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+# UNSUPERVISED PRETRAINING FOR SEQUENCE TO SEQUENCE LEARNING
+
+Prajit Ramachandran∗ University of Illinois at Urbana-Champaign prajitram@gmail.com
+
+Peter J. Liu, Quoc V. Le Google Brain {peterjliu,qvl}@google.com
+
+# ABSTRACT
+
+This work presents a general unsupervised learning method to improve the accuracy of sequence to sequence (seq2seq) models. In our method, the weights of the encoder and decoder of a seq2seq model are initialized with the pretrained weights of two language models and then fine-tuned with labeled data. We apply this method to challenging benchmarks in machine translation and abstractive summarization and find that it significantly improves the subsequent supervised models. Our main result is that the pretraining accelerates training and improves generalization of seq2seq models, achieving state-of-the-art results on the WMT English German task, surpassing a range of methods using both phrase-based machine translation and neural machine translation. Our method achieves an improvement of 1.3 BLEU from the previous best models on both WMT’14 and WMT’15 English German. On summarization, our method beats the supervised learning baseline.
+
+# 1 INTRODUCTION
+
+Sequence to sequence (seq2seq) models (Sutskever et al., 2014; Cho et al., 2014; Kalchbrenner & Blunsom, 2013; Allen, 1987; Neco & Forcada, 1997) are extremely effective on a variety of ˜ tasks that require a mapping between a variable-length input sequence to a variable-length output sequence. The main weakness of sequence to sequence models, and deep networks in general, lies in the fact that they can easily overfit when the amount of supervised training data is small.
+
+In this work, we propose a simple and effective technique for using unsupervised pretraining to improve seq2seq models. Our proposal is to initialize both encoder and decoder networks with pretrained weights of two language models. These pretrained weights are then fine-tuned with the labeled corpus.
+
+We benchmark this method on machine translation for English German and abstractive summarization on CNN and Daily Mail articles. Our main result is that a seq2seq model, with pretraining, exceeds the strongest possible baseline in both neural machine translation and phrase-based machine translation. Our model obtains an improvement of 1.3 BLEU from the previous best models on both WMT’14 and WMT’15 English German. On abstractive summarization, our method achieves competitive results to the strongest baselines.
+
+We also perform ablation study to understand the behaviors of the pretraining method. Our study confirms that among many other possible choices of using a language model in seq2seq with attention, the above proposal works best. Our study also shows that, for translation, the main gains come from the improved generalization due to the pretrained features, whereas for summarization the gains come from the improved optimization due to pretraining the encoder which has been unrolled for hundreds of timesteps. On both tasks, our proposed method always improves generalization on the test sets.
+
+# 2 UNSUPERVISED PRETRAINING FOR SEQUENCE TO SEQUENCE LEARNING
+
+In the following section, we will describe our basic unsupervised pretraining procedure for sequence to sequence learning and how to modify sequence to sequence learning to effectively make use of the pretrained weights. We then show several extensions to improve the basic model.
+
+# 2.1 BASIC PROCEDURE
+
+Given an input sequence $x _ { 1 } , x _ { 2 } , . . . , x _ { m }$ and an output sequence $y _ { n } , y _ { n - 1 } , . . . , y _ { 1 }$ , the objective of sequence to sequence learning is to maximize the likelihood $p ( y _ { n } , y _ { n - 1 } , . . . , y _ { 1 } | x _ { 1 } , x _ { 2 } , . . . , x _ { m } )$ . Common sequence to sequence learning methods decompose this objective as $\begin{array} { r } { p ( \boldsymbol { y } _ { n } , \boldsymbol { y } _ { n - 1 } , . . . , \dot { \boldsymbol { y } _ { 1 } } | \boldsymbol { x } _ { 1 } , \boldsymbol { x } _ { 2 } , . . . , \boldsymbol { x } _ { m } ) ^ { \flat } = \prod _ { t = 1 } ^ { n } p ( \boldsymbol { y } _ { t } | \overset { \sim } { \boldsymbol { y } _ { t - 1 } } , . . . , \boldsymbol { y } _ { 1 } ; \boldsymbol { x } _ { 1 } , \boldsymbol { x } _ { 2 } , . . . , \dot { \boldsymbol { x } } _ { m } ) . } \end{array}$ .
+
+In sequence to sequence learning, an RNN encoder is used to represent $x _ { 1 } , . . . , x _ { m }$ as a hidden vector, which is given to an RNN decoder to produce the output sequence. Our method is based on the observation that without the encoder, the decoder essentially acts like a language model on $y$ ’s. Similarly, the encoder with an additional output layer also acts like a language model. Thus it is natural to use trained languages models to initialize the encoder and decoder.
+
+Therefore, the basic procedure of our approach is to pretrain both the seq2seq encoder and decoder networks with language models, which can be trained on large amounts of unlabeled text data. This can be seen in Figure 1, where the parameters in the shaded boxes are pretrained. In the following we will describe the method in detail using machine translation as an example application.
+
+![](images/f0d4d784a5a5539b916e7bd408d746c140a113beb99fda9af36b6f1ca6493a46.jpg)  
+Figure 1: Pretrained sequence to sequence model. The red parameters are the encoder and the blue parameters are the decoder. All parameters in a shaded box are pretrained, either from the source side (light red) or target side (light blue) language model. Otherwise, they are randomly initialized.
+
+First, two monolingual datasets are collected, one for the source side language, and one for the target side language. A language model $( L M )$ is trained on each dataset independently, giving an LM trained on the source side corpus and an LM trained on the target side corpus.
+
+After two language models are trained, a multi-layer seq2seq model $M$ is constructed. The embedding and first LSTM layers of the encoder and decoder are initialized with the pretrained weights. To be even more efficient, the softmax of the decoder is initialized with the softmax of the pretrained target side LM.
+
+# 2.2 IMPROVING THE MODEL
+
+We also employ three additional methods to further improve the model above. The three methods are: a) Monolingual language modeling losses, b) Residual connections and c) Attention over multiple layers (see Figure 2).
+
+Monolingual language modeling losses: After the seq2seq model $M$ is initialized with the two LMs, it is fine-tuned with a labeled dataset. To ensure that the model does not overfit the labeled data, we regularize the parameters that were pretrained by continuing to train with the monolingual language modeling losses. The seq2seq and language modeling losses are weighted equally.
+
+![](images/eb5223724b1e3bd342df03c0ec6e592c7d69698362b72b6f493c4474eba8d1af.jpg)  
+Figure 2: Two improvements to the baseline model: (a) residual connection, and (b) attention over multiple layers.
+
+Residual connections: As described, the input vector to the decoder softmax layer is a random vector because the high level (non-first) layers of the LSTM are randomly initialized. This slows down training and introduces random gradients to the pretrained parameters, reducing the effectiveness of pretraining. To circumvent this issue, we use a residual connection from the output of the first LSTM layer directly to the input of the softmax (see Figure 2-a).
+
+Attention over multiple layers: In all our models, we use an attention mechanism (Bahdanau et al., 2015), where the model attends over both top and first layer (see Figure 2-b). More concretely, given a query vector $q _ { t }$ from the decoder, encoder states from the first layer $h _ { 1 } ^ { 1 } , \ldots , h _ { T } ^ { 1 }$ , and encoder states from the last layer $h _ { 1 } ^ { L } , \ldots , h _ { T } ^ { L }$ , we compute the attention context vector $c _ { t }$ as follows:
+
+$$
+\alpha _ { i } = \frac { \exp ( q _ { t } \cdot h _ { i } ^ { N } ) } { \sum _ { j = 1 } ^ { T } \exp ( q _ { t } \cdot h _ { j } ^ { N } ) } \qquad c _ { t } ^ { 1 } = \sum _ { i = 1 } ^ { T } \alpha _ { i } h _ { i } ^ { 1 } \qquad c _ { t } ^ { N } = \sum _ { i = 1 } ^ { T } \alpha _ { i } h _ { i } ^ { N } \qquad c _ { t } = [ c _ { t } ^ { 1 } ; c _ { t } ^ { N } ]
+$$
+
+Note that attention weights $\alpha _ { i }$ are only computed once using the top level encoder states.
+
+We also experiment with passing the attention vector $c _ { t }$ as input into the next timestep (Luong et al., 2015b). Instead of passing $c$ into the first LSTM layer, we pass it as input to the second LSTM layer by concatenating it with the output of the first LSTM layer.
+
+We use all three improvements in our experiments. However, in general we notice that the benefits of the attention modifications are minor in comparison with the benefits of the additional language modeling objectives and residual connections.
+
+# 3 EXPERIMENTS
+
+In the following section, we apply our approach to two important tasks in seq2seq learning: machine translation and abstractive summarization. On each task, we compare against the previous best systems. We also perform ablation experiments to understand the behavior of each component of our method.
+
+# 3.1 MACHINE TRANSLATION
+
+Dataset and Evaluation: For machine translation, we evaluate our method on the WMT English German task (Bojar et al., 2015). We used the WMT 14 training dataset, which is slightly smaller than the WMT 15 dataset. Because the dataset has some noisy examples, we used a language detection system to filter the training examples. Sentences pairs where either the source was not English or the target was not German were thrown away. This resulted in around 4 million training examples. Following Sennrich et al. (2015b), we use subword units (Sennrich et al., 2015a)
+
+with 89500 merge operations, giving a vocabulary size around 90000. The validation set is the concatenated newstest2012 and newstest2013, and our test sets are newstest2014 and newstest2015. Evaluation on the validation set was with case-sensitive BLEU (Papineni et al., 2002) on tokenized text using multi-bleu.perl. Evaluation on the test sets was with case-sensitive BLEU on detokenized text using mteval-v13a.pl. The monolingual training datasets are the News Crawl English and German corpora, each of which has more than a billion tokens.
+
+Experimental settings: The language models were trained in the same fashion as (Jozefowicz et al., 2016) We used a 1 layer 4096 dimensional LSTM with the hidden state projected down to 1024 units (Sak et al., 2014) and trained for one week on 32 Tesla K40 GPUs. Our seq2seq model was a 3 layer model, where the second and third layers each have 1000 hidden units. The monolingual objectives, residual connection, and the modified attention were all used. We used the Adam optimizer (Kingma & Ba, 2015) and train with asynchronous SGD on 16 GPUs for speed. We used a learning rate of 5e-5 which is multiplied by 0.8 every 50K steps after an initial 400K steps, gradient clipping with norm 5.0 (Pascanu et al., 2013), and dropout of 0.2 on non-recurrent connections (Zaremba et al., 2014). We used early stopping on validation set perplexity. A beam size of 10 was used for decoding. Our ensemble is constructed with the 5 best performing models on the validation set, which are trained with different hyperparameters.
+
+Results: Table 1 shows the results of our method in comparison with other baselines. Our method achieves a new state-of-the-art for single model performance on both newstest2014 and newstest2015, significantly outperforming the competitive semi-supervised backtranslation technique (Sennrich et al., 2015b). Equally impressive is the fact that our best single model outperforms the previous state of the art ensemble of 4 models. Our ensemble of 5 models matches or exceeds the previous best ensemble of 12 models.
+
+Table 1: English German performance on WMT test sets. Our pretrained model outperforms all other models. Note that the model without pretraining uses the LM objective.   
+
+<table><tr><td rowspan="2">System</td><td rowspan="2">ensemble?</td><td colspan="2">BLEU</td></tr><tr><td>newstest2014</td><td>newstest2015</td></tr><tr><td>Phrase Based MT(Williams et al., 2016)</td><td>1</td><td>21.9</td><td>23.7</td></tr><tr><td>Supervised NMT (Jean et al., 2015)</td><td>single</td><td>-</td><td>22.4</td></tr><tr><td>Edit Distance Transducer NMT (Stahlberg et al.,2016)</td><td>single</td><td>21.7</td><td>24.1</td></tr><tr><td>Edit Distance Transducer NMT (Stahlberg et al., 2016)</td><td>ensemble 8</td><td>22.9</td><td>25.7</td></tr><tr><td>Backtranslation (Sennrich et al.,2015b)</td><td>single</td><td>22.7</td><td>25.7</td></tr><tr><td>Backtranslation (Sennrich et al.,2015b)</td><td>ensemble 4</td><td>23.8</td><td>26.5</td></tr><tr><td>Backtranslation (Sennrich et al.,2015b)</td><td>ensemble 12</td><td>24.7</td><td>27.6</td></tr><tr><td>No pretraining</td><td>single</td><td>21.3</td><td>24.3</td></tr><tr><td>Pretrained seq2seq</td><td>single</td><td>24.0</td><td>27.0</td></tr><tr><td>Pretrained seq2seq</td><td>ensemble 5</td><td>24.7</td><td>28.1</td></tr></table>
+
+Ablation study: In order to better understand the effects of pretraining, we conducted an ablation study by modifying the pretraining scheme. Figure 3 shows the drop in validation BLEU of various ablations compared with the full model. The full model uses LMs trained with monolingual data to initialize the encoder and decoder, in addition to the language modeling objective. In the following, we interpret the findings of the study. Note that some findings are specific to the translation task.
+
+Given the results from the ablation study, we can make the following observations:
+
+• Pretraining the decoder is better than pretraining the encoder: Only pretraining the encoder leads to a 1.6 BLEU point drop while only pretraining the decoder leads to a 1.0 BLEU point drop.   
+• Pretrain as much as possible because the benefits compound: given the drops of no pretraining at all $( - 2 . 0 )$ and only pretraining the encoder $( - 1 . 6 )$ , the additive estimate of the drop of only pretraining the decoder side is $- 2 . 0 - ( - 1 . 6 ) = - 0 . 4$ ; however the actual drop is $- 1 . 0$ which is a much larger drop than the additive estimate.   
+Pretraining the softmax is important: Pretraining only the embeddings and first LSTM layer gives a large drop of 1.6 BLEU points.
+
+![](images/57d26fe90190577ff49dfc6d7f18419158811b996b7254dfe25e06731cc60a96.jpg)  
+Figure 3: English German ablation study measuring the difference in validation BLEU between various ablations and the full model. More negative is worse. The full model uses LMs trained with monolingual data to initialize the encoder and decoder, plus the language modeling objective.
+
+• The language modeling objective is a strong regularizer: The drop in BLEU points of pretraining the entire model and not using the LM objective is as bad as using the LM objective without pretraining. Pretraining on a lot of unlabeled data is essential for learning to extract powerful features: If the model is initialized with LMs that are pretrained on the source part and target part of the parallel corpus, the drop in performance is as large as not pretraining at all. However, performance remains strong when pretrained on the large, non-news Wikipedia corpus.
+
+To understand the contributions of unsupervised pretraining vs. supervised training, we track the performance of pretraining as a function of dataset size. For this, we trained a a model with and without pretraining on random subsets of the English German corpus. Both models use the additional LM objective. The results are summarized in Figure 4. When a $100 \%$ of the labeled data is used, the gap between the pretrained and no pretrain model is 2.0 BLEU points. However, that gap grows when less data is available. When trained on $20 \%$ of the labeled data, the gap becomes 3.8 BLEU points. This demonstrates that the pretrained models degrade less as the labeled dataset becomes smaller.
+
+![](images/fd6efc51ca31158846d3581314b1dd9275c6f461e264a8857db584f1e5681534.jpg)  
+Figure 4: Validation performance of pretraining vs. no pretraining when trained on a subset of the entire labeled dataset for English German translation.
+
+# 3.2 ABSTRACTIVE SUMMARIZATION
+
+Dataset and Evaluation: For a low-resource abstractive summarization task, we use the CNN/Daily Mail corpus from (Hermann et al., 2015). Following Nallapati et al. (2016), we modify the data collection scripts to restore the bullet point summaries. The task is to predict the bullet point summaries from a news article. The dataset has fewer than 300K document-summary pairs. To compare against Nallapati et al. (2016), we used the anonymized corpus. However, for our ablation study, we used the non-anonymized corpus.1 We evaluate our system using full length ROUGE (Lin, 2004). For the anonymized corpus in particular, we considered each highlight as a separate sentence following Nallapati et al. (2016). In this setting, we used the English Gigaword corpus (Napoles et al., 2012) as our larger, unlabeled “monolingual” corpus, although all data used in this task is in English.
+
+Experimental settings: We use subword units (Sennrich et al., 2015a) with 31500 merges, resulting in a vocabulary size of about 32000. We use up to the first 600 tokens of the document and predict the entire summary. Only one language model is trained and it is used to initialize both the encoder and decoder, since the source and target languages are the same. However, the encoder and decoder are not tied. The LM is a one-layer LSTM of size 1024 trained in a similar fashion to Jozefowicz et al. (2016). For the seq2seq model, we use the same settings as the machine translation experiments. The only differences are that we use a 2 layer model with the second layer having 1024 hidden units, and that the learning rate is multiplied by 0.8 every 30K steps after an initial 100K steps.
+
+Results: Table 2 summarizes our results on the anonymized version of the corpus. Our pretrained model is only able to match the previous baseline seq2seq of Nallapati et al. (2016). However, our model is a unidirectional LSTM while they use a bidirectional LSTM. They also use a longer context of 800 tokens, whereas we used a context of 600 tokens due to GPU memory issues. Furthermore, they use pretrained word2vec (Mikolov et al., 2013) vectors to initialize their word embeddings. As we show in our ablation study, just pretraining the embeddings itself gives a large improvement.
+
+Table 2: Results on the anonymized CNN/Daily Mail dataset.   
+
+<table><tr><td rowspan=1 colspan=1>System</td><td rowspan=1 colspan=1>ROUGE-1</td><td rowspan=1 colspan=1>ROUGE-2</td><td rowspan=1 colspan=1>ROUGE-L</td></tr><tr><td rowspan=1 colspan=1>Seq2seq + pretrained embeddings (Nallapati et al., 2016)+ temporal attention (Nallapati et al., 2016)</td><td rowspan=1 colspan=1>32.4935.46</td><td rowspan=1 colspan=1>11.8413.30</td><td rowspan=1 colspan=1>29.4732.65</td></tr><tr><td rowspan=1 colspan=1>Pretrained seq2seq</td><td rowspan=1 colspan=1>32.56</td><td rowspan=1 colspan=1>11.89</td><td rowspan=1 colspan=1>29.44</td></tr></table>
+
+Ablation study: We performed an ablation study similar to the one performed on the machine translation model. The results are reported in Figure 5. Here we report the drops on ROUGE-1, ROUGE-2, and ROUGE-L on the non-anonymized validation set.
+
+Given the results from our ablation study, we can make the following observations:
+
+• Pretraining improves optimization: in contrast with the machine translation model, it is more beneficial to only pretrain the encoder than only the decoder of the summarization model. One interpretation is that pretraining enables the gradient to flow much further back in time than randomly initialized weights. This may also explain why pretraining on the parallel corpus is no worse than pretraining on a larger monolingual corpus. • The language modeling objective is a strong regularizer: A model without the LM objective has a significant drop in ROUGE scores.
+
+Human evaluation: As ROUGE may not be able to capture the quality of summarization, we also performed a small qualitative study to understand the human impression of the summaries produced by different models. We took 200 random documents and compared the performance of a pretrained and non-pretrained system. The document, gold summary, and the two system outputs were presented to a human evaluator who was asked to rate each system output on a scale of 1-5 with 5 being the best score. The system outputs were presented in random order and the evaluator did not know the identity of either output. The evaluator noted if there were repetitive phrases or sentences in either system outputs. Unwanted repetition was also noticed by Nallapati et al. (2016).
+
+![](images/d3b179c66bdf6148ce917c9236d5050079cc7cbcf410d123ed214d8a5af4d647.jpg)  
+Figure 5: Summarization ablation study measuring the difference in validation ROUGE between various ablations and the full model. More negative is worse. The full model uses LMs trained with unlabeled data to initialize the encoder and decoder, plus the language modeling objective.
+
+Table 3 and 4 show the results of the study. In both cases, the pretrained system outperforms the system without pretraining in a statistically significant manner. The better optimization enabled by pretraining improves the generated summaries and decreases unwanted repetition in the output.
+
+$$
+\frac { N P > P ~ \mid ~ N P = P ~ \mid ~ N P < P } { 2 9 } 
+$$
+
+Table 3: The count of how often the no pretrain system $( N P )$ achieves a higher, equal, and lower score than the pretrained system $( P )$ in the side-by-side study where the human evaluator gave each system a score from 1-5. The sign statistical test gives a $\mathsf { p }$ -value of $< 0 . 0 0 0 1$ for rejecting the null hypothesis that there is no difference in the score obtained by either system.
+
+<table><tr><td colspan="2"></td><td colspan="2">No pretrain</td></tr><tr><td colspan="2"></td><td>No repeats</td><td>Repeats</td></tr><tr><td rowspan="2">Pretrain</td><td>No repeats</td><td>67</td><td>65</td></tr><tr><td>Repeats</td><td>24</td><td>44</td></tr></table>
+
+Table 4: The count of how often the pretrain and no pretrain systems contain repeated phrases or sentences in their outputs in the side-by-side study. McNemar’s test gives a $\mathsf { p }$ -value of $< 0 . 0 0 0 1$ for rejecting the null hypothesis that the two systems repeat the same proportion of times. The pretrained system clearly repeats less than the system without pretraining.
+
+# 4 RELATED WORK
+
+Unsupervised pretraining has been intensively studied in the past years, most notably is the work by Dahl et al. (2012) who found that pretraining with deep belief networks improved feedforward acoustic models. More recent acoustic models have found pretraining unnecessary (Xiong et al.,
+
+2016; Zhang et al., 2016; Chan et al., 2015), probably because the reconstruction objective of deep belief networks is too easy. In contrast, we find that pretraining language models by next step prediction significantly improves seq2seq on challenging real world datasets.
+
+Despite its appeal, unsupervised learning is rarely shown to improve supervised training. Dai & Le (2015) was amongst the rare studies which showed the benefits of pretraining in a semi-supervised learning setting. Their method is similar to our method except that they did not have a decoder network and thus could not apply to seq2seq learning. Similarly, Zhang & Zong (2016) found it useful to add an additional task of sentence reordering of source-side monolingual data for neural machine translation. Various forms of transfer or multitask learning with seq2seq framework also have the flavors of our algorithm (Zoph et al., 2016; Luong et al., 2015a; Firat et al., 2016).
+
+Perhaps most closely related to our method is the work by Gulcehre et al. (2015), who combined a language model with an already trained seq2seq model by fine-tuning additional deep output layers. Empirically, their method produces small improvements over the supervised baseline. We suspect that their method does not produce significant gains because (i) the models are trained independently of each other and are not fine-tuned (ii) the LM is combined with the seq2seq model after the last layer, wasting the benefit of the low level LM features, and (iii) only using the LM on the decoder side. Venugopalan et al. (2016) addressed (i) but still experienced minor improvements. Using pretrained GloVe embedding vectors (Pennington et al., 2014) had more impact.
+
+Related to our approach in principle is the work by Chen et al. (2016) who proposed a two-term, theoretically motivated unsupervised objective for unpaired input-output samples. Though they did not apply their method to seq2seq learning, their framework can be modified to do so. In that case, the first term pushes the output to be highly probable under some scoring model, and the second term ensures that the output depends on the input. In the seq2seq setting, we interpret the first term as a pretrained language model scoring the output sequence. In our work, we fold the pretrained language model into the decoder. We believe that using the pretrained language model only for scoring is less efficient that using all the pretrained weights. Our use of labeled examples satisfies the second term. These connections provide a theoretical grounding for our work.
+
+In our experiments, we benchmark our method on machine translation, where other unsupervised methods are shown to give promising results (Sennrich et al., 2015b; Cheng et al., 2016). In backtranslation (Sennrich et al., 2015b), the trained model is used to decode unlabeled data to yield extra labeled data. One can argue that this method may not have a natural analogue to other tasks such as summarization. We note that their technique is complementary to ours, and may lead to additional gains in machine translation. The method of using autoencoders in Cheng et al. (2016) is promising, though it can be argued that autoencoding is an easy objective and language modeling may force the unsupervised models to learn better features.
+
+# 5 CONCLUSION
+
+We presented a novel unsupervised pretraining method to improve sequence to sequence learning. The method can aid in both generalization and optimization. Our scheme involves pretraining two language models in the source and target domain, and initializing the embeddings, first LSTM layers, and softmax of a sequence to sequence model with the weights of the language models. Using our method, we achieved state-of-the-art machine translation results on both WMT’14 and WMT’15 English to German.
+
+A key advantage of this technique is that it is flexible and can be applied to a large variety of tasks, such as summarization, where it surpasses the supervised learning baseline.
+
+# ACKNOWLEDGMENTS
+
+We thank George Dahl, Andrew Dai, Laurent Dinh, Stephan Gouws, Geoffrey Hinton, Rafal Jozefowicz, Pooya Khorrami, Phillip Louis, Ramesh Nallapati, Arvind Neelakantan, Xin Pan, Abi See, Rico Sennrich, Luke Vilnis, Yuan Yu and the Google Brain team for their help with the project.
+
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+
+# APPENDIX
+
+SELECTED SUMMARIZATION OUTPUTS
+
+Table 5: The pretrained model outputs a highly informative summary, while the no pretrain model outputs irrelevant details.   
+
+<table><tr><td>Source Document (cnn ) like phone booths and typewriters ,record stores are a vanishing breed -another victim</td></tr><tr><td>of the digital age .camelot music .virgin megastores .wherehouse music . tower records ． all of them gone ． corporate america has largely abandoned brick - and - mortar music retailing to a scattering of independent stores , many of them in scruffy urban neighborhoods . and that s not necessarily a bad thing . yes ,it s harder in the spotify era to find a place to go buy physical music . but many of the remaining record stores are succeeding - even thriving - by catering to a passionate core of customers and collectors ．on saturday，,hundreds of music retailers will hold events to commemorate record store day,an annual celebration of ,well ,your neighborhood record store .many stores will host live performances ,drawings ,book signings ,special sales of rare or autographed vinyl and other happenings . some will even serve beer.to their diehard customers ,these places are more than mere stores : they are cultural institutions that celebrate music history（the entire duran duran oeuvre ,all in one place ！）,display artifacts（aretha franklin on vinyl！）,and nurture the local music scene（hey,here s acd by your brother s metal band ！）. they also employ knowledgeable clerks who will be happy to debate the relative merits of blood on the tracks and blonde on blonde .or maybe ,like jack black in high fidelity, just mock your lousy taste in music . so</td></tr><tr><td>if you re a music geek ,drop by . but you might think twice before asking if they stock i just called to say i love you .</td></tr><tr><td>Ground Truth summary saturday is record store day,celebrated at music stores around the world .many stores will</td></tr><tr><td>host live performances ,drawings and special sales of rare vinyl .</td></tr><tr><td>No pretrain corporate america has largely abandoned brick - brick - mortar music . many of the remaining</td></tr><tr><td>record stores are succeeding - even thriving-by catering to a passionate core of customers . Pretrained hundreds of music retailers will hold events to commemorate record store day .many stores</td></tr></table>
+
+Table 6: The pretrained model outputs a highly relevant summary but makes a mistake on the feline executioner’s name. The no pretrain model degenerates into irrelevant details and repeats itself.   
+
+<table><tr><td>Source Document (cnn ） hey,look what i did . that smallboast on social media can trigger a whirlwind that</td></tr><tr><td>lindsey allegedly shot an arrow into the back of an orange tabby s head and posted a proud photo this week on facebook of herself smiling ,as she dangled its limp body by the arrow s shaft . lindsey added a comment,cnn affiliate kbtx reported . my first bow kill,lol . the only good feral tomcat is one with an arrow through it s head ！ vet of the year award ... gladly accepted .callers rang the phones hot at washington county s animal clinic ,where lindsey worked ,to vent their outrage .web traffic crashed its website . high price of public shaming on the internet then an animal rescuer said that lindsey s prey was probably not a feral cat but the pet of an elderly couple ,who called him tiger . he had gone missing on wednesday , the same day that lindsey posted the photo of the slain cat.cnn has not been able to confirm the claim .as the firestorm grew ,lindsey wrote in the comments underneath her post : no i did not lose my job .lol ．psshh .like someone would get rid of me .i m awesome ！ that prediction was wrong. the clinic fired lindsey ,covered her name on its marquee with duct tape ,and publicly distanced itself from her actions .our goal now is to go on and try to fix our black eye and hope that people are reasonable and understand that those actions do nt anyway portray what we re for here at washington animal clinic ,said dr. bruce buenger . we put our heart and soul into this place .the clinic told wbtx that lindsey was not available for comment .cnn is reaching out to her ． she removed her controversial post then eventually shut down her facebook page . callers also complained to the brenham police department and washington county animal control,as her facebook post went viral ．the sheriff s office in austin county ，where the cat was apparently shot , is investigating ，and lindsey could face charges .its dispatchers were overloaded with calls,the sheriff posted on facebook .we are asking you to please take it easy on our dispatchers . as soon as the investigation is complete , we will post the relevant information here on this page ,the post read . animal rights activists are pushing for charges . animal cruelty must be taken seriously ,and the guilty parties should be punished to the fullest extent of the law ，said cat advocacy activist becky robinson ．her organization,alley cat allies ,is offering a $ 7,5OO reward for evidence leading to the arrest and conviction of the person who shot the cat . but others stood up for lindsey . she s amazing</td></tr><tr><td>. she s caring ,said customer shannon stoddard . she s a good vet,so maybe her bad choice of posting something on facebook was not good .but i do nt think she should be judged for it ．she dropped off balloons at the animal clinic for lindsey with a thank you note．cnn s jeremy grisham contributed to this report .</td></tr><tr><td>Ground Truth summary dr.kristen lindsey has since removed the post of her holding the dead cat by an arrow .her</td></tr><tr><td>employer fired her ; the sheriff s ofice is investigating.activist offers $7,5OO reward . No pretrain dr. kristen lindsey allegedly shot an arrow into the back of an orange orange tabby s head . it</td></tr><tr><td> s the only good good tomcat is one with an arrow through it s head ! vet vet of the year award</td></tr><tr><td>Pretrained lindsey lindsey ,a texas veterinarian , shot an arrow into the back of an orange tabby s head . she posted a photo of herself smiling ,as she dangled its limp body by the arrow s shaft . lindsey could face charges,the sheriff s department says .</td></tr><tr><td>Source Document eugenie bouchard s run of poor form continued as the top seed was beaten 6 - 3 ,6 - 1 by</td></tr><tr><td>american lauren davis in the second round at the family circle cup in charleston on wednesday ． davis ,21, had lost her only career meeting with bouchard ,but was in control this time against the world no 7 . davis won nine of the final 11 games of the match and broke bouchard s serve twice in the final set to pull off the upset . eugenie bouchard fires down a serve during her second - round match at the family circle cup bouchard shows her frustrations during her straight - sets defeat by lauren davis on wednesday i ve never beaten here before ， so i came out knowing i had nothing to lose ，said davis ,ranked 66th in the world ．bouchard was a semi-finalist last year but had struggled in the lead - up to the charlston green - clay event ,losing three of her last five matches to lower - ranked opponents .davis used precise groundstrokes to keep bouchard on her heels throughout the second set.davis broke bouchard S serve to love to take a 3 -1 lead as the 21 - year - old canadian had a double fault, then sailed a forehand long to fall behind .two games later ，davis hit a backhand to send back bouchard s lO2mph serve for a winner down the left sideline and a 5-1 lead．davis hits a forehand on her way to an impressve win against the canadian top seed bouchard has struggled recently,this time slumping to her fourth defeat in six matches the match ended on bouchard s forehand into the net,davis waving to the cheering crowd．bouchard said</td></tr><tr><td>: as soon as it was over,definitely a bit of anger,but also kind of this confusion，slash , like quest to find what s wrong,like this kind of searching feeling that ，ok ,like i know something s off .i know something s not right .so i want to find it . i was definitely a little bit slow today ,overpowered .usually ,im the one dominating .so it was definitely, just ,i do nt know, just not good .</td></tr><tr><td>Ground Truth summary eugenie bouchard suffered her fourth defeat in six matches . the canadian top seed lost to lauren davis at the family circle cup . world no 66 davis won 6 - 3,6 - 1 in the second round in charleston .davis won nine of the final 11 games of the match to seal victory .click here</td></tr><tr><td>for all the latest news from charleston . No pretrain bouchard beat american lauren davis 6 - 3,6 - 1 in the second round of the family circle cup</td></tr><tr><td>in charleston on wednesday.bouchard had lost her only career meeting with bouchard but was in control this time against the world no 7 .bouchard won nine of the final 11 games of the match and broke bouchard s serve twice in the final set to pull off the upset .</td></tr><tr><td>Pretrained eugenie bouchard was beaten 6 - 3,6 -1 by american lauren davis in the second round . davis had lost her only career meeting with bouchard,but was in control this time against the</td></tr><tr><td>world no 7. davis hit a backhand to send back bouchard s 1O2mph serve for a winner down the left sideline .</td></tr></table>
+
+Table 7: Both models output a relevant summary, but the no pretrain model uses the same name to refer to both players.
+
+Table 8: A failure case. The pretrained model outputs irrelevant details while the no pretrain model successfully summarizes the document.   
+
+<table><tr><td>Source Document （cnn） mike rowe is coming to a river near you .sometimes , you hear about a person who</td></tr><tr><td>makes you feel good about humanity ,but bad about yourself ,rowe says .on thursday s episode of somebody s got ta do it , rowe meets up with chad pregracke ，the founder of living lands &amp; waters ，who does just that . pregracke wants to clean up the nation s rivers one piece of detritus at a time . his quota ? always more . read mike rowe s facebook post on how to break our litter habit . since he founded the nonprofit in 1998 at the ripe age of 23 , pregracke and more than 87,OoO volunteers have collected 8.4 million pounds of trash from u.s. waterways .those efforts helped him earn the 2O13 cnn hero of the year award ,along with numerous other honors ．wherever you are , no matter if there s a stream ,a creek ，a lake , whatever ,that needs to be cleaned up,you can do it . just organize it and do it, he told cnn s anderson cooper after his win . pregracke also gives rowe a tour of the 15O - foot, solar - powered barge that the living lands &amp; waters staff calls home during lengthy cleanups . the part - home ,part - office,part - dumpster has seven bedrooms ,two bathrooms ,a classroom and a kitchen -and just happens to be made from a recycled strip club ．according to the organization s latest annual report，pregracke has made it his mission in 2O15 to remove</td></tr><tr><td>500,00O more pounds of trash .if you d like to help achieve this goal, visit his website to learn how to help : livinglandsandwaters.org / get - involved / .</td></tr><tr><td>Ground Truth summary chad pregracke was the 2O13 cnn hero of the year. mike rowe visited pregracke for an episode</td></tr><tr><td>of somebody s got ta do it . No pretrain</td></tr><tr><td>rowe meets up with chad pregracke , founder of living lands &amp; waters . pregracke and more</td></tr><tr><td>than 87,Ooo volunteers collected 8.4 million pounds of trash from u.s. waterways . Pretrained rowe is the founder of living lands &amp; waters , who does just that . pregracke also gives rowe</td></tr></table>
+
+# SELECTED ENGLISH GERMAN OUTPUTS
+
+<table><tr><td rowspan=1 colspan=1>Source</td></tr><tr><td rowspan=1 colspan=1>Mayor Bloomberg told reporters that, because of that court order, the city had suspended thereopening of the public space and protesters were informed, however, that local laws do notallow them to re-install with camping shops and sleeping bags.</td></tr><tr><td rowspan=1 colspan=1>Ground Truth</td></tr><tr><td rowspan=1 colspan=1>Buirgermeister Bloomberg stellt vor der Presse Klar , das aufgrund dieser richterlichen Anord-nung die erneute Offnung des Platzes fir den Publikumsverkehr und die Demonstrantenaufgehoben worden sei .Die Demonstranten wies er darauf hin,dass die Stadtgesetze ihnennicht erlaubten,sich erneut mit Zelten und Schlafsäcken an diesem Ort einzurichten .</td></tr><tr><td rowspan=1 colspan=1>No pretrain</td></tr><tr><td rowspan=1 colspan=1>Der Burgermeister Bloomberg sagte den Reportern , dass die Stadt aufgrund dieser Gericht-sentscheidung die Wiedereroffnung des offentlichen Raumes und die Information derDemonstranten ausgesetzt habe，dass die lokalen Gesetze ihnen nicht erlauben ，mit denCampingplätzen und Schlafsäcken neu zu installieren .</td></tr><tr><td rowspan=1 colspan=1>Pretrained</td></tr><tr><td rowspan=1 colspan=1>Birgermeister Bloomberg erklärte gegenuber Journalisten ，dass die Stadt aufgrund dieserGerichtsentscheidung die Wiedereroffnung des offentlichen Raums ausgesetzt habe und dassdie Demonstranten daruber informiert wurden ，dass die ortlichen Gesetze es ihnen nichterlauben wuirden , sich mit Campingplätzen und Schlafsälen neu zu installieren .</td></tr></table>
+
+Table 9: The no pretrain model makes a complete mistranslation when outputting ”und die Information der Demonstranten ausgesetzt habe”. That translates to ”the reopening of the public space and the information [noun] of the protesters were suspended”, instead of informing the protesters. Furthermore, it wrongly separated the two sentences, so the first sentence has extra words and the second sentence is left without a subject. The pretrained model does not make any of these mistakes. However, both models make a vocabulary mistake of ”zu installieren”, which is typically only used to refer to installing software. A human evaluator fluent in both German and English said that the pretrained version was better.
+
+<table><tr><td rowspan=1 colspan=1>Source</td></tr><tr><td rowspan=1 colspan=1>The low February temperatures, not only did they cause losses of millions for the agricultural sector, but they limited the possibilities of the state economy to grow,causing a contraction ofthe economic activity in general of 3.6 percent in the first half of the year, mainly supportedby the historic fall of 31.16 per cent in agriculture,which affected the dynamics of othereconomic sectors.</td></tr><tr><td rowspan=1 colspan=1>Ground Truth</td></tr><tr><td rowspan=1 colspan=1>Die niedrigen Temperaturen im Februar verursachten nicht nur Verluste in Millionenhohe inderLandwirtschaft，sondern steckten daruber hinaus dem Wachstum der Staatswirtschaftenge Grenzen und verursachten im ersten Vierteljahr einen allgemeinen Rückgang derWirtschaftstatigkeit um 3,6 Prozent Dieser geht hauptsächlich auf den historischen Abbauder landwirtschaftlichen Entwicklung um 31,16 Prozent zuruck,der sich bremsend auf weit-ere Wirtschaftssektoren auswirkte .</td></tr><tr><td rowspan=1 colspan=1>No pretrain</td></tr><tr><td rowspan=1 colspan=1>Die niedrigen Temperaturen im Februar fuhrten nicht nur zu Verlusten fur die Landwirtschaft,sondern sie beschränkten die Moglichkeiten der staatlichen Wirtschaft，wachsen zu wach-sen，wodurch die Wirtschaftstatigkeit insgesamt von 3,6 Prozent in der ersten Halfte desJahres ,hauptsächlich durch den historischen Rückgang von 31.16 % in der Landwirtschaft ,beeinflusst wurde,was die Dynamik anderer Wirtschaftssektoren betraf .</td></tr><tr><td rowspan=1 colspan=1>Pretrained</td></tr><tr><td rowspan=1 colspan=1>Die niedrigen Temperaturen im Februar fuhrten nicht nur zu Verlusten von Millionen fur denAgrarsektor,sondern beschränkten die Moglichkeiten der Staatswirtschaft, zu wachsen, waszu einer Schrumpfung der Wirtschaftstatigkeit im Allgemeinen von 3,6 Prozent in der erstenHalfte des Jahres fuhrte,hauptsächlich durch den historischen Einbruch von 316 Prozent inder Landwirtschaft,der die Dynamik anderer Wirtschaftsbereiche beeinflusst hatte .</td></tr></table>
+
+Table 10: The human evaluator noted that the pretrained version is better, as it correctly captures the meaning and sentence structure of the middle. The no pretrain model does not misses translating the word ”million”, repeats itself in ”wachsen zu wachsen”, and puts the verb ”beeinflusst wurde” is an unnatural position. However, the pretrained model makes a mistake in the percentage $3 1 6 \%$ instead of $3 1 . 1 6 \%$ ).
+
+Table 11: An example where the English source is poorly worded. Both models output poor translations, but the evaluator noted that the pretrained version is still better than the no pretrain version. Interestingly, both models mistranslate ”radical” as ”radikalislamistisches”, which means ”radical Islam”, which is probably a bias in the training data.   
+
+<table><tr><td rowspan=1 colspan=1>Source</td></tr><tr><td rowspan=1 colspan=1>To facilitate the inception of the Second World War, they allowed bankers and politiciansto create a latent conflict situation by saddling Germany with huge war reparations, therebymaking a radicalist example of the impoverished masses,it remained only to introduce asuffciently convincing culprit and a leader with a simple solution, while also creating a multi-racial Czechoslovakia with a strong German minority to play,and indeed did, the role of afifth colony, once the war had been ignited.</td></tr><tr><td rowspan=1 colspan=1>Ground Truth</td></tr><tr><td rowspan=1 colspan=1>Um den Zweiten Weltkrieg einfacher entfachen zu konnen ，lieBen die Banker durch diePolitik eine latente Konfliktsituation schaffen ，indem sie Deutschland mit gigantischenKriegsreparationen belegten ; dadurch schufen sie die Voraussetzung verarmter Massen ，sodass sie den Deutschen nur noch einen ausreichend starken Fuhrer unterjubeln mussten,derdie Schuldigen benannte und einfache Losungen anbot ; ein weiterer Faktor war die Schaf-fung des Vielvolkerstaates Tschechoslowakei mit einer starken deutschen Minderheit,die dieFunktion einer fuinften Kolonne einnehmen sollte und auch einnahm ,um den Kriegsbrandzu entfachen.</td></tr><tr><td rowspan=1 colspan=1>No pretrain</td></tr><tr><td rowspan=1 colspan=1>Um die Grundung des Zweiten Weltkriegs zu erleichtern ， ermoglichte es den Bankern undPolitikern ,eine latente Konfliktlage zu schaffen,indem sie Deutschland mit enormen Repa-rationsforderungen konfrontierte ,wodurch ein radikalislamistisches Beispiel der verarmtenMassen entstand ,es blieb nur ，einen ausreichend aussagekraftigen Schuldigen und einenFuhrer mit einer einfachen Losung zu etablieren ,während gleichzeitig eine multi-ethnischeTschechoslowakei mit einer starken deutschen Minderheit zu spielen war und tatsächlich dieRolle einer funften Kolonie war .</td></tr><tr><td rowspan=1 colspan=1>Pretrained</td></tr><tr><td rowspan=1 colspan=1>Um die Einfuhrung des Zweiten Weltkrieges zu erleichtern ,lieBen sie Banker und Politikereine latente Konfliktlage schaffen ,indem sie Deutschland mit riesigen Reparationszahlungenbelieferten，wodurch ein radikalislamistisches Beispiel der verarmten Massen entstand,esblieb nur,einen ausreichend üiberzeugenden Schuldigen und einen Fuhrer mit einer einfachenLosung zu präsentieren，während gleichzeitig eine multiethnische Tschechoslowakei miteiner starken deutschen Minderheit geschaffen wurde ,um zu spielen,und tatsächlich,dieRolle einer funften Kolonie,sobald der Krieg entfacht worden war .</td></tr></table>
+
+Table 12: Another example where the English source is poorly worded. Both models get the structure right, but have a variety of problematic translations. Both models miss the meaning of ”total vote count”. They both also translate ”electoral boxes” poorly - the no pretrain model calls it ”electoral paperwork” while the pretrained model calls it ”ballots”. These failures may be because of the poorly worded English source. The human evaluator found them both equally poor.   
