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+# SYNTHETIC AND NATURAL NOISE BOTH BREAK NEURAL MACHINE TRANSLATION
+
+Yonatan Belinkov∗
+
+# Yonatan Bisk∗
+
+Computer Science and   
+Artificial Intelligence Laboratory,   
+Massachusetts Institute of Technology   
+belinkov@mit.edu
+
+Paul G. Allen School of Computer Science & Engineering, University of Washington ybisk@cs.washington.edu
+
+# ABSTRACT
+
+Character-based neural machine translation (NMT) models alleviate out-ofvocabulary issues, learn morphology, and move us closer to completely end-toend translation systems. Unfortunately, they are also very brittle and easily falter when presented with noisy data. In this paper, we confront NMT models with synthetic and natural sources of noise. We find that state-of-the-art models fail to translate even moderately noisy texts that humans have no trouble comprehending. We explore two approaches to increase model robustness: structure-invariant word representations and robust training on noisy texts. We find that a model based on a character convolutional neural network is able to simultaneously learn representations robust to multiple kinds of noise.
+
+# 1 INTRODUCTION
+
+Humans have surprisingly robust language processing systems that can easily overcome typos, misspellings, and the complete omission of letters when reading (Rawlinson, 1976). A particularly extreme and comical exploitation of our robustness came years ago in the form of a popular meme:
+
+“Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae.”
+
+A person’s ability to read this text comes as no surprise to the psychology literature. Saberi & Perrott (1999) found that this robustness extends to audio as well. They experimented with playing parts of audio transcripts backwards and found that it did not affect comprehension. Rayner et al. (2006) found that in noisier settings reading comprehension only slowed by $11 \%$ . McCusker et al. (1981) found that the common case of swapping letters could often go unnoticed by the reader. The exact mechanisms and limitations of our understanding system are unknown. There is some evidence that we rely on word shape (Mayall et al., 1997), that we can switch between whole word recognition and piecing together words from letters (Reicher, 1969; Pelli et al., 2003), and there appears to be no evidence that the first and last letter positions are required to stay constant for comprehension.1
+
+In stark contrast, neural machine translation (NMT) systems, despite their pervasive use, are immensely brittle. For instance, Google Translate produces the following unintelligible translation for a German version of the above meme:2
+
+“After being stubbornly defiant, it is clear to kenie Rlloe in which Reiehnfogle is advancing the boulders in a Wrot that is integral to Sahce, as the utterance and the lukewarm boorstbaen stmimt.”
+
+While typos and noise are not new to NLP, our systems are rarely trained to explicitly address them, as we instead hope that the relevant noise will occur in the training data.
+
+Despite these weaknesses, the move to character-based NMT is important. It helps us tackle the long tailed distribution of out-of-vocabulary words in natural language, as well as reduce computation
+
+load of dealing with large word embedding matrices. NMT models based on characters and other0 34.22 0 34.22 0 34.22 40   
+sub-word units are able to extract stem and morphological information to generalize to unseen words     15.3 21.77 10.4 25.59 7.6 28.52   
+and conjugations. They perform very well in practice on a range of languages (Sennrich et al.,23.2 15.73 15.3 21.56 11.4 25.42 30   
+2016a; Wu et al., 2016). In many cases, these models actually discover an impressive amount of30.8 11.45 20.6 17.91 15.2 22.60   
+morphological information about a language (Belinkov et al., 2017a). Unfortunately, training (and46.3 5.28 30.3 12.22 22.6 17.62   
+testing) on clean data makes models brittle and, arguably, unfit for broad deployment.53.6 3.19 35.8 9.49 26.2 16.52
+
+Figure 1 shows how the performance of two state-of-the-art NMT systems degrades when translating69.1 0.84 45.7 5.36 34.0 12.02 10 German to English as a function of the percent of German words modified. Here we show three types76.7 0.29 51.1 3.39 37.8 10.68 of noise: 1) Random permutation of the word, 2) Swapping a pair of adjacent letters, and 3) Natural0 human errors. We discuss these types of noise and others in depth in section 4.2. The important thing to note is that even small amounts of noise lead to substantial drops in performance.Random Swap Natural
+
+![](images/a0eaf407647ec50ed9174c02e7a537177a58014aa3549a2a542b4922c39bd813.jpg)  
+Random Swap NaturalChar2Char Char2CharFigure 1: Degradation of Nematus (Sennrich et al., 2017) and char2char (Lee et al., 2017) 40 Nematusperformance as noise increases.
+
+30 52.5x+68.2To address these trends and investigate the effects of noise on NMT, we explore two simple strategies   
+0 68.2 0 68.2 0 68.2 0 68.2for increasing model robustness: using structure-invariant representations and robust training on   
+20 35.015.3 55.8 10.4 59.9 7.6 62.7 20 54.56noisy data, a form of adversarial training (Szegedy et al., 2014; Goodfellow et al., 2015). We find   
+23.2 49.6 15.3 55.7 11.4 59.6 30 47.74that a character CNN representation trained on an ensemble of noise types is robust to all kinds of   
+38.0 38.5 25.9 48.8 18.8 53.6 50 34.1noise. We shed some light on the model ability to learn robust representations to multiple types of   
+46.3 33.0 30.3 45.6 22.6 51.3 60 27.28noise, and point to remaining difficulties in handling natural noise. Our goal is two fold: 1) initiate   
+53.6 27.4 35.8 41.6 26.2 49.3 70 20.46a conversation on robust training and modeling techniques in NMT, and 2) promote the creation of   
+0 20 40 60 80  069.1 17.7 45.7 34.3 34.0 43.5 90 6.82better and more linguistically accurate artificial noise to be applied to new languages and tasks.
+
+# 2 ADVERSARIAL EXAMPLES
+
+char2charThe growing literature on adversarial examples has demonstrated how dangerous it can be to use y =  Random Swap Natural Linear y = (-66/100brittle machine learning systems so pervasively in the real world (Biggio et al., 2012; Szegedy et al., x+68.2 )x + 662014; Goodfellow et al., 2015; Mei & Zhu, 2015). Small changes to the input can lead to dramatic 0 68.2 7.7 60.6 5.2 63.3 3.7 64.2 10 59.4failures of deep learning models (Szegedy et al., 2014; Goodfellow et al., 2015). In the machine 20 54.56 15.3 55.3 10.4 60.2 7.6 62.4 20 52.8vision field, changes to the input image that are indistinguishable by humans can lead to misclas30 47.74 23.2 49.5 15.3 57.3 11.4 60.3 30 46.230.8 43.6 20.6 54.2 15.2 58.0 40 39.6sification. This leads to potential for malicious attacks using adversarial examples. An important 40 40.9250 34.1 38.0 38.3 25.9 51.5 18.8 56.7 50 33distinction is often drawn between white-box attacks, where adversarial examples are generated with 60 27.28 46.3 33.3 30.3 48.3 22.6 54.7 60 26.4access to the model parameters, and black-box attacks, where examples are generated without such 70 20.46       61.5 23.2 40.9 42.2 30.1 50.7 80 13.2access (Papernot et al., 2016a; 2017; Narodytska & Kasiviswanathan, 2017; Liu et al., 2017).
+
+90 6.82 76.7 14.1 51.1 35.8 37.8 46.3 100 0While more common in the vision domain, recent work has started exploring adversarial examples for NLP. A few white-box attacks have employed the fast gradient sign method (Goodfellow et al., 2015) or other techniques to find important text edit operations (Papernot et al., 2016b; Samanta & Mehta, 2017; Liang et al., 2017; Ebrahimi et al., 2017). Others have considered black-box adversarar y = ial examples for text classification (Gao et al., 2018) or NLP evaluation (Jia & Liang, 2017). Heigold )x + 66et al. (2017) evaluated character-based models on several types of noise in morphological tagging 0 66and MT, and observed similar trends to our findings. Finally, Sakaguchi et al. (2017) designed a 20 52.8character-level recurrent neural network that can better handle the particular kind of noise present 30 46.2in the meme mentioned above by modeling spelling correction. Here we devise simple methods 40 39.650 33for generating adversarial examples for NMT. We do not assume any access to the NMT models’ 60 26.4gradients, instead relying on synthetic and naturally occurring language errors to generate noise.
+
+The other side of the coin is to improve models’ robustness to adversarial examples (Globerson & Roweis, 2006; Cretu et al., 2008; Rubinstein et al., 2009; Chan et al., 2017). Adversarial training – including adversarial examples in the training data – can improve a model’s ability to cope with such examples at test time (Szegedy et al., 2014; Goodfellow et al., 2015). This kind of defense is sensitive to the type of adversarial examples seen in training, but can be made more robust by ensemble adversarial training – training on examples transfered from multiple pre-trained models (Tramer\` et al., 2017). We explore ensemble training by combining multiple types of noise at training time, and observe similar increased robustness in the machine translation scenario.
+
+Training on and for adversarial noise is an important extension of earlier work on creating robustness in neural networks by incorporating noise to a network’s representations, data, or gradients. Training with noise can provide a form of regularization (Bishop, 1995) and ensure the model is exposed to samples outside the training distribution (Matsuoka, 1992).
+
+# 3 MT SYSTEMS
+
+The rise of end-to-end models in neural machine translation has led to recent interest in understanding how these models operate. Several studies investigated the ability of such models to learn linguistic properties at morphological (Vylomova et al., 2016; Belinkov et al., 2017a; Dalvi et al., 2017), syntactic (Shi et al., 2016; Sennrich, 2017), and semantic levels (Belinkov et al., 2017b). The use of characters or other sub-word units emerges as an important component in these models. Our work complements previous studies by presenting such NMT systems with noisy examples and exploring methods for increasing their robustness.
+
+We experiment with three different NMT systems with access to character information at different levels. First, we use the fully character-level model of Lee et al. (2017). This is a sequence-tosequence model with attention (Sutskever et al., 2014; Bahdanau et al., 2014) that is trained on characters to characters (char2char). It has a complex encoder with convolutional, highway, and recurrent layers, and a standard recurrent decoder. See Lee et al. (2017) for architecture details. This model was shown to have excellent performance on the German English and Czech English language pairs. We use the pre-trained German/Czech English models.
+
+Second, we use Nematus (Sennrich et al., 2017), a popular NMT toolkit that was used in topperforming contributions in shared MT tasks in WMT (Sennrich et al., 2016b) and IWSLT (JunczysDowmunt & Birch, 2016). It is another sequence-to-sequence model with several architecture modifications, especially operating on sub-word units using byte-pair encoding (BPE) (Sennrich et al., 2016a). We experimented with both their single best and ensemble BPE models, but saw no significant difference in their performance under noise, so we report results with their single best WMT models for German/Czech English.
+
+Finally, we train an attentional sequence-to-sequence model with a word representation based on a character convolutional neural network (charCNN). This model retains the notion of a word but learns a character-dependent representation of words. It was shown to perform well on morphologically-rich languages (Kim et al., 2015; Belinkov & Glass, 2016; Costa-jussa & Fonol- \` losa, 2016; Sajjad et al., 2017), thanks to its ability to learn morphologically-informative representations (Belinkov et al., 2017a). The charCNN model has two long short-term memory (Hochreiter & Schmidhuber, 1997) layers in the encoder and decoder. A CNN over characters in each word replaces the word embeddings on the encoder side (for simplicity, the decoder is word-based). We use 1000 filters with a width of 6 characters. The character embedding size is set to 25. The convolutions are followed by Tanh and max-pooling over the length of the word (Kim et al., 2015). We train charCNN with the implementation in Kim (2016); all other settings are kept to default values.
+
+# 4 DATA
+
+# 4.1 MT DATA
+
+We use the TED talks parallel corpus prepared for IWSLT 2016 (Cettolo et al., 2012) for testing all of the NMT systems, as well as for training the charCNN models. We follow the official training/development/test splits. All texts are tokenized with the Moses tokenizer. Table 1 summarizes statistics on the TED talks corpus.
+
+Table 1: Statistics for the source-side of French/German/Czech English parallel corpora.   
+
+<table><tr><td></td><td colspan="3">French</td><td colspan="3">German</td><td colspan="3">Czech Test</td></tr><tr><td></td><td>Train</td><td>Dev</td><td>Test</td><td>Train</td><td>Dev</td><td>Test</td><td>Train</td><td>Dev</td></tr><tr><td>Sentences</td><td>235K</td><td>2.5K</td><td>0.8K</td><td>210K</td><td>2.5K</td><td>1.4K</td><td>122K</td><td>20K 1K</td></tr><tr><td>Words</td><td>5.2M</td><td>55K</td><td>16K</td><td>4M</td><td>50K</td><td>26K</td><td>2.1M 35K</td><td>15K</td></tr></table>
+
+Table 2: Average number of available edits per word in natural noise datasets and the corresponding token recall of those edits on the training and test splits.   
+
+<table><tr><td colspan="3">French</td><td colspan="3">German</td><td colspan="3">Czech</td></tr><tr><td>Words</td><td>Errors Train</td><td>Test</td><td>Words</td><td>Errors</td><td>Train Test</td><td></td><td>Words Errors</td><td>Train Test</td></tr><tr><td>65,156</td><td>2.7</td><td>40% 41%</td><td>1,344</td><td>2.5</td><td>37%</td><td>40%</td><td>6.036 2.6</td><td>46% 51%</td></tr></table>
+
+# 4.2 NOISE: NATURAL AND ARTIFICIAL
+
+We insert noise into the source-side of the parallel MT data by utilizing naturally occurring errors and generating synthetic ones. In order to facilitate future work on noise in NMT, we release code and data for generating the noise used in our experiments.3
+
+# 4.2.1 NATURAL NOISE
+
+Since we do not have access to a parallel corpus with natural noise, we instead harvest naturally occurring errors (typos, misspellings, etc.) from available corpora of edits to build a look-up table of possible lexical replacements. In this work, we restrict ourselves to single word replacements, but several of the corpora below also provide access to phrase replacements.
+
+French Max & Wisniewski (2010) collected Wikipedia edit histories to form the Wikipedia Correction and Paraphrase Corpus (WiCoPaCo). They found the bulk of edits were due to incorrect diacritics, choosing the wrong homophone, and incorrect grammatical conjugation.
+
+German Our German data combines two projects: RWSE Wikipedia Revision Dataset (Zesch, 2012) and The MERLIN corpus of language learners (Wisniewski et al., 2013). These corpora were created to measure spelling difficulty and test models of contextual fitness. Unfortunately, the datasets are quite small so we have combined them here.
+
+Czech Our Czech errors come from manually annotated essays written by non-native speakers (Sebesta et al. ˇ , 2017). Here, the authors found an incredibly diverse set of errors, and therefore phenomena of interest: capitalization, incorrectly replacing voiced and voiceless consonants (e.g. z/s, $\mathrm { g / k } )$ ), missing palatalization (matke/matce), error in valence, pronominal reference, inflection, collo- ˇ quial forms, and so forth. Their analysis gives us the best insight into how difficult it would be to synthetically generate truly natural errors. We found similarly rich errors in German (Section 7.2).
+
+We insert these errors into the source-side of the parallel data by replacing every word in the corpus with an error if one exists in our dataset. When there is more than one possible replacement to choose we sample uniformly. Words for which there is no error are kept as is. Table 2 shows the number of words for which we were able to collect errors in each language, and the average number of errors per word. Despite the small size of the German and Czech datasets, we are able to replace up to half of the words in the corpus with errors. Due to the small size of the German and Czech datasets these percentages decrease for longer words $\cdot > 4$ characters) to $2 5 \%$ and $32 \%$ , respectively.
+
+# 4.2.2 SYNTHETIC NOISE
+
+In addition to naturally collected sources of error, we also experiment with four types of synthetic noise: Swap, Middle Random, Fully Random, and Keyboard Typo.
+
+Table 3: The effect of Natural (Nat) and synthetic noise (Swap swap, Middle Random Mid, Fully Random Rand, and Keyboard Typo Key) on models trained on clean (Vanilla) texts.   
+
+<table><tr><td rowspan="2"></td><td colspan="6">Synthetic</td></tr><tr><td></td><td>Vanilla</td><td>Swap Mid</td><td>Rand</td><td>Key</td><td>Nat</td></tr><tr><td>French</td><td>charCNN</td><td>42.54</td><td>10.52</td><td>9.71</td><td>1.71 8.26</td><td>17.42</td></tr><tr><td rowspan="3">German</td><td>charCNN</td><td>34.79</td><td>9.25</td><td>8.37 1.02</td><td>6.40</td><td>14.02</td></tr><tr><td>char2char</td><td>29.97</td><td>5.68</td><td>5.46 0.28</td><td>2.96</td><td>12.68</td></tr><tr><td>Nematus</td><td>34.22</td><td>3.39</td><td>5.16</td><td>0.29 0.61</td><td>10.68</td></tr><tr><td rowspan="3">Czech</td><td>charCNN</td><td>25.99</td><td>6.56</td><td>6.67</td><td>1.50 7.13</td><td>10.20</td></tr><tr><td>char2char</td><td>25.71</td><td>3.90</td><td>4.24</td><td>0.25 2.88</td><td>11.42</td></tr><tr><td>Nematus</td><td>29.65</td><td>2.94</td><td>4.09</td><td>0.66 1.41</td><td>11.88</td></tr></table>
+
+Table 4: An example noisy text with human and machine translations.   
+
+<table><tr><td>Input</td><td>Luat eienr Stduie der Cambrdige Unievrstit speilt es kenie Rlloe in welcehr Reiehnfogle die Buhcstbaen in eniem Wrot vorkmomen,die eingzie whctige Sahce ist,dsas der ertse und der lettze Buhcstbaen stmimt .</td></tr><tr><td>Human</td><td>According to a study from Cambridge university, it doesn&#x27;t matter which order letters in a word are,the only important thing is that the first and the last letter appear in their correct place. Cambridge Universtte is one of the most important features of the Cambridge Universttten ,</td></tr><tr><td>char2char Nematus</td><td>which is one of the most important features of the Cambridge Universttten . Luat eienr Stduie der Cambrant Unievrstilt splashed it kenie Rlloe in welcehr Reiehnfogle the</td></tr><tr><td>charCNN</td><td>Buhcstbaen in eniem Wred vorkmomen,die eingzie whcene Sahce ist,DSAs der ertse und der lettze Buhcstbaen stmimt . According to the &lt;unk&gt;of the Cambridge University,it &#x27;s a litle bit of crude oil in a little bit of recycling ,which is a little bit of acool cap,which is a little bit of a strong cap,that the</td></tr></table>
+
+Swap : Swap The simplest source of noise is swapping two letters (e.g. noise nosie). This is common when typing quickly and is easily implemented. We perform one swap per word, but do not alter the first or last letters. For this reason, this noise is only applied to words of length $\geq 4$ .
+
+Middle Random : Mid Following the claims of the previously discussed meme, we randomize the order of all the letters in a word except for the first and last (noise nisoe). Again, by necessity, this means we do not alter words shorter than four characters.
+
+Fully Random : Rand As we are unaware of any strong results on the importance of the first and last letters we also include completely randomized words (noise iones). This is a particularly extreme case, but we include it for completeness. This type of noise is applied to all words.
+
+Keyboard Typo : Key Finally, using the traditional keyboards for our languages, we randomly replace one letter in each word with an adjacent key (noise noide). This type of error should be much easier than the random settings as most of the word is left intact, but does introduce a completely new character which will often break the templates a system has learned to rely on.
+
+# 5 FAILURES TO TRANSLATE NOISY TEXTS
+
+Table 3 shows BLEU scores of models trained on clean (Vanilla) texts and tested on clean and noisy texts. All models suffer a significant drop in BLEU when evaluated on noisy texts. This is true for both natural noise and all kinds of synthetic noise. The more noise in the text, the worse the translation quality, with random scrambling producing the lowest BLEU scores.
+
+The degradation in translation quality is especially severe in light of humans’ ability to understand noisy texts. To illustrate this, consider the noisy text in Table 4. Humans are quite good at understanding such scrambled texts in a variety of languages.4 We also verified this by obtaining a translation from a German native-speaker, unfamiliar with the meme. As shown in the table, the speaker had no trouble understanding and translating the sentence properly. In contrast, the state-ofthe-art systems (char2char and Nematus) fail on this text.
+
+Table 5: Google Translate’s performance with natural errors and the gains from using spell checking.   
+
+<table><tr><td colspan="3">French</td><td colspan="3">German</td><td colspan="3">Czech</td></tr><tr><td>Vanilla</td><td>Nat</td><td>Spelling</td><td>Vanilla</td><td>Nat</td><td>Spelling</td><td>Vanilla</td><td>Nat</td><td>Spelling</td></tr><tr><td>43.3</td><td>16.7</td><td>21.4</td><td>38.7</td><td>18.6</td><td>25.0</td><td>26.5</td><td>12.3</td><td>11.2</td></tr></table>
+
+Table 6: Results of meanChar models trained and tested on different noise conditions: Scrambled (Scr), Keyboard Typo (Key), and Natural (Nat).   
+
+<table><tr><td rowspan="2">Test Train</td><td colspan="3">French</td><td colspan="3">German</td><td colspan="3">Czech</td></tr><tr><td>Scr</td><td>Key</td><td>Nat</td><td>Scr</td><td>Key</td><td>Nat</td><td>Scr</td><td>Key</td><td>Nat</td></tr><tr><td>Vanilla</td><td>34.26</td><td>4.27</td><td>12.58</td><td>27.53</td><td>3.34</td><td>9.41</td><td>3.73</td><td>2.06</td><td>3.25</td></tr><tr><td>Key</td><td>31.88</td><td>29.75</td><td>13.16</td><td>10.04</td><td>8.84</td><td>4.45</td><td>2.03</td><td>1.9</td><td>1.42</td></tr><tr><td>Nat</td><td>26.94</td><td>5.30</td><td>27.49</td><td>15.65</td><td>3.06</td><td>26.26</td><td>1.66</td><td>1.52</td><td>1.58</td></tr><tr><td>Rand+Key</td><td>13.60</td><td>11.09</td><td>6.12</td><td>26.59</td><td>22.41</td><td>11.07</td><td>9.97</td><td>7.48</td><td>4.21</td></tr><tr><td>Rand+Nat</td><td>28.28</td><td>5.10</td><td>20.40</td><td>13.87</td><td>3.73</td><td>12.74</td><td>4.89</td><td>2.82</td><td>3.42</td></tr><tr><td>Key+Nat</td><td>31.30</td><td>26.94</td><td>24.24</td><td>6.62</td><td>5.41</td><td>5.75</td><td>1.62</td><td>1.68</td><td>1.58</td></tr><tr><td>Rand+Key+Nat</td><td>3.10</td><td>3.28</td><td>2.76</td><td>8.02</td><td>5.79</td><td>6.36</td><td>1.73</td><td>1.74</td><td>1.66</td></tr></table>
+
+One natural question is if robust spell checkers trained on human errors are sufficient to address this performance gap. To test this, we ran texts with and without natural errors through Google Translate. We then used Google’s spell-checkers to correct the documents. We simply accepted the first suggestion for every detected mistake detected, and report results in Table 5.
+
+We found that in French and German, there was often only a single predicted correction and this corresponds to roughly $+ 5$ or more in BLEU. In Czech, however, there was often a large list of possible conjugations and changes, likely indicating that a rich grammatical model would be necessary to predict the correction. It is also important to note the substantial drops from vanilla text even with spell check. This suggests that natural noise cannot be easily addressed by existing tools.
+
+# 6 DEALING WITH NOISE
+
+# 6.1 STRUCTURE INVARIANT REPRESENTATIONS
+
+The three NMT models are all sensitive to word structure. The char2char and charCNN models both have convolutional layers on character sequences, designed to capture character n-grams. The model in Nematus is based on sub-word units obtained with BPE. It thus relies on character order within and across sub-word units. All these models are therefore sensitive to types of noise generated by character scrambling (Swap, Mid, and Rand). Can we improve model robustness by adding invariance to these kinds of noise? Perhaps the simplest such model is to take the average character embedding as a word representation. This model, referred to as meanChar, first generates a word representation by averaging character embeddings, and then proceeds with a word-level encoder similar to the charCNN model. The meanChar model is by definition insensitive to scrambling, although it is still sensitive to other kinds of noise (Key and Nat).
+
+Table 6 (first row) shows the results of meanChar models trained on vanilla texts and tested on noisy texts (the results on vanilla texts are by definition equal to those on scrambled texts). Overall, the average character embedding proves to be a pretty good representation for translating scrambled texts: while performance drops by about 7 BLEU points below charCNN on vanilla French and German, it is much better than charCNN’s performance on scrambled texts (compare to Table 3). The results of meanChar on Czech are much worse, possibly due to its more complex morphology. However, the meanChar model performance degrades quickly on other kinds of noise as the model trained on vanilla texts was not designed to handle Nat and Key types of noise.
+
+Table 7: Results of charCNN models trained and tested on different noise conditions.   
+
+<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>TestTrain</td><td rowspan=1 colspan=1>Vanilla</td><td rowspan=1 colspan=1>Swap   Mid  Rand   Key   Nat</td><td rowspan=1 colspan=1>Ave</td></tr><tr><td rowspan=2 colspan=1></td><td rowspan=1 colspan=2>Swap</td><td rowspan=1 colspan=1>39.01</td><td rowspan=1 colspan=1>42.56 33.64   2.72   4.85  16.43</td><td rowspan=1 colspan=1>23.20</td></tr><tr><td rowspan=1 colspan=2>Mid</td><td rowspan=1 colspan=1>42.46</td><td rowspan=1 colspan=1>42.19  42.17   3.36   6.20  18.22</td><td rowspan=1 colspan=1>25.77</td></tr><tr><td rowspan=7 colspan=1>French</td><td rowspan=2 colspan=2>RandKey</td><td rowspan=1 colspan=1>39.53</td><td rowspan=1 colspan=1>39.46 39.13  39.73   3.11  16.63</td><td rowspan=1 colspan=1>29.60</td></tr><tr><td rowspan=1 colspan=1>38.49</td><td rowspan=1 colspan=1>10.56   8.69   1.08  38.88  16.86</td><td rowspan=1 colspan=1>19.10</td></tr><tr><td rowspan=1 colspan=2>Nat</td><td rowspan=1 colspan=1>28.77</td><td rowspan=1 colspan=1>12.45   8.39   1.03  6.61  36.00</td><td rowspan=1 colspan=1>15.54</td></tr><tr><td rowspan=2 colspan=2>Rand +KeyRand+Nat</td><td rowspan=1 colspan=1>39.23</td><td rowspan=1 colspan=1>38.85  38.89  39.13  38.22  18.71</td><td rowspan=1 colspan=1>35.51</td></tr><tr><td rowspan=1 colspan=1>36.86</td><td rowspan=1 colspan=1>38.95  38.44  38.63   6.67  33.89</td><td rowspan=1 colspan=1>32.24</td></tr><tr><td rowspan=2 colspan=2>Key+NatRand+Key+Nat</td><td rowspan=2 colspan=1>38.4736.97</td><td rowspan=1 colspan=1>17.33  10.54   1.52 38.62  34.66</td><td rowspan=2 colspan=1>23.5235.70</td></tr><tr><td rowspan=1 colspan=1>36.92 36.65  36.64  35.25  31.77</td></tr><tr><td rowspan=7 colspan=1>German</td><td rowspan=3 colspan=2>SwapMidRand</td><td rowspan=1 colspan=1>32.66</td><td rowspan=1 colspan=1>34.76  29.03   2.19   4.78  13.37</td><td rowspan=1 colspan=1>19.47</td></tr><tr><td rowspan=3 colspan=2>MidRandKey</td><td rowspan=1 colspan=1>34.32</td><td rowspan=1 colspan=1>34.26 34.27   3.50   5.08 14.43</td><td rowspan=1 colspan=1>20.98</td></tr><tr><td rowspan=1 colspan=1>33.65</td><td rowspan=1 colspan=1>33.44  33.75  33.56   3.00  14.47</td><td rowspan=1 colspan=1>25.31</td></tr><tr><td rowspan=1 colspan=1>32.87</td><td rowspan=1 colspan=1>10.13   8.39   1.16 33.28  13.88</td><td rowspan=1 colspan=1>16.62</td></tr><tr><td rowspan=3 colspan=2>NatRand+KeyRand+NatKey +NatRand+Key+Nat</td><td rowspan=1 colspan=1>25.79</td><td rowspan=1 colspan=1>8.20   5.73   0.93   4.80  34.59</td><td rowspan=1 colspan=1>13.34</td></tr><tr><td rowspan=2 colspan=1>32.0332.3730.3931.29</td><td rowspan=1 colspan=1>31.57 31.32  31.58 31.23  15.5932.40 31.91  32.11   4.77  33.00</td><td rowspan=2 colspan=1>28.8927.7620.0230.70</td></tr><tr><td rowspan=1 colspan=1>13.51   8.99   1.53 32.23 33.4630.93 30.54  30.04  29.81  31.60</td></tr><tr><td rowspan=9 colspan=1>Czech</td><td rowspan=9 colspan=2>SwapMidRandKeyNatRand+KeyRand+NatKey+NatRand+Key+Nat</td><td rowspan=1 colspan=1>24.22</td><td rowspan=1 colspan=1>24.90  18.72   2.72   6.00   9.03</td><td rowspan=1 colspan=1>14.27</td></tr><tr><td rowspan=1 colspan=1>23.81</td><td rowspan=1 colspan=1>24.52  24.08   3.96   6.34  9.54</td><td rowspan=1 colspan=1>15.38</td></tr><tr><td rowspan=1 colspan=1>23.44</td><td rowspan=1 colspan=1>23.31  23.24  23.47   3.70   8.10</td><td rowspan=1 colspan=1>17.54</td></tr><tr><td rowspan=1 colspan=1>23.15</td><td rowspan=1 colspan=1>7.06   6.04   1.56 22.80  10.16</td><td rowspan=1 colspan=1>11.80</td></tr><tr><td rowspan=1 colspan=1>18.04</td><td rowspan=1 colspan=1>5.36   4.48   1.47  6.71  21.64</td><td rowspan=1 colspan=1>9.62</td></tr><tr><td rowspan=1 colspan=1>21.46</td><td rowspan=1 colspan=1>20.81  20.90  20.59  19.48   8.72</td><td rowspan=1 colspan=1>18.66</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>20.59</td><td rowspan=1 colspan=1>21.56 20.49  20.53   5.89  18.39</td><td rowspan=1 colspan=1>17.91</td></tr><tr><td rowspan=1 colspan=1>19.55</td><td rowspan=1 colspan=1>6.59   5.72   1.40 21.31  19.54</td><td rowspan=1 colspan=1>12.35</td></tr><tr><td rowspan=1 colspan=1>21.30</td><td rowspan=1 colspan=1>21.33 20.38  19.94 19.25  18.38</td><td rowspan=1 colspan=1>20.10</td></tr></table>
+
+# 6.2 BLACK-BOX ADVERSARIAL TRAINING
+
+To increase model robustness we follow a black-box adversarial training scenario, where the model is presented with adversarial examples that are generated without direct access to the model (Papernot et al., 2016a; 2017; Liu et al., 2017; Narodytska & Kasiviswanathan, 2017; Jia & Liang, 2017). We replace the original training set with a noisy training set, where noise is introduced according to the description in Section 4.2. The noisy training set has exactly the same number of sentences and words as the training set. We have one fixed noisy training set per each noise type.5
+
+As shown in Table 6 (second block), training on noisy text can lead to improved performance. The meanChar models trained on Key perform well on Key in French, but not in the other languages. The models trained on Nat perform well in French and German, but not in Czech. Overall, training the meanChar model on noisy text does not appear to consistently increase its robustness to different kinds of noise. The meanChar model however was not expected to perform well on nonscrambling types of noise. Next we test whether the more complicated charCNN model is more robust to different kinds of noise, by training on noisy texts. The results are shown in Table 7.
+
+In general, charCNN models that are trained on a specific kind of noise perform well on the same kind of noise at test time (results in bold). All models also maintain a fairly good quality on vanilla texts.The robust training is sensitive to the kind of noise. Among the scrambling methods (Swap/Mid/Rand), more noise helps in training: models trained on random noise can still translate Swap/Mid noise, but not vice versa. The three broad classes of noise (scrambling, Key, Nat)
+
+![](images/38b5ca4f366595dec304b147eaa23d2f595cb687cb7abe7b6e0838a1b0a860ea.jpg)  
+Figure 2: Variances of charCNN weights when trained on only Key, Natural, Random noise and on a mix of all three are shown in red, green, blue, and white, respectively
+
+are not mutually-beneficial. Models trained on one do not perform well on the others. In particular, 1only models trained on natural noise can reasonably translate natural noise at test time. We find this result indicates an important difference between computational models and human performance, since humans can decipher random letter orderings without explicit training of this form.
+
+Next, we test whether we can increase training robustness by exposing the model to multiple types of noise during training. Our motivation is to see if models can perform well on more than one kind of noise. We therefore mix up to three kinds of noise by sampling a noise method uniformly at random for each sentence. We then train a model on the mixed noisy training set and test it on both vanilla and (unmixed) noisy versions of the test set. We find that models trained on mixed noise are slightly worse than models trained on unmixed noise. However, the models trained on mixed noise are robust to the specific types of noise they were trained on. In particular, the model trained on a mix of Rand, $\operatorname { K e y }$ , and Nat noise is robust to all noise kinds. Even though it is not the best on any one kind of noise, it achieves the best result on average.
+
+This model is also able to translate the scrambled meme reasonably well:
+
+“According to a study of Cambridge University, it doesn’t matter which technology in a word is going to get the letters in a word that is the only important thing for the first and last letter.”
+
+# 7 ANALYSIS
+
+# 7.1 LEARNING MULTIPLE KINDS OF NOISE IN C H A RCNN
+
+The charCNN model was able to perform well on all kinds of noise by training on a mix of noise types. In particular, it performed well on scrambled characters even though its convolutions should be sensitive to the character order, as opposed to meanChar which is by definition invariant to character order. How then can charCNN learn to be robust to multiple kinds of noise at the same time? We speculate that different convolutional filters learn to be robust to different kinds of noise. A convolutional filter can in principle capture a mean (or sum) operation by employing equal or close to equal weights.
+
+To test this, we analyze the weights learned by charCNN models trained under four conditions: three models trained each on completely scrambled words (Rand), keyboard typos (Key), and natural human errors (Nat), as well as an ensemble model trained on a mix of Rand+Key+Nat kinds of noise. For each model, we compute the variance across the filter width (6 characters) for each one of the 1000 filters and for each one out of 25 character embedding dimensions. Intuitively, this variance captures how much a particular filter learns a uniform vs. non-uniform combination of characters. Then we average the variances across the 1000 filters. This yields 25 averaged variances, one for each character embedding dimension. Low average variance means that different filters tend to learn similar behaviors, while high average variance means that they learn different patterns.
+
+Figure 2 shows a box plot of these averages for our three languages and four training conditions. Clearly, the variances of the weights learned by the Rand model are much smaller than those of the weights learned by any other setting. This makes sense as with random scrambling there are no patterns to detect in the data, so filters resort to close to uniform weights. In contrast, the Key and Nat settings introduce a large set of new patterns for the CNNs to try and learn, leading to high variances. Finally, the ensemble model trained on mixed noise appears to be in the middle as it tries to capture both the uniform relationships of Rand and the more diverse patterns of Nat $^ +$ Key.
+
+Moreover, the variance of variances (size of the box) is smallest in the Rand setting, larger in the mixed noise model, and largest in Key and Nat. This indicates that filters for different character embedding dimensions are more different from one another in Key and Nat models. In contrast, in the Rand model, the variance of variances is close to zero, indicating that in all character embedding dimensions the learned weights are of small variance; they do similar things, that is, the model learned to reproduce a representation similar to the meanChar model. The ensemble model again seems to find a balance between Rand and Key/Nat.
+
+# 7.2 RICHNESS OF NATURAL NOISE
+
+Natural noise appears to be very different from synthetic noise. None of the models that were trained only on synthetic noise were able to perform well on natural noise. We manually analyzed a small sample ${ \sim } 4 0$ examples) of natural noise from the German dataset. We found that the most common sources of noise are phonetic or phonological phenomena in the language $( 3 4 \% )$ and character omissions $( 3 2 \% )$ . The rest are incorrect morphological conjugations of verbs, key swaps, character insertions, orthographic variants, and other errors. Table 8 shows examples of these kinds of noise.
+
+The most common types of natural noise – phonological and omissions – are not directly captured by our synthetic noise generation, and demonstrate that good synthetic errors will likely require more explicit phonemic and linguistic knowledge. This discrepancy helps explain why the models trained on synthetic noise were not particularly successful in translating natural noise.
+
+Table 8: Examples of natural noise from the German errors dataset.   
+
+<table><tr><td>Error type</td><td>Examples</td></tr><tr><td>Phonetic</td><td>Tut/Tud (devoicing of final stops),sieht/zieht (s = /z/ before vowel),Trotzdem/Trozdem (tz=/z/),gekriegt/gekrigt (vowel length),Naturlich/Naturlich/Näturlich (diacritics)</td></tr><tr><td>Omission</td><td>erfahren/erfaren,Babysitter/Babysiter, selbst/sebst,Hausschuhe/Hausschue</td></tr><tr><td>Morphological</td><td>wohnt/wonnen,fortsetzt/forzusetzen,wiinsche/winchen</td></tr><tr><td>Key swap</td><td>Eltern/Eltren,Deine/Diene,nichts/nichst, Bahn/Bhan</td></tr><tr><td>Other</td><td>Agglomerationen/Agromelationen (omission + letter swap),Hausaufgabe/Hausausgabe, Thema/Temer,Detailhandelsfachfrau/Deitellhandfachfrau</td></tr></table>
+
+# 8 CONCLUSION
+
+In this work, we have shown that character-based NMT models are extremely brittle and tend to break when presented with both natural and synthetic kinds of noise. We investigated methods for increasing their robustness by using a structure-invariant word representation and by ensemble training on adversarial examples of different kinds. We found that a character-based CNN can learn to address multiple types of errors that are seen in training. However, we observed rich characteristics of natural human errors that cannot be easily captured by existing models. Future work might investigate using phonetic and syntactic structure to generate more realistic synthetic noise.
+
+We believe that more work is necessary in order to immune NMT models against natural noise. As corpora with natural noise are limited, another approach to future work is to design better NMT architectures that would be robust to noise without seeing it in the training data. New psychology results on how humans cope with natural noise might point to possible solutions to this problem.
+
+# ACKNOWLEDGEMENTS
+
+This work benefited from discussions with Frank Keller. This work was supported by the Qatar Computing Research Institute (QCRI) and Samsung Research.
+
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+Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus. Intriguing properties of neural networks. In International Conference on Learning Representations (ICLR), 2014.
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+Florian Tramer, Alexey Kurakin, Nicolas Papernot, Dan Boneh, and Patrick McDaniel. Ensemble \` Adversarial Training: Attacks and Defenses. arXiv preprint arXiv:1705.07204, 2017.
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+Ekaterina Vylomova, Trevor Cohn, Xuanli He, and Gholamreza Haffari. Word Representation Models for Morphologically Rich Languages in Neural Machine Translation. arXiv preprint arXiv:1606.04217, 2016.
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+Katrin Wisniewski, Karin Schne, Lionel Nicolas, Chiara Vettori, Adriane Boyd, Detmar Meurers, Andrea Abel, and Jirka Hana. MERLIN: An online trilingual learner corpus empirically grounding the European Reference Levels in authentic learner data, 10 2013. URL https://www. ukp.tu-darmstadt.de/data/spelling-correction/rwse-datasets.
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+Yonghui Wu, Mike Schuster, Zhifeng Chen, Quoc V Le, Mohammad Norouzi, Wolfgang Macherey, Maxim Krikun, Yuan Cao, Qin Gao, Klaus Macherey, et al. Google’s neural machine translation system: Bridging the gap between human and machine translation. arXiv preprint arXiv:1609.08144, 2016.
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+Torsten Zesch. Measuring Contextual Fitness Using Error Contexts Extracted from the Wikipedia Revision History. In Proceedings of the 13th Conference of the European Chapter of the Association for Computational Linguistics, pp. 529–538, Avignon, France, April 2012. Association for Computational Linguistics.

