optimal", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 596, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 379, + 608 + ], + "score": 1.0, + "content": "bit-rate for lossy prediction by using supervised augmentations, i.e.,", + "type": "text" + }, + { + "bbox": [ + 379, + 596, + 401, + 608 + ], + "score": 0.92, + "content": "A ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 596, + 505, + 608 + ], + "score": 1.0, + "content": "randomly samples a train", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 606, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 141, + 620 + ], + "score": 1.0, + "content": "example", + "type": "text" + }, + { + "bbox": [ + 142, + 607, + 155, + 617 + ], + "score": 0.89, + "content": "x ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 606, + 427, + 620 + ], + "score": 1.0, + "content": "that has the same label. For MNIST the single-task optimal bit-rate is", + "type": "text" + }, + { + "bbox": [ + 427, + 607, + 505, + 619 + ], + "score": 0.92, + "content": "\\mathrm { H } \\bar { \\vert } Y \\vert = \\mathrm { \\bar { l o g } } ( 1 0 ) \\approx", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 617, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 104, + 617, + 505, + 631 + ], + "score": 1.0, + "content": "3.3 bits. VIC and BINCE respectively achieve 5.7 and 5.9 bits, which shows that our losses are", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 628, + 389, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 389, + 641 + ], + "score": 1.0, + "content": "relatively good despite practical approximations. Details in Appx. F.2.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 106, + 645, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 452, + 658 + ], + "score": 1.0, + "content": "What is the impact of the choice of augmentations? The choice of augmentation", + "type": "text" + }, + { + "bbox": [ + 453, + 646, + 461, + 655 + ], + "score": 0.78, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 644, + 505, + 658 + ], + "score": 1.0, + "content": "implicitly", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 656, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 215, + 668 + ], + "score": 1.0, + "content": "defines the desired task-set", + "type": "text" + }, + { + "bbox": [ + 215, + 657, + 224, + 666 + ], + "score": 0.82, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 656, + 245, + 668 + ], + "score": 1.0, + "content": ", i.e.,", + "type": "text" + }, + { + "bbox": [ + 245, + 657, + 254, + 666 + ], + "score": 0.83, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 656, + 378, + 668 + ], + "score": 1.0, + "content": "is the set of all tasks for which", + "type": "text" + }, + { + "bbox": [ + 378, + 657, + 387, + 666 + ], + "score": 0.76, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 656, + 506, + 668 + ], + "score": 1.0, + "content": "does not remove information.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 667, + 504, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 273, + 679 + ], + "score": 1.0, + "content": "As a result Theorem 2 can be rewritten as", + "type": "text" + }, + { + "bbox": [ + 273, + 667, + 385, + 679 + ], + "score": 0.92, + "content": "R a t e ( \\delta ) = \\operatorname { I } [ X ; A ( X ) ] - \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 385, + 667, + 495, + 679 + ], + "score": 1.0, + "content": ", so the rate decreases when", + "type": "text" + }, + { + "bbox": [ + 495, + 667, + 504, + 677 + ], + "score": 0.68, + "content": "A", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 233, + 690 + ], + "score": 1.0, + "content": "removes more information from", + "type": "text" + }, + { + "bbox": [ + 233, + 679, + 243, + 688 + ], + "score": 0.82, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 677, + 505, + 690 + ], + "score": 1.0, + "content": ". To illustrate this we trained our VIC using three augmentation sets", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 443, + 700 + ], + "score": 1.0, + "content": "on MNIST, all of which keep the true label invariant but progressively discard more", + "type": "text" + }, + { + "bbox": [ + 443, + 689, + 453, + 699 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "information.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 698, + 506, + 714 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 714 + ], + "score": 1.0, + "content": "VIC respectively achieves a rate of 185.3, 79.0, and 5.7 bits, which shows the importance of using", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 711, + 459, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 217, + 723 + ], + "score": 1.0, + "content": "augmentations that remove", + "type": "text" + }, + { + "bbox": [ + 217, + 712, + 227, + 721 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 711, + 459, + 723 + ], + "score": 1.0, + "content": "information. Details and BINCE results are in Appx. 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(Left) Our invariant compressor (VIC, blue) outperforms neural compressors (VC,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 249, + 506, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 506, + 263 + ], + "score": 1.0, + "content": "orange). 5 runs with standard errors in gray. (Right) VIC quantizes the space using disks to remove", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 506, + 273 + ], + "score": 1.0, + "content": "unnecessary angular information. Pink lines are quantization boundaries, dots are code vectors with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 271, + 441, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 389, + 285 + ], + "score": 1.0, + "content": "size proportional to learned probabilities. 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Specif-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 316, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 105, + 316, + 506, + 329 + ], + "score": 1.0, + "content": "ically, VIC retains only radial information by mapping all randomly rotated points (disks) back to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 327, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 506, + 339 + ], + "score": 1.0, + "content": "maximal invariants (pink dots). In contrast, standard neural compressors (VC) attempt to reconstruct", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 338, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 351 + ], + "score": 1.0, + "content": "all information, which requires a finer partition (Fig. 5, top right). As a result (Fig. 5a), VIC needs", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 104, + 348, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 104, + 348, + 180, + 362 + ], + "score": 1.0, + "content": "a smaller bit-rate", + "type": "text" + }, + { + "bbox": [ + 181, + 350, + 187, + 360 + ], + "score": 0.71, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 188, + 348, + 350, + 362 + ], + "score": 1.0, + "content": "-axis) for the same desired performance", + "type": "text" + }, + { + "bbox": [ + 350, + 349, + 372, + 361 + ], + "score": 0.87, + "content": "( \\mathrm { D } _ { \\tau _ { \\sim } }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 348, + 376, + 362 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 376, + 351, + 383, + 359 + ], + "score": 0.68, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 348, + 506, + 362 + ], + "score": 1.0, + "content": "-axis). The area under the RD", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 359, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 209, + 373 + ], + "score": 1.0, + "content": "curve (AURD) for VIC is", + "type": "text" + }, + { + "bbox": [ + 209, + 360, + 249, + 370 + ], + "score": 0.79, + "content": "3 5 . 8 { \\pm } 4 . 2 ", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 359, + 280, + 373 + ], + "score": 1.0, + "content": "against", + "type": "text" + }, + { + "bbox": [ + 280, + 360, + 320, + 370 + ], + "score": 0.84, + "content": "4 8 . 1 { \\pm } 0 . 3 ", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 359, + 506, + 373 + ], + "score": 1.0, + "content": "for VC, i.e., expected bit-rate gains are around", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 370, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 371, + 126, + 381 + ], + "score": 0.87, + "content": "7 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 370, + 506, + 384 + ], + "score": 1.0, + "content": ". Similar gains are achieved for augmented MNIST in Fig. 6 by reconstructing canonical digits.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 11.5, + "bbox_fs": [ + 104, + 294, + 506, + 384 + ] + }, + { + "type": "image", + "bbox": [ + 112, + 394, + 503, + 525 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 112, + 394, + 503, + 525 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 112, + 394, + 503, + 525 + ], + "spans": [ + { + "bbox": [ + 112, + 394, + 503, + 525 + ], + "score": 0.971, + "type": "image", + "image_path": "4444126e4d93d8d0691113b395d75bc5be911978be1e8ca385d5ac3e21dd53b8.jpg" + } + ] + } + ], + "index": 17, + "virtual_lines": [ + { + "bbox": [ + 112, + 394, + 503, + 437.6666666666667 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 112, + 437.6666666666667, + 503, + 481.33333333333337 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 112, + 481.33333333333337, + 503, + 525.0 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 533, + 505, + 577 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "spans": [ + { + "bbox": [ + 105, + 533, + 505, + 546 + ], + "score": 1.0, + "content": "Figure 6: (Left) By reconstructing prototypical digits our VIC (blue) achieves higher compression", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 543, + 505, + 557 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 505, + 557 + ], + "score": 1.0, + "content": "of augmented MNIST digits than standard neural compressors (VC, orange) without hindering", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "downstream classification. 