+
+<table><tr><td rowspan=1 colspan=1>Source</td></tr><tr><td rowspan=1 colspan=1>The total vote count will also be done if at the end of the ordinary calculation is establishedthat the diference between the winner and the candidate placed on second position is equalto or less than one percentage point, as long as there is a request of the representative ofthe political party whose candidate came on the second position, case in which there will beexcluded the electoral boxes that have been considered during the partial recount.</td></tr><tr><td rowspan=1 colspan=1>Ground Truth</td></tr><tr><td rowspan=1 colspan=1>Die Stimmenauszählung kann auch in ihrer Gesamtheit erfolgen ，wenn nach Abschlussder ordentlichen Berechnung festgestelt wird，dass der Unterschied zwischen dem mut-maBlichen Gewinner und dem Kandidaten auf dem zweiten Platz gleich oder geringer als einProzent ist,vorausgesetzt es liegt ein ausdruicklicher Antrag von einem Vertreter der Partei ,deren Kandidat Zweiter geworden ist, vor .In diesem Fall wirden die Wahlpakete ,die einerteilweisen Auszahlung ausgesetzt wurden,ausgeschlossen .</td></tr><tr><td rowspan=1 colspan=1>No pretrain</td></tr><tr><td rowspan=1 colspan=1>Die gesamte Stimmenanzahl wird auch dann erreicht，wenn am Ende der ordentlichenBerechnung festgestellt wird ,dass der Unterschied zwischen dem Sieger und dem Kandi-daten,der auf der zweiten Position liegt ,gleich oder weniger als einen Prozentpunkt beträgt, Vorausgesetzt,dass der Vertreter der Partei,deren Kandidat auf der zweiten Position ist,derFall ist,in dem die Wahlunterlagen,die während der teilweisen Rückzahlung beruicksichtigtwurden,ausgeschlossen werden.</td></tr><tr><td rowspan=1 colspan=1>Pretrained</td></tr><tr><td rowspan=1 colspan=1>Die Gesamtzahl der Stimmzetel wird auch dann durchgefuhrt，wenn am Ende der or-dentlichen Berechnung festgestelt wird, dass der Unterschied zwischen dem Gewinner unddem auf den zweiten Platz platzierten Kandidaten gleich oder weniger als einen Prozent-punkt betragt，solange es einen Antrag des Vertreters der politischen Partei gibt，dessenKandidat auf die zweite Position kam,in dem es die Wahlzettel ausklammert,die währendder Teilzählung berüicksichtigt wurden .</td></tr></table>

parse/train/H1lZJpVFvr/H1lZJpVFvr.md

@@ -0,0 +1,336 @@
+# ROBUST LOCAL FEATURES FOR IMPROVING THE GENERALIZATION OF ADVERSARIAL TRAINING
+
+Chuanbiao Song & Kun He $\mathbf { \mu } ^ { * } \mathbf { \& }$ Jiadong Lin School of Computer Science and Technology Huazhong University of Science and Technology Wuhan, 430074, China {cbsong,brooklet60,jdlin}@hust.edu.cn
+
+Liwei Wang   
+School of Electronics Engineering   
+and Computer Sciences, Peking University   
+Peking, China   
+wanglw@cis.pku.edu.cn
+
+John E. Hopcroft Department of Computer Science Cornell University, NY 14853, USA jeh@cs.cornell.edu
+
+# ABSTRACT
+
+Adversarial training has been demonstrated as one of the most effective methods for training robust models to defend against adversarial examples. However, adversarially trained models often lack adversarially robust generalization on unseen testing data. Recent works show that adversarially trained models are more biased towards global structure features. Instead, in this work, we would like to investigate the relationship between the generalization of adversarial training and the robust local features, as the robust local features generalize well for unseen shape variation. To learn the robust local features, we develop a Random Block Shuffle (RBS) transformation to break up the global structure features on normal adversarial examples. We continue to propose a new approach called Robust Local Features for Adversarial Training (RLFAT), which first learns the robust local features by adversarial training on the RBS-transformed adversarial examples, and then transfers the robust local features into the training of normal adversarial examples. To demonstrate the generality of our argument, we implement RLFAT in currently state-of-the-art adversarial training frameworks. Extensive experiments on STL-10, CIFAR-10 and CIFAR-100 show that RLFAT significantly improves both the adversarially robust generalization and the standard generalization of adversarial training. Additionally, we demonstrate that our models capture more local features of the object on the images, aligning better with human perception.
+
+# 1 INTRODUCTION
+
+Deep learning has achieved a remarkable performance breakthrough on various challenging benchmarks in machine learning fields, such as image classification (Krizhevsky et al., 2012) and speech recognition (Hinton et al., 2012). However, recent studies (Szegedy et al., 2014; Goodfellow et al., 2015) have revealed that deep neural network models are strikingly susceptible to adversarial examples, in which small perturbations around the input are sufficient to mislead the predictions of the target model. Moreover, such perturbations are almost imperceptible to humans and often transfer across diverse models to achieve black-box attacks (Papernot et al., 2017; Liu et al., 2017; Wang et al., 2019; Lin et al., 2020).
+
+Though the emergence of adversarial examples has received significant attention and led to various defend approaches for developing robust models (Madry et al., 2018; Dhillon et al., 2018; Wang & Yu, 2019; Song et al., 2019; Zhang et al., 2019a), many proposed defense methods provide few benefits for the true robustness but mask the gradients on which most attacks rely (Carlini & Wagner, 2017a; Athalye et al., 2018; Uesato et al., 2018; Li et al., 2019). Currently, one of the best techniques to defend against adversarial attacks (Athalye et al., 2018; Li et al., 2019) is adversarial training (Madry et al., 2018; Zhang et al., 2019a), which improves the adversarial robustness by injecting adversarial examples into the training data.
+
+Among substantial works of adversarial training, there still remains a big robust generalization gap between the training data and the testing data (Schmidt et al., 2018; Zhang et al., 2019b; Ding et al., 2019; Zhai et al., 2019). The robustness of adversarial training fails to generalize on unseen testing data. Recent works (Geirhos et al., 2019; Zhang & Zhu, 2019) further show that adversarially trained models capture more on global structure features but normally trained models are more biased towards local features. In intuition, global structure features tend to be robust against adversarial perturbations but hard to generalize for unseen shape variations, instead, local features generalize well for unseen shape variations but are hard to generalize on adversarial perturbation. It naturally raises an intriguing question for adversarial training:
+
+For adversarial training, is it possible to learn the robust local features , which have better adversarially robust generalization and better standard generalization?
+
+To address this question, we investigate the relationship between the generalization of adversarial training and the robust local features, and advocate for learning robust local features for adversarial training. Our main contributions are as follows:
+
+• To our knowledge, this is the first work that sheds light on the relationship between adversarial training and robust local features. Specifically, we develop a Random Block Shuffle (RBS) transformation to study such relationship by breaking up the global structure features on normal adversarial examples.   
+• We propose a novel method called Robust Local Features for Adversarial Training (RLFAT), which first learns the robust local features, and then transfers the information of robust local features into the training on normal adversarial examples.   
+• To demonstrate the generality of our argument, we implement RLFAT in two currently stateof-the-art adversarial training frameworks, PGD Adversarial Training (PGDAT) (Madry et al., 2018) and TRADES (Zhang et al., 2019a). Empirical results show consistent and substantial improvements for both adversarial robustness and standard accuracy on several standard datasets. Moreover, the salience maps of our models on images tend to align better with human perception.
+
+# 2 PRELIMINARIES
+
+In this section, we introduce some notations and provide a brief description on current advanced methods for adversarial attacks and adversarial training.
+
+# 2.1 NOTATION
+
+Let $F ( x )$ be a probabilistic classifier based on a neural network with the logits function $f ( x )$ and the probability distribution $p _ { F } ( \cdot | x )$ . Let $\mathcal { L } ( F ; x , y )$ be the cross entropy loss for image classification. The goal of the adversaries is to find an adversarial example $x ^ { \prime } \in \dot { \mathcal { B } } _ { \epsilon } ^ { p } ( x ) : = \{ x ^ { \prime } : \| x ^ { \prime } - x \| _ { p } \leq \epsilon \}$ in the $\ell _ { p }$ norm bounded perturbations, where $\epsilon$ denotes the magnitude of the perturbations. In this paper, we focus on $p = \infty$ to align with previous works.
+
+# 2.2 ADVERSARIAL ATTACKS
+
+Projected Gradient Descent. Projected Gradient Descent (PGD) (Madry et al., 2018) is a stronger iterative variant of Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2015), which iteratively solves the optimization problem $\begin{array} { r } { \operatorname* { m a x } _ { x ^ { \prime } : \| x ^ { \prime } - x \| _ { \infty } < \epsilon } \mathcal { L } \left( F ; x ^ { \prime } , y \right) } \end{array}$ with a step size $\alpha$ :
+
+$$
+\begin{array} { r l } & { \mathrel { \phantom { = } } x ^ { 0 } \sim \mathcal { U } \left( \mathcal { B } _ { \epsilon } ^ { \infty } ( x ) \right) , } \\ & { \mathrel { \phantom { = } } x ^ { t + 1 } = \Pi _ { \mathcal { B } _ { \epsilon } ^ { \infty } ( x ) } \left( x ^ { t } - \alpha \mathrm { s i g n } \left( \nabla _ { x } \mathcal { L } ( F ; x , y ) | _ { x ^ { t } } \right) \right) , } \end{array}
+$$
+
+where $\mathcal { U }$ denotes the uniform distribution, and $\Pi _ { B _ { \epsilon } ^ { \infty } ( x ) }$ indicates the projection of the set $B _ { \epsilon } ^ { \infty } ( x )$
+
+Carlini-Wagner attack. Carlini-Wagner attack (CW) (2017b) is a sophisticated method to directly solve for the adversarial example $x ^ { a d \overline { { v } } }$ by using an auxiliary variable $w$ :
+
+$$
+x ^ { a d v } = 0 . 5 \cdot \left( \operatorname { t a n h } ( w ) + 1 \right) .
+$$
+
+The objective function to optimize the auxiliary variable $w$ is defined as:
+
+$$
+\operatorname* { m i n } _ { \boldsymbol { w } } \left\| \boldsymbol { x } ^ { a d v } - \boldsymbol { x } \right\| + c \cdot \mathcal { F } \left( \boldsymbol { x } ^ { a d v } \right) ,
+$$
+
+where ${ \mathcal { F } } ( x ^ { a d v } ) = \operatorname* { m a x } \left( f _ { y ^ { \mathrm { t r u e } } } ( x ^ { a d v } ) - \operatorname* { m a x } \left\{ f _ { i } ( x ^ { a d v } ) : i \neq y ^ { \mathrm { t r u e } } \right\} , - k \right)$ . The constant $k$ controls the confidence gap between the adversarial class and the true class.
+
+N attack. $\mathcal { N }$ attack (Li et al., 2019) is a derivative-free black-box adversarial attack and it breaks many of the defense methods based on gradient masking. The basic idea is to learn a probability density distribution over a small region centered around the clean input, such that a sample drawn from this distribution is likely to be an adversarial example.
+
+# 2.3 ADVERSARIAL TRAINING
+
+Despite a wide range of defense methods, Athalye et al. (2018) and Li et al. (2019) have broken most previous defense methods (Dhillon et al., 2018; Buckman et al., 2018; Wang & Yu, 2019; Zhang et al., 2019a), and revealed that adversarial training remains one of the best defense method. The basic idea of adversarial training is to solve the min-max optimization problem, as shown in Eq. (4):
+
+$$
+\operatorname* { m i n } _ { F } \operatorname* { m a x } _ { x ^ { \prime } : \| x ^ { \prime } - x \| _ { \infty } < \epsilon } { \mathcal { L } } \left( F ; x ^ { \prime } , y \right) .
+$$
+
+Here we introduce two currently state-of-the-art adversarial training frameworks.
+
+PGD adversarial training. PGD Adversarial Training (PGDAT) (Madry et al., 2018) leverages the PGD attack to generate adversarial examples, and trains only with the adversarial examples. The objective function is formalized as follows:
+
+$$
+\mathcal { L } _ { \mathrm { P G D } } ( F ; x , y ) = \mathcal { L } ( F ; x _ { \mathrm { P G D } } ^ { \prime } , y ) ,
+$$
+
+where $x _ { \mathrm { P G D } } ^ { \prime }$ is obtained via the PGD attack on the cross entropy $\mathcal { L } ( F ; x , y )$ .
+
+TRADES. Zhang et al. (2019a) propose TRADES to specifically maximize the trade-off of adversarial training between adversarial robustness and standard accuracy by optimizing the following regularized surrogate loss:
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { T R A D E S } } ( F ; x , y ) = \mathcal { L } ( F ; x , y ) + \lambda D _ { \mathrm { K L } } \left( ~ p _ { F } ( \cdot | x ) ~ \| ~ p _ { F } \left( \cdot | x _ { \mathrm { P G D } } ^ { \prime } [ x ] \right) ~ \right) ~ , } \end{array}
+$$
+
+where $x _ { \mathrm { P G D } } ^ { \prime } [ x ]$ is obtained via the PGD attack on the KL-divergence $D _ { \mathrm { K L } } \left( p _ { F } ( \cdot | x ) \parallel p _ { F } \left( \cdot | x ^ { \prime } \right) \right)$ , and $\lambda$ is a hyper-parameter to control the trade-off between adversarial robustness and standard accuracy.
+
+# 3 ROBUST LOCAL FEATURES FOR ADVERSARIAL TRAINING
+
+Unlike adversarially trained models, normally trained models are more biased towards the local features but vulnerable to adversarial examples (Geirhos et al., 2019). It indicates that, in contrast to global structural features, local features seems be more well-generalized but less robust against adversarial perturbation. Based on the basic observation, in this work, we focus on the learning of robust local features on adversarial training, and propose a novel form of adversarial training called RLFAT that learns the robust local features and transfers the robust local features into the training of normal adversarial examples. In this way, our adversarially trained models not only yield strong robustness against adversarial examples but also show great generalization on unseen testing data.
+
+# 3.1 ROBUST LOCAL FEATURE LEARNING
+
+It’s known that adversarial training tends to capture global structure features so as to increase invariance against adversarial perturbations (Zhang & Zhu, 2019; Ilyas et al., 2019). To advocate for the learning of robust local features during adversarial training, we propose a simple and straightforward image transformation called Random Block Shuffle (RBS) to break up the global structure features of the images, at the same time retaining the local features. Specifically, for an input image, we randomly split the target image into $k$ blocks horizontally and randomly shuffle the blocks, and then we perform the same split-shuffle operation vertically on the resulting image. As illustrated in Figure 1, RBS transformation can destroy the global structure features of the images to some extent and retain the local features of the images.
+
+![](images/545bbbe8e3349378274f7a539c2931e5c170a20bd12f02755cf048bfddab598e.jpg)  
+Figure 1: Illustration of the RBS transformation for $k = 3$ . For a better understanding on the RBS transformation, we paint the split image blocks with different colors.
+
+Then we apply the RBS transformation on adversarial training. Different from normal adversarial training, we use the RBS-transformed adversarial examples rather than normal adversarial examples as the adversarial information to encourage the models to learn robust local features. Note that we only use the RBS transformation as a tool to learn the robust local features during adversarial training and will not use RBS transformation in the inference phase. we refer to the form of adversarial training as RBS Adversarial Training (RBSAT).
+
+To demonstrate the generality of our argument, we consider two currently state-of-the-art adversarial training frameworks, PGD Adversarial Training (PGDAT) (Madry et al., 2018) and TRADES (Zhang et al., 2019a), to demonstrate the effectiveness of the robust local features.
+
+We use the following loss function as the alternative to the objective function of PGDAT:
+
+$$
+\mathcal { L } _ { \mathrm { P G D A T } } ^ { \mathrm { R L F L } } ( F ; x , y ) = \mathcal { L } ( F ; \mathrm { R B S } ( x _ { \mathrm { P G D } } ^ { \prime } ) , y ) ,
+$$
+
+where RBS(·) denotes the RBS transformation; $x _ { \mathrm { P G D } } ^ { \prime }$ is obtained via the PGD attack on the cross entropy $\mathcal { L } ( \boldsymbol { F } ; \boldsymbol { x } , \boldsymbol { y } )$ .
+
+imilarly, we use the following loss function as the alternative to the objective function of TRADES:
+
+$$
+\mathcal { L } _ { \mathrm { T R A D E S } } ^ { \mathrm { R L F L } } ( F ; x , y ) = \mathcal { L } ( F ; x , y ) + \lambda D _ { \mathrm { K L } } \left[ p _ { F } ( \cdot | x ) \parallel p _ { F } \left( \cdot | \mathrm { R B S } \left( x _ { \mathrm { P G D } } ^ { \prime } [ x ] \right) \right) \right] ,
+$$
+
+where $x _ { \mathrm { P G D } } ^ { \prime } [ x ]$ is obtained via the PGD attack on the KL-divergence $D _ { \mathrm { K L } } \left( p _ { F } ( \cdot | x ) \parallel p _ { F } \left( \cdot | x ^ { \prime } \right) \right)$ ).
+
+# 3.2 ROBUST LOCAL FEATURE TRANSFER
+
+Since the type of input images in the training phase and the inference phase is different (RBS transformed images for training, versus original images for inference), we consider to transfer the knowledge of the robust local features learned by RBSAT to the normal adversarial examples. Specifically, we present a knowledge transfer scheme, called Robust Local Feature Transfer (RLFT). The goal of RLFT is to learn the representation that minimizes the feature shift between the normal adversarial examples and the RBS-transformed adversarial examples.
+
+In particular, we apply RLFT on the logit layer for high-level feature alignment. Formally, the objective functions of robust local feature transfer for PGDAT and TRADES are formalized as follows, respectively:
+
+$$
+\mathcal { L } _ { \mathrm { P G D A T } } ^ { \mathrm { R L F T } } ( F ; x , y ) = \left\| f ( \mathrm { R B S } ( x _ { \mathrm { P G D } } ^ { \prime } ) ) - f ( x _ { \mathrm { P G D } } ^ { \prime } ) \right\| _ { 2 } ^ { 2 } ,
+$$
+
+$$
+\begin{array} { r } { \mathcal { L } _ { \mathrm { T R A D E S } } ^ { \mathrm { R L F T } } ( F ; x , y ) = \| f ( \mathrm { R B S } ( x _ { \mathrm { P G D } } ^ { \prime } [ x ] ) ) - f ( x _ { \mathrm { P G D } } ^ { \prime } [ x ] ) \| _ { 2 } ^ { 2 } , } \end{array}
+$$
+
+where $f ( \cdot )$ denotes the mapping of the logit layer, and $\left\| \cdot \right\| _ { 2 } ^ { 2 }$ denotes the squared Euclidean norm.
+
+# 3.3 OVERALL OBJECTIVE FUNCTION
+
+Since the quality of robust local feature transfer depends on the quality of the robust local features learned by RBSAT, we integrate RBSAT and RLFT into an end-to-end training framework, which we refer to as RLFAT (Robust Local Features for Adversarial Training). The general training process of RLFAT is summarized in Algorithm 1. Note that the computational cost of RBS transformation (line 7) is negligible in the total computational cost.
+
+# Algorithm 1 Robust Local Features for Adversarial Training (RLFAT).
+
+1: Randomly initialize network $F ( x )$ ;   
+2: Number of iterations $t \gets 0$ ;   
+3: repeat   
+4: $t \gets t + 1$ ;   
+5: Read a minibatch of data $\{ x _ { 1 } , . . . , x _ { m } \}$ from the training set;   
+6: Generate the normal adversarial examples $\{ x _ { 1 } ^ { a d v } , . . . , x _ { m } ^ { \tilde { a } d v } \}$   
+7: 1Obtain the RBS-transformed adversarial examples $\{ \mathrm { R B S } ( x _ { 1 } ^ { a d v } ) , . . . , \mathrm { R B S } ( x _ { m } ^ { a d v } ) \}$ ;   
+8: Calculate the overall loss following Eq. (10).   
+9: Update the parameters of network $F$ through back propagation;
+
+10: until the training converges.
+
+We implement RLFAT in two currently state-of-the-art adversarial training frameworks, PGDAT and TRADES, and have new objective functions to learn the robust and well-generalized feature representations, which we call RLF $\mathrm { \Delta ^ { \prime } A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ :
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { \mathrm { R L F A T } _ { \mathrm { P } } } ( F ; x , y ) = \mathcal { L } _ { \mathrm { P G D A T } } ^ { \mathrm { R L F L } } ( F ; x , y ) + \eta \mathcal { L } _ { \mathrm { P G D A T } } ^ { \mathrm { R L F T } } ( F ; x , y ) , } \\ & { } \\ & { \mathcal { L } _ { \mathrm { R L F A T } _ { \mathrm { T } } } ( F ; x , y ) = \mathcal { L } _ { \mathrm { T R A D E S } } ^ { \mathrm { R L F L } } ( F ; x , y ) + \eta \mathcal { L } _ { \mathrm { T R A D E S } } ^ { \mathrm { R L F T } } ( F ; x , y ) } \end{array}
+$$
+
+where $\eta$ is a hyper-parameter to balance the two terms.
+
+# 4 EXPERIMENTS
+
+In this section, to validate the effectiveness of RLFAT, we empirically evaluate our two implementations, denoted as $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ , and show that our models make significant improvement on both robust accuracy and standard accuracy on standard benchmark datasets, which provides strong support for our main hypothesis. Codes are available online1.
+
+# 4.1 EXPERIMENTAL SETUP
+
+Baselines. Since most previous defense methods provide few benefit in true adversarially robustness (Athalye et al., 2018; Li et al., 2019), we compare the proposed methods with state-of-theart adversarial training defenses, PGD Adversarial Training (PGDAT) (Madry et al., 2018) and TRADES (Zhang et al., 2019a).
+
+Adversarial setting. We consider two attack settings with the bounded $\ell _ { \infty }$ norm: the white-box attack setting and the black-box attack setting. For the white-box attack setting, we consider existing strongest white-box attacks: Projected Gradient Descent (PGD) (Madry et al., 2018) and CarliniWagner attack (CW) (Carlini & Wagner, 2017b). For the black-box attack setting, we perform the powerful black-box attack, $\mathcal { N }$ attack (Li et al., 2019), on a sample of 1,500 test inputs as it is timeconsuming.
+
+Datasets. We compare the proposed methods with the baselines on widely used benchmark datasets, namely CIFAR-10 and CIFAR-100 (Krizhevsky & Hinton, 2009). Since adversarially robust generalization becomes increasingly hard for high dimensional data and little training data (Schmidt et al., 2018), we also consider one challenging dataset: STL-10 (Coates et al.), which contains 5, 000 training images, with $9 6 \times 9 6$ pixels per image.
+
+Neural networks. For STL-10, the architecture we use is a wide ResNet 40-2 (Zagoruyko & Komodakis, 2016). For CIFAR-10 and CIFAR-100, we use a wide ResNet w32-10. For all datasets, we scale the input images to the range of $[ 0 , 1 ]$ .
+
+Hyper-parameters. To avoid posting much concentrate on optimizing the hyper-parameters, for all datasets, we set the hyper-parameter $\lambda$ in TRADES as 6, set the hyper-parameter $\eta$ in RLFATP as 0.5, and set the hyper-parameter $\eta$ in $\mathrm { R L F A T _ { T } }$ as 1. For the training jobs of all our models, we set the hyper-parameters $k$ of the RBS transformation as 2. More details about the hyper-parameters are provided in Appendix A.
+
+# 4.2 EVALUATION RESULTS
+
+We first validate our main hypothesis: for adversarial training, is it possible to learn the robust local features that have better adversarially robust generalization and better standard generalization?
+
+In Table 1, we compare the accuracy of $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ with the competing baselines on three standard datasets. The proposed methods lead to consistent and significant improvements on adversarial robustness as well as standard accuracy over the baseline models on all datasets. With the robust local features, $\mathrm { R L F A T _ { T } }$ achieves better adversarially robust generalization and better standard generalization than TRADES. RLFATP also works similarly, showing a significant improvement on the robustness against all attacks and standard accuracy than PGDAT.
+
+Table 1: The classification accuracy $( \% )$ of defense methods under white-box and black-box attacks on STL-10, CIFAR-10 and CIFAR-100.
+
+(a) STL-10. The magnitude of perturbation is 0.03 in $\ell _ { \infty }$ norm.   
+
+<table><tr><td>Defense</td><td>No attack</td><td>PGD</td><td>CW</td><td>Nattack</td></tr><tr><td>PGDAT</td><td>67.05</td><td>30.00</td><td>31.97</td><td>34.80</td></tr><tr><td>TRADES</td><td>65.24</td><td>38.99</td><td>38.35</td><td>42.07</td></tr><tr><td>RLFATp</td><td>71.47</td><td>38.42</td><td>38.42</td><td>44.80</td></tr><tr><td>RLFATT</td><td>72.38</td><td>43.36</td><td>39.31</td><td>48.13</td></tr></table>
+
+(b) CIFAR-10. The magnitude of perturbation is 0.03 in $\ell _ { \infty }$ norm.   
+
+<table><tr><td>Defense</td><td>No attack</td><td>PGD</td><td>CW</td><td>Nattack</td></tr><tr><td>PGDAT</td><td>82.96</td><td>46.19</td><td>46.41</td><td>46.67</td></tr><tr><td>TRADES</td><td>80.35</td><td>50.95</td><td>49.80</td><td>52.47</td></tr><tr><td>RLFATp</td><td>84.77</td><td>53.97</td><td>52.40</td><td>54.60</td></tr><tr><td>RLFATT</td><td>82.72</td><td>58.75</td><td>51.94</td><td>54.60</td></tr></table>
+
+(c) CIFAR-100. The magnitude of perturbation is 0.03 in $\ell _ { \infty }$ norm.   
+
+<table><tr><td>Defense</td><td>No attack</td><td>PGD</td><td>CW</td><td>Nattack</td></tr><tr><td>PGDAT</td><td>55.86</td><td>23.32</td><td>22.87</td><td>22.47</td></tr><tr><td>TRADES</td><td>52.13</td><td>27.26</td><td>24.66</td><td>25.13</td></tr><tr><td>RLFATp</td><td>56.70</td><td>31.99</td><td>29.04</td><td>32.53</td></tr><tr><td>RLFATT</td><td>58.96</td><td>31.63</td><td>27.54</td><td>30.86</td></tr></table>
+
+The results demonstrate that, the robust local features can significantly improve both the adversarially robust generalization and the standard generalization over the state-of-the-art adversarial training frameworks, and strongly support our hypothesis. That is, for adversarial training, it is possible to learn the robust local features, which have better robust and standard generalization.
+
+# 4.3 LOSS SENSITIVITY UNDER DISTRIBUTION SHIFT
+
+Motivation. Ding et al. (2019) and Zhang et al. (2019b) found that the effectiveness of adversarial training is highly sensitive to the “semantic-loss” shift of the test data distribution, such as gamma mapping. To further investigate the performance of the proposed methods, we quantify the smoothness of the models under the distribution shifts of brightness perturbation and gamma mapping.
+
+Loss sensitivity on brightness perturbation. To quantify the smoothness of models on the shift of the brightness perturbation, we propose to estimate the Lipschitz continuity constant $\ell _ { \mathcal { F } }$ by using the gradients of the loss function with respect to the brightness perturbation of the testing data. We adjust the brightness factor of images in the HSV (hue, saturation, value) color space, which we refer to as $x ^ { b } = \mathcal { V } ( x , \alpha )$ , where $\alpha$ denotes the magnitude of the brightness adjustment. The lower the value of $\ell _ { \mathcal { F } } ^ { b } ( \alpha )$ is, the smoother the loss function of the model is:
+
+$$
+\ell _ { \mathcal { F } } ^ { b } ( \alpha ) = \frac { 1 } { m } \sum _ { i = 1 } ^ { m } \| \nabla _ { x } \mathcal { L } ( F ; \mathcal { V } ( x _ { i } , \alpha ) , y _ { t r u e } ) \| _ { 2 }
+$$
+
+Loss sensitivity on gamma mapping. Gamma mapping (Szeliski, 2011) is a nonlinear elementwise operation used to adjust the exposure of images by applying $\tilde { x } ^ { ( \gamma ) } = x ^ { \gamma }$ on the original image $x$ . Similarly, we approximate the loss sensitivity under gamma mapping, by using the gradients of the loss function with respect to the gamma mapping of the testing data. A smaller value indicates a smoother loss function.
+
+$$
+\ell _ { \mathcal { F } } ^ { g } ( \gamma ) = \frac { 1 } { m } \sum _ { i = 1 } ^ { m } \| \nabla _ { x } \mathcal { L } ( F ; x _ { i } ^ { \gamma } , y _ { t r u e } ) \| _ { 2 }
+$$
+
+Sensitivity analysis. The results for the loss sensitivity of the adversarially trained models under brightness perturbation are reported in Table 2a, where we adopt various magnitude of brightness adjustment on each testing data. In Table 2b, we report the loss sensitivity of adversarially trained models under various gamma mappings. We observe that RLFATT provides the smoothest model under the distribution shifts on all the three datasets. The results suggest that, as compared to PGDAT and TRADES, both $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ show lower gradients of the models on different data distributions, which we can directly attribute to the robust local features.
+
+Table 2: The loss sensitivity of defense methods under different testing data distributions.   
+(a) Loss sensitivity on brightness perturbation for the adversarially trained models.   
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="4">e(-0.15)/(0.15)</td></tr><tr><td>PGDAT</td><td>TRADES</td><td>RLFATp</td><td>RLFATT</td></tr><tr><td>STL-10</td><td>0.85/0.82</td><td>0.46 / 0.48</td><td>0.32 /0.34</td><td>0.22 / 0.23</td></tr><tr><td>CIFAR-10</td><td>1.41/1.36</td><td>0.88 /0.90</td><td>0.70 /0.71</td><td>0.54 / 0.56</td></tr><tr><td>CIFAR-100</td><td>3.93 /3.66</td><td>2.31/2.12</td><td>1.25 /1.31</td><td>1.00 / 0.98</td></tr></table>
+
+(b) Loss sensitivity on gamma mapping for the adversarially trained models.   
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="4">(0.8)/(1.2)</td></tr><tr><td>PGDAT</td><td>TRADES</td><td>RLFATp</td><td>RLFATT</td></tr><tr><td>STL-10</td><td>0.77 / 0.79</td><td>0.44/0.42</td><td>0.30 /0.29</td><td>0.21/ 0.19</td></tr><tr><td>CIFAR-10</td><td>1.27 / 1.20</td><td>0.84 /0.76</td><td>0.69 /0.62</td><td>0.54 / 0.48</td></tr><tr><td>CIFAR-100</td><td>2.82/2.80</td><td>1.78 / 1.76</td><td>1.09 / 1.01</td><td>0.95 / 0.88</td></tr></table>
+
+# 4.4 ABLATION STUDIES
+
+To further gain insights on the performance obtained by the robust local features, we perform ablation studies to dissect the impact of various components (robust local feature learning and robust local feature transfer). As shown in Figure 2, we conduct additional experiments for the ablation studies of $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ on STL-10, CIFAR-10 and CIFAR-100, where we report the standard accuracy over the clean data and the average robust accuracy over all the attacks for each model.
+
+Does robust local feature learning help? We first analyze that as compared to adversarial training on normal adversarial examples, whether adversarial training on RBS-transformed adversarial examples produces better generalization and more robust features. As shown in Figure 2, we observe that Robust Local Features Learning (RLFL) exhibits stable improvements on both standard accuracy and robust accuracy for $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ , providing strong support for our hypothesis.
+
+![](images/84116789f1a34326fcff0ccd94cc1b1ee45dc493726c3fe6ce621fa768a52140.jpg)  
+Figure 2: Ablation studies for $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ to investigate the impact of Robust Local Feature Learning (RLFL) and Robust Local Feature Transfer (RLFT).
+
+Does robust local feature transfer help? We further add Robust Local Feature Transfer (RLFT), the second term in Eq. (10), to get the overall loss of RLFAT. The robust accuracy further increases on all datasets for RLFATP and RLFATT. The standard accuracy further increases also, except for $\mathrm { R L F A T _ { P } }$ on CIFAR-100, but it is still clearly higher than the baseline model PGDAT. It indicates that transferring the robust local features into the training of normal adversarial examples does help promote the standard accuracy and robust accuracy in most cases.
+
+# 4.5 VISUALIZING THE SALIENCE MAPS
+
+We would like to investigate the features of the input images that the models are mostly focused on. Following the work of Zhang & Zhu (2019), we generate the salience maps using SmoothGrad (Smilkov et al., 2017) on STL-10 dataset. The key idea of SmoothGrad is to average the gradients of class activation with respect to noisy copies of an input image. As illustrated in Figure 3, all the adversarially trained models basically capture the global structure features of the object on the images. As compared to PGDAT and TRADES, both $\mathrm { R L F A T _ { P } }$ and $\mathrm { R L F A T _ { T } }$ capture more local feature information of the object, aligning better with human perception. Note that the images are correctly classified by all these models. For more visualization results, see Appendix B.
+
+# 5 CONCLUSION AND FUTURE WORK
+
+Differs to existing adversarially trained models that are more biased towards the global structure features of the images, in this work, we hypothesize that robust local features can improve the generalization of adversarial training. To validate this hypothesis, we propose a new stream of adversarial training approach called Robust Local Features for Adversarial Training (RLFAT) and implement it in currently state-of-the-art adversarial training frameworks, PGDAT and TRADES. We provide strong empirical support for our hypothesis and show that the proposed methods based on RLFAT not only yield better standard generalization but also promote the adversarially robust generalization. Furthermore, we show that the salience maps of our models on images tend to align better with human perception, uncovering certain unexpected benefit of the robust local features for adversarial training.
+
+Our findings open a new avenue for improving adversarial training, whereas there are still a lot to explore along this avenue. First, is it possible to explicitly disentangle the robust local features from the perspective of feature disentanglement? What is the best way to leverage the robust local features? Second, from a methodological standpoint, the discovered relationship may also serve as an inspiration for new adversarial defenses, where not only the robust local features but also the global information is taken into account, as the global information is useful for some tasks. These questions are worth investigation in future work, and we hope that our observations on the benefit of robust local features will inspire more future development.
+
+![](images/23a16e8d2e9f01acf82aa7f4b470717d2eea4c8084747ef48724840b0873c42d.jpg)  
+Figure 3: Salience maps of the four models on sampled images. For each group of images, we have the original image, and the salience maps of the four models sequentially.
+
+# ACKNOWLEDGMENTS
+
+This work is supported by the Fundamental Research Funds for the Central Universities (2019kfyXKJC021) and Microsoft Research Asia.
+
+# REFERENCES
+
+Anish Athalye, Nicholas Carlini, and David A. Wagner. Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In Proceedings of the 35th International Conference on Machine Learning, ICML 2018, pp. 274–283, 2018.
+
+Jacob Buckman, Aurko Roy, Colin Raffel, and Ian J. Goodfellow. Thermometer encoding: One hot way to resist adversarial examples. In 6th International Conference on Learning Representations, ICLR 2018, 2018.
+
+Nicholas Carlini and David A. Wagner. Adversarial examples are not easily detected: Bypassing ten detection methods. In Proceedings of the 10th ACM Workshop on Artificial Intelligence and Security, AISec@CCS 2017, pp. 3–14, 2017a.
+
+Nicholas Carlini and David A. Wagner. Towards evaluating the robustness of neural networks. In 2017 IEEE Symposium on Security and Privacy, SP 2017, pp. 39–57, 2017b.
+
+Adam Coates, Andrew Y. Ng, and Honglak Lee. An analysis of single-layer networks in unsupervised feature learning. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, AISTATS 2011.
+
+Guneet S. Dhillon, Kamyar Azizzadenesheli, Zachary C. Lipton, Jeremy Bernstein, Jean Kossaifi, Aran Khanna, and Animashree Anandkumar. Stochastic activation pruning for robust adversarial defense. In 6th International Conference on Learning Representations, ICLR 2018, 2018.
+
+Gavin Weiguang Ding, Kry Yik Chau Lui, Xiaomeng Jin, Luyu Wang, and Ruitong Huang. On the sensitivity of adversarial robustness to input data distributions. In 7th International Conference on Learning Representations, ICLR 2019, 2019.
+
+Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A. Wichmann, and Wieland Brendel. ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness. In 7th International Conference on Learning Representations, ICLR 2019, 2019.
+
+Ian J. Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial examples. In 3rd International Conference on Learning Representations, ICLR 2015, 2015.
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+Geoffrey Hinton, Li Deng, Dong Yu, George Dahl, Abdel-rahman Mohamed, Navdeep Jaitly, Andrew Senior, Vincent Vanhoucke, Patrick Nguyen, Brian Kingsbury, et al. Deep neural networks for acoustic modeling in speech recognition. IEEE Signal processing magazine, 29, 2012.
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+Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Logan Engstrom, Brandon Tran, and Aleksander Madry. Adversarial examples are not bugs, they are features. CoRR, abs/1905.02175, 2019.
+
+Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. Technical report, Citeseer, 2009.
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+Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012, pp. 1106–1114, 2012.
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+Yandong Li, Lijun Li, Liqiang Wang, Tong Zhang, and Boqing Gong. NATTACK: learning the distributions of adversarial examples for an improved black-box attack on deep neural networks. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, pp. 3866– 3876, 2019.
+
+Jiadong Lin, Chuanbiao Song, Kun He, Liwei Wang, and John E. Hopcroft. Nesterov accelerated gradient and scale invariance for adversarial attacks. In International Conference on Learning Representations, 2020. URL https://openreview.net/forum?id=SJlHwkBYDH.
+
+Yanpei Liu, Xinyun Chen, Chang Liu, and Dawn Song. Delving into transferable adversarial examples and black-box attacks. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings, 2017.
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+Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In 6th International Conference on Learning Representations, ICLR 2018, 2018.
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+Nicolas Papernot, Patrick D. McDaniel, Ian J. Goodfellow, Somesh Jha, Z. Berkay Celik, and Ananthram Swami. Practical black-box attacks against machine learning. In Proceedings of the 2017 ACM on Asia Conference on Computer and Communications Security, AsiaCCS 2017, pp. 506– 519, 2017.
+
+Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry. Adversarially robust generalization requires more data. In Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, pp. 5019–5031, 2018.
+
+Daniel Smilkov, Nikhil Thorat, Been Kim, Fernanda B. Viegas, and Martin Wattenberg. Smooth- ´ grad: removing noise by adding noise. CoRR, abs/1706.03825, 2017.
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+Chuanbiao Song, Kun He, Liwei Wang, and John E. Hopcroft. Improving the generalization of adversarial training with domain adaptation. In 7th International Conference on Learning Representations, ICLR 2019, 2019.
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+Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian J. Goodfellow, and Rob Fergus. Intriguing properties of neural networks. In 2nd International Conference on Learning Representations, ICLR 2014, 2014.
+
+Richard Szeliski. Computer Vision - Algorithms and Applications. Texts in Computer Science. Springer, 2011.
+
+Jonathan Uesato, Brendan O’Donoghue, Pushmeet Kohli, and Aaron van den Oord. Adversarial ¨ risk and the dangers of evaluating against weak attacks. In Proceedings of the 35th International Conference on Machine Learning, ICML 2018, pp. 5032–5041, 2018.
+
+Huaxia Wang and Chun-Nam Yu. A direct approach to robust deep learning using adversarial networks. In 7th International Conference on Learning Representations, ICLR 2019, 2019.
+
+Xiaosen Wang, Kun He, and John E. Hopcroft. AT-GAN: A generative attack model for adversarial transferring on generative adversarial nets. CoRR, abs/1904.07793, 2019.
+
+Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. In Proceedings of the British Machine Vision Conference 2016, BMVC, 2016.
+
+Runtian Zhai, Tianle Cai, Di He, Chen Dan, Kun He, John E. Hopcroft, and Liwei Wang. Adversarially robust generalization just requires more unlabeled data. CoRR, abs/1906.00555, 2019.
+
+Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P. Xing, Laurent El Ghaoui, and Michael I. Jordan. Theoretically principled trade-off between robustness and accuracy. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, pp. 7472–7482, 2019a.
+
+Huan Zhang, Hongge Chen, Zhao Song, Duane S. Boning, Inderjit S. Dhillon, and Cho-Jui Hsieh. The limitations of adversarial training and the blind-spot attack. In 7th International Conference on Learning Representations, ICLR 2019, 2019b.
+
+Tianyuan Zhang and Zhanxing Zhu. Interpreting adversarially trained convolutional neural networks. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, pp. 7502–7511, 2019.
+
+# A HYPER-PARAMETER SETTING
+
+Here we show the details of the training hyper-parameters and the attack hyper-parameters for the experiments.
+
+Training Hyper-parameters. For all training jobs, we use the Adam optimizer with a learning rate of 0.001 and a batch size of 32. For CIFAR-10 and CIFAR-100, we run 79,800 steps for training. For STL-10, we run 29,700 steps for training. For STL-10 and CIFAR-100, the adversarial examples are generated with step size 0.0075, 7 iterations, and $\epsilon = 0 . 0 3$ . For CIFAR-10, the adversarial examples are generated with step size 0.0075, 10 iterations, and $\epsilon = 0 . 0 3$ .
+
+Attack Hyper-parameters. For the PGD attack, we use the same attack parameters as those of the training process. For the CW attack, we use PGD to minimize its loss function with a high confidence parameter $k = 5 0$ ) following the work of Madry et al. (2018). For the $\mathcal { N }$ attack, we set the maximum number of optimization iterations to $T = 2 0 0$ , $b = 3 0 0$ for the sample size, the variance of the isotropic Gaussian $\sigma ^ { 2 } = 0 . 0 1$ , and the learning rate $\eta = 0 . 0 0 8$ .
+
+# B MORE FEATURE VISUALIZATION
+
+We provide more salience maps of the adversarially trained models on sampled images in Figure 4.
+
+![](images/b339bb269ade9b3a8f714984ff893ebffbb2fe065abe469c553f996d532c53d9.jpg)  
+Figure 4: More Salience maps of the four models. For each group of images, we have the original image, and the salience maps of the four models sequentially.