parse/train/BJ8vJebC-/BJ8vJebC-_content_list.json

@@ -0,0 +1,1655 @@
+[
+    {
+        "type": "text",
+        "text": "SYNTHETIC AND NATURAL NOISE BOTH BREAK NEURAL MACHINE TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yonatan Belinkov∗ ",
+        "bbox": [
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+            184
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Yonatan Bisk∗ ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Computer Science and   \nArtificial Intelligence Laboratory,   \nMassachusetts Institute of Technology   \nbelinkov@mit.edu ",
+        "bbox": [
+            184,
+            185,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Paul G. Allen School of Computer Science & Engineering, University of Washington ybisk@cs.washington.edu ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
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+            544,
+            291
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Character-based neural machine translation (NMT) models alleviate out-ofvocabulary issues, learn morphology, and move us closer to completely end-toend translation systems. Unfortunately, they are also very brittle and easily falter when presented with noisy data. In this paper, we confront NMT models with synthetic and natural sources of noise. We find that state-of-the-art models fail to translate even moderately noisy texts that humans have no trouble comprehending. We explore two approaches to increase model robustness: structure-invariant word representations and robust training on noisy texts. We find that a model based on a character convolutional neural network is able to simultaneously learn representations robust to multiple kinds of noise. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            468,
+            336,
+            484
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Humans have surprisingly robust language processing systems that can easily overcome typos, misspellings, and the complete omission of letters when reading (Rawlinson, 1976). A particularly extreme and comical exploitation of our robustness came years ago in the form of a popular meme: ",
+        "bbox": [
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+            500,
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+            541
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "“Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae.” ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "A person’s ability to read this text comes as no surprise to the psychology literature. Saberi & Perrott (1999) found that this robustness extends to audio as well. They experimented with playing parts of audio transcripts backwards and found that it did not affect comprehension. Rayner et al. (2006) found that in noisier settings reading comprehension only slowed by $11 \\%$ . McCusker et al. (1981) found that the common case of swapping letters could often go unnoticed by the reader. The exact mechanisms and limitations of our understanding system are unknown. There is some evidence that we rely on word shape (Mayall et al., 1997), that we can switch between whole word recognition and piecing together words from letters (Reicher, 1969; Pelli et al., 2003), and there appears to be no evidence that the first and last letter positions are required to stay constant for comprehension.1 ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In stark contrast, neural machine translation (NMT) systems, despite their pervasive use, are immensely brittle. For instance, Google Translate produces the following unintelligible translation for a German version of the above meme:2 ",
+        "bbox": [
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+            763
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "“After being stubbornly defiant, it is clear to kenie Rlloe in which Reiehnfogle is advancing the boulders in a Wrot that is integral to Sahce, as the utterance and the lukewarm boorstbaen stmimt.” ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "While typos and noise are not new to NLP, our systems are rarely trained to explicitly address them, as we instead hope that the relevant noise will occur in the training data. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Despite these weaknesses, the move to character-based NMT is important. It helps us tackle the long tailed distribution of out-of-vocabulary words in natural language, as well as reduce computation ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "load of dealing with large word embedding matrices. NMT models based on characters and other0 34.22 0 34.22 0 34.22 40   \nsub-word units are able to extract stem and morphological information to generalize to unseen words     15.3 21.77 10.4 25.59 7.6 28.52   \nand conjugations. They perform very well in practice on a range of languages (Sennrich et al.,23.2 15.73 15.3 21.56 11.4 25.42 30   \n2016a; Wu et al., 2016). In many cases, these models actually discover an impressive amount of30.8 11.45 20.6 17.91 15.2 22.60   \nmorphological information about a language (Belinkov et al., 2017a). Unfortunately, training (and46.3 5.28 30.3 12.22 22.6 17.62   \ntesting) on clean data makes models brittle and, arguably, unfit for broad deployment.53.6 3.19 35.8 9.49 26.2 16.52 ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 1 shows how the performance of two state-of-the-art NMT systems degrades when translating69.1 0.84 45.7 5.36 34.0 12.02 10 German to English as a function of the percent of German words modified. Here we show three types76.7 0.29 51.1 3.39 37.8 10.68 of noise: 1) Random permutation of the word, 2) Swapping a pair of adjacent letters, and 3) Natural0 human errors. We discuss these types of noise and others in depth in section 4.2. The important thing to note is that even small amounts of noise lead to substantial drops in performance.Random Swap Natural ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/a0eaf407647ec50ed9174c02e7a537177a58014aa3549a2a542b4922c39bd813.jpg",
+        "image_caption": [
+            "Random Swap NaturalChar2Char Char2CharFigure 1: Degradation of Nematus (Sennrich et al., 2017) and char2char (Lee et al., 2017) 40 Nematusperformance as noise increases. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "30 52.5x+68.2To address these trends and investigate the effects of noise on NMT, we explore two simple strategies   \n0 68.2 0 68.2 0 68.2 0 68.2for increasing model robustness: using structure-invariant representations and robust training on   \n20 35.015.3 55.8 10.4 59.9 7.6 62.7 20 54.56noisy data, a form of adversarial training (Szegedy et al., 2014; Goodfellow et al., 2015). We find   \n23.2 49.6 15.3 55.7 11.4 59.6 30 47.74that a character CNN representation trained on an ensemble of noise types is robust to all kinds of   \n38.0 38.5 25.9 48.8 18.8 53.6 50 34.1noise. We shed some light on the model ability to learn robust representations to multiple types of   \n46.3 33.0 30.3 45.6 22.6 51.3 60 27.28noise, and point to remaining difficulties in handling natural noise. Our goal is two fold: 1) initiate   \n53.6 27.4 35.8 41.6 26.2 49.3 70 20.46a conversation on robust training and modeling techniques in NMT, and 2) promote the creation of   \n0 20 40 60 80  069.1 17.7 45.7 34.3 34.0 43.5 90 6.82better and more linguistically accurate artificial noise to be applied to new languages and tasks. ",
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+    {
+        "type": "text",
+        "text": "2 ADVERSARIAL EXAMPLES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "char2charThe growing literature on adversarial examples has demonstrated how dangerous it can be to use y =  Random Swap Natural Linear y = (-66/100brittle machine learning systems so pervasively in the real world (Biggio et al., 2012; Szegedy et al., x+68.2 )x + 662014; Goodfellow et al., 2015; Mei & Zhu, 2015). Small changes to the input can lead to dramatic 0 68.2 7.7 60.6 5.2 63.3 3.7 64.2 10 59.4failures of deep learning models (Szegedy et al., 2014; Goodfellow et al., 2015). In the machine 20 54.56 15.3 55.3 10.4 60.2 7.6 62.4 20 52.8vision field, changes to the input image that are indistinguishable by humans can lead to misclas30 47.74 23.2 49.5 15.3 57.3 11.4 60.3 30 46.230.8 43.6 20.6 54.2 15.2 58.0 40 39.6sification. This leads to potential for malicious attacks using adversarial examples. An important 40 40.9250 34.1 38.0 38.3 25.9 51.5 18.8 56.7 50 33distinction is often drawn between white-box attacks, where adversarial examples are generated with 60 27.28 46.3 33.3 30.3 48.3 22.6 54.7 60 26.4access to the model parameters, and black-box attacks, where examples are generated without such 70 20.46       61.5 23.2 40.9 42.2 30.1 50.7 80 13.2access (Papernot et al., 2016a; 2017; Narodytska & Kasiviswanathan, 2017; Liu et al., 2017). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "90 6.82 76.7 14.1 51.1 35.8 37.8 46.3 100 0While more common in the vision domain, recent work has started exploring adversarial examples for NLP. A few white-box attacks have employed the fast gradient sign method (Goodfellow et al., 2015) or other techniques to find important text edit operations (Papernot et al., 2016b; Samanta & Mehta, 2017; Liang et al., 2017; Ebrahimi et al., 2017). Others have considered black-box adversarar y = ial examples for text classification (Gao et al., 2018) or NLP evaluation (Jia & Liang, 2017). Heigold )x + 66et al. (2017) evaluated character-based models on several types of noise in morphological tagging 0 66and MT, and observed similar trends to our findings. Finally, Sakaguchi et al. (2017) designed a 20 52.8character-level recurrent neural network that can better handle the particular kind of noise present 30 46.2in the meme mentioned above by modeling spelling correction. Here we devise simple methods 40 39.650 33for generating adversarial examples for NMT. We do not assume any access to the NMT models’ 60 26.4gradients, instead relying on synthetic and naturally occurring language errors to generate noise. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "The other side of the coin is to improve models’ robustness to adversarial examples (Globerson & Roweis, 2006; Cretu et al., 2008; Rubinstein et al., 2009; Chan et al., 2017). Adversarial training – including adversarial examples in the training data – can improve a model’s ability to cope with such examples at test time (Szegedy et al., 2014; Goodfellow et al., 2015). This kind of defense is sensitive to the type of adversarial examples seen in training, but can be made more robust by ensemble adversarial training – training on examples transfered from multiple pre-trained models (Tramer\\` et al., 2017). We explore ensemble training by combining multiple types of noise at training time, and observe similar increased robustness in the machine translation scenario. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Training on and for adversarial noise is an important extension of earlier work on creating robustness in neural networks by incorporating noise to a network’s representations, data, or gradients. Training with noise can provide a form of regularization (Bishop, 1995) and ensure the model is exposed to samples outside the training distribution (Matsuoka, 1992). ",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 MT SYSTEMS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            296,
+            321,
+            313
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The rise of end-to-end models in neural machine translation has led to recent interest in understanding how these models operate. Several studies investigated the ability of such models to learn linguistic properties at morphological (Vylomova et al., 2016; Belinkov et al., 2017a; Dalvi et al., 2017), syntactic (Shi et al., 2016; Sennrich, 2017), and semantic levels (Belinkov et al., 2017b). The use of characters or other sub-word units emerges as an important component in these models. Our work complements previous studies by presenting such NMT systems with noisy examples and exploring methods for increasing their robustness. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We experiment with three different NMT systems with access to character information at different levels. First, we use the fully character-level model of Lee et al. (2017). This is a sequence-tosequence model with attention (Sutskever et al., 2014; Bahdanau et al., 2014) that is trained on characters to characters (char2char). It has a complex encoder with convolutional, highway, and recurrent layers, and a standard recurrent decoder. See Lee et al. (2017) for architecture details. This model was shown to have excellent performance on the German English and Czech English language pairs. We use the pre-trained German/Czech English models. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Second, we use Nematus (Sennrich et al., 2017), a popular NMT toolkit that was used in topperforming contributions in shared MT tasks in WMT (Sennrich et al., 2016b) and IWSLT (JunczysDowmunt & Birch, 2016). It is another sequence-to-sequence model with several architecture modifications, especially operating on sub-word units using byte-pair encoding (BPE) (Sennrich et al., 2016a). We experimented with both their single best and ensemble BPE models, but saw no significant difference in their performance under noise, so we report results with their single best WMT models for German/Czech English. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Finally, we train an attentional sequence-to-sequence model with a word representation based on a character convolutional neural network (charCNN). This model retains the notion of a word but learns a character-dependent representation of words. It was shown to perform well on morphologically-rich languages (Kim et al., 2015; Belinkov & Glass, 2016; Costa-jussa & Fonol- \\` losa, 2016; Sajjad et al., 2017), thanks to its ability to learn morphologically-informative representations (Belinkov et al., 2017a). The charCNN model has two long short-term memory (Hochreiter & Schmidhuber, 1997) layers in the encoder and decoder. A CNN over characters in each word replaces the word embeddings on the encoder side (for simplicity, the decoder is word-based). We use 1000 filters with a width of 6 characters. The character embedding size is set to 25. The convolutions are followed by Tanh and max-pooling over the length of the word (Kim et al., 2015). We train charCNN with the implementation in Kim (2016); all other settings are kept to default values. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4 DATA ",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "4.1 MT DATA ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We use the TED talks parallel corpus prepared for IWSLT 2016 (Cettolo et al., 2012) for testing all of the NMT systems, as well as for training the charCNN models. We follow the official training/development/test splits. All texts are tokenized with the Moses tokenizer. Table 1 summarizes statistics on the TED talks corpus. ",
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "table",
+        "img_path": "images/ff34da7c1225ba2c00bb95f34fb580f4eef492a60f8281594faf24594f1e8b11.jpg",
+        "table_caption": [
+            "Table 1: Statistics for the source-side of French/German/Czech English parallel corpora. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"3\">French</td><td colspan=\"3\">German</td><td colspan=\"3\">Czech Test</td></tr><tr><td></td><td>Train</td><td>Dev</td><td>Test</td><td>Train</td><td>Dev</td><td>Test</td><td>Train</td><td>Dev</td></tr><tr><td>Sentences</td><td>235K</td><td>2.5K</td><td>0.8K</td><td>210K</td><td>2.5K</td><td>1.4K</td><td>122K</td><td>20K 1K</td></tr><tr><td>Words</td><td>5.2M</td><td>55K</td><td>16K</td><td>4M</td><td>50K</td><td>26K</td><td>2.1M 35K</td><td>15K</td></tr></table>",
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/cd27aadf75f4d83356290ad153766e525d18ba2b8a8e8804a3b4acb215cb038e.jpg",
+        "table_caption": [
+            "Table 2: Average number of available edits per word in natural noise datasets and the corresponding token recall of those edits on the training and test splits. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">French</td><td colspan=\"3\">German</td><td colspan=\"3\">Czech</td></tr><tr><td>Words</td><td>Errors Train</td><td>Test</td><td>Words</td><td>Errors</td><td>Train Test</td><td></td><td>Words Errors</td><td>Train Test</td></tr><tr><td>65,156</td><td>2.7</td><td>40% 41%</td><td>1,344</td><td>2.5</td><td>37%</td><td>40%</td><td>6.036 2.6</td><td>46% 51%</td></tr></table>",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2 NOISE: NATURAL AND ARTIFICIAL ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            313,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We insert noise into the source-side of the parallel MT data by utilizing naturally occurring errors and generating synthetic ones. In order to facilitate future work on noise in NMT, we release code and data for generating the noise used in our experiments.3 ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.2.1 NATURAL NOISE ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since we do not have access to a parallel corpus with natural noise, we instead harvest naturally occurring errors (typos, misspellings, etc.) from available corpora of edits to build a look-up table of possible lexical replacements. In this work, we restrict ourselves to single word replacements, but several of the corpora below also provide access to phrase replacements. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "French Max & Wisniewski (2010) collected Wikipedia edit histories to form the Wikipedia Correction and Paraphrase Corpus (WiCoPaCo). They found the bulk of edits were due to incorrect diacritics, choosing the wrong homophone, and incorrect grammatical conjugation. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "German Our German data combines two projects: RWSE Wikipedia Revision Dataset (Zesch, 2012) and The MERLIN corpus of language learners (Wisniewski et al., 2013). These corpora were created to measure spelling difficulty and test models of contextual fitness. Unfortunately, the datasets are quite small so we have combined them here. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Czech Our Czech errors come from manually annotated essays written by non-native speakers (Sebesta et al. ˇ , 2017). Here, the authors found an incredibly diverse set of errors, and therefore phenomena of interest: capitalization, incorrectly replacing voiced and voiceless consonants (e.g. z/s, $\\mathrm { g / k } )$ ), missing palatalization (matke/matce), error in valence, pronominal reference, inflection, collo- ˇ quial forms, and so forth. Their analysis gives us the best insight into how difficult it would be to synthetically generate truly natural errors. We found similarly rich errors in German (Section 7.2). ",
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+    {
+        "type": "text",
+        "text": "We insert these errors into the source-side of the parallel data by replacing every word in the corpus with an error if one exists in our dataset. When there is more than one possible replacement to choose we sample uniformly. Words for which there is no error are kept as is. Table 2 shows the number of words for which we were able to collect errors in each language, and the average number of errors per word. Despite the small size of the German and Czech datasets, we are able to replace up to half of the words in the corpus with errors. Due to the small size of the German and Czech datasets these percentages decrease for longer words $\\cdot > 4$ characters) to $2 5 \\%$ and $32 \\%$ , respectively. ",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2.2 SYNTHETIC NOISE ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            842,
+            356,
+            856
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In addition to naturally collected sources of error, we also experiment with four types of synthetic noise: Swap, Middle Random, Fully Random, and Keyboard Typo. ",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e854d3b48b19f9b143c2746d1e1b72bb0ca85b70691cbc6b1bbb6df171b41172.jpg",
+        "table_caption": [
+            "Table 3: The effect of Natural (Nat) and synthetic noise (Swap swap, Middle Random Mid, Fully Random Rand, and Keyboard Typo Key) on models trained on clean (Vanilla) texts. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"6\">Synthetic</td></tr><tr><td></td><td>Vanilla</td><td>Swap Mid</td><td>Rand</td><td>Key</td><td>Nat</td></tr><tr><td>French</td><td>charCNN</td><td>42.54</td><td>10.52</td><td>9.71</td><td>1.71 8.26</td><td>17.42</td></tr><tr><td rowspan=\"3\">German</td><td>charCNN</td><td>34.79</td><td>9.25</td><td>8.37 1.02</td><td>6.40</td><td>14.02</td></tr><tr><td>char2char</td><td>29.97</td><td>5.68</td><td>5.46 0.28</td><td>2.96</td><td>12.68</td></tr><tr><td>Nematus</td><td>34.22</td><td>3.39</td><td>5.16</td><td>0.29 0.61</td><td>10.68</td></tr><tr><td rowspan=\"3\">Czech</td><td>charCNN</td><td>25.99</td><td>6.56</td><td>6.67</td><td>1.50 7.13</td><td>10.20</td></tr><tr><td>char2char</td><td>25.71</td><td>3.90</td><td>4.24</td><td>0.25 2.88</td><td>11.42</td></tr><tr><td>Nematus</td><td>29.65</td><td>2.94</td><td>4.09</td><td>0.66 1.41</td><td>11.88</td></tr></table>",
+        "bbox": [
+            235,
+            142,
+            758,
+            292
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/9ad1426a82753cba7613b0db0bb1e36fbb76c0d2ed57ead7190c0feb8cff8841.jpg",
+        "table_caption": [
+            "Table 4: An example noisy text with human and machine translations. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Input</td><td>Luat eienr Stduie der Cambrdige Unievrstit speilt es kenie Rlloe in welcehr Reiehnfogle die Buhcstbaen in eniem Wrot vorkmomen,die eingzie whctige Sahce ist,dsas der ertse und der lettze Buhcstbaen stmimt .</td></tr><tr><td>Human</td><td>According to a study from Cambridge university, it doesn&#x27;t matter which order letters in a word are,the only important thing is that the first and the last letter appear in their correct place. Cambridge Universtte is one of the most important features of the Cambridge Universttten ,</td></tr><tr><td>char2char Nematus</td><td>which is one of the most important features of the Cambridge Universttten . Luat eienr Stduie der Cambrant Unievrstilt splashed it kenie Rlloe in welcehr Reiehnfogle the</td></tr><tr><td>charCNN</td><td>Buhcstbaen in eniem Wred vorkmomen,die eingzie whcene Sahce ist,DSAs der ertse und der lettze Buhcstbaen stmimt . According to the &lt;unk&gt;of the Cambridge University,it &#x27;s a litle bit of crude oil in a little bit of recycling ,which is a little bit of acool cap,which is a little bit of a strong cap,that the</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Swap : Swap The simplest source of noise is swapping two letters (e.g. noise nosie). This is common when typing quickly and is easily implemented. We perform one swap per word, but do not alter the first or last letters. For this reason, this noise is only applied to words of length $\\geq 4$ . ",
+        "bbox": [
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+            516,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Middle Random : Mid Following the claims of the previously discussed meme, we randomize the order of all the letters in a word except for the first and last (noise nisoe). Again, by necessity, this means we do not alter words shorter than four characters. ",
+        "bbox": [
+            174,
+            569,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Fully Random : Rand As we are unaware of any strong results on the importance of the first and last letters we also include completely randomized words (noise iones). This is a particularly extreme case, but we include it for completeness. This type of noise is applied to all words. ",
+        "bbox": [
+            174,
+            622,
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+            665
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Keyboard Typo : Key Finally, using the traditional keyboards for our languages, we randomly replace one letter in each word with an adjacent key (noise noide). This type of error should be much easier than the random settings as most of the word is left intact, but does introduce a completely new character which will often break the templates a system has learned to rely on. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5 FAILURES TO TRANSLATE NOISY TEXTS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            751,
+            544,
+            768
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 3 shows BLEU scores of models trained on clean (Vanilla) texts and tested on clean and noisy texts. All models suffer a significant drop in BLEU when evaluated on noisy texts. This is true for both natural noise and all kinds of synthetic noise. The more noise in the text, the worse the translation quality, with random scrambling producing the lowest BLEU scores. ",
+        "bbox": [
+            174,
+            784,
+            825,
+            838
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The degradation in translation quality is especially severe in light of humans’ ability to understand noisy texts. To illustrate this, consider the noisy text in Table 4. Humans are quite good at understanding such scrambled texts in a variety of languages.4 We also verified this by obtaining a translation from a German native-speaker, unfamiliar with the meme. As shown in the table, the speaker had no trouble understanding and translating the sentence properly. In contrast, the state-ofthe-art systems (char2char and Nematus) fail on this text. ",
+        "bbox": [
+            174,
+            845,
+            823,
+            888
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/e814d0f3ac317975b126ef820411d8f303d3ca776661b1d408951e0c1910c6c8.jpg",
+        "table_caption": [
+            "Table 5: Google Translate’s performance with natural errors and the gains from using spell checking. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"3\">French</td><td colspan=\"3\">German</td><td colspan=\"3\">Czech</td></tr><tr><td>Vanilla</td><td>Nat</td><td>Spelling</td><td>Vanilla</td><td>Nat</td><td>Spelling</td><td>Vanilla</td><td>Nat</td><td>Spelling</td></tr><tr><td>43.3</td><td>16.7</td><td>21.4</td><td>38.7</td><td>18.6</td><td>25.0</td><td>26.5</td><td>12.3</td><td>11.2</td></tr></table>",
+        "bbox": [
+            178,
+            127,
+            818,
+            184
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/07093e11371f2b9c96845524a376f913f568be0ca24d08291cfac78b61f6fd92.jpg",
+        "table_caption": [
+            "Table 6: Results of meanChar models trained and tested on different noise conditions: Scrambled (Scr), Keyboard Typo (Key), and Natural (Nat). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Test Train</td><td colspan=\"3\">French</td><td colspan=\"3\">German</td><td colspan=\"3\">Czech</td></tr><tr><td>Scr</td><td>Key</td><td>Nat</td><td>Scr</td><td>Key</td><td>Nat</td><td>Scr</td><td>Key</td><td>Nat</td></tr><tr><td>Vanilla</td><td>34.26</td><td>4.27</td><td>12.58</td><td>27.53</td><td>3.34</td><td>9.41</td><td>3.73</td><td>2.06</td><td>3.25</td></tr><tr><td>Key</td><td>31.88</td><td>29.75</td><td>13.16</td><td>10.04</td><td>8.84</td><td>4.45</td><td>2.03</td><td>1.9</td><td>1.42</td></tr><tr><td>Nat</td><td>26.94</td><td>5.30</td><td>27.49</td><td>15.65</td><td>3.06</td><td>26.26</td><td>1.66</td><td>1.52</td><td>1.58</td></tr><tr><td>Rand+Key</td><td>13.60</td><td>11.09</td><td>6.12</td><td>26.59</td><td>22.41</td><td>11.07</td><td>9.97</td><td>7.48</td><td>4.21</td></tr><tr><td>Rand+Nat</td><td>28.28</td><td>5.10</td><td>20.40</td><td>13.87</td><td>3.73</td><td>12.74</td><td>4.89</td><td>2.82</td><td>3.42</td></tr><tr><td>Key+Nat</td><td>31.30</td><td>26.94</td><td>24.24</td><td>6.62</td><td>5.41</td><td>5.75</td><td>1.62</td><td>1.68</td><td>1.58</td></tr><tr><td>Rand+Key+Nat</td><td>3.10</td><td>3.28</td><td>2.76</td><td>8.02</td><td>5.79</td><td>6.36</td><td>1.73</td><td>1.74</td><td>1.66</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
+            176,
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+            445
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "One natural question is if robust spell checkers trained on human errors are sufficient to address this performance gap. To test this, we ran texts with and without natural errors through Google Translate. We then used Google’s spell-checkers to correct the documents. We simply accepted the first suggestion for every detected mistake detected, and report results in Table 5. ",
+        "bbox": [
+            174,
+            452,
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+            508
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We found that in French and German, there was often only a single predicted correction and this corresponds to roughly $+ 5$ or more in BLEU. In Czech, however, there was often a large list of possible conjugations and changes, likely indicating that a rich grammatical model would be necessary to predict the correction. It is also important to note the substantial drops from vanilla text even with spell check. This suggests that natural noise cannot be easily addressed by existing tools. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6 DEALING WITH NOISE ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "6.1 STRUCTURE INVARIANT REPRESENTATIONS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            640,
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+            654
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The three NMT models are all sensitive to word structure. The char2char and charCNN models both have convolutional layers on character sequences, designed to capture character n-grams. The model in Nematus is based on sub-word units obtained with BPE. It thus relies on character order within and across sub-word units. All these models are therefore sensitive to types of noise generated by character scrambling (Swap, Mid, and Rand). Can we improve model robustness by adding invariance to these kinds of noise? Perhaps the simplest such model is to take the average character embedding as a word representation. This model, referred to as meanChar, first generates a word representation by averaging character embeddings, and then proceeds with a word-level encoder similar to the charCNN model. The meanChar model is by definition insensitive to scrambling, although it is still sensitive to other kinds of noise (Key and Nat). ",
+        "bbox": [
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+            666,
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+            805
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 6 (first row) shows the results of meanChar models trained on vanilla texts and tested on noisy texts (the results on vanilla texts are by definition equal to those on scrambled texts). Overall, the average character embedding proves to be a pretty good representation for translating scrambled texts: while performance drops by about 7 BLEU points below charCNN on vanilla French and German, it is much better than charCNN’s performance on scrambled texts (compare to Table 3). The results of meanChar on Czech are much worse, possibly due to its more complex morphology. However, the meanChar model performance degrades quickly on other kinds of noise as the model trained on vanilla texts was not designed to handle Nat and Key types of noise. ",
+        "bbox": [
+            174,
+            813,
+            825,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/7581189edf6c2484d5dd9eb74df84b8bddb421a44e67058fb7c825a8060344f7.jpg",
+        "table_caption": [
+            "Table 7: Results of charCNN models trained and tested on different noise conditions. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=2>TestTrain</td><td rowspan=1 colspan=1>Vanilla</td><td rowspan=1 colspan=1>Swap   Mid  Rand   Key   Nat</td><td rowspan=1 colspan=1>Ave</td></tr><tr><td rowspan=2 colspan=1></td><td rowspan=1 colspan=2>Swap</td><td rowspan=1 colspan=1>39.01</td><td rowspan=1 colspan=1>42.56 33.64   2.72   4.85  16.43</td><td rowspan=1 colspan=1>23.20</td></tr><tr><td rowspan=1 colspan=2>Mid</td><td rowspan=1 colspan=1>42.46</td><td rowspan=1 colspan=1>42.19  42.17   3.36   6.20  18.22</td><td rowspan=1 colspan=1>25.77</td></tr><tr><td rowspan=7 colspan=1>French</td><td rowspan=2 colspan=2>RandKey</td><td rowspan=1 colspan=1>39.53</td><td rowspan=1 colspan=1>39.46 39.13  39.73   3.11  16.63</td><td rowspan=1 colspan=1>29.60</td></tr><tr><td rowspan=1 colspan=1>38.49</td><td rowspan=1 colspan=1>10.56   8.69   1.08  38.88  16.86</td><td rowspan=1 colspan=1>19.10</td></tr><tr><td rowspan=1 colspan=2>Nat</td><td rowspan=1 colspan=1>28.77</td><td rowspan=1 colspan=1>12.45   8.39   1.03  6.61  36.00</td><td rowspan=1 colspan=1>15.54</td></tr><tr><td rowspan=2 colspan=2>Rand +KeyRand+Nat</td><td rowspan=1 colspan=1>39.23</td><td rowspan=1 colspan=1>38.85  38.89  39.13  38.22  18.71</td><td rowspan=1 colspan=1>35.51</td></tr><tr><td rowspan=1 colspan=1>36.86</td><td rowspan=1 colspan=1>38.95  38.44  38.63   6.67  33.89</td><td rowspan=1 colspan=1>32.24</td></tr><tr><td rowspan=2 colspan=2>Key+NatRand+Key+Nat</td><td rowspan=2 colspan=1>38.4736.97</td><td rowspan=1 colspan=1>17.33  10.54   1.52 38.62  34.66</td><td rowspan=2 colspan=1>23.5235.70</td></tr><tr><td rowspan=1 colspan=1>36.92 36.65  36.64  35.25  31.77</td></tr><tr><td rowspan=7 colspan=1>German</td><td rowspan=3 colspan=2>SwapMidRand</td><td rowspan=1 colspan=1>32.66</td><td rowspan=1 colspan=1>34.76  29.03   2.19   4.78  13.37</td><td rowspan=1 colspan=1>19.47</td></tr><tr><td rowspan=3 colspan=2>MidRandKey</td><td rowspan=1 colspan=1>34.32</td><td rowspan=1 colspan=1>34.26 34.27   3.50   5.08 14.43</td><td rowspan=1 colspan=1>20.98</td></tr><tr><td rowspan=1 colspan=1>33.65</td><td rowspan=1 colspan=1>33.44  33.75  33.56   3.00  14.47</td><td rowspan=1 colspan=1>25.31</td></tr><tr><td rowspan=1 colspan=1>32.87</td><td rowspan=1 colspan=1>10.13   8.39   1.16 33.28  13.88</td><td rowspan=1 colspan=1>16.62</td></tr><tr><td rowspan=3 colspan=2>NatRand+KeyRand+NatKey +NatRand+Key+Nat</td><td rowspan=1 colspan=1>25.79</td><td rowspan=1 colspan=1>8.20   5.73   0.93   4.80  34.59</td><td rowspan=1 colspan=1>13.34</td></tr><tr><td rowspan=2 colspan=1>32.0332.3730.3931.29</td><td rowspan=1 colspan=1>31.57 31.32  31.58 31.23  15.5932.40 31.91  32.11   4.77  33.00</td><td rowspan=2 colspan=1>28.8927.7620.0230.70</td></tr><tr><td rowspan=1 colspan=1>13.51   8.99   1.53 32.23 33.4630.93 30.54  30.04  29.81  31.60</td></tr><tr><td rowspan=9 colspan=1>Czech</td><td rowspan=9 colspan=2>SwapMidRandKeyNatRand+KeyRand+NatKey+NatRand+Key+Nat</td><td rowspan=1 colspan=1>24.22</td><td rowspan=1 colspan=1>24.90  18.72   2.72   6.00   9.03</td><td rowspan=1 colspan=1>14.27</td></tr><tr><td rowspan=1 colspan=1>23.81</td><td rowspan=1 colspan=1>24.52  24.08   3.96   6.34  9.54</td><td rowspan=1 colspan=1>15.38</td></tr><tr><td rowspan=1 colspan=1>23.44</td><td rowspan=1 colspan=1>23.31  23.24  23.47   3.70   8.10</td><td rowspan=1 colspan=1>17.54</td></tr><tr><td rowspan=1 colspan=1>23.15</td><td rowspan=1 colspan=1>7.06   6.04   1.56 22.80  10.16</td><td rowspan=1 colspan=1>11.80</td></tr><tr><td rowspan=1 colspan=1>18.04</td><td rowspan=1 colspan=1>5.36   4.48   1.47  6.71  21.64</td><td rowspan=1 colspan=1>9.62</td></tr><tr><td rowspan=1 colspan=1>21.46</td><td rowspan=1 colspan=1>20.81  20.90  20.59  19.48   8.72</td><td rowspan=1 colspan=1>18.66</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>20.59</td><td rowspan=1 colspan=1>21.56 20.49  20.53   5.89  18.39</td><td rowspan=1 colspan=1>17.91</td></tr><tr><td rowspan=1 colspan=1>19.55</td><td rowspan=1 colspan=1>6.59   5.72   1.40 21.31  19.54</td><td rowspan=1 colspan=1>12.35</td></tr><tr><td rowspan=1 colspan=1>21.30</td><td rowspan=1 colspan=1>21.33 20.38  19.94 19.25  18.38</td><td rowspan=1 colspan=1>20.10</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "6.2 BLACK-BOX ADVERSARIAL TRAINING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            580,
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+            594
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To increase model robustness we follow a black-box adversarial training scenario, where the model is presented with adversarial examples that are generated without direct access to the model (Papernot et al., 2016a; 2017; Liu et al., 2017; Narodytska & Kasiviswanathan, 2017; Jia & Liang, 2017). We replace the original training set with a noisy training set, where noise is introduced according to the description in Section 4.2. The noisy training set has exactly the same number of sentences and words as the training set. We have one fixed noisy training set per each noise type.5 ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "As shown in Table 6 (second block), training on noisy text can lead to improved performance. The meanChar models trained on Key perform well on Key in French, but not in the other languages. The models trained on Nat perform well in French and German, but not in Czech. Overall, training the meanChar model on noisy text does not appear to consistently increase its robustness to different kinds of noise. The meanChar model however was not expected to perform well on nonscrambling types of noise. Next we test whether the more complicated charCNN model is more robust to different kinds of noise, by training on noisy texts. The results are shown in Table 7. ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In general, charCNN models that are trained on a specific kind of noise perform well on the same kind of noise at test time (results in bold). All models also maintain a fairly good quality on vanilla texts.The robust training is sensitive to the kind of noise. Among the scrambling methods (Swap/Mid/Rand), more noise helps in training: models trained on random noise can still translate Swap/Mid noise, but not vice versa. The three broad classes of noise (scrambling, Key, Nat) ",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/38b5ca4f366595dec304b147eaa23d2f595cb687cb7abe7b6e0838a1b0a860ea.jpg",
+        "image_caption": [
+            "Figure 2: Variances of charCNN weights when trained on only Key, Natural, Random noise and on a mix of all three are shown in red, green, blue, and white, respectively "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            242
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "are not mutually-beneficial. Models trained on one do not perform well on the others. In particular, 1only models trained on natural noise can reasonably translate natural noise at test time. We find this result indicates an important difference between computational models and human performance, since humans can decipher random letter orderings without explicit training of this form. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Next, we test whether we can increase training robustness by exposing the model to multiple types of noise during training. Our motivation is to see if models can perform well on more than one kind of noise. We therefore mix up to three kinds of noise by sampling a noise method uniformly at random for each sentence. We then train a model on the mixed noisy training set and test it on both vanilla and (unmixed) noisy versions of the test set. We find that models trained on mixed noise are slightly worse than models trained on unmixed noise. However, the models trained on mixed noise are robust to the specific types of noise they were trained on. In particular, the model trained on a mix of Rand, $\\operatorname { K e y }$ , and Nat noise is robust to all noise kinds. Even though it is not the best on any one kind of noise, it achieves the best result on average. ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "This model is also able to translate the scrambled meme reasonably well: ",
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+    },
+    {
+        "type": "text",
+        "text": "“According to a study of Cambridge University, it doesn’t matter which technology in a word is going to get the letters in a word that is the only important thing for the first and last letter.” ",
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+    {
+        "type": "text",
+        "text": "7 ANALYSIS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "7.1 LEARNING MULTIPLE KINDS OF NOISE IN C H A RCNN",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The charCNN model was able to perform well on all kinds of noise by training on a mix of noise types. In particular, it performed well on scrambled characters even though its convolutions should be sensitive to the character order, as opposed to meanChar which is by definition invariant to character order. How then can charCNN learn to be robust to multiple kinds of noise at the same time? We speculate that different convolutional filters learn to be robust to different kinds of noise. A convolutional filter can in principle capture a mean (or sum) operation by employing equal or close to equal weights. ",
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+    {
+        "type": "text",
+        "text": "To test this, we analyze the weights learned by charCNN models trained under four conditions: three models trained each on completely scrambled words (Rand), keyboard typos (Key), and natural human errors (Nat), as well as an ensemble model trained on a mix of Rand+Key+Nat kinds of noise. For each model, we compute the variance across the filter width (6 characters) for each one of the 1000 filters and for each one out of 25 character embedding dimensions. Intuitively, this variance captures how much a particular filter learns a uniform vs. non-uniform combination of characters. Then we average the variances across the 1000 filters. This yields 25 averaged variances, one for each character embedding dimension. Low average variance means that different filters tend to learn similar behaviors, while high average variance means that they learn different patterns. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Figure 2 shows a box plot of these averages for our three languages and four training conditions. Clearly, the variances of the weights learned by the Rand model are much smaller than those of the weights learned by any other setting. This makes sense as with random scrambling there are no patterns to detect in the data, so filters resort to close to uniform weights. In contrast, the Key and Nat settings introduce a large set of new patterns for the CNNs to try and learn, leading to high variances. Finally, the ensemble model trained on mixed noise appears to be in the middle as it tries to capture both the uniform relationships of Rand and the more diverse patterns of Nat $^ +$ Key. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Moreover, the variance of variances (size of the box) is smallest in the Rand setting, larger in the mixed noise model, and largest in Key and Nat. This indicates that filters for different character embedding dimensions are more different from one another in Key and Nat models. In contrast, in the Rand model, the variance of variances is close to zero, indicating that in all character embedding dimensions the learned weights are of small variance; they do similar things, that is, the model learned to reproduce a representation similar to the meanChar model. The ensemble model again seems to find a balance between Rand and Key/Nat. ",
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+    },
+    {
+        "type": "text",
+        "text": "7.2 RICHNESS OF NATURAL NOISE ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Natural noise appears to be very different from synthetic noise. None of the models that were trained only on synthetic noise were able to perform well on natural noise. We manually analyzed a small sample ${ \\sim } 4 0$ examples) of natural noise from the German dataset. We found that the most common sources of noise are phonetic or phonological phenomena in the language $( 3 4 \\% )$ and character omissions $( 3 2 \\% )$ . The rest are incorrect morphological conjugations of verbs, key swaps, character insertions, orthographic variants, and other errors. Table 8 shows examples of these kinds of noise. ",
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+    },
+    {
+        "type": "text",
+        "text": "The most common types of natural noise – phonological and omissions – are not directly captured by our synthetic noise generation, and demonstrate that good synthetic errors will likely require more explicit phonemic and linguistic knowledge. This discrepancy helps explain why the models trained on synthetic noise were not particularly successful in translating natural noise. ",
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+        "type": "table",
+        "img_path": "images/f524b76dc6f550c7a73d820c2b556d562214718f2ea30f03443e81556ef7793a.jpg",
+        "table_caption": [
+            "Table 8: Examples of natural noise from the German errors dataset. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Error type</td><td>Examples</td></tr><tr><td>Phonetic</td><td>Tut/Tud (devoicing of final stops),sieht/zieht (s = /z/ before vowel),Trotzdem/Trozdem (tz=/z/),gekriegt/gekrigt (vowel length),Naturlich/Naturlich/Näturlich (diacritics)</td></tr><tr><td>Omission</td><td>erfahren/erfaren,Babysitter/Babysiter, selbst/sebst,Hausschuhe/Hausschue</td></tr><tr><td>Morphological</td><td>wohnt/wonnen,fortsetzt/forzusetzen,wiinsche/winchen</td></tr><tr><td>Key swap</td><td>Eltern/Eltren,Deine/Diene,nichts/nichst, Bahn/Bhan</td></tr><tr><td>Other</td><td>Agglomerationen/Agromelationen (omission + letter swap),Hausaufgabe/Hausausgabe, Thema/Temer,Detailhandelsfachfrau/Deitellhandfachfrau</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "8 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we have shown that character-based NMT models are extremely brittle and tend to break when presented with both natural and synthetic kinds of noise. We investigated methods for increasing their robustness by using a structure-invariant word representation and by ensemble training on adversarial examples of different kinds. We found that a character-based CNN can learn to address multiple types of errors that are seen in training. However, we observed rich characteristics of natural human errors that cannot be easily captured by existing models. Future work might investigate using phonetic and syntactic structure to generate more realistic synthetic noise. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We believe that more work is necessary in order to immune NMT models against natural noise. As corpora with natural noise are limited, another approach to future work is to design better NMT architectures that would be robust to noise without seeing it in the training data. New psychology results on how humans cope with natural noise might point to possible solutions to this problem. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "ACKNOWLEDGEMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This work benefited from discussions with Frank Keller. This work was supported by the Qatar Computing Research Institute (QCRI) and Samsung Research. ",
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parse/train/H1g8p1BYvS/H1g8p1BYvS.md

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+# ADVERSARIAL FILTERS OF DATASET BIASES
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Large-scale benchmark datasets have been among the major driving forces in AI, supporting training of models and measuring their progress. The key assumption is that these benchmarks are realistic approximations of the target tasks in the real world. However, while machine performance on these benchmarks advances rapidly — often surpassing human performance — it still struggles on the target tasks in the wild. This raises an important question: whether the surreal high performance on existing benchmarks are inflated due to spurious biases in them, and if so, how we can effectively revise these benchmarks to better simulate more realistic problem distributions in the real world.
+
+In this paper, we posit that while the real world problems consist of a great deal of long-tail problems, existing benchmarks are overly populated with a great deal of similar (thus non-tail) problems, which in turn, leads to a major overestimation of true AI performance. To address this challenge, we present a novel framework of Adversarial Filters to investigate model-based reduction of dataset biases. We discuss that the optimum bias reduction via AFOPTIMUM is intractable, thus propose AFLITE, an iterative greedy algorithm that adversarially filters out data points to identify a reduced dataset with more realistic problem distributions and considerably less spurious biases.
+
+AFLITE is lightweight and can in principle be applied to any task and dataset. We apply it to popular benchmarks that are practically solved — ImageNet and Natural Language Inference (SNLI, MNLI, QNLI) — and present filtered counterparts as new challenge datasets where the model performance drops considerably (e.g., from $84 \%$ to $24 \%$ for ImageNet and from $92 \%$ to $62 \%$ for SNLI), while human performance remains high. An extensive suite of analysis demonstrates that AFLITE effectively reduces measurable dataset biases in both the synthetic and real datasets. Finally, we introduce new measures of dataset biases based on K-nearest-neighbors to help guide future research on dataset developments and bias reduction.
+
+# 1 INTRODUCTION
+
+Large-scale neural networks have achieved superhuman performance across many popular AI benchmarks, for tasks as diverse as image recognition (ImageNet; Russakovsky et al. (2015)), natural language inference (SNLI; Bowman et al. (2015)), and question answering (SQuAD; Rajpurkar et al. (2016)). Yet these deep models struggle when taken out of these dataset environments and evaluated on adversarial data or problems in the wild (Eykholt et al., 2018; Jia & Liang, 2017). This raises a key question: Does high model performance on today’s benchmark datasets indicate the underlying task is solved, or do those datasets overestimate the true capabilities of current AI systems?
+
+Answering this question is key because benchmarks serve important roles in the community. Not only do they direct progress on core tasks, they also make it easier to tackle the lofty target tasks such as image recognition in the wild through a more practically-scoped dataset such as ImageNet. However, the closed-world assumption of most existing datasets is subject to significant bias (Torralba & Efros, 2011). Much of the data that is easy to obtain and label isn’t necessarily representative of the task we seek to measure. Thus, if left unchecked, artifacts from data collection (Fouhey et al., 2018) or human labeling (Gururangan et al., 2018; Poliak et al., 2018; Tsuchiya, 2018; Geva et al., 2019) can significantly inflate model performance. Though there exist task- and dataset-specific approaches for addressing these biases (Goyal et al., 2017; Geirhos et al., 2018), the complex artifacts that emerge from large-scale dataset creation are challenging to exhaustively identify and remove.
+
+![](images/92d062e2e02496cd00d087cc6083837faa34ec7bcddf685cd2d17227f4c79fd2.jpg)  
+Figure 1: Random ImageNet images for two labels – Monarch Butterfly and Chickadee – that were either selected (left) as adversarial by our AFLITE algorithm, or excluded (right). The heatmap shows pairwise cosine similarity between EfficientNet-B7 features (Tan & Le, 2019). The AFLITE images show significantly greater diversity – such as the cocoon of a butterfly, or the non-canonical chickadee poses – that is in turn reflected by the cosine similarity. This diversity suggests that the AFLITE examples more directly measure progress on the true task of image classification, versus fitting to dataset bias.
+
+In this paper, we present AFLITE – a computationally efficient dataset reduction algorithm, aimed at systematically reducing spurious artifacts in a dataset. AFLITE is general and can be applied to any task and dataset. Our approach leverages a high capacity model to learn dataset specific biases on a small subset, then uses it to identify and filter artifact-prone instances in the remainder of the dataset to yield a final dataset that is possibly closer to the intended task.
+
+We first evaluate the effectiveness of our method on synthetic data and show that AFLITE lowers the performance of models relying on annotation artifacts while preserving the performance of models whose representation captures the underlying tasks. In addition, while AFLITE aims to retain the more challenging, confusing instances, our experiments show that it can successfully remove biased instances that are adversarial to the correct representation of the data.
+
+Finally, we apply the method to several benchmark datasets across various tasks and domains. In language understanding, we apply AFLITE to the SNLI (Bowman et al., 2015) and MNLI (Williams et al., 2018) datasets for natural language inference, and to QNLI (Wang et al., 2018) for question answering. We show a $3 0 \%$ absolute gap in performance in the current state-of-art methods before and after AFLITE. In computer vision, AFLITE reduces the performance of image classification neural methods on ImageNet (Russakovsky et al., 2015), showing a $49 \%$ absolute gap.
+
+# 2 DATASET REDUCTION FOR REPRESENTATION-BIAS MINIMIZATION
+
+In this section, we introduce AFLITE, a general approach for reducing the scope of bias in datasets. Large datasets run the risk of prioritizing performance on the data-rich head of the distribution, where examples are plentiful, and discounting the tail. Our goal is to minimize the ability of a model to exploit biases in the head of the distribution, while preserving the inherent complexity of the tail.
+
+Let $\Phi$ represent a feature representation, defined over a dataset ${ \mathcal { D } } = ( X , Y )$ . With AFLITE, we seek a subset $S \subset \mathcal { D }$ of size $| S | \ge n$ that is maximally resilient to the features uncovered by $\Phi$ . For any identically-distributed train-test split of $\mathcal { D }$ , the features extracted by $\Phi$ should not generalize to the held-out set. Our approach allows for any choice of feature representation.
+
+Formalization More formally, let $\mathcal { M }$ denote a family of classification models (e.g., logistic regression, SVM, or a particular neural architecture) that can be trained on subsets $S$ of $D \doteq ( X , Y )$
+
+using features $\Phi ( X )$ . We define the representation bias of $\Phi$ in $S w x t { \mathcal { M } }$ , denoted ${ \mathcal { R } } ( \Phi , S , { \mathcal { M } } )$ , as the best possible out-of-sample classification accuracy achievable by models in $\mathcal { M }$ when predicting the true labels $Y$ using features $\Phi ( X )$ . For a given target reduced dataset size of at least $n$ , the goal is to find a subset $S \subset D$ , $| S | \ge n$ that minimizes this representation bias in $S$ w.r.t. $\mathcal { M }$ :
+
+$$
+\operatorname* { m i n } _ { S \subset D , | S | \geq n } { \mathcal { R } } ( \Phi , S , { \mathcal { M } } )
+$$
+
+Eq. (1) corresponds to the optimum bias reduction, referred to as AFOPTIMUM. ${ \mathcal { R } } ( \Phi , S , { \mathcal { M } } )$ can be formulated as the expected classification accuracy resulting from the following process. Let $q : 2 ^ { S }  [ 0 , 1 ]$ be a probability distribution over subsets $T = \mathsf { \bar { ( } } X ^ { T } , Y ^ { T } )$ of $D$ . The process is to randomly choose a subset $T$ with probability $q ( T )$ , train a bias estimator $M _ { T } \in \mathcal { M }$ on $D \backslash T$ , and evaluate its classification accuracy $f _ { M _ { T } } ( \Phi ( X ^ { T } ) , Y ^ { T } )$ on $T$ . Note that the resulting classification accuracy on $T$ itself is a random variable, since the training set $D \setminus T$ is random. We define the expected value of this classification accuracy to be the representation bias:
+
+$$
+\mathcal { R } ( \Phi , S , \mathcal { M } ) \stackrel { \Delta } { = } \mathbb { E } _ { T \sim q } \left[ f _ { M _ { T } } ( \Phi ( X ^ { T } ) , Y ^ { T } ) \right]
+$$
+
+While this expression formalizes the intended objective function, it involves a large summation over subsets $T \subset S$ just to compute the representation bias present in a single set $S$ . It does not suggest a practical way to compute the minimization in Eq. (1) without further considering each of the exponentially many subsets $S \subset D$ individually – thus an optimal solution for Equation (2) is intractable. To get around this difficulty, we reformulate the representation bias in $S$ as a sum factored over the $| S |$ individual instances $i \in S$ . This will allow us to efficiently decide whether or not to include $i$ in the targeted, reduced subset we are constructing.
+
+The idea is to aggregate the contribution of each $i$ towards the representation bias expression across all random choices of the training set $D \backslash T$ . We call this the predictability score $p ( i )$ for $i$ : on average, how reliably can the label $y _ { i }$ be predicted using features $\Phi ( x _ { i } )$ when a model from $\mathcal { M }$ is trained on a randomly chosen training set $D \backslash T$ not containing $i$ . The higher the value of $p ( i )$ , the easier it is to correctly classify the instance $( x _ { i } , y _ { i } )$ using model family $\mathcal { M }$ . This is the signal we will use to decide whether to include $i$ in the reduced subset $S$ we are constructing.
+
+With some abuse of notation, for $i \in D$ , let $\begin{array} { r } { q ( i ) \triangleq \sum _ { T \ni i } q ( T ) } \end{array}$ denote the marginal probability of choosing a subset T that contains i. The ratio q(T )q(i) is then the probability of $T$ conditioned on it containing $i$ . Let $f _ { M _ { T } } ( \Phi ( x _ { i } ) , y _ { i } )$ be the classification accuracy of $M _ { T }$ on $i$ . The reformulation of representation bias in terms of predictability scores of individual instances works as follows:
+
+$$
+\begin{array} { r l } { \mathbb { E } _ { \mathcal { F } \sim \infty _ { + } } \left[ f _ { M \tau } \left( \Phi ( X ^ { \tau } ) , Y ^ { \tau } \right) \right] = \displaystyle \sum _ { t \in S } q ( T ) \cdot \frac { 1 } { | T | } \sum _ { i \in T } ^ { T } f _ { M \tau } \left( \Phi ( x _ { i } ) , y _ { i } \right) } & { } \\ & { = \displaystyle \sum _ { \tau \in S } \sum _ { i \in T } q ( T ) \cdot \frac { f _ { M \tau } \left( \Phi ( x _ { i } ) , y _ { i } \right) } { | T | } } \\ & { = \displaystyle \sum _ { \tau \in S } \sum _ { \tau \in S } q ( T ) \cdot \frac { f _ { M \tau } \left( \Phi ( x _ { i } ) , y _ { i } \right) } { | T | } } \\ & { = \displaystyle \sum _ { \tau \in S } \frac { \displaystyle \sum _ { \tau \in S } y } { \displaystyle \sum _ { \tau \in S } y } \cdot \frac { \displaystyle \frac { \bar { q } ( T ) } { \displaystyle \lambda } \sum _ { i \in T } \left( \frac { \bar { q } ( x _ { i } ) } { | T | } \right) \cdot y _ { i } } { | T | } } \\ & { = \displaystyle \sum _ { \tau \in S } q ( t ) \cdot \frac { \displaystyle \sum _ { \tau \in S } \bar { q } ( T ) } { \displaystyle \sum _ { \tau \in S } y } \frac { \displaystyle \bar { q } ( T ) } { \displaystyle \left( \bar { q } ( x _ { i } ) \right) } \frac { f _ { M \tau } \left( \Phi ( x _ { i } ) , y _ { i } \right) } { | T | } } \\ & { = \displaystyle \sum _ { \tau \in S } q ( \bar { q } ) \mathbb { E } _ { \tau \cap S , \tau \in S } \left\{ \frac { f _ { M \tau } \left( \bar { q } ( x _ { i } ) , y _ { i } \right) } { | T | } \right\} } \\ & { = \displaystyle \sum _ { \tau \in S } p ( i ) } \end{array}
+$$
+
+where $p ( i )$ is the predictability score of $i$ defined as:
+
+$$
+p ( i ) \triangleq q ( i ) \mathbb { E } _ { T \subset S , T \ni i } \left[ \frac { f _ { M _ { T } } ( \Phi ( x _ { i } ) , y _ { i } ) } { \vert T \vert } \right]
+$$
+
+While the method works for any probability distribution $q$ with non-zero support on all samples, for simplicity of exposition, we restrict $q$ to be the uniform distribution over all subsets $T \subset S$ of a fixed size. This makes both $| T |$ and $q ( i )$ fixed constants; in particular, $\begin{array} { r } { q ( i ) = \binom { | S | - 1 } { | T | - 1 } / \binom { | S | } { | T | } = \frac { | T | } { | S | } } \end{array}$ |T ||S| . This reduces the predictability score expression of Eq. (3) to the simplified variant $\tilde { p } ( i )$ :
+
+$$
+\tilde { p } ( i ) \triangleq \frac { 1 } { | S | } \mathbb { E } _ { T \subset S , T \ni i } \left[ f _ { M _ { T } } ( \Phi ( x _ { i } ) , y _ { i } ) \right]
+$$
+
+Putting the pieces together, we have a factored reformulation of the representation bias in Eq. (2):
+
+$$
+\mathcal { R } ( \Phi , S , \mathcal { M } ) = \sum _ { i \in S } \tilde { p } ( i )
+$$
+
+Armed with this factored representation, we return to the task of identifying an $S \subset D$ , $| S | \ge n$ that minimizes the representation bias. We use the simplified predictability scores (henceforth simply referred to as predictability scores) as a heuristic metric to decide which $i \in D$ to include in $S$ . We consider three approaches that iteratively filter out the most predictable instances from $D$ to arrive at $S$ . In all cases, we use a fixed training set size $| S \setminus T | = t < n$ . Further, since a larger filtered set is generally desirable, we terminate the filtering process early (i.e., while $\vert S \vert > n )$ if the predictability score for every $i$ falls below a pre-specified early stopping threshold $\tau \in [ 0 , 1 ]$ .
+
+The three approaches are as follows. (A) A simple greedy approach starts with the full set $S = D$ , identifies an $i \in S$ with the highest predictability score, removes it from $S$ , and repeats up to $| D | - n$ times. (B) A greedy slicing approach identifies the instances with the $k$ highest predictability scores, removes all of them from $S$ , and repeats the process up to $\lfloor { \frac { \lfloor D \rfloor - n } { k } } \rfloor$ times. (C) A slice sampling approach where, instead of greedily choosing the top $k$ instances, it randomly samples $k$ instances with probabilities proportional to their predictability scores.1 In this paper, we use the greedy slicing approach in our experiments and refer to it as AFLITE. While the optimum bias reduction via AFOPTIMUM is intractable, its light-weight version, AFLITE, is applicable in practice.
+
+The slice sampling approach can be efficiently implemented using what is known as the Gumbel method or Gumbel trick (Gumbel & Lieblein, 1954; Maddison et al., 2014), which uses random perturbations to turn sampling into a simpler problem of optimization. This has recently found success in several probabilistic inference applications (Kim et al., 2016; Jang et al., 2016; Maddison et al., 2016; Balog et al., 2017; Kool et al., 2019). Starting with the log-predictability scores $\log \tilde { p } ( i )$ for various $i$ , the idea is to perturb them by adding an independent random noise $\gamma _ { i }$ drawn from the standard Gumbel distribution. Interestingly, the maximizer $i ^ { * }$ of $\gamma _ { i } + \log \tilde { p } ( i )$ turns out to be an exact sample drawn from the (unnormalized) distribution defined by $\tilde { p }$ . Note that $i ^ { * }$ is a random variable since the $\gamma _ { i }$ are drawn at random. This result can be generalized (Vieira, 2014) for slice sampling: the $k$ highest values of Gumbel-perturbed log-predictability scores correspond to sampling, without replacement, $k$ items from the probability distribution defined by $\tilde { p }$ . The Gumbel method is typically applied to exponentially large combinatorial spaces, where it is challenging to scale up. In our setting, however, the overhead is minimal since the cost of drawing a random $\gamma _ { i }$ is negligible compared to computing $\tilde { p } ( i )$ .
+
+Implementation Algorithm 1 provides an implementation of AFLITE. The algorithm takes as input a dataset $D = \bar { ( } X , Y )$ , a representation $\Phi ( X )$ we are interested in minimizing the bias in, a model family $\mathcal { M }$ (e.g., linear classifiers), a target dataset size $n$ , size $m$ of the support of the expectation in Eq. (4), training set size $t$ for the classifiers, size $k$ of each slice, and an early-stopping filtering threshold $\tau$ . Importantly, for efficiency, $\Phi ( X )$ is provided to AFLITE in the form of precomputed embeddings for all of $X$ . To obtain $\Phi ( X )$ in practice, we train a first model on a small fraction of the data based on the learning curve in low-data regime, and do not reuse this data for the rest of our experiments. Moreover, this fraction corresponds to the training size $t$ for AFLITE and it remains unchanged across iterations. We follow the iterative filtering approach, starting with $S \ : = \ : D$ and iteratively removing some instances with the highest predictability scores using the
+
+# Algorithm 1: AFLITE
+
+Input: dataset $D = ( X , Y )$ , pre-computed representation $\Phi ( X )$ , model family $\mathcal { M }$ , target dataset size $n$ ,   
+number of random partitions $m$ , training set size $t < n$ , slice size $k \leq n$ , early-stopping threshold $\tau$   
+Output: reduced dataset $S$   
+1 $S = D$   
+2 while $\vert S \vert > n$ do   
+// Filtering phase   
+3 forall $i \in S$ do   
+4 Initialize a multi-set of out-of-sample predictions $E ( i ) = \emptyset$   
+5 for iteration $j : 1 . . m$ do   
+6 Randomly partition $S$ into $( T _ { j } , S \setminus T _ { j } )$ s.t. $| S \setminus T _ { j } | = t$   
+7 Train a classifier ${ \mathcal { L } } \in { \mathcal { M } }$ on $\{ ( \Phi ( x ) , y ) ~ | ~ ( x , y ) \in S \setminus T _ { j } \}$ $\mathcal { L }$ is typically a linear classifier)   
+8 forall $i = ( x , y ) \in T _ { j }$ do   
+9 Add the prediction ${ \mathcal { L } } ( \Phi ( x ) )$ to $E ( i )$   
+10 forall $i = ( x , y ) \in S$ do   
+11 Compute the predictability score $\tilde { p } ( i ) = | \{ \hat { y } \in E ( i ) \ s . t . \ \hat { y } = y \} | / \left| E ( i ) \right|$   
+12 Select up to $k$ instances $S ^ { \prime }$ in $S$ with the highest predictability scores subject to $\tilde { p } ( i ) \geq \tau$   
+13 $S = S \setminus S ^ { \prime }$   
+14 if $| S ^ { \prime } | < k$ then   
+15 break   
+16 return $S$
+
+greedy slicing strategy. Slice size $k$ and number of partitions $m$ are determined by the available computation budget.