5 runs. (Right) The source examples (first row) as well as reconstructions", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 565, + 391, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 391, + 578 + ], + "score": 1.0, + "content": "for the non-invariant (second row) and invariant compressor (last row).", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5 + } + ], + "index": 18.75 + }, + { + "type": "text", + "bbox": [ + 106, + 585, + 505, + 641 + ], + "lines": [ + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 584, + 505, + 597 + ], + "score": 1.0, + "content": "Can we recover the optimal bit-rate? We investigated whether our losses can achieve the optimal", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 596, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 379, + 608 + ], + "score": 1.0, + "content": "bit-rate for lossy prediction by using supervised augmentations, i.e.,", + "type": "text" + }, + { + "bbox": [ + 379, + 596, + 401, + 608 + ], + "score": 0.92, + "content": "A ( x )", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 596, + 505, + 608 + ], + "score": 1.0, + "content": "randomly samples a train", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 606, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 141, + 620 + ], + "score": 1.0, + "content": "example", + "type": "text" + }, + { + "bbox": [ + 142, + 607, + 155, + 617 + ], + "score": 0.89, + "content": "x ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 606, + 427, + 620 + ], + "score": 1.0, + "content": "that has the same label. For MNIST the single-task optimal bit-rate is", + "type": "text" + }, + { + "bbox": [ + 427, + 607, + 505, + 619 + ], + "score": 0.92, + "content": "\\mathrm { H } \\bar { \\vert } Y \\vert = \\mathrm { \\bar { l o g } } ( 1 0 ) \\approx", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 617, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 104, + 617, + 505, + 631 + ], + "score": 1.0, + "content": "3.3 bits. VIC and BINCE respectively achieve 5.7 and 5.9 bits, which shows that our losses are", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 628, + 389, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 389, + 641 + ], + "score": 1.0, + "content": "relatively good despite practical approximations. Details in Appx. F.2.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25, + "bbox_fs": [ + 104, + 584, + 505, + 641 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 645, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 644, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 452, + 658 + ], + "score": 1.0, + "content": "What is the impact of the choice of augmentations? The choice of augmentation", + "type": "text" + }, + { + "bbox": [ + 453, + 646, + 461, + 655 + ], + "score": 0.78, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 644, + 505, + 658 + ], + "score": 1.0, + "content": "implicitly", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 656, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 215, + 668 + ], + "score": 1.0, + "content": "defines the desired task-set", + "type": "text" + }, + { + "bbox": [ + 215, + 657, + 224, + 666 + ], + "score": 0.82, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 656, + 245, + 668 + ], + "score": 1.0, + "content": ", i.e.,", + "type": "text" + }, + { + "bbox": [ + 245, + 657, + 254, + 666 + ], + "score": 0.83, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 656, + 378, + 668 + ], + "score": 1.0, + "content": "is the set of all tasks for which", + "type": "text" + }, + { + "bbox": [ + 378, + 657, + 387, + 666 + ], + "score": 0.76, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 656, + 506, + 668 + ], + "score": 1.0, + "content": "does not remove information.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 667, + 504, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 273, + 679 + ], + "score": 1.0, + "content": "As a result Theorem 2 can be rewritten as", + "type": "text" + }, + { + "bbox": [ + 273, + 667, + 385, + 679 + ], + "score": 0.92, + "content": "R a t e ( \\delta ) = \\operatorname { I } [ X ; A ( X ) ] - \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 385, + 667, + 495, + 679 + ], + "score": 1.0, + "content": ", so the rate decreases when", + "type": "text" + }, + { + "bbox": [ + 495, + 667, + 504, + 677 + ], + "score": 0.68, + "content": "A", + "type": "inline_equation" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 233, + 690 + ], + "score": 1.0, + "content": "removes more information from", + "type": "text" + }, + { + "bbox": [ + 233, + 679, + 243, + 688 + ], + "score": 0.82, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 677, + 505, + 690 + ], + "score": 1.0, + "content": ". To illustrate this we trained our VIC using three augmentation sets", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 688, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 443, + 700 + ], + "score": 1.0, + "content": "on MNIST, all of which keep the true label invariant but progressively discard more", + "type": "text" + }, + { + "bbox": [ + 443, + 689, + 453, + 699 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 688, + 506, + 700 + ], + "score": 1.0, + "content": "information.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 698, + 506, + 714 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 714 + ], + "score": 1.0, + "content": "VIC respectively achieves a rate of 185.3, 79.0, and 5.7 bits, which shows the importance of using", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 711, + 459, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 217, + 723 + ], + "score": 1.0, + "content": "augmentations that remove", + "type": "text" + }, + { + "bbox": [ + 217, + 712, + 227, + 721 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 711, + 459, + 723 + ], + "score": 1.0, + "content": "information. Details and BINCE results are in Appx. F.2.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 644, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 72, + 354, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 71, + 356, + 87 + ], + "spans": [ + { + "bbox": [ + 105, + 71, + 356, + 87 + ], + "score": 1.0, + "content": "5.2 Evaluating our methods with controlled experiments", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 89, + 506, + 133 + ], + "lines": [ + { + "bbox": [ + 105, + 89, + 506, + 102 + ], + "spans": [ + { + "bbox": [ + 105, + 89, + 506, + 102 + ], + "score": 1.0, + "content": "To investigate our methods, we compressed the STL10 dataset [37]. We augment (flipping, color", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 100, + 507, + 112 + ], + "spans": [ + { + "bbox": [ + 105, + 100, + 507, + 112 + ], + "score": 1.0, + "content": "jittering, cropping) the train and test set, to ensure that the task invariance assumptions are satisfied.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 111, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 106, + 111, + 505, + 123 + ], + "score": 1.0, + "content": "We focus on more realistic settings in the next section. 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Both our invariant (VIC) and standard (VC) neural", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 288, + 504, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 504, + 300 + ], + "score": 1.0, + "content": "compressors significantly decreased classification accuracy, which we believe can be explained by", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 433, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 433, + 311 + ], + "score": 1.0, + "content": "the encoders architecture (ResNet18) that we use for consistency (see Appx. 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In", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 338, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 210, + 351 + ], + "score": 1.0, + "content": "contrast, predicting from", + "type": "text" + }, + { + "bbox": [ + 210, + 338, + 219, + 348 + ], + "score": 0.72, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 338, + 358, + 351 + ], + "score": 1.0, + "content": "for VC decreases performance by", + "type": "text" + }, + { + "bbox": [ + 359, + 338, + 378, + 349 + ], + "score": 0.88, + "content": "1 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 338, + 505, + 351 + ], + "score": 1.0, + "content": "(see Appx. F.3). This suggests", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 499, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 224, + 363 + ], + "score": 1.0, + "content": "that invariant reconstructions", + "type": "text" + }, + { + "bbox": [ + 225, + 348, + 235, + 360 + ], + "score": 0.85, + "content": "\\tilde { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 350, + 499, + 363 + ], + "score": 1.0, + "content": "might not be easy to predict from with standard image predictors.