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+    {
+        "type": "text",
+        "text": "ROBUST LOCAL FEATURES FOR IMPROVING THE GENERALIZATION OF ADVERSARIAL TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+            99,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Chuanbiao Song & Kun He $\\mathbf { \\mu } ^ { * } \\mathbf { \\& }$ Jiadong Lin School of Computer Science and Technology Huazhong University of Science and Technology Wuhan, 430074, China {cbsong,brooklet60,jdlin}@hust.edu.cn ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Liwei Wang   \nSchool of Electronics Engineering   \nand Computer Sciences, Peking University   \nPeking, China   \nwanglw@cis.pku.edu.cn ",
+        "bbox": [
+            562,
+            170,
+            843,
+            239
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "John E. Hopcroft Department of Computer Science Cornell University, NY 14853, USA jeh@cs.cornell.edu ",
+        "bbox": [
+            184,
+            261,
+            423,
+            316
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+            353,
+            544,
+            368
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Adversarial training has been demonstrated as one of the most effective methods for training robust models to defend against adversarial examples. However, adversarially trained models often lack adversarially robust generalization on unseen testing data. Recent works show that adversarially trained models are more biased towards global structure features. Instead, in this work, we would like to investigate the relationship between the generalization of adversarial training and the robust local features, as the robust local features generalize well for unseen shape variation. To learn the robust local features, we develop a Random Block Shuffle (RBS) transformation to break up the global structure features on normal adversarial examples. We continue to propose a new approach called Robust Local Features for Adversarial Training (RLFAT), which first learns the robust local features by adversarial training on the RBS-transformed adversarial examples, and then transfers the robust local features into the training of normal adversarial examples. To demonstrate the generality of our argument, we implement RLFAT in currently state-of-the-art adversarial training frameworks. Extensive experiments on STL-10, CIFAR-10 and CIFAR-100 show that RLFAT significantly improves both the adversarially robust generalization and the standard generalization of adversarial training. Additionally, we demonstrate that our models capture more local features of the object on the images, aligning better with human perception. ",
+        "bbox": [
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+            386,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            678,
+            336,
+            694
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Deep learning has achieved a remarkable performance breakthrough on various challenging benchmarks in machine learning fields, such as image classification (Krizhevsky et al., 2012) and speech recognition (Hinton et al., 2012). However, recent studies (Szegedy et al., 2014; Goodfellow et al., 2015) have revealed that deep neural network models are strikingly susceptible to adversarial examples, in which small perturbations around the input are sufficient to mislead the predictions of the target model. Moreover, such perturbations are almost imperceptible to humans and often transfer across diverse models to achieve black-box attacks (Papernot et al., 2017; Liu et al., 2017; Wang et al., 2019; Lin et al., 2020). ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Though the emergence of adversarial examples has received significant attention and led to various defend approaches for developing robust models (Madry et al., 2018; Dhillon et al., 2018; Wang & Yu, 2019; Song et al., 2019; Zhang et al., 2019a), many proposed defense methods provide few benefits for the true robustness but mask the gradients on which most attacks rely (Carlini & Wagner, 2017a; Athalye et al., 2018; Uesato et al., 2018; Li et al., 2019). Currently, one of the best techniques to defend against adversarial attacks (Athalye et al., 2018; Li et al., 2019) is adversarial training (Madry et al., 2018; Zhang et al., 2019a), which improves the adversarial robustness by injecting adversarial examples into the training data. ",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Among substantial works of adversarial training, there still remains a big robust generalization gap between the training data and the testing data (Schmidt et al., 2018; Zhang et al., 2019b; Ding et al., 2019; Zhai et al., 2019). The robustness of adversarial training fails to generalize on unseen testing data. Recent works (Geirhos et al., 2019; Zhang & Zhu, 2019) further show that adversarially trained models capture more on global structure features but normally trained models are more biased towards local features. In intuition, global structure features tend to be robust against adversarial perturbations but hard to generalize for unseen shape variations, instead, local features generalize well for unseen shape variations but are hard to generalize on adversarial perturbation. It naturally raises an intriguing question for adversarial training: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "For adversarial training, is it possible to learn the robust local features , which have better adversarially robust generalization and better standard generalization? ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address this question, we investigate the relationship between the generalization of adversarial training and the robust local features, and advocate for learning robust local features for adversarial training. Our main contributions are as follows: ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• To our knowledge, this is the first work that sheds light on the relationship between adversarial training and robust local features. Specifically, we develop a Random Block Shuffle (RBS) transformation to study such relationship by breaking up the global structure features on normal adversarial examples.   \n• We propose a novel method called Robust Local Features for Adversarial Training (RLFAT), which first learns the robust local features, and then transfers the information of robust local features into the training on normal adversarial examples.   \n• To demonstrate the generality of our argument, we implement RLFAT in two currently stateof-the-art adversarial training frameworks, PGD Adversarial Training (PGDAT) (Madry et al., 2018) and TRADES (Zhang et al., 2019a). Empirical results show consistent and substantial improvements for both adversarial robustness and standard accuracy on several standard datasets. Moreover, the salience maps of our models on images tend to align better with human perception. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 PRELIMINARIES ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In this section, we introduce some notations and provide a brief description on current advanced methods for adversarial attacks and adversarial training. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.1 NOTATION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Let $F ( x )$ be a probabilistic classifier based on a neural network with the logits function $f ( x )$ and the probability distribution $p _ { F } ( \\cdot | x )$ . Let $\\mathcal { L } ( F ; x , y )$ be the cross entropy loss for image classification. The goal of the adversaries is to find an adversarial example $x ^ { \\prime } \\in \\dot { \\mathcal { B } } _ { \\epsilon } ^ { p } ( x ) : = \\{ x ^ { \\prime } : \\| x ^ { \\prime } - x \\| _ { p } \\leq \\epsilon \\}$ in the $\\ell _ { p }$ norm bounded perturbations, where $\\epsilon$ denotes the magnitude of the perturbations. In this paper, we focus on $p = \\infty$ to align with previous works. ",
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+    {
+        "type": "text",
+        "text": "2.2 ADVERSARIAL ATTACKS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Projected Gradient Descent. Projected Gradient Descent (PGD) (Madry et al., 2018) is a stronger iterative variant of Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2015), which iteratively solves the optimization problem $\\begin{array} { r } { \\operatorname* { m a x } _ { x ^ { \\prime } : \\| x ^ { \\prime } - x \\| _ { \\infty } < \\epsilon } \\mathcal { L } \\left( F ; x ^ { \\prime } , y \\right) } \\end{array}$ with a step size $\\alpha$ : ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "equation",
+        "img_path": "images/eccad6509635090fcbd6d1d11158b0f042ab3c907435fa664395ed37e278aeb1.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathrel { \\phantom { = } } x ^ { 0 } \\sim \\mathcal { U } \\left( \\mathcal { B } _ { \\epsilon } ^ { \\infty } ( x ) \\right) , } \\\\ & { \\mathrel { \\phantom { = } } x ^ { t + 1 } = \\Pi _ { \\mathcal { B } _ { \\epsilon } ^ { \\infty } ( x ) } \\left( x ^ { t } - \\alpha \\mathrm { s i g n } \\left( \\nabla _ { x } \\mathcal { L } ( F ; x , y ) | _ { x ^ { t } } \\right) \\right) , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where $\\mathcal { U }$ denotes the uniform distribution, and $\\Pi _ { B _ { \\epsilon } ^ { \\infty } ( x ) }$ indicates the projection of the set $B _ { \\epsilon } ^ { \\infty } ( x )$ ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Carlini-Wagner attack. Carlini-Wagner attack (CW) (2017b) is a sophisticated method to directly solve for the adversarial example $x ^ { a d \\overline { { v } } }$ by using an auxiliary variable $w$ : ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/817469dfc6d2ad3061b4dcac09c7467d1475f1ac70e3434b95e454231f32d6ee.jpg",
+        "text": "$$\nx ^ { a d v } = 0 . 5 \\cdot \\left( \\operatorname { t a n h } ( w ) + 1 \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The objective function to optimize the auxiliary variable $w$ is defined as: ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/28c2c9a5afb82f35efff98a9dc192fe16856aa4ae1ef7c3594a1bf0b83b84611.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { \\boldsymbol { w } } \\left\\| \\boldsymbol { x } ^ { a d v } - \\boldsymbol { x } \\right\\| + c \\cdot \\mathcal { F } \\left( \\boldsymbol { x } ^ { a d v } \\right) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            388,
+            183,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where ${ \\mathcal { F } } ( x ^ { a d v } ) = \\operatorname* { m a x } \\left( f _ { y ^ { \\mathrm { t r u e } } } ( x ^ { a d v } ) - \\operatorname* { m a x } \\left\\{ f _ { i } ( x ^ { a d v } ) : i \\neq y ^ { \\mathrm { t r u e } } \\right\\} , - k \\right)$ . The constant $k$ controls the confidence gap between the adversarial class and the true class. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "N attack. $\\mathcal { N }$ attack (Li et al., 2019) is a derivative-free black-box adversarial attack and it breaks many of the defense methods based on gradient masking. The basic idea is to learn a probability density distribution over a small region centered around the clean input, such that a sample drawn from this distribution is likely to be an adversarial example. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3 ADVERSARIAL TRAINING ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            323,
+            393,
+            338
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Despite a wide range of defense methods, Athalye et al. (2018) and Li et al. (2019) have broken most previous defense methods (Dhillon et al., 2018; Buckman et al., 2018; Wang & Yu, 2019; Zhang et al., 2019a), and revealed that adversarial training remains one of the best defense method. The basic idea of adversarial training is to solve the min-max optimization problem, as shown in Eq. (4): ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/935e52a661c4f623c547135c0f977a6c1992cec413200f4e9f65103c44995aa7.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { F } \\operatorname* { m a x } _ { x ^ { \\prime } : \\| x ^ { \\prime } - x \\| _ { \\infty } < \\epsilon } { \\mathcal { L } } \\left( F ; x ^ { \\prime } , y \\right) .\n$$",
+        "text_format": "latex",
+        "bbox": [
+            395,
+            416,
+            602,
+            444
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here we introduce two currently state-of-the-art adversarial training frameworks. ",
+        "bbox": [
+            173,
+            453,
+            702,
+            468
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "PGD adversarial training. PGD Adversarial Training (PGDAT) (Madry et al., 2018) leverages the PGD attack to generate adversarial examples, and trains only with the adversarial examples. The objective function is formalized as follows: ",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/70ca81c2e923fd0068f6db06554f549cab8a1805e6513f414ce9878b3eff5ca6.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { P G D } } ( F ; x , y ) = \\mathcal { L } ( F ; x _ { \\mathrm { P G D } } ^ { \\prime } , y ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            383,
+            523,
+            614,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $x _ { \\mathrm { P G D } } ^ { \\prime }$ is obtained via the PGD attack on the cross entropy $\\mathcal { L } ( F ; x , y )$ . ",
+        "bbox": [
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+            546,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "TRADES. Zhang et al. (2019a) propose TRADES to specifically maximize the trade-off of adversarial training between adversarial robustness and standard accuracy by optimizing the following regularized surrogate loss: ",
+        "bbox": [
+            174,
+            568,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/b9f2abfd2a78017dbbb4812abeee75f02964026d08b4994ffa5202df34e24249.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { T R A D E S } } ( F ; x , y ) = \\mathcal { L } ( F ; x , y ) + \\lambda D _ { \\mathrm { K L } } \\left( ~ p _ { F } ( \\cdot | x ) ~ \\| ~ p _ { F } \\left( \\cdot | x _ { \\mathrm { P G D } } ^ { \\prime } [ x ] \\right) ~ \\right) ~ , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            256,
+            616,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $x _ { \\mathrm { P G D } } ^ { \\prime } [ x ]$ is obtained via the PGD attack on the KL-divergence $D _ { \\mathrm { K L } } \\left( p _ { F } ( \\cdot | x ) \\parallel p _ { F } \\left( \\cdot | x ^ { \\prime } \\right) \\right)$ , and $\\lambda$ is a hyper-parameter to control the trade-off between adversarial robustness and standard accuracy. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 ROBUST LOCAL FEATURES FOR ADVERSARIAL TRAINING ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Unlike adversarially trained models, normally trained models are more biased towards the local features but vulnerable to adversarial examples (Geirhos et al., 2019). It indicates that, in contrast to global structural features, local features seems be more well-generalized but less robust against adversarial perturbation. Based on the basic observation, in this work, we focus on the learning of robust local features on adversarial training, and propose a novel form of adversarial training called RLFAT that learns the robust local features and transfers the robust local features into the training of normal adversarial examples. In this way, our adversarially trained models not only yield strong robustness against adversarial examples but also show great generalization on unseen testing data. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1 ROBUST LOCAL FEATURE LEARNING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "It’s known that adversarial training tends to capture global structure features so as to increase invariance against adversarial perturbations (Zhang & Zhu, 2019; Ilyas et al., 2019). To advocate for the learning of robust local features during adversarial training, we propose a simple and straightforward image transformation called Random Block Shuffle (RBS) to break up the global structure features of the images, at the same time retaining the local features. Specifically, for an input image, we randomly split the target image into $k$ blocks horizontally and randomly shuffle the blocks, and then we perform the same split-shuffle operation vertically on the resulting image. As illustrated in Figure 1, RBS transformation can destroy the global structure features of the images to some extent and retain the local features of the images. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/545bbbe8e3349378274f7a539c2931e5c170a20bd12f02755cf048bfddab598e.jpg",
+        "image_caption": [
+            "Figure 1: Illustration of the RBS transformation for $k = 3$ . For a better understanding on the RBS transformation, we paint the split image blocks with different colors. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            209,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Then we apply the RBS transformation on adversarial training. Different from normal adversarial training, we use the RBS-transformed adversarial examples rather than normal adversarial examples as the adversarial information to encourage the models to learn robust local features. Note that we only use the RBS transformation as a tool to learn the robust local features during adversarial training and will not use RBS transformation in the inference phase. we refer to the form of adversarial training as RBS Adversarial Training (RBSAT). ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the generality of our argument, we consider two currently state-of-the-art adversarial training frameworks, PGD Adversarial Training (PGDAT) (Madry et al., 2018) and TRADES (Zhang et al., 2019a), to demonstrate the effectiveness of the robust local features. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We use the following loss function as the alternative to the objective function of PGDAT: ",
+        "bbox": [
+            169,
+            535,
+            754,
+            550
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/76592913e9d0e69e67c8c5818aa3286c8baaa25b0e8e02b0ba10a904cf363bf8.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { P G D A T } } ^ { \\mathrm { R L F L } } ( F ; x , y ) = \\mathcal { L } ( F ; \\mathrm { R B S } ( x _ { \\mathrm { P G D } } ^ { \\prime } ) , y ) ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where RBS(·) denotes the RBS transformation; $x _ { \\mathrm { P G D } } ^ { \\prime }$ is obtained via the PGD attack on the cross entropy $\\mathcal { L } ( \\boldsymbol { F } ; \\boldsymbol { x } , \\boldsymbol { y } )$ . ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "imilarly, we use the following loss function as the alternative to the objective function of TRADES: ",
+        "bbox": [
+            189,
+            608,
+            820,
+            622
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5a52b0b73ee93e7f4a91223331fe1ceeeea13f133e1d19c2e5bfa06fe7df0f67.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { T R A D E S } } ^ { \\mathrm { R L F L } } ( F ; x , y ) = \\mathcal { L } ( F ; x , y ) + \\lambda D _ { \\mathrm { K L } } \\left[ p _ { F } ( \\cdot | x ) \\parallel p _ { F } \\left( \\cdot | \\mathrm { R B S } \\left( x _ { \\mathrm { P G D } } ^ { \\prime } [ x ] \\right) \\right) \\right] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            233,
+            626,
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+            643
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $x _ { \\mathrm { P G D } } ^ { \\prime } [ x ]$ is obtained via the PGD attack on the KL-divergence $D _ { \\mathrm { K L } } \\left( p _ { F } ( \\cdot | x ) \\parallel p _ { F } \\left( \\cdot | x ^ { \\prime } \\right) \\right)$ ). ",
+        "bbox": [
+            181,
+            651,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 ROBUST LOCAL FEATURE TRANSFER ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            683,
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+            698
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since the type of input images in the training phase and the inference phase is different (RBS transformed images for training, versus original images for inference), we consider to transfer the knowledge of the robust local features learned by RBSAT to the normal adversarial examples. Specifically, we present a knowledge transfer scheme, called Robust Local Feature Transfer (RLFT). The goal of RLFT is to learn the representation that minimizes the feature shift between the normal adversarial examples and the RBS-transformed adversarial examples. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In particular, we apply RLFT on the logit layer for high-level feature alignment. Formally, the objective functions of robust local feature transfer for PGDAT and TRADES are formalized as follows, respectively: ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/353b0882ac6cfd3e081cd03a1913cec67579379acddd8d2a8c9ad3e761a7fbe9.jpg",
+        "text": "$$\n\\mathcal { L } _ { \\mathrm { P G D A T } } ^ { \\mathrm { R L F T } } ( F ; x , y ) = \\left\\| f ( \\mathrm { R B S } ( x _ { \\mathrm { P G D } } ^ { \\prime } ) ) - f ( x _ { \\mathrm { P G D } } ^ { \\prime } ) \\right\\| _ { 2 } ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            295,
+            844,
+            655,
+            866
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d108be011f2d3f7be3f137e0494c6121363806970c99c955f8c81864c3ec852d.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathcal { L } _ { \\mathrm { T R A D E S } } ^ { \\mathrm { R L F T } } ( F ; x , y ) = \\| f ( \\mathrm { R B S } ( x _ { \\mathrm { P G D } } ^ { \\prime } [ x ] ) ) - f ( x _ { \\mathrm { P G D } } ^ { \\prime } [ x ] ) \\| _ { 2 } ^ { 2 } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            295,
+            883,
+            700,
+            904
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $f ( \\cdot )$ denotes the mapping of the logit layer, and $\\left\\| \\cdot \\right\\| _ { 2 } ^ { 2 }$ denotes the squared Euclidean norm. ",
+        "bbox": [
+            173,
+            907,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3 OVERALL OBJECTIVE FUNCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            103,
+            444,
+            118
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since the quality of robust local feature transfer depends on the quality of the robust local features learned by RBSAT, we integrate RBSAT and RLFT into an end-to-end training framework, which we refer to as RLFAT (Robust Local Features for Adversarial Training). The general training process of RLFAT is summarized in Algorithm 1. Note that the computational cost of RBS transformation (line 7) is negligible in the total computational cost. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Robust Local Features for Adversarial Training (RLFAT). ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            215,
+            640,
+            231
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "1: Randomly initialize network $F ( x )$ ;   \n2: Number of iterations $t \\gets 0$ ;   \n3: repeat   \n4: $t \\gets t + 1$ ;   \n5: Read a minibatch of data $\\{ x _ { 1 } , . . . , x _ { m } \\}$ from the training set;   \n6: Generate the normal adversarial examples $\\{ x _ { 1 } ^ { a d v } , . . . , x _ { m } ^ { \\tilde { a } d v } \\}$   \n7: 1Obtain the RBS-transformed adversarial examples $\\{ \\mathrm { R B S } ( x _ { 1 } ^ { a d v } ) , . . . , \\mathrm { R B S } ( x _ { m } ^ { a d v } ) \\}$ ;   \n8: Calculate the overall loss following Eq. (10).   \n9: Update the parameters of network $F$ through back propagation; ",
+        "bbox": [
+            179,
+            234,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "10: until the training converges. ",
+        "bbox": [
+            176,
+            362,
+            388,
+            375
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We implement RLFAT in two currently state-of-the-art adversarial training frameworks, PGDAT and TRADES, and have new objective functions to learn the robust and well-generalized feature representations, which we call RLF $\\mathrm { \\Delta ^ { \\prime } A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ : ",
+        "bbox": [
+            176,
+            395,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8845c627f5669e55a6b8bc85ac16f558ff292b706c0e67b77ee27a523c08f212.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { \\mathrm { R L F A T } _ { \\mathrm { P } } } ( F ; x , y ) = \\mathcal { L } _ { \\mathrm { P G D A T } } ^ { \\mathrm { R L F L } } ( F ; x , y ) + \\eta \\mathcal { L } _ { \\mathrm { P G D A T } } ^ { \\mathrm { R L F T } } ( F ; x , y ) , } \\\\ & { } \\\\ & { \\mathcal { L } _ { \\mathrm { R L F A T } _ { \\mathrm { T } } } ( F ; x , y ) = \\mathcal { L } _ { \\mathrm { T R A D E S } } ^ { \\mathrm { R L F L } } ( F ; x , y ) + \\eta \\mathcal { L } _ { \\mathrm { T R A D E S } } ^ { \\mathrm { R L F T } } ( F ; x , y ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            284,
+            443,
+            712,
+            505
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\eta$ is a hyper-parameter to balance the two terms. ",
+        "bbox": [
+            176,
+            508,
+            532,
+            523
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            542,
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+            560
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, to validate the effectiveness of RLFAT, we empirically evaluate our two implementations, denoted as $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ , and show that our models make significant improvement on both robust accuracy and standard accuracy on standard benchmark datasets, which provides strong support for our main hypothesis. Codes are available online1. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 EXPERIMENTAL SETUP ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            650,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines. Since most previous defense methods provide few benefit in true adversarially robustness (Athalye et al., 2018; Li et al., 2019), we compare the proposed methods with state-of-theart adversarial training defenses, PGD Adversarial Training (PGDAT) (Madry et al., 2018) and TRADES (Zhang et al., 2019a). ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adversarial setting. We consider two attack settings with the bounded $\\ell _ { \\infty }$ norm: the white-box attack setting and the black-box attack setting. For the white-box attack setting, we consider existing strongest white-box attacks: Projected Gradient Descent (PGD) (Madry et al., 2018) and CarliniWagner attack (CW) (Carlini & Wagner, 2017b). For the black-box attack setting, we perform the powerful black-box attack, $\\mathcal { N }$ attack (Li et al., 2019), on a sample of 1,500 test inputs as it is timeconsuming. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We compare the proposed methods with the baselines on widely used benchmark datasets, namely CIFAR-10 and CIFAR-100 (Krizhevsky & Hinton, 2009). Since adversarially robust generalization becomes increasingly hard for high dimensional data and little training data (Schmidt et al., 2018), we also consider one challenging dataset: STL-10 (Coates et al.), which contains 5, 000 training images, with $9 6 \\times 9 6$ pixels per image. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Neural networks. For STL-10, the architecture we use is a wide ResNet 40-2 (Zagoruyko & Komodakis, 2016). For CIFAR-10 and CIFAR-100, we use a wide ResNet w32-10. For all datasets, we scale the input images to the range of $[ 0 , 1 ]$ . ",
+        "bbox": [
+            176,
+            103,
+            823,
+            147
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Hyper-parameters. To avoid posting much concentrate on optimizing the hyper-parameters, for all datasets, we set the hyper-parameter $\\lambda$ in TRADES as 6, set the hyper-parameter $\\eta$ in RLFATP as 0.5, and set the hyper-parameter $\\eta$ in $\\mathrm { R L F A T _ { T } }$ as 1. For the training jobs of all our models, we set the hyper-parameters $k$ of the RBS transformation as 2. More details about the hyper-parameters are provided in Appendix A. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 EVALUATION RESULTS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            241,
+            370,
+            255
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We first validate our main hypothesis: for adversarial training, is it possible to learn the robust local features that have better adversarially robust generalization and better standard generalization? ",
+        "bbox": [
+            174,
+            266,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In Table 1, we compare the accuracy of $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ with the competing baselines on three standard datasets. The proposed methods lead to consistent and significant improvements on adversarial robustness as well as standard accuracy over the baseline models on all datasets. With the robust local features, $\\mathrm { R L F A T _ { T } }$ achieves better adversarially robust generalization and better standard generalization than TRADES. RLFATP also works similarly, showing a significant improvement on the robustness against all attacks and standard accuracy than PGDAT. ",
+        "bbox": [
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+            301,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1: The classification accuracy $( \\% )$ of defense methods under white-box and black-box attacks on STL-10, CIFAR-10 and CIFAR-100. ",
+        "bbox": [
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+            400,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/7e2edaff72c2e9a8c451b882378802fae559bacd8936b6836995c6184f0fb46a.jpg",
+        "table_caption": [
+            "(a) STL-10. The magnitude of perturbation is 0.03 in $\\ell _ { \\infty }$ norm. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Defense</td><td>No attack</td><td>PGD</td><td>CW</td><td>Nattack</td></tr><tr><td>PGDAT</td><td>67.05</td><td>30.00</td><td>31.97</td><td>34.80</td></tr><tr><td>TRADES</td><td>65.24</td><td>38.99</td><td>38.35</td><td>42.07</td></tr><tr><td>RLFATp</td><td>71.47</td><td>38.42</td><td>38.42</td><td>44.80</td></tr><tr><td>RLFATT</td><td>72.38</td><td>43.36</td><td>39.31</td><td>48.13</td></tr></table>",
+        "bbox": [
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+        "type": "table",
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+        "table_caption": [
+            "(b) CIFAR-10. The magnitude of perturbation is 0.03 in $\\ell _ { \\infty }$ norm. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Defense</td><td>No attack</td><td>PGD</td><td>CW</td><td>Nattack</td></tr><tr><td>PGDAT</td><td>82.96</td><td>46.19</td><td>46.41</td><td>46.67</td></tr><tr><td>TRADES</td><td>80.35</td><td>50.95</td><td>49.80</td><td>52.47</td></tr><tr><td>RLFATp</td><td>84.77</td><td>53.97</td><td>52.40</td><td>54.60</td></tr><tr><td>RLFATT</td><td>82.72</td><td>58.75</td><td>51.94</td><td>54.60</td></tr></table>",
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+    {
+        "type": "table",
+        "img_path": "images/fb426b3107ba88229badef3b38f6458a66c2c6addef40e411a7ecc541c07e032.jpg",
+        "table_caption": [
+            "(c) CIFAR-100. The magnitude of perturbation is 0.03 in $\\ell _ { \\infty }$ norm. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Defense</td><td>No attack</td><td>PGD</td><td>CW</td><td>Nattack</td></tr><tr><td>PGDAT</td><td>55.86</td><td>23.32</td><td>22.87</td><td>22.47</td></tr><tr><td>TRADES</td><td>52.13</td><td>27.26</td><td>24.66</td><td>25.13</td></tr><tr><td>RLFATp</td><td>56.70</td><td>31.99</td><td>29.04</td><td>32.53</td></tr><tr><td>RLFATT</td><td>58.96</td><td>31.63</td><td>27.54</td><td>30.86</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "The results demonstrate that, the robust local features can significantly improve both the adversarially robust generalization and the standard generalization over the state-of-the-art adversarial training frameworks, and strongly support our hypothesis. That is, for adversarial training, it is possible to learn the robust local features, which have better robust and standard generalization. ",
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+    {
+        "type": "text",
+        "text": "4.3 LOSS SENSITIVITY UNDER DISTRIBUTION SHIFT ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Motivation. Ding et al. (2019) and Zhang et al. (2019b) found that the effectiveness of adversarial training is highly sensitive to the “semantic-loss” shift of the test data distribution, such as gamma mapping. To further investigate the performance of the proposed methods, we quantify the smoothness of the models under the distribution shifts of brightness perturbation and gamma mapping. ",
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+    {
+        "type": "text",
+        "text": "Loss sensitivity on brightness perturbation. To quantify the smoothness of models on the shift of the brightness perturbation, we propose to estimate the Lipschitz continuity constant $\\ell _ { \\mathcal { F } }$ by using the gradients of the loss function with respect to the brightness perturbation of the testing data. We adjust the brightness factor of images in the HSV (hue, saturation, value) color space, which we refer to as $x ^ { b } = \\mathcal { V } ( x , \\alpha )$ , where $\\alpha$ denotes the magnitude of the brightness adjustment. The lower the value of $\\ell _ { \\mathcal { F } } ^ { b } ( \\alpha )$ is, the smoother the loss function of the model is: ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "equation",
+        "img_path": "images/47d5e5262f8e95af982b46829621718d01cde4dc8b73bb7c535b7ae0dcb4252b.jpg",
+        "text": "$$\n\\ell _ { \\mathcal { F } } ^ { b } ( \\alpha ) = \\frac { 1 } { m } \\sum _ { i = 1 } ^ { m } \\| \\nabla _ { x } \\mathcal { L } ( F ; \\mathcal { V } ( x _ { i } , \\alpha ) , y _ { t r u e } ) \\| _ { 2 }\n$$",
+        "text_format": "latex",
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Loss sensitivity on gamma mapping. Gamma mapping (Szeliski, 2011) is a nonlinear elementwise operation used to adjust the exposure of images by applying $\\tilde { x } ^ { ( \\gamma ) } = x ^ { \\gamma }$ on the original image $x$ . Similarly, we approximate the loss sensitivity under gamma mapping, by using the gradients of the loss function with respect to the gamma mapping of the testing data. A smaller value indicates a smoother loss function. ",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/cd58b6fa37396d80e498dde4e3633217274140a885d48d3831251b818de2c5d2.jpg",
+        "text": "$$\n\\ell _ { \\mathcal { F } } ^ { g } ( \\gamma ) = \\frac { 1 } { m } \\sum _ { i = 1 } ^ { m } \\| \\nabla _ { x } \\mathcal { L } ( F ; x _ { i } ^ { \\gamma } , y _ { t r u e } ) \\| _ { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Sensitivity analysis. The results for the loss sensitivity of the adversarially trained models under brightness perturbation are reported in Table 2a, where we adopt various magnitude of brightness adjustment on each testing data. In Table 2b, we report the loss sensitivity of adversarially trained models under various gamma mappings. We observe that RLFATT provides the smoothest model under the distribution shifts on all the three datasets. The results suggest that, as compared to PGDAT and TRADES, both $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ show lower gradients of the models on different data distributions, which we can directly attribute to the robust local features. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/3798d8ba9b0cad4c440191d5694c6fec43c45bb446cfe40b9a132188accce025.jpg",
+        "table_caption": [
+            "Table 2: The loss sensitivity of defense methods under different testing data distributions. ",
+            "(a) Loss sensitivity on brightness perturbation for the adversarially trained models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">e(-0.15)/(0.15)</td></tr><tr><td>PGDAT</td><td>TRADES</td><td>RLFATp</td><td>RLFATT</td></tr><tr><td>STL-10</td><td>0.85/0.82</td><td>0.46 / 0.48</td><td>0.32 /0.34</td><td>0.22 / 0.23</td></tr><tr><td>CIFAR-10</td><td>1.41/1.36</td><td>0.88 /0.90</td><td>0.70 /0.71</td><td>0.54 / 0.56</td></tr><tr><td>CIFAR-100</td><td>3.93 /3.66</td><td>2.31/2.12</td><td>1.25 /1.31</td><td>1.00 / 0.98</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/7b9a718e8bf20a98b42f5caf7ce660b8f9ff7df3f08eeece2f31bf610586d199.jpg",
+        "table_caption": [
+            "(b) Loss sensitivity on gamma mapping for the adversarially trained models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Dataset</td><td colspan=\"4\">(0.8)/(1.2)</td></tr><tr><td>PGDAT</td><td>TRADES</td><td>RLFATp</td><td>RLFATT</td></tr><tr><td>STL-10</td><td>0.77 / 0.79</td><td>0.44/0.42</td><td>0.30 /0.29</td><td>0.21/ 0.19</td></tr><tr><td>CIFAR-10</td><td>1.27 / 1.20</td><td>0.84 /0.76</td><td>0.69 /0.62</td><td>0.54 / 0.48</td></tr><tr><td>CIFAR-100</td><td>2.82/2.80</td><td>1.78 / 1.76</td><td>1.09 / 1.01</td><td>0.95 / 0.88</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4 ABLATION STUDIES ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To further gain insights on the performance obtained by the robust local features, we perform ablation studies to dissect the impact of various components (robust local feature learning and robust local feature transfer). As shown in Figure 2, we conduct additional experiments for the ablation studies of $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ on STL-10, CIFAR-10 and CIFAR-100, where we report the standard accuracy over the clean data and the average robust accuracy over all the attacks for each model. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Does robust local feature learning help? We first analyze that as compared to adversarial training on normal adversarial examples, whether adversarial training on RBS-transformed adversarial examples produces better generalization and more robust features. As shown in Figure 2, we observe that Robust Local Features Learning (RLFL) exhibits stable improvements on both standard accuracy and robust accuracy for $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ , providing strong support for our hypothesis. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/84116789f1a34326fcff0ccd94cc1b1ee45dc493726c3fe6ce621fa768a52140.jpg",
+        "image_caption": [
+            "Figure 2: Ablation studies for $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ to investigate the impact of Robust Local Feature Learning (RLFL) and Robust Local Feature Transfer (RLFT). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Does robust local feature transfer help? We further add Robust Local Feature Transfer (RLFT), the second term in Eq. (10), to get the overall loss of RLFAT. The robust accuracy further increases on all datasets for RLFATP and RLFATT. The standard accuracy further increases also, except for $\\mathrm { R L F A T _ { P } }$ on CIFAR-100, but it is still clearly higher than the baseline model PGDAT. It indicates that transferring the robust local features into the training of normal adversarial examples does help promote the standard accuracy and robust accuracy in most cases. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5 VISUALIZING THE SALIENCE MAPS ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            542,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We would like to investigate the features of the input images that the models are mostly focused on. Following the work of Zhang & Zhu (2019), we generate the salience maps using SmoothGrad (Smilkov et al., 2017) on STL-10 dataset. The key idea of SmoothGrad is to average the gradients of class activation with respect to noisy copies of an input image. As illustrated in Figure 3, all the adversarially trained models basically capture the global structure features of the object on the images. As compared to PGDAT and TRADES, both $\\mathrm { R L F A T _ { P } }$ and $\\mathrm { R L F A T _ { T } }$ capture more local feature information of the object, aligning better with human perception. Note that the images are correctly classified by all these models. For more visualization results, see Appendix B. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION AND FUTURE WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            703,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Differs to existing adversarially trained models that are more biased towards the global structure features of the images, in this work, we hypothesize that robust local features can improve the generalization of adversarial training. To validate this hypothesis, we propose a new stream of adversarial training approach called Robust Local Features for Adversarial Training (RLFAT) and implement it in currently state-of-the-art adversarial training frameworks, PGDAT and TRADES. We provide strong empirical support for our hypothesis and show that the proposed methods based on RLFAT not only yield better standard generalization but also promote the adversarially robust generalization. Furthermore, we show that the salience maps of our models on images tend to align better with human perception, uncovering certain unexpected benefit of the robust local features for adversarial training. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our findings open a new avenue for improving adversarial training, whereas there are still a lot to explore along this avenue. First, is it possible to explicitly disentangle the robust local features from the perspective of feature disentanglement? What is the best way to leverage the robust local features? Second, from a methodological standpoint, the discovered relationship may also serve as an inspiration for new adversarial defenses, where not only the robust local features but also the global information is taken into account, as the global information is useful for some tasks. These questions are worth investigation in future work, and we hope that our observations on the benefit of robust local features will inspire more future development. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/23a16e8d2e9f01acf82aa7f4b470717d2eea4c8084747ef48724840b0873c42d.jpg",
+        "image_caption": [
+            "Figure 3: Salience maps of the four models on sampled images. For each group of images, we have the original image, and the salience maps of the four models sequentially. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "This work is supported by the Fundamental Research Funds for the Central Universities (2019kfyXKJC021) and Microsoft Research Asia. ",
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+    },
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+        "text": "Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric P. Xing, Laurent El Ghaoui, and Michael I. Jordan. Theoretically principled trade-off between robustness and accuracy. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, pp. 7472–7482, 2019a. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Huan Zhang, Hongge Chen, Zhao Song, Duane S. Boning, Inderjit S. Dhillon, and Cho-Jui Hsieh. The limitations of adversarial training and the blind-spot attack. In 7th International Conference on Learning Representations, ICLR 2019, 2019b. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Tianyuan Zhang and Zhanxing Zhu. Interpreting adversarially trained convolutional neural networks. In Proceedings of the 36th International Conference on Machine Learning, ICML 2019, pp. 7502–7511, 2019. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A HYPER-PARAMETER SETTING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            457,
+            118
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Here we show the details of the training hyper-parameters and the attack hyper-parameters for the experiments. ",
+        "bbox": [
+            173,
+            133,
+            823,
+            161
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Training Hyper-parameters. For all training jobs, we use the Adam optimizer with a learning rate of 0.001 and a batch size of 32. For CIFAR-10 and CIFAR-100, we run 79,800 steps for training. For STL-10, we run 29,700 steps for training. For STL-10 and CIFAR-100, the adversarial examples are generated with step size 0.0075, 7 iterations, and $\\epsilon = 0 . 0 3$ . For CIFAR-10, the adversarial examples are generated with step size 0.0075, 10 iterations, and $\\epsilon = 0 . 0 3$ . ",
+        "bbox": [
+            174,
+            169,
+            825,
+            238
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Attack Hyper-parameters. For the PGD attack, we use the same attack parameters as those of the training process. For the CW attack, we use PGD to minimize its loss function with a high confidence parameter $k = 5 0$ ) following the work of Madry et al. (2018). For the $\\mathcal { N }$ attack, we set the maximum number of optimization iterations to $T = 2 0 0$ , $b = 3 0 0$ for the sample size, the variance of the isotropic Gaussian $\\sigma ^ { 2 } = 0 . 0 1$ , and the learning rate $\\eta = 0 . 0 0 8$ . ",
+        "bbox": [
+            173,
+            246,
+            825,
+            315
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "B MORE FEATURE VISUALIZATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            335,
+            483,
+            352
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "We provide more salience maps of the adversarially trained models on sampled images in Figure 4. ",
+        "bbox": [
+            173,
+            367,
+            821,
+            382
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "image",
+        "img_path": "images/b339bb269ade9b3a8f714984ff893ebffbb2fe065abe469c553f996d532c53d9.jpg",
+        "image_caption": [
+            "Figure 4: More Salience maps of the four models. For each group of images, we have the original image, and the salience maps of the four models sequentially. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            173,
+            393,
+            823,
+            862
+        ],
+        "page_idx": 11
+    }
+]

parse/train/HJ0NvFzxl/HJ0NvFzxl.md

@@ -0,0 +1,422 @@
+# LEARNING GRAPHICAL STATE TRANSITIONS
+
+Daniel D. Johnson   
+Department of Computer Science   
+Harvey Mudd College   
+301 Platt Boulevard   
+ddjohnson@hmc.edu
+
+# ABSTRACT
+
+Graph-structured data is important in modeling relationships between multiple entities, and can be used to represent states of the world as well as many data structures. Li et al. (2016) describe a model known as a Gated Graph Sequence Neural Network (GGS-NN) that produces sequences from graph-structured input. In this work I introduce the Gated Graph Transformer Neural Network (GGTNN), an extension of GGS-NNs that uses graph-structured data as an intermediate representation. The model can learn to construct and modify graphs in sophisticated ways based on textual input, and also to use the graphs to produce a variety of outputs. For example, the model successfully learns to solve almost all of the bAbI tasks (Weston et al., 2016), and also discovers the rules governing graphical formulations of a simple cellular automaton and a family of Turing machines.
+
+# 1 INTRODUCTION
+
+Many different types of data can be formulated using a graph structure. One form of data that lends itself to a graphical representation is data involving relationships (edges) between entities (nodes). Abstract maps of places and paths between them also have a natural graph representation, where places are nodes and paths are edges. In addition, many data structures can be expressed in graphical form, including linked lists and binary trees.
+
+Substantial research has been done on producing output when given graph-structured input (Kashima et al., 2003; Shervashidze et al., 2011; Perozzi et al., 2014; Bruna et al., 2013; Duvenaud et al., 2015). Of particular relevance to this work are Graph Neural Networks (Gori et al., 2005; Scarselli et al., 2009), or GNNs, which extend recursive neural networks by assigning states to each node in a graph based on the states of adjacent nodes. Recently Li et al. (2016) have modified GNNs to use gated state updates and to produce output sequences. The resulting networks, called GG-NNs and GGS-NNs, are successful at solving a variety of tasks with graph-structured input.
+
+The current work further builds upon GG-NNs and GGS-NNs by allowing graph-structured intermediate representations, as well as graph-structured outputs. This is accomplished using a more flexible graph definition, along with a set of graph transformations which take a graph and other information as input and produce a modified version of the graph. This work also introduces the Gated Graph Transformer Neural Network model (GGT-NN), which combines these transformations with a recurrent input model to incrementally construct a graph given natural language input, and can either produce a final graph representing its current state, or use the graph to produce a natural language output.
+
+Extending GG-NNs in this way opens up a wide variety of applications. Since many types of data can be naturally expressed as a graph, it is possible to train a GGT-NN model to manipulate a meaningful graphical internal state. In this paper I demonstrate the GGT-NN model on the bAbI task dataset, which contains a set of stories about the state of the world. By encoding this state as a graph and providing these graphs to the model at training time, a GGT-NN model can be trained to construct the correct graph from the input sentences and then answer questions based on this internal graph. I also demonstrate that this architecture can learn complex update rules by training it to model a simple 1D cellular automaton and arbitrary 4-state Turing machines. This requires the network to learn how to transform its internal state based on the rules of each task.
+
+![](images/ef5cd43c594e7ef31036550081983820b4a1577a09156a006285b8662ff24e07.jpg)  
+Figure 1: Diagram of the differentiable encoding of a graphical structure, as described in section 3. On the left, the desired graph we wish to represent, in which there are 6 node types (shown as blue, purple, red, orange, green, and yellow) and two edge types (shown as blue/solid and red/dashed). Node 3 and the edge between nodes 6 and 7 have a low strength. On the right, depictions of the node and edge matrices: annotations, strengths, state, and connectivity correspond to $\mathbf { x } _ { v }$ , $s _ { v }$ , $\mathbf { h } _ { v }$ , and $\mathcal { C }$ , respectively. Saturation represents the value in each cell, where white represents 0, and fully saturated represents 1. Note that each node’s annotation only has a single nonzero entry, corresponding to each node having a single well-defined type, with the exception of node 3, which has an annotation that does not correspond to a single type. State vectors are shaded arbitrarily to indicate that they can store network-determined data. The edge connectivity matrix $\mathcal { C }$ is three dimensional, indicated by stacking the blue-edge cell on top of the red-edge cell for a given sourcedestination pair. Also notice the low strength for cell 3 in the strength vector and for the edge between node 6 and node 7 in the connectivity matrix.
+
+# 2 BACKGROUND
+
+# 2.1 GRU
+
+Gated Recurrent Units (GRU) are a type of recurrent network cell introduced by Cho et al. (2014). Each unit uses a reset gate $r$ and an update gate $z$ , and updates according to
+
+$$
+\begin{array} { r l r l } & { \mathbf { r } ^ { ( t ) } = \sigma \left( \mathbf { W } _ { r } \mathbf { x } ^ { ( t ) } + \mathbf { U } _ { r } \mathbf { h } ^ { ( t - 1 ) } + \mathbf { b } _ { r } \right) \quad } & & { \mathbf { z } ^ { ( t ) } = \sigma \left( \mathbf { W } _ { z } \mathbf { x } ^ { ( t ) } + \mathbf { U } _ { z } \mathbf { h } ^ { ( t - 1 ) } + \mathbf { b } _ { z } \right) } \\ & { \widetilde { \mathbf { h } } ^ { ( t ) } = \phi \left( \mathbf { W } \mathbf { x } + \mathbf { U } \left( \mathbf { r } ^ { ( t ) } \odot \mathbf { h } ^ { ( t - 1 ) } \right) + \mathbf { b } \right) \quad } & & { \mathbf { h } ^ { ( t ) } = \mathbf { z } \odot \mathbf { h } ^ { ( t - 1 ) } + \left( 1 - \mathbf { z } \right) \odot \widetilde { \mathbf { h } } ^ { ( t ) } } \end{array}
+$$
+
+where $\sigma$ is the logistic sigmoid function, $\phi$ is an activation function (here tanh is used), $\mathbf { x } ^ { ( t ) }$ is the input vector at timestep $t$ , $\mathbf { h } ^ { ( t ) }$ is the hidden output vector at timestep $t$ , and ${ \bf W } , { \bf U } , { \bf W } _ { r } , { \bf U } _ { r } , { \bf W } _ { z }$ , $\mathbf { U } _ { z }$ , b, ${ \bf b } _ { r }$ and $\mathbf { b } _ { z }$ are learned weights and biases. Note that $\odot$ denotes elementwise multiplication.
+
+# 2.2 GG-NN AND GGS-NN
+
+The Gated Graph Neural Network (GG-NN) is a form of graphical neural network model described by Li et al. (2016). In a GG-NN, a graph $\mathcal { G } = ( \nu , \mathcal { E } )$ consists of a set $V$ of nodes $v$ with unique values and a set $\mathcal { E }$ of directed edges $e = ( v , v ^ { \prime } ) \in \mathcal { V } \times \mathcal { V }$ oriented from $v$ to $v ^ { \prime }$ . Each node has an annotation $\mathbf { x } _ { v } \in \mathbb { R } ^ { N }$ and a hidden state $\mathbf { h } _ { v } \in \mathbb { R } ^ { D }$ , and each edge has a type $y _ { e } \in \{ 1 , \cdots , M \}$ .
+
+GG-NNs operate by first initializing the state $\mathbf { h } _ { v }$ of each node to correspond to the annotation $\mathbf { x } _ { v }$ . Then, a series of propagation steps occur. In each step, information is transferred between nodes across the edges, and the types of edge determine what information is sent. Each node sums the input it receives from all adjacent nodes, and uses that to update its own internal state, in the same manner as a GRU cell. Finally, the states of all nodes are used either to create a graph-level aggregate output, or to classify each individual node.
+
+GGS-NNs extend GG-NNs by performing a large number of propagation-output cycles. At each stage, two versions of the GG-NN propagation process are run. The first is used to predict an output for that timestep, and the second is used to update the annotations of the nodes for the next timestep. This allows GGS-NNs to predict a sequence of outputs from a single graph.
+
+![](images/7d21775c1c752781426ffcd20b664960dc69107bea3e632b40212f682b3ee84f.jpg)  
+Figure 2: Summary of the graph transformations. Input and output are represented as gray squares. a) Node addition $( \mathcal { T } _ { \mathrm { a d d } } )$ , where the input is used by a recurrent network (white box) to produce new nodes, of varying annotations and strengths. b) Node state update $( \mathcal { T } _ { \mathbf { h } } )$ , where each node receives input (dashed line) and updates its internal state. c) Edge update $( \mathcal { T } _ { \mathcal { C } } )$ , where each existing edge (colored) and potential edge (dashed) is added or removed according to the input and states of the adjacent nodes (depicted as solid arrows meeting at circles on each edge). d) Propagation $( \mathcal { T } _ { \mathrm { p r o p } } )$ , where nodes exchange information along the current edges, and update their states. e) Aggregation $( \mathcal { T } _ { \mathrm { r e p r } } )$ , where a single representation is created using an attention mechanism, by summing information from all nodes weighted by relevance (with weights shown by saturation of arrows).
+
+# 3 DIFFERENTIABLE GRAPH TRANSFORMATIONS
+
+In this section, I describe some modifications to the graph structure to make it fully differentiable, and then propose a set of transformations which can be applied to a graph structure in order to transform it. In particular, I redefine a graph $\mathcal { G } = ( \nu , \mathcal { C } ) \in \Gamma$ as a set $V$ of nodes $v$ , and a connectivity matrix $\mathcal { C } \in \mathbb { R } ^ { | \mathcal { V } | \times | \mathcal { V } | \times Y }$ , where $Y$ is the number of possible edge types. As before, each node has an annotation $\mathbf { x } _ { v } \in \mathbb { R } ^ { N }$ and a hidden state $\mathbf { h } _ { v } \in \mathbb { R } ^ { D }$ . However, there is an additional constraint that $\textstyle \sum _ { j = 1 } ^ { N } x _ { v , j } = 1$ . One can then interpret $x _ { v , j }$ as the level of belief that $v$ should have type $j$ out of $N$ possible node types. Each node also has a strength $s _ { v } \in [ 0 , 1 ]$ . This represents the level of belief that node $v$ should exist, where $s _ { v } = 1$ means the node exists, and $s _ { v } = 0$ indicates that the node should not exist and thus should be ignored.