+
+At each filtering phase, we train models (linear classifiers in our implementation) on $m$ different random partitions of the data, and collect their predictions on their corresponding test set. For each instance $i$ , we compute its predictability score as the ratio of the number of times its label $y _ { i }$ is predicted correctly, over the total number of predictions for it. We rank the instances according to their predictability score and use the greedy slicing strategy of removing the top- $k$ instances whose score is not less than the early-stopping threshold $\tau$ . We repeat this process until fewer than $k$ instances pass the $\tau$ threshold in a filtering phase or fewer than $n$ instances remain.
+
+# 3 EXPERIMENTAL ANALYSIS
+
+We evaluate AFLITE across various domains (synthetic, natural language processing, computer vision), different tasks in a given domain (language inference and question answering in NLP), different datasets for a given task (SNLI and MNLI in natural language inference), and different representations for a given dataset (pre-computed embeddings from ESIM+GLoVe, BERT, RoBERTa for the SNLI dataset).
+
+# 3.1 SYNTHETIC EXPERIMENTS
+
+We demonstrate the utility of AFLITE in a synthetic data setting. Our dataset consists of twodimensional data, arranged in concentric circles, at four different levels of separation, as shown in the Figure 2. As is evident, a linear function might not be adequate for separating the two classes; it requires a more complex non-linear model such as an SVM with an RBF kernel. 2
+
+We add class-specific artificially constructed features (artifacts) sampled from two different Gaussian distributions. These features are only added to $7 5 \%$ of the data in each class, while for the rest of the data, we insert random (noise) features. These artifacts make the task solvable through a linear function. Furthermore, for the first dataset, with the largest separation, we flipped the labels of some examples with artifacts, making the data slightly adversarial even to the RBF. Both models can clearly leverage the artifacts, and demonstrate improved performance over a baseline without artifacts.
+
+Table 1: Dev accuracy $( \% )$ on the original SNLI dataset $D$ and the datasets obtained through various representation-bias minimization. The -HypOnly baselines correspond to models trained on the instances restricted to their hypotheses.   
+
+<table><tr><td>Model</td><td>D</td><td>D92k</td><td>D(ΦESIM+GLoVe)</td><td>D(ΦBERT)</td><td>D(ΦRoBERTa)</td></tr><tr><td>ESIM+ELMo (Peters et al.,2018)</td><td>88.7</td><td>86.0</td><td>61.5</td><td>54.2</td><td>51.9</td></tr><tr><td>BERT (Devlin et al., 2019)</td><td>91.3</td><td>87.6</td><td>74.7</td><td>61.8</td><td>57.0</td></tr><tr><td>RoBERTa (Liu et al.,2019b)</td><td>92.6</td><td>88.3</td><td>78.9</td><td>71.4</td><td>62.6</td></tr><tr><td>Max-PPMI baseline</td><td>54.5</td><td>52.0</td><td>41.1</td><td>41.5</td><td>41.9</td></tr><tr><td>BERT-HypOnly</td><td>71.5</td><td>70.1</td><td>52.3</td><td>46.4</td><td>48.4</td></tr><tr><td>RoBERTa-HypOnly</td><td>72.0</td><td>70.4</td><td>53.6</td><td>49.5</td><td>48.5</td></tr><tr><td>Human performance</td><td>88.1</td><td>88.1</td><td>82.3</td><td>80.3</td><td>77.8</td></tr><tr><td>Training set size</td><td>550k</td><td>92k</td><td>138k</td><td>109k</td><td>92k</td></tr></table>
+
+Once we apply AFLITE, as expected, the number of examples with artifacts is reduced considerably, making the task hard once again for the linear model, but still solvable for the non-linear one. The filtered dataset is shown in the bottom half of Fig. 2, and the captions indicate the performance of a linear and an SVM model. For the first dataset, we see that AFLITE removes most of those examples with flipped labels.
+
+![](images/115f14c9115d54ffd350759e4fc7e5da77c8f8f5fbabc34a97b98e2ba25d04eb.jpg)  
+Figure 2: Four sample datasets with artifacts as input to AFLITE (top). Blue and orange indicate two different classes. Only the original two dimensions are shown, not the artifacts. For the leftmost dataset with the highest separation, we flip some labels at random, so even an RBF kernel cannot achieve perfect performance. AFLITE makes the data more challenging for the models (bottom).
+
+# 3.2 NLP EXPERIMENTS
+
+We evaluate AFLITE on two NLP tasks, namely NLI and question answer sentence selection. We use two popular NLI large-scale datasets – SNLI (Bowman et al., 2015) and MNLI (Wang et al., 2018). For the answer sentence selection task, we use QNLI which is a transformed version of the SQuAD question answering dataset (Rajpurkar et al., 2016) converted to binary classification where systems determine whether a sentence contains the answer to a question.
+
+SNLI Each instance in the SNLI dataset consists of a premise-hypothesis pair that belongs to one out of three possible categories (entailment, contradiction, or neutral) based on the relationship between the premise and the hypothesis.
+
+For SNLI, we experiment with three different feature representations derived from strong baseline models: $\Phi _ { B E R T }$ and $\Phi _ { R o B E R T a }$ which are based on BERT (Devlin et al., 2019) and RoBERTa (Liu et al., 2019b), large-scale pretrained masked language models, plus $\Phi _ { E S I M + G L o V e }$ which uses the
+
+Table 2: Dev accuracy $( \% )$ on the original MNLI-matched and QNLI datasets and the datasets obtained through $\Phi _ { R o B E R T a }$ -representation-bias minimization. The -PartialInput baselines correspond to models trained on partial, incomplete input, namely the Hypotheses for MNLI instances and the Answers for QNLI instances.   
+
+<table><tr><td></td><td colspan="2">MNLI</td><td colspan="2">QNLI</td></tr><tr><td>Model</td><td>D</td><td>D(RoBERTa)</td><td>D</td><td>D( RoBERTa)</td></tr><tr><td>BERT (Devlin et al., 2019)</td><td>86.6</td><td>55.8</td><td>92.0</td><td>63.5</td></tr><tr><td>RoBERTa (Liu et al.,2019b)</td><td>90.3</td><td>66.2</td><td>93.7</td><td>77.7</td></tr><tr><td>BERT-PartialInput</td><td>59.7</td><td>43.2</td><td>62.6</td><td>56.6</td></tr><tr><td>RoBERTa-PartialInput</td><td>60.3</td><td>44.4</td><td>63.9</td><td>59.4</td></tr></table>
+
+ESIM model (Chen et al., 2016) with GLoVe word embeddings (Pennington et al., 2014). In all cases, feature representation $\Phi$ is trained on a random sample of $1 0 \%$ of the original training instances, and feature representations are extracted from the final layer before the output layer. These features are pre-computed for all remaining instances while we discard the instances $1 0 \%$ of training) used for training the embeddings in the subsequent steps of our algorithm. Additionally, to measure the ability of a weaker adversary to filter biases only learned by a stronger model, we evaluate the filtered datasets (for SNLI) with three different models: (i) ESIM with ELMo embeddings (Peters et al., 2018), (ii) BERT-large, and (iii) RoBERTa-large models.
+
+Table 1 shows the results for SNLI. In all cases, applying AFLITE substantially reduces overall model accuracy, with typical drops of $1 5 . 3 5 \%$ depending on the models used for learning the feature representations and those used for evaluation of the filtered dataset. In general, performance is lowest when using the strongest model (RoBERTa) for learning feature representations. Results also highlight the ability of weaker adversaries to produce datasets that are still challenging for much stronger models with a drop of $1 3 . 7 \%$ for RoBERTa using $\Phi _ { E S I M + G L o V e }$ as feature representation. We also include a model that uses Point-wise Mutual Information (PMI) between words in a given instance and the target label as a feature. The baseline captures the extent to which datasets exhibit word-association artifacts. While this baseline is relatively weaker than other models, we still show that its performance reduce from $5 4 . 5 \%$ on $D$ to $4 1 . 9 \%$ on the $D ( \phi _ { R o B E R T a } )$ dataset.
+
+It might seem unsurprising that reducing the size of the training set results in lower performance. To control for the confounding factor of the dataset size, we create another filtered dataset $D _ { 9 2 k }$ , sampled randomly from $D$ such that its size is approximately equal to the size of $D ( \phi _ { R o B E R T a } )$ dataset. All models achieve nearly the same performance as their performance on the full dataset – even when trained on just one-fifth the original dataset size. This result further points to the fact that current benchmark datasets contain significant redundancy within its instances.
+
+Finally, to demonstrate the value of the iterative, ensemble-based AFLITE algorithm, we compare with a baseline where using a single model, we filter out the most predictable examples in a single iteration — a non-iterative, single-model version of AFLITE. A RoBERTa-large model trained on this subset (of the same size as $D ( \phi _ { R o B E R T a } ) )$ achieves a dev accuracy of $7 2 . 1 \%$ . Compared to the performance of RoBERTa on $D ( \phi _ { R o B E R T a } )$ $( 6 2 . 6 \%$ , see Table 1), it makes this baseline a sensible yet less effective approach. In particular, this illustrates the need for an iterative procedure involving models trained on multiple partitions of the remaining data in each iteration.
+
+We also report the $\mathbf { k }$ -nearest neighbors distances between examples in the train and heldout data in Table 3. We consider distances for examples within each class, as well as examples across classes. The distances are computed using cosine similarity between pooled features from BERT-based model (features for the [CLS] token, indicating a sentence-pair feature) trained on the original SNLI dataset. Distances are measured between samples from the heldout data, and their nearest neighbors in the training data, before and after filtering. Distances generally increase after filtering, indicating that AFLITE promotes selecting a diverse set of examples from the dataset. The only exception to the rule is the neutral class, where distances to other classes decrease – this is not surprising since the neutral class is known to be associated with the least number of artifacts (Gururangan et al., 2018).
+
+Table 3: KNN-distances by class, before and after applying (RoBERTa-filtered) AFLITE to SNLI.   
+
+<table><tr><td rowspan="2"></td><td colspan="4">Before AFLITE</td><td colspan="4">After AFLITE</td></tr><tr><td>Top1</td><td>Top5</td><td>Top10</td><td>Top50</td><td>Top1</td><td>Top5</td><td>Top10</td><td>Top50</td></tr><tr><td>Entailment</td><td>0.29</td><td>1.32</td><td>2.45</td><td>9.5</td><td>0.32</td><td>1.42</td><td>2.64</td><td>9.98</td></tr><tr><td>Neutral</td><td>0.40</td><td>1.89</td><td>3.68</td><td>16.83</td><td>0.42</td><td>1.97</td><td>3.80</td><td>16.66</td></tr><tr><td>Contradiction</td><td>0.49</td><td>2.41</td><td>4.77</td><td>23.09</td><td>0.52</td><td>2.49</td><td>4.84</td><td>22.10</td></tr><tr><td>Entailment vs others</td><td>0.32</td><td>1.48</td><td>2.87</td><td>12.98</td><td>0.34</td><td>1.53</td><td>2.92</td><td>12.31</td></tr><tr><td>Neutral vs others</td><td>0.43</td><td>2.05</td><td>3.99</td><td>18.42</td><td>0.41</td><td>1.94</td><td>3.72</td><td>16.41</td></tr><tr><td>Contradiction vs others</td><td>0.49</td><td>2.38</td><td>4.70</td><td>22.61</td><td>0.53</td><td>2.51</td><td>4.87</td><td>22.38</td></tr></table>
+
+<table><tr><td></td><td colspan="4">HANS</td><td colspan="3">NLI-Diagnostics</td><td colspan="3">Adversarial-NLI</td></tr><tr><td>Model</td><td>Al</td><td>Lex.</td><td>Subseq.</td><td>Constit.</td><td>All</td><td>Logic</td><td>Knowl.</td><td>Rd1</td><td>Rd2</td><td>Rd3</td></tr><tr><td>RoBERTa</td><td>70.7</td><td>84.4</td><td>35.4</td><td>13.4</td><td>59.3</td><td>52.8</td><td>48.9</td><td>58.5</td><td>48.3</td><td>50.1</td></tr><tr><td>RoBERTa-AFlite</td><td>74.5</td><td>96.3</td><td>56.6</td><td>57.4</td><td>62.0</td><td>53.2</td><td>57.7</td><td>65.1</td><td>49.1</td><td>52.8</td></tr></table>
+
+Table 4: SNLI accuracy $( \% )$ on three out-of-distribution evaluation tasks, comparing RoBERTalarge models pre-trained on the original SNLI data, and on AFLITE-filtered data. On the HANS dataset, both models are evaluated on $A l l$ , as well as on the non-entailment cases of the three syntactic heuristics (Lexical overlap, Subsequence, and Constituent). The NLI-Diagnostics dataset is broken down into the full dataset $( A l l )$ , as well as the instances requiring logical reasoning (Logic) and the ones requiring world and commonsense knowledge (Knowledge). For Adversarial NLI, we finetuned both models on the in-distribution training data for each round (Rd1, Rd2, and Rd3).
+
+MNLI and QNLI Following the same procedure described above, we apply AFLITE on the MNLI and QNLI datasets. Since RoBERTa resulted in the largest drops in performance across the board in SNLI, we only experiment with RoBERTa as adversary for MNLI and QNLI. While RoBERTa achieves over $9 0 \%$ on both original datasets, its performance drops to $6 6 . 2 \%$ for MNLI and to $7 7 . 7 \%$ for QNLI on the reduced datasets. Similarly, partial input baseline performance also decreases substantially on both dataset compared to their performance on the original dataset. Table 2 shows these results. We show that AFLITE consistently result in reduced accuracy on the filtered datasets across multiple NLP benchmark datasets, even after controlling for the size of the training set.
+
+# 3.2.1 OUT-OF-DISTRIBUTION NLI
+
+We measure the performance of AFLITE on three other benchmarks for NLI evaluation, which provide out-of-distribution examples to challenge reliance on dataset biases in the original SNLI data (Glockner et al., 2018; Naik et al., 2018). Such benchmarks approximate the performance of NLI models in the wild. NLI Diagnostics (Wang et al., 2018) is a set of hand-crafted examples designed to demonstrate model performance on several fine-grained semantic categories, such as logical reasoning and commonsense knowledge. HANS (McCoy et al., 2019) contains evaluation examples designed to avoid common structural heuristics (such as word overlap) which could be used by models to correctly predict NLI inputs, without true inferential reasoning. Adversarial NLI (Nie et al., 2019) consists of premises collected from Wikipedia and other news corpora, and human generated hypotheses, arranged at different tiers of the challenge they present to a model, using a human and model in-the-loop procedure. Given that these benchmarks are collected independently of the original SNLI task, the biases from SNLI are less likely to carry over; however these benchmarks might contain their own biases (Liu et al., 2019a).
+
+AFLITE assigns a predictability score to all samples in a dataset, resulting in an ordering of the data. Filtering out examples from the head of the data distribution based on this order yields more accurate benchmarks for measuring true model performance. On the other hand, transferability to out-of-distribution data would involve a greater balance between examples from the head and the tail ends of the data distribution. Hence we evaluate AFLITE for generalization using a larger filtered subset, amounting to only a third of the full training data. We present these results on all the above benchmarks in Table 4. On the two diagnostic datasets (HANS and NLI-Diagnostics), we perform a zero-shot evaluation of the two models. Adversarial NLI allows to test for transfer capabilities, by finetuning these models on each of the three training datasets (Rd1, Rd2 and Rd3). On each of the benchmarks above, the model trained on the AFLITE data consistently outperforms the model trained on the full SNLI data. challenging examples in the HANS benchmark, which targets models purely relying on lexical and syntactic cues. Similarly, our model performs better on the instances in NLI-Diagnostics that require logical reasoning and commonsense knowledge, as opposed to instances that can be solved through lexical entailment alone.
+
+Table 5: Experimental results on ImageNet. We compare between three settings: the original dataset’s train-test splits, using $20 \%$ of the training set but evaluating on the validation set, and using the AFLITE produced training and validation sets. AFLITE produces a training dataset that is also $20 \%$ of the training set size, making it a fair comparison in terms of dataset examples. The results show a significant drop in Top-1 and Top-5 accuracy: the Top-1 accuracy goes down by roughly 40 percentage points per model in this new training and evaluation setting.   
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">100% Train, Original Val</td><td colspan="2">20% Train, , Original Val</td><td colspan="2">AFLITE</td></tr><tr><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td></tr><tr><td>EfficientNet-B0</td><td>76.3</td><td>93.2</td><td>58.5</td><td>81.2</td><td>18.1</td><td>48.1</td></tr><tr><td>EfficientNet-B2</td><td>79.8</td><td>94.9</td><td>60.9</td><td>82.8</td><td>20.7</td><td>53.1</td></tr><tr><td>EfficientNet-B4</td><td>82.6</td><td>96.3</td><td>64.4</td><td>85.8</td><td>23.3</td><td>58.8</td></tr><tr><td>EfficientNet-B7</td><td>84.4</td><td>97.1</td><td>73.8</td><td>90.8</td><td>24.5</td><td>60.6</td></tr><tr><td>ResNet-34</td><td>78.4</td><td>94.4</td><td>51.8</td><td>74.3</td><td>11.1</td><td>30.2</td></tr><tr><td>ResNet-50</td><td>79.2</td><td>94.7</td><td>53.2</td><td>75.5</td><td>12.2</td><td>30.2</td></tr><tr><td>ResNet-101</td><td>80.1</td><td>95.4</td><td>55.6</td><td>77.5</td><td>12.3</td><td>32.1</td></tr><tr><td>ResNet-152</td><td>80.6</td><td>95.5</td><td>56.5</td><td>78.2</td><td>13.2</td><td>33.8</td></tr></table>
+
+# 3.3 IMAGENET EXPERIMENTS
+
+We evaluate AFLITE on image classification through ImageNet (ILSVRC2012) classification. On ImageNet, we use the state-of-the-art EfficientNet-B7 model as our core feature extractor $\Phi$ (Tan & Le, 2019). The EfficientNet model is learned from scratch on a fixed $20 \%$ sample of the ImageNet training set, using AutoAugment data augmentation (Cubuk et al., 2019). We then use the 2560- dimensional features extracted by EfficientNet-B7 as then underlying representation for AFLITE to use to filter the remaining dataset.
+
+In Table 5, we evaluate the robustness of the filtered dataset by considering ImageNet accuracy across the EfficientNet and ResNet model families (He et al., 2016). When lowering the size of the training set – down to $20 \%$ of the original, we find a large drop in performance. The EfficientNet models seem to suffer less – from $8 4 \%$ to $7 3 \%$ on EfficientNet-B7 versus $8 0 . 6 \%$ to $5 6 . 5 \%$ on ResNet-152. However, the biggest performance drop comes from training and evaluating on the AFLITE-filtered dataset: the top performer is still EfficientNet-B7, but its accuracy drops to $2 4 . 5 \%$ top-1. This is despite controlling for dataset size, as well as discrepancy between the training and validation sets.
+
+Overall, these results suggest that image classification – even within a subset of the closed world of ImageNet – is far from solved. These results echo other findings that suggest that common biases that naturally occur in web-scale image data, such as towards canonical poses (Alcorn et al., 2019) or towards texture rather than shape (Geirhos et al., 2018), are problems for ImageNet-trained classifiers. Indeed, the randomly-selected ImageNet images in Figure 1 suggest that the AFLITE algorithm learns to identify subsets of the data that are particularly challenging.
+
+# 4 RELATED WORK
+
+Our proposed framework for artifact reduction is related to the adversarial filtering (AF) algorithm in Zellers et al. (2018), yet distinct in two key ways: our approach is (i) much more broadly applicable (by not requiring over generation of data instances), and (ii) considerably more lightweight (by not requiring re-training a model at each iteration of AF). Variants of this AF approach have recently been used to create other datasets such as HellaSwag (Zellers et al., 2019) and ANLI (Bhagavatula et al., 2019) by iteratively perturbing dataset instances until a target model cannot fit the resulting dataset. While effective, these approaches run into three main pitfalls. First, dataset curators need to explicitly devise a strategy of collecting or generating perturbations of a given instance. Second, the approach runs the risk of distributional bias where a discriminator can learn to distinguish between machine generated instances and human-generated ones. Finally it requires re-training a model at each iteration, which is computationally expensive especially when using a large model such as BERT (Devlin et al., 2019) as the adversary. In contrast, AFLITE focuses on addressing dataset biases from existing datasets instead of adversarially perturbing instances. AFLITE was earlier proposed by Sakaguchi et al. (2019) to create the Winogrande dataset. This paper presents more thorough experiments, theoretical justification and results from generalizing the proposed approach to multiple popular NLP and Vision datasets.
+
+AFLITE is also inspired by Gururangan et al. (2018), who study lexical biased prevalent in the SNLI dataset (Bowman et al., 2015) and use point-wise mutual information (PMI) between a word and an inference class to determine the words that are highly indicative of the target label. Instead of lexical features, we adopt a deeper representation of the instances using their pre-computed dense feature representations. We use an ensemble of linear classifiers trained on random subsets of the data to determine whether the dense feature representations are highly indicative of the target label. If so, we discard the corresponding instances and proceed iteratively.
+
+Li & Vasconcelos (2019) recently proposed REPAIR, a method to remove representation bias by dataset resampling. While resampling is a common technique for balancing datasets, the motivation in REPAIR is to learn a probability distribution over the dataset that favors instances that are hard for a given representation. This approach targets how to train better, less-biased models as opposed to creating datasets with fewer artifacts. In addition, the implementation of REPAIR relies on intraining classification loss as opposed to out-of-sample generalization accuracy. RESOUND (Li et al., 2018) is another method that quantifies the representation biases of datasets. It uses the representation biases to assemble a new K-class dataset with smaller biases by sampling an existing C-class dataset $( C > K )$ ).
+
+Arjovsky et al. (2019) argue that unstable, spurious correlations in the data would generalize poorly to novel test environments. Thus, they propose Invariant Risk Minimization as an objective that promotes learning representations of the data which are stable across environments. Instead of learning optimal classifiers, our aim is to remove instances that exhibit artifacts in a dataset.
+
+# 5 CONCLUSION
+
+We presented AFLITE – a novel iterative greedy algorithm that adversarially filters out data points to arrive at a reduced dataset with more realistic problem distributions and considerably fewer spurious biases. We apply AFLITE to four widely-used datasets, including SNLI and ImageNet, where reported performance is extremely high – and show that state-of-the-art performance on the resulting filtered dataset drops by 30 points for SNLI and drops from $8 4 . 4 \%$ to $2 4 . 5 \%$ Top-1 accuracy for ImageNet. In extensive analysis we show that AFLITE is effective on real as well as synthetic datasets. We hope that dataset creators will employ AFLITE to identify unobservable artifacts before releasing new challenge datasets for the research community in order to have a more reliable estimate of model performance on future AI benchmarks.
+
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parse/train/H1g8p1BYvS/H1g8p1BYvS_content_list.json

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+    {
+        "type": "text",
+        "text": "ADVERSARIAL FILTERS OF DATASET BIASES ",
+        "text_level": 1,
+        "bbox": [
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+            98,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Anonymous authors Paper under double-blind review ",
+        "bbox": [
+            183,
+            145,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
+        "bbox": [
+            454,
+            210,
+            544,
+            224
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Large-scale benchmark datasets have been among the major driving forces in AI, supporting training of models and measuring their progress. The key assumption is that these benchmarks are realistic approximations of the target tasks in the real world. However, while machine performance on these benchmarks advances rapidly — often surpassing human performance — it still struggles on the target tasks in the wild. This raises an important question: whether the surreal high performance on existing benchmarks are inflated due to spurious biases in them, and if so, how we can effectively revise these benchmarks to better simulate more realistic problem distributions in the real world. ",
+        "bbox": [
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+            243,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we posit that while the real world problems consist of a great deal of long-tail problems, existing benchmarks are overly populated with a great deal of similar (thus non-tail) problems, which in turn, leads to a major overestimation of true AI performance. To address this challenge, we present a novel framework of Adversarial Filters to investigate model-based reduction of dataset biases. We discuss that the optimum bias reduction via AFOPTIMUM is intractable, thus propose AFLITE, an iterative greedy algorithm that adversarially filters out data points to identify a reduced dataset with more realistic problem distributions and considerably less spurious biases. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "AFLITE is lightweight and can in principle be applied to any task and dataset. We apply it to popular benchmarks that are practically solved — ImageNet and Natural Language Inference (SNLI, MNLI, QNLI) — and present filtered counterparts as new challenge datasets where the model performance drops considerably (e.g., from $84 \\%$ to $24 \\%$ for ImageNet and from $92 \\%$ to $62 \\%$ for SNLI), while human performance remains high. An extensive suite of analysis demonstrates that AFLITE effectively reduces measurable dataset biases in both the synthetic and real datasets. Finally, we introduce new measures of dataset biases based on K-nearest-neighbors to help guide future research on dataset developments and bias reduction. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Large-scale neural networks have achieved superhuman performance across many popular AI benchmarks, for tasks as diverse as image recognition (ImageNet; Russakovsky et al. (2015)), natural language inference (SNLI; Bowman et al. (2015)), and question answering (SQuAD; Rajpurkar et al. (2016)). Yet these deep models struggle when taken out of these dataset environments and evaluated on adversarial data or problems in the wild (Eykholt et al., 2018; Jia & Liang, 2017). This raises a key question: Does high model performance on today’s benchmark datasets indicate the underlying task is solved, or do those datasets overestimate the true capabilities of current AI systems? ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Answering this question is key because benchmarks serve important roles in the community. Not only do they direct progress on core tasks, they also make it easier to tackle the lofty target tasks such as image recognition in the wild through a more practically-scoped dataset such as ImageNet. However, the closed-world assumption of most existing datasets is subject to significant bias (Torralba & Efros, 2011). Much of the data that is easy to obtain and label isn’t necessarily representative of the task we seek to measure. Thus, if left unchecked, artifacts from data collection (Fouhey et al., 2018) or human labeling (Gururangan et al., 2018; Poliak et al., 2018; Tsuchiya, 2018; Geva et al., 2019) can significantly inflate model performance. Though there exist task- and dataset-specific approaches for addressing these biases (Goyal et al., 2017; Geirhos et al., 2018), the complex artifacts that emerge from large-scale dataset creation are challenging to exhaustively identify and remove. ",
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+    {
+        "type": "image",
+        "img_path": "images/92d062e2e02496cd00d087cc6083837faa34ec7bcddf685cd2d17227f4c79fd2.jpg",
+        "image_caption": [
+            "Figure 1: Random ImageNet images for two labels – Monarch Butterfly and Chickadee – that were either selected (left) as adversarial by our AFLITE algorithm, or excluded (right). The heatmap shows pairwise cosine similarity between EfficientNet-B7 features (Tan & Le, 2019). The AFLITE images show significantly greater diversity – such as the cocoon of a butterfly, or the non-canonical chickadee poses – that is in turn reflected by the cosine similarity. This diversity suggests that the AFLITE examples more directly measure progress on the true task of image classification, versus fitting to dataset bias. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we present AFLITE – a computationally efficient dataset reduction algorithm, aimed at systematically reducing spurious artifacts in a dataset. AFLITE is general and can be applied to any task and dataset. Our approach leverages a high capacity model to learn dataset specific biases on a small subset, then uses it to identify and filter artifact-prone instances in the remainder of the dataset to yield a final dataset that is possibly closer to the intended task. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We first evaluate the effectiveness of our method on synthetic data and show that AFLITE lowers the performance of models relying on annotation artifacts while preserving the performance of models whose representation captures the underlying tasks. In addition, while AFLITE aims to retain the more challenging, confusing instances, our experiments show that it can successfully remove biased instances that are adversarial to the correct representation of the data. ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Finally, we apply the method to several benchmark datasets across various tasks and domains. In language understanding, we apply AFLITE to the SNLI (Bowman et al., 2015) and MNLI (Williams et al., 2018) datasets for natural language inference, and to QNLI (Wang et al., 2018) for question answering. We show a $3 0 \\%$ absolute gap in performance in the current state-of-art methods before and after AFLITE. In computer vision, AFLITE reduces the performance of image classification neural methods on ImageNet (Russakovsky et al., 2015), showing a $49 \\%$ absolute gap. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 DATASET REDUCTION FOR REPRESENTATION-BIAS MINIMIZATION ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this section, we introduce AFLITE, a general approach for reducing the scope of bias in datasets. Large datasets run the risk of prioritizing performance on the data-rich head of the distribution, where examples are plentiful, and discounting the tail. Our goal is to minimize the ability of a model to exploit biases in the head of the distribution, while preserving the inherent complexity of the tail. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Let $\\Phi$ represent a feature representation, defined over a dataset ${ \\mathcal { D } } = ( X , Y )$ . With AFLITE, we seek a subset $S \\subset \\mathcal { D }$ of size $| S | \\ge n$ that is maximally resilient to the features uncovered by $\\Phi$ . For any identically-distributed train-test split of $\\mathcal { D }$ , the features extracted by $\\Phi$ should not generalize to the held-out set. Our approach allows for any choice of feature representation. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Formalization More formally, let $\\mathcal { M }$ denote a family of classification models (e.g., logistic regression, SVM, or a particular neural architecture) that can be trained on subsets $S$ of $D \\doteq ( X , Y )$ ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "using features $\\Phi ( X )$ . We define the representation bias of $\\Phi$ in $S w x t { \\mathcal { M } }$ , denoted ${ \\mathcal { R } } ( \\Phi , S , { \\mathcal { M } } )$ , as the best possible out-of-sample classification accuracy achievable by models in $\\mathcal { M }$ when predicting the true labels $Y$ using features $\\Phi ( X )$ . For a given target reduced dataset size of at least $n$ , the goal is to find a subset $S \\subset D$ , $| S | \\ge n$ that minimizes this representation bias in $S$ w.r.t. $\\mathcal { M }$ : ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/138d356d9bb0487ab7dbe7d48dd75e00379cf72f1cf5496c068c5ec935a5576c.jpg",
+        "text": "$$\n\\operatorname* { m i n } _ { S \\subset D , | S | \\geq n } { \\mathcal { R } } ( \\Phi , S , { \\mathcal { M } } )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Eq. (1) corresponds to the optimum bias reduction, referred to as AFOPTIMUM. ${ \\mathcal { R } } ( \\Phi , S , { \\mathcal { M } } )$ can be formulated as the expected classification accuracy resulting from the following process. Let $q : 2 ^ { S }  [ 0 , 1 ]$ be a probability distribution over subsets $T = \\mathsf { \\bar { ( } } X ^ { T } , Y ^ { T } )$ of $D$ . The process is to randomly choose a subset $T$ with probability $q ( T )$ , train a bias estimator $M _ { T } \\in \\mathcal { M }$ on $D \\backslash T$ , and evaluate its classification accuracy $f _ { M _ { T } } ( \\Phi ( X ^ { T } ) , Y ^ { T } )$ on $T$ . Note that the resulting classification accuracy on $T$ itself is a random variable, since the training set $D \\setminus T$ is random. We define the expected value of this classification accuracy to be the representation bias: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e1f1545e08af5d5b8cac2abe4018edff15a22990692c44a07db6528e69f1c13b.jpg",
+        "text": "$$\n\\mathcal { R } ( \\Phi , S , \\mathcal { M } ) \\stackrel { \\Delta } { = } \\mathbb { E } _ { T \\sim q } \\left[ f _ { M _ { T } } ( \\Phi ( X ^ { T } ) , Y ^ { T } ) \\right]\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "While this expression formalizes the intended objective function, it involves a large summation over subsets $T \\subset S$ just to compute the representation bias present in a single set $S$ . It does not suggest a practical way to compute the minimization in Eq. (1) without further considering each of the exponentially many subsets $S \\subset D$ individually – thus an optimal solution for Equation (2) is intractable. To get around this difficulty, we reformulate the representation bias in $S$ as a sum factored over the $| S |$ individual instances $i \\in S$ . This will allow us to efficiently decide whether or not to include $i$ in the targeted, reduced subset we are constructing. ",
+        "bbox": [
+            173,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The idea is to aggregate the contribution of each $i$ towards the representation bias expression across all random choices of the training set $D \\backslash T$ . We call this the predictability score $p ( i )$ for $i$ : on average, how reliably can the label $y _ { i }$ be predicted using features $\\Phi ( x _ { i } )$ when a model from $\\mathcal { M }$ is trained on a randomly chosen training set $D \\backslash T$ not containing $i$ . The higher the value of $p ( i )$ , the easier it is to correctly classify the instance $( x _ { i } , y _ { i } )$ using model family $\\mathcal { M }$ . This is the signal we will use to decide whether to include $i$ in the reduced subset $S$ we are constructing. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "With some abuse of notation, for $i \\in D$ , let $\\begin{array} { r } { q ( i ) \\triangleq \\sum _ { T \\ni i } q ( T ) } \\end{array}$ denote the marginal probability of choosing a subset T that contains i. The ratio q(T )q(i) is then the probability of $T$ conditioned on it containing $i$ . Let $f _ { M _ { T } } ( \\Phi ( x _ { i } ) , y _ { i } )$ be the classification accuracy of $M _ { T }$ on $i$ . The reformulation of representation bias in terms of predictability scores of individual instances works as follows: ",
+        "bbox": [
+            173,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0503b750dda5e3d0722957d201e3f55182643e45a86a2a0878a4c2aef877f536.jpg",
+        "text": "$$\n\\begin{array} { r l } { \\mathbb { E } _ { \\mathcal { F } \\sim \\infty _ { + } } \\left[ f _ { M \\tau } \\left( \\Phi ( X ^ { \\tau } ) , Y ^ { \\tau } \\right) \\right] = \\displaystyle \\sum _ { t \\in S } q ( T ) \\cdot \\frac { 1 } { | T | } \\sum _ { i \\in T } ^ { T } f _ { M \\tau } \\left( \\Phi ( x _ { i } ) , y _ { i } \\right) } & { } \\\\ & { = \\displaystyle \\sum _ { \\tau \\in S } \\sum _ { i \\in T } q ( T ) \\cdot \\frac { f _ { M \\tau } \\left( \\Phi ( x _ { i } ) , y _ { i } \\right) } { | T | } } \\\\ & { = \\displaystyle \\sum _ { \\tau \\in S } \\sum _ { \\tau \\in S } q ( T ) \\cdot \\frac { f _ { M \\tau } \\left( \\Phi ( x _ { i } ) , y _ { i } \\right) } { | T | } } \\\\ & { = \\displaystyle \\sum _ { \\tau \\in S } \\frac { \\displaystyle \\sum _ { \\tau \\in S } y } { \\displaystyle \\sum _ { \\tau \\in S } y } \\cdot \\frac { \\displaystyle \\frac { \\bar { q } ( T ) } { \\displaystyle \\lambda } \\sum _ { i \\in T } \\left( \\frac { \\bar { q } ( x _ { i } ) } { | T | } \\right) \\cdot y _ { i } } { | T | } } \\\\ & { = \\displaystyle \\sum _ { \\tau \\in S } q ( t ) \\cdot \\frac { \\displaystyle \\sum _ { \\tau \\in S } \\bar { q } ( T ) } { \\displaystyle \\sum _ { \\tau \\in S } y } \\frac { \\displaystyle \\bar { q } ( T ) } { \\displaystyle \\left( \\bar { q } ( x _ { i } ) \\right) } \\frac { f _ { M \\tau } \\left( \\Phi ( x _ { i } ) , y _ { i } \\right) } { | T | } } \\\\ & { = \\displaystyle \\sum _ { \\tau \\in S } q ( \\bar { q } ) \\mathbb { E } _ { \\tau \\cap S , \\tau \\in S } \\left\\{ \\frac { f _ { M \\tau } \\left( \\bar { q } ( x _ { i } ) , y _ { i } \\right) } { | T | } \\right\\} } \\\\ & { = \\displaystyle \\sum _ { \\tau \\in S } p ( i ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
+            287,
+            637,
+            705,
+            862
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where $p ( i )$ is the predictability score of $i$ defined as: ",
+        "bbox": [
+            176,
+            867,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/aac22338ed07ec63429acb42b16308ee7e2b4f421f2cbbf2d25e411ec5923042.jpg",
+        "text": "$$\np ( i ) \\triangleq q ( i ) \\mathbb { E } _ { T \\subset S , T \\ni i } \\left[ \\frac { f _ { M _ { T } } ( \\Phi ( x _ { i } ) , y _ { i } ) } { \\vert T \\vert } \\right]\n$$",
+        "text_format": "latex",
+        "bbox": [
+            361,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "While the method works for any probability distribution $q$ with non-zero support on all samples, for simplicity of exposition, we restrict $q$ to be the uniform distribution over all subsets $T \\subset S$ of a fixed size. This makes both $| T |$ and $q ( i )$ fixed constants; in particular, $\\begin{array} { r } { q ( i ) = \\binom { | S | - 1 } { | T | - 1 } / \\binom { | S | } { | T | } = \\frac { | T | } { | S | } } \\end{array}$ |T ||S| . This reduces the predictability score expression of Eq. (3) to the simplified variant $\\tilde { p } ( i )$ : ",
+        "bbox": [
+            173,
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/9ec60a6f45978a3c40cb5e59f3539de8e48051f81e2402256245d4080fc4e3d6.jpg",
+        "text": "$$\n\\tilde { p } ( i ) \\triangleq \\frac { 1 } { | S | } \\mathbb { E } _ { T \\subset S , T \\ni i } \\left[ f _ { M _ { T } } ( \\Phi ( x _ { i } ) , y _ { i } ) \\right]\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Putting the pieces together, we have a factored reformulation of the representation bias in Eq. (2): ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/8a2bb63a75174d1aac0ccfa546522503995cbc04c902342d2daed0bd3100fc7c.jpg",
+        "text": "$$\n\\mathcal { R } ( \\Phi , S , \\mathcal { M } ) = \\sum _ { i \\in S } \\tilde { p } ( i )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Armed with this factored representation, we return to the task of identifying an $S \\subset D$ , $| S | \\ge n$ that minimizes the representation bias. We use the simplified predictability scores (henceforth simply referred to as predictability scores) as a heuristic metric to decide which $i \\in D$ to include in $S$ . We consider three approaches that iteratively filter out the most predictable instances from $D$ to arrive at $S$ . In all cases, we use a fixed training set size $| S \\setminus T | = t < n$ . Further, since a larger filtered set is generally desirable, we terminate the filtering process early (i.e., while $\\vert S \\vert > n )$ if the predictability score for every $i$ falls below a pre-specified early stopping threshold $\\tau \\in [ 0 , 1 ]$ . ",
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+    {
+        "type": "text",
+        "text": "The three approaches are as follows. (A) A simple greedy approach starts with the full set $S = D$ , identifies an $i \\in S$ with the highest predictability score, removes it from $S$ , and repeats up to $| D | - n$ times. (B) A greedy slicing approach identifies the instances with the $k$ highest predictability scores, removes all of them from $S$ , and repeats the process up to $\\lfloor { \\frac { \\lfloor D \\rfloor - n } { k } } \\rfloor$ times. (C) A slice sampling approach where, instead of greedily choosing the top $k$ instances, it randomly samples $k$ instances with probabilities proportional to their predictability scores.1 In this paper, we use the greedy slicing approach in our experiments and refer to it as AFLITE. While the optimum bias reduction via AFOPTIMUM is intractable, its light-weight version, AFLITE, is applicable in practice. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The slice sampling approach can be efficiently implemented using what is known as the Gumbel method or Gumbel trick (Gumbel & Lieblein, 1954; Maddison et al., 2014), which uses random perturbations to turn sampling into a simpler problem of optimization. This has recently found success in several probabilistic inference applications (Kim et al., 2016; Jang et al., 2016; Maddison et al., 2016; Balog et al., 2017; Kool et al., 2019). Starting with the log-predictability scores $\\log \\tilde { p } ( i )$ for various $i$ , the idea is to perturb them by adding an independent random noise $\\gamma _ { i }$ drawn from the standard Gumbel distribution. Interestingly, the maximizer $i ^ { * }$ of $\\gamma _ { i } + \\log \\tilde { p } ( i )$ turns out to be an exact sample drawn from the (unnormalized) distribution defined by $\\tilde { p }$ . Note that $i ^ { * }$ is a random variable since the $\\gamma _ { i }$ are drawn at random. This result can be generalized (Vieira, 2014) for slice sampling: the $k$ highest values of Gumbel-perturbed log-predictability scores correspond to sampling, without replacement, $k$ items from the probability distribution defined by $\\tilde { p }$ . The Gumbel method is typically applied to exponentially large combinatorial spaces, where it is challenging to scale up. In our setting, however, the overhead is minimal since the cost of drawing a random $\\gamma _ { i }$ is negligible compared to computing $\\tilde { p } ( i )$ . ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Implementation Algorithm 1 provides an implementation of AFLITE. The algorithm takes as input a dataset $D = \\bar { ( } X , Y )$ , a representation $\\Phi ( X )$ we are interested in minimizing the bias in, a model family $\\mathcal { M }$ (e.g., linear classifiers), a target dataset size $n$ , size $m$ of the support of the expectation in Eq. (4), training set size $t$ for the classifiers, size $k$ of each slice, and an early-stopping filtering threshold $\\tau$ . Importantly, for efficiency, $\\Phi ( X )$ is provided to AFLITE in the form of precomputed embeddings for all of $X$ . To obtain $\\Phi ( X )$ in practice, we train a first model on a small fraction of the data based on the learning curve in low-data regime, and do not reuse this data for the rest of our experiments. Moreover, this fraction corresponds to the training size $t$ for AFLITE and it remains unchanged across iterations. We follow the iterative filtering approach, starting with $S \\ : = \\ : D$ and iteratively removing some instances with the highest predictability scores using the ",
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+    {
+        "type": "text",
+        "text": "Algorithm 1: AFLITE ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Input: dataset $D = ( X , Y )$ , pre-computed representation $\\Phi ( X )$ , model family $\\mathcal { M }$ , target dataset size $n$ ,   \nnumber of random partitions $m$ , training set size $t < n$ , slice size $k \\leq n$ , early-stopping threshold $\\tau$   \nOutput: reduced dataset $S$   \n1 $S = D$   \n2 while $\\vert S \\vert > n$ do   \n// Filtering phase   \n3 forall $i \\in S$ do   \n4 Initialize a multi-set of out-of-sample predictions $E ( i ) = \\emptyset$   \n5 for iteration $j : 1 . . m$ do   \n6 Randomly partition $S$ into $( T _ { j } , S \\setminus T _ { j } )$ s.t. $| S \\setminus T _ { j } | = t$   \n7 Train a classifier ${ \\mathcal { L } } \\in { \\mathcal { M } }$ on $\\{ ( \\Phi ( x ) , y ) ~ | ~ ( x , y ) \\in S \\setminus T _ { j } \\}$ $\\mathcal { L }$ is typically a linear classifier)   \n8 forall $i = ( x , y ) \\in T _ { j }$ do   \n9 Add the prediction ${ \\mathcal { L } } ( \\Phi ( x ) )$ to $E ( i )$   \n10 forall $i = ( x , y ) \\in S$ do   \n11 Compute the predictability score $\\tilde { p } ( i ) = | \\{ \\hat { y } \\in E ( i ) \\ s . t . \\ \\hat { y } = y \\} | / \\left| E ( i ) \\right|$   \n12 Select up to $k$ instances $S ^ { \\prime }$ in $S$ with the highest predictability scores subject to $\\tilde { p } ( i ) \\geq \\tau$   \n13 $S = S \\setminus S ^ { \\prime }$   \n14 if $| S ^ { \\prime } | < k$ then   \n15 break   \n16 return $S$ ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "greedy slicing strategy. Slice size $k$ and number of partitions $m$ are determined by the available computation budget. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "At each filtering phase, we train models (linear classifiers in our implementation) on $m$ different random partitions of the data, and collect their predictions on their corresponding test set. For each instance $i$ , we compute its predictability score as the ratio of the number of times its label $y _ { i }$ is predicted correctly, over the total number of predictions for it. We rank the instances according to their predictability score and use the greedy slicing strategy of removing the top- $k$ instances whose score is not less than the early-stopping threshold $\\tau$ . We repeat this process until fewer than $k$ instances pass the $\\tau$ threshold in a filtering phase or fewer than $n$ instances remain. ",
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+    {
+        "type": "text",
+        "text": "3 EXPERIMENTAL ANALYSIS ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We evaluate AFLITE across various domains (synthetic, natural language processing, computer vision), different tasks in a given domain (language inference and question answering in NLP), different datasets for a given task (SNLI and MNLI in natural language inference), and different representations for a given dataset (pre-computed embeddings from ESIM+GLoVe, BERT, RoBERTa for the SNLI dataset). ",
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+    {
+        "type": "text",
+        "text": "3.1 SYNTHETIC EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We demonstrate the utility of AFLITE in a synthetic data setting. Our dataset consists of twodimensional data, arranged in concentric circles, at four different levels of separation, as shown in the Figure 2. As is evident, a linear function might not be adequate for separating the two classes; it requires a more complex non-linear model such as an SVM with an RBF kernel. 2 ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We add class-specific artificially constructed features (artifacts) sampled from two different Gaussian distributions. These features are only added to $7 5 \\%$ of the data in each class, while for the rest of the data, we insert random (noise) features. These artifacts make the task solvable through a linear function. Furthermore, for the first dataset, with the largest separation, we flipped the labels of some examples with artifacts, making the data slightly adversarial even to the RBF. Both models can clearly leverage the artifacts, and demonstrate improved performance over a baseline without artifacts. ",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/062974b3effd84b5e7be5250aa0bd1114d533c7813c0745da7596aea8bd25c7b.jpg",
+        "table_caption": [
+            "Table 1: Dev accuracy $( \\% )$ on the original SNLI dataset $D$ and the datasets obtained through various representation-bias minimization. The -HypOnly baselines correspond to models trained on the instances restricted to their hypotheses. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>D</td><td>D92k</td><td>D(ΦESIM+GLoVe)</td><td>D(ΦBERT)</td><td>D(ΦRoBERTa)</td></tr><tr><td>ESIM+ELMo (Peters et al.,2018)</td><td>88.7</td><td>86.0</td><td>61.5</td><td>54.2</td><td>51.9</td></tr><tr><td>BERT (Devlin et al., 2019)</td><td>91.3</td><td>87.6</td><td>74.7</td><td>61.8</td><td>57.0</td></tr><tr><td>RoBERTa (Liu et al.,2019b)</td><td>92.6</td><td>88.3</td><td>78.9</td><td>71.4</td><td>62.6</td></tr><tr><td>Max-PPMI baseline</td><td>54.5</td><td>52.0</td><td>41.1</td><td>41.5</td><td>41.9</td></tr><tr><td>BERT-HypOnly</td><td>71.5</td><td>70.1</td><td>52.3</td><td>46.4</td><td>48.4</td></tr><tr><td>RoBERTa-HypOnly</td><td>72.0</td><td>70.4</td><td>53.6</td><td>49.5</td><td>48.5</td></tr><tr><td>Human performance</td><td>88.1</td><td>88.1</td><td>82.3</td><td>80.3</td><td>77.8</td></tr><tr><td>Training set size</td><td>550k</td><td>92k</td><td>138k</td><td>109k</td><td>92k</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Once we apply AFLITE, as expected, the number of examples with artifacts is reduced considerably, making the task hard once again for the linear model, but still solvable for the non-linear one. The filtered dataset is shown in the bottom half of Fig. 2, and the captions indicate the performance of a linear and an SVM model. For the first dataset, we see that AFLITE removes most of those examples with flipped labels. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/115f14c9115d54ffd350759e4fc7e5da77c8f8f5fbabc34a97b98e2ba25d04eb.jpg",
+        "image_caption": [
+            "Figure 2: Four sample datasets with artifacts as input to AFLITE (top). Blue and orange indicate two different classes. Only the original two dimensions are shown, not the artifacts. For the leftmost dataset with the highest separation, we flip some labels at random, so even an RBF kernel cannot achieve perfect performance. AFLITE makes the data more challenging for the models (bottom). "
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "3.2 NLP EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We evaluate AFLITE on two NLP tasks, namely NLI and question answer sentence selection. We use two popular NLI large-scale datasets – SNLI (Bowman et al., 2015) and MNLI (Wang et al., 2018). For the answer sentence selection task, we use QNLI which is a transformed version of the SQuAD question answering dataset (Rajpurkar et al., 2016) converted to binary classification where systems determine whether a sentence contains the answer to a question. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "SNLI Each instance in the SNLI dataset consists of a premise-hypothesis pair that belongs to one out of three possible categories (entailment, contradiction, or neutral) based on the relationship between the premise and the hypothesis. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For SNLI, we experiment with three different feature representations derived from strong baseline models: $\\Phi _ { B E R T }$ and $\\Phi _ { R o B E R T a }$ which are based on BERT (Devlin et al., 2019) and RoBERTa (Liu et al., 2019b), large-scale pretrained masked language models, plus $\\Phi _ { E S I M + G L o V e }$ which uses the ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/769868d42b4886f01fb6da884d2ea02bf2a1618db48533da24ed3905bdabddd8.jpg",
+        "table_caption": [