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 366, + 505, + 411 + ], + "lines": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "score": 1.0, + "content": "Are we learning invariant compressors? Invariant compressors should provide RD curves that are", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 376, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 505, + 390 + ], + "score": 1.0, + "content": "robust to test distribution shift in the desired augmentations. We thus trained our VIC by applying the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 166, + 401 + ], + "score": 1.0, + "content": "augmentations", + "type": "text" + }, + { + "bbox": [ + 166, + 388, + 186, + 399 + ], + "score": 0.88, + "content": "5 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 388, + 342, + 401 + ], + "score": 1.0, + "content": "of the time but varying that probability", + "type": "text" + }, + { + "bbox": [ + 342, + 390, + 349, + 400 + ], + "score": 0.78, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 388, + 506, + 401 + ], + "score": 1.0, + "content": "at test time. In Appx. F.3 we show that", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 398, + 354, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 354, + 412 + ], + "score": 1.0, + "content": "this distribution shift have negligible influence on RD curves.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5 + }, + { + "type": "title", + "bbox": [ + 108, + 420, + 405, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 419, + 406, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 406, + 434 + ], + "score": 1.0, + "content": "5.3 A zero-shot compressor using pre-trained self-supervised models", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 436, + 505, + 548 + ], + "lines": [ + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "score": 1.0, + "content": "BINCE includes a standard contrastive SSL loss. So, we investigated whether existing pre-trained", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 506, + 460 + ], + "score": 1.0, + "content": "SSL models [32, 41] can be used to build generic compressors. In particular, we investigated whether", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "CLIP [41] could be quickly turned into a powerful task-centric compressor for computer vision. In the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "introduction, we motivated large compression gains by noting that typical image classification tasks", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 365, + 492 + ], + "score": 1.0, + "content": "can be predicted from detailed captions instead of images (around", + "type": "text" + }, + { + "bbox": [ + 365, + 480, + 393, + 490 + ], + "score": 0.87, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "more bits). CLIP is a vision", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 491, + 507, + 506 + ], + "spans": [ + { + "bbox": [ + 104, + 491, + 350, + 506 + ], + "score": 1.0, + "content": "transformer [42] pre-trained on 400M pairs of images and text", + "type": "text" + }, + { + "bbox": [ + 350, + 491, + 411, + 503 + ], + "score": 0.89, + "content": "( x _ { i m a g e } , x _ { t e x t } ^ { + } )", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 491, + 507, + 506 + ], + "score": 1.0, + "content": "using a contrastive loss.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 103, + 499, + 508, + 520 + ], + "spans": [ + { + "bbox": [ + 103, + 499, + 188, + 520 + ], + "score": 1.0, + "content": "The “augmentation”", + "type": "text" + }, + { + "bbox": [ + 189, + 504, + 197, + 513 + ], + "score": 0.62, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 499, + 309, + 520 + ], + "score": 1.0, + "content": "is then a function that maps", + "type": "text" + }, + { + "bbox": [ + 309, + 505, + 339, + 515 + ], + "score": 0.75, + "content": "x _ { i m a g e }", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 499, + 405, + 520 + ], + "score": 1.0, + "content": "to its associated", + "type": "text" + }, + { + "bbox": [ + 405, + 503, + 426, + 515 + ], + "score": 0.92, + "content": "\\boldsymbol { x } _ { t e x t } ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 499, + 508, + 520 + ], + "score": 1.0, + "content": "and vis-versa. This", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "score": 1.0, + "content": "will partition the images and texts into sets, each of which are associated directly or by transitivity", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "in CLIP’s dataset. This suggests that CLIP is retaining the image information that corresponds to a", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 536, + 454, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 454, + 549 + ], + "score": 1.0, + "content": "detailed caption, and may be turned into a generic compressor for image classification.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 31.5 + }, + { + "type": "text", + "bbox": [ + 107, + 552, + 505, + 662 + ], + "lines": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "CLIP can essentially be seen as a BINCE model with an image-to-text augmentation, but without an", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 564, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 576 + ], + "score": 1.0, + "content": "entropy bottleneck. (For details about the CLIP-BINCE relation see Appx. C.5.) We thus constructed", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "score": 1.0, + "content": "an approximation of our desired image-to-text BINCE compressor by two simple steps. First, we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 583, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 598 + ], + "score": 1.0, + "content": "downloaded and froze CLIP’s parameters. Second, we trained, on the small MSCOCO dataset [43],", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 595, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 506, + 610 + ], + "score": 1.0, + "content": "an entropy bottleneck to compress CLIP’s representation. The latter step can be done by training any", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 605, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 621 + ], + "score": 1.0, + "content": "lossy compressor on CLIP’s representations, we did so using Ballé et al.’s [28] hyperprior entropy", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "score": 1.0, + "content": "model with a learned rounded precision. We then evaluated our resulting compressor on 8 datasets", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 630, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 505, + 642 + ], + "score": 1.0, + "content": "(various classification tasks and image shapes) that were never seen during training (zero-shot), by", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 104, + 639, + 505, + 654 + ], + "spans": [ + { + "bbox": [ + 104, + 639, + 505, + 654 + ], + "score": 1.0, + "content": "training an MLP for downstream predictions on each dataset. One can see this as a multi-task setting", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 651, + 501, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 501, + 663 + ], + "score": 1.0, + "content": "(each dataset is a distinct task). We investigate the case of multiple labels per images in Appx. F.5.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "Can we use pretrained SSL to obtain a generic compressor? Table 2 shows that we can exploit", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 676, + 506, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 692 + ], + "score": 1.0, + "content": "existing state-of-the-art (SOTA) SSL models to get a powerful image compressor, which achieves", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 135, + 699 + ], + "score": 0.88, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "bit-rate gains on ImageNet compared to JPEG (at the quality level used for storing ImageNet).", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 184, + 713 + ], + "score": 1.0, + "content": "The bit-rate gains (", + "type": "text" + }, + { + "bbox": [ + 184, + 700, + 196, + 711 + ], + "score": 0.6, + "content": "1 ^ { \\mathrm { s t } }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "row) are significant across all zero-shot datasets, even for biological tissues", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "(PCam; [44]). Importantly, these gains come at little cost in test performance. Indeed, the test", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 106, + 72, + 354, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 71, + 356, + 87 + ], + "spans": [ + { + "bbox": [ + 105, + 71, + 356, + 87 + ], + "score": 1.0, + "content": "5.2 Evaluating our methods with controlled experiments", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 89, + 506, + 133 + ], + "lines": [ + { + "bbox": [ + 105, + 89, + 506, + 102 + ], + "spans": [ + { + "bbox": [ + 105, + 89, + 506, + 102 + ], + "score": 1.0, + "content": "To investigate our methods, we compressed the STL10 dataset [37]. We augment (flipping, color", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 100, + 507, + 112 + ], + "spans": [ + { + "bbox": [ + 105, + 100, + 507, + 112 + ], + "score": 1.0, + "content": "jittering, cropping) the train and test set, to ensure that the task invariance assumptions are satisfied.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 111, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 106, + 111, + 505, + 123 + ], + "score": 1.0, + "content": "We focus on more realistic settings in the next section. In each experiment, we sampled 100", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 122, + 507, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 122, + 507, + 135 + ], + "score": 1.0, + "content": "combinations of hyper-parameters to ensure equal computational budget across models and baselines.