+
+Similarly, elements of $\mathcal { C }$ are constrained to the range $[ 0 , 1 ]$ , and thus one can interpret $\mathcal { C } _ { v , v ^ { \prime } , y }$ as the level of belief that there should be a directed edge of type $y$ from $v$ to $v ^ { \prime }$ . (Note that it is possible for there to be edges of multiple types between the same two nodes $v$ and $v ^ { \prime }$ , i.e. it is possible for $\mathcal { C } _ { v , v ^ { \prime } , y } = \mathcal { C } _ { v , v ^ { \prime } , y ^ { \prime } } = 1$ where $y \ne y ^ { \prime }$ .) Figure 1 shows the values of $\mathbf { x } _ { v }$ , $s _ { v }$ , $\mathbf { h } _ { v }$ , and $\mathcal { C }$ corresponding to a particular graphical structure.
+
+There are five classes of graph transformation:
+
+a) Node addition $( \mathcal { T } _ { \mathrm { a d d } } )$ , which modifies a graph by adding new nodes and assigning them annotations $\mathbf { x } _ { v }$ and strengths $s _ { v }$ based on an input vector.   
+b) Node state update $( \mathcal { T } _ { \mathbf { h } } )$ , which modifies the internal state of each node using an input vector (similar to a GRU update step). Optionally, different input can be given to nodes of each type, based on direct textual references to specific node types. This version is called a direct reference update $( \mathcal { T } _ { \mathbf { h } , \mathrm { d i r e c t } } )$ .   
+c) Edge update $( \mathcal { T } _ { \mathcal { C } } )$ , which modifies the edges between each pair of nodes based on the internal states of the two nodes and an external input vector.   
+d) Propagation $( \mathcal { T } _ { \mathrm { p r o p } } )$ , which allows nodes to trade information across the existing edges and then update their internal states based on the information received.   
+e) Aggregation $( \mathcal { T } _ { \mathrm { r e p r } } )$ , which uses an attention mechanism to select relevant nodes and then generates a graph-level output.
+
+Each transformation has its own trainable parameters. Together, these transformations can be combined to process a graph in complex ways. An overview of these operations is shown in Figure 2. For details about the implementation of each of these transformations, see Appendix B.
+
+# 4 GATED GRAPH TRANSFORMER NEURAL NETWORK (GGT-NN)
+
+In this section I introduce the Gated Graph Transformer Neural Network (GGT-NN), which is constructed by combining a series of these transformations. Depending on the configuration of the transformations, a GGT-NN can take textual or graph-structured input, and produce textual or graphstructured output. Here I describe one particular GGT-NN configuration, designed to build and modify a graph based on a sequence of input sentences, and then produce an answer to a query.
+
+<table><tr><td colspan="3">Algorithm1 Graph Transformation Pseudocode</td></tr><tr><td colspan="2">1:g↑α</td><td>11: G←Tada(G,[i(k） hgd])</td></tr><tr><td colspan="2">2:for k from 1 to K do</td><td>12: 9←Te(g,i（𝑘)</td></tr><tr><td>3:</td><td>9 ←Th(g,i(k))</td><td>13:end for</td></tr><tr><td>4:</td><td>if direct reference enabled then</td><td>14: 9 ← Tuery(G,iquery)</td></tr><tr><td>5:</td><td>9 ← Th,direct(G,D(𝑘))</td><td>15:if direct reference enabled then</td></tr><tr><td>6:</td><td>end if</td><td></td></tr><tr><td>7:</td><td>if intermediate propagation enabled then</td><td>17:end if</td></tr><tr><td>8:</td><td>9 ← Tprop(S)</td><td>18:9←T（G)）</td></tr><tr><td>9:</td><td>end if</td><td>19: hswer ←Trper(G)）</td></tr><tr><td>10:</td><td>hgd ←Trepr(9)</td><td>20: return foutput(hanswer)</td></tr></table>
+
+When run, the model performs the following: For each sentence $k$ , each word is converted to a one-hot vector $\mathbf { w } _ { l } ^ { ( k ) }$ , and the sequence of words (of length $L$ ) is passed through a GRU layer to produce a sequence of partial-sentence representation vectors ${ \bf p } _ { l } ^ { ( k ) }$ . The full sentence representation vector $\mathbf { i } ^ { ( k ) }$ is initialized to the last partial representation vector $\mathbf { p } _ { L } ^ { ( k ) }$ . Furthermore, a direct-reference input matrix $\mathbf { D } ^ { ( k ) }$ is set to the sum of partial representation vectors corresponding to the words that directly reference a node type, .e. $\begin{array} { r } { \mathbf { D } _ { n } ^ { ( k ) } = \sum _ { l \in R _ { n } } \mathbf { p } _ { l } ^ { ( k ) } } \end{array}$ where $R _ { n }$ is the set of words in sentence $k$ $n$ . This acts like an attention mechanism, by accumulating the partial representation vectors for the words that directly reference each type, and masking out the vectors corresponding to other words.
+
+Next, a series of graph transformations are applied, as depicted in Algorithm 1. Depending on the task, direct reference updates and per-sentence propagation can be enabled or disabled. The output function $f _ { \mathrm { o u t p u t } }$ will depend on the specific type of answer desired. If the answer is a single word, $f _ { \mathrm { o u t p u t } }$ can be a multilayer perceptron followed by a softmax operation. If the answer is a sequence of words, $f _ { \mathrm { o u t p u t } }$ can use a recurrent network (such as a GRU) to produce a sequence of outputs. Note that transformations with different superscripts $\mathcal { T } _ { \mathbf { h } }$ and $\mathcal { T } _ { \mathbf { h } } ^ { \mathrm { q u e r y } }$ , for instance) refer to similar transformations with different learned weights.
+
+Since the processing of the input and all of the graph transformations are differentiable, at this point the network output can be compared with the correct output for that query and used to update the network parameters, including both the GRU parameters used when processing the input and the internal weights associated with each transformation.
+
+# 4.1 SUPERVISION
+
+As with many supervised models, one can evaluate the loss based on the likelihood of producing an incorrect answer, and then minimize the loss by backpropagation. However, based on initial experiments, the model appeared to require additional supervision to extract meaningful graphstructured data. To provide this additional supervision, I found it beneficial to provide the correct graph at each timestep and train the network to produce that graph. This occurs in two stages, first when new nodes are proposed, and then when edges are adjusted. For the edge adjustment, the edge loss between a correct edge matrix $\mathcal { C } ^ { * }$ and the computed edge matrix $\mathcal { C }$ is given by
+
+$$
+{ \mathcal { L } } _ { \mathrm { e d g e } } = - { \mathcal { C } } ^ { * } \cdot \ln ( { \mathcal { C } } ) - ( 1 - { \mathcal { C } } ^ { * } ) \cdot \ln ( 1 - { \mathcal { C } } ) .
+$$
+
+The node adjustment is slightly more complex. Multiple nodes are added in each timestep, but the order of those nodes is arbitrary, and only their existence is important. Thus it should be possible for the network to determine the optimal ordering of the nodes. In fact, this is important because there is no guarantee that the nodes will be ordered consistently in the training data.
+
+Vinyals et al. (2016) demonstrate a simple method for training a network to output unordered sets: the network produces a sequence of outputs, and these outputs are compared with the closest ordering of the training data, i.e., the ordering of the training data which would produce the smallest loss when compared with the network output. Vinyals et al. show that when using this method, the network arbitrarily chooses an ordering which may not be the optimal ordering for the task. However, in this case any ordering should be sufficient, and I found the arbitrary orderings selected in this way to work well in practice. In particular, letting s∗π(v) and $\mathbf { x } _ { \pi ( v ) } ^ { * }$ denote the correct strength and annotations of node $v$ under ordering $\pi$ , the loss becomes
+
+$$
+\mathcal { L } _ { \mathrm { n o d e } } = - \operatorname* { m a x } _ { \pi } \sum _ { v = | \mathcal { V } _ { \mathrm { o d d } } | + 1 } ^ { | \mathcal { V } _ { \mathrm { n e v } } | } s _ { \pi ( v ) } ^ { * } \ln ( s _ { v } ) + ( 1 - s _ { \pi ( v ) } ^ { * } ) \ln ( 1 - s _ { v } ) + \mathbf { x } _ { \pi ( v ) } ^ { * } \cdot \ln ( \mathbf { x } _ { v } ) .
+$$
+
+At this point the correct values C∗, s∗π(v) a nd $\mathbf { x } _ { \pi ( v ) } ^ { * }$ are substituted into the graph for further processing. Note that only the edges and the new nodes are replaced by the supervision. The hidden states of all existing nodes are propagated without adjustment.
+
+# 4.2 OTHER TRANSFORMATION CONFIGURATIONS
+
+The structure described in Algorithm 1 is designed for question-answering tasks. However, due to the composability of the individual graph transformations, other configurations could be used to solve other tasks that operate on structured data.
+
+For instance, if a task consists of tracking relationships between a fixed set of objects, one could construct a version of the model that does not use the new-nodes transformation $( \mathcal { T } _ { \mathrm { a d d } } )$ , but instead only modifies edges. If the task was to extract information from an existing graph, a structure similar to the GGS-NNs could be built by using only the propagation and aggregation transformations. If the task was to construct a graph based on textual input, the query processing steps could be omitted, and instead the final graph could be returned for processing. And if information should be gathered from a sequence of graphs instead of from a single graph, the query processing steps could be modified to run in parallel on the full sequence of graphs and extract information from each graph. This last modification is demonstrated in Appendix D.
+
+# 5 EXPERIMENTS
+
+# 5.1 BABI TASKS
+
+I evaluated the GGT-NN model on the bAbI tasks, a set of simple natural-language tasks, where each task is structured as a sequence of sentences followed by a query (Weston et al., 2016). The generation procedure for the bAbI tasks includes a “Knowledge” object for each sentence, representing the current state of knowledge after that sentence. I exposed this knowledge object in graph format, and used this to train a GGT-NN in supervised mode. The knowledge object provides names for each node type, and direct reference was performed based on these names: if a word in the sentence matched a node type name, it was parsed as a direct reference to all nodes of that type. For details on this graphical format, see Appendix C.
+
+# 5.1.1 ANALYSIS AND RESULTS
+
+I trained two versions of the GGT-NN model for each task: one with and one without direct reference. Tasks 3 and 5, which involve a complex temporal component, were trained with intermediate propagation, whereas all of the other tasks were not because the structure of the tasks made such complexity unnecessary. Most task models were configured to output a single word, but task 19 (pathfinding) used a GRU to output multiple words, and task 8 (listing) was configured to output a strength for each possible word to allow multiple words to be selected without having to consider ordering.
+
+Results are shown in Tables 1 and 2. The GGT-NN model was able to reach $9 5 \%$ accuracy in all but one of the tasks, and reached $100 \%$ accuracy in eleven of them (see Table 2). Additionally, for fourteen of the tasks, the model was able to reach $9 5 \%$ accuracy using 500 or fewer of the 1000 training examples (see Table 1).
+
+The only task that the GGT-NN was unable to solve with $9 5 \%$ accuracy was task 17 (Positional Reasoning), for which the model was not able to attain a high accuracy. Task 17 has a larger number of possible entities than the other tasks: each entity consists of a color (chosen from five options) and a shape (chosen from four shapes), for a total of 20 unique entities that must be represented separately. Additionally, the stories are much shorter than those in other tasks (2 facts for each set of 8 questions). It is likely that these additional complexities caused the network performance to suffer.
+
+Table 1: Number of training examples needed before the GGT-NN model could attain $\leq 5 \%$ error on each of the bAbI tasks. Experiments were run with 50, 100, 250, 500, and 1000 examples. “GGT-NN $^ +$ direct ref.” denotes the performance of the model with direct reference, and “GGTNN” denotes the performance of the model without direct reference. Dashes indicate that the model was unable to reach the desired accuracy with 1000 examples.   
+
+<table><tr><td>Task</td><td>CE-LNN rteeet CE-LNN</td><td>Task</td><td>CE-LNN aatteeat</td><td>CC-LNN</td></tr><tr><td></td><td></td><td>11-Basic Coreference</td><td>100</td><td>1000</td></tr><tr><td>1 - Single Supporting Fact 2 - Two Supporting Facts</td><td>100 1000 250</td><td>12 - Conjunction</td><td>500</td><td>1000</td></tr><tr><td>3 - Three Supporting Facts</td><td>= 1000</td><td>13 - Compound Coref.</td><td>100</td><td>1000</td></tr><tr><td>4 - Two Arg.Relations</td><td>1 1000 1000</td><td>14-Time Reasoning</td><td>1000</td><td>-</td></tr><tr><td>5 - Three Arg.Relations</td><td>500</td><td>15 -Basic Deduction</td><td>500</td><td>500</td></tr><tr><td>6 - Yes/No Questions</td><td>100 1</td><td>16 -Basic Induction</td><td>100</td><td>500</td></tr><tr><td>7 - Counting</td><td>250 =</td><td>17 -Positional Reasoning</td><td>-</td><td>1</td></tr><tr><td>8 -Lists/Sets</td><td>250 1000</td><td>18 - Size Reasoning</td><td>1000</td><td>=</td></tr><tr><td>9 - Simple Negation</td><td>250 1</td><td>19 -Path Finding</td><td>500</td><td>1</td></tr><tr><td>10 - Indefinite Knowledge</td><td>1000 1</td><td>20 -Agent&#x27;s Motivations</td><td>250</td><td>250</td></tr></table>
+
+<table><tr><td></td><td colspan="6">1,000 examples</td><td colspan="5">10,000 examples</td></tr><tr><td>Task</td><td>CECLNN pa teeeer</td><td>CE-LNN</td><td>JLST</td><td>NNLIN</td><td>NIANNN</td><td>Greee</td><td>WLN</td><td>*ANNNN JLN-I</td><td>ONG</td><td>+NNI</td><td>Jeeg</td></tr><tr><td></td><td>0</td><td>0.7</td><td>50.0</td><td>0</td><td>0</td><td>8</td><td>招</td><td></td><td>0</td><td>0</td><td>0</td></tr><tr><td>１２３４</td><td>0</td><td>5.7</td><td>80.0</td><td>0</td><td>8.3</td><td></td><td></td><td></td><td>0.4</td><td>0.3</td><td>0.1</td></tr><tr><td></td><td>1.3</td><td>12.0</td><td>80.0</td><td>0</td><td>40.3</td><td></td><td>3</td><td>2.1</td><td>1.8</td><td>1.1</td><td>4.1</td></tr><tr><td></td><td>1.2</td><td>2.2</td><td>39.0</td><td>0</td><td>2.8</td><td>1.4</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>5</td><td>1.6</td><td>10.9</td><td>30.0</td><td>2.0</td><td>13.1</td><td>4.6</td><td>0.8</td><td>0.8</td><td>0.8</td><td>0.5</td><td>0.3</td></tr><tr><td>6</td><td>0</td><td>7.7</td><td>52.0</td><td>0</td><td>7.6</td><td>30.0</td><td>17.1 1.5</td><td>0.1</td><td>0</td><td>0</td><td>0.2</td></tr><tr><td>7</td><td>0</td><td>5.6</td><td>51.0</td><td>15.0</td><td>17.3</td><td>22.3</td><td>17.8 60</td><td>2.0</td><td>0.6</td><td>2.4</td><td>0</td></tr><tr><td>8</td><td>0</td><td>3.3</td><td>55.0</td><td>9.0</td><td>10.0</td><td>19.2</td><td>13.8 1.7</td><td>0.9</td><td>0.3</td><td>0</td><td>0.5</td></tr><tr><td>9</td><td>0</td><td>11.6</td><td>36.0</td><td>0</td><td>13.2</td><td>31. 1.5</td><td>16.4 0.6</td><td>0.3</td><td>0.2</td><td>0</td><td>0.1</td></tr><tr><td>10</td><td>3.4</td><td>28.6</td><td>56.0</td><td>2.0</td><td>15.1</td><td>15.6</td><td>16.6 19.8</td><td>0</td><td>0.2</td><td>0</td><td>0.6</td></tr><tr><td>11</td><td>0</td><td>0.2</td><td>28.0</td><td>0</td><td>0.9</td><td>8.0</td><td>15.2</td><td>0</td><td>0</td><td>0</td><td>0.3</td></tr><tr><td>12</td><td>0.1</td><td>0.7</td><td>26.0</td><td>0</td><td>0.2</td><td>0.8</td><td>8.9 6.2</td><td>0</td><td>0</td><td>0.2</td><td>0</td></tr><tr><td>13</td><td>0</td><td>0.8</td><td>6.0</td><td>0</td><td>0.4</td><td>9.0</td><td>7.4 7.5</td><td>0</td><td>0</td><td>0</td><td>1 1.3</td></tr><tr><td>14</td><td>2.2</td><td>55.1</td><td>73.0</td><td>1.0</td><td>1.7</td><td>62.9</td><td>24.2 17.5</td><td>0.2</td><td>0.4</td><td>0.2</td><td>0</td></tr><tr><td>15</td><td>0.9</td><td>0</td><td>79.0</td><td>0</td><td>0</td><td>57. .8</td><td>47. 7.0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>16</td><td>0</td><td>0</td><td>77.0</td><td>0</td><td>1.3</td><td>53.2</td><td>49.6 3.6</td><td>51.</td><td>S</td><td></td><td>0.2</td></tr><tr><td>17</td><td>34</td><td>48.0</td><td>49.0</td><td>35.0</td><td>51.0</td><td></td><td></td><td></td><td></td><td></td><td>0.5</td></tr><tr><td>18</td><td></td><td>10.6</td><td>48.0</td><td>5.0</td><td>11.1</td><td>8.8</td><td></td><td>12</td><td></td><td></td><td>0.3</td></tr><tr><td>19</td><td>0</td><td>70.6</td><td>92.0</td><td>64.0</td><td>82.8</td><td>90.4</td><td>4.3</td><td>39.5 2.3</td><td>3.9</td><td>0</td><td>2.3</td></tr><tr><td>20</td><td>0</td><td>1.0</td><td>9.0</td><td>0</td><td>0</td><td>2.6</td><td>1.5</td><td>0</td><td>0 0</td><td>0</td><td>0</td></tr></table>
+
+For comparison, accuracy on the bAbI tasks is also included for a simple sequence-to-sequence LSTM model and for a variety of existing state-of-the-art approaches (see Table 2): a simple sequence-to-sequence LSTM model, as implemented in Weston et al. (2016), a modified Memory Network model (MemNN, Weston et al., 2016), End-To-End Memory Network (MemN2N, Sukhbaatar et al., 2015), Recurrent Entity Network (EntNet, Henaff et al., 2016), Neural Turing Machine (NTM, Graves et al., 2014), Dynamic NTM (D-NTM, Gulcehre et al., 2016), a larger version of the MemN2N model with weight tying and nonlinearity $( \mathrm { M e m N } 2 \mathrm { N } ^ { \ast }$ , Sukhbaatar et al., 2015), Differentiable Neural Computer (DNC, Graves et al., 2016), and Dynamic Memory Network $\mathrm { ( D M N + }$ , Xiong et al., 2016). Although the GGT-NN model was trained using only 1,000 training examples, results using 10,000 examples have also been reproduced here for comparison. Also, it is important to note that the GGT-NN and MemNN models were trained with strong supervision: the GGT-NN model was trained with full graph information, and the MemNN model was trained with information on which sentences were relevant to the query. All other models were trained end-to-end without additional supervision.
+
+Since the GGT-NN and MemNN models are both strongly supervised, it is interesting to note that each approach outperforms the other on a subset of the tasks. In particular, the GGT-NN model with direct reference attains a higher level of accuracy on the following tasks, with an improvement of $0 . 4 \substack { - 6 4 \% }$ depending on the task: task 5 $( 0 . 4 \% )$ , task 7 $( 1 5 \% )$ , task 8 $( 9 \% )$ , task 17 $( 0 . 5 \% )$ , task 18 $( 2 . 9 \% )$ , and task 19 $( 6 4 \% )$ . This may indicate that a graphical representation is superior to a list of sentence memories for solving these tasks. On the other hand, the MemNN model outperforms the GGT-NN model $( 0 . 1 \mathrm { - } 2 . 9 \%$ greater accuracy) on tasks 3, 4, 10, 12, 14, and 15.
+
+Of particular interest is the performance on task 19, the pathfinding task, for which the GGT-NN model with direct reference performs better than all but one of the other models $( \mathrm { D M N } + )$ ), and shows a large improvement over the performance of the MemNN model. This is reasonable, since pathfinding is a task that is naturally suited to a graphical representation. The shortest path between two nodes can be easily found by sending information across all paths away from one of the nodes in a distributed fashion, which the GGT-NN model allows. Note that the preexisting GGS-NN model (discussed in Section 2.2) was also able to successfully learn the pathfinding task, but required the input to be preprocessed into graphical form even when evaluating the model, and thus could not be directly evaluated on the textual form of any of the bAbI tasks (Li et al., 2016). The current results demonstrate that the proposed GGT-NN model is able to solve the pathfinding task when given textual input.
+
+Similarly, both variants of the GGT-NN model show improvement over many other models on task 16, the induction task. Solving the induction task requires being able to infer relationships based on similarities between entities. (One example from this task: Lily is a swan. Lily is white. Bernhard is green. Greg is a swan. What color is Greg? A:white.) In a graphical setting, this can be done by following a sequence of edges $( \mathrm { G r e g } \to \mathrm { s w a n } \to \mathrm { L i l y } \to $ white), and the performance of the GGT-NN model indicates that this task is particularly suited to such a representation.
+
+In general, the GGT-NN model with direct reference performs better than the model without it. The model with direct reference reaches $9 5 \%$ accuracy on 19/20 of the bAbI tasks, while the model without direct reference reaches that level of accuracy on $9 / 2 0$ of the tasks (see Table 2). Additionally, when compared to the direct-reference model, the model without direct reference requires more training examples in order to reach the accuracy threshold (see Table 1). This indicates that, although the model can be used without direct reference, adding direct reference greatly improves the training of the model.
+
+# 5.2 RULE DISCOVERY TASKS
+
+To demonstrate the power of GGT-NN to model a wide variety of graph-based problems, I applied the GGT-NN to two additional tasks. In each task, a sequence of data structures were transformed into a graphical format, and the GGT-NN was tasked with predicting the data for the next timestep
+
+Table 3: Accuracy of GGT-NN on the Rule 30 Automaton and Turing Machine tasks.   
+
+<table><tr><td></td><td>Original Task</td><td>Generalization:20</td><td>Generalization:30</td></tr><tr><td></td><td></td><td></td><td></td></tr><tr><td>Automaton</td><td>100.0%</td><td>87.0%</td><td>69.5%</td></tr><tr><td>Turing</td><td>99.9%</td><td>90.4%</td><td>80.4%</td></tr></table>
+
+![](images/1eba93c492466429914e5eaf632b79c171018c8e7223ee0e87c583c7ce5c49fa.jpg)  
+Figure 3: Visualization of network performance on the Rule 30 Automaton task. Top node (purple) represents zero, bottom node (blue) represents 1, and middle nodes (green, orange, and red) represent individual cells. Blue edges indicate adjacent cells, and gold edges indicate the value of each cell. Three timesteps occur between each row.
+
+based on the current timestep. No additional information was provided as textual input; instead, the network was tasked with learning the rules governing the evolution of the graph structure over time.
+
+# 5.2.1 CELLULAR AUTOMATON TASK
+
+The first task used was a 1-dimensional cellular automaton, specifically the binary cellular automaton known as Rule 30 (Wolfram, 2002). Rule 30 acts on an infinite set of cells, each with a binary state (either 0 or 1). At each timestep, each cell deterministically changes state based on its previous state and the states of its neighbors. In particular, the update rules are
+
+$$
+{ \mathrm { C u r r e n t ~ n e i g h b o r h o o d } } { \left| \begin{array} { l } { 1 1 1 } \\ { ~ \mathbf { n e x t ~ v a l u e } } \end{array} \right| } { \begin{array} { l } { 1 1 1 } \\ { ~ \mathbf { 0 } ~ } \end{array} } { \left| \begin{array} { l } { ~ 1 \mathbf { 0 } ~ } \\ { ~ \mathbf { 0 } ~ } \end{array} \right| } { \begin{array} { l } { ~ \mathbf { 1 0 0 } ~ } \\ { ~ \mathbf { 1 } ~ } \end{array} } { \left| \begin{array} { l } { ~ 0 \mathbf { 1 } 1 } \\ { ~ \mathbf { 1 } ~ } \end{array} \right| } { \begin{array} { l } { ~ 0 \mathbf { 1 0 } ~ } \\ { ~ \mathbf { 1 } ~ } \end{array} } { \left| \begin{array} { l } { ~ 0 \mathbf { 0 } 1 } \\ { ~ \mathbf { 0 } ~ } \end{array} \right| }
+$$
+
+Cell states can be converted into graphical format by treating the cells as a linked list. Each of the cells is represented by a node with edges connecting it to the cell’s neighbors, and a value edge is used to indicate whether the cell is 0 or 1. This format is described in more detail in Appendix C.
+
+# 5.2.2 TURING MACHINES
+
+The second task was simulating an arbitrary 2-symbol 4-state Turing machine. A Turing machine operates on an infinite tape of cells, each containing a symbol from a finite set of possible symbols. It has a head, which points at a particular cell and can read and write the symbol at that cell. It also has an internal state, from a finite set of states. At each timestep, based on the current state and the contents of the cell at the head, the machine writes a new symbol, changes the internal state, and can move the head left or right or leave it in place. The action of the machine depends on a finite set of rules, which specify the actions to take for each state-symbol combination. Note that the version of Turing machine used here has only 2 symbols, and requires that the initial contents of the tape be all 0 (the first symbol) except for finitely many 1s (the second symbol).
+
+When converting a Turing machine to graphical format, the tape of the machine is modeled as a linked list of cells. Additionally, each state of the machine is denoted by a state node, and edges between these nodes encode the transition rules. There is also a head node, which connects both to the current cell and to the current state of the machine. See Appendix C for more details.
+
+# 5.2.3 ANALYSIS AND RESULTS
+
+The GGT-NN model was trained on 1000 examples of the Rule 30 automaton with different initial states, each of which simulated 7 timesteps of the automaton, and 20,000 examples of Turing machines with different rules and initial tape contents, each of which simulated 6 timesteps of the Turing machine. Performance was then evaluated on 1000 new examples generated with the same format. The models were evaluated by picking the most likely graph generated by the model, and comparing it with the correct graph. The percent accuracy denotes the fraction of the examples for which these two graphs were identical at all timesteps. In addition to evaluating the performance on identical tasks, the generalization ability of the models was also assessed. The same trained models were evaluated on versions of the task with 20 and 30 timesteps of simulation.
+
+Results are shown in Table 3. The models successfully learned the assigned tasks, reaching high levels of accuracy for both tasks. Additionally, the models show the ability to generalize to large inputs, giving a perfect output in the majority of extended tasks. For visualization purposes, Figure 3 shows the model at various stages of training when evaluated starting with a single 1 cell.
+
+# 6 COMPARISON WITH RELATED WORK
+
+Many methods have been proposed for combining neural networks with graphs. These methods generally require the input to the network to be in graphical format. For instance, GNNs and GGS-NNs take a graph as input, and propagate information between nodes according to the graph structure (Gori et al., 2005; Scarselli et al., 2009; Li et al., 2016). Similarly, graph convolutional networks extract information from an existing graph structure by using approximations to spectral graph convolutions (Kipf & Welling, 2016). These methods are similar to GGT-NNs in that they all store information in the nodes of a graph and use edges to determine how information flows. However, they all use a graph with fixed structure, and can only accept graphical data. The GGT-NN model, on the other hand, allows the graph structure to be built and modified based on unstructured input.
+
+Giles et al. (1992) describe a method for extracting a finite state machine from a trained recurrent neural network by quantizing the hidden states of the network, recording all possible state transitions, and using them to construct a minimal directed graph representing the state machine. This method, however, requires postprocessing of the network to extract the graph, and is limited to extracting graphs that represent state machines. Additionally, although the FSM extraction method described by Giles et al. (1992) and the GGT-NN model both produce graphs using neural networks, the goals are different: the FSM extraction method aims to learn a single graph that can classify sequences, whereas the GGT-NN model aims to learn a neural network that can manipulate graphs.
+
+The lifted relational neural network (LRNN) is another approach to working with structured data (Sourek et al., 2015). LRNNs require the input to be formatted as a combination of weighted predicate logic statements, encompassing both general rules and specific known facts. For each training example, the statements are used to construct a “ground neural network”, with a connection pattern determined by the dependencies between the statements. LRNNs can learn to extract information by adjusting the weights of each statement, but require the rules to be composed by hand based on the task structure. Furthermore, unlike in GGT-NNs, a LRNN has no internal state associated with the objects it describes (which are instead represented by single neurons), and the relationships between objects cannot be constructed or modified by the network.
+
+Multiple recent architectures have included differentiable internal states. Memory Networks, as described in Weston et al. (2014), and the fully differentiable end-to-end memory networks, described in Sukhbaatar et al. (2015), both utilize a differentiable long-term memory component, consisting of a set of memories that are produced by encoding the input sentences. To answer a query, an attention mechanism is used to select a subset of these memories, and the resulting memories are processed to produce the desired output. Differentiable Neural Computers (DNCs), described in Graves et al. (2016), interact with a fixed-size memory using a set of read and write “heads”, which can be moved within the memory either by searching for particular content or by following temporal “links of association” that track the order in which data was written.
+
+Memory networks and DNCs share with the GGT-NN model the ability to iteratively construct an internal state based on textual input, and use that internal state to answer questions about the underlying structured data. However, in these models, the structure of the internal state is implicit: although the network can store and work with structured data, the actual memory consists of a set of vectors that cannot be easily interpreted, except by monitoring the network access patterns. The GGT-NN model, on the other hand, explicitly models the internal state as a graph with labeled nodes and edges. This allows the produced graph to be extracted, visualized, and potentially used in downstream applications that require graph-structured input.
+
+Hierarchical Attentive Memory (HAM) is a memory-based architecture that consists of a binary tree built on top of an input sequence (Andrychowicz & Kurach, 2016). A recurrent controller accesses the HAM module by performing a top-down search through the tree, at each stage choosing to attend to either the left or right subtrees. Once this process reaches a leaf, the value of the leaf is provided to the controller to use in predicting the next output, and this leaf’s value can be updated with a new value. This architecture is especially suited toward sequence-based tasks, and has been shown to generalize to longer sequences very efficiently due to the tree structure. However, it is unclear whether a HAM module would work well with non-sequential structured data, since the tree structure is fixed by the network.
+
+One advantage of the GGT-NN model over existing works is that it can process data in a distributed fashion. Each node independently processes its surroundings, which can be beneficial for complex tasks such as pathfinding on a graph. This is in contrast to memory networks, DNCs, and HAM modules, which are restricted to processing only a fixed number of locations in a given timestep. On the other hand, the distributed nature of the GGT-NN model means that it is less time and space efficient than these other networks. Since every node can communicate with every other node, the time and space required to run a GGT-NN step scales quadratically with the size of the input. A DNC or memory network, on the other hand, either scales linearly (since it attends to all stored data or memories) or is constant (if restricted to a fixed-size memory), and a HAM module scales logarithmically (due to the tree structure).
+
+# 7 CONCLUSION
+
+The results presented here show that GGT-NNs are able to successfully model a wide variety of tasks using graph-structured states and potentially could be useful in solving many other types of problems. The specific GGT-NN model described here can be used as-is for tasks consisting of a sequence of input sentences and graphs, optionally followed by a query. In addition, due to the modular nature of GGT-NNs, it is possible to reconfigure the order of the transformations to produce a model suitable for a different task.
+
+The GGT-NN architecture has a few advantages over the architectures described in existing works. In contrast to other approaches to working with structured data, GGT-NNs are designed to work with unstructured input, and are able to modify a graphical structure based on the input. And in contrast to memory networks or DNCs, the internal state of the network is explicitly graph structured, and complex computations can be distributed across the nodes of the graph.
+
+One downside of the current model is that the time and space required to train the model increase very quickly as the complexity of the task increases, which limits the model’s applicability. It would be very advantageous to develop optimizations that would allow the model to train faster and with smaller space requirements, such as using sparse edge connections, or only processing some subset of the nodes at each timestep. Another promising direction of future work is in reducing the level of supervision needed to obtain meaningful graphs, for example by combining a few examples that have full graph-level supervision with a larger set of examples that do not have graph-level information, or using additional regularization to enable the GGT-NN model to be trained without any graph information.
+
+There are exciting potential uses for the GGT-NN model. One particularly interesting application would be using GGT-NNs to extract graph-structured information from unstructured textual descriptions. More generally, the graph transformations provided here may allow machine learning to interoperate more flexibly with other data sources and processes with structured inputs and outputs.
+
+# ACKNOWLEDGMENTS
+
+I would like to thank Harvey Mudd College for computing resources. I would also like to thank the developers of the Theano library, which I used to run my experiments. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.
+
+# REFERENCES
+
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+
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+
+# APPENDIX A BACKGROUND ON GG-NNS AND GGS-NNS
+
+This section gives additional background on the implementation of GG-NNs and GGS-NNs, described by Li et al. (2016).
+
+Recall from section 2.2 that GG-NNs represent a graph $\mathcal { G } = ( \nu , \mathcal { E } )$ as a set $V$ of nodes $v$ with unique values $1 , \ldots , | \nu |$ and a set $\mathcal { E }$ of directed edges $e = ( v , v ^ { \prime } ) \in \mathcal { V } \times \mathcal { V }$ oriented from $v$ to $v ^ { \prime }$ . Each node has an annotation $\mathbf { x } _ { v } \in \mathbb { R } ^ { N }$ and a hidden state $\mathbf { h } _ { v } \in \mathbb { R } ^ { D }$ . Additionally, each edge has a type $y _ { e } \in \{ 1 , \cdots , M \}$ .
+
+Initially, $\mathbf { h } _ { v } ^ { ( 1 ) }$ is set to the annotation $\mathbf { x } _ { v }$ padded with zeros. Then nodes exchange information for some fixed number of timesteps $T$ according to the propagation model
+
+$$
+\begin{array} { r l r l } & { \mathbf { h } _ { v } ^ { ( 1 ) } = [ \mathbf { x } _ { v } ^ { \top } , \mathbf { 0 } ] ^ { \top } } & { \mathbf { a } _ { v } ^ { ( t ) } = \mathbf { A } _ { v : } ^ { \top } [ \mathbf { h } _ { 1 } ^ { ( t - 1 ) \top } \cdot \cdot \cdot \mathbf { h } _ { | \mathcal { V } | } ^ { ( t - 1 ) \top } ] ^ { \top } } \\ & { \mathbf { z } _ { v } ^ { ( t ) } = \sigma ( \mathbf { W } _ { z } \mathbf { a } _ { v } ^ { ( t ) } + \mathbf { U } \mathbf { h } _ { v } ^ { ( t - 1 ) } ) } & { \mathbf { r } _ { v } ^ { ( t ) } = \sigma ( \mathbf { W } _ { r } \mathbf { a } _ { v } ^ { ( t ) } + \mathbf { U } _ { r } \mathbf { h } _ { v } ^ { ( t - 1 ) } ) } \\ & { \mathbf { \widehat { h } } _ { v } ^ { ( t ) } = \operatorname { t a n h } ( \mathbf { W } \mathbf { a } _ { v } ^ { ( t ) } + \mathbf { U } \mathbf { ( r } _ { v } ^ { ( t ) } \odot \mathbf { h } _ { v } ^ { ( t - 1 ) } ) ) } & { \mathbf { h } _ { v } ^ { ( t ) } = \big ( 1 - \mathbf { z } _ { v } ^ { ( t ) } \big ) \odot \mathbf { h } _ { v } ^ { ( t - 1 ) } + \mathbf { z } _ { v } ^ { ( t ) } \odot \mathbf { \widehat { h } } _ { v } ^ { ( t ) } . } \end{array}
+$$
+
+Here $\mathbf { a } _ { v } ^ { ( t ) }$ represents the information received by each node from its neighbors in the graph, and the matrix $\mathbf { A } \in \mathbf { \bar { \mathbb { R } } } ^ { D | \mathcal { V } | \times 2 D | \mathcal { V } | }$ has a specific structure that determines how nodes communicate. The first half of $\mathbf { A }$ , denoted $\mathbf { A } ^ { ( o u t ) } \in \mathbb { R } ^ { \tilde { D } | \mathcal { V } | \times D | \mathcal { V } | }$ , corresponds to outgoing edges, whereas the second half $\mathbf { A } ^ { ( i n ) } \in \mathbb { R } ^ { D | \mathcal { V } | \times D | \mathcal { V } | }$ corresponds to incoming edges.
+
+Each edge type corresponds to specific forward and backward propagation matrices $\mathbf { P } _ { y } , \mathbf { P } _ { y } ^ { \prime } \in \mathbb { R } ^ { \tilde { D } \times D }$ which determine how to propagate information across an edge of that type in each direction. The $D \times D$ -sized submatrix of $\mathbf { A } ^ { ( o u t ) }$ in position $i , j$ contains $\mathbf { P } _ { y }$ if an edge of type $y$ connects nodes $n _ { i }$ to $n _ { j }$ , or 0 if no such edge connects in that direction. Similarly, the $D \times D$ - sized submatrix of the matrix $\mathbf { A } ^ { ( i n ) }$ in position $i , j$ contains $\mathbf { P } _ { y } ^ { \prime }$ if an edge of type $y$ connects nodes $n _ { j }$ to $n _ { i }$ , or 0 if no such edge connects in that direction. $\mathbf { A } _ { v : } \in \mathbb { R } ^ { D \times 2 D | \mathcal { V } | }$ is the submatrix of $\mathbf { A }$ corresponding to node $v$ . Thus, multiplication by $\mathbf { A } _ { v }$ : in 1 is equivalent to taking the following sum:
+
+$$
+\mathbf { a } _ { v } ^ { ( t ) } = \sum _ { v ^ { \prime } \in \mathcal { V } } \left( \sum _ { y = 1 } ^ { M } s _ { \mathrm { e d g e } } ( v , v ^ { \prime } , y ) \odot \mathbf { P } _ { y } + s _ { \mathrm { e d g e } } ( v ^ { \prime } , v , y ) \odot \mathbf { P } _ { y } ^ { \prime } \right) \mathbf { h } _ { v ^ { \prime } } ^ { ( t - 1 ) }
+$$
+
+where $s _ { \mathrm { e d g e } } ( v , v ^ { \prime } , y )$ is 1 if $e = ( v , v ^ { \prime } ) \in \mathcal { E }$ and $y _ { e } = y$ , and 0 otherwise.
+
+The output from a GG-NN is flexible depending on the task. For node selection tasks, a node score $o _ { v } \ = \ g ( \mathbf { h } _ { v } ^ { ( T ) } , \mathbf { x } _ { v } )$ is given for each node, and then a softmax operation is applied. Graph-level outputs are obtained by combining an attention mechanism $i$ and a node representation function $j$ , both implemented as neural networks, to produce the output representation
+
+$$
+\begin{array} { r } { \mathbf { h } _ { \mathcal { G } } = \operatorname { t a n h } \left( \sum _ { v \in \mathcal { V } } \sigma ( i \big ( \mathbf { h } _ { v } ^ { ( T ) } , \mathbf { x } _ { v } \big ) \big ) \odot \operatorname { t a n h } ( j \big ( \mathbf { h } _ { v } ^ { ( T ) } , \mathbf { x } _ { v } ) ) \right) } \end{array}
+$$
+
+Gated Graph Sequence Neural Networks (GGS-NN) are an extension of GG-NNs to sequential output o(1), $\mathbf { o } ^ { ( 1 ) } , \ldots , \mathbf { \bar { o } } ^ { ( K ) }$ . At each output step $k$ , the annotation matrix $\mathcal { X }$ is given by $\begin{array} { r l } { \bar { \chi } ^ { } ( k ) } & { { } = } \end{array}$ $[ \mathbf { x } _ { 1 } ^ { ( k ) } , \ldots , \mathbf { x } _ { | \mathcal { V } | } ^ { ( k ) } ] ^ { \top } \in \mathbb { R } ^ { | \mathcal { V } | \times L _ { \mathcal { V } } }$ . A GG-NN $\mathcal { F } _ { \mathbf { o } }$ is trained to predict an output sequence $\mathbf { o } ^ { ( k ) }$ from $\chi ( k )$ , and another GG-NN $\mathcal { F } _ { \mathbf { X } }$ is trained to predict $\chi ( k { + } 1 )$ from $\chi ^ { ( k ) }$ . Prediction of the output at each step is performed as in a normal GG-NN, and prediction of $\chi ( k { + } 1 )$ from the set of all final hidden states $\mathcal { H } ^ { ( k , T ) }$ (after $T$ propagation steps of $\mathcal { F } _ { \mathbf { X } }$ ) occurs according to the equation
+
+$$
+\begin{array} { r } { \mathbf { x } _ { v } ^ { ( k + 1 ) } = \sigma \left( j ( \mathbf { h } _ { v } ^ { ( k , T ) } , \mathbf { x } _ { v } ^ { ( k ) } ) \right) . } \end{array}
+$$
+
+![](images/09134bf13f89db5fbe8b19a73414cfe0b9b12e0650666fd28c035051132a23a6.jpg)  
+Figure 4: Diagram of the operations performed for each class of transformation. Graph state is shown in the format given by Figure 1. Input and output are shown as gray boxes. Black dots represent concatenation, and $^ +$ and $\times$ represent addition and multiplication, respectively. $1 - \#$ represents taking the input value and subtracting it from 1. Note that for simplicity, operations are only shown for single nodes or edges, although the operations act on all nodes and edges in parallel. In particular, the propagation section focuses on information sent and received by the first node only. In that section the strengths of the edges in the connectivity matrix determine what information is sent to each of the other nodes. Light gray connections indicate the value zero, corresponding to situations where a given edge is not present.
+
+# APPENDIX B GRAPH TRANSFORMATION DETAILS
+
+In this section I describe in detail the implementations of each type of differentiable graph transformation.1 A diagram of the implementation of each transformation is shown in Figure 4. Note that it is natural to think of these transformations as operating on a single graphical state, and each modifying the state in place. However, in the technical descriptions of these transformations, the operations will be described as functions that take in an old graph and produce a new one, similarly to unrolling a recurrent network over time.
+
+# B.1 NODE ADDITION
+
+The node addition transformation $\mathcal { T } _ { \mathrm { a d d } } : \Gamma \times \mathbb { R } ^ { \alpha }  \Gamma$ takes as input a graph $\mathcal { G }$ and an input vector $\mathbf { a } \in \mathbb { R } ^ { \alpha }$ , and produces a graph $\mathcal { G } ^ { \prime }$ with additional nodes. The annotation and strength of each new node is determined by a function $f _ { \mathrm { a d d } } : \mathbb { R } ^ { \alpha } \times \mathbb { R } ^ { \beta } \to \mathbb { R } \times \mathbb { R } ^ { N } \times \mathbb { R } ^ { \beta }$ , where $\alpha$ is the length of the input vector, $\beta$ is the length of the internal state vector, and as before $N$ is the number of node types. The new nodes are then produced according to
+
+$$
+\begin{array} { r } { \left( s _ { | V _ { \mathcal { G } } | + i } , \mathbf { x } _ { | V _ { \mathcal { G } } | + i } , \mathbf { h } _ { i } \right) = f _ { \mathrm { a d d } } ( \mathbf { a } , \mathbf { h } _ { i - 1 } ) , } \end{array}
+$$
+
+starting with $\mathbf { h } _ { 0 }$ initialized to some learned initial state, and recurrently computing $s _ { v }$ and $\mathbf { x } _ { v }$ for each new node, up to some maximum number of nodes. Based on initial experiments, I found that implementing $f _ { \mathrm { a d d } }$ as a GRU layer followed by 2 hidden tanh layers was effective, although other recurrent networks would likely be similarly effective. The node hidden states $\mathbf { h } _ { v }$ are initialized to zero. The recurrence should be computed as many times as the maximum number of nodes that might be produced. The recurrent function $f _ { \mathrm { a d d } }$ can learn to output $s _ { v } = 0$ for some nodes to create fewer nodes, if necessary.
+
+Note that in order to use information from all of the existing nodes to produce the new nodes, the input to this transformation should include information provided by an aggregation transformation $\bar { \mathcal { T } _ { \mathrm { r e p r } } }$ , described in section B.5.