+            "Table 2: Dev accuracy $( \\% )$ on the original MNLI-matched and QNLI datasets and the datasets obtained through $\\Phi _ { R o B E R T a }$ -representation-bias minimization. The -PartialInput baselines correspond to models trained on partial, incomplete input, namely the Hypotheses for MNLI instances and the Answers for QNLI instances. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"2\">MNLI</td><td colspan=\"2\">QNLI</td></tr><tr><td>Model</td><td>D</td><td>D(RoBERTa)</td><td>D</td><td>D( RoBERTa)</td></tr><tr><td>BERT (Devlin et al., 2019)</td><td>86.6</td><td>55.8</td><td>92.0</td><td>63.5</td></tr><tr><td>RoBERTa (Liu et al.,2019b)</td><td>90.3</td><td>66.2</td><td>93.7</td><td>77.7</td></tr><tr><td>BERT-PartialInput</td><td>59.7</td><td>43.2</td><td>62.6</td><td>56.6</td></tr><tr><td>RoBERTa-PartialInput</td><td>60.3</td><td>44.4</td><td>63.9</td><td>59.4</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ESIM model (Chen et al., 2016) with GLoVe word embeddings (Pennington et al., 2014). In all cases, feature representation $\\Phi$ is trained on a random sample of $1 0 \\%$ of the original training instances, and feature representations are extracted from the final layer before the output layer. These features are pre-computed for all remaining instances while we discard the instances $1 0 \\%$ of training) used for training the embeddings in the subsequent steps of our algorithm. Additionally, to measure the ability of a weaker adversary to filter biases only learned by a stronger model, we evaluate the filtered datasets (for SNLI) with three different models: (i) ESIM with ELMo embeddings (Peters et al., 2018), (ii) BERT-large, and (iii) RoBERTa-large models. ",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Table 1 shows the results for SNLI. In all cases, applying AFLITE substantially reduces overall model accuracy, with typical drops of $1 5 . 3 5 \\%$ depending on the models used for learning the feature representations and those used for evaluation of the filtered dataset. In general, performance is lowest when using the strongest model (RoBERTa) for learning feature representations. Results also highlight the ability of weaker adversaries to produce datasets that are still challenging for much stronger models with a drop of $1 3 . 7 \\%$ for RoBERTa using $\\Phi _ { E S I M + G L o V e }$ as feature representation. We also include a model that uses Point-wise Mutual Information (PMI) between words in a given instance and the target label as a feature. The baseline captures the extent to which datasets exhibit word-association artifacts. While this baseline is relatively weaker than other models, we still show that its performance reduce from $5 4 . 5 \\%$ on $D$ to $4 1 . 9 \\%$ on the $D ( \\phi _ { R o B E R T a } )$ dataset. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "It might seem unsurprising that reducing the size of the training set results in lower performance. To control for the confounding factor of the dataset size, we create another filtered dataset $D _ { 9 2 k }$ , sampled randomly from $D$ such that its size is approximately equal to the size of $D ( \\phi _ { R o B E R T a } )$ dataset. All models achieve nearly the same performance as their performance on the full dataset – even when trained on just one-fifth the original dataset size. This result further points to the fact that current benchmark datasets contain significant redundancy within its instances. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Finally, to demonstrate the value of the iterative, ensemble-based AFLITE algorithm, we compare with a baseline where using a single model, we filter out the most predictable examples in a single iteration — a non-iterative, single-model version of AFLITE. A RoBERTa-large model trained on this subset (of the same size as $D ( \\phi _ { R o B E R T a } ) )$ achieves a dev accuracy of $7 2 . 1 \\%$ . Compared to the performance of RoBERTa on $D ( \\phi _ { R o B E R T a } )$ $( 6 2 . 6 \\%$ , see Table 1), it makes this baseline a sensible yet less effective approach. In particular, this illustrates the need for an iterative procedure involving models trained on multiple partitions of the remaining data in each iteration. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also report the $\\mathbf { k }$ -nearest neighbors distances between examples in the train and heldout data in Table 3. We consider distances for examples within each class, as well as examples across classes. The distances are computed using cosine similarity between pooled features from BERT-based model (features for the [CLS] token, indicating a sentence-pair feature) trained on the original SNLI dataset. Distances are measured between samples from the heldout data, and their nearest neighbors in the training data, before and after filtering. Distances generally increase after filtering, indicating that AFLITE promotes selecting a diverse set of examples from the dataset. The only exception to the rule is the neutral class, where distances to other classes decrease – this is not surprising since the neutral class is known to be associated with the least number of artifacts (Gururangan et al., 2018). ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0a8fc461e9aee2228b63bb3d311a639e07545e97e689380a00ab532481a0264c.jpg",
+        "table_caption": [
+            "Table 3: KNN-distances by class, before and after applying (RoBERTa-filtered) AFLITE to SNLI. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"4\">Before AFLITE</td><td colspan=\"4\">After AFLITE</td></tr><tr><td>Top1</td><td>Top5</td><td>Top10</td><td>Top50</td><td>Top1</td><td>Top5</td><td>Top10</td><td>Top50</td></tr><tr><td>Entailment</td><td>0.29</td><td>1.32</td><td>2.45</td><td>9.5</td><td>0.32</td><td>1.42</td><td>2.64</td><td>9.98</td></tr><tr><td>Neutral</td><td>0.40</td><td>1.89</td><td>3.68</td><td>16.83</td><td>0.42</td><td>1.97</td><td>3.80</td><td>16.66</td></tr><tr><td>Contradiction</td><td>0.49</td><td>2.41</td><td>4.77</td><td>23.09</td><td>0.52</td><td>2.49</td><td>4.84</td><td>22.10</td></tr><tr><td>Entailment vs others</td><td>0.32</td><td>1.48</td><td>2.87</td><td>12.98</td><td>0.34</td><td>1.53</td><td>2.92</td><td>12.31</td></tr><tr><td>Neutral vs others</td><td>0.43</td><td>2.05</td><td>3.99</td><td>18.42</td><td>0.41</td><td>1.94</td><td>3.72</td><td>16.41</td></tr><tr><td>Contradiction vs others</td><td>0.49</td><td>2.38</td><td>4.70</td><td>22.61</td><td>0.53</td><td>2.51</td><td>4.87</td><td>22.38</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2c74d68bd6c394e658062b437c4ed24a1c1ba009f5a97a514540a8445d8299d3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td colspan=\"4\">HANS</td><td colspan=\"3\">NLI-Diagnostics</td><td colspan=\"3\">Adversarial-NLI</td></tr><tr><td>Model</td><td>Al</td><td>Lex.</td><td>Subseq.</td><td>Constit.</td><td>All</td><td>Logic</td><td>Knowl.</td><td>Rd1</td><td>Rd2</td><td>Rd3</td></tr><tr><td>RoBERTa</td><td>70.7</td><td>84.4</td><td>35.4</td><td>13.4</td><td>59.3</td><td>52.8</td><td>48.9</td><td>58.5</td><td>48.3</td><td>50.1</td></tr><tr><td>RoBERTa-AFlite</td><td>74.5</td><td>96.3</td><td>56.6</td><td>57.4</td><td>62.0</td><td>53.2</td><td>57.7</td><td>65.1</td><td>49.1</td><td>52.8</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 4: SNLI accuracy $( \\% )$ on three out-of-distribution evaluation tasks, comparing RoBERTalarge models pre-trained on the original SNLI data, and on AFLITE-filtered data. On the HANS dataset, both models are evaluated on $A l l$ , as well as on the non-entailment cases of the three syntactic heuristics (Lexical overlap, Subsequence, and Constituent). The NLI-Diagnostics dataset is broken down into the full dataset $( A l l )$ , as well as the instances requiring logical reasoning (Logic) and the ones requiring world and commonsense knowledge (Knowledge). For Adversarial NLI, we finetuned both models on the in-distribution training data for each round (Rd1, Rd2, and Rd3). ",
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+    {
+        "type": "text",
+        "text": "MNLI and QNLI Following the same procedure described above, we apply AFLITE on the MNLI and QNLI datasets. Since RoBERTa resulted in the largest drops in performance across the board in SNLI, we only experiment with RoBERTa as adversary for MNLI and QNLI. While RoBERTa achieves over $9 0 \\%$ on both original datasets, its performance drops to $6 6 . 2 \\%$ for MNLI and to $7 7 . 7 \\%$ for QNLI on the reduced datasets. Similarly, partial input baseline performance also decreases substantially on both dataset compared to their performance on the original dataset. Table 2 shows these results. We show that AFLITE consistently result in reduced accuracy on the filtered datasets across multiple NLP benchmark datasets, even after controlling for the size of the training set. ",
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+    {
+        "type": "text",
+        "text": "3.2.1 OUT-OF-DISTRIBUTION NLI ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We measure the performance of AFLITE on three other benchmarks for NLI evaluation, which provide out-of-distribution examples to challenge reliance on dataset biases in the original SNLI data (Glockner et al., 2018; Naik et al., 2018). Such benchmarks approximate the performance of NLI models in the wild. NLI Diagnostics (Wang et al., 2018) is a set of hand-crafted examples designed to demonstrate model performance on several fine-grained semantic categories, such as logical reasoning and commonsense knowledge. HANS (McCoy et al., 2019) contains evaluation examples designed to avoid common structural heuristics (such as word overlap) which could be used by models to correctly predict NLI inputs, without true inferential reasoning. Adversarial NLI (Nie et al., 2019) consists of premises collected from Wikipedia and other news corpora, and human generated hypotheses, arranged at different tiers of the challenge they present to a model, using a human and model in-the-loop procedure. Given that these benchmarks are collected independently of the original SNLI task, the biases from SNLI are less likely to carry over; however these benchmarks might contain their own biases (Liu et al., 2019a). ",
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+    {
+        "type": "text",
+        "text": "AFLITE assigns a predictability score to all samples in a dataset, resulting in an ordering of the data. Filtering out examples from the head of the data distribution based on this order yields more accurate benchmarks for measuring true model performance. On the other hand, transferability to out-of-distribution data would involve a greater balance between examples from the head and the tail ends of the data distribution. Hence we evaluate AFLITE for generalization using a larger filtered subset, amounting to only a third of the full training data. We present these results on all the above benchmarks in Table 4. On the two diagnostic datasets (HANS and NLI-Diagnostics), we perform a zero-shot evaluation of the two models. Adversarial NLI allows to test for transfer capabilities, by finetuning these models on each of the three training datasets (Rd1, Rd2 and Rd3). On each of the benchmarks above, the model trained on the AFLITE data consistently outperforms the model trained on the full SNLI data. challenging examples in the HANS benchmark, which targets models purely relying on lexical and syntactic cues. Similarly, our model performs better on the instances in NLI-Diagnostics that require logical reasoning and commonsense knowledge, as opposed to instances that can be solved through lexical entailment alone. ",
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+        "type": "table",
+        "img_path": "images/68cae2fa1117ce0ef26090f7849a40943a9c3ce14a6728b71480f3dd54f16316.jpg",
+        "table_caption": [
+            "Table 5: Experimental results on ImageNet. We compare between three settings: the original dataset’s train-test splits, using $20 \\%$ of the training set but evaluating on the validation set, and using the AFLITE produced training and validation sets. AFLITE produces a training dataset that is also $20 \\%$ of the training set size, making it a fair comparison in terms of dataset examples. The results show a significant drop in Top-1 and Top-5 accuracy: the Top-1 accuracy goes down by roughly 40 percentage points per model in this new training and evaluation setting. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">100% Train, Original Val</td><td colspan=\"2\">20% Train, , Original Val</td><td colspan=\"2\">AFLITE</td></tr><tr><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td><td>Top-1</td><td>Top-5</td></tr><tr><td>EfficientNet-B0</td><td>76.3</td><td>93.2</td><td>58.5</td><td>81.2</td><td>18.1</td><td>48.1</td></tr><tr><td>EfficientNet-B2</td><td>79.8</td><td>94.9</td><td>60.9</td><td>82.8</td><td>20.7</td><td>53.1</td></tr><tr><td>EfficientNet-B4</td><td>82.6</td><td>96.3</td><td>64.4</td><td>85.8</td><td>23.3</td><td>58.8</td></tr><tr><td>EfficientNet-B7</td><td>84.4</td><td>97.1</td><td>73.8</td><td>90.8</td><td>24.5</td><td>60.6</td></tr><tr><td>ResNet-34</td><td>78.4</td><td>94.4</td><td>51.8</td><td>74.3</td><td>11.1</td><td>30.2</td></tr><tr><td>ResNet-50</td><td>79.2</td><td>94.7</td><td>53.2</td><td>75.5</td><td>12.2</td><td>30.2</td></tr><tr><td>ResNet-101</td><td>80.1</td><td>95.4</td><td>55.6</td><td>77.5</td><td>12.3</td><td>32.1</td></tr><tr><td>ResNet-152</td><td>80.6</td><td>95.5</td><td>56.5</td><td>78.2</td><td>13.2</td><td>33.8</td></tr></table>",
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+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "3.3 IMAGENET EXPERIMENTS ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We evaluate AFLITE on image classification through ImageNet (ILSVRC2012) classification. On ImageNet, we use the state-of-the-art EfficientNet-B7 model as our core feature extractor $\\Phi$ (Tan & Le, 2019). The EfficientNet model is learned from scratch on a fixed $20 \\%$ sample of the ImageNet training set, using AutoAugment data augmentation (Cubuk et al., 2019). We then use the 2560- dimensional features extracted by EfficientNet-B7 as then underlying representation for AFLITE to use to filter the remaining dataset. ",
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+    },
+    {
+        "type": "text",
+        "text": "In Table 5, we evaluate the robustness of the filtered dataset by considering ImageNet accuracy across the EfficientNet and ResNet model families (He et al., 2016). When lowering the size of the training set – down to $20 \\%$ of the original, we find a large drop in performance. The EfficientNet models seem to suffer less – from $8 4 \\%$ to $7 3 \\%$ on EfficientNet-B7 versus $8 0 . 6 \\%$ to $5 6 . 5 \\%$ on ResNet-152. However, the biggest performance drop comes from training and evaluating on the AFLITE-filtered dataset: the top performer is still EfficientNet-B7, but its accuracy drops to $2 4 . 5 \\%$ top-1. This is despite controlling for dataset size, as well as discrepancy between the training and validation sets. ",
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+    {
+        "type": "text",
+        "text": "Overall, these results suggest that image classification – even within a subset of the closed world of ImageNet – is far from solved. These results echo other findings that suggest that common biases that naturally occur in web-scale image data, such as towards canonical poses (Alcorn et al., 2019) or towards texture rather than shape (Geirhos et al., 2018), are problems for ImageNet-trained classifiers. Indeed, the randomly-selected ImageNet images in Figure 1 suggest that the AFLITE algorithm learns to identify subsets of the data that are particularly challenging. ",
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+    {
+        "type": "text",
+        "text": "4 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our proposed framework for artifact reduction is related to the adversarial filtering (AF) algorithm in Zellers et al. (2018), yet distinct in two key ways: our approach is (i) much more broadly applicable (by not requiring over generation of data instances), and (ii) considerably more lightweight (by not requiring re-training a model at each iteration of AF). Variants of this AF approach have recently been used to create other datasets such as HellaSwag (Zellers et al., 2019) and ANLI (Bhagavatula et al., 2019) by iteratively perturbing dataset instances until a target model cannot fit the resulting dataset. While effective, these approaches run into three main pitfalls. First, dataset curators need to explicitly devise a strategy of collecting or generating perturbations of a given instance. Second, the approach runs the risk of distributional bias where a discriminator can learn to distinguish between machine generated instances and human-generated ones. Finally it requires re-training a model at each iteration, which is computationally expensive especially when using a large model such as BERT (Devlin et al., 2019) as the adversary. In contrast, AFLITE focuses on addressing dataset biases from existing datasets instead of adversarially perturbing instances. AFLITE was earlier proposed by Sakaguchi et al. (2019) to create the Winogrande dataset. This paper presents more thorough experiments, theoretical justification and results from generalizing the proposed approach to multiple popular NLP and Vision datasets. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "AFLITE is also inspired by Gururangan et al. (2018), who study lexical biased prevalent in the SNLI dataset (Bowman et al., 2015) and use point-wise mutual information (PMI) between a word and an inference class to determine the words that are highly indicative of the target label. Instead of lexical features, we adopt a deeper representation of the instances using their pre-computed dense feature representations. We use an ensemble of linear classifiers trained on random subsets of the data to determine whether the dense feature representations are highly indicative of the target label. If so, we discard the corresponding instances and proceed iteratively. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Li & Vasconcelos (2019) recently proposed REPAIR, a method to remove representation bias by dataset resampling. While resampling is a common technique for balancing datasets, the motivation in REPAIR is to learn a probability distribution over the dataset that favors instances that are hard for a given representation. This approach targets how to train better, less-biased models as opposed to creating datasets with fewer artifacts. In addition, the implementation of REPAIR relies on intraining classification loss as opposed to out-of-sample generalization accuracy. RESOUND (Li et al., 2018) is another method that quantifies the representation biases of datasets. It uses the representation biases to assemble a new K-class dataset with smaller biases by sampling an existing C-class dataset $( C > K )$ ). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Arjovsky et al. (2019) argue that unstable, spurious correlations in the data would generalize poorly to novel test environments. Thus, they propose Invariant Risk Minimization as an objective that promotes learning representations of the data which are stable across environments. Instead of learning optimal classifiers, our aim is to remove instances that exhibit artifacts in a dataset. ",
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+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "We presented AFLITE – a novel iterative greedy algorithm that adversarially filters out data points to arrive at a reduced dataset with more realistic problem distributions and considerably fewer spurious biases. We apply AFLITE to four widely-used datasets, including SNLI and ImageNet, where reported performance is extremely high – and show that state-of-the-art performance on the resulting filtered dataset drops by 30 points for SNLI and drops from $8 4 . 4 \\%$ to $2 4 . 5 \\%$ Top-1 accuracy for ImageNet. In extensive analysis we show that AFLITE is effective on real as well as synthetic datasets. We hope that dataset creators will employ AFLITE to identify unobservable artifacts before releasing new challenge datasets for the research community in order to have a more reliable estimate of model performance on future AI benchmarks. ",
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+    {
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parse/train/rk5UYassf/rk5UYassf.md

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+# Regularized siamese neural network for unsupervised outlier detection on brain multiparametric magnetic resonance imaging: application to epilepsy lesion screening
+
+Zara Alaverdyan   
+Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1,   
+UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621, Lyon, France zaruhi.alaverdyan@creatis.insa-lyon.fr
+
+Julien Jung, Romain Bouet Lyon Neuroscience Research Center, CRNL, INSERM U1028, CNRS UMR5292, University Lyon 1, Lyon, France {julien.jung, romain.bouet}@inserm.fr
+
+Carole Lartizien   
+Univ Lyon, INSA-Lyon, Université Claude Bernard Lyon 1,   
+UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621, Lyon, France carole.lartizien@creatis.insa-lyon.fr
+
+# Abstract
+
+Computer aided diagnosis (CAD) systems are designed to assist clinicians in various tasks, including highlighting abnormal regions in medical images. Common methods exploit supervised learning using annotated data sets and perform classification at voxel-level. However, many pathologies are characterized by subtle lesions that may be located anywhere in the organ of interest, have various shapes, sizes and textures. Acquiring a data set adequately representing the heterogeneity of such pathologies is therefore a major issue. Moreover, when a lesion is not visually detected on a scan, outlining it accurately is not feasible. Performing supervised learning on such labeled data would not be reliable. In this study, we consider the problem of detecting subtle epilepsy lesions in multiparametric (T1w, FLAIR) MRI exams considered as normal (MRI-negative). We cast this problem as an outlier detection problem and build on a previously proposed approach that consists in learning a oc-SVM model for each voxel in the brain volume using a small number of clinically-guided features [1]. Our goal in this study is to make a step forward by replacing the handcrafted features with automatically learnt representations using neural networks. We propose a novel version of siamese networks trained on patches extracted from healthy patients’ scans only. This network, composed of stacked convolutional autoencoders as subnetworks, is regularized by the reconstruction error of the patches. It is designed to map patches centered at the same spatial localization to ’close’ representations with respect to the chosen metric (i.e. cosine) in a latent space. Finally, the middle layer representations of the subnetworks are fed into oc-SVM models at voxel-level. The model is trained on 75 healthy subjects and validated on 21 patients with confirmed epilepsy lesions (with 18 MR negative patients) and shows a promising performance.
+
+# 1 Introduction
+
+Computer aided diagnosis (CAD) systems have been introduced as to assist clinicians in various tasks such as organ or lesion segmentation, detection of abnormal regions in a medical image, etc. Recent CAD systems for brain pathologies exploit various modalities of neuroimaging data, such as magnetic resonance imaging (MRI) and positron emission tomography (PET). The vast majority of the existing CAD systems are built upon methods developed in supervised settings, using either manually designed features or currently ubiquitous deep learning architectures as in [2, 3, 4, 5]. Such systems benefit from the available data sets (usually) annotated at voxel-level, and output maps where each voxel is characterized either by a class label, a probability or, less commonly, a score discriminating healthy versus pathological voxels. Supervised learning, however, cannot be applied when the number of pathological cases in the training set is not sufficient to account for the complexity of the task. This is often the case when it comes to detecting some brain pathologies such as small vessel diseases (SVD), multiple sclerosis (MS) or epilepsy, when the lesions are subtle and vary largely in terms of shapes and textures. It is not trivial to obtain a well-annotated data set to represent such a variability. To bypass the problem of insufficient labeled data, some authors recently proposed to formulate such lesion detection tasks in semi-supervised settings, by accounting for both labeled and unlabeled data in a deep architecture for MS lesion segmentation [6] or by exploiting weak labels (the number of lesions in a scan) to detect enlarged perivascular spaces in the basal ganglia [7].
+
+In this study we propose to tackle the problem of epilepsy lesion detection in patients with MRI negative exams, meaning that the lesions were not visually identified by clinicians on the MR scans. Similarly to the above mentioned lesion detection tasks, most of the current epilepsy detection methods perform supervised learning by leveraging annotated lesions delineated on MRI positive patients (the lesions are visually detected on the scans) [8] or by careful a posteriori re-reading of postsurgical scans of MRI negative patients who had undergone surgery and were seizure-free afterwards [1, 9, 10, 11]. While obtaining accurately labeled data for MRI positive patients is feasible, the real challenge is to extract accurate delineations in MRI negative patients. [11] showed that exploiting ’too generously’ annotated lesions on MRI negative scans as labels for supervised learning methods leads to poor detection rate due to the presence of normal tissue in the areas labeled as pathological. Therefore, some recent methods cast epilepsy lesion detection task as an outlier detection problem [1, 11, 12]. Such an approach solely needs a training set of non-pathological images, hence no labeled data is required. [1] used a small number of features modeling the gray-white matter junction (similarly to [13, 14]) while [12] and [11] derived features from surface based morphometry (SBM). All the latter methods targeted a specific type of epilepsy caused by focal cortical dysplasia (FCD); hence the features were chosen as to provide the most common FCD-characteristics to the models.
+
+In this work we build on the method proposed in [1] that learns a one-class SVM (oc-SVM) model for each voxel individually. Our goal is to make a step forward by replacing the handcrafted features with automatically learnt representations using neural networks. Deep learning architectures allow to learn representations that are not limited to the clinically-guided features which have to be designed for each pathology individually; the representations are learnt based on the available data. Moreover, certain architectures provide a convenient framework to learn joint representations of multiparametric/multimodality imaging. Our methodological contribution consists in proposing a variant of siamese neural network designed to learn representations for outlier detection on brain images. The network is composed of stacked convolutional autoencoders and is trained on the patches of healthy brain volumes only, by utilizing a novel loss function adapted to the given context. Such a network allows learning meaningful representations which, coupled with voxel-level oc-SVM classifiers, discriminate various brain abnormalities and can be applied to detect subtle pathologies in general. From the medical application perspective, we attempt to make a step forward in automatically learning representations for epilepsy lesion detection, unlike in the previous studies ([1, 11]). Our approach is not targeted at one specific epilepsy type and thus is more generic and also detects lesions with rather unknown signatures. Moreover, to our knowledge, this is the first study to propose a neural network architecture trained on multiparametric MRI data that can be applied to detect epilepsy lesions.
+
+![](images/379d1acd31862d3fdd86f677c9c5a3757012cdcbec4108d9df3b1da960f0845c.jpg)  
+Figure 1: Siamese neural network composed of stacked convolutional autoencoders as sub-networks. The input consists of a pair of patches of 2 different subjects centered at the same spatial localization in the brain. The middle-layer representation is denoted by $g ( x )$ .
+
+# 2 Method
+
+In this study we propose to use a siamese network to learn patch-level representations in the context of outlier detection. Such an approach is applicable in cases where pathological samples are not available or their number is insufficient to adequately represent the nature of the pathology and hence, supervised learning is not possible.
+
+The motivation behind the architecture choice is the following. Our objective is to map the original patches to a space where the patches belonging to different subjects but centered at the same spatial localization are "close" with respect to a chosen metric. We could consider the patches centered at the same voxel as representatives of the same class (hence, "similar" patches). In this case the number of classes would be equal to the number of voxels in a brain volume (around 4 millions) but the number of samples per class would be equal to the number of subjects. The siamese networks have proved to be efficient in similar scenarios [15, 16] where the number of classes is largely greater than the number of samples per class.
+
+# 2.1 Regularized siamese neural network for representation learning
+
+# 2.1.1 Architecture
+
+The proposed architecture is illustrated on figure 1. Our regularized siamese neural network (rSNN) consists of two identical (same architecture, shared parameters) subnetworks - stacked convolutional autoencoders (sCAE) with $K$ hidden layers and a cost module. The input $\mathbf { x }$ of a SCAE is first encoded to a middle-layer representation by a series of convolutional and max-pooling operations and later decoded with a series of deconvolutions and up-poolings to produce a reconstruction $\hat { \bf x }$ of the input. A convolutional layer $l$ is composed of $N _ { l }$ kernels and biases and can be expressed as
+
+$$
+\mathbf { H } _ { l } ^ { m } = f ( \mathbf { W } _ { l - 1 } ^ { m } * \mathbf { H } _ { l - 1 } + b _ { l - 1 } ^ { m } )
+$$
+
+where $\mathbf { H } _ { l } ^ { m }$ is the $m$ -th feature map of the convolutional layer $l$ , $\mathbf { W } _ { l } ^ { m }$ is the kernel matrix associated with $\mathbf { H } _ { l } ^ { m }$ and $b _ { l } ^ { m }$ is its bias, $f$ is an activation function (usually non-linear). $^ *$ denotes the convolution operation. The parameters are iteratively updated to optimize a loss function that measures the deviation between the output $\hat { \bf x }$ and the input $\mathbf { x }$ .
+
+The siamese network receives a pair of patches $\left( \mathbf { x _ { 1 } } , \mathbf { x _ { 2 } } \right)$ at input, then each patch is propagated through the corresponding subnetwork yielding representations $g ( \mathbf { x _ { t } } ) , t \ = \ ( 1 , 2 )$ in the middle layer which are then passed to the loss function $L$ below. It is important to mention that, unlike in the classical siamese frameworks where the network also receives a binary label that stands for the similarity/dissimilarity of the pair, in our application all the considered pairs are ’similar’ and therefore the label is not present in the loss function. The loss function, however, can be easily modified to meet the general setting.
+
+# 2.1.2 Loss function
+
+Our loss function is designed to maximize the cosine similarity between $g ( \mathbf { x _ { 1 } } )$ and $g ( \mathbf { x _ { 2 } } )$ . In the absence of dissimilar pairs (the notion of dissimilar patches is not defined in our context), it is necessary to add a regularizing term. To this end, we propose to use the mean squared error between the input patches and their reconstructions output by the subnetworks. Without a proper regularization term, the loss function could be driven to 0 by mapping all the patches to a constant value. The proposed loss function for a single pair hence is:
+
+$$
+L ( \mathbf { x _ { 1 } } , \mathbf { x _ { 2 } } ; \Theta ) = \sum _ { t = 1 } ^ { 2 } | | \mathbf { x _ { t } } - { \hat { \mathbf { x _ { t } } } } | | _ { 2 } ^ { 2 } - \alpha c o s ( g ( \mathbf { x _ { 1 } } ) , g ( \mathbf { x _ { 2 } } ) )
+$$
+
+where $\hat { \mathbf { x } } _ { \mathbf { t } }$ is the reconstructed output of subnetwork $t$ of the patch $\mathbf { x _ { t } }$ while $g ( \mathbf { x _ { t } } )$ is its (vectorized) representation in the middle layer and $\alpha$ is a coefficient that controls the tradeoff between the two terms. $\Theta$ represents the parameter set.
+
+# 2.2 Voxel-level outlier detection with oc-SVM classifiers
+
+A oc-SVM classifier [17] is an outlier detection method that seeks to find the optimal hyperplane that separates the given points from the origin in a dot product space defined by some kernel function $\phi$ . The corresponding optimization problem is the following:
+
+$$
+\begin{array} { l } { \displaystyle \underset { \mathbf { w } , \rho , \xi _ { i } } { \operatorname* { m i n } } \quad \displaystyle \frac { 1 } { 2 } | | \mathbf { w } | | ^ { 2 } - \rho + \frac { 1 } { \nu \mathrm { n } } \sum _ { \mathrm { i } = 1 } ^ { \mathrm { n } } \xi _ { \mathrm { i } } } \\ { \displaystyle \mathrm { s u b j e c t ~ t o } \quad \mathbf { w } \cdot \phi ( \mathbf { x _ { i } } ) \geq \rho - \xi _ { \mathrm { i } } , \xi _ { \mathrm { i } } \geq 0 , \mathrm { i } \in [ 1 , \mathrm { n } ] } \end{array}
+$$
+
+where $n$ is the number of training examples, $\mathbf { x _ { i } }$ is the $i$ -th example in the training dataset $X$ , $\xi _ { i }$ -s are slack variables relaxing the inequality constraints as to account for the non-separable classes, w and $\rho$ define the separating hyperplane, $\nu$ is a parameter that sets a boundary to the fraction of outliers allowed. The decision function, then, for an example $\mathbf { x }$ is ${ \bf w } \cdot \phi ( { \bf x } ) - \dot { \rho }$ . This decision function contributes to the signed score output by a oc-SVM model (in a typical scenario examples with negatives scores would be considered outliers).
+
+To validate the usefulness of the features learnt by the proposed method, we use the representations in the middle layer of the subnetworks $( g ( \mathbf { x } ) )$ to train oc-SVM classifiers at voxel level. Each voxel is associated with a classifier, hence the number of classifiers is equal to the number of voxels in a volume (around 4 million voxels). For a given voxel $v _ { i }$ , the associated oc-SVM classifier $C _ { i }$ is trained on the matrix $M _ { i } = [ \bf { x _ { i 1 } } , . . . , \bf { x _ { i n } } ]$ where $\mathbf { x _ { i j } }$ is the feature vector corresponding to the patch centered at $v _ { i }$ of subject $j$ and $n$ is the number of subjects.
+
+For a new patient, each voxel $v _ { i }$ is matched against the corresponding classifier $C _ { i }$ and is assigned the signed score output by the classifier. This yields a distance map $D _ { p }$ for the given patient.
+
+# 2.3 Post-processing
+
+For a given patient, the output of the previous step - the distance map $D _ { p }$ - is then post-processed to obtain the final detections. A 3-step post-processing is proposed as follows.
+
+The first step consists in normalizing the distance maps with respect to the intra-subject spatial variability. For that purpose, the distance maps of the control subjects are computed by performing a $k$ -fold evaluation of the controls in the training set (i.e. for each fold of normal subjects, the distance maps are obtained with oc-SVMs trained on the remaining subjects). These maps are used to estimate the standard deviation of the normal subjects’ distance distribution at voxel-level. For a given patient $p$ , a new map $\acute { D } _ { p }$ is computed by a voxel-wise division of the output distance map $D _ { p }$ over the estimated standard deviations. The final distance map $F _ { p }$ is then derived by averaging $D _ { p }$ and $\acute { D } _ { p }$ i.e. $\begin{array} { r } { F _ { p } = \frac { 1 } { 2 } ( \frac { D _ { p } } { m a x ( a b s ( D _ { p } ) ) } + \frac { \dot { D } _ { p } } { m a x ( a b s ( \dot { D } _ { p } ) } ) ) } \end{array}$ . The reason behind the additional term is that some zones in the brain have more intra-subject variability than others and therefore are more likely to be considered as anomalies. By weighing them by the standard deviation, the score maps account for this effect. The second step consists in thresholding the $F _ { p }$ map to produce a cluster map. We keep the most negative scores up to the score corresponding to a pre-chosen $p$ -value in the patient’s distance score distribution and apply a 26-connectivity rule to identify connected components which we refer to as clusters. The voxel clusters smaller than a fixed size (here, 82 voxels corresponding to the expected cluster size calculated with the SPM analysis of the T1 MRI data) are discarded. This allows quick elimination of small and very negative clusters which usually represent isolated intensity peaks (the size of the majority of the detected clusters varies between 500 and 1500, this threshold therefore does not affect the performance in any significant way). The clusters are what we refer to as detections by the proposed method. By varying the $p$ -value the number of clusters can be controlled according to a clinician’s needs.
+
+The third step consists in ranking the detected clusters to help the analysis of the detections. For each patient individually, a $p$ -value is found that produces at most 15 clusters. Among those, we use the following ranking criterion to assign a rank to a cluster $c _ { i }$
+
+$$
+r a n k ( \mathbf { c _ { i } } ) \sim \lambda * \frac { s c o r e ( \mathbf { c _ { i } } ) } { m i n _ { j } s c o r e ( \mathbf { c _ { j } } ) } + ( 1 - \lambda ) * \frac { s i z e ( \mathbf { c _ { i } } ) } { m a x _ { j } s i z e ( \mathbf { c _ { j } } ) }
+$$
+
+where $s c o r e ( c _ { i } )$ is the average of the voxel scores in the cluster and $s i z e ( c _ { i } )$ is the number of voxels in the cluster. Such a ranking favors large clusters with the most negative average score. Using this ranking, we keep the top $n$ detections and discard the rest. When there is a significant overlap between a detected cluster and the ground truth for a given patient, we consider the cluster a true positive and false positive otherwise.
+
+# 3 Experiments and results
+
+# 3.1 Dataset description and pre-processing
+
+The study was approved by our institutional review board with approval numbers 2012-A00516-37 and 2014-019 B and a written consent was obtained for all participants.
+
+Our database consists of multiparametric (T1-weighted and FLAIR) MR images of 75 healthy subjects and 21 patients. They all had a 3D anatomical T1-weighted brain MRI (TR/TE 2400/3.55; 160 sagittal slices of $1 9 2 \mathrm { ~ x ~ } 1 9 2 \ 1 . 2 \mathrm { m m }$ cubic voxels) and FLAIR (176 sagittal slices of $1 9 6 \times 2 5 6 ~ 1 . 2 \mathrm { m m }$ cubic voxels) on a $1 . 5 \mathrm { T }$ Sonata scanner (Siemens Healthcare, Erlangen, Germany). All the volumes were normalized to the standard brain template of the Montreal Neurological Institute (MNI) [18] using a voxel size of $1 \mathrm { ~ x ~ } 1 \mathrm { ~ x ~ } 1 \mathrm { ~ m m }$ . This processing was performed using the unified segmentation algorithm [19] implemented in SPM12 also correcting for magnetic field inhomogeneities. This spatial normalisation assures a voxel-level correspondence between the subjects. We removed top $1 \%$ intensities and scaled the images between 0 and 1 at image level before feeding the patches to the rSNN.
+
+The method has been validated on 21 patients admitted to our clinical center with confirmed medically intractable epileptogenic lesions: 2 of them were visually detected on the patient FLAIR images (but not on T1w images) and only 1 lesion was identified on both T1w and FLAIR scans. The remaining 18 patients are confirmed MR negative patients. The MR negative patients had undertaken surgeries and have been seizure-free since. The ground truth annotations used in the performance evaluation were obtained by outlining the visible zones of the MR positive patients and by combining the information of post-surgical MR images and the resected zones for MR negative patients.
+
+# 3.2 Feature extraction with SNN
+
+The proposed rSNN consists of two identical subnetworks - stacked convolutional autoencoders with the architecture as in fig. 2. In the mono-modal scenario, they both receive at input $1 5 \mathrm { x } 1 5$ patches extracted from all the available healthy subjects’ volumes of the corresponding modality (T1w or FLAIR) with a stride of 8. In the multi-modal scenario, the input consists of the patches of each modality joint as channels. For each of the patches, a random ’similar pair’ is found among the other subjects yielding in total around 3.5 million pairs. The $\alpha$ parameter in the loss 1 is set to 0 during the first 10 epochs, then grows linearly for 15 epochs until it reaches 0.5 and then plateaus for 5 more epochs. We used ReLU activation function in all the layers except the last one where the sigmoid is used (the input patches are scaled between 0 and 1). The Adam optimizer was used with the learning rate set to 0.001 (the rest of the parameters remained at their default value as implemented in Theano). The architecture itself is not arbitrary. The size of the patches at input was chosen after a number of tested configurations and is justified by the subtle nature of epilepsy lesions. Indeed, larger patch sizes were not successful at detecting subtle lesions. Since the middle-layer representations are used to build oc-SVM models per voxel where the number of samples per model is equal to the number of subjects, having large representation vectors would not be beneficial. As shown on figure 2 the middle layer has 16 feature maps of $2 \mathbf { x } 2$ which, when flattened, yields a 64-dimensional vector.
+
+![](images/8c1689631af765b6514824b37c2b48ac6ee9b2e10d4d832a8dd23349dd997268.jpg)  
+Figure 2: rSNN subnetwork architecture for epilepsy lesion detection. $C$ and $D C$ denote convolutional and deconvolutional layers respectively, $M P$ and $U P$ denote Maxpooling and Uppooling. The C and DC layers are denoted with the number of features maps (e.g. 16 for the first C layer) and the kernel size in parenthesis (e.g. 3x3 for the first C layer). With this configuration, the middle-layer is composed of 16 feature maps of size $2 \mathbf { x } 2$ which yields a 64-dimensional representation vector $g ( \mathbf { x } )$ when flattened.
+
+# 3.3 oc-SVM classifier design
+
+We used oc-SVM classifiers with RBF kernel which gives us two parameters to tune - $\nu$ (upper bound on the fraction of permitted outliers) and $\gamma$ (the kernel parameter). Varying the parameter $\nu$ did not significantly impact the results; the fraction of the outliers is controlled in the post-processing step by the threshold value applied on the distance map. It was set to 0.03 for all the voxels. The $\gamma$ parameter was derived for each voxel $v _ { i }$ individually by estimating the median of the standardized euclidean pairwise distances of the corresponding matrix $M _ { i }$ (see section 2.2) as in [20].
+
+# 3.4 Results
+
+Below we evaluate the performance of the system on 21 patients with confirmed epilepsy lesions. We first demonstrate the advantage of the multi-modal approach versus mono-modal approaches. Fig. 3 shows the true detection rates among the top $n$ clusters for 3 scenarios - voxel-level outlier detection with T1w-only, FLAIR-only and T1w/FLAIR-trained features, for 3 values of $\lambda$ of expression 3, the trade-off coefficient between the cluster size and average score. It clearly demonstrates that features learnt on the combination of multimodality data outperform the individual modalities. Moreover, the figure shows that ranking the clusters by both their average score and size has an advantage over the individual criteria. With this ranking approach, the multimodal model achieves $62 \%$ of true detections among the top 10 clusters. [11] reports a detection rate of $70 \%$ when individual SBM-based features are used; the results vary between 60 and $70 \%$ when considering combinations of some of these SBM features. 2 of the 3 MR positive lesions were detected among the top 2 clusters. This result is expected considering that visually detected lesions have visible markers that allow to distinguish them easily unlike the MR negative patients whose lesions may be detected along with other outliers of similar ’suspiciousness’.
+
+We have also compared the global results of our CAD system to the results obtained with a general linear model (GLM) learned on feature maps derived from T1w images using three settings - 1. junction contrast, 2.extension contrast and 3. the conjunction of both contrasts - for a $p$ -value of 0.001 as done in [1]. These features model the junction between gray and white matters as described in [13, 14]. For a fair comparison, the same clustering and ranking procedures (as described in section 2.3) were applied and only the top 10 clusters were considered. The results are summarized in table 1. While extension contrast detects one additional lesion compared with our mono-modal T1-based approach, the combination of junction and extension contrasts does not achieve our best performance with T1w/FLAIR model. We should also note that without applying the ranking method the original SPM implementation produces much more false positive detections without any significant change in the true positive rate.
+
+![](images/d52c1d823009fafd5fb564e67089e19907bdd7ccc8c2198edcd3710190693a14.jpg)  
+Figure 3: The performance of the CAD system. $\mathbf { X }$ -axis: Top $n$ clusters, y-axis: Detection rate among the top $n$ clusters. From left to right: $\lambda = 1$ (score-only), $\lambda = 0 . 5$ (score and size average) and $\lambda = 0$ (size-only) ranking criteria.
+
+Table 1: Our system versus GLM model on T1w MRI as implemented in SPM software. First column: the true positive rate; the number of detected patients / total number of patients in parenthesis. Second column: the true positive rate calculated on MRI negative patients only. Third column: the average number of false positive detections per patient.   
+
+<table><tr><td></td><td>True positive rate</td><td>True positive rate on MR negative patients</td><td>Average # of false positives</td></tr><tr><td>rSNN +oc-SVMon T1 (ranked, top 10)</td><td>0.38 (8/21)</td><td>0.38 (7/18)</td><td>9</td></tr><tr><td>rSNN + oc-SVM on FLAIR (ranked,top 10)</td><td>0.52 (11/21)</td><td>0.5 (9/18)</td><td>9</td></tr><tr><td>rSNN + oc-SVMon T1/FLAIR (ranked,top 10)</td><td>0.62 (13/21)</td><td>0.61 (11/18)</td><td>9</td></tr><tr><td>SPMJunction on T1 (ranked,top 10)</td><td>0.28 (6/21)</td><td>0.27 (5/18)</td><td>9</td></tr><tr><td>SPM Extension on T1 (ranked,top 10)</td><td>0.43 (9/21)</td><td>0.44 (8/18)</td><td>9</td></tr><tr><td>SPM Junction-Extension on T1 (ranked, top 10)</td><td>0.24 (5/21)</td><td>0.22 (4/18)</td><td>9</td></tr></table>
+
+![](images/0f5acdc24796b148a1840d3364e95dcbe798680b3e3996cab22fe1d2aa6836af.jpg)  
+Figure 4: CAD system output for patients $A ^ { + }$ , $B ^ { - }$ and $C ^ { - }$ respectively ( $^ +$ stands for MR positive patients, − for MR negative patients). Top row: Transverse slices centered at the lesion locations (highlighted in red circles). Bottom row: Maximum intensity projections (MIP) of the cluster maps overlaid on the MRI transverse slices. The maps show the top 1, top 6 and top 3 clusters, respectively.
+
+# 4 Discussion
+
+This study presents a novel method to learn representations that can be used in the task of anomaly detection on brain images. We have formulated a regularized siamese network architecture that learns normal brain representations using a set of non-pathological MR volumes. The features learnt with the network do not target specific pathology but rather allow to capture normal variability from a cohort of healthy subjects. The framework allows integrating multiple modalities and we have shown the performance gain obtained by coupling T1w and FLAIR imaging for the task of detecting subtle epilepsy lesions in MRI negative patients. To our knowledge, this is the first attempt to use deep learning for epilepsy lesion detection.
+
+Most current studies target a specific type of the pathology, referred to as focal cortical dysplasia (FCD), mainly resulting from a malformation of cortical development and leading to drug-resistant epilepsy lesions. Some of these studies use manually designed features characterizing cortical malformations based on surface based morphometry (SBM) [9, 11, 12]. Others associate these morphometric features to the intensity anomalies in T1w MRI mainly caused by heterotopy lesions [1, 8]. Our method seeks to find more complex features in an unsupervised manner in order to identify lesions with unknown signatures. Naturally, such an approach, when applied to a specific pathology, is likely to produce more false positive detections. Although a fair comparison with published results is difficult because of the differences in the patient groups, results reported in table 1 ( $6 2 \%$ sensitivity for 9 false positives per scan) are of the same order as those reported in recent studies for the difficult task of automated detection in MRI-negative patients. Indeed, the system proposed in [11] based on SBM features coupled with semi-supervised hierarchical conditional random fields achieves $70 \%$ sensitivity on a sample of $2 0 \mathrm { T } 1$ weighted MRI negative patients among the top 10 detections per scan. In [1], a CAD system based on morphometric and intensity features coupled with a oc-SVM classifier allows achieving the same $70 \%$ sensitivity with an average of 4 false positives per scan when evaluated on a small cohort of 8 T1w MRI negative patients.
+
+There are different options to improve the diagnostic performance of the proposed system. First, some pathology-specific information could be introduced in the post-processing step, by discarding some of the detected clusters based on shape and/or localization criteria. In the majority of the cases, as shown in figure 4, most of the detected false positive clusters are indeed irregularities that can be easily removed by a trained radiologist. An alternative option is to move towards a semi-supervised setting by enhancing the neural network with a few ’pathological’ patches that could be extracted from MRI positive cases or after a careful analysis of retrospective MRI negative patients, following, for instance, some ideas recently proposed in [21]. More improvement could be achieved by accounting for the complementary information provided by different imaging modalities. T1 and FLAIR modalities, introduced as channels to our network, allowed a significant diagnostic performance gain as shown on figure 3. We expect a further performance gain by exploiting PET imaging as recently demonstrated in [22].
+
+Finally, the proposed method is quite straightforward to implement and to apply in daily practice as the output of the system can be obtained under a couple of minutes.
+
+# 5 Acknowledgements
+
+This work was performed within the framework of the LABEX PRIMES (ANR-11-LABX-0063) of Université de Lyon, within the program "Investissements d’Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The authors sincerely thank Valentin Hoang for his valuable contribution to the SPM analysis.
+
+# References
+
+[1] M. El Azami, A. Hammers, J. Jung, N. Costes, R. Bouet, and C. Lartizien, “Detection of lesions underlying intractable epilepsy on t1-weighted mri as an outlier detection problem,” PloS one, vol. 11, no. 9, p. e0161498, 2016.   
+[2] P. Moeskops, M. A. Viergever, A. M. Mendrik, L. S. de Vries, M. J. Benders, and I. Išgum, “Automatic segmentation of mr brain images with a convolutional neural network,” IEEE transactions on medical imaging, vol. 35, no. 5, pp. 1252–1261, 2016.   
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+[7] F. Dubost, G. Bortsova, H. Adams, A. Ikram, W. J. Niessen, M. Vernooij, and M. De Bruijne, “Gp-unet: Lesion detection from weak labels with a 3d regression network,” in Medical Image Computing and Computer Assisted Intervention (MICCAI 2017) (M. Descoteaux, L. Maier-Hein, A. Franz, P. Jannin, D. L. Collins, and S. Duchesne, eds.), (Cham), pp. 214–221, Springer International Publishing, 2017.   
+[8] R. S. Gill, S.-J. Hong, F. Fadaie, B. Caldairou, B. Bernhardt, N. Bernasconi, and A. Bernasconi, “Automated detection of epileptogenic cortical malformations using multimodal mri,” in Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, pp. 349–356, Springer, 2017.   
+[9] S.-J. Hong, H. Kim, D. Schrader, N. Bernasconi, B. C. Bernhardt, and A. Bernasconi, “Automated detection of cortical dysplasia type ii in mri-negative epilepsy,” Neurology, vol. 83, no. 1, pp. 48–55, 2014.   
+[10] B. Ahmed, C. E. Brodley, K. E. Blackmon, R. Kuzniecky, G. Barash, C. Carlson, B. T. Quinn, W. K. Doyle, J. French, O. Devinsky, and T. Thesen, “Cortical feature analysis and machine learning improves detection of "mri-negative" focal cortical dysplasia.,” Epilepsy and behavior, vol. 48, pp. 21–8, 2015.   
+[11] B. Ahmed, T. Thesen, K. E. Blackmon, R. Kuzniekcy, O. Devinsky, and C. E. Brodley, “Decrypting "cryptogenic" epilepsy: Semi-supervised hierarchical conditional random fields for detecting cortical lesions in mri-negative patients,” Journal of Machine Learning Research, vol. 17, no. 112, pp. 1–30, 2016.   
+[12] T. Thesen, B. T. Quinn, C. Carlson, O. Devinsky, J. DuBois, C. R. McDonald, J. French, R. Leventer, O. Felsovalyi, X. Wang, et al., “Detection of epileptogenic cortical malformations with surface-based mri morphometry,” PloS one, vol. 6, no. 2, p. e16430, 2011.   
+[13] H.-J. Huppertz, C. Grimm, S. Fauser, J. Kassubek, I. Mader, A. Hochmuth, J. Spreer, and A. SchulzeBonhage, “Enhanced visualization of blurred gray–white matter junctions in focal cortical dysplasia by voxel-based 3d mri analysis,” Epilepsy research, vol. 67, no. 1-2, pp. 35–50, 2005.   