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2.5, + "bbox_fs": [ + 105, + 89, + 507, + 135 + ] + }, + { + "type": "table", + "bbox": [ + 110, + 166, + 499, + 210 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 139, + 504, + 162 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 138, + 505, + 153 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 505, + 153 + ], + "score": 1.0, + "content": "Table 1: Invariant compressors (BINCE, VIC) outperform classical (PNG, JPEG, WebP) and neural", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 488, + 164 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 435, + 164 + ], + "score": 1.0, + "content": "(VC) compressors on STL10. BINCE achieves lossless prediction but compresses", + "type": "text" + }, + { + "bbox": [ + 435, + 151, + 459, + 161 + ], + "score": 0.86, + "content": "1 2 1 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 149, + 488, + 164 + ], + "score": 1.0, + "content": "better.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "table_body", + "bbox": [ + 110, + 166, + 499, + 210 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 110, + 166, + 499, + 210 + ], + "spans": [ + { + "bbox": [ + 110, + 166, + 499, + 210 + ], + "score": 0.977, + "html": "
PNG [38]JPEG [39]WebP [40]vcxVIC XVIC ZBINCE
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Compression gains1×3×13×63×269×175×121×
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In Table 1 we compare com-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 232, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 506, + 245 + ], + "score": 1.0, + "content": "pressors at the lowest downstream error that they achieved. As benchmark, we use PNG’s lossless", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 244, + 505, + 256 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 505, + 256 + ], + "score": 1.0, + "content": "compression. Predicting from PNG corresponds to standard image classification, and obtains a rate", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 117, + 267 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 255, + 146, + 265 + ], + "score": 0.55, + "content": "1 . 4 2 \\mathrm { e 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 254, + 219, + 267 + ], + "score": 1.0, + "content": "bits per image for", + "type": "text" + }, + { + "bbox": [ + 219, + 254, + 247, + 265 + ], + "score": 0.89, + "content": "8 0 . 8 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "accuracy. Classical lossy methods (JPEG, WebP) achieved up to", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 264, + 504, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 125, + 276 + ], + "score": 0.87, + "content": "1 3 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 264, + 480, + 278 + ], + "score": 1.0, + "content": "bit-rate gains with little drop in performance. In comparison, our BINCE method achieved", + "type": "text" + }, + { + "bbox": [ + 480, + 266, + 504, + 276 + ], + "score": 0.87, + "content": "1 2 1 \\times", + "type": "inline_equation" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 276, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 506, + 289 + ], + "score": 1.0, + "content": "compression gains with no impact on predictions. Both our invariant (VIC) and standard (VC) neural", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 288, + 504, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 504, + 300 + ], + "score": 1.0, + "content": "compressors significantly decreased classification accuracy, which we believe can be explained by", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 433, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 433, + 311 + ], + "score": 1.0, + "content": "the encoders architecture (ResNet18) that we use for consistency (see Appx. 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In", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 338, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 210, + 351 + ], + "score": 1.0, + "content": "contrast, predicting from", + "type": "text" + }, + { + "bbox": [ + 210, + 338, + 219, + 348 + ], + "score": 0.72, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 338, + 358, + 351 + ], + "score": 1.0, + "content": "for VC decreases performance by", + "type": "text" + }, + { + "bbox": [ + 359, + 338, + 378, + 349 + ], + "score": 0.88, + "content": "1 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 338, + 505, + 351 + ], + "score": 1.0, + "content": "(see Appx. F.3). This suggests", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 499, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 224, + 363 + ], + "score": 1.0, + "content": "that invariant reconstructions", + "type": "text" + }, + { + "bbox": [ + 225, + 348, + 235, + 360 + ], + "score": 0.85, + "content": "\\tilde { X }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 350, + 499, + 363 + ], + "score": 1.0, + "content": "might not be easy to predict from with standard image predictors.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 315, + 505, + 363 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 366, + 505, + 411 + ], + "lines": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 505, + 379 + ], + "score": 1.0, + "content": "Are we learning invariant compressors? Invariant compressors should provide RD curves that are", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 376, + 505, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 505, + 390 + ], + "score": 1.0, + "content": "robust to test distribution shift in the desired augmentations. We thus trained our VIC by applying the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 388, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 166, + 401 + ], + "score": 1.0, + "content": "augmentations", + "type": "text" + }, + { + "bbox": [ + 166, + 388, + 186, + 399 + ], + "score": 0.88, + "content": "5 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 388, + 342, + 401 + ], + "score": 1.0, + "content": "of the time but varying that probability", + "type": "text" + }, + { + "bbox": [ + 342, + 390, + 349, + 400 + ], + "score": 0.78, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 388, + 506, + 401 + ], + "score": 1.0, + "content": "at test time. In Appx. F.3 we show that", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 398, + 354, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 354, + 412 + ], + "score": 1.0, + "content": "this distribution shift have negligible influence on RD curves.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 367, + 506, + 412 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 420, + 405, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 419, + 406, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 406, + 434 + ], + "score": 1.0, + "content": "5.3 A zero-shot compressor using pre-trained self-supervised models", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 436, + 505, + 548 + ], + "lines": [ + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 106, + 436, + 505, + 448 + ], + "score": 1.0, + "content": "BINCE includes a standard contrastive SSL loss. So, we investigated whether existing pre-trained", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 447, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 506, + 460 + ], + "score": 1.0, + "content": "SSL models [32, 41] can be used to build generic compressors. In particular, we investigated whether", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "CLIP [41] could be quickly turned into a powerful task-centric compressor for computer vision. In the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "introduction, we motivated large compression gains by noting that typical image classification tasks", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 480, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 365, + 492 + ], + "score": 1.0, + "content": "can be predicted from detailed captions instead of images (around", + "type": "text" + }, + { + "bbox": [ + 365, + 480, + 393, + 490 + ], + "score": 0.87, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 480, + 506, + 492 + ], + "score": 1.0, + "content": "more bits). 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This", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 528 + ], + "score": 1.0, + "content": "will partition the images and texts into sets, each of which are associated directly or by transitivity", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "in CLIP’s dataset. This suggests that CLIP is retaining the image information that corresponds to a", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 536, + 454, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 454, + 549 + ], + "score": 1.0, + "content": "detailed caption, and may be turned into a generic compressor for image classification.