+
+# B.2 NODE STATE UPDATE
+
+The node state update transformation $\mathcal { T } _ { \mathbf { h } } : \Gamma \times \mathbb { R } ^ { \alpha }  \Gamma$ takes as input a graph $\mathcal { G }$ and an input vector $\mathbf { a } \in \mathbb { R } ^ { \alpha }$ , and produces a graph $\mathcal { G } ^ { \prime }$ with updated node states. This is accomplished by performing a GRU-style update for each node, where the input is a concatenation of a and that node’s annotation vector $\mathbf { x } _ { v }$ and the state is the node’s hidden state, according to
+
+$$
+\begin{array} { r l r l } & { \mathbf { r } _ { v } = \sigma \left( \mathbf { W } _ { r } [ \mathbf { a } \mathbf { x } _ { v } ] + \mathbf { U } _ { r } \mathbf { h } _ { v } + \mathbf { b } _ { r } \right) , } & & { \mathbf { z } _ { v } = \sigma \left( \mathbf { W } _ { z } [ \mathbf { a } \mathbf { x } _ { v } ] + \mathbf { U } _ { z } \mathbf { h } _ { v } + \mathbf { b } _ { z } \right) , } \\ & { \widetilde { \mathbf { h } } _ { v } ^ { \prime } = \operatorname { t a n h } \left( \mathbf { W } [ \mathbf { a } \mathbf { x } _ { v } ] + \mathbf { U } \left( \mathbf { r } \odot \mathbf { h } _ { v } \right) + \mathbf { b } \right) , } & & { \mathbf { h } _ { v } ^ { \prime } = \mathbf { z } _ { v } \odot \mathbf { h } _ { v } + \left( 1 - \mathbf { z } _ { v } \right) \odot \widetilde { \mathbf { h } } _ { v } ^ { \prime } } \end{array}
+$$
+
+# B.2.1 DIRECT REFERENCE UPDATE
+
+For some tasks, performance can be improved by providing information to nodes of a particular type only. For instance, if the input is a sentence, and one word of that sentence directly refers to a node type (e.g., if nodes of type 1 represent Mary, and Mary appears in the sentence), it can be helpful to allow all nodes of type 1 to perform an update using this information. To accomplish this, $\mathcal { T } _ { \mathbf { h } }$ can be modified to take node types into account. (This modification is denoted $\tau _ { \mathrm { h , d i r e c t } }$ .) Instead of a single vector $\mathbf { a } \in \mathbb { R } ^ { \alpha }$ , the direct-reference transformation takes in $\mathbf { A } \in \mathbb { R } ^ { N \times \alpha }$ , where $\mathbf { A } _ { n } \in \mathbb { R } ^ { \alpha }$ is the input vector for nodes with type $n$ . The update equations then become
+
+$$
+\begin{array} { c c } { { \bf a } _ { v } = { \bf x } _ { v } { \bf A } } & { } \\ { { \bf r } _ { v } = \sigma \left( { \bf W } _ { r } [ { \bf a } _ { v } { \bf x } _ { v } ] + { \bf U } _ { r } { \bf h } _ { v } + { \bf b } _ { r } \right) , } & { { \bf z } _ { v } = \sigma \left( { \bf W } _ { z } [ { \bf a } _ { v } { \bf x } _ { v } ] + { \bf U } _ { z } { \bf h } _ { v } + { \bf b } _ { z } \right) , } \\ { { \bf \tilde { h } } _ { v } ^ { \prime } = \operatorname { t a n h } \left( { \bf W } [ { \bf a } _ { v } { \bf x } _ { v } ] + { \bf U } \left( { \bf r } \odot { \bf h } _ { v } \right) + { \bf b } \right) , } & { { \bf h } _ { v } ^ { \prime } = { \bf z } _ { v } \odot { \bf h } _ { v } + \left( 1 - { \bf z } _ { v } \right) \odot { \bf \tilde { h } } _ { v } ^ { \prime } } \end{array}
+$$
+
+# B.3 EDGE UPDATE
+
+The edge update transformation $\mathcal { T } _ { \mathcal { C } } : \Gamma \times \mathbb { R } ^ { \alpha }  \Gamma$ takes a graph $\mathcal { G }$ and an input vector $\mathbf { a } \in \mathbb { R } ^ { \alpha }$ , and produces a graph $\mathcal { G } ^ { \prime }$ with updated edges. For each pair of nodes $( \boldsymbol { v } , \boldsymbol { v } ^ { \prime } )$ , the update equations are
+
+$$
+\begin{array} { r l } & { \mathbf { c } _ { v , v ^ { \prime } } = f _ { \mathrm { s e t } } ( \mathbf { a } , \mathbf { x } _ { v } , \mathbf { h } _ { v } , \mathbf { x } _ { v ^ { \prime } } , \mathbf { h } _ { v ^ { \prime } } ) } \\ & { \mathcal { C } _ { v , v ^ { \prime } } ^ { \prime } = ( 1 - \mathcal { C } _ { v , v ^ { \prime } } ) \odot \mathbf { c } _ { v , v ^ { \prime } } + \mathcal { C } _ { v , v ^ { \prime } } \odot ( 1 - \mathbf { r } _ { v , v ^ { \prime } } ) . } \end{array} \quad \begin{array} { r l } & { \mathbf { r } _ { v , v ^ { \prime } } = f _ { \mathrm { r e s e t } } ( \mathbf { a } , \mathbf { x } _ { v } , \mathbf { h } _ { v } , \mathbf { x } _ { v ^ { \prime } } , \mathbf { h } _ { v ^ { \prime } } ) } \\ & { } \end{array}
+$$
+
+The functions $f _ { \mathrm { s e t } } , f _ { \mathrm { r e s e t } } ~ : ~ \mathbb { R } ^ { \alpha \times 2 N \times 2 D } \  ~ [ 0 , 1 ] ^ { Y }$ are implemented as neural networks. (In my experiments, I used a simple 2-layer fully connected network.) $\mathbf { c } _ { v , v ^ { \prime } , y }$ gives the level of belief in $[ 0 , 1 ]$ that an edge from $v$ to $v ^ { \prime }$ of type $y$ should be created if it does not exist, and $\mathbf { r } _ { v , v ^ { \prime } , y }$ gives the level of belief in $[ 0 , 1 ]$ that an edge from $v$ to $v ^ { \prime }$ of type $y$ should be removed if it does. Setting both to zero results in no change for that edge, and setting both to 1 toggles the edge state.
+
+# B.4 PROPAGATION
+
+The propagation transformation $\mathcal { T } _ { \mathrm { p r o p } } : \Gamma \to \Gamma$ takes a graph ${ \mathcal { G } } = { \mathcal { G } } ^ { ( 0 ) }$ and runs a series of $T$ propagation steps (as in GG-NN), returning the resulting graph $\mathcal { G } ^ { \prime } = \mathcal { G } ^ { ( T ) }$ . The GG-NN propagation step is extended to handle node and edge strengths, as well as to allow more processing to occur to
+
+the information transferred across edges. The full propagation equations for step $t$ are
+
+$$
+\begin{array} { r l } & { \mathbf { a } _ { v } ^ { ( t ) } = \displaystyle \sum _ { v ^ { \prime } \in \mathcal { V } } s _ { v ^ { \prime } } \displaystyle \sum _ { y = 1 } ^ { M } \mathcal { C } _ { v , v ^ { \prime } , y } \odot f _ { y } ^ { \mathrm { f w d } } ( \mathbf { x } _ { v ^ { \prime } } , \mathbf { h } _ { v ^ { \prime } } ^ { ( t - 1 ) } ) + \mathcal { C } _ { v ^ { \prime } , v , y } \odot f _ { y } ^ { \mathrm { f w d } } ( \mathbf { x } _ { v ^ { \prime } } , \mathbf { h } _ { v ^ { \prime } } ^ { ( t - 1 ) } ) } \\ & { \mathbf { z } _ { v } ^ { ( t ) } = \sigma ( \mathbf { W } _ { z } [ \mathbf { a } _ { v } ^ { ( t ) } \ \mathbf { x } _ { v } ] + \mathbf { U } \mathbf { h } _ { v } ^ { ( t - 1 ) } + \mathbf { b } _ { z } ) } \\ & { \mathbf { r } _ { v } ^ { ( t ) } = \sigma ( \mathbf { W } _ { r } [ \mathbf { a } _ { v } ^ { ( t ) } \ \mathbf { x } _ { v } ] + \mathbf { U } _ { r } \mathbf { h } _ { v } ^ { ( t - 1 ) } + \mathbf { b } _ { r } ) } \\ & { \mathbf { \widetilde { h } } _ { v } ^ { ( t ) } = \mathrm { t a n h } ( \mathbf { W } [ \mathbf { a } _ { v } ^ { ( t ) } \ \mathbf { x } _ { v } ] + \mathbf { U } ( \mathbf { r } _ { v } ^ { ( t ) } \odot \mathbf { h } _ { v } ^ { ( t - 1 ) } ) + \mathbf { b } _ { h } ) } \\ & { \mathbf { h } _ { v } ^ { ( t ) } = ( 1 - \mathbf { z } _ { v } ^ { ( t ) } ) \odot \mathbf { h } _ { v } ^ { ( t - 1 ) } + \mathbf { z } _ { v } ^ { ( t ) } \odot \mathbf { \widetilde { h } } _ { v } ^ { ( t ) } . } \end{array}
+$$
+
+Equation 5 has been adjusted in the most significant manner (relative to Equation 2). In particular, $s _ { v ^ { \prime } }$ restricts propagation so that nodes with low strength send less information to adjacent nodes, $s _ { \mathrm { e d g e } }$ has been replaced with $\mathcal { C }$ to allow edges with fractional strength, and the propagation matrices $\mathbf { P } _ { y } , \mathbf { P } _ { z } ^ { \prime }$ have been replaced with arbitrary functions $f _ { y _ { . } } ^ { \mathrm { f w d } } , f _ { y } ^ { \mathrm { b w d } } : \mathbb { R } ^ { N } \times \mathbb { R } ^ { D }  \mathbb { R } ^ { \alpha }$ , where $\alpha$ is the length of the vector a. I used a fully connected layer to implement each function in my experiments. Equations 6, 7, and 8 have also been modified slightly to add a bias term.
+
+# B.5 AGGREGATION
+
+The aggregation transformation $\mathcal { T } _ { \mathrm { r e p r } } : \Gamma \to \mathbb { R } ^ { \alpha }$ produces a graph-level representation vector from a graph. It functions very similarly to the output representation of a GG-NN (equation 3), combining an attention mechanism with a node representation function, but is modified slightly to take into account node strengths. As in GG-NN, both $i$ and $j$ are neural networks, and in practice a single fully connected layer appears to be adequate for both.
+
+$$
+\begin{array} { r } { \mathbf { h } _ { \mathcal { G } } = \operatorname { t a n h } \left( \sum _ { v \in \mathcal { V } } s _ { v } \sigma \big ( i \big ( \mathbf { h } _ { v } ^ { ( T ) } , \mathbf { x } _ { v } \big ) \big ) \odot \operatorname { t a n h } \big ( j \big ( \mathbf { h } _ { v } ^ { ( T ) } , \mathbf { x } _ { v } \big ) \big ) \right) . } \end{array}
+$$
+
+# APPENDIX C GRAPH FORMAT DETAILS
+
+# C.1 BABI TASKS
+
+The knowledge graph object used during generation of the bAbI tasks is structured as a dictionary relating entities to each other with specific relationship types. Entities are identified based on their names, and include people (John, Mary, Sandra), locations (bedroom, kitchen, garden), objects (football, apple, suitcase), animals (mouse, wolf, cat), and colors (white, yellow, green), depending on the particular task. Relationships between entities are also expressed as strings, and are directed: if John is holding the milk there is an “is in” relationship from “milk” to “John”; if Sandra is in the bedroom there is an “is in” relationship from “Sandra” to “bedroom”; if Lily is green there is a “has color” relationship from “Lily” to “green”, etc.
+
+The transformation from the knowledge object to a graph is straightforward: each entity used is assigned to a new node type, and relationships between entities are represented as edges between the corresponding nodes. To avoid confusion from overloaded relationships (such as “is in” being used to represent an object being held by a person as well as a person being in a room), relation names are given a distinct edge type depending on the usage context. For instance, when a person is carrying an object, the generic “is in” relationship becomes an edge of type “gettable is in actor”.
+
+Some of the graph representations had to be modified in order to ensure that they contained all of the necessary information. For instance, task 3 requires the network to remember where items were in the past, but the knowledge object only contained references to their current locations. In these cases, a linked list structure was added to the knowledge object to allow the history information to be represented in the graph.
+
+In particular, each time an item changed locations, a new “record” node was added, with a “previous” edge to the previous history node and a “value” edge to the current location of the item. Each item then connected to the most recent history node using a “history-head” edge. This ensures that the history of each node is present in the graph.
+
+1. John grabbed the milk.   
+2. John travelled to the bedroom.   
+3. Sandra took the football.   
+4. John went to the garden.   
+5. John let go of the milk.   
+6. Sandra let go of the football.   
+7. John got the football.   
+8. John grabbed the milk.   
+Where is the milk?   
+$\begin{array} { r l } & { \mathrm { 1 . ~ i n i t ~ 1 } } \\ & { \mathrm { 2 . ~ i n i t ~ 1 } } \\ & { \mathrm { 3 . ~ i n i t ~ 1 } } \\ & { \mathrm { 4 . ~ i n i t ~ 1 } } \\ & { \mathrm { 5 . ~ i n i t ~ 1 } } \\ & { \mathrm { 6 . ~ i n i t ~ 0 } } \\ & { \mathrm { 7 . ~ i n i t ~ 0 } } \\ & { \mathrm { 8 . ~ i n i t ~ 0 } } \\ & { \mathrm { 9 . ~ i n i t ~ 1 } } \\ & { \mathrm { 1 0 . ~ i n i t ~ 1 } } \end{array}$ 11. init 1   
+12. init 1   
+13. init 0   
+14. simulate   
+15. simulate   
+16. simulate   
+17. simulate   
+18. simulate   
+19. simulate   
+1 20. simulate
+
+![](images/2c34ea3e1cbe4483bbb0315d748361ce7e834d6d8095e097205ca3c36486bb96.jpg)  
+Figure 5: Diagram of one sample story from the bAbI dataset (Task 2), along with a graphical representation of the knowledge state after the italicized sentence.
+
+![](images/1bd521739a8142652bc7990baf791d6be79f95ea969bddc4076b0e596aa625e3.jpg)  
+Figure 6: Diagram of one example from the automaton task, along with a graphical representation of the automaton state after the fourth simulate command (italicized).
+
+![](images/c9c3011cf6664a53330d88027e8ebd96cacbb70f36cac9ad865b9be8d469e828.jpg)  
+Figure 7: Diagram of an example from the Turing machine task, with a graphical representation of the machine state after the second run command (italicized).
+
+In a few of the tasks, specific entities had multi-word representations. While this works for normal input, it makes it difficult to do direct reference, since direct reference is checked on an individual word level. These tasks were modified slightly so that the entities are referred to with single words (e.g. “red square” instead of “red square”).
+
+An example of a graph produced from the bAbI tasks is given in Figure 5.
+
+# C.2 CELLULAR AUTOMATON
+
+The cellular automaton task was mapped to graphical format as follows: Nodes have 5 types: zero, one, init-cell, left-cell, and right-cell. Edges have 2 types: value, and next-r. There is always exactly one “zero” node and one “one” node, and all of the cell nodes form a linked list, with a “value” edge connecting to either zero or one, and a “next-r” edge pointing to the next cell to the right (or no edge for the rightmost cell).
+
+At the start of each training example, there are 13 timesteps with input of the form “init X” where X is 0 or 1. These timesteps indicate the first 13 initial cells. Afterward, there are 7 “simulate” inputs. At each of these timesteps, one new left-cell node is added on the left, one new right-cell node is added on the right, and then all cells update their value according to the Rule 30 update rules.
+
+An example of the graphical format for the cellular automaton task is given in Figure 6.
+
+# C.3 TURING MACHINE
+
+For the Turing machine task, nodes were assigned to 8 types: state-A, state-B, state-C, state-D, head, cell, 0, and 1. Edges have 16 types: head-cell, next-left, head-state, value, and 12 types of the form rule-R-W-D, where R is the symbol read (0 or 1), W is the symbol written (0 or 1), and D is the direction to move afterward (Left, Right, or None). State nodes are connected with rule edges, which together specify the rules governing the Turing machine. Cell nodes are connected to adjacent cells with next-left edges, and to the symbol on the tape with value edges. Finally, the head node is connected to the current state with a head-state edge, and to the current cell of the head with a head-cell edge.
+
+At the start of each training example, each of the rules for the Turing machine are given, in the form “rule state-X R W state-Y D”. Next, the initial state is given in the format “start state-X”, and the initial contents of the tape (of length 4) are given sequentially in the format “input symbol-X”, with the position for the head to start marked by “input symbol-X head”. Finally, there are 6 “run” inputs, after each of which the head node updates its edges and the cell at the head updates its value according to the rules of the Turing machine. If the head leaves the left or right of the tape, a new node is introduced there.
+
+An example of the graphical format for the Turing machine task is given in Figure 7.
+
+# APPENDIX D GRAPH SEQUENCE INPUT
+
+The model described in Section 4 conditions the output of the model on the final graph produced by the network. This is ideal when the graph represents all of the necessary knowledge for solving the task. However, it may also be desirable for each graph to represent a subset of knowledge corresponding to a particular time, and for the output to be based on the sequence of graphs produced. For instance, in the third bAbI task (which requires reasoning about the temporal sequence of events) each graph could represent the state of the word at that particular time, instead of representing the full sequence of events prior to that time. In Appendix C, section C.1, I describe a transformation to the tasks which allows all information to be contained in the graph. But this adds complexity to the graphical structure. If it were possible for the model to take into account the full sequence of graphs, instead of just the final one, we could maintain the simplicity of the graph transformation.
+
+To this end, I present an extension of the GGT-NN model that can produce output using the full graphical sequence. In the extended model, the graphical output of the network after each input sentence is saved for later use. Then, when processing the query, the same set of query transformations are applied to every intermediate graph, producing a sequence of representation vectors hanswer1 , . $\mathbf { h } _ { 1 } ^ { \mathrm { a n s w e r } } , \ldots , \mathbf { h } _ { K } ^ { \mathrm { a n s w e r } }$ , hanswer . These are then combined into a final summary representation vector hanswersummary using a recurrent network such as a GRU layer, from which the output can be produced. The modified pseudocode for this is shown in Algorithm 2.
+
+Table 4: Performance of the sequence-extended GGT-NN on the two bAbI tasks with a temporal component.   
+
+<table><tr><td rowspan=1 colspan=1>Task</td><td rowspan=1 colspan=1>Direct referenceAccuracy</td><td rowspan=1 colspan=1>No direct referenceAccuracy</td></tr><tr><td rowspan=1 colspan=1>3 - Three Supporting Facts5 - Three Arg. Relations</td><td rowspan=1 colspan=1>90.3%89.8%</td><td rowspan=1 colspan=1>65.4%74.2%</td></tr></table>
+
+<table><tr><td colspan="2">Algorithm2 Sequence-Extended Pseudocode</td></tr><tr><td>9↑</td><td>Initialize G to an empty graph</td></tr><tr><td>for k from1 to K do</td><td>Process each sentence</td></tr><tr><td>9k ←Th(Sk-1,i(k))</td><td></td></tr><tr><td>if direct reference enabled then</td><td></td></tr><tr><td>9k ← Tiret(G,D(k))</td><td></td></tr><tr><td>end if</td><td></td></tr><tr><td>if intermediate propagation enabled then</td><td></td></tr><tr><td>9k←Tprop(Sk)</td><td></td></tr><tr><td>end if</td><td></td></tr><tr><td>h←Trepr(G）</td><td></td></tr><tr><td>9k←Tadd(Sk,[i(k） ）hg])</td><td></td></tr><tr><td>9k ←Tc(Sk,i(k)）</td><td></td></tr><tr><td>end for</td><td></td></tr><tr><td>hameary←0</td><td></td></tr><tr><td>for k from1 to K do</td><td>&gt;Process the query for each graph</td></tr><tr><td>9 ←Tuery(, query）</td><td></td></tr><tr><td>if direct reference enabled then</td><td></td></tr><tr><td>t(9k,Dquery)</td><td></td></tr><tr><td>end if</td><td></td></tr><tr><td>Tpy（G） 9k←</td><td></td></tr><tr><td>←Trepery（G）</td><td></td></tr><tr><td>answer r,summeary)</td><td></td></tr><tr><td>end for</td><td></td></tr><tr><td>return fouput(hamary)</td><td></td></tr></table>
+
+I evaluated the extended model on bAbI tasks 3 and 5, the two tasks which asked questions about a sequence of events. (Note that although Task 14 also involves a sequence of events, it uses a set of discrete named time periods and so is not applicable to this modification.) The model was trained on each of these tasks, without the extra record and history nodes used to store the sequence, instead simply using the sequence of graphs to encode the relevant information. Due to the simpler graphs produced, intermediate propagation was also disabled.
+
+Results from training the model are shown in Table 4. The accuracy of the extended model appears to be slightly inferior to the original model in general, although the extended direct-reference model of task 5 performs slightly better than its original counterpart. One possible explanation for the inferiority of the extended model is that the increased amount of query processing made the model more likely to overfit on the training data. Even so, the extended model shows promise, and could be advantageous for modeling complex tasks for which preprocessing the graph would be impractical.

parse/train/Sklf1yrYDr/Sklf1yrYDr.md

@@ -0,0 +1,408 @@
+# BATCHENSEMBLE: AN ALTERNATIVE APPROACH TOEFFICIENT ENSEMBLE AND LIFELONG LEARNING
+
+Yeming $\mathbf { W e n } ^ { 1 , 2 , 3 * }$ , Dustin Tran3 & Jimmy $\mathbf { B a } ^ { 1 , 2 }$ 1University of Toronto, 2Vector Institute, 3Google Brain
+
+# ABSTRACT
+
+Ensembles, where multiple neural networks are trained individually and their predictions are averaged, have been shown to be widely successful for improving both the accuracy and predictive uncertainty of single neural networks. However, an ensemble’s cost for both training and testing increases linearly with the number of networks, which quickly becomes untenable.
+
+In this paper, we propose BatchEnsemble1, an ensemble method whose computational and memory costs are significantly lower than typical ensembles. BatchEnsemble achieves this by defining each weight matrix to be the Hadamard product of a shared weight among all ensemble members and a rank-one matrix per member. Unlike ensembles, BatchEnsemble is not only parallelizable across devices, where one device trains one member, but also parallelizable within a device, where multiple ensemble members are updated simultaneously for a given mini-batch. Across CIFAR-10, CIFAR-100, WMT14 EN-DE/EN-FR translation, and out-of-distribution tasks, BatchEnsemble yields competitive accuracy and uncertainties as typical ensembles; the speedup at test time is 3X and memory reduction is 3X at an ensemble of size 4. We also apply BatchEnsemble to lifelong learning, where on Split-CIFAR-100, BatchEnsemble yields comparable performance to progressive neural networks while having a much lower computational and memory costs. We further show that BatchEnsemble can easily scale up to lifelong learning on Split-ImageNet which involves 100 sequential learning tasks.
+
+# 1 INTRODUCTION
+
+Ensembling is one of the oldest tricks in machine learning literature (Hansen & Salamon, 1990). By combining the outputs of several models, an ensemble can achieve better performance than any of its members. Many researchers demonstrate that a good ensemble is one where the ensemble’s members are both accurate and make independent errors (Perrone & Cooper, 1992; Maclin & Opitz, 1999). In neural networks, SGD (Bottou, 2003) and its variants such as Adam (Kingma & Ba, 2014) are the most common optimization algorithm. The random noise from sampling mini-batches of data in SGD-like algorithms and random initialization of the deep neural networks, combined with the fact that there is a wide variety of local minima solutions in high dimensional optimization problem (Ge et al., 2015; Kawaguchi, 2016; Wen et al., 2019), results in the following observation: deep neural networks trained with different random seeds can converge to very different local minima although they share similar error rates. One of the consequence is that neural networks trained with different random seeds will usually not make all the same errors on the test set, i.e. they may disagree on a prediction given the same input even if the model has converged (Fort et al., 2019).
+
+Ensembles of neural networks benefit from the above observation to achieve better performance by averaging or majority voting on the output of each ensemble member (Xie et al., 2013; Huang et al., 2017). It is shown that ensembles of models perform at least as well as its individual members and diverse ensemble members lead to better performance (Krogh & Vedelsby, 1995). More recently, Lakshminarayanan et al. (2017) showed that deep ensembles give reliable predictive uncertainty estimates while remaining simple and scalable. A further study confirms that deep ensembles generally
+
+achieves the best performance on out-of-distribution uncertainty benchmarks (Ovadia et al., 2019;   
+Gustafsson et al., 2019) compared to other methods such as MC-dropout (Gal & Ghahramani, 2015).
+
+Despite their success on benchmarks, ensembles are limited in practice due to their expensive computational and memory costs, which increase linearly with the ensemble size in both training and testing. Computation-wise, each ensemble member requires a separate neural network forward pass of its inputs. Memory-wise, each ensemble member requires an independent copy of neural network weights, each up to millions (sometimes billions) of parameters. This memory requirement also makes many tasks beyond supervised learning prohibitive. For example, in lifelong learning, a natural idea is to use a separate ensemble member for each task, adaptively growing the total number of parameters by creating a new independent set
+
+![](images/916489bd43820a77d26ecfe4f784345a9f8467d6694706af38148617513b12bc.jpg)  
+Figure 1: The test time cost (blue) and memory cost of BatchEnsemble (orange) w.r.t the ensemble size. The result is relative to single model cost. Testing time cost and memory cost of naive ensemble are plotted in green.
+
+of weights for each new task. No previous work achieves competitive performance on lifelong learning via ensemble methods, as memory is a major bottleneck.
+
+Our contribution: In this paper, we aim to address the computational and memory bottleneck by building a more parameter efficient-ensemble method: BatchEnsemble. We achieve this goal by exploiting a novel ensemble weight generation mechanism: the weight of each ensemble member is generated by the Hadamard product between: a. one shared weight among all ensemble members. b. one rank-one matrix that varies among all members, which we refer to as fast weight in the following sections. Figure 1 compares testing and memory cost between BatchEnsemble and naive ensemble. Unlike typical ensembles, BatchEnsemble is mini-batch friendly, where it is not only parallelizable across devices like typical ensembles but also parallelizable within a device. Moreover, it incurs only minor memory overhead because a large number of weights are shared across ensemble members.
+
+Empirically, we show that BatchEnsemble has the best trade-off among accuracy, running time, and memory on several deep learning architectures and learning tasks: CIFAR-10/100 classification with ResNet32 (He et al., 2016) and WMT14 EN-DE/EN-FR machine translation with Transformer (Vaswani et al., 2017). Additionally, we show that BatchEnsemble is effective in calibrated prediction on out-of-distribution datasets; and uncertainty evaluation on contextual bandits. Finally, we show that BatchEnsemble can be successfully applied in lifelong learning and scale up to 100 sequential learning tasks without catastrophic forgetting and the need of a memory buffer. Section 5 further provides diversity analysis as a tool to understand why BatchEnsemble works well in practice.
+
+# 2 BACKGROUND
+
+In this section, we describe relevant background about ensembles, uncertainty evaluation, and lifelong learning for our proposed method, BatchEnsemble.
+
+# 2.1 ENSEMBLES FOR IMPROVED PERFORMANCE
+
+Bagging, also called bootstrap aggregating, is an algorithm to improve the total generalization performance by combining several different models (Breiman, 1996). Strategies to combine those models such as averaging and majority voting are known as ensemble methods. It is shown that ensembles of models perform at least as well as each of its ensemble members (Krogh & Vedelsby, 1995). Moreover, ensembles achieve the best performance when each of their members makes independent errors (Goodfellow et al., 2015; Hansen & Salamon, 1990).
+
+Related work on ensembles: Ensembles have been studied extensively for improving model performance (Hansen & Salamon, 1990; Perrone & Cooper, 1992; Dietterich, 2000; Maclin & Opitz, 1999). One major direction in ensemble research is how to reduce their cost at test time. Bucila et al. (2006) developed a method to compress large, complex ensembles into smaller and faster models which achieve faster test time prediction. Hinton et al. (2015) developed the above approach further by distilling the knowledge in an ensemble of models into one single neural network. Another major direction in ensemble research is how to reduce their cost at training time. Xie et al. (2013) forms ensembles by combining the output of networks within a number of training checkpoints, named Horizontal Voting Vertical Voting and Horizontal Stacked Ensemble. Additionally, models trained with different regularization and augmentation can be used as ensemble to achieve better performance in semi-supervised learning (Laine & Aila, 2017). More recently, Huang et al. (2017) proposed Snapshot ensemble, in which a single model is trained by cyclic learning rates (Loshchilov & Hutter, 2016; Smith, 2015) so that it is encouraged to visit multiple local minima. Those local minima solutions are then used as ensemble members. Garipov et al. (2018) proposed fast geometric ensemble where it finds modes that can be connected by simple curves, and each mode can taken as one ensemble member. The aforementioned works are complementary to BatchEnsemble, and one could potentially combine these techniques to achieve better performance. BatchEnsemble is efficient in both computation (including training and testing) and memory, along with a minimal change to the current training scheme such as learning rate schedule. For example, the need of cyclic learning rates in Snapshot Ensemble makes it incompatible to Transformer (Vaswani et al., 2017) which requires a warm-up and inverse square root learning rate.
+
+Explicit ensembles are expensive so another line of work lies on what so-called “implicit” ensembles. For example, Dropout (Srivastava et al., 2014) can be interpreted as creating an exponential number of weight-sharing sub-networks, which are implicitly ensembled in test time prediction (Warde-Farley et al., 2014). MC-dropout can be used for uncertainty estimates (Gal & Ghahramani, 2015). Implicit ensemble methods are generally cost-free in training and testing.
+
+# 2.2 ENSEMBLES FOR IMPROVED UNCERTAINTY
+
+Several measures have been proposed to assess the quality of uncertainty estimates, such as calibration (Dawid, 1982; Degroot & Fienberg, 1983). Another important metric is the generalization of predictive uncertainty estimates to out-of-distribution datasets (Hendrycks & Dietterich, 2019). The contextual bandits task was recently proposed to evaluate the quality of predictive uncertainty, where maximizing reward is of direct interest (Riquelme et al., 2018); and which requires good uncertainty estimates in order to balance exploration and exploitation.
+
+Although deep neural networks achieve state-of-the-art performance on a variety of tasks, their predictions are often poorly calibrated (Guo et al., 2017). Bayesian neural networks (Hinton & Neal, 1995), which posit a distribution over the weights rather than a point estimate, are often used for model uncertainty (Dusenberry et al., 2019). However, they require modifications to the traditional neural network training scheme. Deep ensembles have been proposed as a simple and scalable alternative, and have been shown to make well-calibrated uncertainty estimates (Lakshminarayanan et al., 2017). More recently, Ovadia et al. (2019) and Gustafsson et al. (2019) independently benchmarked existing methods for uncertainty modelling on a broad range of datasets and architectures, and observed that ensembles tend to outperform variational Bayesian neural networks in terms of both accuracy and uncertainty, particularly on OOD datasets. Fort et al. (2019) investigates the loss landscape and postulates that variational methods only capture local uncertainty whereas ensembles explore different global modes. It explains why deep ensembles generally perform better.
+
+# 2.3 LIFELONG LEARNING
+
+In lifelong learning, the model trains on a number of tasks in a sequential (online) order, without access to entire previous tasks’ data (Thrun, 1998; Zhao & Schmidhuber, 1996). One core difficulty of lifelong learning is “catastrophic forgetting”: neural networks tend to forget what it has learnt after training on the subsequent tasks (McCloskey, 1989; French, 1999). Previous work on alleviating catastrophic forgetting can be divided into two categories.
+
+In the first category, updates on the current task are regularized so that the neural network does not forget previous tasks. Elastic weight consolidation (EWC) applies a penalty on the parameter update based on the distance between the parameters for the new and the old task using the Fisher information metric (Kirkpatrick et al., 2016). Other methods maintain a memory buffer that stores a number of data points from previous tasks. For example, gradient episodic memory approach penalizes the gradient on the current task so that it does not increase the loss of examples in the memory buffer (Lopez-Paz & Ranzato, 2017; Chaudhry et al., 2018). Another approach combines experience replay algorithms with lifelong learning (Rolnick et al., 2018; Riemer et al., 2018).
+
+In the second category, one increases model capacity as new tasks are added. For example, progressive neural networks (PNN) copy the entire network for the previous task and add new hidden units when adopting to a new task (Rusu et al., 2016). This prevents forgetting on previous tasks by construction (the network on previous tasks remains the same). However, it leads to significant memory consumption when faced with a large number of lifelong learning tasks. Some following methods expand the model in a more parameter efficient way at the cost of introducing an extra learning task and not entirely preventing forgetting. Yoon et al. (2017) applies group sparsity regularization to efficiently expand model capacity; Xu & Zhu (2018) learns to search for the best architectural changes by carefully designed reinforcement learning strategies.
+
+# 3 METHODS
+
+As described above, ensembles suffer from expensive memory and computational costs. In this section, we introduce BatchEnsemble, an efficient way to ensemble deep neural networks.
+
+# 3.1 BATCHENSEMBLE
+
+In this section, we introduce how to ensemble neural networks in an efficient way. Let $W$ be the weights in a neural network layer. Denote the input dimension as $m$ and the output dimension as $n$ , i.e. $W \in \mathbb { R } ^ { m \times n }$ . For ensemble, assuming the ensemble size is $M$ and each ensemble member has weight matrix $\overline { { W } } _ { i }$ . Each ensemble member owns a tuple of trainable vectors $r _ { i }$ and $s _ { i }$ which share the same dimension as output and input $\mathbf { \xi } _ { n }$ and $m$ ) respectively, where $i$ ranges from 1 to $M$ . Our algorithm generates a family of ensemble weights $\overline { { W } } _ { i } ^ { \bullet }$ by the following:
+
+$$
+\overline { { W } } _ { i } = W \circ F _ { i } , \mathrm { w h e r e } F _ { i } = s _ { i } r _ { i } ^ { \top } ,
+$$
+
+For each training example in the mini-batch, it receives an ensemble weight $\overline { { W } } _ { i }$ by elementwise multiplying $W$ , which we refer to as “slow weights”, with a rank-one matrix $F _ { i }$ , which we refer to as “fast weights.” The subscript $i$ represents the selection of ensemble member. Since $W$ is shared across ensemble members, we term it as "shared weight" in the following paper. Figure 2 visualizes BatchEnsemble. Rather than modulating the weight matrices, one can also modulate the neural networks’ intermediate features, which achieves promising performance in visual reasoning tasks (Perez et al., 2017).
+
+![](images/2db93a67bc870357557fbebb57aa2a0dc73dc2b7416ec74146e2221b83791e83.jpg)  
+Figure 2: An illustration on how to generate the ensemble weights for two ensemble members.
+
+Vectorization: We show how to make the above ensemble weight generation mechanism parallelizable within a device, i.e., where one computes a forward pass with respect to multiple ensemble members in parallel. This is achieved by manipulating the matrix computations for a mini-batch (Wen et al., 2018). Let $x$ denote the activations of the incoming neurons in a neural network layer. The next layer’s activations are given by:
+
+$$
+\begin{array} { r l } & { y _ { n } = \phi \left( \overline { { W } } _ { i } ^ { \top } x _ { n } \right) } \\ & { \quad = \phi \left( \left( W \circ s _ { i } r _ { i } ^ { \top } \right) ^ { \top } x _ { n } \right) } \\ & { \quad = \phi \left( \left( W ^ { \top } ( x _ { n } \circ s _ { i } ) \right) \circ r _ { i } \right) , } \end{array}
+$$
+
+where $\phi$ denotes the activation function and the subscript $n$ represents the index in the mini-batch. The output represents next layer’s activations from the $i ^ { t h }$ ensemble member. To vectorize these computations, we define matrices $R$ and $S$ whose rows consist of the vectors $r _ { i }$ and $s _ { i }$ for all examples in the mini-batch. The above equation is vectorized as:
+
+$$
+Y = \phi \left( ( ( X \circ S ) W ) \circ R \right) .
+$$
+
+where $X$ is the mini-batch input. By computing Eqn. 5, we can obtain the next layer’s activations for each ensemble member in a mini-batch friendly way. This allows us to take full advantage of parallel accelerators to implement the ensemble efficiently. To match the input and the ensemble weight, we can divide the input mini-batch into $M$ sub-batches and each sub-batch receives ensemble weight $\overline { { W } } _ { i }$ , $i = \{ 1 , \ldots , M \}$ .
+
+Ensembling During Testing: In our experiments, we take the average of predictions of each ensemble member. Suppose the test batch size is $B$ and there are $M$ ensemble members. To achieve an efficient implementation, one repeats the input mini-batch $M$ times, which leads to an effective batch size $B \cdot M$ . This enables all ensemble members to compute the output of the same $B$ input data points in a single forward pass. It eliminates the need to calculate the output of each ensemble member sequentially and therefore reduces the ensemble’s computational cost.
+
+# 3.2 COMPUTATIONAL COST
+
+The only extra computation in BatchEnsemble over a single neural network is the Hadamard product, which is cheap compared to matrix multiplication. Thus, BatchEnsemble incurs almost no additional computational overhead (Figure 1).2 One limitation of BatchEnsemble is that if we keep the minibatch size the same as single model training, each ensemble member gets only a portion of input data. In practice, the above issue can be remedied by increasing the batch size so that each ensemble member receives the same amount of data as ordinary single model training. Since BatchEnsemble is parallelizable within a device, increasing the batch size incurs almost no computational overhead in both training and testing stages on the hardware that can fully utilize large batch size. Moreover, when increasing the batch size reaches its diminishing return regime, BatchEnsemble can still take advantage from even larger batch size by increasing the ensemble size.
+
+The only memory overhead in BatchEnsemble is the set of vectors, $\{ r _ { 1 } , \ldots , r _ { m } \}$ and $\{ s _ { 1 } , \ldots , s _ { m } \}$ , which are cheap to store compared to the weight matrices. By eliminating the need to store full weight matrices of each ensemble member, BatchEnsemble has almost no additional memory cost. For example, BatchEnsemble of ResNet-32 of size 4 incurs $1 0 \%$ more parameters while naive ensemble incurs 3X more.
+
+# 3.3 BATCHENSEMBLE AS AN APPROACH TO LIFELONG LEARNING
+
+The significant memory cost of ensemble methods limits its application to many real world learning scenarios such as multi-task learning and lifelong learning, where one might apply an independent copy of the model for each task. This is not the case with BatchEnsemble. Specifically, consider a total of $T$ tasks arriving in sequential order. Denote $D _ { t } = ( x _ { i } , y _ { i } , t )$ as the training data in task $t$ where $t \in \{ 1 , 2 , \ldots , T \}$ and $i$ is the index of the data point. Similarly, denote the test data set as $\mathcal { T } _ { t } = ( x _ { i } , y _ { i } , t )$ . At test time, we compute the average performance on $\mathcal { T } _ { t }$ across all tasks seen so far as the evaluation metric. To extend BatchEnsemble to lifelong learning, we compute the neural network prediction in task $t$ with weight $\overline { { W } } _ { t } = W \circ ( r _ { t } s _ { t } ^ { \top } )$ in task $t$ . In other words, each ensemble member is in charge of one lifelong learning task. For the training protocol, we train the shared weight $W$ and two fast weights $r _ { 1 } , s _ { 1 }$ on the first task,
+
+$$
+\operatorname* { m i n } _ { W , s _ { 1 } , r _ { 1 } } L _ { 1 } ( W , s _ { 1 } , r _ { 1 } ; D _ { 1 } ) ,
+$$
+
+where $L _ { 1 }$ is the objective function in the first task such as cross-entropy in image classification. On a subsequent task $t$ , we only train the relevant fast weights $r _ { t } , s _ { t }$ .
+
+$$
+\operatorname* { m i n } _ { s _ { t } , r _ { t } } L _ { t } ( s _ { t } , r _ { t } ; D _ { t } ) .
+$$
+
+BatchEnsemble shares similar advantages as progressive neural networks (PNN): it entirely prevents catastrophic forgetting as the model for previously seen tasks remains the same. This removes the need of storing any data from previous task. In addition, BatchEnsemble has significantly less memory consumption than PNN as only fast weights are trained to adapt to a new task. Therefore, BatchEnsemble can easily scale to up to 100 tasks as we showed in Section 4.1 on split ImageNet. Another benefit of BatchEnsemble is that if future tasks arrive in parallel rather than sequential order, one can train on all the tasks at once (see Section 3.1). We are not aware of any other lifelong learning methods can achieve this.
+
+Table 1: Computational and memory costs on Split-CIFAR100 on LeNet. Numbers are relative to vanilla neural network.   
+
+<table><tr><td></td><td>Vanilla</td><td>BatchE</td><td>DEN</td><td>PNN</td><td>RCL</td></tr><tr><td>Computational</td><td>1</td><td>1.11</td><td>9.58</td><td>1.12</td><td>26.41</td></tr><tr><td>Memory</td><td>1</td><td>1.10</td><td>5.31</td><td>4.16</td><td>2.52</td></tr></table>
+
+Limitations: BatchEnsemble is one step toward toward a full lifelong learning agent that is both immune to catastrophic forgetting and parameter-efficient. On existing benchmarks like split-CIFAR and split-ImageNet, Section 4.1 shows that BatchEnsemble’s rank-1 perturbation per layer provides enough expressiveness for competitive state-of-the-art accuracies. However, one limitation of BatchEnsemble is that only rank-1 perturbations are fit to each lifelong learning task and thus the model’s expressiveness is a valid concern when each task is significantly varied. Another limitation is that the shared weight is only trained on the first task. This implies that only information learnt for the first task can transfer to subsequent tasks. There is no explicit transfer, for example, between the second and third tasks. One solution is to enable lateral connections to features extracted by the weights of previously learned tasks, as done in PNN. However, we found that no lateral connections were needed for Split-CIFAR100 and Split-ImageNet. Therefore we leave the above solution to future work to further improve BatchEnsemble for lifelong learning.
+
+Computational cost compared to other methods: Dynamically expandable networks (Yoon et al., 2017) and reinforced continual learning (Xu & Zhu, 2018) are two recently proposed lifelong learning methods that achieve competitive performance. These two methods can be seen as an improved version progressive neural network (PNN) (Rusu et al., 2016) in terms of memory efficiency. As shown in Xu & Zhu (2018), all three methods result to similar accuracy measure in Split-CIFAR100 task. Therefore, among three evaluation metrics (accuracy, forgetting and cost), we only compare the accuracy of BatchEnsemble to PNN in Section 4.1 and compare the cost in this section. We first compute the cost relative to PNN on Split-CIFAR100 on LeNet and then compute the rest of the numbers base on what were reported in Xu & Zhu (2018). Notice that PNN has no much computational overhead on Split-CIFAR100 because the number of total tasks is limited to 10. Even on the simple setup above, BatchEnsemble gives the best computational and memory efficiency. BatchEnsemble leads to more lower costs on large lifelong learning tasks such as Split-ImageNet.
+
+# 4 EXPERIMENTS
+
+Section 4.1 first demonstrates BatchEnsemble’s effectiveness as an alternative approach to lifelong learning on Split-CIFAR and Split-ImageNet. Section 4.2 and Section 4.3 next evaluate BatchEnsemble on several benchmark datasets with common deep learning architectures, including image classification with ResNet (He et al., 2016) and neural machine translation with Transformer (Vaswani et al., 2017). Section 4.4 demonstrates that BatchEnsemble can be used for calibrated prediction. Finally, we showcase its applications in uncertainty modelling in Appendix C and Appendix D. Detailed description of datasets we used is in Appendix A. Implementation details are in Appendix B.
+
+# 4.1 LIFELONG LEARNING
+
+We showcase BatchEnsemble for lifelong learning on Split-CIFAR100 and Split-ImageNet. SplitCIFAR100 proposed in Rebuffi et al. (2016) is a harder lifelong learning task than MNIST permutations and MNIST rotations (Kirkpatrick et al., 2016), where one introduces a new set of classes upon the arrival of a new task. Each task consists of examples from a disjoint set of $1 0 0 / T$ classes assuming $T$ tasks in total. To show that BatchEnsemble is able to scale to 100 sequential tasks, we also build our own Split-ImageNet dataset which shares the same property as Split-CIFAR100 except more classes (and thus more tasks) and higher image resolutions are involved. More details about these two lifelong learning datasets are provided in Appendix A.