+[14] J. Wagner, B. Weber, H. Urbach, C. E. Elger, and H.-J. Huppertz, “Morphometric mri analysis improves detection of focal cortical dysplasia type ii,” Brain, vol. 134, no. 10, pp. 2844–2854, 2011.   
+[15] J. Bromley, J. W. Bentz, L. Bottou, I. Guyon, Y. LeCun, C. Moore, E. Säckinger, and R. Shah, “Signature verification using a "siamese" time delay neural network,” IJPRAI, vol. 7, no. 4, pp. 669–688, 1993.   
+[16] S. Chopra, R. Hadsell, and Y. LeCun, “Learning a similarity metric discriminatively, with application to face verification,” in Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on, vol. 1, pp. 539–546, IEEE, 2005.   
+[17] B. Schölkopf, J. C. Platt, J. Shawe-Taylor, A. J. Smola, and R. C. Williamson, “Estimating the support of a high-dimensional distribution,” Neural computation, vol. 13, no. 7, pp. 1443–1471, 2001.   
+[18] J. Mazziotta, A. Toga, A. Evans, P. Fox, J. Lancaster, K. Zilles, R. Woods, T. Paus, G. Simpson, B. Pike, et al., “A probabilistic atlas and reference system for the human brain: International consortium for brain mapping (icbm),” Philosophical Transactions of the Royal Society of London B: Biological Sciences, vol. 356, no. 1412, pp. 1293–1322, 2001.   
+[19] J. Ashburner and K. Friston, “Unified segmentation,” Neuroimage, vol. 26, pp. 839–851, 2005.   
+[20] B. Caputo, K. Sim, F. Furesjo, and A. Smola, “Appearance-based object recognition using svms: which kernel should i use?,” in Proc of NIPS workshop on Statistical methods for computational experiments in visual processing and computer vision, Whistler, vol. 2002, 2002.   
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+[22] Y. L. Tan, H. Kim, S. Lee, T. Tihan, L. Ver Hoef, S. G. Mueller, A. J. Barkovich, D. Xu, and R. Knowlton, “Quantitative surface analysis of combined mri and pet enhances detection of focal cortical dysplasias.,” Neuroimage, vol. 166, pp. 10–18, 2018.

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+        "text": "Regularized siamese neural network for unsupervised outlier detection on brain multiparametric magnetic resonance imaging: application to epilepsy lesion screening ",
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+        "text": "Zara Alaverdyan   \nUniv Lyon, INSA-Lyon, Université Claude Bernard Lyon 1,   \nUJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621, Lyon, France zaruhi.alaverdyan@creatis.insa-lyon.fr ",
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+        "text": "Julien Jung, Romain Bouet Lyon Neuroscience Research Center, CRNL, INSERM U1028, CNRS UMR5292, University Lyon 1, Lyon, France {julien.jung, romain.bouet}@inserm.fr ",
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+        "text": "Carole Lartizien   \nUniv Lyon, INSA-Lyon, Université Claude Bernard Lyon 1,   \nUJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621, Lyon, France carole.lartizien@creatis.insa-lyon.fr ",
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+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+        "text": "Computer aided diagnosis (CAD) systems are designed to assist clinicians in various tasks, including highlighting abnormal regions in medical images. Common methods exploit supervised learning using annotated data sets and perform classification at voxel-level. However, many pathologies are characterized by subtle lesions that may be located anywhere in the organ of interest, have various shapes, sizes and textures. Acquiring a data set adequately representing the heterogeneity of such pathologies is therefore a major issue. Moreover, when a lesion is not visually detected on a scan, outlining it accurately is not feasible. Performing supervised learning on such labeled data would not be reliable. In this study, we consider the problem of detecting subtle epilepsy lesions in multiparametric (T1w, FLAIR) MRI exams considered as normal (MRI-negative). We cast this problem as an outlier detection problem and build on a previously proposed approach that consists in learning a oc-SVM model for each voxel in the brain volume using a small number of clinically-guided features [1]. Our goal in this study is to make a step forward by replacing the handcrafted features with automatically learnt representations using neural networks. We propose a novel version of siamese networks trained on patches extracted from healthy patients’ scans only. This network, composed of stacked convolutional autoencoders as subnetworks, is regularized by the reconstruction error of the patches. It is designed to map patches centered at the same spatial localization to ’close’ representations with respect to the chosen metric (i.e. cosine) in a latent space. Finally, the middle layer representations of the subnetworks are fed into oc-SVM models at voxel-level. The model is trained on 75 healthy subjects and validated on 21 patients with confirmed epilepsy lesions (with 18 MR negative patients) and shows a promising performance. ",
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+        "text": "1 Introduction ",
+        "text_level": 1,
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+        "text": "Computer aided diagnosis (CAD) systems have been introduced as to assist clinicians in various tasks such as organ or lesion segmentation, detection of abnormal regions in a medical image, etc. Recent CAD systems for brain pathologies exploit various modalities of neuroimaging data, such as magnetic resonance imaging (MRI) and positron emission tomography (PET). The vast majority of the existing CAD systems are built upon methods developed in supervised settings, using either manually designed features or currently ubiquitous deep learning architectures as in [2, 3, 4, 5]. Such systems benefit from the available data sets (usually) annotated at voxel-level, and output maps where each voxel is characterized either by a class label, a probability or, less commonly, a score discriminating healthy versus pathological voxels. Supervised learning, however, cannot be applied when the number of pathological cases in the training set is not sufficient to account for the complexity of the task. This is often the case when it comes to detecting some brain pathologies such as small vessel diseases (SVD), multiple sclerosis (MS) or epilepsy, when the lesions are subtle and vary largely in terms of shapes and textures. It is not trivial to obtain a well-annotated data set to represent such a variability. To bypass the problem of insufficient labeled data, some authors recently proposed to formulate such lesion detection tasks in semi-supervised settings, by accounting for both labeled and unlabeled data in a deep architecture for MS lesion segmentation [6] or by exploiting weak labels (the number of lesions in a scan) to detect enlarged perivascular spaces in the basal ganglia [7]. ",
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+        "text": "In this study we propose to tackle the problem of epilepsy lesion detection in patients with MRI negative exams, meaning that the lesions were not visually identified by clinicians on the MR scans. Similarly to the above mentioned lesion detection tasks, most of the current epilepsy detection methods perform supervised learning by leveraging annotated lesions delineated on MRI positive patients (the lesions are visually detected on the scans) [8] or by careful a posteriori re-reading of postsurgical scans of MRI negative patients who had undergone surgery and were seizure-free afterwards [1, 9, 10, 11]. While obtaining accurately labeled data for MRI positive patients is feasible, the real challenge is to extract accurate delineations in MRI negative patients. [11] showed that exploiting ’too generously’ annotated lesions on MRI negative scans as labels for supervised learning methods leads to poor detection rate due to the presence of normal tissue in the areas labeled as pathological. Therefore, some recent methods cast epilepsy lesion detection task as an outlier detection problem [1, 11, 12]. Such an approach solely needs a training set of non-pathological images, hence no labeled data is required. [1] used a small number of features modeling the gray-white matter junction (similarly to [13, 14]) while [12] and [11] derived features from surface based morphometry (SBM). All the latter methods targeted a specific type of epilepsy caused by focal cortical dysplasia (FCD); hence the features were chosen as to provide the most common FCD-characteristics to the models. ",
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+        "text": "In this work we build on the method proposed in [1] that learns a one-class SVM (oc-SVM) model for each voxel individually. Our goal is to make a step forward by replacing the handcrafted features with automatically learnt representations using neural networks. Deep learning architectures allow to learn representations that are not limited to the clinically-guided features which have to be designed for each pathology individually; the representations are learnt based on the available data. Moreover, certain architectures provide a convenient framework to learn joint representations of multiparametric/multimodality imaging. Our methodological contribution consists in proposing a variant of siamese neural network designed to learn representations for outlier detection on brain images. The network is composed of stacked convolutional autoencoders and is trained on the patches of healthy brain volumes only, by utilizing a novel loss function adapted to the given context. Such a network allows learning meaningful representations which, coupled with voxel-level oc-SVM classifiers, discriminate various brain abnormalities and can be applied to detect subtle pathologies in general. From the medical application perspective, we attempt to make a step forward in automatically learning representations for epilepsy lesion detection, unlike in the previous studies ([1, 11]). Our approach is not targeted at one specific epilepsy type and thus is more generic and also detects lesions with rather unknown signatures. Moreover, to our knowledge, this is the first study to propose a neural network architecture trained on multiparametric MRI data that can be applied to detect epilepsy lesions. ",
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+        "image_caption": [
+            "Figure 1: Siamese neural network composed of stacked convolutional autoencoders as sub-networks. The input consists of a pair of patches of 2 different subjects centered at the same spatial localization in the brain. The middle-layer representation is denoted by $g ( x )$ . "
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+        "text": "2 Method ",
+        "text_level": 1,
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+    },
+    {
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+        "text": "In this study we propose to use a siamese network to learn patch-level representations in the context of outlier detection. Such an approach is applicable in cases where pathological samples are not available or their number is insufficient to adequately represent the nature of the pathology and hence, supervised learning is not possible. ",
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+        "text": "The motivation behind the architecture choice is the following. Our objective is to map the original patches to a space where the patches belonging to different subjects but centered at the same spatial localization are \"close\" with respect to a chosen metric. We could consider the patches centered at the same voxel as representatives of the same class (hence, \"similar\" patches). In this case the number of classes would be equal to the number of voxels in a brain volume (around 4 millions) but the number of samples per class would be equal to the number of subjects. The siamese networks have proved to be efficient in similar scenarios [15, 16] where the number of classes is largely greater than the number of samples per class. ",
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+        "text": "2.1 Regularized siamese neural network for representation learning ",
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+        "text": "The proposed architecture is illustrated on figure 1. Our regularized siamese neural network (rSNN) consists of two identical (same architecture, shared parameters) subnetworks - stacked convolutional autoencoders (sCAE) with $K$ hidden layers and a cost module. The input $\\mathbf { x }$ of a SCAE is first encoded to a middle-layer representation by a series of convolutional and max-pooling operations and later decoded with a series of deconvolutions and up-poolings to produce a reconstruction $\\hat { \\bf x }$ of the input. A convolutional layer $l$ is composed of $N _ { l }$ kernels and biases and can be expressed as ",
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+        "text": "$$\n\\mathbf { H } _ { l } ^ { m } = f ( \\mathbf { W } _ { l - 1 } ^ { m } * \\mathbf { H } _ { l - 1 } + b _ { l - 1 } ^ { m } )\n$$",
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+        "text": "where $\\mathbf { H } _ { l } ^ { m }$ is the $m$ -th feature map of the convolutional layer $l$ , $\\mathbf { W } _ { l } ^ { m }$ is the kernel matrix associated with $\\mathbf { H } _ { l } ^ { m }$ and $b _ { l } ^ { m }$ is its bias, $f$ is an activation function (usually non-linear). $^ *$ denotes the convolution operation. The parameters are iteratively updated to optimize a loss function that measures the deviation between the output $\\hat { \\bf x }$ and the input $\\mathbf { x }$ . ",
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+        "text": "The siamese network receives a pair of patches $\\left( \\mathbf { x _ { 1 } } , \\mathbf { x _ { 2 } } \\right)$ at input, then each patch is propagated through the corresponding subnetwork yielding representations $g ( \\mathbf { x _ { t } } ) , t \\ = \\ ( 1 , 2 )$ in the middle layer which are then passed to the loss function $L$ below. It is important to mention that, unlike in the classical siamese frameworks where the network also receives a binary label that stands for the similarity/dissimilarity of the pair, in our application all the considered pairs are ’similar’ and therefore the label is not present in the loss function. The loss function, however, can be easily modified to meet the general setting. ",
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+        "text": "2.1.2 Loss function ",
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+        "text": "Our loss function is designed to maximize the cosine similarity between $g ( \\mathbf { x _ { 1 } } )$ and $g ( \\mathbf { x _ { 2 } } )$ . In the absence of dissimilar pairs (the notion of dissimilar patches is not defined in our context), it is necessary to add a regularizing term. To this end, we propose to use the mean squared error between the input patches and their reconstructions output by the subnetworks. Without a proper regularization term, the loss function could be driven to 0 by mapping all the patches to a constant value. The proposed loss function for a single pair hence is: ",
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+        "text": "$$\nL ( \\mathbf { x _ { 1 } } , \\mathbf { x _ { 2 } } ; \\Theta ) = \\sum _ { t = 1 } ^ { 2 } | | \\mathbf { x _ { t } } - { \\hat { \\mathbf { x _ { t } } } } | | _ { 2 } ^ { 2 } - \\alpha c o s ( g ( \\mathbf { x _ { 1 } } ) , g ( \\mathbf { x _ { 2 } } ) )\n$$",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where $\\hat { \\mathbf { x } } _ { \\mathbf { t } }$ is the reconstructed output of subnetwork $t$ of the patch $\\mathbf { x _ { t } }$ while $g ( \\mathbf { x _ { t } } )$ is its (vectorized) representation in the middle layer and $\\alpha$ is a coefficient that controls the tradeoff between the two terms. $\\Theta$ represents the parameter set. ",
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+        "type": "text",
+        "text": "2.2 Voxel-level outlier detection with oc-SVM classifiers ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "A oc-SVM classifier [17] is an outlier detection method that seeks to find the optimal hyperplane that separates the given points from the origin in a dot product space defined by some kernel function $\\phi$ . The corresponding optimization problem is the following: ",
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+        "type": "equation",
+        "img_path": "images/8d6cfe422f8006d9c2903196fb701b57b77c86308c7131d009c07640f336a280.jpg",
+        "text": "$$\n\\begin{array} { l } { \\displaystyle \\underset { \\mathbf { w } , \\rho , \\xi _ { i } } { \\operatorname* { m i n } } \\quad \\displaystyle \\frac { 1 } { 2 } | | \\mathbf { w } | | ^ { 2 } - \\rho + \\frac { 1 } { \\nu \\mathrm { n } } \\sum _ { \\mathrm { i } = 1 } ^ { \\mathrm { n } } \\xi _ { \\mathrm { i } } } \\\\ { \\displaystyle \\mathrm { s u b j e c t ~ t o } \\quad \\mathbf { w } \\cdot \\phi ( \\mathbf { x _ { i } } ) \\geq \\rho - \\xi _ { \\mathrm { i } } , \\xi _ { \\mathrm { i } } \\geq 0 , \\mathrm { i } \\in [ 1 , \\mathrm { n } ] } \\end{array}\n$$",
+        "text_format": "latex",
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+    },
+    {
+        "type": "text",
+        "text": "where $n$ is the number of training examples, $\\mathbf { x _ { i } }$ is the $i$ -th example in the training dataset $X$ , $\\xi _ { i }$ -s are slack variables relaxing the inequality constraints as to account for the non-separable classes, w and $\\rho$ define the separating hyperplane, $\\nu$ is a parameter that sets a boundary to the fraction of outliers allowed. The decision function, then, for an example $\\mathbf { x }$ is ${ \\bf w } \\cdot \\phi ( { \\bf x } ) - \\dot { \\rho }$ . This decision function contributes to the signed score output by a oc-SVM model (in a typical scenario examples with negatives scores would be considered outliers). ",
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+    {
+        "type": "text",
+        "text": "To validate the usefulness of the features learnt by the proposed method, we use the representations in the middle layer of the subnetworks $( g ( \\mathbf { x } ) )$ to train oc-SVM classifiers at voxel level. Each voxel is associated with a classifier, hence the number of classifiers is equal to the number of voxels in a volume (around 4 million voxels). For a given voxel $v _ { i }$ , the associated oc-SVM classifier $C _ { i }$ is trained on the matrix $M _ { i } = [ \\bf { x _ { i 1 } } , . . . , \\bf { x _ { i n } } ]$ where $\\mathbf { x _ { i j } }$ is the feature vector corresponding to the patch centered at $v _ { i }$ of subject $j$ and $n$ is the number of subjects. ",
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+        "type": "text",
+        "text": "For a new patient, each voxel $v _ { i }$ is matched against the corresponding classifier $C _ { i }$ and is assigned the signed score output by the classifier. This yields a distance map $D _ { p }$ for the given patient. ",
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+        "type": "text",
+        "text": "2.3 Post-processing ",
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+        "type": "text",
+        "text": "For a given patient, the output of the previous step - the distance map $D _ { p }$ - is then post-processed to obtain the final detections. A 3-step post-processing is proposed as follows. ",
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+    {
+        "type": "text",
+        "text": "The first step consists in normalizing the distance maps with respect to the intra-subject spatial variability. For that purpose, the distance maps of the control subjects are computed by performing a $k$ -fold evaluation of the controls in the training set (i.e. for each fold of normal subjects, the distance maps are obtained with oc-SVMs trained on the remaining subjects). These maps are used to estimate the standard deviation of the normal subjects’ distance distribution at voxel-level. For a given patient $p$ , a new map $\\acute { D } _ { p }$ is computed by a voxel-wise division of the output distance map $D _ { p }$ over the estimated standard deviations. The final distance map $F _ { p }$ is then derived by averaging $D _ { p }$ and $\\acute { D } _ { p }$ i.e. $\\begin{array} { r } { F _ { p } = \\frac { 1 } { 2 } ( \\frac { D _ { p } } { m a x ( a b s ( D _ { p } ) ) } + \\frac { \\dot { D } _ { p } } { m a x ( a b s ( \\dot { D } _ { p } ) } ) ) } \\end{array}$ . The reason behind the additional term is that some zones in the brain have more intra-subject variability than others and therefore are more likely to be considered as anomalies. By weighing them by the standard deviation, the score maps account for this effect. The second step consists in thresholding the $F _ { p }$ map to produce a cluster map. We keep the most negative scores up to the score corresponding to a pre-chosen $p$ -value in the patient’s distance score distribution and apply a 26-connectivity rule to identify connected components which we refer to as clusters. The voxel clusters smaller than a fixed size (here, 82 voxels corresponding to the expected cluster size calculated with the SPM analysis of the T1 MRI data) are discarded. This allows quick elimination of small and very negative clusters which usually represent isolated intensity peaks (the size of the majority of the detected clusters varies between 500 and 1500, this threshold therefore does not affect the performance in any significant way). The clusters are what we refer to as detections by the proposed method. By varying the $p$ -value the number of clusters can be controlled according to a clinician’s needs. ",
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+        "type": "text",
+        "text": "",
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+        "type": "text",
+        "text": "The third step consists in ranking the detected clusters to help the analysis of the detections. For each patient individually, a $p$ -value is found that produces at most 15 clusters. Among those, we use the following ranking criterion to assign a rank to a cluster $c _ { i }$ ",
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+    {
+        "type": "equation",
+        "img_path": "images/8497df7c82fa844db1b58f6bfa190c6cbc3293bb3d1eb586085230ee4de4ea74.jpg",
+        "text": "$$\nr a n k ( \\mathbf { c _ { i } } ) \\sim \\lambda * \\frac { s c o r e ( \\mathbf { c _ { i } } ) } { m i n _ { j } s c o r e ( \\mathbf { c _ { j } } ) } + ( 1 - \\lambda ) * \\frac { s i z e ( \\mathbf { c _ { i } } ) } { m a x _ { j } s i z e ( \\mathbf { c _ { j } } ) }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where $s c o r e ( c _ { i } )$ is the average of the voxel scores in the cluster and $s i z e ( c _ { i } )$ is the number of voxels in the cluster. Such a ranking favors large clusters with the most negative average score. Using this ranking, we keep the top $n$ detections and discard the rest. When there is a significant overlap between a detected cluster and the ground truth for a given patient, we consider the cluster a true positive and false positive otherwise. ",
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+    {
+        "type": "text",
+        "text": "3 Experiments and results ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1 Dataset description and pre-processing ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The study was approved by our institutional review board with approval numbers 2012-A00516-37 and 2014-019 B and a written consent was obtained for all participants. ",
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+    {
+        "type": "text",
+        "text": "Our database consists of multiparametric (T1-weighted and FLAIR) MR images of 75 healthy subjects and 21 patients. They all had a 3D anatomical T1-weighted brain MRI (TR/TE 2400/3.55; 160 sagittal slices of $1 9 2 \\mathrm { ~ x ~ } 1 9 2 \\ 1 . 2 \\mathrm { m m }$ cubic voxels) and FLAIR (176 sagittal slices of $1 9 6 \\times 2 5 6 ~ 1 . 2 \\mathrm { m m }$ cubic voxels) on a $1 . 5 \\mathrm { T }$ Sonata scanner (Siemens Healthcare, Erlangen, Germany). All the volumes were normalized to the standard brain template of the Montreal Neurological Institute (MNI) [18] using a voxel size of $1 \\mathrm { ~ x ~ } 1 \\mathrm { ~ x ~ } 1 \\mathrm { ~ m m }$ . This processing was performed using the unified segmentation algorithm [19] implemented in SPM12 also correcting for magnetic field inhomogeneities. This spatial normalisation assures a voxel-level correspondence between the subjects. We removed top $1 \\%$ intensities and scaled the images between 0 and 1 at image level before feeding the patches to the rSNN. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The method has been validated on 21 patients admitted to our clinical center with confirmed medically intractable epileptogenic lesions: 2 of them were visually detected on the patient FLAIR images (but not on T1w images) and only 1 lesion was identified on both T1w and FLAIR scans. The remaining 18 patients are confirmed MR negative patients. The MR negative patients had undertaken surgeries and have been seizure-free since. The ground truth annotations used in the performance evaluation were obtained by outlining the visible zones of the MR positive patients and by combining the information of post-surgical MR images and the resected zones for MR negative patients. ",
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+    {
+        "type": "text",
+        "text": "3.2 Feature extraction with SNN ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The proposed rSNN consists of two identical subnetworks - stacked convolutional autoencoders with the architecture as in fig. 2. In the mono-modal scenario, they both receive at input $1 5 \\mathrm { x } 1 5$ patches extracted from all the available healthy subjects’ volumes of the corresponding modality (T1w or FLAIR) with a stride of 8. In the multi-modal scenario, the input consists of the patches of each modality joint as channels. For each of the patches, a random ’similar pair’ is found among the other subjects yielding in total around 3.5 million pairs. The $\\alpha$ parameter in the loss 1 is set to 0 during the first 10 epochs, then grows linearly for 15 epochs until it reaches 0.5 and then plateaus for 5 more epochs. We used ReLU activation function in all the layers except the last one where the sigmoid is used (the input patches are scaled between 0 and 1). The Adam optimizer was used with the learning rate set to 0.001 (the rest of the parameters remained at their default value as implemented in Theano). The architecture itself is not arbitrary. The size of the patches at input was chosen after a number of tested configurations and is justified by the subtle nature of epilepsy lesions. Indeed, larger patch sizes were not successful at detecting subtle lesions. Since the middle-layer representations are used to build oc-SVM models per voxel where the number of samples per model is equal to the number of subjects, having large representation vectors would not be beneficial. As shown on figure 2 the middle layer has 16 feature maps of $2 \\mathbf { x } 2$ which, when flattened, yields a 64-dimensional vector. ",
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+        "img_path": "images/8c1689631af765b6514824b37c2b48ac6ee9b2e10d4d832a8dd23349dd997268.jpg",
+        "image_caption": [
+            "Figure 2: rSNN subnetwork architecture for epilepsy lesion detection. $C$ and $D C$ denote convolutional and deconvolutional layers respectively, $M P$ and $U P$ denote Maxpooling and Uppooling. The C and DC layers are denoted with the number of features maps (e.g. 16 for the first C layer) and the kernel size in parenthesis (e.g. 3x3 for the first C layer). With this configuration, the middle-layer is composed of 16 feature maps of size $2 \\mathbf { x } 2$ which yields a 64-dimensional representation vector $g ( \\mathbf { x } )$ when flattened. "
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+    {
+        "type": "text",
+        "text": "3.3 oc-SVM classifier design ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We used oc-SVM classifiers with RBF kernel which gives us two parameters to tune - $\\nu$ (upper bound on the fraction of permitted outliers) and $\\gamma$ (the kernel parameter). Varying the parameter $\\nu$ did not significantly impact the results; the fraction of the outliers is controlled in the post-processing step by the threshold value applied on the distance map. It was set to 0.03 for all the voxels. The $\\gamma$ parameter was derived for each voxel $v _ { i }$ individually by estimating the median of the standardized euclidean pairwise distances of the corresponding matrix $M _ { i }$ (see section 2.2) as in [20]. ",
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+    {
+        "type": "text",
+        "text": "3.4 Results ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Below we evaluate the performance of the system on 21 patients with confirmed epilepsy lesions. We first demonstrate the advantage of the multi-modal approach versus mono-modal approaches. Fig. 3 shows the true detection rates among the top $n$ clusters for 3 scenarios - voxel-level outlier detection with T1w-only, FLAIR-only and T1w/FLAIR-trained features, for 3 values of $\\lambda$ of expression 3, the trade-off coefficient between the cluster size and average score. It clearly demonstrates that features learnt on the combination of multimodality data outperform the individual modalities. Moreover, the figure shows that ranking the clusters by both their average score and size has an advantage over the individual criteria. With this ranking approach, the multimodal model achieves $62 \\%$ of true detections among the top 10 clusters. [11] reports a detection rate of $70 \\%$ when individual SBM-based features are used; the results vary between 60 and $70 \\%$ when considering combinations of some of these SBM features. 2 of the 3 MR positive lesions were detected among the top 2 clusters. This result is expected considering that visually detected lesions have visible markers that allow to distinguish them easily unlike the MR negative patients whose lesions may be detected along with other outliers of similar ’suspiciousness’. ",
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+    {
+        "type": "text",
+        "text": "We have also compared the global results of our CAD system to the results obtained with a general linear model (GLM) learned on feature maps derived from T1w images using three settings - 1. junction contrast, 2.extension contrast and 3. the conjunction of both contrasts - for a $p$ -value of 0.001 as done in [1]. These features model the junction between gray and white matters as described in [13, 14]. For a fair comparison, the same clustering and ranking procedures (as described in section 2.3) were applied and only the top 10 clusters were considered. The results are summarized in table 1. While extension contrast detects one additional lesion compared with our mono-modal T1-based approach, the combination of junction and extension contrasts does not achieve our best performance with T1w/FLAIR model. We should also note that without applying the ranking method the original SPM implementation produces much more false positive detections without any significant change in the true positive rate. ",
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+        "img_path": "images/d52c1d823009fafd5fb564e67089e19907bdd7ccc8c2198edcd3710190693a14.jpg",
+        "image_caption": [
+            "Figure 3: The performance of the CAD system. $\\mathbf { X }$ -axis: Top $n$ clusters, y-axis: Detection rate among the top $n$ clusters. From left to right: $\\lambda = 1$ (score-only), $\\lambda = 0 . 5$ (score and size average) and $\\lambda = 0$ (size-only) ranking criteria. "
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/afd5ac78aee4c635a16998a900ce4eb359cc7a4e647f872180b87a84e0751a61.jpg",
+        "table_caption": [
+            "Table 1: Our system versus GLM model on T1w MRI as implemented in SPM software. First column: the true positive rate; the number of detected patients / total number of patients in parenthesis. Second column: the true positive rate calculated on MRI negative patients only. Third column: the average number of false positive detections per patient. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>True positive rate</td><td>True positive rate on MR negative patients</td><td>Average # of false positives</td></tr><tr><td>rSNN +oc-SVMon T1 (ranked, top 10)</td><td>0.38 (8/21)</td><td>0.38 (7/18)</td><td>9</td></tr><tr><td>rSNN + oc-SVM on FLAIR (ranked,top 10)</td><td>0.52 (11/21)</td><td>0.5 (9/18)</td><td>9</td></tr><tr><td>rSNN + oc-SVMon T1/FLAIR (ranked,top 10)</td><td>0.62 (13/21)</td><td>0.61 (11/18)</td><td>9</td></tr><tr><td>SPMJunction on T1 (ranked,top 10)</td><td>0.28 (6/21)</td><td>0.27 (5/18)</td><td>9</td></tr><tr><td>SPM Extension on T1 (ranked,top 10)</td><td>0.43 (9/21)</td><td>0.44 (8/18)</td><td>9</td></tr><tr><td>SPM Junction-Extension on T1 (ranked, top 10)</td><td>0.24 (5/21)</td><td>0.22 (4/18)</td><td>9</td></tr></table>",
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+    {
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+        "img_path": "images/0f5acdc24796b148a1840d3364e95dcbe798680b3e3996cab22fe1d2aa6836af.jpg",
+        "image_caption": [
+            "Figure 4: CAD system output for patients $A ^ { + }$ , $B ^ { - }$ and $C ^ { - }$ respectively ( $^ +$ stands for MR positive patients, − for MR negative patients). Top row: Transverse slices centered at the lesion locations (highlighted in red circles). Bottom row: Maximum intensity projections (MIP) of the cluster maps overlaid on the MRI transverse slices. The maps show the top 1, top 6 and top 3 clusters, respectively. "
+        ],
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+    {
+        "type": "text",
+        "text": "4 Discussion ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This study presents a novel method to learn representations that can be used in the task of anomaly detection on brain images. We have formulated a regularized siamese network architecture that learns normal brain representations using a set of non-pathological MR volumes. The features learnt with the network do not target specific pathology but rather allow to capture normal variability from a cohort of healthy subjects. The framework allows integrating multiple modalities and we have shown the performance gain obtained by coupling T1w and FLAIR imaging for the task of detecting subtle epilepsy lesions in MRI negative patients. To our knowledge, this is the first attempt to use deep learning for epilepsy lesion detection. ",
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+    {
+        "type": "text",
+        "text": "Most current studies target a specific type of the pathology, referred to as focal cortical dysplasia (FCD), mainly resulting from a malformation of cortical development and leading to drug-resistant epilepsy lesions. Some of these studies use manually designed features characterizing cortical malformations based on surface based morphometry (SBM) [9, 11, 12]. Others associate these morphometric features to the intensity anomalies in T1w MRI mainly caused by heterotopy lesions [1, 8]. Our method seeks to find more complex features in an unsupervised manner in order to identify lesions with unknown signatures. Naturally, such an approach, when applied to a specific pathology, is likely to produce more false positive detections. Although a fair comparison with published results is difficult because of the differences in the patient groups, results reported in table 1 ( $6 2 \\%$ sensitivity for 9 false positives per scan) are of the same order as those reported in recent studies for the difficult task of automated detection in MRI-negative patients. Indeed, the system proposed in [11] based on SBM features coupled with semi-supervised hierarchical conditional random fields achieves $70 \\%$ sensitivity on a sample of $2 0 \\mathrm { T } 1$ weighted MRI negative patients among the top 10 detections per scan. In [1], a CAD system based on morphometric and intensity features coupled with a oc-SVM classifier allows achieving the same $70 \\%$ sensitivity with an average of 4 false positives per scan when evaluated on a small cohort of 8 T1w MRI negative patients. ",
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+        "text": "There are different options to improve the diagnostic performance of the proposed system. First, some pathology-specific information could be introduced in the post-processing step, by discarding some of the detected clusters based on shape and/or localization criteria. In the majority of the cases, as shown in figure 4, most of the detected false positive clusters are indeed irregularities that can be easily removed by a trained radiologist. An alternative option is to move towards a semi-supervised setting by enhancing the neural network with a few ’pathological’ patches that could be extracted from MRI positive cases or after a careful analysis of retrospective MRI negative patients, following, for instance, some ideas recently proposed in [21]. More improvement could be achieved by accounting for the complementary information provided by different imaging modalities. T1 and FLAIR modalities, introduced as channels to our network, allowed a significant diagnostic performance gain as shown on figure 3. We expect a further performance gain by exploiting PET imaging as recently demonstrated in [22]. ",
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+        "text": "Finally, the proposed method is quite straightforward to implement and to apply in daily practice as the output of the system can be obtained under a couple of minutes. ",
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+    {
+        "type": "text",
+        "text": "5 Acknowledgements ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+    },
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+        "text": "This work was performed within the framework of the LABEX PRIMES (ANR-11-LABX-0063) of Université de Lyon, within the program \"Investissements d’Avenir\" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The authors sincerely thank Valentin Hoang for his valuable contribution to the SPM analysis. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
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+        ],
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+    },
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+        "text": "[1] M. El Azami, A. Hammers, J. Jung, N. Costes, R. Bouet, and C. Lartizien, “Detection of lesions underlying intractable epilepsy on t1-weighted mri as an outlier detection problem,” PloS one, vol. 11, no. 9, p. e0161498, 2016.   \n[2] P. Moeskops, M. A. Viergever, A. M. Mendrik, L. S. de Vries, M. J. Benders, and I. Išgum, “Automatic segmentation of mr brain images with a convolutional neural network,” IEEE transactions on medical imaging, vol. 35, no. 5, pp. 1252–1261, 2016.   \n[3] K. Kamnitsas, C. Ledig, V. F. Newcombe, J. P. Simpson, A. D. Kane, D. K. Menon, D. Rueckert, and B. Glocker, “Efficient multi-scale 3d cnn with fully connected crf for accurate brain lesion segmentation,” Medical Image Analysis, vol. 36, pp. 61 – 78, 2017.   \n[4] M. Ghafoorian, N. Karssemeijer, T. Heskes, M. Bergkamp, J. Wissink, J. Obels, K. Keizer, F.-E. de Leeuw, B. van Ginneken, E. Marchiori, and B. 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De Bruijne, “Gp-unet: Lesion detection from weak labels with a 3d regression network,” in Medical Image Computing and Computer Assisted Intervention (MICCAI 2017) (M. Descoteaux, L. Maier-Hein, A. Franz, P. Jannin, D. L. Collins, and S. Duchesne, eds.), (Cham), pp. 214–221, Springer International Publishing, 2017.   \n[8] R. S. Gill, S.-J. Hong, F. Fadaie, B. Caldairou, B. Bernhardt, N. Bernasconi, and A. Bernasconi, “Automated detection of epileptogenic cortical malformations using multimodal mri,” in Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, pp. 349–356, Springer, 2017.   \n[9] S.-J. Hong, H. Kim, D. Schrader, N. Bernasconi, B. C. Bernhardt, and A. Bernasconi, “Automated detection of cortical dysplasia type ii in mri-negative epilepsy,” Neurology, vol. 83, no. 1, pp. 48–55, 2014.   \n[10] B. Ahmed, C. E. Brodley, K. E. Blackmon, R. Kuzniecky, G. Barash, C. Carlson, B. T. Quinn, W. K. Doyle, J. French, O. Devinsky, and T. Thesen, “Cortical feature analysis and machine learning improves detection of \"mri-negative\" focal cortical dysplasia.,” Epilepsy and behavior, vol. 48, pp. 21–8, 2015.   \n[11] B. Ahmed, T. Thesen, K. E. Blackmon, R. Kuzniekcy, O. Devinsky, and C. E. Brodley, “Decrypting \"cryptogenic\" epilepsy: Semi-supervised hierarchical conditional random fields for detecting cortical lesions in mri-negative patients,” Journal of Machine Learning Research, vol. 17, no. 112, pp. 1–30, 2016.   \n[12] T. Thesen, B. T. Quinn, C. Carlson, O. Devinsky, J. DuBois, C. R. McDonald, J. French, R. Leventer, O. Felsovalyi, X. Wang, et al., “Detection of epileptogenic cortical malformations with surface-based mri morphometry,” PloS one, vol. 6, no. 2, p. e16430, 2011.   \n[13] H.-J. Huppertz, C. Grimm, S. Fauser, J. Kassubek, I. Mader, A. Hochmuth, J. Spreer, and A. SchulzeBonhage, “Enhanced visualization of blurred gray–white matter junctions in focal cortical dysplasia by voxel-based 3d mri analysis,” Epilepsy research, vol. 67, no. 1-2, pp. 35–50, 2005.   \n[14] J. Wagner, B. Weber, H. Urbach, C. E. Elger, and H.-J. Huppertz, “Morphometric mri analysis improves detection of focal cortical dysplasia type ii,” Brain, vol. 134, no. 10, pp. 2844–2854, 2011.   \n[15] J. Bromley, J. W. Bentz, L. Bottou, I. Guyon, Y. LeCun, C. Moore, E. Säckinger, and R. Shah, “Signature verification using a \"siamese\" time delay neural network,” IJPRAI, vol. 7, no. 4, pp. 669–688, 1993.   \n[16] S. Chopra, R. Hadsell, and Y. LeCun, “Learning a similarity metric discriminatively, with application to face verification,” in Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on, vol. 1, pp. 539–546, IEEE, 2005.   \n[17] B. Schölkopf, J. C. Platt, J. Shawe-Taylor, A. J. Smola, and R. C. Williamson, “Estimating the support of a high-dimensional distribution,” Neural computation, vol. 13, no. 7, pp. 1443–1471, 2001.   \n[18] J. Mazziotta, A. Toga, A. Evans, P. Fox, J. Lancaster, K. Zilles, R. Woods, T. Paus, G. Simpson, B. Pike, et al., “A probabilistic atlas and reference system for the human brain: International consortium for brain mapping (icbm),” Philosophical Transactions of the Royal Society of London B: Biological Sciences, vol. 356, no. 1412, pp. 1293–1322, 2001.   \n[19] J. Ashburner and K. Friston, “Unified segmentation,” Neuroimage, vol. 26, pp. 839–851, 2005.   \n[20] B. Caputo, K. Sim, F. Furesjo, and A. Smola, “Appearance-based object recognition using svms: which kernel should i use?,” in Proc of NIPS workshop on Statistical methods for computational experiments in visual processing and computer vision, Whistler, vol. 2002, 2002.   \n[21] M. P. Shah, S. N. Merchant, and S. P. Awate, “Abnormality detection using deep neural networks with robust quasi-norm autoencoding and semi-supervised learning,” in IEEE International Symposium on Biomedical Imaging (ISBI 2018), pp. 568–572.   \n[22] Y. L. Tan, H. Kim, S. Lee, T. Tihan, L. Ver Hoef, S. G. Mueller, A. J. Barkovich, D. Xu, and R. Knowlton, “Quantitative surface analysis of combined mri and pet enhances detection of focal cortical dysplasias.,” Neuroimage, vol. 166, pp. 10–18, 2018. ",
+        "bbox": [
+            178,
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+        "page_idx": 7
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+    {
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+            168,
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+    },
+    {
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+        "page_idx": 9
+    }
+]

parse/train/vllRjSTWcLs/vllRjSTWcLs.md

@@ -0,0 +1,316 @@
+# Rethinking Space-Time Networks with Improved Memory Coverage for Efficient Video Object Segmentation
+
+Ho Kei Cheng† University of Illinois Urbana-Champaign hokeikc2@illinois.edu
+
+Yu-Wing Tai   
+Kuaishou   
+Technology   
+yuwing@gmail.com
+
+Chi-Keung Tang The Hong Kong University of Science and Technology cktang@cs.ust.hk
+
+# Abstract
+
+This paper presents a simple yet effective approach to modeling space-time correspondences in the context of video object segmentation. Unlike most existing approaches, we establish correspondences directly between frames without reencoding the mask features for every object, leading to a highly efficient and robust framework. With the correspondences, every node in the current query frame is inferred by aggregating features from the past in an associative fashion. We cast the aggregation process as a voting problem and find that the existing inner-product affinity leads to poor use of memory with a small (fixed) subset of memory nodes dominating the votes, regardless of the query. In light of this phenomenon, we propose using the negative squared Euclidean distance instead to compute the affinities. We validate that every memory node now has a chance to contribute, and experimentally show that such diversified voting is beneficial to both memory efficiency and inference accuracy. The synergy of correspondence networks and diversified voting works exceedingly well, achieves new state-of-the-art results on both DAVIS and YouTubeVOS datasets while running significantly faster at $^ { 2 0 + }$ FPS for multiple objects without bells and whistles.
+
+# 1 Introduction
+
+Video object segmentation (VOS) aims to identify and segment target instances in a video sequence. This work focuses on the semi-supervised setting where the first-frame segmentation is given and the algorithm needs to infer the segmentation for the remaining frames. This task is an extension of video object tracking [1, 2], requiring detailed object masks instead of simple bounding boxes. A high-performing algorithm should be able to delineate an object from the background or other distractors (e.g., similar instances) under partial or complete occlusion, appearance changes, and object deformation [3].
+
+Most current methods either fit a model using the initial segmentation [4, 5, 6, 7, 8, 9] or leverage temporal propagation [10, 11, 12, 13, 14, 15, 16], particularly with spatio-temporal matching [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. Space-Time Memory networks [18] are especially popular recently due to its high performance and simplicity – many variants [22, 16, 23, 21, 24, 28, 29, 30], including competitions’ winners [31, 32], have been developed to improve the speed, reduce memory usage, or to regularize the memory readout process of STM.
+
+In this work, we aim to subtract from STM to arrive at a minimalistic form of matching networks, dubbed Space-Time Correspondence Network (STCN) 1. Specifically, we start from the basic premise that correspondences are target-agnostic. Instead of building a specific memory bank and therefore affinity for every object in the video as in STM, we build a single affinity matrix using only RGB relations. For querying, each target object passes through the same affinity matrix for feature transfer. This is not only more efficient but also more robust – the model is forced to learn all object relations beyond just the labeled ones. With the learned affinity, the algorithm can propagate features from the first frame to the rest of the video sequence, with intermediate features stored as memory.
+
+While STCN already reaches state-of-the-art performance and speed in this simple form, we further probe into the inner workings of the construction of affinities. Traditionally, affinities are constructed from dot products followed by a softmax as in attention mechanisms [18, 33]. This however implicitly encoded “confidence” (magnitude) with high-confidence points dominating the affinities all the time, regardless of query features. Some memory nodes will therefore be always suppressed, and the (large) memory bank will be underutilized, reducing effective diversity and robustness. We find this to be harmful, and propose using the negative squared Euclidean distance as a similarity measure with an efficient implementation instead. Though simple, this small change ensures that every memory node has a chance to contribute significantly (given the right query), leading to better performance, higher robustness, and more efficient use of memory.
+
+Our contribution is three-fold:
+
+• We propose STCN with direct image-to-image correspondence that is simpler, more efficient, and more effective than STM.   
+• We examine the affinity in detail, and propose using L2 similarity in place of dot product for a better memory coverage, where every memory node contributes instead of just a few.   
+• The synergy of the above two results in a simple and strong method, which suppresses previous state-of-the-art performance without additional complications while running fast at $^ { 2 0 + }$ FPS.
+
+# 2 Related Works
+
+Correspondence Learning Finding correspondences is one of the most fundamental problems in computer vision. Local correspondences have been used heavily in optical flow [34, 35, 36] and object tracking [37, 38, 39] with fast running time and high performance. More explicit correspondence learning has also been achieved with deep learning [40, 41, 42].
+
+Few-shots learning can be considered as a matching problem where the query is compared with every element in the support set [43, 44, 45, 46]. Typical approaches use a Siamese network [47] and compare the embedded query/support features using a similarity measure such as cosine similarity [43], squared Euclidean distance [48], or even a learned function [49]. Our task can also be formulated as a few-shots problem, where our memory bank acts as the support set. This connection helps us with the choice of similarity function, albeit we are dealing with a million times more pointwise comparisons.
+
+Video Object Segmentation Early VOS methods [4, 5, 50] employ online first-frame finetuning which is very slow in inference and have been gradually phased out. Faster approaches have been proposed such as a more efficient online learning algorithm [8, 6, 7], MRF graph inference [51], temporal CNN [52], capsule routing [53], tracking [11, 13, 15, 54, 55, 56, 57], embedding learning [10, 58, 59] and space-time matching [17, 18, 19, 20]. Embedding learning bears a high similarity to space-time matching, both attempting to learn a deep feature representation of an object that remains consistent across a video. Usually embedding learning methods are more constrained [10, 58], adopting local search window and hard one-to-one matching.
+
+We are particularly interested in the class of Space-Time Memory networks (STM) [18] which are the backbone for many follow-up state-of-the-art VOS methods. STM constructs a memory bank for each object in the video, and matches every query frame to the memory bank to perform “memory readout”. Newly inferred frames can be added to the memory, and then the algorithm propagates forward in time. Derivatives either apply STM at other tasks [21, 60], improve the training data or augmentation policy [21, 22], augment the memory readout process [16, 21, 22, 24, 28], use optical flow [29], or reduce the size of the memory bank by limiting its growth [23, 30]. MAST [61] is an adjacent research that focused on unsupervised learning with a photometric reconstruction loss. Without the input mask, they use Siamese networks on RGB images to build the correspondence out of necessity. In this work, we deliberately build such connections and establish that building correspondences between images is a better choice, even when input masks are available, rather than a concession.
+
+We propose to overhaul STM into STCN where the construction of affinity is redefined to be between frames only. We also take a close look at the similarity function, which has always been the dot product in all STM variants, make changes and comparisons according to our findings. The resultant framework is both faster and better while still principled. STCN is even fundamentally simpler than STM, and we hope that STCN can be adopted as the new and efficient backbone for future works.
+
+# 3 Space-Time Correspondence Networks (STCN)
+
+Given a video sequence and the first-frame annotation, we process the frames sequentially and maintain a memory bank of features. For each query frame, we extract a key feature which is compared with the keys in the memory bank, and retrieve corresponding value features from memory using key affinities as in STM [18].
+
+![](images/34d3120c9edd09edfc84a96a19bf7049cd284a0bec343bbc927b48cbda2d2d98.jpg)  
+Figure 1: Left: The general framework of the popularly used Space-Time Memory (STM) networks, ignoring fine-level variations. Objects are encoded separately, and affinities are specific to each object. Right: Our proposed Space-Time Correspondence Networks (STCN). We use Siamese key encoders to compute affinity directly from RGB images, making it more robust and efficient. Note that the query key can be cached and reused later as a memory key (unlike in STM) as it is independent of the mask.
+
+# 3.1 Feature Extraction
+
+Figure 1 illustrates the overall flow of STCN. While STM [18] parameterizes a Query Encoder (image as input) and a Memory Encoder (image and mask as input) with two ResNet50 [62], we instead construct a Key Encoder (image as input) and a Value Encoder (image and mask as input) with a ResNet50 and a ResNet18 respectively. Thus, unlike in STM [18], the key features (and thus the resultant affinity) can be extracted independently without the mask, computed only once for each frame, and symmetric between memory and query.2 The rationales are 1) Correspondences (key features) are more difficult to extract than value, hence a deeper network, and 2) Correspondences should exist between frames in a video, and there is little reason to introduce the mask as a distraction. From another perspective, we are using a Siamese structure [47] which is widely adopted in few-shots learning [63, 49] for computing the key features, as if our memory bank is the few-shots support set. As the key features are independent of the mask, we can reuse the “query key” later as a “memory key” if we decide to turn the query frame into a memory frame during propagation (strategy to be discussed in Section 3.3). This means the key encoder is used exactly once per image in the entire process, despite the two appearances in Figure 1 (which is for brevity).
+
+Architecture. Following the STM practice [18], we take res4 features with stride 16 from the base ResNets as our backbone features and discard res5. A $3 \times 3$ convolutional layer without non-linearity is used as a projection head from the backbone feature to either the key space ( $C ^ { k }$ dimensional) or the value space $C ^ { v }$ dimensional). We set $C ^ { v }$ to be 512 following STM and discuss the choice of $C ^ { k }$ in Section 4.1.
+
+Feature reuse. As seen from Figure 1, both the key encoder and the value encoder are processing the same frame, albeit with different inputs. It is natural to reuse features from the key encoder (with fewer inputs and a deeper network) at the value encoder. To avoid bloating the feature dimensions and for simplicity, we concatenate the last layer features from both encoders (before the projection head) and process them with two ResBlocks [62] and a CBAM block3 [64] as the final value output.
+
+# 3.2 Memory Reading and Decoding
+
+Given $T$ memory frames and a query frame, the feature extraction step would generate the followings: memory key $\mathbf { k } ^ { M } \in \mathbb { R } ^ { C ^ { k } \times T H W }$ , memory value $\mathbf { v } ^ { M } \in \mathbb { R } ^ { C ^ { v } \times T H W }$ , and query key $\mathbf { k } ^ { Q } \in \mathbb { R } ^ { C ^ { k } \times H W }$ , where H and W are (stride 16) spatial dimensions. Then, for any similarity measure c : RCk × $c : \mathbb { R } ^ { C ^ { k } } \times \mathbb { R } ^ { C ^ { k } } $ $\mathbb { R }$ , we can compute the pairwise affinity matrix $\mathbf { S }$ and the softmax-normalized affinity matrix $\mathbf { W }$ , where S $, \mathbf { W } \in \dot { \mathbb { R } } ^ { T H W \times \dot { H } W }$ with:
+
+$$
+{ \bf S } _ { i j } = c ( { \bf k } _ { i } ^ { M } , { \bf k } _ { j } ^ { Q } ) \qquad { \bf W } _ { i j } = \frac { \exp { ( { \bf S } _ { i j } ) } } { \sum _ { n } { ( \exp { ( { \bf S } _ { n j } ) } ) } } ,
+$$
+
+where $\mathbf { k } _ { i }$ denotes the feature vector at the $i$ -th position. The similarities are normalized by $\sqrt { C ^ { k } }$ as in standard practice [18, 33] and is not shown for brevity. In STM [18], the dot product is used as $c$ Memory reading regularization like KMN [22] or top- $k$ filtering [21] can be applied at this step.