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 31.5, + "bbox_fs": [ + 103, + 436, + 508, + 549 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 552, + 505, + 662 + ], + "lines": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 506, + 565 + ], + "score": 1.0, + "content": "CLIP can essentially be seen as a BINCE model with an image-to-text augmentation, but without an", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 564, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 576 + ], + "score": 1.0, + "content": "entropy bottleneck. (For details about the CLIP-BINCE relation see Appx. C.5.) We thus constructed", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "score": 1.0, + "content": "an approximation of our desired image-to-text BINCE compressor by two simple steps. First, we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 583, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 598 + ], + "score": 1.0, + "content": "downloaded and froze CLIP’s parameters. Second, we trained, on the small MSCOCO dataset [43],", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 595, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 506, + 610 + ], + "score": 1.0, + "content": "an entropy bottleneck to compress CLIP’s representation. The latter step can be done by training any", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 605, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 621 + ], + "score": 1.0, + "content": "lossy compressor on CLIP’s representations, we did so using Ballé et al.’s [28] hyperprior entropy", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 631 + ], + "score": 1.0, + "content": "model with a learned rounded precision. We then evaluated our resulting compressor on 8 datasets", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 630, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 630, + 505, + 642 + ], + "score": 1.0, + "content": "(various classification tasks and image shapes) that were never seen during training (zero-shot), by", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 104, + 639, + 505, + 654 + ], + "spans": [ + { + "bbox": [ + 104, + 639, + 505, + 654 + ], + "score": 1.0, + "content": "training an MLP for downstream predictions on each dataset. One can see this as a multi-task setting", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 651, + 501, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 501, + 663 + ], + "score": 1.0, + "content": "(each dataset is a distinct task). We investigate the case of multiple labels per images in Appx. F.5.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 41.5, + "bbox_fs": [ + 104, + 552, + 506, + 663 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "Can we use pretrained SSL to obtain a generic compressor? Table 2 shows that we can exploit", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 676, + 506, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 692 + ], + "score": 1.0, + "content": "existing state-of-the-art (SOTA) SSL models to get a powerful image compressor, which achieves", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 135, + 699 + ], + "score": 0.88, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "bit-rate gains on ImageNet compared to JPEG (at the quality level used for storing ImageNet).", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 184, + 713 + ], + "score": 1.0, + "content": "The bit-rate gains (", + "type": "text" + }, + { + "bbox": [ + 184, + 700, + 196, + 711 + ], + "score": 0.6, + "content": "1 ^ { \\mathrm { s t } }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "row) are significant across all zero-shot datasets, even for biological tissues", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "(PCam; [44]). Importantly, these gains come at little cost in test performance. Indeed, the test", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 294, + 183 + ], + "score": 1.0, + "content": "accuracies of MLPs from our representations (", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 294, + 170, + 308, + 181 + ], + "score": 0.77, + "content": "2 ^ { \\mathrm { n d } }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 308, + 170, + 505, + 183 + ], + "score": 1.0, + "content": "row) is similar to a near SOTA model trained on", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 181, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 216, + 194 + ], + "score": 1.0, + "content": "the uncompressed images", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 217, + 181, + 230, + 192 + ], + "score": 0.84, + "content": "3 ^ { \\mathrm { r d } }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 230, + 181, + 506, + 194 + ], + "score": 1.0, + "content": "row is from Radford et al. [41]). These results are not surprising as", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 192, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 505, + 206 + ], + "score": 1.0, + "content": "JPEG is optimized to retain perceptual rather than classification information. Note that the large", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 203, + 466, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 203, + 466, + 216 + ], + "score": 1.0, + "content": "variance in rate gains come from JPEG rates due to different images shapes (see Table 3).", + "type": "text", + "cross_page": true + } + ], + "index": 8 + } + ], + "index": 49, + "bbox_fs": [ + 105, + 667, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 112, + 93, + 497, + 152 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 66, + 503, + 89 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 65, + 505, + 79 + ], + "spans": [ + { + "bbox": [ + 105, + 65, + 505, + 79 + ], + "score": 1.0, + "content": "Table 2: Converting a pretrained SSL model into a zero-shot compressor achieves substantial bit-rate", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 77, + 484, + 91 + ], + "spans": [ + { + "bbox": [ + 105, + 77, + 484, + 91 + ], + "score": 1.0, + "content": "gains while allowing test accuracies similar to supervised models predicting from raw images.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 112, + 93, + 497, + 152 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 112, + 93, + 497, + 152 + ], + "spans": [ + { + "bbox": [ + 112, + 93, + 497, + 152 + ], + "score": 0.979, + "html": "
ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
Rate gains vs JPEG1104×35×64×131×7×109×150×126×
Our Acc. [%]76.398.780.979.695.288.389.593.4
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Rate gains vs JPEG1104×35×64×131×7×109×150×126×
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In Table 3 we compare the pretrained CLIP, to our", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 435, + 460 + ], + "score": 1.0, + "content": "CLIP compressor with an entropy bottleneck (EB) trained at different values for", + "type": "text" + }, + { + "bbox": [ + 435, + 447, + 443, + 459 + ], + "score": 0.81, + "content": "\\beta", + "type": "inline_equation" + }, + { + "bbox": [ + 443, + 447, + 505, + 460 + ], + "score": 1.0, + "content": ". When trained", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 459, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 154, + 470 + ], + "score": 1.0, + "content": "with a high", + "type": "text" + }, + { + "bbox": [ + 155, + 459, + 162, + 469 + ], + "score": 0.79, + "content": "\\beta", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 459, + 344, + 470 + ], + "score": 1.0, + "content": ", our EB improves bit-rates by an average of", + "type": "text" + }, + { + "bbox": [ + 345, + 459, + 359, + 469 + ], + "score": 0.87, + "content": "6 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 459, + 505, + 470 + ], + "score": 1.0, + "content": "without impacting predictions. For", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 469, + 506, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 228, + 481 + ], + "score": 1.0, + "content": "our compressor from Table 2", + "type": "text" + }, + { + "bbox": [ + 228, + 469, + 279, + 480 + ], + "score": 0.54, + "content": "\\mathbf { ( C L I P + E B \\ } \\beta \\mathbf { \\Lambda }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 469, + 370, + 481 + ], + "score": 1.0, + "content": ") the gains increase to", + "type": "text" + }, + { + "bbox": [ + 370, + 469, + 389, + 479 + ], + "score": 0.88, + "content": "1 1 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 469, + 506, + 481 + ], + "score": 1.0, + "content": "with little predictive impact.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 479, + 506, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 284, + 492 + ], + "score": 1.0, + "content": "The sacrifice in predictions is more clear for", + "type": "text" + }, + { + "bbox": [ + 284, + 480, + 303, + 490 + ], + "score": 0.88, + "content": "1 6 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 479, + 378, + 492 + ], + "score": 1.0, + "content": "bit-rate gains (low", + "type": "text" + }, + { + "bbox": [ + 378, + 480, + 386, + 491 + ], + "score": 0.77, + "content": "\\beta", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 479, + 506, + 492 + ], + "score": 1.0, + "content": "). This shows that CLIP’s raw", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 491, + 493, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 493, + 503 + ], + "score": 1.0, + "content": "representations retain unnecessary information as it not explicitly trained to discard information.