+
+We consider $T = 2 0$ tasks on Split-CIFAR100, following the setup of Lopez-Paz & Ranzato (2017). We used ResNet-18 with slightly fewer number of filters across all convolutional layers. Note that for the purpose of making use of the task descriptor, we build a different final dense layer per task. We compare BatchEnsemble to progressive neural networks (PNN) (Rusu et al., 2016), vanilla neural networks, and elastic weight consolidation (EWC) on Split-CIFAR100. Xu & Zhu (2018) reported similar accuracies among DEN (Yoon et al., 2017), RCL (Xu & Zhu, 2018) and PNN. Therefore we compare accuracy only to PNN which has an official implementation and only compare computational and memory costs to DEN and RCL in Table 1.
+
+![](images/5e7678611432061aa2d03c69ecf48394cb04706d5c76a1a38fc4655825f0f9be.jpg)  
+Figure 3: Performance for lifelong learning. (a): Validation accuracy for each Split-ImageNet task. Standard deviation is computed over 5 random seeds. (b): BatchEnsemble and several other methods on Split-CIFAR100. BatchEnsemble achieves the best trade-off among Accuracy (↑), Forget (↓), and Time & Memory (↓) costs. VAN: Vanilla neural network. EWC: Elastic weight consolidation (Kirkpatrick et al., 2016). PNN: Progressive neural network (Rusu et al., 2016). BNTuned: Fine tuning Batch Norm layer per subsequent tasks. BatchE: BatchEnsemble. Upperbound: Individual ResNet-50 per task.
+
+Figure 3b displays results on Split-CIFAR100 over three metrics including accuracy, forgetting, and cost. The accuracy measures the average validation accuracy over total 20 tasks after lifelong learning ends. Average forgetting over all tasks is also presented in Figure 3b. Forgetting on task $t$ is measured by the difference between accuracy of task $t$ right after training on it and at the end of lifelong learning. It measures the degree of catastrophic forgetting. As showed in Figure 3b, BatchEnsemble achieves comparable accuracy as PNN while having 4X speed-up and 50X less memory consumption. It also preserves the no-forgetting property of PNN. Therefore BatchEnsemble has the best trade-off among all compared methods.
+
+For Split-ImageNet, we consider $T = 1 0 0$ tasks and apply ResNet-50 followed by a final linear classifier per task. The parameter overhead of BatchEnsemble on Split-ImageNet over 100 sequential tasks is $2 0 \%$ : the total number of parameters is 30M v.s. 25M (vanilla ResNet-50). PNN is not capable of learning 100 sequential tasks due to the significant memory consumption; other methods noted above have also not shown results at ImageNet scale. Therefore we adopt two of our baselines. The first baseline is “BN-Tuned”, which fine-tunes batch normalization parameters per task and which has previously shown strong performance for multi-task learning (Mudrakarta et al., 2018). To make a fair comparison, we augment the number of filters in BN-Tuned so that both methods have the same number of parameters. The second baseline is a naive ensemble which trains an individual ResNet-50 per task. This provides a rough upper bound on the BatchEnsemble’s expressiveness per task. Note BatchEnsemble and both baselines are immune to catastrophic forgetting. So we consider validation accuracy on each subsequent task as evaluation metric. Figure 3a shows that BatchEnsemble outperforms BN-Tuned consistently. This demonstrates that BatchEnsemble is a practical method for lifelong learning that scales to a large number of sequential tasks.
+
+# 4.2 MACHINE TRANSLATION
+
+In this section, we evaluate BatchEnsemble on the Transformer (Vaswani et al., 2017) and the large-scale machine translation tasks WMT14 EN-DE/EN-FR. We apply BatchEnsemble to all selfattention layers with an ensemble size of 4. The ensemble in a self-attention layer can be interpreted as each ensemble member keeps their own attention mechanism and makes independent decisions. We conduct our experiments on WMT16 English-German dataset and WMT14 English-French dataset with Transformer base (65M parameters) and Transformer big (213M parameters). We maintain exactly the same training scheme and hyper-parameters between single Transformer model and BatchEnsemble Transformer model.
+
+![](images/8bb712157a9b2dcbe4f181c52a5b0912a5775a7a2c189f0cd3badd3f2730a545.jpg)  
+Figure 4: Comparison between BatchEnsemble and single model on WMT English-German and English-French. Training stops after the model reaches targeted validation perplexity. BatchEnsemble gives a faster convergence by taking the advantage of multiple models. (a): Validation loss of WMT16 English-German task. (b): Validation loss of WMT14 English-French task. Big: Tranformer big model. Base: Transformer base model. BE: BatchEnsemble. Single: Single model.
+
+As the result shown in Figure 4, BatchEnsemble achieves a much faster convergence than a single model. Big BatchEnsemble Transformer is roughly $1 . 5 \mathrm { X }$ faster than single big Transformer on WMT16 English-German. In addition, the BatchEnsemble Transformer also gives a lower validation perplexity than big Transformer (Table 2). This suggests that BatchEnsemble is promising for bigger Transformer models. We also compared BatchEnsemble to dropout ensemble (MC-drop in Table 2). Transformer single model itself uses dropout layers. We run multiple forward passes with different sampled dropout maskd during testing. The sample size is 16 which is already 16X more expensive than BatchEnsemble. As Table 2 showed, dropout ensemble doesn’t give better performance than single model. However, Appendix B shows that while BatchEnemble’s test BLEU score increases faster over the course of training, BatchEnsemble which gives lower validation loss does not achieve a better BLEU score over the single model.
+
+Table 2: Perplexity on Newstest2013 with big Transformer. BatchEnsemble with ensemble size 4.   
+
+<table><tr><td colspan="2">Single</td><td>MC-drop</td><td>BatchE</td></tr><tr><td>EN-DE</td><td>4.30</td><td>4.30</td><td>4.26</td></tr><tr><td>EN-FR</td><td>2.76</td><td>2.77</td><td>2.74</td></tr></table>
+
+# 4.3 CLASSIFICATION
+
+We evaluate BatchEnsemble on classification tasks with CIFAR-10/100 dataset (Krizhevsky, 2009). We run our evaluation on ResNet32 (He et al., 2016). To achieve $1 0 0 \%$ training accuracy on CIFAR100, we use 4X more filters than the standard ResNet-32. In this section, we compare to MC-dropout (Gal & Ghahramani, 2015), which is also a memory efficient ensemble method. We add one more dense layer fol
+
+Table 3: Validation accuracy on ResNet32. Ensemble with size 4. MC-drop stands for Dropout ensemble (Gal & Ghahramani, 2015).   
+
+<table><tr><td></td><td>Single</td><td>MC-drop</td><td>BatchE</td><td>NaiveE</td></tr><tr><td>C10</td><td>95.31</td><td>95.72</td><td>95.94</td><td>96.30</td></tr><tr><td>C100</td><td>78.32</td><td>78.89</td><td>80.32</td><td>81.02</td></tr></table>
+
+lowed by dropout before the final linear classifier so that the number of parameters of MC-dropout are the same as BatchEnsemble. Most hyper-parameters are shared across the single model, BatchEnsemble, and MC-dropout. More details about hyper-parameters are in Appendix B. Note that we increase the training iterations for BatchEnsemble to reach its best performance because each ensemble member gets only a portion of input data.
+
+We train both BatchEnsemble model and MC-dropout with 375 epochs on CIFAR-10/100, which is $5 0 \%$ more iterations than single model. Although the training duration is longer, BatchEnsemble is still significantly faster than training individual model sequentially. Another implementation that leads to the same performance is to increase the mini-batch size. For example, if we use 4X large minibatch size then there is no need to increase the training iterations. Table 3 shows that BatchEnsemble reaches better accuracy than single model and MC-dropout. We also calculate the accuracy of naive ensemble, whose members consist of individually trained single models. Its accuracy can be viewed as the upper bound of efficient ensembling methods. For fairness, we also compare BatchEnsemble to naive ensemble of small models in Appendix F.
+
+![](images/7c6bb26bed5e211b80c70b34f40ef43ed091d86ff9185c424955634eb0d29285.jpg)  
+Figure 5: Calibration on CIFAR-10 corruptions: boxplots showing a comparison of ECE under all types of corruptions on CIFAR-10. Each box shows the quartiles summarizing the results across all types of skew while the error bars indicate the min and max across different skew types. Ensemble/BatchEnsemble: Naive/Batch ensemble of $4 { \mathrm { R e s N e t } } 3 2 { \mathrm { x } } 4$ models. Dropout-8: Dropout ensemble with sample size 8. BEDrop-8: BatchEnsemble of 4 models $^ +$ Dropout ensemble with sample size 8. A similar measurement can be found in Ovadia et al. (2019).
+
+# 4.4 CALIBRATION ON CORRUPTED DATASET
+
+In this section, we measure the calibrated prediction of BatchEnsemble on corrupted datasets. Other uncertainty modelling tasks such as contextual bandits are delegated to Appendix C and Appendix D.
+
+Other than unseen classes, corruption is another type of out-of-distribution examples. It is common that the collected data is corrupted or mislabelled. Thus, measuring uncertainty modelling under corruption is practically meaningful. We want our model to preserve uncertainty or calibration in this case. In this section, we evaluate the calibration of different methods on recently proposed CIFAR-10 corruption dataset (Hendrycks & Dietterich, 2019). The dataset consists of over 30 types of corruptions to the images. Notice that the corrupted dataset is used as a testset without training on it. Given the predictions on CIFAR-10 corruption, we can compare accuracy and calibration measure such as ECE loss for single neural network, naive ensemnble, and BatchEnsemble. Ovadia et al. (2019) benchmarked a number of methods on CIFAR-10 corruption. Their results showed that naive ensemble achieves the best performance on both accuracy and ECE loss, outperforming other methods including dropout ensemble, temperature scaling and variational methods significantly. Dropout ensemble is the state-of-the-art memory efficient ensemble method.
+
+The scope of this paper is on efficient ensembles. Thus, in this section, we mainly compare BatchEnsemble to dropout ensemble on CIFAR-10 corruption. Naive ensemble is also plotted as an upper bound of our method. As showed in Figure 5, BatchEnsemble and dropout ensemble achieve comparable accuracy on corrupted dataset on all skew intensities. Calibration is a more important metric than accuracy when the dataset is corrupted. We observed that BatchEnsemble achieves better average calibration than dropout as the skew intensity increases. Moreover, dropout ensemble requires multiple forward passes to get the best performance. Ovadia et al. (2019) used sample size 128 while we found no significant difference between sample size 128 and 8. Note that even for sample size is 8, it is 8X more expensive than BatchEnsemble in the testing time cost. Finally, we showed that combining BatchEnsemble and dropout ensemble leads to better accuracy and calibration. It is competitive to naive ensemble while keeping memory consumption efficient. It is also an evidence that BatchEnsemble is an orthogonal method to dropout ensemble; combining these two can potentially obtain better performance.
+
+# 5 DIVERSITY ANALYSIS
+
+As mentioned in Section 2, more diversity among ensembling members leads to better performance. Therefore, beyond accuracy and uncertainty metrics, we are particularly interested in how much diversity rank-1 perturbation provides. We compare BatchEnsemble to dropout ensemble and naive ensemble over the newly proposed diversity metric (Fort et al., 2019). The metric measures the disagreement among ensemble members on test set. We computed it over different amount of training data. See Appendix E for details on diversity metric and plots.
+
+In this section, we give an intuitive explanation of why BatchEnsemble leads to more diverse members with fewer training data. If only limited training data is available, the parameters of the neural network would remain close to their initialization after convergence. In the extreme case where only one training data point is available, the optimization quickly converges and most of the parameters are not updated. This suggests that the diversity of initialization entirely determines the diversity of ensembling system. Naive ensemble has fully independent random initializations. BatchEnsemble has peudo-independent random initializations. In comparison, all ensemble members of dropout ensemble share the same initialized parameters. Therefore, both naive ensemble and BatchEnsemble significantly outperform dropout ensemble in diversity with limited training data.
+
+More importantly, Figure 8 provides insightful advice on when BatchEnsemble achieves the best gain in practice. We observe that diversity of BatchEnsemble is comparable to naive ensemble when training data is limited. This explains why BatchEnsemble has higher gains on CIFAR-100 than CIFAR-10, because there are only 500 training points for each class on CIFAR-100 whereas 5000 on CIFAR-10. Thus, CIFAR-100 has more limited training data compared to CIFAR-10. Another implication is that BatchEnsemble can benefit more from heavily over-parameterized neural networks. The reason is that given the fixed amount of training data, increasing the number of parameters essentially converges to the case where the training data is limited. In practice, the best way to make full use of increasing computational power is to design deeper and wider neural networks. This suggests that BatchEnsemble benefits more from the development of computational power; because it has better gain on over-parameterized neural networks.
+
+# 6 CONCLUSION
+
+We introduced BatchEnsemble, an efficient method for ensembling and lifelong learning. BatchEnsemble can be used to improve the accuracy and uncertainty of any neural network like typical ensemble methods. More importantly, BatchEnsemble removes the computation and memory bottleneck of typical ensemble methods, enabling its successful application to not only faster ensembles but also lifelong learning on up to 100 tasks. We believe BatchEnsemble has great potential to improve in lifelong learning. Our work may serve as a starting point for a new research area.
+
+# ACKNOWLEDGMENTS
+
+YW was supported by University of Toronto Fellowship, Faculty of Arts And Science and Vector Scholarships in Artificial Intelligence (VSAI).
+
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+# A DATASET DETAILS
+
+CIFAR: We consider two CIFAR datasets, CIFAR-10 and CIFAR-100 (Krizhevsky, 2009). Each consists of a training set of size 50K and a test set of size 10K. They are natural images with $3 2 \mathbf { x } 3 2$ pixels. In our experiments, we follow the standard data pre-processing schemes including zero-padding with 4 pixels on each sise, random crop and horizon flip (Romero et al., 2015; Huang et al., 2016; Srivastava et al., 2015).
+
+WMT: In machine translation tasks, we consider the standard training datasets WMT16 EnglishGerman and WMT14 English-French. WMT16 English-German dataset consists of roughly 4.5M sentence pairs. We follow the same pre-processing schemes in (Vaswani et al., 2017).Source and target tokens are processed into 37K shared sub-word units based on byte-pair encoding (BPE) (Britz et al., 2017). Newstest2013 and Newstest2014 are used as validation set and test set respectively. WMT14 English-French consists of a much larger dataset sized at 36M sentences pairs. We split the tokens into a 32K word-piece vocabulary (Wu et al., 2016).
+
+Split-CIFAR100: The dataset has the same set of images as CIFAR-100 dataset (Krizhevsky, 2009). It randomly splits the entire dataset into $\mathrm { T }$ tasks so each task consists of $1 0 0 / T$ classes of images. To leverage the task descriptor in the data, different final linear classifier is trained on top of feature extractor per task. This simplifies the task to be a $1 0 0 / T$ class classification problem in each task. i.e. random prediction has accuracy $T / 1 0 0$ . Notice that since we are not under the setting of single epoch training, standard data pre-processing including padding, random crop and random horizontal flip are applied to the training set.
+
+Split-ImageNet: The dataset has the same set of images as ImageNet dataset (Deng et al., 2009). It randomly splits the entire dataset into $\mathrm { T }$ tasks so each task consists of $1 0 0 0 / T$ classes of images. Same as Split-CIFAR100, each task has its own final linear classifier. Data preprocessing (He et al., 2016) is applied to the training data.
+
+# B IMPLEMENTATION DETAILS
+
+In this section, we discuss some implementation details of BatchEnsemble.
+
+Weight Decay: In the BatchEnsemble, the weight of each ensemble member is never explicitly calculated because we obtain the activations directly by computing Eqn. 5. To maintain the goal of no additional computational cost, we can instead regularize the mean weight $\overline { W }$ over ensemble members, which can be efficiently calculated as $\begin{array} { r } { \overline { { W } } = \frac { 1 } { B } W \circ S ^ { \top } R } \end{array}$ , where $W$ is the shared weight among ensemble members, $S$ and $R$ are the matrices in Eqn. 5. We can also only regularize the
+
+![](images/6b6bb89dfa16bfc2ad35be0e9c541cbe034e90f5e789cffed3585264905c70e9.jpg)  
+Figure 6: BLEU on English-German task.
+
+shared weight and leave the fast weights unregularized because it only accounts for a small portion of model parameters. In practice, we find the above two schemes work equally.
+
+Diversity Encouragement: Additional loss term such as KL divergence among ensemble members can be added to encourage diversity. However, we find it sufficient for BatchEnsemble to have desired diversity by initializing the fast weight ( $s _ { i }$ and $r _ { i }$ in Eqn. 1) to be random sign vectors. Also note that the scheme that each ensemble member is trained with different sub-batch of input can encourage diversity as well. The diversity analysis is provided in Appendix G.
+
+Machine Translation: The Transformer base is trained for 100K steps and the Transformer big is trained for 180K steps. The training steps of big model are shorter than Vaswani et al. (2017) because we terminate the training when it reaches the targeted perplexity on validation set. Experiments are run on 4 NVIDIA P100 GPUs. The BLEU score of Big Transformer on English-German task is in Figure 6. Although BatchEnsemble has lower perplexity as we showed in Section 4.2, we didn’t observe a better BLEU score. Noted that the BLEU score in Figure 6 is lower than what Vaswani et al. (2017) reported. It is because in order to correctly evaluate model performance at a given timestep, we didn’t use the averaging checkpoint trick. The dropout rate of Transformer base is 0.1 and 0.3 for
+
+Transformer big on English-German while remaining 0.1 on English-French. For dropout ensemble, we ran a grid search between 0.05 and 0.3 in the testing time and report the best validation perplexity.
+
+Classification: We train the model with mini-batch size 128. We also keep the standard learning rate schedule for ResNet. The learning rate decreases from 0.1 to 0.01, from 0.01 to 0.001 at halfway of training and $7 5 \%$ of training. The weight decay coefficient is set to be $1 0 ^ { - 4 }$ . We use an ensemble size of 4, which means each ensemble member receives 32 training examples if we maintain the mini-batch size of 128. It is because Batch Normalization (Ioffe & Szegedy, 2015) requires at least 32 examples to be effective on CIFAR dataset. As for the training budget, we train the single model for 250 epochs
+
+# C PREDICTIVE UNCERTAINTY
+
+In this section, we evaluate the predictive uncertainty of BatchEnsemble on out-of-distribution tasks and ECE loss.
+
+(a) Histogram of the predictive entropy on test examples from known classes, CIFAR-10 (left) and unknown classes, CIFAR-100 (right).
+
+Similar to Lakshminarayanan et al. (2017), we first evaluate BatchEnsemble on out-ofdistribution examples from unseen classes. It is known that deep neural network tends to make over-confident predictions even if the prediction is wrong or the input comes from unseen classes. Ensembles of models can give better uncertainty prediction when the test data is out of the distribution of training data. To measure the uncertainty on the prediction, we calculate the predictive entropy of Single neural network, naive ensemble and BatchEnsemble. The result is presented in Figure 7a. As we expected, single model produces over-confident predictions on unseen examples, whereas ensemble methods exhibit higher uncertainty on unseen classes, including both BatchEnsemble and naive ensemble. It suggests our ensemble weight generation mechanism doesn’t degrade uncertainty modelling.
+
+![](images/15f2cdcf564edacf6fe14fc6dc8e30c6c80bed59e404e613004d200a408f5fb8.jpg)
+
+(b) Expected Calibration Error. Ensemble of size 4. Lower ECE reflects better calibration.   
+
+<table><tr><td></td><td>Single</td><td>MC-drop</td><td>BatchE</td><td>NaiveE</td></tr><tr><td>C10</td><td>3.27</td><td>2.89</td><td>2.37</td><td>2.32</td></tr><tr><td>C100</td><td>9.28</td><td>8.99</td><td>8.89</td><td>6.82</td></tr></table>
+
+We also calculate the Expected Calibration Error (Naeini et al., 2015) (ECE) of single model, naive ensemble and BatchEnsemble on both CIFAR-10 and CIFAR-100 in Table 7b. To calculate ECE, we group model predictions into $\mathbf { M }$ interval bins based on the predictive confidence (each bin has size $\mathbf { \frac { \partial T } { \partial \mathbf { u } } } )$ ). Let $B _ { m }$ denote the set of samples whose predictive probability falls into the interval $\textstyle \left( { \frac { m - 1 } { M } } , { \frac { m } { M } } \right]$ for $m \in \{ 1 , \ldots M \}$ . Let $\operatorname { a c c } ( B _ { m } )$ and conf $( B _ { m } )$ be the averaged accuracy and averaged confidence of the examples in the bin $B _ { m }$ . The ECE can de defined as the following,
+
+$$
+\mathrm { E C E } = \sum _ { m = 1 } ^ { M } \frac { | B _ { m } | } { n } | \mathrm { a c c } ( B _ { m } ) - \mathrm { c o n f } ( B _ { m } ) |
+$$
+
+where $n$ is the number of samples. ECE as a criteria of model calibration, measures the difference in expectation between confidence and accuracy (Guo et al., 2017). It shows that BatchEnsemble makes more calibrated prediction compared to single neural networks.
+
+# D UNCERTAINTY ON BANDITS
+
+In this section, we conduct analysis beyond accuracy, where we show that BatchEnsemble can be used for uncertainty modelling in contextual bandits.
+
+For uncertainty modelling, we evaluate our BatchEnsemble method on the recently proposed bandits benchmark (Riquelme et al., 2018). Bandit data comes from different empirical problems that highlight several aspects of decision making. No single algorithm can outperform every other algorithm on every bandit problem. Thus, average performance of the algorithm over different problems is used to evaluate the quality of uncertainty estimation. The key factor to achieve good performance in contextual bandits is to learn a reliable uncertainty model. In our experiment, Thompson sampling samples from the policy given by one of the ensemble members. The fact that Dropout which is an implicit ensemble method achieves competitive performance on bandits problem suggests that ensemble can be used as uncertainty modelling. Indeed, Table 4 shows that BatchEnsemble with an ensemble size 8 achieves the best mean value on the bandits task. Both BatchEnsemble with ensemble size 4 and 8 outperform Dropout in terms of average performance. We also evaluate BatchEnsemble on CIFAR-10 corrupted dataset (Hendrycks & Dietterich, 2019) in Appendix C. Figure 5 shows that BatchEnsemble achieves promising accuracy, uncertainty and cost trade-off among all methods we compared. Moreover, combining BatchEnsemble and dropout ensemble leads to better uncertainty prediction.
+
+Table 4: Contextual bandits regret. Results are relative to the cumulative regret of the Uniform algorithm. We report the mean and standard error of the mean over 30 trials. Ensemble size with 4, 8. We remove the methods with mean rank greater than 10.   
+
+<table><tr><td></td><td>M.RANK</td><td>M.VALUE</td><td>MUSHROOM</td><td>STATLOG</td><td>FINANCIAL</td><td>JESTER</td><td>WHEEL</td></tr><tr><td>NaiveEnsemble4</td><td>5.30</td><td>34.64</td><td>13.44 ± 3.83</td><td>7.10 ± 1.15</td><td>11.31 ± 1.48</td><td>72.73 ± 6.32</td><td>68.63 ± 21.97</td></tr><tr><td>NaiveEnsemble8</td><td>6.50</td><td>34.91</td><td>13.59 ± 3.13</td><td>7.15 ± 0.98</td><td>11.64 ± 1.57</td><td>73.54 ± 6.14</td><td>68.65 ± 19.32</td></tr><tr><td>BatchEnsemble4</td><td>6.30</td><td>34.52</td><td>15.22 ± 5.21</td><td>11.53 ± 5.06</td><td>10.24 ± 2.66</td><td>72.65 ± 6.27</td><td>62.94 ± 26.12</td></tr><tr><td>BatchEnsemble8</td><td>5.70</td><td>33.95</td><td>13.48 ± 3.36</td><td>9.85 ± 3.67</td><td>13.17 ± 2.87</td><td>71.84 ± 6.47</td><td>61.41 ± 26.18</td></tr><tr><td>Dropout</td><td>8.20</td><td>36.73</td><td>15.05 ± 8.23</td><td>9.31 ± 3.19</td><td>13.53 ± 2.98</td><td>71.90 ± 6.31</td><td>73.86 ± 22.48</td></tr><tr><td>LinFullPost</td><td>9.40</td><td>49.60</td><td>97.42 ± 4.52</td><td>19.00 ±1.03</td><td>10.24 ± 0.92</td><td>78.40 ± 4.85</td><td>42.94 ± 12.68</td></tr><tr><td>MultitaskGP</td><td>5.90</td><td>34.59</td><td>12.87 ± 4.70</td><td>8.04 ± 3.77</td><td>8.50 ± 0.80</td><td>74.03 ± 5.96</td><td>69.52 ± 18.55</td></tr><tr><td>RMS</td><td>9.40</td><td>39.18</td><td>16.31 ± 6.13</td><td>10.44 ± 5.02</td><td>11.75 ± 2.64</td><td>73.38 ± 4.70</td><td>84.02 ± 24.67</td></tr><tr><td>Uniform</td><td>16.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td><td>100.00</td></tr></table>
+
+# E DIVERSITY ANALYSIS
+
+# E.1 DIVERSITY METRIC
+
+Final performance metrics such as accuracy and uncertainty score we provided in Section 4 obscures many insights of our models. In this section, we provide visualization of some commonly used diversity metrics proposed in Fort et al. (2019). The diversity score used in the experiments below quantify the difference of two functions, by measuring fraction of the test data points on which their predictions disagree. This metric is 0 when two functions are making identical predictions, and 1 when they differ on every single example in the test set. We also normalize the diversity metric by the error rate to account for the case where random predictions provide the best diversity. There are other diversity metrics we can use such as the KL-divergence between the probability distributions. It doesn’t make significant difference in our experiments, so we chose the fraction of disagreement for simplicity. We compare BatchEnsemble to dropout ensemble and naive ensemble. For BatchEnsemble and naive ensemble, we first select a model as our base model. We calculated the diversity measure of other ensembling members against the base model. We also plotted the diversity of the base model as a reference, which is trivially zero. For dropout ensemble, we sample a number of dropout masks and take the prediction of the first dropout mask as the base model. The disagreement fraction of the rest dropout masks can be computed against the base model.
+
+In Figure 8, we plotted the diversity measures of BatchEnsemble, dropout ensemble and naive ensemble. According to the ensembling theory 2, the more diversity among ensembling members leads to better total accuracy. As Table 3 showed, naive ensemble achieves the best accuracy and then followed by BatchEnsemble and dropout ensemble. Therefore, we expect the diversity measure of BatchEnsemble is in the middle of naive ensemble and dropout ensemble. Figure 8a confirms our hypothesis. Note that naive ensemble, which only differs from random initializations, is very effective at sampling diverse and accurate solutions. This is aligned to the observation in Fort et al. (2019). Notice that naive ensemble incurs 4X more memory cost and 3X more inference time than Rank-1 Net. Thus, we can conclude that BatchEnsemble achieves the best trade-off among accuracy, diversity and efficiency in all methods we compared. The diversity gap between naive ensemble and BatchEnsemble is due to the limited expressiveness of rank-1 perturbation. This provides scope for future research direction.
+
+![](images/0cf2310b00f419ecf4dca46460162ac08dec7809c52722a13063bf7988f2acda.jpg)  
+Figure 8: Comparison among BatchEnsemble, naive ensemble and dropout ensemble over diversity metric. Each point in the plot represents a trained model where $\mathbf { X }$ -axis represents its accuracy on validation set and y-axis represents its diversity against the base model. The base model trivially has 0 diversity. We plot the diversity of models trained on different proportions of training data, respectively $1 0 0 \%$ , $5 0 \%$ , $2 0 \%$ and $1 0 \%$ .
+
+# E.2 DIVERSITY METRIC ON PARTIAL TRAINING SET
+
+There are two sources of uncertainty: aleatoric uncertainty and epistemic uncertainty. Epistemic uncertainty accounts for the uncertainty in the model we train. We focus more on epistemic uncertainty because the aleatoric uncertainty is difficult to measure. The simplest to magnify epistemic uncertainty is to reduce the number of training data points. Under this case, we want our model to be more uncertain to reflect the lack of training data. Ovadia et al. (2019) showed that more diversity among ensembling member leads to larger uncertainty score. There, under the case where only limited training data is provided, we hope that our ensembling method can produce more diverse member, compared to training on full dataset.
+
+We repeated the experiments in Appendix E.1 with the exactly same diversity metric on models trained with proportional CIFAR-10 dataset. Figure 8b, Figure 8c and Figure 8d plotted the diversity measure with $5 \bar { 0 } \%$ , $2 0 \%$ , and $1 0 \%$ CIFAR-10 training data, respectively. The results showed that BatchEnsemble is on par with naive ensemble under limited training data. In Figure 8b, it shows that when we reduce the number of training data to a half, BatchEnsemble achieves comparable diversity to naive ensemble. It outperforms dropout ensemble by a significant margin. Figure 8c and Figure 8d confirm the conclusion under even fewer training data points. Given the fact that diversity reflects epistemic uncertainty, we want our model to have more diversity when only limited training data is available. However, Figure 8 showed that dropout ensemble has the same diversity on $1 0 0 \%$ , $5 0 \%$ , and $2 0 \%$ training data. This is a significant flaw of dropout ensemble. In conclusion, BatchEnsemble leads to much more diverse member than dropout ensemble under the case of limited training data. To supplement Figure 8, we provide the ensembling accuracy of BatchEnsemble, naive ensemble and dropout ensemble trained on proportional training set in Table 5.
+
+Table 5: Validation accuracy on ResNet32 with proportional training data. Ensemble with size 4. MC-drop stands for dropout ensemble (Gal & Ghahramani, 2015). Single represents the accuracy of the base model in naive ensemble in Figure 8.   
+
+<table><tr><td></td><td>Single</td><td>MC-drop</td><td>BatchEnsemble</td><td>NaiveEnsemble</td></tr><tr><td>CIFAR-10</td><td>95.22</td><td>95.40</td><td>95.61</td><td>96.09</td></tr><tr><td>CIFAR-10 (50%)</td><td>92.20</td><td>92.43</td><td>92.93</td><td>93.01</td></tr><tr><td>CIFAR-10 (20%)</td><td>82.32</td><td>84.5</td><td>86.08</td><td>86.17</td></tr><tr><td>CIFAR-10 (10%)</td><td>69.37</td><td>71.3</td><td>76.75</td><td>76.77</td></tr></table>
+
+# F COMPARISON TO NAIVE ENSEMBLE OF SMALL MODELS
+
+In this section, we compare BatchEnsemble to naive ensemble of small models on CIFAR-10/100 dataset. To maintain the same memory consumption as BatchEnsemble, we trained 4 independent ResNet14x4 models and evaluate the naive ensemble on these 4 models. This setup of naive ensemble still has roughly $1 0 \%$ memory overhead to BatchEnsemble. The results are reported in Table 6. It shows that naive ensemble of small models achieves lower accuracy than BatchEnsemble. It illustrates that given the same memory budget, BatchEnsemble is a better choice over naive ensemble.
+
+Table 6: Supplementary result to Table 3. NaiveSmall is naive ensemble of 4 ResNet14x4 models. Vanilla, MC-drop and BatchEnsemble are still ResNet32x4 as in Table 3.   
+
+<table><tr><td></td><td>Vanilla</td><td>MC-drop</td><td>BatchEnsemble</td><td>NaiveSmall</td></tr><tr><td>CIFAR10</td><td>95.31</td><td>95.72</td><td>95.94</td><td>95.59</td></tr><tr><td>CIFAR100</td><td>78.32</td><td>78.89</td><td>80.32</td><td>79.09</td></tr></table>
+
+# G PREDICTIVE DIVERSITY
+
+As we discussed in Section 2, ensemble benefits from the diversity among its members. We focus on the set of test examples on CIFAR-10 where single model makes confident incorrect predictions while ensemble model predicts correctly. We used the final models we reported in Section 4.3. In Figure 9, we randomly select examples from the above set and plot the prediction map of single model, each ensemble member and mean ensemble. As we can see, although some of the ensemble members make mistakes on thoes examples, the mean prediction takes the advantage of the model averaging and achieves better accuracy on CIFAR-10 classification task. We notice that BatchEnsemble preserves the diversity among ensemble members as naive ensemble.
+
+![](images/aca4431e9b48283221469ddfd9af7de34571eea72635c49fb0eac611a4f9ba85.jpg)  
+Figure 9: Visualizing prediction diversity among BatchEnsemble (top row) and naive ensemble (bottom row) members on selected test examples on CIFAR-10. The y-axis label denotes mean prediction of ensemble (Mean), individual ensemble member prediction (from E1 to E4) and single model prediction (Single). Correct class is labelled as red. BatchEnsemble preserves the model diversity as naive ensemble.

parse/train/T4gXBOXoIUr/T4gXBOXoIUr.md

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+# CONTRASTIVE LEARNING OF MEDICAL VISUAL REPRESENTATIONS FROM PAIRED IMAGES AND TEXT
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Learning visual representations of medical images is core to medical image understanding but its progress has been held back by the small size of hand-labeled datasets. Existing work commonly relies on transferring weights from ImageNet pretraining, which is suboptimal due to drastically different image characteristics, or rule-based label extraction from the textual report data paired with medical images, which is inaccurate and hard to generalize. We propose an alternative unsupervised strategy to learn medical visual representations directly from the naturally occurring pairing of images and textual data. Our method of pretraining medical image encoders with the paired text data via a bidirectional contrastive objective between the two modalities is domain-agnostic, and requires no additional expert input. We test our method by transferring our pretrained weights to 4 medical image classification tasks and 2 zero-shot retrieval tasks, and show that our method leads to image representations that considerably outperform strong baselines in most settings. Notably, in all 4 classification tasks, our method requires only $10 \%$ as much labeled training data as an ImageNet initialized counterpart to achieve better or comparable performance, demonstrating superior data efficiency.
+
+# 1 INTRODUCTION
+
+Medical image understanding has the potential to transform healthcare and has seen rapid progress with the use of deep neural architectures (Gulshan et al., 2016; Esteva et al., 2017; De Fauw et al., 2018; Rajpurkar et al., 2018b). Yet, with expert-level performance achieved only in some specialties and under some circumstances, medical image understanding remains a difficult task for the majority of specialties, mainly due to its challenging nature and the extreme scarcity of annotated data.
+
+Existing work has followed two general approaches to obtain annotations for medical imaging tasks. The first approach has been using high-quality annotations created by medical experts (Abramoff et al., 2016; Gulshan et al., \` 2016; Shih et al., 2019; Wang & Wong, 2020). However, the high cost of this approach has resulted in datasets that are mostly orders of magnitude smaller than natural image datasets such as ImageNet (Russakovsky et al., 2015). To remedy this, existing work has relied heavily on transferring model weights from ImageNet pretraining (Wang et al., 2017; Esteva et al., 2017; Irvin et al., 2019). This approach is suboptimal because, as shown in Figure 1, medical image understanding often requires representations of very fine-grained visual features that are drastically different from those required for identifying objects in natural images. As a result, Raghu et al. (2019) found that ImageNet pretraining often provides little to no benefit compared to simple random initialization.
+
+![](images/fd93c765bd58da6d8fed1129f74b53255e91c9f25b9d77c8d70ea6b4d0e69c57.jpg)  
+Figure 1: Two example chest radiograph images with different abnormality categories, along with sentences from their paired textual report and example views indicative of their characteristics.
+
+A second popular approach is to use expert-crafted rules to extract labels from the textual reports accompanying the medical images. This approach has led to datasets of larger scale, since the text data paired with medical images are often produced naturally by medical experts in their routine workflow and abundant in a typical hospital’s IT systems. Nevertheless, this rule-based label extraction approach has two limitations: 1) the rules are often inaccurate and limited to a few major categories (Wang et al., 2017), leading to very inefficient use of the textual report data; 2) these rules are often domain-specific and sensitive to the style of the text, making cross-domain and cross-institution generalization difficult (Irvin et al., 2019).
+
+In efforts to make more efficient use of unlabeled image data, several recent studies have shown promising results from contrastive representation learning from natural images (Chen et al., 2020a; He et al., 2020; Grill et al., 2020). However, as we will show, applying these image view-based contrastive methods to medical images provides only marginal benefits compared to ImageNet pretraining, a result mostly due to the high inter-class similarity of the medical images as in Figure 1.
+
+In this work, we aim to improve visual representations of medical images by combining the benefits of both learning from abundant textual data and unsupervised statistical approaches. We present Contrastive VIsual Representation Learning from Text (ConVIRT), a framework for learning visual representations by exploiting the naturally occurring pairing of images and textual data. ConVIRT improves visual representations by maximizing the agreement between true image-text pairs versus random pairs via a bidirectional contrastive objective between the image and text modalities. We apply ConVIRT to the pretraining of medical image encoders, and show that it leads to higherquality in-domain image representations that capture the subtlety of visual features required for medical image understanding tasks.
+
+Compared to existing methods, ConVIRT has the advantages of utilizing the paired text data in a way agnostic to the medical specialty and requiring no additional expert input. This allows us to evaluate ConVIRT by transferring our pretrained weights to 4 different medical image classification tasks covering 2 different specialties. We find that the resulting models outperform all baseline initialization approaches, including the standard ImageNet pretraining and several strong baselines that also utilize the paired text data. Most notably, in all 4 tasks, ConVIRT requires only $10 \%$ as much labeled training data as an ImageNet initialized counterpart to achieve better or comparable performance. We further evaluate ConVIRT on two new zero-shot retrieval tasks, an image-image and a text-image retrieval task, and also find it superior to all baselines. To facilitate future research, we will make our code and the collected retrieval datasets available.
+
+# 2 METHOD
+
+# 2.1 TASK DEFINITION
+
+We start by giving a formal description of our representation learning setting. We assume paired input $\left( \mathbf { x } _ { v } , \mathbf { x } _ { u } \right)$ where $\mathbf { x } _ { v }$ represents one or a group of images, and $\mathbf { x } _ { u }$ represents a text sequence which describes the imaging information in $\mathbf { x } _ { v }$ . Our goal is to learn a parameterized image encoder function $f _ { v }$ , which maps an image to a fixed-dimensional vector. We are then interested in transferring the learned image encoder function $f _ { v }$ into downstream tasks, such as classification or image retrieval. In this work, we model the encoder function $f _ { v }$ as a convolutional neural network (CNN).
+
+We note that paired image-text data $\left( \mathbf { x } _ { v } , \mathbf { x } _ { u } \right)$ naturally exists for many medical domains. Medical experts such as radiologists produce textual descriptions of images as part of their routine workflow, some of which are also made publicly available (Demner-Fushman et al., 2016; Johnson et al., 2019).
+
+# 2.2 CONTRASTIVE VISUAL REPRESENTATION LEARNING FROM TEXT
+
+An overview of our method, ConVIRT, for learning $f _ { v }$ is shown in Figure 2. At a high level, our method converts each input image $\mathbf { x } _ { v }$ and text $\mathbf { x } _ { u }$ into $d$ -dimensional vector representations $\mathbf { v }$ and u respectively, following a similar processing pipeline. For each input image $\mathbf { x } _ { v }$ , our method starts by drawing a random view $\tilde { \mathbf { x } } _ { v }$ from $\mathbf { x } _ { v }$ with a sampled transformation function $t _ { v } \sim \tau$ , where $\tau$ represents a family of stochastic image transformation functions described later. Next, the encoder function $f _ { v }$ transforms $\tilde { \mathbf { x } } _ { v }$ into a fixed-dimensional vector $\mathbf { h } _ { v }$ , followed by a non-linear projection function $g _ { v }$ which further transforms $\mathbf { h } _ { v }$ into vector $\mathbf { v }$ :
+
+$$
+\begin{array} { r } { \mathbf { v } = g _ { v } ( f _ { v } ( \tilde { \mathbf { x } } _ { v } ) ) , } \end{array}
+$$
+
+where $\mathbf { v } \in \mathbb { R } ^ { d }$ . Similarly, for each text input $\mathbf { x } _ { u }$ , we obtain a span $\tilde { \mathbf { x } } _ { u }$ from it following a sampling function $t _ { u }$ , and then a text representation $\mathbf { u }$ with: $\mathbf { u } = g _ { u } ( f _ { u } ( \tilde { \mathbf { x } } _ { u } ) )$ , where $f _ { u }$ is a text encoder, $g _ { u }$ a projection, and $\mathbf { u } \in \mathbb { R } ^ { d }$ . The projection functions $g _ { v }$ and $g _ { u }$ project representations for both modalities from their encoder space to the same $d$ -dimensional space for contrastive learning.
+
+![](images/597326df4567d7ca02062d452b178ffd35be6dedc8e5729eb7f9fa9428df410b.jpg)  
+Figure 2: Overview of our ConVIRT framework. The blue and green shades represent the image and text encoding pipelines, respectively. Our method relies on maximizing the agreement between the true image-text representation pairs with bidirectional losses $\ell ^ { ( v  u ) }$ and $\ell ^ { ( u  v ) }$ .
+
+At training time, we sample a minibatch of $N$ input pairs $( \mathbf { x } _ { v } , \mathbf { x } _ { u } )$ from training data, and calculate their representation pairs $( \mathbf { v } , \mathbf { u } )$ . We use $( \mathbf { v } _ { i } , \mathbf { u } _ { i } )$ to denote the $i$ -th pair. The training objective of ConVIRT involves two loss functions. The first loss function is an image-to-text contrastive loss for the $i$ -th pair:
+
+$$
+\ell _ { i } ^ { ( v  u ) } = - \log \frac { \exp ( \langle { \bf v } _ { i } , { \bf u } _ { i } \rangle / \tau ) } { \sum _ { k = 1 } ^ { N } \exp ( \langle { \bf v } _ { i } , { \bf u } _ { k } \rangle / \tau ) } ,
+$$
+
+where $\left. \mathbf { v } _ { i } , \mathbf { u } _ { i } \right.$ represents the cosine similarity, i.e., $\langle \mathbf { v } , \mathbf { u } \rangle = \mathbf { v } ^ { \top } \mathbf { u } / \| \mathbf { v } \| \| \mathbf { u } \|$ ; and $\tau \in \mathbb { R } ^ { + }$ represents a temperature parameter. This loss takes the same form as the InfoNCE loss (Oord et al., 2018), and minimizing it leads to encoders that maximally preserve the mutual information between the true pairs under the representation functions. Intuitively, it is the log loss of an $N$ -way classifier that tries to predict $( \mathbf { v } _ { i } , \mathbf { u } _ { i } )$ as the true pair. Note that unlike previous work which use a contrastive loss between inputs of the same modality (Chen et al., 2020a; He et al., 2020), our image-to-text contrastive loss is asymmetric for each input modality. We therefore define a similar text-to-image contrastive loss as:
+
+$$
+\ell _ { i } ^ { ( u  v ) } = - \log \frac { \exp ( \langle { \bf u } _ { i } , { \bf v } _ { i } \rangle / \tau ) } { \sum _ { k = 1 } ^ { N } \exp ( \langle { \bf u } _ { i } , { \bf v } _ { k } \rangle / \tau ) } .
+$$
+
+Our final training loss is then computed as a weighted combination of the two losses averaged over all positive image-text pairs in each minibatch:
+
+$$
+\mathcal { L } = \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \Big ( \lambda \ell _ { i } ^ { ( v  u ) } + ( 1 - \lambda ) \ell _ { i } ^ { ( u  v ) } \Big ) ,
+$$
+
+where $\lambda \in [ 0 , 1 ]$ is a scalar weight.
+
+# 2.3 REALIZATION
+
+We note that our ConVIRT framework defined above is agnostic to the specific choice of image and text encoders, transformations and projection functions. In this work, following previous work (Chen et al., 2020a), we model $g _ { v }$ and $g _ { u }$ as separate learnable single-hidden-layer neural networks, i.e., $g _ { v } ( \cdot ) = \mathbf { W } ^ { ( 2 ) } \sigma ( \mathbf { W } ^ { ( 1 ) } ( \cdot ) )$ where $\sigma$ is a ReLU non-linearity, and similarly for $g _ { u }$ .
+
+For the image encoder $f _ { v }$ , we use the ResNet50 architecture (He et al., 2016) for all experiments, as it is the architecture of choice for much medical imaging work and is shown to achieve competitive performance. For the text encoder $f _ { u }$ , we use a BERT encoder (Devlin et al., 2019) followed by a max-pooling layer over all output vectors. We initialize our BERT encoder with the ClinicalBERT model (Alsentzer et al., 2019) pretrained on the MIMIC clinical notes, which achieved state-of-theart performance on a suite of clinical NLP tasks. At training time we allow the encoder to adapt to our contrastive task by freezing the embeddings and the first 6 layers of this BERT encoder and fine-tuning the last 6 layers.