+
+With the normalized affinity matrix $\mathbf { W }$ , the aggregated readout feature $\mathbf { v } ^ { Q } \in \mathbb { R } ^ { C ^ { v } \times H W }$ for the query frame can be computed as a weighted sum of the memory features with an efficient matrix multiplication:
+
+$$
+\begin{array} { r } { \mathbf { v } ^ { Q } = \mathbf { v } ^ { M } \mathbf { W } , } \end{array}
+$$
+
+which is then passed to the decoder for mask generation.
+
+In the case of multi-object segmentation, only Equation 2 has to be repeated as W is defined between image features only, and thus is the same for different objects. In the case of STM [18], W must be recomputed instead. Detailed running time analysis can be found in Section 6.2.
+
+Decoder. Our decoder structure stays close to that of the STM [18] as it is not the focus of this paper. Features are processed and upsampled at a scale of two gradually with higher-resolution features from the key encoder incorporated using skip-connections. The final layer of the decoder produces a stride 4 mask which is bilinearly upsampled to the original resolution. In the case of multiple objects, soft aggregation [18] of the output masks is used.
+
+# 3.3 Memory Management
+
+So far we have assumed the existence of a memory bank of size $T$ . Here, we will describe the construction of the memory bank. For each memory frame, we store two items: memory key and memory value. Note that all memory frames (except the first one) are once query frames. The memory key is simply reused from the query key, as described in Section 3.1 without extra computation. The memory value is computed after mask generation of that frame, independently for each object as the value encoder takes both the image and the object mask as inputs.
+
+STM [18] consider every fifth query frame as a memory frame, and the immediately previous frame as a temporary memory frame to ensure accurate matching. In the case of STCN, we find that it is unnecessary, and in fact harmful, to include the last frame as temporary memory. This is a direct consequence of using shared key encoders – 1) key features are sufficiently robust to match well without the need for close-range (temporal) propagation, and 2) the temporary memory key would otherwise be too similar to that of the query, as the image context usually changes smoothly and we do not have the encoding noises resultant from distinct encoders, leading to drifting.4 This modification also reduces the number of calls to the value encoder, contributing a significant speedup.
+
+Table 1: Performance comparison between STM and STCN under different memory configurations on the DAVIS 2017 validation set [65].   
+
+<table><tr><td rowspan="2"></td><td colspan="2">STM</td><td colspan="2">STCN</td></tr><tr><td>Every 5th + Last</td><td>Every 5th only </td><td>Every 5th + Last</td><td>Every 5th only</td></tr><tr><td>J&amp;F</td><td>82.7</td><td>81.0</td><td>83.1</td><td>85.4</td></tr><tr><td>FPS</td><td>12.3</td><td>16.7</td><td>15.4</td><td>20.2</td></tr></table>
+
+Table 1 tabulates the performance comparisons between STM and STCN. For a video of length $L$ with $m \geq 1$ objects, and a final memory bank of size $T < L$ , STM [18] would need to invoke the memory encoder and compute the affinity $m L$ times. Our proposed STCN, on the other hand, only invokes the value encoder $m T$ times and computes the affinity $L$ times. It is therefore evident that STCN is significantly faster. Section 6.2 provides a breakdown of running time.
+
+# 4 Computing Affinity
+
+The similarity function $c : \mathbb { R } ^ { C ^ { k } } \times \mathbb { R } ^ { C ^ { k } } \to \mathbb { R }$ plays a crucial role in both STM and STCN, as it supports the construction of affinity that is central to both correspondences and memory reading. It also has to be fast and memory-efficient as there can be up to 50M pairwise relations $( T H W \times H W )$ to compute for just one query frame.
+
+To recap, we need to compute the similarity between a memory key $\mathbf { k } ^ { M } \in \mathbb { R } ^ { C ^ { k } \times H W }$ and a query key $\mathbf { k } ^ { Q } \in \mathbb { R } ^ { C ^ { k } \times H W }$ . The resultant pairwise affinity matrix is denoted as $\mathbf { S } \in \mathbb { R } ^ { T H W \times H W }$ , with $\mathbf { S } _ { i j } = c ( \mathbf { k } _ { i } ^ { M } , \mathbf { k } _ { j } ^ { Q } )$ denoting the similarity between $\mathbf { k } _ { i } ^ { M }$ (the memory feature vector at the $i$ -th position) and $\mathbf { k } _ { j } ^ { Q }$ (the query feature vector at the $j$ -th position).
+
+In the case of dot product, it can be implemented very efficiently with a matrix multiplication:
+
+$$
+\mathbf { S } _ { i j } ^ { \mathrm { d o t } } = \mathbf { k } _ { i } ^ { M } \cdot \mathbf { k } _ { j } ^ { Q } \qquad \Rightarrow \qquad \mathbf { S } ^ { \mathrm { d o t } } = \left( \mathbf { k } ^ { M } \right) ^ { T } \mathbf { k } ^ { Q }
+$$
+
+In the following, we will also discuss the use of cosine similarity and negative squared Euclidean distance as similarity functions. They are defined as (with efficient implementation discussed later):
+
+$$
+\mathbf { S } _ { i j } ^ { \mathrm { c o s } } = \frac { \mathbf { k } _ { i } ^ { M } \cdot \mathbf { k } _ { j } ^ { Q } } { \left\| \mathbf { k } _ { i } ^ { M } \right\| _ { 2 } \times \left\| \mathbf { k } _ { j } ^ { Q } \right\| _ { 2 } } \qquad \mathbf { S } _ { i j } ^ { \mathrm { L 2 } } = - \left\| \mathbf { k } _ { i } ^ { M } - \mathbf { k } _ { j } ^ { Q } \right\| _ { 2 } ^ { 2 }
+$$
+
+For brevity, we will use the shorthand “L2” or “L2 similarity” to denote the negative squared Euclidean distance in the rest of the paper. The ranges for dot product, cosine similarity and L2 similarity are $( - \infty , \infty )$ , $[ - 1 , 1 ]$ , and $( - \infty , 0 ]$ respectively. Note that cosine similarity has a limited range. Non-related points are encouraged to have a low similarity score through back-propagation such that they have a close-to-zero affinity (Eq. 1), and thus no value is propagated (Eq. 2).
+
+# 4.1 A Closer Look at the Affinity
+
+The affinity matrix is core to STCN and deserves close attention. Previous works [18, 21, 22, 23, 24], almost by default, use the dot product as the similarity function – but is this a good choice?
+
+Cosine similarity computes the angle between two vectors and is often regarded as the normalized dot product. Reversely, we can consider dot product as a scaled version of cosine similarity, with the scale equals to the product of vectors’ norms. Note that this is query-agnostic, meaning that every similarity with a memory key $\mathbf { k } _ { i } ^ { M }$ will be scaled by its norm. If we cast the aggregation process (Eq. 2) as voting with similarity representing the weights, memory keys with large magnitudes will predominately suppress any representation from other memory nodes.
+
+Figure 2 visualizes this phenomenon in a 2D feature space. For dot product, only a subset of points (labeled as triangles) has a chance to contribute the most for any query. Outliers (top-right red) can suppress existing clusters; clusters with dominant value in one dimension (top-left cyan) can suppress other clusters; some points may be able to contribute the most in a region even it is outside of the region (bottom-right beige). These undesirable situations will however not happen if the proposed L2 similarity is used: a Voronoi diagram [66] is formed and every memory point can be fully utilized, leading to a diversified, queryspecific voting mechanism with ease.
+
+Figure 3 shows a closer look at the same problem with soft weights. With dot product, the blue/green point has low weights for every possible query in the first quadrant while a smooth transition is created with our proposed L2 similarity. Note that cosine similarity has the same benefits, but its limited range $[ - 1 , 1 ]$ means that an extra softmax temperature hyperparameter is required to shape the affinity distribution, or one more parameter to tune. L2 works well without extra temperature tuning in our experiments.
+
+![](images/85c612c1417c295449077b1f5b10298a127f21cb1e0f8ccce53ff2cc79ff656e.jpg)  
+Figure 2: Regions are colored as the “most similar” point under a measure. Left: Dot product; right: L2 similarity.
+
+![](images/4ac22e17c8ad47f6fa57e87c08cd25985158a51a114b24ae89615ef513bd4476.jpg)  
+Figure 3: Visualization of the softmax contributions from three points. Left: Dot product; right: L2 similarity.
+
+Connection to self-attention, and whether some points are more important than others. Dotproducts have been used extensively in self-attention models [33, 67, 68]. One way to look at the dot-product affinity positively is to consider the points with large magnitudes as more important – naturally they should enjoy a higher influence. Admittedly, this is probably true in NLP [33] where a stop word (“the”) is almost useless compared to a noun (“London”) or in video classification [67] where the foreground human is far more important than a pixel in the plain blue sky. This is however not true for STCN where pixels are more or less equal. It is beneficial to match every pixel in the query frame accurately, including the background (also noted by [10]). After all, if we can know that a pixel is part of the background, we would also know that it does not belong to the foreground. In fact, we find STCN can track the background fairly well (floor, lake, etc.) even when it is never explicitly trained to do so. The notion of relative importance therefore does not generally apply in our context.
+
+Efficient implementation. The naïve implementation of negative squared Euclidean distance in Eq. 4 needs to materialize a $C ^ { k } \times T H W ^ { \mathbf { \hat { \nu } } } \times H W$ element-wise difference matrix which is then squared and summed. This process is much slower than simple dot product and cannot be run on the same hardware. A simple decomposition greatly simplifies the implementation, as noted in [69]:
+
+$$
+\mathbf { S } _ { i j } ^ { \mathbf { L } 2 } = - \left\| \mathbf { k } _ { i } ^ { M } - \mathbf { k } _ { j } ^ { Q } \right\| _ { 2 } ^ { 2 } = 2 \mathbf { k } _ { i } ^ { M } \cdot \mathbf { k } _ { j } ^ { Q } - \left\| \mathbf { k } _ { i } ^ { M } \right\| _ { 2 } ^ { 2 } - \left\| \mathbf { k } _ { j } ^ { Q } \right\| _ { 2 } ^ { 2 }
+$$
+
+which has only slightly more computation than the baseline dot product, and can be implemented with standard matrix operations. In fact, we can further drop the last term as softmax is invariant to translation in the target dimension (details in the supplementary material). For cosine similarity, we first normalize the input vectors, then compute dot product. Table 2 tabulates the actual computational and memory costs.
+
+# 4.2 Experimental Verification
+
+Here, we verify three claims: 1) the aforementioned phenomenon does happen in a high-dimension key space for real-data and a fully-trained model; 2) using L2 similarity diversifies the voting; 3) L2 similarity brings about higher efficiency and performance.
+
+Affinity distribution. We verify the first two claims by training two different models with dot product and L2 similarity respectively as the similarity function and plot the maximum contribution given by each memory node in its lifetime. We use the same setting for the two models and report the distribution on the DAVIS 2017 [65] dataset.
+
+![](images/20466405f829cea9fe78bb766259729256e3a5385ef434da1072cbc7673c1041.jpg)  
+Figure 4 shows the pertinent distributions. Under the L2 similarity measure, a lot more memory nodes contribute a fair share. Specifically, around $3 \%$ memory nodes never contribute more than $1 \%$ weight under dot product while only $0 . 0 6 \%$ suffer the same fate with L2. Under dot product, $31 \%$ memory nodes contribute less than $10 \%$ weight at best while the same only happen for $7 \%$ of the memory with L2 similarity. To measure the distribution inequality, we additionally compute the Gini coefficient [70] (the higher it is, the more unequal the distribution). The Gini coefficient for dot product is 44.0, while the Gini coefficient for L2 similarity is much lower at 31.8.   
+Figure 4: The curves show the number of memory nodes that have contributed above a certain threshold at least once.
+
+Performance and efficiency. Next, we show that using L2 similarity does improve performance with negligible overhead. We compare three similarity measures: dot product, cosine similarity, and L2 similarity. For cosine similarity, we use a softmax temperature of 0.01 while a default temperature of 1 is used for both dot product and L2 similarity. This scaling is crucial for cosine similarity only since it is the only one with a limited output range $[ - 1 , 1 ]$ . Searching for an extra hyperparameter is computationally demanding – we simply picked one that converges fairly quickly without collapsing. Table 2 tabulates the main results.
+
+Interestingly, we find that reducing the key space dimension $( C ^ { k } )$ is beneficial to both cosine similarity and L2 similarity but not dot product. This can be explained in the context of Section $4 . 1 -$ the network needs more dimensions so that it can spread the memory key features out to save them from being suppressed by high-magnitude points. Cosine similarity and L2 similarity do not suffer from this problem and can utilize the full key space. The reduced key space in turn benefits memory efficiency and improves running time.
+
+Table 2: Performance comparison between different similarity functions and key space dimensionality $( C ^ { k } )$ in STCN on the DAVIS 2017 validation set [65]. The number of floating-point operations (FLOPs) are computed for Eq. 3 and Eq. 4 only with $T = 1 0$ . L2 works the best with a reduced key space and a small computational overhead.   
+
+<table><tr><td>Similarity function</td><td>Ck</td><td>J&amp;F</td><td>#FLOPs (G)</td><td>Size of keys (MB)</td></tr><tr><td>Dot product</td><td>128</td><td>84.1</td><td>6.26</td><td>8.70</td></tr><tr><td>Cosine similarity</td><td>128</td><td>82.6</td><td>6.26</td><td>8.70</td></tr><tr><td>L2 similarity</td><td>128</td><td>85.0</td><td>6.33</td><td>8.70</td></tr><tr><td>Dot product</td><td>64</td><td>83.2</td><td>3.13</td><td>4.35</td></tr><tr><td>Cosine similarity</td><td>64</td><td>83.4</td><td>3.13</td><td>4.35</td></tr><tr><td>L2 similarity</td><td>64</td><td>85.4</td><td>3.20</td><td>4.35</td></tr></table>
+
+# 5 Implementation Details
+
+Models are trained with two 11GB 2080Ti GPUs with the Adam optimizer [71] using PyTorch [72]. Following previous practices [18, 21], we first pretrain the model on static image datasets [73, 74, 75, 76, 77] with synthetic deformation then perform main training on YouTubeVOS [78] and DAVIS [3, 65]. We also experimented with the synthetic dataset BL30K [79, 80] proposed in [21] which is not used unless otherwise specified. We use a batch size of 16 during pretraining and a batch size of 8 during main training. Pre-training takes about 36 hours and main training takes around 16 hours with batchnorm layers frozen during training following [18]. Bootstrapped cross entropy is used following [21]. The full set of hyperparameters can be found in the open-sourced code.
+
+In each iteration, we pick three temporally ordered frames (with the ground-truth mask for the first frame) from a video to form a training sample [18]. First, we predict the second frame using the first frame as memory. The prediction will be saved as the second memory frame, and then the third frame will be predicted using the union of the first and the second frame. The temporal distance between the frames will first gradually increase from 5 to 25 as a curriculum learning schedule and anneal back to 5 towards the end of training. This process follows the implementation of MiVOS [21].
+
+For memory-read augmentation, we experimented with kernelized memory reading [22] and top- $k$ filtering [21]. We find that top- $k$ works well universally and improves running time while kernelized memory reading is slower and does not always help. We find that $k = 2 0$ always works better for STCN (original paper uses $k = 5 0$ ) and we adopt top- $k$ filtering in all our experiments with $k = 2 0$ . For fairness, we also re-run all experiments in MiVOS [21] with $k = 2 0$ , and pick the best result in their favor. We use L2 similarity with $C ^ { k } = 6 4$ in all experiments unless otherwise specified.
+
+For inference, a 2080Ti GPU is used with full floating point precision for a fair running time comparison. We memorize every 5th frame and no temporary frame is used as discussed in Section 3.3.
+
+# 6 Experiments
+
+We mainly conduct experiments in the DAVIS 2017 validation [65] set and the YouTubeVOS 2018 [78] validation set. For completeness, we also include results in the single object DAVIS 2016 validation [3] set and the expanded YouTubeVOS 2019 [78] validation set. Results for the DAVIS 2017 test-dev [65] set are included in the supplementary material. We first conduct quantitative comparisons with previous methods, and then analyze the running time for each component in STCN. For reference, we also present results without pretraining on stataic images. Ablation studies have been included in previous sections (Table 1 and Table 2).
+
+# 6.1 Evaluations
+
+Table 3 tabulates the comparisons of STCN with previous methods in semi-supervised video object segmentation benchmarks. For DAVIS 2017 [65], we compare the standard metrics: region similarity $\mathcal { I }$ , contour accuracy $\mathcal { F }$ , and their average $\mathcal { T } \& \mathcal { F }$ . For YouTubeVOS [78], we report $\mathcal { I }$ and $\mathcal { F }$ for both seen and unseen categories, and the averaged overall score $\mathcal { G }$ . For comparing the speed, we compute the multi-object FPS that is the total number of output frames divided by the total processing time for the entire DAVIS 2017 [65] validation set. We either copy the FPS directly from papers/project websites, or estimate based on their single object inference FPS (simply labeled as $< ^ { 5 }$ ). We use $4 8 0 \mathrm { p }$ resolution videos for both DAVIS and YouTubeVOS. Table 4, 5, 6, and 7 tabulate additional results. For the interactive setting, we replace the propagation module of MiVOS [21] with STCN.
+
+Visualizations. Figure 6 visualizes the learned correspondences. Note that our correspondences are general and mask-free, naturally associating every pixel (including background bystanders) even when it is only trained with foreground masks. Figure 7 visualizes our semi-supervised mask propagation results with the last row being a failure case (Section 7).
+
+Leaderboard results. Our method is also very competitive on the public VOS challenge leaderboard [78]. Methods on the leaderboard are typically cutting-edge, with engineering extensions like deeper network, multi-scale inference, and model ensemble. They usually represent the highest achievable performance at the time. On the latest YouTubeVOS 2019 validation split [78], our base model $( 8 4 . 2 \mathcal { G } )$ outperforms the previous challenge winner [32] (based on STM [18], $8 2 . 0 \mathcal { G } ,$ by a large margin. With ensemble and multi-scale testing (details in the supplementary material), our method is ranked first place $( 8 6 . 7 \mathcal { G } )$ at the time of submission on the still active leaderboard.
+
+# 6.2 Running Time Analysis
+
+Here, we analyze the running time of each component in STM and STCN on DAVIS 2017 [65]. For a fair comparison, we use our own implementation of STM, enabled top- $k$ filtering [21], and set $C ^ { k } = 6 4$ for both methods such that all the speed improvements come from the fundamental differences between STM and STCN. Our affinity matching time is lower because we compute a single affinity between raw images while STM [18] compute one for every object. Our value encoder takes much less time than the memory encoder in STM [18] because of our light network, feature reuse, and robust memory bank/management as discussed in Section 3.3.
+
+![](images/89a35847b37f478010454e025f80b2632afe824314b17113d6ef63cdf069a911.jpg)  
+Figure 5: Average running time of each component in STM and STCN.
+
+Table 3: Comparisons between different methods on DAVIS 2017 and YouTubeVOS 2018 validation sets. Subscripts $S$ and $U$ denote seen or unseen respectively. FPS is measured for multi-object scenarios and is measured on DAVIS 2017. Methods are ranked by YouTubeVOS performance; STM is re-timed on our hardware (see supplementary material); our model is the fastest among methods that are better than STM [18]; \* denotes contemporary work.   
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">YouTubeVOS 2018 [78]</td><td colspan="4">DAVIS 2017 [65]</td></tr><tr><td>g</td><td>Js</td><td>Fs</td><td>Ju</td><td>Fu</td><td>J&amp;F</td><td>J</td><td>F</td><td>FPS</td></tr><tr><td>OSMN[8]</td><td>51.2</td><td>60.0</td><td>60.1</td><td>40.6</td><td>44.0</td><td>54.8</td><td>52.5</td><td>57.1</td><td>&lt;7.1</td></tr><tr><td>RGMP [55]</td><td>53.8</td><td>59.5</td><td>=</td><td>45.2</td><td>1</td><td>66.7</td><td>64.8</td><td>68.6</td><td>&lt;7.7</td></tr><tr><td>RVOS[12]</td><td>56.8</td><td>63.6</td><td>67.2</td><td>45.5</td><td>51.0</td><td>50.3</td><td>48.0</td><td>52.6</td><td>&lt;15</td></tr><tr><td>Track-Seg [54]</td><td>63.6</td><td>67.1</td><td>70.2</td><td>55.3</td><td>61.7</td><td>72.3</td><td>68.6</td><td>76.0</td><td>&lt;39</td></tr><tr><td>PReMVOS [81]</td><td>66.9</td><td>71.4</td><td>75.9</td><td>56.5</td><td>63.7</td><td>77.8</td><td>73.9</td><td>81.7</td><td>&lt;0.03</td></tr><tr><td>TVOS [82]</td><td>67.8</td><td>67.1</td><td>69.4</td><td>63.0</td><td>71.6</td><td>72.3</td><td>69.9</td><td>74.7</td><td>37</td></tr><tr><td>FRTM-VOS [6]</td><td>72.1</td><td>72.3</td><td>76.2</td><td>65.9</td><td>74.1</td><td>76.7</td><td>1</td><td>1</td><td>&lt;21.9</td></tr><tr><td>GC [24]</td><td>73.2</td><td>72.6</td><td>68.9</td><td>75.6</td><td>75.7</td><td>71.4</td><td>69.3</td><td>73.5</td><td>&lt;25</td></tr><tr><td>SwiftNet* [30]</td><td>77.8</td><td>77.8</td><td>81.8</td><td>72.3</td><td>79.5</td><td>81.1</td><td>78.3</td><td>83.9</td><td>25</td></tr><tr><td>STM[18]</td><td>79.4</td><td>79.7</td><td>84.2</td><td>72.8</td><td>80.9</td><td>81.8</td><td>79.2</td><td>84.3</td><td>10.2</td></tr><tr><td>AFB-URR[23]</td><td>79.6</td><td>78.8</td><td>83.1</td><td>74.1</td><td>82.6</td><td>74.6</td><td>73.0</td><td>76.1</td><td>4</td></tr><tr><td>GraphMem[16]</td><td>80.2</td><td>80.7</td><td>85.1</td><td>74.0</td><td>80.9</td><td>82.8</td><td>80.2</td><td>85.2</td><td>5</td></tr><tr><td>MiVOS* [21]</td><td>80.4</td><td>80.0</td><td>84.6</td><td>74.8</td><td>82.4</td><td>83.3</td><td>80.6</td><td>85.9</td><td>11.2</td></tr><tr><td>CFBI[10]</td><td>81.4</td><td>81.1</td><td>85.8</td><td>75.3</td><td>83.4</td><td>81.9</td><td>79.1</td><td>84.6</td><td>5.9</td></tr><tr><td>KMN[22]</td><td>81.4</td><td>81.4</td><td>85.6</td><td>75.3</td><td>83.3</td><td>82.8</td><td>80.0</td><td>85.6</td><td>&lt;8.4</td></tr><tr><td>RMNet*[29]</td><td>81.5</td><td>82.1</td><td>85.7</td><td>75.7</td><td>82.4</td><td>83.5</td><td>81.0</td><td>86.0</td><td>&lt;11.9</td></tr><tr><td>LWL [7]</td><td>81.5</td><td>80.4</td><td>84.9</td><td>76.4</td><td>84.4</td><td>81.6</td><td>79.1</td><td>84.1</td><td>&lt;6.0</td></tr><tr><td>CFBI+* [83]</td><td>82.0</td><td>81.2</td><td>86.0</td><td>76.2</td><td>84.6</td><td>82.9</td><td>80.1</td><td>85.7</td><td>5.6</td></tr><tr><td>LCM* [28]</td><td>82.0</td><td>82.2</td><td>86.7</td><td>75.7</td><td>83.4</td><td>83.5</td><td>80.5</td><td>86.5</td><td>~9.2</td></tr><tr><td>Ours</td><td>83.0</td><td>81.9</td><td>86.5</td><td>77.9</td><td>85.7</td><td>85.4</td><td>82.2</td><td>88.6</td><td>20.2</td></tr><tr><td>MiVOS*[21] + BL30K Ours +BL30K</td><td>82.6 84.3</td><td>81.1 83.2</td><td>85.6 87.9</td><td>77.7 79.0</td><td>86.2 87.3</td><td>84.5 85.3</td><td>81.7 82.0</td><td>87.4</td><td>11.2</td></tr></table>
+
+![](images/0c2526ce8ca45ab9ca5422616a63e9ebec9e443d6aabd859cf7cee21a45f697e.jpg)  
+Figure 6: Visualization of the correspondences. Labels are hand-picked in the source frame (leftmost) and are propagated to the rest directly without intermediate memory. We label all the peaks (e.g., the two yellow diamonds representing the front/back wheel – our algorithm cannot distinguish them). The bystander in white (labeled with an orange crescent) is occluded in the last frame and the resultant affinity does not have a distinct peak (not labeled).
+
+# 7 Limitations
+
+To alienate our method from other possible enhancement, we only use fundamentally simple global matching. Like STM [18], we have no notion of temporal consistency as we do not employ local matching [58, 10, 17] or optical flow [29]. This means we may incorrectly segment objects that are far away with similar appearance. One such failure case is shown on the last row of Figure 7. We expect that given our framework’s simplicity, our method can be readily extended to include temporal consistency consideration for further improvement.
+
+# 8 Conclusion
+
+We present STCN, a simple, effective, and efficient framework for video object segmentation. We propose to use direct image-to-image correspondence for efficiency and more robust matching, and examine the inner workings of affinity in details $^ { - \mathbf { L } 2 }$ similarity is proposed as a result of our observations. With its clear technical advantages, We hope that STCN can serve as a new baseline backbone for future contributions.
+
+Table 4: Results on the DAVIS 2016 validation set.   
+
+<table><tr><td>Method</td><td>J&amp;F</td><td>J</td><td>F</td></tr><tr><td>OSMN [8]</td><td>73.5</td><td>74.0</td><td>72.9</td></tr><tr><td>MaskTrack [15]</td><td>77.6</td><td>79.7</td><td>75.4</td></tr><tr><td>OSVOS [5]</td><td>80.2</td><td>79.8</td><td>80.6</td></tr><tr><td>FAVOS [14]</td><td>81.0</td><td>82.4</td><td>79.5</td></tr><tr><td>FEELVOS[58]</td><td>81.7</td><td>81.1</td><td>82.2</td></tr><tr><td>RGMP [55]</td><td>81.8</td><td>81.5</td><td>82.0</td></tr><tr><td>Track-Seg [54]</td><td>83.1</td><td>82.6</td><td>83.6</td></tr><tr><td>FRTM-VOS [6]</td><td>83.5</td><td>=</td><td>-</td></tr><tr><td>CINN [51]</td><td>84.2</td><td>83.4</td><td>85.0</td></tr><tr><td>OnAVOS [50]</td><td>85.5</td><td>86.1</td><td>84.9</td></tr><tr><td>PReMVOS[81]</td><td>86.8</td><td>84.9</td><td>88.6</td></tr><tr><td>GC [24]</td><td>86.8</td><td>87.6</td><td>85.7</td></tr><tr><td>RMNet [29]</td><td>88.8</td><td>88.9</td><td>88.7</td></tr><tr><td>STM[18]</td><td>89.3</td><td>88.7</td><td>89.9</td></tr><tr><td>CFBI[10]</td><td>89.4</td><td>88.3</td><td>90.5</td></tr><tr><td>CFBI+ [83]</td><td>89.9</td><td>88.7</td><td>91.1</td></tr><tr><td>MiVOS [21]</td><td>90.0</td><td>88.9</td><td>91.1</td></tr><tr><td>SwiftNet [30]</td><td>90.4</td><td>90.5</td><td>90.3</td></tr><tr><td>KMN [22]</td><td>90.5</td><td>89.5</td><td>91.5</td></tr><tr><td>LCM [28]</td><td>90.7</td><td>91.4</td><td>89.9</td></tr><tr><td>Ours</td><td>91.6</td><td>90.8</td><td>92.5</td></tr><tr><td>MiVOS [21] + BL30K</td><td>91.0</td><td>89.6</td><td>92.4</td></tr><tr><td>Ours+BL30K</td><td>91.7</td><td>90.4</td><td>93.0</td></tr></table>
+
+Table 5: Results on the YouTubeVOS 2019 validation set.   
+
+<table><tr><td>Method</td><td>9</td><td></td><td></td><td>Js Fs Ju Ju</td></tr><tr><td>MiVOS [21]</td><td>80.3</td><td>79.3 83.7</td><td>75.3</td><td>82.8</td></tr><tr><td>CFBI[10]</td><td>81.0 80.6</td><td>85.1</td><td>75.2</td><td>83.0</td></tr><tr><td>Ours</td><td>82.7 81.1</td><td>85.4</td><td>78.2</td><td>85.9</td></tr><tr><td>MiVOS[21] + BL30K 82.4 80.6 84.7 78.1</td><td></td><td></td><td></td><td>86.4</td></tr><tr><td>Ours +BL30K</td><td>84.2</td><td>82.6 87.0</td><td>79.4 87.7</td><td></td></tr></table>
+
+Table 6: Results on the DAVIS interactive track [65]. BL30K [21] used for both MiVOS and ours.   
+
+<table><tr><td>Method</td><td>AUC-J&amp;F</td><td>J&amp;F@60s</td><td>Time (s)</td></tr><tr><td>ATNet [84]</td><td>80.9</td><td>82.7</td><td>55+</td></tr><tr><td>STM [85]</td><td>80.3</td><td>84.8</td><td>37</td></tr><tr><td>GIS [86]</td><td>85.6</td><td>86.6</td><td>34</td></tr><tr><td>MiVOS [21]</td><td>87.9</td><td>88.5</td><td>12</td></tr><tr><td>Ours</td><td>88.4</td><td>88.8</td><td>7.3</td></tr></table>
+
+Table 7: Effects of pretraining on static images/maintraining on the DAVIS 2017 validation set.   
+
+<table><tr><td></td><td>J&amp;F</td><td>J</td><td>F</td></tr><tr><td>Pre-training only</td><td>75.8</td><td>73.1</td><td>78.6</td></tr><tr><td>Main training only</td><td>82.5</td><td>79.3</td><td>85.7</td></tr><tr><td>Both</td><td>85.4</td><td>82.2</td><td>88.6</td></tr></table>
+
+![](images/94e37f4502159e43cad81f95b2efe5f2ac0471328649960cf9653bf5649ea78d.jpg)  
+Figure 7: Visualization of semi-supervised VOS results with the first column being the reference masks to be propagated. The first two examples show comparisons of our method with STM [18] and MiVOS [21]. In the second example, zoom-ins inset (orange) are shown with the corresponding ground-truths inset (green) to highlight their differences. The last row shows a failure case: we cannot distinguish the real duck from the duck picture, as no temporal consistency clue is used in our method.
+
+Broader Impacts Malicious use of VOS software can bring potential negative societal impacts, including but not limited to unauthorized mass surveillance or privacy infringing human/vehicle tracking. We believe that the task itself is neutral with positive uses as well, such as video editing for amateurs or making safe self-driving cars.
+
+# Acknowledgment
+
+This research is supported in part by Kuaishou Technology and the Research Grant Council of the Hong Kong SAR under grant no. 16201818.
+
+# References
+
+[1] Anton Milan, Laura Leal-Taixé, Ian Reid, Stefan Roth, and Konrad Schindler. MOT16: A benchmark for multi-object tracking. In arXiv preprint arXiv:1603.00831, 2016.   
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parse/train/vllRjSTWcLs/vllRjSTWcLs_content_list.json

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+    {
+        "type": "text",
+        "text": "Rethinking Space-Time Networks with Improved Memory Coverage for Efficient Video Object Segmentation ",
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+    {
+        "type": "text",
+        "text": "Ho Kei Cheng† University of Illinois Urbana-Champaign hokeikc2@illinois.edu ",
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+    {
+        "type": "text",
+        "text": "Yu-Wing Tai   \nKuaishou   \nTechnology   \nyuwing@gmail.com ",
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+    {
+        "type": "text",
+        "text": "Chi-Keung Tang The Hong Kong University of Science and Technology cktang@cs.ust.hk ",
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+        "page_idx": 0
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+        "type": "text",
+        "text": "Abstract ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper presents a simple yet effective approach to modeling space-time correspondences in the context of video object segmentation. Unlike most existing approaches, we establish correspondences directly between frames without reencoding the mask features for every object, leading to a highly efficient and robust framework. With the correspondences, every node in the current query frame is inferred by aggregating features from the past in an associative fashion. We cast the aggregation process as a voting problem and find that the existing inner-product affinity leads to poor use of memory with a small (fixed) subset of memory nodes dominating the votes, regardless of the query. In light of this phenomenon, we propose using the negative squared Euclidean distance instead to compute the affinities. We validate that every memory node now has a chance to contribute, and experimentally show that such diversified voting is beneficial to both memory efficiency and inference accuracy. The synergy of correspondence networks and diversified voting works exceedingly well, achieves new state-of-the-art results on both DAVIS and YouTubeVOS datasets while running significantly faster at $^ { 2 0 + }$ FPS for multiple objects without bells and whistles. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "1 Introduction ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Video object segmentation (VOS) aims to identify and segment target instances in a video sequence. This work focuses on the semi-supervised setting where the first-frame segmentation is given and the algorithm needs to infer the segmentation for the remaining frames. This task is an extension of video object tracking [1, 2], requiring detailed object masks instead of simple bounding boxes. A high-performing algorithm should be able to delineate an object from the background or other distractors (e.g., similar instances) under partial or complete occlusion, appearance changes, and object deformation [3]. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Most current methods either fit a model using the initial segmentation [4, 5, 6, 7, 8, 9] or leverage temporal propagation [10, 11, 12, 13, 14, 15, 16], particularly with spatio-temporal matching [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]. Space-Time Memory networks [18] are especially popular recently due to its high performance and simplicity – many variants [22, 16, 23, 21, 24, 28, 29, 30], including competitions’ winners [31, 32], have been developed to improve the speed, reduce memory usage, or to regularize the memory readout process of STM. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we aim to subtract from STM to arrive at a minimalistic form of matching networks, dubbed Space-Time Correspondence Network (STCN) 1. Specifically, we start from the basic premise that correspondences are target-agnostic. Instead of building a specific memory bank and therefore affinity for every object in the video as in STM, we build a single affinity matrix using only RGB relations. For querying, each target object passes through the same affinity matrix for feature transfer. This is not only more efficient but also more robust – the model is forced to learn all object relations beyond just the labeled ones. With the learned affinity, the algorithm can propagate features from the first frame to the rest of the video sequence, with intermediate features stored as memory. ",
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+    {
+        "type": "text",
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+    {
+        "type": "text",
+        "text": "While STCN already reaches state-of-the-art performance and speed in this simple form, we further probe into the inner workings of the construction of affinities. Traditionally, affinities are constructed from dot products followed by a softmax as in attention mechanisms [18, 33]. This however implicitly encoded “confidence” (magnitude) with high-confidence points dominating the affinities all the time, regardless of query features. Some memory nodes will therefore be always suppressed, and the (large) memory bank will be underutilized, reducing effective diversity and robustness. We find this to be harmful, and propose using the negative squared Euclidean distance as a similarity measure with an efficient implementation instead. Though simple, this small change ensures that every memory node has a chance to contribute significantly (given the right query), leading to better performance, higher robustness, and more efficient use of memory. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our contribution is three-fold: ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "• We propose STCN with direct image-to-image correspondence that is simpler, more efficient, and more effective than STM.   \n• We examine the affinity in detail, and propose using L2 similarity in place of dot product for a better memory coverage, where every memory node contributes instead of just a few.   \n• The synergy of the above two results in a simple and strong method, which suppresses previous state-of-the-art performance without additional complications while running fast at $^ { 2 0 + }$ FPS. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2 Related Works ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            474,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Correspondence Learning Finding correspondences is one of the most fundamental problems in computer vision. Local correspondences have been used heavily in optical flow [34, 35, 36] and object tracking [37, 38, 39] with fast running time and high performance. More explicit correspondence learning has also been achieved with deep learning [40, 41, 42]. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Few-shots learning can be considered as a matching problem where the query is compared with every element in the support set [43, 44, 45, 46]. Typical approaches use a Siamese network [47] and compare the embedded query/support features using a similarity measure such as cosine similarity [43], squared Euclidean distance [48], or even a learned function [49]. Our task can also be formulated as a few-shots problem, where our memory bank acts as the support set. This connection helps us with the choice of similarity function, albeit we are dealing with a million times more pointwise comparisons. ",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Video Object Segmentation Early VOS methods [4, 5, 50] employ online first-frame finetuning which is very slow in inference and have been gradually phased out. Faster approaches have been proposed such as a more efficient online learning algorithm [8, 6, 7], MRF graph inference [51], temporal CNN [52], capsule routing [53], tracking [11, 13, 15, 54, 55, 56, 57], embedding learning [10, 58, 59] and space-time matching [17, 18, 19, 20]. Embedding learning bears a high similarity to space-time matching, both attempting to learn a deep feature representation of an object that remains consistent across a video. Usually embedding learning methods are more constrained [10, 58], adopting local search window and hard one-to-one matching. ",
+        "bbox": [
+            174,
+            655,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "We are particularly interested in the class of Space-Time Memory networks (STM) [18] which are the backbone for many follow-up state-of-the-art VOS methods. STM constructs a memory bank for each object in the video, and matches every query frame to the memory bank to perform “memory readout”. Newly inferred frames can be added to the memory, and then the algorithm propagates forward in time. Derivatives either apply STM at other tasks [21, 60], improve the training data or augmentation policy [21, 22], augment the memory readout process [16, 21, 22, 24, 28], use optical flow [29], or reduce the size of the memory bank by limiting its growth [23, 30]. MAST [61] is an adjacent research that focused on unsupervised learning with a photometric reconstruction loss. Without the input mask, they use Siamese networks on RGB images to build the correspondence out of necessity. In this work, we deliberately build such connections and establish that building correspondences between images is a better choice, even when input masks are available, rather than a concession. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We propose to overhaul STM into STCN where the construction of affinity is redefined to be between frames only. We also take a close look at the similarity function, which has always been the dot product in all STM variants, make changes and comparisons according to our findings. The resultant framework is both faster and better while still principled. STCN is even fundamentally simpler than STM, and we hope that STCN can be adopted as the new and efficient backbone for future works. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3 Space-Time Correspondence Networks (STCN) ",
+        "text_level": 1,
+        "bbox": [
+            173,
+            213,
+            601,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a video sequence and the first-frame annotation, we process the frames sequentially and maintain a memory bank of features. For each query frame, we extract a key feature which is compared with the keys in the memory bank, and retrieve corresponding value features from memory using key affinities as in STM [18]. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/34d3120c9edd09edfc84a96a19bf7049cd284a0bec343bbc927b48cbda2d2d98.jpg",
+        "image_caption": [
+            "Figure 1: Left: The general framework of the popularly used Space-Time Memory (STM) networks, ignoring fine-level variations. Objects are encoded separately, and affinities are specific to each object. Right: Our proposed Space-Time Correspondence Networks (STCN). We use Siamese key encoders to compute affinity directly from RGB images, making it more robust and efficient. Note that the query key can be cached and reused later as a memory key (unlike in STM) as it is independent of the mask. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "3.1 Feature Extraction ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Figure 1 illustrates the overall flow of STCN. While STM [18] parameterizes a Query Encoder (image as input) and a Memory Encoder (image and mask as input) with two ResNet50 [62], we instead construct a Key Encoder (image as input) and a Value Encoder (image and mask as input) with a ResNet50 and a ResNet18 respectively. Thus, unlike in STM [18], the key features (and thus the resultant affinity) can be extracted independently without the mask, computed only once for each frame, and symmetric between memory and query.2 The rationales are 1) Correspondences (key features) are more difficult to extract than value, hence a deeper network, and 2) Correspondences should exist between frames in a video, and there is little reason to introduce the mask as a distraction. From another perspective, we are using a Siamese structure [47] which is widely adopted in few-shots learning [63, 49] for computing the key features, as if our memory bank is the few-shots support set. As the key features are independent of the mask, we can reuse the “query key” later as a “memory key” if we decide to turn the query frame into a memory frame during propagation (strategy to be discussed in Section 3.3). This means the key encoder is used exactly once per image in the entire process, despite the two appearances in Figure 1 (which is for brevity). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Architecture. Following the STM practice [18], we take res4 features with stride 16 from the base ResNets as our backbone features and discard res5. A $3 \\times 3$ convolutional layer without non-linearity is used as a projection head from the backbone feature to either the key space ( $C ^ { k }$ dimensional) or the value space $C ^ { v }$ dimensional). We set $C ^ { v }$ to be 512 following STM and discuss the choice of $C ^ { k }$ in Section 4.1. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Feature reuse. As seen from Figure 1, both the key encoder and the value encoder are processing the same frame, albeit with different inputs. It is natural to reuse features from the key encoder (with fewer inputs and a deeper network) at the value encoder. To avoid bloating the feature dimensions and for simplicity, we concatenate the last layer features from both encoders (before the projection head) and process them with two ResBlocks [62] and a CBAM block3 [64] as the final value output. ",
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+    {
+        "type": "text",
+        "text": "3.2 Memory Reading and Decoding ",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Given $T$ memory frames and a query frame, the feature extraction step would generate the followings: memory key $\\mathbf { k } ^ { M } \\in \\mathbb { R } ^ { C ^ { k } \\times T H W }$ , memory value $\\mathbf { v } ^ { M } \\in \\mathbb { R } ^ { C ^ { v } \\times T H W }$ , and query key $\\mathbf { k } ^ { Q } \\in \\mathbb { R } ^ { C ^ { k } \\times H W }$ , where H and W are (stride 16) spatial dimensions. Then, for any similarity measure c : RCk × $c : \\mathbb { R } ^ { C ^ { k } } \\times \\mathbb { R } ^ { C ^ { k } } $ $\\mathbb { R }$ , we can compute the pairwise affinity matrix $\\mathbf { S }$ and the softmax-normalized affinity matrix $\\mathbf { W }$ , where S $, \\mathbf { W } \\in \\dot { \\mathbb { R } } ^ { T H W \\times \\dot { H } W }$ with: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6f4099c0b20e02c0c8268ad3459f5e12be158542173279cf22951382617da9f2.jpg",
+        "text": "$$\n{ \\bf S } _ { i j } = c ( { \\bf k } _ { i } ^ { M } , { \\bf k } _ { j } ^ { Q } ) \\qquad { \\bf W } _ { i j } = \\frac { \\exp { ( { \\bf S } _ { i j } ) } } { \\sum _ { n } { ( \\exp { ( { \\bf S } _ { n j } ) } ) } } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $\\mathbf { k } _ { i }$ denotes the feature vector at the $i$ -th position. The similarities are normalized by $\\sqrt { C ^ { k } }$ as in standard practice [18, 33] and is not shown for brevity. In STM [18], the dot product is used as $c$ Memory reading regularization like KMN [22] or top- $k$ filtering [21] can be applied at this step. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "With the normalized affinity matrix $\\mathbf { W }$ , the aggregated readout feature $\\mathbf { v } ^ { Q } \\in \\mathbb { R } ^ { C ^ { v } \\times H W }$ for the query frame can be computed as a weighted sum of the memory features with an efficient matrix multiplication: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/a3620dd2f15a79f02e6964e846ee2b0630fdac8da887441f76787b905dfe69c6.jpg",
+        "text": "$$\n\\begin{array} { r } { \\mathbf { v } ^ { Q } = \\mathbf { v } ^ { M } \\mathbf { W } , } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which is then passed to the decoder for mask generation. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In the case of multi-object segmentation, only Equation 2 has to be repeated as W is defined between image features only, and thus is the same for different objects. In the case of STM [18], W must be recomputed instead. Detailed running time analysis can be found in Section 6.2. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Decoder. Our decoder structure stays close to that of the STM [18] as it is not the focus of this paper. Features are processed and upsampled at a scale of two gradually with higher-resolution features from the key encoder incorporated using skip-connections. The final layer of the decoder produces a stride 4 mask which is bilinearly upsampled to the original resolution. In the case of multiple objects, soft aggregation [18] of the output masks is used. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3 Memory Management ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "So far we have assumed the existence of a memory bank of size $T$ . Here, we will describe the construction of the memory bank. For each memory frame, we store two items: memory key and memory value. Note that all memory frames (except the first one) are once query frames. The memory key is simply reused from the query key, as described in Section 3.1 without extra computation. The memory value is computed after mask generation of that frame, independently for each object as the value encoder takes both the image and the object mask as inputs. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "STM [18] consider every fifth query frame as a memory frame, and the immediately previous frame as a temporary memory frame to ensure accurate matching. In the case of STCN, we find that it is unnecessary, and in fact harmful, to include the last frame as temporary memory. This is a direct consequence of using shared key encoders – 1) key features are sufficiently robust to match well without the need for close-range (temporal) propagation, and 2) the temporary memory key would otherwise be too similar to that of the query, as the image context usually changes smoothly and we do not have the encoding noises resultant from distinct encoders, leading to drifting.4 This modification also reduces the number of calls to the value encoder, contributing a significant speedup. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0f15ec4cf897c6e96fbb67080b8deddeb65098d82027c7558cb7438e93aa3c80.jpg",
+        "table_caption": [
+            "Table 1: Performance comparison between STM and STCN under different memory configurations on the DAVIS 2017 validation set [65]. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">STM</td><td colspan=\"2\">STCN</td></tr><tr><td>Every 5th + Last</td><td>Every 5th only </td><td>Every 5th + Last</td><td>Every 5th only</td></tr><tr><td>J&amp;F</td><td>82.7</td><td>81.0</td><td>83.1</td><td>85.4</td></tr><tr><td>FPS</td><td>12.3</td><td>16.7</td><td>15.4</td><td>20.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1 tabulates the performance comparisons between STM and STCN. For a video of length $L$ with $m \\geq 1$ objects, and a final memory bank of size $T < L$ , STM [18] would need to invoke the memory encoder and compute the affinity $m L$ times. Our proposed STCN, on the other hand, only invokes the value encoder $m T$ times and computes the affinity $L$ times. It is therefore evident that STCN is significantly faster. Section 6.2 provides a breakdown of running time. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 Computing Affinity ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The similarity function $c : \\mathbb { R } ^ { C ^ { k } } \\times \\mathbb { R } ^ { C ^ { k } } \\to \\mathbb { R }$ plays a crucial role in both STM and STCN, as it supports the construction of affinity that is central to both correspondences and memory reading. It also has to be fast and memory-efficient as there can be up to 50M pairwise relations $( T H W \\times H W )$ to compute for just one query frame. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To recap, we need to compute the similarity between a memory key $\\mathbf { k } ^ { M } \\in \\mathbb { R } ^ { C ^ { k } \\times H W }$ and a query key $\\mathbf { k } ^ { Q } \\in \\mathbb { R } ^ { C ^ { k } \\times H W }$ . The resultant pairwise affinity matrix is denoted as $\\mathbf { S } \\in \\mathbb { R } ^ { T H W \\times H W }$ , with $\\mathbf { S } _ { i j } = c ( \\mathbf { k } _ { i } ^ { M } , \\mathbf { k } _ { j } ^ { Q } )$ denoting the similarity between $\\mathbf { k } _ { i } ^ { M }$ (the memory feature vector at the $i$ -th position) and $\\mathbf { k } _ { j } ^ { Q }$ (the query feature vector at the $j$ -th position). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In the case of dot product, it can be implemented very efficiently with a matrix multiplication: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/97c84f516f697b024bd3ea97ea5c17c59b7700cda61a2f6a7da44716d561437f.jpg",
+        "text": "$$\n\\mathbf { S } _ { i j } ^ { \\mathrm { d o t } } = \\mathbf { k } _ { i } ^ { M } \\cdot \\mathbf { k } _ { j } ^ { Q } \\qquad \\Rightarrow \\qquad \\mathbf { S } ^ { \\mathrm { d o t } } = \\left( \\mathbf { k } ^ { M } \\right) ^ { T } \\mathbf { k } ^ { Q }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the following, we will also discuss the use of cosine similarity and negative squared Euclidean distance as similarity functions. They are defined as (with efficient implementation discussed later): ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/c1eb43bc3e972622f7eb90e15dae2067a5a6676e34185a2d1d85157ea739700b.jpg",