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 435, + 506, + 503 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 507, + 505, + 551 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 520 + ], + "score": 1.0, + "content": "How would end-to-end BINCE compare to staggered training? Compression gains can likely be", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 518, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 506, + 530 + ], + "score": 1.0, + "content": "larger by end-to-end training of BINCE, which would require access to CLIP’s original dataset.7 To", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 529, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 506, + 541 + ], + "score": 1.0, + "content": "get an idea of potential gains we compared end-to-end and staggered BINCE on augmented MNIST", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 539, + 492, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 492, + 553 + ], + "score": 1.0, + "content": "in Appx. F.2. We found significant rate improvements (358 to 131 bits) for similar test accuracy.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 506, + 506, + 553 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 556, + 505, + 633 + ], + "lines": [ + { + "bbox": [ + 106, + 556, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 506, + 570 + ], + "score": 1.0, + "content": "Our CLIP compressor is simple to use. In Appx. E.7, we provide a minimal script (150 lines) to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 567, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 506, + 579 + ], + "score": 1.0, + "content": "train a generic compressor in less than five minutes on a single GPU. The script contains an efficient", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 578, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 506, + 591 + ], + "score": 1.0, + "content": "entropy coder for our model (200 images/second), which shows its practicality. As usual in SSL,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 589, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 506, + 601 + ], + "score": 1.0, + "content": "the compressed representations are also more computationally efficient to work with than standard", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 599, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 104, + 599, + 406, + 613 + ], + "score": 1.0, + "content": "compressors. 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This", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 621, + 484, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 484, + 635 + ], + "score": 1.0, + "content": "shows that our pipeline can improve computational efficiency in addition to storage efficiency.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32, + "bbox_fs": [ + 104, + 556, + 506, + 635 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 637, + 504, + 704 + ], + "lines": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "What augmentations to use for SSL compression? Table 4 compares two ResNet50 pretrained with", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 649, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 661 + ], + "score": 1.0, + "content": "contrastive learning using invariance to text-image (CLIP) or standard image augmentations (SimCLR", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 660, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 506, + 673 + ], + "score": 1.0, + "content": "[32]) such as cropping or flipping. We see that CLIP’s augmentation usually give better compression", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 671, + 506, + 683 + ], + "spans": [ + { + "bbox": [ + 105, + 671, + 506, + 683 + ], + "score": 1.0, + "content": "and downstream performance, which shows the importance of the choice of augmentations. This also", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 681, + 506, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 506, + 694 + ], + "score": 1.0, + "content": "supports our motivation of using text-image augmentations, which are likely label-preserving for a", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 694, + 408, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 694, + 408, + 705 + ], + "score": 1.0, + "content": "vast amount of tasks but discard large amounts of unnecessary information.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 638, + 506, + 705 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 119, + 93, + 489, + 162 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 66, + 504, + 89 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 66, + 506, + 79 + ], + "spans": [ + { + "bbox": [ + 105, + 66, + 506, + 79 + ], + "score": 1.0, + "content": "Table 4: Text-image invariance is better than invariance to standard augmentations for image classifi-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 77, + 505, + 90 + ], + "spans": [ + { + "bbox": [ + 105, + 77, + 505, + 90 + ], + "score": 1.0, + "content": "cation. 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D we discuss more related work, including invariances in compression and the link to SSL.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 220, + 505, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "score": 1.0, + "content": "Task-centric compression. To our knowledge, our paper is the first to formalize compression", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 232, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 505, + 243 + ], + "score": 1.0, + "content": "only for predictions. IB [11] uses a task-centric distortion, but is not used for compression as it", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "score": 1.0, + "content": "requires supervised training, so there are no advantages compared to compressing predicted labels.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 252, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 506, + 267 + ], + "score": 1.0, + "content": "Some authors used heuristics to bypass the supervised issue, e.g., focusing on low frequencies", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "for classification [45] or high frequencies for segmentation [46]. Other authors have incorporated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 275, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 275, + 506, + 288 + ], + "score": 1.0, + "content": "predictive errors to perceptual distortions [47, 48], but cannot compress without the perceptual", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 106, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "distortion for the same reason as IB. One exception is Weber et al.’s [49] compressor, which (when", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 297, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 297, + 506, + 309 + ], + "score": 1.0, + "content": "removing their perceptual distortion) minimizes MSE in the hidden layers of a pretrained classifier.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 306, + 507, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 507, + 321 + ], + "score": 1.0, + "content": "Even more related is Singh et al.’s [50] work on compressing pretrained features for transfer learning,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "score": 1.0, + "content": "which is practice is similar to our compression of SSL features. Their work do not provide theoretical", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 328, + 454, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 454, + 343 + ], + "score": 1.0, + "content": "justifications, and are constrained to tasks that are similar to those used for pretraining.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 108, + 356, + 246, + 370 + ], + "lines": [ + { + "bbox": [ + 104, + 354, + 248, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 354, + 248, + 371 + ], + "score": 1.0, + "content": "7 Discussion and Outlook", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 379, + 505, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 393 + ], + "score": 1.0, + "content": "Given the ever increasing amount of data that is processed by task-specific algorithms, it is necessary", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 391, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 505, + 403 + ], + "score": 1.0, + "content": "to rethink the current task-agnostic compression paradigm. We formalized the first compression", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 399, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 506, + 415 + ], + "score": 1.0, + "content": "framework for retaining only the information necessary for high performance on desired tasks. Using", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 411, + 506, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 426 + ], + "score": 1.0, + "content": "our theory, we provide two unsupervised objectives for training neural compressors. Experimentally,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 460, + 436 + ], + "score": 1.0, + "content": "we show that these compressors can achieve bit-rates that are orders of magnitude", + "type": "text" + }, + { + "bbox": [ + 461, + 424, + 490, + 434 + ], + "score": 0.85, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 491, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "on", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 434, + 475, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 475, + 448 + ], + "score": 1.0, + "content": "ImageNet) smaller than standard image compressors without losing predictive performance.