+
+For the image transformation family $\tau$ where $t _ { v }$ is sampled from, we use sequential applications of five random transformations: cropping, horizontal flipping, affine transformation, color jittering and Gaussian blur. Different from recent work on contrastive visual representation learning (Chen et al., 2020a;b), we only apply brightness and contrast adjustments in color jittering, due to the monochrome nature of the medical images. For the text transformation function $t _ { u }$ , we apply a simple uniform sampling of a sentence from the input document $\mathbf { x } _ { u }$ (i.e., $\tilde { \mathbf { x } } _ { u }$ is a randomly sampled sentence from $\mathbf { x } _ { u }$ for each minibatch). We did not use a more aggressive transformation mainly because sampling at the sentence level can preserve the semantic meaning of the sampled spans.
+
+# 3 EXPERIMENTS
+
+# 3.1 DATA FOR PRETRAINING
+
+We test our ConVIRT framework by pretraining two separate image encoders covering different medical specialties using two separate paired image-text datasets:
+
+• Chest image encoder: We use version 2 of the public MIMIC-CXR database (Johnson et al., 2019), which is a collection of chest radiograph images paired with their textual reports, and since its release has become a standard resource for studying multi-modal modeling of medical images. After preprocessing, this dataset contains a total of about $2 1 7 \mathrm { k }$ image-text pairs, with each pair containing an average of 1.7 images and 6.0 sentences. • Bony image encoder: We obtain a collection of musculoskeletal image-text pairs from the Rhode Island Hospital system. Following chest images, musculoskeletal images constitute the second most common type of radiograph images in a typical hospital. This dataset contains a total of $4 8 \mathrm { k }$ image-text pairs, with each pair containing an average of 2.5 images and 8.0 sentences.
+
+We include model implementation and pretraining details in Appendix A.
+
+# 3.2 EVALUATION TASKS & DATA
+
+We evaluate our pretrained image encoders on three downstream medical imaging tasks: image classification, zero-shot image-image retrieval and zero-shot text-image retrieval.
+
+Image Classification. We evaluate our pretrained image representations on four representative medical image classification tasks: 1) RSNA Pneumonia Detection (Wang et al., 2017; Shih et al., 2019), which involves binary classification of a chest radiograph image into either a pneumonia or a normal category; 2) CheXpert image classification (Irvin et al., 2019), which involves multi-label binary classification of a chest image for five individual labels, i.e., atelectasis, cardiomegaly, consolidation, edema and pleural effusion; 3) COVIDx image classification (Wang & Wong, 2020), which involves multi-class classification of a chest image into one of COVID19, non-COVID pneumonia or normal categories; and 4) MURA bony abnormality detection (Rajpurkar et al., 2018a), which involves binary classification of a musculoskeletal image into abnormal or normal. We report test accuracy for COVIDx given its balanced test set, and report the standard area under the receiver operating characteristic curve (AUC) metric for other tasks following previous work.
+
+Following previous work (Henaff et al., 2020; Chen et al., 2020a; He et al., 2020), for all tasks, we ´ evaluate each pretrained image encoder under two individual settings: a linear classification setting, where the pretrained CNN weights are frozen and only a linear classification head is trained for the task; and a fine-tuning setting, where both the CNN weights and the linear head are fine-tuned. The two settings complement each other for evaluation purposes: while the linear setting directly evaluates the quality of the extracted image features with the pretrained CNN, the fine-tuning setting more closely resembles how the pretrained CNN weights are used in practical applications.
+
+To further compare the data efficiency of different pretraining methods, for each setting we evaluate the image encoders with $1 \%$ , $10 \%$ and all training data, respectively (except for the COVIDx dataset where we omit the $1 \%$ setting due to the scarcity of data for some categories). To control the variance in results, for all settings and models, we report average results aggregated over 5 independent training runs. We include further dataset processing and model training details in Appendix B.
+
+Zero-shot Image-image Retrieval. This evaluation is similar to the conventional content-based image retrieval setting in which we search for images of a particular category using a representative query image. For evaluation, a group of query images and a larger collection of candidate images, each with a categorical label, are given to a pretrained CNN encoder. We encode each query and candidate image with this encoder, and then for each query, rank all candidates by their cosine similarities to the query in descending order. Since a widely-used annotated benchmark for this setting is not available, we create our own dataset by re-using existing annotations in the CheXpert dataset (Irvin et al., 2019) and additional expert annotations from a board-certified radiologist. The resulting dataset covers 8 different chest abnormality categories, each with 10 expert-annotated query and 200 candidate images. We include the detailed collection and annotation procedure in Appendix C, and refer to this dataset as CheXpert $\mathbf { 8 \times 2 0 0 }$ Retrieval Dataset. We focus our evaluation on retrieval precision, and evaluate our models with Precision $@ k$ metrics where $k = 5 , 1 0 , 1 0 0$ .
+
+Zero-shot Text-image Retrieval. This setting is similar to the image-image retrieval setting, but instead of using query images, we retrieve images of a particular category with textual queries. For this purpose, we ask a radiologist to write 5 diverse and representative textual descriptions for each of the 8 abnormality categories for the same CheXpert $8 \mathrm { x } 2 0 0$ candidate images (see Appendix D for details). At test time, for each query we encode its text with the learned text encoder $f _ { u }$ and then retrieve from candidate images in a similar way. This evaluation not only evaluates the quality of the learned image representations, but also the alignment between the text representations and the image representations. We again use Precision $@ k$ metrics where $k = 5 , 1 0 , 1 0 0$ .
+
+# 3.3 BASELINE METHODS
+
+We compare ConVIRT against the following standard or competitive initialization methods:
+
+• Random Init.: For all tasks we initialize the ResNet50 with its default random initialization. • ImageNet Init.: We use CNN weights pretrained on ImageNet (Russakovsky et al., 2015), which remains a dominant initialization approach for medical imaging work (Raghu et al., 2019). Caption-LSTM: We initialize the CNN weights with ImageNet, and then pretrain it with an image captioning task using the standard CNN-LSTM with attention architecture (Xu et al., 2015). For the captioning task, we train the model to decode the paired textual report from the encoded image representations. Compared to the random or ImageNet initializations, this is an “in-domain” initialization baseline which uses the paired text data for representation learning. Caption-Transformer: In this initialization we replace the CNN-LSTM model in Caption-LSTM with a CNN-Transformer-based captioning model in Cornia et al. (2020), which recently achieves state-of-the-art results on the COCO image captioning benchmark (Lin et al., 2014). Contrastive-Binary: This baseline differs from our method by contrasting the paired image and text representations with a binary classification head, as is widely done in visual-linguistic pretraining work (Tan & Bansal, 2019; Su et al., 2020). For each input pair, we first project encoder outputs $\mathbf { h } _ { v }$ and $\mathbf { h } _ { u }$ into the same dimension with linear layers, concatenate them, and use a MLP network to predict a binary probability of whether the input is a real or a “fake” pair, which we train with a binary cross-entropy loss. During training, for each $( \mathbf { x } _ { v } , \mathbf { x } _ { u } )$ pair in the training set, we construct a “fake” pair by replacing $\mathbf { x } _ { u }$ with a randomly sampled one from the dataset. We expect that the binary classification task requires the encoder to learn reasonable representations of the input images, and therefore is a stronger in-domain initialization baseline.
+
+For fair comparison, for all baselines that require paired image-text data, we use the same datasets as in our contrastive pretraining. For the captioning-based methods, we always use the model checkpoints that achieve the best CIDEr score (Vedantam et al., 2015) on a held-out validation set.
+
+# 4 RESULTS
+
+# 4.1 CLASSIFICATION TASKS
+
+Linear Classification. We present all linear classification results for the medical imaging tasks in Table 1a. We find that compared to random initialization, ImageNet initialization provides markedly better representations, despite pretrained on a very different domain of images; in-domain image initialization methods that use paired image-text data further improve over ImageNet initialization in almost all settings. Among the in-domain initialization methods, our proposed ConVIRT pretraining achieves the best overall results in all settings. Notably, we find on three out of the four tasks, with only $1 \%$ training data ConVIRT is able to achieve classification results better than the default ImageNet initialization with $100 \%$ training data, highlighting the high quality of the learned representations from ConVIRT.
+
+Table 1: Results for the medical image classification tasks: (a) linear classification; (b) fine-tuning setting. All results are averaged over 5 independent models. Best results for each setting are in boldface. COVIDx $1 \%$ setting is omitted due to the scarcity of labels in COVIDx.   
+
+<table><tr><td colspan="10">(a)</td></tr><tr><td></td><td colspan="3">RSNA (AUC)</td><td colspan="3">CheXpert (AUC)</td><td colspan="2">COVIDx (Accu.)</td><td colspan="3">MURA (AUC)</td></tr><tr><td>Method</td><td>1%</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td></tr><tr><td colspan="10">General initialization methods</td><td></td><td></td></tr><tr><td>Random Init.</td><td>55.0</td><td>67.3</td><td>72.3</td><td>58.2</td><td>63.7</td><td>66.2</td><td>69.2</td><td>73.5</td><td>50.9</td><td>56.8</td><td>62.0</td></tr><tr><td>ImageNet Init.</td><td>82.8</td><td>85.4</td><td>86.9</td><td>75.7</td><td>79.7</td><td>81.0</td><td>83.7</td><td>88.6</td><td>63.8</td><td>74.1</td><td>79.0</td></tr><tr><td colspan="10">In-domain initialization methods</td><td></td></tr><tr><td>Caption-Transformer</td><td>84.8</td><td>87.5</td><td>89.5</td><td>77.2</td><td>82.6</td><td>83.9</td><td>80.0</td><td>89.0</td><td>66.5</td><td>76.3</td><td>81.8</td></tr><tr><td>Caption-LSTM</td><td>89.8</td><td>90.8</td><td>91.3</td><td>85.2</td><td>85.3</td><td>86.2</td><td>84.5</td><td>91.7</td><td>75.2</td><td>81.5</td><td>84.1</td></tr><tr><td>Contrastive-Binary</td><td>88.9</td><td>90.5</td><td>90.8</td><td>84.5</td><td>85.6</td><td>85.8</td><td>80.5</td><td>90.8</td><td>76.8</td><td>81.7</td><td>85.3</td></tr><tr><td>ConVIRT (Ours)</td><td>90.7</td><td>91.7</td><td>92.1</td><td>85.9</td><td>86.8</td><td>87.3</td><td>85.9</td><td>91.7</td><td>81.2</td><td>85.1</td><td>87.6</td></tr><tr><td colspan="10"></td></tr><tr><td></td><td>RSNA (AUC)</td><td></td><td></td><td></td><td>(b) CheXpert (AUC)</td><td></td><td></td><td>COVIDx (Accu.)</td><td></td><td>MURA (AUC)</td><td></td></tr><tr><td colspan="10">Method</td></tr><tr><td>General initialization methods</td><td>1%</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td></tr><tr><td>Random Init.</td><td>71.9</td><td>82.2</td><td>88.5</td><td>70.4</td><td>81.1</td><td>85.8</td><td>75.4</td><td>87.7</td><td>56.8</td><td>61.6</td><td>79.1</td></tr><tr><td colspan="10">ImageNet Init.</td></tr><tr><td></td><td>83.1</td><td>87.3</td><td>90.8</td><td>80.1</td><td>84.8</td><td>87.6</td><td>84.4</td><td>90.3</td><td>72.1</td><td>81.8</td><td>87.0</td></tr><tr><td colspan="10">In-domain initialization methods</td></tr><tr><td>Caption-Transformer</td><td>86.3</td><td>89.2</td><td>92.1</td><td>81.5</td><td>86.4</td><td>88.2</td><td>88.3</td><td>92.3</td><td>75.2</td><td>83.2</td><td>87.6</td></tr><tr><td>Caption-LSTM</td><td>87.2</td><td>88.0</td><td>91.0</td><td>83.5</td><td>85.8</td><td>87.8</td><td>83.8</td><td>90.8</td><td>78.7</td><td>83.3</td><td>87.8</td></tr><tr><td>Contrastive-Binary</td><td>87.7</td><td>89.9</td><td>91.2</td><td>86.2</td><td>86.1</td><td>87.7</td><td>89.5</td><td>90.5</td><td>80.6</td><td>84.0</td><td>88.4</td></tr><tr><td>ConVIRT (Ours)</td><td>88.8</td><td>91.5</td><td>92.7</td><td>87.0</td><td>88.1</td><td>88.1</td><td>90.3</td><td>92.4</td><td>81.3</td><td>86.5</td><td>89.0</td></tr></table>
+
+Fine-tuning. We show the fine-tuning evaluation results in Table 1b. Similar to the linear setting, we find that: 1) ImageNet initialization is again better than random initialization with smaller margins; 2) all in-domain initialization methods are better than the popular ImageNet initialization in most settings; and 3) our proposed ConVIRT pretraining again achieves the best overall results in 10 out of the 11 settings, with the exception of the CheXpert dataset with all training data used, where the result of ConVIRT is similar to that of the Caption-Transformer result. Most notably, on all datasets, with only $10 \%$ labeled training data ConVIRT achieves classification results that are better or close to the ImageNet initialization with $100 \%$ training data results.
+
+We also notice that our conclusion of using ImageNet versus random initialization is different from Raghu et al. (2019): while they showed comparable results from the two strategies, we find that using ImageNet initialization is still superior than random initialization in most results, justifying its popularity. Upon closer examination, we conjecture that this is likely due to under-optimization of their models: while our ResNet50 with random initialization achieves an average AUC of 85.8 on the CheXpert dataset, their ResNet50 model only achieved 83.5 AUC on the same evaluation set.
+
+# 4.2 RETRIEVAL TASKS
+
+We present the zero-shot image-image and text-image retrieval results in Table 2. For the imageimage retrieval setting, we present additional results from fine-tuning our pretrained model on all CheXpert training data, and use them as “upper bounds” of the results obtained from the use of supervised labels. We find that: 1) using ImageNet pretrained CNN weights in a zero-shot image retrieval setting is only better than random guess by small margins; 2) all in-domain pretrained CNN weights achieve much better retrieval performance than ImageNet weights; and 3) our proposed ConVIRT pretraining achieves the best overall retrieval results on all metrics. We find that while Contrastive-Binary performs notably better than other baselines in the image-image retrieval setting, its text-image retrieval results are far from ConVIRT pretraining. We conjecture that the lack of an explicit similarity-based loss function in the Contrastive-Binary baseline results in misaligned representations in the image and text space, leading to poor results in text-image retrieval.
+
+Table 2: Zero-shot image-image and text-image retrieval results on the CheXpert $8 \times 2 0 0$ datasets. Random shows results from a random guess; ConVIRT + CheXpert Supervised shows results from further fine-tuning the pretrained weights with supervised training data. Text-image retrieval results are not obtained for some methods due to the lack of text encoders.   
+
+<table><tr><td></td><td colspan="3"> Image-Image Retrieval</td><td colspan="3">Text-Image Retrieval</td></tr><tr><td>Method</td><td>Prec@5</td><td>Prec@10</td><td>Prec @50</td><td>Prec@5</td><td>Prec@10</td><td>Prec@50</td></tr><tr><td>Random</td><td>12.5</td><td>12.5</td><td>12.5</td><td>12.5</td><td>12.5</td><td>12.5</td></tr><tr><td>ImageNet</td><td>14.8</td><td>14.4</td><td>15.0</td><td>1</td><td>1</td><td>1</td></tr><tr><td>In-domain initialization methods</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Caption-Transformer</td><td>29.8</td><td>28.0</td><td>23.0</td><td></td><td>1</td><td></td></tr><tr><td>Caption-LSTM</td><td>34.8</td><td>32.9</td><td>28.1</td><td></td><td>1</td><td></td></tr><tr><td>Contrastive-Binary</td><td>38.8</td><td>36.6</td><td>29.7</td><td>15.5</td><td>14.5</td><td>13.7</td></tr><tr><td>ConVIRT(Ours)</td><td>45.0</td><td>42.9</td><td>35.7</td><td>60.0</td><td> 57.5</td><td>48.8</td></tr><tr><td>Fine-tuned</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ConVIRT + CheXpert Supervised</td><td>56.8</td><td>56.3</td><td>48.9</td><td></td><td></td><td></td></tr></table>
+
+To understand how well ConVIRT pretraining helps separate images from different abnormality categories in its encoding space, in Figure 3 we present t-SNE plots (Maaten & Hinton, 2008) of candidate images in the CheXpert 8x200 dataset for five selected categories, from the ImageNet pretrained CNN encoder and the ConVIRT pretrained encoder. It is worth noting that clustering images in our setting is much more challenging than that in the general object classification setting due to the high inter-class similarity of the medical images. Nevertheless we find that ConVIRT pretraining achieves a better clus
+
+![](images/a5873cd26f221e3ba37c5caa7ca052356a54e35ade633fa6de6a7effac4a611a.jpg)  
+Figure 3: t-SNE visualizations of encoded image representations from different pretraining methods.
+
+tering of the images in the t-SNE plots. On the other hand, the lack of clear separations between groups suggests room for further improvement.
+
+# 5 ANALYSIS AND DISCUSSION
+
+Comparisons to Image-only Contrastive Learning. ConVIRT shows superior results against baselines in evaluation, but an important question remains as to how it compares against existing image-only contrastive visual representation learning methods. We study this by running two popular such methods, SimCLR (Chen et al., 2020a) and MoCo v2 (Chen et al., 2020b), on the same collection of images that we used in our pretraining. We present the results in Table 3 and include model training details in Appendix E. We find that compared to ImageNet initial
+
+Table 3: Comparisons of ConVIRT to imageonly unsupervised image representation learning approaches.   
+
+<table><tr><td>RSNA Linear Method (1%, AUC)</td><td>(1%,AUC)</td><td>r CheXpert Linear Image-Image (Prec@10)</td></tr><tr><td> ImageNet</td><td>82.8</td><td>75.7 14.4</td></tr><tr><td>SimCLR</td><td>86.3</td><td>77.4 17.6 81.3</td></tr><tr><td>MoCo v2</td><td>86.6</td><td>20.6</td></tr><tr><td>ConVIRT</td><td>90.7</td><td>85.9 42.9</td></tr></table>
+
+ization, both contrastive methods lead to marginal to moderate improvements on the classification
+
+![](images/dccbf6a127f3b58075349a46ccf4447bd6fae637b9ff71419e18a9ff2e635acc.jpg)  
+Figure 4: Saliency maps on sampled images for 4 abnormality categories in the CheXpert dataset. For each image we present maps for ImageNet, SimCLR, MoCo v2 and our ConVIRT initializations. Ground truth regions that are indicative of the abnormalities are shown as red boxes in the images.
+
+and retrieval tasks. However, our training strategy substantially outperforms both methods on all tasks, demonstrating its effective use of information from the paired text data.
+
+To understand the representational difference that has led to this difference in performance, for all four initialization methods, we visualize in Figure 4 the saliency maps (Simonyan et al., 2014) corresponding to the correct class on sampled images from the CheXpert dataset. Models for all initialization methods are trained with $1 \%$ CheXpert training data under the linear classification setting (with pretrained CNN weights frozen). We find that ImageNet pretraining has led to models that focus on trivial visual features that are mostly irrelevant to the task, and that the model with ConVIRT pretrained weights has focused on much more relevant areas than those with SimCLR and MoCo v2 pretraining, suggesting more effective representation learning. For example, for atelectasis, while the ConVIRT model has correctly focused on the bottom of the lung regions, the SimCLR model has much more scattered focus and the MoCo model has incorrectly focused on the heart region.
+
+Correlation Between Contrastive Loss and End Task Performance. To understand the relation between a model’s performance on the ConVIRT pretraining task and its performance on the downstream tasks, we ran an analysis where for every 5 epochs during the pretraining, we transferred the pretrained checkpoint to the downstream tasks and evaluate its performance. The pretraining was run for a total of 200 epochs, and 40 points were obtained with varying validation loss and end task results. Figure 5 presents the results of the models’ validation loss on the pretraining task, and its achieved performance on the RSNA $1 \%$ data linear evaluation and the two retrieval tasks. For all three tasks, we find a clear positive correlation between the pretraining performance and the end task performance. This corroborates that by learning with the ConVIRT objective, the image encoder learns gradually improved representations for the end tasks, and suggests that further improvement on the pretraining task may have positive impact on the end task performance.
+
+Hyperparameter Analysis. We run experiments to study the impact of hyperparameters, and find that: 1) similar to previous work on image-only contrastive learning (Chen et al., 2020a), the pretraining results are most sensitive to the choice of the temperature value $\tau$ ; 2) unlike previous work, changing batch size does not lead to substantial change in the classification results; and 3) using linear projection heads instead of non-linear ones notably hurts the retrieval results. We include our detailed comparisons in Appendix F.
+
+![](images/3d4a9febb985168506013d364451209ea06b6fa625f5eb89099a3ba3dd7423a1.jpg)  
+Figure 5: (a) shows pretraining validation loss at different epochs; (b)-(d) shows correlation between the pretraining loss and the performance of three end tasks. For (a) the $\mathbf { X }$ -axis shows the training epoch number, and for (b)-(d) the $\mathbf { X }$ -axis shows the negative value of the pretraining loss (i.e., $- \mathcal { L } )$ on a held-out validation set.
+
+# 6 RELATED WORK
+
+Our work is most relevant to existing work on medical image classification, which we have covered in Section 1, and textual report generation from medical images (Wang et al., 2018; Jing et al., 2018; Liu et al., 2019). A dominant approach for initializing medical image encoders in this work has been using encoder weights pretrained on ImageNet, despite the drastic difference in image characteristics (Raghu et al., 2019). Instead, our work proposes an alternative in-domain pretraining strategy, and compares ImageNet pretraining with different pretraining approaches that also use the paired text data. To our knowledge our work represents the first systematic attempt in this direction.
+
+Our work is inspired by the recent line of work on image view-based contrastive visual representation learning (Henaff et al., 2020; Chen et al., 2020a; He et al., 2020; Grill et al., 2020), but differs ´ from existing studies by the contrastive learning with text modality, which as we show in Section 5, is more effective in learning high-quality representations of medical images.
+
+Another line of work related to ours is visual-linguistic representation learning (Lu et al., 2019; Tan & Bansal, 2019; Su et al., 2020). Among existing studies, Ilharco et al. (2020) and Gupta et al. (2020) used a cross-modality contrastive objective related to ours, but for the purpose of probing visual-linguistic models and learning phrase grounding, respectively. Our work differs from this line of work in several crucial ways: 1) existing work in visual-linguistic learning focused on learning visual representations from paired text via a binary contrastive prediction task, whereas we showed the superior performance of the new cross-modality NCE objectives in our setting; 2) existing work has primarily used object representations extracted from image segmentation models in their preprocessing steps, making them less applicable to medical image understanding tasks where anatomical segmentations are extremely hard to obtain; 3) while existing work has run evaluation primarily on visual-linguistic tasks such as visual question answering, we instead focus on evaluation with classification and retrieval tasks which are at the center of medical image understanding research.
+
+# 7 CONCLUSION
+
+We presented ConVIRT, an unsupervised method for learning medical visual representations from naturally occurring pairing of images and text. Our method relies on contrasting the image representations with the paired text data via a bidirectional objective between the two modalities. On 4 medical image classification tasks and 2 image retrieval tasks, ConVIRT outperformed other strong in-domain initialization methods that also use the text data, and led to representations with notably higher quality. Compared to ImageNet pretraining, ConVIRT is able to achieve the same level of classification accuracy with an order of magnitude less labeled data. We hope that our work can inspire future work that makes more efficient use of textual data for medical image understanding.
+
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+
+# A MODEL IMPLEMENTATION AND PRETRAINING DETAILS
+
+Dataset Preprocessing. For the MIMIC-CXR chest radiograph dataset, we use the publicly available JPG version of it.1 For both the MIMIC-CXR chest dataset and the Rhode Island Hospital bone image datasets, we resize the image files to have a size of 256 on the larger side. For the textual radiology report data, we first tokenize all reports with the default English tokenizer in version 4.0.0 of the CoreNLP library (Manning et al., 2014). Next, we keep only the Findings and Impression sections and remove all other sections. We remove all image-text pairings from the dataset where the text section is empty or has less than 3 tokens. This preprocessing procedure gives us about $2 1 7 \mathrm { k }$ total image-text pairs for pretraining our chest image encoder and 48k total pairs for pretraining our bone image encoder.
+
+Image and Text Encoders. For the image encoder, we use the standard ResNet50 implementation provided by the torchvision library. For the text encoder, we use the BERT base encoder offered by the Transformers library (Wolf et al., 2019) and initialize it with the ClinicalBERT model (Alsentzer et al., 2019) pretrained on the MIMIC clinical notes. We also experimented with training a specialized BERT encoder on a large collection of radiology notes but found that it made no substantial difference in the pretraining results. At pretraining time we freeze the embeddings and the first 6 layers of this BERT encoder, and only fine-tune the last 6 layers for our contrastive task.
+
+Other Hyperparameters. For contrastive learning, we use projection layers with an output dimension $d = 5 1 2$ , a temperature value $\tau = 0 . 1$ , a loss weight $\lambda = 0 . 7 5$ . These hyperparameter settings are obtained by comparing the linear evaluation validation scores on the RSNA image classification task with the pretrained ResNet50 weights. For the image transformation family $\tau$ , we adopt the implementations offered by the torchvision library.2 We apply random cropping with a ratio sampled from [0.6, 1.0]; horizontal flipping with $p = 0 . 5$ ; affine transformation with a degree sampled from $[ - 2 0 , 2 0 ]$ , max horizontal and vertical translation fractions of 0.1, and a scaling factor sampled from [0.95, 1.05]; color jittering with brightness and contrast adjustment ratios sampled from [0.6, 1.4]; and Gaussian blur with $\sigma \in [ 0 . 1 , 3 . 0 ]$ . All images are resized to $2 2 4 \times 2 2 4$ after the transformation $t _ { v }$ is applied. Limited by computational resources, we arrive at these image transformation parameters via preliminary experiments rather than a systematic search.
+
+Pretraining Details. At pretraining time, for each dataset, we randomly sample 5k image-text pairs to form a held-out validation set. We we use the Adam optimizer (Kingma & Ba, 2015) with an initial learning rate of 1e-4 and weight decay of 1e-6. We initialize the image encoder with ImageNet pretrained weights at the beginning of pretraining, and use a fixed batch size of 32. We calculate the validation loss every 5000 steps, and if the validation loss does not decrease after 5 straight evaluation runs, we anneal the learning rate by a factor of 0.5. We stop pretraining after 200 evaluation runs, and save the model checkpoint that achieves the lowest validation loss. For efficiency, we employ mixed-precision training, and for reference, the whole pretraining run on the MIMIC-CXR dataset took about 3 days on a single Titan RTX GPU card.
+
+# B IMAGE CLASSIFICATION EXPERIMENTS
+
+We prepared and used the 4 image classification datasets following the procedures below:
+
+1. RSNA Pneumonia Detection (Wang et al., 2017; Shih et al., 2019): we used the original version of this dataset available at its Kaggle page,3 which contains 25184/1500/3000 annotated images in its training/validation/test sets, respectively.
+
+2. CheXpert image classification (Irvin et al., 2019): we downloaded the original version of this dataset from its official website.4 Since the original expert-labeled test set of this dataset is hidden and not included as part of the release, we instead followed Raghu et al. (2019) and used the original expert-labeled validation set as our test set, and randomly sampled 5000 images from the original training set for validation purpose. The resulting dataset contains 218414/5000/234 images in each split.
+
+3. COVIDx image classification (Wang & Wong, 2020): we prepared this dataset following the scripts provided by its authors.5 We used the version 4 of this dataset, the latest version at the time of this work. We additionally randomly sampled 300 images from the training set for validation, resulting in a dataset with 13598/300/300 images in each split.
+
+4. MURA bony abnormality detection (Rajpurkar et al., 2018a): we downloaded the original version of this dataset from its website.6 Similar to the CheXpert dataset, we again used the original validation set as our test set, and randomly sampled $10 \%$ images from the training set for validation, resulting in a dataset with 33078/3730/3197 images in each split. Different from the other 3 datasets, the MURA dataset uses patient-level evaluation, meaning that the prediction results from different images of the same patient needs to be aggregated to produce a final prediction for the patient, which is then scored against the gold patient label. We therefore followed Rajpurkar et al. (2018a) and at test time aggregated result for a patient by averaging the predicted probabilities from multiple images.
+
+Classification Model Training Details. For all models that require ImageNet pretrained initialization, we use the pretrained weights from torchvision, which achieves an ImageNet top-5 error rate of $7 . 1 3 \%$ . For all datasets, we first zero-pad the input image to be square, and then resize it to be $2 2 4 \times 2 2 4$ . For training, we use the Adam optimizer with an initial learning rate of 1e-3 for the COVIDx task and 1e-4 for the other three tasks. We additionally apply a weight decay of 1e-6 and a dropout before the last classification layer with $p = 0 . 2$ in all tasks. All classification models are trained with a batch size of 64. In the fine-tuning evaluation setting, we first “warmup” the classification head by freezing the CNN weights and only training the classification head with a learning rate of 1e-3 for 200 steps, after which we unfreeze the CNN weights and fine-tune the entire network together. Validation score is obtained after each epoch of training and we anneal the learning rate by a factor of 0.5 if the validation score is not improved after 3 epochs. The training is stopped after no validation improvement is observed for 10 straight epochs, at which point the model checkpoint with the highest validation score is evaluated on the test set.
+
+# C IMAGE-IMAGE RETRIEVAL DATASET COLLECTION
+
+We create the CheXpert $8 \times 2 0 0$ Retrieval Dataset with 8 different abnormality categories commonly found in Chest radiograph images, including atelectasis, cardiomegaly, edema, fracture, pleural effusion, pneumonia, pneumothorax and a special no finding category indicating that no obvious abnormality is found in the image. We create the dataset by reusing existing rule-labeled annotations in the CheXpert dataset (Irvin et al., 2019) and additional expert annotations. To create the candidate images for a category label $\ell$ , we go through all images in the CheXpert training set, and keep an image as a candidate image if only its label for $\ell$ is positive and all other categories negative. We only include images with this “exclusive positivity” as candidate images, mainly to avoid confounding results between categories in retrieval evaluation.
+
+To create the query images for a category $\ell$ , we again first pre-select 50 exclusively positive images for this category in the CheXpert training set (with all candidate images excluded). Next, we ask a board-certified radiologist to examine each of the 50 images, and exclude images that: 1) might indicate additional abnormalities other than \`, 2) have uncommon color or contrast distortions in the image, or 3) are not well posed during the capture of the image. This procedure is mainly to avoid including query images that have uncommon features and may therefore bias the retrieval evaluation results. At the end, we aggregate the annotation results from the radiologist and keep 10 query images for each abnormality category.
+
+# D TEXT-IMAGE RETRIEVAL DATASET COLLECTION
+
+For the text-image retrieval dataset, we first reuse all candidate images from the CheXpert $8 \times 2 0 0$ image-image retrieval dataset described above, with 200 images for each of 8 categories. To create the textual queries for each abnormality category, we ask a board-certified radiologist to write at least 5 different sentences that he will use to describe this abnormality in radiology reporting. We additionally set the following requirements: 1) the sentences must describe the category with no ambiguity and must not include other categories; 2) the sentences must be diverse from each other; and 3) the sentences should not include very specific anatomic locations or rare clinical observations. At the end, we aggregate the results and keep 5 textual queries for each abnormality category. For reference, we present example textual queries in Table 4.
+
+Table 4: Example textual queries for each of the 8 categories in the text-image retrieval task.   
+
+<table><tr><td>Image Category</td><td>Example Textual Query</td></tr><tr><td>Atelectasis</td><td>Platelike opacity likely represents atelectasis.</td></tr><tr><td>Cardiomegaly</td><td>The cardiac silhouette is enlarged.</td></tr><tr><td>Edema</td><td>The presence of hazy opacity suggests interstitial pulmonary edema.</td></tr><tr><td>Fracture</td><td>A cortical step off indicates the presence of a fracture.</td></tr><tr><td>Pleural Effusion</td><td>The pleural space is partially filled with fluid.</td></tr><tr><td>Pneumonia</td><td>A pulmonary opacity with ill defined borders likely represents pneumonia.</td></tr><tr><td>Pneumothorax</td><td>A medial pneumothorax is present adjacent to the heart.</td></tr><tr><td>No Finding</td><td>No clinically significant radiographic abnormalities.</td></tr></table>
+
+# E EXPERIMENTS ON IMAGE-ONLY CONTRASTIVE LEARNING METHODS
+
+We run experiments with two popular image-only contrastive visual representation learning methods: SimCLR (Chen et al., 2020a) and MoCo v2 (Chen et al., 2020b). For a fair comparison, in both experiments we use the exact same set of images from the MIMIC-CXR dataset that we use in the pretraining of our method and the baselines. Our settings for each method are:
+
+• SimCLR: We use the open PyTorch implementation available at https://github.com/ sthalles/SimCLR. For image encoder we use ResNet50. We use cosine similarity in the loss function, set the temperature value to 0.1 and set the output dimension to 128. We use the default image augmentation functions in the paper except for the color jittering transformation where we set the saturation and hue adjustment to 0 due to the monochrome nature of our medical images. For training, we use the Adam optimizer with an initial learning rate of 3e-4 and weight decay of 1e-4. We set batch size to 128 and run training on a single GPU card for 100 epochs, as we find that increasing the batch size or number of epochs does not lead to improved results. We use the default settings for all other parameters.
+
+• MoCo v2: We use the authors’ PyTorch implementation available at https://github.com/ facebookresearch/moco. For image encoder we use ResNet50. We follow the default MoCo v2 setting and use a temperature value of 0.07 and an output dimension of 128. Similarly, we adopt the default image augmentation functions except for the color jittering transformation where we set the saturation and hue adjustment to 0. For training, we use the SGD optimizer with a learning rate of 0.0075 and weight decay of 1e-4. We use a batch size of 64 and a queue size of 4096, and run parallel training on two GPU cards for 100 epochs, as we find that further increasing the batch size or number of epochs does not lead to improved results. During training, we anneal the learning rate by a factor of 0.1 at the 60th and 80th epochs.
+
+# F HYPERPARAMETER ANALYSIS
+
+Similar to previous work on unsupervised image representation learning (Chen et al., 2020a; He et al., 2020), we first find that the effectiveness of $\mathrm { C o n V I R T }$ pretraining is most sensitive to the temperature value $\tau$ . As shown in Table 5, using a temperature much lower than the ideal value $( \tau = 0 . 0 1 )$ hurts the retrieval results, and a temperature much larger $\tau = 1 \mathrm { \Delta }$ ) notably hurts the performance on all tasks. Unlike previous work, we find that using a smaller or larger batch size hurts the retrieval performance, but neither setup brings substantial impact to the classification results. Lastly, we find that replacing the non-linear projection heads in $g _ { v }$ and $g _ { u }$ with linear layers hurts the retrieval results moderately, suggesting worse representations. However, this is again not reflected notably in the RSNA classification results.
+
+Table 5: Evaluation results with different hyperparameters, for the RSNA $1 \%$ data linear evaluation, image-image retrieval and text-image retrieval tasks. bs represents batch size and linear proj. represents using linear projection layers for $g _ { v }$ and $g _ { u }$ . Our default model uses $\tau = 0 . 1$ , ${ \mathfrak { b s } } = 3 2$ and non-linear projections.   