+        "text": "$$\n\\mathbf { S } _ { i j } ^ { \\mathrm { c o s } } = \\frac { \\mathbf { k } _ { i } ^ { M } \\cdot \\mathbf { k } _ { j } ^ { Q } } { \\left\\| \\mathbf { k } _ { i } ^ { M } \\right\\| _ { 2 } \\times \\left\\| \\mathbf { k } _ { j } ^ { Q } \\right\\| _ { 2 } } \\qquad \\mathbf { S } _ { i j } ^ { \\mathrm { L 2 } } = - \\left\\| \\mathbf { k } _ { i } ^ { M } - \\mathbf { k } _ { j } ^ { Q } \\right\\| _ { 2 } ^ { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For brevity, we will use the shorthand “L2” or “L2 similarity” to denote the negative squared Euclidean distance in the rest of the paper. The ranges for dot product, cosine similarity and L2 similarity are $( - \\infty , \\infty )$ , $[ - 1 , 1 ]$ , and $( - \\infty , 0 ]$ respectively. Note that cosine similarity has a limited range. Non-related points are encouraged to have a low similarity score through back-propagation such that they have a close-to-zero affinity (Eq. 1), and thus no value is propagated (Eq. 2). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1 A Closer Look at the Affinity ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "The affinity matrix is core to STCN and deserves close attention. Previous works [18, 21, 22, 23, 24], almost by default, use the dot product as the similarity function – but is this a good choice? ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Cosine similarity computes the angle between two vectors and is often regarded as the normalized dot product. Reversely, we can consider dot product as a scaled version of cosine similarity, with the scale equals to the product of vectors’ norms. Note that this is query-agnostic, meaning that every similarity with a memory key $\\mathbf { k } _ { i } ^ { M }$ will be scaled by its norm. If we cast the aggregation process (Eq. 2) as voting with similarity representing the weights, memory keys with large magnitudes will predominately suppress any representation from other memory nodes. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Figure 2 visualizes this phenomenon in a 2D feature space. For dot product, only a subset of points (labeled as triangles) has a chance to contribute the most for any query. Outliers (top-right red) can suppress existing clusters; clusters with dominant value in one dimension (top-left cyan) can suppress other clusters; some points may be able to contribute the most in a region even it is outside of the region (bottom-right beige). These undesirable situations will however not happen if the proposed L2 similarity is used: a Voronoi diagram [66] is formed and every memory point can be fully utilized, leading to a diversified, queryspecific voting mechanism with ease. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figure 3 shows a closer look at the same problem with soft weights. With dot product, the blue/green point has low weights for every possible query in the first quadrant while a smooth transition is created with our proposed L2 similarity. Note that cosine similarity has the same benefits, but its limited range $[ - 1 , 1 ]$ means that an extra softmax temperature hyperparameter is required to shape the affinity distribution, or one more parameter to tune. L2 works well without extra temperature tuning in our experiments. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/85c612c1417c295449077b1f5b10298a127f21cb1e0f8ccce53ff2cc79ff656e.jpg",
+        "image_caption": [
+            "Figure 2: Regions are colored as the “most similar” point under a measure. Left: Dot product; right: L2 similarity. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            566,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/4ac22e17c8ad47f6fa57e87c08cd25985158a51a114b24ae89615ef513bd4476.jpg",
+        "image_caption": [
+            "Figure 3: Visualization of the softmax contributions from three points. Left: Dot product; right: L2 similarity. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Connection to self-attention, and whether some points are more important than others. Dotproducts have been used extensively in self-attention models [33, 67, 68]. One way to look at the dot-product affinity positively is to consider the points with large magnitudes as more important – naturally they should enjoy a higher influence. Admittedly, this is probably true in NLP [33] where a stop word (“the”) is almost useless compared to a noun (“London”) or in video classification [67] where the foreground human is far more important than a pixel in the plain blue sky. This is however not true for STCN where pixels are more or less equal. It is beneficial to match every pixel in the query frame accurately, including the background (also noted by [10]). After all, if we can know that a pixel is part of the background, we would also know that it does not belong to the foreground. In fact, we find STCN can track the background fairly well (floor, lake, etc.) even when it is never explicitly trained to do so. The notion of relative importance therefore does not generally apply in our context. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Efficient implementation. The naïve implementation of negative squared Euclidean distance in Eq. 4 needs to materialize a $C ^ { k } \\times T H W ^ { \\mathbf { \\hat { \\nu } } } \\times H W$ element-wise difference matrix which is then squared and summed. This process is much slower than simple dot product and cannot be run on the same hardware. A simple decomposition greatly simplifies the implementation, as noted in [69]: ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "img_path": "images/3a0f07338cccdf6b826adf0b79495fb368164bf9c205a4232f702559ff76fa87.jpg",
+        "text": "$$\n\\mathbf { S } _ { i j } ^ { \\mathbf { L } 2 } = - \\left\\| \\mathbf { k } _ { i } ^ { M } - \\mathbf { k } _ { j } ^ { Q } \\right\\| _ { 2 } ^ { 2 } = 2 \\mathbf { k } _ { i } ^ { M } \\cdot \\mathbf { k } _ { j } ^ { Q } - \\left\\| \\mathbf { k } _ { i } ^ { M } \\right\\| _ { 2 } ^ { 2 } - \\left\\| \\mathbf { k } _ { j } ^ { Q } \\right\\| _ { 2 } ^ { 2 }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "which has only slightly more computation than the baseline dot product, and can be implemented with standard matrix operations. In fact, we can further drop the last term as softmax is invariant to translation in the target dimension (details in the supplementary material). For cosine similarity, we first normalize the input vectors, then compute dot product. Table 2 tabulates the actual computational and memory costs. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2 Experimental Verification ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Here, we verify three claims: 1) the aforementioned phenomenon does happen in a high-dimension key space for real-data and a fully-trained model; 2) using L2 similarity diversifies the voting; 3) L2 similarity brings about higher efficiency and performance. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Affinity distribution. We verify the first two claims by training two different models with dot product and L2 similarity respectively as the similarity function and plot the maximum contribution given by each memory node in its lifetime. We use the same setting for the two models and report the distribution on the DAVIS 2017 [65] dataset. ",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/20466405f829cea9fe78bb766259729256e3a5385ef434da1072cbc7673c1041.jpg",
+        "image_caption": [
+            "Figure 4 shows the pertinent distributions. Under the L2 similarity measure, a lot more memory nodes contribute a fair share. Specifically, around $3 \\%$ memory nodes never contribute more than $1 \\%$ weight under dot product while only $0 . 0 6 \\%$ suffer the same fate with L2. Under dot product, $31 \\%$ memory nodes contribute less than $10 \\%$ weight at best while the same only happen for $7 \\%$ of the memory with L2 similarity. To measure the distribution inequality, we additionally compute the Gini coefficient [70] (the higher it is, the more unequal the distribution). The Gini coefficient for dot product is 44.0, while the Gini coefficient for L2 similarity is much lower at 31.8. ",
+            "Figure 4: The curves show the number of memory nodes that have contributed above a certain threshold at least once. "
+        ],
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+    {
+        "type": "text",
+        "text": "Performance and efficiency. Next, we show that using L2 similarity does improve performance with negligible overhead. We compare three similarity measures: dot product, cosine similarity, and L2 similarity. For cosine similarity, we use a softmax temperature of 0.01 while a default temperature of 1 is used for both dot product and L2 similarity. This scaling is crucial for cosine similarity only since it is the only one with a limited output range $[ - 1 , 1 ]$ . Searching for an extra hyperparameter is computationally demanding – we simply picked one that converges fairly quickly without collapsing. Table 2 tabulates the main results. ",
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+    {
+        "type": "text",
+        "text": "Interestingly, we find that reducing the key space dimension $( C ^ { k } )$ is beneficial to both cosine similarity and L2 similarity but not dot product. This can be explained in the context of Section $4 . 1 -$ the network needs more dimensions so that it can spread the memory key features out to save them from being suppressed by high-magnitude points. Cosine similarity and L2 similarity do not suffer from this problem and can utilize the full key space. The reduced key space in turn benefits memory efficiency and improves running time. ",
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+    {
+        "type": "table",
+        "img_path": "images/74b6a86b6d4c3de104b67905188fbfb26e6b849c736430015cfb0c8832170cb5.jpg",
+        "table_caption": [
+            "Table 2: Performance comparison between different similarity functions and key space dimensionality $( C ^ { k } )$ in STCN on the DAVIS 2017 validation set [65]. The number of floating-point operations (FLOPs) are computed for Eq. 3 and Eq. 4 only with $T = 1 0$ . L2 works the best with a reduced key space and a small computational overhead. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Similarity function</td><td>Ck</td><td>J&amp;F</td><td>#FLOPs (G)</td><td>Size of keys (MB)</td></tr><tr><td>Dot product</td><td>128</td><td>84.1</td><td>6.26</td><td>8.70</td></tr><tr><td>Cosine similarity</td><td>128</td><td>82.6</td><td>6.26</td><td>8.70</td></tr><tr><td>L2 similarity</td><td>128</td><td>85.0</td><td>6.33</td><td>8.70</td></tr><tr><td>Dot product</td><td>64</td><td>83.2</td><td>3.13</td><td>4.35</td></tr><tr><td>Cosine similarity</td><td>64</td><td>83.4</td><td>3.13</td><td>4.35</td></tr><tr><td>L2 similarity</td><td>64</td><td>85.4</td><td>3.20</td><td>4.35</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5 Implementation Details ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Models are trained with two 11GB 2080Ti GPUs with the Adam optimizer [71] using PyTorch [72]. Following previous practices [18, 21], we first pretrain the model on static image datasets [73, 74, 75, 76, 77] with synthetic deformation then perform main training on YouTubeVOS [78] and DAVIS [3, 65]. We also experimented with the synthetic dataset BL30K [79, 80] proposed in [21] which is not used unless otherwise specified. We use a batch size of 16 during pretraining and a batch size of 8 during main training. Pre-training takes about 36 hours and main training takes around 16 hours with batchnorm layers frozen during training following [18]. Bootstrapped cross entropy is used following [21]. The full set of hyperparameters can be found in the open-sourced code. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In each iteration, we pick three temporally ordered frames (with the ground-truth mask for the first frame) from a video to form a training sample [18]. First, we predict the second frame using the first frame as memory. The prediction will be saved as the second memory frame, and then the third frame will be predicted using the union of the first and the second frame. The temporal distance between the frames will first gradually increase from 5 to 25 as a curriculum learning schedule and anneal back to 5 towards the end of training. This process follows the implementation of MiVOS [21]. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For memory-read augmentation, we experimented with kernelized memory reading [22] and top- $k$ filtering [21]. We find that top- $k$ works well universally and improves running time while kernelized memory reading is slower and does not always help. We find that $k = 2 0$ always works better for STCN (original paper uses $k = 5 0$ ) and we adopt top- $k$ filtering in all our experiments with $k = 2 0$ . For fairness, we also re-run all experiments in MiVOS [21] with $k = 2 0$ , and pick the best result in their favor. We use L2 similarity with $C ^ { k } = 6 4$ in all experiments unless otherwise specified. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For inference, a 2080Ti GPU is used with full floating point precision for a fair running time comparison. We memorize every 5th frame and no temporary frame is used as discussed in Section 3.3. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6 Experiments ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We mainly conduct experiments in the DAVIS 2017 validation [65] set and the YouTubeVOS 2018 [78] validation set. For completeness, we also include results in the single object DAVIS 2016 validation [3] set and the expanded YouTubeVOS 2019 [78] validation set. Results for the DAVIS 2017 test-dev [65] set are included in the supplementary material. We first conduct quantitative comparisons with previous methods, and then analyze the running time for each component in STCN. For reference, we also present results without pretraining on stataic images. Ablation studies have been included in previous sections (Table 1 and Table 2). ",
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+    },
+    {
+        "type": "text",
+        "text": "6.1 Evaluations ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 3 tabulates the comparisons of STCN with previous methods in semi-supervised video object segmentation benchmarks. For DAVIS 2017 [65], we compare the standard metrics: region similarity $\\mathcal { I }$ , contour accuracy $\\mathcal { F }$ , and their average $\\mathcal { T } \\& \\mathcal { F }$ . For YouTubeVOS [78], we report $\\mathcal { I }$ and $\\mathcal { F }$ for both seen and unseen categories, and the averaged overall score $\\mathcal { G }$ . For comparing the speed, we compute the multi-object FPS that is the total number of output frames divided by the total processing time for the entire DAVIS 2017 [65] validation set. We either copy the FPS directly from papers/project websites, or estimate based on their single object inference FPS (simply labeled as $< ^ { 5 }$ ). We use $4 8 0 \\mathrm { p }$ resolution videos for both DAVIS and YouTubeVOS. Table 4, 5, 6, and 7 tabulate additional results. For the interactive setting, we replace the propagation module of MiVOS [21] with STCN. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Visualizations. Figure 6 visualizes the learned correspondences. Note that our correspondences are general and mask-free, naturally associating every pixel (including background bystanders) even when it is only trained with foreground masks. Figure 7 visualizes our semi-supervised mask propagation results with the last row being a failure case (Section 7). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Leaderboard results. Our method is also very competitive on the public VOS challenge leaderboard [78]. Methods on the leaderboard are typically cutting-edge, with engineering extensions like deeper network, multi-scale inference, and model ensemble. They usually represent the highest achievable performance at the time. On the latest YouTubeVOS 2019 validation split [78], our base model $( 8 4 . 2 \\mathcal { G } )$ outperforms the previous challenge winner [32] (based on STM [18], $8 2 . 0 \\mathcal { G } ,$ by a large margin. With ensemble and multi-scale testing (details in the supplementary material), our method is ranked first place $( 8 6 . 7 \\mathcal { G } )$ at the time of submission on the still active leaderboard. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "",
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+    {
+        "type": "text",
+        "text": "6.2 Running Time Analysis ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Here, we analyze the running time of each component in STM and STCN on DAVIS 2017 [65]. For a fair comparison, we use our own implementation of STM, enabled top- $k$ filtering [21], and set $C ^ { k } = 6 4$ for both methods such that all the speed improvements come from the fundamental differences between STM and STCN. Our affinity matching time is lower because we compute a single affinity between raw images while STM [18] compute one for every object. Our value encoder takes much less time than the memory encoder in STM [18] because of our light network, feature reuse, and robust memory bank/management as discussed in Section 3.3. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/89a35847b37f478010454e025f80b2632afe824314b17113d6ef63cdf069a911.jpg",
+        "image_caption": [
+            "Figure 5: Average running time of each component in STM and STCN. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            611,
+            638,
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/bff86f85d2cbf5e4cd06243cae1ac3a7162d0a642899c319846e01cc78102c59.jpg",
+        "table_caption": [
+            "Table 3: Comparisons between different methods on DAVIS 2017 and YouTubeVOS 2018 validation sets. Subscripts $S$ and $U$ denote seen or unseen respectively. FPS is measured for multi-object scenarios and is measured on DAVIS 2017. Methods are ranked by YouTubeVOS performance; STM is re-timed on our hardware (see supplementary material); our model is the fastest among methods that are better than STM [18]; \\* denotes contemporary work. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"5\">YouTubeVOS 2018 [78]</td><td colspan=\"4\">DAVIS 2017 [65]</td></tr><tr><td>g</td><td>Js</td><td>Fs</td><td>Ju</td><td>Fu</td><td>J&amp;F</td><td>J</td><td>F</td><td>FPS</td></tr><tr><td>OSMN[8]</td><td>51.2</td><td>60.0</td><td>60.1</td><td>40.6</td><td>44.0</td><td>54.8</td><td>52.5</td><td>57.1</td><td>&lt;7.1</td></tr><tr><td>RGMP [55]</td><td>53.8</td><td>59.5</td><td>=</td><td>45.2</td><td>1</td><td>66.7</td><td>64.8</td><td>68.6</td><td>&lt;7.7</td></tr><tr><td>RVOS[12]</td><td>56.8</td><td>63.6</td><td>67.2</td><td>45.5</td><td>51.0</td><td>50.3</td><td>48.0</td><td>52.6</td><td>&lt;15</td></tr><tr><td>Track-Seg [54]</td><td>63.6</td><td>67.1</td><td>70.2</td><td>55.3</td><td>61.7</td><td>72.3</td><td>68.6</td><td>76.0</td><td>&lt;39</td></tr><tr><td>PReMVOS [81]</td><td>66.9</td><td>71.4</td><td>75.9</td><td>56.5</td><td>63.7</td><td>77.8</td><td>73.9</td><td>81.7</td><td>&lt;0.03</td></tr><tr><td>TVOS [82]</td><td>67.8</td><td>67.1</td><td>69.4</td><td>63.0</td><td>71.6</td><td>72.3</td><td>69.9</td><td>74.7</td><td>37</td></tr><tr><td>FRTM-VOS [6]</td><td>72.1</td><td>72.3</td><td>76.2</td><td>65.9</td><td>74.1</td><td>76.7</td><td>1</td><td>1</td><td>&lt;21.9</td></tr><tr><td>GC [24]</td><td>73.2</td><td>72.6</td><td>68.9</td><td>75.6</td><td>75.7</td><td>71.4</td><td>69.3</td><td>73.5</td><td>&lt;25</td></tr><tr><td>SwiftNet* [30]</td><td>77.8</td><td>77.8</td><td>81.8</td><td>72.3</td><td>79.5</td><td>81.1</td><td>78.3</td><td>83.9</td><td>25</td></tr><tr><td>STM[18]</td><td>79.4</td><td>79.7</td><td>84.2</td><td>72.8</td><td>80.9</td><td>81.8</td><td>79.2</td><td>84.3</td><td>10.2</td></tr><tr><td>AFB-URR[23]</td><td>79.6</td><td>78.8</td><td>83.1</td><td>74.1</td><td>82.6</td><td>74.6</td><td>73.0</td><td>76.1</td><td>4</td></tr><tr><td>GraphMem[16]</td><td>80.2</td><td>80.7</td><td>85.1</td><td>74.0</td><td>80.9</td><td>82.8</td><td>80.2</td><td>85.2</td><td>5</td></tr><tr><td>MiVOS* [21]</td><td>80.4</td><td>80.0</td><td>84.6</td><td>74.8</td><td>82.4</td><td>83.3</td><td>80.6</td><td>85.9</td><td>11.2</td></tr><tr><td>CFBI[10]</td><td>81.4</td><td>81.1</td><td>85.8</td><td>75.3</td><td>83.4</td><td>81.9</td><td>79.1</td><td>84.6</td><td>5.9</td></tr><tr><td>KMN[22]</td><td>81.4</td><td>81.4</td><td>85.6</td><td>75.3</td><td>83.3</td><td>82.8</td><td>80.0</td><td>85.6</td><td>&lt;8.4</td></tr><tr><td>RMNet*[29]</td><td>81.5</td><td>82.1</td><td>85.7</td><td>75.7</td><td>82.4</td><td>83.5</td><td>81.0</td><td>86.0</td><td>&lt;11.9</td></tr><tr><td>LWL [7]</td><td>81.5</td><td>80.4</td><td>84.9</td><td>76.4</td><td>84.4</td><td>81.6</td><td>79.1</td><td>84.1</td><td>&lt;6.0</td></tr><tr><td>CFBI+* [83]</td><td>82.0</td><td>81.2</td><td>86.0</td><td>76.2</td><td>84.6</td><td>82.9</td><td>80.1</td><td>85.7</td><td>5.6</td></tr><tr><td>LCM* [28]</td><td>82.0</td><td>82.2</td><td>86.7</td><td>75.7</td><td>83.4</td><td>83.5</td><td>80.5</td><td>86.5</td><td>~9.2</td></tr><tr><td>Ours</td><td>83.0</td><td>81.9</td><td>86.5</td><td>77.9</td><td>85.7</td><td>85.4</td><td>82.2</td><td>88.6</td><td>20.2</td></tr><tr><td>MiVOS*[21] + BL30K Ours +BL30K</td><td>82.6 84.3</td><td>81.1 83.2</td><td>85.6 87.9</td><td>77.7 79.0</td><td>86.2 87.3</td><td>84.5 85.3</td><td>81.7 82.0</td><td>87.4</td><td>11.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "image",
+        "img_path": "images/0c2526ce8ca45ab9ca5422616a63e9ebec9e443d6aabd859cf7cee21a45f697e.jpg",
+        "image_caption": [
+            "Figure 6: Visualization of the correspondences. Labels are hand-picked in the source frame (leftmost) and are propagated to the rest directly without intermediate memory. We label all the peaks (e.g., the two yellow diamonds representing the front/back wheel – our algorithm cannot distinguish them). The bystander in white (labeled with an orange crescent) is occluded in the last frame and the resultant affinity does not have a distinct peak (not labeled). "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "7 Limitations ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "To alienate our method from other possible enhancement, we only use fundamentally simple global matching. Like STM [18], we have no notion of temporal consistency as we do not employ local matching [58, 10, 17] or optical flow [29]. This means we may incorrectly segment objects that are far away with similar appearance. One such failure case is shown on the last row of Figure 7. We expect that given our framework’s simplicity, our method can be readily extended to include temporal consistency consideration for further improvement. ",
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+    },
+    {
+        "type": "text",
+        "text": "8 Conclusion ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We present STCN, a simple, effective, and efficient framework for video object segmentation. We propose to use direct image-to-image correspondence for efficiency and more robust matching, and examine the inner workings of affinity in details $^ { - \\mathbf { L } 2 }$ similarity is proposed as a result of our observations. With its clear technical advantages, We hope that STCN can serve as a new baseline backbone for future contributions. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "table",
+        "img_path": "images/ce87789368e97b8f282ad1b95fe2fc4cb3d91be33ec8d36a5eb99434fdbbef2c.jpg",
+        "table_caption": [
+            "Table 4: Results on the DAVIS 2016 validation set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>J&amp;F</td><td>J</td><td>F</td></tr><tr><td>OSMN [8]</td><td>73.5</td><td>74.0</td><td>72.9</td></tr><tr><td>MaskTrack [15]</td><td>77.6</td><td>79.7</td><td>75.4</td></tr><tr><td>OSVOS [5]</td><td>80.2</td><td>79.8</td><td>80.6</td></tr><tr><td>FAVOS [14]</td><td>81.0</td><td>82.4</td><td>79.5</td></tr><tr><td>FEELVOS[58]</td><td>81.7</td><td>81.1</td><td>82.2</td></tr><tr><td>RGMP [55]</td><td>81.8</td><td>81.5</td><td>82.0</td></tr><tr><td>Track-Seg [54]</td><td>83.1</td><td>82.6</td><td>83.6</td></tr><tr><td>FRTM-VOS [6]</td><td>83.5</td><td>=</td><td>-</td></tr><tr><td>CINN [51]</td><td>84.2</td><td>83.4</td><td>85.0</td></tr><tr><td>OnAVOS [50]</td><td>85.5</td><td>86.1</td><td>84.9</td></tr><tr><td>PReMVOS[81]</td><td>86.8</td><td>84.9</td><td>88.6</td></tr><tr><td>GC [24]</td><td>86.8</td><td>87.6</td><td>85.7</td></tr><tr><td>RMNet [29]</td><td>88.8</td><td>88.9</td><td>88.7</td></tr><tr><td>STM[18]</td><td>89.3</td><td>88.7</td><td>89.9</td></tr><tr><td>CFBI[10]</td><td>89.4</td><td>88.3</td><td>90.5</td></tr><tr><td>CFBI+ [83]</td><td>89.9</td><td>88.7</td><td>91.1</td></tr><tr><td>MiVOS [21]</td><td>90.0</td><td>88.9</td><td>91.1</td></tr><tr><td>SwiftNet [30]</td><td>90.4</td><td>90.5</td><td>90.3</td></tr><tr><td>KMN [22]</td><td>90.5</td><td>89.5</td><td>91.5</td></tr><tr><td>LCM [28]</td><td>90.7</td><td>91.4</td><td>89.9</td></tr><tr><td>Ours</td><td>91.6</td><td>90.8</td><td>92.5</td></tr><tr><td>MiVOS [21] + BL30K</td><td>91.0</td><td>89.6</td><td>92.4</td></tr><tr><td>Ours+BL30K</td><td>91.7</td><td>90.4</td><td>93.0</td></tr></table>",
+        "bbox": [
+            183,
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+            443
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/2b913abd832e573862cb6f169891e93a67fffa0675c5e3113bee8c262e5e4a62.jpg",
+        "table_caption": [
+            "Table 5: Results on the YouTubeVOS 2019 validation set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>9</td><td></td><td></td><td>Js Fs Ju Ju</td></tr><tr><td>MiVOS [21]</td><td>80.3</td><td>79.3 83.7</td><td>75.3</td><td>82.8</td></tr><tr><td>CFBI[10]</td><td>81.0 80.6</td><td>85.1</td><td>75.2</td><td>83.0</td></tr><tr><td>Ours</td><td>82.7 81.1</td><td>85.4</td><td>78.2</td><td>85.9</td></tr><tr><td>MiVOS[21] + BL30K 82.4 80.6 84.7 78.1</td><td></td><td></td><td></td><td>86.4</td></tr><tr><td>Ours +BL30K</td><td>84.2</td><td>82.6 87.0</td><td>79.4 87.7</td><td></td></tr></table>",
+        "bbox": [
+            485,
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+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "table",
+        "img_path": "images/5c1f8d42ee3f6ffe13249432da8e5721f850860730270b2b2e9d714385fbd4d6.jpg",
+        "table_caption": [
+            "Table 6: Results on the DAVIS interactive track [65]. BL30K [21] used for both MiVOS and ours. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>AUC-J&amp;F</td><td>J&amp;F@60s</td><td>Time (s)</td></tr><tr><td>ATNet [84]</td><td>80.9</td><td>82.7</td><td>55+</td></tr><tr><td>STM [85]</td><td>80.3</td><td>84.8</td><td>37</td></tr><tr><td>GIS [86]</td><td>85.6</td><td>86.6</td><td>34</td></tr><tr><td>MiVOS [21]</td><td>87.9</td><td>88.5</td><td>12</td></tr><tr><td>Ours</td><td>88.4</td><td>88.8</td><td>7.3</td></tr></table>",
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+    },
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+        "type": "table",
+        "img_path": "images/cf5da519123ed06550d3a355c0e157932df312b0c854b66cc60c1bd48732ab18.jpg",
+        "table_caption": [
+            "Table 7: Effects of pretraining on static images/maintraining on the DAVIS 2017 validation set. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>J&amp;F</td><td>J</td><td>F</td></tr><tr><td>Pre-training only</td><td>75.8</td><td>73.1</td><td>78.6</td></tr><tr><td>Main training only</td><td>82.5</td><td>79.3</td><td>85.7</td></tr><tr><td>Both</td><td>85.4</td><td>82.2</td><td>88.6</td></tr></table>",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/94e37f4502159e43cad81f95b2efe5f2ac0471328649960cf9653bf5649ea78d.jpg",
+        "image_caption": [
+            "Figure 7: Visualization of semi-supervised VOS results with the first column being the reference masks to be propagated. The first two examples show comparisons of our method with STM [18] and MiVOS [21]. In the second example, zoom-ins inset (orange) are shown with the corresponding ground-truths inset (green) to highlight their differences. The last row shows a failure case: we cannot distinguish the real duck from the duck picture, as no temporal consistency clue is used in our method. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Broader Impacts Malicious use of VOS software can bring potential negative societal impacts, including but not limited to unauthorized mass surveillance or privacy infringing human/vehicle tracking. We believe that the task itself is neutral with positive uses as well, such as video editing for amateurs or making safe self-driving cars. ",
+        "bbox": [
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+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgment ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            89,
+            321,
+            106
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "This research is supported in part by Kuaishou Technology and the Research Grant Council of the Hong Kong SAR under grant no. 16201818. ",
+        "bbox": [
+            176,
+            119,
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+            148
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            167,
+            266,
+            183
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
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parse/train/yT7-k6Q6gda/yT7-k6Q6gda.md

@@ -0,0 +1,460 @@
+# CATASTROPHIC FISHER EXPLOSION: EARLY PHASE FISHER MATRIX IMPACTS GENERALIZATION
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+The early phase of training has been shown to be important in two ways for deep neural networks. First, the degree of regularization in this phase significantly impacts the final generalization. Second, it is accompanied by a rapid change in the local loss curvature influenced by regularization choices. Connecting these two findings, we show that stochastic gradient descent (SGD) implicitly penalizes the trace of the Fisher Information Matrix (FIM) from the beginning of training. We argue it is an implicit regularizer in SGD by showing that explicitly penalizing the trace of the FIM can significantly improve generalization. We further show that the early value of the trace of the FIM correlates strongly with the final generalization. We highlight that in the absence of implicit or explicit regularization, the trace of the FIM can increase to a large value early in training, to which we refer as catastrophic Fisher explosion. Finally, to gain insight into the regularization effect of penalizing the trace of the FIM, we show that it limits memorization by reducing the learning speed of examples with noisy labels more than that of the clean examples, and 2) trajectories with a low initial trace of the FIM end in flat minima, which are commonly associated with good generalization.
+
+# 1 INTRODUCTION
+
+Implicit regularization in gradient-based training of deep neural networks (DNNs) remains relatively poorly understood, despite being considered a critical component in their empirical success (Neyshabur, 2017; Zhang et al., 2016; Jiang et al., 2020b). Recent work suggests that the early phase of training of DNNs might hold the key to understanding these implicit regularization effects. Golatkar et al. (2019); Keskar et al. (2017); Sagun et al. (2018); Achille et al. (2019) show that by introducing regularization later, a drop in performance due to lack of regularization in this phase is hard to recover from, while on the other hand, removing regularization after the early phase has a relatively small effect on the final performance.
+
+Other works show that the early phase of training also has a dramatic effect on the trajectory in terms of properties such as the local curvature of the loss surface or the gradient norm (Jastrzebski et al., 2020; Frankle et al., 2020). In particular, Achille et al. (2019); Jastrz˛ebski et al. (2019); Golatkar et al. (2019); Lewkowycz et al. (2020); Leclerc & Madry (2020) independently suggest that rapid changes in the local curvature of the loss surface in the early phase critically affects the final generalization. Closely related to our work, Lewkowycz et al. (2020); Jastrz˛ebski et al. (2019) show that using a large learning rate has a dramatic effect on the early optimization trajectory in terms of the loss curvature. These observations lead to a question: what is the mechanism by which regularization in the early phase impacts the optimization trajectory and generalization? We investigate this question mainly through the lens of the Fisher Information Matrix (FIM), a matrix that can be seen as approximating the local curvature of the loss surface in DNNs (Martens, 2020; Thomas et al., 2020).
+
+Our main contribution is to show that the implicit regularization effect of using a large learning rate or a small batch size can be modeled as an implicit penalization of the trace of the FIM $( \mathrm { T r } ( \mathbf { F } ) )$ from the very beginning of training. We demonstrate on image classification tasks that the value of $\operatorname { T r } ( \mathbf { F } )$ early in training correlates with the final generalization performance across settings with different learning rates or batch sizes. We then show evidence that explicitly regularizing $\operatorname { T r } ( \mathbf { F } )$ (which we call Fisher penalty) significantly improves generalization in training with a sub-optimal learning rate. On the other hand, growth of $\operatorname { T r } ( \mathbf { F } )$ early in training, which may occur in practice when using a relatively small learning rate, coincides with poor generalization. We call this phenomenon the catastrophic Fisher explosion. Figure 1 illustrates this effect on the TinyImageNet dataset (Le & Yang, 2015).
+
+![](images/e3ebeb7411d3dac8e18f12947af3479c29c6a9c5d44a902b8fa594ef7e2f9627.jpg)  
+Figure 1: The catastrophic Fisher explosion phenomenon demonstrated for Wide ResNet trained using stochastic gradient descent on the TinyImageNet dataset. Training is done with either a learning rate optimized using grid search $\zeta _ { 1 1 } = 0 . 0 3 1 6$ , red), or a small learning rate $\dot { \eta } _ { 2 } = 0 . 0 0 1$ , blue). Training with $\eta _ { 2 }$ leads to large overfitting (left) and a sharp increase in the trace of the Fisher Information Matrix (FIM, middle). The trace of the FIM is closely related to the gradient norm (right).
+
+![](images/b2020287c1e9258742e6bcdd95efaf2a185f4d7d2886a57b79aa11e4b6f1b047.jpg)  
+Figure 2: Association between the value of $\operatorname { T r } ( \mathbf { F } )$ in the initial phase of training $( \mathrm { { T r } ( { F _ { i } } ) } )$ and test accuracy on ImageNet, CIFAR-10 and CIFAR-100 datasets. Each point corresponds to multiple seeds and a specific value of learning rate. $\operatorname { T r } ( \mathbf { F _ { i } } )$ is recorded during the early phase of training (2-7 epochs, see the main text for details). The plots show that early $\operatorname { T r } ( \mathbf { F } )$ is predictive of final generalization. Analogous results illustrating the influence of batch size are shown in Appendix A.1
+
+Our second contribution is an analysis of why implicitly or explicitly regularizing $\operatorname { T r } ( \mathbf { F } )$ impacts generalization. We reveal two effects of implicit or explicit regularization of $\operatorname { T r } ( \mathbf { F } )$ : (1) penalizing ${ \bar { \mathrm { T r } } } ( \mathbf { F } )$ discourages memorizing noisy labels, (2) small $\operatorname { T r } ( \mathbf { F } )$ in the early phase of training biases optimization towards a flat minimum, as characterized by the trace of the Hessian.
+
+# 2 IMPLICIT AND EXPLICIT REGULARIZATION OF THE FIM
+
+Fisher Information Matrix Consider a probabilistic classification model $p _ { \pmb { \theta } } ( \pmb { y } | \pmb { x } )$ , where $\pmb { \theta }$ denotes its parameters. Let $\ell ( x , y ; \theta )$ be the cross-entropy loss function calculated for input $_ { \textbf { \em x } }$ and label $y$ . Let bject $\begin{array} { r } { g ( \pmb { x } , y ; \pmb { \theta } ) = \frac { \partial } { \partial \pmb { \theta } } \ell ( \pmb { x } , y ; \pmb { \theta } ) } \end{array}$ denote the gradient Information Matrix mputed for an example defined as $( { \pmb x } , y )$ . The central $\mathbf { F }$
+
+$$
+\mathbf { F } ( \pmb { \theta } ) = \mathbb { E } _ { \pmb { x } \sim \mathcal { X } , \hat { \pmb { y } } \sim p _ { \theta } ( y | \pmb { x } ) } [ g ( \pmb { x } , \hat { y } ) g ( \pmb { x } , \hat { y } ) ^ { T } ] ,
+$$
+
+where the expectation is often approximated using the empirical distribution $\hat { \mathcal X }$ induced by the training set. We denote its trace by $\operatorname { T r } ( \mathbf { F } )$ . Later, we also look into the Hessian $\begin{array} { r } { { \bf H } ( \pmb \theta ) = \frac { \partial ^ { 2 } } { \partial \pmb \theta ^ { 2 } } \ell ( \pmb x , y ; \pmb \theta ) } \end{array}$ . We denote its trace by $\mathrm { T r } ( \mathbf { H } )$ .
+
+The FIM can be seen as an approximation to the Hessian (Martens, 2020). In particular, as $p ( \boldsymbol { y } | \mathbf { x } ; \boldsymbol { \theta } )  \hat { p } ( \boldsymbol { y } | \mathbf { x } )$ , where $\hat { p } ( y | \mathbf x )$ is the empirical label distribution, the FIM converges to the
+
+Hessian. Thomas et al. (2020) showed on image classifications tasks that $\operatorname { T r } ( \mathbf { H } ) \approx \operatorname { T r } ( \mathbf { F } )$ along the optimization trajectory, which we also evidence in Appendix F.
+
+Fisher Penalty Several studies have presented evidence that the early phase has a drastic effect on the trajectory in terms of the local curvature of the loss surface (Achille et al., 2019; Jastrz˛ebski et al., 2019; Gur-Ari et al., 2018; Lewkowycz et al., 2020; Leclerc & Madry, 2020). In particular, Lewkowycz et al. (2020); Jastrz˛ebski et al. (2019) show that using a large learning rate in stochastic gradient descent biases training towards low curvature regions of the loss surface very early in training. For example, using a large learning rate in SGD was shown to result in a rapid decay of $\mathrm { T r } ( \mathbf { H } )$ along the optimization trajectory Jastrz˛ebski et al. (2019).
+
+Our main contribution is to propose and investigate a specific mechanism by which using a large learning rate or a small batch size implicitly influences final generalization. Our first insight is to shift the focus from studying the Hessian, to studying properties of the FIM. Concretely, we hypothesize that using a large learning rate or a small batch size improves generalization by implicitly penalizing $\operatorname { T r } ( \mathbf { F } )$ from the very beginning of training.
+
+The benefit of studying the FIM is that it can be directly and efficiently manipulated during training. In order to study the effect of implicit regularization of $\operatorname { T r } ( \mathbf { F } )$ , we introduce a regularizer, which we refer to as Fisher penalty, explicitly penalizing $\operatorname { T r } ( \mathbf { F } )$ . We derive this regularizer in the following way. First, we note that $\operatorname { T r } ( \mathbf { F } )$ can be written as $\begin{array} { r } { \mathrm { T r } ( \mathbf { F } ) = \mathbb { E } _ { \boldsymbol { x } \sim \mathcal { X } , \hat { \boldsymbol { y } } \sim p _ { \boldsymbol { \theta } } ( \boldsymbol { y } \vert \mathbf { x } ) } \left[ \Vert \frac { \partial } { \partial \boldsymbol { \theta } } \boldsymbol { \ell } ( \mathbf { x } , \hat { \boldsymbol { y } } ) \Vert _ { 2 } ^ { 2 } \right] . } \end{array}$
+
+To regularize $\operatorname { T r } ( \mathbf { F } )$ , we add the following term to the loss function:
+
+$$
+\ell ^ { \prime } ( x _ { 1 : B } , y _ { 1 : B } ; \pmb \theta ) = \frac { 1 } { B } \sum _ { i = 1 } ^ { B } \ell ( { \pmb x } _ { i } , y _ { i } ; \pmb \theta ) + \alpha \left\| \frac { 1 } { B } \sum _ { i = 1 } ^ { B } g ( { \pmb x } _ { i } , \hat { y } _ { i } ) \right\| ^ { 2 } ,
+$$
+
+where $\left( \pmb { x } _ { 1 : B } , \pmb { y } _ { 1 : B } \right)$ is a mini-batch, $\hat { y } _ { i }$ is sampled from $p _ { \pmb { \theta } } ( \pmb { y } | \pmb { x } _ { i } )$ , and $\alpha$ is a hyperparameter. We refer to this regularizer as Fisher penalty. The formulation is based on the empirical observation that $\begin{array} { r l } & { \left\| \frac { 1 } { B } \sum _ { i = 1 } ^ { B } g ( \pmb { x } _ { i } , \hat { y } _ { i } ) \right\| ^ { 2 } } \end{array}$ 2 and $\operatorname { T r } ( \mathbf { F } )$ correlate well during training. Crucially, this allows us to reduce the added computational cost of Fisher penalty to that of a single additional backpropagation call (Drucker & Le Cun, 1992). Finally, we compute the gradient of the second term only every 10 optimization steps, and in a given iteration use the most recently computed gradient. We discuss these approximations in detail in Appendix C.
+
+Catastrophic Fisher Explosion To illustrate the concepts mentioned in this section, we train a Wide ResNet model (depth 44, width 3) (Zagoruyko & Komodakis, 2016) on the TinyImageNet dataset with SGD and two different learning rates. We illustrate in Figure 1 that the small learning rate leads to dramatic overfitting, which coincides with a sharp increase in $\operatorname { T r } ( \mathbf { F } )$ in the early phase of training. We also show in Appendix D that these effects cannot be explained by the difference in learning speed between runs with smaller and learning rates. We call this phenomenon the catastrophic Fisher explosion.
+
+# 3 EARLY-PHASE $\mathrm { T r } ( \mathbf F )$ CORRELATES WITH FINAL GENERALIZATION
+
+Using a large learning rate $( \eta )$ or a small batch size $( S )$ in SGD steers optimization to a lower curvature region of the loss surface. However, it remains a hotly debated topic whether this explains their strong regularization effect (Dinh et al., 2017; He et al., 2019; Maddox et al., 2020; Tsuzuku et al., 2019; Yoshida & Miyato, 2017). We begin by studying the connection between $\operatorname { T r } ( \mathbf { F } )$ and generalization in experiments across which we vary $\eta$ or $S$ in SGD.
+
+Experimental setup We run our experiments in two settings: (1) ResNet-18 with Fixup He et al. (2015); Zhang et al. (2019) trained on the ImageNet dataset (Deng et al., 2009), (2) ResNet-26 initialized with Arpit et al. (2019) trained on the CIFAR-10 and CIFAR-100 datasets (Krizhevsky, 2009). We train each architecture using SGD, with various values of $\eta , S .$ , and random seed.
+
+We define $\operatorname { T r } ( \mathbf { F _ { i } } )$ as $\operatorname { T r } ( \mathbf { F } )$ during the initial phase of training. The early-phase $\operatorname { T r } ( \mathbf { F } )$ is measured when the training loss crosses a task-specific threshold $\epsilon$ . For ImageNet, we use learning rates 0.001,
+
+Table 1: Using a 10-30x smaller learning rate (Baseline) results in up to $9 \%$ degradation in test accuracy on popular image classification benchmarks (c.f. to optimal $\eta ^ { * }$ ). Adding Fisher penalty (FP) substantially improves generalization and closes the gap to $\eta ^ { * }$ . We do not use data augmentation with CIFAR-10 and CIFAR-100 to ensure that using a small learning rate does not lead to under-fitting.   
+
+<table><tr><td>Setting</td><td>m*</td><td>Baseline</td><td>GPx</td><td>GP</td><td>FP</td><td>GPr</td></tr><tr><td>WResNet/TinyImageNet (aug.)</td><td>54.67%</td><td>52.57%</td><td>52.79%</td><td>56.44%</td><td>56.73%</td><td>55.41%</td></tr><tr><td>DenseNet/C100(w/o aug.)</td><td>66.09%</td><td>58.51%</td><td>62.12%</td><td>64.42%</td><td>66.41%</td><td>66.39%</td></tr><tr><td>VGG11/C100 (w/o aug.）</td><td>45.86%</td><td>36.86%</td><td>45.26%</td><td>47.35%</td><td>49.87%</td><td>48.26%</td></tr><tr><td>WResNet/C100 (w/o aug.)</td><td>53.96%</td><td>46.38%</td><td>58.68%</td><td>57.68%</td><td>57.05%</td><td>58.15%</td></tr><tr><td>SimpleCNN/C10(w/o aug.)</td><td>76.94%</td><td>71.32%</td><td>75.68%</td><td>75.73%</td><td>79.66%</td><td>79.76%</td></tr></table>
+
+0.01, 0.1, and $\epsilon = 3 . 5$ . For CIFAR-10, we use learning rates 0.007, 0.01, 0.05, and $\epsilon = 1 . 2$ . For CIFAR-100, we use learning rates 0.001, 0.005, 0.01, and $\epsilon = 3 . 5$ . In all cases, training loss reaches $\epsilon$ between 2 and 7 epochs across different hyper-parameter settings. We repeat similar experiments for different batch sizes in Appendix A.1. The remaining training details can be found in Appendix G.1.
+
+Results Figure 2 shows the correlation between $\operatorname { T r } ( \mathbf { F _ { i } } )$ and test accuracy across runs with different learning rates. We show results for CIFAR-10 and CIFAR-100 when varying the batch size in Figure 7 in the Appendix. We find that $\mathrm { { T r } ( \mathbf { F _ { i } } ) }$ correlates well with the final generalization in our setting, which provides initial evidence for the importance of $\operatorname { T r } ( \mathbf { F } )$ . It also serves as a stepping stone towards developing a more granular understanding of the role of implicit regularization of $\operatorname { T r } ( \mathbf { F } )$ in the following sections.
+
+# 4 FISHER PENALTY
+
+To better understand the significance of the identified correlation between $\operatorname { T r } ( \mathbf { F _ { i } } )$ and generalization, we now run experiments in which we directly penalize $\operatorname { T r } ( \mathbf { F } )$ . We focus our attention on the identified effect of high learning rate on $\operatorname { T r } ( \mathbf { F } )$ .
+
+Experimental setting We use a similar setting as in the previous section, but we include larger models. We run experiments using Wide ResNet (Zagoruyko & Komodakis, 2016) (depth 44 and width 3, with or without BN layers), SimpleCNN (without BN layers), DenseNet $\mathrm { L } { = } 4 0$ , $\mathrm { K } { = } 1 2$ ) (Huang et al., 2017) and VGG-11 (Simonyan & Zisserman, 2015). We train these models on either the CIFAR-10 or the CIFAR-100 datasets. Due to larger computational cost, we replace ImageNet with the TinyImageNet dataset (Le & Yang, 2015) in these experiments.
+
+To investigate if the correlation of $\operatorname { T r } ( \mathbf { F _ { i } } )$ and final generalization holds more generally, we apply Fisher penalty in two settings. First, we use a learning rate $1 0 – 3 0 \mathrm { x }$ smaller than the optimal one, which both incur up to $9 \%$ degradation in test accuracy and results in large value of $\operatorname { T r } ( \mathbf { F _ { i } } )$ . We also remove data augmentation from the CIFAR-10 and the CIFAR-100 datasets to ensure that training with small learning rate does not result in underfitting. In the second setting, we add Fisher penalty in training with an optimized learning rate using grid search $( \eta ^ { * } )$ and train with data augmentation.
+
+Fisher penalty penalizes the gradient norm computed using labels sampled from $p _ { \pmb { \theta } } ( \pmb { y } | \pmb { x } )$ . We hyFir size that a similar, but weaker, effect can be introducee compare FP to penalizing the input gradient norm $\begin{array} { r } { \| \pmb { g } _ { x } \| = \frac { \partial ^ { \smile } } { \partial \pmb { x } } \ell ( \pmb { x } , y ) } \end{array}$ norm regularizers., which we denote $\mathrm { G P _ { x } }$ (Varga et al., 2018; Rifai et al., 2011; Drucker & Le Cun, 1992). We also experiment with penalizing the vanilla mini-batch gradient Gulrajani et al. (2017), which we denote by GP. Finally, we experiment with penalizing the mini-batch gradient computed with random labels $\begin{array} { r } { \| \dot { \pmb g } _ { r } \| = \frac { \partial } { \partial \pmb x } \ell ( \pmb x , \hat { y } ) } \end{array}$ where $\hat { y }$ is sampled from a uniform distribution over the label set $( \mathrm { G P _ { r } } )$ . We are not aware of any prior work using GP or $\mathrm { G P _ { r } }$ in supervised training, with the exception of Alizadeh et al. (2020) where the authors penalized $\ell _ { 1 }$ norm of gradients to compress the network towards the end of training.
+
+We tune the hyperparameters on the validation set. More specifically for $\alpha$ , we test 10 different values spaced uniformly between $1 0 ^ { - 1 } \times v$ to $1 0 ^ { 1 } \times v$ on a logarithmic scale with $v \in \mathbb { R } _ { + }$ . For TinyImageNet we test 5 alternatives instead. To pick the optimal learning rate, we evaluate 5 values spaced equally on a logarithmic scale. We include the remaining experimental details in the Appendix G.2.
+
+Table 2: Fisher penalty (FP) improves generalization in 4 out of 5 settings when applied with the optimal learning rate $\eta ^ { * }$ and trained using standard data augmentation. In 3 out of 5 settings the difference between FP and $\eta ^ { * }$ is small (below $1 \%$ ), which is expected given that FP is aimed at reproducing the regularization effect of large $\eta$ , and we compare to training with the optimal $\eta ^ { * }$ .   
+
+<table><tr><td>Setting</td><td>m*</td><td>FP</td></tr><tr><td>DenseNet/C100 (aug.)</td><td>74.41±0.47%</td><td>74.19±0.51%</td></tr><tr><td>VGG11/C100 (aug.)</td><td>59.82±1.23%</td><td>65.08±0.53%</td></tr><tr><td>WResNet/C100 (aug.)</td><td>69.48±0.30%</td><td>71.53±1.22%</td></tr><tr><td>SimpleCNN/C10 (aug.)</td><td>87.16±0.16%</td><td>87.52±0.50%</td></tr><tr><td>WResNet/TinyImageNet (aug.)</td><td>54.70±0.04%</td><td>60.00±0.07 %</td></tr></table>
+
+![](images/43f0eb346c353e1372e8e5d3ed68da3c2418b55a49ba194fae26afc8ac5ec278.jpg)  
+Figure 3: Training with FP or $\mathrm { G P _ { x } }$ improves generalization and limits early peak of $\operatorname { T r } ( \mathbf { F } )$ . Each subfigure shows validation accuracy (left) and $\operatorname { T r } ( \mathbf { F } )$ (right) for training with $\eta ^ { * }$ or a small learning rate (blue) and for training with either $\mathrm { G P _ { x } }$ or FP (red). Curves were smoothed for clarity.
+
+Fisher Penalty improves generalization Table 1 summarizes the results of the main experiment. First, we observe that a suboptimal learning rate $1 0 – 3 0 \mathrm { x }$ lower than the optimal) leads to dramatic overfitting. We observe a degradation of up to $9 \%$ in test accuracy, while achieving perfect training accuracy (see Table 6 in the Appendix).
+
+Fisher penalty closes the gap in test accuracy between the small and optimal learning rate, and even achieves better performance than the optimal learning rate. A similar performance was observed when minimizing $\| g _ { r } \|$ . We will come back to this observation in the next section.
+
+GP and $\mathrm { G P _ { x } }$ reduce the early value of $\operatorname { T r } ( \mathbf { F } )$ (see Table 4 in the Appendix). They, however, generally perform worse than $\operatorname { T r } ( \mathbf { F } )$ or $\mathrm { G P _ { r } }$ and do not fully close the gap between small and optimal learning rate. We hypothesize they improve generalization by a similar but less direct mechanism than $\operatorname { T r } ( \mathbf { F } )$ and $\mathrm { G P _ { r } }$ .
+
+In the second experimental setting, we apply FP to a network trained with the optimal learning rate $\eta ^ { * }$ . According to Table 2, Fisher Penalty improves generalization in 4 out of 5 settings. The gap between the baseline and FP is small in 3 out of 5 settings (below $1 \%$ ), which is natural given that we already regularize training implicitly by using the optimal $\eta$ and data augmentation.
+
+Geometry and generalization in the early phase of training Here, we investigate the temporal aspect of Fisher Penalty on CIFAR-10 and CIFAR-100. In particular, we study whether early penalization of $\operatorname { T r } ( \mathbf { F } )$ matters for final generalization.