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5 + }, + { + "type": "text", + "bbox": [ + 107, + 450, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 105, + 448, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 506, + 464 + ], + "score": 1.0, + "content": "There are a number of caveats that should be addressed. First, to achieve better rates, our theory", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 462, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 506, + 474 + ], + "score": 1.0, + "content": "requires an irrecoverable loss of information. This can be an issue if the set of desired tasks", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "changes. For example, if one uses text-image invariances then it may be impossible to perform image", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "segmentation from the compressed representations. One solution would be to keep an original copy", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "and use invariant compression for duplicated data, e.g., for the thousands copies of ImageNet. A", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "score": 1.0, + "content": "second issue is the interpretability of the compressed representations. This can be partially addressed", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 516, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 506, + 529 + ], + "score": 1.0, + "content": "by reconstructing prototypical data as in Fig. 1 (post-hoc decoders could be trained for BINCE).", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "score": 1.0, + "content": "A third caveat is that the compressed representations may be harder to learn from, e.g., neural", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "networks may struggle to predict from representations even if the information is retained. Although", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 548, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 506, + 563 + ], + "score": 1.0, + "content": "our experiments actually showed the opposite, this should be addressed theoretically, e.g., using", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "decodable information [51, 52]. 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Finding such an", + "type": "text" + }, + { + "bbox": [ + 475, + 571, + 484, + 581 + ], + "score": 0.65, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 569, + 506, + 585 + ], + "score": 1.0, + "content": "may", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 581, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 595 + ], + "score": 1.0, + "content": "be challenging for some tasks. 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CLIP and SimCLR are both ResNet50 pretrained with InfoNCE but different augmentations.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 119, + 93, + 489, + 162 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 119, + 93, + 489, + 162 + ], + "spans": [ + { + "bbox": [ + 119, + 93, + 489, + 162 + ], + "score": 0.98, + "html": "
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D we discuss more related work, including invariances in compression and the link to SSL.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 203, + 505, + 216 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 220, + 505, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 505, + 233 + ], + "score": 1.0, + "content": "Task-centric compression. To our knowledge, our paper is the first to formalize compression", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 232, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 505, + 243 + ], + "score": 1.0, + "content": "only for predictions. IB [11] uses a task-centric distortion, but is not used for compression as it", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "score": 1.0, + "content": "requires supervised training, so there are no advantages compared to compressing predicted labels.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 252, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 506, + 267 + ], + "score": 1.0, + "content": "Some authors used heuristics to bypass the supervised issue, e.g., focusing on low frequencies", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "for classification [45] or high frequencies for segmentation [46]. Other authors have incorporated", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 275, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 275, + 506, + 288 + ], + "score": 1.0, + "content": "predictive errors to perceptual distortions [47, 48], but cannot compress without the perceptual", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 106, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "distortion for the same reason as IB. One exception is Weber et al.’s [49] compressor, which (when", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 297, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 297, + 506, + 309 + ], + "score": 1.0, + "content": "removing their perceptual distortion) minimizes MSE in the hidden layers of a pretrained classifier.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 306, + 507, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 507, + 321 + ], + "score": 1.0, + "content": "Even more related is Singh et al.’s [50] work on compressing pretrained features for transfer learning,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "score": 1.0, + "content": "which is practice is similar to our compression of SSL features. Their work do not provide theoretical", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 328, + 454, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 328, + 454, + 343 + ], + "score": 1.0, + "content": "justifications, and are constrained to tasks that are similar to those used for pretraining.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 219, + 507, + 343 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 356, + 246, + 370 + ], + "lines": [ + { + "bbox": [ + 104, + 354, + 248, + 371 + ], + "spans": [ + { + "bbox": [ + 104, + 354, + 248, + 371 + ], + "score": 1.0, + "content": "7 Discussion and Outlook", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 379, + 505, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 378, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 505, + 393 + ], + "score": 1.0, + "content": "Given the ever increasing amount of data that is processed by task-specific algorithms, it is necessary", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 391, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 391, + 505, + 403 + ], + "score": 1.0, + "content": "to rethink the current task-agnostic compression paradigm. We formalized the first compression", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 399, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 506, + 415 + ], + "score": 1.0, + "content": "framework for retaining only the information necessary for high performance on desired tasks. Using", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 411, + 506, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 426 + ], + "score": 1.0, + "content": "our theory, we provide two unsupervised objectives for training neural compressors. Experimentally,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 460, + 436 + ], + "score": 1.0, + "content": "we show that these compressors can achieve bit-rates that are orders of magnitude", + "type": "text" + }, + { + "bbox": [ + 461, + 424, + 490, + 434 + ], + "score": 0.85, + "content": "1 0 0 0 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 491, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "on", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 434, + 475, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 475, + 448 + ], + "score": 1.0, + "content": "ImageNet) smaller than standard image compressors without losing predictive performance.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 378, + 506, + 448 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 450, + 505, + 603 + ], + "lines": [ + { + "bbox": [ + 105, + 448, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 506, + 464 + ], + "score": 1.0, + "content": "There are a number of caveats that should be addressed. First, to achieve better rates, our theory", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 462, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 506, + 474 + ], + "score": 1.0, + "content": "requires an irrecoverable loss of information. This can be an issue if the set of desired tasks", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "changes. For example, if one uses text-image invariances then it may be impossible to perform image", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "segmentation from the compressed representations. One solution would be to keep an original copy", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "and use invariant compression for duplicated data, e.g., for the thousands copies of ImageNet. A", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "score": 1.0, + "content": "second issue is the interpretability of the compressed representations. This can be partially addressed", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 516, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 506, + 529 + ], + "score": 1.0, + "content": "by reconstructing prototypical data as in Fig. 1 (post-hoc decoders could be trained for BINCE).", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 541 + ], + "score": 1.0, + "content": "A third caveat is that the compressed representations may be harder to learn from, e.g., neural", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "networks may struggle to predict from representations even if the information is retained. Although", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 548, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 506, + 563 + ], + "score": 1.0, + "content": "our experiments actually showed the opposite, this should be addressed theoretically, e.g., using", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "decodable information [51, 52]. 