+
+<table><tr><td>Settings</td><td>RSNA Linear (1%, AUC)</td><td>Image-Image (Prec@10)</td><td>Text-Image (Prec@10)</td></tr><tr><td>ConVIRT (default)</td><td>90.7</td><td>42.9</td><td>57.5</td></tr><tr><td>T = 0.01</td><td>90.7</td><td>40.5</td><td>21.0</td></tr><tr><td>T=1</td><td>89.6</td><td>25.0</td><td>31.0</td></tr><tr><td>bs = 16</td><td>90.3</td><td>40.0</td><td>55.8</td></tr><tr><td>bs =128</td><td>90.3</td><td>39.3</td><td>50.3</td></tr><tr><td> linear proj.</td><td>90.6</td><td>40.8</td><td>55.8</td></tr></table>

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+        "text": "CONTRASTIVE LEARNING OF MEDICAL VISUAL REPRESENTATIONS FROM PAIRED IMAGES AND TEXT ",
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+        "text": "Anonymous authors Paper under double-blind review ",
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+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        "text": "Learning visual representations of medical images is core to medical image understanding but its progress has been held back by the small size of hand-labeled datasets. Existing work commonly relies on transferring weights from ImageNet pretraining, which is suboptimal due to drastically different image characteristics, or rule-based label extraction from the textual report data paired with medical images, which is inaccurate and hard to generalize. We propose an alternative unsupervised strategy to learn medical visual representations directly from the naturally occurring pairing of images and textual data. Our method of pretraining medical image encoders with the paired text data via a bidirectional contrastive objective between the two modalities is domain-agnostic, and requires no additional expert input. We test our method by transferring our pretrained weights to 4 medical image classification tasks and 2 zero-shot retrieval tasks, and show that our method leads to image representations that considerably outperform strong baselines in most settings. Notably, in all 4 classification tasks, our method requires only $10 \\%$ as much labeled training data as an ImageNet initialized counterpart to achieve better or comparable performance, demonstrating superior data efficiency. ",
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+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
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+        "text": "Medical image understanding has the potential to transform healthcare and has seen rapid progress with the use of deep neural architectures (Gulshan et al., 2016; Esteva et al., 2017; De Fauw et al., 2018; Rajpurkar et al., 2018b). Yet, with expert-level performance achieved only in some specialties and under some circumstances, medical image understanding remains a difficult task for the majority of specialties, mainly due to its challenging nature and the extreme scarcity of annotated data. ",
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+        "text": "Existing work has followed two general approaches to obtain annotations for medical imaging tasks. The first approach has been using high-quality annotations created by medical experts (Abramoff et al., 2016; Gulshan et al., \\` 2016; Shih et al., 2019; Wang & Wong, 2020). However, the high cost of this approach has resulted in datasets that are mostly orders of magnitude smaller than natural image datasets such as ImageNet (Russakovsky et al., 2015). To remedy this, existing work has relied heavily on transferring model weights from ImageNet pretraining (Wang et al., 2017; Esteva et al., 2017; Irvin et al., 2019). This approach is suboptimal because, as shown in Figure 1, medical image understanding often requires representations of very fine-grained visual features that are drastically different from those required for identifying objects in natural images. As a result, Raghu et al. (2019) found that ImageNet pretraining often provides little to no benefit compared to simple random initialization. ",
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+        "image_caption": [
+            "Figure 1: Two example chest radiograph images with different abnormality categories, along with sentences from their paired textual report and example views indicative of their characteristics. "
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+        "text": "A second popular approach is to use expert-crafted rules to extract labels from the textual reports accompanying the medical images. This approach has led to datasets of larger scale, since the text data paired with medical images are often produced naturally by medical experts in their routine workflow and abundant in a typical hospital’s IT systems. Nevertheless, this rule-based label extraction approach has two limitations: 1) the rules are often inaccurate and limited to a few major categories (Wang et al., 2017), leading to very inefficient use of the textual report data; 2) these rules are often domain-specific and sensitive to the style of the text, making cross-domain and cross-institution generalization difficult (Irvin et al., 2019). ",
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+        "text": "In efforts to make more efficient use of unlabeled image data, several recent studies have shown promising results from contrastive representation learning from natural images (Chen et al., 2020a; He et al., 2020; Grill et al., 2020). However, as we will show, applying these image view-based contrastive methods to medical images provides only marginal benefits compared to ImageNet pretraining, a result mostly due to the high inter-class similarity of the medical images as in Figure 1. ",
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+        "text": "In this work, we aim to improve visual representations of medical images by combining the benefits of both learning from abundant textual data and unsupervised statistical approaches. We present Contrastive VIsual Representation Learning from Text (ConVIRT), a framework for learning visual representations by exploiting the naturally occurring pairing of images and textual data. ConVIRT improves visual representations by maximizing the agreement between true image-text pairs versus random pairs via a bidirectional contrastive objective between the image and text modalities. We apply ConVIRT to the pretraining of medical image encoders, and show that it leads to higherquality in-domain image representations that capture the subtlety of visual features required for medical image understanding tasks. ",
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+        "text": "Compared to existing methods, ConVIRT has the advantages of utilizing the paired text data in a way agnostic to the medical specialty and requiring no additional expert input. This allows us to evaluate ConVIRT by transferring our pretrained weights to 4 different medical image classification tasks covering 2 different specialties. We find that the resulting models outperform all baseline initialization approaches, including the standard ImageNet pretraining and several strong baselines that also utilize the paired text data. Most notably, in all 4 tasks, ConVIRT requires only $10 \\%$ as much labeled training data as an ImageNet initialized counterpart to achieve better or comparable performance. We further evaluate ConVIRT on two new zero-shot retrieval tasks, an image-image and a text-image retrieval task, and also find it superior to all baselines. To facilitate future research, we will make our code and the collected retrieval datasets available. ",
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+        "type": "text",
+        "text": "2 METHOD ",
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+        "type": "text",
+        "text": "2.1 TASK DEFINITION ",
+        "text_level": 1,
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+        "text": "We start by giving a formal description of our representation learning setting. We assume paired input $\\left( \\mathbf { x } _ { v } , \\mathbf { x } _ { u } \\right)$ where $\\mathbf { x } _ { v }$ represents one or a group of images, and $\\mathbf { x } _ { u }$ represents a text sequence which describes the imaging information in $\\mathbf { x } _ { v }$ . Our goal is to learn a parameterized image encoder function $f _ { v }$ , which maps an image to a fixed-dimensional vector. We are then interested in transferring the learned image encoder function $f _ { v }$ into downstream tasks, such as classification or image retrieval. In this work, we model the encoder function $f _ { v }$ as a convolutional neural network (CNN). ",
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+        "text": "We note that paired image-text data $\\left( \\mathbf { x } _ { v } , \\mathbf { x } _ { u } \\right)$ naturally exists for many medical domains. Medical experts such as radiologists produce textual descriptions of images as part of their routine workflow, some of which are also made publicly available (Demner-Fushman et al., 2016; Johnson et al., 2019). ",
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+        "type": "text",
+        "text": "2.2 CONTRASTIVE VISUAL REPRESENTATION LEARNING FROM TEXT ",
+        "text_level": 1,
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+        "text": "An overview of our method, ConVIRT, for learning $f _ { v }$ is shown in Figure 2. At a high level, our method converts each input image $\\mathbf { x } _ { v }$ and text $\\mathbf { x } _ { u }$ into $d$ -dimensional vector representations $\\mathbf { v }$ and u respectively, following a similar processing pipeline. For each input image $\\mathbf { x } _ { v }$ , our method starts by drawing a random view $\\tilde { \\mathbf { x } } _ { v }$ from $\\mathbf { x } _ { v }$ with a sampled transformation function $t _ { v } \\sim \\tau$ , where $\\tau$ represents a family of stochastic image transformation functions described later. Next, the encoder function $f _ { v }$ transforms $\\tilde { \\mathbf { x } } _ { v }$ into a fixed-dimensional vector $\\mathbf { h } _ { v }$ , followed by a non-linear projection function $g _ { v }$ which further transforms $\\mathbf { h } _ { v }$ into vector $\\mathbf { v }$ : ",
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+        "type": "equation",
+        "img_path": "images/7536bae74ac706832d4847945e961f3338f9971f5caa53917b8e7b8ac1ac44f1.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { v } = g _ { v } ( f _ { v } ( \\tilde { \\mathbf { x } } _ { v } ) ) , } \\end{array}\n$$",
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+        "type": "text",
+        "text": "where $\\mathbf { v } \\in \\mathbb { R } ^ { d }$ . Similarly, for each text input $\\mathbf { x } _ { u }$ , we obtain a span $\\tilde { \\mathbf { x } } _ { u }$ from it following a sampling function $t _ { u }$ , and then a text representation $\\mathbf { u }$ with: $\\mathbf { u } = g _ { u } ( f _ { u } ( \\tilde { \\mathbf { x } } _ { u } ) )$ , where $f _ { u }$ is a text encoder, $g _ { u }$ a projection, and $\\mathbf { u } \\in \\mathbb { R } ^ { d }$ . The projection functions $g _ { v }$ and $g _ { u }$ project representations for both modalities from their encoder space to the same $d$ -dimensional space for contrastive learning. ",
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+        "type": "image",
+        "img_path": "images/597326df4567d7ca02062d452b178ffd35be6dedc8e5729eb7f9fa9428df410b.jpg",
+        "image_caption": [
+            "Figure 2: Overview of our ConVIRT framework. The blue and green shades represent the image and text encoding pipelines, respectively. Our method relies on maximizing the agreement between the true image-text representation pairs with bidirectional losses $\\ell ^ { ( v  u ) }$ and $\\ell ^ { ( u  v ) }$ . "
+        ],
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+        "type": "text",
+        "text": "",
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+        "text": "At training time, we sample a minibatch of $N$ input pairs $( \\mathbf { x } _ { v } , \\mathbf { x } _ { u } )$ from training data, and calculate their representation pairs $( \\mathbf { v } , \\mathbf { u } )$ . We use $( \\mathbf { v } _ { i } , \\mathbf { u } _ { i } )$ to denote the $i$ -th pair. The training objective of ConVIRT involves two loss functions. The first loss function is an image-to-text contrastive loss for the $i$ -th pair: ",
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+        "type": "equation",
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+        "text": "$$\n\\ell _ { i } ^ { ( v  u ) } = - \\log \\frac { \\exp ( \\langle { \\bf v } _ { i } , { \\bf u } _ { i } \\rangle / \\tau ) } { \\sum _ { k = 1 } ^ { N } \\exp ( \\langle { \\bf v } _ { i } , { \\bf u } _ { k } \\rangle / \\tau ) } ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\left. \\mathbf { v } _ { i } , \\mathbf { u } _ { i } \\right.$ represents the cosine similarity, i.e., $\\langle \\mathbf { v } , \\mathbf { u } \\rangle = \\mathbf { v } ^ { \\top } \\mathbf { u } / \\| \\mathbf { v } \\| \\| \\mathbf { u } \\|$ ; and $\\tau \\in \\mathbb { R } ^ { + }$ represents a temperature parameter. This loss takes the same form as the InfoNCE loss (Oord et al., 2018), and minimizing it leads to encoders that maximally preserve the mutual information between the true pairs under the representation functions. Intuitively, it is the log loss of an $N$ -way classifier that tries to predict $( \\mathbf { v } _ { i } , \\mathbf { u } _ { i } )$ as the true pair. Note that unlike previous work which use a contrastive loss between inputs of the same modality (Chen et al., 2020a; He et al., 2020), our image-to-text contrastive loss is asymmetric for each input modality. We therefore define a similar text-to-image contrastive loss as: ",
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+        "type": "equation",
+        "img_path": "images/d9e35c768a4ced1d91134a88f099afe686c9764ce2613fdd51c623ca50785248.jpg",
+        "text": "$$\n\\ell _ { i } ^ { ( u  v ) } = - \\log \\frac { \\exp ( \\langle { \\bf u } _ { i } , { \\bf v } _ { i } \\rangle / \\tau ) } { \\sum _ { k = 1 } ^ { N } \\exp ( \\langle { \\bf u } _ { i } , { \\bf v } _ { k } \\rangle / \\tau ) } .\n$$",
+        "text_format": "latex",
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+        "text": "Our final training loss is then computed as a weighted combination of the two losses averaged over all positive image-text pairs in each minibatch: ",
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+    {
+        "type": "equation",
+        "img_path": "images/c284069bece9bc85041daf2ff4d5a3f7c3843b91ec97c698c871e8f91d59bcb6.jpg",
+        "text": "$$\n\\mathcal { L } = \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\Big ( \\lambda \\ell _ { i } ^ { ( v  u ) } + ( 1 - \\lambda ) \\ell _ { i } ^ { ( u  v ) } \\Big ) ,\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\lambda \\in [ 0 , 1 ]$ is a scalar weight. ",
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+    {
+        "type": "text",
+        "text": "2.3 REALIZATION ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We note that our ConVIRT framework defined above is agnostic to the specific choice of image and text encoders, transformations and projection functions. In this work, following previous work (Chen et al., 2020a), we model $g _ { v }$ and $g _ { u }$ as separate learnable single-hidden-layer neural networks, i.e., $g _ { v } ( \\cdot ) = \\mathbf { W } ^ { ( 2 ) } \\sigma ( \\mathbf { W } ^ { ( 1 ) } ( \\cdot ) )$ where $\\sigma$ is a ReLU non-linearity, and similarly for $g _ { u }$ . ",
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+        "type": "text",
+        "text": "For the image encoder $f _ { v }$ , we use the ResNet50 architecture (He et al., 2016) for all experiments, as it is the architecture of choice for much medical imaging work and is shown to achieve competitive performance. For the text encoder $f _ { u }$ , we use a BERT encoder (Devlin et al., 2019) followed by a max-pooling layer over all output vectors. We initialize our BERT encoder with the ClinicalBERT model (Alsentzer et al., 2019) pretrained on the MIMIC clinical notes, which achieved state-of-theart performance on a suite of clinical NLP tasks. At training time we allow the encoder to adapt to our contrastive task by freezing the embeddings and the first 6 layers of this BERT encoder and fine-tuning the last 6 layers. ",
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+    {
+        "type": "text",
+        "text": "For the image transformation family $\\tau$ where $t _ { v }$ is sampled from, we use sequential applications of five random transformations: cropping, horizontal flipping, affine transformation, color jittering and Gaussian blur. Different from recent work on contrastive visual representation learning (Chen et al., 2020a;b), we only apply brightness and contrast adjustments in color jittering, due to the monochrome nature of the medical images. For the text transformation function $t _ { u }$ , we apply a simple uniform sampling of a sentence from the input document $\\mathbf { x } _ { u }$ (i.e., $\\tilde { \\mathbf { x } } _ { u }$ is a randomly sampled sentence from $\\mathbf { x } _ { u }$ for each minibatch). We did not use a more aggressive transformation mainly because sampling at the sentence level can preserve the semantic meaning of the sampled spans. ",
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+    {
+        "type": "text",
+        "text": "3 EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 DATA FOR PRETRAINING ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We test our ConVIRT framework by pretraining two separate image encoders covering different medical specialties using two separate paired image-text datasets: ",
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+        "text": "• Chest image encoder: We use version 2 of the public MIMIC-CXR database (Johnson et al., 2019), which is a collection of chest radiograph images paired with their textual reports, and since its release has become a standard resource for studying multi-modal modeling of medical images. After preprocessing, this dataset contains a total of about $2 1 7 \\mathrm { k }$ image-text pairs, with each pair containing an average of 1.7 images and 6.0 sentences. • Bony image encoder: We obtain a collection of musculoskeletal image-text pairs from the Rhode Island Hospital system. Following chest images, musculoskeletal images constitute the second most common type of radiograph images in a typical hospital. This dataset contains a total of $4 8 \\mathrm { k }$ image-text pairs, with each pair containing an average of 2.5 images and 8.0 sentences. ",
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+        "type": "text",
+        "text": "We include model implementation and pretraining details in Appendix A. ",
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+    {
+        "type": "text",
+        "text": "3.2 EVALUATION TASKS & DATA ",
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+        "type": "text",
+        "text": "We evaluate our pretrained image encoders on three downstream medical imaging tasks: image classification, zero-shot image-image retrieval and zero-shot text-image retrieval. ",
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+        "type": "text",
+        "text": "Image Classification. We evaluate our pretrained image representations on four representative medical image classification tasks: 1) RSNA Pneumonia Detection (Wang et al., 2017; Shih et al., 2019), which involves binary classification of a chest radiograph image into either a pneumonia or a normal category; 2) CheXpert image classification (Irvin et al., 2019), which involves multi-label binary classification of a chest image for five individual labels, i.e., atelectasis, cardiomegaly, consolidation, edema and pleural effusion; 3) COVIDx image classification (Wang & Wong, 2020), which involves multi-class classification of a chest image into one of COVID19, non-COVID pneumonia or normal categories; and 4) MURA bony abnormality detection (Rajpurkar et al., 2018a), which involves binary classification of a musculoskeletal image into abnormal or normal. We report test accuracy for COVIDx given its balanced test set, and report the standard area under the receiver operating characteristic curve (AUC) metric for other tasks following previous work. ",
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+        "type": "text",
+        "text": "Following previous work (Henaff et al., 2020; Chen et al., 2020a; He et al., 2020), for all tasks, we ´ evaluate each pretrained image encoder under two individual settings: a linear classification setting, where the pretrained CNN weights are frozen and only a linear classification head is trained for the task; and a fine-tuning setting, where both the CNN weights and the linear head are fine-tuned. The two settings complement each other for evaluation purposes: while the linear setting directly evaluates the quality of the extracted image features with the pretrained CNN, the fine-tuning setting more closely resembles how the pretrained CNN weights are used in practical applications. ",
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+    {
+        "type": "text",
+        "text": "To further compare the data efficiency of different pretraining methods, for each setting we evaluate the image encoders with $1 \\%$ , $10 \\%$ and all training data, respectively (except for the COVIDx dataset where we omit the $1 \\%$ setting due to the scarcity of data for some categories). To control the variance in results, for all settings and models, we report average results aggregated over 5 independent training runs. We include further dataset processing and model training details in Appendix B. ",
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+    {
+        "type": "text",
+        "text": "Zero-shot Image-image Retrieval. This evaluation is similar to the conventional content-based image retrieval setting in which we search for images of a particular category using a representative query image. For evaluation, a group of query images and a larger collection of candidate images, each with a categorical label, are given to a pretrained CNN encoder. We encode each query and candidate image with this encoder, and then for each query, rank all candidates by their cosine similarities to the query in descending order. Since a widely-used annotated benchmark for this setting is not available, we create our own dataset by re-using existing annotations in the CheXpert dataset (Irvin et al., 2019) and additional expert annotations from a board-certified radiologist. The resulting dataset covers 8 different chest abnormality categories, each with 10 expert-annotated query and 200 candidate images. We include the detailed collection and annotation procedure in Appendix C, and refer to this dataset as CheXpert $\\mathbf { 8 \\times 2 0 0 }$ Retrieval Dataset. We focus our evaluation on retrieval precision, and evaluate our models with Precision $@ k$ metrics where $k = 5 , 1 0 , 1 0 0$ . ",
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+    {
+        "type": "text",
+        "text": "Zero-shot Text-image Retrieval. This setting is similar to the image-image retrieval setting, but instead of using query images, we retrieve images of a particular category with textual queries. For this purpose, we ask a radiologist to write 5 diverse and representative textual descriptions for each of the 8 abnormality categories for the same CheXpert $8 \\mathrm { x } 2 0 0$ candidate images (see Appendix D for details). At test time, for each query we encode its text with the learned text encoder $f _ { u }$ and then retrieve from candidate images in a similar way. This evaluation not only evaluates the quality of the learned image representations, but also the alignment between the text representations and the image representations. We again use Precision $@ k$ metrics where $k = 5 , 1 0 , 1 0 0$ . ",
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+    {
+        "type": "text",
+        "text": "3.3 BASELINE METHODS",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We compare ConVIRT against the following standard or competitive initialization methods: ",
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+        "type": "text",
+        "text": "• Random Init.: For all tasks we initialize the ResNet50 with its default random initialization. • ImageNet Init.: We use CNN weights pretrained on ImageNet (Russakovsky et al., 2015), which remains a dominant initialization approach for medical imaging work (Raghu et al., 2019). Caption-LSTM: We initialize the CNN weights with ImageNet, and then pretrain it with an image captioning task using the standard CNN-LSTM with attention architecture (Xu et al., 2015). For the captioning task, we train the model to decode the paired textual report from the encoded image representations. Compared to the random or ImageNet initializations, this is an “in-domain” initialization baseline which uses the paired text data for representation learning. Caption-Transformer: In this initialization we replace the CNN-LSTM model in Caption-LSTM with a CNN-Transformer-based captioning model in Cornia et al. (2020), which recently achieves state-of-the-art results on the COCO image captioning benchmark (Lin et al., 2014). Contrastive-Binary: This baseline differs from our method by contrasting the paired image and text representations with a binary classification head, as is widely done in visual-linguistic pretraining work (Tan & Bansal, 2019; Su et al., 2020). For each input pair, we first project encoder outputs $\\mathbf { h } _ { v }$ and $\\mathbf { h } _ { u }$ into the same dimension with linear layers, concatenate them, and use a MLP network to predict a binary probability of whether the input is a real or a “fake” pair, which we train with a binary cross-entropy loss. During training, for each $( \\mathbf { x } _ { v } , \\mathbf { x } _ { u } )$ pair in the training set, we construct a “fake” pair by replacing $\\mathbf { x } _ { u }$ with a randomly sampled one from the dataset. We expect that the binary classification task requires the encoder to learn reasonable representations of the input images, and therefore is a stronger in-domain initialization baseline. ",
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+    {
+        "type": "text",
+        "text": "For fair comparison, for all baselines that require paired image-text data, we use the same datasets as in our contrastive pretraining. For the captioning-based methods, we always use the model checkpoints that achieve the best CIDEr score (Vedantam et al., 2015) on a held-out validation set. ",
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+    {
+        "type": "text",
+        "text": "4 RESULTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1 CLASSIFICATION TASKS ",
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+        "type": "text",
+        "text": "Linear Classification. We present all linear classification results for the medical imaging tasks in Table 1a. We find that compared to random initialization, ImageNet initialization provides markedly better representations, despite pretrained on a very different domain of images; in-domain image initialization methods that use paired image-text data further improve over ImageNet initialization in almost all settings. Among the in-domain initialization methods, our proposed ConVIRT pretraining achieves the best overall results in all settings. Notably, we find on three out of the four tasks, with only $1 \\%$ training data ConVIRT is able to achieve classification results better than the default ImageNet initialization with $100 \\%$ training data, highlighting the high quality of the learned representations from ConVIRT. ",
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+    {
+        "type": "table",
+        "img_path": "images/6a58d6e56065d9455dc9a30c32bb8b5fdcb3ac453b9a04fe13644f1ad3d8f040.jpg",
+        "table_caption": [
+            "Table 1: Results for the medical image classification tasks: (a) linear classification; (b) fine-tuning setting. All results are averaged over 5 independent models. Best results for each setting are in boldface. COVIDx $1 \\%$ setting is omitted due to the scarcity of labels in COVIDx. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"10\">(a)</td></tr><tr><td></td><td colspan=\"3\">RSNA (AUC)</td><td colspan=\"3\">CheXpert (AUC)</td><td colspan=\"2\">COVIDx (Accu.)</td><td colspan=\"3\">MURA (AUC)</td></tr><tr><td>Method</td><td>1%</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td></tr><tr><td colspan=\"10\">General initialization methods</td><td></td><td></td></tr><tr><td>Random Init.</td><td>55.0</td><td>67.3</td><td>72.3</td><td>58.2</td><td>63.7</td><td>66.2</td><td>69.2</td><td>73.5</td><td>50.9</td><td>56.8</td><td>62.0</td></tr><tr><td>ImageNet Init.</td><td>82.8</td><td>85.4</td><td>86.9</td><td>75.7</td><td>79.7</td><td>81.0</td><td>83.7</td><td>88.6</td><td>63.8</td><td>74.1</td><td>79.0</td></tr><tr><td colspan=\"10\">In-domain initialization methods</td><td></td></tr><tr><td>Caption-Transformer</td><td>84.8</td><td>87.5</td><td>89.5</td><td>77.2</td><td>82.6</td><td>83.9</td><td>80.0</td><td>89.0</td><td>66.5</td><td>76.3</td><td>81.8</td></tr><tr><td>Caption-LSTM</td><td>89.8</td><td>90.8</td><td>91.3</td><td>85.2</td><td>85.3</td><td>86.2</td><td>84.5</td><td>91.7</td><td>75.2</td><td>81.5</td><td>84.1</td></tr><tr><td>Contrastive-Binary</td><td>88.9</td><td>90.5</td><td>90.8</td><td>84.5</td><td>85.6</td><td>85.8</td><td>80.5</td><td>90.8</td><td>76.8</td><td>81.7</td><td>85.3</td></tr><tr><td>ConVIRT (Ours)</td><td>90.7</td><td>91.7</td><td>92.1</td><td>85.9</td><td>86.8</td><td>87.3</td><td>85.9</td><td>91.7</td><td>81.2</td><td>85.1</td><td>87.6</td></tr><tr><td colspan=\"10\"></td></tr><tr><td></td><td>RSNA (AUC)</td><td></td><td></td><td></td><td>(b) CheXpert (AUC)</td><td></td><td></td><td>COVIDx (Accu.)</td><td></td><td>MURA (AUC)</td><td></td></tr><tr><td colspan=\"10\">Method</td></tr><tr><td>General initialization methods</td><td>1%</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td><td>10%</td><td>all</td><td>1%</td><td>10%</td><td>all</td></tr><tr><td>Random Init.</td><td>71.9</td><td>82.2</td><td>88.5</td><td>70.4</td><td>81.1</td><td>85.8</td><td>75.4</td><td>87.7</td><td>56.8</td><td>61.6</td><td>79.1</td></tr><tr><td colspan=\"10\">ImageNet Init.</td></tr><tr><td></td><td>83.1</td><td>87.3</td><td>90.8</td><td>80.1</td><td>84.8</td><td>87.6</td><td>84.4</td><td>90.3</td><td>72.1</td><td>81.8</td><td>87.0</td></tr><tr><td colspan=\"10\">In-domain initialization methods</td></tr><tr><td>Caption-Transformer</td><td>86.3</td><td>89.2</td><td>92.1</td><td>81.5</td><td>86.4</td><td>88.2</td><td>88.3</td><td>92.3</td><td>75.2</td><td>83.2</td><td>87.6</td></tr><tr><td>Caption-LSTM</td><td>87.2</td><td>88.0</td><td>91.0</td><td>83.5</td><td>85.8</td><td>87.8</td><td>83.8</td><td>90.8</td><td>78.7</td><td>83.3</td><td>87.8</td></tr><tr><td>Contrastive-Binary</td><td>87.7</td><td>89.9</td><td>91.2</td><td>86.2</td><td>86.1</td><td>87.7</td><td>89.5</td><td>90.5</td><td>80.6</td><td>84.0</td><td>88.4</td></tr><tr><td>ConVIRT (Ours)</td><td>88.8</td><td>91.5</td><td>92.7</td><td>87.0</td><td>88.1</td><td>88.1</td><td>90.3</td><td>92.4</td><td>81.3</td><td>86.5</td><td>89.0</td></tr></table>",
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+        "text": "Fine-tuning. We show the fine-tuning evaluation results in Table 1b. Similar to the linear setting, we find that: 1) ImageNet initialization is again better than random initialization with smaller margins; 2) all in-domain initialization methods are better than the popular ImageNet initialization in most settings; and 3) our proposed ConVIRT pretraining again achieves the best overall results in 10 out of the 11 settings, with the exception of the CheXpert dataset with all training data used, where the result of ConVIRT is similar to that of the Caption-Transformer result. Most notably, on all datasets, with only $10 \\%$ labeled training data ConVIRT achieves classification results that are better or close to the ImageNet initialization with $100 \\%$ training data results. ",
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+        "text": "We also notice that our conclusion of using ImageNet versus random initialization is different from Raghu et al. (2019): while they showed comparable results from the two strategies, we find that using ImageNet initialization is still superior than random initialization in most results, justifying its popularity. Upon closer examination, we conjecture that this is likely due to under-optimization of their models: while our ResNet50 with random initialization achieves an average AUC of 85.8 on the CheXpert dataset, their ResNet50 model only achieved 83.5 AUC on the same evaluation set. ",
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+    {
+        "type": "text",
+        "text": "4.2 RETRIEVAL TASKS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We present the zero-shot image-image and text-image retrieval results in Table 2. For the imageimage retrieval setting, we present additional results from fine-tuning our pretrained model on all CheXpert training data, and use them as “upper bounds” of the results obtained from the use of supervised labels. We find that: 1) using ImageNet pretrained CNN weights in a zero-shot image retrieval setting is only better than random guess by small margins; 2) all in-domain pretrained CNN weights achieve much better retrieval performance than ImageNet weights; and 3) our proposed ConVIRT pretraining achieves the best overall retrieval results on all metrics. We find that while Contrastive-Binary performs notably better than other baselines in the image-image retrieval setting, its text-image retrieval results are far from ConVIRT pretraining. We conjecture that the lack of an explicit similarity-based loss function in the Contrastive-Binary baseline results in misaligned representations in the image and text space, leading to poor results in text-image retrieval. ",
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+        "img_path": "images/92a488f48e3ba71511bcd8c9fc798617439319390ff0d6385bbb11e958816e67.jpg",
+        "table_caption": [
+            "Table 2: Zero-shot image-image and text-image retrieval results on the CheXpert $8 \\times 2 0 0$ datasets. Random shows results from a random guess; ConVIRT + CheXpert Supervised shows results from further fine-tuning the pretrained weights with supervised training data. Text-image retrieval results are not obtained for some methods due to the lack of text encoders. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\"> Image-Image Retrieval</td><td colspan=\"3\">Text-Image Retrieval</td></tr><tr><td>Method</td><td>Prec@5</td><td>Prec@10</td><td>Prec @50</td><td>Prec@5</td><td>Prec@10</td><td>Prec@50</td></tr><tr><td>Random</td><td>12.5</td><td>12.5</td><td>12.5</td><td>12.5</td><td>12.5</td><td>12.5</td></tr><tr><td>ImageNet</td><td>14.8</td><td>14.4</td><td>15.0</td><td>1</td><td>1</td><td>1</td></tr><tr><td>In-domain initialization methods</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Caption-Transformer</td><td>29.8</td><td>28.0</td><td>23.0</td><td></td><td>1</td><td></td></tr><tr><td>Caption-LSTM</td><td>34.8</td><td>32.9</td><td>28.1</td><td></td><td>1</td><td></td></tr><tr><td>Contrastive-Binary</td><td>38.8</td><td>36.6</td><td>29.7</td><td>15.5</td><td>14.5</td><td>13.7</td></tr><tr><td>ConVIRT(Ours)</td><td>45.0</td><td>42.9</td><td>35.7</td><td>60.0</td><td> 57.5</td><td>48.8</td></tr><tr><td>Fine-tuned</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ConVIRT + CheXpert Supervised</td><td>56.8</td><td>56.3</td><td>48.9</td><td></td><td></td><td></td></tr></table>",
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+        "type": "text",
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+    {
+        "type": "text",
+        "text": "To understand how well ConVIRT pretraining helps separate images from different abnormality categories in its encoding space, in Figure 3 we present t-SNE plots (Maaten & Hinton, 2008) of candidate images in the CheXpert 8x200 dataset for five selected categories, from the ImageNet pretrained CNN encoder and the ConVIRT pretrained encoder. It is worth noting that clustering images in our setting is much more challenging than that in the general object classification setting due to the high inter-class similarity of the medical images. Nevertheless we find that ConVIRT pretraining achieves a better clus",
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+    {
+        "type": "image",
+        "img_path": "images/a5873cd26f221e3ba37c5caa7ca052356a54e35ade633fa6de6a7effac4a611a.jpg",
+        "image_caption": [
+            "Figure 3: t-SNE visualizations of encoded image representations from different pretraining methods. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "tering of the images in the t-SNE plots. On the other hand, the lack of clear separations between groups suggests room for further improvement. ",
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+    {
+        "type": "text",
+        "text": "5 ANALYSIS AND DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Comparisons to Image-only Contrastive Learning. ConVIRT shows superior results against baselines in evaluation, but an important question remains as to how it compares against existing image-only contrastive visual representation learning methods. We study this by running two popular such methods, SimCLR (Chen et al., 2020a) and MoCo v2 (Chen et al., 2020b), on the same collection of images that we used in our pretraining. We present the results in Table 3 and include model training details in Appendix E. We find that compared to ImageNet initial",
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+    {
+        "type": "table",
+        "img_path": "images/b508d2b4c6267b636590c809bedf194e39332dc596d172dfaa9d288dd859bfc9.jpg",
+        "table_caption": [
+            "Table 3: Comparisons of ConVIRT to imageonly unsupervised image representation learning approaches. "
+        ],
+        "table_footnote": [
+            "ization, both contrastive methods lead to marginal to moderate improvements on the classification "
+        ],
+        "table_body": "<table><tr><td>RSNA Linear Method (1%, AUC)</td><td>(1%,AUC)</td><td>r CheXpert Linear Image-Image (Prec@10)</td></tr><tr><td> ImageNet</td><td>82.8</td><td>75.7 14.4</td></tr><tr><td>SimCLR</td><td>86.3</td><td>77.4 17.6 81.3</td></tr><tr><td>MoCo v2</td><td>86.6</td><td>20.6</td></tr><tr><td>ConVIRT</td><td>90.7</td><td>85.9 42.9</td></tr></table>",
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+    {
+        "type": "image",
+        "img_path": "images/dccbf6a127f3b58075349a46ccf4447bd6fae637b9ff71419e18a9ff2e635acc.jpg",
+        "image_caption": [
+            "Figure 4: Saliency maps on sampled images for 4 abnormality categories in the CheXpert dataset. For each image we present maps for ImageNet, SimCLR, MoCo v2 and our ConVIRT initializations. Ground truth regions that are indicative of the abnormalities are shown as red boxes in the images. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "and retrieval tasks. However, our training strategy substantially outperforms both methods on all tasks, demonstrating its effective use of information from the paired text data. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "To understand the representational difference that has led to this difference in performance, for all four initialization methods, we visualize in Figure 4 the saliency maps (Simonyan et al., 2014) corresponding to the correct class on sampled images from the CheXpert dataset. Models for all initialization methods are trained with $1 \\%$ CheXpert training data under the linear classification setting (with pretrained CNN weights frozen). We find that ImageNet pretraining has led to models that focus on trivial visual features that are mostly irrelevant to the task, and that the model with ConVIRT pretrained weights has focused on much more relevant areas than those with SimCLR and MoCo v2 pretraining, suggesting more effective representation learning. For example, for atelectasis, while the ConVIRT model has correctly focused on the bottom of the lung regions, the SimCLR model has much more scattered focus and the MoCo model has incorrectly focused on the heart region. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Correlation Between Contrastive Loss and End Task Performance. To understand the relation between a model’s performance on the ConVIRT pretraining task and its performance on the downstream tasks, we ran an analysis where for every 5 epochs during the pretraining, we transferred the pretrained checkpoint to the downstream tasks and evaluate its performance. The pretraining was run for a total of 200 epochs, and 40 points were obtained with varying validation loss and end task results. Figure 5 presents the results of the models’ validation loss on the pretraining task, and its achieved performance on the RSNA $1 \\%$ data linear evaluation and the two retrieval tasks. For all three tasks, we find a clear positive correlation between the pretraining performance and the end task performance. This corroborates that by learning with the ConVIRT objective, the image encoder learns gradually improved representations for the end tasks, and suggests that further improvement on the pretraining task may have positive impact on the end task performance. ",
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+    {
+        "type": "text",
+        "text": "Hyperparameter Analysis. We run experiments to study the impact of hyperparameters, and find that: 1) similar to previous work on image-only contrastive learning (Chen et al., 2020a), the pretraining results are most sensitive to the choice of the temperature value $\\tau$ ; 2) unlike previous work, changing batch size does not lead to substantial change in the classification results; and 3) using linear projection heads instead of non-linear ones notably hurts the retrieval results. We include our detailed comparisons in Appendix F. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/3d4a9febb985168506013d364451209ea06b6fa625f5eb89099a3ba3dd7423a1.jpg",
+        "image_caption": [
+            "Figure 5: (a) shows pretraining validation loss at different epochs; (b)-(d) shows correlation between the pretraining loss and the performance of three end tasks. For (a) the $\\mathbf { X }$ -axis shows the training epoch number, and for (b)-(d) the $\\mathbf { X }$ -axis shows the negative value of the pretraining loss (i.e., $- \\mathcal { L } )$ on a held-out validation set. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "6 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our work is most relevant to existing work on medical image classification, which we have covered in Section 1, and textual report generation from medical images (Wang et al., 2018; Jing et al., 2018; Liu et al., 2019). A dominant approach for initializing medical image encoders in this work has been using encoder weights pretrained on ImageNet, despite the drastic difference in image characteristics (Raghu et al., 2019). Instead, our work proposes an alternative in-domain pretraining strategy, and compares ImageNet pretraining with different pretraining approaches that also use the paired text data. To our knowledge our work represents the first systematic attempt in this direction. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our work is inspired by the recent line of work on image view-based contrastive visual representation learning (Henaff et al., 2020; Chen et al., 2020a; He et al., 2020; Grill et al., 2020), but differs ´ from existing studies by the contrastive learning with text modality, which as we show in Section 5, is more effective in learning high-quality representations of medical images. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Another line of work related to ours is visual-linguistic representation learning (Lu et al., 2019; Tan & Bansal, 2019; Su et al., 2020). Among existing studies, Ilharco et al. (2020) and Gupta et al. (2020) used a cross-modality contrastive objective related to ours, but for the purpose of probing visual-linguistic models and learning phrase grounding, respectively. Our work differs from this line of work in several crucial ways: 1) existing work in visual-linguistic learning focused on learning visual representations from paired text via a binary contrastive prediction task, whereas we showed the superior performance of the new cross-modality NCE objectives in our setting; 2) existing work has primarily used object representations extracted from image segmentation models in their preprocessing steps, making them less applicable to medical image understanding tasks where anatomical segmentations are extremely hard to obtain; 3) while existing work has run evaluation primarily on visual-linguistic tasks such as visual question answering, we instead focus on evaluation with classification and retrieval tasks which are at the center of medical image understanding research. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "7 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We presented ConVIRT, an unsupervised method for learning medical visual representations from naturally occurring pairing of images and text. Our method relies on contrasting the image representations with the paired text data via a bidirectional objective between the two modalities. On 4 medical image classification tasks and 2 image retrieval tasks, ConVIRT outperformed other strong in-domain initialization methods that also use the text data, and led to representations with notably higher quality. Compared to ImageNet pretraining, ConVIRT is able to achieve the same level of classification accuracy with an order of magnitude less labeled data. We hope that our work can inspire future work that makes more efficient use of textual data for medical image understanding. ",
+        "bbox": [
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+    {
+        "type": "text",
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+        "text": "Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pierric Cistac, Tim Rault, Rmi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame, Quentin Lhoest, and Alexander M. Rush. HuggingFace’s Transformers: Stateof-the-art natural language processing. arXiv preprint arXiv:1910.03771, 2019. ",
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+        "text": "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 International Conference on Machine Learning (ICML), 2015. ",
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+    {
+        "type": "text",
+        "text": "A MODEL IMPLEMENTATION AND PRETRAINING DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            102,
+            671,
+            118
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Dataset Preprocessing. For the MIMIC-CXR chest radiograph dataset, we use the publicly available JPG version of it.1 For both the MIMIC-CXR chest dataset and the Rhode Island Hospital bone image datasets, we resize the image files to have a size of 256 on the larger side. For the textual radiology report data, we first tokenize all reports with the default English tokenizer in version 4.0.0 of the CoreNLP library (Manning et al., 2014). Next, we keep only the Findings and Impression sections and remove all other sections. We remove all image-text pairings from the dataset where the text section is empty or has less than 3 tokens. This preprocessing procedure gives us about $2 1 7 \\mathrm { k }$ total image-text pairs for pretraining our chest image encoder and 48k total pairs for pretraining our bone image encoder. ",
+        "bbox": [
+            174,
+            132,
+            825,
+            258
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Image and Text Encoders. For the image encoder, we use the standard ResNet50 implementation provided by the torchvision library. For the text encoder, we use the BERT base encoder offered by the Transformers library (Wolf et al., 2019) and initialize it with the ClinicalBERT model (Alsentzer et al., 2019) pretrained on the MIMIC clinical notes. We also experimented with training a specialized BERT encoder on a large collection of radiology notes but found that it made no substantial difference in the pretraining results. At pretraining time we freeze the embeddings and the first 6 layers of this BERT encoder, and only fine-tune the last 6 layers for our contrastive task. ",
+        "bbox": [
+            174,
+            273,
+            825,
+            371
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Other Hyperparameters. For contrastive learning, we use projection layers with an output dimension $d = 5 1 2$ , a temperature value $\\tau = 0 . 1$ , a loss weight $\\lambda = 0 . 7 5$ . These hyperparameter settings are obtained by comparing the linear evaluation validation scores on the RSNA image classification task with the pretrained ResNet50 weights. For the image transformation family $\\tau$ , we adopt the implementations offered by the torchvision library.2 We apply random cropping with a ratio sampled from [0.6, 1.0]; horizontal flipping with $p = 0 . 5$ ; affine transformation with a degree sampled from $[ - 2 0 , 2 0 ]$ , max horizontal and vertical translation fractions of 0.1, and a scaling factor sampled from [0.95, 1.05]; color jittering with brightness and contrast adjustment ratios sampled from [0.6, 1.4]; and Gaussian blur with $\\sigma \\in [ 0 . 1 , 3 . 0 ]$ . All images are resized to $2 2 4 \\times 2 2 4$ after the transformation $t _ { v }$ is applied. Limited by computational resources, we arrive at these image transformation parameters via preliminary experiments rather than a systematic search. ",
+        "bbox": [
+            174,
+            386,
+            825,
+            539
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "Pretraining Details. At pretraining time, for each dataset, we randomly sample 5k image-text pairs to form a held-out validation set. We we use the Adam optimizer (Kingma & Ba, 2015) with an initial learning rate of 1e-4 and weight decay of 1e-6. We initialize the image encoder with ImageNet pretrained weights at the beginning of pretraining, and use a fixed batch size of 32. We calculate the validation loss every 5000 steps, and if the validation loss does not decrease after 5 straight evaluation runs, we anneal the learning rate by a factor of 0.5. We stop pretraining after 200 evaluation runs, and save the model checkpoint that achieves the lowest validation loss. For efficiency, we employ mixed-precision training, and for reference, the whole pretraining run on the MIMIC-CXR dataset took about 3 days on a single Titan RTX GPU card. ",
+        "bbox": [
+            173,
+            554,
+            825,
+            679
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "B IMAGE CLASSIFICATION EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            699,
+            537,
+            715
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "We prepared and used the 4 image classification datasets following the procedures below: ",
+        "bbox": [
+            173,
+            729,
+            758,
+            744
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "1. RSNA Pneumonia Detection (Wang et al., 2017; Shih et al., 2019): we used the original version of this dataset available at its Kaggle page,3 which contains 25184/1500/3000 annotated images in its training/validation/test sets, respectively. ",
+        "bbox": [
+            176,
+            757,
+            823,
+            799
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "2. CheXpert image classification (Irvin et al., 2019): we downloaded the original version of this dataset from its official website.4 Since the original expert-labeled test set of this dataset is hidden and not included as part of the release, we instead followed Raghu et al. (2019) and used the original expert-labeled validation set as our test set, and randomly sampled 5000 images from the original training set for validation purpose. The resulting dataset contains 218414/5000/234 images in each split. ",
+        "bbox": [
+            176,
+            803,
+            823,
+            859
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            186,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "3. COVIDx image classification (Wang & Wong, 2020): we prepared this dataset following the scripts provided by its authors.5 We used the version 4 of this dataset, the latest version at the time of this work. We additionally randomly sampled 300 images from the training set for validation, resulting in a dataset with 13598/300/300 images in each split. ",
+        "bbox": [
+            176,
+            136,
+            823,
+            190
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "4. MURA bony abnormality detection (Rajpurkar et al., 2018a): we downloaded the original version of this dataset from its website.6 Similar to the CheXpert dataset, we again used the original validation set as our test set, and randomly sampled $10 \\%$ images from the training set for validation, resulting in a dataset with 33078/3730/3197 images in each split. Different from the other 3 datasets, the MURA dataset uses patient-level evaluation, meaning that the prediction results from different images of the same patient needs to be aggregated to produce a final prediction for the patient, which is then scored against the gold patient label. We therefore followed Rajpurkar et al. (2018a) and at test time aggregated result for a patient by averaging the predicted probabilities from multiple images. ",
+        "bbox": [
+            173,
+            195,
+            825,
+            320
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "Classification Model Training Details. For all models that require ImageNet pretrained initialization, we use the pretrained weights from torchvision, which achieves an ImageNet top-5 error rate of $7 . 1 3 \\%$ . For all datasets, we first zero-pad the input image to be square, and then resize it to be $2 2 4 \\times 2 2 4$ . For training, we use the Adam optimizer with an initial learning rate of 1e-3 for the COVIDx task and 1e-4 for the other three tasks. We additionally apply a weight decay of 1e-6 and a dropout before the last classification layer with $p = 0 . 2$ in all tasks. All classification models are trained with a batch size of 64. In the fine-tuning evaluation setting, we first “warmup” the classification head by freezing the CNN weights and only training the classification head with a learning rate of 1e-3 for 200 steps, after which we unfreeze the CNN weights and fine-tune the entire network together. Validation score is obtained after each epoch of training and we anneal the learning rate by a factor of 0.5 if the validation score is not improved after 3 epochs. The training is stopped after no validation improvement is observed for 10 straight epochs, at which point the model checkpoint with the highest validation score is evaluated on the test set. ",
+        "bbox": [
+            174,
+            335,
+            825,
+            515
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "C IMAGE-IMAGE RETRIEVAL DATASET COLLECTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            535,
+            627,
+            551
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "We create the CheXpert $8 \\times 2 0 0$ Retrieval Dataset with 8 different abnormality categories commonly found in Chest radiograph images, including atelectasis, cardiomegaly, edema, fracture, pleural effusion, pneumonia, pneumothorax and a special no finding category indicating that no obvious abnormality is found in the image. We create the dataset by reusing existing rule-labeled annotations in the CheXpert dataset (Irvin et al., 2019) and additional expert annotations. To create the candidate images for a category label $\\ell$ , we go through all images in the CheXpert training set, and keep an image as a candidate image if only its label for $\\ell$ is positive and all other categories negative. We only include images with this “exclusive positivity” as candidate images, mainly to avoid confounding results between categories in retrieval evaluation. ",
+        "bbox": [
+            174,
+            565,
+            825,
+            690
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "To create the query images for a category $\\ell$ , we again first pre-select 50 exclusively positive images for this category in the CheXpert training set (with all candidate images excluded). Next, we ask a board-certified radiologist to examine each of the 50 images, and exclude images that: 1) might indicate additional abnormalities other than \\`, 2) have uncommon color or contrast distortions in the image, or 3) are not well posed during the capture of the image. This procedure is mainly to avoid including query images that have uncommon features and may therefore bias the retrieval evaluation results. At the end, we aggregate the annotation results from the radiologist and keep 10 query images for each abnormality category. ",
+        "bbox": [
+            174,
+            698,
+            825,
+            809
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "D TEXT-IMAGE RETRIEVAL DATASET COLLECTION ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            829,
+            616,
+            844
+        ],
+        "page_idx": 13
+    },
+    {
+        "type": "text",
+        "text": "For the text-image retrieval dataset, we first reuse all candidate images from the CheXpert $8 \\times 2 0 0$ image-image retrieval dataset described above, with 200 images for each of 8 categories. To create the textual queries for each abnormality category, we ask a board-certified radiologist to write at least 5 different sentences that he will use to describe this abnormality in radiology reporting. We additionally set the following requirements: 1) the sentences must describe the category with no ambiguity and must not include other categories; 2) the sentences must be diverse from each other; and 3) the sentences should not include very specific anatomic locations or rare clinical observations. At the end, we aggregate the results and keep 5 textual queries for each abnormality category. For reference, we present example textual queries in Table 4. ",
+        "bbox": [
+            176,
+            859,
+            823,
+            887
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+        "type": "table",
+        "img_path": "images/e32d378233ff1e45c3b81410bd729e5a6748b91742d17ab10728913368fbba82.jpg",
+        "table_caption": [
+            "Table 4: Example textual queries for each of the 8 categories in the text-image retrieval task. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Image Category</td><td>Example Textual Query</td></tr><tr><td>Atelectasis</td><td>Platelike opacity likely represents atelectasis.</td></tr><tr><td>Cardiomegaly</td><td>The cardiac silhouette is enlarged.</td></tr><tr><td>Edema</td><td>The presence of hazy opacity suggests interstitial pulmonary edema.</td></tr><tr><td>Fracture</td><td>A cortical step off indicates the presence of a fracture.</td></tr><tr><td>Pleural Effusion</td><td>The pleural space is partially filled with fluid.</td></tr><tr><td>Pneumonia</td><td>A pulmonary opacity with ill defined borders likely represents pneumonia.</td></tr><tr><td>Pneumothorax</td><td>A medial pneumothorax is present adjacent to the heart.</td></tr><tr><td>No Finding</td><td>No clinically significant radiographic abnormalities.</td></tr></table>",
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+        "text": "",
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+    {
+        "type": "text",
+        "text": "E EXPERIMENTS ON IMAGE-ONLY CONTRASTIVE LEARNING METHODS ",
+        "text_level": 1,
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+        "text": "We run experiments with two popular image-only contrastive visual representation learning methods: SimCLR (Chen et al., 2020a) and MoCo v2 (Chen et al., 2020b). For a fair comparison, in both experiments we use the exact same set of images from the MIMIC-CXR dataset that we use in the pretraining of our method and the baselines. Our settings for each method are: ",
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+        "text": "• SimCLR: We use the open PyTorch implementation available at https://github.com/ sthalles/SimCLR. For image encoder we use ResNet50. We use cosine similarity in the loss function, set the temperature value to 0.1 and set the output dimension to 128. We use the default image augmentation functions in the paper except for the color jittering transformation where we set the saturation and hue adjustment to 0 due to the monochrome nature of our medical images. For training, we use the Adam optimizer with an initial learning rate of 3e-4 and weight decay of 1e-4. We set batch size to 128 and run training on a single GPU card for 100 epochs, as we find that increasing the batch size or number of epochs does not lead to improved results. We use the default settings for all other parameters. ",
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+        "text": "• MoCo v2: We use the authors’ PyTorch implementation available at https://github.com/ facebookresearch/moco. For image encoder we use ResNet50. We follow the default MoCo v2 setting and use a temperature value of 0.07 and an output dimension of 128. Similarly, we adopt the default image augmentation functions except for the color jittering transformation where we set the saturation and hue adjustment to 0. For training, we use the SGD optimizer with a learning rate of 0.0075 and weight decay of 1e-4. We use a batch size of 64 and a queue size of 4096, and run parallel training on two GPU cards for 100 epochs, as we find that further increasing the batch size or number of epochs does not lead to improved results. During training, we anneal the learning rate by a factor of 0.1 at the 60th and 80th epochs. ",
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+    {
+        "type": "text",
+        "text": "F HYPERPARAMETER ANALYSIS ",
+        "text_level": 1,
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+        "text": "Similar to previous work on unsupervised image representation learning (Chen et al., 2020a; He et al., 2020), we first find that the effectiveness of $\\mathrm { C o n V I R T }$ pretraining is most sensitive to the temperature value $\\tau$ . As shown in Table 5, using a temperature much lower than the ideal value $( \\tau = 0 . 0 1 )$ hurts the retrieval results, and a temperature much larger $\\tau = 1 \\mathrm { \\Delta }$ ) notably hurts the performance on all tasks. Unlike previous work, we find that using a smaller or larger batch size hurts the retrieval performance, but neither setup brings substantial impact to the classification results. Lastly, we find that replacing the non-linear projection heads in $g _ { v }$ and $g _ { u }$ with linear layers hurts the retrieval results moderately, suggesting worse representations. However, this is again not reflected notably in the RSNA classification results. ",
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+    {
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+        "img_path": "images/7ee83c7838fd5eb240e992a6deba2890e0f1e7854badea78606e0995e7618aba.jpg",
+        "table_caption": [
+            "Table 5: Evaluation results with different hyperparameters, for the RSNA $1 \\%$ data linear evaluation, image-image retrieval and text-image retrieval tasks. bs represents batch size and linear proj. represents using linear projection layers for $g _ { v }$ and $g _ { u }$ . Our default model uses $\\tau = 0 . 1$ , ${ \\mathfrak { b s } } = 3 2$ and non-linear projections. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Settings</td><td>RSNA Linear (1%, AUC)</td><td>Image-Image (Prec@10)</td><td>Text-Image (Prec@10)</td></tr><tr><td>ConVIRT (default)</td><td>90.7</td><td>42.9</td><td>57.5</td></tr><tr><td>T = 0.01</td><td>90.7</td><td>40.5</td><td>21.0</td></tr><tr><td>T=1</td><td>89.6</td><td>25.0</td><td>31.0</td></tr><tr><td>bs = 16</td><td>90.3</td><td>40.0</td><td>55.8</td></tr><tr><td>bs =128</td><td>90.3</td><td>39.3</td><td>50.3</td></tr><tr><td> linear proj.</td><td>90.6</td><td>40.8</td><td>55.8</td></tr></table>",
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+        "text": "",
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+]