+
+First, we observe that all gradient-norm regularizers reduce the early value of $\operatorname { T r } ( \mathbf { F } )$ closer to $\operatorname { T r } ( \mathbf { F } )$ achieved when trained with the optimal learning rate $\eta ^ { * }$ . We show this effect with Wide ResNet and VGG-11 on CIFAR-100 in Figure 3, and for other experimental settings in the Appendix. We also tabulate the maximum achieved values of $\operatorname { T r } ( \mathbf { F } )$ over the optimization trajectory in Appendix A.2.
+
+![](images/8ce904557cc7e22826007bf7e77e02a0e24439f18434c27a2b85e5ee6489c3c7.jpg)  
+Figure 4: Each subplot summarizes an experiment in which we apply Fisher Penalty starting from a certain epoch $\mathbf { \dot { x } }$ axis) and measure the final test accuracy (y axis). Fisher Penalty has to be applied from the beginning of training to close the generalization gap to the optimal learning rate (c.f. the red horizontal line to the blue horizontal line).
+
+To test the importance of explicitly penalizing $\operatorname { T r } ( \mathbf { F } )$ early in training, we start applying it after a certain number of epoch $E \in \{ 1 , 2 , 4 , 8 , 1 6 , 3 2 , 6 4 , 1 2 8 \}$ . We use the best hyperparameter set from the previous experiments. Figure 4 summarizes the results. For both datasets, we observe a consistent pattern. When FP is applied starting from a later epoch, final generalization is significantly worse, and the generalization gap arising from a suboptimal learning rate is not closed.
+
+# 4.1 FISHER PENALTY REDUCES MEMORIZATION
+
+It is not self-evident how regularizing $\operatorname { T r } ( \mathbf { F } )$ influences generalization. In this section, we provide evidence that regularizing $\operatorname { T r } ( \mathbf { F } )$ slows down learning on data with noisy labels. To study this, we replace labels of the examples in the CIFAR-100 dataset $2 5 \%$ or $50 \%$ of the training set) with labels sampled uniformly. While label noise in real datasets is not uniform, methods that perform well with uniform label noise generally are more robust to label noise in real datasets (Jiang et al., 2020a). We also know that datasets such as CIFAR-100 contain many labeling errors (Song et al., 2020). As such, examining how $\operatorname { T r } ( \mathbf { F } )$ reduces memorization of synthetic label noise provides an insight into how it improves generalization in our prior experiments.
+
+We expect FP to reduce memorization. When the predictive distribution $p _ { \pmb { \theta } } ( \pmb { y } | \pmb { x } )$ and the true label distribution $p ^ { * } ( y | \pmb { x } )$ are both uniform, $\operatorname { T r } ( \mathbf { F } )$ of the specific example $_ { \textbf { \em x } }$ is equivalent to the squared loss gradient norm of the sample example. The proposed Fisher penalty thus minimizes the contribution of the loss gradient from the training examples whose labels were sampled uniformly. In other words, the Fisher penalty implicitly suppresses learning noisy examples, under the assumption that clean examples’ label distributions are not uniform.
+
+To study whether the above happens in practice, we compare FP to $\mathrm { G P _ { x } }$ , $\mathrm { G P _ { r } }$ , and mixup (Zhang et al., 2018). While mixup is not the state-of-the-art approach to learning with noisy labels, it is competitive among approaches that do not require additional data nor multiple stages of training. In particular, it is a component in several state-of-the-art approaches (Li et al., 2020; Song et al., 2020). For gradient norm based regularizers, we evaluate 6 different hyperparameter values spaced uniformly on a logarithmic scale, and for mixup we evaluate $\beta \in \{ 0 . 2 , 0 . 4 , 0 . 8 , 1 . 6 , 3 . 2 , 6 . 4 \}$ . We experiment with the Wide ResNet and VGG-11 models. We describe remaining experimental details in the Appendix G.3.
+
+Results We begin by studying the learning dynamics on data with noisy labels through the lens of training accuracy and mini-batch gradient norm. We show the results for VGG-11 and ResNet-50 in Figure 5 and Figure 9 in the Appendix. We observe that FP limits the ability of the model to memorize data more strongly than it limits its ability to learn from clean data. We can further confirm our interpretation of the effect $\operatorname { T r } ( \mathbf { F } )$ has on training by studying the gradient norms. As visible in Figure 5, the gradient norm on examples with noisy labels is larger than on clean examples, and the ratio is closer to 1 when large regularization is applied.
+
+We report test accuracy (at the best validation point) in Table 3. We observe that $\operatorname { T r } ( \mathbf { F } )$ reduces memorization competitively to mixup. Furthermore, FP performs similarly to $\mathrm { G P _ { r } }$ , which agrees with our interpretation of why FP limits learning on examples with noisy labels.
+
+![](images/7a321bba955d23a1a40fbb9eae9e586fa508ab1dd3635b670494059f72f4c041.jpg)  
+Figure 6: Small $\operatorname { T r } ( \mathbf { F } )$ during the early phase of training is more likely to reach wider minima. Left: two ResNet-56 models are trained with two different levels of regularization for 20 epochs on CIFAR-100. $\operatorname { T r } ( \mathbf { F } )$ at the end of 20 epochs $( \mathrm { { T r } ( { F _ { i } } ) ) }$ is shown. Middle: Each model is then continued trained using the low regularization configuration with different random seeds. A histogram of $\mathrm { T r } ( \mathbf { H } )$ at best test accuracy along the trajectory $( \mathrm { T r } ( \mathbf { H } _ { \mathbf { f } } ) ,$ ) is shown. Right: a histogram of test accuracy.
+
+Table 3: Fisher Penalty (FP) and $\mathrm { G P _ { r } }$ both reduce memorization competitively to mixup. We measure test accuracy at the best validation point in training with either $2 5 \%$ or $50 \%$ examples with noisy labels in the CIFAR-100 dataset.   
+
+<table><tr><td>Noise</td><td>Setting</td><td>Baseline</td><td>Mixup</td><td>GPx</td><td>FP</td><td>GPr</td></tr><tr><td rowspan="2">25%</td><td>VGG-11/C100</td><td>41.74%</td><td>52.31%</td><td>45.94%</td><td>60.18%</td><td>58.46%</td></tr><tr><td>ResNet-52/C100</td><td>53.30%</td><td>61.61%</td><td>52.70%</td><td>58.31%</td><td>57.60%</td></tr><tr><td rowspan="2">50%</td><td>VGG-11/C100</td><td>30.05%</td><td>39.15%</td><td>34.26%</td><td> 51.33%</td><td>50.33%</td></tr><tr><td>ResNet-52/C100</td><td>43.35%</td><td> 51.71%</td><td>42.99%</td><td>47.99%</td><td>50.08%</td></tr></table>
+
+![](images/b5a5a955b191ef658f4f7bbc350b8eed0acf63330f974199503c4ddc5190a1a2.jpg)  
+Figure 5: Fisher penalty slows down training on data with noisy labels more strongly than it slows down training on clean data for VGG-11 on CIFAR-100. This likely happens because FP penalizes more strongly gradient norm on data with noisy labels. Left plot shows the training accuracy on examples with clean/noisy labels (solid/dashed line). Middle plot shows the gradient norm evaluated on examples with clean/noisy labels (solid/dashed). Right plot shows the ratio of gradient norm on clean to noisy data. Red to blue color represents the regularization coefficient (from $1 0 ^ { - 2 }$ to $1 0 ^ { 1 }$ ).
+
+# 5 EARLY $\mathrm { T r } ( \mathbf F )$ INFLUENCES FINAL CURVATURE
+
+To provide further insight why it is important to regularize $\operatorname { T r } ( \mathbf { F } )$ during the early phase of training, we establish a connection between the early phase of training and the wide minima hypothesis (Hochreiter & Schmidhuber, 1997; Keskar et al., 2017) which states that flat minima typically correspond to better generalization. Here, we use $\mathrm { T r } ( \mathbf { H } )$ as a measure of flatness.
+
+Experimental setting We investigate how likely it is for an optimization trajectory to end up in a wide minimum in two scenarios. 1) When optimization exhibits small $\operatorname { T r } ( \mathbf { F } )$ early on. 2) When optimization exhibits large $\operatorname { T r } ( \mathbf { F } )$ early on. Specifically, we train two separate ResNet-26 models for 20 epochs using high and low regularization configurations. At epoch 20 we record $\operatorname { T r } ( \mathbf { F } )$ for each model. We then use these two models as initialization for 8 separate models each, and continue training using the low regularization configuration with different random seeds. The motivation behind this experiment is to show that the degree of regularization in the early phase biases the model towards minima with certain flatness $( \mathrm { T r } ( \mathbf { H } ) )$ even though no further high regularization configurations are used during the rest of the training. For all these runs, we record the best test accuracy along the optimization trajectory along with $\mathrm { T r } ( \mathbf { H } )$ at the point corresponding to the best test accuracy. We describe the remaining experimental details in Appendix G.4.
+
+Results We present the result in Figure 6 for the CIFAR-100 datasets, and for CIFAR-10 in Appendix A.4. A training run that shows a lower $\operatorname { T r } ( \mathbf { F } )$ during the early phase is more likely to end up in a wider minimum as opposed to one that reaches large $\operatorname { T r } ( \mathbf { F } )$ during the early phase. This happens despite that the late phases of both sets of models use the low regularization configuration. The latter runs have a high variance in the best test accuracy and always end up in sharper minima. In Appendix G.4 we also show evolution of $\mathrm { T r } ( \mathbf { H } )$ throughout training, which suggests that this behavior can be attributed to curvature stabilization happening early during training.
+
+# 6 RELATED WORK
+
+SGD’s implicit regularization effect has been argued to be a critical component of the empirical success of DNNs (Neyshabur, 2017; Zhang et al., 2016). Much of it is attributed to the choice of hyperparameters (Keskar et al., 2017; Smith & Le, 2018; Jastrzebski et al., 2017), the low complexity bias induced by gradient descent (Xu, 2018; Jacot et al., 2018; Hu et al., 2020) or the cross-entropy loss function (Poggio et al., 2018; Soudry et al., 2018). However, a more mechanistic understanding of how SGD implicitly regularizes DNNs remains a largely unsolved problem.
+
+Prior work on replicating SGD’s implicit regularization focused mainly on the loss curvature at the final minimum (Hochreiter & Schmidhuber, 1997). Chaudhari et al. (2019) propose a Langevin dynamics based algorithm for finding update directions that point towards wide minima. Wen et al. (2018) propose to find wide minima by averaging gradients at the neighborhood of the current parameter state. In contrast, we shift the focus to the FIM and the early phase of training. This new perspective allows us to more directly test our theory by explicitly penalizing $\operatorname { T r } ( \mathbf { F } )$ .
+
+Penalizing $\operatorname { T r } ( \mathbf { F } )$ is related to regularizing the input gradient norm, which was shown to be an effective regularizer for deep neural networks (Drucker & Le Cun, 1992; Varga et al., 2018). Chatterjee (2020); Fort et al. (2020) show that SGD avoids memorization by extracting commonalities between examples due to following gradient descent directions shared between examples. Our work is complementary. We argue that SGD implicitly penalizes $\operatorname { T r } ( \mathbf { F } )$ , which also reduces memorization. Concurrently, Barrett & Dherin (2020) show that SGD implicitly penalizes the gradient norm for large learning rates and propose GP as an explicit regularizer. Similarly, we found that SGD implicitly regularizes $\operatorname { T r } ( \mathbf { F } )$ , which is the squared gradient norm under labels sampled from $p _ { \pmb { \theta } } ( \pmb { y } | \pmb { x } )$ . In contrast to them, we connected the implicit regularization effect of SGD to large curvature in the early phase. We also found GP to be a generally less effective regularizer than FP.
+
+# 7 CONCLUSION
+
+Inspired by recent findings of rapid changes to the local curvature of the loss surface that happen in the early phase of training (Achille et al., 2019; Jastrz˛ebski et al., 2019; Lewkowycz et al., 2020), we investigated more closely the connection between the loss geometry in the early phase of training of neural networks and generalization.
+
+We proposed and investigated a hypothesis that SGD influences generalization by implicitly penalizing the trace of the Fisher Information Matrix $( \mathrm { T r } ( \mathbf { F } ) )$ from the very beginning of training. We show that (1) the value of early $\operatorname { T r } ( \mathbf { F } )$ correlates with final generalization, and (2) explicitly regularizing $\operatorname { T r } ( \mathbf { F } )$ can substantially improve generalization.
+
+To gain further insight into the mechanism by which penalizing $\operatorname { T r } ( \mathbf { F } )$ improves generalization, we investigated training on noisy data. We found that penalizing $\operatorname { T r } ( \mathbf { F } )$ reduces memorization by penalizing examples with noisy labels more strongly than clean ones, which seems to happen because it penalizes more strongly their gradient norm. This sheds new light onto implicit regularization effects in SGD, and suggests the utility of penalizing $\operatorname { T r } ( \mathbf { F } )$ as an explicit regularizer.
+
+An interesting topic for the future is to put our findings in the context of transfer and continual learning. We hypothesize that catastrophic Fisher explosion (the initial growth of $\cdot$ to a large value) can negatively impact not only generalization, but also transferability of the model.
+
+# REFERENCES
+
+Alessandro Achille, Matteo Rovere, and Stefano Soatto. Critical learning periods in deep networks. In International Conference on Learning Representations, 2019.
+
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+
+# APPPENDIX
+
+A ADDITIONAL RESULTS
+
+# A.1 EARLY PHASE $\operatorname { T r } ( \mathbf { F } )$ CORRELATES WITH FINAL GENERALIZATION
+
+In this section, we present the additional experimental results for Section 3. The experiments with varying batch size for CIFAR-100 and CIFAR-10 are shown in Figure 7. The conclusions are the same as discussed in the main text in Section 3.
+
+![](images/4afdbb1947f55d4032370085055a11399ea5d42f098e6eccfa388035053e29bc.jpg)  
+Figure 7: Association between early phase values of $\operatorname { T r } ( \mathbf { F } )$ and generalization, holds on the CIFAR10 and the CIFAR-100 datasets. Each point corresponds to multiple runs with randomly chosen seeds and a specific value of batch size. $\mathrm { T r } \mathbf { F } _ { i }$ is recorded during early phase (2-7 epochs, see main text for details), while the test accuracy is the maximum value along the entire optimization path (averaged across runs with the same batch size). The horizontal and vertical error bars show the standard deviation of values across runs. The plots show that early phase $\operatorname { T r } ( \mathbf { F } )$ is predictive of final generalization.
+
+# A.2 FISHER PENALTY
+
+We first show additional metrics for experiments summarized in Table 1. In Table 6 we show the final training accuracy. Table 4 confirms that generally all gradient norm regularizers reduce the maximum value of $\operatorname { T r } ( \mathbf { F } )$ (we measure $\operatorname { T r } ( \mathbf { F } )$ starting from after one epoch of training because $\operatorname { T r } ( \mathbf { F } )$ explodes in networks with batch normalization layers at initialization). Finally, Table 5 confirms that the regularizers incurred a relatively small additional computational cost.
+
+![](images/86f65c41dd28dda537c5a94df3abd78a9811447560c57fd1d2b5055918882c27.jpg)  
+Figure 8 is a counterpart of Figure 3 for the other two models on the CIFAR-10 and the CIFAR-100 datasets.   
+Figure 8: Same as Figure 3, but for DenseNet on CIFAR-100, and SimpleCNN on CIFAR-10. Curves were smoothed for visual clarity.
+
+Table 4: The maximum value of $\operatorname { T r } ( \mathbf { F } )$ along the optimization trajectory for experiments on CIFAR-10 or CIFAR-100 included in Table 1.   
+
+<table><tr><td>Setting</td><td>n*</td><td>Baseline</td><td>GPx</td><td>GP</td><td>FP</td><td>GP</td></tr><tr><td>DenseNet/C100 (w/o aug.)</td><td>24.68</td><td>98.17</td><td>83.64</td><td>64.33</td><td>66.24</td><td>73.66</td></tr><tr><td>VGG11/C100 (w/o aug.)</td><td>50.88</td><td>148.19</td><td>102.95</td><td>58.53</td><td>64.93</td><td>62.96</td></tr><tr><td>WResNet/C100 (w/o aug.)</td><td>26.21</td><td>91.39</td><td>41.43</td><td>40.94</td><td>56.53</td><td>39.31</td></tr><tr><td>SCNN/C10 (w/o aug.)</td><td>24.21</td><td>52.05</td><td>47.96</td><td>25.03</td><td>19.63</td><td>25.35</td></tr></table>
+
+Table 5: Time per epoch (in seconds) for experiments in Table 1.   
+
+<table><tr><td>Setting</td><td>m*</td><td>Baseline</td><td>GPx</td><td>GP</td><td>FP</td><td>GP</td></tr><tr><td>WResNet/TinyImageNet (aug.)</td><td>214.45</td><td>142.69</td><td>233.14</td><td>143.78</td><td>208.62</td><td>371.74</td></tr><tr><td>DenseNet/C100 (w/o aug.)</td><td>78.88</td><td>57.40</td><td>77.89</td><td>78.66</td><td>97.25</td><td>75.96</td></tr><tr><td>VGG11/C100 (w/o aug.)</td><td>30.50</td><td>35.27</td><td>31.54</td><td>32.52</td><td>43.41</td><td>42.40</td></tr><tr><td>WResNet/C100 (w/o aug.)</td><td>49.64</td><td>47.99</td><td>71.33</td><td>61.36</td><td>76.93</td><td>53.25</td></tr><tr><td>SCNN/C10 (w/o aug.)</td><td>18.64</td><td>19.51</td><td>26.09</td><td>19.91</td><td>21.21</td><td>20.55</td></tr></table>
+
+Table 6: The final epoch training accuracy for experiments shown in Table 1. Experiments with small learning rate reach no lower accuracy than experiments corresponding to a large learning rate $\eta ^ { * }$ .   
+
+<table><tr><td>Setting</td><td>m*</td><td>Baseline</td><td>GPx</td><td>GP</td><td>FP</td><td>GP</td></tr><tr><td>WResNet/TinyImageNet (aug.)</td><td>99.84%</td><td>99.96%</td><td>99.97%</td><td>93.84%</td><td>81.05%</td><td>86.46%</td></tr><tr><td>DenseNet/C100 (w/o aug)</td><td>99.98%</td><td>99.97%</td><td>99.96%</td><td>99.91%</td><td>99.91%</td><td>99.39%</td></tr><tr><td>VGG11/C100 (w/o aug)</td><td>99.98%</td><td>99.98%</td><td>99.85%</td><td>99.62%</td><td>97.73%</td><td>86.32%</td></tr><tr><td>WResNet/C100 (w/o aug)</td><td>99.98%</td><td>99.98%</td><td>99.97%</td><td>99.96%</td><td>99.99%</td><td>99.94%</td></tr><tr><td>SCNN/C10 (w/o aug)</td><td>100.00%</td><td>100.00%</td><td>97.79%</td><td>100.00%</td><td>93.80%</td><td>94.64%</td></tr></table>
+
+# A.3 FISHER PENALTY REDUCES MEMORIZATION
+
+In this section, we describe additional experimental results for Section 4.1. Figure 9 is the same as Figure 5, but for ResNet-50.
+
+![](images/ee4d5e480ffe2a7bf5a738d6821a048af4c55570966df6f0d7babfee2233f1fa.jpg)  
+Figure 9: Same as Figure 5, but for ResNet-50.
+
+# A.4 EARLY $\operatorname { T r } ( \mathbf { F } )$ INFLUENCES FINAL CURVATURE
+
+In this section, we present additional experimental results for Section 5. The experiment on CIFAR-10 is shown in Figure 10. The conclusions are the same as discussed in the main text in Section 5.
+
+![](images/63ef5905624a61a4354e721d63489d6eb823dae11cee3b9edd580fc50bfa206e.jpg)  
+Figure 10: Small $\operatorname { T r } ( \mathbf { F } )$ during the early phase of training is more likely to reach wider minima as measured by $\mathrm { T r } ( \mathbf { H } )$ . Left: 2 models are trained with different levels of regularization for 20 epochs on CIFAR-10. $\operatorname { T r } ( \mathbf { F } )$ at the end of 20 epochs (denoted as $\operatorname { T r } ( \mathbf { F _ { i } } ) )$ ) is shown. Middle: Each model is then used as initialization and trained until convergence using the low regularization configuration with different random seeds. A histogram of $\mathrm { T r } ( \mathbf { H } )$ at the point corresponding to the best test accuracy along the trajectory (denoted by $\mathrm { T r } ( \mathbf { H } _ { \mathbf { f } } ) \dot { { \mathbf { \phi } } }$ ) is shown. Right: a histogram of the best test accuracy corresponding to middle figure is shown.
+
+![](images/056f59edf57a0b5750e6f703ffb0d8514f41e171c59f9478570a120a42f71370.jpg)  
+Figure 11: The value of $\mathrm { T r } ( \mathbf { H } )$ over the course of training. Each point corresponds to runs with different seeds and a specific value of learning rate $\eta$ and batch size $S$ . $\ell$ and TA respectively denote the minimum training loss and the maximum test accuracy along the entire trajectory for the corresponding runs (averaged across seeds). The plots show that flatter optimization trajectories become biased towards flatter minima early during training, at a coarse scale of hyper-parameter values (red vs blue).
+
+Next, to understand why smaller $\operatorname { T r } ( \mathbf { F } )$ during early phase is more likely to end up in a wider final minimum, we track $\mathrm { T r } ( \mathbf { H } )$ during the entire coarse of training and show that it stabilizes early during training. In this experiment, we create two sets of hyper-parameters: coarse-grained and fine-grained. For CIFAR-10, we use batch size $S \in A \cup B$ , where $A = \{ 4 8 0 , 5 0 0 , 5 2 0 \}$ and $B = \{ 8 0 , 1 0 0 , 1 2 0 \}$ . For all batch size configurations, a learning rate of 0.02 is used. Overloading the symbols $A$ and $B$ for CIFAR-100, we use learning rate $\eta ~ \in ~ A \cup B$ , where $A = \{ 0 . 0 0 0 \bar { 8 } , 0 . 0 0 \bar { 1 } , 0 . 0 0 1 2 \}$ and $B = \{ 0 . 0 0 8 , 0 . 0 1 , 0 . 0 1 2 \}$ . For all learning rate configurations, a batch size of 100 is used. In both cases, the elements within each set ( $A$ and $B$ ) vary on a fine-grained scale, while the elements across the two sets vary on a coarse-grained scale. The remaining details and additional experiments can be found in Appendix G.4. The experiments are shown in Figure 11. Notice that after initialization (index 0 on $\mathbf { X }$ -axis), the first value is computed at epoch 10 (at which point previous experiments show that entanglement starts to hold with late phase).
+
+We make three observations in this experiment. First, the relative ordering of $\mathrm { T r } ( \mathbf { H } )$ values for runs between sets $A$ vs $B$ stay the same after the first 10 epochs. Second, the degree of entanglement is higher between any two epochs when looking at runs across sets $A$ and $B$ , while it is weaker when looking at runs within any one the sets. Finally, test accuracies for set $B$ runs are always higher than those of set $A$ runs, but this trend is not strong for runs within any one set. Note that the minimum loss values are roughly at a similar scale for each dataset and they are all at or below $1 0 ^ { - 2 }$ .
+
+# B COMPUTATION OF $\mathrm { T r } ( \mathbf { H } )$
+
+We computed $\mathrm { T r } ( \mathbf { H } )$ in our experiments using the Hutchinson’s estimator Hutchinson (1990),
+
+$$
+\begin{array} { r l } & { T r ( \mathbf { H } ) = T r ( \mathbf { H } ) = T r ( \mathbf { H } ) } \\ & { \quad = T r ( \mathbf { H } \cdot \mathbf { B } [ \varrho \mathbf { z } ^ { T } ] ) } \\ & { \quad = \mathbb { E } [ T r ( \mathbf { H } \cdot \mathbf { z } \mathbf { z } ^ { T } ) ] } \\ & { \quad = \mathbb { E } [ T r ( \mathbf { H } \cdot \mathbf { z } ) ^ { T } ] } \\ & { \quad = \mathbb { E } [ \varrho ^ { T } \mathbf { H } \cdot \mathbf { z } ] } \\ & { \quad \approx \frac { 1 } { M } \frac { 1 } { \omega _ { \mathrm { m } } ^ { T } } \mathbf { z } ^ { T } \mathbf { H } \cdot \mathbf { z } _ { i } } \\ & { \quad = \frac { 1 } { M } \sum _ { i = 1 } ^ { M } \tau _ { i } ^ { T } \frac { \partial } { \partial \theta } \left( \frac { \partial \mathcal { E } } { \partial \theta ^ { T } } \right) \cdot \mathbf { z } _ { i } } \\ & { \quad = \frac { 1 } { M } \frac { 1 } { \omega _ { \mathrm { m } } ^ { T } } z _ { i } ^ { T } \frac { \partial } { \partial \theta } \left( \frac { \partial \mathcal { E } ^ { T } } { \partial \theta } \mathbf { z } _ { i } \right) , } \end{array}
+$$
+
+where I is the identity matrix, $\mathbf { z }$ is a multi-variate standard Gaussian random variable, and $\mathbf { z } _ { i }$ ’s are i.i.d. instances of $\mathbf { z }$ . The larger the value of $M$ , the more accurate the approximation is. We used $M = 3 0$ . To make the above computation efficient, note that the gradient $\frac { \partial \ell } { \partial \theta }$ only needs to be computed once and it can be re-used in the summation over the $M$ samples.
+
+# C APPROXIMATIONS IN FISHER PENALTY
+
+In this section, we describe the approximations made in Fisher Penalty in detail. Recall, that $\operatorname { T r } ( \mathbf { F } )$ can be expressed as
+
+$$
+\mathrm { T r } ( \mathbf { F } ) = \mathbb { E } _ { \boldsymbol { x } \sim \mathcal { X } , \hat { \boldsymbol { y } } \sim p _ { \boldsymbol { \theta } } ( \boldsymbol { y } \vert \mathbf { x } ) } \left[ \Vert \frac { \partial } { \partial \boldsymbol { \theta } } \boldsymbol { \ell } ( \mathbf { x } , \hat { \boldsymbol { y } } ) \Vert _ { 2 } ^ { 2 } \right] .
+$$
+
+In the preliminary experiments, we found empirically that we can use the norm of the expected gradient rather than the expected norm of the gradient, which is a more direct expression of $\operatorname { T r } ( \mathbf { F } )$ :
+
+$$
+\begin{array} { r } { \nabla \mathbb { E } _ { x \sim \mathcal { X } , \hat { y } \sim p _ { \theta } ( y | x ) } \left[ \left\| \frac { \partial } { \partial \theta } \ell ( \pmb { x } , \hat { y } ) \right\| _ { 2 } ^ { 2 } \right] \approx \displaystyle \frac { 1 } { N } \sum _ { n = 1 } ^ { N } \frac { 1 } { M } \sum _ { m = 1 } ^ { M } \nabla \left\| \frac { \partial } { \partial \theta } \ell ( \pmb { x } _ { n } , \hat { y } _ { n m } ) \right\| _ { 2 } ^ { 2 } } \\ { \geq \nabla \left\| \frac { 1 } { N M } \sum _ { n = 1 } ^ { N } \sum _ { m = 1 } ^ { M } \frac { \partial } { \partial \theta } \ell ( \pmb { x } _ { n } , \hat { y } _ { n m } ) \right\| _ { 2 } ^ { 2 } , } \end{array}
+$$
+
+where $N$ and $M$ are the minibatch size and the number of samples from $p _ { \theta } ( y | \pmb { x } _ { n } )$ , respectively. This greatly improves the computational efficiency. With $N = B$ and $M = 1$ , we end up with the following learning objective function:
+
+$$
+\ell ^ { \prime } ( x _ { 1 : B } , y _ { 1 : B } ; \pmb \theta ) = \frac { 1 } { B } \sum _ { i = 1 } ^ { B } \ell ( { \pmb x } _ { i } , y _ { i } ; \pmb \theta ) + \alpha \left\| \frac { 1 } { B } \sum _ { i = 1 } ^ { B } g ( { \pmb x } _ { i } , \hat { y } _ { i } ) \right\| ^ { 2 } .
+$$
+
+We found empirically that $\begin{array} { r l } & { \left\| \frac { 1 } { B } \sum _ { i = 1 } ^ { B } g ( \pmb { x } _ { i } , \hat { y } _ { i } ) \right\| ^ { 2 } } \end{array}$ , which we denote by $\mathrm { T r } ( \mathbf { F } ^ { B } )$ , and $\operatorname { T r } ( \mathbf { F } )$ correlate well during training. To demonstrate this, we train SimpleCNN on the CIFAR-10 dataset with 5 different learning rates (from $1 0 ^ { - 3 }$ to $1 0 ^ { - 1 }$ ). The outcome is shown in Figure 12. We see that for most of the training, with the exception of the final phase, $\mathrm { T r } ( \mathbf { F } ^ { B } )$ and $\operatorname { T r } ( \mathbf { F } )$ correlate extremely well. Equally importantly, we find that using a large learning affects both $\mathrm { T r } ( \mathbf { F } ^ { B } )$ and $\operatorname { T r } ( \mathbf { F } )$ , which further suggests the two are closely connected.
+
+![](images/86d3ea80c56f74dc85b6c95e62926e6e682bf3498c67bb68d870bfb0a1ef8f6f.jpg)  
+Figure 12: Correlation between $\operatorname { T r } ( \mathbf { F } )$ and $\mathrm { T r } ( \mathbf { F } ^ { B } )$ for SimpleCNN trained on the CIFAR-10 dataset. Blue to red color denotes learning rates from $1 0 ^ { - 3 }$ to $1 0 ^ { - 1 }$ . The value of $\operatorname { T r } ( \mathbf { F } )$ and $\mathrm { T r } ( \mathbf { F } ^ { B } )$ correlate strongly for the most of the training trajectory. Using large learning rate reduces both $\operatorname { T r } ( \mathbf { F } )$ and $\mathrm { T r } ( \mathbf { F } ^ { \mathbf { \breve { B } } } )$ .
+
+![](images/4adecb439e7a7276cc7e9f8ef4e6fa3fa38b3957ffb8621bcfe30a68138dc2b6.jpg)  
+Figure 13: A comparison between the effect of recomputing Fisher Penalty gradient every 10 iterations (left) or every iteration (right), with respect to validation accuracy and $\operatorname { T r } ( \mathbf { F } )$ . We denote by $f$ the frequency with which we update the gradient. Both experiments result in approximately $80 \%$ test accuracy with the best configuration.
+
+![](images/b18b19773aee4f7fe7547a9e97644b4b1cd76d1e0ce056ce07e2cc6c1b475ab3.jpg)  
+Figure 14: Using Fisher Penalty without the approximation results in a similar generalization performance. We penalize the norm of the gradient rather than norm of the mini-batch gradient (as in Equation 2). We observe that this variant of Fisher Penalty improves generalization to a similar degree as the version of Fisher Penalty used in the paper (c.f. Figure 13.), achieving $\cdot$ test accuracy.
+
+We also update the gradient of $\mathrm { T r } ( \mathbf { F } ^ { B } )$ only every 10 optimization steps. We found empirically it does not affect generalization performance nor the ability to regularize $\operatorname { T r } ( \mathbf { F } )$ in our setting. However, we acknowledge that it is plausible that this choice would have to be reconsidered in training with very large learning rates or with larger models.
+
+Figure 13 compares learning curves of training with FP recomputed every optimization step, or every 10 optimization steps. For each, we tune the hyperparameter $\alpha$ , checking 10 values equally spaced between $1 0 ^ { - 2 }$ and $1 0 ^ { 0 }$ on a logarithmic scale. We observe that for the optimal value of $\alpha$ both validation accuracy and $\operatorname { T r } ( \mathbf { F } )$ are similar between the two runs. Both experiments achieve approximately $80 \%$ test accuracy.
+
+Finally, to ensure that using the approximation in Equation 2 does not negatively affect how Fisher Penalty improves generalization or reduces the value of $\operatorname { T r } ( \mathbf { F } )$ , we experiment with a variant of Fisher Penalty without the approximation. Please recall that we always measure $\mathrm { T r } ( \mathbf { F } )$ (i.e. we do not use approximations in computing $\operatorname { T r } ( \mathbf { F } )$ that is reported in the plots), regardless of what variant of penalty is used in regularizing the training.
+
+Specifically, we augment the loss function with the norm of the gradient computed on the first example in the mini-batch as follows
+
+$$
+\ell ^ { \prime } ( x _ { 1 : B } , y _ { 1 : B } ; \pmb \theta ) = \frac { 1 } { B } \sum _ { i = 1 } ^ { B } \ell ( { \pmb x } _ { i } , y _ { i } ; \pmb \theta ) + \alpha \left\| g ( { \pmb x } _ { 1 } , \hat { y } _ { 1 } ) \right\| ^ { 2 } .
+$$
+
+We apply this penalty in each optimization step. We tune the hyperparameter $\cdot$ , checking 10 values equally spaced between $\cdot$ and $\cdot$ on a logarithmic scale.
+
+Figure 14 summarizes the results. We observe that the best value of $\cdot$ yields $7 9 . 7 \%$ test accuracy, compared to $\cdot$ test accuracy yielded by the Fisher Penalty. The effect on $\cdot$ is also very similar. We observe that the best run corresponds to maximum value of $\cdot$ of 24.16, compared to that of 21.38 achieved by Fisher Penalty. These results suggest that the approximation used in Fisher Penalty only improves the generalization and flattening effects of Fisher Penalty.
+
+# D A CLOSER LOOK AT THE SURPRISING EFFECT OF LEARNING RATE ON THE LOSS GEOMETRY IN THE EARLY PHASE OF TRAINING
+
+It is intuitive to hypothesize that the catastrophic Fisher explosion (the initial growth of the value of $\cdot$ ) occurs during training with a large learning rate, but is overlooked due to not sufficiently fine-grained computation of $\cdot$ . In this section we show evidence against this hypothesis based on the literature mentioned in the main text. We also run additional experiments in which we compute the value of $\operatorname { T r } ( \mathbf { F } )$ at each iteration.
+
+The surprising effect of the learning rate on the geometry of the loss surface (e.g. the value of $\cdot$ ) was demonstrated in prior works (Jastrz˛ebski et al., 2019; Golatkar et al., 2019; Lewkowycz et al., 2020; Leclerc & Madry, 2020). In particular, Jastrzebski et al. (2020); Lewkowycz et al. (2020) show that training with large learning rate rapidly escapes regions of high curvature, where curvature is understood as the spectral norm of the Hessian evaluated at the current point of the loss surface. Perhaps the most direct experimental data against this hypothesis can be found in Anonymous (2021) in Figure 1, where training with Gradient Descent finds regions of the loss surface with large curvature for small learning rate rapidly in the early phase of training.
+
+We also run the following experiment to provide further evidence against the hypothesis. We train SimpleCNN on the CIFAR-10 dataset using two different learning rates, while computing the value of $\cdot$ for every mini-batch. We use 128 random samples in each iteration to estimate $\cdot$ .
+
+We find that training with a large learning rate never (even for a single optimization step) enters a region with the value of $\operatorname { T r } ( \mathbf { F } )$ as large as reached during training with a small learning rate. Figure 15 shows the experimental data.
+
+We also found similar to hold when varying the batch size, see Section E, which further shows that the observed effects cannot be explained by the difference in learning speed incurred by using a small learning rate.
+
+To summarize, both the published evidence of Jastrzebski et al. (2020); Lewkowycz et al. (2020); Anonymous (2021), as well as our additional experiments are inconsistent with the hypothesis that the results in this paper can be explained by differences in training speed between experiments using large and small learning rates.
+
+![](images/78bd5ee69baa2ac17885df8dfa174f463cb205a4563812370577ec74cf5bc94f.jpg)  
+Figure 15: Training with a large learning rate never (even for a single optimization step) enters a region with as large value of $\cdot$ as the maximum value of $\cdot$ reached during training with a small learning rate. We run the experiment using SimpleCNN on the CIFAR-10 dataset with two different learning rates. The left plot shows the value of $\operatorname { T r } ( \mathbf { F } )$ computed at each iteration, and the right plot shows training accuracy computed on the current mini-batch (curve has been smoothed for clarity).
+
+# E CATASTROPHIC FISHER EXPLOSION HOLDS IN TRAINING WITH LARGE BATCH-SIZE
+
+In this section, we show evidence that the conclusions transfer to large batch size training. Namely, we show that (1) catastrophic Fisher explosion also occurs in large batch size training, and (2) Fisher Penalty can improve generalization and close the generalization gap due to using a large batch size (Keskar et al., 2017).
+
+![](images/88d894bf26dc9f32949eedeb4378b3ac93541cec6b9b796aeb30490c170a5776.jpg)  
+Figure 16: Catastrophic Fisher explosion in large batch size training. Experiment run on the CIFAR10 and dataset the SimpleCNN model. The left plot shows the value of $\cdot$ computed at each iteration, and the right plot shows training accuracy computed on the current mini-batch (curve has been smoothed for clarity).
+
+We first train SimpleCNN on the CIFAR-10 dataset using three different batch sizes, while computing the value of $\cdot$ for every mini-batch. We use 128 random samples in each iteration to estimate $\cdot$ . Figure 16 summarizes the experiment. We observe that training with a large batch size enters a region of the loss surface with a substantially larger value of $\cdot$ than the small batch size.
+
+Next, we run a variant of one of the experiments in Table 1. Instead of using a suboptimal (smaller) learning rate, we use a suboptimal (larger) batch size. Specifically, we train SimpleCNN on the CIFAR-10 dataset (without augmentation) with a $\cdot$ larger batch size while keeping learning rate the same. Using a larger batch size results in $3 . 2 4 \%$ lower test accuracy ( $7 6 . 9 4 \%$ compared to ${ \bar { 7 } } 3 . 7 \%$ test accuracy, c.f. with Table 1).
+
+We next experiment with Fisher Penalty. We apply the penalty in each optimization step and use the first 128 examples when computing the penalty. We also use a $2 \mathrm { x }$ lower learning rate, which stabilizes training but does not improve generalization on its own (training with this learning rate reaches $\cdot$ test accuracy). Figure 17 shows $\mathrm { T r } ( \mathbf { F } )$ and validation accuracy during training for different values of the penalty. We observe that Fisher Penalty improves test accuracy from $7 3 . 5 9 \%$ to $7 8 . 7 \%$ . Applying Fisher Penalty also effectively reduces the peak value of $\mathrm { T r } ( \mathbf { F } ) /$ i
+
+Taken together, the results suggest that Catastrophic Fisher explosion holds in large batch size training; using a small batch size improves generalization by a similar mechanism as using a large batch size, which can be introduced explicitly in the form of Fisher Penalty.
+
+![](images/1818eda78f1a8287dcc03b60b299742cbf1e291c049c2bd0fa9c4a24f0810d00.jpg)  
+Figure 17: Fisher Penalty improves in large batch size training. Experiment run on the CIFAR-10 dataset (without augmentation) and the SimpleCNN model. Warmer color corresponds to larger coefficient used in Fisher Penalty.
+
+# F $\mathrm { T r } ( \mathbf { H } )$ AND $\mathrm { T r } ( \mathbf F )$ CORRELATE STRONGLY
+
+We demonstrate a strong correlation between $\mathrm { T r } ( \mathbf { H } )$ and $\operatorname { T r } ( \mathbf { F } )$ for DenseNet, ResNet-56 and SimpleCNN in Figure 18. We calculate $\operatorname { T r } ( \mathbf { F } )$ using a mini-batch. We see that $\operatorname { T r } ( \mathbf { F } )$ has a smaller magnitude (because we use the mini-batch gradient which has lower variance), but correlates extremely well with $\mathrm { T r } ( \mathbf { H } )$ .
+
+![](images/04b02357d2fd9445daf7f56873824a57c5c016a4ba2f86145670da52a9c6cee4.jpg)  
+Figure 18: Correlation between $\operatorname { T r } ( \mathbf { F } )$ and $\mathrm { T r } ( \mathbf { H } )$ .
+
+# G ADDITIONAL EXPERIMENTAL DETAILS
+
+G.1 EARLY PHASE $\operatorname { T r } ( \mathbf { F } )$ CORRELATES WITH FINAL GENERALIZATION
+
+Here, we describe additional details for experiments in Section 3.
+
+In the experiments with batch size, for CIFAR-10, we use batch sizes 100, 500 and 700, and $\epsilon = 1 . 2$ For CIFAR-100, we use batch sizes 100, 300 and 700, and $\epsilon = 3 . 5$ . These thresholds are crossed between 2 and 7 epochs across different hyperparameter settings. The remaining details for CIFAR100 and CIFAR-10 are the same as described in main text. The optimization details for these datasets are as follows.
+
+ImageNet: No data augmentation was used in order to allow training loss to converge to small values. We use a batch size of 256. Training is done using SGD with momentum set to 0.9, weight decay set to $1 e - 4$ , and with base learning rate as per the aforementioned details. Learning rate is dropped by a factor of 0.1 after 29 epochs and training is ended at around 50 epochs at which most runs converge to small loss values. No batch normalization is used and weight are initialized using Fixup Zhang et al. (2019). For each hyperparameter setting, we run two experiments with different random seeds due to the computational overhead. We compute $\operatorname { T r } ( \mathbf { F } )$ using 2500 samples (similarly to ?).
+
+CIFAR-10: We used random flipping as data augmentation. In the experiments with variation in learning rates, we use a batch size of 256. In the experiments with variation in batch size, we use a learning rate of 0.02. Training is done using SGD with momentum set to 0.9, weight decay set to $1 e - 5$ , and with base learning rate as per the aforementioned details. Learning rate is dropped by a factor of 0.5 at epochs 60, 120, and 170, and training is ended at 200 epochs at which most runs converge to small loss values. No batch normalization is used and weight are initialized using Arpit et al. (2019). For each hyperparameter setting, we run 32 experiments with different random seeds. We compute $\operatorname { T r } ( \mathbf { F } )$ using 5000 samples.
+
+CIFAR-100: No data augmentation was used for CIFAR-100 to allow training loss to converge to small values. We used random flipping as data augmentation for CIFAR-10. In the experiments with variation in learning rates, we use a batch size of 100. In the experiments with variation in batch size, we use a learning rates of 0.02. Training is done using SGD with momentum set to 0.9, weight decay set to $1 e - 5$ , and with base learning rate as per the aforementioned details. Learning rate is dropped by a factor of 0.5 at epochs 60, 120, and 170, and training is ended at 200 epochs at which most runs converge to small loss values. No batch normalization is used and weight are initialized using Arpit et al. (2019). For each hyperparameter setting, we run 32 experiments with different random seeds. We compute $\operatorname { T r } ( \mathbf { F } )$ using 5000 samples.
+
+# G.2 FISHER PENALTY
+
+Here, we describe the remaining details for the experiments in Section 4. We first describe how we tune hyperparameters in these experiments. In the remainder of this section, we describe each setting used in detail .
+
+Tuning hyperparameters In all experiments, we refer to the optimal learning rate $\eta ^ { * }$ as the learning rate optimized using grid search. In most experiments we check 5 different learning rate values uniformly spaced on a logarithmic scale, usually between $1 0 ^ { - 2 }$ and $1 0 ^ { 0 }$ . In some experiments we adapt the range to ensure that the range includes the optimal learning rate. We tune the learning rate only once for each configuration (i.e. we do not repeat it for different random seeds).
+
+In the first setting, for most experiments involving gradient norm regularizers, we use $1 0 \times$ smaller learning rate than $\eta ^ { * }$ . For TinyImageNet, we use $3 0 \times$ smaller learning rate than $\eta ^ { * }$ . To pick the regularization coefficient $\alpha$ , we evaluate 10 different values uniformly spaced on a logarithmic scale between $1 0 ^ { - 1 } \times v$ to $1 0 ^ { 1 } \times v$ with $v \in \mathbb { R } _ { + }$ . We choose the best performing $\alpha$ according to best validation accuracy. We pick the value of $v$ manually with the aim that the optimal $\alpha$ is included in this range. We generally found that $v = 0 . 0 1$ works well for GP, $\mathrm { G P _ { r } }$ , and FP. For $\mathrm { G P _ { x } }$ we found in some experiments that it is necessary to pick larger values of $v$ .
+
+Measuring $\operatorname { T r } ( \mathbf { F } )$ We measure $\operatorname { T r } ( \mathbf { F } )$ using the number of examples equal to the batch size used in training. For experiments with Batch Normalization layers, we use Batch Normalization in evaluation mode due to the practical reason that computing $\operatorname { T r } ( \mathbf { F } )$ uses batch size of 1, and hence $\operatorname { T r } ( \mathbf { F } )$ is not defined for a network with Batch Normalization layers in training mode.
+
+DenseNet on the CIFAR-100 dataset We use the DenseNet $( \mathrm { L } { = } 4 0 , \mathrm { k } { = } 1 2$ ) configuration from Huang et al. (2017). We largely follow the experimental setting in Huang et al. (2017). We use the standard data augmentation (where noted) and data normalization for CIFAR-100. We hold out random 5000 examples as the validation set. We train the model using SGD with momentum of 0.9, a batch size of 128, and weight decay of 0.0001. Following Huang et al. (2017), we train for 300 epochs and decay the learning rate by a factor of 0.1 after epochs 150 and 225. To reduce variance, in testing we update Batch Normalization statistics using 100 batches from the training set.
+
+Wide ResNet on the CIFAR-100 dataset We train Wide ResNet (depth 44 and width 3, without Batch Normalization layers). We largely follow experimental setting in He et al. (2015).We use the standard data augmentation and data normalization for CIFAR-100. We hold out random 5000 examples as the validation set. We train the model using SGD with momentum of 0.9, a batch size of 128, weight decay of 0.0010. Following He et al. (2015), we train for 300 epochs and decay the learning rate by a factor of 0.1 after epochs 150 and 225. We remove Batch Normalization layers. To ensure stable training we use the SkipInit initialization (De & Smith, 2020).
+
+VGG-11 on the CIFAR-100 dataset We adapt the VGG-11 model (Simonyan & Zisserman, 2015) to CIFAR-100. We do not use dropout nor Batch Normalization layers. We hold out random 5000 examples as the validation set. We use the standard data augmentation (where noted) and data normalization for CIFAR-100. We train the model using SGD with momentum of 0.9, a batch size of 128, and weight decay of 0.0001. We train the model for 300 epochs, and decay the learning rate by a factor of 0.1 after every 40 epochs starting from epoch 80.
+
+SimpleCNN on the CIFAR-10 dataset We also run experiments on the CNN example architecture from the Keras example repository (Chollet & others, $2 0 \dot { 1 } \dot { 5 } ) ^ { 1 }$ , which we change slightly. Specifically, we remove dropout and reduce the size of the final fully-connected layer to 128. We train it for 300 epochs and decay the learning rate by a factor of 0.1 after the epochs 150 and 225. We train the model using SGD with momentum of 0.9, a batch size of 128.
+
+Wide ResNet on the TinyImageNet dataset We train Wide ResNet (depth 44 and width 3, with Batch Normalization layers) on TinyImageNet Le & Yang (2015). TinyImageNet consists of subset of 100,000 examples from ImageNet that we downsized to $3 2 \times 3 2$ pixels. We train the model using SGD with momentum of 0.9, a batch size of 128, and weight decay of 0.0001. We train for 300 epochs and decay the learning rate by a factor of 0.1 after epochs 150 and 225. We train the model using SGD with momentum of 0.9, a batch size of 128. We do not use validation in TinyImageNet due to its larger size. To reduce variance, in testing we update Batch Normalization statistics using 100 batches from the training set.
+
+# G.3 FISHER PENALTY REDUCES MEMORIZATION
+
+Here, we describe additional experimental details for Section 4.1. We use two configurations described in Section G.2: VGG-11 trained on CIFAR-100 dataset, and Wide ResNe trained on the CIFAR-100 dataset. We tune the regularization coefficient $\alpha$ in the range $\{ 0 . 0 1 , 0 . 1 , 0 . 3 1 , 1 0 \}$ , with the exception of $\mathrm { G P _ { x } }$ for which we use the range $\{ 1 0 , 3 0 , 1 0 0 , 3 0 0 , 1 0 0 0 \}$ . We tuned mixup coefficient in the range $\{ 0 . 4 , 0 . 8 , 1 . 6 , 3 . 2 , 6 . 4 \}$ . We removed weight decay in these experiments.
+
+# G.4 EARLY $\operatorname { T r } ( \mathbf { F } )$ INFLUENCES FINAL CURVATURE
+
+CIFAR-10: We used random flipping as data augmentation for CIFAR-10. We use a learning rate of 0.02 for all experiments. Training is done using SGD with momentum 0.9, weight decay $1 e - 5$ , and with batch size as shown in figures. Learning rate is drop by a factor of 0.5 at 80, 150, and 200 epochs, and training is ended at 250 epochs. No batch normalization is used and weight are initialized using Arpit et al. (2019). For each batch size, we run 32 experiments with different random seeds. We compute $\operatorname { T r } ( \mathbf { F } )$ using 5000 samples.
+
+CIFAR-100: No data augmentation is used. We use a batch size of 100 for all experiments. Training is done using SGD with momentum 0.9, weight decay $1 e - 5$ , and with base learning rate as shown in figures. Learning rate is drop by a factor of 0.5 at 80, 150, and 200 epochs, and training is ended at 250 epochs. No batch normalization is used and weight are initialized using Arpit et al. (2019). For each learning rate, we run 32 experiments with different random seeds. We compute $\operatorname { T r } ( \mathbf { F } )$ using 5000 samples.