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Finding such an", + "type": "text" + }, + { + "bbox": [ + 475, + 571, + 484, + 581 + ], + "score": 0.65, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 485, + 569, + 506, + 585 + ], + "score": 1.0, + "content": "may", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 581, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 595 + ], + "score": 1.0, + "content": "be challenging for some tasks. 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If you ran experiments...", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12, + "bbox_fs": [ + 108, + 222, + 222, + 237 + ] + }, + { + "type": "list", + "bbox": [ + 120, + 239, + 506, + 369 + ], + "lines": [ + { + "bbox": [ + 118, + 238, + 506, + 252 + ], + "spans": [ + { + "bbox": [ + 118, + 238, + 506, + 252 + ], + "score": 1.0, + "content": "(a) Did you include the code, data, and instructions needed to reproduce the main experimental", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true + }, + { + "bbox": [ + 136, + 250, + 505, + 262 + ], + "spans": [ + { + "bbox": [ + 136, + 250, + 505, + 262 + ], + "score": 1.0, + "content": "results (either in the supplemental material or as a URL)? [Yes] The code to train our main", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 136, + 261, + 460, + 273 + ], + "spans": [ + { + "bbox": [ + 136, + 261, + 460, + 273 + ], + "score": 1.0, + "content": "compressor is in Appx. E.7, the code to replicate all our results is at anonymous.", + "type": "text" + } + ], + "index": 15, + "is_list_end_line": true + }, + { + "bbox": [ + 120, + 272, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 120, + 272, + 505, + 284 + ], + "score": 1.0, + "content": "(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true + }, + { + "bbox": [ + 135, + 281, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 135, + 281, + 506, + 296 + ], + "score": 1.0, + "content": "chosen)? [Yes] The most important training details can be found at Appx. E. Minor hyperpa-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 135, + 293, + 337, + 306 + ], + "spans": [ + { + "bbox": [ + 135, + 293, + 337, + 306 + ], + "score": 1.0, + "content": "rameters can be found in our code at anonymous.", + "type": "text" + } + ], + "index": 18, + "is_list_end_line": true + }, + { + "bbox": [ + 120, + 304, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 120, + 305, + 134, + 317 + ], + "score": 1.0, + "content": "(c)", + "type": "text" + }, + { + "bbox": [ + 135, + 304, + 506, + 317 + ], + "score": 1.0, + "content": "Did you report error bars (e.g., with respect to the random seed after running experiments", + "type": "text" + } + ], + "index": 19, + "is_list_start_line": true + }, + { + "bbox": [ + 135, + 315, + 506, + 328 + ], + "spans": [ + { + "bbox": [ + 135, + 315, + 506, + 328 + ], + "score": 1.0, + "content": "multiple times)? [Yes] We report error bars for MNIST (Appx. F.2) and Banana (Appx. F.1).", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 135, + 325, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 135, + 325, + 506, + 339 + ], + "score": 1.0, + "content": "For larger experiments we sampled a fixed number of hyperparameters for each model and", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 135, + 336, + 335, + 350 + ], + "spans": [ + { + "bbox": [ + 135, + 336, + 335, + 350 + ], + "score": 1.0, + "content": "baseline (see Appx. E), and report the best result.", + "type": "text" + } + ], + "index": 22, + "is_list_end_line": true + }, + { + "bbox": [ + 119, + 348, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 119, + 348, + 506, + 361 + ], + "score": 1.0, + "content": "(d) Did you include the total amount of compute and the type of resources used (e.g., type of", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true + }, + { + "bbox": [ + 135, + 358, + 330, + 371 + ], + "spans": [ + { + "bbox": [ + 135, + 358, + 330, + 371 + ], + "score": 1.0, + "content": "GPUs, internal cluster, or cloud provider)? [No]", + "type": "text" + } + ], + "index": 24, + "is_list_end_line": true + } + ], + "index": 18.5, + "bbox_fs": [ + 118, + 238, + 506, + 371 + ] + }, + { + "type": "text", + "bbox": [ + 111, + 371, + 483, + 381 + ], + "lines": [ + { + "bbox": [ + 109, + 368, + 485, + 383 + ], + "spans": [ + { + "bbox": [ + 109, + 368, + 485, + 383 + ], + "score": 1.0, + "content": "4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets...", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25, + "bbox_fs": [ + 109, + 368, + 485, + 383 + ] + }, + { + "type": "list", + "bbox": [ + 120, + 385, + 506, + 517 + ], + "lines": [ + { + "bbox": [ + 119, + 384, + 447, + 398 + ], + "spans": [ + { + "bbox": [ + 119, + 384, + 447, + 398 + ], + "score": 1.0, + "content": "(a) If your work uses existing assets, did you cite the creators? [Yes] In Appx. E.", + "type": "text" + } + ], + "index": 26, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 120, + 396, + 329, + 408 + ], + "spans": [ + { + "bbox": [ + 120, + 396, + 329, + 408 + ], + "score": 1.0, + "content": "(b) Did you mention the license of the assets? [No]", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 120, + 406, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 120, + 406, + 506, + 420 + ], + "score": 1.0, + "content": "(c) Did you include any new assets either in the supplemental material or as a URL? [Yes] Our", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 136, + 418, + 372, + 430 + ], + "spans": [ + { + "bbox": [ + 136, + 418, + 372, + 430 + ], + "score": 1.0, + "content": "clip compressor in Appx. E.7 and our code at anonymous.", + "type": "text" + } + ], + "index": 29, + "is_list_end_line": true + }, + { + "bbox": [ + 120, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 120, + 429, + 134, + 441 + ], + "score": 1.0, + "content": "(d)", + "type": "text" + }, + { + "bbox": [ + 136, + 429, + 505, + 441 + ], + "score": 1.0, + "content": "Did you discuss whether and how consent was obtained from people whose data you’re", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 136, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 136, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "using/curating? [No] We do not propose any new dataset. The main possible issues come", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 135, + 450, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 135, + 450, + 505, + 463 + ], + "score": 1.0, + "content": "from the CLIP dataset [41], for which the data collection procedure is discussed in details in", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 136, + 461, + 184, + 475 + ], + "spans": [ + { + "bbox": [ + 136, + 461, + 184, + 475 + ], + "score": 1.0, + "content": "their paper.", + "type": "text" + } + ], + "index": 33, + "is_list_end_line": true + }, + { + "bbox": [ + 120, + 473, + 505, + 485 + ], + "spans": [ + { + "bbox": [ + 120, + 473, + 505, + 485 + ], + "score": 1.0, + "content": "(e) Did you discuss whether the data you are using/curating contains personally identifiable", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true + }, + { + "bbox": [ + 136, + 483, + 506, + 496 + ], + "spans": [ + { + "bbox": [ + 136, + 483, + 506, + 496 + ], + "score": 1.0, + "content": "information or offensive content? [No] We do not propose any new dataset. The main possible", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 135, + 494, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 135, + 494, + 505, + 506 + ], + "score": 1.0, + "content": "issues come from the CLIP dataset [41], for which the data collection procedure is discussed", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 135, + 504, + 232, + 518 + ], + "spans": [ + { + "bbox": [ + 135, + 504, + 232, + 518 + ], + "score": 1.0, + "content": "in details in their paper.", + "type": "text" + } + ], + "index": 37, + "is_list_end_line": true + } + ], + "index": 31.5, + "bbox_fs": [ + 119, + 384, + 506, + 518 + ] + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/train/wZrOOO9XBn/wZrOOO9XBn_model.json b/parse/train/wZrOOO9XBn/wZrOOO9XBn_model.json new file mode 100644 index 0000000000000000000000000000000000000000..023c8abd9f84bc3512c8ec391f408c077900437d --- /dev/null +++ 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PNG [38]JPEG [39]WebP [40]vcxVIC XVIC ZBINCE
Decrease in test acc.00.71.121.025.116.10.0
Compression gains1×3×13×63×269×175×121×
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ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
JPEG1.49e64.71e49.60e41.92e51.05e41.54e51.81e51.69e5
CLIP1.52e41.52e41.52e41.52e41.52e41.52e41.52e41.52e4
Brr+EB high β2.47e32.46e32.61e32.59e32.53e32.39e32.33e32.46e3
+EB β1.35e31.34e31.49e31.47e31.41e31.27e31.21e31.34e3
+EB low β9.63e29.52e21.09e31.07e31.02e38.89e28.35e29.53e2
CLIP76.598.684.580.895.388.589.793.2
+EB high β76.698.782.780.495.388.589.693.5
Trrs sss+EB β76.398.780.979.695.288.389.593.4
+EB low β76.098.780.178.994.887.688.692.9
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ImageNetSTLPCamCarsCIFAR10FoodPetsCaltech
Rate gains vs JPEG1104×35×64×131×7×109×150×126×
Our Acc. [%]76.398.780.979.695.288.389.593.4
Supervised Acc. [%]76.199.082.649.196.781.890.494.5
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